TSTP Solution File: GRA009+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : GRA009+1 : TPTP v5.0.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art09.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 09:56:56 EST 2010
% Result : Theorem 6.56s
% Output : CNFRefutation 6.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 89
% Number of leaves : 12
% Syntax : Number of formulae : 338 ( 25 unt; 0 def)
% Number of atoms : 1582 ( 671 equ)
% Maximal formula atoms : 37 ( 4 avg)
% Number of connectives : 1951 ( 707 ~;1047 |; 167 &)
% ( 7 <=>; 20 =>; 1 <=; 2 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 4 ( 2 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 : 492 ( 33 sgn 190 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] :
( edge(X1)
=> ( vertex(head_of(X1))
& vertex(tail_of(X1)) ) ),
file('/tmp/tmpfUWJdZ/sel_GRA009+1.p_1',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/tmpfUWJdZ/sel_GRA009+1.p_1',sequential_defn) ).
fof(3,axiom,
! [X1] :
( edge(X1)
=> head_of(X1) != tail_of(X1) ),
file('/tmp/tmpfUWJdZ/sel_GRA009+1.p_1',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/tmpfUWJdZ/sel_GRA009+1.p_1',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/tmpfUWJdZ/sel_GRA009+1.p_1',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/tmpfUWJdZ/sel_GRA009+1.p_1',precedes_properties) ).
fof(7,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/tmpfUWJdZ/sel_GRA009+1.p_1',shortest_path_properties) ).
fof(8,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/tmpfUWJdZ/sel_GRA009+1.p_1',precedes_defn) ).
fof(9,conjecture,
( complete
=> ! [X4,X5,X7,X2,X3] :
( ( shortest_path(X4,X5,X7)
& on_path(X2,X7)
& on_path(X3,X7)
& sequential(X2,X3) )
=> ? [X8] : triangle(X2,X3,X8) ) ),
file('/tmp/tmpfUWJdZ/sel_GRA009+1.p_1',complete_means_path_and_stuff_means_triangles) ).
fof(14,axiom,
! [X2,X3,X8] :
( triangle(X2,X3,X8)
<=> ( edge(X2)
& edge(X3)
& edge(X8)
& sequential(X2,X3)
& sequential(X3,X8)
& sequential(X8,X2) ) ),
file('/tmp/tmpfUWJdZ/sel_GRA009+1.p_1',triangle_defn) ).
fof(15,negated_conjecture,
~ ( complete
=> ! [X4,X5,X7,X2,X3] :
( ( shortest_path(X4,X5,X7)
& on_path(X2,X7)
& on_path(X3,X7)
& sequential(X2,X3) )
=> ? [X8] : triangle(X2,X3,X8) ) ),
inference(assume_negation,[status(cth)],[9]) ).
fof(16,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(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)],[6,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)],[7,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)],[8,theory(equality)]) ).
fof(20,plain,
! [X1] :
( ~ edge(X1)
| ( vertex(head_of(X1))
& vertex(tail_of(X1)) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(21,plain,
! [X2] :
( ~ edge(X2)
| ( vertex(head_of(X2))
& vertex(tail_of(X2)) ) ),
inference(variable_rename,[status(thm)],[20]) ).
fof(22,plain,
! [X2] :
( ( vertex(head_of(X2))
| ~ edge(X2) )
& ( vertex(tail_of(X2))
| ~ edge(X2) ) ),
inference(distribute,[status(thm)],[21]) ).
cnf(23,plain,
( vertex(tail_of(X1))
| ~ edge(X1) ),
inference(split_conjunct,[status(thm)],[22]) ).
cnf(24,plain,
( vertex(head_of(X1))
| ~ edge(X1) ),
inference(split_conjunct,[status(thm)],[22]) ).
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]) ).
cnf(29,plain,
( head_of(X1) = tail_of(X2)
| ~ sequential(X1,X2) ),
inference(split_conjunct,[status(thm)],[27]) ).
cnf(30,plain,
( ~ sequential(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[27]) ).
cnf(31,plain,
( edge(X2)
| ~ sequential(X1,X2) ),
inference(split_conjunct,[status(thm)],[27]) ).
cnf(32,plain,
( edge(X1)
| ~ sequential(X1,X2) ),
inference(split_conjunct,[status(thm)],[27]) ).
fof(33,plain,
! [X1] :
( ~ edge(X1)
| head_of(X1) != tail_of(X1) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(34,plain,
! [X2] :
( ~ edge(X2)
| head_of(X2) != tail_of(X2) ),
inference(variable_rename,[status(thm)],[33]) ).
cnf(35,plain,
( head_of(X1) != tail_of(X1)
| ~ edge(X1) ),
inference(split_conjunct,[status(thm)],[34]) ).
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,
( ~ 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)],[16]) ).
fof(47,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)],[46]) ).
fof(48,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)],[47]) ).
fof(49,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)],[48]) ).
fof(50,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)],[49]) ).
cnf(51,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)],[50]) ).
cnf(52,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)],[50]) ).
cnf(53,plain,
( X1 = X2
| X1 = head_of(esk2_2(X1,X2))
| X1 = tail_of(esk2_2(X1,X2))
| ~ complete
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(split_conjunct,[status(thm)],[50]) ).
cnf(54,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)],[50]) ).
cnf(56,plain,
( X1 = X2
| edge(esk2_2(X1,X2))
| ~ complete
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(split_conjunct,[status(thm)],[50]) ).
fof(57,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(58,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)],[57]) ).
fof(59,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)],[58]) ).
fof(60,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)],[59]) ).
fof(61,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)],[60]) ).
cnf(62,plain,
( on_path(X5,X3)
| ~ path(X1,X2,X3)
| ~ precedes(X4,X5,X3) ),
inference(split_conjunct,[status(thm)],[61]) ).
cnf(63,plain,
( on_path(X4,X3)
| ~ path(X1,X2,X3)
| ~ precedes(X4,X5,X3) ),
inference(split_conjunct,[status(thm)],[61]) ).
cnf(64,plain,
( sequential(X4,X5)
| precedes(esk3_5(X3,X1,X2,X4,X5),X5,X3)
| ~ path(X1,X2,X3)
| ~ precedes(X4,X5,X3) ),
inference(split_conjunct,[status(thm)],[61]) ).
cnf(65,plain,
( sequential(X4,X5)
| sequential(X4,esk3_5(X3,X1,X2,X4,X5))
| ~ path(X1,X2,X3)
| ~ precedes(X4,X5,X3) ),
inference(split_conjunct,[status(thm)],[61]) ).
fof(67,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(68,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)],[67]) ).
fof(69,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)],[68]) ).
fof(70,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)],[69]) ).
cnf(71,plain,
( ~ precedes(X1,X2,X3)
| ~ shortest_path(X4,X5,X3)
| ~ precedes(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[70]) ).
cnf(72,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)],[70]) ).
fof(73,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(74,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)],[73]) ).
fof(75,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)],[74]) ).
fof(76,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)],[75]) ).
cnf(77,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)],[76]) ).
fof(79,negated_conjecture,
( complete
& ? [X4,X5,X7,X2,X3] :
( shortest_path(X4,X5,X7)
& on_path(X2,X7)
& on_path(X3,X7)
& sequential(X2,X3)
& ! [X8] : ~ triangle(X2,X3,X8) ) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(80,negated_conjecture,
( complete
& ? [X9,X10,X11,X12,X13] :
( shortest_path(X9,X10,X11)
& on_path(X12,X11)
& on_path(X13,X11)
& sequential(X12,X13)
& ! [X14] : ~ triangle(X12,X13,X14) ) ),
inference(variable_rename,[status(thm)],[79]) ).
fof(81,negated_conjecture,
( complete
& shortest_path(esk4_0,esk5_0,esk6_0)
& on_path(esk7_0,esk6_0)
& on_path(esk8_0,esk6_0)
& sequential(esk7_0,esk8_0)
& ! [X14] : ~ triangle(esk7_0,esk8_0,X14) ),
inference(skolemize,[status(esa)],[80]) ).
fof(82,negated_conjecture,
! [X14] :
( ~ triangle(esk7_0,esk8_0,X14)
& shortest_path(esk4_0,esk5_0,esk6_0)
& on_path(esk7_0,esk6_0)
& on_path(esk8_0,esk6_0)
& sequential(esk7_0,esk8_0)
& complete ),
inference(shift_quantors,[status(thm)],[81]) ).
cnf(83,negated_conjecture,
complete,
inference(split_conjunct,[status(thm)],[82]) ).
cnf(84,negated_conjecture,
sequential(esk7_0,esk8_0),
inference(split_conjunct,[status(thm)],[82]) ).
cnf(85,negated_conjecture,
on_path(esk8_0,esk6_0),
inference(split_conjunct,[status(thm)],[82]) ).
cnf(86,negated_conjecture,
on_path(esk7_0,esk6_0),
inference(split_conjunct,[status(thm)],[82]) ).
cnf(87,negated_conjecture,
shortest_path(esk4_0,esk5_0,esk6_0),
inference(split_conjunct,[status(thm)],[82]) ).
cnf(88,negated_conjecture,
~ triangle(esk7_0,esk8_0,X1),
inference(split_conjunct,[status(thm)],[82]) ).
fof(106,plain,
! [X2,X3,X8] :
( ( ~ triangle(X2,X3,X8)
| ( edge(X2)
& edge(X3)
& edge(X8)
& sequential(X2,X3)
& sequential(X3,X8)
& sequential(X8,X2) ) )
& ( ~ edge(X2)
| ~ edge(X3)
| ~ edge(X8)
| ~ sequential(X2,X3)
| ~ sequential(X3,X8)
| ~ sequential(X8,X2)
| triangle(X2,X3,X8) ) ),
inference(fof_nnf,[status(thm)],[14]) ).
fof(107,plain,
! [X9,X10,X11] :
( ( ~ triangle(X9,X10,X11)
| ( edge(X9)
& edge(X10)
& edge(X11)
& sequential(X9,X10)
& sequential(X10,X11)
& sequential(X11,X9) ) )
& ( ~ edge(X9)
| ~ edge(X10)
| ~ edge(X11)
| ~ sequential(X9,X10)
| ~ sequential(X10,X11)
| ~ sequential(X11,X9)
| triangle(X9,X10,X11) ) ),
inference(variable_rename,[status(thm)],[106]) ).
fof(108,plain,
! [X9,X10,X11] :
( ( edge(X9)
| ~ triangle(X9,X10,X11) )
& ( edge(X10)
| ~ triangle(X9,X10,X11) )
& ( edge(X11)
| ~ triangle(X9,X10,X11) )
& ( sequential(X9,X10)
| ~ triangle(X9,X10,X11) )
& ( sequential(X10,X11)
| ~ triangle(X9,X10,X11) )
& ( sequential(X11,X9)
| ~ triangle(X9,X10,X11) )
& ( ~ edge(X9)
| ~ edge(X10)
| ~ edge(X11)
| ~ sequential(X9,X10)
| ~ sequential(X10,X11)
| ~ sequential(X11,X9)
| triangle(X9,X10,X11) ) ),
inference(distribute,[status(thm)],[107]) ).
cnf(109,plain,
( triangle(X1,X2,X3)
| ~ sequential(X3,X1)
| ~ sequential(X2,X3)
| ~ sequential(X1,X2)
| ~ edge(X3)
| ~ edge(X2)
| ~ edge(X1) ),
inference(split_conjunct,[status(thm)],[108]) ).
cnf(116,negated_conjecture,
edge(esk8_0),
inference(spm,[status(thm)],[31,84,theory(equality)]) ).
cnf(117,negated_conjecture,
edge(esk7_0),
inference(spm,[status(thm)],[32,84,theory(equality)]) ).
cnf(118,plain,
~ sequential(X1,X1),
inference(er,[status(thm)],[30,theory(equality)]) ).
cnf(120,negated_conjecture,
tail_of(esk8_0) = head_of(esk7_0),
inference(spm,[status(thm)],[29,84,theory(equality)]) ).
cnf(121,negated_conjecture,
path(esk4_0,esk5_0,esk6_0),
inference(spm,[status(thm)],[44,87,theory(equality)]) ).
cnf(122,plain,
( X1 = X2
| edge(esk2_2(X1,X2))
| $false
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(rw,[status(thm)],[56,83,theory(equality)]) ).
cnf(123,plain,
( X1 = X2
| edge(esk2_2(X1,X2))
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(cn,[status(thm)],[122,theory(equality)]) ).
cnf(124,plain,
( triangle(X1,X2,X3)
| ~ sequential(X3,X1)
| ~ sequential(X2,X3)
| ~ sequential(X1,X2)
| ~ edge(X3)
| ~ edge(X2) ),
inference(csr,[status(thm)],[109,32]) ).
cnf(125,plain,
( triangle(X1,X2,X3)
| ~ sequential(X3,X1)
| ~ sequential(X2,X3)
| ~ sequential(X1,X2)
| ~ edge(X3) ),
inference(csr,[status(thm)],[124,32]) ).
cnf(126,plain,
( triangle(X1,X2,X3)
| ~ sequential(X3,X1)
| ~ sequential(X2,X3)
| ~ sequential(X1,X2) ),
inference(csr,[status(thm)],[125,32]) ).
cnf(127,negated_conjecture,
( ~ sequential(X1,esk7_0)
| ~ sequential(esk8_0,X1)
| ~ sequential(esk7_0,esk8_0) ),
inference(spm,[status(thm)],[88,126,theory(equality)]) ).
cnf(134,negated_conjecture,
( ~ sequential(X1,esk7_0)
| ~ sequential(esk8_0,X1)
| $false ),
inference(rw,[status(thm)],[127,84,theory(equality)]) ).
cnf(135,negated_conjecture,
( ~ sequential(X1,esk7_0)
| ~ sequential(esk8_0,X1) ),
inference(cn,[status(thm)],[134,theory(equality)]) ).
cnf(136,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)],[54,83,theory(equality)]) ).
cnf(137,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)],[136,theory(equality)]) ).
cnf(138,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)],[137,24,theory(equality)]) ).
cnf(139,plain,
( head_of(esk2_2(X1,tail_of(X2))) = X1
| head_of(esk2_2(X1,tail_of(X2))) = tail_of(X2)
| X1 = tail_of(X2)
| ~ vertex(X1)
| ~ edge(X2) ),
inference(spm,[status(thm)],[137,23,theory(equality)]) ).
cnf(144,plain,
( edge(esk3_5(X1,X2,X3,X4,X5))
| sequential(X4,X5)
| ~ precedes(X4,X5,X1)
| ~ path(X2,X3,X1) ),
inference(spm,[status(thm)],[31,65,theory(equality)]) ).
cnf(146,plain,
( tail_of(esk3_5(X1,X2,X3,X4,X5)) = head_of(X4)
| sequential(X4,X5)
| ~ precedes(X4,X5,X1)
| ~ path(X2,X3,X1) ),
inference(spm,[status(thm)],[29,65,theory(equality)]) ).
cnf(147,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)],[52,83,theory(equality)]) ).
cnf(148,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)],[147,theory(equality)]) ).
cnf(151,plain,
( esk2_2(X1,X2) = X3
| sequential(esk2_2(X1,X2),X3)
| tail_of(esk2_2(X1,X2)) = X2
| X1 = X2
| tail_of(X3) != X2
| ~ edge(X3)
| ~ edge(esk2_2(X1,X2))
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(spm,[status(thm)],[28,148,theory(equality)]) ).
cnf(154,plain,
( X1 = X2
| head_of(esk2_2(X1,X2)) = X1
| tail_of(esk2_2(X1,X2)) = X1
| $false
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(rw,[status(thm)],[53,83,theory(equality)]) ).
cnf(155,plain,
( X1 = X2
| head_of(esk2_2(X1,X2)) = X1
| tail_of(esk2_2(X1,X2)) = X1
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(cn,[status(thm)],[154,theory(equality)]) ).
cnf(158,plain,
( esk2_2(X1,X2) = X3
| sequential(esk2_2(X1,X2),X3)
| tail_of(esk2_2(X1,X2)) = X1
| X1 = X2
| tail_of(X3) != X1
| ~ edge(X3)
| ~ edge(esk2_2(X1,X2))
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(spm,[status(thm)],[28,155,theory(equality)]) ).
cnf(160,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)],[51,83,theory(equality)]) ).
cnf(161,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)],[160,theory(equality)]) ).
cnf(162,plain,
( tail_of(esk2_2(X1,head_of(X2))) = X1
| tail_of(esk2_2(X1,head_of(X2))) = head_of(X2)
| X1 = head_of(X2)
| ~ vertex(X1)
| ~ edge(X2) ),
inference(spm,[status(thm)],[161,24,theory(equality)]) ).
cnf(163,plain,
( tail_of(esk2_2(X1,tail_of(X2))) = X1
| tail_of(esk2_2(X1,tail_of(X2))) = tail_of(X2)
| X1 = tail_of(X2)
| ~ vertex(X1)
| ~ edge(X2) ),
inference(spm,[status(thm)],[161,23,theory(equality)]) ).
cnf(168,plain,
( on_path(esk3_5(X1,X2,X3,X4,X5),X1)
| sequential(X4,X5)
| ~ path(X6,X7,X1)
| ~ precedes(X4,X5,X1)
| ~ path(X2,X3,X1) ),
inference(spm,[status(thm)],[63,64,theory(equality)]) ).
cnf(169,plain,
( sequential(X4,X5)
| ~ precedes(X5,esk3_5(X1,X2,X3,X4,X5),X1)
| ~ shortest_path(X6,X7,X1)
| ~ precedes(X4,X5,X1)
| ~ path(X2,X3,X1) ),
inference(spm,[status(thm)],[71,64,theory(equality)]) ).
cnf(176,negated_conjecture,
( precedes(X1,X2,esk6_0)
| ~ on_path(X2,esk6_0)
| ~ on_path(X1,esk6_0)
| ~ sequential(X1,X2) ),
inference(spm,[status(thm)],[77,121,theory(equality)]) ).
cnf(178,negated_conjecture,
( vertex(tail_of(esk8_0))
| ~ edge(esk7_0) ),
inference(spm,[status(thm)],[24,120,theory(equality)]) ).
cnf(179,negated_conjecture,
( tail_of(esk8_0) != tail_of(esk7_0)
| ~ edge(esk7_0) ),
inference(spm,[status(thm)],[35,120,theory(equality)]) ).
cnf(180,negated_conjecture,
( esk7_0 = X1
| sequential(esk7_0,X1)
| tail_of(X1) != tail_of(esk8_0)
| ~ edge(X1)
| ~ edge(esk7_0) ),
inference(spm,[status(thm)],[28,120,theory(equality)]) ).
cnf(181,negated_conjecture,
( vertex(tail_of(esk8_0))
| $false ),
inference(rw,[status(thm)],[178,117,theory(equality)]) ).
cnf(182,negated_conjecture,
vertex(tail_of(esk8_0)),
inference(cn,[status(thm)],[181,theory(equality)]) ).
cnf(183,negated_conjecture,
( tail_of(esk8_0) != tail_of(esk7_0)
| $false ),
inference(rw,[status(thm)],[179,117,theory(equality)]) ).
cnf(184,negated_conjecture,
tail_of(esk8_0) != tail_of(esk7_0),
inference(cn,[status(thm)],[183,theory(equality)]) ).
cnf(185,negated_conjecture,
( esk7_0 = X1
| sequential(esk7_0,X1)
| tail_of(X1) != tail_of(esk8_0)
| ~ edge(X1)
| $false ),
inference(rw,[status(thm)],[180,117,theory(equality)]) ).
cnf(186,negated_conjecture,
( esk7_0 = X1
| sequential(esk7_0,X1)
| tail_of(X1) != tail_of(esk8_0)
| ~ edge(X1) ),
inference(cn,[status(thm)],[185,theory(equality)]) ).
cnf(190,negated_conjecture,
( head_of(esk2_2(X1,tail_of(esk8_0))) = X1
| head_of(esk2_2(X1,tail_of(esk8_0))) = tail_of(esk8_0)
| X1 = tail_of(esk8_0)
| ~ vertex(X1) ),
inference(spm,[status(thm)],[137,182,theory(equality)]) ).
cnf(191,negated_conjecture,
( tail_of(esk2_2(X1,tail_of(esk8_0))) = X1
| tail_of(esk2_2(X1,tail_of(esk8_0))) = tail_of(esk8_0)
| X1 = tail_of(esk8_0)
| ~ vertex(X1) ),
inference(spm,[status(thm)],[161,182,theory(equality)]) ).
cnf(207,negated_conjecture,
( precedes(X1,esk7_0,esk6_0)
| ~ on_path(X1,esk6_0)
| ~ sequential(X1,esk7_0) ),
inference(spm,[status(thm)],[176,86,theory(equality)]) ).
cnf(208,negated_conjecture,
( precedes(X1,esk8_0,esk6_0)
| ~ on_path(X1,esk6_0)
| ~ sequential(X1,esk8_0) ),
inference(spm,[status(thm)],[176,85,theory(equality)]) ).
cnf(212,negated_conjecture,
( precedes(esk8_0,esk7_0,esk6_0)
| ~ sequential(esk8_0,esk7_0) ),
inference(spm,[status(thm)],[207,85,theory(equality)]) ).
cnf(217,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)],[138,23,theory(equality)]) ).
cnf(220,negated_conjecture,
( ~ precedes(esk7_0,esk8_0,esk6_0)
| ~ shortest_path(X1,X2,esk6_0)
| ~ sequential(esk8_0,esk7_0) ),
inference(spm,[status(thm)],[71,212,theory(equality)]) ).
cnf(226,negated_conjecture,
( ~ precedes(esk7_0,esk8_0,esk6_0)
| ~ sequential(esk8_0,esk7_0) ),
inference(spm,[status(thm)],[220,87,theory(equality)]) ).
cnf(234,negated_conjecture,
( precedes(esk7_0,esk8_0,esk6_0)
| ~ sequential(esk7_0,esk8_0) ),
inference(spm,[status(thm)],[208,86,theory(equality)]) ).
cnf(238,negated_conjecture,
( precedes(esk7_0,esk8_0,esk6_0)
| $false ),
inference(rw,[status(thm)],[234,84,theory(equality)]) ).
cnf(239,negated_conjecture,
precedes(esk7_0,esk8_0,esk6_0),
inference(cn,[status(thm)],[238,theory(equality)]) ).
cnf(242,negated_conjecture,
( head_of(esk2_2(tail_of(esk8_0),tail_of(X1))) = tail_of(X1)
| head_of(esk2_2(tail_of(esk8_0),tail_of(X1))) = tail_of(esk8_0)
| tail_of(esk8_0) = tail_of(X1)
| ~ edge(X1) ),
inference(spm,[status(thm)],[139,182,theory(equality)]) ).
cnf(243,plain,
( head_of(esk2_2(head_of(X1),tail_of(X2))) = tail_of(X2)
| head_of(esk2_2(head_of(X1),tail_of(X2))) = head_of(X1)
| head_of(X1) = tail_of(X2)
| ~ edge(X2)
| ~ edge(X1) ),
inference(spm,[status(thm)],[139,24,theory(equality)]) ).
cnf(257,negated_conjecture,
( head_of(esk8_0) != head_of(X1)
| tail_of(esk7_0) != tail_of(X1)
| ~ shortest_path(X2,X3,esk6_0) ),
inference(spm,[status(thm)],[72,239,theory(equality)]) ).
cnf(259,negated_conjecture,
( $false
| ~ sequential(esk8_0,esk7_0) ),
inference(rw,[status(thm)],[226,239,theory(equality)]) ).
cnf(260,negated_conjecture,
~ sequential(esk8_0,esk7_0),
inference(cn,[status(thm)],[259,theory(equality)]) ).
fof(285,plain,
( ~ epred5_0
<=> ! [X1] :
( tail_of(esk7_0) != tail_of(X1)
| head_of(esk8_0) != head_of(X1) ) ),
introduced(definition),
[split] ).
cnf(286,plain,
( epred5_0
| tail_of(esk7_0) != tail_of(X1)
| head_of(esk8_0) != head_of(X1) ),
inference(split_equiv,[status(thm)],[285]) ).
fof(287,plain,
( ~ epred6_0
<=> ! [X3,X2] : ~ shortest_path(X2,X3,esk6_0) ),
introduced(definition),
[split] ).
cnf(288,plain,
( epred6_0
| ~ shortest_path(X2,X3,esk6_0) ),
inference(split_equiv,[status(thm)],[287]) ).
cnf(289,negated_conjecture,
( ~ epred6_0
| ~ epred5_0 ),
inference(apply_def,[status(esa)],[inference(apply_def,[status(esa)],[257,285,theory(equality)]),287,theory(equality)]),
[split] ).
cnf(290,negated_conjecture,
epred6_0,
inference(spm,[status(thm)],[288,87,theory(equality)]) ).
cnf(292,negated_conjecture,
( $false
| ~ epred5_0 ),
inference(rw,[status(thm)],[289,290,theory(equality)]) ).
cnf(293,negated_conjecture,
~ epred5_0,
inference(cn,[status(thm)],[292,theory(equality)]) ).
cnf(296,negated_conjecture,
( epred5_0
| tail_of(esk2_2(X1,X2)) = X1
| X1 = X2
| tail_of(esk7_0) != tail_of(esk2_2(X1,X2))
| head_of(esk8_0) != X1
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(spm,[status(thm)],[286,155,theory(equality)]) ).
cnf(315,negated_conjecture,
( tail_of(esk2_2(X1,X2)) = X1
| X1 = X2
| tail_of(esk2_2(X1,X2)) != tail_of(esk7_0)
| head_of(esk8_0) != X1
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(sr,[status(thm)],[296,293,theory(equality)]) ).
cnf(326,negated_conjecture,
( esk7_0 = esk3_5(X1,X2,X3,X4,X5)
| sequential(esk7_0,esk3_5(X1,X2,X3,X4,X5))
| sequential(X4,X5)
| head_of(X4) != tail_of(esk8_0)
| ~ edge(esk3_5(X1,X2,X3,X4,X5))
| ~ precedes(X4,X5,X1)
| ~ path(X2,X3,X1) ),
inference(spm,[status(thm)],[186,146,theory(equality)]) ).
cnf(373,plain,
( tail_of(esk2_2(X1,X2)) = X2
| esk2_2(X1,X2) = X3
| X1 = X2
| sequential(esk2_2(X1,X2),X3)
| tail_of(X3) != X2
| ~ vertex(X2)
| ~ vertex(X1)
| ~ edge(X3) ),
inference(csr,[status(thm)],[151,123]) ).
cnf(374,plain,
( tail_of(esk2_2(X1,tail_of(X2))) = tail_of(X2)
| esk2_2(X1,tail_of(X2)) = X2
| X1 = tail_of(X2)
| sequential(esk2_2(X1,tail_of(X2)),X2)
| ~ vertex(tail_of(X2))
| ~ vertex(X1)
| ~ edge(X2) ),
inference(er,[status(thm)],[373,theory(equality)]) ).
cnf(415,plain,
( tail_of(esk2_2(X1,X2)) = X1
| esk2_2(X1,X2) = X3
| X1 = X2
| sequential(esk2_2(X1,X2),X3)
| tail_of(X3) != X1
| ~ vertex(X2)
| ~ vertex(X1)
| ~ edge(X3) ),
inference(csr,[status(thm)],[158,123]) ).
cnf(416,plain,
( tail_of(esk2_2(tail_of(X1),X2)) = tail_of(X1)
| esk2_2(tail_of(X1),X2) = X1
| tail_of(X1) = X2
| sequential(esk2_2(tail_of(X1),X2),X1)
| ~ vertex(X2)
| ~ vertex(tail_of(X1))
| ~ edge(X1) ),
inference(er,[status(thm)],[415,theory(equality)]) ).
cnf(422,negated_conjecture,
( head_of(esk2_2(tail_of(X1),tail_of(esk8_0))) = tail_of(esk8_0)
| head_of(esk2_2(tail_of(X1),tail_of(esk8_0))) = tail_of(X1)
| tail_of(X1) = tail_of(esk8_0)
| ~ edge(X1) ),
inference(spm,[status(thm)],[190,23,theory(equality)]) ).
cnf(425,plain,
( tail_of(esk2_2(tail_of(X1),head_of(X2))) = head_of(X2)
| tail_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)],[162,23,theory(equality)]) ).
cnf(452,negated_conjecture,
( tail_of(esk2_2(tail_of(X1),tail_of(esk8_0))) = tail_of(esk8_0)
| tail_of(esk2_2(tail_of(X1),tail_of(esk8_0))) = tail_of(X1)
| tail_of(X1) = tail_of(esk8_0)
| ~ edge(X1) ),
inference(spm,[status(thm)],[191,23,theory(equality)]) ).
cnf(453,negated_conjecture,
( tail_of(esk2_2(tail_of(esk8_0),tail_of(X1))) = tail_of(X1)
| tail_of(esk2_2(tail_of(esk8_0),tail_of(X1))) = tail_of(esk8_0)
| tail_of(esk8_0) = tail_of(X1)
| ~ edge(X1) ),
inference(spm,[status(thm)],[163,182,theory(equality)]) ).
cnf(454,plain,
( tail_of(esk2_2(head_of(X1),tail_of(X2))) = tail_of(X2)
| tail_of(esk2_2(head_of(X1),tail_of(X2))) = head_of(X1)
| head_of(X1) = tail_of(X2)
| ~ edge(X2)
| ~ edge(X1) ),
inference(spm,[status(thm)],[163,24,theory(equality)]) ).
cnf(492,negated_conjecture,
( on_path(esk3_5(esk6_0,X1,X2,X3,X4),esk6_0)
| sequential(X3,X4)
| ~ precedes(X3,X4,esk6_0)
| ~ path(X1,X2,esk6_0) ),
inference(spm,[status(thm)],[168,121,theory(equality)]) ).
cnf(503,negated_conjecture,
( precedes(X1,esk3_5(esk6_0,X2,X3,X4,X5),esk6_0)
| sequential(X4,X5)
| ~ on_path(X1,esk6_0)
| ~ sequential(X1,esk3_5(esk6_0,X2,X3,X4,X5))
| ~ precedes(X4,X5,esk6_0)
| ~ path(X2,X3,esk6_0) ),
inference(spm,[status(thm)],[176,492,theory(equality)]) ).
cnf(611,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)],[217,116,theory(equality)]) ).
cnf(626,negated_conjecture,
( head_of(esk2_2(tail_of(esk8_0),tail_of(esk7_0))) = tail_of(esk8_0)
| head_of(esk2_2(tail_of(esk8_0),tail_of(esk7_0))) = tail_of(esk7_0)
| tail_of(esk8_0) = tail_of(esk7_0) ),
inference(spm,[status(thm)],[242,117,theory(equality)]) ).
cnf(631,negated_conjecture,
( head_of(esk2_2(tail_of(esk8_0),tail_of(esk7_0))) = tail_of(esk8_0)
| head_of(esk2_2(tail_of(esk8_0),tail_of(esk7_0))) = tail_of(esk7_0) ),
inference(sr,[status(thm)],[626,184,theory(equality)]) ).
cnf(633,negated_conjecture,
( head_of(esk2_2(head_of(X1),tail_of(esk7_0))) = head_of(X1)
| head_of(esk2_2(head_of(X1),tail_of(esk7_0))) = tail_of(esk7_0)
| head_of(X1) = tail_of(esk7_0)
| ~ edge(X1) ),
inference(spm,[status(thm)],[243,117,theory(equality)]) ).
cnf(640,negated_conjecture,
( head_of(esk2_2(tail_of(esk8_0),tail_of(esk7_0))) = tail_of(esk7_0)
| tail_of(esk8_0) != tail_of(esk2_2(tail_of(esk8_0),tail_of(esk7_0)))
| ~ edge(esk2_2(tail_of(esk8_0),tail_of(esk7_0))) ),
inference(spm,[status(thm)],[35,631,theory(equality)]) ).
cnf(642,negated_conjecture,
( tail_of(esk2_2(tail_of(esk8_0),tail_of(esk7_0))) = tail_of(esk7_0)
| tail_of(esk8_0) = tail_of(esk7_0)
| head_of(esk2_2(tail_of(esk8_0),tail_of(esk7_0))) = tail_of(esk7_0)
| ~ vertex(tail_of(esk7_0))
| ~ vertex(tail_of(esk8_0)) ),
inference(spm,[status(thm)],[148,631,theory(equality)]) ).
cnf(644,negated_conjecture,
( epred5_0
| head_of(esk2_2(tail_of(esk8_0),tail_of(esk7_0))) = tail_of(esk7_0)
| tail_of(esk7_0) != tail_of(esk2_2(tail_of(esk8_0),tail_of(esk7_0)))
| head_of(esk8_0) != tail_of(esk8_0) ),
inference(spm,[status(thm)],[286,631,theory(equality)]) ).
cnf(647,negated_conjecture,
( tail_of(esk2_2(tail_of(esk8_0),tail_of(esk7_0))) = tail_of(esk7_0)
| tail_of(esk8_0) = tail_of(esk7_0)
| head_of(esk2_2(tail_of(esk8_0),tail_of(esk7_0))) = tail_of(esk7_0)
| ~ vertex(tail_of(esk7_0))
| $false ),
inference(rw,[status(thm)],[642,182,theory(equality)]) ).
cnf(648,negated_conjecture,
( tail_of(esk2_2(tail_of(esk8_0),tail_of(esk7_0))) = tail_of(esk7_0)
| tail_of(esk8_0) = tail_of(esk7_0)
| head_of(esk2_2(tail_of(esk8_0),tail_of(esk7_0))) = tail_of(esk7_0)
| ~ vertex(tail_of(esk7_0)) ),
inference(cn,[status(thm)],[647,theory(equality)]) ).
cnf(649,negated_conjecture,
( tail_of(esk2_2(tail_of(esk8_0),tail_of(esk7_0))) = tail_of(esk7_0)
| head_of(esk2_2(tail_of(esk8_0),tail_of(esk7_0))) = tail_of(esk7_0)
| ~ vertex(tail_of(esk7_0)) ),
inference(sr,[status(thm)],[648,184,theory(equality)]) ).
cnf(650,negated_conjecture,
( head_of(esk2_2(tail_of(esk8_0),tail_of(esk7_0))) = tail_of(esk7_0)
| tail_of(esk2_2(tail_of(esk8_0),tail_of(esk7_0))) != tail_of(esk7_0)
| head_of(esk8_0) != tail_of(esk8_0) ),
inference(sr,[status(thm)],[644,293,theory(equality)]) ).
cnf(654,negated_conjecture,
( tail_of(esk2_2(tail_of(esk8_0),tail_of(esk7_0))) = tail_of(esk8_0)
| tail_of(esk7_0) = tail_of(esk8_0)
| ~ vertex(tail_of(esk7_0))
| ~ vertex(tail_of(esk8_0))
| tail_of(esk2_2(tail_of(esk8_0),tail_of(esk7_0))) != tail_of(esk7_0)
| head_of(esk8_0) != tail_of(esk8_0) ),
inference(spm,[status(thm)],[155,650,theory(equality)]) ).
cnf(661,negated_conjecture,
( tail_of(esk2_2(tail_of(esk8_0),tail_of(esk7_0))) = tail_of(esk8_0)
| tail_of(esk7_0) = tail_of(esk8_0)
| ~ vertex(tail_of(esk7_0))
| $false
| tail_of(esk2_2(tail_of(esk8_0),tail_of(esk7_0))) != tail_of(esk7_0)
| head_of(esk8_0) != tail_of(esk8_0) ),
inference(rw,[status(thm)],[654,182,theory(equality)]) ).
cnf(662,negated_conjecture,
( tail_of(esk2_2(tail_of(esk8_0),tail_of(esk7_0))) = tail_of(esk8_0)
| tail_of(esk7_0) = tail_of(esk8_0)
| ~ vertex(tail_of(esk7_0))
| tail_of(esk2_2(tail_of(esk8_0),tail_of(esk7_0))) != tail_of(esk7_0)
| head_of(esk8_0) != tail_of(esk8_0) ),
inference(cn,[status(thm)],[661,theory(equality)]) ).
cnf(663,negated_conjecture,
( tail_of(esk2_2(tail_of(esk8_0),tail_of(esk7_0))) = tail_of(esk8_0)
| ~ vertex(tail_of(esk7_0))
| tail_of(esk2_2(tail_of(esk8_0),tail_of(esk7_0))) != tail_of(esk7_0)
| head_of(esk8_0) != tail_of(esk8_0) ),
inference(sr,[status(thm)],[662,184,theory(equality)]) ).
cnf(671,negated_conjecture,
( tail_of(esk2_2(tail_of(esk8_0),tail_of(esk7_0))) = tail_of(esk8_0)
| tail_of(esk7_0) = tail_of(esk8_0)
| tail_of(esk2_2(tail_of(esk8_0),tail_of(esk7_0))) = tail_of(esk7_0)
| ~ vertex(tail_of(esk7_0))
| ~ vertex(tail_of(esk8_0)) ),
inference(spm,[status(thm)],[155,649,theory(equality)]) ).
cnf(678,negated_conjecture,
( tail_of(esk2_2(tail_of(esk8_0),tail_of(esk7_0))) = tail_of(esk8_0)
| tail_of(esk7_0) = tail_of(esk8_0)
| tail_of(esk2_2(tail_of(esk8_0),tail_of(esk7_0))) = tail_of(esk7_0)
| ~ vertex(tail_of(esk7_0))
| $false ),
inference(rw,[status(thm)],[671,182,theory(equality)]) ).
cnf(679,negated_conjecture,
( tail_of(esk2_2(tail_of(esk8_0),tail_of(esk7_0))) = tail_of(esk8_0)
| tail_of(esk7_0) = tail_of(esk8_0)
| tail_of(esk2_2(tail_of(esk8_0),tail_of(esk7_0))) = tail_of(esk7_0)
| ~ vertex(tail_of(esk7_0)) ),
inference(cn,[status(thm)],[678,theory(equality)]) ).
cnf(680,negated_conjecture,
( tail_of(esk2_2(tail_of(esk8_0),tail_of(esk7_0))) = tail_of(esk8_0)
| tail_of(esk2_2(tail_of(esk8_0),tail_of(esk7_0))) = tail_of(esk7_0)
| ~ vertex(tail_of(esk7_0)) ),
inference(sr,[status(thm)],[679,184,theory(equality)]) ).
cnf(708,negated_conjecture,
( vertex(tail_of(esk7_0))
| ~ edge(esk2_2(tail_of(esk8_0),tail_of(esk7_0)))
| tail_of(esk2_2(tail_of(esk8_0),tail_of(esk7_0))) != tail_of(esk8_0) ),
inference(spm,[status(thm)],[24,640,theory(equality)]) ).
cnf(726,negated_conjecture,
( tail_of(esk2_2(tail_of(esk8_0),tail_of(esk7_0))) = tail_of(esk8_0)
| head_of(esk8_0) != tail_of(esk8_0)
| ~ vertex(tail_of(esk7_0)) ),
inference(csr,[status(thm)],[663,680]) ).
cnf(728,negated_conjecture,
( X1 = esk2_2(tail_of(esk8_0),tail_of(esk7_0))
| sequential(X1,esk2_2(tail_of(esk8_0),tail_of(esk7_0)))
| tail_of(esk8_0) != head_of(X1)
| ~ edge(esk2_2(tail_of(esk8_0),tail_of(esk7_0)))
| ~ edge(X1)
| head_of(esk8_0) != tail_of(esk8_0)
| ~ vertex(tail_of(esk7_0)) ),
inference(spm,[status(thm)],[28,726,theory(equality)]) ).
cnf(816,negated_conjecture,
( head_of(esk2_2(tail_of(esk7_0),tail_of(esk8_0))) = tail_of(esk8_0)
| head_of(esk2_2(tail_of(esk7_0),tail_of(esk8_0))) = tail_of(esk7_0)
| tail_of(esk7_0) = tail_of(esk8_0) ),
inference(spm,[status(thm)],[422,117,theory(equality)]) ).
cnf(822,negated_conjecture,
( head_of(esk2_2(tail_of(esk7_0),tail_of(esk8_0))) = tail_of(esk8_0)
| head_of(esk2_2(tail_of(esk7_0),tail_of(esk8_0))) = tail_of(esk7_0) ),
inference(sr,[status(thm)],[816,184,theory(equality)]) ).
cnf(825,negated_conjecture,
( head_of(esk2_2(tail_of(esk7_0),tail_of(esk8_0))) = tail_of(esk7_0)
| tail_of(esk8_0) != tail_of(esk2_2(tail_of(esk7_0),tail_of(esk8_0)))
| ~ edge(esk2_2(tail_of(esk7_0),tail_of(esk8_0))) ),
inference(spm,[status(thm)],[35,822,theory(equality)]) ).
cnf(902,negated_conjecture,
( vertex(tail_of(esk7_0))
| ~ edge(esk2_2(tail_of(esk7_0),tail_of(esk8_0)))
| tail_of(esk2_2(tail_of(esk7_0),tail_of(esk8_0))) != tail_of(esk8_0) ),
inference(spm,[status(thm)],[24,825,theory(equality)]) ).
cnf(1020,negated_conjecture,
( esk3_5(X1,X2,X3,X4,X5) = esk7_0
| sequential(esk7_0,esk3_5(X1,X2,X3,X4,X5))
| sequential(X4,X5)
| head_of(X4) != tail_of(esk8_0)
| ~ precedes(X4,X5,X1)
| ~ path(X2,X3,X1) ),
inference(csr,[status(thm)],[326,144]) ).
cnf(1216,negated_conjecture,
( tail_of(esk2_2(tail_of(esk7_0),tail_of(esk8_0))) = tail_of(esk8_0)
| tail_of(esk2_2(tail_of(esk7_0),tail_of(esk8_0))) = tail_of(esk7_0)
| tail_of(esk7_0) = tail_of(esk8_0) ),
inference(spm,[status(thm)],[452,117,theory(equality)]) ).
cnf(1223,negated_conjecture,
( tail_of(esk2_2(tail_of(esk7_0),tail_of(esk8_0))) = tail_of(esk8_0)
| tail_of(esk2_2(tail_of(esk7_0),tail_of(esk8_0))) = tail_of(esk7_0) ),
inference(sr,[status(thm)],[1216,184,theory(equality)]) ).
cnf(1247,negated_conjecture,
( vertex(tail_of(esk7_0))
| tail_of(esk2_2(tail_of(esk7_0),tail_of(esk8_0))) = tail_of(esk7_0)
| ~ edge(esk2_2(tail_of(esk7_0),tail_of(esk8_0))) ),
inference(spm,[status(thm)],[902,1223,theory(equality)]) ).
cnf(1253,negated_conjecture,
( vertex(tail_of(esk7_0))
| ~ edge(esk2_2(tail_of(esk7_0),tail_of(esk8_0))) ),
inference(spm,[status(thm)],[23,1247,theory(equality)]) ).
cnf(1277,negated_conjecture,
( tail_of(esk2_2(tail_of(esk8_0),tail_of(esk7_0))) = tail_of(esk8_0)
| tail_of(esk2_2(tail_of(esk8_0),tail_of(esk7_0))) = tail_of(esk7_0)
| tail_of(esk8_0) = tail_of(esk7_0) ),
inference(spm,[status(thm)],[453,117,theory(equality)]) ).
cnf(1284,negated_conjecture,
( tail_of(esk2_2(tail_of(esk8_0),tail_of(esk7_0))) = tail_of(esk8_0)
| tail_of(esk2_2(tail_of(esk8_0),tail_of(esk7_0))) = tail_of(esk7_0) ),
inference(sr,[status(thm)],[1277,184,theory(equality)]) ).
cnf(1308,negated_conjecture,
( vertex(tail_of(esk7_0))
| tail_of(esk2_2(tail_of(esk8_0),tail_of(esk7_0))) = tail_of(esk7_0)
| ~ edge(esk2_2(tail_of(esk8_0),tail_of(esk7_0))) ),
inference(spm,[status(thm)],[708,1284,theory(equality)]) ).
cnf(1314,negated_conjecture,
( vertex(tail_of(esk7_0))
| ~ edge(esk2_2(tail_of(esk8_0),tail_of(esk7_0))) ),
inference(spm,[status(thm)],[23,1308,theory(equality)]) ).
cnf(1463,plain,
( tail_of(esk2_2(X1,tail_of(X2))) = tail_of(X2)
| esk2_2(X1,tail_of(X2)) = X2
| X1 = tail_of(X2)
| sequential(esk2_2(X1,tail_of(X2)),X2)
| ~ vertex(X1)
| ~ edge(X2) ),
inference(csr,[status(thm)],[374,23]) ).
cnf(1464,negated_conjecture,
( tail_of(esk2_2(tail_of(esk8_0),tail_of(X1))) = tail_of(X1)
| esk2_2(tail_of(esk8_0),tail_of(X1)) = X1
| tail_of(esk8_0) = tail_of(X1)
| sequential(esk2_2(tail_of(esk8_0),tail_of(X1)),X1)
| ~ edge(X1) ),
inference(spm,[status(thm)],[1463,182,theory(equality)]) ).
cnf(1465,plain,
( tail_of(esk2_2(head_of(X1),tail_of(X2))) = tail_of(X2)
| esk2_2(head_of(X1),tail_of(X2)) = X2
| head_of(X1) = tail_of(X2)
| sequential(esk2_2(head_of(X1),tail_of(X2)),X2)
| ~ edge(X2)
| ~ edge(X1) ),
inference(spm,[status(thm)],[1463,24,theory(equality)]) ).
cnf(1466,plain,
( tail_of(esk2_2(tail_of(X1),tail_of(X2))) = tail_of(X2)
| esk2_2(tail_of(X1),tail_of(X2)) = X2
| tail_of(X1) = tail_of(X2)
| sequential(esk2_2(tail_of(X1),tail_of(X2)),X2)
| ~ edge(X2)
| ~ edge(X1) ),
inference(spm,[status(thm)],[1463,23,theory(equality)]) ).
cnf(1711,negated_conjecture,
( sequential(X1,X2)
| ~ precedes(X1,X2,esk6_0)
| ~ path(X3,X4,esk6_0)
| ~ shortest_path(X5,X6,esk6_0)
| ~ on_path(X2,esk6_0)
| ~ sequential(X2,esk3_5(esk6_0,X3,X4,X1,X2)) ),
inference(spm,[status(thm)],[169,503,theory(equality)]) ).
cnf(1734,negated_conjecture,
( sequential(X1,X2)
| ~ precedes(X1,X2,esk6_0)
| ~ path(X3,X4,esk6_0)
| ~ shortest_path(X5,X6,esk6_0)
| ~ sequential(X2,esk3_5(esk6_0,X3,X4,X1,X2)) ),
inference(csr,[status(thm)],[1711,62]) ).
cnf(1737,negated_conjecture,
( sequential(X1,esk7_0)
| esk3_5(esk6_0,X2,X3,X1,esk7_0) = esk7_0
| ~ precedes(X1,esk7_0,esk6_0)
| ~ path(X2,X3,esk6_0)
| ~ shortest_path(X4,X5,esk6_0)
| head_of(X1) != tail_of(esk8_0) ),
inference(spm,[status(thm)],[1734,1020,theory(equality)]) ).
cnf(1770,negated_conjecture,
( esk3_5(esk6_0,X1,X2,X3,esk7_0) = esk7_0
| sequential(X3,esk7_0)
| head_of(X3) != tail_of(esk8_0)
| ~ precedes(X3,esk7_0,esk6_0)
| ~ path(X1,X2,esk6_0) ),
inference(spm,[status(thm)],[1737,87,theory(equality)]) ).
cnf(1775,negated_conjecture,
( sequential(X1,esk7_0)
| ~ precedes(X1,esk7_0,esk6_0)
| ~ path(X2,X3,esk6_0)
| head_of(X1) != tail_of(esk8_0) ),
inference(spm,[status(thm)],[65,1770,theory(equality)]) ).
cnf(1823,negated_conjecture,
( sequential(X1,esk7_0)
| head_of(X1) != tail_of(esk8_0)
| ~ precedes(X1,esk7_0,esk6_0) ),
inference(spm,[status(thm)],[1775,121,theory(equality)]) ).
cnf(1824,negated_conjecture,
( sequential(esk7_0,esk7_0)
| ~ precedes(esk7_0,esk7_0,esk6_0) ),
inference(spm,[status(thm)],[1823,120,theory(equality)]) ).
cnf(1844,negated_conjecture,
~ precedes(esk7_0,esk7_0,esk6_0),
inference(sr,[status(thm)],[1824,118,theory(equality)]) ).
cnf(2230,plain,
( tail_of(esk2_2(tail_of(X1),X2)) = tail_of(X1)
| esk2_2(tail_of(X1),X2) = X1
| tail_of(X1) = X2
| sequential(esk2_2(tail_of(X1),X2),X1)
| ~ vertex(X2)
| ~ edge(X1) ),
inference(csr,[status(thm)],[416,23]) ).
cnf(2231,negated_conjecture,
( tail_of(esk2_2(tail_of(X1),tail_of(esk8_0))) = tail_of(X1)
| esk2_2(tail_of(X1),tail_of(esk8_0)) = X1
| tail_of(X1) = tail_of(esk8_0)
| sequential(esk2_2(tail_of(X1),tail_of(esk8_0)),X1)
| ~ edge(X1) ),
inference(spm,[status(thm)],[2230,182,theory(equality)]) ).
cnf(2232,plain,
( tail_of(esk2_2(tail_of(X1),head_of(X2))) = tail_of(X1)
| esk2_2(tail_of(X1),head_of(X2)) = X1
| tail_of(X1) = head_of(X2)
| sequential(esk2_2(tail_of(X1),head_of(X2)),X1)
| ~ edge(X1)
| ~ edge(X2) ),
inference(spm,[status(thm)],[2230,24,theory(equality)]) ).
cnf(2442,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)],[611,117,theory(equality)]) ).
cnf(2449,negated_conjecture,
( tail_of(esk2_2(tail_of(X1),head_of(esk8_0))) = tail_of(X1)
| tail_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)],[425,116,theory(equality)]) ).
cnf(2506,negated_conjecture,
( epred5_0
| 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)],[286,2442,theory(equality)]) ).
cnf(2523,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(esk2_2(tail_of(esk7_0),head_of(esk8_0))) != tail_of(esk7_0) ),
inference(sr,[status(thm)],[2506,293,theory(equality)]) ).
cnf(2525,negated_conjecture,
( head_of(esk8_0) = tail_of(esk7_0)
| tail_of(esk7_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)],[35,2523,theory(equality)]) ).
cnf(2765,negated_conjecture,
( tail_of(esk2_2(head_of(X1),tail_of(esk7_0))) = head_of(X1)
| tail_of(esk2_2(head_of(X1),tail_of(esk7_0))) = tail_of(esk7_0)
| head_of(X1) = tail_of(esk7_0)
| ~ edge(X1) ),
inference(spm,[status(thm)],[454,117,theory(equality)]) ).
cnf(3172,negated_conjecture,
( tail_of(esk2_2(tail_of(esk7_0),head_of(esk8_0))) = head_of(esk8_0)
| tail_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)],[2449,117,theory(equality)]) ).
cnf(3217,negated_conjecture,
( vertex(head_of(esk8_0))
| tail_of(esk2_2(tail_of(esk7_0),head_of(esk8_0))) = tail_of(esk7_0)
| head_of(esk8_0) = tail_of(esk7_0)
| ~ edge(esk2_2(tail_of(esk7_0),head_of(esk8_0))) ),
inference(spm,[status(thm)],[23,3172,theory(equality)]) ).
cnf(3237,negated_conjecture,
( head_of(esk8_0) = tail_of(esk7_0)
| vertex(head_of(esk8_0))
| ~ edge(esk2_2(tail_of(esk7_0),head_of(esk8_0))) ),
inference(csr,[status(thm)],[3217,2525]) ).
cnf(4703,negated_conjecture,
( tail_of(esk2_2(tail_of(esk8_0),tail_of(esk7_0))) = tail_of(esk7_0)
| esk2_2(tail_of(esk8_0),tail_of(esk7_0)) = esk7_0
| tail_of(esk8_0) = tail_of(esk7_0)
| sequential(esk2_2(tail_of(esk8_0),tail_of(esk7_0)),esk7_0) ),
inference(spm,[status(thm)],[1464,117,theory(equality)]) ).
cnf(4710,negated_conjecture,
( tail_of(esk2_2(tail_of(esk8_0),tail_of(esk7_0))) = tail_of(esk7_0)
| esk2_2(tail_of(esk8_0),tail_of(esk7_0)) = esk7_0
| sequential(esk2_2(tail_of(esk8_0),tail_of(esk7_0)),esk7_0) ),
inference(sr,[status(thm)],[4703,184,theory(equality)]) ).
cnf(4759,negated_conjecture,
( tail_of(esk7_0) = tail_of(esk8_0)
| esk2_2(tail_of(esk8_0),tail_of(esk7_0)) = esk7_0
| sequential(esk2_2(tail_of(esk8_0),tail_of(esk7_0)),esk7_0)
| head_of(esk8_0) != tail_of(esk8_0)
| ~ vertex(tail_of(esk7_0))
| ~ vertex(tail_of(esk8_0)) ),
inference(spm,[status(thm)],[315,4710,theory(equality)]) ).
cnf(4784,negated_conjecture,
( tail_of(esk7_0) = tail_of(esk8_0)
| esk2_2(tail_of(esk8_0),tail_of(esk7_0)) = esk7_0
| sequential(esk2_2(tail_of(esk8_0),tail_of(esk7_0)),esk7_0)
| head_of(esk8_0) != tail_of(esk8_0)
| ~ vertex(tail_of(esk7_0))
| $false ),
inference(rw,[status(thm)],[4759,182,theory(equality)]) ).
cnf(4785,negated_conjecture,
( tail_of(esk7_0) = tail_of(esk8_0)
| esk2_2(tail_of(esk8_0),tail_of(esk7_0)) = esk7_0
| sequential(esk2_2(tail_of(esk8_0),tail_of(esk7_0)),esk7_0)
| head_of(esk8_0) != tail_of(esk8_0)
| ~ vertex(tail_of(esk7_0)) ),
inference(cn,[status(thm)],[4784,theory(equality)]) ).
cnf(4786,negated_conjecture,
( esk2_2(tail_of(esk8_0),tail_of(esk7_0)) = esk7_0
| sequential(esk2_2(tail_of(esk8_0),tail_of(esk7_0)),esk7_0)
| head_of(esk8_0) != tail_of(esk8_0)
| ~ vertex(tail_of(esk7_0)) ),
inference(sr,[status(thm)],[4785,184,theory(equality)]) ).
cnf(4804,negated_conjecture,
( esk2_2(tail_of(esk8_0),tail_of(esk7_0)) = esk7_0
| ~ sequential(esk8_0,esk2_2(tail_of(esk8_0),tail_of(esk7_0)))
| head_of(esk8_0) != tail_of(esk8_0)
| ~ vertex(tail_of(esk7_0)) ),
inference(spm,[status(thm)],[135,4786,theory(equality)]) ).
cnf(5339,negated_conjecture,
( tail_of(esk2_2(tail_of(esk7_0),tail_of(esk8_0))) = tail_of(esk7_0)
| esk2_2(tail_of(esk7_0),tail_of(esk8_0)) = esk7_0
| tail_of(esk7_0) = tail_of(esk8_0)
| sequential(esk2_2(tail_of(esk7_0),tail_of(esk8_0)),esk7_0) ),
inference(spm,[status(thm)],[2231,117,theory(equality)]) ).
cnf(5347,negated_conjecture,
( tail_of(esk2_2(tail_of(esk7_0),tail_of(esk8_0))) = tail_of(esk7_0)
| esk2_2(tail_of(esk7_0),tail_of(esk8_0)) = esk7_0
| sequential(esk2_2(tail_of(esk7_0),tail_of(esk8_0)),esk7_0) ),
inference(sr,[status(thm)],[5339,184,theory(equality)]) ).
cnf(9168,negated_conjecture,
( X1 = esk2_2(tail_of(esk8_0),tail_of(esk7_0))
| sequential(X1,esk2_2(tail_of(esk8_0),tail_of(esk7_0)))
| head_of(esk8_0) != tail_of(esk8_0)
| head_of(X1) != tail_of(esk8_0)
| ~ edge(esk2_2(tail_of(esk8_0),tail_of(esk7_0)))
| ~ edge(X1) ),
inference(csr,[status(thm)],[728,1314]) ).
cnf(9169,negated_conjecture,
( X1 = esk2_2(tail_of(esk8_0),tail_of(esk7_0))
| sequential(X1,esk2_2(tail_of(esk8_0),tail_of(esk7_0)))
| tail_of(esk8_0) = tail_of(esk7_0)
| head_of(esk8_0) != tail_of(esk8_0)
| head_of(X1) != tail_of(esk8_0)
| ~ edge(X1)
| ~ vertex(tail_of(esk7_0))
| ~ vertex(tail_of(esk8_0)) ),
inference(spm,[status(thm)],[9168,123,theory(equality)]) ).
cnf(9172,negated_conjecture,
( X1 = esk2_2(tail_of(esk8_0),tail_of(esk7_0))
| sequential(X1,esk2_2(tail_of(esk8_0),tail_of(esk7_0)))
| tail_of(esk8_0) = tail_of(esk7_0)
| head_of(esk8_0) != tail_of(esk8_0)
| head_of(X1) != tail_of(esk8_0)
| ~ edge(X1)
| ~ vertex(tail_of(esk7_0))
| $false ),
inference(rw,[status(thm)],[9169,182,theory(equality)]) ).
cnf(9173,negated_conjecture,
( X1 = esk2_2(tail_of(esk8_0),tail_of(esk7_0))
| sequential(X1,esk2_2(tail_of(esk8_0),tail_of(esk7_0)))
| tail_of(esk8_0) = tail_of(esk7_0)
| head_of(esk8_0) != tail_of(esk8_0)
| head_of(X1) != tail_of(esk8_0)
| ~ edge(X1)
| ~ vertex(tail_of(esk7_0)) ),
inference(cn,[status(thm)],[9172,theory(equality)]) ).
cnf(9174,negated_conjecture,
( X1 = esk2_2(tail_of(esk8_0),tail_of(esk7_0))
| sequential(X1,esk2_2(tail_of(esk8_0),tail_of(esk7_0)))
| head_of(esk8_0) != tail_of(esk8_0)
| head_of(X1) != tail_of(esk8_0)
| ~ edge(X1)
| ~ vertex(tail_of(esk7_0)) ),
inference(sr,[status(thm)],[9173,184,theory(equality)]) ).
cnf(9296,negated_conjecture,
( esk2_2(tail_of(esk8_0),tail_of(esk7_0)) = esk7_0
| esk8_0 = esk2_2(tail_of(esk8_0),tail_of(esk7_0))
| head_of(esk8_0) != tail_of(esk8_0)
| ~ vertex(tail_of(esk7_0))
| ~ edge(esk8_0) ),
inference(spm,[status(thm)],[4804,9174,theory(equality)]) ).
cnf(9301,negated_conjecture,
( esk2_2(tail_of(esk8_0),tail_of(esk7_0)) = esk7_0
| esk8_0 = esk2_2(tail_of(esk8_0),tail_of(esk7_0))
| head_of(esk8_0) != tail_of(esk8_0)
| ~ vertex(tail_of(esk7_0))
| $false ),
inference(rw,[status(thm)],[9296,116,theory(equality)]) ).
cnf(9302,negated_conjecture,
( esk2_2(tail_of(esk8_0),tail_of(esk7_0)) = esk7_0
| esk8_0 = esk2_2(tail_of(esk8_0),tail_of(esk7_0))
| head_of(esk8_0) != tail_of(esk8_0)
| ~ vertex(tail_of(esk7_0)) ),
inference(cn,[status(thm)],[9301,theory(equality)]) ).
cnf(9303,negated_conjecture,
( esk2_2(tail_of(esk8_0),tail_of(esk7_0)) = esk7_0
| esk8_0 != esk7_0
| head_of(esk8_0) != tail_of(esk8_0)
| ~ vertex(tail_of(esk7_0)) ),
inference(ef,[status(thm)],[9302,theory(equality)]) ).
cnf(9332,negated_conjecture,
( tail_of(esk8_0) = tail_of(esk7_0)
| esk8_0 = esk7_0
| sequential(esk8_0,esk7_0)
| esk2_2(tail_of(esk8_0),tail_of(esk7_0)) = esk7_0
| head_of(esk8_0) != tail_of(esk8_0)
| ~ vertex(tail_of(esk7_0)) ),
inference(spm,[status(thm)],[4710,9302,theory(equality)]) ).
cnf(9414,negated_conjecture,
( esk8_0 = esk7_0
| sequential(esk8_0,esk7_0)
| esk2_2(tail_of(esk8_0),tail_of(esk7_0)) = esk7_0
| head_of(esk8_0) != tail_of(esk8_0)
| ~ vertex(tail_of(esk7_0)) ),
inference(sr,[status(thm)],[9332,184,theory(equality)]) ).
cnf(9415,negated_conjecture,
( esk8_0 = esk7_0
| esk2_2(tail_of(esk8_0),tail_of(esk7_0)) = esk7_0
| head_of(esk8_0) != tail_of(esk8_0)
| ~ vertex(tail_of(esk7_0)) ),
inference(sr,[status(thm)],[9414,260,theory(equality)]) ).
cnf(9446,negated_conjecture,
( tail_of(esk7_0) = tail_of(esk8_0)
| head_of(esk8_0) != tail_of(esk8_0)
| ~ vertex(tail_of(esk7_0))
| ~ vertex(tail_of(esk8_0))
| esk8_0 != esk7_0 ),
inference(spm,[status(thm)],[315,9303,theory(equality)]) ).
cnf(9491,negated_conjecture,
( tail_of(esk7_0) = tail_of(esk8_0)
| head_of(esk8_0) != tail_of(esk8_0)
| ~ vertex(tail_of(esk7_0))
| $false
| esk8_0 != esk7_0 ),
inference(rw,[status(thm)],[9446,182,theory(equality)]) ).
cnf(9492,negated_conjecture,
( tail_of(esk7_0) = tail_of(esk8_0)
| head_of(esk8_0) != tail_of(esk8_0)
| ~ vertex(tail_of(esk7_0))
| esk8_0 != esk7_0 ),
inference(cn,[status(thm)],[9491,theory(equality)]) ).
cnf(9493,negated_conjecture,
( head_of(esk8_0) != tail_of(esk8_0)
| ~ vertex(tail_of(esk7_0))
| esk8_0 != esk7_0 ),
inference(sr,[status(thm)],[9492,184,theory(equality)]) ).
cnf(9572,negated_conjecture,
( esk2_2(tail_of(esk8_0),tail_of(esk7_0)) = esk7_0
| head_of(esk8_0) != tail_of(esk8_0)
| ~ vertex(tail_of(esk7_0)) ),
inference(csr,[status(thm)],[9415,9493]) ).
cnf(9575,negated_conjecture,
( tail_of(esk7_0) = tail_of(esk8_0)
| head_of(esk8_0) != tail_of(esk8_0)
| ~ vertex(tail_of(esk7_0))
| ~ vertex(tail_of(esk8_0)) ),
inference(spm,[status(thm)],[315,9572,theory(equality)]) ).
cnf(9620,negated_conjecture,
( tail_of(esk7_0) = tail_of(esk8_0)
| head_of(esk8_0) != tail_of(esk8_0)
| ~ vertex(tail_of(esk7_0))
| $false ),
inference(rw,[status(thm)],[9575,182,theory(equality)]) ).
cnf(9621,negated_conjecture,
( tail_of(esk7_0) = tail_of(esk8_0)
| head_of(esk8_0) != tail_of(esk8_0)
| ~ vertex(tail_of(esk7_0)) ),
inference(cn,[status(thm)],[9620,theory(equality)]) ).
cnf(9622,negated_conjecture,
( head_of(esk8_0) != tail_of(esk8_0)
| ~ vertex(tail_of(esk7_0)) ),
inference(sr,[status(thm)],[9621,184,theory(equality)]) ).
cnf(9832,negated_conjecture,
( head_of(esk8_0) != tail_of(esk8_0)
| ~ edge(esk7_0) ),
inference(spm,[status(thm)],[9622,23,theory(equality)]) ).
cnf(9834,negated_conjecture,
( head_of(esk8_0) != tail_of(esk8_0)
| $false ),
inference(rw,[status(thm)],[9832,117,theory(equality)]) ).
cnf(9835,negated_conjecture,
head_of(esk8_0) != tail_of(esk8_0),
inference(cn,[status(thm)],[9834,theory(equality)]) ).
cnf(23384,negated_conjecture,
( tail_of(esk2_2(head_of(X1),tail_of(esk7_0))) = tail_of(esk7_0)
| esk2_2(head_of(X1),tail_of(esk7_0)) = esk7_0
| head_of(X1) = tail_of(esk7_0)
| sequential(esk2_2(head_of(X1),tail_of(esk7_0)),esk7_0)
| ~ edge(X1) ),
inference(spm,[status(thm)],[1465,117,theory(equality)]) ).
cnf(23547,negated_conjecture,
( tail_of(esk7_0) = head_of(X1)
| esk2_2(head_of(X1),tail_of(esk7_0)) = esk7_0
| sequential(esk2_2(head_of(X1),tail_of(esk7_0)),esk7_0)
| head_of(esk8_0) != head_of(X1)
| ~ vertex(tail_of(esk7_0))
| ~ vertex(head_of(X1))
| ~ edge(X1) ),
inference(spm,[status(thm)],[315,23384,theory(equality)]) ).
cnf(23685,negated_conjecture,
( esk2_2(head_of(X1),tail_of(esk7_0)) = esk7_0
| head_of(X1) = tail_of(esk7_0)
| sequential(esk2_2(head_of(X1),tail_of(esk7_0)),esk7_0)
| head_of(esk8_0) != head_of(X1)
| ~ vertex(tail_of(esk7_0))
| ~ edge(X1) ),
inference(csr,[status(thm)],[23547,24]) ).
cnf(23692,negated_conjecture,
( esk2_2(head_of(X1),tail_of(esk7_0)) = esk7_0
| head_of(X1) = tail_of(esk7_0)
| ~ sequential(esk8_0,esk2_2(head_of(X1),tail_of(esk7_0)))
| head_of(esk8_0) != head_of(X1)
| ~ vertex(tail_of(esk7_0))
| ~ edge(X1) ),
inference(spm,[status(thm)],[135,23685,theory(equality)]) ).
cnf(24396,negated_conjecture,
( tail_of(esk2_2(tail_of(X1),tail_of(esk8_0))) = tail_of(esk8_0)
| esk2_2(tail_of(X1),tail_of(esk8_0)) = esk8_0
| tail_of(X1) = tail_of(esk8_0)
| sequential(esk2_2(tail_of(X1),tail_of(esk8_0)),esk8_0)
| ~ edge(X1) ),
inference(spm,[status(thm)],[1466,116,theory(equality)]) ).
cnf(24605,negated_conjecture,
( tail_of(esk8_0) = tail_of(esk7_0)
| esk2_2(tail_of(esk7_0),tail_of(esk8_0)) = esk7_0
| sequential(esk2_2(tail_of(esk7_0),tail_of(esk8_0)),esk7_0)
| esk2_2(tail_of(esk7_0),tail_of(esk8_0)) = esk8_0
| sequential(esk2_2(tail_of(esk7_0),tail_of(esk8_0)),esk8_0)
| ~ edge(esk7_0) ),
inference(spm,[status(thm)],[5347,24396,theory(equality)]) ).
cnf(24659,negated_conjecture,
( tail_of(esk8_0) = tail_of(esk7_0)
| esk2_2(tail_of(esk7_0),tail_of(esk8_0)) = esk7_0
| sequential(esk2_2(tail_of(esk7_0),tail_of(esk8_0)),esk7_0)
| esk2_2(tail_of(esk7_0),tail_of(esk8_0)) = esk8_0
| sequential(esk2_2(tail_of(esk7_0),tail_of(esk8_0)),esk8_0)
| $false ),
inference(rw,[status(thm)],[24605,117,theory(equality)]) ).
cnf(24660,negated_conjecture,
( tail_of(esk8_0) = tail_of(esk7_0)
| esk2_2(tail_of(esk7_0),tail_of(esk8_0)) = esk7_0
| sequential(esk2_2(tail_of(esk7_0),tail_of(esk8_0)),esk7_0)
| esk2_2(tail_of(esk7_0),tail_of(esk8_0)) = esk8_0
| sequential(esk2_2(tail_of(esk7_0),tail_of(esk8_0)),esk8_0) ),
inference(cn,[status(thm)],[24659,theory(equality)]) ).
cnf(24661,negated_conjecture,
( esk2_2(tail_of(esk7_0),tail_of(esk8_0)) = esk7_0
| sequential(esk2_2(tail_of(esk7_0),tail_of(esk8_0)),esk7_0)
| esk2_2(tail_of(esk7_0),tail_of(esk8_0)) = esk8_0
| sequential(esk2_2(tail_of(esk7_0),tail_of(esk8_0)),esk8_0) ),
inference(sr,[status(thm)],[24660,184,theory(equality)]) ).
cnf(24731,negated_conjecture,
( edge(esk2_2(tail_of(esk7_0),tail_of(esk8_0)))
| esk2_2(tail_of(esk7_0),tail_of(esk8_0)) = esk8_0
| esk2_2(tail_of(esk7_0),tail_of(esk8_0)) = esk7_0
| sequential(esk2_2(tail_of(esk7_0),tail_of(esk8_0)),esk7_0) ),
inference(spm,[status(thm)],[32,24661,theory(equality)]) ).
cnf(24737,negated_conjecture,
( esk2_2(tail_of(esk7_0),tail_of(esk8_0)) = esk8_0
| esk2_2(tail_of(esk7_0),tail_of(esk8_0)) = esk7_0
| edge(esk2_2(tail_of(esk7_0),tail_of(esk8_0))) ),
inference(csr,[status(thm)],[24731,32]) ).
cnf(24745,negated_conjecture,
( vertex(tail_of(esk7_0))
| esk2_2(tail_of(esk7_0),tail_of(esk8_0)) = esk7_0
| esk2_2(tail_of(esk7_0),tail_of(esk8_0)) = esk8_0 ),
inference(spm,[status(thm)],[1253,24737,theory(equality)]) ).
cnf(24776,negated_conjecture,
( vertex(tail_of(esk7_0))
| esk2_2(tail_of(esk7_0),tail_of(esk8_0)) = esk7_0
| ~ edge(esk8_0) ),
inference(spm,[status(thm)],[1253,24745,theory(equality)]) ).
cnf(24836,negated_conjecture,
( vertex(tail_of(esk7_0))
| esk2_2(tail_of(esk7_0),tail_of(esk8_0)) = esk7_0
| $false ),
inference(rw,[status(thm)],[24776,116,theory(equality)]) ).
cnf(24837,negated_conjecture,
( vertex(tail_of(esk7_0))
| esk2_2(tail_of(esk7_0),tail_of(esk8_0)) = esk7_0 ),
inference(cn,[status(thm)],[24836,theory(equality)]) ).
cnf(24930,negated_conjecture,
( vertex(tail_of(esk7_0))
| ~ edge(esk7_0) ),
inference(spm,[status(thm)],[1253,24837,theory(equality)]) ).
cnf(24994,negated_conjecture,
( vertex(tail_of(esk7_0))
| $false ),
inference(rw,[status(thm)],[24930,117,theory(equality)]) ).
cnf(24995,negated_conjecture,
vertex(tail_of(esk7_0)),
inference(cn,[status(thm)],[24994,theory(equality)]) ).
cnf(25105,negated_conjecture,
( head_of(esk2_2(X1,tail_of(esk7_0))) = X1
| head_of(esk2_2(X1,tail_of(esk7_0))) = tail_of(esk7_0)
| X1 = tail_of(esk7_0)
| ~ vertex(X1) ),
inference(spm,[status(thm)],[137,24995,theory(equality)]) ).
cnf(25107,negated_conjecture,
( head_of(esk2_2(tail_of(esk7_0),head_of(X1))) = head_of(X1)
| head_of(esk2_2(tail_of(esk7_0),head_of(X1))) = tail_of(esk7_0)
| tail_of(esk7_0) = head_of(X1)
| ~ edge(X1) ),
inference(spm,[status(thm)],[138,24995,theory(equality)]) ).
cnf(25132,negated_conjecture,
( esk2_2(head_of(X1),tail_of(esk7_0)) = esk7_0
| head_of(X1) = tail_of(esk7_0)
| head_of(esk8_0) != head_of(X1)
| ~ sequential(esk8_0,esk2_2(head_of(X1),tail_of(esk7_0)))
| $false
| ~ edge(X1) ),
inference(rw,[status(thm)],[23692,24995,theory(equality)]) ).
cnf(25133,negated_conjecture,
( esk2_2(head_of(X1),tail_of(esk7_0)) = esk7_0
| head_of(X1) = tail_of(esk7_0)
| head_of(esk8_0) != head_of(X1)
| ~ sequential(esk8_0,esk2_2(head_of(X1),tail_of(esk7_0)))
| ~ edge(X1) ),
inference(cn,[status(thm)],[25132,theory(equality)]) ).
cnf(26711,negated_conjecture,
( tail_of(esk2_2(tail_of(esk7_0),head_of(X1))) = tail_of(esk7_0)
| head_of(X1) = tail_of(esk7_0)
| head_of(esk2_2(tail_of(esk7_0),head_of(X1))) = tail_of(esk7_0)
| ~ vertex(head_of(X1))
| ~ vertex(tail_of(esk7_0))
| ~ edge(X1) ),
inference(spm,[status(thm)],[155,25107,theory(equality)]) ).
cnf(26714,negated_conjecture,
( epred5_0
| head_of(esk2_2(tail_of(esk7_0),head_of(X1))) = tail_of(esk7_0)
| head_of(X1) = tail_of(esk7_0)
| tail_of(esk7_0) != tail_of(esk2_2(tail_of(esk7_0),head_of(X1)))
| head_of(esk8_0) != head_of(X1)
| ~ edge(X1) ),
inference(spm,[status(thm)],[286,25107,theory(equality)]) ).
cnf(26876,negated_conjecture,
( tail_of(esk2_2(tail_of(esk7_0),head_of(X1))) = tail_of(esk7_0)
| head_of(X1) = tail_of(esk7_0)
| head_of(esk2_2(tail_of(esk7_0),head_of(X1))) = tail_of(esk7_0)
| ~ vertex(head_of(X1))
| $false
| ~ edge(X1) ),
inference(rw,[status(thm)],[26711,24995,theory(equality)]) ).
cnf(26877,negated_conjecture,
( tail_of(esk2_2(tail_of(esk7_0),head_of(X1))) = tail_of(esk7_0)
| head_of(X1) = tail_of(esk7_0)
| head_of(esk2_2(tail_of(esk7_0),head_of(X1))) = tail_of(esk7_0)
| ~ vertex(head_of(X1))
| ~ edge(X1) ),
inference(cn,[status(thm)],[26876,theory(equality)]) ).
cnf(26878,negated_conjecture,
( head_of(esk2_2(tail_of(esk7_0),head_of(X1))) = tail_of(esk7_0)
| head_of(X1) = tail_of(esk7_0)
| tail_of(esk2_2(tail_of(esk7_0),head_of(X1))) != tail_of(esk7_0)
| head_of(esk8_0) != head_of(X1)
| ~ edge(X1) ),
inference(sr,[status(thm)],[26714,293,theory(equality)]) ).
cnf(27490,negated_conjecture,
( tail_of(esk2_2(tail_of(esk7_0),head_of(X1))) = tail_of(esk7_0)
| head_of(esk2_2(tail_of(esk7_0),head_of(X1))) = tail_of(esk7_0)
| head_of(X1) = tail_of(esk7_0)
| ~ edge(X1) ),
inference(csr,[status(thm)],[26877,24]) ).
cnf(27733,negated_conjecture,
( head_of(esk2_2(tail_of(esk7_0),head_of(X1))) = tail_of(esk7_0)
| head_of(X1) = tail_of(esk7_0)
| head_of(esk8_0) != head_of(X1)
| ~ edge(X1) ),
inference(csr,[status(thm)],[26878,27490]) ).
cnf(27738,negated_conjecture,
( tail_of(esk2_2(tail_of(esk7_0),head_of(X1))) = head_of(X1)
| tail_of(esk7_0) = head_of(X1)
| ~ vertex(head_of(X1))
| ~ vertex(tail_of(esk7_0))
| head_of(esk8_0) != head_of(X1)
| ~ edge(X1) ),
inference(spm,[status(thm)],[148,27733,theory(equality)]) ).
cnf(27894,negated_conjecture,
( tail_of(esk2_2(tail_of(esk7_0),head_of(X1))) = head_of(X1)
| tail_of(esk7_0) = head_of(X1)
| ~ vertex(head_of(X1))
| $false
| head_of(esk8_0) != head_of(X1)
| ~ edge(X1) ),
inference(rw,[status(thm)],[27738,24995,theory(equality)]) ).
cnf(27895,negated_conjecture,
( tail_of(esk2_2(tail_of(esk7_0),head_of(X1))) = head_of(X1)
| tail_of(esk7_0) = head_of(X1)
| ~ vertex(head_of(X1))
| head_of(esk8_0) != head_of(X1)
| ~ edge(X1) ),
inference(cn,[status(thm)],[27894,theory(equality)]) ).
cnf(28107,negated_conjecture,
( tail_of(esk2_2(tail_of(esk7_0),head_of(X1))) = head_of(X1)
| head_of(X1) = tail_of(esk7_0)
| head_of(esk8_0) != head_of(X1)
| ~ edge(X1) ),
inference(csr,[status(thm)],[27895,24]) ).
cnf(37401,negated_conjecture,
( tail_of(esk2_2(tail_of(esk7_0),head_of(X1))) = tail_of(esk7_0)
| esk2_2(tail_of(esk7_0),head_of(X1)) = esk7_0
| tail_of(esk7_0) = head_of(X1)
| sequential(esk2_2(tail_of(esk7_0),head_of(X1)),esk7_0)
| ~ edge(X1) ),
inference(spm,[status(thm)],[2232,117,theory(equality)]) ).
cnf(37972,negated_conjecture,
( tail_of(esk7_0) = head_of(X1)
| esk2_2(tail_of(esk7_0),head_of(X1)) = esk7_0
| sequential(esk2_2(tail_of(esk7_0),head_of(X1)),esk7_0)
| head_of(esk8_0) != head_of(X1)
| ~ edge(X1) ),
inference(spm,[status(thm)],[28107,37401,theory(equality)]) ).
cnf(38102,negated_conjecture,
( edge(esk2_2(tail_of(esk7_0),head_of(X1)))
| esk2_2(tail_of(esk7_0),head_of(X1)) = esk7_0
| head_of(X1) = tail_of(esk7_0)
| head_of(esk8_0) != head_of(X1)
| ~ edge(X1) ),
inference(spm,[status(thm)],[32,37972,theory(equality)]) ).
cnf(38234,negated_conjecture,
( head_of(esk8_0) = tail_of(esk7_0)
| vertex(head_of(esk8_0))
| esk2_2(tail_of(esk7_0),head_of(esk8_0)) = esk7_0
| ~ edge(esk8_0) ),
inference(spm,[status(thm)],[3237,38102,theory(equality)]) ).
cnf(38298,negated_conjecture,
( head_of(esk8_0) = tail_of(esk7_0)
| vertex(head_of(esk8_0))
| esk2_2(tail_of(esk7_0),head_of(esk8_0)) = esk7_0
| $false ),
inference(rw,[status(thm)],[38234,116,theory(equality)]) ).
cnf(38299,negated_conjecture,
( head_of(esk8_0) = tail_of(esk7_0)
| vertex(head_of(esk8_0))
| esk2_2(tail_of(esk7_0),head_of(esk8_0)) = esk7_0 ),
inference(cn,[status(thm)],[38298,theory(equality)]) ).
cnf(38339,negated_conjecture,
( head_of(esk7_0) = tail_of(esk7_0)
| head_of(esk7_0) = head_of(esk8_0)
| head_of(esk8_0) = tail_of(esk7_0)
| vertex(head_of(esk8_0)) ),
inference(spm,[status(thm)],[2442,38299,theory(equality)]) ).
cnf(38401,negated_conjecture,
( tail_of(esk8_0) = tail_of(esk7_0)
| head_of(esk7_0) = head_of(esk8_0)
| head_of(esk8_0) = tail_of(esk7_0)
| vertex(head_of(esk8_0)) ),
inference(rw,[status(thm)],[38339,120,theory(equality)]) ).
cnf(38402,negated_conjecture,
( tail_of(esk8_0) = tail_of(esk7_0)
| tail_of(esk8_0) = head_of(esk8_0)
| head_of(esk8_0) = tail_of(esk7_0)
| vertex(head_of(esk8_0)) ),
inference(rw,[status(thm)],[38401,120,theory(equality)]) ).
cnf(38403,negated_conjecture,
( head_of(esk8_0) = tail_of(esk8_0)
| head_of(esk8_0) = tail_of(esk7_0)
| vertex(head_of(esk8_0)) ),
inference(sr,[status(thm)],[38402,184,theory(equality)]) ).
cnf(38404,negated_conjecture,
( head_of(esk8_0) = tail_of(esk7_0)
| vertex(head_of(esk8_0)) ),
inference(sr,[status(thm)],[38403,9835,theory(equality)]) ).
cnf(38547,negated_conjecture,
( head_of(esk2_2(head_of(esk8_0),tail_of(esk7_0))) = tail_of(esk7_0)
| head_of(esk2_2(head_of(esk8_0),tail_of(esk7_0))) = head_of(esk8_0)
| head_of(esk8_0) = tail_of(esk7_0) ),
inference(spm,[status(thm)],[25105,38404,theory(equality)]) ).
cnf(39195,negated_conjecture,
( tail_of(esk2_2(head_of(esk8_0),tail_of(esk7_0))) = tail_of(esk7_0)
| head_of(esk8_0) = tail_of(esk7_0)
| head_of(esk2_2(head_of(esk8_0),tail_of(esk7_0))) = tail_of(esk7_0)
| ~ vertex(tail_of(esk7_0))
| ~ vertex(head_of(esk8_0)) ),
inference(spm,[status(thm)],[148,38547,theory(equality)]) ).
cnf(39197,negated_conjecture,
( epred5_0
| head_of(esk2_2(head_of(esk8_0),tail_of(esk7_0))) = tail_of(esk7_0)
| head_of(esk8_0) = tail_of(esk7_0)
| tail_of(esk7_0) != tail_of(esk2_2(head_of(esk8_0),tail_of(esk7_0))) ),
inference(spm,[status(thm)],[286,38547,theory(equality)]) ).
cnf(39327,negated_conjecture,
( tail_of(esk2_2(head_of(esk8_0),tail_of(esk7_0))) = tail_of(esk7_0)
| head_of(esk8_0) = tail_of(esk7_0)
| head_of(esk2_2(head_of(esk8_0),tail_of(esk7_0))) = tail_of(esk7_0)
| $false
| ~ vertex(head_of(esk8_0)) ),
inference(rw,[status(thm)],[39195,24995,theory(equality)]) ).
cnf(39328,negated_conjecture,
( tail_of(esk2_2(head_of(esk8_0),tail_of(esk7_0))) = tail_of(esk7_0)
| head_of(esk8_0) = tail_of(esk7_0)
| head_of(esk2_2(head_of(esk8_0),tail_of(esk7_0))) = tail_of(esk7_0)
| ~ vertex(head_of(esk8_0)) ),
inference(cn,[status(thm)],[39327,theory(equality)]) ).
cnf(39329,negated_conjecture,
( head_of(esk2_2(head_of(esk8_0),tail_of(esk7_0))) = tail_of(esk7_0)
| head_of(esk8_0) = tail_of(esk7_0)
| tail_of(esk2_2(head_of(esk8_0),tail_of(esk7_0))) != tail_of(esk7_0) ),
inference(sr,[status(thm)],[39197,293,theory(equality)]) ).
cnf(41007,negated_conjecture,
( tail_of(esk2_2(head_of(esk8_0),tail_of(esk7_0))) = tail_of(esk7_0)
| head_of(esk2_2(head_of(esk8_0),tail_of(esk7_0))) = tail_of(esk7_0)
| head_of(esk8_0) = tail_of(esk7_0) ),
inference(csr,[status(thm)],[39328,38404]) ).
cnf(41008,negated_conjecture,
( head_of(esk2_2(head_of(esk8_0),tail_of(esk7_0))) = tail_of(esk7_0)
| head_of(esk8_0) = tail_of(esk7_0) ),
inference(csr,[status(thm)],[41007,39329]) ).
cnf(41012,negated_conjecture,
( tail_of(esk2_2(head_of(esk8_0),tail_of(esk7_0))) = head_of(esk8_0)
| tail_of(esk7_0) = head_of(esk8_0)
| ~ vertex(tail_of(esk7_0))
| ~ vertex(head_of(esk8_0)) ),
inference(spm,[status(thm)],[155,41008,theory(equality)]) ).
cnf(41121,negated_conjecture,
( tail_of(esk2_2(head_of(esk8_0),tail_of(esk7_0))) = head_of(esk8_0)
| tail_of(esk7_0) = head_of(esk8_0)
| $false
| ~ vertex(head_of(esk8_0)) ),
inference(rw,[status(thm)],[41012,24995,theory(equality)]) ).
cnf(41122,negated_conjecture,
( tail_of(esk2_2(head_of(esk8_0),tail_of(esk7_0))) = head_of(esk8_0)
| tail_of(esk7_0) = head_of(esk8_0)
| ~ vertex(head_of(esk8_0)) ),
inference(cn,[status(thm)],[41121,theory(equality)]) ).
cnf(41180,negated_conjecture,
( tail_of(esk2_2(head_of(esk8_0),tail_of(esk7_0))) = head_of(esk8_0)
| head_of(esk8_0) = tail_of(esk7_0) ),
inference(csr,[status(thm)],[41122,38404]) ).
cnf(41182,negated_conjecture,
( X1 = esk2_2(head_of(esk8_0),tail_of(esk7_0))
| sequential(X1,esk2_2(head_of(esk8_0),tail_of(esk7_0)))
| head_of(esk8_0) = tail_of(esk7_0)
| head_of(esk8_0) != head_of(X1)
| ~ edge(esk2_2(head_of(esk8_0),tail_of(esk7_0)))
| ~ edge(X1) ),
inference(spm,[status(thm)],[28,41180,theory(equality)]) ).
cnf(54325,negated_conjecture,
( X1 = esk2_2(head_of(esk8_0),tail_of(esk7_0))
| head_of(esk8_0) = tail_of(esk7_0)
| sequential(X1,esk2_2(head_of(esk8_0),tail_of(esk7_0)))
| head_of(esk8_0) != head_of(X1)
| ~ edge(X1)
| ~ vertex(tail_of(esk7_0))
| ~ vertex(head_of(esk8_0)) ),
inference(spm,[status(thm)],[41182,123,theory(equality)]) ).
cnf(54328,negated_conjecture,
( X1 = esk2_2(head_of(esk8_0),tail_of(esk7_0))
| head_of(esk8_0) = tail_of(esk7_0)
| sequential(X1,esk2_2(head_of(esk8_0),tail_of(esk7_0)))
| head_of(esk8_0) != head_of(X1)
| ~ edge(X1)
| $false
| ~ vertex(head_of(esk8_0)) ),
inference(rw,[status(thm)],[54325,24995,theory(equality)]) ).
cnf(54329,negated_conjecture,
( X1 = esk2_2(head_of(esk8_0),tail_of(esk7_0))
| head_of(esk8_0) = tail_of(esk7_0)
| sequential(X1,esk2_2(head_of(esk8_0),tail_of(esk7_0)))
| head_of(esk8_0) != head_of(X1)
| ~ edge(X1)
| ~ vertex(head_of(esk8_0)) ),
inference(cn,[status(thm)],[54328,theory(equality)]) ).
cnf(54353,negated_conjecture,
( X1 = esk2_2(head_of(esk8_0),tail_of(esk7_0))
| head_of(esk8_0) = tail_of(esk7_0)
| sequential(X1,esk2_2(head_of(esk8_0),tail_of(esk7_0)))
| head_of(esk8_0) != head_of(X1)
| ~ edge(X1) ),
inference(csr,[status(thm)],[54329,38404]) ).
cnf(54364,negated_conjecture,
( esk2_2(head_of(esk8_0),tail_of(esk7_0)) = esk7_0
| head_of(esk8_0) = tail_of(esk7_0)
| esk8_0 = esk2_2(head_of(esk8_0),tail_of(esk7_0))
| ~ edge(esk8_0) ),
inference(spm,[status(thm)],[25133,54353,theory(equality)]) ).
cnf(54369,negated_conjecture,
( esk2_2(head_of(esk8_0),tail_of(esk7_0)) = esk7_0
| head_of(esk8_0) = tail_of(esk7_0)
| esk8_0 = esk2_2(head_of(esk8_0),tail_of(esk7_0))
| $false ),
inference(rw,[status(thm)],[54364,116,theory(equality)]) ).
cnf(54370,negated_conjecture,
( esk2_2(head_of(esk8_0),tail_of(esk7_0)) = esk7_0
| head_of(esk8_0) = tail_of(esk7_0)
| esk8_0 = esk2_2(head_of(esk8_0),tail_of(esk7_0)) ),
inference(cn,[status(thm)],[54369,theory(equality)]) ).
cnf(54390,negated_conjecture,
( tail_of(esk8_0) = tail_of(esk7_0)
| tail_of(esk8_0) = head_of(esk8_0)
| head_of(esk8_0) = tail_of(esk7_0)
| esk2_2(head_of(esk8_0),tail_of(esk7_0)) = esk7_0
| ~ edge(esk8_0) ),
inference(spm,[status(thm)],[2765,54370,theory(equality)]) ).
cnf(54492,negated_conjecture,
( tail_of(esk8_0) = tail_of(esk7_0)
| tail_of(esk8_0) = head_of(esk8_0)
| head_of(esk8_0) = tail_of(esk7_0)
| esk2_2(head_of(esk8_0),tail_of(esk7_0)) = esk7_0
| $false ),
inference(rw,[status(thm)],[54390,116,theory(equality)]) ).
cnf(54493,negated_conjecture,
( tail_of(esk8_0) = tail_of(esk7_0)
| tail_of(esk8_0) = head_of(esk8_0)
| head_of(esk8_0) = tail_of(esk7_0)
| esk2_2(head_of(esk8_0),tail_of(esk7_0)) = esk7_0 ),
inference(cn,[status(thm)],[54492,theory(equality)]) ).
cnf(54494,negated_conjecture,
( head_of(esk8_0) = tail_of(esk8_0)
| head_of(esk8_0) = tail_of(esk7_0)
| esk2_2(head_of(esk8_0),tail_of(esk7_0)) = esk7_0 ),
inference(sr,[status(thm)],[54493,184,theory(equality)]) ).
cnf(54495,negated_conjecture,
( head_of(esk8_0) = tail_of(esk7_0)
| esk2_2(head_of(esk8_0),tail_of(esk7_0)) = esk7_0 ),
inference(sr,[status(thm)],[54494,9835,theory(equality)]) ).
cnf(54659,negated_conjecture,
( head_of(esk7_0) = tail_of(esk7_0)
| head_of(esk7_0) = head_of(esk8_0)
| head_of(esk8_0) = tail_of(esk7_0)
| ~ edge(esk8_0) ),
inference(spm,[status(thm)],[633,54495,theory(equality)]) ).
cnf(54720,negated_conjecture,
( tail_of(esk8_0) = tail_of(esk7_0)
| head_of(esk7_0) = head_of(esk8_0)
| head_of(esk8_0) = tail_of(esk7_0)
| ~ edge(esk8_0) ),
inference(rw,[status(thm)],[54659,120,theory(equality)]) ).
cnf(54721,negated_conjecture,
( tail_of(esk8_0) = tail_of(esk7_0)
| tail_of(esk8_0) = head_of(esk8_0)
| head_of(esk8_0) = tail_of(esk7_0)
| ~ edge(esk8_0) ),
inference(rw,[status(thm)],[54720,120,theory(equality)]) ).
cnf(54722,negated_conjecture,
( tail_of(esk8_0) = tail_of(esk7_0)
| tail_of(esk8_0) = head_of(esk8_0)
| head_of(esk8_0) = tail_of(esk7_0)
| $false ),
inference(rw,[status(thm)],[54721,116,theory(equality)]) ).
cnf(54723,negated_conjecture,
( tail_of(esk8_0) = tail_of(esk7_0)
| tail_of(esk8_0) = head_of(esk8_0)
| head_of(esk8_0) = tail_of(esk7_0) ),
inference(cn,[status(thm)],[54722,theory(equality)]) ).
cnf(54724,negated_conjecture,
( head_of(esk8_0) = tail_of(esk8_0)
| head_of(esk8_0) = tail_of(esk7_0) ),
inference(sr,[status(thm)],[54723,184,theory(equality)]) ).
cnf(54725,negated_conjecture,
head_of(esk8_0) = tail_of(esk7_0),
inference(sr,[status(thm)],[54724,9835,theory(equality)]) ).
cnf(54849,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)],[28,54725,theory(equality)]) ).
cnf(55516,negated_conjecture,
( esk8_0 = X1
| sequential(esk8_0,X1)
| tail_of(X1) != tail_of(esk7_0)
| ~ edge(X1)
| $false ),
inference(rw,[status(thm)],[54849,116,theory(equality)]) ).
cnf(55517,negated_conjecture,
( esk8_0 = X1
| sequential(esk8_0,X1)
| tail_of(X1) != tail_of(esk7_0)
| ~ edge(X1) ),
inference(cn,[status(thm)],[55516,theory(equality)]) ).
cnf(55712,negated_conjecture,
( esk8_0 = esk7_0
| sequential(esk8_0,esk7_0)
| ~ edge(esk7_0) ),
inference(er,[status(thm)],[55517,theory(equality)]) ).
cnf(55758,negated_conjecture,
( esk8_0 = esk7_0
| sequential(esk8_0,esk7_0)
| $false ),
inference(rw,[status(thm)],[55712,117,theory(equality)]) ).
cnf(55759,negated_conjecture,
( esk8_0 = esk7_0
| sequential(esk8_0,esk7_0) ),
inference(cn,[status(thm)],[55758,theory(equality)]) ).
cnf(55760,negated_conjecture,
esk8_0 = esk7_0,
inference(sr,[status(thm)],[55759,260,theory(equality)]) ).
cnf(55763,negated_conjecture,
precedes(esk7_0,esk7_0,esk6_0),
inference(rw,[status(thm)],[239,55760,theory(equality)]) ).
cnf(55764,negated_conjecture,
$false,
inference(sr,[status(thm)],[55763,1844,theory(equality)]) ).
cnf(55765,negated_conjecture,
$false,
55764,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GRA/GRA009+1.p
% --creating new selector for [GRA001+0.ax]
% -running prover on /tmp/tmpfUWJdZ/sel_GRA009+1.p_1 with time limit 29
% -prover status Theorem
% Problem GRA009+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GRA/GRA009+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GRA/GRA009+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
%
%------------------------------------------------------------------------------