TSTP Solution File: GRA008+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : GRA008+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 09:56:35 EST 2010
% Result : Theorem 7.25s
% Output : CNFRefutation 7.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 89
% Number of leaves : 12
% Syntax : Number of formulae : 336 ( 24 unt; 0 def)
% Number of atoms : 1568 ( 662 equ)
% Maximal formula atoms : 37 ( 4 avg)
% Number of connectives : 1946 ( 714 ~;1041 |; 161 &)
% ( 7 <=>; 20 =>; 1 <=; 2 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 4 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-5 aty)
% Number of variables : 508 ( 41 sgn 190 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] :
( edge(X1)
=> ( vertex(head_of(X1))
& vertex(tail_of(X1)) ) ),
file('/tmp/tmp2znHc3/sel_GRA008+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/tmp2znHc3/sel_GRA008+1.p_1',sequential_defn) ).
fof(3,axiom,
! [X1] :
( edge(X1)
=> head_of(X1) != tail_of(X1) ),
file('/tmp/tmp2znHc3/sel_GRA008+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/tmp2znHc3/sel_GRA008+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/tmp2znHc3/sel_GRA008+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/tmp2znHc3/sel_GRA008+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/tmp2znHc3/sel_GRA008+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/tmp2znHc3/sel_GRA008+1.p_1',precedes_defn) ).
fof(13,conjecture,
( complete
=> ! [X4,X5,X2,X3,X7] :
( ( shortest_path(X4,X5,X7)
& precedes(X2,X3,X7)
& sequential(X2,X3) )
=> ? [X8] : triangle(X2,X3,X8) ) ),
file('/tmp/tmp2znHc3/sel_GRA008+1.p_1',sequential_is_triangle) ).
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/tmp2znHc3/sel_GRA008+1.p_1',triangle_defn) ).
fof(15,negated_conjecture,
~ ( complete
=> ! [X4,X5,X2,X3,X7] :
( ( shortest_path(X4,X5,X7)
& precedes(X2,X3,X7)
& sequential(X2,X3) )
=> ? [X8] : triangle(X2,X3,X8) ) ),
inference(assume_negation,[status(cth)],[13]) ).
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]) ).
cnf(78,plain,
( precedes(X4,X5,X3)
| ~ path(X1,X2,X3)
| ~ on_path(X5,X3)
| ~ on_path(X4,X3)
| ~ precedes(X6,X5,X3)
| ~ sequential(X4,X6) ),
inference(split_conjunct,[status(thm)],[76]) ).
fof(96,negated_conjecture,
( complete
& ? [X4,X5,X2,X3,X7] :
( shortest_path(X4,X5,X7)
& precedes(X2,X3,X7)
& sequential(X2,X3)
& ! [X8] : ~ triangle(X2,X3,X8) ) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(97,negated_conjecture,
( complete
& ? [X9,X10,X11,X12,X13] :
( shortest_path(X9,X10,X13)
& precedes(X11,X12,X13)
& sequential(X11,X12)
& ! [X14] : ~ triangle(X11,X12,X14) ) ),
inference(variable_rename,[status(thm)],[96]) ).
fof(98,negated_conjecture,
( complete
& shortest_path(esk6_0,esk7_0,esk10_0)
& precedes(esk8_0,esk9_0,esk10_0)
& sequential(esk8_0,esk9_0)
& ! [X14] : ~ triangle(esk8_0,esk9_0,X14) ),
inference(skolemize,[status(esa)],[97]) ).
fof(99,negated_conjecture,
! [X14] :
( ~ triangle(esk8_0,esk9_0,X14)
& shortest_path(esk6_0,esk7_0,esk10_0)
& precedes(esk8_0,esk9_0,esk10_0)
& sequential(esk8_0,esk9_0)
& complete ),
inference(shift_quantors,[status(thm)],[98]) ).
cnf(100,negated_conjecture,
complete,
inference(split_conjunct,[status(thm)],[99]) ).
cnf(101,negated_conjecture,
sequential(esk8_0,esk9_0),
inference(split_conjunct,[status(thm)],[99]) ).
cnf(102,negated_conjecture,
precedes(esk8_0,esk9_0,esk10_0),
inference(split_conjunct,[status(thm)],[99]) ).
cnf(103,negated_conjecture,
shortest_path(esk6_0,esk7_0,esk10_0),
inference(split_conjunct,[status(thm)],[99]) ).
cnf(104,negated_conjecture,
~ triangle(esk8_0,esk9_0,X1),
inference(split_conjunct,[status(thm)],[99]) ).
fof(105,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(106,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)],[105]) ).
fof(107,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)],[106]) ).
cnf(108,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)],[107]) ).
cnf(115,negated_conjecture,
edge(esk9_0),
inference(spm,[status(thm)],[31,101,theory(equality)]) ).
cnf(116,negated_conjecture,
edge(esk8_0),
inference(spm,[status(thm)],[32,101,theory(equality)]) ).
cnf(117,plain,
~ sequential(X1,X1),
inference(er,[status(thm)],[30,theory(equality)]) ).
cnf(119,negated_conjecture,
tail_of(esk9_0) = head_of(esk8_0),
inference(spm,[status(thm)],[29,101,theory(equality)]) ).
cnf(120,negated_conjecture,
path(esk6_0,esk7_0,esk10_0),
inference(spm,[status(thm)],[44,103,theory(equality)]) ).
cnf(122,negated_conjecture,
( on_path(esk9_0,esk10_0)
| ~ path(X1,X2,esk10_0) ),
inference(spm,[status(thm)],[62,102,theory(equality)]) ).
cnf(124,plain,
( X1 = X2
| edge(esk2_2(X1,X2))
| $false
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(rw,[status(thm)],[56,100,theory(equality)]) ).
cnf(125,plain,
( X1 = X2
| edge(esk2_2(X1,X2))
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(cn,[status(thm)],[124,theory(equality)]) ).
cnf(127,negated_conjecture,
( head_of(esk9_0) != head_of(X1)
| tail_of(esk8_0) != tail_of(X1)
| ~ shortest_path(X2,X3,esk10_0) ),
inference(spm,[status(thm)],[72,102,theory(equality)]) ).
cnf(128,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(130,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(131,plain,
( triangle(X1,X2,X3)
| ~ sequential(X3,X1)
| ~ sequential(X2,X3)
| ~ sequential(X1,X2)
| ~ edge(X3)
| ~ edge(X2) ),
inference(csr,[status(thm)],[108,32]) ).
cnf(132,plain,
( triangle(X1,X2,X3)
| ~ sequential(X3,X1)
| ~ sequential(X2,X3)
| ~ sequential(X1,X2)
| ~ edge(X3) ),
inference(csr,[status(thm)],[131,32]) ).
cnf(133,plain,
( triangle(X1,X2,X3)
| ~ sequential(X3,X1)
| ~ sequential(X2,X3)
| ~ sequential(X1,X2) ),
inference(csr,[status(thm)],[132,32]) ).
cnf(134,negated_conjecture,
( ~ sequential(X1,esk8_0)
| ~ sequential(esk9_0,X1)
| ~ sequential(esk8_0,esk9_0) ),
inference(spm,[status(thm)],[104,133,theory(equality)]) ).
cnf(141,negated_conjecture,
( ~ sequential(X1,esk8_0)
| ~ sequential(esk9_0,X1)
| $false ),
inference(rw,[status(thm)],[134,101,theory(equality)]) ).
cnf(142,negated_conjecture,
( ~ sequential(X1,esk8_0)
| ~ sequential(esk9_0,X1) ),
inference(cn,[status(thm)],[141,theory(equality)]) ).
cnf(143,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)],[54,100,theory(equality)]) ).
cnf(144,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)],[143,theory(equality)]) ).
cnf(145,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)],[144,24,theory(equality)]) ).
cnf(146,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)],[144,23,theory(equality)]) ).
cnf(151,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(153,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(156,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)],[52,100,theory(equality)]) ).
cnf(157,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)],[156,theory(equality)]) ).
cnf(160,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)],[28,157,theory(equality)]) ).
cnf(161,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)],[53,100,theory(equality)]) ).
cnf(162,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)],[161,theory(equality)]) ).
cnf(165,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)],[28,162,theory(equality)]) ).
cnf(167,plain,
( precedes(X4,X5,X3)
| ~ on_path(X4,X3)
| ~ precedes(X6,X5,X3)
| ~ path(X1,X2,X3)
| ~ sequential(X4,X6) ),
inference(csr,[status(thm)],[78,62]) ).
cnf(169,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)],[51,100,theory(equality)]) ).
cnf(170,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)],[169,theory(equality)]) ).
cnf(171,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)],[170,24,theory(equality)]) ).
cnf(172,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)],[170,23,theory(equality)]) ).
cnf(180,negated_conjecture,
( precedes(X1,X2,esk10_0)
| ~ on_path(X2,esk10_0)
| ~ on_path(X1,esk10_0)
| ~ sequential(X1,X2) ),
inference(spm,[status(thm)],[77,120,theory(equality)]) ).
cnf(181,negated_conjecture,
( precedes(X1,X2,esk10_0)
| ~ on_path(X1,esk10_0)
| ~ precedes(X3,X2,esk10_0)
| ~ sequential(X1,X3) ),
inference(spm,[status(thm)],[167,120,theory(equality)]) ).
cnf(182,negated_conjecture,
( vertex(tail_of(esk9_0))
| ~ edge(esk8_0) ),
inference(spm,[status(thm)],[24,119,theory(equality)]) ).
cnf(183,negated_conjecture,
( tail_of(esk9_0) != tail_of(esk8_0)
| ~ edge(esk8_0) ),
inference(spm,[status(thm)],[35,119,theory(equality)]) ).
cnf(184,negated_conjecture,
( esk8_0 = X1
| sequential(esk8_0,X1)
| tail_of(X1) != tail_of(esk9_0)
| ~ edge(X1)
| ~ edge(esk8_0) ),
inference(spm,[status(thm)],[28,119,theory(equality)]) ).
cnf(185,negated_conjecture,
( vertex(tail_of(esk9_0))
| $false ),
inference(rw,[status(thm)],[182,116,theory(equality)]) ).
cnf(186,negated_conjecture,
vertex(tail_of(esk9_0)),
inference(cn,[status(thm)],[185,theory(equality)]) ).
cnf(187,negated_conjecture,
( tail_of(esk9_0) != tail_of(esk8_0)
| $false ),
inference(rw,[status(thm)],[183,116,theory(equality)]) ).
cnf(188,negated_conjecture,
tail_of(esk9_0) != tail_of(esk8_0),
inference(cn,[status(thm)],[187,theory(equality)]) ).
cnf(189,negated_conjecture,
( esk8_0 = X1
| sequential(esk8_0,X1)
| tail_of(X1) != tail_of(esk9_0)
| ~ edge(X1)
| $false ),
inference(rw,[status(thm)],[184,116,theory(equality)]) ).
cnf(190,negated_conjecture,
( esk8_0 = X1
| sequential(esk8_0,X1)
| tail_of(X1) != tail_of(esk9_0)
| ~ edge(X1) ),
inference(cn,[status(thm)],[189,theory(equality)]) ).
cnf(198,negated_conjecture,
( head_of(esk2_2(X1,tail_of(esk9_0))) = X1
| head_of(esk2_2(X1,tail_of(esk9_0))) = tail_of(esk9_0)
| X1 = tail_of(esk9_0)
| ~ vertex(X1) ),
inference(spm,[status(thm)],[144,186,theory(equality)]) ).
cnf(199,negated_conjecture,
( tail_of(esk2_2(X1,tail_of(esk9_0))) = X1
| tail_of(esk2_2(X1,tail_of(esk9_0))) = tail_of(esk9_0)
| X1 = tail_of(esk9_0)
| ~ vertex(X1) ),
inference(spm,[status(thm)],[170,186,theory(equality)]) ).
cnf(202,negated_conjecture,
on_path(esk9_0,esk10_0),
inference(spm,[status(thm)],[122,120,theory(equality)]) ).
fof(218,plain,
( ~ epred3_0
<=> ! [X1] :
( tail_of(esk8_0) != tail_of(X1)
| head_of(esk9_0) != head_of(X1) ) ),
introduced(definition),
[split] ).
cnf(219,plain,
( epred3_0
| tail_of(esk8_0) != tail_of(X1)
| head_of(esk9_0) != head_of(X1) ),
inference(split_equiv,[status(thm)],[218]) ).
fof(220,plain,
( ~ epred4_0
<=> ! [X3,X2] : ~ shortest_path(X2,X3,esk10_0) ),
introduced(definition),
[split] ).
cnf(221,plain,
( epred4_0
| ~ shortest_path(X2,X3,esk10_0) ),
inference(split_equiv,[status(thm)],[220]) ).
cnf(222,negated_conjecture,
( ~ epred4_0
| ~ epred3_0 ),
inference(apply_def,[status(esa)],[inference(apply_def,[status(esa)],[127,218,theory(equality)]),220,theory(equality)]),
[split] ).
cnf(223,negated_conjecture,
epred4_0,
inference(spm,[status(thm)],[221,103,theory(equality)]) ).
cnf(225,negated_conjecture,
( $false
| ~ epred3_0 ),
inference(rw,[status(thm)],[222,223,theory(equality)]) ).
cnf(226,negated_conjecture,
~ epred3_0,
inference(cn,[status(thm)],[225,theory(equality)]) ).
cnf(233,negated_conjecture,
( tail_of(esk8_0) != tail_of(X1)
| head_of(esk9_0) != head_of(X1) ),
inference(sr,[status(thm)],[219,226,theory(equality)]) ).
cnf(236,negated_conjecture,
( tail_of(esk2_2(X1,X2)) = X1
| X1 = X2
| tail_of(esk8_0) != tail_of(esk2_2(X1,X2))
| head_of(esk9_0) != X1
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(spm,[status(thm)],[233,162,theory(equality)]) ).
cnf(241,negated_conjecture,
( precedes(X1,esk9_0,esk10_0)
| ~ on_path(X1,esk10_0)
| ~ sequential(X1,esk8_0) ),
inference(spm,[status(thm)],[181,102,theory(equality)]) ).
cnf(243,negated_conjecture,
( precedes(esk9_0,esk9_0,esk10_0)
| ~ sequential(esk9_0,esk8_0) ),
inference(spm,[status(thm)],[241,202,theory(equality)]) ).
cnf(248,negated_conjecture,
( ~ precedes(esk9_0,esk9_0,esk10_0)
| ~ shortest_path(X1,X2,esk10_0)
| ~ sequential(esk9_0,esk8_0) ),
inference(spm,[status(thm)],[71,243,theory(equality)]) ).
cnf(263,negated_conjecture,
( ~ shortest_path(X1,X2,esk10_0)
| ~ sequential(esk9_0,esk8_0) ),
inference(csr,[status(thm)],[248,243]) ).
cnf(264,negated_conjecture,
~ sequential(esk9_0,esk8_0),
inference(spm,[status(thm)],[263,103,theory(equality)]) ).
cnf(278,negated_conjecture,
( esk8_0 = esk3_5(X1,X2,X3,X4,X5)
| sequential(esk8_0,esk3_5(X1,X2,X3,X4,X5))
| sequential(X4,X5)
| head_of(X4) != tail_of(esk9_0)
| ~ edge(esk3_5(X1,X2,X3,X4,X5))
| ~ precedes(X4,X5,X1)
| ~ path(X2,X3,X1) ),
inference(spm,[status(thm)],[190,130,theory(equality)]) ).
cnf(289,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)],[145,23,theory(equality)]) ).
cnf(314,negated_conjecture,
( head_of(esk2_2(tail_of(esk9_0),tail_of(X1))) = tail_of(X1)
| head_of(esk2_2(tail_of(esk9_0),tail_of(X1))) = tail_of(esk9_0)
| tail_of(esk9_0) = tail_of(X1)
| ~ edge(X1) ),
inference(spm,[status(thm)],[146,186,theory(equality)]) ).
cnf(315,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)],[146,24,theory(equality)]) ).
cnf(406,negated_conjecture,
( head_of(esk2_2(tail_of(X1),tail_of(esk9_0))) = tail_of(esk9_0)
| head_of(esk2_2(tail_of(X1),tail_of(esk9_0))) = tail_of(X1)
| tail_of(X1) = tail_of(esk9_0)
| ~ edge(X1) ),
inference(spm,[status(thm)],[198,23,theory(equality)]) ).
cnf(439,negated_conjecture,
( tail_of(esk2_2(tail_of(X1),tail_of(esk9_0))) = tail_of(esk9_0)
| tail_of(esk2_2(tail_of(X1),tail_of(esk9_0))) = tail_of(X1)
| tail_of(X1) = tail_of(esk9_0)
| ~ edge(X1) ),
inference(spm,[status(thm)],[199,23,theory(equality)]) ).
cnf(440,negated_conjecture,
( on_path(esk3_5(esk10_0,X1,X2,X3,X4),esk10_0)
| sequential(X3,X4)
| ~ precedes(X3,X4,esk10_0)
| ~ path(X1,X2,esk10_0) ),
inference(spm,[status(thm)],[153,120,theory(equality)]) ).
cnf(452,negated_conjecture,
( precedes(X1,esk3_5(esk10_0,X2,X3,X4,X5),esk10_0)
| sequential(X4,X5)
| ~ on_path(X1,esk10_0)
| ~ sequential(X1,esk3_5(esk10_0,X2,X3,X4,X5))
| ~ precedes(X4,X5,esk10_0)
| ~ path(X2,X3,esk10_0) ),
inference(spm,[status(thm)],[180,440,theory(equality)]) ).
cnf(471,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)],[160,125]) ).
cnf(472,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)],[471,theory(equality)]) ).
cnf(500,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)],[165,125]) ).
cnf(501,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)],[500,theory(equality)]) ).
cnf(535,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)],[171,23,theory(equality)]) ).
cnf(542,negated_conjecture,
( tail_of(esk2_2(tail_of(esk9_0),tail_of(X1))) = tail_of(X1)
| tail_of(esk2_2(tail_of(esk9_0),tail_of(X1))) = tail_of(esk9_0)
| tail_of(esk9_0) = tail_of(X1)
| ~ edge(X1) ),
inference(spm,[status(thm)],[172,186,theory(equality)]) ).
cnf(543,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)],[172,24,theory(equality)]) ).
cnf(627,negated_conjecture,
( esk3_5(X1,X2,X3,X4,X5) = esk8_0
| sequential(esk8_0,esk3_5(X1,X2,X3,X4,X5))
| sequential(X4,X5)
| head_of(X4) != tail_of(esk9_0)
| ~ precedes(X4,X5,X1)
| ~ path(X2,X3,X1) ),
inference(csr,[status(thm)],[278,128]) ).
cnf(750,negated_conjecture,
( head_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk9_0)
| head_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
| tail_of(esk9_0) = tail_of(esk8_0) ),
inference(spm,[status(thm)],[314,116,theory(equality)]) ).
cnf(755,negated_conjecture,
( head_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk9_0)
| head_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0) ),
inference(sr,[status(thm)],[750,188,theory(equality)]) ).
cnf(756,negated_conjecture,
( head_of(esk2_2(tail_of(X1),head_of(esk9_0))) = tail_of(X1)
| head_of(esk2_2(tail_of(X1),head_of(esk9_0))) = head_of(esk9_0)
| tail_of(X1) = head_of(esk9_0)
| ~ edge(X1) ),
inference(spm,[status(thm)],[289,115,theory(equality)]) ).
cnf(768,negated_conjecture,
( head_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
| tail_of(esk9_0) != tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0)))
| ~ edge(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) ),
inference(spm,[status(thm)],[35,755,theory(equality)]) ).
cnf(770,negated_conjecture,
( tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
| tail_of(esk9_0) = tail_of(esk8_0)
| head_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
| ~ vertex(tail_of(esk8_0))
| ~ vertex(tail_of(esk9_0)) ),
inference(spm,[status(thm)],[157,755,theory(equality)]) ).
cnf(771,negated_conjecture,
( head_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
| tail_of(esk8_0) != tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0)))
| head_of(esk9_0) != tail_of(esk9_0) ),
inference(spm,[status(thm)],[233,755,theory(equality)]) ).
cnf(775,negated_conjecture,
( tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
| tail_of(esk9_0) = tail_of(esk8_0)
| head_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
| ~ vertex(tail_of(esk8_0))
| $false ),
inference(rw,[status(thm)],[770,186,theory(equality)]) ).
cnf(776,negated_conjecture,
( tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
| tail_of(esk9_0) = tail_of(esk8_0)
| head_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
| ~ vertex(tail_of(esk8_0)) ),
inference(cn,[status(thm)],[775,theory(equality)]) ).
cnf(777,negated_conjecture,
( tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
| head_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
| ~ vertex(tail_of(esk8_0)) ),
inference(sr,[status(thm)],[776,188,theory(equality)]) ).
cnf(804,negated_conjecture,
( tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk9_0)
| tail_of(esk8_0) = tail_of(esk9_0)
| tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
| ~ vertex(tail_of(esk8_0))
| ~ vertex(tail_of(esk9_0)) ),
inference(spm,[status(thm)],[162,777,theory(equality)]) ).
cnf(810,negated_conjecture,
( tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk9_0)
| tail_of(esk8_0) = tail_of(esk9_0)
| tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
| ~ vertex(tail_of(esk8_0))
| $false ),
inference(rw,[status(thm)],[804,186,theory(equality)]) ).
cnf(811,negated_conjecture,
( tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk9_0)
| tail_of(esk8_0) = tail_of(esk9_0)
| tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
| ~ vertex(tail_of(esk8_0)) ),
inference(cn,[status(thm)],[810,theory(equality)]) ).
cnf(812,negated_conjecture,
( tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk9_0)
| tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
| ~ vertex(tail_of(esk8_0)) ),
inference(sr,[status(thm)],[811,188,theory(equality)]) ).
cnf(825,negated_conjecture,
( tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk9_0)
| tail_of(esk8_0) = tail_of(esk9_0)
| ~ vertex(tail_of(esk8_0))
| ~ vertex(tail_of(esk9_0))
| tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) != tail_of(esk8_0)
| head_of(esk9_0) != tail_of(esk9_0) ),
inference(spm,[status(thm)],[162,771,theory(equality)]) ).
cnf(832,negated_conjecture,
( tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk9_0)
| tail_of(esk8_0) = tail_of(esk9_0)
| ~ vertex(tail_of(esk8_0))
| $false
| tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) != tail_of(esk8_0)
| head_of(esk9_0) != tail_of(esk9_0) ),
inference(rw,[status(thm)],[825,186,theory(equality)]) ).
cnf(833,negated_conjecture,
( tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk9_0)
| tail_of(esk8_0) = tail_of(esk9_0)
| ~ vertex(tail_of(esk8_0))
| tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) != tail_of(esk8_0)
| head_of(esk9_0) != tail_of(esk9_0) ),
inference(cn,[status(thm)],[832,theory(equality)]) ).
cnf(834,negated_conjecture,
( tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk9_0)
| ~ vertex(tail_of(esk8_0))
| tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) != tail_of(esk8_0)
| head_of(esk9_0) != tail_of(esk9_0) ),
inference(sr,[status(thm)],[833,188,theory(equality)]) ).
cnf(946,negated_conjecture,
( vertex(tail_of(esk8_0))
| ~ edge(esk2_2(tail_of(esk9_0),tail_of(esk8_0)))
| tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) != tail_of(esk9_0) ),
inference(spm,[status(thm)],[24,768,theory(equality)]) ).
cnf(1035,negated_conjecture,
( tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk9_0)
| head_of(esk9_0) != tail_of(esk9_0)
| ~ vertex(tail_of(esk8_0)) ),
inference(csr,[status(thm)],[834,812]) ).
cnf(1037,negated_conjecture,
( X1 = esk2_2(tail_of(esk9_0),tail_of(esk8_0))
| sequential(X1,esk2_2(tail_of(esk9_0),tail_of(esk8_0)))
| tail_of(esk9_0) != head_of(X1)
| ~ edge(esk2_2(tail_of(esk9_0),tail_of(esk8_0)))
| ~ edge(X1)
| head_of(esk9_0) != tail_of(esk9_0)
| ~ vertex(tail_of(esk8_0)) ),
inference(spm,[status(thm)],[28,1035,theory(equality)]) ).
cnf(1082,negated_conjecture,
( head_of(esk2_2(head_of(X1),tail_of(esk8_0))) = head_of(X1)
| head_of(esk2_2(head_of(X1),tail_of(esk8_0))) = tail_of(esk8_0)
| head_of(X1) = tail_of(esk8_0)
| ~ edge(X1) ),
inference(spm,[status(thm)],[315,116,theory(equality)]) ).
cnf(1266,negated_conjecture,
( head_of(esk2_2(tail_of(esk8_0),tail_of(esk9_0))) = tail_of(esk9_0)
| head_of(esk2_2(tail_of(esk8_0),tail_of(esk9_0))) = tail_of(esk8_0)
| tail_of(esk8_0) = tail_of(esk9_0) ),
inference(spm,[status(thm)],[406,116,theory(equality)]) ).
cnf(1271,negated_conjecture,
( head_of(esk2_2(tail_of(esk8_0),tail_of(esk9_0))) = tail_of(esk9_0)
| head_of(esk2_2(tail_of(esk8_0),tail_of(esk9_0))) = tail_of(esk8_0) ),
inference(sr,[status(thm)],[1266,188,theory(equality)]) ).
cnf(1276,negated_conjecture,
( head_of(esk2_2(tail_of(esk8_0),tail_of(esk9_0))) = tail_of(esk8_0)
| tail_of(esk9_0) != tail_of(esk2_2(tail_of(esk8_0),tail_of(esk9_0)))
| ~ edge(esk2_2(tail_of(esk8_0),tail_of(esk9_0))) ),
inference(spm,[status(thm)],[35,1271,theory(equality)]) ).
cnf(1477,negated_conjecture,
( sequential(X1,X2)
| ~ precedes(X1,X2,esk10_0)
| ~ path(X3,X4,esk10_0)
| ~ shortest_path(X5,X6,esk10_0)
| ~ on_path(X2,esk10_0)
| ~ sequential(X2,esk3_5(esk10_0,X3,X4,X1,X2)) ),
inference(spm,[status(thm)],[151,452,theory(equality)]) ).
cnf(1504,negated_conjecture,
( sequential(X1,X2)
| ~ precedes(X1,X2,esk10_0)
| ~ path(X3,X4,esk10_0)
| ~ shortest_path(X5,X6,esk10_0)
| ~ sequential(X2,esk3_5(esk10_0,X3,X4,X1,X2)) ),
inference(csr,[status(thm)],[1477,62]) ).
cnf(1508,negated_conjecture,
( sequential(X1,esk8_0)
| esk3_5(esk10_0,X2,X3,X1,esk8_0) = esk8_0
| ~ precedes(X1,esk8_0,esk10_0)
| ~ path(X2,X3,esk10_0)
| ~ shortest_path(X4,X5,esk10_0)
| head_of(X1) != tail_of(esk9_0) ),
inference(spm,[status(thm)],[1504,627,theory(equality)]) ).
cnf(1570,negated_conjecture,
( esk3_5(esk10_0,X1,X2,X3,esk8_0) = esk8_0
| sequential(X3,esk8_0)
| head_of(X3) != tail_of(esk9_0)
| ~ precedes(X3,esk8_0,esk10_0)
| ~ path(X1,X2,esk10_0) ),
inference(spm,[status(thm)],[1508,103,theory(equality)]) ).
cnf(1571,negated_conjecture,
( sequential(X1,esk8_0)
| ~ precedes(X1,esk8_0,esk10_0)
| ~ path(X2,X3,esk10_0)
| head_of(X1) != tail_of(esk9_0) ),
inference(spm,[status(thm)],[65,1570,theory(equality)]) ).
cnf(1620,negated_conjecture,
( sequential(X1,esk8_0)
| head_of(X1) != tail_of(esk9_0)
| ~ precedes(X1,esk8_0,esk10_0) ),
inference(spm,[status(thm)],[1571,120,theory(equality)]) ).
cnf(1621,negated_conjecture,
( sequential(esk8_0,esk8_0)
| ~ precedes(esk8_0,esk8_0,esk10_0) ),
inference(spm,[status(thm)],[1620,119,theory(equality)]) ).
cnf(1636,negated_conjecture,
~ precedes(esk8_0,esk8_0,esk10_0),
inference(sr,[status(thm)],[1621,117,theory(equality)]) ).
cnf(1732,negated_conjecture,
( vertex(tail_of(esk8_0))
| ~ edge(esk2_2(tail_of(esk8_0),tail_of(esk9_0)))
| tail_of(esk2_2(tail_of(esk8_0),tail_of(esk9_0))) != tail_of(esk9_0) ),
inference(spm,[status(thm)],[24,1276,theory(equality)]) ).
cnf(2376,negated_conjecture,
( tail_of(esk2_2(tail_of(esk8_0),tail_of(esk9_0))) = tail_of(esk9_0)
| tail_of(esk2_2(tail_of(esk8_0),tail_of(esk9_0))) = tail_of(esk8_0)
| tail_of(esk8_0) = tail_of(esk9_0) ),
inference(spm,[status(thm)],[439,116,theory(equality)]) ).
cnf(2381,negated_conjecture,
( tail_of(esk2_2(tail_of(esk8_0),tail_of(esk9_0))) = tail_of(esk9_0)
| tail_of(esk2_2(tail_of(esk8_0),tail_of(esk9_0))) = tail_of(esk8_0) ),
inference(sr,[status(thm)],[2376,188,theory(equality)]) ).
cnf(2406,negated_conjecture,
( vertex(tail_of(esk8_0))
| tail_of(esk2_2(tail_of(esk8_0),tail_of(esk9_0))) = tail_of(esk8_0)
| ~ edge(esk2_2(tail_of(esk8_0),tail_of(esk9_0))) ),
inference(spm,[status(thm)],[1732,2381,theory(equality)]) ).
cnf(2421,negated_conjecture,
( vertex(tail_of(esk8_0))
| ~ edge(esk2_2(tail_of(esk8_0),tail_of(esk9_0))) ),
inference(spm,[status(thm)],[23,2406,theory(equality)]) ).
cnf(2522,negated_conjecture,
( tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk9_0)
| tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
| tail_of(esk9_0) = tail_of(esk8_0) ),
inference(spm,[status(thm)],[542,116,theory(equality)]) ).
cnf(2527,negated_conjecture,
( tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk9_0)
| tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0) ),
inference(sr,[status(thm)],[2522,188,theory(equality)]) ).
cnf(2546,negated_conjecture,
( vertex(tail_of(esk8_0))
| tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
| ~ edge(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) ),
inference(spm,[status(thm)],[946,2527,theory(equality)]) ).
cnf(2565,negated_conjecture,
( vertex(tail_of(esk8_0))
| ~ edge(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) ),
inference(spm,[status(thm)],[23,2546,theory(equality)]) ).
cnf(3000,negated_conjecture,
( head_of(esk2_2(tail_of(esk8_0),head_of(esk9_0))) = head_of(esk9_0)
| head_of(esk2_2(tail_of(esk8_0),head_of(esk9_0))) = tail_of(esk8_0)
| tail_of(esk8_0) = head_of(esk9_0) ),
inference(spm,[status(thm)],[756,116,theory(equality)]) ).
cnf(3043,negated_conjecture,
( head_of(esk2_2(tail_of(esk8_0),head_of(esk9_0))) = tail_of(esk8_0)
| head_of(esk9_0) = tail_of(esk8_0)
| tail_of(esk8_0) != tail_of(esk2_2(tail_of(esk8_0),head_of(esk9_0))) ),
inference(spm,[status(thm)],[233,3000,theory(equality)]) ).
cnf(3058,negated_conjecture,
( head_of(esk9_0) = tail_of(esk8_0)
| tail_of(esk8_0) != tail_of(esk2_2(tail_of(esk8_0),head_of(esk9_0)))
| ~ edge(esk2_2(tail_of(esk8_0),head_of(esk9_0))) ),
inference(spm,[status(thm)],[35,3043,theory(equality)]) ).
cnf(3627,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)],[472,23]) ).
cnf(3628,negated_conjecture,
( tail_of(esk2_2(tail_of(esk9_0),tail_of(X1))) = tail_of(X1)
| esk2_2(tail_of(esk9_0),tail_of(X1)) = X1
| tail_of(esk9_0) = tail_of(X1)
| sequential(esk2_2(tail_of(esk9_0),tail_of(X1)),X1)
| ~ edge(X1) ),
inference(spm,[status(thm)],[3627,186,theory(equality)]) ).
cnf(3629,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)],[3627,24,theory(equality)]) ).
cnf(3630,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)],[3627,23,theory(equality)]) ).
cnf(4045,negated_conjecture,
( tail_of(esk2_2(tail_of(X1),head_of(esk9_0))) = tail_of(X1)
| tail_of(esk2_2(tail_of(X1),head_of(esk9_0))) = head_of(esk9_0)
| tail_of(X1) = head_of(esk9_0)
| ~ edge(X1) ),
inference(spm,[status(thm)],[535,115,theory(equality)]) ).
cnf(4178,negated_conjecture,
( tail_of(esk2_2(tail_of(esk8_0),head_of(esk9_0))) = head_of(esk9_0)
| tail_of(esk2_2(tail_of(esk8_0),head_of(esk9_0))) = tail_of(esk8_0)
| tail_of(esk8_0) = head_of(esk9_0) ),
inference(spm,[status(thm)],[4045,116,theory(equality)]) ).
cnf(4204,negated_conjecture,
( vertex(head_of(esk9_0))
| tail_of(esk2_2(tail_of(esk8_0),head_of(esk9_0))) = tail_of(esk8_0)
| head_of(esk9_0) = tail_of(esk8_0)
| ~ edge(esk2_2(tail_of(esk8_0),head_of(esk9_0))) ),
inference(spm,[status(thm)],[23,4178,theory(equality)]) ).
cnf(4231,negated_conjecture,
( head_of(esk9_0) = tail_of(esk8_0)
| vertex(head_of(esk9_0))
| ~ edge(esk2_2(tail_of(esk8_0),head_of(esk9_0))) ),
inference(csr,[status(thm)],[4204,3058]) ).
cnf(4295,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)],[501,23]) ).
cnf(4296,negated_conjecture,
( tail_of(esk2_2(tail_of(X1),tail_of(esk9_0))) = tail_of(X1)
| esk2_2(tail_of(X1),tail_of(esk9_0)) = X1
| tail_of(X1) = tail_of(esk9_0)
| sequential(esk2_2(tail_of(X1),tail_of(esk9_0)),X1)
| ~ edge(X1) ),
inference(spm,[status(thm)],[4295,186,theory(equality)]) ).
cnf(4297,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)],[4295,24,theory(equality)]) ).
cnf(4350,negated_conjecture,
( tail_of(esk2_2(head_of(X1),tail_of(esk8_0))) = head_of(X1)
| tail_of(esk2_2(head_of(X1),tail_of(esk8_0))) = tail_of(esk8_0)
| head_of(X1) = tail_of(esk8_0)
| ~ edge(X1) ),
inference(spm,[status(thm)],[543,116,theory(equality)]) ).
cnf(6043,negated_conjecture,
( tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
| esk2_2(tail_of(esk9_0),tail_of(esk8_0)) = esk8_0
| tail_of(esk9_0) = tail_of(esk8_0)
| sequential(esk2_2(tail_of(esk9_0),tail_of(esk8_0)),esk8_0) ),
inference(spm,[status(thm)],[3628,116,theory(equality)]) ).
cnf(6050,negated_conjecture,
( tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
| esk2_2(tail_of(esk9_0),tail_of(esk8_0)) = esk8_0
| sequential(esk2_2(tail_of(esk9_0),tail_of(esk8_0)),esk8_0) ),
inference(sr,[status(thm)],[6043,188,theory(equality)]) ).
cnf(6060,negated_conjecture,
( tail_of(esk8_0) = tail_of(esk9_0)
| esk2_2(tail_of(esk9_0),tail_of(esk8_0)) = esk8_0
| sequential(esk2_2(tail_of(esk9_0),tail_of(esk8_0)),esk8_0)
| head_of(esk9_0) != tail_of(esk9_0)
| ~ vertex(tail_of(esk8_0))
| ~ vertex(tail_of(esk9_0)) ),
inference(spm,[status(thm)],[236,6050,theory(equality)]) ).
cnf(6094,negated_conjecture,
( tail_of(esk8_0) = tail_of(esk9_0)
| esk2_2(tail_of(esk9_0),tail_of(esk8_0)) = esk8_0
| sequential(esk2_2(tail_of(esk9_0),tail_of(esk8_0)),esk8_0)
| head_of(esk9_0) != tail_of(esk9_0)
| ~ vertex(tail_of(esk8_0))
| $false ),
inference(rw,[status(thm)],[6060,186,theory(equality)]) ).
cnf(6095,negated_conjecture,
( tail_of(esk8_0) = tail_of(esk9_0)
| esk2_2(tail_of(esk9_0),tail_of(esk8_0)) = esk8_0
| sequential(esk2_2(tail_of(esk9_0),tail_of(esk8_0)),esk8_0)
| head_of(esk9_0) != tail_of(esk9_0)
| ~ vertex(tail_of(esk8_0)) ),
inference(cn,[status(thm)],[6094,theory(equality)]) ).
cnf(6096,negated_conjecture,
( esk2_2(tail_of(esk9_0),tail_of(esk8_0)) = esk8_0
| sequential(esk2_2(tail_of(esk9_0),tail_of(esk8_0)),esk8_0)
| head_of(esk9_0) != tail_of(esk9_0)
| ~ vertex(tail_of(esk8_0)) ),
inference(sr,[status(thm)],[6095,188,theory(equality)]) ).
cnf(6122,negated_conjecture,
( esk2_2(tail_of(esk9_0),tail_of(esk8_0)) = esk8_0
| ~ sequential(esk9_0,esk2_2(tail_of(esk9_0),tail_of(esk8_0)))
| head_of(esk9_0) != tail_of(esk9_0)
| ~ vertex(tail_of(esk8_0)) ),
inference(spm,[status(thm)],[142,6096,theory(equality)]) ).
cnf(6610,negated_conjecture,
( tail_of(esk2_2(tail_of(esk8_0),tail_of(esk9_0))) = tail_of(esk8_0)
| esk2_2(tail_of(esk8_0),tail_of(esk9_0)) = esk8_0
| tail_of(esk8_0) = tail_of(esk9_0)
| sequential(esk2_2(tail_of(esk8_0),tail_of(esk9_0)),esk8_0) ),
inference(spm,[status(thm)],[4296,116,theory(equality)]) ).
cnf(6618,negated_conjecture,
( tail_of(esk2_2(tail_of(esk8_0),tail_of(esk9_0))) = tail_of(esk8_0)
| esk2_2(tail_of(esk8_0),tail_of(esk9_0)) = esk8_0
| sequential(esk2_2(tail_of(esk8_0),tail_of(esk9_0)),esk8_0) ),
inference(sr,[status(thm)],[6610,188,theory(equality)]) ).
cnf(16962,negated_conjecture,
( X1 = esk2_2(tail_of(esk9_0),tail_of(esk8_0))
| sequential(X1,esk2_2(tail_of(esk9_0),tail_of(esk8_0)))
| head_of(esk9_0) != tail_of(esk9_0)
| head_of(X1) != tail_of(esk9_0)
| ~ edge(esk2_2(tail_of(esk9_0),tail_of(esk8_0)))
| ~ edge(X1) ),
inference(csr,[status(thm)],[1037,2565]) ).
cnf(16963,negated_conjecture,
( X1 = esk2_2(tail_of(esk9_0),tail_of(esk8_0))
| sequential(X1,esk2_2(tail_of(esk9_0),tail_of(esk8_0)))
| tail_of(esk9_0) = tail_of(esk8_0)
| head_of(esk9_0) != tail_of(esk9_0)
| head_of(X1) != tail_of(esk9_0)
| ~ edge(X1)
| ~ vertex(tail_of(esk8_0))
| ~ vertex(tail_of(esk9_0)) ),
inference(spm,[status(thm)],[16962,125,theory(equality)]) ).
cnf(16966,negated_conjecture,
( X1 = esk2_2(tail_of(esk9_0),tail_of(esk8_0))
| sequential(X1,esk2_2(tail_of(esk9_0),tail_of(esk8_0)))
| tail_of(esk9_0) = tail_of(esk8_0)
| head_of(esk9_0) != tail_of(esk9_0)
| head_of(X1) != tail_of(esk9_0)
| ~ edge(X1)
| ~ vertex(tail_of(esk8_0))
| $false ),
inference(rw,[status(thm)],[16963,186,theory(equality)]) ).
cnf(16967,negated_conjecture,
( X1 = esk2_2(tail_of(esk9_0),tail_of(esk8_0))
| sequential(X1,esk2_2(tail_of(esk9_0),tail_of(esk8_0)))
| tail_of(esk9_0) = tail_of(esk8_0)
| head_of(esk9_0) != tail_of(esk9_0)
| head_of(X1) != tail_of(esk9_0)
| ~ edge(X1)
| ~ vertex(tail_of(esk8_0)) ),
inference(cn,[status(thm)],[16966,theory(equality)]) ).
cnf(16968,negated_conjecture,
( X1 = esk2_2(tail_of(esk9_0),tail_of(esk8_0))
| sequential(X1,esk2_2(tail_of(esk9_0),tail_of(esk8_0)))
| head_of(esk9_0) != tail_of(esk9_0)
| head_of(X1) != tail_of(esk9_0)
| ~ edge(X1)
| ~ vertex(tail_of(esk8_0)) ),
inference(sr,[status(thm)],[16967,188,theory(equality)]) ).
cnf(17284,negated_conjecture,
( esk2_2(tail_of(esk9_0),tail_of(esk8_0)) = esk8_0
| esk9_0 = esk2_2(tail_of(esk9_0),tail_of(esk8_0))
| head_of(esk9_0) != tail_of(esk9_0)
| ~ vertex(tail_of(esk8_0))
| ~ edge(esk9_0) ),
inference(spm,[status(thm)],[6122,16968,theory(equality)]) ).
cnf(17292,negated_conjecture,
( esk2_2(tail_of(esk9_0),tail_of(esk8_0)) = esk8_0
| esk9_0 = esk2_2(tail_of(esk9_0),tail_of(esk8_0))
| head_of(esk9_0) != tail_of(esk9_0)
| ~ vertex(tail_of(esk8_0))
| $false ),
inference(rw,[status(thm)],[17284,115,theory(equality)]) ).
cnf(17293,negated_conjecture,
( esk2_2(tail_of(esk9_0),tail_of(esk8_0)) = esk8_0
| esk9_0 = esk2_2(tail_of(esk9_0),tail_of(esk8_0))
| head_of(esk9_0) != tail_of(esk9_0)
| ~ vertex(tail_of(esk8_0)) ),
inference(cn,[status(thm)],[17292,theory(equality)]) ).
cnf(17296,negated_conjecture,
( esk2_2(tail_of(esk9_0),tail_of(esk8_0)) = esk8_0
| esk9_0 != esk8_0
| head_of(esk9_0) != tail_of(esk9_0)
| ~ vertex(tail_of(esk8_0)) ),
inference(ef,[status(thm)],[17293,theory(equality)]) ).
cnf(17328,negated_conjecture,
( tail_of(esk9_0) = tail_of(esk8_0)
| esk9_0 = esk8_0
| sequential(esk9_0,esk8_0)
| esk2_2(tail_of(esk9_0),tail_of(esk8_0)) = esk8_0
| head_of(esk9_0) != tail_of(esk9_0)
| ~ vertex(tail_of(esk8_0)) ),
inference(spm,[status(thm)],[6050,17293,theory(equality)]) ).
cnf(17444,negated_conjecture,
( esk9_0 = esk8_0
| sequential(esk9_0,esk8_0)
| esk2_2(tail_of(esk9_0),tail_of(esk8_0)) = esk8_0
| head_of(esk9_0) != tail_of(esk9_0)
| ~ vertex(tail_of(esk8_0)) ),
inference(sr,[status(thm)],[17328,188,theory(equality)]) ).
cnf(17445,negated_conjecture,
( esk9_0 = esk8_0
| esk2_2(tail_of(esk9_0),tail_of(esk8_0)) = esk8_0
| head_of(esk9_0) != tail_of(esk9_0)
| ~ vertex(tail_of(esk8_0)) ),
inference(sr,[status(thm)],[17444,264,theory(equality)]) ).
cnf(17572,negated_conjecture,
( tail_of(esk8_0) = tail_of(esk9_0)
| head_of(esk9_0) != tail_of(esk9_0)
| ~ vertex(tail_of(esk8_0))
| ~ vertex(tail_of(esk9_0))
| esk9_0 != esk8_0 ),
inference(spm,[status(thm)],[236,17296,theory(equality)]) ).
cnf(17647,negated_conjecture,
( tail_of(esk8_0) = tail_of(esk9_0)
| head_of(esk9_0) != tail_of(esk9_0)
| ~ vertex(tail_of(esk8_0))
| $false
| esk9_0 != esk8_0 ),
inference(rw,[status(thm)],[17572,186,theory(equality)]) ).
cnf(17648,negated_conjecture,
( tail_of(esk8_0) = tail_of(esk9_0)
| head_of(esk9_0) != tail_of(esk9_0)
| ~ vertex(tail_of(esk8_0))
| esk9_0 != esk8_0 ),
inference(cn,[status(thm)],[17647,theory(equality)]) ).
cnf(17649,negated_conjecture,
( head_of(esk9_0) != tail_of(esk9_0)
| ~ vertex(tail_of(esk8_0))
| esk9_0 != esk8_0 ),
inference(sr,[status(thm)],[17648,188,theory(equality)]) ).
cnf(17840,negated_conjecture,
( head_of(esk9_0) != tail_of(esk9_0)
| esk9_0 != esk8_0
| ~ edge(esk8_0) ),
inference(spm,[status(thm)],[17649,23,theory(equality)]) ).
cnf(17843,negated_conjecture,
( head_of(esk9_0) != tail_of(esk9_0)
| esk9_0 != esk8_0
| $false ),
inference(rw,[status(thm)],[17840,116,theory(equality)]) ).
cnf(17844,negated_conjecture,
( head_of(esk9_0) != tail_of(esk9_0)
| esk9_0 != esk8_0 ),
inference(cn,[status(thm)],[17843,theory(equality)]) ).
cnf(17848,negated_conjecture,
( esk2_2(tail_of(esk9_0),tail_of(esk8_0)) = esk8_0
| head_of(esk9_0) != tail_of(esk9_0)
| ~ vertex(tail_of(esk8_0)) ),
inference(csr,[status(thm)],[17445,17844]) ).
cnf(17851,negated_conjecture,
( tail_of(esk8_0) = tail_of(esk9_0)
| head_of(esk9_0) != tail_of(esk9_0)
| ~ vertex(tail_of(esk8_0))
| ~ vertex(tail_of(esk9_0)) ),
inference(spm,[status(thm)],[236,17848,theory(equality)]) ).
cnf(17926,negated_conjecture,
( tail_of(esk8_0) = tail_of(esk9_0)
| head_of(esk9_0) != tail_of(esk9_0)
| ~ vertex(tail_of(esk8_0))
| $false ),
inference(rw,[status(thm)],[17851,186,theory(equality)]) ).
cnf(17927,negated_conjecture,
( tail_of(esk8_0) = tail_of(esk9_0)
| head_of(esk9_0) != tail_of(esk9_0)
| ~ vertex(tail_of(esk8_0)) ),
inference(cn,[status(thm)],[17926,theory(equality)]) ).
cnf(17928,negated_conjecture,
( head_of(esk9_0) != tail_of(esk9_0)
| ~ vertex(tail_of(esk8_0)) ),
inference(sr,[status(thm)],[17927,188,theory(equality)]) ).
cnf(18127,negated_conjecture,
( head_of(esk9_0) != tail_of(esk9_0)
| ~ edge(esk8_0) ),
inference(spm,[status(thm)],[17928,23,theory(equality)]) ).
cnf(18130,negated_conjecture,
( head_of(esk9_0) != tail_of(esk9_0)
| $false ),
inference(rw,[status(thm)],[18127,116,theory(equality)]) ).
cnf(18131,negated_conjecture,
head_of(esk9_0) != tail_of(esk9_0),
inference(cn,[status(thm)],[18130,theory(equality)]) ).
cnf(27976,negated_conjecture,
( tail_of(esk2_2(head_of(X1),tail_of(esk8_0))) = tail_of(esk8_0)
| esk2_2(head_of(X1),tail_of(esk8_0)) = esk8_0
| head_of(X1) = tail_of(esk8_0)
| sequential(esk2_2(head_of(X1),tail_of(esk8_0)),esk8_0)
| ~ edge(X1) ),
inference(spm,[status(thm)],[3629,116,theory(equality)]) ).
cnf(28400,negated_conjecture,
( tail_of(esk8_0) = head_of(X1)
| esk2_2(head_of(X1),tail_of(esk8_0)) = esk8_0
| sequential(esk2_2(head_of(X1),tail_of(esk8_0)),esk8_0)
| head_of(esk9_0) != head_of(X1)
| ~ vertex(tail_of(esk8_0))
| ~ vertex(head_of(X1))
| ~ edge(X1) ),
inference(spm,[status(thm)],[236,27976,theory(equality)]) ).
cnf(28784,negated_conjecture,
( esk2_2(head_of(X1),tail_of(esk8_0)) = esk8_0
| head_of(X1) = tail_of(esk8_0)
| sequential(esk2_2(head_of(X1),tail_of(esk8_0)),esk8_0)
| head_of(esk9_0) != head_of(X1)
| ~ vertex(tail_of(esk8_0))
| ~ edge(X1) ),
inference(csr,[status(thm)],[28400,24]) ).
cnf(28791,negated_conjecture,
( esk2_2(head_of(X1),tail_of(esk8_0)) = esk8_0
| head_of(X1) = tail_of(esk8_0)
| ~ sequential(esk9_0,esk2_2(head_of(X1),tail_of(esk8_0)))
| head_of(esk9_0) != head_of(X1)
| ~ vertex(tail_of(esk8_0))
| ~ edge(X1) ),
inference(spm,[status(thm)],[142,28784,theory(equality)]) ).
cnf(29928,negated_conjecture,
( tail_of(esk2_2(tail_of(X1),tail_of(esk9_0))) = tail_of(esk9_0)
| esk2_2(tail_of(X1),tail_of(esk9_0)) = esk9_0
| tail_of(X1) = tail_of(esk9_0)
| sequential(esk2_2(tail_of(X1),tail_of(esk9_0)),esk9_0)
| ~ edge(X1) ),
inference(spm,[status(thm)],[3630,115,theory(equality)]) ).
cnf(30054,negated_conjecture,
( tail_of(esk9_0) = tail_of(esk8_0)
| esk2_2(tail_of(esk8_0),tail_of(esk9_0)) = esk8_0
| sequential(esk2_2(tail_of(esk8_0),tail_of(esk9_0)),esk8_0)
| esk2_2(tail_of(esk8_0),tail_of(esk9_0)) = esk9_0
| sequential(esk2_2(tail_of(esk8_0),tail_of(esk9_0)),esk9_0)
| ~ edge(esk8_0) ),
inference(spm,[status(thm)],[6618,29928,theory(equality)]) ).
cnf(30114,negated_conjecture,
( tail_of(esk9_0) = tail_of(esk8_0)
| esk2_2(tail_of(esk8_0),tail_of(esk9_0)) = esk8_0
| sequential(esk2_2(tail_of(esk8_0),tail_of(esk9_0)),esk8_0)
| esk2_2(tail_of(esk8_0),tail_of(esk9_0)) = esk9_0
| sequential(esk2_2(tail_of(esk8_0),tail_of(esk9_0)),esk9_0)
| $false ),
inference(rw,[status(thm)],[30054,116,theory(equality)]) ).
cnf(30115,negated_conjecture,
( tail_of(esk9_0) = tail_of(esk8_0)
| esk2_2(tail_of(esk8_0),tail_of(esk9_0)) = esk8_0
| sequential(esk2_2(tail_of(esk8_0),tail_of(esk9_0)),esk8_0)
| esk2_2(tail_of(esk8_0),tail_of(esk9_0)) = esk9_0
| sequential(esk2_2(tail_of(esk8_0),tail_of(esk9_0)),esk9_0) ),
inference(cn,[status(thm)],[30114,theory(equality)]) ).
cnf(30116,negated_conjecture,
( esk2_2(tail_of(esk8_0),tail_of(esk9_0)) = esk8_0
| sequential(esk2_2(tail_of(esk8_0),tail_of(esk9_0)),esk8_0)
| esk2_2(tail_of(esk8_0),tail_of(esk9_0)) = esk9_0
| sequential(esk2_2(tail_of(esk8_0),tail_of(esk9_0)),esk9_0) ),
inference(sr,[status(thm)],[30115,188,theory(equality)]) ).
cnf(30161,negated_conjecture,
( edge(esk2_2(tail_of(esk8_0),tail_of(esk9_0)))
| esk2_2(tail_of(esk8_0),tail_of(esk9_0)) = esk9_0
| esk2_2(tail_of(esk8_0),tail_of(esk9_0)) = esk8_0
| sequential(esk2_2(tail_of(esk8_0),tail_of(esk9_0)),esk8_0) ),
inference(spm,[status(thm)],[32,30116,theory(equality)]) ).
cnf(30167,negated_conjecture,
( esk2_2(tail_of(esk8_0),tail_of(esk9_0)) = esk9_0
| esk2_2(tail_of(esk8_0),tail_of(esk9_0)) = esk8_0
| edge(esk2_2(tail_of(esk8_0),tail_of(esk9_0))) ),
inference(csr,[status(thm)],[30161,32]) ).
cnf(30175,negated_conjecture,
( vertex(tail_of(esk8_0))
| esk2_2(tail_of(esk8_0),tail_of(esk9_0)) = esk8_0
| esk2_2(tail_of(esk8_0),tail_of(esk9_0)) = esk9_0 ),
inference(spm,[status(thm)],[2421,30167,theory(equality)]) ).
cnf(30212,negated_conjecture,
( vertex(tail_of(esk8_0))
| esk2_2(tail_of(esk8_0),tail_of(esk9_0)) = esk8_0
| ~ edge(esk9_0) ),
inference(spm,[status(thm)],[2421,30175,theory(equality)]) ).
cnf(30303,negated_conjecture,
( vertex(tail_of(esk8_0))
| esk2_2(tail_of(esk8_0),tail_of(esk9_0)) = esk8_0
| $false ),
inference(rw,[status(thm)],[30212,115,theory(equality)]) ).
cnf(30304,negated_conjecture,
( vertex(tail_of(esk8_0))
| esk2_2(tail_of(esk8_0),tail_of(esk9_0)) = esk8_0 ),
inference(cn,[status(thm)],[30303,theory(equality)]) ).
cnf(30463,negated_conjecture,
( vertex(tail_of(esk8_0))
| ~ edge(esk8_0) ),
inference(spm,[status(thm)],[2421,30304,theory(equality)]) ).
cnf(30552,negated_conjecture,
( vertex(tail_of(esk8_0))
| $false ),
inference(rw,[status(thm)],[30463,116,theory(equality)]) ).
cnf(30553,negated_conjecture,
vertex(tail_of(esk8_0)),
inference(cn,[status(thm)],[30552,theory(equality)]) ).
cnf(30707,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)],[144,30553,theory(equality)]) ).
cnf(30709,negated_conjecture,
( head_of(esk2_2(tail_of(esk8_0),head_of(X1))) = head_of(X1)
| head_of(esk2_2(tail_of(esk8_0),head_of(X1))) = tail_of(esk8_0)
| tail_of(esk8_0) = head_of(X1)
| ~ edge(X1) ),
inference(spm,[status(thm)],[145,30553,theory(equality)]) ).
cnf(30733,negated_conjecture,
( esk2_2(head_of(X1),tail_of(esk8_0)) = esk8_0
| head_of(X1) = tail_of(esk8_0)
| head_of(esk9_0) != head_of(X1)
| ~ sequential(esk9_0,esk2_2(head_of(X1),tail_of(esk8_0)))
| $false
| ~ edge(X1) ),
inference(rw,[status(thm)],[28791,30553,theory(equality)]) ).
cnf(30734,negated_conjecture,
( esk2_2(head_of(X1),tail_of(esk8_0)) = esk8_0
| head_of(X1) = tail_of(esk8_0)
| head_of(esk9_0) != head_of(X1)
| ~ sequential(esk9_0,esk2_2(head_of(X1),tail_of(esk8_0)))
| ~ edge(X1) ),
inference(cn,[status(thm)],[30733,theory(equality)]) ).
cnf(32282,negated_conjecture,
( tail_of(esk2_2(tail_of(esk8_0),head_of(X1))) = tail_of(esk8_0)
| head_of(X1) = tail_of(esk8_0)
| head_of(esk2_2(tail_of(esk8_0),head_of(X1))) = tail_of(esk8_0)
| ~ vertex(head_of(X1))
| ~ vertex(tail_of(esk8_0))
| ~ edge(X1) ),
inference(spm,[status(thm)],[162,30709,theory(equality)]) ).
cnf(32284,negated_conjecture,
( head_of(esk2_2(tail_of(esk8_0),head_of(X1))) = tail_of(esk8_0)
| head_of(X1) = tail_of(esk8_0)
| tail_of(esk8_0) != tail_of(esk2_2(tail_of(esk8_0),head_of(X1)))
| head_of(esk9_0) != head_of(X1)
| ~ edge(X1) ),
inference(spm,[status(thm)],[233,30709,theory(equality)]) ).
cnf(32417,negated_conjecture,
( tail_of(esk2_2(tail_of(esk8_0),head_of(X1))) = tail_of(esk8_0)
| head_of(X1) = tail_of(esk8_0)
| head_of(esk2_2(tail_of(esk8_0),head_of(X1))) = tail_of(esk8_0)
| ~ vertex(head_of(X1))
| $false
| ~ edge(X1) ),
inference(rw,[status(thm)],[32282,30553,theory(equality)]) ).
cnf(32418,negated_conjecture,
( tail_of(esk2_2(tail_of(esk8_0),head_of(X1))) = tail_of(esk8_0)
| head_of(X1) = tail_of(esk8_0)
| head_of(esk2_2(tail_of(esk8_0),head_of(X1))) = tail_of(esk8_0)
| ~ vertex(head_of(X1))
| ~ edge(X1) ),
inference(cn,[status(thm)],[32417,theory(equality)]) ).
cnf(32995,negated_conjecture,
( tail_of(esk2_2(tail_of(esk8_0),head_of(X1))) = tail_of(esk8_0)
| head_of(esk2_2(tail_of(esk8_0),head_of(X1))) = tail_of(esk8_0)
| head_of(X1) = tail_of(esk8_0)
| ~ edge(X1) ),
inference(csr,[status(thm)],[32418,24]) ).
cnf(33260,negated_conjecture,
( head_of(esk2_2(tail_of(esk8_0),head_of(X1))) = tail_of(esk8_0)
| head_of(X1) = tail_of(esk8_0)
| head_of(esk9_0) != head_of(X1)
| ~ edge(X1) ),
inference(csr,[status(thm)],[32284,32995]) ).
cnf(33265,negated_conjecture,
( tail_of(esk2_2(tail_of(esk8_0),head_of(X1))) = head_of(X1)
| tail_of(esk8_0) = head_of(X1)
| ~ vertex(head_of(X1))
| ~ vertex(tail_of(esk8_0))
| head_of(esk9_0) != head_of(X1)
| ~ edge(X1) ),
inference(spm,[status(thm)],[157,33260,theory(equality)]) ).
cnf(33391,negated_conjecture,
( tail_of(esk2_2(tail_of(esk8_0),head_of(X1))) = head_of(X1)
| tail_of(esk8_0) = head_of(X1)
| ~ vertex(head_of(X1))
| $false
| head_of(esk9_0) != head_of(X1)
| ~ edge(X1) ),
inference(rw,[status(thm)],[33265,30553,theory(equality)]) ).
cnf(33392,negated_conjecture,
( tail_of(esk2_2(tail_of(esk8_0),head_of(X1))) = head_of(X1)
| tail_of(esk8_0) = head_of(X1)
| ~ vertex(head_of(X1))
| head_of(esk9_0) != head_of(X1)
| ~ edge(X1) ),
inference(cn,[status(thm)],[33391,theory(equality)]) ).
cnf(33590,negated_conjecture,
( tail_of(esk2_2(tail_of(esk8_0),head_of(X1))) = head_of(X1)
| head_of(X1) = tail_of(esk8_0)
| head_of(esk9_0) != head_of(X1)
| ~ edge(X1) ),
inference(csr,[status(thm)],[33392,24]) ).
cnf(42262,negated_conjecture,
( tail_of(esk2_2(tail_of(esk8_0),head_of(X1))) = tail_of(esk8_0)
| esk2_2(tail_of(esk8_0),head_of(X1)) = esk8_0
| tail_of(esk8_0) = head_of(X1)
| sequential(esk2_2(tail_of(esk8_0),head_of(X1)),esk8_0)
| ~ edge(X1) ),
inference(spm,[status(thm)],[4297,116,theory(equality)]) ).
cnf(42767,negated_conjecture,
( tail_of(esk8_0) = head_of(X1)
| esk2_2(tail_of(esk8_0),head_of(X1)) = esk8_0
| sequential(esk2_2(tail_of(esk8_0),head_of(X1)),esk8_0)
| head_of(esk9_0) != head_of(X1)
| ~ edge(X1) ),
inference(spm,[status(thm)],[33590,42262,theory(equality)]) ).
cnf(43083,negated_conjecture,
( edge(esk2_2(tail_of(esk8_0),head_of(X1)))
| esk2_2(tail_of(esk8_0),head_of(X1)) = esk8_0
| head_of(X1) = tail_of(esk8_0)
| head_of(esk9_0) != head_of(X1)
| ~ edge(X1) ),
inference(spm,[status(thm)],[32,42767,theory(equality)]) ).
cnf(43265,negated_conjecture,
( head_of(esk9_0) = tail_of(esk8_0)
| vertex(head_of(esk9_0))
| esk2_2(tail_of(esk8_0),head_of(esk9_0)) = esk8_0
| ~ edge(esk9_0) ),
inference(spm,[status(thm)],[4231,43083,theory(equality)]) ).
cnf(43323,negated_conjecture,
( head_of(esk9_0) = tail_of(esk8_0)
| vertex(head_of(esk9_0))
| esk2_2(tail_of(esk8_0),head_of(esk9_0)) = esk8_0
| $false ),
inference(rw,[status(thm)],[43265,115,theory(equality)]) ).
cnf(43324,negated_conjecture,
( head_of(esk9_0) = tail_of(esk8_0)
| vertex(head_of(esk9_0))
| esk2_2(tail_of(esk8_0),head_of(esk9_0)) = esk8_0 ),
inference(cn,[status(thm)],[43323,theory(equality)]) ).
cnf(43355,negated_conjecture,
( head_of(esk8_0) = tail_of(esk8_0)
| head_of(esk8_0) = head_of(esk9_0)
| head_of(esk9_0) = tail_of(esk8_0)
| vertex(head_of(esk9_0)) ),
inference(spm,[status(thm)],[3000,43324,theory(equality)]) ).
cnf(43429,negated_conjecture,
( tail_of(esk9_0) = tail_of(esk8_0)
| head_of(esk8_0) = head_of(esk9_0)
| head_of(esk9_0) = tail_of(esk8_0)
| vertex(head_of(esk9_0)) ),
inference(rw,[status(thm)],[43355,119,theory(equality)]) ).
cnf(43430,negated_conjecture,
( tail_of(esk9_0) = tail_of(esk8_0)
| tail_of(esk9_0) = head_of(esk9_0)
| head_of(esk9_0) = tail_of(esk8_0)
| vertex(head_of(esk9_0)) ),
inference(rw,[status(thm)],[43429,119,theory(equality)]) ).
cnf(43431,negated_conjecture,
( head_of(esk9_0) = tail_of(esk9_0)
| head_of(esk9_0) = tail_of(esk8_0)
| vertex(head_of(esk9_0)) ),
inference(sr,[status(thm)],[43430,188,theory(equality)]) ).
cnf(43432,negated_conjecture,
( head_of(esk9_0) = tail_of(esk8_0)
| vertex(head_of(esk9_0)) ),
inference(sr,[status(thm)],[43431,18131,theory(equality)]) ).
cnf(43616,negated_conjecture,
( head_of(esk2_2(head_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
| head_of(esk2_2(head_of(esk9_0),tail_of(esk8_0))) = head_of(esk9_0)
| head_of(esk9_0) = tail_of(esk8_0) ),
inference(spm,[status(thm)],[30707,43432,theory(equality)]) ).
cnf(44292,negated_conjecture,
( tail_of(esk2_2(head_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
| head_of(esk9_0) = tail_of(esk8_0)
| head_of(esk2_2(head_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
| ~ vertex(tail_of(esk8_0))
| ~ vertex(head_of(esk9_0)) ),
inference(spm,[status(thm)],[157,43616,theory(equality)]) ).
cnf(44293,negated_conjecture,
( head_of(esk2_2(head_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
| head_of(esk9_0) = tail_of(esk8_0)
| tail_of(esk8_0) != tail_of(esk2_2(head_of(esk9_0),tail_of(esk8_0))) ),
inference(spm,[status(thm)],[233,43616,theory(equality)]) ).
cnf(44421,negated_conjecture,
( tail_of(esk2_2(head_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
| head_of(esk9_0) = tail_of(esk8_0)
| head_of(esk2_2(head_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
| $false
| ~ vertex(head_of(esk9_0)) ),
inference(rw,[status(thm)],[44292,30553,theory(equality)]) ).
cnf(44422,negated_conjecture,
( tail_of(esk2_2(head_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
| head_of(esk9_0) = tail_of(esk8_0)
| head_of(esk2_2(head_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
| ~ vertex(head_of(esk9_0)) ),
inference(cn,[status(thm)],[44421,theory(equality)]) ).
cnf(45726,negated_conjecture,
( tail_of(esk2_2(head_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
| head_of(esk2_2(head_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
| head_of(esk9_0) = tail_of(esk8_0) ),
inference(csr,[status(thm)],[44422,43432]) ).
cnf(45727,negated_conjecture,
( head_of(esk2_2(head_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
| head_of(esk9_0) = tail_of(esk8_0) ),
inference(csr,[status(thm)],[45726,44293]) ).
cnf(45731,negated_conjecture,
( tail_of(esk2_2(head_of(esk9_0),tail_of(esk8_0))) = head_of(esk9_0)
| tail_of(esk8_0) = head_of(esk9_0)
| ~ vertex(tail_of(esk8_0))
| ~ vertex(head_of(esk9_0)) ),
inference(spm,[status(thm)],[162,45727,theory(equality)]) ).
cnf(45834,negated_conjecture,
( tail_of(esk2_2(head_of(esk9_0),tail_of(esk8_0))) = head_of(esk9_0)
| tail_of(esk8_0) = head_of(esk9_0)
| $false
| ~ vertex(head_of(esk9_0)) ),
inference(rw,[status(thm)],[45731,30553,theory(equality)]) ).
cnf(45835,negated_conjecture,
( tail_of(esk2_2(head_of(esk9_0),tail_of(esk8_0))) = head_of(esk9_0)
| tail_of(esk8_0) = head_of(esk9_0)
| ~ vertex(head_of(esk9_0)) ),
inference(cn,[status(thm)],[45834,theory(equality)]) ).
cnf(45883,negated_conjecture,
( tail_of(esk2_2(head_of(esk9_0),tail_of(esk8_0))) = head_of(esk9_0)
| head_of(esk9_0) = tail_of(esk8_0) ),
inference(csr,[status(thm)],[45835,43432]) ).
cnf(45885,negated_conjecture,
( X1 = esk2_2(head_of(esk9_0),tail_of(esk8_0))
| sequential(X1,esk2_2(head_of(esk9_0),tail_of(esk8_0)))
| head_of(esk9_0) = tail_of(esk8_0)
| head_of(esk9_0) != head_of(X1)
| ~ edge(esk2_2(head_of(esk9_0),tail_of(esk8_0)))
| ~ edge(X1) ),
inference(spm,[status(thm)],[28,45883,theory(equality)]) ).
cnf(56712,negated_conjecture,
( X1 = esk2_2(head_of(esk9_0),tail_of(esk8_0))
| head_of(esk9_0) = tail_of(esk8_0)
| sequential(X1,esk2_2(head_of(esk9_0),tail_of(esk8_0)))
| head_of(esk9_0) != head_of(X1)
| ~ edge(X1)
| ~ vertex(tail_of(esk8_0))
| ~ vertex(head_of(esk9_0)) ),
inference(spm,[status(thm)],[45885,125,theory(equality)]) ).
cnf(56715,negated_conjecture,
( X1 = esk2_2(head_of(esk9_0),tail_of(esk8_0))
| head_of(esk9_0) = tail_of(esk8_0)
| sequential(X1,esk2_2(head_of(esk9_0),tail_of(esk8_0)))
| head_of(esk9_0) != head_of(X1)
| ~ edge(X1)
| $false
| ~ vertex(head_of(esk9_0)) ),
inference(rw,[status(thm)],[56712,30553,theory(equality)]) ).
cnf(56716,negated_conjecture,
( X1 = esk2_2(head_of(esk9_0),tail_of(esk8_0))
| head_of(esk9_0) = tail_of(esk8_0)
| sequential(X1,esk2_2(head_of(esk9_0),tail_of(esk8_0)))
| head_of(esk9_0) != head_of(X1)
| ~ edge(X1)
| ~ vertex(head_of(esk9_0)) ),
inference(cn,[status(thm)],[56715,theory(equality)]) ).
cnf(56892,negated_conjecture,
( X1 = esk2_2(head_of(esk9_0),tail_of(esk8_0))
| head_of(esk9_0) = tail_of(esk8_0)
| sequential(X1,esk2_2(head_of(esk9_0),tail_of(esk8_0)))
| head_of(esk9_0) != head_of(X1)
| ~ edge(X1) ),
inference(csr,[status(thm)],[56716,43432]) ).
cnf(56903,negated_conjecture,
( esk2_2(head_of(esk9_0),tail_of(esk8_0)) = esk8_0
| head_of(esk9_0) = tail_of(esk8_0)
| esk9_0 = esk2_2(head_of(esk9_0),tail_of(esk8_0))
| ~ edge(esk9_0) ),
inference(spm,[status(thm)],[30734,56892,theory(equality)]) ).
cnf(56908,negated_conjecture,
( esk2_2(head_of(esk9_0),tail_of(esk8_0)) = esk8_0
| head_of(esk9_0) = tail_of(esk8_0)
| esk9_0 = esk2_2(head_of(esk9_0),tail_of(esk8_0))
| $false ),
inference(rw,[status(thm)],[56903,115,theory(equality)]) ).
cnf(56909,negated_conjecture,
( esk2_2(head_of(esk9_0),tail_of(esk8_0)) = esk8_0
| head_of(esk9_0) = tail_of(esk8_0)
| esk9_0 = esk2_2(head_of(esk9_0),tail_of(esk8_0)) ),
inference(cn,[status(thm)],[56908,theory(equality)]) ).
cnf(56925,negated_conjecture,
( tail_of(esk9_0) = tail_of(esk8_0)
| tail_of(esk9_0) = head_of(esk9_0)
| head_of(esk9_0) = tail_of(esk8_0)
| esk2_2(head_of(esk9_0),tail_of(esk8_0)) = esk8_0
| ~ edge(esk9_0) ),
inference(spm,[status(thm)],[4350,56909,theory(equality)]) ).
cnf(57038,negated_conjecture,
( tail_of(esk9_0) = tail_of(esk8_0)
| tail_of(esk9_0) = head_of(esk9_0)
| head_of(esk9_0) = tail_of(esk8_0)
| esk2_2(head_of(esk9_0),tail_of(esk8_0)) = esk8_0
| $false ),
inference(rw,[status(thm)],[56925,115,theory(equality)]) ).
cnf(57039,negated_conjecture,
( tail_of(esk9_0) = tail_of(esk8_0)
| tail_of(esk9_0) = head_of(esk9_0)
| head_of(esk9_0) = tail_of(esk8_0)
| esk2_2(head_of(esk9_0),tail_of(esk8_0)) = esk8_0 ),
inference(cn,[status(thm)],[57038,theory(equality)]) ).
cnf(57040,negated_conjecture,
( head_of(esk9_0) = tail_of(esk9_0)
| head_of(esk9_0) = tail_of(esk8_0)
| esk2_2(head_of(esk9_0),tail_of(esk8_0)) = esk8_0 ),
inference(sr,[status(thm)],[57039,188,theory(equality)]) ).
cnf(57041,negated_conjecture,
( head_of(esk9_0) = tail_of(esk8_0)
| esk2_2(head_of(esk9_0),tail_of(esk8_0)) = esk8_0 ),
inference(sr,[status(thm)],[57040,18131,theory(equality)]) ).
cnf(57236,negated_conjecture,
( head_of(esk8_0) = tail_of(esk8_0)
| head_of(esk8_0) = head_of(esk9_0)
| head_of(esk9_0) = tail_of(esk8_0)
| ~ edge(esk9_0) ),
inference(spm,[status(thm)],[1082,57041,theory(equality)]) ).
cnf(57311,negated_conjecture,
( tail_of(esk9_0) = tail_of(esk8_0)
| head_of(esk8_0) = head_of(esk9_0)
| head_of(esk9_0) = tail_of(esk8_0)
| ~ edge(esk9_0) ),
inference(rw,[status(thm)],[57236,119,theory(equality)]) ).
cnf(57312,negated_conjecture,
( tail_of(esk9_0) = tail_of(esk8_0)
| tail_of(esk9_0) = head_of(esk9_0)
| head_of(esk9_0) = tail_of(esk8_0)
| ~ edge(esk9_0) ),
inference(rw,[status(thm)],[57311,119,theory(equality)]) ).
cnf(57313,negated_conjecture,
( tail_of(esk9_0) = tail_of(esk8_0)
| tail_of(esk9_0) = head_of(esk9_0)
| head_of(esk9_0) = tail_of(esk8_0)
| $false ),
inference(rw,[status(thm)],[57312,115,theory(equality)]) ).
cnf(57314,negated_conjecture,
( tail_of(esk9_0) = tail_of(esk8_0)
| tail_of(esk9_0) = head_of(esk9_0)
| head_of(esk9_0) = tail_of(esk8_0) ),
inference(cn,[status(thm)],[57313,theory(equality)]) ).
cnf(57315,negated_conjecture,
( head_of(esk9_0) = tail_of(esk9_0)
| head_of(esk9_0) = tail_of(esk8_0) ),
inference(sr,[status(thm)],[57314,188,theory(equality)]) ).
cnf(57316,negated_conjecture,
head_of(esk9_0) = tail_of(esk8_0),
inference(sr,[status(thm)],[57315,18131,theory(equality)]) ).
cnf(57494,negated_conjecture,
( esk9_0 = X1
| sequential(esk9_0,X1)
| tail_of(X1) != tail_of(esk8_0)
| ~ edge(X1)
| ~ edge(esk9_0) ),
inference(spm,[status(thm)],[28,57316,theory(equality)]) ).
cnf(58242,negated_conjecture,
( esk9_0 = X1
| sequential(esk9_0,X1)
| tail_of(X1) != tail_of(esk8_0)
| ~ edge(X1)
| $false ),
inference(rw,[status(thm)],[57494,115,theory(equality)]) ).
cnf(58243,negated_conjecture,
( esk9_0 = X1
| sequential(esk9_0,X1)
| tail_of(X1) != tail_of(esk8_0)
| ~ edge(X1) ),
inference(cn,[status(thm)],[58242,theory(equality)]) ).
cnf(58565,negated_conjecture,
( esk9_0 = esk8_0
| sequential(esk9_0,esk8_0)
| ~ edge(esk8_0) ),
inference(er,[status(thm)],[58243,theory(equality)]) ).
cnf(58610,negated_conjecture,
( esk9_0 = esk8_0
| sequential(esk9_0,esk8_0)
| $false ),
inference(rw,[status(thm)],[58565,116,theory(equality)]) ).
cnf(58611,negated_conjecture,
( esk9_0 = esk8_0
| sequential(esk9_0,esk8_0) ),
inference(cn,[status(thm)],[58610,theory(equality)]) ).
cnf(58612,negated_conjecture,
esk9_0 = esk8_0,
inference(sr,[status(thm)],[58611,264,theory(equality)]) ).
cnf(58623,negated_conjecture,
precedes(esk8_0,esk8_0,esk10_0),
inference(rw,[status(thm)],[102,58612,theory(equality)]) ).
cnf(58624,negated_conjecture,
$false,
inference(sr,[status(thm)],[58623,1636,theory(equality)]) ).
cnf(58625,negated_conjecture,
$false,
58624,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GRA/GRA008+1.p
% --creating new selector for [GRA001+0.ax]
% -running prover on /tmp/tmp2znHc3/sel_GRA008+1.p_1 with time limit 29
% -prover status Theorem
% Problem GRA008+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GRA/GRA008+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GRA/GRA008+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
%
%------------------------------------------------------------------------------