%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GRA009+2 : TPTP v9.3.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:19:42 AM UTC 2026
% Result : Theorem 9.62s 1.86s
% Output : CNFRefutation 9.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 18
% Syntax : Number of formulae : 652 ( 147 unt; 0 typ; 0 def)
% Number of atoms : 7667 (3173 equ; 0 cnn)
% Maximal formula atoms : 9 ( 11 avg)
% Number of connectives : 16984 (4812 ~;2886 |; 150 &;9049 @)
% ( 9 <=>; 63 =>; 6 <=; 9 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 39 usr; 14 con; 0-6 aty)
% Number of variables : 2471 ( 0 ^;2435 !; 36 ?;2471 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_complete,type,
complete: $o ).
thf(tp_edge,type,
edge: $i > $o ).
thf(tp_edges,type,
edges: $i ).
thf(tp_empty,type,
empty: $i ).
thf(tp_graph,type,
graph: $i ).
thf(tp_head_of,type,
head_of: $i > $i ).
thf(tp_in_path,type,
in_path: $i > $i > $o ).
thf(tp_length_of,type,
length_of: $i > $i ).
thf(tp_less_or_equal,type,
less_or_equal: $i > $i > $o ).
thf(tp_minus,type,
minus: $i > $i > $i ).
thf(tp_n1,type,
n1: $i ).
thf(tp_number_of_in,type,
number_of_in: $i > $i > $i ).
thf(tp_on_path,type,
on_path: $i > $i > $o ).
thf(tp_path,type,
path: $i > $i > $i > $o ).
thf(tp_path_cons,type,
path_cons: $i > $i > $i ).
thf(tp_precedes,type,
precedes: $i > $i > $i > $o ).
thf(tp_sK10_SY189,type,
sK10_SY189: $i > $i > $i ).
thf(tp_sK11_SY163,type,
sK11_SY163: $i > $i > $i > $i ).
thf(tp_sK12_SY207,type,
sK12_SY207: $i > $i > $i > $i > $i > $i ).
thf(tp_sK13_SY209,type,
sK13_SY209: $i > $i > $i > $i ).
thf(tp_sK14_SY209,type,
sK14_SY209: $i > $i > $i > $i ).
thf(tp_sK15_SY207,type,
sK15_SY207: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK16_SY209,type,
sK16_SY209: $i > $i > $i > $i > $i ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK2_SY141,type,
sK2_SY141: $i ).
thf(tp_sK3_SY175,type,
sK3_SY175: $i ).
thf(tp_sK4_SY143,type,
sK4_SY143: $i ).
thf(tp_sK5_SY197,type,
sK5_SY197: $i ).
thf(tp_sK6_SY169,type,
sK6_SY169: $i > $i > $i > $i ).
thf(tp_sK7_SY99,type,
sK7_SY99: $i > $i > $i > $i ).
thf(tp_sK8_SY210,type,
sK8_SY210: $i > $i > $i > $i ).
thf(tp_sK9_SY190,type,
sK9_SY190: $i > $i > $i > $i > $i ).
thf(tp_sequential,type,
sequential: $i > $i > $o ).
thf(tp_sequential_pairs,type,
sequential_pairs: $i ).
thf(tp_shortest_path,type,
shortest_path: $i > $i > $i > $o ).
thf(tp_tail_of,type,
tail_of: $i > $i ).
thf(tp_triangle,type,
triangle: $i > $i > $i > $o ).
thf(tp_triangles,type,
triangles: $i ).
thf(tp_vertex,type,
vertex: $i > $o ).
thf(1,axiom,
! [Things: $i,InThese: $i] : ( less_or_equal @ ( number_of_in @ Things @ InThese ) @ ( number_of_in @ Things @ graph ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',graph_has_them_all) ).
thf(2,axiom,
! [P: $i,V1: $i,V2: $i] :
( ( ( path @ V1 @ V2 @ P )
& ! [E1: $i,E2: $i] :
( ( ( on_path @ E1 @ P )
& ( on_path @ E2 @ P )
& ( sequential @ E1 @ E2 ) )
=> ? [E3: $i] : ( triangle @ E1 @ E2 @ E3 ) ) )
=> ( ( number_of_in @ sequential_pairs @ P )
= ( number_of_in @ triangles @ P ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sequential_pairs_and_triangles) ).
thf(3,axiom,
! [V1: $i,V2: $i,P: $i] :
( ( path @ V1 @ V2 @ P )
=> ( ( number_of_in @ sequential_pairs @ P )
= ( minus @ ( length_of @ P ) @ n1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',path_length_sequential_pairs) ).
thf(4,axiom,
! [V1: $i,V2: $i,P: $i] :
( ( path @ V1 @ V2 @ P )
=> ( ( length_of @ P )
= ( number_of_in @ edges @ P ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',length_defn) ).
thf(5,axiom,
! [E1: $i,E2: $i,E3: $i] :
( ( triangle @ E1 @ E2 @ E3 )
<=> ( ( edge @ E1 )
& ( edge @ E2 )
& ( edge @ E3 )
& ( sequential @ E1 @ E2 )
& ( sequential @ E2 @ E3 )
& ( sequential @ E3 @ E1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',triangle_defn) ).
thf(6,axiom,
! [V1: $i,V2: $i,E1: $i,E2: $i,P: $i] :
( ( ( shortest_path @ V1 @ V2 @ P )
& ( precedes @ E1 @ E2 @ P ) )
=> ( ~ ? [E3: $i] :
( ( ( tail_of @ E3 )
= ( tail_of @ E1 ) )
& ( ( head_of @ E3 )
= ( head_of @ E2 ) ) )
& ~ ( precedes @ E2 @ E1 @ P ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',shortest_path_properties) ).
thf(7,axiom,
! [V1: $i,V2: $i,SP: $i] :
( ( shortest_path @ V1 @ V2 @ SP )
<=> ( ( path @ V1 @ V2 @ SP )
& ( V1 != V2 )
& ! [P: $i] :
( ( path @ V1 @ V2 @ P )
=> ( less_or_equal @ ( length_of @ SP ) @ ( length_of @ P ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',shortest_path_defn) ).
thf(8,axiom,
! [P: $i,V1: $i,V2: $i] :
( ( path @ V1 @ V2 @ P )
=> ! [E1: $i,E2: $i] :
( ( precedes @ E1 @ E2 @ P )
=> ( ( on_path @ E1 @ P )
& ( on_path @ E2 @ P )
& ( ( sequential @ E1 @ E2 )
<~> ? [E3: $i] :
( ( sequential @ E1 @ E3 )
& ( precedes @ E3 @ E2 @ P ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',precedes_properties) ).
thf(9,axiom,
! [P: $i,V1: $i,V2: $i] :
( ( path @ V1 @ V2 @ P )
=> ! [E1: $i,E2: $i] :
( ( precedes @ E1 @ E2 @ P )
<= ( ( on_path @ E1 @ P )
& ( on_path @ E2 @ P )
& ( ( sequential @ E1 @ E2 )
| ? [E3: $i] :
( ( sequential @ E1 @ E3 )
& ( precedes @ E3 @ E2 @ P ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',precedes_defn) ).
thf(10,axiom,
! [E1: $i,E2: $i] :
( ( sequential @ E1 @ E2 )
<=> ( ( edge @ E1 )
& ( edge @ E2 )
& ( E1 != E2 )
& ( ( head_of @ E1 )
= ( tail_of @ E2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sequential_defn) ).
thf(11,axiom,
! [V1: $i,V2: $i,P: $i,V: $i] :
( ( ( path @ V1 @ V2 @ P )
& ( in_path @ V @ P ) )
=> ( ( vertex @ V )
& ? [E: $i] :
( ( on_path @ E @ P )
& ( ( V
= ( head_of @ E ) )
| ( V
= ( tail_of @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in_path_properties) ).
thf(12,axiom,
! [V1: $i,V2: $i,P: $i,E: $i] :
( ( ( path @ V1 @ V2 @ P )
& ( on_path @ E @ P ) )
=> ( ( edge @ E )
& ( in_path @ ( head_of @ E ) @ P )
& ( in_path @ ( tail_of @ E ) @ P ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',on_path_properties) ).
thf(13,axiom,
! [V1: $i,V2: $i,P: $i] :
( ( path @ V1 @ V2 @ P )
=> ( ( vertex @ V1 )
& ( vertex @ V2 )
& ? [E: $i] :
( ( edge @ E )
& ( V1
= ( tail_of @ E ) )
& ( ( ( V2
= ( head_of @ E ) )
& ( P
= ( path_cons @ E @ empty ) ) )
<~> ? [TP: $i] :
( ( path @ ( head_of @ E ) @ V2 @ TP )
& ( P
= ( path_cons @ E @ TP ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',path_properties) ).
thf(14,axiom,
! [V1: $i,V2: $i,P: $i] :
( ( path @ V1 @ V2 @ P )
<= ( ( vertex @ V1 )
& ( vertex @ V2 )
& ? [E: $i] :
( ( edge @ E )
& ( V1
= ( tail_of @ E ) )
& ( ( ( V2
= ( head_of @ E ) )
& ( P
= ( path_cons @ E @ empty ) ) )
| ? [TP: $i] :
( ( path @ ( head_of @ E ) @ V2 @ TP )
& ( P
= ( path_cons @ E @ TP ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',path_defn) ).
thf(15,axiom,
( complete
=> ! [V1: $i,V2: $i] :
( ( ( vertex @ V1 )
& ( vertex @ V2 )
& ( V1 != V2 ) )
=> ? [E: $i] :
( ( edge @ E )
& ( ( ( V1
= ( head_of @ E ) )
& ( V2
= ( tail_of @ E ) ) )
<~> ( ( V2
= ( head_of @ E ) )
& ( V1
= ( tail_of @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complete_properties) ).
thf(16,axiom,
! [E: $i] :
( ( edge @ E )
=> ( ( vertex @ ( head_of @ E ) )
& ( vertex @ ( tail_of @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',edge_ends_are_vertices) ).
thf(17,axiom,
! [E: $i] :
( ( edge @ E )
=> ( ( head_of @ E )
!= ( tail_of @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',no_loops) ).
thf(18,conjecture,
( complete
=> ! [P: $i,V1: $i,V2: $i] :
( ( shortest_path @ V1 @ V2 @ P )
=> ! [E1: $i,E2: $i] :
( ( ( on_path @ E1 @ P )
& ( on_path @ E2 @ P )
& ( sequential @ E1 @ E2 ) )
=> ? [E3: $i] : ( triangle @ E1 @ E2 @ E3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complete_means_path_means_stuff_means_triangles) ).
thf(19,negated_conjecture,
( ( complete
=> ! [P: $i,V1: $i,V2: $i] :
( ( shortest_path @ V1 @ V2 @ P )
=> ! [E1: $i,E2: $i] :
( ( ( on_path @ E1 @ P )
& ( on_path @ E2 @ P )
& ( sequential @ E1 @ E2 ) )
=> ? [E3: $i] : ( triangle @ E1 @ E2 @ E3 ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[18]) ).
thf(20,plain,
( ( complete
=> ! [P: $i,V1: $i,V2: $i] :
( ( shortest_path @ V1 @ V2 @ P )
=> ! [E1: $i,E2: $i] :
( ( ( on_path @ E1 @ P )
& ( on_path @ E2 @ P )
& ( sequential @ E1 @ E2 ) )
=> ? [E3: $i] : ( triangle @ E1 @ E2 @ E3 ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[19]) ).
thf(21,plain,
( ( ! [Things: $i,InThese: $i] : ( less_or_equal @ ( number_of_in @ Things @ InThese ) @ ( number_of_in @ Things @ graph ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(22,plain,
( ( ! [P: $i,V1: $i,V2: $i] :
( ( ( path @ V1 @ V2 @ P )
& ! [E1: $i,E2: $i] :
( ( ( on_path @ E1 @ P )
& ( on_path @ E2 @ P )
& ( sequential @ E1 @ E2 ) )
=> ? [E3: $i] : ( triangle @ E1 @ E2 @ E3 ) ) )
=> ( ( number_of_in @ sequential_pairs @ P )
= ( number_of_in @ triangles @ P ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(23,plain,
( ( ! [V1: $i,V2: $i,P: $i] :
( ( path @ V1 @ V2 @ P )
=> ( ( number_of_in @ sequential_pairs @ P )
= ( minus @ ( length_of @ P ) @ n1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(24,plain,
( ( ! [V1: $i,V2: $i,P: $i] :
( ( path @ V1 @ V2 @ P )
=> ( ( length_of @ P )
= ( number_of_in @ edges @ P ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(25,plain,
( ( ! [E1: $i,E2: $i,E3: $i] :
( ( triangle @ E1 @ E2 @ E3 )
<=> ( ( edge @ E1 )
& ( edge @ E2 )
& ( edge @ E3 )
& ( sequential @ E1 @ E2 )
& ( sequential @ E2 @ E3 )
& ( sequential @ E3 @ E1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(26,plain,
( ( ! [V1: $i,V2: $i,E1: $i,E2: $i,P: $i] :
( ( ( shortest_path @ V1 @ V2 @ P )
& ( precedes @ E1 @ E2 @ P ) )
=> ( ~ ? [E3: $i] :
( ( ( tail_of @ E3 )
= ( tail_of @ E1 ) )
& ( ( head_of @ E3 )
= ( head_of @ E2 ) ) )
& ~ ( precedes @ E2 @ E1 @ P ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(27,plain,
( ( ! [V1: $i,V2: $i,SP: $i] :
( ( shortest_path @ V1 @ V2 @ SP )
<=> ( ( path @ V1 @ V2 @ SP )
& ( V1 != V2 )
& ! [P: $i] :
( ( path @ V1 @ V2 @ P )
=> ( less_or_equal @ ( length_of @ SP ) @ ( length_of @ P ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(28,plain,
( ( ! [P: $i,V1: $i,V2: $i] :
( ( path @ V1 @ V2 @ P )
=> ! [E1: $i,E2: $i] :
( ( precedes @ E1 @ E2 @ P )
=> ( ( on_path @ E1 @ P )
& ( on_path @ E2 @ P )
& ( ( sequential @ E1 @ E2 )
<~> ? [E3: $i] :
( ( sequential @ E1 @ E3 )
& ( precedes @ E3 @ E2 @ P ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(29,plain,
( ( ! [P: $i,V1: $i,V2: $i] :
( ( path @ V1 @ V2 @ P )
=> ! [E1: $i,E2: $i] :
( ( precedes @ E1 @ E2 @ P )
<= ( ( on_path @ E1 @ P )
& ( on_path @ E2 @ P )
& ( ( sequential @ E1 @ E2 )
| ? [E3: $i] :
( ( sequential @ E1 @ E3 )
& ( precedes @ E3 @ E2 @ P ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(30,plain,
( ( ! [E1: $i,E2: $i] :
( ( sequential @ E1 @ E2 )
<=> ( ( edge @ E1 )
& ( edge @ E2 )
& ( E1 != E2 )
& ( ( head_of @ E1 )
= ( tail_of @ E2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(31,plain,
( ( ! [V1: $i,V2: $i,P: $i,V: $i] :
( ( ( path @ V1 @ V2 @ P )
& ( in_path @ V @ P ) )
=> ( ( vertex @ V )
& ? [E: $i] :
( ( on_path @ E @ P )
& ( ( V
= ( head_of @ E ) )
| ( V
= ( tail_of @ E ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(32,plain,
( ( ! [V1: $i,V2: $i,P: $i,E: $i] :
( ( ( path @ V1 @ V2 @ P )
& ( on_path @ E @ P ) )
=> ( ( edge @ E )
& ( in_path @ ( head_of @ E ) @ P )
& ( in_path @ ( tail_of @ E ) @ P ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(33,plain,
( ( ! [V1: $i,V2: $i,P: $i] :
( ( path @ V1 @ V2 @ P )
=> ( ( vertex @ V1 )
& ( vertex @ V2 )
& ? [E: $i] :
( ( edge @ E )
& ( V1
= ( tail_of @ E ) )
& ( ( ( V2
= ( head_of @ E ) )
& ( P
= ( path_cons @ E @ empty ) ) )
<~> ? [TP: $i] :
( ( path @ ( head_of @ E ) @ V2 @ TP )
& ( P
= ( path_cons @ E @ TP ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(34,plain,
( ( ! [V1: $i,V2: $i,P: $i] :
( ( path @ V1 @ V2 @ P )
<= ( ( vertex @ V1 )
& ( vertex @ V2 )
& ? [E: $i] :
( ( edge @ E )
& ( V1
= ( tail_of @ E ) )
& ( ( ( V2
= ( head_of @ E ) )
& ( P
= ( path_cons @ E @ empty ) ) )
| ? [TP: $i] :
( ( path @ ( head_of @ E ) @ V2 @ TP )
& ( P
= ( path_cons @ E @ TP ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(35,plain,
( ( complete
=> ! [V1: $i,V2: $i] :
( ( ( vertex @ V1 )
& ( vertex @ V2 )
& ( V1 != V2 ) )
=> ? [E: $i] :
( ( edge @ E )
& ( ( ( V1
= ( head_of @ E ) )
& ( V2
= ( tail_of @ E ) ) )
<~> ( ( V2
= ( head_of @ E ) )
& ( V1
= ( tail_of @ E ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(36,plain,
( ( ! [E: $i] :
( ( edge @ E )
=> ( ( vertex @ ( head_of @ E ) )
& ( vertex @ ( tail_of @ E ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(37,plain,
( ( ! [E: $i] :
( ( edge @ E )
=> ( ( head_of @ E )
!= ( tail_of @ E ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(38,plain,
complete = $true,
inference(standard_cnf,[status(thm)],[20]) ).
thf(39,plain,
( ( ! [P: $i,V1: $i,V2: $i] :
( ( shortest_path @ V1 @ V2 @ P )
=> ! [E1: $i,E2: $i] :
( ( ( on_path @ E1 @ P )
& ( on_path @ E2 @ P )
& ( sequential @ E1 @ E2 ) )
=> ? [E3: $i] : ( triangle @ E1 @ E2 @ E3 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[20]) ).
thf(40,plain,
( ( ~ ! [P: $i,V1: $i,V2: $i] :
( ( shortest_path @ V1 @ V2 @ P )
=> ! [E1: $i,E2: $i] :
( ( ( on_path @ E1 @ P )
& ( on_path @ E2 @ P )
& ( sequential @ E1 @ E2 ) )
=> ? [E3: $i] : ( triangle @ E1 @ E2 @ E3 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[39]) ).
thf(41,plain,
( ( ! [E: $i] :
( ( edge @ E )
=> ( ( head_of @ E )
!= ( tail_of @ E ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(42,plain,
( ( ! [E: $i] :
( ( edge @ E )
=> ( ( vertex @ ( head_of @ E ) )
& ( vertex @ ( tail_of @ E ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(43,plain,
( ( complete
=> ! [V1: $i,V2: $i] :
( ( ( vertex @ V1 )
& ( vertex @ V2 )
& ( V1 != V2 ) )
=> ? [E: $i] :
( ( edge @ E )
& ( ( ( V1
= ( head_of @ E ) )
& ( V2
= ( tail_of @ E ) ) )
<~> ( ( V2
= ( head_of @ E ) )
& ( V1
= ( tail_of @ E ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(44,plain,
( ( ! [V1: $i,V2: $i,P: $i] :
( ( path @ V1 @ V2 @ P )
<= ( ( vertex @ V1 )
& ( vertex @ V2 )
& ? [E: $i] :
( ( edge @ E )
& ( V1
= ( tail_of @ E ) )
& ( ( ( V2
= ( head_of @ E ) )
& ( P
= ( path_cons @ E @ empty ) ) )
| ? [TP: $i] :
( ( path @ ( head_of @ E ) @ V2 @ TP )
& ( P
= ( path_cons @ E @ TP ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(45,plain,
( ( ! [V1: $i,V2: $i,P: $i] :
( ( path @ V1 @ V2 @ P )
=> ( ( vertex @ V1 )
& ( vertex @ V2 )
& ? [E: $i] :
( ( edge @ E )
& ( V1
= ( tail_of @ E ) )
& ( ( ( V2
= ( head_of @ E ) )
& ( P
= ( path_cons @ E @ empty ) ) )
<~> ? [TP: $i] :
( ( path @ ( head_of @ E ) @ V2 @ TP )
& ( P
= ( path_cons @ E @ TP ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(46,plain,
( ( ! [V1: $i,V2: $i,P: $i,E: $i] :
( ( ( path @ V1 @ V2 @ P )
& ( on_path @ E @ P ) )
=> ( ( edge @ E )
& ( in_path @ ( head_of @ E ) @ P )
& ( in_path @ ( tail_of @ E ) @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(47,plain,
( ( ! [V1: $i,V2: $i,P: $i,V: $i] :
( ( ( path @ V1 @ V2 @ P )
& ( in_path @ V @ P ) )
=> ( ( vertex @ V )
& ? [E: $i] :
( ( on_path @ E @ P )
& ( ( V
= ( head_of @ E ) )
| ( V
= ( tail_of @ E ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(48,plain,
( ( ! [E1: $i,E2: $i] :
( ( sequential @ E1 @ E2 )
<=> ( ( edge @ E1 )
& ( edge @ E2 )
& ( E1 != E2 )
& ( ( head_of @ E1 )
= ( tail_of @ E2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(49,plain,
( ( ! [P: $i,V1: $i,V2: $i] :
( ( path @ V1 @ V2 @ P )
=> ! [E1: $i,E2: $i] :
( ( precedes @ E1 @ E2 @ P )
<= ( ( on_path @ E1 @ P )
& ( on_path @ E2 @ P )
& ( ( sequential @ E1 @ E2 )
| ? [E3: $i] :
( ( sequential @ E1 @ E3 )
& ( precedes @ E3 @ E2 @ P ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(50,plain,
( ( ! [P: $i,V1: $i,V2: $i] :
( ( path @ V1 @ V2 @ P )
=> ! [E1: $i,E2: $i] :
( ( precedes @ E1 @ E2 @ P )
=> ( ( on_path @ E1 @ P )
& ( on_path @ E2 @ P )
& ( ( sequential @ E1 @ E2 )
<~> ? [E3: $i] :
( ( sequential @ E1 @ E3 )
& ( precedes @ E3 @ E2 @ P ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(51,plain,
( ( ! [V1: $i,V2: $i,SP: $i] :
( ( shortest_path @ V1 @ V2 @ SP )
<=> ( ( path @ V1 @ V2 @ SP )
& ( V1 != V2 )
& ! [P: $i] :
( ( path @ V1 @ V2 @ P )
=> ( less_or_equal @ ( length_of @ SP ) @ ( length_of @ P ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(52,plain,
( ( ! [V1: $i,V2: $i,E1: $i,E2: $i,P: $i] :
( ( ( shortest_path @ V1 @ V2 @ P )
& ( precedes @ E1 @ E2 @ P ) )
=> ( ~ ? [E3: $i] :
( ( ( tail_of @ E3 )
= ( tail_of @ E1 ) )
& ( ( head_of @ E3 )
= ( head_of @ E2 ) ) )
& ~ ( precedes @ E2 @ E1 @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(53,plain,
( ( ! [E1: $i,E2: $i,E3: $i] :
( ( triangle @ E1 @ E2 @ E3 )
<=> ( ( edge @ E1 )
& ( edge @ E2 )
& ( edge @ E3 )
& ( sequential @ E1 @ E2 )
& ( sequential @ E2 @ E3 )
& ( sequential @ E3 @ E1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(54,plain,
( ( ! [V1: $i,V2: $i,P: $i] :
( ( path @ V1 @ V2 @ P )
=> ( ( length_of @ P )
= ( number_of_in @ edges @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(55,plain,
( ( ! [V1: $i,V2: $i,P: $i] :
( ( path @ V1 @ V2 @ P )
=> ( ( number_of_in @ sequential_pairs @ P )
= ( minus @ ( length_of @ P ) @ n1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(56,plain,
( ( ! [P: $i,V1: $i,V2: $i] :
( ( ( path @ V1 @ V2 @ P )
& ! [E1: $i,E2: $i] :
( ( ( on_path @ E1 @ P )
& ( on_path @ E2 @ P )
& ( sequential @ E1 @ E2 ) )
=> ? [E3: $i] : ( triangle @ E1 @ E2 @ E3 ) ) )
=> ( ( number_of_in @ sequential_pairs @ P )
= ( number_of_in @ triangles @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(57,plain,
( ( ! [Things: $i,InThese: $i] : ( less_or_equal @ ( number_of_in @ Things @ InThese ) @ ( number_of_in @ Things @ graph ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(58,plain,
complete = $true,
inference(copy,[status(thm)],[38]) ).
thf(59,plain,
( ( ~ ! [P: $i,V1: $i,V2: $i] :
( ( shortest_path @ V1 @ V2 @ P )
=> ! [E1: $i,E2: $i] :
( ( ( on_path @ E1 @ P )
& ( on_path @ E2 @ P )
& ( sequential @ E1 @ E2 ) )
=> ? [E3: $i] : ( triangle @ E1 @ E2 @ E3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(60,plain,
( ( ~ complete
| ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ~ ( ~ ( vertex @ SX0 )
| ~ ( vertex @ SX1 ) )
| ~ ( ( SX0 != SX1 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( edge @ SX2 )
| ~ ~ ~ ( ~ ( ~ ~ ( ( SX0
!= ( head_of @ SX2 ) )
| ( SX1
!= ( tail_of @ SX2 ) ) )
| ~ ( ( SX1
!= ( head_of @ SX2 ) )
| ( SX0
!= ( tail_of @ SX2 ) ) ) )
| ~ ( ~ ~ ( ( SX1
!= ( head_of @ SX2 ) )
| ( SX0
!= ( tail_of @ SX2 ) ) )
| ~ ( ( SX0
!= ( head_of @ SX2 ) )
| ( SX1
!= ( tail_of @ SX2 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(61,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( shortest_path @ SX0 @ SX1 @ SX2 )
| ~ ( ~ ~ ( ~ ( path @ SX0 @ SX1 @ SX2 )
| ~ ( ( SX0 != SX1 ) ) )
| ~ ! [SX3: $i] :
( ~ ( path @ SX0 @ SX1 @ SX3 )
| ( less_or_equal @ ( length_of @ SX2 ) @ ( length_of @ SX3 ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( path @ SX0 @ SX1 @ SX2 )
| ~ ( ( SX0 != SX1 ) ) )
| ~ ! [SX3: $i] :
( ~ ( path @ SX0 @ SX1 @ SX3 )
| ( less_or_equal @ ( length_of @ SX2 ) @ ( length_of @ SX3 ) ) ) )
| ( shortest_path @ SX0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(62,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( path @ SX0 @ SX1 @ SX2 )
| ~ ( on_path @ SX3 @ SX2 ) )
| ~ ( ~ ~ ( ~ ( edge @ SX3 )
| ~ ( in_path @ ( head_of @ SX3 ) @ SX2 ) )
| ~ ( in_path @ ( tail_of @ SX3 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(63,plain,
( ( ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ~ ( ~ ( vertex @ ( head_of @ SX0 ) )
| ~ ( vertex @ ( tail_of @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(64,plain,
( ( ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( ( head_of @ SX0 )
!= ( tail_of @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(65,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( path @ SX0 @ SX1 @ SX2 )
| ~ ~ ( ~ ~ ( ~ ( vertex @ SX0 )
| ~ ( vertex @ SX1 ) )
| ~ ~ ! [SX3: $i] :
~ ~ ( ~ ~ ( ~ ( edge @ SX3 )
| ( SX0
!= ( tail_of @ SX3 ) ) )
| ~ ( ~ ( ( SX1
!= ( head_of @ SX3 ) )
| ( SX2
!= ( path_cons @ SX3 @ empty ) ) )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( path @ ( head_of @ SX3 ) @ SX1 @ SX4 )
| ( SX2
!= ( path_cons @ SX3 @ SX4 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(66,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( path @ SX0 @ SX1 @ SX2 )
| ~ ( in_path @ SX3 @ SX2 ) )
| ~ ( ~ ( vertex @ SX3 )
| ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( on_path @ SX4 @ SX2 )
| ~ ( ( SX3
= ( head_of @ SX4 ) )
| ( SX3
= ( tail_of @ SX4 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(67,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( triangle @ SX0 @ SX1 @ SX2 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SX0 )
| ~ ( edge @ SX1 ) )
| ~ ( edge @ SX2 ) )
| ~ ( sequential @ SX0 @ SX1 ) )
| ~ ( sequential @ SX1 @ SX2 ) )
| ~ ( sequential @ SX2 @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SX0 )
| ~ ( edge @ SX1 ) )
| ~ ( edge @ SX2 ) )
| ~ ( sequential @ SX0 @ SX1 ) )
| ~ ( sequential @ SX1 @ SX2 ) )
| ~ ( sequential @ SX2 @ SX0 ) )
| ( triangle @ SX0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(68,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( path @ SX0 @ SX1 @ SX2 )
| ( ( length_of @ SX2 )
= ( number_of_in @ edges @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(69,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( path @ SX0 @ SX1 @ SX2 )
| ~ ( ~ ~ ( ~ ( vertex @ SX0 )
| ~ ( vertex @ SX1 ) )
| ~ ~ ! [SX3: $i] :
~ ~ ( ~ ~ ( ~ ( edge @ SX3 )
| ( SX0
!= ( tail_of @ SX3 ) ) )
| ~ ~ ~ ( ~ ( ~ ~ ( ( SX1
!= ( head_of @ SX3 ) )
| ( SX2
!= ( path_cons @ SX3 @ empty ) ) )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( path @ ( head_of @ SX3 ) @ SX1 @ SX4 )
| ( SX2
!= ( path_cons @ SX3 @ SX4 ) ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( path @ ( head_of @ SX3 ) @ SX1 @ SX4 )
| ( SX2
!= ( path_cons @ SX3 @ SX4 ) ) )
| ~ ( ( SX1
!= ( head_of @ SX3 ) )
| ( SX2
!= ( path_cons @ SX3 @ empty ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(70,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( sequential @ SX0 @ SX1 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SX0 )
| ~ ( edge @ SX1 ) )
| ~ ( ( SX0 != SX1 ) ) )
| ( ( head_of @ SX0 )
!= ( tail_of @ SX1 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SX0 )
| ~ ( edge @ SX1 ) )
| ~ ( ( SX0 != SX1 ) ) )
| ( ( head_of @ SX0 )
!= ( tail_of @ SX1 ) ) )
| ( sequential @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(71,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( path @ SX1 @ SX2 @ SX0 )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ~ ( ~ ~ ( ~ ( on_path @ SX3 @ SX0 )
| ~ ( on_path @ SX4 @ SX0 ) )
| ~ ( sequential @ SX3 @ SX4 ) )
| ~ ! [SX5: $i] :
~ ( triangle @ SX3 @ SX4 @ SX5 ) ) )
| ( ( number_of_in @ sequential_pairs @ SX0 )
= ( number_of_in @ triangles @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(72,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( shortest_path @ SX1 @ SX2 @ SX0 )
| ! [SX3: $i,SX4: $i] :
( ~ ~ ( ~ ~ ( ~ ( on_path @ SX3 @ SX0 )
| ~ ( on_path @ SX4 @ SX0 ) )
| ~ ( sequential @ SX3 @ SX4 ) )
| ~ ! [SX5: $i] :
~ ( triangle @ SX3 @ SX4 @ SX5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(73,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( path @ SX0 @ SX1 @ SX2 )
| ( ( number_of_in @ sequential_pairs @ SX2 )
= ( minus @ ( length_of @ SX2 ) @ n1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(74,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ~ ( ~ ( shortest_path @ SX0 @ SX1 @ SX4 )
| ~ ( precedes @ SX2 @ SX3 @ SX4 ) )
| ~ ( ~ ~ ~ ! [SX5: $i] :
~ ~ ( ( ( tail_of @ SX5 )
!= ( tail_of @ SX2 ) )
| ( ( head_of @ SX5 )
!= ( head_of @ SX3 ) ) )
| ~ ~ ( precedes @ SX3 @ SX2 @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(75,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( path @ SX1 @ SX2 @ SX0 )
| ! [SX3: $i,SX4: $i] :
( ( precedes @ SX3 @ SX4 @ SX0 )
| ~ ~ ( ~ ~ ( ~ ( on_path @ SX3 @ SX0 )
| ~ ( on_path @ SX4 @ SX0 ) )
| ~ ( ( sequential @ SX3 @ SX4 )
| ~ ! [SX5: $i] :
~ ~ ( ~ ( sequential @ SX3 @ SX5 )
| ~ ( precedes @ SX5 @ SX4 @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(76,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( path @ SX1 @ SX2 @ SX0 )
| ! [SX3: $i,SX4: $i] :
( ~ ( precedes @ SX3 @ SX4 @ SX0 )
| ~ ( ~ ~ ( ~ ( on_path @ SX3 @ SX0 )
| ~ ( on_path @ SX4 @ SX0 ) )
| ~ ~ ~ ( ~ ( ~ ( sequential @ SX3 @ SX4 )
| ~ ! [SX5: $i] :
~ ~ ( ~ ( sequential @ SX3 @ SX5 )
| ~ ( precedes @ SX5 @ SX4 @ SX0 ) ) )
| ~ ( ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( sequential @ SX3 @ SX5 )
| ~ ( precedes @ SX5 @ SX4 @ SX0 ) )
| ( sequential @ SX3 @ SX4 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(77,plain,
! [SV1: $i] :
( ( ! [SY71: $i] : ( less_or_equal @ ( number_of_in @ SV1 @ SY71 ) @ ( number_of_in @ SV1 @ graph ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(78,plain,
( ( ( ~ complete ) = $true )
| ( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ~ ( ~ ( vertex @ SX0 )
| ~ ( vertex @ SX1 ) )
| ~ ( ( SX0 != SX1 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( edge @ SX2 )
| ~ ~ ~ ( ~ ( ~ ~ ( ( SX0
!= ( head_of @ SX2 ) )
| ( SX1
!= ( tail_of @ SX2 ) ) )
| ~ ( ( SX1
!= ( head_of @ SX2 ) )
| ( SX0
!= ( tail_of @ SX2 ) ) ) )
| ~ ( ~ ~ ( ( SX1
!= ( head_of @ SX2 ) )
| ( SX0
!= ( tail_of @ SX2 ) ) )
| ~ ( ( SX0
!= ( head_of @ SX2 ) )
| ( SX1
!= ( tail_of @ SX2 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(79,plain,
! [SV2: $i] :
( ( ! [SY72: $i,SY73: $i] :
~ ( ~ ( ~ ( shortest_path @ SV2 @ SY72 @ SY73 )
| ~ ( ~ ~ ( ~ ( path @ SV2 @ SY72 @ SY73 )
| ~ ( ( SV2 != SY72 ) ) )
| ~ ! [SY74: $i] :
( ~ ( path @ SV2 @ SY72 @ SY74 )
| ( less_or_equal @ ( length_of @ SY73 ) @ ( length_of @ SY74 ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( path @ SV2 @ SY72 @ SY73 )
| ~ ( ( SV2 != SY72 ) ) )
| ~ ! [SY75: $i] :
( ~ ( path @ SV2 @ SY72 @ SY75 )
| ( less_or_equal @ ( length_of @ SY73 ) @ ( length_of @ SY75 ) ) ) )
| ( shortest_path @ SV2 @ SY72 @ SY73 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(80,plain,
! [SV3: $i] :
( ( ! [SY76: $i,SY77: $i,SY78: $i] :
( ~ ~ ( ~ ( path @ SV3 @ SY76 @ SY77 )
| ~ ( on_path @ SY78 @ SY77 ) )
| ~ ( ~ ~ ( ~ ( edge @ SY78 )
| ~ ( in_path @ ( head_of @ SY78 ) @ SY77 ) )
| ~ ( in_path @ ( tail_of @ SY78 ) @ SY77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(81,plain,
! [SV4: $i] :
( ( ~ ( edge @ SV4 )
| ~ ( ~ ( vertex @ ( head_of @ SV4 ) )
| ~ ( vertex @ ( tail_of @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(82,plain,
! [SV5: $i] :
( ( ~ ( edge @ SV5 )
| ( ( head_of @ SV5 )
!= ( tail_of @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(83,plain,
! [SV6: $i] :
( ( ! [SY79: $i,SY80: $i] :
( ( path @ SV6 @ SY79 @ SY80 )
| ~ ~ ( ~ ~ ( ~ ( vertex @ SV6 )
| ~ ( vertex @ SY79 ) )
| ~ ~ ! [SY81: $i] :
~ ~ ( ~ ~ ( ~ ( edge @ SY81 )
| ( SV6
!= ( tail_of @ SY81 ) ) )
| ~ ( ~ ( ( SY79
!= ( head_of @ SY81 ) )
| ( SY80
!= ( path_cons @ SY81 @ empty ) ) )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( path @ ( head_of @ SY81 ) @ SY79 @ SX4 )
| ( SY80
!= ( path_cons @ SY81 @ SX4 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(84,plain,
! [SV7: $i] :
( ( ! [SY83: $i,SY84: $i,SY85: $i] :
( ~ ~ ( ~ ( path @ SV7 @ SY83 @ SY84 )
| ~ ( in_path @ SY85 @ SY84 ) )
| ~ ( ~ ( vertex @ SY85 )
| ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( on_path @ SX4 @ SY84 )
| ~ ( ( SY85
= ( head_of @ SX4 ) )
| ( SY85
= ( tail_of @ SX4 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(85,plain,
! [SV8: $i] :
( ( ! [SY87: $i,SY88: $i] :
~ ( ~ ( ~ ( triangle @ SV8 @ SY87 @ SY88 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV8 )
| ~ ( edge @ SY87 ) )
| ~ ( edge @ SY88 ) )
| ~ ( sequential @ SV8 @ SY87 ) )
| ~ ( sequential @ SY87 @ SY88 ) )
| ~ ( sequential @ SY88 @ SV8 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV8 )
| ~ ( edge @ SY87 ) )
| ~ ( edge @ SY88 ) )
| ~ ( sequential @ SV8 @ SY87 ) )
| ~ ( sequential @ SY87 @ SY88 ) )
| ~ ( sequential @ SY88 @ SV8 ) )
| ( triangle @ SV8 @ SY87 @ SY88 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(86,plain,
! [SV9: $i] :
( ( ! [SY89: $i,SY90: $i] :
( ~ ( path @ SV9 @ SY89 @ SY90 )
| ( ( length_of @ SY90 )
= ( number_of_in @ edges @ SY90 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(87,plain,
! [SV10: $i] :
( ( ! [SY91: $i,SY92: $i] :
( ~ ( path @ SV10 @ SY91 @ SY92 )
| ~ ( ~ ~ ( ~ ( vertex @ SV10 )
| ~ ( vertex @ SY91 ) )
| ~ ~ ! [SY93: $i] :
~ ~ ( ~ ~ ( ~ ( edge @ SY93 )
| ( SV10
!= ( tail_of @ SY93 ) ) )
| ~ ~ ~ ( ~ ( ~ ~ ( ( SY91
!= ( head_of @ SY93 ) )
| ( SY92
!= ( path_cons @ SY93 @ empty ) ) )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( path @ ( head_of @ SY93 ) @ SY91 @ SX4 )
| ( SY92
!= ( path_cons @ SY93 @ SX4 ) ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( path @ ( head_of @ SY93 ) @ SY91 @ SX4 )
| ( SY92
!= ( path_cons @ SY93 @ SX4 ) ) )
| ~ ( ( SY91
!= ( head_of @ SY93 ) )
| ( SY92
!= ( path_cons @ SY93 @ empty ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(88,plain,
! [SV11: $i] :
( ( ! [SY96: $i] :
~ ( ~ ( ~ ( sequential @ SV11 @ SY96 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV11 )
| ~ ( edge @ SY96 ) )
| ~ ( ( SV11 != SY96 ) ) )
| ( ( head_of @ SV11 )
!= ( tail_of @ SY96 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV11 )
| ~ ( edge @ SY96 ) )
| ~ ( ( SV11 != SY96 ) ) )
| ( ( head_of @ SV11 )
!= ( tail_of @ SY96 ) ) )
| ( sequential @ SV11 @ SY96 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(89,plain,
! [SV12: $i] :
( ( ! [SY97: $i,SY98: $i] :
( ~ ~ ( ~ ( path @ SY97 @ SY98 @ SV12 )
| ~ ! [SY99: $i,SY100: $i] :
( ~ ~ ( ~ ~ ( ~ ( on_path @ SY99 @ SV12 )
| ~ ( on_path @ SY100 @ SV12 ) )
| ~ ( sequential @ SY99 @ SY100 ) )
| ~ ! [SX5: $i] :
~ ( triangle @ SY99 @ SY100 @ SX5 ) ) )
| ( ( number_of_in @ sequential_pairs @ SV12 )
= ( number_of_in @ triangles @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(90,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( shortest_path @ SX1 @ SX2 @ SX0 )
| ! [SX3: $i,SX4: $i] :
( ~ ~ ( ~ ~ ( ~ ( on_path @ SX3 @ SX0 )
| ~ ( on_path @ SX4 @ SX0 ) )
| ~ ( sequential @ SX3 @ SX4 ) )
| ~ ! [SX5: $i] :
~ ( triangle @ SX3 @ SX4 @ SX5 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(91,plain,
! [SV13: $i] :
( ( ! [SY102: $i,SY103: $i] :
( ~ ( path @ SV13 @ SY102 @ SY103 )
| ( ( number_of_in @ sequential_pairs @ SY103 )
= ( minus @ ( length_of @ SY103 ) @ n1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(92,plain,
! [SV14: $i] :
( ( ! [SY104: $i,SY105: $i,SY106: $i,SY107: $i] :
( ~ ~ ( ~ ( shortest_path @ SV14 @ SY104 @ SY107 )
| ~ ( precedes @ SY105 @ SY106 @ SY107 ) )
| ~ ( ~ ~ ~ ! [SX5: $i] :
~ ~ ( ( ( tail_of @ SX5 )
!= ( tail_of @ SY105 ) )
| ( ( head_of @ SX5 )
!= ( head_of @ SY106 ) ) )
| ~ ~ ( precedes @ SY106 @ SY105 @ SY107 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(93,plain,
! [SV15: $i] :
( ( ! [SY109: $i,SY110: $i] :
( ~ ( path @ SY109 @ SY110 @ SV15 )
| ! [SY111: $i,SY112: $i] :
( ( precedes @ SY111 @ SY112 @ SV15 )
| ~ ~ ( ~ ~ ( ~ ( on_path @ SY111 @ SV15 )
| ~ ( on_path @ SY112 @ SV15 ) )
| ~ ( ( sequential @ SY111 @ SY112 )
| ~ ! [SY113: $i] :
~ ~ ( ~ ( sequential @ SY111 @ SY113 )
| ~ ( precedes @ SY113 @ SY112 @ SV15 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(94,plain,
! [SV16: $i] :
( ( ! [SY114: $i,SY115: $i] :
( ~ ( path @ SY114 @ SY115 @ SV16 )
| ! [SY116: $i,SY117: $i] :
( ~ ( precedes @ SY116 @ SY117 @ SV16 )
| ~ ( ~ ~ ( ~ ( on_path @ SY116 @ SV16 )
| ~ ( on_path @ SY117 @ SV16 ) )
| ~ ~ ~ ( ~ ( ~ ( sequential @ SY116 @ SY117 )
| ~ ! [SY118: $i] :
~ ~ ( ~ ( sequential @ SY116 @ SY118 )
| ~ ( precedes @ SY118 @ SY117 @ SV16 ) ) )
| ~ ( ~ ~ ! [SY119: $i] :
~ ~ ( ~ ( sequential @ SY116 @ SY119 )
| ~ ( precedes @ SY119 @ SY117 @ SV16 ) )
| ( sequential @ SY116 @ SY117 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(95,plain,
! [SV17: $i,SV1: $i] :
( ( less_or_equal @ ( number_of_in @ SV1 @ SV17 ) @ ( number_of_in @ SV1 @ graph ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(96,plain,
( ( complete = $false )
| ( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ~ ( ~ ( vertex @ SX0 )
| ~ ( vertex @ SX1 ) )
| ~ ( ( SX0 != SX1 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( edge @ SX2 )
| ~ ~ ~ ( ~ ( ~ ~ ( ( SX0
!= ( head_of @ SX2 ) )
| ( SX1
!= ( tail_of @ SX2 ) ) )
| ~ ( ( SX1
!= ( head_of @ SX2 ) )
| ( SX0
!= ( tail_of @ SX2 ) ) ) )
| ~ ( ~ ~ ( ( SX1
!= ( head_of @ SX2 ) )
| ( SX0
!= ( tail_of @ SX2 ) ) )
| ~ ( ( SX0
!= ( head_of @ SX2 ) )
| ( SX1
!= ( tail_of @ SX2 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(97,plain,
! [SV18: $i,SV2: $i] :
( ( ! [SY120: $i] :
~ ( ~ ( ~ ( shortest_path @ SV2 @ SV18 @ SY120 )
| ~ ( ~ ~ ( ~ ( path @ SV2 @ SV18 @ SY120 )
| ~ ( ( SV2 != SV18 ) ) )
| ~ ! [SY121: $i] :
( ~ ( path @ SV2 @ SV18 @ SY121 )
| ( less_or_equal @ ( length_of @ SY120 ) @ ( length_of @ SY121 ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( path @ SV2 @ SV18 @ SY120 )
| ~ ( ( SV2 != SV18 ) ) )
| ~ ! [SY122: $i] :
( ~ ( path @ SV2 @ SV18 @ SY122 )
| ( less_or_equal @ ( length_of @ SY120 ) @ ( length_of @ SY122 ) ) ) )
| ( shortest_path @ SV2 @ SV18 @ SY120 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(98,plain,
! [SV19: $i,SV3: $i] :
( ( ! [SY123: $i,SY124: $i] :
( ~ ~ ( ~ ( path @ SV3 @ SV19 @ SY123 )
| ~ ( on_path @ SY124 @ SY123 ) )
| ~ ( ~ ~ ( ~ ( edge @ SY124 )
| ~ ( in_path @ ( head_of @ SY124 ) @ SY123 ) )
| ~ ( in_path @ ( tail_of @ SY124 ) @ SY123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(99,plain,
! [SV4: $i] :
( ( ( ~ ( edge @ SV4 ) )
= $true )
| ( ( ~ ( ~ ( vertex @ ( head_of @ SV4 ) )
| ~ ( vertex @ ( tail_of @ SV4 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(100,plain,
! [SV5: $i] :
( ( ( ~ ( edge @ SV5 ) )
= $true )
| ( ( ( head_of @ SV5 )
!= ( tail_of @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(101,plain,
! [SV20: $i,SV6: $i] :
( ( ! [SY125: $i] :
( ( path @ SV6 @ SV20 @ SY125 )
| ~ ~ ( ~ ~ ( ~ ( vertex @ SV6 )
| ~ ( vertex @ SV20 ) )
| ~ ~ ! [SY126: $i] :
~ ~ ( ~ ~ ( ~ ( edge @ SY126 )
| ( SV6
!= ( tail_of @ SY126 ) ) )
| ~ ( ~ ( ( SV20
!= ( head_of @ SY126 ) )
| ( SY125
!= ( path_cons @ SY126 @ empty ) ) )
| ~ ! [SY127: $i] :
~ ~ ( ~ ( path @ ( head_of @ SY126 ) @ SV20 @ SY127 )
| ( SY125
!= ( path_cons @ SY126 @ SY127 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(102,plain,
! [SV21: $i,SV7: $i] :
( ( ! [SY128: $i,SY129: $i] :
( ~ ~ ( ~ ( path @ SV7 @ SV21 @ SY128 )
| ~ ( in_path @ SY129 @ SY128 ) )
| ~ ( ~ ( vertex @ SY129 )
| ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( on_path @ SX4 @ SY128 )
| ~ ( ( SY129
= ( head_of @ SX4 ) )
| ( SY129
= ( tail_of @ SX4 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(103,plain,
! [SV22: $i,SV8: $i] :
( ( ! [SY131: $i] :
~ ( ~ ( ~ ( triangle @ SV8 @ SV22 @ SY131 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV8 )
| ~ ( edge @ SV22 ) )
| ~ ( edge @ SY131 ) )
| ~ ( sequential @ SV8 @ SV22 ) )
| ~ ( sequential @ SV22 @ SY131 ) )
| ~ ( sequential @ SY131 @ SV8 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV8 )
| ~ ( edge @ SV22 ) )
| ~ ( edge @ SY131 ) )
| ~ ( sequential @ SV8 @ SV22 ) )
| ~ ( sequential @ SV22 @ SY131 ) )
| ~ ( sequential @ SY131 @ SV8 ) )
| ( triangle @ SV8 @ SV22 @ SY131 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(104,plain,
! [SV23: $i,SV9: $i] :
( ( ! [SY132: $i] :
( ~ ( path @ SV9 @ SV23 @ SY132 )
| ( ( length_of @ SY132 )
= ( number_of_in @ edges @ SY132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(105,plain,
! [SV24: $i,SV10: $i] :
( ( ! [SY133: $i] :
( ~ ( path @ SV10 @ SV24 @ SY133 )
| ~ ( ~ ~ ( ~ ( vertex @ SV10 )
| ~ ( vertex @ SV24 ) )
| ~ ~ ! [SY134: $i] :
~ ~ ( ~ ~ ( ~ ( edge @ SY134 )
| ( SV10
!= ( tail_of @ SY134 ) ) )
| ~ ~ ~ ( ~ ( ~ ~ ( ( SV24
!= ( head_of @ SY134 ) )
| ( SY133
!= ( path_cons @ SY134 @ empty ) ) )
| ~ ! [SY135: $i] :
~ ~ ( ~ ( path @ ( head_of @ SY134 ) @ SV24 @ SY135 )
| ( SY133
!= ( path_cons @ SY134 @ SY135 ) ) ) )
| ~ ( ~ ~ ! [SY136: $i] :
~ ~ ( ~ ( path @ ( head_of @ SY134 ) @ SV24 @ SY136 )
| ( SY133
!= ( path_cons @ SY134 @ SY136 ) ) )
| ~ ( ( SV24
!= ( head_of @ SY134 ) )
| ( SY133
!= ( path_cons @ SY134 @ empty ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(106,plain,
! [SV25: $i,SV11: $i] :
( ( ~ ( ~ ( ~ ( sequential @ SV11 @ SV25 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV11 )
| ~ ( edge @ SV25 ) )
| ~ ( ( SV11 != SV25 ) ) )
| ( ( head_of @ SV11 )
!= ( tail_of @ SV25 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV11 )
| ~ ( edge @ SV25 ) )
| ~ ( ( SV11 != SV25 ) ) )
| ( ( head_of @ SV11 )
!= ( tail_of @ SV25 ) ) )
| ( sequential @ SV11 @ SV25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(107,plain,
! [SV12: $i,SV26: $i] :
( ( ! [SY137: $i] :
( ~ ~ ( ~ ( path @ SV26 @ SY137 @ SV12 )
| ~ ! [SY99: $i,SY100: $i] :
( ~ ~ ( ~ ~ ( ~ ( on_path @ SY99 @ SV12 )
| ~ ( on_path @ SY100 @ SV12 ) )
| ~ ( sequential @ SY99 @ SY100 ) )
| ~ ! [SX5: $i] :
~ ( triangle @ SY99 @ SY100 @ SX5 ) ) )
| ( ( number_of_in @ sequential_pairs @ SV12 )
= ( number_of_in @ triangles @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(108,plain,
( ( ! [SY141: $i,SY142: $i] :
( ~ ( shortest_path @ SY141 @ SY142 @ sK1_SX0 )
| ! [SY143: $i,SY144: $i] :
( ~ ~ ( ~ ~ ( ~ ( on_path @ SY143 @ sK1_SX0 )
| ~ ( on_path @ SY144 @ sK1_SX0 ) )
| ~ ( sequential @ SY143 @ SY144 ) )
| ~ ! [SX5: $i] :
~ ( triangle @ SY143 @ SY144 @ SX5 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[90]) ).
thf(109,plain,
! [SV27: $i,SV13: $i] :
( ( ! [SY146: $i] :
( ~ ( path @ SV13 @ SV27 @ SY146 )
| ( ( number_of_in @ sequential_pairs @ SY146 )
= ( minus @ ( length_of @ SY146 ) @ n1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(110,plain,
! [SV28: $i,SV14: $i] :
( ( ! [SY147: $i,SY148: $i,SY149: $i] :
( ~ ~ ( ~ ( shortest_path @ SV14 @ SV28 @ SY149 )
| ~ ( precedes @ SY147 @ SY148 @ SY149 ) )
| ~ ( ~ ~ ~ ! [SX5: $i] :
~ ~ ( ( ( tail_of @ SX5 )
!= ( tail_of @ SY147 ) )
| ( ( head_of @ SX5 )
!= ( head_of @ SY148 ) ) )
| ~ ~ ( precedes @ SY148 @ SY147 @ SY149 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(111,plain,
! [SV15: $i,SV29: $i] :
( ( ! [SY151: $i] :
( ~ ( path @ SV29 @ SY151 @ SV15 )
| ! [SY111: $i,SY112: $i] :
( ( precedes @ SY111 @ SY112 @ SV15 )
| ~ ~ ( ~ ~ ( ~ ( on_path @ SY111 @ SV15 )
| ~ ( on_path @ SY112 @ SV15 ) )
| ~ ( ( sequential @ SY111 @ SY112 )
| ~ ! [SY113: $i] :
~ ~ ( ~ ( sequential @ SY111 @ SY113 )
| ~ ( precedes @ SY113 @ SY112 @ SV15 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(112,plain,
! [SV16: $i,SV30: $i] :
( ( ! [SY155: $i] :
( ~ ( path @ SV30 @ SY155 @ SV16 )
| ! [SY116: $i,SY117: $i] :
( ~ ( precedes @ SY116 @ SY117 @ SV16 )
| ~ ( ~ ~ ( ~ ( on_path @ SY116 @ SV16 )
| ~ ( on_path @ SY117 @ SV16 ) )
| ~ ~ ~ ( ~ ( ~ ( sequential @ SY116 @ SY117 )
| ~ ! [SY118: $i] :
~ ~ ( ~ ( sequential @ SY116 @ SY118 )
| ~ ( precedes @ SY118 @ SY117 @ SV16 ) ) )
| ~ ( ~ ~ ! [SY119: $i] :
~ ~ ( ~ ( sequential @ SY116 @ SY119 )
| ~ ( precedes @ SY119 @ SY117 @ SV16 ) )
| ( sequential @ SY116 @ SY117 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(113,plain,
! [SV31: $i] :
( ( ( ! [SY160: $i] :
( ~ ~ ( ~ ~ ( ~ ( vertex @ SV31 )
| ~ ( vertex @ SY160 ) )
| ~ ( ( SV31 != SY160 ) ) )
| ~ ! [SY161: $i] :
~ ~ ( ~ ( edge @ SY161 )
| ~ ~ ~ ( ~ ( ~ ~ ( ( SV31
!= ( head_of @ SY161 ) )
| ( SY160
!= ( tail_of @ SY161 ) ) )
| ~ ( ( SY160
!= ( head_of @ SY161 ) )
| ( SV31
!= ( tail_of @ SY161 ) ) ) )
| ~ ( ~ ~ ( ( SY160
!= ( head_of @ SY161 ) )
| ( SV31
!= ( tail_of @ SY161 ) ) )
| ~ ( ( SV31
!= ( head_of @ SY161 ) )
| ( SY160
!= ( tail_of @ SY161 ) ) ) ) ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(114,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ~ ( ~ ( ~ ( shortest_path @ SV2 @ SV18 @ SV32 )
| ~ ( ~ ~ ( ~ ( path @ SV2 @ SV18 @ SV32 )
| ~ ( ( SV2 != SV18 ) ) )
| ~ ! [SY162: $i] :
( ~ ( path @ SV2 @ SV18 @ SY162 )
| ( less_or_equal @ ( length_of @ SV32 ) @ ( length_of @ SY162 ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( path @ SV2 @ SV18 @ SV32 )
| ~ ( ( SV2 != SV18 ) ) )
| ~ ! [SY163: $i] :
( ~ ( path @ SV2 @ SV18 @ SY163 )
| ( less_or_equal @ ( length_of @ SV32 ) @ ( length_of @ SY163 ) ) ) )
| ( shortest_path @ SV2 @ SV18 @ SV32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(115,plain,
! [SV33: $i,SV19: $i,SV3: $i] :
( ( ! [SY164: $i] :
( ~ ~ ( ~ ( path @ SV3 @ SV19 @ SV33 )
| ~ ( on_path @ SY164 @ SV33 ) )
| ~ ( ~ ~ ( ~ ( edge @ SY164 )
| ~ ( in_path @ ( head_of @ SY164 ) @ SV33 ) )
| ~ ( in_path @ ( tail_of @ SY164 ) @ SV33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(116,plain,
! [SV4: $i] :
( ( ( edge @ SV4 )
= $false )
| ( ( ~ ( ~ ( vertex @ ( head_of @ SV4 ) )
| ~ ( vertex @ ( tail_of @ SV4 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(117,plain,
! [SV5: $i] :
( ( ( edge @ SV5 )
= $false )
| ( ( ( head_of @ SV5 )
!= ( tail_of @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(118,plain,
! [SV34: $i,SV20: $i,SV6: $i] :
( ( ( path @ SV6 @ SV20 @ SV34 )
| ~ ~ ( ~ ~ ( ~ ( vertex @ SV6 )
| ~ ( vertex @ SV20 ) )
| ~ ~ ! [SY165: $i] :
~ ~ ( ~ ~ ( ~ ( edge @ SY165 )
| ( SV6
!= ( tail_of @ SY165 ) ) )
| ~ ( ~ ( ( SV20
!= ( head_of @ SY165 ) )
| ( SV34
!= ( path_cons @ SY165 @ empty ) ) )
| ~ ! [SY166: $i] :
~ ~ ( ~ ( path @ ( head_of @ SY165 ) @ SV20 @ SY166 )
| ( SV34
!= ( path_cons @ SY165 @ SY166 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(119,plain,
! [SV35: $i,SV21: $i,SV7: $i] :
( ( ! [SY167: $i] :
( ~ ~ ( ~ ( path @ SV7 @ SV21 @ SV35 )
| ~ ( in_path @ SY167 @ SV35 ) )
| ~ ( ~ ( vertex @ SY167 )
| ~ ~ ! [SY168: $i] :
~ ~ ( ~ ( on_path @ SY168 @ SV35 )
| ~ ( ( SY167
= ( head_of @ SY168 ) )
| ( SY167
= ( tail_of @ SY168 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(120,plain,
! [SV36: $i,SV22: $i,SV8: $i] :
( ( ~ ( ~ ( ~ ( triangle @ SV8 @ SV22 @ SV36 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV8 )
| ~ ( edge @ SV22 ) )
| ~ ( edge @ SV36 ) )
| ~ ( sequential @ SV8 @ SV22 ) )
| ~ ( sequential @ SV22 @ SV36 ) )
| ~ ( sequential @ SV36 @ SV8 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV8 )
| ~ ( edge @ SV22 ) )
| ~ ( edge @ SV36 ) )
| ~ ( sequential @ SV8 @ SV22 ) )
| ~ ( sequential @ SV22 @ SV36 ) )
| ~ ( sequential @ SV36 @ SV8 ) )
| ( triangle @ SV8 @ SV22 @ SV36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(121,plain,
! [SV37: $i,SV23: $i,SV9: $i] :
( ( ~ ( path @ SV9 @ SV23 @ SV37 )
| ( ( length_of @ SV37 )
= ( number_of_in @ edges @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(122,plain,
! [SV38: $i,SV24: $i,SV10: $i] :
( ( ~ ( path @ SV10 @ SV24 @ SV38 )
| ~ ( ~ ~ ( ~ ( vertex @ SV10 )
| ~ ( vertex @ SV24 ) )
| ~ ~ ! [SY169: $i] :
~ ~ ( ~ ~ ( ~ ( edge @ SY169 )
| ( SV10
!= ( tail_of @ SY169 ) ) )
| ~ ~ ~ ( ~ ( ~ ~ ( ( SV24
!= ( head_of @ SY169 ) )
| ( SV38
!= ( path_cons @ SY169 @ empty ) ) )
| ~ ! [SY170: $i] :
~ ~ ( ~ ( path @ ( head_of @ SY169 ) @ SV24 @ SY170 )
| ( SV38
!= ( path_cons @ SY169 @ SY170 ) ) ) )
| ~ ( ~ ~ ! [SY171: $i] :
~ ~ ( ~ ( path @ ( head_of @ SY169 ) @ SV24 @ SY171 )
| ( SV38
!= ( path_cons @ SY169 @ SY171 ) ) )
| ~ ( ( SV24
!= ( head_of @ SY169 ) )
| ( SV38
!= ( path_cons @ SY169 @ empty ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(123,plain,
! [SV25: $i,SV11: $i] :
( ( ~ ( ~ ( sequential @ SV11 @ SV25 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV11 )
| ~ ( edge @ SV25 ) )
| ~ ( ( SV11 != SV25 ) ) )
| ( ( head_of @ SV11 )
!= ( tail_of @ SV25 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV11 )
| ~ ( edge @ SV25 ) )
| ~ ( ( SV11 != SV25 ) ) )
| ( ( head_of @ SV11 )
!= ( tail_of @ SV25 ) ) )
| ( sequential @ SV11 @ SV25 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(124,plain,
! [SV12: $i,SV39: $i,SV26: $i] :
( ( ~ ~ ( ~ ( path @ SV26 @ SV39 @ SV12 )
| ~ ! [SY99: $i,SY100: $i] :
( ~ ~ ( ~ ~ ( ~ ( on_path @ SY99 @ SV12 )
| ~ ( on_path @ SY100 @ SV12 ) )
| ~ ( sequential @ SY99 @ SY100 ) )
| ~ ! [SX5: $i] :
~ ( triangle @ SY99 @ SY100 @ SX5 ) ) )
| ( ( number_of_in @ sequential_pairs @ SV12 )
= ( number_of_in @ triangles @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(125,plain,
( ( ! [SY175: $i] :
( ~ ( shortest_path @ sK2_SY141 @ SY175 @ sK1_SX0 )
| ! [SY143: $i,SY144: $i] :
( ~ ~ ( ~ ~ ( ~ ( on_path @ SY143 @ sK1_SX0 )
| ~ ( on_path @ SY144 @ sK1_SX0 ) )
| ~ ( sequential @ SY143 @ SY144 ) )
| ~ ! [SX5: $i] :
~ ( triangle @ SY143 @ SY144 @ SX5 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[108]) ).
thf(126,plain,
! [SV40: $i,SV27: $i,SV13: $i] :
( ( ~ ( path @ SV13 @ SV27 @ SV40 )
| ( ( number_of_in @ sequential_pairs @ SV40 )
= ( minus @ ( length_of @ SV40 ) @ n1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(127,plain,
! [SV41: $i,SV28: $i,SV14: $i] :
( ( ! [SY179: $i,SY180: $i] :
( ~ ~ ( ~ ( shortest_path @ SV14 @ SV28 @ SY180 )
| ~ ( precedes @ SV41 @ SY179 @ SY180 ) )
| ~ ( ~ ~ ~ ! [SY181: $i] :
~ ~ ( ( ( tail_of @ SY181 )
!= ( tail_of @ SV41 ) )
| ( ( head_of @ SY181 )
!= ( head_of @ SY179 ) ) )
| ~ ~ ( precedes @ SY179 @ SV41 @ SY180 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(128,plain,
! [SV15: $i,SV42: $i,SV29: $i] :
( ( ~ ( path @ SV29 @ SV42 @ SV15 )
| ! [SY111: $i,SY112: $i] :
( ( precedes @ SY111 @ SY112 @ SV15 )
| ~ ~ ( ~ ~ ( ~ ( on_path @ SY111 @ SV15 )
| ~ ( on_path @ SY112 @ SV15 ) )
| ~ ( ( sequential @ SY111 @ SY112 )
| ~ ! [SY113: $i] :
~ ~ ( ~ ( sequential @ SY111 @ SY113 )
| ~ ( precedes @ SY113 @ SY112 @ SV15 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(129,plain,
! [SV16: $i,SV43: $i,SV30: $i] :
( ( ~ ( path @ SV30 @ SV43 @ SV16 )
| ! [SY116: $i,SY117: $i] :
( ~ ( precedes @ SY116 @ SY117 @ SV16 )
| ~ ( ~ ~ ( ~ ( on_path @ SY116 @ SV16 )
| ~ ( on_path @ SY117 @ SV16 ) )
| ~ ~ ~ ( ~ ( ~ ( sequential @ SY116 @ SY117 )
| ~ ! [SY118: $i] :
~ ~ ( ~ ( sequential @ SY116 @ SY118 )
| ~ ( precedes @ SY118 @ SY117 @ SV16 ) ) )
| ~ ( ~ ~ ! [SY119: $i] :
~ ~ ( ~ ( sequential @ SY116 @ SY119 )
| ~ ( precedes @ SY119 @ SY117 @ SV16 ) )
| ( sequential @ SY116 @ SY117 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(130,plain,
! [SV44: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( vertex @ SV31 )
| ~ ( vertex @ SV44 ) )
| ~ ( ( SV31 != SV44 ) ) )
| ~ ! [SY189: $i] :
~ ~ ( ~ ( edge @ SY189 )
| ~ ~ ~ ( ~ ( ~ ~ ( ( SV31
!= ( head_of @ SY189 ) )
| ( SV44
!= ( tail_of @ SY189 ) ) )
| ~ ( ( SV44
!= ( head_of @ SY189 ) )
| ( SV31
!= ( tail_of @ SY189 ) ) ) )
| ~ ( ~ ~ ( ( SV44
!= ( head_of @ SY189 ) )
| ( SV31
!= ( tail_of @ SY189 ) ) )
| ~ ( ( SV31
!= ( head_of @ SY189 ) )
| ( SV44
!= ( tail_of @ SY189 ) ) ) ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(131,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ~ ( ~ ( shortest_path @ SV2 @ SV18 @ SV32 )
| ~ ( ~ ~ ( ~ ( path @ SV2 @ SV18 @ SV32 )
| ~ ( ( SV2 != SV18 ) ) )
| ~ ! [SY162: $i] :
( ~ ( path @ SV2 @ SV18 @ SY162 )
| ( less_or_equal @ ( length_of @ SV32 ) @ ( length_of @ SY162 ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( path @ SV2 @ SV18 @ SV32 )
| ~ ( ( SV2 != SV18 ) ) )
| ~ ! [SY163: $i] :
( ~ ( path @ SV2 @ SV18 @ SY163 )
| ( less_or_equal @ ( length_of @ SV32 ) @ ( length_of @ SY163 ) ) ) )
| ( shortest_path @ SV2 @ SV18 @ SV32 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(132,plain,
! [SV45: $i,SV33: $i,SV19: $i,SV3: $i] :
( ( ~ ~ ( ~ ( path @ SV3 @ SV19 @ SV33 )
| ~ ( on_path @ SV45 @ SV33 ) )
| ~ ( ~ ~ ( ~ ( edge @ SV45 )
| ~ ( in_path @ ( head_of @ SV45 ) @ SV33 ) )
| ~ ( in_path @ ( tail_of @ SV45 ) @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(133,plain,
! [SV4: $i] :
( ( ( ~ ( vertex @ ( head_of @ SV4 ) )
| ~ ( vertex @ ( tail_of @ SV4 ) ) )
= $false )
| ( ( edge @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(134,plain,
! [SV5: $i] :
( ( ( ( head_of @ SV5 )
= ( tail_of @ SV5 ) )
= $false )
| ( ( edge @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(135,plain,
! [SV34: $i,SV20: $i,SV6: $i] :
( ( ( path @ SV6 @ SV20 @ SV34 )
= $true )
| ( ( ~ ~ ( ~ ~ ( ~ ( vertex @ SV6 )
| ~ ( vertex @ SV20 ) )
| ~ ~ ! [SY165: $i] :
~ ~ ( ~ ~ ( ~ ( edge @ SY165 )
| ( SV6
!= ( tail_of @ SY165 ) ) )
| ~ ( ~ ( ( SV20
!= ( head_of @ SY165 ) )
| ( SV34
!= ( path_cons @ SY165 @ empty ) ) )
| ~ ! [SY166: $i] :
~ ~ ( ~ ( path @ ( head_of @ SY165 ) @ SV20 @ SY166 )
| ( SV34
!= ( path_cons @ SY165 @ SY166 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(136,plain,
! [SV46: $i,SV35: $i,SV21: $i,SV7: $i] :
( ( ~ ~ ( ~ ( path @ SV7 @ SV21 @ SV35 )
| ~ ( in_path @ SV46 @ SV35 ) )
| ~ ( ~ ( vertex @ SV46 )
| ~ ~ ! [SY190: $i] :
~ ~ ( ~ ( on_path @ SY190 @ SV35 )
| ~ ( ( SV46
= ( head_of @ SY190 ) )
| ( SV46
= ( tail_of @ SY190 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(137,plain,
! [SV36: $i,SV22: $i,SV8: $i] :
( ( ~ ( ~ ( triangle @ SV8 @ SV22 @ SV36 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV8 )
| ~ ( edge @ SV22 ) )
| ~ ( edge @ SV36 ) )
| ~ ( sequential @ SV8 @ SV22 ) )
| ~ ( sequential @ SV22 @ SV36 ) )
| ~ ( sequential @ SV36 @ SV8 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV8 )
| ~ ( edge @ SV22 ) )
| ~ ( edge @ SV36 ) )
| ~ ( sequential @ SV8 @ SV22 ) )
| ~ ( sequential @ SV22 @ SV36 ) )
| ~ ( sequential @ SV36 @ SV8 ) )
| ( triangle @ SV8 @ SV22 @ SV36 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(138,plain,
! [SV37: $i,SV23: $i,SV9: $i] :
( ( ( ~ ( path @ SV9 @ SV23 @ SV37 ) )
= $true )
| ( ( ( length_of @ SV37 )
= ( number_of_in @ edges @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(139,plain,
! [SV38: $i,SV24: $i,SV10: $i] :
( ( ( ~ ( path @ SV10 @ SV24 @ SV38 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( vertex @ SV10 )
| ~ ( vertex @ SV24 ) )
| ~ ~ ! [SY169: $i] :
~ ~ ( ~ ~ ( ~ ( edge @ SY169 )
| ( SV10
!= ( tail_of @ SY169 ) ) )
| ~ ~ ~ ( ~ ( ~ ~ ( ( SV24
!= ( head_of @ SY169 ) )
| ( SV38
!= ( path_cons @ SY169 @ empty ) ) )
| ~ ! [SY170: $i] :
~ ~ ( ~ ( path @ ( head_of @ SY169 ) @ SV24 @ SY170 )
| ( SV38
!= ( path_cons @ SY169 @ SY170 ) ) ) )
| ~ ( ~ ~ ! [SY171: $i] :
~ ~ ( ~ ( path @ ( head_of @ SY169 ) @ SV24 @ SY171 )
| ( SV38
!= ( path_cons @ SY169 @ SY171 ) ) )
| ~ ( ( SV24
!= ( head_of @ SY169 ) )
| ( SV38
!= ( path_cons @ SY169 @ empty ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[122]) ).
thf(140,plain,
! [SV25: $i,SV11: $i] :
( ( ~ ( ~ ( sequential @ SV11 @ SV25 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV11 )
| ~ ( edge @ SV25 ) )
| ~ ( ( SV11 != SV25 ) ) )
| ( ( head_of @ SV11 )
!= ( tail_of @ SV25 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[123]) ).
thf(141,plain,
! [SV25: $i,SV11: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV11 )
| ~ ( edge @ SV25 ) )
| ~ ( ( SV11 != SV25 ) ) )
| ( ( head_of @ SV11 )
!= ( tail_of @ SV25 ) ) )
| ( sequential @ SV11 @ SV25 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[123]) ).
thf(142,plain,
! [SV12: $i,SV39: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ( path @ SV26 @ SV39 @ SV12 )
| ~ ! [SY99: $i,SY100: $i] :
( ~ ~ ( ~ ~ ( ~ ( on_path @ SY99 @ SV12 )
| ~ ( on_path @ SY100 @ SV12 ) )
| ~ ( sequential @ SY99 @ SY100 ) )
| ~ ! [SX5: $i] :
~ ( triangle @ SY99 @ SY100 @ SX5 ) ) ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV12 )
= ( number_of_in @ triangles @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(143,plain,
( ( ~ ( shortest_path @ sK2_SY141 @ sK3_SY175 @ sK1_SX0 )
| ! [SY143: $i,SY144: $i] :
( ~ ~ ( ~ ~ ( ~ ( on_path @ SY143 @ sK1_SX0 )
| ~ ( on_path @ SY144 @ sK1_SX0 ) )
| ~ ( sequential @ SY143 @ SY144 ) )
| ~ ! [SX5: $i] :
~ ( triangle @ SY143 @ SY144 @ SX5 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[125]) ).
thf(144,plain,
! [SV40: $i,SV27: $i,SV13: $i] :
( ( ( ~ ( path @ SV13 @ SV27 @ SV40 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV40 )
= ( minus @ ( length_of @ SV40 ) @ n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(145,plain,
! [SV47: $i,SV41: $i,SV28: $i,SV14: $i] :
( ( ! [SY194: $i] :
( ~ ~ ( ~ ( shortest_path @ SV14 @ SV28 @ SY194 )
| ~ ( precedes @ SV41 @ SV47 @ SY194 ) )
| ~ ( ~ ~ ~ ! [SY195: $i] :
~ ~ ( ( ( tail_of @ SY195 )
!= ( tail_of @ SV41 ) )
| ( ( head_of @ SY195 )
!= ( head_of @ SV47 ) ) )
| ~ ~ ( precedes @ SV47 @ SV41 @ SY194 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(146,plain,
! [SV15: $i,SV42: $i,SV29: $i] :
( ( ( ~ ( path @ SV29 @ SV42 @ SV15 ) )
= $true )
| ( ( ! [SY111: $i,SY112: $i] :
( ( precedes @ SY111 @ SY112 @ SV15 )
| ~ ~ ( ~ ~ ( ~ ( on_path @ SY111 @ SV15 )
| ~ ( on_path @ SY112 @ SV15 ) )
| ~ ( ( sequential @ SY111 @ SY112 )
| ~ ! [SY113: $i] :
~ ~ ( ~ ( sequential @ SY111 @ SY113 )
| ~ ( precedes @ SY113 @ SY112 @ SV15 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(147,plain,
! [SV16: $i,SV43: $i,SV30: $i] :
( ( ( ~ ( path @ SV30 @ SV43 @ SV16 ) )
= $true )
| ( ( ! [SY116: $i,SY117: $i] :
( ~ ( precedes @ SY116 @ SY117 @ SV16 )
| ~ ( ~ ~ ( ~ ( on_path @ SY116 @ SV16 )
| ~ ( on_path @ SY117 @ SV16 ) )
| ~ ~ ~ ( ~ ( ~ ( sequential @ SY116 @ SY117 )
| ~ ! [SY118: $i] :
~ ~ ( ~ ( sequential @ SY116 @ SY118 )
| ~ ( precedes @ SY118 @ SY117 @ SV16 ) ) )
| ~ ( ~ ~ ! [SY119: $i] :
~ ~ ( ~ ( sequential @ SY116 @ SY119 )
| ~ ( precedes @ SY119 @ SY117 @ SV16 ) )
| ( sequential @ SY116 @ SY117 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(148,plain,
! [SV44: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( vertex @ SV31 )
| ~ ( vertex @ SV44 ) )
| ~ ( ( SV31 != SV44 ) ) ) )
= $true )
| ( ( ~ ! [SY189: $i] :
~ ~ ( ~ ( edge @ SY189 )
| ~ ~ ~ ( ~ ( ~ ~ ( ( SV31
!= ( head_of @ SY189 ) )
| ( SV44
!= ( tail_of @ SY189 ) ) )
| ~ ( ( SV44
!= ( head_of @ SY189 ) )
| ( SV31
!= ( tail_of @ SY189 ) ) ) )
| ~ ( ~ ~ ( ( SV44
!= ( head_of @ SY189 ) )
| ( SV31
!= ( tail_of @ SY189 ) ) )
| ~ ( ( SV31
!= ( head_of @ SY189 ) )
| ( SV44
!= ( tail_of @ SY189 ) ) ) ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(149,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ~ ( ~ ( shortest_path @ SV2 @ SV18 @ SV32 )
| ~ ( ~ ~ ( ~ ( path @ SV2 @ SV18 @ SV32 )
| ~ ( ( SV2 != SV18 ) ) )
| ~ ! [SY162: $i] :
( ~ ( path @ SV2 @ SV18 @ SY162 )
| ( less_or_equal @ ( length_of @ SV32 ) @ ( length_of @ SY162 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[131]) ).
thf(150,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( path @ SV2 @ SV18 @ SV32 )
| ~ ( ( SV2 != SV18 ) ) )
| ~ ! [SY163: $i] :
( ~ ( path @ SV2 @ SV18 @ SY163 )
| ( less_or_equal @ ( length_of @ SV32 ) @ ( length_of @ SY163 ) ) ) )
| ( shortest_path @ SV2 @ SV18 @ SV32 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[131]) ).
thf(151,plain,
! [SV45: $i,SV33: $i,SV19: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( path @ SV3 @ SV19 @ SV33 )
| ~ ( on_path @ SV45 @ SV33 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( edge @ SV45 )
| ~ ( in_path @ ( head_of @ SV45 ) @ SV33 ) )
| ~ ( in_path @ ( tail_of @ SV45 ) @ SV33 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(152,plain,
! [SV4: $i] :
( ( ( ~ ( vertex @ ( head_of @ SV4 ) ) )
= $false )
| ( ( edge @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[133]) ).
thf(153,plain,
! [SV4: $i] :
( ( ( ~ ( vertex @ ( tail_of @ SV4 ) ) )
= $false )
| ( ( edge @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[133]) ).
thf(154,plain,
! [SV34: $i,SV20: $i,SV6: $i] :
( ( ( ~ ( ~ ~ ( ~ ( vertex @ SV6 )
| ~ ( vertex @ SV20 ) )
| ~ ~ ! [SY165: $i] :
~ ~ ( ~ ~ ( ~ ( edge @ SY165 )
| ( SV6
!= ( tail_of @ SY165 ) ) )
| ~ ( ~ ( ( SV20
!= ( head_of @ SY165 ) )
| ( SV34
!= ( path_cons @ SY165 @ empty ) ) )
| ~ ! [SY166: $i] :
~ ~ ( ~ ( path @ ( head_of @ SY165 ) @ SV20 @ SY166 )
| ( SV34
!= ( path_cons @ SY165 @ SY166 ) ) ) ) ) ) )
= $false )
| ( ( path @ SV6 @ SV20 @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(155,plain,
! [SV46: $i,SV35: $i,SV21: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( path @ SV7 @ SV21 @ SV35 )
| ~ ( in_path @ SV46 @ SV35 ) ) )
= $true )
| ( ( ~ ( ~ ( vertex @ SV46 )
| ~ ~ ! [SY190: $i] :
~ ~ ( ~ ( on_path @ SY190 @ SV35 )
| ~ ( ( SV46
= ( head_of @ SY190 ) )
| ( SV46
= ( tail_of @ SY190 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(156,plain,
! [SV36: $i,SV22: $i,SV8: $i] :
( ( ~ ( ~ ( triangle @ SV8 @ SV22 @ SV36 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV8 )
| ~ ( edge @ SV22 ) )
| ~ ( edge @ SV36 ) )
| ~ ( sequential @ SV8 @ SV22 ) )
| ~ ( sequential @ SV22 @ SV36 ) )
| ~ ( sequential @ SV36 @ SV8 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[137]) ).
thf(157,plain,
! [SV36: $i,SV22: $i,SV8: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV8 )
| ~ ( edge @ SV22 ) )
| ~ ( edge @ SV36 ) )
| ~ ( sequential @ SV8 @ SV22 ) )
| ~ ( sequential @ SV22 @ SV36 ) )
| ~ ( sequential @ SV36 @ SV8 ) )
| ( triangle @ SV8 @ SV22 @ SV36 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[137]) ).
thf(158,plain,
! [SV37: $i,SV23: $i,SV9: $i] :
( ( ( path @ SV9 @ SV23 @ SV37 )
= $false )
| ( ( ( length_of @ SV37 )
= ( number_of_in @ edges @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(159,plain,
! [SV38: $i,SV24: $i,SV10: $i] :
( ( ( path @ SV10 @ SV24 @ SV38 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( vertex @ SV10 )
| ~ ( vertex @ SV24 ) )
| ~ ~ ! [SY169: $i] :
~ ~ ( ~ ~ ( ~ ( edge @ SY169 )
| ( SV10
!= ( tail_of @ SY169 ) ) )
| ~ ~ ~ ( ~ ( ~ ~ ( ( SV24
!= ( head_of @ SY169 ) )
| ( SV38
!= ( path_cons @ SY169 @ empty ) ) )
| ~ ! [SY170: $i] :
~ ~ ( ~ ( path @ ( head_of @ SY169 ) @ SV24 @ SY170 )
| ( SV38
!= ( path_cons @ SY169 @ SY170 ) ) ) )
| ~ ( ~ ~ ! [SY171: $i] :
~ ~ ( ~ ( path @ ( head_of @ SY169 ) @ SV24 @ SY171 )
| ( SV38
!= ( path_cons @ SY169 @ SY171 ) ) )
| ~ ( ( SV24
!= ( head_of @ SY169 ) )
| ( SV38
!= ( path_cons @ SY169 @ empty ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(160,plain,
! [SV25: $i,SV11: $i] :
( ( ~ ( sequential @ SV11 @ SV25 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV11 )
| ~ ( edge @ SV25 ) )
| ~ ( ( SV11 != SV25 ) ) )
| ( ( head_of @ SV11 )
!= ( tail_of @ SV25 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[140]) ).
thf(161,plain,
! [SV25: $i,SV11: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV11 )
| ~ ( edge @ SV25 ) )
| ~ ( ( SV11 != SV25 ) ) )
| ( ( head_of @ SV11 )
!= ( tail_of @ SV25 ) ) )
| ( sequential @ SV11 @ SV25 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(162,plain,
! [SV12: $i,SV39: $i,SV26: $i] :
( ( ( ~ ( ~ ( path @ SV26 @ SV39 @ SV12 )
| ~ ! [SY99: $i,SY100: $i] :
( ~ ~ ( ~ ~ ( ~ ( on_path @ SY99 @ SV12 )
| ~ ( on_path @ SY100 @ SV12 ) )
| ~ ( sequential @ SY99 @ SY100 ) )
| ~ ! [SX5: $i] :
~ ( triangle @ SY99 @ SY100 @ SX5 ) ) ) )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV12 )
= ( number_of_in @ triangles @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(163,plain,
( ( ~ ( shortest_path @ sK2_SY141 @ sK3_SY175 @ sK1_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[143]) ).
thf(164,plain,
( ( ! [SY143: $i,SY144: $i] :
( ~ ~ ( ~ ~ ( ~ ( on_path @ SY143 @ sK1_SX0 )
| ~ ( on_path @ SY144 @ sK1_SX0 ) )
| ~ ( sequential @ SY143 @ SY144 ) )
| ~ ! [SX5: $i] :
~ ( triangle @ SY143 @ SY144 @ SX5 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[143]) ).
thf(165,plain,
! [SV40: $i,SV27: $i,SV13: $i] :
( ( ( path @ SV13 @ SV27 @ SV40 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV40 )
= ( minus @ ( length_of @ SV40 ) @ n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(166,plain,
! [SV47: $i,SV41: $i,SV48: $i,SV28: $i,SV14: $i] :
( ( ~ ~ ( ~ ( shortest_path @ SV14 @ SV28 @ SV48 )
| ~ ( precedes @ SV41 @ SV47 @ SV48 ) )
| ~ ( ~ ~ ~ ! [SY195: $i] :
~ ~ ( ( ( tail_of @ SY195 )
!= ( tail_of @ SV41 ) )
| ( ( head_of @ SY195 )
!= ( head_of @ SV47 ) ) )
| ~ ~ ( precedes @ SV47 @ SV41 @ SV48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(167,plain,
! [SV15: $i,SV42: $i,SV29: $i] :
( ( ( path @ SV29 @ SV42 @ SV15 )
= $false )
| ( ( ! [SY111: $i,SY112: $i] :
( ( precedes @ SY111 @ SY112 @ SV15 )
| ~ ~ ( ~ ~ ( ~ ( on_path @ SY111 @ SV15 )
| ~ ( on_path @ SY112 @ SV15 ) )
| ~ ( ( sequential @ SY111 @ SY112 )
| ~ ! [SY113: $i] :
~ ~ ( ~ ( sequential @ SY111 @ SY113 )
| ~ ( precedes @ SY113 @ SY112 @ SV15 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(168,plain,
! [SV16: $i,SV43: $i,SV30: $i] :
( ( ( path @ SV30 @ SV43 @ SV16 )
= $false )
| ( ( ! [SY116: $i,SY117: $i] :
( ~ ( precedes @ SY116 @ SY117 @ SV16 )
| ~ ( ~ ~ ( ~ ( on_path @ SY116 @ SV16 )
| ~ ( on_path @ SY117 @ SV16 ) )
| ~ ~ ~ ( ~ ( ~ ( sequential @ SY116 @ SY117 )
| ~ ! [SY118: $i] :
~ ~ ( ~ ( sequential @ SY116 @ SY118 )
| ~ ( precedes @ SY118 @ SY117 @ SV16 ) ) )
| ~ ( ~ ~ ! [SY119: $i] :
~ ~ ( ~ ( sequential @ SY116 @ SY119 )
| ~ ( precedes @ SY119 @ SY117 @ SV16 ) )
| ( sequential @ SY116 @ SY117 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(169,plain,
! [SV44: $i,SV31: $i] :
( ( ( ~ ( ~ ~ ( ~ ( vertex @ SV31 )
| ~ ( vertex @ SV44 ) )
| ~ ( ( SV31 != SV44 ) ) ) )
= $false )
| ( ( ~ ! [SY189: $i] :
~ ~ ( ~ ( edge @ SY189 )
| ~ ~ ~ ( ~ ( ~ ~ ( ( SV31
!= ( head_of @ SY189 ) )
| ( SV44
!= ( tail_of @ SY189 ) ) )
| ~ ( ( SV44
!= ( head_of @ SY189 ) )
| ( SV31
!= ( tail_of @ SY189 ) ) ) )
| ~ ( ~ ~ ( ( SV44
!= ( head_of @ SY189 ) )
| ( SV31
!= ( tail_of @ SY189 ) ) )
| ~ ( ( SV31
!= ( head_of @ SY189 ) )
| ( SV44
!= ( tail_of @ SY189 ) ) ) ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(170,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ~ ( shortest_path @ SV2 @ SV18 @ SV32 )
| ~ ( ~ ~ ( ~ ( path @ SV2 @ SV18 @ SV32 )
| ~ ( ( SV2 != SV18 ) ) )
| ~ ! [SY162: $i] :
( ~ ( path @ SV2 @ SV18 @ SY162 )
| ( less_or_equal @ ( length_of @ SV32 ) @ ( length_of @ SY162 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(171,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( path @ SV2 @ SV18 @ SV32 )
| ~ ( ( SV2 != SV18 ) ) )
| ~ ! [SY163: $i] :
( ~ ( path @ SV2 @ SV18 @ SY163 )
| ( less_or_equal @ ( length_of @ SV32 ) @ ( length_of @ SY163 ) ) ) )
| ( shortest_path @ SV2 @ SV18 @ SV32 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[150]) ).
thf(172,plain,
! [SV45: $i,SV33: $i,SV19: $i,SV3: $i] :
( ( ( ~ ( ~ ( path @ SV3 @ SV19 @ SV33 )
| ~ ( on_path @ SV45 @ SV33 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( edge @ SV45 )
| ~ ( in_path @ ( head_of @ SV45 ) @ SV33 ) )
| ~ ( in_path @ ( tail_of @ SV45 ) @ SV33 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(173,plain,
! [SV4: $i] :
( ( ( vertex @ ( head_of @ SV4 ) )
= $true )
| ( ( edge @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[152]) ).
thf(174,plain,
! [SV4: $i] :
( ( ( vertex @ ( tail_of @ SV4 ) )
= $true )
| ( ( edge @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[153]) ).
thf(175,plain,
! [SV34: $i,SV20: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( vertex @ SV6 )
| ~ ( vertex @ SV20 ) )
| ~ ~ ! [SY165: $i] :
~ ~ ( ~ ~ ( ~ ( edge @ SY165 )
| ( SV6
!= ( tail_of @ SY165 ) ) )
| ~ ( ~ ( ( SV20
!= ( head_of @ SY165 ) )
| ( SV34
!= ( path_cons @ SY165 @ empty ) ) )
| ~ ! [SY166: $i] :
~ ~ ( ~ ( path @ ( head_of @ SY165 ) @ SV20 @ SY166 )
| ( SV34
!= ( path_cons @ SY165 @ SY166 ) ) ) ) ) )
= $true )
| ( ( path @ SV6 @ SV20 @ SV34 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[154]) ).
thf(176,plain,
! [SV46: $i,SV35: $i,SV21: $i,SV7: $i] :
( ( ( ~ ( ~ ( path @ SV7 @ SV21 @ SV35 )
| ~ ( in_path @ SV46 @ SV35 ) ) )
= $false )
| ( ( ~ ( ~ ( vertex @ SV46 )
| ~ ~ ! [SY190: $i] :
~ ~ ( ~ ( on_path @ SY190 @ SV35 )
| ~ ( ( SV46
= ( head_of @ SY190 ) )
| ( SV46
= ( tail_of @ SY190 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(177,plain,
! [SV36: $i,SV22: $i,SV8: $i] :
( ( ~ ( triangle @ SV8 @ SV22 @ SV36 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV8 )
| ~ ( edge @ SV22 ) )
| ~ ( edge @ SV36 ) )
| ~ ( sequential @ SV8 @ SV22 ) )
| ~ ( sequential @ SV22 @ SV36 ) )
| ~ ( sequential @ SV36 @ SV8 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[156]) ).
thf(178,plain,
! [SV36: $i,SV22: $i,SV8: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV8 )
| ~ ( edge @ SV22 ) )
| ~ ( edge @ SV36 ) )
| ~ ( sequential @ SV8 @ SV22 ) )
| ~ ( sequential @ SV22 @ SV36 ) )
| ~ ( sequential @ SV36 @ SV8 ) )
| ( triangle @ SV8 @ SV22 @ SV36 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[157]) ).
thf(179,plain,
! [SV38: $i,SV24: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( vertex @ SV10 )
| ~ ( vertex @ SV24 ) )
| ~ ~ ! [SY169: $i] :
~ ~ ( ~ ~ ( ~ ( edge @ SY169 )
| ( SV10
!= ( tail_of @ SY169 ) ) )
| ~ ~ ~ ( ~ ( ~ ~ ( ( SV24
!= ( head_of @ SY169 ) )
| ( SV38
!= ( path_cons @ SY169 @ empty ) ) )
| ~ ! [SY170: $i] :
~ ~ ( ~ ( path @ ( head_of @ SY169 ) @ SV24 @ SY170 )
| ( SV38
!= ( path_cons @ SY169 @ SY170 ) ) ) )
| ~ ( ~ ~ ! [SY171: $i] :
~ ~ ( ~ ( path @ ( head_of @ SY169 ) @ SV24 @ SY171 )
| ( SV38
!= ( path_cons @ SY169 @ SY171 ) ) )
| ~ ( ( SV24
!= ( head_of @ SY169 ) )
| ( SV38
!= ( path_cons @ SY169 @ empty ) ) ) ) ) ) )
= $false )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(180,plain,
! [SV25: $i,SV11: $i] :
( ( ( ~ ( sequential @ SV11 @ SV25 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV11 )
| ~ ( edge @ SV25 ) )
| ~ ( ( SV11 != SV25 ) ) )
| ( ( head_of @ SV11 )
!= ( tail_of @ SV25 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[160]) ).
thf(181,plain,
! [SV25: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV11 )
| ~ ( edge @ SV25 ) )
| ~ ( ( SV11 != SV25 ) ) )
| ( ( head_of @ SV11 )
!= ( tail_of @ SV25 ) ) ) )
= $true )
| ( ( sequential @ SV11 @ SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(182,plain,
! [SV12: $i,SV39: $i,SV26: $i] :
( ( ( ~ ( path @ SV26 @ SV39 @ SV12 )
| ~ ! [SY99: $i,SY100: $i] :
( ~ ~ ( ~ ~ ( ~ ( on_path @ SY99 @ SV12 )
| ~ ( on_path @ SY100 @ SV12 ) )
| ~ ( sequential @ SY99 @ SY100 ) )
| ~ ! [SX5: $i] :
~ ( triangle @ SY99 @ SY100 @ SX5 ) ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV12 )
= ( number_of_in @ triangles @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[162]) ).
thf(183,plain,
( ( shortest_path @ sK2_SY141 @ sK3_SY175 @ sK1_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[163]) ).
thf(184,plain,
( ( ! [SY197: $i] :
( ~ ~ ( ~ ~ ( ~ ( on_path @ sK4_SY143 @ sK1_SX0 )
| ~ ( on_path @ SY197 @ sK1_SX0 ) )
| ~ ( sequential @ sK4_SY143 @ SY197 ) )
| ~ ! [SY198: $i] :
~ ( triangle @ sK4_SY143 @ SY197 @ SY198 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[164]) ).
thf(185,plain,
! [SV47: $i,SV41: $i,SV48: $i,SV28: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( shortest_path @ SV14 @ SV28 @ SV48 )
| ~ ( precedes @ SV41 @ SV47 @ SV48 ) ) )
= $true )
| ( ( ~ ( ~ ~ ~ ! [SY195: $i] :
~ ~ ( ( ( tail_of @ SY195 )
!= ( tail_of @ SV41 ) )
| ( ( head_of @ SY195 )
!= ( head_of @ SV47 ) ) )
| ~ ~ ( precedes @ SV47 @ SV41 @ SV48 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(186,plain,
! [SV42: $i,SV29: $i,SV15: $i,SV49: $i] :
( ( ( ! [SY199: $i] :
( ( precedes @ SV49 @ SY199 @ SV15 )
| ~ ~ ( ~ ~ ( ~ ( on_path @ SV49 @ SV15 )
| ~ ( on_path @ SY199 @ SV15 ) )
| ~ ( ( sequential @ SV49 @ SY199 )
| ~ ! [SY200: $i] :
~ ~ ( ~ ( sequential @ SV49 @ SY200 )
| ~ ( precedes @ SY200 @ SY199 @ SV15 ) ) ) ) ) )
= $true )
| ( ( path @ SV29 @ SV42 @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(187,plain,
! [SV43: $i,SV30: $i,SV16: $i,SV50: $i] :
( ( ( ! [SY201: $i] :
( ~ ( precedes @ SV50 @ SY201 @ SV16 )
| ~ ( ~ ~ ( ~ ( on_path @ SV50 @ SV16 )
| ~ ( on_path @ SY201 @ SV16 ) )
| ~ ~ ~ ( ~ ( ~ ( sequential @ SV50 @ SY201 )
| ~ ! [SY202: $i] :
~ ~ ( ~ ( sequential @ SV50 @ SY202 )
| ~ ( precedes @ SY202 @ SY201 @ SV16 ) ) )
| ~ ( ~ ~ ! [SY203: $i] :
~ ~ ( ~ ( sequential @ SV50 @ SY203 )
| ~ ( precedes @ SY203 @ SY201 @ SV16 ) )
| ( sequential @ SV50 @ SY201 ) ) ) ) ) )
= $true )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(188,plain,
! [SV44: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ( vertex @ SV31 )
| ~ ( vertex @ SV44 ) )
| ~ ( ( SV31 != SV44 ) ) )
= $true )
| ( ( ~ ! [SY189: $i] :
~ ~ ( ~ ( edge @ SY189 )
| ~ ~ ~ ( ~ ( ~ ~ ( ( SV31
!= ( head_of @ SY189 ) )
| ( SV44
!= ( tail_of @ SY189 ) ) )
| ~ ( ( SV44
!= ( head_of @ SY189 ) )
| ( SV31
!= ( tail_of @ SY189 ) ) ) )
| ~ ( ~ ~ ( ( SV44
!= ( head_of @ SY189 ) )
| ( SV31
!= ( tail_of @ SY189 ) ) )
| ~ ( ( SV31
!= ( head_of @ SY189 ) )
| ( SV44
!= ( tail_of @ SY189 ) ) ) ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[169]) ).
thf(189,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ( ~ ( shortest_path @ SV2 @ SV18 @ SV32 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( path @ SV2 @ SV18 @ SV32 )
| ~ ( ( SV2 != SV18 ) ) )
| ~ ! [SY162: $i] :
( ~ ( path @ SV2 @ SV18 @ SY162 )
| ( less_or_equal @ ( length_of @ SV32 ) @ ( length_of @ SY162 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(190,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( path @ SV2 @ SV18 @ SV32 )
| ~ ( ( SV2 != SV18 ) ) )
| ~ ! [SY163: $i] :
( ~ ( path @ SV2 @ SV18 @ SY163 )
| ( less_or_equal @ ( length_of @ SV32 ) @ ( length_of @ SY163 ) ) ) ) )
= $true )
| ( ( shortest_path @ SV2 @ SV18 @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(191,plain,
! [SV45: $i,SV33: $i,SV19: $i,SV3: $i] :
( ( ( ~ ( path @ SV3 @ SV19 @ SV33 )
| ~ ( on_path @ SV45 @ SV33 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( edge @ SV45 )
| ~ ( in_path @ ( head_of @ SV45 ) @ SV33 ) )
| ~ ( in_path @ ( tail_of @ SV45 ) @ SV33 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[172]) ).
thf(192,plain,
! [SV34: $i,SV20: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( vertex @ SV6 )
| ~ ( vertex @ SV20 ) ) )
= $true )
| ( ( ~ ~ ! [SY165: $i] :
~ ~ ( ~ ~ ( ~ ( edge @ SY165 )
| ( SV6
!= ( tail_of @ SY165 ) ) )
| ~ ( ~ ( ( SV20
!= ( head_of @ SY165 ) )
| ( SV34
!= ( path_cons @ SY165 @ empty ) ) )
| ~ ! [SY166: $i] :
~ ~ ( ~ ( path @ ( head_of @ SY165 ) @ SV20 @ SY166 )
| ( SV34
!= ( path_cons @ SY165 @ SY166 ) ) ) ) ) )
= $true )
| ( ( path @ SV6 @ SV20 @ SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(193,plain,
! [SV46: $i,SV35: $i,SV21: $i,SV7: $i] :
( ( ( ~ ( path @ SV7 @ SV21 @ SV35 )
| ~ ( in_path @ SV46 @ SV35 ) )
= $true )
| ( ( ~ ( ~ ( vertex @ SV46 )
| ~ ~ ! [SY190: $i] :
~ ~ ( ~ ( on_path @ SY190 @ SV35 )
| ~ ( ( SV46
= ( head_of @ SY190 ) )
| ( SV46
= ( tail_of @ SY190 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[176]) ).
thf(194,plain,
! [SV36: $i,SV22: $i,SV8: $i] :
( ( ( ~ ( triangle @ SV8 @ SV22 @ SV36 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV8 )
| ~ ( edge @ SV22 ) )
| ~ ( edge @ SV36 ) )
| ~ ( sequential @ SV8 @ SV22 ) )
| ~ ( sequential @ SV22 @ SV36 ) )
| ~ ( sequential @ SV36 @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(195,plain,
! [SV36: $i,SV22: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV8 )
| ~ ( edge @ SV22 ) )
| ~ ( edge @ SV36 ) )
| ~ ( sequential @ SV8 @ SV22 ) )
| ~ ( sequential @ SV22 @ SV36 ) )
| ~ ( sequential @ SV36 @ SV8 ) ) )
= $true )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(196,plain,
! [SV38: $i,SV24: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( vertex @ SV10 )
| ~ ( vertex @ SV24 ) ) )
= $false )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[179]) ).
thf(197,plain,
! [SV38: $i,SV24: $i,SV10: $i] :
( ( ( ~ ~ ! [SY169: $i] :
~ ~ ( ~ ~ ( ~ ( edge @ SY169 )
| ( SV10
!= ( tail_of @ SY169 ) ) )
| ~ ~ ~ ( ~ ( ~ ~ ( ( SV24
!= ( head_of @ SY169 ) )
| ( SV38
!= ( path_cons @ SY169 @ empty ) ) )
| ~ ! [SY170: $i] :
~ ~ ( ~ ( path @ ( head_of @ SY169 ) @ SV24 @ SY170 )
| ( SV38
!= ( path_cons @ SY169 @ SY170 ) ) ) )
| ~ ( ~ ~ ! [SY171: $i] :
~ ~ ( ~ ( path @ ( head_of @ SY169 ) @ SV24 @ SY171 )
| ( SV38
!= ( path_cons @ SY169 @ SY171 ) ) )
| ~ ( ( SV24
!= ( head_of @ SY169 ) )
| ( SV38
!= ( path_cons @ SY169 @ empty ) ) ) ) ) ) )
= $false )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[179]) ).
thf(198,plain,
! [SV25: $i,SV11: $i] :
( ( ( sequential @ SV11 @ SV25 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV11 )
| ~ ( edge @ SV25 ) )
| ~ ( ( SV11 != SV25 ) ) )
| ( ( head_of @ SV11 )
!= ( tail_of @ SV25 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(199,plain,
! [SV25: $i,SV11: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV11 )
| ~ ( edge @ SV25 ) )
| ~ ( ( SV11 != SV25 ) ) )
| ( ( head_of @ SV11 )
!= ( tail_of @ SV25 ) ) ) )
= $false )
| ( ( sequential @ SV11 @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(200,plain,
! [SV12: $i,SV39: $i,SV26: $i] :
( ( ( ~ ( path @ SV26 @ SV39 @ SV12 ) )
= $true )
| ( ( ~ ! [SY99: $i,SY100: $i] :
( ~ ~ ( ~ ~ ( ~ ( on_path @ SY99 @ SV12 )
| ~ ( on_path @ SY100 @ SV12 ) )
| ~ ( sequential @ SY99 @ SY100 ) )
| ~ ! [SX5: $i] :
~ ( triangle @ SY99 @ SY100 @ SX5 ) ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV12 )
= ( number_of_in @ triangles @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(201,plain,
( ( ~ ~ ( ~ ~ ( ~ ( on_path @ sK4_SY143 @ sK1_SX0 )
| ~ ( on_path @ sK5_SY197 @ sK1_SX0 ) )
| ~ ( sequential @ sK4_SY143 @ sK5_SY197 ) )
| ~ ! [SY204: $i] :
~ ( triangle @ sK4_SY143 @ sK5_SY197 @ SY204 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[184]) ).
thf(202,plain,
! [SV47: $i,SV41: $i,SV48: $i,SV28: $i,SV14: $i] :
( ( ( ~ ( ~ ( shortest_path @ SV14 @ SV28 @ SV48 )
| ~ ( precedes @ SV41 @ SV47 @ SV48 ) ) )
= $false )
| ( ( ~ ( ~ ~ ~ ! [SY195: $i] :
~ ~ ( ( ( tail_of @ SY195 )
!= ( tail_of @ SV41 ) )
| ( ( head_of @ SY195 )
!= ( head_of @ SV47 ) ) )
| ~ ~ ( precedes @ SV47 @ SV41 @ SV48 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(203,plain,
! [SV42: $i,SV29: $i,SV15: $i,SV51: $i,SV49: $i] :
( ( ( ( precedes @ SV49 @ SV51 @ SV15 )
| ~ ~ ( ~ ~ ( ~ ( on_path @ SV49 @ SV15 )
| ~ ( on_path @ SV51 @ SV15 ) )
| ~ ( ( sequential @ SV49 @ SV51 )
| ~ ! [SY205: $i] :
~ ~ ( ~ ( sequential @ SV49 @ SY205 )
| ~ ( precedes @ SY205 @ SV51 @ SV15 ) ) ) ) )
= $true )
| ( ( path @ SV29 @ SV42 @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(204,plain,
! [SV43: $i,SV30: $i,SV16: $i,SV52: $i,SV50: $i] :
( ( ( ~ ( precedes @ SV50 @ SV52 @ SV16 )
| ~ ( ~ ~ ( ~ ( on_path @ SV50 @ SV16 )
| ~ ( on_path @ SV52 @ SV16 ) )
| ~ ~ ~ ( ~ ( ~ ( sequential @ SV50 @ SV52 )
| ~ ! [SY206: $i] :
~ ~ ( ~ ( sequential @ SV50 @ SY206 )
| ~ ( precedes @ SY206 @ SV52 @ SV16 ) ) )
| ~ ( ~ ~ ! [SY207: $i] :
~ ~ ( ~ ( sequential @ SV50 @ SY207 )
| ~ ( precedes @ SY207 @ SV52 @ SV16 ) )
| ( sequential @ SV50 @ SV52 ) ) ) ) )
= $true )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(205,plain,
! [SV44: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ( vertex @ SV31 )
| ~ ( vertex @ SV44 ) ) )
= $true )
| ( ( ~ ( ( SV31 != SV44 ) ) )
= $true )
| ( ( ~ ! [SY189: $i] :
~ ~ ( ~ ( edge @ SY189 )
| ~ ~ ~ ( ~ ( ~ ~ ( ( SV31
!= ( head_of @ SY189 ) )
| ( SV44
!= ( tail_of @ SY189 ) ) )
| ~ ( ( SV44
!= ( head_of @ SY189 ) )
| ( SV31
!= ( tail_of @ SY189 ) ) ) )
| ~ ( ~ ~ ( ( SV44
!= ( head_of @ SY189 ) )
| ( SV31
!= ( tail_of @ SY189 ) ) )
| ~ ( ( SV31
!= ( head_of @ SY189 ) )
| ( SV44
!= ( tail_of @ SY189 ) ) ) ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(206,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ( shortest_path @ SV2 @ SV18 @ SV32 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( path @ SV2 @ SV18 @ SV32 )
| ~ ( ( SV2 != SV18 ) ) )
| ~ ! [SY162: $i] :
( ~ ( path @ SV2 @ SV18 @ SY162 )
| ( less_or_equal @ ( length_of @ SV32 ) @ ( length_of @ SY162 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(207,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ( ~ ( ~ ~ ( ~ ( path @ SV2 @ SV18 @ SV32 )
| ~ ( ( SV2 != SV18 ) ) )
| ~ ! [SY163: $i] :
( ~ ( path @ SV2 @ SV18 @ SY163 )
| ( less_or_equal @ ( length_of @ SV32 ) @ ( length_of @ SY163 ) ) ) ) )
= $false )
| ( ( shortest_path @ SV2 @ SV18 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(208,plain,
! [SV45: $i,SV33: $i,SV19: $i,SV3: $i] :
( ( ( ~ ( path @ SV3 @ SV19 @ SV33 ) )
= $true )
| ( ( ~ ( on_path @ SV45 @ SV33 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( edge @ SV45 )
| ~ ( in_path @ ( head_of @ SV45 ) @ SV33 ) )
| ~ ( in_path @ ( tail_of @ SV45 ) @ SV33 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(209,plain,
! [SV34: $i,SV20: $i,SV6: $i] :
( ( ( ~ ( ~ ( vertex @ SV6 )
| ~ ( vertex @ SV20 ) ) )
= $false )
| ( ( ~ ~ ! [SY165: $i] :
~ ~ ( ~ ~ ( ~ ( edge @ SY165 )
| ( SV6
!= ( tail_of @ SY165 ) ) )
| ~ ( ~ ( ( SV20
!= ( head_of @ SY165 ) )
| ( SV34
!= ( path_cons @ SY165 @ empty ) ) )
| ~ ! [SY166: $i] :
~ ~ ( ~ ( path @ ( head_of @ SY165 ) @ SV20 @ SY166 )
| ( SV34
!= ( path_cons @ SY165 @ SY166 ) ) ) ) ) )
= $true )
| ( ( path @ SV6 @ SV20 @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(210,plain,
! [SV46: $i,SV35: $i,SV21: $i,SV7: $i] :
( ( ( ~ ( path @ SV7 @ SV21 @ SV35 ) )
= $true )
| ( ( ~ ( in_path @ SV46 @ SV35 ) )
= $true )
| ( ( ~ ( ~ ( vertex @ SV46 )
| ~ ~ ! [SY190: $i] :
~ ~ ( ~ ( on_path @ SY190 @ SV35 )
| ~ ( ( SV46
= ( head_of @ SY190 ) )
| ( SV46
= ( tail_of @ SY190 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(211,plain,
! [SV36: $i,SV22: $i,SV8: $i] :
( ( ( triangle @ SV8 @ SV22 @ SV36 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV8 )
| ~ ( edge @ SV22 ) )
| ~ ( edge @ SV36 ) )
| ~ ( sequential @ SV8 @ SV22 ) )
| ~ ( sequential @ SV22 @ SV36 ) )
| ~ ( sequential @ SV36 @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(212,plain,
! [SV36: $i,SV22: $i,SV8: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV8 )
| ~ ( edge @ SV22 ) )
| ~ ( edge @ SV36 ) )
| ~ ( sequential @ SV8 @ SV22 ) )
| ~ ( sequential @ SV22 @ SV36 ) )
| ~ ( sequential @ SV36 @ SV8 ) ) )
= $false )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(213,plain,
! [SV38: $i,SV24: $i,SV10: $i] :
( ( ( ~ ( ~ ( vertex @ SV10 )
| ~ ( vertex @ SV24 ) ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[196]) ).
thf(214,plain,
! [SV38: $i,SV24: $i,SV10: $i] :
( ( ( ~ ! [SY169: $i] :
~ ~ ( ~ ~ ( ~ ( edge @ SY169 )
| ( SV10
!= ( tail_of @ SY169 ) ) )
| ~ ~ ~ ( ~ ( ~ ~ ( ( SV24
!= ( head_of @ SY169 ) )
| ( SV38
!= ( path_cons @ SY169 @ empty ) ) )
| ~ ! [SY170: $i] :
~ ~ ( ~ ( path @ ( head_of @ SY169 ) @ SV24 @ SY170 )
| ( SV38
!= ( path_cons @ SY169 @ SY170 ) ) ) )
| ~ ( ~ ~ ! [SY171: $i] :
~ ~ ( ~ ( path @ ( head_of @ SY169 ) @ SV24 @ SY171 )
| ( SV38
!= ( path_cons @ SY169 @ SY171 ) ) )
| ~ ( ( SV24
!= ( head_of @ SY169 ) )
| ( SV38
!= ( path_cons @ SY169 @ empty ) ) ) ) ) ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[197]) ).
thf(215,plain,
! [SV25: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( edge @ SV11 )
| ~ ( edge @ SV25 ) )
| ~ ( ( SV11 != SV25 ) ) )
| ( ( head_of @ SV11 )
!= ( tail_of @ SV25 ) ) )
= $false )
| ( ( sequential @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(216,plain,
! [SV25: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( edge @ SV11 )
| ~ ( edge @ SV25 ) )
| ~ ( ( SV11 != SV25 ) ) )
| ( ( head_of @ SV11 )
!= ( tail_of @ SV25 ) ) )
= $true )
| ( ( sequential @ SV11 @ SV25 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[199]) ).
thf(217,plain,
! [SV12: $i,SV39: $i,SV26: $i] :
( ( ( path @ SV26 @ SV39 @ SV12 )
= $false )
| ( ( ~ ! [SY99: $i,SY100: $i] :
( ~ ~ ( ~ ~ ( ~ ( on_path @ SY99 @ SV12 )
| ~ ( on_path @ SY100 @ SV12 ) )
| ~ ( sequential @ SY99 @ SY100 ) )
| ~ ! [SX5: $i] :
~ ( triangle @ SY99 @ SY100 @ SX5 ) ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV12 )
= ( number_of_in @ triangles @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(218,plain,
( ( ~ ~ ( ~ ~ ( ~ ( on_path @ sK4_SY143 @ sK1_SX0 )
| ~ ( on_path @ sK5_SY197 @ sK1_SX0 ) )
| ~ ( sequential @ sK4_SY143 @ sK5_SY197 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[201]) ).
thf(219,plain,
( ( ~ ! [SY204: $i] :
~ ( triangle @ sK4_SY143 @ sK5_SY197 @ SY204 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[201]) ).
thf(220,plain,
! [SV47: $i,SV41: $i,SV48: $i,SV28: $i,SV14: $i] :
( ( ( ~ ( shortest_path @ SV14 @ SV28 @ SV48 )
| ~ ( precedes @ SV41 @ SV47 @ SV48 ) )
= $true )
| ( ( ~ ( ~ ~ ~ ! [SY195: $i] :
~ ~ ( ( ( tail_of @ SY195 )
!= ( tail_of @ SV41 ) )
| ( ( head_of @ SY195 )
!= ( head_of @ SV47 ) ) )
| ~ ~ ( precedes @ SV47 @ SV41 @ SV48 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[202]) ).
thf(221,plain,
! [SV42: $i,SV29: $i,SV15: $i,SV51: $i,SV49: $i] :
( ( ( precedes @ SV49 @ SV51 @ SV15 )
= $true )
| ( ( ~ ~ ( ~ ~ ( ~ ( on_path @ SV49 @ SV15 )
| ~ ( on_path @ SV51 @ SV15 ) )
| ~ ( ( sequential @ SV49 @ SV51 )
| ~ ! [SY205: $i] :
~ ~ ( ~ ( sequential @ SV49 @ SY205 )
| ~ ( precedes @ SY205 @ SV51 @ SV15 ) ) ) ) )
= $true )
| ( ( path @ SV29 @ SV42 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[203]) ).
thf(222,plain,
! [SV43: $i,SV30: $i,SV16: $i,SV52: $i,SV50: $i] :
( ( ( ~ ( precedes @ SV50 @ SV52 @ SV16 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( on_path @ SV50 @ SV16 )
| ~ ( on_path @ SV52 @ SV16 ) )
| ~ ~ ~ ( ~ ( ~ ( sequential @ SV50 @ SV52 )
| ~ ! [SY206: $i] :
~ ~ ( ~ ( sequential @ SV50 @ SY206 )
| ~ ( precedes @ SY206 @ SV52 @ SV16 ) ) )
| ~ ( ~ ~ ! [SY207: $i] :
~ ~ ( ~ ( sequential @ SV50 @ SY207 )
| ~ ( precedes @ SY207 @ SV52 @ SV16 ) )
| ( sequential @ SV50 @ SV52 ) ) ) ) )
= $true )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[204]) ).
thf(223,plain,
! [SV44: $i,SV31: $i] :
( ( ( ~ ( ~ ( vertex @ SV31 )
| ~ ( vertex @ SV44 ) ) )
= $false )
| ( ( ~ ( ( SV31 != SV44 ) ) )
= $true )
| ( ( ~ ! [SY189: $i] :
~ ~ ( ~ ( edge @ SY189 )
| ~ ~ ~ ( ~ ( ~ ~ ( ( SV31
!= ( head_of @ SY189 ) )
| ( SV44
!= ( tail_of @ SY189 ) ) )
| ~ ( ( SV44
!= ( head_of @ SY189 ) )
| ( SV31
!= ( tail_of @ SY189 ) ) ) )
| ~ ( ~ ~ ( ( SV44
!= ( head_of @ SY189 ) )
| ( SV31
!= ( tail_of @ SY189 ) ) )
| ~ ( ( SV31
!= ( head_of @ SY189 ) )
| ( SV44
!= ( tail_of @ SY189 ) ) ) ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(224,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( path @ SV2 @ SV18 @ SV32 )
| ~ ( ( SV2 != SV18 ) ) )
| ~ ! [SY162: $i] :
( ~ ( path @ SV2 @ SV18 @ SY162 )
| ( less_or_equal @ ( length_of @ SV32 ) @ ( length_of @ SY162 ) ) ) )
= $false )
| ( ( shortest_path @ SV2 @ SV18 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(225,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( path @ SV2 @ SV18 @ SV32 )
| ~ ( ( SV2 != SV18 ) ) )
| ~ ! [SY163: $i] :
( ~ ( path @ SV2 @ SV18 @ SY163 )
| ( less_or_equal @ ( length_of @ SV32 ) @ ( length_of @ SY163 ) ) ) )
= $true )
| ( ( shortest_path @ SV2 @ SV18 @ SV32 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[207]) ).
thf(226,plain,
! [SV45: $i,SV33: $i,SV19: $i,SV3: $i] :
( ( ( path @ SV3 @ SV19 @ SV33 )
= $false )
| ( ( ~ ( on_path @ SV45 @ SV33 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( edge @ SV45 )
| ~ ( in_path @ ( head_of @ SV45 ) @ SV33 ) )
| ~ ( in_path @ ( tail_of @ SV45 ) @ SV33 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(227,plain,
! [SV34: $i,SV20: $i,SV6: $i] :
( ( ( ~ ( vertex @ SV6 )
| ~ ( vertex @ SV20 ) )
= $true )
| ( ( ~ ~ ! [SY165: $i] :
~ ~ ( ~ ~ ( ~ ( edge @ SY165 )
| ( SV6
!= ( tail_of @ SY165 ) ) )
| ~ ( ~ ( ( SV20
!= ( head_of @ SY165 ) )
| ( SV34
!= ( path_cons @ SY165 @ empty ) ) )
| ~ ! [SY166: $i] :
~ ~ ( ~ ( path @ ( head_of @ SY165 ) @ SV20 @ SY166 )
| ( SV34
!= ( path_cons @ SY165 @ SY166 ) ) ) ) ) )
= $true )
| ( ( path @ SV6 @ SV20 @ SV34 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[209]) ).
thf(228,plain,
! [SV46: $i,SV35: $i,SV21: $i,SV7: $i] :
( ( ( path @ SV7 @ SV21 @ SV35 )
= $false )
| ( ( ~ ( in_path @ SV46 @ SV35 ) )
= $true )
| ( ( ~ ( ~ ( vertex @ SV46 )
| ~ ~ ! [SY190: $i] :
~ ~ ( ~ ( on_path @ SY190 @ SV35 )
| ~ ( ( SV46
= ( head_of @ SY190 ) )
| ( SV46
= ( tail_of @ SY190 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(229,plain,
! [SV36: $i,SV22: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV8 )
| ~ ( edge @ SV22 ) )
| ~ ( edge @ SV36 ) )
| ~ ( sequential @ SV8 @ SV22 ) )
| ~ ( sequential @ SV22 @ SV36 ) )
| ~ ( sequential @ SV36 @ SV8 ) )
= $false )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(230,plain,
! [SV36: $i,SV22: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV8 )
| ~ ( edge @ SV22 ) )
| ~ ( edge @ SV36 ) )
| ~ ( sequential @ SV8 @ SV22 ) )
| ~ ( sequential @ SV22 @ SV36 ) )
| ~ ( sequential @ SV36 @ SV8 ) )
= $true )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[212]) ).
thf(231,plain,
! [SV38: $i,SV24: $i,SV10: $i] :
( ( ( ~ ( vertex @ SV10 )
| ~ ( vertex @ SV24 ) )
= $false )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(232,plain,
! [SV38: $i,SV24: $i,SV10: $i] :
( ( ( ! [SY169: $i] :
~ ~ ( ~ ~ ( ~ ( edge @ SY169 )
| ( SV10
!= ( tail_of @ SY169 ) ) )
| ~ ~ ~ ( ~ ( ~ ~ ( ( SV24
!= ( head_of @ SY169 ) )
| ( SV38
!= ( path_cons @ SY169 @ empty ) ) )
| ~ ! [SY170: $i] :
~ ~ ( ~ ( path @ ( head_of @ SY169 ) @ SV24 @ SY170 )
| ( SV38
!= ( path_cons @ SY169 @ SY170 ) ) ) )
| ~ ( ~ ~ ! [SY171: $i] :
~ ~ ( ~ ( path @ ( head_of @ SY169 ) @ SV24 @ SY171 )
| ( SV38
!= ( path_cons @ SY169 @ SY171 ) ) )
| ~ ( ( SV24
!= ( head_of @ SY169 ) )
| ( SV38
!= ( path_cons @ SY169 @ empty ) ) ) ) ) ) )
= $false )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(233,plain,
! [SV25: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( edge @ SV11 )
| ~ ( edge @ SV25 ) )
| ~ ( ( SV11 != SV25 ) ) ) )
= $false )
| ( ( sequential @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[215]) ).
thf(234,plain,
! [SV25: $i,SV11: $i] :
( ( ( ( head_of @ SV11 )
!= ( tail_of @ SV25 ) )
= $false )
| ( ( sequential @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[215]) ).
thf(235,plain,
! [SV25: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( edge @ SV11 )
| ~ ( edge @ SV25 ) )
| ~ ( ( SV11 != SV25 ) ) ) )
= $true )
| ( ( ( head_of @ SV11 )
!= ( tail_of @ SV25 ) )
= $true )
| ( ( sequential @ SV11 @ SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(236,plain,
! [SV39: $i,SV26: $i,SV12: $i] :
( ( ( ! [SY99: $i,SY100: $i] :
( ~ ~ ( ~ ~ ( ~ ( on_path @ SY99 @ SV12 )
| ~ ( on_path @ SY100 @ SV12 ) )
| ~ ( sequential @ SY99 @ SY100 ) )
| ~ ! [SX5: $i] :
~ ( triangle @ SY99 @ SY100 @ SX5 ) ) )
= $false )
| ( ( path @ SV26 @ SV39 @ SV12 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV12 )
= ( number_of_in @ triangles @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(237,plain,
( ( ~ ( ~ ~ ( ~ ( on_path @ sK4_SY143 @ sK1_SX0 )
| ~ ( on_path @ sK5_SY197 @ sK1_SX0 ) )
| ~ ( sequential @ sK4_SY143 @ sK5_SY197 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[218]) ).
thf(238,plain,
( ( ! [SY204: $i] :
~ ( triangle @ sK4_SY143 @ sK5_SY197 @ SY204 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[219]) ).
thf(239,plain,
! [SV47: $i,SV41: $i,SV48: $i,SV28: $i,SV14: $i] :
( ( ( ~ ( shortest_path @ SV14 @ SV28 @ SV48 ) )
= $true )
| ( ( ~ ( precedes @ SV41 @ SV47 @ SV48 ) )
= $true )
| ( ( ~ ( ~ ~ ~ ! [SY195: $i] :
~ ~ ( ( ( tail_of @ SY195 )
!= ( tail_of @ SV41 ) )
| ( ( head_of @ SY195 )
!= ( head_of @ SV47 ) ) )
| ~ ~ ( precedes @ SV47 @ SV41 @ SV48 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(240,plain,
! [SV42: $i,SV29: $i,SV51: $i,SV15: $i,SV49: $i] :
( ( ( ~ ( ~ ~ ( ~ ( on_path @ SV49 @ SV15 )
| ~ ( on_path @ SV51 @ SV15 ) )
| ~ ( ( sequential @ SV49 @ SV51 )
| ~ ! [SY205: $i] :
~ ~ ( ~ ( sequential @ SV49 @ SY205 )
| ~ ( precedes @ SY205 @ SV51 @ SV15 ) ) ) ) )
= $false )
| ( ( precedes @ SV49 @ SV51 @ SV15 )
= $true )
| ( ( path @ SV29 @ SV42 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(241,plain,
! [SV43: $i,SV30: $i,SV16: $i,SV52: $i,SV50: $i] :
( ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( on_path @ SV50 @ SV16 )
| ~ ( on_path @ SV52 @ SV16 ) )
| ~ ~ ~ ( ~ ( ~ ( sequential @ SV50 @ SV52 )
| ~ ! [SY206: $i] :
~ ~ ( ~ ( sequential @ SV50 @ SY206 )
| ~ ( precedes @ SY206 @ SV52 @ SV16 ) ) )
| ~ ( ~ ~ ! [SY207: $i] :
~ ~ ( ~ ( sequential @ SV50 @ SY207 )
| ~ ( precedes @ SY207 @ SV52 @ SV16 ) )
| ( sequential @ SV50 @ SV52 ) ) ) ) )
= $true )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(242,plain,
! [SV44: $i,SV31: $i] :
( ( ( ~ ( vertex @ SV31 )
| ~ ( vertex @ SV44 ) )
= $true )
| ( ( ~ ( ( SV31 != SV44 ) ) )
= $true )
| ( ( ~ ! [SY189: $i] :
~ ~ ( ~ ( edge @ SY189 )
| ~ ~ ~ ( ~ ( ~ ~ ( ( SV31
!= ( head_of @ SY189 ) )
| ( SV44
!= ( tail_of @ SY189 ) ) )
| ~ ( ( SV44
!= ( head_of @ SY189 ) )
| ( SV31
!= ( tail_of @ SY189 ) ) ) )
| ~ ( ~ ~ ( ( SV44
!= ( head_of @ SY189 ) )
| ( SV31
!= ( tail_of @ SY189 ) ) )
| ~ ( ( SV31
!= ( head_of @ SY189 ) )
| ( SV44
!= ( tail_of @ SY189 ) ) ) ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[223]) ).
thf(243,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( path @ SV2 @ SV18 @ SV32 )
| ~ ( ( SV2 != SV18 ) ) ) )
= $false )
| ( ( shortest_path @ SV2 @ SV18 @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[224]) ).
thf(244,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ( ~ ! [SY162: $i] :
( ~ ( path @ SV2 @ SV18 @ SY162 )
| ( less_or_equal @ ( length_of @ SV32 ) @ ( length_of @ SY162 ) ) ) )
= $false )
| ( ( shortest_path @ SV2 @ SV18 @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[224]) ).
thf(245,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( path @ SV2 @ SV18 @ SV32 )
| ~ ( ( SV2 != SV18 ) ) ) )
= $true )
| ( ( ~ ! [SY163: $i] :
( ~ ( path @ SV2 @ SV18 @ SY163 )
| ( less_or_equal @ ( length_of @ SV32 ) @ ( length_of @ SY163 ) ) ) )
= $true )
| ( ( shortest_path @ SV2 @ SV18 @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(246,plain,
! [SV19: $i,SV3: $i,SV33: $i,SV45: $i] :
( ( ( on_path @ SV45 @ SV33 )
= $false )
| ( ( path @ SV3 @ SV19 @ SV33 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( edge @ SV45 )
| ~ ( in_path @ ( head_of @ SV45 ) @ SV33 ) )
| ~ ( in_path @ ( tail_of @ SV45 ) @ SV33 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(247,plain,
! [SV34: $i,SV20: $i,SV6: $i] :
( ( ( ~ ( vertex @ SV6 ) )
= $true )
| ( ( ~ ( vertex @ SV20 ) )
= $true )
| ( ( ~ ~ ! [SY165: $i] :
~ ~ ( ~ ~ ( ~ ( edge @ SY165 )
| ( SV6
!= ( tail_of @ SY165 ) ) )
| ~ ( ~ ( ( SV20
!= ( head_of @ SY165 ) )
| ( SV34
!= ( path_cons @ SY165 @ empty ) ) )
| ~ ! [SY166: $i] :
~ ~ ( ~ ( path @ ( head_of @ SY165 ) @ SV20 @ SY166 )
| ( SV34
!= ( path_cons @ SY165 @ SY166 ) ) ) ) ) )
= $true )
| ( ( path @ SV6 @ SV20 @ SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(248,plain,
! [SV21: $i,SV7: $i,SV35: $i,SV46: $i] :
( ( ( in_path @ SV46 @ SV35 )
= $false )
| ( ( path @ SV7 @ SV21 @ SV35 )
= $false )
| ( ( ~ ( ~ ( vertex @ SV46 )
| ~ ~ ! [SY190: $i] :
~ ~ ( ~ ( on_path @ SY190 @ SV35 )
| ~ ( ( SV46
= ( head_of @ SY190 ) )
| ( SV46
= ( tail_of @ SY190 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(249,plain,
! [SV36: $i,SV22: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV8 )
| ~ ( edge @ SV22 ) )
| ~ ( edge @ SV36 ) )
| ~ ( sequential @ SV8 @ SV22 ) )
| ~ ( sequential @ SV22 @ SV36 ) ) )
= $false )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[229]) ).
thf(250,plain,
! [SV22: $i,SV8: $i,SV36: $i] :
( ( ( ~ ( sequential @ SV36 @ SV8 ) )
= $false )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[229]) ).
thf(251,plain,
! [SV36: $i,SV22: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV8 )
| ~ ( edge @ SV22 ) )
| ~ ( edge @ SV36 ) )
| ~ ( sequential @ SV8 @ SV22 ) )
| ~ ( sequential @ SV22 @ SV36 ) ) )
= $true )
| ( ( ~ ( sequential @ SV36 @ SV8 ) )
= $true )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[230]) ).
thf(252,plain,
! [SV38: $i,SV24: $i,SV10: $i] :
( ( ( ~ ( vertex @ SV10 ) )
= $false )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[231]) ).
thf(253,plain,
! [SV38: $i,SV10: $i,SV24: $i] :
( ( ( ~ ( vertex @ SV24 ) )
= $false )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[231]) ).
thf(254,plain,
! [SV10: $i,SV24: $i,SV38: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( edge @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) )
| ( SV10
!= ( tail_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) ) )
| ~ ~ ~ ( ~ ( ~ ~ ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) ) )
| ~ ! [SY208: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY208 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY208 ) ) ) )
| ~ ( ~ ~ ! [SY209: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY209 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY209 ) ) )
| ~ ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) ) ) ) ) ) )
= $false )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[232]) ).
thf(255,plain,
! [SV25: $i,SV11: $i] :
( ( ( ~ ( ~ ~ ( ~ ( edge @ SV11 )
| ~ ( edge @ SV25 ) )
| ~ ( ( SV11 != SV25 ) ) ) )
= $true )
| ( ( sequential @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[233]) ).
thf(256,plain,
! [SV25: $i,SV11: $i] :
( ( ( ( head_of @ SV11 )
= ( tail_of @ SV25 ) )
= $true )
| ( ( sequential @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[234]) ).
thf(257,plain,
! [SV25: $i,SV11: $i] :
( ( ( ~ ( ~ ~ ( ~ ( edge @ SV11 )
| ~ ( edge @ SV25 ) )
| ~ ( ( SV11 != SV25 ) ) ) )
= $false )
| ( ( ( head_of @ SV11 )
!= ( tail_of @ SV25 ) )
= $true )
| ( ( sequential @ SV11 @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(258,plain,
! [SV12: $i,SV26: $i,SV39: $i] :
( ( ( ! [SY210: $i] :
( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK7_SY99 @ SV39 @ SV26 @ SV12 ) @ SV12 )
| ~ ( on_path @ SY210 @ SV12 ) )
| ~ ( sequential @ ( sK7_SY99 @ SV39 @ SV26 @ SV12 ) @ SY210 ) )
| ~ ! [SY211: $i] :
~ ( triangle @ ( sK7_SY99 @ SV39 @ SV26 @ SV12 ) @ SY210 @ SY211 ) ) )
= $false )
| ( ( path @ SV26 @ SV39 @ SV12 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV12 )
= ( number_of_in @ triangles @ SV12 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[236]) ).
thf(259,plain,
( ( ~ ~ ( ~ ( on_path @ sK4_SY143 @ sK1_SX0 )
| ~ ( on_path @ sK5_SY197 @ sK1_SX0 ) )
| ~ ( sequential @ sK4_SY143 @ sK5_SY197 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(260,plain,
! [SV53: $i] :
( ( ~ ( triangle @ sK4_SY143 @ sK5_SY197 @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(261,plain,
! [SV47: $i,SV41: $i,SV48: $i,SV28: $i,SV14: $i] :
( ( ( shortest_path @ SV14 @ SV28 @ SV48 )
= $false )
| ( ( ~ ( precedes @ SV41 @ SV47 @ SV48 ) )
= $true )
| ( ( ~ ( ~ ~ ~ ! [SY195: $i] :
~ ~ ( ( ( tail_of @ SY195 )
!= ( tail_of @ SV41 ) )
| ( ( head_of @ SY195 )
!= ( head_of @ SV47 ) ) )
| ~ ~ ( precedes @ SV47 @ SV41 @ SV48 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(262,plain,
! [SV42: $i,SV29: $i,SV51: $i,SV15: $i,SV49: $i] :
( ( ( ~ ~ ( ~ ( on_path @ SV49 @ SV15 )
| ~ ( on_path @ SV51 @ SV15 ) )
| ~ ( ( sequential @ SV49 @ SV51 )
| ~ ! [SY205: $i] :
~ ~ ( ~ ( sequential @ SV49 @ SY205 )
| ~ ( precedes @ SY205 @ SV51 @ SV15 ) ) ) )
= $true )
| ( ( precedes @ SV49 @ SV51 @ SV15 )
= $true )
| ( ( path @ SV29 @ SV42 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[240]) ).
thf(263,plain,
! [SV43: $i,SV30: $i,SV52: $i,SV16: $i,SV50: $i] :
( ( ( ~ ~ ( ~ ( on_path @ SV50 @ SV16 )
| ~ ( on_path @ SV52 @ SV16 ) )
| ~ ~ ~ ( ~ ( ~ ( sequential @ SV50 @ SV52 )
| ~ ! [SY206: $i] :
~ ~ ( ~ ( sequential @ SV50 @ SY206 )
| ~ ( precedes @ SY206 @ SV52 @ SV16 ) ) )
| ~ ( ~ ~ ! [SY207: $i] :
~ ~ ( ~ ( sequential @ SV50 @ SY207 )
| ~ ( precedes @ SY207 @ SV52 @ SV16 ) )
| ( sequential @ SV50 @ SV52 ) ) ) )
= $false )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(264,plain,
! [SV44: $i,SV31: $i] :
( ( ( ~ ( vertex @ SV31 ) )
= $true )
| ( ( ~ ( vertex @ SV44 ) )
= $true )
| ( ( ~ ( ( SV31 != SV44 ) ) )
= $true )
| ( ( ~ ! [SY189: $i] :
~ ~ ( ~ ( edge @ SY189 )
| ~ ~ ~ ( ~ ( ~ ~ ( ( SV31
!= ( head_of @ SY189 ) )
| ( SV44
!= ( tail_of @ SY189 ) ) )
| ~ ( ( SV44
!= ( head_of @ SY189 ) )
| ( SV31
!= ( tail_of @ SY189 ) ) ) )
| ~ ( ~ ~ ( ( SV44
!= ( head_of @ SY189 ) )
| ( SV31
!= ( tail_of @ SY189 ) ) )
| ~ ( ( SV31
!= ( head_of @ SY189 ) )
| ( SV44
!= ( tail_of @ SY189 ) ) ) ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[242]) ).
thf(265,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ( ~ ( ~ ( path @ SV2 @ SV18 @ SV32 )
| ~ ( ( SV2 != SV18 ) ) ) )
= $true )
| ( ( shortest_path @ SV2 @ SV18 @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[243]) ).
thf(266,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ( ! [SY162: $i] :
( ~ ( path @ SV2 @ SV18 @ SY162 )
| ( less_or_equal @ ( length_of @ SV32 ) @ ( length_of @ SY162 ) ) ) )
= $true )
| ( ( shortest_path @ SV2 @ SV18 @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[244]) ).
thf(267,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ( ~ ( ~ ( path @ SV2 @ SV18 @ SV32 )
| ~ ( ( SV2 != SV18 ) ) ) )
= $false )
| ( ( ~ ! [SY163: $i] :
( ~ ( path @ SV2 @ SV18 @ SY163 )
| ( less_or_equal @ ( length_of @ SV32 ) @ ( length_of @ SY163 ) ) ) )
= $true )
| ( ( shortest_path @ SV2 @ SV18 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(268,plain,
! [SV19: $i,SV3: $i,SV33: $i,SV45: $i] :
( ( ( ~ ~ ( ~ ( edge @ SV45 )
| ~ ( in_path @ ( head_of @ SV45 ) @ SV33 ) )
| ~ ( in_path @ ( tail_of @ SV45 ) @ SV33 ) )
= $false )
| ( ( path @ SV3 @ SV19 @ SV33 )
= $false )
| ( ( on_path @ SV45 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(269,plain,
! [SV34: $i,SV20: $i,SV6: $i] :
( ( ( vertex @ SV6 )
= $false )
| ( ( ~ ( vertex @ SV20 ) )
= $true )
| ( ( ~ ~ ! [SY165: $i] :
~ ~ ( ~ ~ ( ~ ( edge @ SY165 )
| ( SV6
!= ( tail_of @ SY165 ) ) )
| ~ ( ~ ( ( SV20
!= ( head_of @ SY165 ) )
| ( SV34
!= ( path_cons @ SY165 @ empty ) ) )
| ~ ! [SY166: $i] :
~ ~ ( ~ ( path @ ( head_of @ SY165 ) @ SV20 @ SY166 )
| ( SV34
!= ( path_cons @ SY165 @ SY166 ) ) ) ) ) )
= $true )
| ( ( path @ SV6 @ SV20 @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(270,plain,
! [SV21: $i,SV7: $i,SV35: $i,SV46: $i] :
( ( ( ~ ( vertex @ SV46 )
| ~ ~ ! [SY190: $i] :
~ ~ ( ~ ( on_path @ SY190 @ SV35 )
| ~ ( ( SV46
= ( head_of @ SY190 ) )
| ( SV46
= ( tail_of @ SY190 ) ) ) ) )
= $false )
| ( ( path @ SV7 @ SV21 @ SV35 )
= $false )
| ( ( in_path @ SV46 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(271,plain,
! [SV36: $i,SV22: $i,SV8: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV8 )
| ~ ( edge @ SV22 ) )
| ~ ( edge @ SV36 ) )
| ~ ( sequential @ SV8 @ SV22 ) )
| ~ ( sequential @ SV22 @ SV36 ) ) )
= $true )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[249]) ).
thf(272,plain,
! [SV22: $i,SV8: $i,SV36: $i] :
( ( ( sequential @ SV36 @ SV8 )
= $true )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[250]) ).
thf(273,plain,
! [SV36: $i,SV22: $i,SV8: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV8 )
| ~ ( edge @ SV22 ) )
| ~ ( edge @ SV36 ) )
| ~ ( sequential @ SV8 @ SV22 ) )
| ~ ( sequential @ SV22 @ SV36 ) ) )
= $false )
| ( ( ~ ( sequential @ SV36 @ SV8 ) )
= $true )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(274,plain,
! [SV38: $i,SV24: $i,SV10: $i] :
( ( ( vertex @ SV10 )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[252]) ).
thf(275,plain,
! [SV38: $i,SV10: $i,SV24: $i] :
( ( ( vertex @ SV24 )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[253]) ).
thf(276,plain,
! [SV10: $i,SV24: $i,SV38: $i] :
( ( ( ~ ( ~ ~ ( ~ ( edge @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) )
| ( SV10
!= ( tail_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) ) )
| ~ ~ ~ ( ~ ( ~ ~ ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) ) )
| ~ ! [SY208: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY208 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY208 ) ) ) )
| ~ ( ~ ~ ! [SY209: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY209 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY209 ) ) )
| ~ ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) ) ) ) ) ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[254]) ).
thf(277,plain,
! [SV25: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( edge @ SV11 )
| ~ ( edge @ SV25 ) )
| ~ ( ( SV11 != SV25 ) ) )
= $false )
| ( ( sequential @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(278,plain,
! [SV25: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( edge @ SV11 )
| ~ ( edge @ SV25 ) )
| ~ ( ( SV11 != SV25 ) ) )
= $true )
| ( ( ( head_of @ SV11 )
!= ( tail_of @ SV25 ) )
= $true )
| ( ( sequential @ SV11 @ SV25 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[257]) ).
thf(279,plain,
! [SV12: $i,SV26: $i,SV39: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK7_SY99 @ SV39 @ SV26 @ SV12 ) @ SV12 )
| ~ ( on_path @ ( sK8_SY210 @ SV12 @ SV26 @ SV39 ) @ SV12 ) )
| ~ ( sequential @ ( sK7_SY99 @ SV39 @ SV26 @ SV12 ) @ ( sK8_SY210 @ SV12 @ SV26 @ SV39 ) ) )
| ~ ! [SY212: $i] :
~ ( triangle @ ( sK7_SY99 @ SV39 @ SV26 @ SV12 ) @ ( sK8_SY210 @ SV12 @ SV26 @ SV39 ) @ SY212 ) )
= $false )
| ( ( path @ SV26 @ SV39 @ SV12 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV12 )
= ( number_of_in @ triangles @ SV12 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[258]) ).
thf(280,plain,
( ( ~ ~ ( ~ ( on_path @ sK4_SY143 @ sK1_SX0 )
| ~ ( on_path @ sK5_SY197 @ sK1_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[259]) ).
thf(281,plain,
( ( ~ ( sequential @ sK4_SY143 @ sK5_SY197 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[259]) ).
thf(282,plain,
! [SV53: $i] :
( ( triangle @ sK4_SY143 @ sK5_SY197 @ SV53 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(283,plain,
! [SV28: $i,SV14: $i,SV48: $i,SV47: $i,SV41: $i] :
( ( ( precedes @ SV41 @ SV47 @ SV48 )
= $false )
| ( ( shortest_path @ SV14 @ SV28 @ SV48 )
= $false )
| ( ( ~ ( ~ ~ ~ ! [SY195: $i] :
~ ~ ( ( ( tail_of @ SY195 )
!= ( tail_of @ SV41 ) )
| ( ( head_of @ SY195 )
!= ( head_of @ SV47 ) ) )
| ~ ~ ( precedes @ SV47 @ SV41 @ SV48 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(284,plain,
! [SV42: $i,SV29: $i,SV51: $i,SV15: $i,SV49: $i] :
( ( ( ~ ~ ( ~ ( on_path @ SV49 @ SV15 )
| ~ ( on_path @ SV51 @ SV15 ) ) )
= $true )
| ( ( ~ ( ( sequential @ SV49 @ SV51 )
| ~ ! [SY205: $i] :
~ ~ ( ~ ( sequential @ SV49 @ SY205 )
| ~ ( precedes @ SY205 @ SV51 @ SV15 ) ) ) )
= $true )
| ( ( precedes @ SV49 @ SV51 @ SV15 )
= $true )
| ( ( path @ SV29 @ SV42 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[262]) ).
thf(285,plain,
! [SV43: $i,SV30: $i,SV52: $i,SV16: $i,SV50: $i] :
( ( ( ~ ~ ( ~ ( on_path @ SV50 @ SV16 )
| ~ ( on_path @ SV52 @ SV16 ) ) )
= $false )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[263]) ).
thf(286,plain,
! [SV43: $i,SV30: $i,SV16: $i,SV52: $i,SV50: $i] :
( ( ( ~ ~ ~ ( ~ ( ~ ( sequential @ SV50 @ SV52 )
| ~ ! [SY206: $i] :
~ ~ ( ~ ( sequential @ SV50 @ SY206 )
| ~ ( precedes @ SY206 @ SV52 @ SV16 ) ) )
| ~ ( ~ ~ ! [SY207: $i] :
~ ~ ( ~ ( sequential @ SV50 @ SY207 )
| ~ ( precedes @ SY207 @ SV52 @ SV16 ) )
| ( sequential @ SV50 @ SV52 ) ) ) )
= $false )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[263]) ).
thf(287,plain,
! [SV44: $i,SV31: $i] :
( ( ( vertex @ SV31 )
= $false )
| ( ( ~ ( vertex @ SV44 ) )
= $true )
| ( ( ~ ( ( SV31 != SV44 ) ) )
= $true )
| ( ( ~ ! [SY189: $i] :
~ ~ ( ~ ( edge @ SY189 )
| ~ ~ ~ ( ~ ( ~ ~ ( ( SV31
!= ( head_of @ SY189 ) )
| ( SV44
!= ( tail_of @ SY189 ) ) )
| ~ ( ( SV44
!= ( head_of @ SY189 ) )
| ( SV31
!= ( tail_of @ SY189 ) ) ) )
| ~ ( ~ ~ ( ( SV44
!= ( head_of @ SY189 ) )
| ( SV31
!= ( tail_of @ SY189 ) ) )
| ~ ( ( SV31
!= ( head_of @ SY189 ) )
| ( SV44
!= ( tail_of @ SY189 ) ) ) ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(288,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ( ~ ( path @ SV2 @ SV18 @ SV32 )
| ~ ( ( SV2 != SV18 ) ) )
= $false )
| ( ( shortest_path @ SV2 @ SV18 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[265]) ).
thf(289,plain,
! [SV32: $i,SV54: $i,SV18: $i,SV2: $i] :
( ( ( ~ ( path @ SV2 @ SV18 @ SV54 )
| ( less_or_equal @ ( length_of @ SV32 ) @ ( length_of @ SV54 ) ) )
= $true )
| ( ( shortest_path @ SV2 @ SV18 @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(290,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ( ~ ( path @ SV2 @ SV18 @ SV32 )
| ~ ( ( SV2 != SV18 ) ) )
= $true )
| ( ( ~ ! [SY163: $i] :
( ~ ( path @ SV2 @ SV18 @ SY163 )
| ( less_or_equal @ ( length_of @ SV32 ) @ ( length_of @ SY163 ) ) ) )
= $true )
| ( ( shortest_path @ SV2 @ SV18 @ SV32 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[267]) ).
thf(291,plain,
! [SV19: $i,SV3: $i,SV33: $i,SV45: $i] :
( ( ( ~ ~ ( ~ ( edge @ SV45 )
| ~ ( in_path @ ( head_of @ SV45 ) @ SV33 ) ) )
= $false )
| ( ( path @ SV3 @ SV19 @ SV33 )
= $false )
| ( ( on_path @ SV45 @ SV33 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[268]) ).
thf(292,plain,
! [SV19: $i,SV3: $i,SV33: $i,SV45: $i] :
( ( ( ~ ( in_path @ ( tail_of @ SV45 ) @ SV33 ) )
= $false )
| ( ( path @ SV3 @ SV19 @ SV33 )
= $false )
| ( ( on_path @ SV45 @ SV33 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[268]) ).
thf(293,plain,
! [SV34: $i,SV6: $i,SV20: $i] :
( ( ( vertex @ SV20 )
= $false )
| ( ( vertex @ SV6 )
= $false )
| ( ( ~ ~ ! [SY165: $i] :
~ ~ ( ~ ~ ( ~ ( edge @ SY165 )
| ( SV6
!= ( tail_of @ SY165 ) ) )
| ~ ( ~ ( ( SV20
!= ( head_of @ SY165 ) )
| ( SV34
!= ( path_cons @ SY165 @ empty ) ) )
| ~ ! [SY166: $i] :
~ ~ ( ~ ( path @ ( head_of @ SY165 ) @ SV20 @ SY166 )
| ( SV34
!= ( path_cons @ SY165 @ SY166 ) ) ) ) ) )
= $true )
| ( ( path @ SV6 @ SV20 @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(294,plain,
! [SV35: $i,SV21: $i,SV7: $i,SV46: $i] :
( ( ( ~ ( vertex @ SV46 ) )
= $false )
| ( ( path @ SV7 @ SV21 @ SV35 )
= $false )
| ( ( in_path @ SV46 @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[270]) ).
thf(295,plain,
! [SV21: $i,SV7: $i,SV46: $i,SV35: $i] :
( ( ( ~ ~ ! [SY190: $i] :
~ ~ ( ~ ( on_path @ SY190 @ SV35 )
| ~ ( ( SV46
= ( head_of @ SY190 ) )
| ( SV46
= ( tail_of @ SY190 ) ) ) ) )
= $false )
| ( ( path @ SV7 @ SV21 @ SV35 )
= $false )
| ( ( in_path @ SV46 @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[270]) ).
thf(296,plain,
! [SV36: $i,SV22: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV8 )
| ~ ( edge @ SV22 ) )
| ~ ( edge @ SV36 ) )
| ~ ( sequential @ SV8 @ SV22 ) )
| ~ ( sequential @ SV22 @ SV36 ) )
= $false )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[271]) ).
thf(297,plain,
! [SV36: $i,SV22: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV8 )
| ~ ( edge @ SV22 ) )
| ~ ( edge @ SV36 ) )
| ~ ( sequential @ SV8 @ SV22 ) )
| ~ ( sequential @ SV22 @ SV36 ) )
= $true )
| ( ( ~ ( sequential @ SV36 @ SV8 ) )
= $true )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[273]) ).
thf(298,plain,
! [SV10: $i,SV24: $i,SV38: $i] :
( ( ( ~ ~ ( ~ ( edge @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) )
| ( SV10
!= ( tail_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) ) )
| ~ ~ ~ ( ~ ( ~ ~ ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) ) )
| ~ ! [SY208: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY208 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY208 ) ) ) )
| ~ ( ~ ~ ! [SY209: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY209 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY209 ) ) )
| ~ ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) ) ) ) ) )
= $false )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(299,plain,
! [SV25: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( edge @ SV11 )
| ~ ( edge @ SV25 ) ) )
= $false )
| ( ( sequential @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[277]) ).
thf(300,plain,
! [SV25: $i,SV11: $i] :
( ( ( ~ ( ( SV11 != SV25 ) ) )
= $false )
| ( ( sequential @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[277]) ).
thf(301,plain,
! [SV25: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( edge @ SV11 )
| ~ ( edge @ SV25 ) ) )
= $true )
| ( ( ~ ( ( SV11 != SV25 ) ) )
= $true )
| ( ( ( head_of @ SV11 )
!= ( tail_of @ SV25 ) )
= $true )
| ( ( sequential @ SV11 @ SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[278]) ).
thf(302,plain,
! [SV12: $i,SV26: $i,SV39: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK7_SY99 @ SV39 @ SV26 @ SV12 ) @ SV12 )
| ~ ( on_path @ ( sK8_SY210 @ SV12 @ SV26 @ SV39 ) @ SV12 ) )
| ~ ( sequential @ ( sK7_SY99 @ SV39 @ SV26 @ SV12 ) @ ( sK8_SY210 @ SV12 @ SV26 @ SV39 ) ) ) )
= $false )
| ( ( path @ SV26 @ SV39 @ SV12 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV12 )
= ( number_of_in @ triangles @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[279]) ).
thf(303,plain,
! [SV12: $i,SV26: $i,SV39: $i] :
( ( ( ~ ! [SY212: $i] :
~ ( triangle @ ( sK7_SY99 @ SV39 @ SV26 @ SV12 ) @ ( sK8_SY210 @ SV12 @ SV26 @ SV39 ) @ SY212 ) )
= $false )
| ( ( path @ SV26 @ SV39 @ SV12 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV12 )
= ( number_of_in @ triangles @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[279]) ).
thf(304,plain,
( ( ~ ( ~ ( on_path @ sK4_SY143 @ sK1_SX0 )
| ~ ( on_path @ sK5_SY197 @ sK1_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[280]) ).
thf(305,plain,
( ( sequential @ sK4_SY143 @ sK5_SY197 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[281]) ).
thf(306,plain,
! [SV28: $i,SV14: $i,SV48: $i,SV47: $i,SV41: $i] :
( ( ( ~ ~ ~ ! [SY195: $i] :
~ ~ ( ( ( tail_of @ SY195 )
!= ( tail_of @ SV41 ) )
| ( ( head_of @ SY195 )
!= ( head_of @ SV47 ) ) )
| ~ ~ ( precedes @ SV47 @ SV41 @ SV48 ) )
= $false )
| ( ( shortest_path @ SV14 @ SV28 @ SV48 )
= $false )
| ( ( precedes @ SV41 @ SV47 @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(307,plain,
! [SV42: $i,SV29: $i,SV51: $i,SV15: $i,SV49: $i] :
( ( ( ~ ( ~ ( on_path @ SV49 @ SV15 )
| ~ ( on_path @ SV51 @ SV15 ) ) )
= $false )
| ( ( ~ ( ( sequential @ SV49 @ SV51 )
| ~ ! [SY205: $i] :
~ ~ ( ~ ( sequential @ SV49 @ SY205 )
| ~ ( precedes @ SY205 @ SV51 @ SV15 ) ) ) )
= $true )
| ( ( precedes @ SV49 @ SV51 @ SV15 )
= $true )
| ( ( path @ SV29 @ SV42 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(308,plain,
! [SV43: $i,SV30: $i,SV52: $i,SV16: $i,SV50: $i] :
( ( ( ~ ( ~ ( on_path @ SV50 @ SV16 )
| ~ ( on_path @ SV52 @ SV16 ) ) )
= $true )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[285]) ).
thf(309,plain,
! [SV43: $i,SV30: $i,SV16: $i,SV52: $i,SV50: $i] :
( ( ( ~ ~ ( ~ ( ~ ( sequential @ SV50 @ SV52 )
| ~ ! [SY206: $i] :
~ ~ ( ~ ( sequential @ SV50 @ SY206 )
| ~ ( precedes @ SY206 @ SV52 @ SV16 ) ) )
| ~ ( ~ ~ ! [SY207: $i] :
~ ~ ( ~ ( sequential @ SV50 @ SY207 )
| ~ ( precedes @ SY207 @ SV52 @ SV16 ) )
| ( sequential @ SV50 @ SV52 ) ) ) )
= $true )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[286]) ).
thf(310,plain,
! [SV31: $i,SV44: $i] :
( ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( ~ ( ( SV31 != SV44 ) ) )
= $true )
| ( ( ~ ! [SY189: $i] :
~ ~ ( ~ ( edge @ SY189 )
| ~ ~ ~ ( ~ ( ~ ~ ( ( SV31
!= ( head_of @ SY189 ) )
| ( SV44
!= ( tail_of @ SY189 ) ) )
| ~ ( ( SV44
!= ( head_of @ SY189 ) )
| ( SV31
!= ( tail_of @ SY189 ) ) ) )
| ~ ( ~ ~ ( ( SV44
!= ( head_of @ SY189 ) )
| ( SV31
!= ( tail_of @ SY189 ) ) )
| ~ ( ( SV31
!= ( head_of @ SY189 ) )
| ( SV44
!= ( tail_of @ SY189 ) ) ) ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(311,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ( ~ ( path @ SV2 @ SV18 @ SV32 ) )
= $false )
| ( ( shortest_path @ SV2 @ SV18 @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[288]) ).
thf(312,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ( ~ ( ( SV2 != SV18 ) ) )
= $false )
| ( ( shortest_path @ SV2 @ SV18 @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[288]) ).
thf(313,plain,
! [SV32: $i,SV54: $i,SV18: $i,SV2: $i] :
( ( ( ~ ( path @ SV2 @ SV18 @ SV54 ) )
= $true )
| ( ( less_or_equal @ ( length_of @ SV32 ) @ ( length_of @ SV54 ) )
= $true )
| ( ( shortest_path @ SV2 @ SV18 @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[289]) ).
thf(314,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ( ~ ( path @ SV2 @ SV18 @ SV32 ) )
= $true )
| ( ( ~ ( ( SV2 != SV18 ) ) )
= $true )
| ( ( ~ ! [SY163: $i] :
( ~ ( path @ SV2 @ SV18 @ SY163 )
| ( less_or_equal @ ( length_of @ SV32 ) @ ( length_of @ SY163 ) ) ) )
= $true )
| ( ( shortest_path @ SV2 @ SV18 @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[290]) ).
thf(315,plain,
! [SV19: $i,SV3: $i,SV33: $i,SV45: $i] :
( ( ( ~ ( ~ ( edge @ SV45 )
| ~ ( in_path @ ( head_of @ SV45 ) @ SV33 ) ) )
= $true )
| ( ( path @ SV3 @ SV19 @ SV33 )
= $false )
| ( ( on_path @ SV45 @ SV33 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[291]) ).
thf(316,plain,
! [SV19: $i,SV3: $i,SV33: $i,SV45: $i] :
( ( ( in_path @ ( tail_of @ SV45 ) @ SV33 )
= $true )
| ( ( path @ SV3 @ SV19 @ SV33 )
= $false )
| ( ( on_path @ SV45 @ SV33 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[292]) ).
thf(317,plain,
! [SV34: $i,SV20: $i,SV6: $i] :
( ( ( ~ ! [SY165: $i] :
~ ~ ( ~ ~ ( ~ ( edge @ SY165 )
| ( SV6
!= ( tail_of @ SY165 ) ) )
| ~ ( ~ ( ( SV20
!= ( head_of @ SY165 ) )
| ( SV34
!= ( path_cons @ SY165 @ empty ) ) )
| ~ ! [SY166: $i] :
~ ~ ( ~ ( path @ ( head_of @ SY165 ) @ SV20 @ SY166 )
| ( SV34
!= ( path_cons @ SY165 @ SY166 ) ) ) ) ) )
= $false )
| ( ( vertex @ SV6 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV6 @ SV20 @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[293]) ).
thf(318,plain,
! [SV35: $i,SV21: $i,SV7: $i,SV46: $i] :
( ( ( vertex @ SV46 )
= $true )
| ( ( path @ SV7 @ SV21 @ SV35 )
= $false )
| ( ( in_path @ SV46 @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[294]) ).
thf(319,plain,
! [SV21: $i,SV7: $i,SV46: $i,SV35: $i] :
( ( ( ~ ! [SY190: $i] :
~ ~ ( ~ ( on_path @ SY190 @ SV35 )
| ~ ( ( SV46
= ( head_of @ SY190 ) )
| ( SV46
= ( tail_of @ SY190 ) ) ) ) )
= $true )
| ( ( path @ SV7 @ SV21 @ SV35 )
= $false )
| ( ( in_path @ SV46 @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[295]) ).
thf(320,plain,
! [SV36: $i,SV22: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV8 )
| ~ ( edge @ SV22 ) )
| ~ ( edge @ SV36 ) )
| ~ ( sequential @ SV8 @ SV22 ) ) )
= $false )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[296]) ).
thf(321,plain,
! [SV8: $i,SV36: $i,SV22: $i] :
( ( ( ~ ( sequential @ SV22 @ SV36 ) )
= $false )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[296]) ).
thf(322,plain,
! [SV36: $i,SV22: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV8 )
| ~ ( edge @ SV22 ) )
| ~ ( edge @ SV36 ) )
| ~ ( sequential @ SV8 @ SV22 ) ) )
= $true )
| ( ( ~ ( sequential @ SV22 @ SV36 ) )
= $true )
| ( ( ~ ( sequential @ SV36 @ SV8 ) )
= $true )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[297]) ).
thf(323,plain,
! [SV10: $i,SV24: $i,SV38: $i] :
( ( ( ~ ~ ( ~ ( edge @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) )
| ( SV10
!= ( tail_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) ) ) )
= $false )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[298]) ).
thf(324,plain,
! [SV10: $i,SV38: $i,SV24: $i] :
( ( ( ~ ~ ~ ( ~ ( ~ ~ ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) ) )
| ~ ! [SY208: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY208 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY208 ) ) ) )
| ~ ( ~ ~ ! [SY209: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY209 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY209 ) ) )
| ~ ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) ) ) ) ) )
= $false )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[298]) ).
thf(325,plain,
! [SV25: $i,SV11: $i] :
( ( ( ~ ( ~ ( edge @ SV11 )
| ~ ( edge @ SV25 ) ) )
= $true )
| ( ( sequential @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[299]) ).
thf(326,plain,
! [SV25: $i,SV11: $i] :
( ( ( SV11 != SV25 )
= $true )
| ( ( sequential @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[300]) ).
thf(327,plain,
! [SV25: $i,SV11: $i] :
( ( ( ~ ( ~ ( edge @ SV11 )
| ~ ( edge @ SV25 ) ) )
= $false )
| ( ( ~ ( ( SV11 != SV25 ) ) )
= $true )
| ( ( ( head_of @ SV11 )
!= ( tail_of @ SV25 ) )
= $true )
| ( ( sequential @ SV11 @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(328,plain,
! [SV12: $i,SV26: $i,SV39: $i] :
( ( ( ~ ( ~ ~ ( ~ ( on_path @ ( sK7_SY99 @ SV39 @ SV26 @ SV12 ) @ SV12 )
| ~ ( on_path @ ( sK8_SY210 @ SV12 @ SV26 @ SV39 ) @ SV12 ) )
| ~ ( sequential @ ( sK7_SY99 @ SV39 @ SV26 @ SV12 ) @ ( sK8_SY210 @ SV12 @ SV26 @ SV39 ) ) ) )
= $true )
| ( ( path @ SV26 @ SV39 @ SV12 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV12 )
= ( number_of_in @ triangles @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[302]) ).
thf(329,plain,
! [SV12: $i,SV26: $i,SV39: $i] :
( ( ( ! [SY212: $i] :
~ ( triangle @ ( sK7_SY99 @ SV39 @ SV26 @ SV12 ) @ ( sK8_SY210 @ SV12 @ SV26 @ SV39 ) @ SY212 ) )
= $true )
| ( ( path @ SV26 @ SV39 @ SV12 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV12 )
= ( number_of_in @ triangles @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[303]) ).
thf(330,plain,
( ( ~ ( on_path @ sK4_SY143 @ sK1_SX0 )
| ~ ( on_path @ sK5_SY197 @ sK1_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(331,plain,
! [SV48: $i,SV28: $i,SV14: $i,SV47: $i,SV41: $i] :
( ( ( ~ ~ ~ ! [SY195: $i] :
~ ~ ( ( ( tail_of @ SY195 )
!= ( tail_of @ SV41 ) )
| ( ( head_of @ SY195 )
!= ( head_of @ SV47 ) ) ) )
= $false )
| ( ( shortest_path @ SV14 @ SV28 @ SV48 )
= $false )
| ( ( precedes @ SV41 @ SV47 @ SV48 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[306]) ).
thf(332,plain,
! [SV28: $i,SV14: $i,SV48: $i,SV41: $i,SV47: $i] :
( ( ( ~ ~ ( precedes @ SV47 @ SV41 @ SV48 ) )
= $false )
| ( ( shortest_path @ SV14 @ SV28 @ SV48 )
= $false )
| ( ( precedes @ SV41 @ SV47 @ SV48 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[306]) ).
thf(333,plain,
! [SV42: $i,SV29: $i,SV51: $i,SV15: $i,SV49: $i] :
( ( ( ~ ( on_path @ SV49 @ SV15 )
| ~ ( on_path @ SV51 @ SV15 ) )
= $true )
| ( ( ~ ( ( sequential @ SV49 @ SV51 )
| ~ ! [SY205: $i] :
~ ~ ( ~ ( sequential @ SV49 @ SY205 )
| ~ ( precedes @ SY205 @ SV51 @ SV15 ) ) ) )
= $true )
| ( ( precedes @ SV49 @ SV51 @ SV15 )
= $true )
| ( ( path @ SV29 @ SV42 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[307]) ).
thf(334,plain,
! [SV43: $i,SV30: $i,SV52: $i,SV16: $i,SV50: $i] :
( ( ( ~ ( on_path @ SV50 @ SV16 )
| ~ ( on_path @ SV52 @ SV16 ) )
= $false )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(335,plain,
! [SV43: $i,SV30: $i,SV16: $i,SV52: $i,SV50: $i] :
( ( ( ~ ( ~ ( ~ ( sequential @ SV50 @ SV52 )
| ~ ! [SY206: $i] :
~ ~ ( ~ ( sequential @ SV50 @ SY206 )
| ~ ( precedes @ SY206 @ SV52 @ SV16 ) ) )
| ~ ( ~ ~ ! [SY207: $i] :
~ ~ ( ~ ( sequential @ SV50 @ SY207 )
| ~ ( precedes @ SY207 @ SV52 @ SV16 ) )
| ( sequential @ SV50 @ SV52 ) ) ) )
= $false )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[309]) ).
thf(336,plain,
! [SV44: $i,SV31: $i] :
( ( ( SV31 != SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( vertex @ SV44 )
= $false )
| ( ( ~ ! [SY189: $i] :
~ ~ ( ~ ( edge @ SY189 )
| ~ ~ ~ ( ~ ( ~ ~ ( ( SV31
!= ( head_of @ SY189 ) )
| ( SV44
!= ( tail_of @ SY189 ) ) )
| ~ ( ( SV44
!= ( head_of @ SY189 ) )
| ( SV31
!= ( tail_of @ SY189 ) ) ) )
| ~ ( ~ ~ ( ( SV44
!= ( head_of @ SY189 ) )
| ( SV31
!= ( tail_of @ SY189 ) ) )
| ~ ( ( SV31
!= ( head_of @ SY189 ) )
| ( SV44
!= ( tail_of @ SY189 ) ) ) ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[310]) ).
thf(337,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ( path @ SV2 @ SV18 @ SV32 )
= $true )
| ( ( shortest_path @ SV2 @ SV18 @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[311]) ).
thf(338,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ( SV2 != SV18 )
= $true )
| ( ( shortest_path @ SV2 @ SV18 @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[312]) ).
thf(339,plain,
! [SV32: $i,SV54: $i,SV18: $i,SV2: $i] :
( ( ( path @ SV2 @ SV18 @ SV54 )
= $false )
| ( ( less_or_equal @ ( length_of @ SV32 ) @ ( length_of @ SV54 ) )
= $true )
| ( ( shortest_path @ SV2 @ SV18 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[313]) ).
thf(340,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ( path @ SV2 @ SV18 @ SV32 )
= $false )
| ( ( ~ ( ( SV2 != SV18 ) ) )
= $true )
| ( ( ~ ! [SY163: $i] :
( ~ ( path @ SV2 @ SV18 @ SY163 )
| ( less_or_equal @ ( length_of @ SV32 ) @ ( length_of @ SY163 ) ) ) )
= $true )
| ( ( shortest_path @ SV2 @ SV18 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(341,plain,
! [SV19: $i,SV3: $i,SV33: $i,SV45: $i] :
( ( ( ~ ( edge @ SV45 )
| ~ ( in_path @ ( head_of @ SV45 ) @ SV33 ) )
= $false )
| ( ( path @ SV3 @ SV19 @ SV33 )
= $false )
| ( ( on_path @ SV45 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(342,plain,
! [SV34: $i,SV20: $i,SV6: $i] :
( ( ( ! [SY165: $i] :
~ ~ ( ~ ~ ( ~ ( edge @ SY165 )
| ( SV6
!= ( tail_of @ SY165 ) ) )
| ~ ( ~ ( ( SV20
!= ( head_of @ SY165 ) )
| ( SV34
!= ( path_cons @ SY165 @ empty ) ) )
| ~ ! [SY166: $i] :
~ ~ ( ~ ( path @ ( head_of @ SY165 ) @ SV20 @ SY166 )
| ( SV34
!= ( path_cons @ SY165 @ SY166 ) ) ) ) ) )
= $true )
| ( ( vertex @ SV6 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV6 @ SV20 @ SV34 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[317]) ).
thf(343,plain,
! [SV21: $i,SV7: $i,SV46: $i,SV35: $i] :
( ( ( ! [SY190: $i] :
~ ~ ( ~ ( on_path @ SY190 @ SV35 )
| ~ ( ( SV46
= ( head_of @ SY190 ) )
| ( SV46
= ( tail_of @ SY190 ) ) ) ) )
= $false )
| ( ( path @ SV7 @ SV21 @ SV35 )
= $false )
| ( ( in_path @ SV46 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[319]) ).
thf(344,plain,
! [SV36: $i,SV22: $i,SV8: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV8 )
| ~ ( edge @ SV22 ) )
| ~ ( edge @ SV36 ) )
| ~ ( sequential @ SV8 @ SV22 ) ) )
= $true )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[320]) ).
thf(345,plain,
! [SV8: $i,SV36: $i,SV22: $i] :
( ( ( sequential @ SV22 @ SV36 )
= $true )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[321]) ).
thf(346,plain,
! [SV36: $i,SV22: $i,SV8: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV8 )
| ~ ( edge @ SV22 ) )
| ~ ( edge @ SV36 ) )
| ~ ( sequential @ SV8 @ SV22 ) ) )
= $false )
| ( ( ~ ( sequential @ SV22 @ SV36 ) )
= $true )
| ( ( ~ ( sequential @ SV36 @ SV8 ) )
= $true )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[322]) ).
thf(347,plain,
! [SV10: $i,SV24: $i,SV38: $i] :
( ( ( ~ ( ~ ( edge @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) )
| ( SV10
!= ( tail_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) ) ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[323]) ).
thf(348,plain,
! [SV10: $i,SV38: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ( ~ ~ ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) ) )
| ~ ! [SY208: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY208 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY208 ) ) ) )
| ~ ( ~ ~ ! [SY209: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY209 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY209 ) ) )
| ~ ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) ) ) ) ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[324]) ).
thf(349,plain,
! [SV25: $i,SV11: $i] :
( ( ( ~ ( edge @ SV11 )
| ~ ( edge @ SV25 ) )
= $false )
| ( ( sequential @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(350,plain,
! [SV25: $i,SV11: $i] :
( ( ( SV11 = SV25 )
= $false )
| ( ( sequential @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(351,plain,
! [SV25: $i,SV11: $i] :
( ( ( ~ ( edge @ SV11 )
| ~ ( edge @ SV25 ) )
= $true )
| ( ( ~ ( ( SV11 != SV25 ) ) )
= $true )
| ( ( ( head_of @ SV11 )
!= ( tail_of @ SV25 ) )
= $true )
| ( ( sequential @ SV11 @ SV25 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[327]) ).
thf(352,plain,
! [SV12: $i,SV26: $i,SV39: $i] :
( ( ( ~ ~ ( ~ ( on_path @ ( sK7_SY99 @ SV39 @ SV26 @ SV12 ) @ SV12 )
| ~ ( on_path @ ( sK8_SY210 @ SV12 @ SV26 @ SV39 ) @ SV12 ) )
| ~ ( sequential @ ( sK7_SY99 @ SV39 @ SV26 @ SV12 ) @ ( sK8_SY210 @ SV12 @ SV26 @ SV39 ) ) )
= $false )
| ( ( path @ SV26 @ SV39 @ SV12 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV12 )
= ( number_of_in @ triangles @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(353,plain,
! [SV55: $i,SV12: $i,SV26: $i,SV39: $i] :
( ( ( ~ ( triangle @ ( sK7_SY99 @ SV39 @ SV26 @ SV12 ) @ ( sK8_SY210 @ SV12 @ SV26 @ SV39 ) @ SV55 ) )
= $true )
| ( ( path @ SV26 @ SV39 @ SV12 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV12 )
= ( number_of_in @ triangles @ SV12 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[329]) ).
thf(354,plain,
( ( ~ ( on_path @ sK4_SY143 @ sK1_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[330]) ).
thf(355,plain,
( ( ~ ( on_path @ sK5_SY197 @ sK1_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[330]) ).
thf(356,plain,
! [SV48: $i,SV28: $i,SV14: $i,SV47: $i,SV41: $i] :
( ( ( ~ ~ ! [SY195: $i] :
~ ~ ( ( ( tail_of @ SY195 )
!= ( tail_of @ SV41 ) )
| ( ( head_of @ SY195 )
!= ( head_of @ SV47 ) ) ) )
= $true )
| ( ( shortest_path @ SV14 @ SV28 @ SV48 )
= $false )
| ( ( precedes @ SV41 @ SV47 @ SV48 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[331]) ).
thf(357,plain,
! [SV28: $i,SV14: $i,SV48: $i,SV41: $i,SV47: $i] :
( ( ( ~ ( precedes @ SV47 @ SV41 @ SV48 ) )
= $true )
| ( ( shortest_path @ SV14 @ SV28 @ SV48 )
= $false )
| ( ( precedes @ SV41 @ SV47 @ SV48 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[332]) ).
thf(358,plain,
! [SV42: $i,SV29: $i,SV51: $i,SV15: $i,SV49: $i] :
( ( ( ~ ( on_path @ SV49 @ SV15 ) )
= $true )
| ( ( ~ ( on_path @ SV51 @ SV15 ) )
= $true )
| ( ( ~ ( ( sequential @ SV49 @ SV51 )
| ~ ! [SY205: $i] :
~ ~ ( ~ ( sequential @ SV49 @ SY205 )
| ~ ( precedes @ SY205 @ SV51 @ SV15 ) ) ) )
= $true )
| ( ( precedes @ SV49 @ SV51 @ SV15 )
= $true )
| ( ( path @ SV29 @ SV42 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[333]) ).
thf(359,plain,
! [SV43: $i,SV30: $i,SV52: $i,SV16: $i,SV50: $i] :
( ( ( ~ ( on_path @ SV50 @ SV16 ) )
= $false )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[334]) ).
thf(360,plain,
! [SV43: $i,SV30: $i,SV50: $i,SV16: $i,SV52: $i] :
( ( ( ~ ( on_path @ SV52 @ SV16 ) )
= $false )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[334]) ).
thf(361,plain,
! [SV43: $i,SV30: $i,SV16: $i,SV52: $i,SV50: $i] :
( ( ( ~ ( ~ ( sequential @ SV50 @ SV52 )
| ~ ! [SY206: $i] :
~ ~ ( ~ ( sequential @ SV50 @ SY206 )
| ~ ( precedes @ SY206 @ SV52 @ SV16 ) ) )
| ~ ( ~ ~ ! [SY207: $i] :
~ ~ ( ~ ( sequential @ SV50 @ SY207 )
| ~ ( precedes @ SY207 @ SV52 @ SV16 ) )
| ( sequential @ SV50 @ SV52 ) ) )
= $true )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[335]) ).
thf(362,plain,
! [SV44: $i,SV31: $i] :
( ( ( SV31 = SV44 )
= $true )
| ( ( vertex @ SV31 )
= $false )
| ( ( vertex @ SV44 )
= $false )
| ( ( ~ ! [SY189: $i] :
~ ~ ( ~ ( edge @ SY189 )
| ~ ~ ~ ( ~ ( ~ ~ ( ( SV31
!= ( head_of @ SY189 ) )
| ( SV44
!= ( tail_of @ SY189 ) ) )
| ~ ( ( SV44
!= ( head_of @ SY189 ) )
| ( SV31
!= ( tail_of @ SY189 ) ) ) )
| ~ ( ~ ~ ( ( SV44
!= ( head_of @ SY189 ) )
| ( SV31
!= ( tail_of @ SY189 ) ) )
| ~ ( ( SV31
!= ( head_of @ SY189 ) )
| ( SV44
!= ( tail_of @ SY189 ) ) ) ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[336]) ).
thf(363,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ( SV2 = SV18 )
= $false )
| ( ( shortest_path @ SV2 @ SV18 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[338]) ).
thf(364,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ( SV2 != SV18 )
= $false )
| ( ( path @ SV2 @ SV18 @ SV32 )
= $false )
| ( ( ~ ! [SY163: $i] :
( ~ ( path @ SV2 @ SV18 @ SY163 )
| ( less_or_equal @ ( length_of @ SV32 ) @ ( length_of @ SY163 ) ) ) )
= $true )
| ( ( shortest_path @ SV2 @ SV18 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[340]) ).
thf(365,plain,
! [SV33: $i,SV19: $i,SV3: $i,SV45: $i] :
( ( ( ~ ( edge @ SV45 ) )
= $false )
| ( ( path @ SV3 @ SV19 @ SV33 )
= $false )
| ( ( on_path @ SV45 @ SV33 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[341]) ).
thf(366,plain,
! [SV19: $i,SV3: $i,SV33: $i,SV45: $i] :
( ( ( ~ ( in_path @ ( head_of @ SV45 ) @ SV33 ) )
= $false )
| ( ( path @ SV3 @ SV19 @ SV33 )
= $false )
| ( ( on_path @ SV45 @ SV33 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[341]) ).
thf(367,plain,
! [SV34: $i,SV20: $i,SV6: $i,SV56: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( edge @ SV56 )
| ( SV6
!= ( tail_of @ SV56 ) ) )
| ~ ( ~ ( ( SV20
!= ( head_of @ SV56 ) )
| ( SV34
!= ( path_cons @ SV56 @ empty ) ) )
| ~ ! [SY213: $i] :
~ ~ ( ~ ( path @ ( head_of @ SV56 ) @ SV20 @ SY213 )
| ( SV34
!= ( path_cons @ SV56 @ SY213 ) ) ) ) ) )
= $true )
| ( ( vertex @ SV6 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV6 @ SV20 @ SV34 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[342]) ).
thf(368,plain,
! [SV35: $i,SV46: $i,SV7: $i,SV21: $i] :
( ( ( ~ ~ ( ~ ( on_path @ ( sK9_SY190 @ SV21 @ SV7 @ SV46 @ SV35 ) @ SV35 )
| ~ ( ( SV46
= ( head_of @ ( sK9_SY190 @ SV21 @ SV7 @ SV46 @ SV35 ) ) )
| ( SV46
= ( tail_of @ ( sK9_SY190 @ SV21 @ SV7 @ SV46 @ SV35 ) ) ) ) ) )
= $false )
| ( ( path @ SV7 @ SV21 @ SV35 )
= $false )
| ( ( in_path @ SV46 @ SV35 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[343]) ).
thf(369,plain,
! [SV36: $i,SV22: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( edge @ SV8 )
| ~ ( edge @ SV22 ) )
| ~ ( edge @ SV36 ) )
| ~ ( sequential @ SV8 @ SV22 ) )
= $false )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(370,plain,
! [SV36: $i,SV22: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( edge @ SV8 )
| ~ ( edge @ SV22 ) )
| ~ ( edge @ SV36 ) )
| ~ ( sequential @ SV8 @ SV22 ) )
= $true )
| ( ( ~ ( sequential @ SV22 @ SV36 ) )
= $true )
| ( ( ~ ( sequential @ SV36 @ SV8 ) )
= $true )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[346]) ).
thf(371,plain,
! [SV10: $i,SV24: $i,SV38: $i] :
( ( ( ~ ( edge @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) )
| ( SV10
!= ( tail_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) ) )
= $false )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[347]) ).
thf(372,plain,
! [SV10: $i,SV38: $i,SV24: $i] :
( ( ( ~ ( ~ ( ~ ~ ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) ) )
| ~ ! [SY208: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY208 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY208 ) ) ) )
| ~ ( ~ ~ ! [SY209: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY209 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY209 ) ) )
| ~ ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) ) ) ) ) )
= $false )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[348]) ).
thf(373,plain,
! [SV25: $i,SV11: $i] :
( ( ( ~ ( edge @ SV11 ) )
= $false )
| ( ( sequential @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[349]) ).
thf(374,plain,
! [SV11: $i,SV25: $i] :
( ( ( ~ ( edge @ SV25 ) )
= $false )
| ( ( sequential @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[349]) ).
thf(375,plain,
! [SV25: $i,SV11: $i] :
( ( ( ~ ( edge @ SV11 ) )
= $true )
| ( ( ~ ( edge @ SV25 ) )
= $true )
| ( ( ~ ( ( SV11 != SV25 ) ) )
= $true )
| ( ( ( head_of @ SV11 )
!= ( tail_of @ SV25 ) )
= $true )
| ( ( sequential @ SV11 @ SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[351]) ).
thf(376,plain,
! [SV12: $i,SV26: $i,SV39: $i] :
( ( ( ~ ~ ( ~ ( on_path @ ( sK7_SY99 @ SV39 @ SV26 @ SV12 ) @ SV12 )
| ~ ( on_path @ ( sK8_SY210 @ SV12 @ SV26 @ SV39 ) @ SV12 ) ) )
= $false )
| ( ( path @ SV26 @ SV39 @ SV12 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV12 )
= ( number_of_in @ triangles @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[352]) ).
thf(377,plain,
! [SV12: $i,SV26: $i,SV39: $i] :
( ( ( ~ ( sequential @ ( sK7_SY99 @ SV39 @ SV26 @ SV12 ) @ ( sK8_SY210 @ SV12 @ SV26 @ SV39 ) ) )
= $false )
| ( ( path @ SV26 @ SV39 @ SV12 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV12 )
= ( number_of_in @ triangles @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[352]) ).
thf(378,plain,
! [SV55: $i,SV12: $i,SV26: $i,SV39: $i] :
( ( ( triangle @ ( sK7_SY99 @ SV39 @ SV26 @ SV12 ) @ ( sK8_SY210 @ SV12 @ SV26 @ SV39 ) @ SV55 )
= $false )
| ( ( path @ SV26 @ SV39 @ SV12 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV12 )
= ( number_of_in @ triangles @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[353]) ).
thf(379,plain,
( ( on_path @ sK4_SY143 @ sK1_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[354]) ).
thf(380,plain,
( ( on_path @ sK5_SY197 @ sK1_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[355]) ).
thf(381,plain,
! [SV48: $i,SV28: $i,SV14: $i,SV47: $i,SV41: $i] :
( ( ( ~ ! [SY195: $i] :
~ ~ ( ( ( tail_of @ SY195 )
!= ( tail_of @ SV41 ) )
| ( ( head_of @ SY195 )
!= ( head_of @ SV47 ) ) ) )
= $false )
| ( ( shortest_path @ SV14 @ SV28 @ SV48 )
= $false )
| ( ( precedes @ SV41 @ SV47 @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[356]) ).
thf(382,plain,
! [SV28: $i,SV14: $i,SV48: $i,SV41: $i,SV47: $i] :
( ( ( precedes @ SV47 @ SV41 @ SV48 )
= $false )
| ( ( shortest_path @ SV14 @ SV28 @ SV48 )
= $false )
| ( ( precedes @ SV41 @ SV47 @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(383,plain,
! [SV42: $i,SV29: $i,SV51: $i,SV15: $i,SV49: $i] :
( ( ( on_path @ SV49 @ SV15 )
= $false )
| ( ( ~ ( on_path @ SV51 @ SV15 ) )
= $true )
| ( ( ~ ( ( sequential @ SV49 @ SV51 )
| ~ ! [SY205: $i] :
~ ~ ( ~ ( sequential @ SV49 @ SY205 )
| ~ ( precedes @ SY205 @ SV51 @ SV15 ) ) ) )
= $true )
| ( ( precedes @ SV49 @ SV51 @ SV15 )
= $true )
| ( ( path @ SV29 @ SV42 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[358]) ).
thf(384,plain,
! [SV43: $i,SV30: $i,SV52: $i,SV16: $i,SV50: $i] :
( ( ( on_path @ SV50 @ SV16 )
= $true )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[359]) ).
thf(385,plain,
! [SV43: $i,SV30: $i,SV50: $i,SV16: $i,SV52: $i] :
( ( ( on_path @ SV52 @ SV16 )
= $true )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[360]) ).
thf(386,plain,
! [SV43: $i,SV30: $i,SV16: $i,SV52: $i,SV50: $i] :
( ( ( ~ ( ~ ( sequential @ SV50 @ SV52 )
| ~ ! [SY206: $i] :
~ ~ ( ~ ( sequential @ SV50 @ SY206 )
| ~ ( precedes @ SY206 @ SV52 @ SV16 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY207: $i] :
~ ~ ( ~ ( sequential @ SV50 @ SY207 )
| ~ ( precedes @ SY207 @ SV52 @ SV16 ) )
| ( sequential @ SV50 @ SV52 ) ) )
= $true )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[361]) ).
thf(387,plain,
! [SV44: $i,SV31: $i] :
( ( ( ! [SY189: $i] :
~ ~ ( ~ ( edge @ SY189 )
| ~ ~ ~ ( ~ ( ~ ~ ( ( SV31
!= ( head_of @ SY189 ) )
| ( SV44
!= ( tail_of @ SY189 ) ) )
| ~ ( ( SV44
!= ( head_of @ SY189 ) )
| ( SV31
!= ( tail_of @ SY189 ) ) ) )
| ~ ( ~ ~ ( ( SV44
!= ( head_of @ SY189 ) )
| ( SV31
!= ( tail_of @ SY189 ) ) )
| ~ ( ( SV31
!= ( head_of @ SY189 ) )
| ( SV44
!= ( tail_of @ SY189 ) ) ) ) ) ) )
= $false )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[362]) ).
thf(388,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ( SV2 = SV18 )
= $true )
| ( ( path @ SV2 @ SV18 @ SV32 )
= $false )
| ( ( ~ ! [SY163: $i] :
( ~ ( path @ SV2 @ SV18 @ SY163 )
| ( less_or_equal @ ( length_of @ SV32 ) @ ( length_of @ SY163 ) ) ) )
= $true )
| ( ( shortest_path @ SV2 @ SV18 @ SV32 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[364]) ).
thf(389,plain,
! [SV33: $i,SV19: $i,SV3: $i,SV45: $i] :
( ( ( edge @ SV45 )
= $true )
| ( ( path @ SV3 @ SV19 @ SV33 )
= $false )
| ( ( on_path @ SV45 @ SV33 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[365]) ).
thf(390,plain,
! [SV19: $i,SV3: $i,SV33: $i,SV45: $i] :
( ( ( in_path @ ( head_of @ SV45 ) @ SV33 )
= $true )
| ( ( path @ SV3 @ SV19 @ SV33 )
= $false )
| ( ( on_path @ SV45 @ SV33 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[366]) ).
thf(391,plain,
! [SV34: $i,SV20: $i,SV6: $i,SV56: $i] :
( ( ( ~ ( ~ ~ ( ~ ( edge @ SV56 )
| ( SV6
!= ( tail_of @ SV56 ) ) )
| ~ ( ~ ( ( SV20
!= ( head_of @ SV56 ) )
| ( SV34
!= ( path_cons @ SV56 @ empty ) ) )
| ~ ! [SY213: $i] :
~ ~ ( ~ ( path @ ( head_of @ SV56 ) @ SV20 @ SY213 )
| ( SV34
!= ( path_cons @ SV56 @ SY213 ) ) ) ) ) )
= $false )
| ( ( vertex @ SV6 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV6 @ SV20 @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[367]) ).
thf(392,plain,
! [SV35: $i,SV46: $i,SV7: $i,SV21: $i] :
( ( ( ~ ( ~ ( on_path @ ( sK9_SY190 @ SV21 @ SV7 @ SV46 @ SV35 ) @ SV35 )
| ~ ( ( SV46
= ( head_of @ ( sK9_SY190 @ SV21 @ SV7 @ SV46 @ SV35 ) ) )
| ( SV46
= ( tail_of @ ( sK9_SY190 @ SV21 @ SV7 @ SV46 @ SV35 ) ) ) ) ) )
= $true )
| ( ( path @ SV7 @ SV21 @ SV35 )
= $false )
| ( ( in_path @ SV46 @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[368]) ).
thf(393,plain,
! [SV36: $i,SV22: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( edge @ SV8 )
| ~ ( edge @ SV22 ) )
| ~ ( edge @ SV36 ) ) )
= $false )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[369]) ).
thf(394,plain,
! [SV36: $i,SV22: $i,SV8: $i] :
( ( ( ~ ( sequential @ SV8 @ SV22 ) )
= $false )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[369]) ).
thf(395,plain,
! [SV36: $i,SV22: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( edge @ SV8 )
| ~ ( edge @ SV22 ) )
| ~ ( edge @ SV36 ) ) )
= $true )
| ( ( ~ ( sequential @ SV8 @ SV22 ) )
= $true )
| ( ( ~ ( sequential @ SV22 @ SV36 ) )
= $true )
| ( ( ~ ( sequential @ SV36 @ SV8 ) )
= $true )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[370]) ).
thf(396,plain,
! [SV10: $i,SV24: $i,SV38: $i] :
( ( ( ~ ( edge @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
= $false )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[371]) ).
thf(397,plain,
! [SV24: $i,SV38: $i,SV10: $i] :
( ( ( SV10
!= ( tail_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
= $false )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[371]) ).
thf(398,plain,
! [SV10: $i,SV38: $i,SV24: $i] :
( ( ( ~ ( ~ ~ ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) ) )
| ~ ! [SY208: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY208 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY208 ) ) ) )
| ~ ( ~ ~ ! [SY209: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY209 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY209 ) ) )
| ~ ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) ) ) ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[372]) ).
thf(399,plain,
! [SV25: $i,SV11: $i] :
( ( ( edge @ SV11 )
= $true )
| ( ( sequential @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[373]) ).
thf(400,plain,
! [SV11: $i,SV25: $i] :
( ( ( edge @ SV25 )
= $true )
| ( ( sequential @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[374]) ).
thf(401,plain,
! [SV25: $i,SV11: $i] :
( ( ( edge @ SV11 )
= $false )
| ( ( ~ ( edge @ SV25 ) )
= $true )
| ( ( ~ ( ( SV11 != SV25 ) ) )
= $true )
| ( ( ( head_of @ SV11 )
!= ( tail_of @ SV25 ) )
= $true )
| ( ( sequential @ SV11 @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[375]) ).
thf(402,plain,
! [SV12: $i,SV26: $i,SV39: $i] :
( ( ( ~ ( ~ ( on_path @ ( sK7_SY99 @ SV39 @ SV26 @ SV12 ) @ SV12 )
| ~ ( on_path @ ( sK8_SY210 @ SV12 @ SV26 @ SV39 ) @ SV12 ) ) )
= $true )
| ( ( path @ SV26 @ SV39 @ SV12 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV12 )
= ( number_of_in @ triangles @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[376]) ).
thf(403,plain,
! [SV12: $i,SV26: $i,SV39: $i] :
( ( ( sequential @ ( sK7_SY99 @ SV39 @ SV26 @ SV12 ) @ ( sK8_SY210 @ SV12 @ SV26 @ SV39 ) )
= $true )
| ( ( path @ SV26 @ SV39 @ SV12 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV12 )
= ( number_of_in @ triangles @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[377]) ).
thf(404,plain,
! [SV48: $i,SV28: $i,SV14: $i,SV47: $i,SV41: $i] :
( ( ( ! [SY195: $i] :
~ ~ ( ( ( tail_of @ SY195 )
!= ( tail_of @ SV41 ) )
| ( ( head_of @ SY195 )
!= ( head_of @ SV47 ) ) ) )
= $true )
| ( ( shortest_path @ SV14 @ SV28 @ SV48 )
= $false )
| ( ( precedes @ SV41 @ SV47 @ SV48 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[381]) ).
thf(405,plain,
! [SV42: $i,SV29: $i,SV49: $i,SV15: $i,SV51: $i] :
( ( ( on_path @ SV51 @ SV15 )
= $false )
| ( ( on_path @ SV49 @ SV15 )
= $false )
| ( ( ~ ( ( sequential @ SV49 @ SV51 )
| ~ ! [SY205: $i] :
~ ~ ( ~ ( sequential @ SV49 @ SY205 )
| ~ ( precedes @ SY205 @ SV51 @ SV15 ) ) ) )
= $true )
| ( ( precedes @ SV49 @ SV51 @ SV15 )
= $true )
| ( ( path @ SV29 @ SV42 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[383]) ).
thf(406,plain,
! [SV43: $i,SV30: $i,SV16: $i,SV52: $i,SV50: $i] :
( ( ( ~ ( sequential @ SV50 @ SV52 )
| ~ ! [SY206: $i] :
~ ~ ( ~ ( sequential @ SV50 @ SY206 )
| ~ ( precedes @ SY206 @ SV52 @ SV16 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY207: $i] :
~ ~ ( ~ ( sequential @ SV50 @ SY207 )
| ~ ( precedes @ SY207 @ SV52 @ SV16 ) )
| ( sequential @ SV50 @ SV52 ) ) )
= $true )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[386]) ).
thf(407,plain,
! [SV31: $i,SV44: $i] :
( ( ( ~ ~ ( ~ ( edge @ ( sK10_SY189 @ SV44 @ SV31 ) )
| ~ ~ ~ ( ~ ( ~ ~ ( ( SV31
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) )
| ~ ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) ) )
| ~ ( ~ ~ ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) )
| ~ ( ( SV31
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) ) ) ) ) )
= $false )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_forall_neg,[status(esa)],[387]) ).
thf(408,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ( ! [SY163: $i] :
( ~ ( path @ SV2 @ SV18 @ SY163 )
| ( less_or_equal @ ( length_of @ SV32 ) @ ( length_of @ SY163 ) ) ) )
= $false )
| ( ( path @ SV2 @ SV18 @ SV32 )
= $false )
| ( ( SV2 = SV18 )
= $true )
| ( ( shortest_path @ SV2 @ SV18 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[388]) ).
thf(409,plain,
! [SV34: $i,SV20: $i,SV6: $i,SV56: $i] :
( ( ( ~ ~ ( ~ ( edge @ SV56 )
| ( SV6
!= ( tail_of @ SV56 ) ) )
| ~ ( ~ ( ( SV20
!= ( head_of @ SV56 ) )
| ( SV34
!= ( path_cons @ SV56 @ empty ) ) )
| ~ ! [SY213: $i] :
~ ~ ( ~ ( path @ ( head_of @ SV56 ) @ SV20 @ SY213 )
| ( SV34
!= ( path_cons @ SV56 @ SY213 ) ) ) ) )
= $true )
| ( ( vertex @ SV6 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV6 @ SV20 @ SV34 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[391]) ).
thf(410,plain,
! [SV35: $i,SV46: $i,SV7: $i,SV21: $i] :
( ( ( ~ ( on_path @ ( sK9_SY190 @ SV21 @ SV7 @ SV46 @ SV35 ) @ SV35 )
| ~ ( ( SV46
= ( head_of @ ( sK9_SY190 @ SV21 @ SV7 @ SV46 @ SV35 ) ) )
| ( SV46
= ( tail_of @ ( sK9_SY190 @ SV21 @ SV7 @ SV46 @ SV35 ) ) ) ) )
= $false )
| ( ( path @ SV7 @ SV21 @ SV35 )
= $false )
| ( ( in_path @ SV46 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(411,plain,
! [SV36: $i,SV22: $i,SV8: $i] :
( ( ( ~ ( ~ ~ ( ~ ( edge @ SV8 )
| ~ ( edge @ SV22 ) )
| ~ ( edge @ SV36 ) ) )
= $true )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[393]) ).
thf(412,plain,
! [SV36: $i,SV22: $i,SV8: $i] :
( ( ( sequential @ SV8 @ SV22 )
= $true )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[394]) ).
thf(413,plain,
! [SV36: $i,SV22: $i,SV8: $i] :
( ( ( ~ ( ~ ~ ( ~ ( edge @ SV8 )
| ~ ( edge @ SV22 ) )
| ~ ( edge @ SV36 ) ) )
= $false )
| ( ( ~ ( sequential @ SV8 @ SV22 ) )
= $true )
| ( ( ~ ( sequential @ SV22 @ SV36 ) )
= $true )
| ( ( ~ ( sequential @ SV36 @ SV8 ) )
= $true )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[395]) ).
thf(414,plain,
! [SV10: $i,SV24: $i,SV38: $i] :
( ( ( edge @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[396]) ).
thf(415,plain,
! [SV24: $i,SV38: $i,SV10: $i] :
( ( ( SV10
= ( tail_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[397]) ).
thf(416,plain,
! [SV10: $i,SV38: $i,SV24: $i] :
( ( ( ~ ( ~ ~ ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) ) )
| ~ ! [SY208: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY208 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY208 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY209: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY209 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY209 ) ) )
| ~ ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) ) ) ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[398]) ).
thf(417,plain,
! [SV11: $i,SV25: $i] :
( ( ( edge @ SV25 )
= $false )
| ( ( edge @ SV11 )
= $false )
| ( ( ~ ( ( SV11 != SV25 ) ) )
= $true )
| ( ( ( head_of @ SV11 )
!= ( tail_of @ SV25 ) )
= $true )
| ( ( sequential @ SV11 @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[401]) ).
thf(418,plain,
! [SV12: $i,SV26: $i,SV39: $i] :
( ( ( ~ ( on_path @ ( sK7_SY99 @ SV39 @ SV26 @ SV12 ) @ SV12 )
| ~ ( on_path @ ( sK8_SY210 @ SV12 @ SV26 @ SV39 ) @ SV12 ) )
= $false )
| ( ( path @ SV26 @ SV39 @ SV12 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV12 )
= ( number_of_in @ triangles @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[402]) ).
thf(419,plain,
! [SV48: $i,SV28: $i,SV14: $i,SV47: $i,SV41: $i,SV57: $i] :
( ( ( ~ ~ ( ( ( tail_of @ SV57 )
!= ( tail_of @ SV41 ) )
| ( ( head_of @ SV57 )
!= ( head_of @ SV47 ) ) ) )
= $true )
| ( ( shortest_path @ SV14 @ SV28 @ SV48 )
= $false )
| ( ( precedes @ SV41 @ SV47 @ SV48 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[404]) ).
thf(420,plain,
! [SV42: $i,SV29: $i,SV15: $i,SV51: $i,SV49: $i] :
( ( ( ( sequential @ SV49 @ SV51 )
| ~ ! [SY205: $i] :
~ ~ ( ~ ( sequential @ SV49 @ SY205 )
| ~ ( precedes @ SY205 @ SV51 @ SV15 ) ) )
= $false )
| ( ( on_path @ SV49 @ SV15 )
= $false )
| ( ( on_path @ SV51 @ SV15 )
= $false )
| ( ( precedes @ SV49 @ SV51 @ SV15 )
= $true )
| ( ( path @ SV29 @ SV42 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[405]) ).
thf(421,plain,
! [SV43: $i,SV30: $i,SV16: $i,SV52: $i,SV50: $i] :
( ( ( ~ ( sequential @ SV50 @ SV52 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY207: $i] :
~ ~ ( ~ ( sequential @ SV50 @ SY207 )
| ~ ( precedes @ SY207 @ SV52 @ SV16 ) )
| ( sequential @ SV50 @ SV52 ) ) )
= $true )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[406]) ).
thf(422,plain,
! [SV43: $i,SV30: $i,SV16: $i,SV52: $i,SV50: $i] :
( ( ( ~ ! [SY206: $i] :
~ ~ ( ~ ( sequential @ SV50 @ SY206 )
| ~ ( precedes @ SY206 @ SV52 @ SV16 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY207: $i] :
~ ~ ( ~ ( sequential @ SV50 @ SY207 )
| ~ ( precedes @ SY207 @ SV52 @ SV16 ) )
| ( sequential @ SV50 @ SV52 ) ) )
= $true )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[406]) ).
thf(423,plain,
! [SV31: $i,SV44: $i] :
( ( ( ~ ( ~ ( edge @ ( sK10_SY189 @ SV44 @ SV31 ) )
| ~ ~ ~ ( ~ ( ~ ~ ( ( SV31
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) )
| ~ ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) ) )
| ~ ( ~ ~ ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) )
| ~ ( ( SV31
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) ) ) ) ) )
= $true )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[407]) ).
thf(424,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ( ~ ( path @ SV2 @ SV18 @ ( sK11_SY163 @ SV32 @ SV18 @ SV2 ) )
| ( less_or_equal @ ( length_of @ SV32 ) @ ( length_of @ ( sK11_SY163 @ SV32 @ SV18 @ SV2 ) ) ) )
= $false )
| ( ( path @ SV2 @ SV18 @ SV32 )
= $false )
| ( ( SV2 = SV18 )
= $true )
| ( ( shortest_path @ SV2 @ SV18 @ SV32 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[408]) ).
thf(425,plain,
! [SV34: $i,SV20: $i,SV6: $i,SV56: $i] :
( ( ( ~ ~ ( ~ ( edge @ SV56 )
| ( SV6
!= ( tail_of @ SV56 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV20
!= ( head_of @ SV56 ) )
| ( SV34
!= ( path_cons @ SV56 @ empty ) ) )
| ~ ! [SY213: $i] :
~ ~ ( ~ ( path @ ( head_of @ SV56 ) @ SV20 @ SY213 )
| ( SV34
!= ( path_cons @ SV56 @ SY213 ) ) ) ) )
= $true )
| ( ( vertex @ SV6 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV6 @ SV20 @ SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[409]) ).
thf(426,plain,
! [SV35: $i,SV46: $i,SV7: $i,SV21: $i] :
( ( ( ~ ( on_path @ ( sK9_SY190 @ SV21 @ SV7 @ SV46 @ SV35 ) @ SV35 ) )
= $false )
| ( ( path @ SV7 @ SV21 @ SV35 )
= $false )
| ( ( in_path @ SV46 @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[410]) ).
thf(427,plain,
! [SV35: $i,SV7: $i,SV21: $i,SV46: $i] :
( ( ( ~ ( ( SV46
= ( head_of @ ( sK9_SY190 @ SV21 @ SV7 @ SV46 @ SV35 ) ) )
| ( SV46
= ( tail_of @ ( sK9_SY190 @ SV21 @ SV7 @ SV46 @ SV35 ) ) ) ) )
= $false )
| ( ( path @ SV7 @ SV21 @ SV35 )
= $false )
| ( ( in_path @ SV46 @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[410]) ).
thf(428,plain,
! [SV36: $i,SV22: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( edge @ SV8 )
| ~ ( edge @ SV22 ) )
| ~ ( edge @ SV36 ) )
= $false )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[411]) ).
thf(429,plain,
! [SV36: $i,SV22: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( edge @ SV8 )
| ~ ( edge @ SV22 ) )
| ~ ( edge @ SV36 ) )
= $true )
| ( ( ~ ( sequential @ SV8 @ SV22 ) )
= $true )
| ( ( ~ ( sequential @ SV22 @ SV36 ) )
= $true )
| ( ( ~ ( sequential @ SV36 @ SV8 ) )
= $true )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[413]) ).
thf(430,plain,
! [SV10: $i,SV38: $i,SV24: $i] :
( ( ( ~ ~ ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) ) )
| ~ ! [SY208: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY208 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY208 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY209: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY209 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY209 ) ) )
| ~ ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) ) ) ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[416]) ).
thf(431,plain,
! [SV25: $i,SV11: $i] :
( ( ( SV11 != SV25 )
= $false )
| ( ( edge @ SV11 )
= $false )
| ( ( edge @ SV25 )
= $false )
| ( ( ( head_of @ SV11 )
!= ( tail_of @ SV25 ) )
= $true )
| ( ( sequential @ SV11 @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(432,plain,
! [SV12: $i,SV26: $i,SV39: $i] :
( ( ( ~ ( on_path @ ( sK7_SY99 @ SV39 @ SV26 @ SV12 ) @ SV12 ) )
= $false )
| ( ( path @ SV26 @ SV39 @ SV12 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV12 )
= ( number_of_in @ triangles @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[418]) ).
thf(433,plain,
! [SV39: $i,SV26: $i,SV12: $i] :
( ( ( ~ ( on_path @ ( sK8_SY210 @ SV12 @ SV26 @ SV39 ) @ SV12 ) )
= $false )
| ( ( path @ SV26 @ SV39 @ SV12 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV12 )
= ( number_of_in @ triangles @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[418]) ).
thf(434,plain,
! [SV48: $i,SV28: $i,SV14: $i,SV47: $i,SV41: $i,SV57: $i] :
( ( ( ~ ( ( ( tail_of @ SV57 )
!= ( tail_of @ SV41 ) )
| ( ( head_of @ SV57 )
!= ( head_of @ SV47 ) ) ) )
= $false )
| ( ( shortest_path @ SV14 @ SV28 @ SV48 )
= $false )
| ( ( precedes @ SV41 @ SV47 @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[419]) ).
thf(435,plain,
! [SV42: $i,SV29: $i,SV15: $i,SV51: $i,SV49: $i] :
( ( ( sequential @ SV49 @ SV51 )
= $false )
| ( ( on_path @ SV49 @ SV15 )
= $false )
| ( ( on_path @ SV51 @ SV15 )
= $false )
| ( ( precedes @ SV49 @ SV51 @ SV15 )
= $true )
| ( ( path @ SV29 @ SV42 @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[420]) ).
thf(436,plain,
! [SV42: $i,SV29: $i,SV15: $i,SV51: $i,SV49: $i] :
( ( ( ~ ! [SY205: $i] :
~ ~ ( ~ ( sequential @ SV49 @ SY205 )
| ~ ( precedes @ SY205 @ SV51 @ SV15 ) ) )
= $false )
| ( ( on_path @ SV49 @ SV15 )
= $false )
| ( ( on_path @ SV51 @ SV15 )
= $false )
| ( ( precedes @ SV49 @ SV51 @ SV15 )
= $true )
| ( ( path @ SV29 @ SV42 @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[420]) ).
thf(437,plain,
! [SV43: $i,SV30: $i,SV16: $i,SV52: $i,SV50: $i] :
( ( ( sequential @ SV50 @ SV52 )
= $true )
| ( ( ~ ( ~ ~ ! [SY207: $i] :
~ ~ ( ~ ( sequential @ SV50 @ SY207 )
| ~ ( precedes @ SY207 @ SV52 @ SV16 ) )
| ( sequential @ SV50 @ SV52 ) ) )
= $true )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[421]) ).
thf(438,plain,
! [SV43: $i,SV30: $i,SV16: $i,SV52: $i,SV50: $i] :
( ( ( ! [SY206: $i] :
~ ~ ( ~ ( sequential @ SV50 @ SY206 )
| ~ ( precedes @ SY206 @ SV52 @ SV16 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY207: $i] :
~ ~ ( ~ ( sequential @ SV50 @ SY207 )
| ~ ( precedes @ SY207 @ SV52 @ SV16 ) )
| ( sequential @ SV50 @ SV52 ) ) )
= $true )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[422]) ).
thf(439,plain,
! [SV31: $i,SV44: $i] :
( ( ( ~ ( edge @ ( sK10_SY189 @ SV44 @ SV31 ) )
| ~ ~ ~ ( ~ ( ~ ~ ( ( SV31
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) )
| ~ ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) ) )
| ~ ( ~ ~ ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) )
| ~ ( ( SV31
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) ) ) ) )
= $false )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[423]) ).
thf(440,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ( ~ ( path @ SV2 @ SV18 @ ( sK11_SY163 @ SV32 @ SV18 @ SV2 ) ) )
= $false )
| ( ( path @ SV2 @ SV18 @ SV32 )
= $false )
| ( ( SV2 = SV18 )
= $true )
| ( ( shortest_path @ SV2 @ SV18 @ SV32 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[424]) ).
thf(441,plain,
! [SV2: $i,SV18: $i,SV32: $i] :
( ( ( less_or_equal @ ( length_of @ SV32 ) @ ( length_of @ ( sK11_SY163 @ SV32 @ SV18 @ SV2 ) ) )
= $false )
| ( ( path @ SV2 @ SV18 @ SV32 )
= $false )
| ( ( SV2 = SV18 )
= $true )
| ( ( shortest_path @ SV2 @ SV18 @ SV32 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[424]) ).
thf(442,plain,
! [SV34: $i,SV20: $i,SV6: $i,SV56: $i] :
( ( ( ~ ( ~ ( edge @ SV56 )
| ( SV6
!= ( tail_of @ SV56 ) ) ) )
= $false )
| ( ( ~ ( ~ ( ( SV20
!= ( head_of @ SV56 ) )
| ( SV34
!= ( path_cons @ SV56 @ empty ) ) )
| ~ ! [SY213: $i] :
~ ~ ( ~ ( path @ ( head_of @ SV56 ) @ SV20 @ SY213 )
| ( SV34
!= ( path_cons @ SV56 @ SY213 ) ) ) ) )
= $true )
| ( ( vertex @ SV6 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV6 @ SV20 @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(443,plain,
! [SV35: $i,SV46: $i,SV7: $i,SV21: $i] :
( ( ( on_path @ ( sK9_SY190 @ SV21 @ SV7 @ SV46 @ SV35 ) @ SV35 )
= $true )
| ( ( path @ SV7 @ SV21 @ SV35 )
= $false )
| ( ( in_path @ SV46 @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[426]) ).
thf(444,plain,
! [SV35: $i,SV7: $i,SV21: $i,SV46: $i] :
( ( ( ( SV46
= ( head_of @ ( sK9_SY190 @ SV21 @ SV7 @ SV46 @ SV35 ) ) )
| ( SV46
= ( tail_of @ ( sK9_SY190 @ SV21 @ SV7 @ SV46 @ SV35 ) ) ) )
= $true )
| ( ( path @ SV7 @ SV21 @ SV35 )
= $false )
| ( ( in_path @ SV46 @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[427]) ).
thf(445,plain,
! [SV36: $i,SV22: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( edge @ SV8 )
| ~ ( edge @ SV22 ) ) )
= $false )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[428]) ).
thf(446,plain,
! [SV22: $i,SV8: $i,SV36: $i] :
( ( ( ~ ( edge @ SV36 ) )
= $false )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[428]) ).
thf(447,plain,
! [SV36: $i,SV22: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( edge @ SV8 )
| ~ ( edge @ SV22 ) ) )
= $true )
| ( ( ~ ( edge @ SV36 ) )
= $true )
| ( ( ~ ( sequential @ SV8 @ SV22 ) )
= $true )
| ( ( ~ ( sequential @ SV22 @ SV36 ) )
= $true )
| ( ( ~ ( sequential @ SV36 @ SV8 ) )
= $true )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[429]) ).
thf(448,plain,
! [SV10: $i,SV38: $i,SV24: $i] :
( ( ( ~ ~ ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY209: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY209 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY209 ) ) )
| ~ ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) ) ) ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[430]) ).
thf(449,plain,
! [SV10: $i,SV24: $i,SV38: $i] :
( ( ( ~ ! [SY208: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY208 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY208 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY209: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY209 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY209 ) ) )
| ~ ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) ) ) ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[430]) ).
thf(450,plain,
! [SV25: $i,SV11: $i] :
( ( ( SV11 = SV25 )
= $true )
| ( ( edge @ SV11 )
= $false )
| ( ( edge @ SV25 )
= $false )
| ( ( ( head_of @ SV11 )
!= ( tail_of @ SV25 ) )
= $true )
| ( ( sequential @ SV11 @ SV25 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[431]) ).
thf(451,plain,
! [SV12: $i,SV26: $i,SV39: $i] :
( ( ( on_path @ ( sK7_SY99 @ SV39 @ SV26 @ SV12 ) @ SV12 )
= $true )
| ( ( path @ SV26 @ SV39 @ SV12 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV12 )
= ( number_of_in @ triangles @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[432]) ).
thf(452,plain,
! [SV39: $i,SV26: $i,SV12: $i] :
( ( ( on_path @ ( sK8_SY210 @ SV12 @ SV26 @ SV39 ) @ SV12 )
= $true )
| ( ( path @ SV26 @ SV39 @ SV12 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV12 )
= ( number_of_in @ triangles @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[433]) ).
thf(453,plain,
! [SV48: $i,SV28: $i,SV14: $i,SV47: $i,SV41: $i,SV57: $i] :
( ( ( ( ( tail_of @ SV57 )
!= ( tail_of @ SV41 ) )
| ( ( head_of @ SV57 )
!= ( head_of @ SV47 ) ) )
= $true )
| ( ( shortest_path @ SV14 @ SV28 @ SV48 )
= $false )
| ( ( precedes @ SV41 @ SV47 @ SV48 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[434]) ).
thf(454,plain,
! [SV42: $i,SV29: $i,SV15: $i,SV51: $i,SV49: $i] :
( ( ( ! [SY205: $i] :
~ ~ ( ~ ( sequential @ SV49 @ SY205 )
| ~ ( precedes @ SY205 @ SV51 @ SV15 ) ) )
= $true )
| ( ( on_path @ SV49 @ SV15 )
= $false )
| ( ( on_path @ SV51 @ SV15 )
= $false )
| ( ( precedes @ SV49 @ SV51 @ SV15 )
= $true )
| ( ( path @ SV29 @ SV42 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[436]) ).
thf(455,plain,
! [SV43: $i,SV30: $i,SV16: $i,SV52: $i,SV50: $i] :
( ( ( ~ ~ ! [SY207: $i] :
~ ~ ( ~ ( sequential @ SV50 @ SY207 )
| ~ ( precedes @ SY207 @ SV52 @ SV16 ) )
| ( sequential @ SV50 @ SV52 ) )
= $false )
| ( ( sequential @ SV50 @ SV52 )
= $true )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[437]) ).
thf(456,plain,
! [SV43: $i,SV30: $i,SV16: $i,SV52: $i,SV58: $i,SV50: $i] :
( ( ( ~ ~ ( ~ ( sequential @ SV50 @ SV58 )
| ~ ( precedes @ SV58 @ SV52 @ SV16 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY207: $i] :
~ ~ ( ~ ( sequential @ SV50 @ SY207 )
| ~ ( precedes @ SY207 @ SV52 @ SV16 ) )
| ( sequential @ SV50 @ SV52 ) ) )
= $true )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(457,plain,
! [SV31: $i,SV44: $i] :
( ( ( ~ ( edge @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[439]) ).
thf(458,plain,
! [SV44: $i,SV31: $i] :
( ( ( ~ ~ ~ ( ~ ( ~ ~ ( ( SV31
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) )
| ~ ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) ) )
| ~ ( ~ ~ ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) )
| ~ ( ( SV31
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) ) ) ) )
= $false )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[439]) ).
thf(459,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ( path @ SV2 @ SV18 @ ( sK11_SY163 @ SV32 @ SV18 @ SV2 ) )
= $true )
| ( ( path @ SV2 @ SV18 @ SV32 )
= $false )
| ( ( SV2 = SV18 )
= $true )
| ( ( shortest_path @ SV2 @ SV18 @ SV32 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[440]) ).
thf(460,plain,
! [SV34: $i,SV20: $i,SV6: $i,SV56: $i] :
( ( ( ~ ( edge @ SV56 )
| ( SV6
!= ( tail_of @ SV56 ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV20
!= ( head_of @ SV56 ) )
| ( SV34
!= ( path_cons @ SV56 @ empty ) ) )
| ~ ! [SY213: $i] :
~ ~ ( ~ ( path @ ( head_of @ SV56 ) @ SV20 @ SY213 )
| ( SV34
!= ( path_cons @ SV56 @ SY213 ) ) ) ) )
= $true )
| ( ( vertex @ SV6 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV6 @ SV20 @ SV34 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[442]) ).
thf(461,plain,
! [SV35: $i,SV7: $i,SV21: $i,SV46: $i] :
( ( ( SV46
= ( head_of @ ( sK9_SY190 @ SV21 @ SV7 @ SV46 @ SV35 ) ) )
= $true )
| ( ( SV46
= ( tail_of @ ( sK9_SY190 @ SV21 @ SV7 @ SV46 @ SV35 ) ) )
= $true )
| ( ( path @ SV7 @ SV21 @ SV35 )
= $false )
| ( ( in_path @ SV46 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[444]) ).
thf(462,plain,
! [SV36: $i,SV22: $i,SV8: $i] :
( ( ( ~ ( ~ ( edge @ SV8 )
| ~ ( edge @ SV22 ) ) )
= $true )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[445]) ).
thf(463,plain,
! [SV22: $i,SV8: $i,SV36: $i] :
( ( ( edge @ SV36 )
= $true )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[446]) ).
thf(464,plain,
! [SV36: $i,SV22: $i,SV8: $i] :
( ( ( ~ ( ~ ( edge @ SV8 )
| ~ ( edge @ SV22 ) ) )
= $false )
| ( ( ~ ( edge @ SV36 ) )
= $true )
| ( ( ~ ( sequential @ SV8 @ SV22 ) )
= $true )
| ( ( ~ ( sequential @ SV22 @ SV36 ) )
= $true )
| ( ( ~ ( sequential @ SV36 @ SV8 ) )
= $true )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[447]) ).
thf(465,plain,
! [SV10: $i,SV38: $i,SV24: $i] :
( ( ( ~ ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY209: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY209 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY209 ) ) )
| ~ ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) ) ) ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[448]) ).
thf(466,plain,
! [SV10: $i,SV24: $i,SV38: $i] :
( ( ( ! [SY208: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY208 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY208 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY209: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY209 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY209 ) ) )
| ~ ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) ) ) ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[449]) ).
thf(467,plain,
! [SV25: $i,SV11: $i] :
( ( ( ( head_of @ SV11 )
= ( tail_of @ SV25 ) )
= $false )
| ( ( edge @ SV25 )
= $false )
| ( ( edge @ SV11 )
= $false )
| ( ( SV11 = SV25 )
= $true )
| ( ( sequential @ SV11 @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[450]) ).
thf(468,plain,
! [SV48: $i,SV28: $i,SV14: $i,SV47: $i,SV41: $i,SV57: $i] :
( ( ( ( tail_of @ SV57 )
!= ( tail_of @ SV41 ) )
= $true )
| ( ( ( head_of @ SV57 )
!= ( head_of @ SV47 ) )
= $true )
| ( ( shortest_path @ SV14 @ SV28 @ SV48 )
= $false )
| ( ( precedes @ SV41 @ SV47 @ SV48 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[453]) ).
thf(469,plain,
! [SV42: $i,SV29: $i,SV15: $i,SV51: $i,SV59: $i,SV49: $i] :
( ( ( ~ ~ ( ~ ( sequential @ SV49 @ SV59 )
| ~ ( precedes @ SV59 @ SV51 @ SV15 ) ) )
= $true )
| ( ( on_path @ SV49 @ SV15 )
= $false )
| ( ( on_path @ SV51 @ SV15 )
= $false )
| ( ( precedes @ SV49 @ SV51 @ SV15 )
= $true )
| ( ( path @ SV29 @ SV42 @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[454]) ).
thf(470,plain,
! [SV43: $i,SV30: $i,SV16: $i,SV52: $i,SV50: $i] :
( ( ( ~ ~ ! [SY207: $i] :
~ ~ ( ~ ( sequential @ SV50 @ SY207 )
| ~ ( precedes @ SY207 @ SV52 @ SV16 ) ) )
= $false )
| ( ( sequential @ SV50 @ SV52 )
= $true )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[455]) ).
thf(471,plain,
! [SV43: $i,SV30: $i,SV16: $i,SV52: $i,SV50: $i] :
( ( ( sequential @ SV50 @ SV52 )
= $false )
| ( ( sequential @ SV50 @ SV52 )
= $true )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[455]) ).
thf(472,plain,
! [SV43: $i,SV30: $i,SV16: $i,SV52: $i,SV58: $i,SV50: $i] :
( ( ( ~ ( ~ ( sequential @ SV50 @ SV58 )
| ~ ( precedes @ SV58 @ SV52 @ SV16 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY207: $i] :
~ ~ ( ~ ( sequential @ SV50 @ SY207 )
| ~ ( precedes @ SY207 @ SV52 @ SV16 ) )
| ( sequential @ SV50 @ SV52 ) ) )
= $true )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[456]) ).
thf(473,plain,
! [SV31: $i,SV44: $i] :
( ( ( edge @ ( sK10_SY189 @ SV44 @ SV31 ) )
= $true )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[457]) ).
thf(474,plain,
! [SV44: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ( ~ ~ ( ( SV31
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) )
| ~ ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) ) )
| ~ ( ~ ~ ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) )
| ~ ( ( SV31
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) ) ) ) )
= $true )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[458]) ).
thf(475,plain,
! [SV34: $i,SV20: $i,SV6: $i,SV56: $i] :
( ( ( ~ ( edge @ SV56 ) )
= $true )
| ( ( SV6
!= ( tail_of @ SV56 ) )
= $true )
| ( ( ~ ( ~ ( ( SV20
!= ( head_of @ SV56 ) )
| ( SV34
!= ( path_cons @ SV56 @ empty ) ) )
| ~ ! [SY213: $i] :
~ ~ ( ~ ( path @ ( head_of @ SV56 ) @ SV20 @ SY213 )
| ( SV34
!= ( path_cons @ SV56 @ SY213 ) ) ) ) )
= $true )
| ( ( vertex @ SV6 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV6 @ SV20 @ SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[460]) ).
thf(476,plain,
! [SV36: $i,SV22: $i,SV8: $i] :
( ( ( ~ ( edge @ SV8 )
| ~ ( edge @ SV22 ) )
= $false )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[462]) ).
thf(477,plain,
! [SV36: $i,SV22: $i,SV8: $i] :
( ( ( ~ ( edge @ SV8 )
| ~ ( edge @ SV22 ) )
= $true )
| ( ( ~ ( edge @ SV36 ) )
= $true )
| ( ( ~ ( sequential @ SV8 @ SV22 ) )
= $true )
| ( ( ~ ( sequential @ SV22 @ SV36 ) )
= $true )
| ( ( ~ ( sequential @ SV36 @ SV8 ) )
= $true )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[464]) ).
thf(478,plain,
! [SV10: $i,SV38: $i,SV24: $i] :
( ( ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY209: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY209 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY209 ) ) )
| ~ ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) ) ) ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[465]) ).
thf(479,plain,
! [SV60: $i,SV10: $i,SV24: $i,SV38: $i] :
( ( ( ~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SV60 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SV60 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY209: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY209 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY209 ) ) )
| ~ ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) ) ) ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(480,plain,
! [SV48: $i,SV28: $i,SV14: $i,SV47: $i,SV41: $i,SV57: $i] :
( ( ( ( tail_of @ SV57 )
= ( tail_of @ SV41 ) )
= $false )
| ( ( ( head_of @ SV57 )
!= ( head_of @ SV47 ) )
= $true )
| ( ( shortest_path @ SV14 @ SV28 @ SV48 )
= $false )
| ( ( precedes @ SV41 @ SV47 @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[468]) ).
thf(481,plain,
! [SV42: $i,SV29: $i,SV15: $i,SV51: $i,SV59: $i,SV49: $i] :
( ( ( ~ ( ~ ( sequential @ SV49 @ SV59 )
| ~ ( precedes @ SV59 @ SV51 @ SV15 ) ) )
= $false )
| ( ( on_path @ SV49 @ SV15 )
= $false )
| ( ( on_path @ SV51 @ SV15 )
= $false )
| ( ( precedes @ SV49 @ SV51 @ SV15 )
= $true )
| ( ( path @ SV29 @ SV42 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[469]) ).
thf(482,plain,
! [SV43: $i,SV30: $i,SV16: $i,SV52: $i,SV50: $i] :
( ( ( ~ ! [SY207: $i] :
~ ~ ( ~ ( sequential @ SV50 @ SY207 )
| ~ ( precedes @ SY207 @ SV52 @ SV16 ) ) )
= $true )
| ( ( sequential @ SV50 @ SV52 )
= $true )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[470]) ).
thf(483,plain,
! [SV43: $i,SV30: $i,SV16: $i,SV52: $i,SV58: $i,SV50: $i] :
( ( ( ~ ( sequential @ SV50 @ SV58 )
| ~ ( precedes @ SV58 @ SV52 @ SV16 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY207: $i] :
~ ~ ( ~ ( sequential @ SV50 @ SY207 )
| ~ ( precedes @ SY207 @ SV52 @ SV16 ) )
| ( sequential @ SV50 @ SV52 ) ) )
= $true )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[472]) ).
thf(484,plain,
! [SV44: $i,SV31: $i] :
( ( ( ~ ( ~ ( ~ ~ ( ( SV31
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) )
| ~ ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) ) )
| ~ ( ~ ~ ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) )
| ~ ( ( SV31
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) ) ) ) )
= $false )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[474]) ).
thf(485,plain,
! [SV34: $i,SV20: $i,SV6: $i,SV56: $i] :
( ( ( edge @ SV56 )
= $false )
| ( ( SV6
!= ( tail_of @ SV56 ) )
= $true )
| ( ( ~ ( ~ ( ( SV20
!= ( head_of @ SV56 ) )
| ( SV34
!= ( path_cons @ SV56 @ empty ) ) )
| ~ ! [SY213: $i] :
~ ~ ( ~ ( path @ ( head_of @ SV56 ) @ SV20 @ SY213 )
| ( SV34
!= ( path_cons @ SV56 @ SY213 ) ) ) ) )
= $true )
| ( ( vertex @ SV6 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV6 @ SV20 @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[475]) ).
thf(486,plain,
! [SV36: $i,SV22: $i,SV8: $i] :
( ( ( ~ ( edge @ SV8 ) )
= $false )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[476]) ).
thf(487,plain,
! [SV36: $i,SV8: $i,SV22: $i] :
( ( ( ~ ( edge @ SV22 ) )
= $false )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[476]) ).
thf(488,plain,
! [SV36: $i,SV22: $i,SV8: $i] :
( ( ( ~ ( edge @ SV8 ) )
= $true )
| ( ( ~ ( edge @ SV22 ) )
= $true )
| ( ( ~ ( edge @ SV36 ) )
= $true )
| ( ( ~ ( sequential @ SV8 @ SV22 ) )
= $true )
| ( ( ~ ( sequential @ SV22 @ SV36 ) )
= $true )
| ( ( ~ ( sequential @ SV36 @ SV8 ) )
= $true )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[477]) ).
thf(489,plain,
! [SV10: $i,SV38: $i,SV24: $i] :
( ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY209: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY209 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY209 ) ) )
| ~ ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) ) ) ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[478]) ).
thf(490,plain,
! [SV10: $i,SV24: $i,SV38: $i] :
( ( ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY209: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY209 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY209 ) ) )
| ~ ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) ) ) ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[478]) ).
thf(491,plain,
! [SV60: $i,SV10: $i,SV24: $i,SV38: $i] :
( ( ( ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SV60 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SV60 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY209: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY209 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY209 ) ) )
| ~ ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) ) ) ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[479]) ).
thf(492,plain,
! [SV48: $i,SV28: $i,SV14: $i,SV41: $i,SV47: $i,SV57: $i] :
( ( ( ( head_of @ SV57 )
= ( head_of @ SV47 ) )
= $false )
| ( ( ( tail_of @ SV57 )
= ( tail_of @ SV41 ) )
= $false )
| ( ( shortest_path @ SV14 @ SV28 @ SV48 )
= $false )
| ( ( precedes @ SV41 @ SV47 @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[480]) ).
thf(493,plain,
! [SV42: $i,SV29: $i,SV15: $i,SV51: $i,SV59: $i,SV49: $i] :
( ( ( ~ ( sequential @ SV49 @ SV59 )
| ~ ( precedes @ SV59 @ SV51 @ SV15 ) )
= $true )
| ( ( on_path @ SV49 @ SV15 )
= $false )
| ( ( on_path @ SV51 @ SV15 )
= $false )
| ( ( precedes @ SV49 @ SV51 @ SV15 )
= $true )
| ( ( path @ SV29 @ SV42 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[481]) ).
thf(494,plain,
! [SV43: $i,SV30: $i,SV16: $i,SV52: $i,SV50: $i] :
( ( ( ! [SY207: $i] :
~ ~ ( ~ ( sequential @ SV50 @ SY207 )
| ~ ( precedes @ SY207 @ SV52 @ SV16 ) ) )
= $false )
| ( ( sequential @ SV50 @ SV52 )
= $true )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[482]) ).
thf(495,plain,
! [SV43: $i,SV30: $i,SV16: $i,SV52: $i,SV58: $i,SV50: $i] :
( ( ( ~ ( sequential @ SV50 @ SV58 ) )
= $true )
| ( ( ~ ( precedes @ SV58 @ SV52 @ SV16 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY207: $i] :
~ ~ ( ~ ( sequential @ SV50 @ SY207 )
| ~ ( precedes @ SY207 @ SV52 @ SV16 ) )
| ( sequential @ SV50 @ SV52 ) ) )
= $true )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[483]) ).
thf(496,plain,
! [SV44: $i,SV31: $i] :
( ( ( ~ ( ~ ~ ( ( SV31
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) )
| ~ ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) ) )
| ~ ( ~ ~ ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) )
| ~ ( ( SV31
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) ) ) )
= $true )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[484]) ).
thf(497,plain,
! [SV34: $i,SV20: $i,SV56: $i,SV6: $i] :
( ( ( SV6
= ( tail_of @ SV56 ) )
= $false )
| ( ( edge @ SV56 )
= $false )
| ( ( ~ ( ~ ( ( SV20
!= ( head_of @ SV56 ) )
| ( SV34
!= ( path_cons @ SV56 @ empty ) ) )
| ~ ! [SY213: $i] :
~ ~ ( ~ ( path @ ( head_of @ SV56 ) @ SV20 @ SY213 )
| ( SV34
!= ( path_cons @ SV56 @ SY213 ) ) ) ) )
= $true )
| ( ( vertex @ SV6 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV6 @ SV20 @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[485]) ).
thf(498,plain,
! [SV36: $i,SV22: $i,SV8: $i] :
( ( ( edge @ SV8 )
= $true )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[486]) ).
thf(499,plain,
! [SV36: $i,SV8: $i,SV22: $i] :
( ( ( edge @ SV22 )
= $true )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[487]) ).
thf(500,plain,
! [SV36: $i,SV22: $i,SV8: $i] :
( ( ( edge @ SV8 )
= $false )
| ( ( ~ ( edge @ SV22 ) )
= $true )
| ( ( ~ ( edge @ SV36 ) )
= $true )
| ( ( ~ ( sequential @ SV8 @ SV22 ) )
= $true )
| ( ( ~ ( sequential @ SV22 @ SV36 ) )
= $true )
| ( ( ~ ( sequential @ SV36 @ SV8 ) )
= $true )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[488]) ).
thf(501,plain,
! [SV10: $i,SV38: $i,SV24: $i] :
( ( ( SV24
= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY209: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY209 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY209 ) ) )
| ~ ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) ) ) ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[489]) ).
thf(502,plain,
! [SV10: $i,SV24: $i,SV38: $i] :
( ( ( SV38
= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY209: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY209 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY209 ) ) )
| ~ ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) ) ) ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[490]) ).
thf(503,plain,
! [SV60: $i,SV10: $i,SV24: $i,SV38: $i] :
( ( ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SV60 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SV60 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY209: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY209 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY209 ) ) )
| ~ ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) ) ) ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[491]) ).
thf(504,plain,
! [SV42: $i,SV29: $i,SV15: $i,SV51: $i,SV59: $i,SV49: $i] :
( ( ( ~ ( sequential @ SV49 @ SV59 ) )
= $true )
| ( ( ~ ( precedes @ SV59 @ SV51 @ SV15 ) )
= $true )
| ( ( on_path @ SV49 @ SV15 )
= $false )
| ( ( on_path @ SV51 @ SV15 )
= $false )
| ( ( precedes @ SV49 @ SV51 @ SV15 )
= $true )
| ( ( path @ SV29 @ SV42 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[493]) ).
thf(505,plain,
! [SV52: $i,SV16: $i,SV30: $i,SV43: $i,SV50: $i] :
( ( ( ~ ~ ( ~ ( sequential @ SV50 @ ( sK12_SY207 @ SV43 @ SV30 @ SV16 @ SV52 @ SV50 ) )
| ~ ( precedes @ ( sK12_SY207 @ SV43 @ SV30 @ SV16 @ SV52 @ SV50 ) @ SV52 @ SV16 ) ) )
= $false )
| ( ( sequential @ SV50 @ SV52 )
= $true )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[494]) ).
thf(506,plain,
! [SV43: $i,SV30: $i,SV16: $i,SV52: $i,SV58: $i,SV50: $i] :
( ( ( sequential @ SV50 @ SV58 )
= $false )
| ( ( ~ ( precedes @ SV58 @ SV52 @ SV16 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY207: $i] :
~ ~ ( ~ ( sequential @ SV50 @ SY207 )
| ~ ( precedes @ SY207 @ SV52 @ SV16 ) )
| ( sequential @ SV50 @ SV52 ) ) )
= $true )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[495]) ).
thf(507,plain,
! [SV44: $i,SV31: $i] :
( ( ( ~ ( ~ ~ ( ( SV31
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) )
| ~ ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) )
| ~ ( ( SV31
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) ) ) )
= $true )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[496]) ).
thf(508,plain,
! [SV6: $i,SV34: $i,SV56: $i,SV20: $i] :
( ( ( ~ ( ( SV20
!= ( head_of @ SV56 ) )
| ( SV34
!= ( path_cons @ SV56 @ empty ) ) )
| ~ ! [SY213: $i] :
~ ~ ( ~ ( path @ ( head_of @ SV56 ) @ SV20 @ SY213 )
| ( SV34
!= ( path_cons @ SV56 @ SY213 ) ) ) )
= $false )
| ( ( edge @ SV56 )
= $false )
| ( ( SV6
= ( tail_of @ SV56 ) )
= $false )
| ( ( vertex @ SV6 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV6 @ SV20 @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[497]) ).
thf(509,plain,
! [SV36: $i,SV8: $i,SV22: $i] :
( ( ( edge @ SV22 )
= $false )
| ( ( edge @ SV8 )
= $false )
| ( ( ~ ( edge @ SV36 ) )
= $true )
| ( ( ~ ( sequential @ SV8 @ SV22 ) )
= $true )
| ( ( ~ ( sequential @ SV22 @ SV36 ) )
= $true )
| ( ( ~ ( sequential @ SV36 @ SV8 ) )
= $true )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[500]) ).
thf(510,plain,
! [SV10: $i,SV24: $i,SV38: $i] :
( ( ( ~ ~ ! [SY209: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY209 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY209 ) ) )
| ~ ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) ) ) )
= $false )
| ( ( SV24
= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[501]) ).
thf(511,plain,
! [SV10: $i,SV24: $i,SV38: $i] :
( ( ( ~ ~ ! [SY209: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY209 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY209 ) ) )
| ~ ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) ) ) )
= $false )
| ( ( SV38
= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[502]) ).
thf(512,plain,
! [SV60: $i,SV10: $i,SV24: $i,SV38: $i] :
( ( ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SV60 ) )
= $true )
| ( ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SV60 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY209: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY209 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY209 ) ) )
| ~ ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) ) ) ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[503]) ).
thf(513,plain,
! [SV42: $i,SV29: $i,SV15: $i,SV51: $i,SV59: $i,SV49: $i] :
( ( ( sequential @ SV49 @ SV59 )
= $false )
| ( ( ~ ( precedes @ SV59 @ SV51 @ SV15 ) )
= $true )
| ( ( on_path @ SV49 @ SV15 )
= $false )
| ( ( on_path @ SV51 @ SV15 )
= $false )
| ( ( precedes @ SV49 @ SV51 @ SV15 )
= $true )
| ( ( path @ SV29 @ SV42 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[504]) ).
thf(514,plain,
! [SV52: $i,SV16: $i,SV30: $i,SV43: $i,SV50: $i] :
( ( ( ~ ( ~ ( sequential @ SV50 @ ( sK12_SY207 @ SV43 @ SV30 @ SV16 @ SV52 @ SV50 ) )
| ~ ( precedes @ ( sK12_SY207 @ SV43 @ SV30 @ SV16 @ SV52 @ SV50 ) @ SV52 @ SV16 ) ) )
= $true )
| ( ( sequential @ SV50 @ SV52 )
= $true )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[505]) ).
thf(515,plain,
! [SV43: $i,SV30: $i,SV50: $i,SV16: $i,SV52: $i,SV58: $i] :
( ( ( precedes @ SV58 @ SV52 @ SV16 )
= $false )
| ( ( sequential @ SV50 @ SV58 )
= $false )
| ( ( ~ ( ~ ~ ! [SY207: $i] :
~ ~ ( ~ ( sequential @ SV50 @ SY207 )
| ~ ( precedes @ SY207 @ SV52 @ SV16 ) )
| ( sequential @ SV50 @ SV52 ) ) )
= $true )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[506]) ).
thf(516,plain,
! [SV44: $i,SV31: $i] :
( ( ( ~ ~ ( ( SV31
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) )
| ~ ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) )
| ~ ( ( SV31
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) ) ) )
= $true )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[507]) ).
thf(517,plain,
! [SV6: $i,SV34: $i,SV56: $i,SV20: $i] :
( ( ( ~ ( ( SV20
!= ( head_of @ SV56 ) )
| ( SV34
!= ( path_cons @ SV56 @ empty ) ) ) )
= $false )
| ( ( edge @ SV56 )
= $false )
| ( ( SV6
= ( tail_of @ SV56 ) )
= $false )
| ( ( vertex @ SV6 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV6 @ SV20 @ SV34 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[508]) ).
thf(518,plain,
! [SV6: $i,SV34: $i,SV20: $i,SV56: $i] :
( ( ( ~ ! [SY213: $i] :
~ ~ ( ~ ( path @ ( head_of @ SV56 ) @ SV20 @ SY213 )
| ( SV34
!= ( path_cons @ SV56 @ SY213 ) ) ) )
= $false )
| ( ( edge @ SV56 )
= $false )
| ( ( SV6
= ( tail_of @ SV56 ) )
= $false )
| ( ( vertex @ SV6 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV6 @ SV20 @ SV34 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[508]) ).
thf(519,plain,
! [SV22: $i,SV8: $i,SV36: $i] :
( ( ( edge @ SV36 )
= $false )
| ( ( edge @ SV8 )
= $false )
| ( ( edge @ SV22 )
= $false )
| ( ( ~ ( sequential @ SV8 @ SV22 ) )
= $true )
| ( ( ~ ( sequential @ SV22 @ SV36 ) )
= $true )
| ( ( ~ ( sequential @ SV36 @ SV8 ) )
= $true )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[509]) ).
thf(520,plain,
! [SV10: $i,SV24: $i,SV38: $i] :
( ( ( ~ ~ ! [SY209: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY209 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY209 ) ) ) )
= $false )
| ( ( SV24
= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[510]) ).
thf(521,plain,
! [SV10: $i,SV38: $i,SV24: $i] :
( ( ( ~ ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) ) ) )
= $false )
| ( ( SV24
= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[510]) ).
thf(522,plain,
! [SV10: $i,SV24: $i,SV38: $i] :
( ( ( ~ ~ ! [SY209: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY209 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY209 ) ) ) )
= $false )
| ( ( SV38
= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[511]) ).
thf(523,plain,
! [SV10: $i,SV38: $i,SV24: $i] :
( ( ( ~ ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) ) ) )
= $false )
| ( ( SV38
= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[511]) ).
thf(524,plain,
! [SV60: $i,SV10: $i,SV24: $i,SV38: $i] :
( ( ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SV60 )
= $false )
| ( ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SV60 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY209: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY209 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY209 ) ) )
| ~ ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) ) ) ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[512]) ).
thf(525,plain,
! [SV42: $i,SV29: $i,SV49: $i,SV15: $i,SV51: $i,SV59: $i] :
( ( ( precedes @ SV59 @ SV51 @ SV15 )
= $false )
| ( ( sequential @ SV49 @ SV59 )
= $false )
| ( ( on_path @ SV49 @ SV15 )
= $false )
| ( ( on_path @ SV51 @ SV15 )
= $false )
| ( ( precedes @ SV49 @ SV51 @ SV15 )
= $true )
| ( ( path @ SV29 @ SV42 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[513]) ).
thf(526,plain,
! [SV52: $i,SV16: $i,SV30: $i,SV43: $i,SV50: $i] :
( ( ( ~ ( sequential @ SV50 @ ( sK12_SY207 @ SV43 @ SV30 @ SV16 @ SV52 @ SV50 ) )
| ~ ( precedes @ ( sK12_SY207 @ SV43 @ SV30 @ SV16 @ SV52 @ SV50 ) @ SV52 @ SV16 ) )
= $false )
| ( ( sequential @ SV50 @ SV52 )
= $true )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[514]) ).
thf(527,plain,
! [SV43: $i,SV30: $i,SV58: $i,SV16: $i,SV52: $i,SV50: $i] :
( ( ( ~ ~ ! [SY207: $i] :
~ ~ ( ~ ( sequential @ SV50 @ SY207 )
| ~ ( precedes @ SY207 @ SV52 @ SV16 ) )
| ( sequential @ SV50 @ SV52 ) )
= $false )
| ( ( sequential @ SV50 @ SV58 )
= $false )
| ( ( precedes @ SV58 @ SV52 @ SV16 )
= $false )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[515]) ).
thf(528,plain,
! [SV44: $i,SV31: $i] :
( ( ( ~ ~ ( ( SV31
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) )
| ~ ( ( SV31
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) ) ) )
= $true )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[516]) ).
thf(529,plain,
! [SV31: $i,SV44: $i] :
( ( ( ~ ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) )
| ~ ( ( SV31
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) ) ) )
= $true )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[516]) ).
thf(530,plain,
! [SV6: $i,SV34: $i,SV56: $i,SV20: $i] :
( ( ( ( SV20
!= ( head_of @ SV56 ) )
| ( SV34
!= ( path_cons @ SV56 @ empty ) ) )
= $true )
| ( ( edge @ SV56 )
= $false )
| ( ( SV6
= ( tail_of @ SV56 ) )
= $false )
| ( ( vertex @ SV6 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV6 @ SV20 @ SV34 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[517]) ).
thf(531,plain,
! [SV6: $i,SV34: $i,SV20: $i,SV56: $i] :
( ( ( ! [SY213: $i] :
~ ~ ( ~ ( path @ ( head_of @ SV56 ) @ SV20 @ SY213 )
| ( SV34
!= ( path_cons @ SV56 @ SY213 ) ) ) )
= $true )
| ( ( edge @ SV56 )
= $false )
| ( ( SV6
= ( tail_of @ SV56 ) )
= $false )
| ( ( vertex @ SV6 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV6 @ SV20 @ SV34 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[518]) ).
thf(532,plain,
! [SV36: $i,SV22: $i,SV8: $i] :
( ( ( sequential @ SV8 @ SV22 )
= $false )
| ( ( edge @ SV22 )
= $false )
| ( ( edge @ SV8 )
= $false )
| ( ( edge @ SV36 )
= $false )
| ( ( ~ ( sequential @ SV22 @ SV36 ) )
= $true )
| ( ( ~ ( sequential @ SV36 @ SV8 ) )
= $true )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[519]) ).
thf(533,plain,
! [SV10: $i,SV24: $i,SV38: $i] :
( ( ( ~ ! [SY209: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY209 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY209 ) ) ) )
= $true )
| ( ( SV24
= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[520]) ).
thf(534,plain,
! [SV10: $i,SV38: $i,SV24: $i] :
( ( ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) ) )
= $true )
| ( ( SV24
= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[521]) ).
thf(535,plain,
! [SV10: $i,SV24: $i,SV38: $i] :
( ( ( ~ ! [SY209: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY209 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY209 ) ) ) )
= $true )
| ( ( SV38
= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[522]) ).
thf(536,plain,
! [SV10: $i,SV38: $i,SV24: $i] :
( ( ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) ) )
= $true )
| ( ( SV38
= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[523]) ).
thf(537,plain,
! [SV60: $i,SV10: $i,SV24: $i,SV38: $i] :
( ( ( SV38
= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SV60 ) )
= $false )
| ( ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SV60 )
= $false )
| ( ( ~ ( ~ ~ ! [SY209: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY209 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY209 ) ) )
| ~ ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) ) ) ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[524]) ).
thf(538,plain,
! [SV52: $i,SV16: $i,SV30: $i,SV43: $i,SV50: $i] :
( ( ( ~ ( sequential @ SV50 @ ( sK12_SY207 @ SV43 @ SV30 @ SV16 @ SV52 @ SV50 ) ) )
= $false )
| ( ( sequential @ SV50 @ SV52 )
= $true )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[526]) ).
thf(539,plain,
! [SV50: $i,SV52: $i,SV16: $i,SV30: $i,SV43: $i] :
( ( ( ~ ( precedes @ ( sK12_SY207 @ SV43 @ SV30 @ SV16 @ SV52 @ SV50 ) @ SV52 @ SV16 ) )
= $false )
| ( ( sequential @ SV50 @ SV52 )
= $true )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[526]) ).
thf(540,plain,
! [SV43: $i,SV30: $i,SV58: $i,SV16: $i,SV52: $i,SV50: $i] :
( ( ( ~ ~ ! [SY207: $i] :
~ ~ ( ~ ( sequential @ SV50 @ SY207 )
| ~ ( precedes @ SY207 @ SV52 @ SV16 ) ) )
= $false )
| ( ( sequential @ SV50 @ SV58 )
= $false )
| ( ( precedes @ SV58 @ SV52 @ SV16 )
= $false )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[527]) ).
thf(541,plain,
! [SV43: $i,SV30: $i,SV16: $i,SV58: $i,SV52: $i,SV50: $i] :
( ( ( sequential @ SV50 @ SV52 )
= $false )
| ( ( sequential @ SV50 @ SV58 )
= $false )
| ( ( precedes @ SV58 @ SV52 @ SV16 )
= $false )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[527]) ).
thf(542,plain,
! [SV44: $i,SV31: $i] :
( ( ( ~ ( ( SV31
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) )
| ~ ( ( SV31
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) ) ) )
= $true )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[528]) ).
thf(543,plain,
! [SV31: $i,SV44: $i] :
( ( ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) )
| ~ ( ( SV31
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) ) ) )
= $true )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[529]) ).
thf(544,plain,
! [SV6: $i,SV34: $i,SV56: $i,SV20: $i] :
( ( ( SV20
!= ( head_of @ SV56 ) )
= $true )
| ( ( SV34
!= ( path_cons @ SV56 @ empty ) )
= $true )
| ( ( edge @ SV56 )
= $false )
| ( ( SV6
= ( tail_of @ SV56 ) )
= $false )
| ( ( vertex @ SV6 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV6 @ SV20 @ SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[530]) ).
thf(545,plain,
! [SV6: $i,SV34: $i,SV61: $i,SV20: $i,SV56: $i] :
( ( ( ~ ~ ( ~ ( path @ ( head_of @ SV56 ) @ SV20 @ SV61 )
| ( SV34
!= ( path_cons @ SV56 @ SV61 ) ) ) )
= $true )
| ( ( edge @ SV56 )
= $false )
| ( ( SV6
= ( tail_of @ SV56 ) )
= $false )
| ( ( vertex @ SV6 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV6 @ SV20 @ SV34 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(546,plain,
! [SV8: $i,SV36: $i,SV22: $i] :
( ( ( sequential @ SV22 @ SV36 )
= $false )
| ( ( edge @ SV36 )
= $false )
| ( ( edge @ SV8 )
= $false )
| ( ( edge @ SV22 )
= $false )
| ( ( sequential @ SV8 @ SV22 )
= $false )
| ( ( ~ ( sequential @ SV36 @ SV8 ) )
= $true )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[532]) ).
thf(547,plain,
! [SV10: $i,SV24: $i,SV38: $i] :
( ( ( ! [SY209: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY209 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY209 ) ) ) )
= $false )
| ( ( SV24
= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[533]) ).
thf(548,plain,
! [SV10: $i,SV38: $i,SV24: $i] :
( ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
= $true )
| ( ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) )
= $true )
| ( ( SV24
= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[534]) ).
thf(549,plain,
! [SV10: $i,SV24: $i,SV38: $i] :
( ( ( ! [SY209: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY209 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY209 ) ) ) )
= $false )
| ( ( SV38
= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[535]) ).
thf(550,plain,
! [SV10: $i,SV38: $i,SV24: $i] :
( ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
= $true )
| ( ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) )
= $true )
| ( ( SV38
= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[536]) ).
thf(551,plain,
! [SV60: $i,SV10: $i,SV24: $i,SV38: $i] :
( ( ( ~ ~ ! [SY209: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY209 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY209 ) ) )
| ~ ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) ) ) )
= $false )
| ( ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SV60 )
= $false )
| ( ( SV38
= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SV60 ) )
= $false )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[537]) ).
thf(552,plain,
! [SV52: $i,SV16: $i,SV30: $i,SV43: $i,SV50: $i] :
( ( ( sequential @ SV50 @ ( sK12_SY207 @ SV43 @ SV30 @ SV16 @ SV52 @ SV50 ) )
= $true )
| ( ( sequential @ SV50 @ SV52 )
= $true )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[538]) ).
thf(553,plain,
! [SV50: $i,SV52: $i,SV16: $i,SV30: $i,SV43: $i] :
( ( ( precedes @ ( sK12_SY207 @ SV43 @ SV30 @ SV16 @ SV52 @ SV50 ) @ SV52 @ SV16 )
= $true )
| ( ( sequential @ SV50 @ SV52 )
= $true )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[539]) ).
thf(554,plain,
! [SV43: $i,SV30: $i,SV58: $i,SV16: $i,SV52: $i,SV50: $i] :
( ( ( ~ ! [SY207: $i] :
~ ~ ( ~ ( sequential @ SV50 @ SY207 )
| ~ ( precedes @ SY207 @ SV52 @ SV16 ) ) )
= $true )
| ( ( sequential @ SV50 @ SV58 )
= $false )
| ( ( precedes @ SV58 @ SV52 @ SV16 )
= $false )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[540]) ).
thf(555,plain,
! [SV44: $i,SV31: $i] :
( ( ( ( SV31
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) )
| ~ ( ( SV31
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) ) ) )
= $true )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[542]) ).
thf(556,plain,
! [SV31: $i,SV44: $i] :
( ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $true )
| ( ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) )
| ~ ( ( SV31
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) ) ) )
= $true )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[543]) ).
thf(557,plain,
! [SV6: $i,SV34: $i,SV56: $i,SV20: $i] :
( ( ( SV20
= ( head_of @ SV56 ) )
= $false )
| ( ( SV34
!= ( path_cons @ SV56 @ empty ) )
= $true )
| ( ( edge @ SV56 )
= $false )
| ( ( SV6
= ( tail_of @ SV56 ) )
= $false )
| ( ( vertex @ SV6 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV6 @ SV20 @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[544]) ).
thf(558,plain,
! [SV6: $i,SV34: $i,SV61: $i,SV20: $i,SV56: $i] :
( ( ( ~ ( ~ ( path @ ( head_of @ SV56 ) @ SV20 @ SV61 )
| ( SV34
!= ( path_cons @ SV56 @ SV61 ) ) ) )
= $false )
| ( ( edge @ SV56 )
= $false )
| ( ( SV6
= ( tail_of @ SV56 ) )
= $false )
| ( ( vertex @ SV6 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV6 @ SV20 @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[545]) ).
thf(559,plain,
! [SV22: $i,SV8: $i,SV36: $i] :
( ( ( sequential @ SV36 @ SV8 )
= $false )
| ( ( sequential @ SV8 @ SV22 )
= $false )
| ( ( edge @ SV22 )
= $false )
| ( ( edge @ SV8 )
= $false )
| ( ( edge @ SV36 )
= $false )
| ( ( sequential @ SV22 @ SV36 )
= $false )
| ( ( triangle @ SV8 @ SV22 @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[546]) ).
thf(560,plain,
! [SV10: $i,SV24: $i,SV38: $i] :
( ( ( ~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ ( sK13_SY209 @ SV10 @ SV24 @ SV38 ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ ( sK13_SY209 @ SV10 @ SV24 @ SV38 ) ) ) ) )
= $false )
| ( ( SV24
= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[547]) ).
thf(561,plain,
! [SV10: $i,SV38: $i,SV24: $i] :
( ( ( SV24
= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
= $false )
| ( ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) )
= $true )
| ( ( SV24
= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[548]) ).
thf(562,plain,
! [SV10: $i,SV24: $i,SV38: $i] :
( ( ( ~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ ( sK14_SY209 @ SV10 @ SV24 @ SV38 ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ ( sK14_SY209 @ SV10 @ SV24 @ SV38 ) ) ) ) )
= $false )
| ( ( SV38
= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[549]) ).
thf(563,plain,
! [SV10: $i,SV38: $i,SV24: $i] :
( ( ( SV24
= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
= $false )
| ( ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) )
= $true )
| ( ( SV38
= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[550]) ).
thf(564,plain,
! [SV60: $i,SV10: $i,SV24: $i,SV38: $i] :
( ( ( ~ ~ ! [SY209: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY209 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY209 ) ) ) )
= $false )
| ( ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SV60 )
= $false )
| ( ( SV38
= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SV60 ) )
= $false )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[551]) ).
thf(565,plain,
! [SV60: $i,SV10: $i,SV38: $i,SV24: $i] :
( ( ( ~ ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) ) ) )
= $false )
| ( ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SV60 )
= $false )
| ( ( SV38
= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SV60 ) )
= $false )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[551]) ).
thf(566,plain,
! [SV43: $i,SV30: $i,SV58: $i,SV16: $i,SV52: $i,SV50: $i] :
( ( ( ! [SY207: $i] :
~ ~ ( ~ ( sequential @ SV50 @ SY207 )
| ~ ( precedes @ SY207 @ SV52 @ SV16 ) ) )
= $false )
| ( ( sequential @ SV50 @ SV58 )
= $false )
| ( ( precedes @ SV58 @ SV52 @ SV16 )
= $false )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[554]) ).
thf(567,plain,
! [SV44: $i,SV31: $i] :
( ( ( SV31
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) )
| ~ ( ( SV31
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) ) ) )
= $true )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[555]) ).
thf(568,plain,
! [SV31: $i,SV44: $i] :
( ( ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) )
| ~ ( ( SV31
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) ) ) )
= $true )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[555]) ).
thf(569,plain,
! [SV31: $i,SV44: $i] :
( ( ( SV44
= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) )
| ~ ( ( SV31
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) ) ) )
= $true )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[556]) ).
thf(570,plain,
! [SV6: $i,SV20: $i,SV56: $i,SV34: $i] :
( ( ( SV34
= ( path_cons @ SV56 @ empty ) )
= $false )
| ( ( SV20
= ( head_of @ SV56 ) )
= $false )
| ( ( edge @ SV56 )
= $false )
| ( ( SV6
= ( tail_of @ SV56 ) )
= $false )
| ( ( vertex @ SV6 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV6 @ SV20 @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[557]) ).
thf(571,plain,
! [SV6: $i,SV34: $i,SV61: $i,SV20: $i,SV56: $i] :
( ( ( ~ ( path @ ( head_of @ SV56 ) @ SV20 @ SV61 )
| ( SV34
!= ( path_cons @ SV56 @ SV61 ) ) )
= $true )
| ( ( edge @ SV56 )
= $false )
| ( ( SV6
= ( tail_of @ SV56 ) )
= $false )
| ( ( vertex @ SV6 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV6 @ SV20 @ SV34 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[558]) ).
thf(572,plain,
! [SV10: $i,SV24: $i,SV38: $i] :
( ( ( ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ ( sK13_SY209 @ SV10 @ SV24 @ SV38 ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ ( sK13_SY209 @ SV10 @ SV24 @ SV38 ) ) ) ) )
= $true )
| ( ( SV24
= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[560]) ).
thf(573,plain,
! [SV10: $i,SV24: $i,SV38: $i] :
( ( ( SV38
= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) )
= $false )
| ( ( SV24
= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
= $false )
| ( ( SV24
= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[561]) ).
thf(574,plain,
! [SV10: $i,SV24: $i,SV38: $i] :
( ( ( ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ ( sK14_SY209 @ SV10 @ SV24 @ SV38 ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ ( sK14_SY209 @ SV10 @ SV24 @ SV38 ) ) ) ) )
= $true )
| ( ( SV38
= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[562]) ).
thf(575,plain,
! [SV10: $i,SV24: $i,SV38: $i] :
( ( ( SV38
= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) )
= $false )
| ( ( SV24
= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
= $false )
| ( ( SV38
= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[563]) ).
thf(576,plain,
! [SV60: $i,SV10: $i,SV24: $i,SV38: $i] :
( ( ( ~ ! [SY209: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY209 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY209 ) ) ) )
= $true )
| ( ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SV60 )
= $false )
| ( ( SV38
= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SV60 ) )
= $false )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[564]) ).
thf(577,plain,
! [SV60: $i,SV10: $i,SV38: $i,SV24: $i] :
( ( ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) ) )
= $true )
| ( ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SV60 )
= $false )
| ( ( SV38
= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SV60 ) )
= $false )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[565]) ).
thf(578,plain,
! [SV52: $i,SV16: $i,SV58: $i,SV30: $i,SV43: $i,SV50: $i] :
( ( ( ~ ~ ( ~ ( sequential @ SV50 @ ( sK15_SY207 @ SV43 @ SV30 @ SV58 @ SV16 @ SV52 @ SV50 ) )
| ~ ( precedes @ ( sK15_SY207 @ SV43 @ SV30 @ SV58 @ SV16 @ SV52 @ SV50 ) @ SV52 @ SV16 ) ) )
= $false )
| ( ( sequential @ SV50 @ SV58 )
= $false )
| ( ( precedes @ SV58 @ SV52 @ SV16 )
= $false )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[566]) ).
thf(579,plain,
! [SV44: $i,SV31: $i] :
( ( ( SV31
= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) )
| ~ ( ( SV31
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) ) ) )
= $true )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[567]) ).
thf(580,plain,
! [SV31: $i,SV44: $i] :
( ( ( SV44
= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) )
| ~ ( ( SV31
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) ) ) )
= $true )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[568]) ).
thf(581,plain,
! [SV44: $i,SV31: $i] :
( ( ( SV31
= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( SV44
= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) )
| ~ ( ( SV31
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) ) ) )
= $true )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[569]) ).
thf(582,plain,
! [SV6: $i,SV34: $i,SV61: $i,SV20: $i,SV56: $i] :
( ( ( ~ ( path @ ( head_of @ SV56 ) @ SV20 @ SV61 ) )
= $true )
| ( ( SV34
!= ( path_cons @ SV56 @ SV61 ) )
= $true )
| ( ( edge @ SV56 )
= $false )
| ( ( SV6
= ( tail_of @ SV56 ) )
= $false )
| ( ( vertex @ SV6 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV6 @ SV20 @ SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[571]) ).
thf(583,plain,
! [SV10: $i,SV24: $i,SV38: $i] :
( ( ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ ( sK13_SY209 @ SV10 @ SV24 @ SV38 ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ ( sK13_SY209 @ SV10 @ SV24 @ SV38 ) ) ) )
= $false )
| ( ( SV24
= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[572]) ).
thf(584,plain,
! [SV10: $i,SV24: $i,SV38: $i] :
( ( ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ ( sK14_SY209 @ SV10 @ SV24 @ SV38 ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ ( sK14_SY209 @ SV10 @ SV24 @ SV38 ) ) ) )
= $false )
| ( ( SV38
= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[574]) ).
thf(585,plain,
! [SV60: $i,SV10: $i,SV24: $i,SV38: $i] :
( ( ( ! [SY209: $i] :
~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SY209 )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SY209 ) ) ) )
= $false )
| ( ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SV60 )
= $false )
| ( ( SV38
= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SV60 ) )
= $false )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[576]) ).
thf(586,plain,
! [SV60: $i,SV10: $i,SV38: $i,SV24: $i] :
( ( ( SV24
!= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
= $true )
| ( ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) )
= $true )
| ( ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SV60 )
= $false )
| ( ( SV38
= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SV60 ) )
= $false )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[577]) ).
thf(587,plain,
! [SV52: $i,SV16: $i,SV58: $i,SV30: $i,SV43: $i,SV50: $i] :
( ( ( ~ ( ~ ( sequential @ SV50 @ ( sK15_SY207 @ SV43 @ SV30 @ SV58 @ SV16 @ SV52 @ SV50 ) )
| ~ ( precedes @ ( sK15_SY207 @ SV43 @ SV30 @ SV58 @ SV16 @ SV52 @ SV50 ) @ SV52 @ SV16 ) ) )
= $true )
| ( ( sequential @ SV50 @ SV58 )
= $false )
| ( ( precedes @ SV58 @ SV52 @ SV16 )
= $false )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[578]) ).
thf(588,plain,
! [SV31: $i,SV44: $i] :
( ( ( ~ ~ ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) )
| ~ ( ( SV31
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) ) )
= $false )
| ( ( SV31
= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $true )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[579]) ).
thf(589,plain,
! [SV31: $i,SV44: $i] :
( ( ( ~ ~ ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) )
| ~ ( ( SV31
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) ) )
= $false )
| ( ( SV44
= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $true )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[580]) ).
thf(590,plain,
! [SV31: $i,SV44: $i] :
( ( ( ~ ~ ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) )
| ~ ( ( SV31
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) ) )
= $false )
| ( ( SV44
= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( SV31
= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[581]) ).
thf(591,plain,
! [SV6: $i,SV34: $i,SV61: $i,SV20: $i,SV56: $i] :
( ( ( path @ ( head_of @ SV56 ) @ SV20 @ SV61 )
= $false )
| ( ( SV34
!= ( path_cons @ SV56 @ SV61 ) )
= $true )
| ( ( edge @ SV56 )
= $false )
| ( ( SV6
= ( tail_of @ SV56 ) )
= $false )
| ( ( vertex @ SV6 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV6 @ SV20 @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[582]) ).
thf(592,plain,
! [SV10: $i,SV24: $i,SV38: $i] :
( ( ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ ( sK13_SY209 @ SV10 @ SV24 @ SV38 ) ) )
= $false )
| ( ( SV24
= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[583]) ).
thf(593,plain,
! [SV10: $i,SV24: $i,SV38: $i] :
( ( ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ ( sK13_SY209 @ SV10 @ SV24 @ SV38 ) ) )
= $false )
| ( ( SV24
= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[583]) ).
thf(594,plain,
! [SV10: $i,SV24: $i,SV38: $i] :
( ( ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ ( sK14_SY209 @ SV10 @ SV24 @ SV38 ) ) )
= $false )
| ( ( SV38
= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[584]) ).
thf(595,plain,
! [SV10: $i,SV24: $i,SV38: $i] :
( ( ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ ( sK14_SY209 @ SV10 @ SV24 @ SV38 ) ) )
= $false )
| ( ( SV38
= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[584]) ).
thf(596,plain,
! [SV60: $i,SV10: $i,SV24: $i,SV38: $i] :
( ( ( ~ ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ ( sK16_SY209 @ SV60 @ SV10 @ SV24 @ SV38 ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ ( sK16_SY209 @ SV60 @ SV10 @ SV24 @ SV38 ) ) ) ) )
= $false )
| ( ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SV60 )
= $false )
| ( ( SV38
= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SV60 ) )
= $false )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[585]) ).
thf(597,plain,
! [SV60: $i,SV10: $i,SV38: $i,SV24: $i] :
( ( ( SV24
= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
= $false )
| ( ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) )
= $true )
| ( ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SV60 )
= $false )
| ( ( SV38
= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SV60 ) )
= $false )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[586]) ).
thf(598,plain,
! [SV52: $i,SV16: $i,SV58: $i,SV30: $i,SV43: $i,SV50: $i] :
( ( ( ~ ( sequential @ SV50 @ ( sK15_SY207 @ SV43 @ SV30 @ SV58 @ SV16 @ SV52 @ SV50 ) )
| ~ ( precedes @ ( sK15_SY207 @ SV43 @ SV30 @ SV58 @ SV16 @ SV52 @ SV50 ) @ SV52 @ SV16 ) )
= $false )
| ( ( sequential @ SV50 @ SV58 )
= $false )
| ( ( precedes @ SV58 @ SV52 @ SV16 )
= $false )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[587]) ).
thf(599,plain,
! [SV31: $i,SV44: $i] :
( ( ( ~ ~ ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) ) )
= $false )
| ( ( SV31
= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $true )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[588]) ).
thf(600,plain,
! [SV44: $i,SV31: $i] :
( ( ( ~ ( ( SV31
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) ) )
= $false )
| ( ( SV31
= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $true )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[588]) ).
thf(601,plain,
! [SV31: $i,SV44: $i] :
( ( ( ~ ~ ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) ) )
= $false )
| ( ( SV44
= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $true )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[589]) ).
thf(602,plain,
! [SV44: $i,SV31: $i] :
( ( ( ~ ( ( SV31
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) ) )
= $false )
| ( ( SV44
= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $true )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[589]) ).
thf(603,plain,
! [SV31: $i,SV44: $i] :
( ( ( ~ ~ ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) ) )
= $false )
| ( ( SV44
= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( SV31
= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[590]) ).
thf(604,plain,
! [SV44: $i,SV31: $i] :
( ( ( ~ ( ( SV31
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) ) )
= $false )
| ( ( SV44
= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( SV31
= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[590]) ).
thf(605,plain,
! [SV6: $i,SV20: $i,SV61: $i,SV56: $i,SV34: $i] :
( ( ( SV34
= ( path_cons @ SV56 @ SV61 ) )
= $false )
| ( ( path @ ( head_of @ SV56 ) @ SV20 @ SV61 )
= $false )
| ( ( edge @ SV56 )
= $false )
| ( ( SV6
= ( tail_of @ SV56 ) )
= $false )
| ( ( vertex @ SV6 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV6 @ SV20 @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[591]) ).
thf(606,plain,
! [SV10: $i,SV24: $i,SV38: $i] :
( ( ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ ( sK13_SY209 @ SV10 @ SV24 @ SV38 ) )
= $true )
| ( ( SV24
= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[592]) ).
thf(607,plain,
! [SV10: $i,SV24: $i,SV38: $i] :
( ( ( SV38
= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ ( sK13_SY209 @ SV10 @ SV24 @ SV38 ) ) )
= $true )
| ( ( SV24
= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[593]) ).
thf(608,plain,
! [SV10: $i,SV24: $i,SV38: $i] :
( ( ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ ( sK14_SY209 @ SV10 @ SV24 @ SV38 ) )
= $true )
| ( ( SV38
= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[594]) ).
thf(609,plain,
! [SV10: $i,SV24: $i,SV38: $i] :
( ( ( SV38
= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ ( sK14_SY209 @ SV10 @ SV24 @ SV38 ) ) )
= $true )
| ( ( SV38
= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) )
= $true )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[595]) ).
thf(610,plain,
! [SV60: $i,SV10: $i,SV24: $i,SV38: $i] :
( ( ( ~ ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ ( sK16_SY209 @ SV60 @ SV10 @ SV24 @ SV38 ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ ( sK16_SY209 @ SV60 @ SV10 @ SV24 @ SV38 ) ) ) ) )
= $true )
| ( ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SV60 )
= $false )
| ( ( SV38
= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SV60 ) )
= $false )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[596]) ).
thf(611,plain,
! [SV60: $i,SV10: $i,SV24: $i,SV38: $i] :
( ( ( SV38
= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ empty ) )
= $false )
| ( ( SV24
= ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) )
= $false )
| ( ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SV60 )
= $false )
| ( ( SV38
= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SV60 ) )
= $false )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[597]) ).
thf(612,plain,
! [SV52: $i,SV16: $i,SV58: $i,SV30: $i,SV43: $i,SV50: $i] :
( ( ( ~ ( sequential @ SV50 @ ( sK15_SY207 @ SV43 @ SV30 @ SV58 @ SV16 @ SV52 @ SV50 ) ) )
= $false )
| ( ( sequential @ SV50 @ SV58 )
= $false )
| ( ( precedes @ SV58 @ SV52 @ SV16 )
= $false )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[598]) ).
thf(613,plain,
! [SV50: $i,SV52: $i,SV16: $i,SV58: $i,SV30: $i,SV43: $i] :
( ( ( ~ ( precedes @ ( sK15_SY207 @ SV43 @ SV30 @ SV58 @ SV16 @ SV52 @ SV50 ) @ SV52 @ SV16 ) )
= $false )
| ( ( sequential @ SV50 @ SV58 )
= $false )
| ( ( precedes @ SV58 @ SV52 @ SV16 )
= $false )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[598]) ).
thf(614,plain,
! [SV31: $i,SV44: $i] :
( ( ( ~ ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) ) )
= $true )
| ( ( SV31
= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $true )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[599]) ).
thf(615,plain,
! [SV44: $i,SV31: $i] :
( ( ( ( SV31
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) )
= $true )
| ( ( SV31
= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $true )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[600]) ).
thf(616,plain,
! [SV31: $i,SV44: $i] :
( ( ( ~ ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) ) )
= $true )
| ( ( SV44
= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $true )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[601]) ).
thf(617,plain,
! [SV44: $i,SV31: $i] :
( ( ( ( SV31
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) )
= $true )
| ( ( SV44
= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $true )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[602]) ).
thf(618,plain,
! [SV31: $i,SV44: $i] :
( ( ( ~ ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) ) )
= $true )
| ( ( SV44
= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( SV31
= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[603]) ).
thf(619,plain,
! [SV44: $i,SV31: $i] :
( ( ( ( SV31
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) )
= $true )
| ( ( SV44
= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( SV31
= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[604]) ).
thf(620,plain,
! [SV60: $i,SV10: $i,SV24: $i,SV38: $i] :
( ( ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ ( sK16_SY209 @ SV60 @ SV10 @ SV24 @ SV38 ) )
| ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ ( sK16_SY209 @ SV60 @ SV10 @ SV24 @ SV38 ) ) ) )
= $false )
| ( ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SV60 )
= $false )
| ( ( SV38
= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SV60 ) )
= $false )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[610]) ).
thf(621,plain,
! [SV52: $i,SV16: $i,SV58: $i,SV30: $i,SV43: $i,SV50: $i] :
( ( ( sequential @ SV50 @ ( sK15_SY207 @ SV43 @ SV30 @ SV58 @ SV16 @ SV52 @ SV50 ) )
= $true )
| ( ( sequential @ SV50 @ SV58 )
= $false )
| ( ( precedes @ SV58 @ SV52 @ SV16 )
= $false )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[612]) ).
thf(622,plain,
! [SV50: $i,SV52: $i,SV16: $i,SV58: $i,SV30: $i,SV43: $i] :
( ( ( precedes @ ( sK15_SY207 @ SV43 @ SV30 @ SV58 @ SV16 @ SV52 @ SV50 ) @ SV52 @ SV16 )
= $true )
| ( ( sequential @ SV50 @ SV58 )
= $false )
| ( ( precedes @ SV58 @ SV52 @ SV16 )
= $false )
| ( ( precedes @ SV50 @ SV52 @ SV16 )
= $false )
| ( ( path @ SV30 @ SV43 @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[613]) ).
thf(623,plain,
! [SV31: $i,SV44: $i] :
( ( ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) )
= $false )
| ( ( SV31
= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $true )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[614]) ).
thf(624,plain,
! [SV44: $i,SV31: $i] :
( ( ( SV31
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $true )
| ( ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $true )
| ( ( SV31
= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $true )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[615]) ).
thf(625,plain,
! [SV31: $i,SV44: $i] :
( ( ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) )
= $false )
| ( ( SV44
= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $true )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[616]) ).
thf(626,plain,
! [SV44: $i,SV31: $i] :
( ( ( SV31
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $true )
| ( ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $true )
| ( ( SV44
= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $true )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[617]) ).
thf(627,plain,
! [SV31: $i,SV44: $i] :
( ( ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
| ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) ) )
= $false )
| ( ( SV44
= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( SV31
= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[618]) ).
thf(628,plain,
! [SV44: $i,SV31: $i] :
( ( ( SV31
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $true )
| ( ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $true )
| ( ( SV44
= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( SV31
= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[619]) ).
thf(629,plain,
! [SV60: $i,SV10: $i,SV24: $i,SV38: $i] :
( ( ( ~ ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ ( sK16_SY209 @ SV60 @ SV10 @ SV24 @ SV38 ) ) )
= $false )
| ( ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SV60 )
= $false )
| ( ( SV38
= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SV60 ) )
= $false )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[620]) ).
thf(630,plain,
! [SV60: $i,SV10: $i,SV24: $i,SV38: $i] :
( ( ( SV38
!= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ ( sK16_SY209 @ SV60 @ SV10 @ SV24 @ SV38 ) ) )
= $false )
| ( ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SV60 )
= $false )
| ( ( SV38
= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SV60 ) )
= $false )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[620]) ).
thf(631,plain,
! [SV31: $i,SV44: $i] :
( ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( SV31
= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $true )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[623]) ).
thf(632,plain,
! [SV44: $i,SV31: $i] :
( ( ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( SV31
= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $true )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[623]) ).
thf(633,plain,
! [SV44: $i,SV31: $i] :
( ( ( SV31
= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $true )
| ( ( SV31
= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $true )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[624]) ).
thf(634,plain,
! [SV31: $i,SV44: $i] :
( ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( SV44
= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $true )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[625]) ).
thf(635,plain,
! [SV44: $i,SV31: $i] :
( ( ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( SV44
= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $true )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[625]) ).
thf(636,plain,
! [SV44: $i,SV31: $i] :
( ( ( SV31
= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $true )
| ( ( SV44
= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $true )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[626]) ).
thf(637,plain,
! [SV31: $i,SV44: $i] :
( ( ( SV44
!= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( SV44
= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( SV31
= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[627]) ).
thf(638,plain,
! [SV44: $i,SV31: $i] :
( ( ( SV31
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( SV44
= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( SV31
= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[627]) ).
thf(639,plain,
! [SV44: $i,SV31: $i] :
( ( ( SV31
= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( SV44
!= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $true )
| ( ( SV44
= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( SV31
= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[628]) ).
thf(640,plain,
! [SV60: $i,SV10: $i,SV24: $i,SV38: $i] :
( ( ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ ( sK16_SY209 @ SV60 @ SV10 @ SV24 @ SV38 ) )
= $true )
| ( ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SV60 )
= $false )
| ( ( SV38
= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SV60 ) )
= $false )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[629]) ).
thf(641,plain,
! [SV60: $i,SV10: $i,SV24: $i,SV38: $i] :
( ( ( SV38
= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ ( sK16_SY209 @ SV60 @ SV10 @ SV24 @ SV38 ) ) )
= $true )
| ( ( path @ ( head_of @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) ) @ SV24 @ SV60 )
= $false )
| ( ( SV38
= ( path_cons @ ( sK6_SY169 @ SV38 @ SV24 @ SV10 ) @ SV60 ) )
= $false )
| ( ( path @ SV10 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[630]) ).
thf(642,plain,
! [SV31: $i,SV44: $i] :
( ( ( SV44
= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $true )
| ( ( SV31
= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $true )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[631]) ).
thf(643,plain,
! [SV44: $i,SV31: $i] :
( ( ( SV31
= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $true )
| ( ( SV31
= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $true )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[632]) ).
thf(644,plain,
! [SV31: $i,SV44: $i] :
( ( ( SV44
= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( SV31
= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( SV31
= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $true )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[633]) ).
thf(645,plain,
! [SV31: $i,SV44: $i] :
( ( ( SV44
= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $true )
| ( ( SV44
= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $true )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[634]) ).
thf(646,plain,
! [SV44: $i,SV31: $i] :
( ( ( SV31
= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $true )
| ( ( SV44
= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $true )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[635]) ).
thf(647,plain,
! [SV31: $i,SV44: $i] :
( ( ( SV44
= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( SV31
= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( SV44
= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $true )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[636]) ).
thf(648,plain,
! [SV31: $i,SV44: $i] :
( ( ( SV44
= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $true )
| ( ( SV44
= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( SV31
= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[637]) ).
thf(649,plain,
! [SV44: $i,SV31: $i] :
( ( ( SV31
= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $true )
| ( ( SV44
= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( SV31
= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[638]) ).
thf(650,plain,
! [SV31: $i,SV44: $i] :
( ( ( SV44
= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( SV31
= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( SV44
= ( head_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( SV31
= ( tail_of @ ( sK10_SY189 @ SV44 @ SV31 ) ) )
= $false )
| ( ( vertex @ SV44 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( ( SV31 = SV44 )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[639]) ).
thf(651,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[58,650,649,648,647,646,645,644,643,642,641,640,622,621,611,609,608,607,606,605,575,573,570,559,553,552,541,525,499,498,492,473,471,467,463,461,459,452,451,443,441,435,415,414,412,403,400,399,390,389,385,384,382,380,379,378,363,350,345,339,337,318,316,305,282,275,274,272,256,183,174,173,165,158,134,95]) ).
thf(652,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[651]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRA009+2 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.16 % Computer : n017.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Tue Oct 6 10:17:45 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.62/1.86
% 9.62/1.86 No.of.Axioms: 17
% 9.62/1.86
% 9.62/1.86 Length.of.Defs: 0
% 9.62/1.86
% 9.62/1.86 Contains.Choice.Funs: false
% 9.62/1.86 ......................
% 9.62/1.86
% 9.62/1.86 ********************************
% 9.62/1.86 * All subproblems solved! *
% 9.62/1.86 ********************************
% 9.62/1.86 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:18,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:651,loop_count:0,foatp_calls:1,translation:fof_full)
% 9.62/1.86
% 9.62/1.86 %**** Beginning of derivation protocol ****
% 9.62/1.86 % SZS output start CNFRefutation
% See solution above
% 9.62/1.87
% 9.62/1.87 %**** End of derivation protocol ****
% 9.62/1.87 %**** no. of clauses in derivation: 652 ****
% 9.62/1.87 %**** clause counter: 651 ****
% 9.62/1.87
% 9.62/1.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:18,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:651,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------