TSTP Solution File: GRA003+1 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GRA003+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 07:19:13 EDT 2022
% Result : Theorem 1.81s 1.99s
% Output : CNFRefutation 7.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 55
% Syntax : Number of formulae : 3963 (1487 unt; 37 typ; 0 def)
% Number of atoms : 40771 (15662 equ; 0 cnn)
% Maximal formula atoms : 9 ( 10 avg)
% Number of connectives : 94404 (18807 ~;16963 |; 490 &;58088 @)
% ( 6 <=>; 40 =>; 4 <=; 6 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 54 ( 54 >; 0 *; 0 +; 0 <<)
% Number of symbols : 40 ( 37 usr; 14 con; 0-4 aty)
% Number of variables : 16676 ( 0 ^16656 !; 20 ?;16676 :)
% 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_E,type,
sK10_E: $i > $i > $i > $i > $i ).
thf(tp_sK11_E,type,
sK11_E: $i > $i > $i > $i ).
thf(tp_sK12_SY85,type,
sK12_SY85: $i > $i > $i > $i ).
thf(tp_sK13_SY84,type,
sK13_SY84: $i > $i > $i > $i ).
thf(tp_sK14_E,type,
sK14_E: $i > $i > $i ).
thf(tp_sK1_V1,type,
sK1_V1: $i ).
thf(tp_sK2_SY70,type,
sK2_SY70: $i ).
thf(tp_sK3_SY74,type,
sK3_SY74: $i ).
thf(tp_sK4_SY77,type,
sK4_SY77: $i ).
thf(tp_sK5_SY79,type,
sK5_SY79: $i ).
thf(tp_sK6_E1,type,
sK6_E1: $i > $i ).
thf(tp_sK7_SY80,type,
sK7_SY80: $i > $i ).
thf(tp_sK8_P,type,
sK8_P: $i > $i > $i > $i ).
thf(tp_sK9_E3,type,
sK9_E3: $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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',complete_properties) ).
thf(16,axiom,
! [E: $i] :
( ( edge @ E )
=> ( ( vertex @ ( head_of @ E ) )
& ( vertex @ ( tail_of @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',edge_ends_are_vertices) ).
thf(17,axiom,
! [E: $i] :
( ( edge @ E )
=> ( ( head_of @ E )
!= ( tail_of @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_loops) ).
thf(18,conjecture,
! [V1: $i,V2: $i,E1: $i,E2: $i,P: $i] :
( ( ( shortest_path @ V1 @ V2 @ P )
& ( precedes @ E1 @ E2 @ P ) )
=> ( ( vertex @ V1 )
& ( vertex @ V2 )
& ( V1 != V2 )
& ( edge @ E1 )
& ( edge @ E2 )
& ( E1 != E2 )
& ( path @ V1 @ V2 @ P ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',vertices_and_edges) ).
thf(19,negated_conjecture,
( ( ! [V1: $i,V2: $i,E1: $i,E2: $i,P: $i] :
( ( ( shortest_path @ V1 @ V2 @ P )
& ( precedes @ E1 @ E2 @ P ) )
=> ( ( vertex @ V1 )
& ( vertex @ V2 )
& ( V1 != V2 )
& ( edge @ E1 )
& ( edge @ E2 )
& ( E1 != E2 )
& ( path @ V1 @ V2 @ P ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[18]) ).
thf(20,plain,
( ( ! [V1: $i,V2: $i,E1: $i,E2: $i,P: $i] :
( ( ( shortest_path @ V1 @ V2 @ P )
& ( precedes @ E1 @ E2 @ P ) )
=> ( ( vertex @ V1 )
& ( vertex @ V2 )
& ( V1 != V2 )
& ( edge @ E1 )
& ( edge @ E2 )
& ( E1 != E2 )
& ( path @ V1 @ V2 @ P ) ) ) )
= $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,
( ( ! [SY70: $i,SY71: $i,SY72: $i,SY73: $i] :
( ( ( shortest_path @ sK1_V1 @ SY70 @ SY73 )
& ( precedes @ SY71 @ SY72 @ SY73 ) )
=> ( ( vertex @ sK1_V1 )
& ( vertex @ SY70 )
& ( sK1_V1 != SY70 )
& ( edge @ SY71 )
& ( edge @ SY72 )
& ( SY71 != SY72 )
& ( path @ sK1_V1 @ SY70 @ SY73 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[20]) ).
thf(39,plain,
( ( ! [SY74: $i,SY75: $i,SY76: $i] :
( ( ( shortest_path @ sK1_V1 @ sK2_SY70 @ SY76 )
& ( precedes @ SY74 @ SY75 @ SY76 ) )
=> ( ( vertex @ sK1_V1 )
& ( vertex @ sK2_SY70 )
& ( sK1_V1 != sK2_SY70 )
& ( edge @ SY74 )
& ( edge @ SY75 )
& ( SY74 != SY75 )
& ( path @ sK1_V1 @ sK2_SY70 @ SY76 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[38]) ).
thf(40,plain,
( ( ! [SY77: $i,SY78: $i] :
( ( ( shortest_path @ sK1_V1 @ sK2_SY70 @ SY78 )
& ( precedes @ sK3_SY74 @ SY77 @ SY78 ) )
=> ( ( vertex @ sK1_V1 )
& ( vertex @ sK2_SY70 )
& ( sK1_V1 != sK2_SY70 )
& ( edge @ sK3_SY74 )
& ( edge @ SY77 )
& ( sK3_SY74 != SY77 )
& ( path @ sK1_V1 @ sK2_SY70 @ SY78 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[39]) ).
thf(41,plain,
( ( ! [SY79: $i] :
( ( ( shortest_path @ sK1_V1 @ sK2_SY70 @ SY79 )
& ( precedes @ sK3_SY74 @ sK4_SY77 @ SY79 ) )
=> ( ( vertex @ sK1_V1 )
& ( vertex @ sK2_SY70 )
& ( sK1_V1 != sK2_SY70 )
& ( edge @ sK3_SY74 )
& ( edge @ sK4_SY77 )
& ( sK3_SY74 != sK4_SY77 )
& ( path @ sK1_V1 @ sK2_SY70 @ SY79 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[40]) ).
thf(42,plain,
( ( ( ( shortest_path @ sK1_V1 @ sK2_SY70 @ sK5_SY79 )
& ( precedes @ sK3_SY74 @ sK4_SY77 @ sK5_SY79 ) )
=> ( ( vertex @ sK1_V1 )
& ( vertex @ sK2_SY70 )
& ( sK1_V1 != sK2_SY70 )
& ( edge @ sK3_SY74 )
& ( edge @ sK4_SY77 )
& ( sK3_SY74 != sK4_SY77 )
& ( path @ sK1_V1 @ sK2_SY70 @ sK5_SY79 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[41]) ).
thf(43,plain,
( ( shortest_path @ sK1_V1 @ sK2_SY70 @ sK5_SY79 )
= $true ),
inference(standard_cnf,[status(thm)],[42]) ).
thf(44,plain,
( ( precedes @ sK3_SY74 @ sK4_SY77 @ sK5_SY79 )
= $true ),
inference(standard_cnf,[status(thm)],[42]) ).
thf(45,plain,
( ( ( vertex @ sK1_V1 )
& ( vertex @ sK2_SY70 )
& ( sK1_V1 != sK2_SY70 )
& ( edge @ sK3_SY74 )
& ( edge @ sK4_SY77 )
& ( sK3_SY74 != sK4_SY77 )
& ( path @ sK1_V1 @ sK2_SY70 @ sK5_SY79 ) )
= $false ),
inference(standard_cnf,[status(thm)],[42]) ).
thf(46,plain,
( ( vertex @ sK1_V1 )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[45]) ).
thf(47,plain,
( ( vertex @ sK2_SY70 )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[45]) ).
thf(48,plain,
( ( ( sK1_V1 != sK2_SY70 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[45]) ).
thf(49,plain,
( ( edge @ sK3_SY74 )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[45]) ).
thf(50,plain,
( ( edge @ sK4_SY77 )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[45]) ).
thf(51,plain,
( ( ( sK3_SY74 != sK4_SY77 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[45]) ).
thf(52,plain,
( ( path @ sK1_V1 @ sK2_SY70 @ sK5_SY79 )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[45]) ).
thf(53,plain,
( ( ~ ( vertex @ sK1_V1 ) )
= $true ),
inference(polarity_switch,[status(thm)],[46]) ).
thf(54,plain,
( ( ~ ( vertex @ sK2_SY70 ) )
= $true ),
inference(polarity_switch,[status(thm)],[47]) ).
thf(55,plain,
( ( ~ ( ( sK1_V1 != sK2_SY70 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[48]) ).
thf(56,plain,
( ( ~ ( edge @ sK3_SY74 ) )
= $true ),
inference(polarity_switch,[status(thm)],[49]) ).
thf(57,plain,
( ( ~ ( edge @ sK4_SY77 ) )
= $true ),
inference(polarity_switch,[status(thm)],[50]) ).
thf(58,plain,
( ( ~ ( ( sK3_SY74 != sK4_SY77 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[51]) ).
thf(59,plain,
( ( ~ ( path @ sK1_V1 @ sK2_SY70 @ sK5_SY79 ) )
= $true ),
inference(polarity_switch,[status(thm)],[52]) ).
thf(60,plain,
( ( sK1_V1 = sK2_SY70 )
= $true ),
inference(extcnf_combined,[status(esa)],[55]) ).
thf(61,plain,
( ( sK3_SY74 = sK4_SY77 )
= $true ),
inference(extcnf_combined,[status(esa)],[58]) ).
thf(62,plain,
( ( ! [P: $i] :
( ( ( on_path @ ( sK6_E1 @ P ) @ P )
& ( on_path @ ( sK7_SY80 @ P ) @ P )
& ( sequential @ ( sK6_E1 @ P ) @ ( sK7_SY80 @ P ) )
& ! [SY82: $i] :
~ ( triangle @ ( sK6_E1 @ P ) @ ( sK7_SY80 @ P ) @ SY82 ) )
| ! [V1: $i,V2: $i] :
~ ( path @ V1 @ V2 @ P )
| ( ( number_of_in @ sequential_pairs @ P )
= ( number_of_in @ triangles @ P ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(63,plain,
( ( ! [V1: $i,V2: $i,P: $i] :
( ~ ( path @ V1 @ V2 @ P )
| ( ( number_of_in @ sequential_pairs @ P )
= ( minus @ ( length_of @ P ) @ n1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(64,plain,
( ( ! [V1: $i,V2: $i,P: $i] :
( ~ ( path @ V1 @ V2 @ P )
| ( ( length_of @ P )
= ( number_of_in @ edges @ P ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(65,plain,
( ( ! [E1: $i] :
( ! [E2: $i,E3: $i] :
( ~ ( edge @ E1 )
| ~ ( edge @ E2 )
| ~ ( edge @ E3 )
| ~ ( sequential @ E1 @ E2 )
| ~ ( sequential @ E2 @ E3 )
| ~ ( sequential @ E3 @ E1 )
| ( triangle @ E1 @ E2 @ E3 ) )
& ( ! [E2: $i,E3: $i] :
~ ( triangle @ E1 @ E2 @ E3 )
| ( edge @ E1 ) )
& ! [E2: $i] :
( ! [E3: $i] :
~ ( triangle @ E1 @ E2 @ E3 )
| ( edge @ E2 ) )
& ! [E2: $i,E3: $i] :
( ~ ( triangle @ E1 @ E2 @ E3 )
| ( edge @ E3 ) )
& ! [E2: $i] :
( ! [E3: $i] :
~ ( triangle @ E1 @ E2 @ E3 )
| ( sequential @ E1 @ E2 ) )
& ! [E2: $i,E3: $i] :
( ~ ( triangle @ E1 @ E2 @ E3 )
| ( sequential @ E2 @ E3 ) )
& ! [E2: $i,E3: $i] :
( ~ ( triangle @ E1 @ E2 @ E3 )
| ( sequential @ E3 @ E1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(66,plain,
( ( ! [V1: $i,V2: $i,E1: $i] :
( ! [E2: $i] :
( ! [P: $i] :
( ~ ( precedes @ E1 @ E2 @ P )
| ~ ( shortest_path @ V1 @ V2 @ P ) )
| ! [E3: $i] :
( ( ( tail_of @ E3 )
!= ( tail_of @ E1 ) )
| ( ( head_of @ E3 )
!= ( head_of @ E2 ) ) ) )
& ! [E2: $i,P: $i] :
( ~ ( precedes @ E1 @ E2 @ P )
| ~ ( shortest_path @ V1 @ V2 @ P )
| ~ ( precedes @ E2 @ E1 @ P ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[26]) ).
thf(67,plain,
( ( ! [V1: $i] :
( ! [V2: $i,SP: $i] :
( ( ( path @ V1 @ V2 @ ( sK8_P @ SP @ V2 @ V1 ) )
& ~ ( less_or_equal @ ( length_of @ SP ) @ ( length_of @ ( sK8_P @ SP @ V2 @ V1 ) ) ) )
| ( V1 = V2 )
| ~ ( path @ V1 @ V2 @ SP )
| ( shortest_path @ V1 @ V2 @ SP ) )
& ! [V2: $i,SP: $i] :
( ~ ( shortest_path @ V1 @ V2 @ SP )
| ! [P: $i] :
( ~ ( path @ V1 @ V2 @ P )
| ( less_or_equal @ ( length_of @ SP ) @ ( length_of @ P ) ) ) )
& ! [V2: $i] :
( ! [SP: $i] :
~ ( shortest_path @ V1 @ V2 @ SP )
| ( V1 != V2 ) )
& ! [V2: $i,SP: $i] :
( ~ ( shortest_path @ V1 @ V2 @ SP )
| ( path @ V1 @ V2 @ SP ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[27]) ).
thf(68,plain,
( ( ! [P: $i] :
( ! [V1: $i,V2: $i] :
~ ( path @ V1 @ V2 @ P )
| ( ! [E1: $i] :
( ! [E2: $i] :
~ ( precedes @ E1 @ E2 @ P )
| ( on_path @ E1 @ P ) )
& ! [E1: $i,E2: $i] :
( ~ ( precedes @ E1 @ E2 @ P )
| ( on_path @ E2 @ P ) )
& ! [E1: $i,E2: $i] :
( ~ ( precedes @ E1 @ E2 @ P )
| ! [E3: $i] :
( ~ ( precedes @ E3 @ E2 @ P )
| ~ ( sequential @ E1 @ E3 ) )
| ~ ( sequential @ E1 @ E2 ) )
& ! [E1: $i,E2: $i] :
( ~ ( precedes @ E1 @ E2 @ P )
| ( ( precedes @ ( sK9_E3 @ E2 @ E1 @ P ) @ E2 @ P )
& ( sequential @ E1 @ ( sK9_E3 @ E2 @ E1 @ P ) ) )
| ( sequential @ E1 @ E2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[28]) ).
thf(69,plain,
( ( ! [P: $i] :
( ! [V1: $i,V2: $i] :
~ ( path @ V1 @ V2 @ P )
| ( ! [E1: $i,E2: $i] :
( ~ ( on_path @ E1 @ P )
| ~ ( on_path @ E2 @ P )
| ! [E3: $i] :
( ~ ( precedes @ E3 @ E2 @ P )
| ~ ( sequential @ E1 @ E3 ) )
| ( precedes @ E1 @ E2 @ P ) )
& ! [E1: $i,E2: $i] :
( ~ ( on_path @ E1 @ P )
| ~ ( on_path @ E2 @ P )
| ~ ( sequential @ E1 @ E2 )
| ( precedes @ E1 @ E2 @ P ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[29]) ).
thf(70,plain,
( ( ! [E1: $i,E2: $i] :
( ( E1 = E2 )
| ~ ( edge @ E1 )
| ~ ( edge @ E2 )
| ( ( head_of @ E1 )
!= ( tail_of @ E2 ) )
| ( sequential @ E1 @ E2 ) )
& ! [E1: $i,E2: $i] :
( ~ ( sequential @ E1 @ E2 )
| ( E1 != E2 ) )
& ! [E1: $i] :
( ! [E2: $i] :
~ ( sequential @ E1 @ E2 )
| ( edge @ E1 ) )
& ! [E1: $i,E2: $i] :
( ~ ( sequential @ E1 @ E2 )
| ( edge @ E2 ) )
& ! [E1: $i,E2: $i] :
( ~ ( sequential @ E1 @ E2 )
| ( ( head_of @ E1 )
= ( tail_of @ E2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[30]) ).
thf(71,plain,
( ( ! [V1: $i,V2: $i] :
( ! [P: $i,V: $i] :
( ~ ( in_path @ V @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( ( on_path @ ( sK10_E @ V @ P @ V2 @ V1 ) @ P )
& ( ( V
= ( head_of @ ( sK10_E @ V @ P @ V2 @ V1 ) ) )
| ( V
= ( tail_of @ ( sK10_E @ V @ P @ V2 @ V1 ) ) ) ) ) )
& ! [P: $i,V: $i] :
( ~ ( in_path @ V @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( vertex @ V ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[31]) ).
thf(72,plain,
( ( ! [V1: $i,V2: $i] :
( ! [P: $i,E: $i] :
( ~ ( on_path @ E @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( edge @ E ) )
& ! [P: $i,E: $i] :
( ~ ( on_path @ E @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( in_path @ ( head_of @ E ) @ P ) )
& ! [P: $i,E: $i] :
( ~ ( on_path @ E @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( in_path @ ( tail_of @ E ) @ P ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[32]) ).
thf(73,plain,
( ( ! [V1: $i] :
( ( ! [V2: $i,P: $i] :
~ ( path @ V1 @ V2 @ P )
| ( vertex @ V1 ) )
& ! [V2: $i] :
( ! [P: $i] :
~ ( path @ V1 @ V2 @ P )
| ( vertex @ V2 ) )
& ! [V2: $i,P: $i] :
( ~ ( path @ V1 @ V2 @ P )
| ( ( V1
= ( tail_of @ ( sK11_E @ P @ V2 @ V1 ) ) )
& ( edge @ ( sK11_E @ P @ V2 @ V1 ) )
& ( ( V2
!= ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) )
| ( P
!= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ empty ) )
| ! [SY83: $i] :
( ( P
!= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ SY83 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) @ V2 @ SY83 ) ) )
& ( ( V2
= ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) )
| ( ( P
= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ ( sK13_SY84 @ P @ V2 @ V1 ) ) )
& ( path @ ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) @ V2 @ ( sK13_SY84 @ P @ V2 @ V1 ) ) ) )
& ( ( P
= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ empty ) )
| ( ( P
= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ ( sK12_SY85 @ P @ V2 @ V1 ) ) )
& ( path @ ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) @ V2 @ ( sK12_SY85 @ P @ V2 @ V1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[33]) ).
thf(74,plain,
( ( ! [V1: $i,V2: $i,P: $i] :
( ~ ( vertex @ V1 )
| ~ ( vertex @ V2 )
| ( ! [E: $i] :
( ( V1
!= ( tail_of @ E ) )
| ~ ( edge @ E )
| ( V2
!= ( head_of @ E ) )
| ( P
!= ( path_cons @ E @ empty ) ) )
& ! [E: $i] :
( ( V1
!= ( tail_of @ E ) )
| ~ ( edge @ E )
| ! [TP: $i] :
( ( P
!= ( path_cons @ E @ TP ) )
| ~ ( path @ ( head_of @ E ) @ V2 @ TP ) ) ) )
| ( path @ V1 @ V2 @ P ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[34]) ).
thf(75,plain,
( ( ~ complete
| ! [V1: $i,V2: $i] :
( ( V1 = V2 )
| ~ ( vertex @ V1 )
| ~ ( vertex @ V2 )
| ( ( ( V1
!= ( head_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V2
!= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V2
!= ( head_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V1
!= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( ( V1
= ( head_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V2
= ( head_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( ( V1
= ( head_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V1
= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( ( V2
= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V2
= ( head_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( ( V2
= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V1
= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( edge @ ( sK14_E @ V2 @ V1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[35]) ).
thf(76,plain,
( ( ! [E: $i] :
( ~ ( edge @ E )
| ( vertex @ ( head_of @ E ) ) )
& ! [E: $i] :
( ~ ( edge @ E )
| ( vertex @ ( tail_of @ E ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[36]) ).
thf(77,plain,
( ( ! [E: $i] :
( ~ ( edge @ E )
| ( ( head_of @ E )
!= ( tail_of @ E ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[37]) ).
thf(78,plain,
( ( ! [E: $i] :
( ~ ( edge @ E )
| ( ( head_of @ E )
!= ( tail_of @ E ) ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(79,plain,
( ( ! [E: $i] :
( ~ ( edge @ E )
| ( vertex @ ( head_of @ E ) ) )
& ! [E: $i] :
( ~ ( edge @ E )
| ( vertex @ ( tail_of @ E ) ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(80,plain,
( ( ~ complete
| ! [V1: $i,V2: $i] :
( ( V1 = V2 )
| ~ ( vertex @ V1 )
| ~ ( vertex @ V2 )
| ( ( ( V1
!= ( head_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V2
!= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V2
!= ( head_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V1
!= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( ( V1
= ( head_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V2
= ( head_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( ( V1
= ( head_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V1
= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( ( V2
= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V2
= ( head_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( ( V2
= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V1
= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( edge @ ( sK14_E @ V2 @ V1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(81,plain,
( ( ! [V1: $i,V2: $i,P: $i] :
( ~ ( vertex @ V1 )
| ~ ( vertex @ V2 )
| ( ! [E: $i] :
( ( V1
!= ( tail_of @ E ) )
| ~ ( edge @ E )
| ( V2
!= ( head_of @ E ) )
| ( P
!= ( path_cons @ E @ empty ) ) )
& ! [E: $i] :
( ( V1
!= ( tail_of @ E ) )
| ~ ( edge @ E )
| ! [TP: $i] :
( ( P
!= ( path_cons @ E @ TP ) )
| ~ ( path @ ( head_of @ E ) @ V2 @ TP ) ) ) )
| ( path @ V1 @ V2 @ P ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(82,plain,
( ( ! [V1: $i] :
( ( ! [V2: $i,P: $i] :
~ ( path @ V1 @ V2 @ P )
| ( vertex @ V1 ) )
& ! [V2: $i] :
( ! [P: $i] :
~ ( path @ V1 @ V2 @ P )
| ( vertex @ V2 ) )
& ! [V2: $i,P: $i] :
( ~ ( path @ V1 @ V2 @ P )
| ( ( V1
= ( tail_of @ ( sK11_E @ P @ V2 @ V1 ) ) )
& ( edge @ ( sK11_E @ P @ V2 @ V1 ) )
& ( ( V2
!= ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) )
| ( P
!= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ empty ) )
| ! [SY83: $i] :
( ( P
!= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ SY83 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) @ V2 @ SY83 ) ) )
& ( ( V2
= ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) )
| ( ( P
= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ ( sK13_SY84 @ P @ V2 @ V1 ) ) )
& ( path @ ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) @ V2 @ ( sK13_SY84 @ P @ V2 @ V1 ) ) ) )
& ( ( P
= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ empty ) )
| ( ( P
= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ ( sK12_SY85 @ P @ V2 @ V1 ) ) )
& ( path @ ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) @ V2 @ ( sK12_SY85 @ P @ V2 @ V1 ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(83,plain,
( ( ! [V1: $i,V2: $i] :
( ! [P: $i,E: $i] :
( ~ ( on_path @ E @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( edge @ E ) )
& ! [P: $i,E: $i] :
( ~ ( on_path @ E @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( in_path @ ( head_of @ E ) @ P ) )
& ! [P: $i,E: $i] :
( ~ ( on_path @ E @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( in_path @ ( tail_of @ E ) @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(84,plain,
( ( ! [V1: $i,V2: $i] :
( ! [P: $i,V: $i] :
( ~ ( in_path @ V @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( ( on_path @ ( sK10_E @ V @ P @ V2 @ V1 ) @ P )
& ( ( V
= ( head_of @ ( sK10_E @ V @ P @ V2 @ V1 ) ) )
| ( V
= ( tail_of @ ( sK10_E @ V @ P @ V2 @ V1 ) ) ) ) ) )
& ! [P: $i,V: $i] :
( ~ ( in_path @ V @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( vertex @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(85,plain,
( ( ! [E1: $i,E2: $i] :
( ( E1 = E2 )
| ~ ( edge @ E1 )
| ~ ( edge @ E2 )
| ( ( head_of @ E1 )
!= ( tail_of @ E2 ) )
| ( sequential @ E1 @ E2 ) )
& ! [E1: $i,E2: $i] :
( ~ ( sequential @ E1 @ E2 )
| ( E1 != E2 ) )
& ! [E1: $i] :
( ! [E2: $i] :
~ ( sequential @ E1 @ E2 )
| ( edge @ E1 ) )
& ! [E1: $i,E2: $i] :
( ~ ( sequential @ E1 @ E2 )
| ( edge @ E2 ) )
& ! [E1: $i,E2: $i] :
( ~ ( sequential @ E1 @ E2 )
| ( ( head_of @ E1 )
= ( tail_of @ E2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(86,plain,
( ( ! [P: $i] :
( ! [V1: $i,V2: $i] :
~ ( path @ V1 @ V2 @ P )
| ( ! [E1: $i,E2: $i] :
( ~ ( on_path @ E1 @ P )
| ~ ( on_path @ E2 @ P )
| ! [E3: $i] :
( ~ ( precedes @ E3 @ E2 @ P )
| ~ ( sequential @ E1 @ E3 ) )
| ( precedes @ E1 @ E2 @ P ) )
& ! [E1: $i,E2: $i] :
( ~ ( on_path @ E1 @ P )
| ~ ( on_path @ E2 @ P )
| ~ ( sequential @ E1 @ E2 )
| ( precedes @ E1 @ E2 @ P ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(87,plain,
( ( ! [P: $i] :
( ! [V1: $i,V2: $i] :
~ ( path @ V1 @ V2 @ P )
| ( ! [E1: $i] :
( ! [E2: $i] :
~ ( precedes @ E1 @ E2 @ P )
| ( on_path @ E1 @ P ) )
& ! [E1: $i,E2: $i] :
( ~ ( precedes @ E1 @ E2 @ P )
| ( on_path @ E2 @ P ) )
& ! [E1: $i,E2: $i] :
( ~ ( precedes @ E1 @ E2 @ P )
| ! [E3: $i] :
( ~ ( precedes @ E3 @ E2 @ P )
| ~ ( sequential @ E1 @ E3 ) )
| ~ ( sequential @ E1 @ E2 ) )
& ! [E1: $i,E2: $i] :
( ~ ( precedes @ E1 @ E2 @ P )
| ( ( precedes @ ( sK9_E3 @ E2 @ E1 @ P ) @ E2 @ P )
& ( sequential @ E1 @ ( sK9_E3 @ E2 @ E1 @ P ) ) )
| ( sequential @ E1 @ E2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(88,plain,
( ( ! [V1: $i] :
( ! [V2: $i,SP: $i] :
( ( ( path @ V1 @ V2 @ ( sK8_P @ SP @ V2 @ V1 ) )
& ~ ( less_or_equal @ ( length_of @ SP ) @ ( length_of @ ( sK8_P @ SP @ V2 @ V1 ) ) ) )
| ( V1 = V2 )
| ~ ( path @ V1 @ V2 @ SP )
| ( shortest_path @ V1 @ V2 @ SP ) )
& ! [V2: $i,SP: $i] :
( ~ ( shortest_path @ V1 @ V2 @ SP )
| ! [P: $i] :
( ~ ( path @ V1 @ V2 @ P )
| ( less_or_equal @ ( length_of @ SP ) @ ( length_of @ P ) ) ) )
& ! [V2: $i] :
( ! [SP: $i] :
~ ( shortest_path @ V1 @ V2 @ SP )
| ( V1 != V2 ) )
& ! [V2: $i,SP: $i] :
( ~ ( shortest_path @ V1 @ V2 @ SP )
| ( path @ V1 @ V2 @ SP ) ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(89,plain,
( ( ! [V1: $i,V2: $i,E1: $i] :
( ! [E2: $i] :
( ! [P: $i] :
( ~ ( precedes @ E1 @ E2 @ P )
| ~ ( shortest_path @ V1 @ V2 @ P ) )
| ! [E3: $i] :
( ( ( tail_of @ E3 )
!= ( tail_of @ E1 ) )
| ( ( head_of @ E3 )
!= ( head_of @ E2 ) ) ) )
& ! [E2: $i,P: $i] :
( ~ ( precedes @ E1 @ E2 @ P )
| ~ ( shortest_path @ V1 @ V2 @ P )
| ~ ( precedes @ E2 @ E1 @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(90,plain,
( ( ! [E1: $i] :
( ! [E2: $i,E3: $i] :
( ~ ( edge @ E1 )
| ~ ( edge @ E2 )
| ~ ( edge @ E3 )
| ~ ( sequential @ E1 @ E2 )
| ~ ( sequential @ E2 @ E3 )
| ~ ( sequential @ E3 @ E1 )
| ( triangle @ E1 @ E2 @ E3 ) )
& ( ! [E2: $i,E3: $i] :
~ ( triangle @ E1 @ E2 @ E3 )
| ( edge @ E1 ) )
& ! [E2: $i] :
( ! [E3: $i] :
~ ( triangle @ E1 @ E2 @ E3 )
| ( edge @ E2 ) )
& ! [E2: $i,E3: $i] :
( ~ ( triangle @ E1 @ E2 @ E3 )
| ( edge @ E3 ) )
& ! [E2: $i] :
( ! [E3: $i] :
~ ( triangle @ E1 @ E2 @ E3 )
| ( sequential @ E1 @ E2 ) )
& ! [E2: $i,E3: $i] :
( ~ ( triangle @ E1 @ E2 @ E3 )
| ( sequential @ E2 @ E3 ) )
& ! [E2: $i,E3: $i] :
( ~ ( triangle @ E1 @ E2 @ E3 )
| ( sequential @ E3 @ E1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(91,plain,
( ( ! [V1: $i,V2: $i,P: $i] :
( ~ ( path @ V1 @ V2 @ P )
| ( ( length_of @ P )
= ( number_of_in @ edges @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(92,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)],[63]) ).
thf(93,plain,
( ( ! [P: $i] :
( ( ( on_path @ ( sK6_E1 @ P ) @ P )
& ( on_path @ ( sK7_SY80 @ P ) @ P )
& ( sequential @ ( sK6_E1 @ P ) @ ( sK7_SY80 @ P ) )
& ! [SY82: $i] :
~ ( triangle @ ( sK6_E1 @ P ) @ ( sK7_SY80 @ P ) @ SY82 ) )
| ! [V1: $i,V2: $i] :
~ ( path @ V1 @ V2 @ P )
| ( ( number_of_in @ sequential_pairs @ P )
= ( number_of_in @ triangles @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(94,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(95,plain,
( ( precedes @ sK3_SY74 @ sK4_SY77 @ sK5_SY79 )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(96,plain,
( ( shortest_path @ sK1_V1 @ sK2_SY70 @ sK5_SY79 )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(97,plain,
( ( ~ ( vertex @ sK1_V1 ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(98,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i,SX2: $i] :
~ ( path @ SX1 @ SX2 @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( on_path @ SX1 @ SX0 )
| ~ ( on_path @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( precedes @ SX3 @ SX2 @ SX0 )
| ~ ( sequential @ SX1 @ SX3 ) )
| ( precedes @ SX1 @ SX2 @ SX0 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( on_path @ SX1 @ SX0 )
| ~ ( on_path @ SX2 @ SX0 )
| ~ ( sequential @ SX1 @ SX2 )
| ( precedes @ SX1 @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(99,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( path @ SX0 @ SX1 @ ( sK8_P @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SX2 ) @ ( length_of @ ( sK8_P @ SX2 @ SX1 @ SX0 ) ) ) )
| ( SX0 = SX1 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ( shortest_path @ SX0 @ SX1 @ SX2 ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( shortest_path @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( path @ SX0 @ SX1 @ SX3 )
| ( less_or_equal @ ( length_of @ SX2 ) @ ( length_of @ SX3 ) ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( shortest_path @ SX0 @ SX1 @ SX2 )
| ( SX0 != SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( shortest_path @ SX0 @ SX1 @ SX2 )
| ( path @ SX0 @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(100,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( on_path @ SX3 @ SX2 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ( edge @ SX3 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( on_path @ SX3 @ SX2 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ( in_path @ ( head_of @ SX3 ) @ SX2 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( on_path @ SX3 @ SX2 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ( in_path @ ( tail_of @ SX3 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(101,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SX0 ) @ SX0 )
| ~ ( on_path @ ( sK7_SY80 @ SX0 ) @ SX0 ) )
| ~ ( sequential @ ( sK6_E1 @ SX0 ) @ ( sK7_SY80 @ SX0 ) ) )
| ~ ! [SX1: $i] :
~ ( triangle @ ( sK6_E1 @ SX0 ) @ ( sK7_SY80 @ SX0 ) @ SX1 ) )
| ! [SX1: $i,SX2: $i] :
~ ( path @ SX1 @ SX2 @ SX0 )
| ( ( number_of_in @ sequential_pairs @ SX0 )
= ( number_of_in @ triangles @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(102,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in_path @ SX3 @ SX2 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ~ ( ~ ( on_path @ ( sK10_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( ( SX3
= ( head_of @ ( sK10_E @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ( SX3
= ( tail_of @ ( sK10_E @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( in_path @ SX3 @ SX2 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ( vertex @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(103,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i,SX2: $i] :
~ ( path @ SX1 @ SX2 @ SX0 )
| ~ ( ~ ~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( precedes @ SX1 @ SX2 @ SX0 )
| ( on_path @ SX1 @ SX0 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( precedes @ SX1 @ SX2 @ SX0 )
| ( on_path @ SX2 @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( precedes @ SX1 @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( precedes @ SX3 @ SX2 @ SX0 )
| ~ ( sequential @ SX1 @ SX3 ) )
| ~ ( sequential @ SX1 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( precedes @ SX1 @ SX2 @ SX0 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SX2 @ SX1 @ SX0 ) @ SX2 @ SX0 )
| ~ ( sequential @ SX1 @ ( sK9_E3 @ SX2 @ SX1 @ SX0 ) ) )
| ( sequential @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(104,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( edge @ SX0 )
| ~ ( edge @ SX1 )
| ~ ( edge @ SX2 )
| ~ ( sequential @ SX0 @ SX1 )
| ~ ( sequential @ SX1 @ SX2 )
| ~ ( sequential @ SX2 @ SX0 )
| ( triangle @ SX0 @ SX1 @ SX2 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SX1: $i,SX2: $i] :
~ ( triangle @ SX0 @ SX1 @ SX2 )
| ( edge @ SX0 ) )
| ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( triangle @ SX0 @ SX1 @ SX2 )
| ( edge @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( triangle @ SX0 @ SX1 @ SX2 )
| ( edge @ SX2 ) ) )
| ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( triangle @ SX0 @ SX1 @ SX2 )
| ( sequential @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( triangle @ SX0 @ SX1 @ SX2 )
| ( sequential @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( triangle @ SX0 @ SX1 @ SX2 )
| ( sequential @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(105,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( edge @ SX0 )
| ~ ( edge @ SX1 )
| ( ( head_of @ SX0 )
!= ( tail_of @ SX1 ) )
| ( sequential @ SX0 @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(106,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( vertex @ SX0 )
| ~ ( vertex @ SX1 )
| ~ ( ~ ! [SX3: $i] :
( ( SX0
!= ( tail_of @ SX3 ) )
| ~ ( edge @ SX3 )
| ( SX1
!= ( head_of @ SX3 ) )
| ( SX2
!= ( path_cons @ SX3 @ empty ) ) )
| ~ ! [SX3: $i] :
( ( SX0
!= ( tail_of @ SX3 ) )
| ~ ( edge @ SX3 )
| ! [SX4: $i] :
( ( SX2
!= ( path_cons @ SX3 @ SX4 ) )
| ~ ( path @ ( head_of @ SX3 ) @ SX1 @ SX4 ) ) ) )
| ( path @ SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(107,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( head_of @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( tail_of @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(108,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
( ~ ( precedes @ SX2 @ SX3 @ SX4 )
| ~ ( shortest_path @ SX0 @ SX1 @ SX4 ) )
| ! [SX4: $i] :
( ( ( tail_of @ SX4 )
!= ( tail_of @ SX2 ) )
| ( ( head_of @ SX4 )
!= ( head_of @ SX3 ) ) ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( precedes @ SX2 @ SX3 @ SX4 )
| ~ ( shortest_path @ SX0 @ SX1 @ SX4 )
| ~ ( precedes @ SX3 @ SX2 @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(109,plain,
( ( ! [SX0: $i] :
~ ( ~ ~ ( ~ ( ! [SX1: $i,SX2: $i] :
~ ( path @ SX0 @ SX1 @ SX2 )
| ( vertex @ SX0 ) )
| ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( path @ SX0 @ SX1 @ SX2 )
| ( vertex @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( path @ SX0 @ SX1 @ SX2 )
| ~ ( ~ ~ ( ( SX0
!= ( tail_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( edge @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ( SX1
!= ( head_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) )
| ( SX2
!= ( path_cons @ ( sK11_E @ SX2 @ SX1 @ SX0 ) @ empty ) )
| ! [SX3: $i] :
( ( SX2
!= ( path_cons @ ( sK11_E @ SX2 @ SX1 @ SX0 ) @ SX3 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) @ SX1 @ SX3 ) ) )
| ~ ~ ( ~ ( ( SX1
= ( head_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( ( SX2
!= ( path_cons @ ( sK11_E @ SX2 @ SX1 @ SX0 ) @ ( sK13_SY84 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) @ SX1 @ ( sK13_SY84 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX2
= ( path_cons @ ( sK11_E @ SX2 @ SX1 @ SX0 ) @ empty ) )
| ~ ( ( SX2
!= ( path_cons @ ( sK11_E @ SX2 @ SX1 @ SX0 ) @ ( sK12_SY85 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) @ SX1 @ ( sK12_SY85 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(110,plain,
( ( ~ complete
| ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( vertex @ SX0 )
| ~ ( vertex @ SX1 )
| ~ ( ~ ~ ( ~ ( ( SX0
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
| ~ ~ ( ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(111,plain,
! [SV1: $i] :
( ( ~ ( edge @ SV1 )
| ( ( head_of @ SV1 )
!= ( tail_of @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(112,plain,
! [SV2: $i] :
( ( ! [SY86: $i,SY87: $i] :
( ~ ( path @ SV2 @ SY86 @ SY87 )
| ( ( length_of @ SY87 )
= ( number_of_in @ edges @ SY87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(113,plain,
! [SV3: $i] :
( ( ! [SY88: $i,SY89: $i] :
( ~ ( path @ SV3 @ SY88 @ SY89 )
| ( ( number_of_in @ sequential_pairs @ SY89 )
= ( minus @ ( length_of @ SY89 ) @ n1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(114,plain,
! [SV4: $i] :
( ( ! [SY90: $i] : ( less_or_equal @ ( number_of_in @ SV4 @ SY90 ) @ ( number_of_in @ SV4 @ graph ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(115,plain,
( ( vertex @ sK1_V1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(116,plain,
! [SV5: $i] :
( ( ! [SY91: $i,SY92: $i] :
~ ( path @ SY91 @ SY92 @ SV5 )
| ~ ( ~ ! [SY93: $i,SY94: $i] :
( ~ ( on_path @ SY93 @ SV5 )
| ~ ( on_path @ SY94 @ SV5 )
| ! [SY95: $i] :
( ~ ( precedes @ SY95 @ SY94 @ SV5 )
| ~ ( sequential @ SY93 @ SY95 ) )
| ( precedes @ SY93 @ SY94 @ SV5 ) )
| ~ ! [SY96: $i,SY97: $i] :
( ~ ( on_path @ SY96 @ SV5 )
| ~ ( on_path @ SY97 @ SV5 )
| ~ ( sequential @ SY96 @ SY97 )
| ( precedes @ SY96 @ SY97 @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(117,plain,
! [SV6: $i] :
( ( ~ ( ~ ! [SY98: $i,SY99: $i] :
( ~ ( ~ ( path @ SV6 @ SY98 @ ( sK8_P @ SY99 @ SY98 @ SV6 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY99 ) @ ( length_of @ ( sK8_P @ SY99 @ SY98 @ SV6 ) ) ) )
| ( SV6 = SY98 )
| ~ ( path @ SV6 @ SY98 @ SY99 )
| ( shortest_path @ SV6 @ SY98 @ SY99 ) )
| ~ ~ ( ~ ! [SY100: $i,SY101: $i] :
( ~ ( shortest_path @ SV6 @ SY100 @ SY101 )
| ! [SY102: $i] :
( ~ ( path @ SV6 @ SY100 @ SY102 )
| ( less_or_equal @ ( length_of @ SY101 ) @ ( length_of @ SY102 ) ) ) )
| ~ ~ ( ~ ! [SY103: $i] :
( ! [SY104: $i] :
~ ( shortest_path @ SV6 @ SY103 @ SY104 )
| ( SV6 != SY103 ) )
| ~ ! [SY105: $i,SY106: $i] :
( ~ ( shortest_path @ SV6 @ SY105 @ SY106 )
| ( path @ SV6 @ SY105 @ SY106 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(118,plain,
! [SV7: $i] :
( ( ! [SY107: $i] :
~ ( ~ ~ ( ~ ! [SY108: $i,SY109: $i] :
( ~ ( on_path @ SY109 @ SY108 )
| ~ ( path @ SV7 @ SY107 @ SY108 )
| ( edge @ SY109 ) )
| ~ ! [SY110: $i,SY111: $i] :
( ~ ( on_path @ SY111 @ SY110 )
| ~ ( path @ SV7 @ SY107 @ SY110 )
| ( in_path @ ( head_of @ SY111 ) @ SY110 ) ) )
| ~ ! [SY112: $i,SY113: $i] :
( ~ ( on_path @ SY113 @ SY112 )
| ~ ( path @ SV7 @ SY107 @ SY112 )
| ( in_path @ ( tail_of @ SY113 ) @ SY112 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(119,plain,
! [SV8: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV8 ) @ SV8 )
| ~ ( on_path @ ( sK7_SY80 @ SV8 ) @ SV8 ) )
| ~ ( sequential @ ( sK6_E1 @ SV8 ) @ ( sK7_SY80 @ SV8 ) ) )
| ~ ! [SY114: $i] :
~ ( triangle @ ( sK6_E1 @ SV8 ) @ ( sK7_SY80 @ SV8 ) @ SY114 ) )
| ! [SY115: $i,SY116: $i] :
~ ( path @ SY115 @ SY116 @ SV8 )
| ( ( number_of_in @ sequential_pairs @ SV8 )
= ( number_of_in @ triangles @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(120,plain,
! [SV9: $i] :
( ( ! [SY117: $i] :
~ ( ~ ! [SY118: $i,SY119: $i] :
( ~ ( in_path @ SY119 @ SY118 )
| ~ ( path @ SV9 @ SY117 @ SY118 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY119 @ SY118 @ SY117 @ SV9 ) @ SY118 )
| ~ ( ( SY119
= ( head_of @ ( sK10_E @ SY119 @ SY118 @ SY117 @ SV9 ) ) )
| ( SY119
= ( tail_of @ ( sK10_E @ SY119 @ SY118 @ SY117 @ SV9 ) ) ) ) ) )
| ~ ! [SY120: $i,SY121: $i] :
( ~ ( in_path @ SY121 @ SY120 )
| ~ ( path @ SV9 @ SY117 @ SY120 )
| ( vertex @ SY121 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(121,plain,
! [SV10: $i] :
( ( ! [SY122: $i,SY123: $i] :
~ ( path @ SY122 @ SY123 @ SV10 )
| ~ ( ~ ~ ( ~ ! [SY124: $i] :
( ! [SY125: $i] :
~ ( precedes @ SY124 @ SY125 @ SV10 )
| ( on_path @ SY124 @ SV10 ) )
| ~ ! [SY126: $i,SY127: $i] :
( ~ ( precedes @ SY126 @ SY127 @ SV10 )
| ( on_path @ SY127 @ SV10 ) ) )
| ~ ~ ( ~ ! [SY128: $i,SY129: $i] :
( ~ ( precedes @ SY128 @ SY129 @ SV10 )
| ! [SY130: $i] :
( ~ ( precedes @ SY130 @ SY129 @ SV10 )
| ~ ( sequential @ SY128 @ SY130 ) )
| ~ ( sequential @ SY128 @ SY129 ) )
| ~ ! [SY131: $i,SY132: $i] :
( ~ ( precedes @ SY131 @ SY132 @ SV10 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY132 @ SY131 @ SV10 ) @ SY132 @ SV10 )
| ~ ( sequential @ SY131 @ ( sK9_E3 @ SY132 @ SY131 @ SV10 ) ) )
| ( sequential @ SY131 @ SY132 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(122,plain,
! [SV11: $i] :
( ( ~ ( ~ ! [SY133: $i,SY134: $i] :
( ~ ( edge @ SV11 )
| ~ ( edge @ SY133 )
| ~ ( edge @ SY134 )
| ~ ( sequential @ SV11 @ SY133 )
| ~ ( sequential @ SY133 @ SY134 )
| ~ ( sequential @ SY134 @ SV11 )
| ( triangle @ SV11 @ SY133 @ SY134 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY135: $i,SY136: $i] :
~ ( triangle @ SV11 @ SY135 @ SY136 )
| ( edge @ SV11 ) )
| ~ ! [SY137: $i] :
( ! [SY138: $i] :
~ ( triangle @ SV11 @ SY137 @ SY138 )
| ( edge @ SY137 ) ) )
| ~ ! [SY139: $i,SY140: $i] :
( ~ ( triangle @ SV11 @ SY139 @ SY140 )
| ( edge @ SY140 ) ) )
| ~ ! [SY141: $i] :
( ! [SY142: $i] :
~ ( triangle @ SV11 @ SY141 @ SY142 )
| ( sequential @ SV11 @ SY141 ) ) )
| ~ ! [SY143: $i,SY144: $i] :
( ~ ( triangle @ SV11 @ SY143 @ SY144 )
| ( sequential @ SY143 @ SY144 ) ) )
| ~ ! [SY145: $i,SY146: $i] :
( ~ ( triangle @ SV11 @ SY145 @ SY146 )
| ( sequential @ SY146 @ SV11 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(123,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( edge @ SX0 )
| ~ ( edge @ SX1 )
| ( ( head_of @ SX0 )
!= ( tail_of @ SX1 ) )
| ( sequential @ SX0 @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(124,plain,
! [SV12: $i] :
( ( ! [SY147: $i,SY148: $i] :
( ~ ( vertex @ SV12 )
| ~ ( vertex @ SY147 )
| ~ ( ~ ! [SY149: $i] :
( ( SV12
!= ( tail_of @ SY149 ) )
| ~ ( edge @ SY149 )
| ( SY147
!= ( head_of @ SY149 ) )
| ( SY148
!= ( path_cons @ SY149 @ empty ) ) )
| ~ ! [SY150: $i] :
( ( SV12
!= ( tail_of @ SY150 ) )
| ~ ( edge @ SY150 )
| ! [SX4: $i] :
( ( SY148
!= ( path_cons @ SY150 @ SX4 ) )
| ~ ( path @ ( head_of @ SY150 ) @ SY147 @ SX4 ) ) ) )
| ( path @ SV12 @ SY147 @ SY148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(125,plain,
( ( ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( head_of @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( tail_of @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(126,plain,
! [SV13: $i] :
( ( ! [SY152: $i,SY153: $i] :
~ ( ~ ! [SY154: $i] :
( ! [SY155: $i] :
( ~ ( precedes @ SY153 @ SY154 @ SY155 )
| ~ ( shortest_path @ SV13 @ SY152 @ SY155 ) )
| ! [SX4: $i] :
( ( ( tail_of @ SX4 )
!= ( tail_of @ SY153 ) )
| ( ( head_of @ SX4 )
!= ( head_of @ SY154 ) ) ) )
| ~ ! [SY157: $i,SY158: $i] :
( ~ ( precedes @ SY153 @ SY157 @ SY158 )
| ~ ( shortest_path @ SV13 @ SY152 @ SY158 )
| ~ ( precedes @ SY157 @ SY153 @ SY158 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(127,plain,
! [SV14: $i] :
( ( ~ ( ~ ~ ( ~ ( ! [SY159: $i,SY160: $i] :
~ ( path @ SV14 @ SY159 @ SY160 )
| ( vertex @ SV14 ) )
| ~ ! [SY161: $i] :
( ! [SY162: $i] :
~ ( path @ SV14 @ SY161 @ SY162 )
| ( vertex @ SY161 ) ) )
| ~ ! [SY163: $i,SY164: $i] :
( ~ ( path @ SV14 @ SY163 @ SY164 )
| ~ ( ~ ~ ( ( SV14
!= ( tail_of @ ( sK11_E @ SY164 @ SY163 @ SV14 ) ) )
| ~ ( edge @ ( sK11_E @ SY164 @ SY163 @ SV14 ) ) )
| ~ ~ ( ~ ( ( SY163
!= ( head_of @ ( sK11_E @ SY164 @ SY163 @ SV14 ) ) )
| ( SY164
!= ( path_cons @ ( sK11_E @ SY164 @ SY163 @ SV14 ) @ empty ) )
| ! [SY165: $i] :
( ( SY164
!= ( path_cons @ ( sK11_E @ SY164 @ SY163 @ SV14 ) @ SY165 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY164 @ SY163 @ SV14 ) ) @ SY163 @ SY165 ) ) )
| ~ ~ ( ~ ( ( SY163
= ( head_of @ ( sK11_E @ SY164 @ SY163 @ SV14 ) ) )
| ~ ( ( SY164
!= ( path_cons @ ( sK11_E @ SY164 @ SY163 @ SV14 ) @ ( sK13_SY84 @ SY164 @ SY163 @ SV14 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY164 @ SY163 @ SV14 ) ) @ SY163 @ ( sK13_SY84 @ SY164 @ SY163 @ SV14 ) ) ) )
| ~ ( ( SY164
= ( path_cons @ ( sK11_E @ SY164 @ SY163 @ SV14 ) @ empty ) )
| ~ ( ( SY164
!= ( path_cons @ ( sK11_E @ SY164 @ SY163 @ SV14 ) @ ( sK12_SY85 @ SY164 @ SY163 @ SV14 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY164 @ SY163 @ SV14 ) ) @ SY163 @ ( sK12_SY85 @ SY164 @ SY163 @ SV14 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(128,plain,
( ( ( ~ complete )
= $true )
| ( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( vertex @ SX0 )
| ~ ( vertex @ SX1 )
| ~ ( ~ ~ ( ~ ( ( SX0
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
| ~ ~ ( ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(129,plain,
! [SV1: $i] :
( ( ( ~ ( edge @ SV1 ) )
= $true )
| ( ( ( ( head_of @ SV1 )
!= ( tail_of @ SV1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(130,plain,
! [SV15: $i,SV2: $i] :
( ( ! [SY166: $i] :
( ~ ( path @ SV2 @ SV15 @ SY166 )
| ( ( length_of @ SY166 )
= ( number_of_in @ edges @ SY166 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(131,plain,
! [SV16: $i,SV3: $i] :
( ( ! [SY167: $i] :
( ~ ( path @ SV3 @ SV16 @ SY167 )
| ( ( number_of_in @ sequential_pairs @ SY167 )
= ( minus @ ( length_of @ SY167 ) @ n1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(132,plain,
! [SV17: $i,SV4: $i] :
( ( less_or_equal @ ( number_of_in @ SV4 @ SV17 ) @ ( number_of_in @ SV4 @ graph ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(133,plain,
! [SV5: $i] :
( ( ( ! [SY91: $i,SY92: $i] :
~ ( path @ SY91 @ SY92 @ SV5 ) )
= $true )
| ( ( ~ ( ~ ! [SY93: $i,SY94: $i] :
( ~ ( on_path @ SY93 @ SV5 )
| ~ ( on_path @ SY94 @ SV5 )
| ! [SY95: $i] :
( ~ ( precedes @ SY95 @ SY94 @ SV5 )
| ~ ( sequential @ SY93 @ SY95 ) )
| ( precedes @ SY93 @ SY94 @ SV5 ) )
| ~ ! [SY96: $i,SY97: $i] :
( ~ ( on_path @ SY96 @ SV5 )
| ~ ( on_path @ SY97 @ SV5 )
| ~ ( sequential @ SY96 @ SY97 )
| ( precedes @ SY96 @ SY97 @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(134,plain,
! [SV6: $i] :
( ( ~ ! [SY98: $i,SY99: $i] :
( ~ ( ~ ( path @ SV6 @ SY98 @ ( sK8_P @ SY99 @ SY98 @ SV6 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY99 ) @ ( length_of @ ( sK8_P @ SY99 @ SY98 @ SV6 ) ) ) )
| ( SV6 = SY98 )
| ~ ( path @ SV6 @ SY98 @ SY99 )
| ( shortest_path @ SV6 @ SY98 @ SY99 ) )
| ~ ~ ( ~ ! [SY100: $i,SY101: $i] :
( ~ ( shortest_path @ SV6 @ SY100 @ SY101 )
| ! [SY102: $i] :
( ~ ( path @ SV6 @ SY100 @ SY102 )
| ( less_or_equal @ ( length_of @ SY101 ) @ ( length_of @ SY102 ) ) ) )
| ~ ~ ( ~ ! [SY103: $i] :
( ! [SY104: $i] :
~ ( shortest_path @ SV6 @ SY103 @ SY104 )
| ( SV6 != SY103 ) )
| ~ ! [SY105: $i,SY106: $i] :
( ~ ( shortest_path @ SV6 @ SY105 @ SY106 )
| ( path @ SV6 @ SY105 @ SY106 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(135,plain,
! [SV18: $i,SV7: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY168: $i,SY169: $i] :
( ~ ( on_path @ SY169 @ SY168 )
| ~ ( path @ SV7 @ SV18 @ SY168 )
| ( edge @ SY169 ) )
| ~ ! [SY170: $i,SY171: $i] :
( ~ ( on_path @ SY171 @ SY170 )
| ~ ( path @ SV7 @ SV18 @ SY170 )
| ( in_path @ ( head_of @ SY171 ) @ SY170 ) ) )
| ~ ! [SY172: $i,SY173: $i] :
( ~ ( on_path @ SY173 @ SY172 )
| ~ ( path @ SV7 @ SV18 @ SY172 )
| ( in_path @ ( tail_of @ SY173 ) @ SY172 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(136,plain,
! [SV8: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV8 ) @ SV8 )
| ~ ( on_path @ ( sK7_SY80 @ SV8 ) @ SV8 ) )
| ~ ( sequential @ ( sK6_E1 @ SV8 ) @ ( sK7_SY80 @ SV8 ) ) )
| ~ ! [SY114: $i] :
~ ( triangle @ ( sK6_E1 @ SV8 ) @ ( sK7_SY80 @ SV8 ) @ SY114 ) )
| ! [SY115: $i,SY116: $i] :
~ ( path @ SY115 @ SY116 @ SV8 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV8 )
= ( number_of_in @ triangles @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(137,plain,
! [SV19: $i,SV9: $i] :
( ( ~ ( ~ ! [SY174: $i,SY175: $i] :
( ~ ( in_path @ SY175 @ SY174 )
| ~ ( path @ SV9 @ SV19 @ SY174 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY175 @ SY174 @ SV19 @ SV9 ) @ SY174 )
| ~ ( ( SY175
= ( head_of @ ( sK10_E @ SY175 @ SY174 @ SV19 @ SV9 ) ) )
| ( SY175
= ( tail_of @ ( sK10_E @ SY175 @ SY174 @ SV19 @ SV9 ) ) ) ) ) )
| ~ ! [SY176: $i,SY177: $i] :
( ~ ( in_path @ SY177 @ SY176 )
| ~ ( path @ SV9 @ SV19 @ SY176 )
| ( vertex @ SY177 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(138,plain,
! [SV10: $i] :
( ( ( ! [SY122: $i,SY123: $i] :
~ ( path @ SY122 @ SY123 @ SV10 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY124: $i] :
( ! [SY125: $i] :
~ ( precedes @ SY124 @ SY125 @ SV10 )
| ( on_path @ SY124 @ SV10 ) )
| ~ ! [SY126: $i,SY127: $i] :
( ~ ( precedes @ SY126 @ SY127 @ SV10 )
| ( on_path @ SY127 @ SV10 ) ) )
| ~ ~ ( ~ ! [SY128: $i,SY129: $i] :
( ~ ( precedes @ SY128 @ SY129 @ SV10 )
| ! [SY130: $i] :
( ~ ( precedes @ SY130 @ SY129 @ SV10 )
| ~ ( sequential @ SY128 @ SY130 ) )
| ~ ( sequential @ SY128 @ SY129 ) )
| ~ ! [SY131: $i,SY132: $i] :
( ~ ( precedes @ SY131 @ SY132 @ SV10 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY132 @ SY131 @ SV10 ) @ SY132 @ SV10 )
| ~ ( sequential @ SY131 @ ( sK9_E3 @ SY132 @ SY131 @ SV10 ) ) )
| ( sequential @ SY131 @ SY132 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(139,plain,
! [SV11: $i] :
( ( ~ ! [SY133: $i,SY134: $i] :
( ~ ( edge @ SV11 )
| ~ ( edge @ SY133 )
| ~ ( edge @ SY134 )
| ~ ( sequential @ SV11 @ SY133 )
| ~ ( sequential @ SY133 @ SY134 )
| ~ ( sequential @ SY134 @ SV11 )
| ( triangle @ SV11 @ SY133 @ SY134 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY135: $i,SY136: $i] :
~ ( triangle @ SV11 @ SY135 @ SY136 )
| ( edge @ SV11 ) )
| ~ ! [SY137: $i] :
( ! [SY138: $i] :
~ ( triangle @ SV11 @ SY137 @ SY138 )
| ( edge @ SY137 ) ) )
| ~ ! [SY139: $i,SY140: $i] :
( ~ ( triangle @ SV11 @ SY139 @ SY140 )
| ( edge @ SY140 ) ) )
| ~ ! [SY141: $i] :
( ! [SY142: $i] :
~ ( triangle @ SV11 @ SY141 @ SY142 )
| ( sequential @ SV11 @ SY141 ) ) )
| ~ ! [SY143: $i,SY144: $i] :
( ~ ( triangle @ SV11 @ SY143 @ SY144 )
| ( sequential @ SY143 @ SY144 ) ) )
| ~ ! [SY145: $i,SY146: $i] :
( ~ ( triangle @ SV11 @ SY145 @ SY146 )
| ( sequential @ SY146 @ SV11 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(140,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( edge @ SX0 )
| ~ ( edge @ SX1 )
| ( ( head_of @ SX0 )
!= ( tail_of @ SX1 ) )
| ( sequential @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[123]) ).
thf(141,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[123]) ).
thf(142,plain,
! [SV20: $i,SV12: $i] :
( ( ! [SY178: $i] :
( ~ ( vertex @ SV12 )
| ~ ( vertex @ SV20 )
| ~ ( ~ ! [SY179: $i] :
( ( SV12
!= ( tail_of @ SY179 ) )
| ~ ( edge @ SY179 )
| ( SV20
!= ( head_of @ SY179 ) )
| ( SY178
!= ( path_cons @ SY179 @ empty ) ) )
| ~ ! [SY180: $i] :
( ( SV12
!= ( tail_of @ SY180 ) )
| ~ ( edge @ SY180 )
| ! [SY181: $i] :
( ( SY178
!= ( path_cons @ SY180 @ SY181 ) )
| ~ ( path @ ( head_of @ SY180 ) @ SV20 @ SY181 ) ) ) )
| ( path @ SV12 @ SV20 @ SY178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(143,plain,
( ( ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( head_of @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[125]) ).
thf(144,plain,
( ( ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( tail_of @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[125]) ).
thf(145,plain,
! [SV21: $i,SV13: $i] :
( ( ! [SY182: $i] :
~ ( ~ ! [SY183: $i] :
( ! [SY184: $i] :
( ~ ( precedes @ SY182 @ SY183 @ SY184 )
| ~ ( shortest_path @ SV13 @ SV21 @ SY184 ) )
| ! [SX4: $i] :
( ( ( tail_of @ SX4 )
!= ( tail_of @ SY182 ) )
| ( ( head_of @ SX4 )
!= ( head_of @ SY183 ) ) ) )
| ~ ! [SY186: $i,SY187: $i] :
( ~ ( precedes @ SY182 @ SY186 @ SY187 )
| ~ ( shortest_path @ SV13 @ SV21 @ SY187 )
| ~ ( precedes @ SY186 @ SY182 @ SY187 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(146,plain,
! [SV14: $i] :
( ( ~ ~ ( ~ ( ! [SY159: $i,SY160: $i] :
~ ( path @ SV14 @ SY159 @ SY160 )
| ( vertex @ SV14 ) )
| ~ ! [SY161: $i] :
( ! [SY162: $i] :
~ ( path @ SV14 @ SY161 @ SY162 )
| ( vertex @ SY161 ) ) )
| ~ ! [SY163: $i,SY164: $i] :
( ~ ( path @ SV14 @ SY163 @ SY164 )
| ~ ( ~ ~ ( ( SV14
!= ( tail_of @ ( sK11_E @ SY164 @ SY163 @ SV14 ) ) )
| ~ ( edge @ ( sK11_E @ SY164 @ SY163 @ SV14 ) ) )
| ~ ~ ( ~ ( ( SY163
!= ( head_of @ ( sK11_E @ SY164 @ SY163 @ SV14 ) ) )
| ( SY164
!= ( path_cons @ ( sK11_E @ SY164 @ SY163 @ SV14 ) @ empty ) )
| ! [SY165: $i] :
( ( SY164
!= ( path_cons @ ( sK11_E @ SY164 @ SY163 @ SV14 ) @ SY165 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY164 @ SY163 @ SV14 ) ) @ SY163 @ SY165 ) ) )
| ~ ~ ( ~ ( ( SY163
= ( head_of @ ( sK11_E @ SY164 @ SY163 @ SV14 ) ) )
| ~ ( ( SY164
!= ( path_cons @ ( sK11_E @ SY164 @ SY163 @ SV14 ) @ ( sK13_SY84 @ SY164 @ SY163 @ SV14 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY164 @ SY163 @ SV14 ) ) @ SY163 @ ( sK13_SY84 @ SY164 @ SY163 @ SV14 ) ) ) )
| ~ ( ( SY164
= ( path_cons @ ( sK11_E @ SY164 @ SY163 @ SV14 ) @ empty ) )
| ~ ( ( SY164
!= ( path_cons @ ( sK11_E @ SY164 @ SY163 @ SV14 ) @ ( sK12_SY85 @ SY164 @ SY163 @ SV14 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY164 @ SY163 @ SV14 ) ) @ SY163 @ ( sK12_SY85 @ SY164 @ SY163 @ SV14 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(147,plain,
( ( complete = $false )
| ( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( vertex @ SX0 )
| ~ ( vertex @ SX1 )
| ~ ( ~ ~ ( ~ ( ( SX0
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
| ~ ~ ( ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(148,plain,
! [SV1: $i] :
( ( ( edge @ SV1 )
= $false )
| ( ( ( ( head_of @ SV1 )
!= ( tail_of @ SV1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(149,plain,
! [SV22: $i,SV15: $i,SV2: $i] :
( ( ~ ( path @ SV2 @ SV15 @ SV22 )
| ( ( length_of @ SV22 )
= ( number_of_in @ edges @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(150,plain,
! [SV23: $i,SV16: $i,SV3: $i] :
( ( ~ ( path @ SV3 @ SV16 @ SV23 )
| ( ( number_of_in @ sequential_pairs @ SV23 )
= ( minus @ ( length_of @ SV23 ) @ n1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(151,plain,
! [SV5: $i,SV24: $i] :
( ( ( ! [SY188: $i] :
~ ( path @ SV24 @ SY188 @ SV5 ) )
= $true )
| ( ( ~ ( ~ ! [SY93: $i,SY94: $i] :
( ~ ( on_path @ SY93 @ SV5 )
| ~ ( on_path @ SY94 @ SV5 )
| ! [SY95: $i] :
( ~ ( precedes @ SY95 @ SY94 @ SV5 )
| ~ ( sequential @ SY93 @ SY95 ) )
| ( precedes @ SY93 @ SY94 @ SV5 ) )
| ~ ! [SY96: $i,SY97: $i] :
( ~ ( on_path @ SY96 @ SV5 )
| ~ ( on_path @ SY97 @ SV5 )
| ~ ( sequential @ SY96 @ SY97 )
| ( precedes @ SY96 @ SY97 @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(152,plain,
! [SV6: $i] :
( ( ~ ! [SY98: $i,SY99: $i] :
( ~ ( ~ ( path @ SV6 @ SY98 @ ( sK8_P @ SY99 @ SY98 @ SV6 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY99 ) @ ( length_of @ ( sK8_P @ SY99 @ SY98 @ SV6 ) ) ) )
| ( SV6 = SY98 )
| ~ ( path @ SV6 @ SY98 @ SY99 )
| ( shortest_path @ SV6 @ SY98 @ SY99 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[134]) ).
thf(153,plain,
! [SV6: $i] :
( ( ~ ~ ( ~ ! [SY100: $i,SY101: $i] :
( ~ ( shortest_path @ SV6 @ SY100 @ SY101 )
| ! [SY102: $i] :
( ~ ( path @ SV6 @ SY100 @ SY102 )
| ( less_or_equal @ ( length_of @ SY101 ) @ ( length_of @ SY102 ) ) ) )
| ~ ~ ( ~ ! [SY103: $i] :
( ! [SY104: $i] :
~ ( shortest_path @ SV6 @ SY103 @ SY104 )
| ( SV6 != SY103 ) )
| ~ ! [SY105: $i,SY106: $i] :
( ~ ( shortest_path @ SV6 @ SY105 @ SY106 )
| ( path @ SV6 @ SY105 @ SY106 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[134]) ).
thf(154,plain,
! [SV18: $i,SV7: $i] :
( ( ~ ~ ( ~ ! [SY168: $i,SY169: $i] :
( ~ ( on_path @ SY169 @ SY168 )
| ~ ( path @ SV7 @ SV18 @ SY168 )
| ( edge @ SY169 ) )
| ~ ! [SY170: $i,SY171: $i] :
( ~ ( on_path @ SY171 @ SY170 )
| ~ ( path @ SV7 @ SV18 @ SY170 )
| ( in_path @ ( head_of @ SY171 ) @ SY170 ) ) )
| ~ ! [SY172: $i,SY173: $i] :
( ~ ( on_path @ SY173 @ SY172 )
| ~ ( path @ SV7 @ SV18 @ SY172 )
| ( in_path @ ( tail_of @ SY173 ) @ SY172 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(155,plain,
! [SV8: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV8 ) @ SV8 )
| ~ ( on_path @ ( sK7_SY80 @ SV8 ) @ SV8 ) )
| ~ ( sequential @ ( sK6_E1 @ SV8 ) @ ( sK7_SY80 @ SV8 ) ) )
| ~ ! [SY114: $i] :
~ ( triangle @ ( sK6_E1 @ SV8 ) @ ( sK7_SY80 @ SV8 ) @ SY114 ) ) )
= $true )
| ( ( ! [SY115: $i,SY116: $i] :
~ ( path @ SY115 @ SY116 @ SV8 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV8 )
= ( number_of_in @ triangles @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(156,plain,
! [SV19: $i,SV9: $i] :
( ( ~ ! [SY174: $i,SY175: $i] :
( ~ ( in_path @ SY175 @ SY174 )
| ~ ( path @ SV9 @ SV19 @ SY174 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY175 @ SY174 @ SV19 @ SV9 ) @ SY174 )
| ~ ( ( SY175
= ( head_of @ ( sK10_E @ SY175 @ SY174 @ SV19 @ SV9 ) ) )
| ( SY175
= ( tail_of @ ( sK10_E @ SY175 @ SY174 @ SV19 @ SV9 ) ) ) ) ) )
| ~ ! [SY176: $i,SY177: $i] :
( ~ ( in_path @ SY177 @ SY176 )
| ~ ( path @ SV9 @ SV19 @ SY176 )
| ( vertex @ SY177 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(157,plain,
! [SV10: $i,SV25: $i] :
( ( ( ! [SY189: $i] :
~ ( path @ SV25 @ SY189 @ SV10 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY124: $i] :
( ! [SY125: $i] :
~ ( precedes @ SY124 @ SY125 @ SV10 )
| ( on_path @ SY124 @ SV10 ) )
| ~ ! [SY126: $i,SY127: $i] :
( ~ ( precedes @ SY126 @ SY127 @ SV10 )
| ( on_path @ SY127 @ SV10 ) ) )
| ~ ~ ( ~ ! [SY128: $i,SY129: $i] :
( ~ ( precedes @ SY128 @ SY129 @ SV10 )
| ! [SY130: $i] :
( ~ ( precedes @ SY130 @ SY129 @ SV10 )
| ~ ( sequential @ SY128 @ SY130 ) )
| ~ ( sequential @ SY128 @ SY129 ) )
| ~ ! [SY131: $i,SY132: $i] :
( ~ ( precedes @ SY131 @ SY132 @ SV10 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY132 @ SY131 @ SV10 ) @ SY132 @ SV10 )
| ~ ( sequential @ SY131 @ ( sK9_E3 @ SY132 @ SY131 @ SV10 ) ) )
| ( sequential @ SY131 @ SY132 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(158,plain,
! [SV11: $i] :
( ( ~ ! [SY133: $i,SY134: $i] :
( ~ ( edge @ SV11 )
| ~ ( edge @ SY133 )
| ~ ( edge @ SY134 )
| ~ ( sequential @ SV11 @ SY133 )
| ~ ( sequential @ SY133 @ SY134 )
| ~ ( sequential @ SY134 @ SV11 )
| ( triangle @ SV11 @ SY133 @ SY134 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[139]) ).
thf(159,plain,
! [SV11: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY135: $i,SY136: $i] :
~ ( triangle @ SV11 @ SY135 @ SY136 )
| ( edge @ SV11 ) )
| ~ ! [SY137: $i] :
( ! [SY138: $i] :
~ ( triangle @ SV11 @ SY137 @ SY138 )
| ( edge @ SY137 ) ) )
| ~ ! [SY139: $i,SY140: $i] :
( ~ ( triangle @ SV11 @ SY139 @ SY140 )
| ( edge @ SY140 ) ) )
| ~ ! [SY141: $i] :
( ! [SY142: $i] :
~ ( triangle @ SV11 @ SY141 @ SY142 )
| ( sequential @ SV11 @ SY141 ) ) )
| ~ ! [SY143: $i,SY144: $i] :
( ~ ( triangle @ SV11 @ SY143 @ SY144 )
| ( sequential @ SY143 @ SY144 ) ) )
| ~ ! [SY145: $i,SY146: $i] :
( ~ ( triangle @ SV11 @ SY145 @ SY146 )
| ( sequential @ SY146 @ SV11 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[139]) ).
thf(160,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( edge @ SX0 )
| ~ ( edge @ SX1 )
| ( ( head_of @ SX0 )
!= ( tail_of @ SX1 ) )
| ( sequential @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[140]) ).
thf(161,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(162,plain,
! [SV26: $i,SV20: $i,SV12: $i] :
( ( ~ ( vertex @ SV12 )
| ~ ( vertex @ SV20 )
| ~ ( ~ ! [SY190: $i] :
( ( SV12
!= ( tail_of @ SY190 ) )
| ~ ( edge @ SY190 )
| ( SV20
!= ( head_of @ SY190 ) )
| ( SV26
!= ( path_cons @ SY190 @ empty ) ) )
| ~ ! [SY191: $i] :
( ( SV12
!= ( tail_of @ SY191 ) )
| ~ ( edge @ SY191 )
| ! [SY192: $i] :
( ( SV26
!= ( path_cons @ SY191 @ SY192 ) )
| ~ ( path @ ( head_of @ SY191 ) @ SV20 @ SY192 ) ) ) )
| ( path @ SV12 @ SV20 @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(163,plain,
( ( ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( head_of @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[143]) ).
thf(164,plain,
( ( ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( tail_of @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[144]) ).
thf(165,plain,
! [SV21: $i,SV13: $i,SV27: $i] :
( ( ~ ( ~ ! [SY193: $i] :
( ! [SY194: $i] :
( ~ ( precedes @ SV27 @ SY193 @ SY194 )
| ~ ( shortest_path @ SV13 @ SV21 @ SY194 ) )
| ! [SY195: $i] :
( ( ( tail_of @ SY195 )
!= ( tail_of @ SV27 ) )
| ( ( head_of @ SY195 )
!= ( head_of @ SY193 ) ) ) )
| ~ ! [SY196: $i,SY197: $i] :
( ~ ( precedes @ SV27 @ SY196 @ SY197 )
| ~ ( shortest_path @ SV13 @ SV21 @ SY197 )
| ~ ( precedes @ SY196 @ SV27 @ SY197 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(166,plain,
! [SV14: $i] :
( ( ~ ~ ( ~ ( ! [SY159: $i,SY160: $i] :
~ ( path @ SV14 @ SY159 @ SY160 )
| ( vertex @ SV14 ) )
| ~ ! [SY161: $i] :
( ! [SY162: $i] :
~ ( path @ SV14 @ SY161 @ SY162 )
| ( vertex @ SY161 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[146]) ).
thf(167,plain,
! [SV14: $i] :
( ( ~ ! [SY163: $i,SY164: $i] :
( ~ ( path @ SV14 @ SY163 @ SY164 )
| ~ ( ~ ~ ( ( SV14
!= ( tail_of @ ( sK11_E @ SY164 @ SY163 @ SV14 ) ) )
| ~ ( edge @ ( sK11_E @ SY164 @ SY163 @ SV14 ) ) )
| ~ ~ ( ~ ( ( SY163
!= ( head_of @ ( sK11_E @ SY164 @ SY163 @ SV14 ) ) )
| ( SY164
!= ( path_cons @ ( sK11_E @ SY164 @ SY163 @ SV14 ) @ empty ) )
| ! [SY165: $i] :
( ( SY164
!= ( path_cons @ ( sK11_E @ SY164 @ SY163 @ SV14 ) @ SY165 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY164 @ SY163 @ SV14 ) ) @ SY163 @ SY165 ) ) )
| ~ ~ ( ~ ( ( SY163
= ( head_of @ ( sK11_E @ SY164 @ SY163 @ SV14 ) ) )
| ~ ( ( SY164
!= ( path_cons @ ( sK11_E @ SY164 @ SY163 @ SV14 ) @ ( sK13_SY84 @ SY164 @ SY163 @ SV14 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY164 @ SY163 @ SV14 ) ) @ SY163 @ ( sK13_SY84 @ SY164 @ SY163 @ SV14 ) ) ) )
| ~ ( ( SY164
= ( path_cons @ ( sK11_E @ SY164 @ SY163 @ SV14 ) @ empty ) )
| ~ ( ( SY164
!= ( path_cons @ ( sK11_E @ SY164 @ SY163 @ SV14 ) @ ( sK12_SY85 @ SY164 @ SY163 @ SV14 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY164 @ SY163 @ SV14 ) ) @ SY163 @ ( sK12_SY85 @ SY164 @ SY163 @ SV14 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[146]) ).
thf(168,plain,
! [SV28: $i] :
( ( ( ! [SY198: $i] :
( ( SV28 = SY198 )
| ~ ( vertex @ SV28 )
| ~ ( vertex @ SY198 )
| ~ ( ~ ~ ( ~ ( ( SV28
!= ( head_of @ ( sK14_E @ SY198 @ SV28 ) ) )
| ( SY198
!= ( tail_of @ ( sK14_E @ SY198 @ SV28 ) ) )
| ( SY198
!= ( head_of @ ( sK14_E @ SY198 @ SV28 ) ) )
| ( SV28
!= ( tail_of @ ( sK14_E @ SY198 @ SV28 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV28
= ( head_of @ ( sK14_E @ SY198 @ SV28 ) ) )
| ( SY198
= ( head_of @ ( sK14_E @ SY198 @ SV28 ) ) ) )
| ~ ( ( SV28
= ( head_of @ ( sK14_E @ SY198 @ SV28 ) ) )
| ( SV28
= ( tail_of @ ( sK14_E @ SY198 @ SV28 ) ) ) ) )
| ~ ~ ( ~ ( ( SY198
= ( tail_of @ ( sK14_E @ SY198 @ SV28 ) ) )
| ( SY198
= ( head_of @ ( sK14_E @ SY198 @ SV28 ) ) ) )
| ~ ( ( SY198
= ( tail_of @ ( sK14_E @ SY198 @ SV28 ) ) )
| ( SV28
= ( tail_of @ ( sK14_E @ SY198 @ SV28 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SY198 @ SV28 ) ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(169,plain,
! [SV1: $i] :
( ( ( ( head_of @ SV1 )
= ( tail_of @ SV1 ) )
= $false )
| ( ( edge @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(170,plain,
! [SV22: $i,SV15: $i,SV2: $i] :
( ( ( ~ ( path @ SV2 @ SV15 @ SV22 ) )
= $true )
| ( ( ( length_of @ SV22 )
= ( number_of_in @ edges @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(171,plain,
! [SV23: $i,SV16: $i,SV3: $i] :
( ( ( ~ ( path @ SV3 @ SV16 @ SV23 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV23 )
= ( minus @ ( length_of @ SV23 ) @ n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(172,plain,
! [SV5: $i,SV29: $i,SV24: $i] :
( ( ( ~ ( path @ SV24 @ SV29 @ SV5 ) )
= $true )
| ( ( ~ ( ~ ! [SY93: $i,SY94: $i] :
( ~ ( on_path @ SY93 @ SV5 )
| ~ ( on_path @ SY94 @ SV5 )
| ! [SY95: $i] :
( ~ ( precedes @ SY95 @ SY94 @ SV5 )
| ~ ( sequential @ SY93 @ SY95 ) )
| ( precedes @ SY93 @ SY94 @ SV5 ) )
| ~ ! [SY96: $i,SY97: $i] :
( ~ ( on_path @ SY96 @ SV5 )
| ~ ( on_path @ SY97 @ SV5 )
| ~ ( sequential @ SY96 @ SY97 )
| ( precedes @ SY96 @ SY97 @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(173,plain,
! [SV6: $i] :
( ( ! [SY98: $i,SY99: $i] :
( ~ ( ~ ( path @ SV6 @ SY98 @ ( sK8_P @ SY99 @ SY98 @ SV6 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY99 ) @ ( length_of @ ( sK8_P @ SY99 @ SY98 @ SV6 ) ) ) )
| ( SV6 = SY98 )
| ~ ( path @ SV6 @ SY98 @ SY99 )
| ( shortest_path @ SV6 @ SY98 @ SY99 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[152]) ).
thf(174,plain,
! [SV6: $i] :
( ( ~ ( ~ ! [SY100: $i,SY101: $i] :
( ~ ( shortest_path @ SV6 @ SY100 @ SY101 )
| ! [SY102: $i] :
( ~ ( path @ SV6 @ SY100 @ SY102 )
| ( less_or_equal @ ( length_of @ SY101 ) @ ( length_of @ SY102 ) ) ) )
| ~ ~ ( ~ ! [SY103: $i] :
( ! [SY104: $i] :
~ ( shortest_path @ SV6 @ SY103 @ SY104 )
| ( SV6 != SY103 ) )
| ~ ! [SY105: $i,SY106: $i] :
( ~ ( shortest_path @ SV6 @ SY105 @ SY106 )
| ( path @ SV6 @ SY105 @ SY106 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[153]) ).
thf(175,plain,
! [SV18: $i,SV7: $i] :
( ( ~ ~ ( ~ ! [SY168: $i,SY169: $i] :
( ~ ( on_path @ SY169 @ SY168 )
| ~ ( path @ SV7 @ SV18 @ SY168 )
| ( edge @ SY169 ) )
| ~ ! [SY170: $i,SY171: $i] :
( ~ ( on_path @ SY171 @ SY170 )
| ~ ( path @ SV7 @ SV18 @ SY170 )
| ( in_path @ ( head_of @ SY171 ) @ SY170 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[154]) ).
thf(176,plain,
! [SV18: $i,SV7: $i] :
( ( ~ ! [SY172: $i,SY173: $i] :
( ~ ( on_path @ SY173 @ SY172 )
| ~ ( path @ SV7 @ SV18 @ SY172 )
| ( in_path @ ( tail_of @ SY173 ) @ SY172 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[154]) ).
thf(177,plain,
! [SV8: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV8 ) @ SV8 )
| ~ ( on_path @ ( sK7_SY80 @ SV8 ) @ SV8 ) )
| ~ ( sequential @ ( sK6_E1 @ SV8 ) @ ( sK7_SY80 @ SV8 ) ) )
| ~ ! [SY114: $i] :
~ ( triangle @ ( sK6_E1 @ SV8 ) @ ( sK7_SY80 @ SV8 ) @ SY114 ) )
= $false )
| ( ( ! [SY115: $i,SY116: $i] :
~ ( path @ SY115 @ SY116 @ SV8 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV8 )
= ( number_of_in @ triangles @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(178,plain,
! [SV19: $i,SV9: $i] :
( ( ~ ! [SY174: $i,SY175: $i] :
( ~ ( in_path @ SY175 @ SY174 )
| ~ ( path @ SV9 @ SV19 @ SY174 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY175 @ SY174 @ SV19 @ SV9 ) @ SY174 )
| ~ ( ( SY175
= ( head_of @ ( sK10_E @ SY175 @ SY174 @ SV19 @ SV9 ) ) )
| ( SY175
= ( tail_of @ ( sK10_E @ SY175 @ SY174 @ SV19 @ SV9 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[156]) ).
thf(179,plain,
! [SV19: $i,SV9: $i] :
( ( ~ ! [SY176: $i,SY177: $i] :
( ~ ( in_path @ SY177 @ SY176 )
| ~ ( path @ SV9 @ SV19 @ SY176 )
| ( vertex @ SY177 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[156]) ).
thf(180,plain,
! [SV10: $i,SV30: $i,SV25: $i] :
( ( ( ~ ( path @ SV25 @ SV30 @ SV10 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY124: $i] :
( ! [SY125: $i] :
~ ( precedes @ SY124 @ SY125 @ SV10 )
| ( on_path @ SY124 @ SV10 ) )
| ~ ! [SY126: $i,SY127: $i] :
( ~ ( precedes @ SY126 @ SY127 @ SV10 )
| ( on_path @ SY127 @ SV10 ) ) )
| ~ ~ ( ~ ! [SY128: $i,SY129: $i] :
( ~ ( precedes @ SY128 @ SY129 @ SV10 )
| ! [SY130: $i] :
( ~ ( precedes @ SY130 @ SY129 @ SV10 )
| ~ ( sequential @ SY128 @ SY130 ) )
| ~ ( sequential @ SY128 @ SY129 ) )
| ~ ! [SY131: $i,SY132: $i] :
( ~ ( precedes @ SY131 @ SY132 @ SV10 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY132 @ SY131 @ SV10 ) @ SY132 @ SV10 )
| ~ ( sequential @ SY131 @ ( sK9_E3 @ SY132 @ SY131 @ SV10 ) ) )
| ( sequential @ SY131 @ SY132 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(181,plain,
! [SV11: $i] :
( ( ! [SY133: $i,SY134: $i] :
( ~ ( edge @ SV11 )
| ~ ( edge @ SY133 )
| ~ ( edge @ SY134 )
| ~ ( sequential @ SV11 @ SY133 )
| ~ ( sequential @ SY133 @ SY134 )
| ~ ( sequential @ SY134 @ SV11 )
| ( triangle @ SV11 @ SY133 @ SY134 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[158]) ).
thf(182,plain,
! [SV11: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY135: $i,SY136: $i] :
~ ( triangle @ SV11 @ SY135 @ SY136 )
| ( edge @ SV11 ) )
| ~ ! [SY137: $i] :
( ! [SY138: $i] :
~ ( triangle @ SV11 @ SY137 @ SY138 )
| ( edge @ SY137 ) ) )
| ~ ! [SY139: $i,SY140: $i] :
( ~ ( triangle @ SV11 @ SY139 @ SY140 )
| ( edge @ SY140 ) ) )
| ~ ! [SY141: $i] :
( ! [SY142: $i] :
~ ( triangle @ SV11 @ SY141 @ SY142 )
| ( sequential @ SV11 @ SY141 ) ) )
| ~ ! [SY143: $i,SY144: $i] :
( ~ ( triangle @ SV11 @ SY143 @ SY144 )
| ( sequential @ SY143 @ SY144 ) ) )
| ~ ! [SY145: $i,SY146: $i] :
( ~ ( triangle @ SV11 @ SY145 @ SY146 )
| ( sequential @ SY146 @ SV11 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[159]) ).
thf(183,plain,
! [SV31: $i] :
( ( ! [SY199: $i] :
( ( SV31 = SY199 )
| ~ ( edge @ SV31 )
| ~ ( edge @ SY199 )
| ( ( head_of @ SV31 )
!= ( tail_of @ SY199 ) )
| ( sequential @ SV31 @ SY199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(184,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(185,plain,
! [SV26: $i,SV20: $i,SV12: $i] :
( ( ( ~ ( vertex @ SV12 )
| ~ ( vertex @ SV20 )
| ~ ( ~ ! [SY190: $i] :
( ( SV12
!= ( tail_of @ SY190 ) )
| ~ ( edge @ SY190 )
| ( SV20
!= ( head_of @ SY190 ) )
| ( SV26
!= ( path_cons @ SY190 @ empty ) ) )
| ~ ! [SY191: $i] :
( ( SV12
!= ( tail_of @ SY191 ) )
| ~ ( edge @ SY191 )
| ! [SY192: $i] :
( ( SV26
!= ( path_cons @ SY191 @ SY192 ) )
| ~ ( path @ ( head_of @ SY191 ) @ SV20 @ SY192 ) ) ) ) )
= $true )
| ( ( path @ SV12 @ SV20 @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(186,plain,
! [SV32: $i] :
( ( ~ ( edge @ SV32 )
| ( vertex @ ( head_of @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(187,plain,
! [SV33: $i] :
( ( ~ ( edge @ SV33 )
| ( vertex @ ( tail_of @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(188,plain,
! [SV21: $i,SV13: $i,SV27: $i] :
( ( ~ ! [SY193: $i] :
( ! [SY194: $i] :
( ~ ( precedes @ SV27 @ SY193 @ SY194 )
| ~ ( shortest_path @ SV13 @ SV21 @ SY194 ) )
| ! [SY195: $i] :
( ( ( tail_of @ SY195 )
!= ( tail_of @ SV27 ) )
| ( ( head_of @ SY195 )
!= ( head_of @ SY193 ) ) ) )
| ~ ! [SY196: $i,SY197: $i] :
( ~ ( precedes @ SV27 @ SY196 @ SY197 )
| ~ ( shortest_path @ SV13 @ SV21 @ SY197 )
| ~ ( precedes @ SY196 @ SV27 @ SY197 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(189,plain,
! [SV14: $i] :
( ( ~ ( ~ ( ! [SY159: $i,SY160: $i] :
~ ( path @ SV14 @ SY159 @ SY160 )
| ( vertex @ SV14 ) )
| ~ ! [SY161: $i] :
( ! [SY162: $i] :
~ ( path @ SV14 @ SY161 @ SY162 )
| ( vertex @ SY161 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[166]) ).
thf(190,plain,
! [SV14: $i] :
( ( ! [SY163: $i,SY164: $i] :
( ~ ( path @ SV14 @ SY163 @ SY164 )
| ~ ( ~ ~ ( ( SV14
!= ( tail_of @ ( sK11_E @ SY164 @ SY163 @ SV14 ) ) )
| ~ ( edge @ ( sK11_E @ SY164 @ SY163 @ SV14 ) ) )
| ~ ~ ( ~ ( ( SY163
!= ( head_of @ ( sK11_E @ SY164 @ SY163 @ SV14 ) ) )
| ( SY164
!= ( path_cons @ ( sK11_E @ SY164 @ SY163 @ SV14 ) @ empty ) )
| ! [SY165: $i] :
( ( SY164
!= ( path_cons @ ( sK11_E @ SY164 @ SY163 @ SV14 ) @ SY165 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY164 @ SY163 @ SV14 ) ) @ SY163 @ SY165 ) ) )
| ~ ~ ( ~ ( ( SY163
= ( head_of @ ( sK11_E @ SY164 @ SY163 @ SV14 ) ) )
| ~ ( ( SY164
!= ( path_cons @ ( sK11_E @ SY164 @ SY163 @ SV14 ) @ ( sK13_SY84 @ SY164 @ SY163 @ SV14 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY164 @ SY163 @ SV14 ) ) @ SY163 @ ( sK13_SY84 @ SY164 @ SY163 @ SV14 ) ) ) )
| ~ ( ( SY164
= ( path_cons @ ( sK11_E @ SY164 @ SY163 @ SV14 ) @ empty ) )
| ~ ( ( SY164
!= ( path_cons @ ( sK11_E @ SY164 @ SY163 @ SV14 ) @ ( sK12_SY85 @ SY164 @ SY163 @ SV14 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY164 @ SY163 @ SV14 ) ) @ SY163 @ ( sK12_SY85 @ SY164 @ SY163 @ SV14 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[167]) ).
thf(191,plain,
! [SV34: $i,SV28: $i] :
( ( ( ( SV28 = SV34 )
| ~ ( vertex @ SV28 )
| ~ ( vertex @ SV34 )
| ~ ( ~ ~ ( ~ ( ( SV28
!= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
!= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
!= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
!= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV28
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
| ~ ( ( SV28
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) ) )
| ~ ~ ( ~ ( ( SV34
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
| ~ ( ( SV34
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV34 @ SV28 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(192,plain,
! [SV22: $i,SV15: $i,SV2: $i] :
( ( ( path @ SV2 @ SV15 @ SV22 )
= $false )
| ( ( ( length_of @ SV22 )
= ( number_of_in @ edges @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(193,plain,
! [SV23: $i,SV16: $i,SV3: $i] :
( ( ( path @ SV3 @ SV16 @ SV23 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV23 )
= ( minus @ ( length_of @ SV23 ) @ n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(194,plain,
! [SV5: $i,SV29: $i,SV24: $i] :
( ( ( path @ SV24 @ SV29 @ SV5 )
= $false )
| ( ( ~ ( ~ ! [SY93: $i,SY94: $i] :
( ~ ( on_path @ SY93 @ SV5 )
| ~ ( on_path @ SY94 @ SV5 )
| ! [SY95: $i] :
( ~ ( precedes @ SY95 @ SY94 @ SV5 )
| ~ ( sequential @ SY93 @ SY95 ) )
| ( precedes @ SY93 @ SY94 @ SV5 ) )
| ~ ! [SY96: $i,SY97: $i] :
( ~ ( on_path @ SY96 @ SV5 )
| ~ ( on_path @ SY97 @ SV5 )
| ~ ( sequential @ SY96 @ SY97 )
| ( precedes @ SY96 @ SY97 @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(195,plain,
! [SV35: $i,SV6: $i] :
( ( ! [SY200: $i] :
( ~ ( ~ ( path @ SV6 @ SV35 @ ( sK8_P @ SY200 @ SV35 @ SV6 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY200 ) @ ( length_of @ ( sK8_P @ SY200 @ SV35 @ SV6 ) ) ) )
| ( SV6 = SV35 )
| ~ ( path @ SV6 @ SV35 @ SY200 )
| ( shortest_path @ SV6 @ SV35 @ SY200 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(196,plain,
! [SV6: $i] :
( ( ~ ! [SY100: $i,SY101: $i] :
( ~ ( shortest_path @ SV6 @ SY100 @ SY101 )
| ! [SY102: $i] :
( ~ ( path @ SV6 @ SY100 @ SY102 )
| ( less_or_equal @ ( length_of @ SY101 ) @ ( length_of @ SY102 ) ) ) )
| ~ ~ ( ~ ! [SY103: $i] :
( ! [SY104: $i] :
~ ( shortest_path @ SV6 @ SY103 @ SY104 )
| ( SV6 != SY103 ) )
| ~ ! [SY105: $i,SY106: $i] :
( ~ ( shortest_path @ SV6 @ SY105 @ SY106 )
| ( path @ SV6 @ SY105 @ SY106 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(197,plain,
! [SV18: $i,SV7: $i] :
( ( ~ ( ~ ! [SY168: $i,SY169: $i] :
( ~ ( on_path @ SY169 @ SY168 )
| ~ ( path @ SV7 @ SV18 @ SY168 )
| ( edge @ SY169 ) )
| ~ ! [SY170: $i,SY171: $i] :
( ~ ( on_path @ SY171 @ SY170 )
| ~ ( path @ SV7 @ SV18 @ SY170 )
| ( in_path @ ( head_of @ SY171 ) @ SY170 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[175]) ).
thf(198,plain,
! [SV18: $i,SV7: $i] :
( ( ! [SY172: $i,SY173: $i] :
( ~ ( on_path @ SY173 @ SY172 )
| ~ ( path @ SV7 @ SV18 @ SY172 )
| ( in_path @ ( tail_of @ SY173 ) @ SY172 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[176]) ).
thf(199,plain,
! [SV8: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV8 ) @ SV8 )
| ~ ( on_path @ ( sK7_SY80 @ SV8 ) @ SV8 ) )
| ~ ( sequential @ ( sK6_E1 @ SV8 ) @ ( sK7_SY80 @ SV8 ) ) ) )
= $false )
| ( ( ! [SY115: $i,SY116: $i] :
~ ( path @ SY115 @ SY116 @ SV8 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV8 )
= ( number_of_in @ triangles @ SV8 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[177]) ).
thf(200,plain,
! [SV8: $i] :
( ( ( ~ ! [SY114: $i] :
~ ( triangle @ ( sK6_E1 @ SV8 ) @ ( sK7_SY80 @ SV8 ) @ SY114 ) )
= $false )
| ( ( ! [SY115: $i,SY116: $i] :
~ ( path @ SY115 @ SY116 @ SV8 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV8 )
= ( number_of_in @ triangles @ SV8 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[177]) ).
thf(201,plain,
! [SV19: $i,SV9: $i] :
( ( ! [SY174: $i,SY175: $i] :
( ~ ( in_path @ SY175 @ SY174 )
| ~ ( path @ SV9 @ SV19 @ SY174 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY175 @ SY174 @ SV19 @ SV9 ) @ SY174 )
| ~ ( ( SY175
= ( head_of @ ( sK10_E @ SY175 @ SY174 @ SV19 @ SV9 ) ) )
| ( SY175
= ( tail_of @ ( sK10_E @ SY175 @ SY174 @ SV19 @ SV9 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[178]) ).
thf(202,plain,
! [SV19: $i,SV9: $i] :
( ( ! [SY176: $i,SY177: $i] :
( ~ ( in_path @ SY177 @ SY176 )
| ~ ( path @ SV9 @ SV19 @ SY176 )
| ( vertex @ SY177 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[179]) ).
thf(203,plain,
! [SV10: $i,SV30: $i,SV25: $i] :
( ( ( path @ SV25 @ SV30 @ SV10 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY124: $i] :
( ! [SY125: $i] :
~ ( precedes @ SY124 @ SY125 @ SV10 )
| ( on_path @ SY124 @ SV10 ) )
| ~ ! [SY126: $i,SY127: $i] :
( ~ ( precedes @ SY126 @ SY127 @ SV10 )
| ( on_path @ SY127 @ SV10 ) ) )
| ~ ~ ( ~ ! [SY128: $i,SY129: $i] :
( ~ ( precedes @ SY128 @ SY129 @ SV10 )
| ! [SY130: $i] :
( ~ ( precedes @ SY130 @ SY129 @ SV10 )
| ~ ( sequential @ SY128 @ SY130 ) )
| ~ ( sequential @ SY128 @ SY129 ) )
| ~ ! [SY131: $i,SY132: $i] :
( ~ ( precedes @ SY131 @ SY132 @ SV10 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY132 @ SY131 @ SV10 ) @ SY132 @ SV10 )
| ~ ( sequential @ SY131 @ ( sK9_E3 @ SY132 @ SY131 @ SV10 ) ) )
| ( sequential @ SY131 @ SY132 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(204,plain,
! [SV36: $i,SV11: $i] :
( ( ! [SY201: $i] :
( ~ ( edge @ SV11 )
| ~ ( edge @ SV36 )
| ~ ( edge @ SY201 )
| ~ ( sequential @ SV11 @ SV36 )
| ~ ( sequential @ SV36 @ SY201 )
| ~ ( sequential @ SY201 @ SV11 )
| ( triangle @ SV11 @ SV36 @ SY201 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(205,plain,
! [SV11: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY135: $i,SY136: $i] :
~ ( triangle @ SV11 @ SY135 @ SY136 )
| ( edge @ SV11 ) )
| ~ ! [SY137: $i] :
( ! [SY138: $i] :
~ ( triangle @ SV11 @ SY137 @ SY138 )
| ( edge @ SY137 ) ) )
| ~ ! [SY139: $i,SY140: $i] :
( ~ ( triangle @ SV11 @ SY139 @ SY140 )
| ( edge @ SY140 ) ) )
| ~ ! [SY141: $i] :
( ! [SY142: $i] :
~ ( triangle @ SV11 @ SY141 @ SY142 )
| ( sequential @ SV11 @ SY141 ) ) )
| ~ ! [SY143: $i,SY144: $i] :
( ~ ( triangle @ SV11 @ SY143 @ SY144 )
| ( sequential @ SY143 @ SY144 ) ) )
| ~ ! [SY145: $i,SY146: $i] :
( ~ ( triangle @ SV11 @ SY145 @ SY146 )
| ( sequential @ SY146 @ SV11 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(206,plain,
! [SV37: $i,SV31: $i] :
( ( ( SV31 = SV37 )
| ~ ( edge @ SV31 )
| ~ ( edge @ SV37 )
| ( ( head_of @ SV31 )
!= ( tail_of @ SV37 ) )
| ( sequential @ SV31 @ SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(207,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[184]) ).
thf(208,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[184]) ).
thf(209,plain,
! [SV26: $i,SV20: $i,SV12: $i] :
( ( ( ~ ( vertex @ SV12 )
| ~ ( vertex @ SV20 ) )
= $true )
| ( ( ~ ( ~ ! [SY190: $i] :
( ( SV12
!= ( tail_of @ SY190 ) )
| ~ ( edge @ SY190 )
| ( SV20
!= ( head_of @ SY190 ) )
| ( SV26
!= ( path_cons @ SY190 @ empty ) ) )
| ~ ! [SY191: $i] :
( ( SV12
!= ( tail_of @ SY191 ) )
| ~ ( edge @ SY191 )
| ! [SY192: $i] :
( ( SV26
!= ( path_cons @ SY191 @ SY192 ) )
| ~ ( path @ ( head_of @ SY191 ) @ SV20 @ SY192 ) ) ) ) )
= $true )
| ( ( path @ SV12 @ SV20 @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(210,plain,
! [SV32: $i] :
( ( ( ~ ( edge @ SV32 ) )
= $true )
| ( ( vertex @ ( head_of @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(211,plain,
! [SV33: $i] :
( ( ( ~ ( edge @ SV33 ) )
= $true )
| ( ( vertex @ ( tail_of @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(212,plain,
! [SV21: $i,SV13: $i,SV27: $i] :
( ( ~ ! [SY193: $i] :
( ! [SY194: $i] :
( ~ ( precedes @ SV27 @ SY193 @ SY194 )
| ~ ( shortest_path @ SV13 @ SV21 @ SY194 ) )
| ! [SY195: $i] :
( ( ( tail_of @ SY195 )
!= ( tail_of @ SV27 ) )
| ( ( head_of @ SY195 )
!= ( head_of @ SY193 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[188]) ).
thf(213,plain,
! [SV21: $i,SV13: $i,SV27: $i] :
( ( ~ ! [SY196: $i,SY197: $i] :
( ~ ( precedes @ SV27 @ SY196 @ SY197 )
| ~ ( shortest_path @ SV13 @ SV21 @ SY197 )
| ~ ( precedes @ SY196 @ SV27 @ SY197 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[188]) ).
thf(214,plain,
! [SV14: $i] :
( ( ~ ( ! [SY159: $i,SY160: $i] :
~ ( path @ SV14 @ SY159 @ SY160 )
| ( vertex @ SV14 ) )
| ~ ! [SY161: $i] :
( ! [SY162: $i] :
~ ( path @ SV14 @ SY161 @ SY162 )
| ( vertex @ SY161 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(215,plain,
! [SV38: $i,SV14: $i] :
( ( ! [SY202: $i] :
( ~ ( path @ SV14 @ SV38 @ SY202 )
| ~ ( ~ ~ ( ( SV14
!= ( tail_of @ ( sK11_E @ SY202 @ SV38 @ SV14 ) ) )
| ~ ( edge @ ( sK11_E @ SY202 @ SV38 @ SV14 ) ) )
| ~ ~ ( ~ ( ( SV38
!= ( head_of @ ( sK11_E @ SY202 @ SV38 @ SV14 ) ) )
| ( SY202
!= ( path_cons @ ( sK11_E @ SY202 @ SV38 @ SV14 ) @ empty ) )
| ! [SY203: $i] :
( ( SY202
!= ( path_cons @ ( sK11_E @ SY202 @ SV38 @ SV14 ) @ SY203 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY202 @ SV38 @ SV14 ) ) @ SV38 @ SY203 ) ) )
| ~ ~ ( ~ ( ( SV38
= ( head_of @ ( sK11_E @ SY202 @ SV38 @ SV14 ) ) )
| ~ ( ( SY202
!= ( path_cons @ ( sK11_E @ SY202 @ SV38 @ SV14 ) @ ( sK13_SY84 @ SY202 @ SV38 @ SV14 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY202 @ SV38 @ SV14 ) ) @ SV38 @ ( sK13_SY84 @ SY202 @ SV38 @ SV14 ) ) ) )
| ~ ( ( SY202
= ( path_cons @ ( sK11_E @ SY202 @ SV38 @ SV14 ) @ empty ) )
| ~ ( ( SY202
!= ( path_cons @ ( sK11_E @ SY202 @ SV38 @ SV14 ) @ ( sK12_SY85 @ SY202 @ SV38 @ SV14 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY202 @ SV38 @ SV14 ) ) @ SV38 @ ( sK12_SY85 @ SY202 @ SV38 @ SV14 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(216,plain,
! [SV34: $i,SV28: $i] :
( ( ( ( SV28 = SV34 )
| ~ ( vertex @ SV28 )
| ~ ( vertex @ SV34 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV28
!= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
!= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
!= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
!= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV28
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
| ~ ( ( SV28
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) ) )
| ~ ~ ( ~ ( ( SV34
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
| ~ ( ( SV34
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV34 @ SV28 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(217,plain,
! [SV29: $i,SV24: $i,SV5: $i] :
( ( ( ~ ! [SY93: $i,SY94: $i] :
( ~ ( on_path @ SY93 @ SV5 )
| ~ ( on_path @ SY94 @ SV5 )
| ! [SY95: $i] :
( ~ ( precedes @ SY95 @ SY94 @ SV5 )
| ~ ( sequential @ SY93 @ SY95 ) )
| ( precedes @ SY93 @ SY94 @ SV5 ) )
| ~ ! [SY96: $i,SY97: $i] :
( ~ ( on_path @ SY96 @ SV5 )
| ~ ( on_path @ SY97 @ SV5 )
| ~ ( sequential @ SY96 @ SY97 )
| ( precedes @ SY96 @ SY97 @ SV5 ) ) )
= $false )
| ( ( path @ SV24 @ SV29 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(218,plain,
! [SV39: $i,SV35: $i,SV6: $i] :
( ( ~ ( ~ ( path @ SV6 @ SV35 @ ( sK8_P @ SV39 @ SV35 @ SV6 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SV39 ) @ ( length_of @ ( sK8_P @ SV39 @ SV35 @ SV6 ) ) ) )
| ( SV6 = SV35 )
| ~ ( path @ SV6 @ SV35 @ SV39 )
| ( shortest_path @ SV6 @ SV35 @ SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(219,plain,
! [SV6: $i] :
( ( ~ ! [SY100: $i,SY101: $i] :
( ~ ( shortest_path @ SV6 @ SY100 @ SY101 )
| ! [SY102: $i] :
( ~ ( path @ SV6 @ SY100 @ SY102 )
| ( less_or_equal @ ( length_of @ SY101 ) @ ( length_of @ SY102 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[196]) ).
thf(220,plain,
! [SV6: $i] :
( ( ~ ~ ( ~ ! [SY103: $i] :
( ! [SY104: $i] :
~ ( shortest_path @ SV6 @ SY103 @ SY104 )
| ( SV6 != SY103 ) )
| ~ ! [SY105: $i,SY106: $i] :
( ~ ( shortest_path @ SV6 @ SY105 @ SY106 )
| ( path @ SV6 @ SY105 @ SY106 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[196]) ).
thf(221,plain,
! [SV18: $i,SV7: $i] :
( ( ~ ! [SY168: $i,SY169: $i] :
( ~ ( on_path @ SY169 @ SY168 )
| ~ ( path @ SV7 @ SV18 @ SY168 )
| ( edge @ SY169 ) )
| ~ ! [SY170: $i,SY171: $i] :
( ~ ( on_path @ SY171 @ SY170 )
| ~ ( path @ SV7 @ SV18 @ SY170 )
| ( in_path @ ( head_of @ SY171 ) @ SY170 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(222,plain,
! [SV18: $i,SV7: $i,SV40: $i] :
( ( ! [SY204: $i] :
( ~ ( on_path @ SY204 @ SV40 )
| ~ ( path @ SV7 @ SV18 @ SV40 )
| ( in_path @ ( tail_of @ SY204 ) @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(223,plain,
! [SV8: $i] :
( ( ( ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV8 ) @ SV8 )
| ~ ( on_path @ ( sK7_SY80 @ SV8 ) @ SV8 ) )
| ~ ( sequential @ ( sK6_E1 @ SV8 ) @ ( sK7_SY80 @ SV8 ) ) ) )
= $true )
| ( ( ! [SY115: $i,SY116: $i] :
~ ( path @ SY115 @ SY116 @ SV8 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV8 )
= ( number_of_in @ triangles @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[199]) ).
thf(224,plain,
! [SV8: $i] :
( ( ( ! [SY114: $i] :
~ ( triangle @ ( sK6_E1 @ SV8 ) @ ( sK7_SY80 @ SV8 ) @ SY114 ) )
= $true )
| ( ( ! [SY115: $i,SY116: $i] :
~ ( path @ SY115 @ SY116 @ SV8 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV8 )
= ( number_of_in @ triangles @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[200]) ).
thf(225,plain,
! [SV19: $i,SV9: $i,SV41: $i] :
( ( ! [SY205: $i] :
( ~ ( in_path @ SY205 @ SV41 )
| ~ ( path @ SV9 @ SV19 @ SV41 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY205 @ SV41 @ SV19 @ SV9 ) @ SV41 )
| ~ ( ( SY205
= ( head_of @ ( sK10_E @ SY205 @ SV41 @ SV19 @ SV9 ) ) )
| ( SY205
= ( tail_of @ ( sK10_E @ SY205 @ SV41 @ SV19 @ SV9 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(226,plain,
! [SV19: $i,SV9: $i,SV42: $i] :
( ( ! [SY206: $i] :
( ~ ( in_path @ SY206 @ SV42 )
| ~ ( path @ SV9 @ SV19 @ SV42 )
| ( vertex @ SY206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(227,plain,
! [SV30: $i,SV25: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ! [SY124: $i] :
( ! [SY125: $i] :
~ ( precedes @ SY124 @ SY125 @ SV10 )
| ( on_path @ SY124 @ SV10 ) )
| ~ ! [SY126: $i,SY127: $i] :
( ~ ( precedes @ SY126 @ SY127 @ SV10 )
| ( on_path @ SY127 @ SV10 ) ) )
| ~ ~ ( ~ ! [SY128: $i,SY129: $i] :
( ~ ( precedes @ SY128 @ SY129 @ SV10 )
| ! [SY130: $i] :
( ~ ( precedes @ SY130 @ SY129 @ SV10 )
| ~ ( sequential @ SY128 @ SY130 ) )
| ~ ( sequential @ SY128 @ SY129 ) )
| ~ ! [SY131: $i,SY132: $i] :
( ~ ( precedes @ SY131 @ SY132 @ SV10 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY132 @ SY131 @ SV10 ) @ SY132 @ SV10 )
| ~ ( sequential @ SY131 @ ( sK9_E3 @ SY132 @ SY131 @ SV10 ) ) )
| ( sequential @ SY131 @ SY132 ) ) ) )
= $false )
| ( ( path @ SV25 @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(228,plain,
! [SV43: $i,SV36: $i,SV11: $i] :
( ( ~ ( edge @ SV11 )
| ~ ( edge @ SV36 )
| ~ ( edge @ SV43 )
| ~ ( sequential @ SV11 @ SV36 )
| ~ ( sequential @ SV36 @ SV43 )
| ~ ( sequential @ SV43 @ SV11 )
| ( triangle @ SV11 @ SV36 @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(229,plain,
! [SV11: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY135: $i,SY136: $i] :
~ ( triangle @ SV11 @ SY135 @ SY136 )
| ( edge @ SV11 ) )
| ~ ! [SY137: $i] :
( ! [SY138: $i] :
~ ( triangle @ SV11 @ SY137 @ SY138 )
| ( edge @ SY137 ) ) )
| ~ ! [SY139: $i,SY140: $i] :
( ~ ( triangle @ SV11 @ SY139 @ SY140 )
| ( edge @ SY140 ) ) )
| ~ ! [SY141: $i] :
( ! [SY142: $i] :
~ ( triangle @ SV11 @ SY141 @ SY142 )
| ( sequential @ SV11 @ SY141 ) ) )
| ~ ! [SY143: $i,SY144: $i] :
( ~ ( triangle @ SV11 @ SY143 @ SY144 )
| ( sequential @ SY143 @ SY144 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[205]) ).
thf(230,plain,
! [SV11: $i] :
( ( ~ ! [SY145: $i,SY146: $i] :
( ~ ( triangle @ SV11 @ SY145 @ SY146 )
| ( sequential @ SY146 @ SV11 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[205]) ).
thf(231,plain,
! [SV37: $i,SV31: $i] :
( ( ( ( SV31 = SV37 )
| ~ ( edge @ SV31 )
| ~ ( edge @ SV37 )
| ( ( head_of @ SV31 )
!= ( tail_of @ SV37 ) ) )
= $true )
| ( ( sequential @ SV31 @ SV37 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[206]) ).
thf(232,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[207]) ).
thf(233,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[208]) ).
thf(234,plain,
! [SV26: $i,SV20: $i,SV12: $i] :
( ( ( ~ ( vertex @ SV12 ) )
= $true )
| ( ( ~ ( vertex @ SV20 ) )
= $true )
| ( ( ~ ( ~ ! [SY190: $i] :
( ( SV12
!= ( tail_of @ SY190 ) )
| ~ ( edge @ SY190 )
| ( SV20
!= ( head_of @ SY190 ) )
| ( SV26
!= ( path_cons @ SY190 @ empty ) ) )
| ~ ! [SY191: $i] :
( ( SV12
!= ( tail_of @ SY191 ) )
| ~ ( edge @ SY191 )
| ! [SY192: $i] :
( ( SV26
!= ( path_cons @ SY191 @ SY192 ) )
| ~ ( path @ ( head_of @ SY191 ) @ SV20 @ SY192 ) ) ) ) )
= $true )
| ( ( path @ SV12 @ SV20 @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(235,plain,
! [SV32: $i] :
( ( ( edge @ SV32 )
= $false )
| ( ( vertex @ ( head_of @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(236,plain,
! [SV33: $i] :
( ( ( edge @ SV33 )
= $false )
| ( ( vertex @ ( tail_of @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(237,plain,
! [SV21: $i,SV13: $i,SV27: $i] :
( ( ! [SY193: $i] :
( ! [SY194: $i] :
( ~ ( precedes @ SV27 @ SY193 @ SY194 )
| ~ ( shortest_path @ SV13 @ SV21 @ SY194 ) )
| ! [SY195: $i] :
( ( ( tail_of @ SY195 )
!= ( tail_of @ SV27 ) )
| ( ( head_of @ SY195 )
!= ( head_of @ SY193 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[212]) ).
thf(238,plain,
! [SV21: $i,SV13: $i,SV27: $i] :
( ( ! [SY196: $i,SY197: $i] :
( ~ ( precedes @ SV27 @ SY196 @ SY197 )
| ~ ( shortest_path @ SV13 @ SV21 @ SY197 )
| ~ ( precedes @ SY196 @ SV27 @ SY197 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[213]) ).
thf(239,plain,
! [SV14: $i] :
( ( ~ ( ! [SY159: $i,SY160: $i] :
~ ( path @ SV14 @ SY159 @ SY160 )
| ( vertex @ SV14 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[214]) ).
thf(240,plain,
! [SV14: $i] :
( ( ~ ! [SY161: $i] :
( ! [SY162: $i] :
~ ( path @ SV14 @ SY161 @ SY162 )
| ( vertex @ SY161 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[214]) ).
thf(241,plain,
! [SV44: $i,SV38: $i,SV14: $i] :
( ( ~ ( path @ SV14 @ SV38 @ SV44 )
| ~ ( ~ ~ ( ( SV14
!= ( tail_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( edge @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
| ~ ~ ( ~ ( ( SV38
!= ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
| ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ empty ) )
| ! [SY207: $i] :
( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ SY207 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ SY207 ) ) )
| ~ ~ ( ~ ( ( SV38
= ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ ( sK13_SY84 @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ ( sK13_SY84 @ SV44 @ SV38 @ SV14 ) ) ) )
| ~ ( ( SV44
= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ empty ) )
| ~ ( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ ( sK12_SY85 @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ ( sK12_SY85 @ SV44 @ SV38 @ SV14 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(242,plain,
! [SV34: $i,SV28: $i] :
( ( ( SV28 = SV34 )
= $true )
| ( ( ~ ( vertex @ SV28 )
| ~ ( vertex @ SV34 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV28
!= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
!= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
!= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
!= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV28
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
| ~ ( ( SV28
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) ) )
| ~ ~ ( ~ ( ( SV34
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
| ~ ( ( SV34
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV34 @ SV28 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(243,plain,
! [SV29: $i,SV24: $i,SV5: $i] :
( ( ( ~ ! [SY93: $i,SY94: $i] :
( ~ ( on_path @ SY93 @ SV5 )
| ~ ( on_path @ SY94 @ SV5 )
| ! [SY95: $i] :
( ~ ( precedes @ SY95 @ SY94 @ SV5 )
| ~ ( sequential @ SY93 @ SY95 ) )
| ( precedes @ SY93 @ SY94 @ SV5 ) ) )
= $false )
| ( ( path @ SV24 @ SV29 @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[217]) ).
thf(244,plain,
! [SV29: $i,SV24: $i,SV5: $i] :
( ( ( ~ ! [SY96: $i,SY97: $i] :
( ~ ( on_path @ SY96 @ SV5 )
| ~ ( on_path @ SY97 @ SV5 )
| ~ ( sequential @ SY96 @ SY97 )
| ( precedes @ SY96 @ SY97 @ SV5 ) ) )
= $false )
| ( ( path @ SV24 @ SV29 @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[217]) ).
thf(245,plain,
! [SV39: $i,SV35: $i,SV6: $i] :
( ( ( ~ ( ~ ( path @ SV6 @ SV35 @ ( sK8_P @ SV39 @ SV35 @ SV6 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SV39 ) @ ( length_of @ ( sK8_P @ SV39 @ SV35 @ SV6 ) ) ) )
| ( SV6 = SV35 )
| ~ ( path @ SV6 @ SV35 @ SV39 ) )
= $true )
| ( ( shortest_path @ SV6 @ SV35 @ SV39 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[218]) ).
thf(246,plain,
! [SV6: $i] :
( ( ! [SY100: $i,SY101: $i] :
( ~ ( shortest_path @ SV6 @ SY100 @ SY101 )
| ! [SY102: $i] :
( ~ ( path @ SV6 @ SY100 @ SY102 )
| ( less_or_equal @ ( length_of @ SY101 ) @ ( length_of @ SY102 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[219]) ).
thf(247,plain,
! [SV6: $i] :
( ( ~ ( ~ ! [SY103: $i] :
( ! [SY104: $i] :
~ ( shortest_path @ SV6 @ SY103 @ SY104 )
| ( SV6 != SY103 ) )
| ~ ! [SY105: $i,SY106: $i] :
( ~ ( shortest_path @ SV6 @ SY105 @ SY106 )
| ( path @ SV6 @ SY105 @ SY106 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[220]) ).
thf(248,plain,
! [SV18: $i,SV7: $i] :
( ( ~ ! [SY168: $i,SY169: $i] :
( ~ ( on_path @ SY169 @ SY168 )
| ~ ( path @ SV7 @ SV18 @ SY168 )
| ( edge @ SY169 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[221]) ).
thf(249,plain,
! [SV18: $i,SV7: $i] :
( ( ~ ! [SY170: $i,SY171: $i] :
( ~ ( on_path @ SY171 @ SY170 )
| ~ ( path @ SV7 @ SV18 @ SY170 )
| ( in_path @ ( head_of @ SY171 ) @ SY170 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[221]) ).
thf(250,plain,
! [SV18: $i,SV7: $i,SV40: $i,SV45: $i] :
( ( ~ ( on_path @ SV45 @ SV40 )
| ~ ( path @ SV7 @ SV18 @ SV40 )
| ( in_path @ ( tail_of @ SV45 ) @ SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(251,plain,
! [SV8: $i] :
( ( ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV8 ) @ SV8 )
| ~ ( on_path @ ( sK7_SY80 @ SV8 ) @ SV8 ) )
| ~ ( sequential @ ( sK6_E1 @ SV8 ) @ ( sK7_SY80 @ SV8 ) ) )
= $false )
| ( ( ! [SY115: $i,SY116: $i] :
~ ( path @ SY115 @ SY116 @ SV8 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV8 )
= ( number_of_in @ triangles @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(252,plain,
! [SV46: $i,SV8: $i] :
( ( ( ~ ( triangle @ ( sK6_E1 @ SV8 ) @ ( sK7_SY80 @ SV8 ) @ SV46 ) )
= $true )
| ( ( ! [SY115: $i,SY116: $i] :
~ ( path @ SY115 @ SY116 @ SV8 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV8 )
= ( number_of_in @ triangles @ SV8 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(253,plain,
! [SV19: $i,SV9: $i,SV41: $i,SV47: $i] :
( ( ~ ( in_path @ SV47 @ SV41 )
| ~ ( path @ SV9 @ SV19 @ SV41 )
| ~ ( ~ ( on_path @ ( sK10_E @ SV47 @ SV41 @ SV19 @ SV9 ) @ SV41 )
| ~ ( ( SV47
= ( head_of @ ( sK10_E @ SV47 @ SV41 @ SV19 @ SV9 ) ) )
| ( SV47
= ( tail_of @ ( sK10_E @ SV47 @ SV41 @ SV19 @ SV9 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(254,plain,
! [SV19: $i,SV9: $i,SV42: $i,SV48: $i] :
( ( ~ ( in_path @ SV48 @ SV42 )
| ~ ( path @ SV9 @ SV19 @ SV42 )
| ( vertex @ SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(255,plain,
! [SV30: $i,SV25: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ! [SY124: $i] :
( ! [SY125: $i] :
~ ( precedes @ SY124 @ SY125 @ SV10 )
| ( on_path @ SY124 @ SV10 ) )
| ~ ! [SY126: $i,SY127: $i] :
( ~ ( precedes @ SY126 @ SY127 @ SV10 )
| ( on_path @ SY127 @ SV10 ) ) ) )
= $false )
| ( ( path @ SV25 @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[227]) ).
thf(256,plain,
! [SV30: $i,SV25: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ! [SY128: $i,SY129: $i] :
( ~ ( precedes @ SY128 @ SY129 @ SV10 )
| ! [SY130: $i] :
( ~ ( precedes @ SY130 @ SY129 @ SV10 )
| ~ ( sequential @ SY128 @ SY130 ) )
| ~ ( sequential @ SY128 @ SY129 ) )
| ~ ! [SY131: $i,SY132: $i] :
( ~ ( precedes @ SY131 @ SY132 @ SV10 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY132 @ SY131 @ SV10 ) @ SY132 @ SV10 )
| ~ ( sequential @ SY131 @ ( sK9_E3 @ SY132 @ SY131 @ SV10 ) ) )
| ( sequential @ SY131 @ SY132 ) ) ) )
= $false )
| ( ( path @ SV25 @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[227]) ).
thf(257,plain,
! [SV43: $i,SV36: $i,SV11: $i] :
( ( ( ~ ( edge @ SV11 )
| ~ ( edge @ SV36 )
| ~ ( edge @ SV43 )
| ~ ( sequential @ SV11 @ SV36 )
| ~ ( sequential @ SV36 @ SV43 )
| ~ ( sequential @ SV43 @ SV11 ) )
= $true )
| ( ( triangle @ SV11 @ SV36 @ SV43 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[228]) ).
thf(258,plain,
! [SV11: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY135: $i,SY136: $i] :
~ ( triangle @ SV11 @ SY135 @ SY136 )
| ( edge @ SV11 ) )
| ~ ! [SY137: $i] :
( ! [SY138: $i] :
~ ( triangle @ SV11 @ SY137 @ SY138 )
| ( edge @ SY137 ) ) )
| ~ ! [SY139: $i,SY140: $i] :
( ~ ( triangle @ SV11 @ SY139 @ SY140 )
| ( edge @ SY140 ) ) )
| ~ ! [SY141: $i] :
( ! [SY142: $i] :
~ ( triangle @ SV11 @ SY141 @ SY142 )
| ( sequential @ SV11 @ SY141 ) ) )
| ~ ! [SY143: $i,SY144: $i] :
( ~ ( triangle @ SV11 @ SY143 @ SY144 )
| ( sequential @ SY143 @ SY144 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[229]) ).
thf(259,plain,
! [SV11: $i] :
( ( ! [SY145: $i,SY146: $i] :
( ~ ( triangle @ SV11 @ SY145 @ SY146 )
| ( sequential @ SY146 @ SV11 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[230]) ).
thf(260,plain,
! [SV37: $i,SV31: $i] :
( ( ( ( SV31 = SV37 )
| ~ ( edge @ SV31 )
| ~ ( edge @ SV37 ) )
= $true )
| ( ( ( ( head_of @ SV31 )
!= ( tail_of @ SV37 ) ) )
= $true )
| ( ( sequential @ SV31 @ SV37 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[231]) ).
thf(261,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(262,plain,
! [SV49: $i] :
( ( ! [SY208: $i] :
( ~ ( sequential @ SV49 @ SY208 )
| ( ( head_of @ SV49 )
= ( tail_of @ SY208 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(263,plain,
! [SV26: $i,SV20: $i,SV12: $i] :
( ( ( vertex @ SV12 )
= $false )
| ( ( ~ ( vertex @ SV20 ) )
= $true )
| ( ( ~ ( ~ ! [SY190: $i] :
( ( SV12
!= ( tail_of @ SY190 ) )
| ~ ( edge @ SY190 )
| ( SV20
!= ( head_of @ SY190 ) )
| ( SV26
!= ( path_cons @ SY190 @ empty ) ) )
| ~ ! [SY191: $i] :
( ( SV12
!= ( tail_of @ SY191 ) )
| ~ ( edge @ SY191 )
| ! [SY192: $i] :
( ( SV26
!= ( path_cons @ SY191 @ SY192 ) )
| ~ ( path @ ( head_of @ SY191 ) @ SV20 @ SY192 ) ) ) ) )
= $true )
| ( ( path @ SV12 @ SV20 @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(264,plain,
! [SV21: $i,SV13: $i,SV50: $i,SV27: $i] :
( ( ! [SY209: $i] :
( ~ ( precedes @ SV27 @ SV50 @ SY209 )
| ~ ( shortest_path @ SV13 @ SV21 @ SY209 ) )
| ! [SY210: $i] :
( ( ( tail_of @ SY210 )
!= ( tail_of @ SV27 ) )
| ( ( head_of @ SY210 )
!= ( head_of @ SV50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(265,plain,
! [SV21: $i,SV13: $i,SV51: $i,SV27: $i] :
( ( ! [SY211: $i] :
( ~ ( precedes @ SV27 @ SV51 @ SY211 )
| ~ ( shortest_path @ SV13 @ SV21 @ SY211 )
| ~ ( precedes @ SV51 @ SV27 @ SY211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(266,plain,
! [SV14: $i] :
( ( ! [SY159: $i,SY160: $i] :
~ ( path @ SV14 @ SY159 @ SY160 )
| ( vertex @ SV14 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[239]) ).
thf(267,plain,
! [SV14: $i] :
( ( ! [SY161: $i] :
( ! [SY162: $i] :
~ ( path @ SV14 @ SY161 @ SY162 )
| ( vertex @ SY161 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[240]) ).
thf(268,plain,
! [SV44: $i,SV38: $i,SV14: $i] :
( ( ( ~ ( path @ SV14 @ SV38 @ SV44 ) )
= $true )
| ( ( ~ ( ~ ~ ( ( SV14
!= ( tail_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( edge @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
| ~ ~ ( ~ ( ( SV38
!= ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
| ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ empty ) )
| ! [SY207: $i] :
( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ SY207 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ SY207 ) ) )
| ~ ~ ( ~ ( ( SV38
= ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ ( sK13_SY84 @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ ( sK13_SY84 @ SV44 @ SV38 @ SV14 ) ) ) )
| ~ ( ( SV44
= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ empty ) )
| ~ ( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ ( sK12_SY85 @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ ( sK12_SY85 @ SV44 @ SV38 @ SV14 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[241]) ).
thf(269,plain,
! [SV34: $i,SV28: $i] :
( ( ( ~ ( vertex @ SV28 ) )
= $true )
| ( ( ~ ( vertex @ SV34 ) )
= $true )
| ( ( SV28 = SV34 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV28
!= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
!= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
!= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
!= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV28
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
| ~ ( ( SV28
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) ) )
| ~ ~ ( ~ ( ( SV34
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
| ~ ( ( SV34
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV34 @ SV28 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[242]) ).
thf(270,plain,
! [SV29: $i,SV24: $i,SV5: $i] :
( ( ( ! [SY93: $i,SY94: $i] :
( ~ ( on_path @ SY93 @ SV5 )
| ~ ( on_path @ SY94 @ SV5 )
| ! [SY95: $i] :
( ~ ( precedes @ SY95 @ SY94 @ SV5 )
| ~ ( sequential @ SY93 @ SY95 ) )
| ( precedes @ SY93 @ SY94 @ SV5 ) ) )
= $true )
| ( ( path @ SV24 @ SV29 @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[243]) ).
thf(271,plain,
! [SV29: $i,SV24: $i,SV5: $i] :
( ( ( ! [SY96: $i,SY97: $i] :
( ~ ( on_path @ SY96 @ SV5 )
| ~ ( on_path @ SY97 @ SV5 )
| ~ ( sequential @ SY96 @ SY97 )
| ( precedes @ SY96 @ SY97 @ SV5 ) ) )
= $true )
| ( ( path @ SV24 @ SV29 @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[244]) ).
thf(272,plain,
! [SV39: $i,SV35: $i,SV6: $i] :
( ( ( ~ ( ~ ( path @ SV6 @ SV35 @ ( sK8_P @ SV39 @ SV35 @ SV6 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SV39 ) @ ( length_of @ ( sK8_P @ SV39 @ SV35 @ SV6 ) ) ) ) )
= $true )
| ( ( ( SV6 = SV35 )
| ~ ( path @ SV6 @ SV35 @ SV39 ) )
= $true )
| ( ( shortest_path @ SV6 @ SV35 @ SV39 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[245]) ).
thf(273,plain,
! [SV52: $i,SV6: $i] :
( ( ! [SY212: $i] :
( ~ ( shortest_path @ SV6 @ SV52 @ SY212 )
| ! [SY213: $i] :
( ~ ( path @ SV6 @ SV52 @ SY213 )
| ( less_or_equal @ ( length_of @ SY212 ) @ ( length_of @ SY213 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[246]) ).
thf(274,plain,
! [SV6: $i] :
( ( ~ ! [SY103: $i] :
( ! [SY104: $i] :
~ ( shortest_path @ SV6 @ SY103 @ SY104 )
| ( SV6 != SY103 ) )
| ~ ! [SY105: $i,SY106: $i] :
( ~ ( shortest_path @ SV6 @ SY105 @ SY106 )
| ( path @ SV6 @ SY105 @ SY106 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(275,plain,
! [SV18: $i,SV7: $i] :
( ( ! [SY168: $i,SY169: $i] :
( ~ ( on_path @ SY169 @ SY168 )
| ~ ( path @ SV7 @ SV18 @ SY168 )
| ( edge @ SY169 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[248]) ).
thf(276,plain,
! [SV18: $i,SV7: $i] :
( ( ! [SY170: $i,SY171: $i] :
( ~ ( on_path @ SY171 @ SY170 )
| ~ ( path @ SV7 @ SV18 @ SY170 )
| ( in_path @ ( head_of @ SY171 ) @ SY170 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[249]) ).
thf(277,plain,
! [SV18: $i,SV7: $i,SV40: $i,SV45: $i] :
( ( ( ~ ( on_path @ SV45 @ SV40 )
| ~ ( path @ SV7 @ SV18 @ SV40 ) )
= $true )
| ( ( in_path @ ( tail_of @ SV45 ) @ SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[250]) ).
thf(278,plain,
! [SV8: $i] :
( ( ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV8 ) @ SV8 )
| ~ ( on_path @ ( sK7_SY80 @ SV8 ) @ SV8 ) ) )
= $false )
| ( ( ! [SY115: $i,SY116: $i] :
~ ( path @ SY115 @ SY116 @ SV8 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV8 )
= ( number_of_in @ triangles @ SV8 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[251]) ).
thf(279,plain,
! [SV8: $i] :
( ( ( ~ ( sequential @ ( sK6_E1 @ SV8 ) @ ( sK7_SY80 @ SV8 ) ) )
= $false )
| ( ( ! [SY115: $i,SY116: $i] :
~ ( path @ SY115 @ SY116 @ SV8 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV8 )
= ( number_of_in @ triangles @ SV8 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[251]) ).
thf(280,plain,
! [SV46: $i,SV8: $i] :
( ( ( triangle @ ( sK6_E1 @ SV8 ) @ ( sK7_SY80 @ SV8 ) @ SV46 )
= $false )
| ( ( ! [SY115: $i,SY116: $i] :
~ ( path @ SY115 @ SY116 @ SV8 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV8 )
= ( number_of_in @ triangles @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(281,plain,
! [SV19: $i,SV9: $i,SV41: $i,SV47: $i] :
( ( ( ~ ( in_path @ SV47 @ SV41 )
| ~ ( path @ SV9 @ SV19 @ SV41 ) )
= $true )
| ( ( ~ ( ~ ( on_path @ ( sK10_E @ SV47 @ SV41 @ SV19 @ SV9 ) @ SV41 )
| ~ ( ( SV47
= ( head_of @ ( sK10_E @ SV47 @ SV41 @ SV19 @ SV9 ) ) )
| ( SV47
= ( tail_of @ ( sK10_E @ SV47 @ SV41 @ SV19 @ SV9 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[253]) ).
thf(282,plain,
! [SV19: $i,SV9: $i,SV42: $i,SV48: $i] :
( ( ( ~ ( in_path @ SV48 @ SV42 )
| ~ ( path @ SV9 @ SV19 @ SV42 ) )
= $true )
| ( ( vertex @ SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[254]) ).
thf(283,plain,
! [SV30: $i,SV25: $i,SV10: $i] :
( ( ( ~ ( ~ ! [SY124: $i] :
( ! [SY125: $i] :
~ ( precedes @ SY124 @ SY125 @ SV10 )
| ( on_path @ SY124 @ SV10 ) )
| ~ ! [SY126: $i,SY127: $i] :
( ~ ( precedes @ SY126 @ SY127 @ SV10 )
| ( on_path @ SY127 @ SV10 ) ) ) )
= $true )
| ( ( path @ SV25 @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[255]) ).
thf(284,plain,
! [SV30: $i,SV25: $i,SV10: $i] :
( ( ( ~ ( ~ ! [SY128: $i,SY129: $i] :
( ~ ( precedes @ SY128 @ SY129 @ SV10 )
| ! [SY130: $i] :
( ~ ( precedes @ SY130 @ SY129 @ SV10 )
| ~ ( sequential @ SY128 @ SY130 ) )
| ~ ( sequential @ SY128 @ SY129 ) )
| ~ ! [SY131: $i,SY132: $i] :
( ~ ( precedes @ SY131 @ SY132 @ SV10 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY132 @ SY131 @ SV10 ) @ SY132 @ SV10 )
| ~ ( sequential @ SY131 @ ( sK9_E3 @ SY132 @ SY131 @ SV10 ) ) )
| ( sequential @ SY131 @ SY132 ) ) ) )
= $true )
| ( ( path @ SV25 @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[256]) ).
thf(285,plain,
! [SV43: $i,SV36: $i,SV11: $i] :
( ( ( ~ ( edge @ SV11 )
| ~ ( edge @ SV36 )
| ~ ( edge @ SV43 )
| ~ ( sequential @ SV11 @ SV36 )
| ~ ( sequential @ SV36 @ SV43 ) )
= $true )
| ( ( ~ ( sequential @ SV43 @ SV11 ) )
= $true )
| ( ( triangle @ SV11 @ SV36 @ SV43 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[257]) ).
thf(286,plain,
! [SV11: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY135: $i,SY136: $i] :
~ ( triangle @ SV11 @ SY135 @ SY136 )
| ( edge @ SV11 ) )
| ~ ! [SY137: $i] :
( ! [SY138: $i] :
~ ( triangle @ SV11 @ SY137 @ SY138 )
| ( edge @ SY137 ) ) )
| ~ ! [SY139: $i,SY140: $i] :
( ~ ( triangle @ SV11 @ SY139 @ SY140 )
| ( edge @ SY140 ) ) )
| ~ ! [SY141: $i] :
( ! [SY142: $i] :
~ ( triangle @ SV11 @ SY141 @ SY142 )
| ( sequential @ SV11 @ SY141 ) ) )
| ~ ! [SY143: $i,SY144: $i] :
( ~ ( triangle @ SV11 @ SY143 @ SY144 )
| ( sequential @ SY143 @ SY144 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(287,plain,
! [SV53: $i,SV11: $i] :
( ( ! [SY214: $i] :
( ~ ( triangle @ SV11 @ SV53 @ SY214 )
| ( sequential @ SY214 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[259]) ).
thf(288,plain,
! [SV37: $i,SV31: $i] :
( ( ( SV31 = SV37 )
= $true )
| ( ( ~ ( edge @ SV31 )
| ~ ( edge @ SV37 ) )
= $true )
| ( ( ( ( head_of @ SV31 )
!= ( tail_of @ SV37 ) ) )
= $true )
| ( ( sequential @ SV31 @ SV37 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[260]) ).
thf(289,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[261]) ).
thf(290,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[261]) ).
thf(291,plain,
! [SV54: $i,SV49: $i] :
( ( ~ ( sequential @ SV49 @ SV54 )
| ( ( head_of @ SV49 )
= ( tail_of @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(292,plain,
! [SV26: $i,SV12: $i,SV20: $i] :
( ( ( vertex @ SV20 )
= $false )
| ( ( vertex @ SV12 )
= $false )
| ( ( ~ ( ~ ! [SY190: $i] :
( ( SV12
!= ( tail_of @ SY190 ) )
| ~ ( edge @ SY190 )
| ( SV20
!= ( head_of @ SY190 ) )
| ( SV26
!= ( path_cons @ SY190 @ empty ) ) )
| ~ ! [SY191: $i] :
( ( SV12
!= ( tail_of @ SY191 ) )
| ~ ( edge @ SY191 )
| ! [SY192: $i] :
( ( SV26
!= ( path_cons @ SY191 @ SY192 ) )
| ~ ( path @ ( head_of @ SY191 ) @ SV20 @ SY192 ) ) ) ) )
= $true )
| ( ( path @ SV12 @ SV20 @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(293,plain,
! [SV21: $i,SV13: $i,SV50: $i,SV27: $i] :
( ( ( ! [SY209: $i] :
( ~ ( precedes @ SV27 @ SV50 @ SY209 )
| ~ ( shortest_path @ SV13 @ SV21 @ SY209 ) ) )
= $true )
| ( ( ! [SY210: $i] :
( ( ( tail_of @ SY210 )
!= ( tail_of @ SV27 ) )
| ( ( head_of @ SY210 )
!= ( head_of @ SV50 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[264]) ).
thf(294,plain,
! [SV21: $i,SV13: $i,SV55: $i,SV51: $i,SV27: $i] :
( ( ~ ( precedes @ SV27 @ SV51 @ SV55 )
| ~ ( shortest_path @ SV13 @ SV21 @ SV55 )
| ~ ( precedes @ SV51 @ SV27 @ SV55 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(295,plain,
! [SV14: $i] :
( ( ( ! [SY159: $i,SY160: $i] :
~ ( path @ SV14 @ SY159 @ SY160 ) )
= $true )
| ( ( vertex @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[266]) ).
thf(296,plain,
! [SV56: $i,SV14: $i] :
( ( ! [SY215: $i] :
~ ( path @ SV14 @ SV56 @ SY215 )
| ( vertex @ SV56 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(297,plain,
! [SV44: $i,SV38: $i,SV14: $i] :
( ( ( path @ SV14 @ SV38 @ SV44 )
= $false )
| ( ( ~ ( ~ ~ ( ( SV14
!= ( tail_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( edge @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
| ~ ~ ( ~ ( ( SV38
!= ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
| ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ empty ) )
| ! [SY207: $i] :
( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ SY207 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ SY207 ) ) )
| ~ ~ ( ~ ( ( SV38
= ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ ( sK13_SY84 @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ ( sK13_SY84 @ SV44 @ SV38 @ SV14 ) ) ) )
| ~ ( ( SV44
= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ empty ) )
| ~ ( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ ( sK12_SY85 @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ ( sK12_SY85 @ SV44 @ SV38 @ SV14 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[268]) ).
thf(298,plain,
! [SV34: $i,SV28: $i] :
( ( ( vertex @ SV28 )
= $false )
| ( ( ~ ( vertex @ SV34 ) )
= $true )
| ( ( SV28 = SV34 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV28
!= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
!= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
!= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
!= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV28
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
| ~ ( ( SV28
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) ) )
| ~ ~ ( ~ ( ( SV34
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
| ~ ( ( SV34
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV34 @ SV28 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(299,plain,
! [SV29: $i,SV24: $i,SV5: $i,SV57: $i] :
( ( ( ! [SY216: $i] :
( ~ ( on_path @ SV57 @ SV5 )
| ~ ( on_path @ SY216 @ SV5 )
| ! [SY217: $i] :
( ~ ( precedes @ SY217 @ SY216 @ SV5 )
| ~ ( sequential @ SV57 @ SY217 ) )
| ( precedes @ SV57 @ SY216 @ SV5 ) ) )
= $true )
| ( ( path @ SV24 @ SV29 @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(300,plain,
! [SV29: $i,SV24: $i,SV5: $i,SV58: $i] :
( ( ( ! [SY218: $i] :
( ~ ( on_path @ SV58 @ SV5 )
| ~ ( on_path @ SY218 @ SV5 )
| ~ ( sequential @ SV58 @ SY218 )
| ( precedes @ SV58 @ SY218 @ SV5 ) ) )
= $true )
| ( ( path @ SV24 @ SV29 @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(301,plain,
! [SV39: $i,SV35: $i,SV6: $i] :
( ( ( ~ ( path @ SV6 @ SV35 @ ( sK8_P @ SV39 @ SV35 @ SV6 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SV39 ) @ ( length_of @ ( sK8_P @ SV39 @ SV35 @ SV6 ) ) ) )
= $false )
| ( ( ( SV6 = SV35 )
| ~ ( path @ SV6 @ SV35 @ SV39 ) )
= $true )
| ( ( shortest_path @ SV6 @ SV35 @ SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(302,plain,
! [SV59: $i,SV52: $i,SV6: $i] :
( ( ~ ( shortest_path @ SV6 @ SV52 @ SV59 )
| ! [SY219: $i] :
( ~ ( path @ SV6 @ SV52 @ SY219 )
| ( less_or_equal @ ( length_of @ SV59 ) @ ( length_of @ SY219 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(303,plain,
! [SV6: $i] :
( ( ~ ! [SY103: $i] :
( ! [SY104: $i] :
~ ( shortest_path @ SV6 @ SY103 @ SY104 )
| ( SV6 != SY103 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[274]) ).
thf(304,plain,
! [SV6: $i] :
( ( ~ ! [SY105: $i,SY106: $i] :
( ~ ( shortest_path @ SV6 @ SY105 @ SY106 )
| ( path @ SV6 @ SY105 @ SY106 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[274]) ).
thf(305,plain,
! [SV18: $i,SV7: $i,SV60: $i] :
( ( ! [SY220: $i] :
( ~ ( on_path @ SY220 @ SV60 )
| ~ ( path @ SV7 @ SV18 @ SV60 )
| ( edge @ SY220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(306,plain,
! [SV18: $i,SV7: $i,SV61: $i] :
( ( ! [SY221: $i] :
( ~ ( on_path @ SY221 @ SV61 )
| ~ ( path @ SV7 @ SV18 @ SV61 )
| ( in_path @ ( head_of @ SY221 ) @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(307,plain,
! [SV18: $i,SV7: $i,SV40: $i,SV45: $i] :
( ( ( ~ ( on_path @ SV45 @ SV40 ) )
= $true )
| ( ( ~ ( path @ SV7 @ SV18 @ SV40 ) )
= $true )
| ( ( in_path @ ( tail_of @ SV45 ) @ SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[277]) ).
thf(308,plain,
! [SV8: $i] :
( ( ( ~ ( ~ ( on_path @ ( sK6_E1 @ SV8 ) @ SV8 )
| ~ ( on_path @ ( sK7_SY80 @ SV8 ) @ SV8 ) ) )
= $true )
| ( ( ! [SY115: $i,SY116: $i] :
~ ( path @ SY115 @ SY116 @ SV8 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV8 )
= ( number_of_in @ triangles @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[278]) ).
thf(309,plain,
! [SV8: $i] :
( ( ( sequential @ ( sK6_E1 @ SV8 ) @ ( sK7_SY80 @ SV8 ) )
= $true )
| ( ( ! [SY115: $i,SY116: $i] :
~ ( path @ SY115 @ SY116 @ SV8 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV8 )
= ( number_of_in @ triangles @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[279]) ).
thf(310,plain,
! [SV46: $i,SV8: $i,SV62: $i] :
( ( ( ! [SY222: $i] :
~ ( path @ SV62 @ SY222 @ SV8 ) )
= $true )
| ( ( triangle @ ( sK6_E1 @ SV8 ) @ ( sK7_SY80 @ SV8 ) @ SV46 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV8 )
= ( number_of_in @ triangles @ SV8 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(311,plain,
! [SV19: $i,SV9: $i,SV41: $i,SV47: $i] :
( ( ( ~ ( in_path @ SV47 @ SV41 ) )
= $true )
| ( ( ~ ( path @ SV9 @ SV19 @ SV41 ) )
= $true )
| ( ( ~ ( ~ ( on_path @ ( sK10_E @ SV47 @ SV41 @ SV19 @ SV9 ) @ SV41 )
| ~ ( ( SV47
= ( head_of @ ( sK10_E @ SV47 @ SV41 @ SV19 @ SV9 ) ) )
| ( SV47
= ( tail_of @ ( sK10_E @ SV47 @ SV41 @ SV19 @ SV9 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[281]) ).
thf(312,plain,
! [SV19: $i,SV9: $i,SV42: $i,SV48: $i] :
( ( ( ~ ( in_path @ SV48 @ SV42 ) )
= $true )
| ( ( ~ ( path @ SV9 @ SV19 @ SV42 ) )
= $true )
| ( ( vertex @ SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[282]) ).
thf(313,plain,
! [SV30: $i,SV25: $i,SV10: $i] :
( ( ( ~ ! [SY124: $i] :
( ! [SY125: $i] :
~ ( precedes @ SY124 @ SY125 @ SV10 )
| ( on_path @ SY124 @ SV10 ) )
| ~ ! [SY126: $i,SY127: $i] :
( ~ ( precedes @ SY126 @ SY127 @ SV10 )
| ( on_path @ SY127 @ SV10 ) ) )
= $false )
| ( ( path @ SV25 @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(314,plain,
! [SV30: $i,SV25: $i,SV10: $i] :
( ( ( ~ ! [SY128: $i,SY129: $i] :
( ~ ( precedes @ SY128 @ SY129 @ SV10 )
| ! [SY130: $i] :
( ~ ( precedes @ SY130 @ SY129 @ SV10 )
| ~ ( sequential @ SY128 @ SY130 ) )
| ~ ( sequential @ SY128 @ SY129 ) )
| ~ ! [SY131: $i,SY132: $i] :
( ~ ( precedes @ SY131 @ SY132 @ SV10 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY132 @ SY131 @ SV10 ) @ SY132 @ SV10 )
| ~ ( sequential @ SY131 @ ( sK9_E3 @ SY132 @ SY131 @ SV10 ) ) )
| ( sequential @ SY131 @ SY132 ) ) )
= $false )
| ( ( path @ SV25 @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(315,plain,
! [SV43: $i,SV36: $i,SV11: $i] :
( ( ( ~ ( edge @ SV11 )
| ~ ( edge @ SV36 )
| ~ ( edge @ SV43 )
| ~ ( sequential @ SV11 @ SV36 ) )
= $true )
| ( ( ~ ( sequential @ SV36 @ SV43 ) )
= $true )
| ( ( ~ ( sequential @ SV43 @ SV11 ) )
= $true )
| ( ( triangle @ SV11 @ SV36 @ SV43 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[285]) ).
thf(316,plain,
! [SV11: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY135: $i,SY136: $i] :
~ ( triangle @ SV11 @ SY135 @ SY136 )
| ( edge @ SV11 ) )
| ~ ! [SY137: $i] :
( ! [SY138: $i] :
~ ( triangle @ SV11 @ SY137 @ SY138 )
| ( edge @ SY137 ) ) )
| ~ ! [SY139: $i,SY140: $i] :
( ~ ( triangle @ SV11 @ SY139 @ SY140 )
| ( edge @ SY140 ) ) )
| ~ ! [SY141: $i] :
( ! [SY142: $i] :
~ ( triangle @ SV11 @ SY141 @ SY142 )
| ( sequential @ SV11 @ SY141 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[286]) ).
thf(317,plain,
! [SV11: $i] :
( ( ~ ! [SY143: $i,SY144: $i] :
( ~ ( triangle @ SV11 @ SY143 @ SY144 )
| ( sequential @ SY143 @ SY144 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[286]) ).
thf(318,plain,
! [SV63: $i,SV53: $i,SV11: $i] :
( ( ~ ( triangle @ SV11 @ SV53 @ SV63 )
| ( sequential @ SV63 @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(319,plain,
! [SV37: $i,SV31: $i] :
( ( ( ~ ( edge @ SV31 ) )
= $true )
| ( ( ~ ( edge @ SV37 ) )
= $true )
| ( ( SV31 = SV37 )
= $true )
| ( ( ( ( head_of @ SV31 )
!= ( tail_of @ SV37 ) ) )
= $true )
| ( ( sequential @ SV31 @ SV37 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[288]) ).
thf(320,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[289]) ).
thf(321,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[290]) ).
thf(322,plain,
! [SV54: $i,SV49: $i] :
( ( ( ~ ( sequential @ SV49 @ SV54 ) )
= $true )
| ( ( ( head_of @ SV49 )
= ( tail_of @ SV54 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[291]) ).
thf(323,plain,
! [SV26: $i,SV20: $i,SV12: $i] :
( ( ( ~ ! [SY190: $i] :
( ( SV12
!= ( tail_of @ SY190 ) )
| ~ ( edge @ SY190 )
| ( SV20
!= ( head_of @ SY190 ) )
| ( SV26
!= ( path_cons @ SY190 @ empty ) ) )
| ~ ! [SY191: $i] :
( ( SV12
!= ( tail_of @ SY191 ) )
| ~ ( edge @ SY191 )
| ! [SY192: $i] :
( ( SV26
!= ( path_cons @ SY191 @ SY192 ) )
| ~ ( path @ ( head_of @ SY191 ) @ SV20 @ SY192 ) ) ) )
= $false )
| ( ( vertex @ SV12 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV12 @ SV20 @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(324,plain,
! [SV21: $i,SV13: $i,SV64: $i,SV50: $i,SV27: $i] :
( ( ( ~ ( precedes @ SV27 @ SV50 @ SV64 )
| ~ ( shortest_path @ SV13 @ SV21 @ SV64 ) )
= $true )
| ( ( ! [SY210: $i] :
( ( ( tail_of @ SY210 )
!= ( tail_of @ SV27 ) )
| ( ( head_of @ SY210 )
!= ( head_of @ SV50 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(325,plain,
! [SV21: $i,SV13: $i,SV55: $i,SV51: $i,SV27: $i] :
( ( ( ~ ( precedes @ SV27 @ SV51 @ SV55 )
| ~ ( shortest_path @ SV13 @ SV21 @ SV55 ) )
= $true )
| ( ( ~ ( precedes @ SV51 @ SV27 @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[294]) ).
thf(326,plain,
! [SV65: $i,SV14: $i] :
( ( ( ! [SY223: $i] :
~ ( path @ SV14 @ SV65 @ SY223 ) )
= $true )
| ( ( vertex @ SV14 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(327,plain,
! [SV56: $i,SV14: $i] :
( ( ( ! [SY215: $i] :
~ ( path @ SV14 @ SV56 @ SY215 ) )
= $true )
| ( ( vertex @ SV56 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[296]) ).
thf(328,plain,
! [SV38: $i,SV44: $i,SV14: $i] :
( ( ( ~ ~ ( ( SV14
!= ( tail_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( edge @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
| ~ ~ ( ~ ( ( SV38
!= ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
| ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ empty ) )
| ! [SY207: $i] :
( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ SY207 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ SY207 ) ) )
| ~ ~ ( ~ ( ( SV38
= ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ ( sK13_SY84 @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ ( sK13_SY84 @ SV44 @ SV38 @ SV14 ) ) ) )
| ~ ( ( SV44
= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ empty ) )
| ~ ( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ ( sK12_SY85 @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ ( sK12_SY85 @ SV44 @ SV38 @ SV14 ) ) ) ) ) ) )
= $false )
| ( ( path @ SV14 @ SV38 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[297]) ).
thf(329,plain,
! [SV28: $i,SV34: $i] :
( ( ( vertex @ SV34 )
= $false )
| ( ( vertex @ SV28 )
= $false )
| ( ( SV28 = SV34 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV28
!= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
!= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
!= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
!= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV28
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
| ~ ( ( SV28
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) ) )
| ~ ~ ( ~ ( ( SV34
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
| ~ ( ( SV34
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV34 @ SV28 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[298]) ).
thf(330,plain,
! [SV29: $i,SV24: $i,SV66: $i,SV5: $i,SV57: $i] :
( ( ( ~ ( on_path @ SV57 @ SV5 )
| ~ ( on_path @ SV66 @ SV5 )
| ! [SY224: $i] :
( ~ ( precedes @ SY224 @ SV66 @ SV5 )
| ~ ( sequential @ SV57 @ SY224 ) )
| ( precedes @ SV57 @ SV66 @ SV5 ) )
= $true )
| ( ( path @ SV24 @ SV29 @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(331,plain,
! [SV29: $i,SV24: $i,SV67: $i,SV5: $i,SV58: $i] :
( ( ( ~ ( on_path @ SV58 @ SV5 )
| ~ ( on_path @ SV67 @ SV5 )
| ~ ( sequential @ SV58 @ SV67 )
| ( precedes @ SV58 @ SV67 @ SV5 ) )
= $true )
| ( ( path @ SV24 @ SV29 @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(332,plain,
! [SV39: $i,SV35: $i,SV6: $i] :
( ( ( ~ ( path @ SV6 @ SV35 @ ( sK8_P @ SV39 @ SV35 @ SV6 ) ) )
= $false )
| ( ( ( SV6 = SV35 )
| ~ ( path @ SV6 @ SV35 @ SV39 ) )
= $true )
| ( ( shortest_path @ SV6 @ SV35 @ SV39 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[301]) ).
thf(333,plain,
! [SV6: $i,SV35: $i,SV39: $i] :
( ( ( ~ ~ ( less_or_equal @ ( length_of @ SV39 ) @ ( length_of @ ( sK8_P @ SV39 @ SV35 @ SV6 ) ) ) )
= $false )
| ( ( ( SV6 = SV35 )
| ~ ( path @ SV6 @ SV35 @ SV39 ) )
= $true )
| ( ( shortest_path @ SV6 @ SV35 @ SV39 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[301]) ).
thf(334,plain,
! [SV59: $i,SV52: $i,SV6: $i] :
( ( ( ~ ( shortest_path @ SV6 @ SV52 @ SV59 ) )
= $true )
| ( ( ! [SY219: $i] :
( ~ ( path @ SV6 @ SV52 @ SY219 )
| ( less_or_equal @ ( length_of @ SV59 ) @ ( length_of @ SY219 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[302]) ).
thf(335,plain,
! [SV6: $i] :
( ( ! [SY103: $i] :
( ! [SY104: $i] :
~ ( shortest_path @ SV6 @ SY103 @ SY104 )
| ( SV6 != SY103 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[303]) ).
thf(336,plain,
! [SV6: $i] :
( ( ! [SY105: $i,SY106: $i] :
( ~ ( shortest_path @ SV6 @ SY105 @ SY106 )
| ( path @ SV6 @ SY105 @ SY106 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[304]) ).
thf(337,plain,
! [SV18: $i,SV7: $i,SV60: $i,SV68: $i] :
( ( ~ ( on_path @ SV68 @ SV60 )
| ~ ( path @ SV7 @ SV18 @ SV60 )
| ( edge @ SV68 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(338,plain,
! [SV18: $i,SV7: $i,SV61: $i,SV69: $i] :
( ( ~ ( on_path @ SV69 @ SV61 )
| ~ ( path @ SV7 @ SV18 @ SV61 )
| ( in_path @ ( head_of @ SV69 ) @ SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(339,plain,
! [SV18: $i,SV7: $i,SV40: $i,SV45: $i] :
( ( ( on_path @ SV45 @ SV40 )
= $false )
| ( ( ~ ( path @ SV7 @ SV18 @ SV40 ) )
= $true )
| ( ( in_path @ ( tail_of @ SV45 ) @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(340,plain,
! [SV8: $i] :
( ( ( ~ ( on_path @ ( sK6_E1 @ SV8 ) @ SV8 )
| ~ ( on_path @ ( sK7_SY80 @ SV8 ) @ SV8 ) )
= $false )
| ( ( ! [SY115: $i,SY116: $i] :
~ ( path @ SY115 @ SY116 @ SV8 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV8 )
= ( number_of_in @ triangles @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(341,plain,
! [SV8: $i,SV70: $i] :
( ( ( ! [SY225: $i] :
~ ( path @ SV70 @ SY225 @ SV8 ) )
= $true )
| ( ( sequential @ ( sK6_E1 @ SV8 ) @ ( sK7_SY80 @ SV8 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV8 )
= ( number_of_in @ triangles @ SV8 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(342,plain,
! [SV46: $i,SV8: $i,SV71: $i,SV62: $i] :
( ( ( ~ ( path @ SV62 @ SV71 @ SV8 ) )
= $true )
| ( ( triangle @ ( sK6_E1 @ SV8 ) @ ( sK7_SY80 @ SV8 ) @ SV46 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV8 )
= ( number_of_in @ triangles @ SV8 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(343,plain,
! [SV19: $i,SV9: $i,SV41: $i,SV47: $i] :
( ( ( in_path @ SV47 @ SV41 )
= $false )
| ( ( ~ ( path @ SV9 @ SV19 @ SV41 ) )
= $true )
| ( ( ~ ( ~ ( on_path @ ( sK10_E @ SV47 @ SV41 @ SV19 @ SV9 ) @ SV41 )
| ~ ( ( SV47
= ( head_of @ ( sK10_E @ SV47 @ SV41 @ SV19 @ SV9 ) ) )
| ( SV47
= ( tail_of @ ( sK10_E @ SV47 @ SV41 @ SV19 @ SV9 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[311]) ).
thf(344,plain,
! [SV19: $i,SV9: $i,SV42: $i,SV48: $i] :
( ( ( in_path @ SV48 @ SV42 )
= $false )
| ( ( ~ ( path @ SV9 @ SV19 @ SV42 ) )
= $true )
| ( ( vertex @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(345,plain,
! [SV30: $i,SV25: $i,SV10: $i] :
( ( ( ~ ! [SY124: $i] :
( ! [SY125: $i] :
~ ( precedes @ SY124 @ SY125 @ SV10 )
| ( on_path @ SY124 @ SV10 ) ) )
= $false )
| ( ( path @ SV25 @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[313]) ).
thf(346,plain,
! [SV30: $i,SV25: $i,SV10: $i] :
( ( ( ~ ! [SY126: $i,SY127: $i] :
( ~ ( precedes @ SY126 @ SY127 @ SV10 )
| ( on_path @ SY127 @ SV10 ) ) )
= $false )
| ( ( path @ SV25 @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[313]) ).
thf(347,plain,
! [SV30: $i,SV25: $i,SV10: $i] :
( ( ( ~ ! [SY128: $i,SY129: $i] :
( ~ ( precedes @ SY128 @ SY129 @ SV10 )
| ! [SY130: $i] :
( ~ ( precedes @ SY130 @ SY129 @ SV10 )
| ~ ( sequential @ SY128 @ SY130 ) )
| ~ ( sequential @ SY128 @ SY129 ) ) )
= $false )
| ( ( path @ SV25 @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[314]) ).
thf(348,plain,
! [SV30: $i,SV25: $i,SV10: $i] :
( ( ( ~ ! [SY131: $i,SY132: $i] :
( ~ ( precedes @ SY131 @ SY132 @ SV10 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY132 @ SY131 @ SV10 ) @ SY132 @ SV10 )
| ~ ( sequential @ SY131 @ ( sK9_E3 @ SY132 @ SY131 @ SV10 ) ) )
| ( sequential @ SY131 @ SY132 ) ) )
= $false )
| ( ( path @ SV25 @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[314]) ).
thf(349,plain,
! [SV43: $i,SV36: $i,SV11: $i] :
( ( ( ~ ( edge @ SV11 )
| ~ ( edge @ SV36 )
| ~ ( edge @ SV43 ) )
= $true )
| ( ( ~ ( sequential @ SV11 @ SV36 ) )
= $true )
| ( ( ~ ( sequential @ SV36 @ SV43 ) )
= $true )
| ( ( ~ ( sequential @ SV43 @ SV11 ) )
= $true )
| ( ( triangle @ SV11 @ SV36 @ SV43 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[315]) ).
thf(350,plain,
! [SV11: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY135: $i,SY136: $i] :
~ ( triangle @ SV11 @ SY135 @ SY136 )
| ( edge @ SV11 ) )
| ~ ! [SY137: $i] :
( ! [SY138: $i] :
~ ( triangle @ SV11 @ SY137 @ SY138 )
| ( edge @ SY137 ) ) )
| ~ ! [SY139: $i,SY140: $i] :
( ~ ( triangle @ SV11 @ SY139 @ SY140 )
| ( edge @ SY140 ) ) )
| ~ ! [SY141: $i] :
( ! [SY142: $i] :
~ ( triangle @ SV11 @ SY141 @ SY142 )
| ( sequential @ SV11 @ SY141 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[316]) ).
thf(351,plain,
! [SV11: $i] :
( ( ! [SY143: $i,SY144: $i] :
( ~ ( triangle @ SV11 @ SY143 @ SY144 )
| ( sequential @ SY143 @ SY144 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[317]) ).
thf(352,plain,
! [SV63: $i,SV53: $i,SV11: $i] :
( ( ( ~ ( triangle @ SV11 @ SV53 @ SV63 ) )
= $true )
| ( ( sequential @ SV63 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[318]) ).
thf(353,plain,
! [SV37: $i,SV31: $i] :
( ( ( edge @ SV31 )
= $false )
| ( ( ~ ( edge @ SV37 ) )
= $true )
| ( ( SV31 = SV37 )
= $true )
| ( ( ( ( head_of @ SV31 )
!= ( tail_of @ SV37 ) ) )
= $true )
| ( ( sequential @ SV31 @ SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[319]) ).
thf(354,plain,
! [SV72: $i] :
( ( ! [SY226: $i] :
( ~ ( sequential @ SV72 @ SY226 )
| ( SV72 != SY226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(355,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(356,plain,
! [SV54: $i,SV49: $i] :
( ( ( sequential @ SV49 @ SV54 )
= $false )
| ( ( ( head_of @ SV49 )
= ( tail_of @ SV54 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[322]) ).
thf(357,plain,
! [SV26: $i,SV20: $i,SV12: $i] :
( ( ( ~ ! [SY190: $i] :
( ( SV12
!= ( tail_of @ SY190 ) )
| ~ ( edge @ SY190 )
| ( SV20
!= ( head_of @ SY190 ) )
| ( SV26
!= ( path_cons @ SY190 @ empty ) ) ) )
= $false )
| ( ( vertex @ SV12 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV12 @ SV20 @ SV26 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[323]) ).
thf(358,plain,
! [SV20: $i,SV26: $i,SV12: $i] :
( ( ( ~ ! [SY191: $i] :
( ( SV12
!= ( tail_of @ SY191 ) )
| ~ ( edge @ SY191 )
| ! [SY192: $i] :
( ( SV26
!= ( path_cons @ SY191 @ SY192 ) )
| ~ ( path @ ( head_of @ SY191 ) @ SV20 @ SY192 ) ) ) )
= $false )
| ( ( vertex @ SV12 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV12 @ SV20 @ SV26 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[323]) ).
thf(359,plain,
! [SV21: $i,SV13: $i,SV64: $i,SV50: $i,SV27: $i] :
( ( ( ~ ( precedes @ SV27 @ SV50 @ SV64 ) )
= $true )
| ( ( ~ ( shortest_path @ SV13 @ SV21 @ SV64 ) )
= $true )
| ( ( ! [SY210: $i] :
( ( ( tail_of @ SY210 )
!= ( tail_of @ SV27 ) )
| ( ( head_of @ SY210 )
!= ( head_of @ SV50 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[324]) ).
thf(360,plain,
! [SV21: $i,SV13: $i,SV55: $i,SV51: $i,SV27: $i] :
( ( ( ~ ( precedes @ SV27 @ SV51 @ SV55 ) )
= $true )
| ( ( ~ ( shortest_path @ SV13 @ SV21 @ SV55 ) )
= $true )
| ( ( ~ ( precedes @ SV51 @ SV27 @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[325]) ).
thf(361,plain,
! [SV73: $i,SV65: $i,SV14: $i] :
( ( ( ~ ( path @ SV14 @ SV65 @ SV73 ) )
= $true )
| ( ( vertex @ SV14 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[326]) ).
thf(362,plain,
! [SV74: $i,SV56: $i,SV14: $i] :
( ( ( ~ ( path @ SV14 @ SV56 @ SV74 ) )
= $true )
| ( ( vertex @ SV56 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(363,plain,
! [SV38: $i,SV44: $i,SV14: $i] :
( ( ( ~ ~ ( ( SV14
!= ( tail_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( edge @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) ) )
= $false )
| ( ( path @ SV14 @ SV38 @ SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[328]) ).
thf(364,plain,
! [SV14: $i,SV44: $i,SV38: $i] :
( ( ( ~ ~ ( ~ ( ( SV38
!= ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
| ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ empty ) )
| ! [SY207: $i] :
( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ SY207 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ SY207 ) ) )
| ~ ~ ( ~ ( ( SV38
= ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ ( sK13_SY84 @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ ( sK13_SY84 @ SV44 @ SV38 @ SV14 ) ) ) )
| ~ ( ( SV44
= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ empty ) )
| ~ ( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ ( sK12_SY85 @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ ( sK12_SY85 @ SV44 @ SV38 @ SV14 ) ) ) ) ) ) )
= $false )
| ( ( path @ SV14 @ SV38 @ SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[328]) ).
thf(365,plain,
! [SV34: $i,SV28: $i] :
( ( ( ~ ~ ( ~ ( ( SV28
!= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
!= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
!= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
!= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV28
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
| ~ ( ( SV28
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) ) )
| ~ ~ ( ~ ( ( SV34
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
| ~ ( ( SV34
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV34 @ SV28 ) ) )
= $false )
| ( ( SV28 = SV34 )
= $true )
| ( ( vertex @ SV28 )
= $false )
| ( ( vertex @ SV34 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[329]) ).
thf(366,plain,
! [SV29: $i,SV24: $i,SV66: $i,SV5: $i,SV57: $i] :
( ( ( ~ ( on_path @ SV57 @ SV5 )
| ~ ( on_path @ SV66 @ SV5 )
| ! [SY224: $i] :
( ~ ( precedes @ SY224 @ SV66 @ SV5 )
| ~ ( sequential @ SV57 @ SY224 ) ) )
= $true )
| ( ( precedes @ SV57 @ SV66 @ SV5 )
= $true )
| ( ( path @ SV24 @ SV29 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[330]) ).
thf(367,plain,
! [SV29: $i,SV24: $i,SV67: $i,SV5: $i,SV58: $i] :
( ( ( ~ ( on_path @ SV58 @ SV5 )
| ~ ( on_path @ SV67 @ SV5 )
| ~ ( sequential @ SV58 @ SV67 ) )
= $true )
| ( ( precedes @ SV58 @ SV67 @ SV5 )
= $true )
| ( ( path @ SV24 @ SV29 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[331]) ).
thf(368,plain,
! [SV39: $i,SV35: $i,SV6: $i] :
( ( ( path @ SV6 @ SV35 @ ( sK8_P @ SV39 @ SV35 @ SV6 ) )
= $true )
| ( ( ( SV6 = SV35 )
| ~ ( path @ SV6 @ SV35 @ SV39 ) )
= $true )
| ( ( shortest_path @ SV6 @ SV35 @ SV39 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[332]) ).
thf(369,plain,
! [SV6: $i,SV35: $i,SV39: $i] :
( ( ( ~ ( less_or_equal @ ( length_of @ SV39 ) @ ( length_of @ ( sK8_P @ SV39 @ SV35 @ SV6 ) ) ) )
= $true )
| ( ( ( SV6 = SV35 )
| ~ ( path @ SV6 @ SV35 @ SV39 ) )
= $true )
| ( ( shortest_path @ SV6 @ SV35 @ SV39 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[333]) ).
thf(370,plain,
! [SV59: $i,SV52: $i,SV6: $i] :
( ( ( shortest_path @ SV6 @ SV52 @ SV59 )
= $false )
| ( ( ! [SY219: $i] :
( ~ ( path @ SV6 @ SV52 @ SY219 )
| ( less_or_equal @ ( length_of @ SV59 ) @ ( length_of @ SY219 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(371,plain,
! [SV75: $i,SV6: $i] :
( ( ! [SY227: $i] :
~ ( shortest_path @ SV6 @ SV75 @ SY227 )
| ( SV6 != SV75 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[335]) ).
thf(372,plain,
! [SV76: $i,SV6: $i] :
( ( ! [SY228: $i] :
( ~ ( shortest_path @ SV6 @ SV76 @ SY228 )
| ( path @ SV6 @ SV76 @ SY228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[336]) ).
thf(373,plain,
! [SV18: $i,SV7: $i,SV60: $i,SV68: $i] :
( ( ( ~ ( on_path @ SV68 @ SV60 )
| ~ ( path @ SV7 @ SV18 @ SV60 ) )
= $true )
| ( ( edge @ SV68 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[337]) ).
thf(374,plain,
! [SV18: $i,SV7: $i,SV61: $i,SV69: $i] :
( ( ( ~ ( on_path @ SV69 @ SV61 )
| ~ ( path @ SV7 @ SV18 @ SV61 ) )
= $true )
| ( ( in_path @ ( head_of @ SV69 ) @ SV61 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[338]) ).
thf(375,plain,
! [SV45: $i,SV40: $i,SV18: $i,SV7: $i] :
( ( ( path @ SV7 @ SV18 @ SV40 )
= $false )
| ( ( on_path @ SV45 @ SV40 )
= $false )
| ( ( in_path @ ( tail_of @ SV45 ) @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(376,plain,
! [SV8: $i] :
( ( ( ~ ( on_path @ ( sK6_E1 @ SV8 ) @ SV8 ) )
= $false )
| ( ( ! [SY115: $i,SY116: $i] :
~ ( path @ SY115 @ SY116 @ SV8 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV8 )
= ( number_of_in @ triangles @ SV8 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[340]) ).
thf(377,plain,
! [SV8: $i] :
( ( ( ~ ( on_path @ ( sK7_SY80 @ SV8 ) @ SV8 ) )
= $false )
| ( ( ! [SY115: $i,SY116: $i] :
~ ( path @ SY115 @ SY116 @ SV8 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV8 )
= ( number_of_in @ triangles @ SV8 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[340]) ).
thf(378,plain,
! [SV8: $i,SV77: $i,SV70: $i] :
( ( ( ~ ( path @ SV70 @ SV77 @ SV8 ) )
= $true )
| ( ( sequential @ ( sK6_E1 @ SV8 ) @ ( sK7_SY80 @ SV8 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV8 )
= ( number_of_in @ triangles @ SV8 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(379,plain,
! [SV46: $i,SV8: $i,SV71: $i,SV62: $i] :
( ( ( path @ SV62 @ SV71 @ SV8 )
= $false )
| ( ( triangle @ ( sK6_E1 @ SV8 ) @ ( sK7_SY80 @ SV8 ) @ SV46 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV8 )
= ( number_of_in @ triangles @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[342]) ).
thf(380,plain,
! [SV47: $i,SV41: $i,SV19: $i,SV9: $i] :
( ( ( path @ SV9 @ SV19 @ SV41 )
= $false )
| ( ( in_path @ SV47 @ SV41 )
= $false )
| ( ( ~ ( ~ ( on_path @ ( sK10_E @ SV47 @ SV41 @ SV19 @ SV9 ) @ SV41 )
| ~ ( ( SV47
= ( head_of @ ( sK10_E @ SV47 @ SV41 @ SV19 @ SV9 ) ) )
| ( SV47
= ( tail_of @ ( sK10_E @ SV47 @ SV41 @ SV19 @ SV9 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(381,plain,
! [SV48: $i,SV42: $i,SV19: $i,SV9: $i] :
( ( ( path @ SV9 @ SV19 @ SV42 )
= $false )
| ( ( in_path @ SV48 @ SV42 )
= $false )
| ( ( vertex @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(382,plain,
! [SV30: $i,SV25: $i,SV10: $i] :
( ( ( ! [SY124: $i] :
( ! [SY125: $i] :
~ ( precedes @ SY124 @ SY125 @ SV10 )
| ( on_path @ SY124 @ SV10 ) ) )
= $true )
| ( ( path @ SV25 @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[345]) ).
thf(383,plain,
! [SV30: $i,SV25: $i,SV10: $i] :
( ( ( ! [SY126: $i,SY127: $i] :
( ~ ( precedes @ SY126 @ SY127 @ SV10 )
| ( on_path @ SY127 @ SV10 ) ) )
= $true )
| ( ( path @ SV25 @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[346]) ).
thf(384,plain,
! [SV30: $i,SV25: $i,SV10: $i] :
( ( ( ! [SY128: $i,SY129: $i] :
( ~ ( precedes @ SY128 @ SY129 @ SV10 )
| ! [SY130: $i] :
( ~ ( precedes @ SY130 @ SY129 @ SV10 )
| ~ ( sequential @ SY128 @ SY130 ) )
| ~ ( sequential @ SY128 @ SY129 ) ) )
= $true )
| ( ( path @ SV25 @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[347]) ).
thf(385,plain,
! [SV30: $i,SV25: $i,SV10: $i] :
( ( ( ! [SY131: $i,SY132: $i] :
( ~ ( precedes @ SY131 @ SY132 @ SV10 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY132 @ SY131 @ SV10 ) @ SY132 @ SV10 )
| ~ ( sequential @ SY131 @ ( sK9_E3 @ SY132 @ SY131 @ SV10 ) ) )
| ( sequential @ SY131 @ SY132 ) ) )
= $true )
| ( ( path @ SV25 @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[348]) ).
thf(386,plain,
! [SV43: $i,SV36: $i,SV11: $i] :
( ( ( ~ ( edge @ SV11 )
| ~ ( edge @ SV36 ) )
= $true )
| ( ( ~ ( edge @ SV43 ) )
= $true )
| ( ( ~ ( sequential @ SV11 @ SV36 ) )
= $true )
| ( ( ~ ( sequential @ SV36 @ SV43 ) )
= $true )
| ( ( ~ ( sequential @ SV43 @ SV11 ) )
= $true )
| ( ( triangle @ SV11 @ SV36 @ SV43 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[349]) ).
thf(387,plain,
! [SV11: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( ! [SY135: $i,SY136: $i] :
~ ( triangle @ SV11 @ SY135 @ SY136 )
| ( edge @ SV11 ) )
| ~ ! [SY137: $i] :
( ! [SY138: $i] :
~ ( triangle @ SV11 @ SY137 @ SY138 )
| ( edge @ SY137 ) ) )
| ~ ! [SY139: $i,SY140: $i] :
( ~ ( triangle @ SV11 @ SY139 @ SY140 )
| ( edge @ SY140 ) ) )
| ~ ! [SY141: $i] :
( ! [SY142: $i] :
~ ( triangle @ SV11 @ SY141 @ SY142 )
| ( sequential @ SV11 @ SY141 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[350]) ).
thf(388,plain,
! [SV78: $i,SV11: $i] :
( ( ! [SY229: $i] :
( ~ ( triangle @ SV11 @ SV78 @ SY229 )
| ( sequential @ SV78 @ SY229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[351]) ).
thf(389,plain,
! [SV63: $i,SV53: $i,SV11: $i] :
( ( ( triangle @ SV11 @ SV53 @ SV63 )
= $false )
| ( ( sequential @ SV63 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[352]) ).
thf(390,plain,
! [SV31: $i,SV37: $i] :
( ( ( edge @ SV37 )
= $false )
| ( ( edge @ SV31 )
= $false )
| ( ( SV31 = SV37 )
= $true )
| ( ( ( ( head_of @ SV31 )
!= ( tail_of @ SV37 ) ) )
= $true )
| ( ( sequential @ SV31 @ SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[353]) ).
thf(391,plain,
! [SV79: $i,SV72: $i] :
( ( ~ ( sequential @ SV72 @ SV79 )
| ( SV72 != SV79 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(392,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[355]) ).
thf(393,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[355]) ).
thf(394,plain,
! [SV26: $i,SV20: $i,SV12: $i] :
( ( ( ! [SY190: $i] :
( ( SV12
!= ( tail_of @ SY190 ) )
| ~ ( edge @ SY190 )
| ( SV20
!= ( head_of @ SY190 ) )
| ( SV26
!= ( path_cons @ SY190 @ empty ) ) ) )
= $true )
| ( ( vertex @ SV12 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV12 @ SV20 @ SV26 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[357]) ).
thf(395,plain,
! [SV20: $i,SV26: $i,SV12: $i] :
( ( ( ! [SY191: $i] :
( ( SV12
!= ( tail_of @ SY191 ) )
| ~ ( edge @ SY191 )
| ! [SY192: $i] :
( ( SV26
!= ( path_cons @ SY191 @ SY192 ) )
| ~ ( path @ ( head_of @ SY191 ) @ SV20 @ SY192 ) ) ) )
= $true )
| ( ( vertex @ SV12 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV12 @ SV20 @ SV26 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[358]) ).
thf(396,plain,
! [SV21: $i,SV13: $i,SV64: $i,SV50: $i,SV27: $i] :
( ( ( precedes @ SV27 @ SV50 @ SV64 )
= $false )
| ( ( ~ ( shortest_path @ SV13 @ SV21 @ SV64 ) )
= $true )
| ( ( ! [SY210: $i] :
( ( ( tail_of @ SY210 )
!= ( tail_of @ SV27 ) )
| ( ( head_of @ SY210 )
!= ( head_of @ SV50 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[359]) ).
thf(397,plain,
! [SV21: $i,SV13: $i,SV55: $i,SV51: $i,SV27: $i] :
( ( ( precedes @ SV27 @ SV51 @ SV55 )
= $false )
| ( ( ~ ( shortest_path @ SV13 @ SV21 @ SV55 ) )
= $true )
| ( ( ~ ( precedes @ SV51 @ SV27 @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[360]) ).
thf(398,plain,
! [SV73: $i,SV65: $i,SV14: $i] :
( ( ( path @ SV14 @ SV65 @ SV73 )
= $false )
| ( ( vertex @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(399,plain,
! [SV74: $i,SV56: $i,SV14: $i] :
( ( ( path @ SV14 @ SV56 @ SV74 )
= $false )
| ( ( vertex @ SV56 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[362]) ).
thf(400,plain,
! [SV38: $i,SV44: $i,SV14: $i] :
( ( ( ~ ( ( SV14
!= ( tail_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( edge @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) ) )
= $true )
| ( ( path @ SV14 @ SV38 @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[363]) ).
thf(401,plain,
! [SV14: $i,SV44: $i,SV38: $i] :
( ( ( ~ ( ~ ( ( SV38
!= ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
| ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ empty ) )
| ! [SY207: $i] :
( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ SY207 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ SY207 ) ) )
| ~ ~ ( ~ ( ( SV38
= ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ ( sK13_SY84 @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ ( sK13_SY84 @ SV44 @ SV38 @ SV14 ) ) ) )
| ~ ( ( SV44
= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ empty ) )
| ~ ( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ ( sK12_SY85 @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ ( sK12_SY85 @ SV44 @ SV38 @ SV14 ) ) ) ) ) ) )
= $true )
| ( ( path @ SV14 @ SV38 @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[364]) ).
thf(402,plain,
! [SV34: $i,SV28: $i] :
( ( ( ~ ~ ( ~ ( ( SV28
!= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
!= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
!= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
!= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV28
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
| ~ ( ( SV28
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) ) )
| ~ ~ ( ~ ( ( SV34
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
| ~ ( ( SV34
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) ) ) ) ) )
= $false )
| ( ( SV28 = SV34 )
= $true )
| ( ( vertex @ SV28 )
= $false )
| ( ( vertex @ SV34 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[365]) ).
thf(403,plain,
! [SV28: $i,SV34: $i] :
( ( ( ~ ( edge @ ( sK14_E @ SV34 @ SV28 ) ) )
= $false )
| ( ( SV28 = SV34 )
= $true )
| ( ( vertex @ SV28 )
= $false )
| ( ( vertex @ SV34 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[365]) ).
thf(404,plain,
! [SV29: $i,SV24: $i,SV66: $i,SV5: $i,SV57: $i] :
( ( ( ~ ( on_path @ SV57 @ SV5 )
| ~ ( on_path @ SV66 @ SV5 ) )
= $true )
| ( ( ! [SY224: $i] :
( ~ ( precedes @ SY224 @ SV66 @ SV5 )
| ~ ( sequential @ SV57 @ SY224 ) ) )
= $true )
| ( ( precedes @ SV57 @ SV66 @ SV5 )
= $true )
| ( ( path @ SV24 @ SV29 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[366]) ).
thf(405,plain,
! [SV29: $i,SV24: $i,SV67: $i,SV5: $i,SV58: $i] :
( ( ( ~ ( on_path @ SV58 @ SV5 )
| ~ ( on_path @ SV67 @ SV5 ) )
= $true )
| ( ( ~ ( sequential @ SV58 @ SV67 ) )
= $true )
| ( ( precedes @ SV58 @ SV67 @ SV5 )
= $true )
| ( ( path @ SV24 @ SV29 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[367]) ).
thf(406,plain,
! [SV39: $i,SV35: $i,SV6: $i] :
( ( ( SV6 = SV35 )
= $true )
| ( ( ~ ( path @ SV6 @ SV35 @ SV39 ) )
= $true )
| ( ( path @ SV6 @ SV35 @ ( sK8_P @ SV39 @ SV35 @ SV6 ) )
= $true )
| ( ( shortest_path @ SV6 @ SV35 @ SV39 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[368]) ).
thf(407,plain,
! [SV6: $i,SV35: $i,SV39: $i] :
( ( ( less_or_equal @ ( length_of @ SV39 ) @ ( length_of @ ( sK8_P @ SV39 @ SV35 @ SV6 ) ) )
= $false )
| ( ( ( SV6 = SV35 )
| ~ ( path @ SV6 @ SV35 @ SV39 ) )
= $true )
| ( ( shortest_path @ SV6 @ SV35 @ SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[369]) ).
thf(408,plain,
! [SV59: $i,SV80: $i,SV52: $i,SV6: $i] :
( ( ( ~ ( path @ SV6 @ SV52 @ SV80 )
| ( less_or_equal @ ( length_of @ SV59 ) @ ( length_of @ SV80 ) ) )
= $true )
| ( ( shortest_path @ SV6 @ SV52 @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[370]) ).
thf(409,plain,
! [SV75: $i,SV6: $i] :
( ( ( ! [SY227: $i] :
~ ( shortest_path @ SV6 @ SV75 @ SY227 ) )
= $true )
| ( ( ( SV6 != SV75 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[371]) ).
thf(410,plain,
! [SV81: $i,SV76: $i,SV6: $i] :
( ( ~ ( shortest_path @ SV6 @ SV76 @ SV81 )
| ( path @ SV6 @ SV76 @ SV81 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[372]) ).
thf(411,plain,
! [SV18: $i,SV7: $i,SV60: $i,SV68: $i] :
( ( ( ~ ( on_path @ SV68 @ SV60 ) )
= $true )
| ( ( ~ ( path @ SV7 @ SV18 @ SV60 ) )
= $true )
| ( ( edge @ SV68 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[373]) ).
thf(412,plain,
! [SV18: $i,SV7: $i,SV61: $i,SV69: $i] :
( ( ( ~ ( on_path @ SV69 @ SV61 ) )
= $true )
| ( ( ~ ( path @ SV7 @ SV18 @ SV61 ) )
= $true )
| ( ( in_path @ ( head_of @ SV69 ) @ SV61 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[374]) ).
thf(413,plain,
! [SV8: $i] :
( ( ( on_path @ ( sK6_E1 @ SV8 ) @ SV8 )
= $true )
| ( ( ! [SY115: $i,SY116: $i] :
~ ( path @ SY115 @ SY116 @ SV8 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV8 )
= ( number_of_in @ triangles @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[376]) ).
thf(414,plain,
! [SV8: $i] :
( ( ( on_path @ ( sK7_SY80 @ SV8 ) @ SV8 )
= $true )
| ( ( ! [SY115: $i,SY116: $i] :
~ ( path @ SY115 @ SY116 @ SV8 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV8 )
= ( number_of_in @ triangles @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[377]) ).
thf(415,plain,
! [SV8: $i,SV77: $i,SV70: $i] :
( ( ( path @ SV70 @ SV77 @ SV8 )
= $false )
| ( ( sequential @ ( sK6_E1 @ SV8 ) @ ( sK7_SY80 @ SV8 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV8 )
= ( number_of_in @ triangles @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(416,plain,
! [SV9: $i,SV19: $i,SV41: $i,SV47: $i] :
( ( ( ~ ( on_path @ ( sK10_E @ SV47 @ SV41 @ SV19 @ SV9 ) @ SV41 )
| ~ ( ( SV47
= ( head_of @ ( sK10_E @ SV47 @ SV41 @ SV19 @ SV9 ) ) )
| ( SV47
= ( tail_of @ ( sK10_E @ SV47 @ SV41 @ SV19 @ SV9 ) ) ) ) )
= $false )
| ( ( in_path @ SV47 @ SV41 )
= $false )
| ( ( path @ SV9 @ SV19 @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(417,plain,
! [SV30: $i,SV25: $i,SV10: $i,SV82: $i] :
( ( ( ! [SY230: $i] :
~ ( precedes @ SV82 @ SY230 @ SV10 )
| ( on_path @ SV82 @ SV10 ) )
= $true )
| ( ( path @ SV25 @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(418,plain,
! [SV30: $i,SV25: $i,SV10: $i,SV83: $i] :
( ( ( ! [SY231: $i] :
( ~ ( precedes @ SV83 @ SY231 @ SV10 )
| ( on_path @ SY231 @ SV10 ) ) )
= $true )
| ( ( path @ SV25 @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[383]) ).
thf(419,plain,
! [SV30: $i,SV25: $i,SV10: $i,SV84: $i] :
( ( ( ! [SY232: $i] :
( ~ ( precedes @ SV84 @ SY232 @ SV10 )
| ! [SY233: $i] :
( ~ ( precedes @ SY233 @ SY232 @ SV10 )
| ~ ( sequential @ SV84 @ SY233 ) )
| ~ ( sequential @ SV84 @ SY232 ) ) )
= $true )
| ( ( path @ SV25 @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[384]) ).
thf(420,plain,
! [SV30: $i,SV25: $i,SV10: $i,SV85: $i] :
( ( ( ! [SY234: $i] :
( ~ ( precedes @ SV85 @ SY234 @ SV10 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY234 @ SV85 @ SV10 ) @ SY234 @ SV10 )
| ~ ( sequential @ SV85 @ ( sK9_E3 @ SY234 @ SV85 @ SV10 ) ) )
| ( sequential @ SV85 @ SY234 ) ) )
= $true )
| ( ( path @ SV25 @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(421,plain,
! [SV43: $i,SV36: $i,SV11: $i] :
( ( ( ~ ( edge @ SV11 ) )
= $true )
| ( ( ~ ( edge @ SV36 ) )
= $true )
| ( ( ~ ( edge @ SV43 ) )
= $true )
| ( ( ~ ( sequential @ SV11 @ SV36 ) )
= $true )
| ( ( ~ ( sequential @ SV36 @ SV43 ) )
= $true )
| ( ( ~ ( sequential @ SV43 @ SV11 ) )
= $true )
| ( ( triangle @ SV11 @ SV36 @ SV43 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[386]) ).
thf(422,plain,
! [SV11: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( ! [SY135: $i,SY136: $i] :
~ ( triangle @ SV11 @ SY135 @ SY136 )
| ( edge @ SV11 ) )
| ~ ! [SY137: $i] :
( ! [SY138: $i] :
~ ( triangle @ SV11 @ SY137 @ SY138 )
| ( edge @ SY137 ) ) )
| ~ ! [SY139: $i,SY140: $i] :
( ~ ( triangle @ SV11 @ SY139 @ SY140 )
| ( edge @ SY140 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[387]) ).
thf(423,plain,
! [SV11: $i] :
( ( ~ ! [SY141: $i] :
( ! [SY142: $i] :
~ ( triangle @ SV11 @ SY141 @ SY142 )
| ( sequential @ SV11 @ SY141 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[387]) ).
thf(424,plain,
! [SV86: $i,SV78: $i,SV11: $i] :
( ( ~ ( triangle @ SV11 @ SV78 @ SV86 )
| ( sequential @ SV78 @ SV86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(425,plain,
! [SV37: $i,SV31: $i] :
( ( ( ( head_of @ SV31 )
= ( tail_of @ SV37 ) )
= $false )
| ( ( SV31 = SV37 )
= $true )
| ( ( edge @ SV31 )
= $false )
| ( ( edge @ SV37 )
= $false )
| ( ( sequential @ SV31 @ SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[390]) ).
thf(426,plain,
! [SV79: $i,SV72: $i] :
( ( ( ~ ( sequential @ SV72 @ SV79 ) )
= $true )
| ( ( ( SV72 != SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[391]) ).
thf(427,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[392]) ).
thf(428,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[393]) ).
thf(429,plain,
! [SV26: $i,SV20: $i,SV87: $i,SV12: $i] :
( ( ( ( SV12
!= ( tail_of @ SV87 ) )
| ~ ( edge @ SV87 )
| ( SV20
!= ( head_of @ SV87 ) )
| ( SV26
!= ( path_cons @ SV87 @ empty ) ) )
= $true )
| ( ( vertex @ SV12 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV12 @ SV20 @ SV26 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[394]) ).
thf(430,plain,
! [SV20: $i,SV26: $i,SV88: $i,SV12: $i] :
( ( ( ( SV12
!= ( tail_of @ SV88 ) )
| ~ ( edge @ SV88 )
| ! [SY235: $i] :
( ( SV26
!= ( path_cons @ SV88 @ SY235 ) )
| ~ ( path @ ( head_of @ SV88 ) @ SV20 @ SY235 ) ) )
= $true )
| ( ( vertex @ SV12 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV12 @ SV20 @ SV26 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(431,plain,
! [SV50: $i,SV27: $i,SV64: $i,SV21: $i,SV13: $i] :
( ( ( shortest_path @ SV13 @ SV21 @ SV64 )
= $false )
| ( ( precedes @ SV27 @ SV50 @ SV64 )
= $false )
| ( ( ! [SY210: $i] :
( ( ( tail_of @ SY210 )
!= ( tail_of @ SV27 ) )
| ( ( head_of @ SY210 )
!= ( head_of @ SV50 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[396]) ).
thf(432,plain,
! [SV51: $i,SV27: $i,SV55: $i,SV21: $i,SV13: $i] :
( ( ( shortest_path @ SV13 @ SV21 @ SV55 )
= $false )
| ( ( precedes @ SV27 @ SV51 @ SV55 )
= $false )
| ( ( ~ ( precedes @ SV51 @ SV27 @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[397]) ).
thf(433,plain,
! [SV38: $i,SV44: $i,SV14: $i] :
( ( ( ( SV14
!= ( tail_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( edge @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
= $false )
| ( ( path @ SV14 @ SV38 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[400]) ).
thf(434,plain,
! [SV14: $i,SV44: $i,SV38: $i] :
( ( ( ~ ( ( SV38
!= ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
| ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ empty ) )
| ! [SY207: $i] :
( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ SY207 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ SY207 ) ) )
| ~ ~ ( ~ ( ( SV38
= ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ ( sK13_SY84 @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ ( sK13_SY84 @ SV44 @ SV38 @ SV14 ) ) ) )
| ~ ( ( SV44
= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ empty ) )
| ~ ( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ ( sK12_SY85 @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ ( sK12_SY85 @ SV44 @ SV38 @ SV14 ) ) ) ) ) )
= $false )
| ( ( path @ SV14 @ SV38 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[401]) ).
thf(435,plain,
! [SV34: $i,SV28: $i] :
( ( ( ~ ( ~ ( ( SV28
!= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
!= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
!= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
!= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV28
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
| ~ ( ( SV28
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) ) )
| ~ ~ ( ~ ( ( SV34
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
| ~ ( ( SV34
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) ) ) ) ) )
= $true )
| ( ( SV28 = SV34 )
= $true )
| ( ( vertex @ SV28 )
= $false )
| ( ( vertex @ SV34 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[402]) ).
thf(436,plain,
! [SV28: $i,SV34: $i] :
( ( ( edge @ ( sK14_E @ SV34 @ SV28 ) )
= $true )
| ( ( SV28 = SV34 )
= $true )
| ( ( vertex @ SV28 )
= $false )
| ( ( vertex @ SV34 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[403]) ).
thf(437,plain,
! [SV29: $i,SV24: $i,SV66: $i,SV5: $i,SV57: $i] :
( ( ( ~ ( on_path @ SV57 @ SV5 ) )
= $true )
| ( ( ~ ( on_path @ SV66 @ SV5 ) )
= $true )
| ( ( ! [SY224: $i] :
( ~ ( precedes @ SY224 @ SV66 @ SV5 )
| ~ ( sequential @ SV57 @ SY224 ) ) )
= $true )
| ( ( precedes @ SV57 @ SV66 @ SV5 )
= $true )
| ( ( path @ SV24 @ SV29 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[404]) ).
thf(438,plain,
! [SV29: $i,SV24: $i,SV67: $i,SV5: $i,SV58: $i] :
( ( ( ~ ( on_path @ SV58 @ SV5 ) )
= $true )
| ( ( ~ ( on_path @ SV67 @ SV5 ) )
= $true )
| ( ( ~ ( sequential @ SV58 @ SV67 ) )
= $true )
| ( ( precedes @ SV58 @ SV67 @ SV5 )
= $true )
| ( ( path @ SV24 @ SV29 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[405]) ).
thf(439,plain,
! [SV39: $i,SV35: $i,SV6: $i] :
( ( ( path @ SV6 @ SV35 @ SV39 )
= $false )
| ( ( SV6 = SV35 )
= $true )
| ( ( path @ SV6 @ SV35 @ ( sK8_P @ SV39 @ SV35 @ SV6 ) )
= $true )
| ( ( shortest_path @ SV6 @ SV35 @ SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[406]) ).
thf(440,plain,
! [SV39: $i,SV35: $i,SV6: $i] :
( ( ( SV6 = SV35 )
= $true )
| ( ( ~ ( path @ SV6 @ SV35 @ SV39 ) )
= $true )
| ( ( less_or_equal @ ( length_of @ SV39 ) @ ( length_of @ ( sK8_P @ SV39 @ SV35 @ SV6 ) ) )
= $false )
| ( ( shortest_path @ SV6 @ SV35 @ SV39 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[407]) ).
thf(441,plain,
! [SV59: $i,SV80: $i,SV52: $i,SV6: $i] :
( ( ( ~ ( path @ SV6 @ SV52 @ SV80 ) )
= $true )
| ( ( less_or_equal @ ( length_of @ SV59 ) @ ( length_of @ SV80 ) )
= $true )
| ( ( shortest_path @ SV6 @ SV52 @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[408]) ).
thf(442,plain,
! [SV89: $i,SV75: $i,SV6: $i] :
( ( ( ~ ( shortest_path @ SV6 @ SV75 @ SV89 ) )
= $true )
| ( ( ( SV6 != SV75 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(443,plain,
! [SV81: $i,SV76: $i,SV6: $i] :
( ( ( ~ ( shortest_path @ SV6 @ SV76 @ SV81 ) )
= $true )
| ( ( path @ SV6 @ SV76 @ SV81 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[410]) ).
thf(444,plain,
! [SV18: $i,SV7: $i,SV60: $i,SV68: $i] :
( ( ( on_path @ SV68 @ SV60 )
= $false )
| ( ( ~ ( path @ SV7 @ SV18 @ SV60 ) )
= $true )
| ( ( edge @ SV68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[411]) ).
thf(445,plain,
! [SV18: $i,SV7: $i,SV61: $i,SV69: $i] :
( ( ( on_path @ SV69 @ SV61 )
= $false )
| ( ( ~ ( path @ SV7 @ SV18 @ SV61 ) )
= $true )
| ( ( in_path @ ( head_of @ SV69 ) @ SV61 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[412]) ).
thf(446,plain,
! [SV8: $i,SV90: $i] :
( ( ( ! [SY236: $i] :
~ ( path @ SV90 @ SY236 @ SV8 ) )
= $true )
| ( ( on_path @ ( sK6_E1 @ SV8 ) @ SV8 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV8 )
= ( number_of_in @ triangles @ SV8 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[413]) ).
thf(447,plain,
! [SV8: $i,SV91: $i] :
( ( ( ! [SY237: $i] :
~ ( path @ SV91 @ SY237 @ SV8 ) )
= $true )
| ( ( on_path @ ( sK7_SY80 @ SV8 ) @ SV8 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV8 )
= ( number_of_in @ triangles @ SV8 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[414]) ).
thf(448,plain,
! [SV9: $i,SV19: $i,SV41: $i,SV47: $i] :
( ( ( ~ ( on_path @ ( sK10_E @ SV47 @ SV41 @ SV19 @ SV9 ) @ SV41 ) )
= $false )
| ( ( in_path @ SV47 @ SV41 )
= $false )
| ( ( path @ SV9 @ SV19 @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[416]) ).
thf(449,plain,
! [SV9: $i,SV19: $i,SV41: $i,SV47: $i] :
( ( ( ~ ( ( SV47
= ( head_of @ ( sK10_E @ SV47 @ SV41 @ SV19 @ SV9 ) ) )
| ( SV47
= ( tail_of @ ( sK10_E @ SV47 @ SV41 @ SV19 @ SV9 ) ) ) ) )
= $false )
| ( ( in_path @ SV47 @ SV41 )
= $false )
| ( ( path @ SV9 @ SV19 @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[416]) ).
thf(450,plain,
! [SV30: $i,SV25: $i,SV10: $i,SV82: $i] :
( ( ( ! [SY230: $i] :
~ ( precedes @ SV82 @ SY230 @ SV10 ) )
= $true )
| ( ( on_path @ SV82 @ SV10 )
= $true )
| ( ( path @ SV25 @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[417]) ).
thf(451,plain,
! [SV30: $i,SV25: $i,SV10: $i,SV92: $i,SV83: $i] :
( ( ( ~ ( precedes @ SV83 @ SV92 @ SV10 )
| ( on_path @ SV92 @ SV10 ) )
= $true )
| ( ( path @ SV25 @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[418]) ).
thf(452,plain,
! [SV30: $i,SV25: $i,SV10: $i,SV93: $i,SV84: $i] :
( ( ( ~ ( precedes @ SV84 @ SV93 @ SV10 )
| ! [SY238: $i] :
( ~ ( precedes @ SY238 @ SV93 @ SV10 )
| ~ ( sequential @ SV84 @ SY238 ) )
| ~ ( sequential @ SV84 @ SV93 ) )
= $true )
| ( ( path @ SV25 @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[419]) ).
thf(453,plain,
! [SV30: $i,SV25: $i,SV10: $i,SV94: $i,SV85: $i] :
( ( ( ~ ( precedes @ SV85 @ SV94 @ SV10 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SV94 @ SV85 @ SV10 ) @ SV94 @ SV10 )
| ~ ( sequential @ SV85 @ ( sK9_E3 @ SV94 @ SV85 @ SV10 ) ) )
| ( sequential @ SV85 @ SV94 ) )
= $true )
| ( ( path @ SV25 @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[420]) ).
thf(454,plain,
! [SV43: $i,SV36: $i,SV11: $i] :
( ( ( edge @ SV11 )
= $false )
| ( ( ~ ( edge @ SV36 ) )
= $true )
| ( ( ~ ( edge @ SV43 ) )
= $true )
| ( ( ~ ( sequential @ SV11 @ SV36 ) )
= $true )
| ( ( ~ ( sequential @ SV36 @ SV43 ) )
= $true )
| ( ( ~ ( sequential @ SV43 @ SV11 ) )
= $true )
| ( ( triangle @ SV11 @ SV36 @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[421]) ).
thf(455,plain,
! [SV11: $i] :
( ( ~ ( ~ ~ ( ~ ( ! [SY135: $i,SY136: $i] :
~ ( triangle @ SV11 @ SY135 @ SY136 )
| ( edge @ SV11 ) )
| ~ ! [SY137: $i] :
( ! [SY138: $i] :
~ ( triangle @ SV11 @ SY137 @ SY138 )
| ( edge @ SY137 ) ) )
| ~ ! [SY139: $i,SY140: $i] :
( ~ ( triangle @ SV11 @ SY139 @ SY140 )
| ( edge @ SY140 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[422]) ).
thf(456,plain,
! [SV11: $i] :
( ( ! [SY141: $i] :
( ! [SY142: $i] :
~ ( triangle @ SV11 @ SY141 @ SY142 )
| ( sequential @ SV11 @ SY141 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[423]) ).
thf(457,plain,
! [SV86: $i,SV78: $i,SV11: $i] :
( ( ( ~ ( triangle @ SV11 @ SV78 @ SV86 ) )
= $true )
| ( ( sequential @ SV78 @ SV86 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[424]) ).
thf(458,plain,
! [SV79: $i,SV72: $i] :
( ( ( sequential @ SV72 @ SV79 )
= $false )
| ( ( ( SV72 != SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[426]) ).
thf(459,plain,
! [SV95: $i] :
( ( ! [SY239: $i] :
~ ( sequential @ SV95 @ SY239 )
| ( edge @ SV95 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(460,plain,
! [SV96: $i] :
( ( ! [SY240: $i] :
( ~ ( sequential @ SV96 @ SY240 )
| ( edge @ SY240 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(461,plain,
! [SV26: $i,SV20: $i,SV87: $i,SV12: $i] :
( ( ( ( SV12
!= ( tail_of @ SV87 ) )
| ~ ( edge @ SV87 ) )
= $true )
| ( ( ( SV20
!= ( head_of @ SV87 ) )
| ( SV26
!= ( path_cons @ SV87 @ empty ) ) )
= $true )
| ( ( vertex @ SV12 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV12 @ SV20 @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[429]) ).
thf(462,plain,
! [SV20: $i,SV26: $i,SV88: $i,SV12: $i] :
( ( ( ( SV12
!= ( tail_of @ SV88 ) )
| ~ ( edge @ SV88 ) )
= $true )
| ( ( ! [SY235: $i] :
( ( SV26
!= ( path_cons @ SV88 @ SY235 ) )
| ~ ( path @ ( head_of @ SV88 ) @ SV20 @ SY235 ) ) )
= $true )
| ( ( vertex @ SV12 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV12 @ SV20 @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[430]) ).
thf(463,plain,
! [SV21: $i,SV13: $i,SV64: $i,SV50: $i,SV27: $i,SV97: $i] :
( ( ( ( ( tail_of @ SV97 )
!= ( tail_of @ SV27 ) )
| ( ( head_of @ SV97 )
!= ( head_of @ SV50 ) ) )
= $true )
| ( ( precedes @ SV27 @ SV50 @ SV64 )
= $false )
| ( ( shortest_path @ SV13 @ SV21 @ SV64 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(464,plain,
! [SV21: $i,SV13: $i,SV55: $i,SV27: $i,SV51: $i] :
( ( ( precedes @ SV51 @ SV27 @ SV55 )
= $false )
| ( ( precedes @ SV27 @ SV51 @ SV55 )
= $false )
| ( ( shortest_path @ SV13 @ SV21 @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[432]) ).
thf(465,plain,
! [SV38: $i,SV44: $i,SV14: $i] :
( ( ( ( SV14
!= ( tail_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) ) )
= $false )
| ( ( path @ SV14 @ SV38 @ SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[433]) ).
thf(466,plain,
! [SV14: $i,SV38: $i,SV44: $i] :
( ( ( ~ ( edge @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
= $false )
| ( ( path @ SV14 @ SV38 @ SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[433]) ).
thf(467,plain,
! [SV14: $i,SV44: $i,SV38: $i] :
( ( ( ~ ( ( SV38
!= ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
| ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ empty ) )
| ! [SY207: $i] :
( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ SY207 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ SY207 ) ) ) )
= $false )
| ( ( path @ SV14 @ SV38 @ SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[434]) ).
thf(468,plain,
! [SV14: $i,SV44: $i,SV38: $i] :
( ( ( ~ ~ ( ~ ( ( SV38
= ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ ( sK13_SY84 @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ ( sK13_SY84 @ SV44 @ SV38 @ SV14 ) ) ) )
| ~ ( ( SV44
= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ empty ) )
| ~ ( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ ( sK12_SY85 @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ ( sK12_SY85 @ SV44 @ SV38 @ SV14 ) ) ) ) ) )
= $false )
| ( ( path @ SV14 @ SV38 @ SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[434]) ).
thf(469,plain,
! [SV34: $i,SV28: $i] :
( ( ( ~ ( ( SV28
!= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
!= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
!= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
!= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV28
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
| ~ ( ( SV28
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) ) )
| ~ ~ ( ~ ( ( SV34
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
| ~ ( ( SV34
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) ) ) ) )
= $false )
| ( ( SV28 = SV34 )
= $true )
| ( ( vertex @ SV28 )
= $false )
| ( ( vertex @ SV34 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[435]) ).
thf(470,plain,
! [SV29: $i,SV24: $i,SV66: $i,SV5: $i,SV57: $i] :
( ( ( on_path @ SV57 @ SV5 )
= $false )
| ( ( ~ ( on_path @ SV66 @ SV5 ) )
= $true )
| ( ( ! [SY224: $i] :
( ~ ( precedes @ SY224 @ SV66 @ SV5 )
| ~ ( sequential @ SV57 @ SY224 ) ) )
= $true )
| ( ( precedes @ SV57 @ SV66 @ SV5 )
= $true )
| ( ( path @ SV24 @ SV29 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[437]) ).
thf(471,plain,
! [SV29: $i,SV24: $i,SV67: $i,SV5: $i,SV58: $i] :
( ( ( on_path @ SV58 @ SV5 )
= $false )
| ( ( ~ ( on_path @ SV67 @ SV5 ) )
= $true )
| ( ( ~ ( sequential @ SV58 @ SV67 ) )
= $true )
| ( ( precedes @ SV58 @ SV67 @ SV5 )
= $true )
| ( ( path @ SV24 @ SV29 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(472,plain,
! [SV39: $i,SV35: $i,SV6: $i] :
( ( ( path @ SV6 @ SV35 @ SV39 )
= $false )
| ( ( SV6 = SV35 )
= $true )
| ( ( less_or_equal @ ( length_of @ SV39 ) @ ( length_of @ ( sK8_P @ SV39 @ SV35 @ SV6 ) ) )
= $false )
| ( ( shortest_path @ SV6 @ SV35 @ SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[440]) ).
thf(473,plain,
! [SV59: $i,SV80: $i,SV52: $i,SV6: $i] :
( ( ( path @ SV6 @ SV52 @ SV80 )
= $false )
| ( ( less_or_equal @ ( length_of @ SV59 ) @ ( length_of @ SV80 ) )
= $true )
| ( ( shortest_path @ SV6 @ SV52 @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[441]) ).
thf(474,plain,
! [SV89: $i,SV75: $i,SV6: $i] :
( ( ( shortest_path @ SV6 @ SV75 @ SV89 )
= $false )
| ( ( ( SV6 != SV75 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[442]) ).
thf(475,plain,
! [SV81: $i,SV76: $i,SV6: $i] :
( ( ( shortest_path @ SV6 @ SV76 @ SV81 )
= $false )
| ( ( path @ SV6 @ SV76 @ SV81 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[443]) ).
thf(476,plain,
! [SV68: $i,SV60: $i,SV18: $i,SV7: $i] :
( ( ( path @ SV7 @ SV18 @ SV60 )
= $false )
| ( ( on_path @ SV68 @ SV60 )
= $false )
| ( ( edge @ SV68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[444]) ).
thf(477,plain,
! [SV69: $i,SV61: $i,SV18: $i,SV7: $i] :
( ( ( path @ SV7 @ SV18 @ SV61 )
= $false )
| ( ( on_path @ SV69 @ SV61 )
= $false )
| ( ( in_path @ ( head_of @ SV69 ) @ SV61 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[445]) ).
thf(478,plain,
! [SV8: $i,SV98: $i,SV90: $i] :
( ( ( ~ ( path @ SV90 @ SV98 @ SV8 ) )
= $true )
| ( ( on_path @ ( sK6_E1 @ SV8 ) @ SV8 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV8 )
= ( number_of_in @ triangles @ SV8 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(479,plain,
! [SV8: $i,SV99: $i,SV91: $i] :
( ( ( ~ ( path @ SV91 @ SV99 @ SV8 ) )
= $true )
| ( ( on_path @ ( sK7_SY80 @ SV8 ) @ SV8 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV8 )
= ( number_of_in @ triangles @ SV8 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(480,plain,
! [SV9: $i,SV19: $i,SV41: $i,SV47: $i] :
( ( ( on_path @ ( sK10_E @ SV47 @ SV41 @ SV19 @ SV9 ) @ SV41 )
= $true )
| ( ( in_path @ SV47 @ SV41 )
= $false )
| ( ( path @ SV9 @ SV19 @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[448]) ).
thf(481,plain,
! [SV9: $i,SV19: $i,SV41: $i,SV47: $i] :
( ( ( ( SV47
= ( head_of @ ( sK10_E @ SV47 @ SV41 @ SV19 @ SV9 ) ) )
| ( SV47
= ( tail_of @ ( sK10_E @ SV47 @ SV41 @ SV19 @ SV9 ) ) ) )
= $true )
| ( ( in_path @ SV47 @ SV41 )
= $false )
| ( ( path @ SV9 @ SV19 @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[449]) ).
thf(482,plain,
! [SV30: $i,SV25: $i,SV10: $i,SV100: $i,SV82: $i] :
( ( ( ~ ( precedes @ SV82 @ SV100 @ SV10 ) )
= $true )
| ( ( on_path @ SV82 @ SV10 )
= $true )
| ( ( path @ SV25 @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(483,plain,
! [SV30: $i,SV25: $i,SV10: $i,SV92: $i,SV83: $i] :
( ( ( ~ ( precedes @ SV83 @ SV92 @ SV10 ) )
= $true )
| ( ( on_path @ SV92 @ SV10 )
= $true )
| ( ( path @ SV25 @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[451]) ).
thf(484,plain,
! [SV30: $i,SV25: $i,SV10: $i,SV93: $i,SV84: $i] :
( ( ( ~ ( precedes @ SV84 @ SV93 @ SV10 ) )
= $true )
| ( ( ! [SY238: $i] :
( ~ ( precedes @ SY238 @ SV93 @ SV10 )
| ~ ( sequential @ SV84 @ SY238 ) )
| ~ ( sequential @ SV84 @ SV93 ) )
= $true )
| ( ( path @ SV25 @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[452]) ).
thf(485,plain,
! [SV30: $i,SV25: $i,SV10: $i,SV94: $i,SV85: $i] :
( ( ( ~ ( precedes @ SV85 @ SV94 @ SV10 ) )
= $true )
| ( ( ~ ( ~ ( precedes @ ( sK9_E3 @ SV94 @ SV85 @ SV10 ) @ SV94 @ SV10 )
| ~ ( sequential @ SV85 @ ( sK9_E3 @ SV94 @ SV85 @ SV10 ) ) )
| ( sequential @ SV85 @ SV94 ) )
= $true )
| ( ( path @ SV25 @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[453]) ).
thf(486,plain,
! [SV43: $i,SV11: $i,SV36: $i] :
( ( ( edge @ SV36 )
= $false )
| ( ( edge @ SV11 )
= $false )
| ( ( ~ ( edge @ SV43 ) )
= $true )
| ( ( ~ ( sequential @ SV11 @ SV36 ) )
= $true )
| ( ( ~ ( sequential @ SV36 @ SV43 ) )
= $true )
| ( ( ~ ( sequential @ SV43 @ SV11 ) )
= $true )
| ( ( triangle @ SV11 @ SV36 @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[454]) ).
thf(487,plain,
! [SV11: $i] :
( ( ~ ~ ( ~ ( ! [SY135: $i,SY136: $i] :
~ ( triangle @ SV11 @ SY135 @ SY136 )
| ( edge @ SV11 ) )
| ~ ! [SY137: $i] :
( ! [SY138: $i] :
~ ( triangle @ SV11 @ SY137 @ SY138 )
| ( edge @ SY137 ) ) )
| ~ ! [SY139: $i,SY140: $i] :
( ~ ( triangle @ SV11 @ SY139 @ SY140 )
| ( edge @ SY140 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[455]) ).
thf(488,plain,
! [SV101: $i,SV11: $i] :
( ( ! [SY241: $i] :
~ ( triangle @ SV11 @ SV101 @ SY241 )
| ( sequential @ SV11 @ SV101 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(489,plain,
! [SV86: $i,SV78: $i,SV11: $i] :
( ( ( triangle @ SV11 @ SV78 @ SV86 )
= $false )
| ( ( sequential @ SV78 @ SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[457]) ).
thf(490,plain,
! [SV79: $i,SV72: $i] :
( ( ( SV72 = SV79 )
= $false )
| ( ( sequential @ SV72 @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[458]) ).
thf(491,plain,
! [SV95: $i] :
( ( ( ! [SY239: $i] :
~ ( sequential @ SV95 @ SY239 ) )
= $true )
| ( ( edge @ SV95 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[459]) ).
thf(492,plain,
! [SV102: $i,SV96: $i] :
( ( ~ ( sequential @ SV96 @ SV102 )
| ( edge @ SV102 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[460]) ).
thf(493,plain,
! [SV26: $i,SV20: $i,SV87: $i,SV12: $i] :
( ( ( ( SV12
!= ( tail_of @ SV87 ) ) )
= $true )
| ( ( ~ ( edge @ SV87 ) )
= $true )
| ( ( ( SV20
!= ( head_of @ SV87 ) )
| ( SV26
!= ( path_cons @ SV87 @ empty ) ) )
= $true )
| ( ( vertex @ SV12 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV12 @ SV20 @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[461]) ).
thf(494,plain,
! [SV20: $i,SV26: $i,SV88: $i,SV12: $i] :
( ( ( ( SV12
!= ( tail_of @ SV88 ) ) )
= $true )
| ( ( ~ ( edge @ SV88 ) )
= $true )
| ( ( ! [SY235: $i] :
( ( SV26
!= ( path_cons @ SV88 @ SY235 ) )
| ~ ( path @ ( head_of @ SV88 ) @ SV20 @ SY235 ) ) )
= $true )
| ( ( vertex @ SV12 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV12 @ SV20 @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[462]) ).
thf(495,plain,
! [SV21: $i,SV13: $i,SV64: $i,SV50: $i,SV27: $i,SV97: $i] :
( ( ( ( ( tail_of @ SV97 )
!= ( tail_of @ SV27 ) ) )
= $true )
| ( ( ( ( head_of @ SV97 )
!= ( head_of @ SV50 ) ) )
= $true )
| ( ( precedes @ SV27 @ SV50 @ SV64 )
= $false )
| ( ( shortest_path @ SV13 @ SV21 @ SV64 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[463]) ).
thf(496,plain,
! [SV38: $i,SV44: $i,SV14: $i] :
( ( ( SV14
= ( tail_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
= $true )
| ( ( path @ SV14 @ SV38 @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[465]) ).
thf(497,plain,
! [SV14: $i,SV38: $i,SV44: $i] :
( ( ( edge @ ( sK11_E @ SV44 @ SV38 @ SV14 ) )
= $true )
| ( ( path @ SV14 @ SV38 @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[466]) ).
thf(498,plain,
! [SV14: $i,SV44: $i,SV38: $i] :
( ( ( ( SV38
!= ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
| ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ empty ) )
| ! [SY207: $i] :
( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ SY207 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ SY207 ) ) )
= $true )
| ( ( path @ SV14 @ SV38 @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[467]) ).
thf(499,plain,
! [SV14: $i,SV44: $i,SV38: $i] :
( ( ( ~ ( ~ ( ( SV38
= ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ ( sK13_SY84 @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ ( sK13_SY84 @ SV44 @ SV38 @ SV14 ) ) ) )
| ~ ( ( SV44
= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ empty ) )
| ~ ( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ ( sK12_SY85 @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ ( sK12_SY85 @ SV44 @ SV38 @ SV14 ) ) ) ) ) )
= $true )
| ( ( path @ SV14 @ SV38 @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[468]) ).
thf(500,plain,
! [SV34: $i,SV28: $i] :
( ( ( ~ ( ( SV28
!= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
!= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
!= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
!= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) ) )
= $false )
| ( ( SV28 = SV34 )
= $true )
| ( ( vertex @ SV28 )
= $false )
| ( ( vertex @ SV34 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[469]) ).
thf(501,plain,
! [SV34: $i,SV28: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( SV28
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
| ~ ( ( SV28
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) ) )
| ~ ~ ( ~ ( ( SV34
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
| ~ ( ( SV34
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) ) ) ) )
= $false )
| ( ( SV28 = SV34 )
= $true )
| ( ( vertex @ SV28 )
= $false )
| ( ( vertex @ SV34 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[469]) ).
thf(502,plain,
! [SV29: $i,SV24: $i,SV57: $i,SV5: $i,SV66: $i] :
( ( ( on_path @ SV66 @ SV5 )
= $false )
| ( ( on_path @ SV57 @ SV5 )
= $false )
| ( ( ! [SY224: $i] :
( ~ ( precedes @ SY224 @ SV66 @ SV5 )
| ~ ( sequential @ SV57 @ SY224 ) ) )
= $true )
| ( ( precedes @ SV57 @ SV66 @ SV5 )
= $true )
| ( ( path @ SV24 @ SV29 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[470]) ).
thf(503,plain,
! [SV29: $i,SV24: $i,SV58: $i,SV5: $i,SV67: $i] :
( ( ( on_path @ SV67 @ SV5 )
= $false )
| ( ( on_path @ SV58 @ SV5 )
= $false )
| ( ( ~ ( sequential @ SV58 @ SV67 ) )
= $true )
| ( ( precedes @ SV58 @ SV67 @ SV5 )
= $true )
| ( ( path @ SV24 @ SV29 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[471]) ).
thf(504,plain,
! [SV89: $i,SV75: $i,SV6: $i] :
( ( ( SV6 = SV75 )
= $false )
| ( ( shortest_path @ SV6 @ SV75 @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[474]) ).
thf(505,plain,
! [SV8: $i,SV98: $i,SV90: $i] :
( ( ( path @ SV90 @ SV98 @ SV8 )
= $false )
| ( ( on_path @ ( sK6_E1 @ SV8 ) @ SV8 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV8 )
= ( number_of_in @ triangles @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[478]) ).
thf(506,plain,
! [SV8: $i,SV99: $i,SV91: $i] :
( ( ( path @ SV91 @ SV99 @ SV8 )
= $false )
| ( ( on_path @ ( sK7_SY80 @ SV8 ) @ SV8 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV8 )
= ( number_of_in @ triangles @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[479]) ).
thf(507,plain,
! [SV9: $i,SV19: $i,SV41: $i,SV47: $i] :
( ( ( SV47
= ( head_of @ ( sK10_E @ SV47 @ SV41 @ SV19 @ SV9 ) ) )
= $true )
| ( ( SV47
= ( tail_of @ ( sK10_E @ SV47 @ SV41 @ SV19 @ SV9 ) ) )
= $true )
| ( ( in_path @ SV47 @ SV41 )
= $false )
| ( ( path @ SV9 @ SV19 @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[481]) ).
thf(508,plain,
! [SV30: $i,SV25: $i,SV10: $i,SV100: $i,SV82: $i] :
( ( ( precedes @ SV82 @ SV100 @ SV10 )
= $false )
| ( ( on_path @ SV82 @ SV10 )
= $true )
| ( ( path @ SV25 @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[482]) ).
thf(509,plain,
! [SV30: $i,SV25: $i,SV10: $i,SV92: $i,SV83: $i] :
( ( ( precedes @ SV83 @ SV92 @ SV10 )
= $false )
| ( ( on_path @ SV92 @ SV10 )
= $true )
| ( ( path @ SV25 @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[483]) ).
thf(510,plain,
! [SV30: $i,SV25: $i,SV10: $i,SV93: $i,SV84: $i] :
( ( ( precedes @ SV84 @ SV93 @ SV10 )
= $false )
| ( ( ! [SY238: $i] :
( ~ ( precedes @ SY238 @ SV93 @ SV10 )
| ~ ( sequential @ SV84 @ SY238 ) )
| ~ ( sequential @ SV84 @ SV93 ) )
= $true )
| ( ( path @ SV25 @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[484]) ).
thf(511,plain,
! [SV30: $i,SV25: $i,SV10: $i,SV94: $i,SV85: $i] :
( ( ( precedes @ SV85 @ SV94 @ SV10 )
= $false )
| ( ( ~ ( ~ ( precedes @ ( sK9_E3 @ SV94 @ SV85 @ SV10 ) @ SV94 @ SV10 )
| ~ ( sequential @ SV85 @ ( sK9_E3 @ SV94 @ SV85 @ SV10 ) ) )
| ( sequential @ SV85 @ SV94 ) )
= $true )
| ( ( path @ SV25 @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[485]) ).
thf(512,plain,
! [SV36: $i,SV11: $i,SV43: $i] :
( ( ( edge @ SV43 )
= $false )
| ( ( edge @ SV11 )
= $false )
| ( ( edge @ SV36 )
= $false )
| ( ( ~ ( sequential @ SV11 @ SV36 ) )
= $true )
| ( ( ~ ( sequential @ SV36 @ SV43 ) )
= $true )
| ( ( ~ ( sequential @ SV43 @ SV11 ) )
= $true )
| ( ( triangle @ SV11 @ SV36 @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[486]) ).
thf(513,plain,
! [SV11: $i] :
( ( ~ ~ ( ~ ( ! [SY135: $i,SY136: $i] :
~ ( triangle @ SV11 @ SY135 @ SY136 )
| ( edge @ SV11 ) )
| ~ ! [SY137: $i] :
( ! [SY138: $i] :
~ ( triangle @ SV11 @ SY137 @ SY138 )
| ( edge @ SY137 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[487]) ).
thf(514,plain,
! [SV11: $i] :
( ( ~ ! [SY139: $i,SY140: $i] :
( ~ ( triangle @ SV11 @ SY139 @ SY140 )
| ( edge @ SY140 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[487]) ).
thf(515,plain,
! [SV101: $i,SV11: $i] :
( ( ( ! [SY241: $i] :
~ ( triangle @ SV11 @ SV101 @ SY241 ) )
= $true )
| ( ( sequential @ SV11 @ SV101 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[488]) ).
thf(516,plain,
! [SV103: $i,SV95: $i] :
( ( ( ~ ( sequential @ SV95 @ SV103 ) )
= $true )
| ( ( edge @ SV95 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(517,plain,
! [SV102: $i,SV96: $i] :
( ( ( ~ ( sequential @ SV96 @ SV102 ) )
= $true )
| ( ( edge @ SV102 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[492]) ).
thf(518,plain,
! [SV26: $i,SV20: $i,SV87: $i,SV12: $i] :
( ( ( SV12
= ( tail_of @ SV87 ) )
= $false )
| ( ( ~ ( edge @ SV87 ) )
= $true )
| ( ( ( SV20
!= ( head_of @ SV87 ) )
| ( SV26
!= ( path_cons @ SV87 @ empty ) ) )
= $true )
| ( ( vertex @ SV12 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV12 @ SV20 @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[493]) ).
thf(519,plain,
! [SV20: $i,SV26: $i,SV88: $i,SV12: $i] :
( ( ( SV12
= ( tail_of @ SV88 ) )
= $false )
| ( ( ~ ( edge @ SV88 ) )
= $true )
| ( ( ! [SY235: $i] :
( ( SV26
!= ( path_cons @ SV88 @ SY235 ) )
| ~ ( path @ ( head_of @ SV88 ) @ SV20 @ SY235 ) ) )
= $true )
| ( ( vertex @ SV12 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV12 @ SV20 @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[494]) ).
thf(520,plain,
! [SV21: $i,SV13: $i,SV64: $i,SV50: $i,SV27: $i,SV97: $i] :
( ( ( ( tail_of @ SV97 )
= ( tail_of @ SV27 ) )
= $false )
| ( ( ( ( head_of @ SV97 )
!= ( head_of @ SV50 ) ) )
= $true )
| ( ( precedes @ SV27 @ SV50 @ SV64 )
= $false )
| ( ( shortest_path @ SV13 @ SV21 @ SV64 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[495]) ).
thf(521,plain,
! [SV14: $i,SV44: $i,SV38: $i] :
( ( ( ( SV38
!= ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
| ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ empty ) ) )
= $true )
| ( ( ! [SY207: $i] :
( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ SY207 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ SY207 ) ) )
= $true )
| ( ( path @ SV14 @ SV38 @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[498]) ).
thf(522,plain,
! [SV14: $i,SV44: $i,SV38: $i] :
( ( ( ~ ( ( SV38
= ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ ( sK13_SY84 @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ ( sK13_SY84 @ SV44 @ SV38 @ SV14 ) ) ) )
| ~ ( ( SV44
= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ empty ) )
| ~ ( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ ( sK12_SY85 @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ ( sK12_SY85 @ SV44 @ SV38 @ SV14 ) ) ) ) )
= $false )
| ( ( path @ SV14 @ SV38 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[499]) ).
thf(523,plain,
! [SV34: $i,SV28: $i] :
( ( ( ( SV28
!= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
!= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
!= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
!= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
= $true )
| ( ( SV28 = SV34 )
= $true )
| ( ( vertex @ SV28 )
= $false )
| ( ( vertex @ SV34 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[500]) ).
thf(524,plain,
! [SV34: $i,SV28: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( SV28
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
| ~ ( ( SV28
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) ) )
| ~ ~ ( ~ ( ( SV34
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
| ~ ( ( SV34
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) ) ) ) )
= $true )
| ( ( SV28 = SV34 )
= $true )
| ( ( vertex @ SV28 )
= $false )
| ( ( vertex @ SV34 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[501]) ).
thf(525,plain,
! [SV29: $i,SV24: $i,SV57: $i,SV5: $i,SV66: $i,SV104: $i] :
( ( ( ~ ( precedes @ SV104 @ SV66 @ SV5 )
| ~ ( sequential @ SV57 @ SV104 ) )
= $true )
| ( ( on_path @ SV57 @ SV5 )
= $false )
| ( ( on_path @ SV66 @ SV5 )
= $false )
| ( ( precedes @ SV57 @ SV66 @ SV5 )
= $true )
| ( ( path @ SV24 @ SV29 @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(526,plain,
! [SV29: $i,SV24: $i,SV5: $i,SV67: $i,SV58: $i] :
( ( ( sequential @ SV58 @ SV67 )
= $false )
| ( ( on_path @ SV58 @ SV5 )
= $false )
| ( ( on_path @ SV67 @ SV5 )
= $false )
| ( ( precedes @ SV58 @ SV67 @ SV5 )
= $true )
| ( ( path @ SV24 @ SV29 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[503]) ).
thf(527,plain,
! [SV30: $i,SV25: $i,SV84: $i,SV10: $i,SV93: $i] :
( ( ( ! [SY238: $i] :
( ~ ( precedes @ SY238 @ SV93 @ SV10 )
| ~ ( sequential @ SV84 @ SY238 ) ) )
= $true )
| ( ( ~ ( sequential @ SV84 @ SV93 ) )
= $true )
| ( ( precedes @ SV84 @ SV93 @ SV10 )
= $false )
| ( ( path @ SV25 @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[510]) ).
thf(528,plain,
! [SV30: $i,SV25: $i,SV10: $i,SV85: $i,SV94: $i] :
( ( ( ~ ( ~ ( precedes @ ( sK9_E3 @ SV94 @ SV85 @ SV10 ) @ SV94 @ SV10 )
| ~ ( sequential @ SV85 @ ( sK9_E3 @ SV94 @ SV85 @ SV10 ) ) ) )
= $true )
| ( ( sequential @ SV85 @ SV94 )
= $true )
| ( ( precedes @ SV85 @ SV94 @ SV10 )
= $false )
| ( ( path @ SV25 @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[511]) ).
thf(529,plain,
! [SV43: $i,SV36: $i,SV11: $i] :
( ( ( sequential @ SV11 @ SV36 )
= $false )
| ( ( edge @ SV36 )
= $false )
| ( ( edge @ SV11 )
= $false )
| ( ( edge @ SV43 )
= $false )
| ( ( ~ ( sequential @ SV36 @ SV43 ) )
= $true )
| ( ( ~ ( sequential @ SV43 @ SV11 ) )
= $true )
| ( ( triangle @ SV11 @ SV36 @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[512]) ).
thf(530,plain,
! [SV11: $i] :
( ( ~ ( ~ ( ! [SY135: $i,SY136: $i] :
~ ( triangle @ SV11 @ SY135 @ SY136 )
| ( edge @ SV11 ) )
| ~ ! [SY137: $i] :
( ! [SY138: $i] :
~ ( triangle @ SV11 @ SY137 @ SY138 )
| ( edge @ SY137 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[513]) ).
thf(531,plain,
! [SV11: $i] :
( ( ! [SY139: $i,SY140: $i] :
( ~ ( triangle @ SV11 @ SY139 @ SY140 )
| ( edge @ SY140 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[514]) ).
thf(532,plain,
! [SV105: $i,SV101: $i,SV11: $i] :
( ( ( ~ ( triangle @ SV11 @ SV101 @ SV105 ) )
= $true )
| ( ( sequential @ SV11 @ SV101 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(533,plain,
! [SV103: $i,SV95: $i] :
( ( ( sequential @ SV95 @ SV103 )
= $false )
| ( ( edge @ SV95 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[516]) ).
thf(534,plain,
! [SV102: $i,SV96: $i] :
( ( ( sequential @ SV96 @ SV102 )
= $false )
| ( ( edge @ SV102 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[517]) ).
thf(535,plain,
! [SV26: $i,SV20: $i,SV12: $i,SV87: $i] :
( ( ( edge @ SV87 )
= $false )
| ( ( SV12
= ( tail_of @ SV87 ) )
= $false )
| ( ( ( SV20
!= ( head_of @ SV87 ) )
| ( SV26
!= ( path_cons @ SV87 @ empty ) ) )
= $true )
| ( ( vertex @ SV12 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV12 @ SV20 @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[518]) ).
thf(536,plain,
! [SV20: $i,SV26: $i,SV12: $i,SV88: $i] :
( ( ( edge @ SV88 )
= $false )
| ( ( SV12
= ( tail_of @ SV88 ) )
= $false )
| ( ( ! [SY235: $i] :
( ( SV26
!= ( path_cons @ SV88 @ SY235 ) )
| ~ ( path @ ( head_of @ SV88 ) @ SV20 @ SY235 ) ) )
= $true )
| ( ( vertex @ SV12 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV12 @ SV20 @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[519]) ).
thf(537,plain,
! [SV21: $i,SV13: $i,SV64: $i,SV27: $i,SV50: $i,SV97: $i] :
( ( ( ( head_of @ SV97 )
= ( head_of @ SV50 ) )
= $false )
| ( ( ( tail_of @ SV97 )
= ( tail_of @ SV27 ) )
= $false )
| ( ( precedes @ SV27 @ SV50 @ SV64 )
= $false )
| ( ( shortest_path @ SV13 @ SV21 @ SV64 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[520]) ).
thf(538,plain,
! [SV14: $i,SV44: $i,SV38: $i] :
( ( ( ( SV38
!= ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) ) )
= $true )
| ( ( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ empty ) ) )
= $true )
| ( ( ! [SY207: $i] :
( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ SY207 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ SY207 ) ) )
= $true )
| ( ( path @ SV14 @ SV38 @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[521]) ).
thf(539,plain,
! [SV14: $i,SV44: $i,SV38: $i] :
( ( ( ~ ( ( SV38
= ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ ( sK13_SY84 @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ ( sK13_SY84 @ SV44 @ SV38 @ SV14 ) ) ) ) )
= $false )
| ( ( path @ SV14 @ SV38 @ SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[522]) ).
thf(540,plain,
! [SV14: $i,SV38: $i,SV44: $i] :
( ( ( ~ ( ( SV44
= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ empty ) )
| ~ ( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ ( sK12_SY85 @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ ( sK12_SY85 @ SV44 @ SV38 @ SV14 ) ) ) ) )
= $false )
| ( ( path @ SV14 @ SV38 @ SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[522]) ).
thf(541,plain,
! [SV34: $i,SV28: $i] :
( ( ( ( SV28
!= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
!= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
= $true )
| ( ( ( SV34
!= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
!= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
= $true )
| ( ( SV28 = SV34 )
= $true )
| ( ( vertex @ SV28 )
= $false )
| ( ( vertex @ SV34 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[523]) ).
thf(542,plain,
! [SV34: $i,SV28: $i] :
( ( ( ~ ~ ( ~ ( ( SV28
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
| ~ ( ( SV28
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) ) )
| ~ ~ ( ~ ( ( SV34
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
| ~ ( ( SV34
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) ) ) )
= $false )
| ( ( SV28 = SV34 )
= $true )
| ( ( vertex @ SV28 )
= $false )
| ( ( vertex @ SV34 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[524]) ).
thf(543,plain,
! [SV29: $i,SV24: $i,SV57: $i,SV5: $i,SV66: $i,SV104: $i] :
( ( ( ~ ( precedes @ SV104 @ SV66 @ SV5 ) )
= $true )
| ( ( ~ ( sequential @ SV57 @ SV104 ) )
= $true )
| ( ( on_path @ SV57 @ SV5 )
= $false )
| ( ( on_path @ SV66 @ SV5 )
= $false )
| ( ( precedes @ SV57 @ SV66 @ SV5 )
= $true )
| ( ( path @ SV24 @ SV29 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[525]) ).
thf(544,plain,
! [SV30: $i,SV25: $i,SV84: $i,SV10: $i,SV93: $i,SV106: $i] :
( ( ( ~ ( precedes @ SV106 @ SV93 @ SV10 )
| ~ ( sequential @ SV84 @ SV106 ) )
= $true )
| ( ( ~ ( sequential @ SV84 @ SV93 ) )
= $true )
| ( ( precedes @ SV84 @ SV93 @ SV10 )
= $false )
| ( ( path @ SV25 @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[527]) ).
thf(545,plain,
! [SV30: $i,SV25: $i,SV10: $i,SV85: $i,SV94: $i] :
( ( ( ~ ( precedes @ ( sK9_E3 @ SV94 @ SV85 @ SV10 ) @ SV94 @ SV10 )
| ~ ( sequential @ SV85 @ ( sK9_E3 @ SV94 @ SV85 @ SV10 ) ) )
= $false )
| ( ( sequential @ SV85 @ SV94 )
= $true )
| ( ( precedes @ SV85 @ SV94 @ SV10 )
= $false )
| ( ( path @ SV25 @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[528]) ).
thf(546,plain,
! [SV11: $i,SV43: $i,SV36: $i] :
( ( ( sequential @ SV36 @ SV43 )
= $false )
| ( ( edge @ SV43 )
= $false )
| ( ( edge @ SV11 )
= $false )
| ( ( edge @ SV36 )
= $false )
| ( ( sequential @ SV11 @ SV36 )
= $false )
| ( ( ~ ( sequential @ SV43 @ SV11 ) )
= $true )
| ( ( triangle @ SV11 @ SV36 @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[529]) ).
thf(547,plain,
! [SV11: $i] :
( ( ~ ( ! [SY135: $i,SY136: $i] :
~ ( triangle @ SV11 @ SY135 @ SY136 )
| ( edge @ SV11 ) )
| ~ ! [SY137: $i] :
( ! [SY138: $i] :
~ ( triangle @ SV11 @ SY137 @ SY138 )
| ( edge @ SY137 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[530]) ).
thf(548,plain,
! [SV107: $i,SV11: $i] :
( ( ! [SY242: $i] :
( ~ ( triangle @ SV11 @ SV107 @ SY242 )
| ( edge @ SY242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(549,plain,
! [SV105: $i,SV101: $i,SV11: $i] :
( ( ( triangle @ SV11 @ SV101 @ SV105 )
= $false )
| ( ( sequential @ SV11 @ SV101 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[532]) ).
thf(550,plain,
! [SV12: $i,SV26: $i,SV87: $i,SV20: $i] :
( ( ( ( SV20
!= ( head_of @ SV87 ) ) )
= $true )
| ( ( ( SV26
!= ( path_cons @ SV87 @ empty ) ) )
= $true )
| ( ( SV12
= ( tail_of @ SV87 ) )
= $false )
| ( ( edge @ SV87 )
= $false )
| ( ( vertex @ SV12 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV12 @ SV20 @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[535]) ).
thf(551,plain,
! [SV12: $i,SV20: $i,SV108: $i,SV88: $i,SV26: $i] :
( ( ( ( SV26
!= ( path_cons @ SV88 @ SV108 ) )
| ~ ( path @ ( head_of @ SV88 ) @ SV20 @ SV108 ) )
= $true )
| ( ( SV12
= ( tail_of @ SV88 ) )
= $false )
| ( ( edge @ SV88 )
= $false )
| ( ( vertex @ SV12 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV12 @ SV20 @ SV26 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(552,plain,
! [SV14: $i,SV44: $i,SV38: $i] :
( ( ( SV38
= ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
= $false )
| ( ( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ empty ) ) )
= $true )
| ( ( ! [SY207: $i] :
( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ SY207 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ SY207 ) ) )
= $true )
| ( ( path @ SV14 @ SV38 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[538]) ).
thf(553,plain,
! [SV14: $i,SV44: $i,SV38: $i] :
( ( ( ( SV38
= ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ ( sK13_SY84 @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ ( sK13_SY84 @ SV44 @ SV38 @ SV14 ) ) ) )
= $true )
| ( ( path @ SV14 @ SV38 @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[539]) ).
thf(554,plain,
! [SV14: $i,SV38: $i,SV44: $i] :
( ( ( ( SV44
= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ empty ) )
| ~ ( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ ( sK12_SY85 @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ ( sK12_SY85 @ SV44 @ SV38 @ SV14 ) ) ) )
= $true )
| ( ( path @ SV14 @ SV38 @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[540]) ).
thf(555,plain,
! [SV34: $i,SV28: $i] :
( ( ( ( SV28
!= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
= $true )
| ( ( ( SV34
!= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
= $true )
| ( ( ( SV34
!= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
!= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
= $true )
| ( ( SV28 = SV34 )
= $true )
| ( ( vertex @ SV28 )
= $false )
| ( ( vertex @ SV34 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[541]) ).
thf(556,plain,
! [SV34: $i,SV28: $i] :
( ( ( ~ ~ ( ~ ( ( SV28
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
| ~ ( ( SV28
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) ) ) )
= $false )
| ( ( SV28 = SV34 )
= $true )
| ( ( vertex @ SV28 )
= $false )
| ( ( vertex @ SV34 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[542]) ).
thf(557,plain,
! [SV28: $i,SV34: $i] :
( ( ( ~ ~ ( ~ ( ( SV34
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
| ~ ( ( SV34
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) ) ) )
= $false )
| ( ( SV28 = SV34 )
= $true )
| ( ( vertex @ SV28 )
= $false )
| ( ( vertex @ SV34 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[542]) ).
thf(558,plain,
! [SV29: $i,SV24: $i,SV57: $i,SV5: $i,SV66: $i,SV104: $i] :
( ( ( precedes @ SV104 @ SV66 @ SV5 )
= $false )
| ( ( ~ ( sequential @ SV57 @ SV104 ) )
= $true )
| ( ( on_path @ SV57 @ SV5 )
= $false )
| ( ( on_path @ SV66 @ SV5 )
= $false )
| ( ( precedes @ SV57 @ SV66 @ SV5 )
= $true )
| ( ( path @ SV24 @ SV29 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[543]) ).
thf(559,plain,
! [SV30: $i,SV25: $i,SV84: $i,SV10: $i,SV93: $i,SV106: $i] :
( ( ( ~ ( precedes @ SV106 @ SV93 @ SV10 ) )
= $true )
| ( ( ~ ( sequential @ SV84 @ SV106 ) )
= $true )
| ( ( ~ ( sequential @ SV84 @ SV93 ) )
= $true )
| ( ( precedes @ SV84 @ SV93 @ SV10 )
= $false )
| ( ( path @ SV25 @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[544]) ).
thf(560,plain,
! [SV30: $i,SV25: $i,SV10: $i,SV85: $i,SV94: $i] :
( ( ( ~ ( precedes @ ( sK9_E3 @ SV94 @ SV85 @ SV10 ) @ SV94 @ SV10 ) )
= $false )
| ( ( sequential @ SV85 @ SV94 )
= $true )
| ( ( precedes @ SV85 @ SV94 @ SV10 )
= $false )
| ( ( path @ SV25 @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[545]) ).
thf(561,plain,
! [SV30: $i,SV25: $i,SV10: $i,SV94: $i,SV85: $i] :
( ( ( ~ ( sequential @ SV85 @ ( sK9_E3 @ SV94 @ SV85 @ SV10 ) ) )
= $false )
| ( ( sequential @ SV85 @ SV94 )
= $true )
| ( ( precedes @ SV85 @ SV94 @ SV10 )
= $false )
| ( ( path @ SV25 @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[545]) ).
thf(562,plain,
! [SV36: $i,SV11: $i,SV43: $i] :
( ( ( sequential @ SV43 @ SV11 )
= $false )
| ( ( sequential @ SV11 @ SV36 )
= $false )
| ( ( edge @ SV36 )
= $false )
| ( ( edge @ SV11 )
= $false )
| ( ( edge @ SV43 )
= $false )
| ( ( sequential @ SV36 @ SV43 )
= $false )
| ( ( triangle @ SV11 @ SV36 @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[546]) ).
thf(563,plain,
! [SV11: $i] :
( ( ~ ( ! [SY135: $i,SY136: $i] :
~ ( triangle @ SV11 @ SY135 @ SY136 )
| ( edge @ SV11 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[547]) ).
thf(564,plain,
! [SV11: $i] :
( ( ~ ! [SY137: $i] :
( ! [SY138: $i] :
~ ( triangle @ SV11 @ SY137 @ SY138 )
| ( edge @ SY137 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[547]) ).
thf(565,plain,
! [SV109: $i,SV107: $i,SV11: $i] :
( ( ~ ( triangle @ SV11 @ SV107 @ SV109 )
| ( edge @ SV109 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[548]) ).
thf(566,plain,
! [SV12: $i,SV26: $i,SV87: $i,SV20: $i] :
( ( ( SV20
= ( head_of @ SV87 ) )
= $false )
| ( ( ( SV26
!= ( path_cons @ SV87 @ empty ) ) )
= $true )
| ( ( SV12
= ( tail_of @ SV87 ) )
= $false )
| ( ( edge @ SV87 )
= $false )
| ( ( vertex @ SV12 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV12 @ SV20 @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[550]) ).
thf(567,plain,
! [SV12: $i,SV20: $i,SV108: $i,SV88: $i,SV26: $i] :
( ( ( ( SV26
!= ( path_cons @ SV88 @ SV108 ) ) )
= $true )
| ( ( ~ ( path @ ( head_of @ SV88 ) @ SV20 @ SV108 ) )
= $true )
| ( ( SV12
= ( tail_of @ SV88 ) )
= $false )
| ( ( edge @ SV88 )
= $false )
| ( ( vertex @ SV12 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV12 @ SV20 @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[551]) ).
thf(568,plain,
! [SV14: $i,SV38: $i,SV44: $i] :
( ( ( SV44
= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ empty ) )
= $false )
| ( ( SV38
= ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
= $false )
| ( ( ! [SY207: $i] :
( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ SY207 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ SY207 ) ) )
= $true )
| ( ( path @ SV14 @ SV38 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[552]) ).
thf(569,plain,
! [SV14: $i,SV44: $i,SV38: $i] :
( ( ( SV38
= ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
= $true )
| ( ( ~ ( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ ( sK13_SY84 @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ ( sK13_SY84 @ SV44 @ SV38 @ SV14 ) ) ) )
= $true )
| ( ( path @ SV14 @ SV38 @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[553]) ).
thf(570,plain,
! [SV14: $i,SV38: $i,SV44: $i] :
( ( ( SV44
= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ empty ) )
= $true )
| ( ( ~ ( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ ( sK12_SY85 @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ ( sK12_SY85 @ SV44 @ SV38 @ SV14 ) ) ) )
= $true )
| ( ( path @ SV14 @ SV38 @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[554]) ).
thf(571,plain,
! [SV34: $i,SV28: $i] :
( ( ( SV28
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
= $false )
| ( ( ( SV34
!= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
= $true )
| ( ( ( SV34
!= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
!= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
= $true )
| ( ( SV28 = SV34 )
= $true )
| ( ( vertex @ SV28 )
= $false )
| ( ( vertex @ SV34 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[555]) ).
thf(572,plain,
! [SV34: $i,SV28: $i] :
( ( ( ~ ( ~ ( ( SV28
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
| ~ ( ( SV28
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) ) ) )
= $true )
| ( ( SV28 = SV34 )
= $true )
| ( ( vertex @ SV28 )
= $false )
| ( ( vertex @ SV34 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[556]) ).
thf(573,plain,
! [SV28: $i,SV34: $i] :
( ( ( ~ ( ~ ( ( SV34
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
| ~ ( ( SV34
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) ) ) )
= $true )
| ( ( SV28 = SV34 )
= $true )
| ( ( vertex @ SV28 )
= $false )
| ( ( vertex @ SV34 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[557]) ).
thf(574,plain,
! [SV29: $i,SV24: $i,SV5: $i,SV66: $i,SV104: $i,SV57: $i] :
( ( ( sequential @ SV57 @ SV104 )
= $false )
| ( ( precedes @ SV104 @ SV66 @ SV5 )
= $false )
| ( ( on_path @ SV57 @ SV5 )
= $false )
| ( ( on_path @ SV66 @ SV5 )
= $false )
| ( ( precedes @ SV57 @ SV66 @ SV5 )
= $true )
| ( ( path @ SV24 @ SV29 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[558]) ).
thf(575,plain,
! [SV30: $i,SV25: $i,SV84: $i,SV10: $i,SV93: $i,SV106: $i] :
( ( ( precedes @ SV106 @ SV93 @ SV10 )
= $false )
| ( ( ~ ( sequential @ SV84 @ SV106 ) )
= $true )
| ( ( ~ ( sequential @ SV84 @ SV93 ) )
= $true )
| ( ( precedes @ SV84 @ SV93 @ SV10 )
= $false )
| ( ( path @ SV25 @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[559]) ).
thf(576,plain,
! [SV30: $i,SV25: $i,SV10: $i,SV85: $i,SV94: $i] :
( ( ( precedes @ ( sK9_E3 @ SV94 @ SV85 @ SV10 ) @ SV94 @ SV10 )
= $true )
| ( ( sequential @ SV85 @ SV94 )
= $true )
| ( ( precedes @ SV85 @ SV94 @ SV10 )
= $false )
| ( ( path @ SV25 @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[560]) ).
thf(577,plain,
! [SV30: $i,SV25: $i,SV10: $i,SV94: $i,SV85: $i] :
( ( ( sequential @ SV85 @ ( sK9_E3 @ SV94 @ SV85 @ SV10 ) )
= $true )
| ( ( sequential @ SV85 @ SV94 )
= $true )
| ( ( precedes @ SV85 @ SV94 @ SV10 )
= $false )
| ( ( path @ SV25 @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[561]) ).
thf(578,plain,
! [SV11: $i] :
( ( ! [SY135: $i,SY136: $i] :
~ ( triangle @ SV11 @ SY135 @ SY136 )
| ( edge @ SV11 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[563]) ).
thf(579,plain,
! [SV11: $i] :
( ( ! [SY137: $i] :
( ! [SY138: $i] :
~ ( triangle @ SV11 @ SY137 @ SY138 )
| ( edge @ SY137 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[564]) ).
thf(580,plain,
! [SV109: $i,SV107: $i,SV11: $i] :
( ( ( ~ ( triangle @ SV11 @ SV107 @ SV109 ) )
= $true )
| ( ( edge @ SV109 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[565]) ).
thf(581,plain,
! [SV12: $i,SV20: $i,SV87: $i,SV26: $i] :
( ( ( SV26
= ( path_cons @ SV87 @ empty ) )
= $false )
| ( ( SV20
= ( head_of @ SV87 ) )
= $false )
| ( ( SV12
= ( tail_of @ SV87 ) )
= $false )
| ( ( edge @ SV87 )
= $false )
| ( ( vertex @ SV12 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV12 @ SV20 @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[566]) ).
thf(582,plain,
! [SV12: $i,SV20: $i,SV108: $i,SV88: $i,SV26: $i] :
( ( ( SV26
= ( path_cons @ SV88 @ SV108 ) )
= $false )
| ( ( ~ ( path @ ( head_of @ SV88 ) @ SV20 @ SV108 ) )
= $true )
| ( ( SV12
= ( tail_of @ SV88 ) )
= $false )
| ( ( edge @ SV88 )
= $false )
| ( ( vertex @ SV12 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV12 @ SV20 @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[567]) ).
thf(583,plain,
! [SV110: $i,SV14: $i,SV38: $i,SV44: $i] :
( ( ( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ SV110 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ SV110 ) )
= $true )
| ( ( SV38
= ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
= $false )
| ( ( SV44
= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ empty ) )
= $false )
| ( ( path @ SV14 @ SV38 @ SV44 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(584,plain,
! [SV14: $i,SV38: $i,SV44: $i] :
( ( ( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ ( sK13_SY84 @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ ( sK13_SY84 @ SV44 @ SV38 @ SV14 ) ) )
= $false )
| ( ( SV38
= ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
= $true )
| ( ( path @ SV14 @ SV38 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[569]) ).
thf(585,plain,
! [SV14: $i,SV38: $i,SV44: $i] :
( ( ( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ ( sK12_SY85 @ SV44 @ SV38 @ SV14 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ ( sK12_SY85 @ SV44 @ SV38 @ SV14 ) ) )
= $false )
| ( ( SV44
= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ empty ) )
= $true )
| ( ( path @ SV14 @ SV38 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[570]) ).
thf(586,plain,
! [SV28: $i,SV34: $i] :
( ( ( SV34
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
= $false )
| ( ( SV28
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
= $false )
| ( ( ( SV34
!= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
!= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
= $true )
| ( ( SV28 = SV34 )
= $true )
| ( ( vertex @ SV28 )
= $false )
| ( ( vertex @ SV34 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[571]) ).
thf(587,plain,
! [SV34: $i,SV28: $i] :
( ( ( ~ ( ( SV28
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
| ~ ( ( SV28
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) ) )
= $false )
| ( ( SV28 = SV34 )
= $true )
| ( ( vertex @ SV28 )
= $false )
| ( ( vertex @ SV34 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[572]) ).
thf(588,plain,
! [SV28: $i,SV34: $i] :
( ( ( ~ ( ( SV34
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
| ~ ( ( SV34
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) ) )
= $false )
| ( ( SV28 = SV34 )
= $true )
| ( ( vertex @ SV28 )
= $false )
| ( ( vertex @ SV34 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[573]) ).
thf(589,plain,
! [SV30: $i,SV25: $i,SV10: $i,SV93: $i,SV106: $i,SV84: $i] :
( ( ( sequential @ SV84 @ SV106 )
= $false )
| ( ( precedes @ SV106 @ SV93 @ SV10 )
= $false )
| ( ( ~ ( sequential @ SV84 @ SV93 ) )
= $true )
| ( ( precedes @ SV84 @ SV93 @ SV10 )
= $false )
| ( ( path @ SV25 @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[575]) ).
thf(590,plain,
! [SV11: $i] :
( ( ( ! [SY135: $i,SY136: $i] :
~ ( triangle @ SV11 @ SY135 @ SY136 ) )
= $true )
| ( ( edge @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[578]) ).
thf(591,plain,
! [SV111: $i,SV11: $i] :
( ( ! [SY243: $i] :
~ ( triangle @ SV11 @ SV111 @ SY243 )
| ( edge @ SV111 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[579]) ).
thf(592,plain,
! [SV109: $i,SV107: $i,SV11: $i] :
( ( ( triangle @ SV11 @ SV107 @ SV109 )
= $false )
| ( ( edge @ SV109 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[580]) ).
thf(593,plain,
! [SV12: $i,SV26: $i,SV108: $i,SV20: $i,SV88: $i] :
( ( ( path @ ( head_of @ SV88 ) @ SV20 @ SV108 )
= $false )
| ( ( SV26
= ( path_cons @ SV88 @ SV108 ) )
= $false )
| ( ( SV12
= ( tail_of @ SV88 ) )
= $false )
| ( ( edge @ SV88 )
= $false )
| ( ( vertex @ SV12 )
= $false )
| ( ( vertex @ SV20 )
= $false )
| ( ( path @ SV12 @ SV20 @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[582]) ).
thf(594,plain,
! [SV110: $i,SV14: $i,SV38: $i,SV44: $i] :
( ( ( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ SV110 ) ) )
= $true )
| ( ( ~ ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ SV110 ) )
= $true )
| ( ( SV38
= ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
= $false )
| ( ( SV44
= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ empty ) )
= $false )
| ( ( path @ SV14 @ SV38 @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[583]) ).
thf(595,plain,
! [SV14: $i,SV38: $i,SV44: $i] :
( ( ( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ ( sK13_SY84 @ SV44 @ SV38 @ SV14 ) ) ) )
= $false )
| ( ( SV38
= ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
= $true )
| ( ( path @ SV14 @ SV38 @ SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[584]) ).
thf(596,plain,
! [SV14: $i,SV38: $i,SV44: $i] :
( ( ( ~ ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ ( sK13_SY84 @ SV44 @ SV38 @ SV14 ) ) )
= $false )
| ( ( SV38
= ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
= $true )
| ( ( path @ SV14 @ SV38 @ SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[584]) ).
thf(597,plain,
! [SV14: $i,SV38: $i,SV44: $i] :
( ( ( ( SV44
!= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ ( sK12_SY85 @ SV44 @ SV38 @ SV14 ) ) ) )
= $false )
| ( ( SV44
= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ empty ) )
= $true )
| ( ( path @ SV14 @ SV38 @ SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[585]) ).
thf(598,plain,
! [SV14: $i,SV38: $i,SV44: $i] :
( ( ( ~ ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ ( sK12_SY85 @ SV44 @ SV38 @ SV14 ) ) )
= $false )
| ( ( SV44
= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ empty ) )
= $true )
| ( ( path @ SV14 @ SV38 @ SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[585]) ).
thf(599,plain,
! [SV28: $i,SV34: $i] :
( ( ( ( SV34
!= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
= $true )
| ( ( ( SV28
!= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
= $true )
| ( ( SV28
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
= $false )
| ( ( SV34
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
= $false )
| ( ( SV28 = SV34 )
= $true )
| ( ( vertex @ SV28 )
= $false )
| ( ( vertex @ SV34 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[586]) ).
thf(600,plain,
! [SV34: $i,SV28: $i] :
( ( ( ~ ( ( SV28
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) ) ) )
= $false )
| ( ( SV28 = SV34 )
= $true )
| ( ( vertex @ SV28 )
= $false )
| ( ( vertex @ SV34 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[587]) ).
thf(601,plain,
! [SV34: $i,SV28: $i] :
( ( ( ~ ( ( SV28
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) ) )
= $false )
| ( ( SV28 = SV34 )
= $true )
| ( ( vertex @ SV28 )
= $false )
| ( ( vertex @ SV34 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[587]) ).
thf(602,plain,
! [SV28: $i,SV34: $i] :
( ( ( ~ ( ( SV34
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) ) ) )
= $false )
| ( ( SV28 = SV34 )
= $true )
| ( ( vertex @ SV28 )
= $false )
| ( ( vertex @ SV34 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[588]) ).
thf(603,plain,
! [SV28: $i,SV34: $i] :
( ( ( ~ ( ( SV34
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) ) )
= $false )
| ( ( SV28 = SV34 )
= $true )
| ( ( vertex @ SV28 )
= $false )
| ( ( vertex @ SV34 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[588]) ).
thf(604,plain,
! [SV30: $i,SV25: $i,SV10: $i,SV106: $i,SV93: $i,SV84: $i] :
( ( ( sequential @ SV84 @ SV93 )
= $false )
| ( ( precedes @ SV106 @ SV93 @ SV10 )
= $false )
| ( ( sequential @ SV84 @ SV106 )
= $false )
| ( ( precedes @ SV84 @ SV93 @ SV10 )
= $false )
| ( ( path @ SV25 @ SV30 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[589]) ).
thf(605,plain,
! [SV112: $i,SV11: $i] :
( ( ( ! [SY244: $i] :
~ ( triangle @ SV11 @ SV112 @ SY244 ) )
= $true )
| ( ( edge @ SV11 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[590]) ).
thf(606,plain,
! [SV111: $i,SV11: $i] :
( ( ( ! [SY243: $i] :
~ ( triangle @ SV11 @ SV111 @ SY243 ) )
= $true )
| ( ( edge @ SV111 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[591]) ).
thf(607,plain,
! [SV110: $i,SV14: $i,SV38: $i,SV44: $i] :
( ( ( SV44
= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ SV110 ) )
= $false )
| ( ( ~ ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ SV110 ) )
= $true )
| ( ( SV38
= ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
= $false )
| ( ( SV44
= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ empty ) )
= $false )
| ( ( path @ SV14 @ SV38 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[594]) ).
thf(608,plain,
! [SV14: $i,SV38: $i,SV44: $i] :
( ( ( SV44
= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ ( sK13_SY84 @ SV44 @ SV38 @ SV14 ) ) )
= $true )
| ( ( SV38
= ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
= $true )
| ( ( path @ SV14 @ SV38 @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[595]) ).
thf(609,plain,
! [SV14: $i,SV38: $i,SV44: $i] :
( ( ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ ( sK13_SY84 @ SV44 @ SV38 @ SV14 ) )
= $true )
| ( ( SV38
= ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
= $true )
| ( ( path @ SV14 @ SV38 @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[596]) ).
thf(610,plain,
! [SV14: $i,SV38: $i,SV44: $i] :
( ( ( SV44
= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ ( sK12_SY85 @ SV44 @ SV38 @ SV14 ) ) )
= $true )
| ( ( SV44
= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ empty ) )
= $true )
| ( ( path @ SV14 @ SV38 @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[597]) ).
thf(611,plain,
! [SV14: $i,SV38: $i,SV44: $i] :
( ( ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ ( sK12_SY85 @ SV44 @ SV38 @ SV14 ) )
= $true )
| ( ( SV44
= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ empty ) )
= $true )
| ( ( path @ SV14 @ SV38 @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[598]) ).
thf(612,plain,
! [SV28: $i,SV34: $i] :
( ( ( SV34
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
= $false )
| ( ( ( SV28
!= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
= $true )
| ( ( SV28
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
= $false )
| ( ( SV34
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
= $false )
| ( ( SV28 = SV34 )
= $true )
| ( ( vertex @ SV28 )
= $false )
| ( ( vertex @ SV34 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[599]) ).
thf(613,plain,
! [SV34: $i,SV28: $i] :
( ( ( ( SV28
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
= $true )
| ( ( SV28 = SV34 )
= $true )
| ( ( vertex @ SV28 )
= $false )
| ( ( vertex @ SV34 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[600]) ).
thf(614,plain,
! [SV34: $i,SV28: $i] :
( ( ( ( SV28
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
= $true )
| ( ( SV28 = SV34 )
= $true )
| ( ( vertex @ SV28 )
= $false )
| ( ( vertex @ SV34 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[601]) ).
thf(615,plain,
! [SV28: $i,SV34: $i] :
( ( ( ( SV34
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV34
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
= $true )
| ( ( SV28 = SV34 )
= $true )
| ( ( vertex @ SV28 )
= $false )
| ( ( vertex @ SV34 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[602]) ).
thf(616,plain,
! [SV28: $i,SV34: $i] :
( ( ( ( SV34
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
| ( SV28
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) ) )
= $true )
| ( ( SV28 = SV34 )
= $true )
| ( ( vertex @ SV28 )
= $false )
| ( ( vertex @ SV34 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[603]) ).
thf(617,plain,
! [SV113: $i,SV112: $i,SV11: $i] :
( ( ( ~ ( triangle @ SV11 @ SV112 @ SV113 ) )
= $true )
| ( ( edge @ SV11 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[605]) ).
thf(618,plain,
! [SV114: $i,SV111: $i,SV11: $i] :
( ( ( ~ ( triangle @ SV11 @ SV111 @ SV114 ) )
= $true )
| ( ( edge @ SV111 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[606]) ).
thf(619,plain,
! [SV110: $i,SV14: $i,SV38: $i,SV44: $i] :
( ( ( path @ ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) @ SV38 @ SV110 )
= $false )
| ( ( SV44
= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ SV110 ) )
= $false )
| ( ( SV38
= ( head_of @ ( sK11_E @ SV44 @ SV38 @ SV14 ) ) )
= $false )
| ( ( SV44
= ( path_cons @ ( sK11_E @ SV44 @ SV38 @ SV14 ) @ empty ) )
= $false )
| ( ( path @ SV14 @ SV38 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[607]) ).
thf(620,plain,
! [SV34: $i,SV28: $i] :
( ( ( SV28
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
= $false )
| ( ( SV34
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
= $false )
| ( ( SV28
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
= $false )
| ( ( SV34
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
= $false )
| ( ( SV28 = SV34 )
= $true )
| ( ( vertex @ SV28 )
= $false )
| ( ( vertex @ SV34 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[612]) ).
thf(621,plain,
! [SV34: $i,SV28: $i] :
( ( ( SV28
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
= $true )
| ( ( SV34
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
= $true )
| ( ( SV28 = SV34 )
= $true )
| ( ( vertex @ SV28 )
= $false )
| ( ( vertex @ SV34 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[613]) ).
thf(622,plain,
! [SV34: $i,SV28: $i] :
( ( ( SV28
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
= $true )
| ( ( SV28
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
= $true )
| ( ( SV28 = SV34 )
= $true )
| ( ( vertex @ SV28 )
= $false )
| ( ( vertex @ SV34 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[614]) ).
thf(623,plain,
! [SV28: $i,SV34: $i] :
( ( ( SV34
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
= $true )
| ( ( SV34
= ( head_of @ ( sK14_E @ SV34 @ SV28 ) ) )
= $true )
| ( ( SV28 = SV34 )
= $true )
| ( ( vertex @ SV28 )
= $false )
| ( ( vertex @ SV34 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[615]) ).
thf(624,plain,
! [SV28: $i,SV34: $i] :
( ( ( SV34
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
= $true )
| ( ( SV28
= ( tail_of @ ( sK14_E @ SV34 @ SV28 ) ) )
= $true )
| ( ( SV28 = SV34 )
= $true )
| ( ( vertex @ SV28 )
= $false )
| ( ( vertex @ SV34 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[616]) ).
thf(625,plain,
! [SV113: $i,SV112: $i,SV11: $i] :
( ( ( triangle @ SV11 @ SV112 @ SV113 )
= $false )
| ( ( edge @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[617]) ).
thf(626,plain,
! [SV114: $i,SV111: $i,SV11: $i] :
( ( ( triangle @ SV11 @ SV111 @ SV114 )
= $false )
| ( ( edge @ SV111 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[618]) ).
thf(627,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[95,626,625,624,623,622,621,620,619,611,610,609,608,604,593,592,581,577,576,574,562,549,537,534,533,526,509,508,507,506,505,504,497,496,490,489,480,477,476,475,473,472,464,439,436,425,415,399,398,389,381,379,375,356,236,235,193,192,169,132,115,96]) ).
thf(628,plain,
( ( ! [E: $i] :
( ~ ( edge @ E )
| ( ( head_of @ E )
!= ( tail_of @ E ) ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(629,plain,
( ( ! [E: $i] :
( ~ ( edge @ E )
| ( vertex @ ( head_of @ E ) ) )
& ! [E: $i] :
( ~ ( edge @ E )
| ( vertex @ ( tail_of @ E ) ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(630,plain,
( ( ~ complete
| ! [V1: $i,V2: $i] :
( ( V1 = V2 )
| ~ ( vertex @ V1 )
| ~ ( vertex @ V2 )
| ( ( ( V1
!= ( head_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V2
!= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V2
!= ( head_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V1
!= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( ( V1
= ( head_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V2
= ( head_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( ( V1
= ( head_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V1
= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( ( V2
= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V2
= ( head_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( ( V2
= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V1
= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( edge @ ( sK14_E @ V2 @ V1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(631,plain,
( ( ! [V1: $i,V2: $i,P: $i] :
( ~ ( vertex @ V1 )
| ~ ( vertex @ V2 )
| ( ! [E: $i] :
( ( V1
!= ( tail_of @ E ) )
| ~ ( edge @ E )
| ( V2
!= ( head_of @ E ) )
| ( P
!= ( path_cons @ E @ empty ) ) )
& ! [E: $i] :
( ( V1
!= ( tail_of @ E ) )
| ~ ( edge @ E )
| ! [TP: $i] :
( ( P
!= ( path_cons @ E @ TP ) )
| ~ ( path @ ( head_of @ E ) @ V2 @ TP ) ) ) )
| ( path @ V1 @ V2 @ P ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(632,plain,
( ( ! [V1: $i] :
( ( ! [V2: $i,P: $i] :
~ ( path @ V1 @ V2 @ P )
| ( vertex @ V1 ) )
& ! [V2: $i] :
( ! [P: $i] :
~ ( path @ V1 @ V2 @ P )
| ( vertex @ V2 ) )
& ! [V2: $i,P: $i] :
( ~ ( path @ V1 @ V2 @ P )
| ( ( V1
= ( tail_of @ ( sK11_E @ P @ V2 @ V1 ) ) )
& ( edge @ ( sK11_E @ P @ V2 @ V1 ) )
& ( ( V2
!= ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) )
| ( P
!= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ empty ) )
| ! [SY83: $i] :
( ( P
!= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ SY83 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) @ V2 @ SY83 ) ) )
& ( ( V2
= ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) )
| ( ( P
= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ ( sK13_SY84 @ P @ V2 @ V1 ) ) )
& ( path @ ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) @ V2 @ ( sK13_SY84 @ P @ V2 @ V1 ) ) ) )
& ( ( P
= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ empty ) )
| ( ( P
= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ ( sK12_SY85 @ P @ V2 @ V1 ) ) )
& ( path @ ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) @ V2 @ ( sK12_SY85 @ P @ V2 @ V1 ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(633,plain,
( ( ! [V1: $i,V2: $i] :
( ! [P: $i,E: $i] :
( ~ ( on_path @ E @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( edge @ E ) )
& ! [P: $i,E: $i] :
( ~ ( on_path @ E @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( in_path @ ( head_of @ E ) @ P ) )
& ! [P: $i,E: $i] :
( ~ ( on_path @ E @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( in_path @ ( tail_of @ E ) @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(634,plain,
( ( ! [V1: $i,V2: $i] :
( ! [P: $i,V: $i] :
( ~ ( in_path @ V @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( ( on_path @ ( sK10_E @ V @ P @ V2 @ V1 ) @ P )
& ( ( V
= ( head_of @ ( sK10_E @ V @ P @ V2 @ V1 ) ) )
| ( V
= ( tail_of @ ( sK10_E @ V @ P @ V2 @ V1 ) ) ) ) ) )
& ! [P: $i,V: $i] :
( ~ ( in_path @ V @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( vertex @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(635,plain,
( ( ! [E1: $i,E2: $i] :
( ( E1 = E2 )
| ~ ( edge @ E1 )
| ~ ( edge @ E2 )
| ( ( head_of @ E1 )
!= ( tail_of @ E2 ) )
| ( sequential @ E1 @ E2 ) )
& ! [E1: $i,E2: $i] :
( ~ ( sequential @ E1 @ E2 )
| ( E1 != E2 ) )
& ! [E1: $i] :
( ! [E2: $i] :
~ ( sequential @ E1 @ E2 )
| ( edge @ E1 ) )
& ! [E1: $i,E2: $i] :
( ~ ( sequential @ E1 @ E2 )
| ( edge @ E2 ) )
& ! [E1: $i,E2: $i] :
( ~ ( sequential @ E1 @ E2 )
| ( ( head_of @ E1 )
= ( tail_of @ E2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(636,plain,
( ( ! [P: $i] :
( ! [V1: $i,V2: $i] :
~ ( path @ V1 @ V2 @ P )
| ( ! [E1: $i,E2: $i] :
( ~ ( on_path @ E1 @ P )
| ~ ( on_path @ E2 @ P )
| ! [E3: $i] :
( ~ ( precedes @ E3 @ E2 @ P )
| ~ ( sequential @ E1 @ E3 ) )
| ( precedes @ E1 @ E2 @ P ) )
& ! [E1: $i,E2: $i] :
( ~ ( on_path @ E1 @ P )
| ~ ( on_path @ E2 @ P )
| ~ ( sequential @ E1 @ E2 )
| ( precedes @ E1 @ E2 @ P ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(637,plain,
( ( ! [P: $i] :
( ! [V1: $i,V2: $i] :
~ ( path @ V1 @ V2 @ P )
| ( ! [E1: $i] :
( ! [E2: $i] :
~ ( precedes @ E1 @ E2 @ P )
| ( on_path @ E1 @ P ) )
& ! [E1: $i,E2: $i] :
( ~ ( precedes @ E1 @ E2 @ P )
| ( on_path @ E2 @ P ) )
& ! [E1: $i,E2: $i] :
( ~ ( precedes @ E1 @ E2 @ P )
| ! [E3: $i] :
( ~ ( precedes @ E3 @ E2 @ P )
| ~ ( sequential @ E1 @ E3 ) )
| ~ ( sequential @ E1 @ E2 ) )
& ! [E1: $i,E2: $i] :
( ~ ( precedes @ E1 @ E2 @ P )
| ( ( precedes @ ( sK9_E3 @ E2 @ E1 @ P ) @ E2 @ P )
& ( sequential @ E1 @ ( sK9_E3 @ E2 @ E1 @ P ) ) )
| ( sequential @ E1 @ E2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(638,plain,
( ( ! [V1: $i] :
( ! [V2: $i,SP: $i] :
( ( ( path @ V1 @ V2 @ ( sK8_P @ SP @ V2 @ V1 ) )
& ~ ( less_or_equal @ ( length_of @ SP ) @ ( length_of @ ( sK8_P @ SP @ V2 @ V1 ) ) ) )
| ( V1 = V2 )
| ~ ( path @ V1 @ V2 @ SP )
| ( shortest_path @ V1 @ V2 @ SP ) )
& ! [V2: $i,SP: $i] :
( ~ ( shortest_path @ V1 @ V2 @ SP )
| ! [P: $i] :
( ~ ( path @ V1 @ V2 @ P )
| ( less_or_equal @ ( length_of @ SP ) @ ( length_of @ P ) ) ) )
& ! [V2: $i] :
( ! [SP: $i] :
~ ( shortest_path @ V1 @ V2 @ SP )
| ( V1 != V2 ) )
& ! [V2: $i,SP: $i] :
( ~ ( shortest_path @ V1 @ V2 @ SP )
| ( path @ V1 @ V2 @ SP ) ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(639,plain,
( ( ! [V1: $i,V2: $i,E1: $i] :
( ! [E2: $i] :
( ! [P: $i] :
( ~ ( precedes @ E1 @ E2 @ P )
| ~ ( shortest_path @ V1 @ V2 @ P ) )
| ! [E3: $i] :
( ( ( tail_of @ E3 )
!= ( tail_of @ E1 ) )
| ( ( head_of @ E3 )
!= ( head_of @ E2 ) ) ) )
& ! [E2: $i,P: $i] :
( ~ ( precedes @ E1 @ E2 @ P )
| ~ ( shortest_path @ V1 @ V2 @ P )
| ~ ( precedes @ E2 @ E1 @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(640,plain,
( ( ! [E1: $i] :
( ! [E2: $i,E3: $i] :
( ~ ( edge @ E1 )
| ~ ( edge @ E2 )
| ~ ( edge @ E3 )
| ~ ( sequential @ E1 @ E2 )
| ~ ( sequential @ E2 @ E3 )
| ~ ( sequential @ E3 @ E1 )
| ( triangle @ E1 @ E2 @ E3 ) )
& ( ! [E2: $i,E3: $i] :
~ ( triangle @ E1 @ E2 @ E3 )
| ( edge @ E1 ) )
& ! [E2: $i] :
( ! [E3: $i] :
~ ( triangle @ E1 @ E2 @ E3 )
| ( edge @ E2 ) )
& ! [E2: $i,E3: $i] :
( ~ ( triangle @ E1 @ E2 @ E3 )
| ( edge @ E3 ) )
& ! [E2: $i] :
( ! [E3: $i] :
~ ( triangle @ E1 @ E2 @ E3 )
| ( sequential @ E1 @ E2 ) )
& ! [E2: $i,E3: $i] :
( ~ ( triangle @ E1 @ E2 @ E3 )
| ( sequential @ E2 @ E3 ) )
& ! [E2: $i,E3: $i] :
( ~ ( triangle @ E1 @ E2 @ E3 )
| ( sequential @ E3 @ E1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(641,plain,
( ( ! [V1: $i,V2: $i,P: $i] :
( ~ ( path @ V1 @ V2 @ P )
| ( ( length_of @ P )
= ( number_of_in @ edges @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(642,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)],[63]) ).
thf(643,plain,
( ( ! [P: $i] :
( ( ( on_path @ ( sK6_E1 @ P ) @ P )
& ( on_path @ ( sK7_SY80 @ P ) @ P )
& ( sequential @ ( sK6_E1 @ P ) @ ( sK7_SY80 @ P ) )
& ! [SY82: $i] :
~ ( triangle @ ( sK6_E1 @ P ) @ ( sK7_SY80 @ P ) @ SY82 ) )
| ! [V1: $i,V2: $i] :
~ ( path @ V1 @ V2 @ P )
| ( ( number_of_in @ sequential_pairs @ P )
= ( number_of_in @ triangles @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(644,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(645,plain,
( ( precedes @ sK3_SY74 @ sK4_SY77 @ sK5_SY79 )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(646,plain,
( ( shortest_path @ sK1_V1 @ sK2_SY70 @ sK5_SY79 )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(647,plain,
( ( ~ ( vertex @ sK2_SY70 ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(648,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SX0 ) @ SX0 )
| ~ ( on_path @ ( sK7_SY80 @ SX0 ) @ SX0 ) )
| ~ ( sequential @ ( sK6_E1 @ SX0 ) @ ( sK7_SY80 @ SX0 ) ) )
| ~ ! [SX1: $i] :
~ ( triangle @ ( sK6_E1 @ SX0 ) @ ( sK7_SY80 @ SX0 ) @ SX1 ) )
| ! [SX1: $i,SX2: $i] :
~ ( path @ SX1 @ SX2 @ SX0 )
| ( ( number_of_in @ sequential_pairs @ SX0 )
= ( number_of_in @ triangles @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[643]) ).
thf(649,plain,
( ( ~ complete
| ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( vertex @ SX0 )
| ~ ( vertex @ SX1 )
| ~ ( ~ ~ ( ~ ( ( SX0
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
| ~ ~ ( ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[630]) ).
thf(650,plain,
( ( ! [SX0: $i] :
~ ( ~ ~ ( ~ ( ! [SX1: $i,SX2: $i] :
~ ( path @ SX0 @ SX1 @ SX2 )
| ( vertex @ SX0 ) )
| ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( path @ SX0 @ SX1 @ SX2 )
| ( vertex @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( path @ SX0 @ SX1 @ SX2 )
| ~ ( ~ ~ ( ( SX0
!= ( tail_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( edge @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ( SX1
!= ( head_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) )
| ( SX2
!= ( path_cons @ ( sK11_E @ SX2 @ SX1 @ SX0 ) @ empty ) )
| ! [SX3: $i] :
( ( SX2
!= ( path_cons @ ( sK11_E @ SX2 @ SX1 @ SX0 ) @ SX3 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) @ SX1 @ SX3 ) ) )
| ~ ~ ( ~ ( ( SX1
= ( head_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( ( SX2
!= ( path_cons @ ( sK11_E @ SX2 @ SX1 @ SX0 ) @ ( sK13_SY84 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) @ SX1 @ ( sK13_SY84 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX2
= ( path_cons @ ( sK11_E @ SX2 @ SX1 @ SX0 ) @ empty ) )
| ~ ( ( SX2
!= ( path_cons @ ( sK11_E @ SX2 @ SX1 @ SX0 ) @ ( sK12_SY85 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) @ SX1 @ ( sK12_SY85 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[632]) ).
thf(651,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( on_path @ SX3 @ SX2 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ( edge @ SX3 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( on_path @ SX3 @ SX2 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ( in_path @ ( head_of @ SX3 ) @ SX2 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( on_path @ SX3 @ SX2 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ( in_path @ ( tail_of @ SX3 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[633]) ).
thf(652,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( vertex @ SX0 )
| ~ ( vertex @ SX1 )
| ~ ( ~ ! [SX3: $i] :
( ( SX0
!= ( tail_of @ SX3 ) )
| ~ ( edge @ SX3 )
| ( SX1
!= ( head_of @ SX3 ) )
| ( SX2
!= ( path_cons @ SX3 @ empty ) ) )
| ~ ! [SX3: $i] :
( ( SX0
!= ( tail_of @ SX3 ) )
| ~ ( edge @ SX3 )
| ! [SX4: $i] :
( ( SX2
!= ( path_cons @ SX3 @ SX4 ) )
| ~ ( path @ ( head_of @ SX3 ) @ SX1 @ SX4 ) ) ) )
| ( path @ SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[631]) ).
thf(653,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i,SX2: $i] :
~ ( path @ SX1 @ SX2 @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( on_path @ SX1 @ SX0 )
| ~ ( on_path @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( precedes @ SX3 @ SX2 @ SX0 )
| ~ ( sequential @ SX1 @ SX3 ) )
| ( precedes @ SX1 @ SX2 @ SX0 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( on_path @ SX1 @ SX0 )
| ~ ( on_path @ SX2 @ SX0 )
| ~ ( sequential @ SX1 @ SX2 )
| ( precedes @ SX1 @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[636]) ).
thf(654,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i,SX2: $i] :
~ ( path @ SX1 @ SX2 @ SX0 )
| ~ ( ~ ~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( precedes @ SX1 @ SX2 @ SX0 )
| ( on_path @ SX1 @ SX0 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( precedes @ SX1 @ SX2 @ SX0 )
| ( on_path @ SX2 @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( precedes @ SX1 @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( precedes @ SX3 @ SX2 @ SX0 )
| ~ ( sequential @ SX1 @ SX3 ) )
| ~ ( sequential @ SX1 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( precedes @ SX1 @ SX2 @ SX0 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SX2 @ SX1 @ SX0 ) @ SX2 @ SX0 )
| ~ ( sequential @ SX1 @ ( sK9_E3 @ SX2 @ SX1 @ SX0 ) ) )
| ( sequential @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[637]) ).
thf(655,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
( ~ ( precedes @ SX2 @ SX3 @ SX4 )
| ~ ( shortest_path @ SX0 @ SX1 @ SX4 ) )
| ! [SX4: $i] :
( ( ( tail_of @ SX4 )
!= ( tail_of @ SX2 ) )
| ( ( head_of @ SX4 )
!= ( head_of @ SX3 ) ) ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( precedes @ SX2 @ SX3 @ SX4 )
| ~ ( shortest_path @ SX0 @ SX1 @ SX4 )
| ~ ( precedes @ SX3 @ SX2 @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[639]) ).
thf(656,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( head_of @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( tail_of @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[629]) ).
thf(657,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( path @ SX0 @ SX1 @ ( sK8_P @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SX2 ) @ ( length_of @ ( sK8_P @ SX2 @ SX1 @ SX0 ) ) ) )
| ( SX0 = SX1 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ( shortest_path @ SX0 @ SX1 @ SX2 ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( shortest_path @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( path @ SX0 @ SX1 @ SX3 )
| ( less_or_equal @ ( length_of @ SX2 ) @ ( length_of @ SX3 ) ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( shortest_path @ SX0 @ SX1 @ SX2 )
| ( SX0 != SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( shortest_path @ SX0 @ SX1 @ SX2 )
| ( path @ SX0 @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[638]) ).
thf(658,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( edge @ SX0 )
| ~ ( edge @ SX1 )
| ( ( head_of @ SX0 )
!= ( tail_of @ SX1 ) )
| ( sequential @ SX0 @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[635]) ).
thf(659,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( edge @ SX0 )
| ~ ( edge @ SX1 )
| ~ ( edge @ SX2 )
| ~ ( sequential @ SX0 @ SX1 )
| ~ ( sequential @ SX1 @ SX2 )
| ~ ( sequential @ SX2 @ SX0 )
| ( triangle @ SX0 @ SX1 @ SX2 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SX1: $i,SX2: $i] :
~ ( triangle @ SX0 @ SX1 @ SX2 )
| ( edge @ SX0 ) )
| ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( triangle @ SX0 @ SX1 @ SX2 )
| ( edge @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( triangle @ SX0 @ SX1 @ SX2 )
| ( edge @ SX2 ) ) )
| ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( triangle @ SX0 @ SX1 @ SX2 )
| ( sequential @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( triangle @ SX0 @ SX1 @ SX2 )
| ( sequential @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( triangle @ SX0 @ SX1 @ SX2 )
| ( sequential @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[640]) ).
thf(660,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in_path @ SX3 @ SX2 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ~ ( ~ ( on_path @ ( sK10_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( ( SX3
= ( head_of @ ( sK10_E @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ( SX3
= ( tail_of @ ( sK10_E @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( in_path @ SX3 @ SX2 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ( vertex @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[634]) ).
thf(661,plain,
! [SV115: $i] :
( ( ~ ( edge @ SV115 )
| ( ( head_of @ SV115 )
!= ( tail_of @ SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[628]) ).
thf(662,plain,
! [SV116: $i] :
( ( ! [SY245: $i,SY246: $i] :
( ~ ( path @ SV116 @ SY245 @ SY246 )
| ( ( length_of @ SY246 )
= ( number_of_in @ edges @ SY246 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(663,plain,
! [SV117: $i] :
( ( ! [SY247: $i,SY248: $i] :
( ~ ( path @ SV117 @ SY247 @ SY248 )
| ( ( number_of_in @ sequential_pairs @ SY248 )
= ( minus @ ( length_of @ SY248 ) @ n1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(664,plain,
! [SV118: $i] :
( ( ! [SY249: $i] : ( less_or_equal @ ( number_of_in @ SV118 @ SY249 ) @ ( number_of_in @ SV118 @ graph ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(665,plain,
( ( vertex @ sK2_SY70 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[647]) ).
thf(666,plain,
! [SV119: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV119 ) @ SV119 )
| ~ ( on_path @ ( sK7_SY80 @ SV119 ) @ SV119 ) )
| ~ ( sequential @ ( sK6_E1 @ SV119 ) @ ( sK7_SY80 @ SV119 ) ) )
| ~ ! [SY250: $i] :
~ ( triangle @ ( sK6_E1 @ SV119 ) @ ( sK7_SY80 @ SV119 ) @ SY250 ) )
| ! [SY251: $i,SY252: $i] :
~ ( path @ SY251 @ SY252 @ SV119 )
| ( ( number_of_in @ sequential_pairs @ SV119 )
= ( number_of_in @ triangles @ SV119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(667,plain,
( ( ( ~ complete )
= $true )
| ( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( vertex @ SX0 )
| ~ ( vertex @ SX1 )
| ~ ( ~ ~ ( ~ ( ( SX0
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
| ~ ~ ( ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[649]) ).
thf(668,plain,
! [SV120: $i] :
( ( ~ ( ~ ~ ( ~ ( ! [SY253: $i,SY254: $i] :
~ ( path @ SV120 @ SY253 @ SY254 )
| ( vertex @ SV120 ) )
| ~ ! [SY255: $i] :
( ! [SY256: $i] :
~ ( path @ SV120 @ SY255 @ SY256 )
| ( vertex @ SY255 ) ) )
| ~ ! [SY257: $i,SY258: $i] :
( ~ ( path @ SV120 @ SY257 @ SY258 )
| ~ ( ~ ~ ( ( SV120
!= ( tail_of @ ( sK11_E @ SY258 @ SY257 @ SV120 ) ) )
| ~ ( edge @ ( sK11_E @ SY258 @ SY257 @ SV120 ) ) )
| ~ ~ ( ~ ( ( SY257
!= ( head_of @ ( sK11_E @ SY258 @ SY257 @ SV120 ) ) )
| ( SY258
!= ( path_cons @ ( sK11_E @ SY258 @ SY257 @ SV120 ) @ empty ) )
| ! [SY259: $i] :
( ( SY258
!= ( path_cons @ ( sK11_E @ SY258 @ SY257 @ SV120 ) @ SY259 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY258 @ SY257 @ SV120 ) ) @ SY257 @ SY259 ) ) )
| ~ ~ ( ~ ( ( SY257
= ( head_of @ ( sK11_E @ SY258 @ SY257 @ SV120 ) ) )
| ~ ( ( SY258
!= ( path_cons @ ( sK11_E @ SY258 @ SY257 @ SV120 ) @ ( sK13_SY84 @ SY258 @ SY257 @ SV120 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY258 @ SY257 @ SV120 ) ) @ SY257 @ ( sK13_SY84 @ SY258 @ SY257 @ SV120 ) ) ) )
| ~ ( ( SY258
= ( path_cons @ ( sK11_E @ SY258 @ SY257 @ SV120 ) @ empty ) )
| ~ ( ( SY258
!= ( path_cons @ ( sK11_E @ SY258 @ SY257 @ SV120 ) @ ( sK12_SY85 @ SY258 @ SY257 @ SV120 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY258 @ SY257 @ SV120 ) ) @ SY257 @ ( sK12_SY85 @ SY258 @ SY257 @ SV120 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(669,plain,
! [SV121: $i] :
( ( ! [SY260: $i] :
~ ( ~ ~ ( ~ ! [SY261: $i,SY262: $i] :
( ~ ( on_path @ SY262 @ SY261 )
| ~ ( path @ SV121 @ SY260 @ SY261 )
| ( edge @ SY262 ) )
| ~ ! [SY263: $i,SY264: $i] :
( ~ ( on_path @ SY264 @ SY263 )
| ~ ( path @ SV121 @ SY260 @ SY263 )
| ( in_path @ ( head_of @ SY264 ) @ SY263 ) ) )
| ~ ! [SY265: $i,SY266: $i] :
( ~ ( on_path @ SY266 @ SY265 )
| ~ ( path @ SV121 @ SY260 @ SY265 )
| ( in_path @ ( tail_of @ SY266 ) @ SY265 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(670,plain,
! [SV122: $i] :
( ( ! [SY267: $i,SY268: $i] :
( ~ ( vertex @ SV122 )
| ~ ( vertex @ SY267 )
| ~ ( ~ ! [SY269: $i] :
( ( SV122
!= ( tail_of @ SY269 ) )
| ~ ( edge @ SY269 )
| ( SY267
!= ( head_of @ SY269 ) )
| ( SY268
!= ( path_cons @ SY269 @ empty ) ) )
| ~ ! [SY270: $i] :
( ( SV122
!= ( tail_of @ SY270 ) )
| ~ ( edge @ SY270 )
| ! [SX4: $i] :
( ( SY268
!= ( path_cons @ SY270 @ SX4 ) )
| ~ ( path @ ( head_of @ SY270 ) @ SY267 @ SX4 ) ) ) )
| ( path @ SV122 @ SY267 @ SY268 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[652]) ).
thf(671,plain,
! [SV123: $i] :
( ( ! [SY272: $i,SY273: $i] :
~ ( path @ SY272 @ SY273 @ SV123 )
| ~ ( ~ ! [SY274: $i,SY275: $i] :
( ~ ( on_path @ SY274 @ SV123 )
| ~ ( on_path @ SY275 @ SV123 )
| ! [SY276: $i] :
( ~ ( precedes @ SY276 @ SY275 @ SV123 )
| ~ ( sequential @ SY274 @ SY276 ) )
| ( precedes @ SY274 @ SY275 @ SV123 ) )
| ~ ! [SY277: $i,SY278: $i] :
( ~ ( on_path @ SY277 @ SV123 )
| ~ ( on_path @ SY278 @ SV123 )
| ~ ( sequential @ SY277 @ SY278 )
| ( precedes @ SY277 @ SY278 @ SV123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(672,plain,
! [SV124: $i] :
( ( ! [SY279: $i,SY280: $i] :
~ ( path @ SY279 @ SY280 @ SV124 )
| ~ ( ~ ~ ( ~ ! [SY281: $i] :
( ! [SY282: $i] :
~ ( precedes @ SY281 @ SY282 @ SV124 )
| ( on_path @ SY281 @ SV124 ) )
| ~ ! [SY283: $i,SY284: $i] :
( ~ ( precedes @ SY283 @ SY284 @ SV124 )
| ( on_path @ SY284 @ SV124 ) ) )
| ~ ~ ( ~ ! [SY285: $i,SY286: $i] :
( ~ ( precedes @ SY285 @ SY286 @ SV124 )
| ! [SY287: $i] :
( ~ ( precedes @ SY287 @ SY286 @ SV124 )
| ~ ( sequential @ SY285 @ SY287 ) )
| ~ ( sequential @ SY285 @ SY286 ) )
| ~ ! [SY288: $i,SY289: $i] :
( ~ ( precedes @ SY288 @ SY289 @ SV124 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY289 @ SY288 @ SV124 ) @ SY289 @ SV124 )
| ~ ( sequential @ SY288 @ ( sK9_E3 @ SY289 @ SY288 @ SV124 ) ) )
| ( sequential @ SY288 @ SY289 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(673,plain,
! [SV125: $i] :
( ( ! [SY290: $i,SY291: $i] :
~ ( ~ ! [SY292: $i] :
( ! [SY293: $i] :
( ~ ( precedes @ SY291 @ SY292 @ SY293 )
| ~ ( shortest_path @ SV125 @ SY290 @ SY293 ) )
| ! [SX4: $i] :
( ( ( tail_of @ SX4 )
!= ( tail_of @ SY291 ) )
| ( ( head_of @ SX4 )
!= ( head_of @ SY292 ) ) ) )
| ~ ! [SY295: $i,SY296: $i] :
( ~ ( precedes @ SY291 @ SY295 @ SY296 )
| ~ ( shortest_path @ SV125 @ SY290 @ SY296 )
| ~ ( precedes @ SY295 @ SY291 @ SY296 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(674,plain,
( ( ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( head_of @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( tail_of @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[656]) ).
thf(675,plain,
! [SV126: $i] :
( ( ~ ( ~ ! [SY297: $i,SY298: $i] :
( ~ ( ~ ( path @ SV126 @ SY297 @ ( sK8_P @ SY298 @ SY297 @ SV126 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY298 ) @ ( length_of @ ( sK8_P @ SY298 @ SY297 @ SV126 ) ) ) )
| ( SV126 = SY297 )
| ~ ( path @ SV126 @ SY297 @ SY298 )
| ( shortest_path @ SV126 @ SY297 @ SY298 ) )
| ~ ~ ( ~ ! [SY299: $i,SY300: $i] :
( ~ ( shortest_path @ SV126 @ SY299 @ SY300 )
| ! [SY301: $i] :
( ~ ( path @ SV126 @ SY299 @ SY301 )
| ( less_or_equal @ ( length_of @ SY300 ) @ ( length_of @ SY301 ) ) ) )
| ~ ~ ( ~ ! [SY302: $i] :
( ! [SY303: $i] :
~ ( shortest_path @ SV126 @ SY302 @ SY303 )
| ( SV126 != SY302 ) )
| ~ ! [SY304: $i,SY305: $i] :
( ~ ( shortest_path @ SV126 @ SY304 @ SY305 )
| ( path @ SV126 @ SY304 @ SY305 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(676,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( edge @ SX0 )
| ~ ( edge @ SX1 )
| ( ( head_of @ SX0 )
!= ( tail_of @ SX1 ) )
| ( sequential @ SX0 @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[658]) ).
thf(677,plain,
! [SV127: $i] :
( ( ~ ( ~ ! [SY306: $i,SY307: $i] :
( ~ ( edge @ SV127 )
| ~ ( edge @ SY306 )
| ~ ( edge @ SY307 )
| ~ ( sequential @ SV127 @ SY306 )
| ~ ( sequential @ SY306 @ SY307 )
| ~ ( sequential @ SY307 @ SV127 )
| ( triangle @ SV127 @ SY306 @ SY307 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY308: $i,SY309: $i] :
~ ( triangle @ SV127 @ SY308 @ SY309 )
| ( edge @ SV127 ) )
| ~ ! [SY310: $i] :
( ! [SY311: $i] :
~ ( triangle @ SV127 @ SY310 @ SY311 )
| ( edge @ SY310 ) ) )
| ~ ! [SY312: $i,SY313: $i] :
( ~ ( triangle @ SV127 @ SY312 @ SY313 )
| ( edge @ SY313 ) ) )
| ~ ! [SY314: $i] :
( ! [SY315: $i] :
~ ( triangle @ SV127 @ SY314 @ SY315 )
| ( sequential @ SV127 @ SY314 ) ) )
| ~ ! [SY316: $i,SY317: $i] :
( ~ ( triangle @ SV127 @ SY316 @ SY317 )
| ( sequential @ SY316 @ SY317 ) ) )
| ~ ! [SY318: $i,SY319: $i] :
( ~ ( triangle @ SV127 @ SY318 @ SY319 )
| ( sequential @ SY319 @ SV127 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[659]) ).
thf(678,plain,
! [SV128: $i] :
( ( ! [SY320: $i] :
~ ( ~ ! [SY321: $i,SY322: $i] :
( ~ ( in_path @ SY322 @ SY321 )
| ~ ( path @ SV128 @ SY320 @ SY321 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY322 @ SY321 @ SY320 @ SV128 ) @ SY321 )
| ~ ( ( SY322
= ( head_of @ ( sK10_E @ SY322 @ SY321 @ SY320 @ SV128 ) ) )
| ( SY322
= ( tail_of @ ( sK10_E @ SY322 @ SY321 @ SY320 @ SV128 ) ) ) ) ) )
| ~ ! [SY323: $i,SY324: $i] :
( ~ ( in_path @ SY324 @ SY323 )
| ~ ( path @ SV128 @ SY320 @ SY323 )
| ( vertex @ SY324 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(679,plain,
! [SV115: $i] :
( ( ( ~ ( edge @ SV115 ) )
= $true )
| ( ( ( ( head_of @ SV115 )
!= ( tail_of @ SV115 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[661]) ).
thf(680,plain,
! [SV129: $i,SV116: $i] :
( ( ! [SY325: $i] :
( ~ ( path @ SV116 @ SV129 @ SY325 )
| ( ( length_of @ SY325 )
= ( number_of_in @ edges @ SY325 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[662]) ).
thf(681,plain,
! [SV130: $i,SV117: $i] :
( ( ! [SY326: $i] :
( ~ ( path @ SV117 @ SV130 @ SY326 )
| ( ( number_of_in @ sequential_pairs @ SY326 )
= ( minus @ ( length_of @ SY326 ) @ n1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(682,plain,
! [SV131: $i,SV118: $i] :
( ( less_or_equal @ ( number_of_in @ SV118 @ SV131 ) @ ( number_of_in @ SV118 @ graph ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(683,plain,
! [SV119: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV119 ) @ SV119 )
| ~ ( on_path @ ( sK7_SY80 @ SV119 ) @ SV119 ) )
| ~ ( sequential @ ( sK6_E1 @ SV119 ) @ ( sK7_SY80 @ SV119 ) ) )
| ~ ! [SY250: $i] :
~ ( triangle @ ( sK6_E1 @ SV119 ) @ ( sK7_SY80 @ SV119 ) @ SY250 ) )
| ! [SY251: $i,SY252: $i] :
~ ( path @ SY251 @ SY252 @ SV119 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV119 )
= ( number_of_in @ triangles @ SV119 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[666]) ).
thf(684,plain,
( ( complete = $false )
| ( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( vertex @ SX0 )
| ~ ( vertex @ SX1 )
| ~ ( ~ ~ ( ~ ( ( SX0
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
| ~ ~ ( ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[667]) ).
thf(685,plain,
! [SV120: $i] :
( ( ~ ~ ( ~ ( ! [SY253: $i,SY254: $i] :
~ ( path @ SV120 @ SY253 @ SY254 )
| ( vertex @ SV120 ) )
| ~ ! [SY255: $i] :
( ! [SY256: $i] :
~ ( path @ SV120 @ SY255 @ SY256 )
| ( vertex @ SY255 ) ) )
| ~ ! [SY257: $i,SY258: $i] :
( ~ ( path @ SV120 @ SY257 @ SY258 )
| ~ ( ~ ~ ( ( SV120
!= ( tail_of @ ( sK11_E @ SY258 @ SY257 @ SV120 ) ) )
| ~ ( edge @ ( sK11_E @ SY258 @ SY257 @ SV120 ) ) )
| ~ ~ ( ~ ( ( SY257
!= ( head_of @ ( sK11_E @ SY258 @ SY257 @ SV120 ) ) )
| ( SY258
!= ( path_cons @ ( sK11_E @ SY258 @ SY257 @ SV120 ) @ empty ) )
| ! [SY259: $i] :
( ( SY258
!= ( path_cons @ ( sK11_E @ SY258 @ SY257 @ SV120 ) @ SY259 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY258 @ SY257 @ SV120 ) ) @ SY257 @ SY259 ) ) )
| ~ ~ ( ~ ( ( SY257
= ( head_of @ ( sK11_E @ SY258 @ SY257 @ SV120 ) ) )
| ~ ( ( SY258
!= ( path_cons @ ( sK11_E @ SY258 @ SY257 @ SV120 ) @ ( sK13_SY84 @ SY258 @ SY257 @ SV120 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY258 @ SY257 @ SV120 ) ) @ SY257 @ ( sK13_SY84 @ SY258 @ SY257 @ SV120 ) ) ) )
| ~ ( ( SY258
= ( path_cons @ ( sK11_E @ SY258 @ SY257 @ SV120 ) @ empty ) )
| ~ ( ( SY258
!= ( path_cons @ ( sK11_E @ SY258 @ SY257 @ SV120 ) @ ( sK12_SY85 @ SY258 @ SY257 @ SV120 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY258 @ SY257 @ SV120 ) ) @ SY257 @ ( sK12_SY85 @ SY258 @ SY257 @ SV120 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[668]) ).
thf(686,plain,
! [SV132: $i,SV121: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY327: $i,SY328: $i] :
( ~ ( on_path @ SY328 @ SY327 )
| ~ ( path @ SV121 @ SV132 @ SY327 )
| ( edge @ SY328 ) )
| ~ ! [SY329: $i,SY330: $i] :
( ~ ( on_path @ SY330 @ SY329 )
| ~ ( path @ SV121 @ SV132 @ SY329 )
| ( in_path @ ( head_of @ SY330 ) @ SY329 ) ) )
| ~ ! [SY331: $i,SY332: $i] :
( ~ ( on_path @ SY332 @ SY331 )
| ~ ( path @ SV121 @ SV132 @ SY331 )
| ( in_path @ ( tail_of @ SY332 ) @ SY331 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[669]) ).
thf(687,plain,
! [SV133: $i,SV122: $i] :
( ( ! [SY333: $i] :
( ~ ( vertex @ SV122 )
| ~ ( vertex @ SV133 )
| ~ ( ~ ! [SY334: $i] :
( ( SV122
!= ( tail_of @ SY334 ) )
| ~ ( edge @ SY334 )
| ( SV133
!= ( head_of @ SY334 ) )
| ( SY333
!= ( path_cons @ SY334 @ empty ) ) )
| ~ ! [SY335: $i] :
( ( SV122
!= ( tail_of @ SY335 ) )
| ~ ( edge @ SY335 )
| ! [SY336: $i] :
( ( SY333
!= ( path_cons @ SY335 @ SY336 ) )
| ~ ( path @ ( head_of @ SY335 ) @ SV133 @ SY336 ) ) ) )
| ( path @ SV122 @ SV133 @ SY333 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[670]) ).
thf(688,plain,
! [SV123: $i] :
( ( ( ! [SY272: $i,SY273: $i] :
~ ( path @ SY272 @ SY273 @ SV123 ) )
= $true )
| ( ( ~ ( ~ ! [SY274: $i,SY275: $i] :
( ~ ( on_path @ SY274 @ SV123 )
| ~ ( on_path @ SY275 @ SV123 )
| ! [SY276: $i] :
( ~ ( precedes @ SY276 @ SY275 @ SV123 )
| ~ ( sequential @ SY274 @ SY276 ) )
| ( precedes @ SY274 @ SY275 @ SV123 ) )
| ~ ! [SY277: $i,SY278: $i] :
( ~ ( on_path @ SY277 @ SV123 )
| ~ ( on_path @ SY278 @ SV123 )
| ~ ( sequential @ SY277 @ SY278 )
| ( precedes @ SY277 @ SY278 @ SV123 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[671]) ).
thf(689,plain,
! [SV124: $i] :
( ( ( ! [SY279: $i,SY280: $i] :
~ ( path @ SY279 @ SY280 @ SV124 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY281: $i] :
( ! [SY282: $i] :
~ ( precedes @ SY281 @ SY282 @ SV124 )
| ( on_path @ SY281 @ SV124 ) )
| ~ ! [SY283: $i,SY284: $i] :
( ~ ( precedes @ SY283 @ SY284 @ SV124 )
| ( on_path @ SY284 @ SV124 ) ) )
| ~ ~ ( ~ ! [SY285: $i,SY286: $i] :
( ~ ( precedes @ SY285 @ SY286 @ SV124 )
| ! [SY287: $i] :
( ~ ( precedes @ SY287 @ SY286 @ SV124 )
| ~ ( sequential @ SY285 @ SY287 ) )
| ~ ( sequential @ SY285 @ SY286 ) )
| ~ ! [SY288: $i,SY289: $i] :
( ~ ( precedes @ SY288 @ SY289 @ SV124 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY289 @ SY288 @ SV124 ) @ SY289 @ SV124 )
| ~ ( sequential @ SY288 @ ( sK9_E3 @ SY289 @ SY288 @ SV124 ) ) )
| ( sequential @ SY288 @ SY289 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[672]) ).
thf(690,plain,
! [SV134: $i,SV125: $i] :
( ( ! [SY337: $i] :
~ ( ~ ! [SY338: $i] :
( ! [SY339: $i] :
( ~ ( precedes @ SY337 @ SY338 @ SY339 )
| ~ ( shortest_path @ SV125 @ SV134 @ SY339 ) )
| ! [SX4: $i] :
( ( ( tail_of @ SX4 )
!= ( tail_of @ SY337 ) )
| ( ( head_of @ SX4 )
!= ( head_of @ SY338 ) ) ) )
| ~ ! [SY341: $i,SY342: $i] :
( ~ ( precedes @ SY337 @ SY341 @ SY342 )
| ~ ( shortest_path @ SV125 @ SV134 @ SY342 )
| ~ ( precedes @ SY341 @ SY337 @ SY342 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(691,plain,
( ( ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( head_of @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[674]) ).
thf(692,plain,
( ( ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( tail_of @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[674]) ).
thf(693,plain,
! [SV126: $i] :
( ( ~ ! [SY297: $i,SY298: $i] :
( ~ ( ~ ( path @ SV126 @ SY297 @ ( sK8_P @ SY298 @ SY297 @ SV126 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY298 ) @ ( length_of @ ( sK8_P @ SY298 @ SY297 @ SV126 ) ) ) )
| ( SV126 = SY297 )
| ~ ( path @ SV126 @ SY297 @ SY298 )
| ( shortest_path @ SV126 @ SY297 @ SY298 ) )
| ~ ~ ( ~ ! [SY299: $i,SY300: $i] :
( ~ ( shortest_path @ SV126 @ SY299 @ SY300 )
| ! [SY301: $i] :
( ~ ( path @ SV126 @ SY299 @ SY301 )
| ( less_or_equal @ ( length_of @ SY300 ) @ ( length_of @ SY301 ) ) ) )
| ~ ~ ( ~ ! [SY302: $i] :
( ! [SY303: $i] :
~ ( shortest_path @ SV126 @ SY302 @ SY303 )
| ( SV126 != SY302 ) )
| ~ ! [SY304: $i,SY305: $i] :
( ~ ( shortest_path @ SV126 @ SY304 @ SY305 )
| ( path @ SV126 @ SY304 @ SY305 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[675]) ).
thf(694,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( edge @ SX0 )
| ~ ( edge @ SX1 )
| ( ( head_of @ SX0 )
!= ( tail_of @ SX1 ) )
| ( sequential @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[676]) ).
thf(695,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[676]) ).
thf(696,plain,
! [SV127: $i] :
( ( ~ ! [SY306: $i,SY307: $i] :
( ~ ( edge @ SV127 )
| ~ ( edge @ SY306 )
| ~ ( edge @ SY307 )
| ~ ( sequential @ SV127 @ SY306 )
| ~ ( sequential @ SY306 @ SY307 )
| ~ ( sequential @ SY307 @ SV127 )
| ( triangle @ SV127 @ SY306 @ SY307 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY308: $i,SY309: $i] :
~ ( triangle @ SV127 @ SY308 @ SY309 )
| ( edge @ SV127 ) )
| ~ ! [SY310: $i] :
( ! [SY311: $i] :
~ ( triangle @ SV127 @ SY310 @ SY311 )
| ( edge @ SY310 ) ) )
| ~ ! [SY312: $i,SY313: $i] :
( ~ ( triangle @ SV127 @ SY312 @ SY313 )
| ( edge @ SY313 ) ) )
| ~ ! [SY314: $i] :
( ! [SY315: $i] :
~ ( triangle @ SV127 @ SY314 @ SY315 )
| ( sequential @ SV127 @ SY314 ) ) )
| ~ ! [SY316: $i,SY317: $i] :
( ~ ( triangle @ SV127 @ SY316 @ SY317 )
| ( sequential @ SY316 @ SY317 ) ) )
| ~ ! [SY318: $i,SY319: $i] :
( ~ ( triangle @ SV127 @ SY318 @ SY319 )
| ( sequential @ SY319 @ SV127 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[677]) ).
thf(697,plain,
! [SV135: $i,SV128: $i] :
( ( ~ ( ~ ! [SY343: $i,SY344: $i] :
( ~ ( in_path @ SY344 @ SY343 )
| ~ ( path @ SV128 @ SV135 @ SY343 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY344 @ SY343 @ SV135 @ SV128 ) @ SY343 )
| ~ ( ( SY344
= ( head_of @ ( sK10_E @ SY344 @ SY343 @ SV135 @ SV128 ) ) )
| ( SY344
= ( tail_of @ ( sK10_E @ SY344 @ SY343 @ SV135 @ SV128 ) ) ) ) ) )
| ~ ! [SY345: $i,SY346: $i] :
( ~ ( in_path @ SY346 @ SY345 )
| ~ ( path @ SV128 @ SV135 @ SY345 )
| ( vertex @ SY346 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(698,plain,
! [SV115: $i] :
( ( ( edge @ SV115 )
= $false )
| ( ( ( ( head_of @ SV115 )
!= ( tail_of @ SV115 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[679]) ).
thf(699,plain,
! [SV136: $i,SV129: $i,SV116: $i] :
( ( ~ ( path @ SV116 @ SV129 @ SV136 )
| ( ( length_of @ SV136 )
= ( number_of_in @ edges @ SV136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(700,plain,
! [SV137: $i,SV130: $i,SV117: $i] :
( ( ~ ( path @ SV117 @ SV130 @ SV137 )
| ( ( number_of_in @ sequential_pairs @ SV137 )
= ( minus @ ( length_of @ SV137 ) @ n1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(701,plain,
! [SV119: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV119 ) @ SV119 )
| ~ ( on_path @ ( sK7_SY80 @ SV119 ) @ SV119 ) )
| ~ ( sequential @ ( sK6_E1 @ SV119 ) @ ( sK7_SY80 @ SV119 ) ) )
| ~ ! [SY250: $i] :
~ ( triangle @ ( sK6_E1 @ SV119 ) @ ( sK7_SY80 @ SV119 ) @ SY250 ) ) )
= $true )
| ( ( ! [SY251: $i,SY252: $i] :
~ ( path @ SY251 @ SY252 @ SV119 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV119 )
= ( number_of_in @ triangles @ SV119 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[683]) ).
thf(702,plain,
! [SV138: $i] :
( ( ( ! [SY347: $i] :
( ( SV138 = SY347 )
| ~ ( vertex @ SV138 )
| ~ ( vertex @ SY347 )
| ~ ( ~ ~ ( ~ ( ( SV138
!= ( head_of @ ( sK14_E @ SY347 @ SV138 ) ) )
| ( SY347
!= ( tail_of @ ( sK14_E @ SY347 @ SV138 ) ) )
| ( SY347
!= ( head_of @ ( sK14_E @ SY347 @ SV138 ) ) )
| ( SV138
!= ( tail_of @ ( sK14_E @ SY347 @ SV138 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV138
= ( head_of @ ( sK14_E @ SY347 @ SV138 ) ) )
| ( SY347
= ( head_of @ ( sK14_E @ SY347 @ SV138 ) ) ) )
| ~ ( ( SV138
= ( head_of @ ( sK14_E @ SY347 @ SV138 ) ) )
| ( SV138
= ( tail_of @ ( sK14_E @ SY347 @ SV138 ) ) ) ) )
| ~ ~ ( ~ ( ( SY347
= ( tail_of @ ( sK14_E @ SY347 @ SV138 ) ) )
| ( SY347
= ( head_of @ ( sK14_E @ SY347 @ SV138 ) ) ) )
| ~ ( ( SY347
= ( tail_of @ ( sK14_E @ SY347 @ SV138 ) ) )
| ( SV138
= ( tail_of @ ( sK14_E @ SY347 @ SV138 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SY347 @ SV138 ) ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(703,plain,
! [SV120: $i] :
( ( ~ ~ ( ~ ( ! [SY253: $i,SY254: $i] :
~ ( path @ SV120 @ SY253 @ SY254 )
| ( vertex @ SV120 ) )
| ~ ! [SY255: $i] :
( ! [SY256: $i] :
~ ( path @ SV120 @ SY255 @ SY256 )
| ( vertex @ SY255 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[685]) ).
thf(704,plain,
! [SV120: $i] :
( ( ~ ! [SY257: $i,SY258: $i] :
( ~ ( path @ SV120 @ SY257 @ SY258 )
| ~ ( ~ ~ ( ( SV120
!= ( tail_of @ ( sK11_E @ SY258 @ SY257 @ SV120 ) ) )
| ~ ( edge @ ( sK11_E @ SY258 @ SY257 @ SV120 ) ) )
| ~ ~ ( ~ ( ( SY257
!= ( head_of @ ( sK11_E @ SY258 @ SY257 @ SV120 ) ) )
| ( SY258
!= ( path_cons @ ( sK11_E @ SY258 @ SY257 @ SV120 ) @ empty ) )
| ! [SY259: $i] :
( ( SY258
!= ( path_cons @ ( sK11_E @ SY258 @ SY257 @ SV120 ) @ SY259 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY258 @ SY257 @ SV120 ) ) @ SY257 @ SY259 ) ) )
| ~ ~ ( ~ ( ( SY257
= ( head_of @ ( sK11_E @ SY258 @ SY257 @ SV120 ) ) )
| ~ ( ( SY258
!= ( path_cons @ ( sK11_E @ SY258 @ SY257 @ SV120 ) @ ( sK13_SY84 @ SY258 @ SY257 @ SV120 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY258 @ SY257 @ SV120 ) ) @ SY257 @ ( sK13_SY84 @ SY258 @ SY257 @ SV120 ) ) ) )
| ~ ( ( SY258
= ( path_cons @ ( sK11_E @ SY258 @ SY257 @ SV120 ) @ empty ) )
| ~ ( ( SY258
!= ( path_cons @ ( sK11_E @ SY258 @ SY257 @ SV120 ) @ ( sK12_SY85 @ SY258 @ SY257 @ SV120 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY258 @ SY257 @ SV120 ) ) @ SY257 @ ( sK12_SY85 @ SY258 @ SY257 @ SV120 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[685]) ).
thf(705,plain,
! [SV132: $i,SV121: $i] :
( ( ~ ~ ( ~ ! [SY327: $i,SY328: $i] :
( ~ ( on_path @ SY328 @ SY327 )
| ~ ( path @ SV121 @ SV132 @ SY327 )
| ( edge @ SY328 ) )
| ~ ! [SY329: $i,SY330: $i] :
( ~ ( on_path @ SY330 @ SY329 )
| ~ ( path @ SV121 @ SV132 @ SY329 )
| ( in_path @ ( head_of @ SY330 ) @ SY329 ) ) )
| ~ ! [SY331: $i,SY332: $i] :
( ~ ( on_path @ SY332 @ SY331 )
| ~ ( path @ SV121 @ SV132 @ SY331 )
| ( in_path @ ( tail_of @ SY332 ) @ SY331 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[686]) ).
thf(706,plain,
! [SV139: $i,SV133: $i,SV122: $i] :
( ( ~ ( vertex @ SV122 )
| ~ ( vertex @ SV133 )
| ~ ( ~ ! [SY348: $i] :
( ( SV122
!= ( tail_of @ SY348 ) )
| ~ ( edge @ SY348 )
| ( SV133
!= ( head_of @ SY348 ) )
| ( SV139
!= ( path_cons @ SY348 @ empty ) ) )
| ~ ! [SY349: $i] :
( ( SV122
!= ( tail_of @ SY349 ) )
| ~ ( edge @ SY349 )
| ! [SY350: $i] :
( ( SV139
!= ( path_cons @ SY349 @ SY350 ) )
| ~ ( path @ ( head_of @ SY349 ) @ SV133 @ SY350 ) ) ) )
| ( path @ SV122 @ SV133 @ SV139 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(707,plain,
! [SV123: $i,SV140: $i] :
( ( ( ! [SY351: $i] :
~ ( path @ SV140 @ SY351 @ SV123 ) )
= $true )
| ( ( ~ ( ~ ! [SY274: $i,SY275: $i] :
( ~ ( on_path @ SY274 @ SV123 )
| ~ ( on_path @ SY275 @ SV123 )
| ! [SY276: $i] :
( ~ ( precedes @ SY276 @ SY275 @ SV123 )
| ~ ( sequential @ SY274 @ SY276 ) )
| ( precedes @ SY274 @ SY275 @ SV123 ) )
| ~ ! [SY277: $i,SY278: $i] :
( ~ ( on_path @ SY277 @ SV123 )
| ~ ( on_path @ SY278 @ SV123 )
| ~ ( sequential @ SY277 @ SY278 )
| ( precedes @ SY277 @ SY278 @ SV123 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(708,plain,
! [SV124: $i,SV141: $i] :
( ( ( ! [SY352: $i] :
~ ( path @ SV141 @ SY352 @ SV124 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY281: $i] :
( ! [SY282: $i] :
~ ( precedes @ SY281 @ SY282 @ SV124 )
| ( on_path @ SY281 @ SV124 ) )
| ~ ! [SY283: $i,SY284: $i] :
( ~ ( precedes @ SY283 @ SY284 @ SV124 )
| ( on_path @ SY284 @ SV124 ) ) )
| ~ ~ ( ~ ! [SY285: $i,SY286: $i] :
( ~ ( precedes @ SY285 @ SY286 @ SV124 )
| ! [SY287: $i] :
( ~ ( precedes @ SY287 @ SY286 @ SV124 )
| ~ ( sequential @ SY285 @ SY287 ) )
| ~ ( sequential @ SY285 @ SY286 ) )
| ~ ! [SY288: $i,SY289: $i] :
( ~ ( precedes @ SY288 @ SY289 @ SV124 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY289 @ SY288 @ SV124 ) @ SY289 @ SV124 )
| ~ ( sequential @ SY288 @ ( sK9_E3 @ SY289 @ SY288 @ SV124 ) ) )
| ( sequential @ SY288 @ SY289 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(709,plain,
! [SV134: $i,SV125: $i,SV142: $i] :
( ( ~ ( ~ ! [SY353: $i] :
( ! [SY354: $i] :
( ~ ( precedes @ SV142 @ SY353 @ SY354 )
| ~ ( shortest_path @ SV125 @ SV134 @ SY354 ) )
| ! [SY355: $i] :
( ( ( tail_of @ SY355 )
!= ( tail_of @ SV142 ) )
| ( ( head_of @ SY355 )
!= ( head_of @ SY353 ) ) ) )
| ~ ! [SY356: $i,SY357: $i] :
( ~ ( precedes @ SV142 @ SY356 @ SY357 )
| ~ ( shortest_path @ SV125 @ SV134 @ SY357 )
| ~ ( precedes @ SY356 @ SV142 @ SY357 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(710,plain,
( ( ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( head_of @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[691]) ).
thf(711,plain,
( ( ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( tail_of @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[692]) ).
thf(712,plain,
! [SV126: $i] :
( ( ~ ! [SY297: $i,SY298: $i] :
( ~ ( ~ ( path @ SV126 @ SY297 @ ( sK8_P @ SY298 @ SY297 @ SV126 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY298 ) @ ( length_of @ ( sK8_P @ SY298 @ SY297 @ SV126 ) ) ) )
| ( SV126 = SY297 )
| ~ ( path @ SV126 @ SY297 @ SY298 )
| ( shortest_path @ SV126 @ SY297 @ SY298 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[693]) ).
thf(713,plain,
! [SV126: $i] :
( ( ~ ~ ( ~ ! [SY299: $i,SY300: $i] :
( ~ ( shortest_path @ SV126 @ SY299 @ SY300 )
| ! [SY301: $i] :
( ~ ( path @ SV126 @ SY299 @ SY301 )
| ( less_or_equal @ ( length_of @ SY300 ) @ ( length_of @ SY301 ) ) ) )
| ~ ~ ( ~ ! [SY302: $i] :
( ! [SY303: $i] :
~ ( shortest_path @ SV126 @ SY302 @ SY303 )
| ( SV126 != SY302 ) )
| ~ ! [SY304: $i,SY305: $i] :
( ~ ( shortest_path @ SV126 @ SY304 @ SY305 )
| ( path @ SV126 @ SY304 @ SY305 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[693]) ).
thf(714,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( edge @ SX0 )
| ~ ( edge @ SX1 )
| ( ( head_of @ SX0 )
!= ( tail_of @ SX1 ) )
| ( sequential @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[694]) ).
thf(715,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[695]) ).
thf(716,plain,
! [SV127: $i] :
( ( ~ ! [SY306: $i,SY307: $i] :
( ~ ( edge @ SV127 )
| ~ ( edge @ SY306 )
| ~ ( edge @ SY307 )
| ~ ( sequential @ SV127 @ SY306 )
| ~ ( sequential @ SY306 @ SY307 )
| ~ ( sequential @ SY307 @ SV127 )
| ( triangle @ SV127 @ SY306 @ SY307 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[696]) ).
thf(717,plain,
! [SV127: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY308: $i,SY309: $i] :
~ ( triangle @ SV127 @ SY308 @ SY309 )
| ( edge @ SV127 ) )
| ~ ! [SY310: $i] :
( ! [SY311: $i] :
~ ( triangle @ SV127 @ SY310 @ SY311 )
| ( edge @ SY310 ) ) )
| ~ ! [SY312: $i,SY313: $i] :
( ~ ( triangle @ SV127 @ SY312 @ SY313 )
| ( edge @ SY313 ) ) )
| ~ ! [SY314: $i] :
( ! [SY315: $i] :
~ ( triangle @ SV127 @ SY314 @ SY315 )
| ( sequential @ SV127 @ SY314 ) ) )
| ~ ! [SY316: $i,SY317: $i] :
( ~ ( triangle @ SV127 @ SY316 @ SY317 )
| ( sequential @ SY316 @ SY317 ) ) )
| ~ ! [SY318: $i,SY319: $i] :
( ~ ( triangle @ SV127 @ SY318 @ SY319 )
| ( sequential @ SY319 @ SV127 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[696]) ).
thf(718,plain,
! [SV135: $i,SV128: $i] :
( ( ~ ! [SY343: $i,SY344: $i] :
( ~ ( in_path @ SY344 @ SY343 )
| ~ ( path @ SV128 @ SV135 @ SY343 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY344 @ SY343 @ SV135 @ SV128 ) @ SY343 )
| ~ ( ( SY344
= ( head_of @ ( sK10_E @ SY344 @ SY343 @ SV135 @ SV128 ) ) )
| ( SY344
= ( tail_of @ ( sK10_E @ SY344 @ SY343 @ SV135 @ SV128 ) ) ) ) ) )
| ~ ! [SY345: $i,SY346: $i] :
( ~ ( in_path @ SY346 @ SY345 )
| ~ ( path @ SV128 @ SV135 @ SY345 )
| ( vertex @ SY346 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[697]) ).
thf(719,plain,
! [SV115: $i] :
( ( ( ( head_of @ SV115 )
= ( tail_of @ SV115 ) )
= $false )
| ( ( edge @ SV115 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[698]) ).
thf(720,plain,
! [SV136: $i,SV129: $i,SV116: $i] :
( ( ( ~ ( path @ SV116 @ SV129 @ SV136 ) )
= $true )
| ( ( ( length_of @ SV136 )
= ( number_of_in @ edges @ SV136 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[699]) ).
thf(721,plain,
! [SV137: $i,SV130: $i,SV117: $i] :
( ( ( ~ ( path @ SV117 @ SV130 @ SV137 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV137 )
= ( minus @ ( length_of @ SV137 ) @ n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[700]) ).
thf(722,plain,
! [SV119: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV119 ) @ SV119 )
| ~ ( on_path @ ( sK7_SY80 @ SV119 ) @ SV119 ) )
| ~ ( sequential @ ( sK6_E1 @ SV119 ) @ ( sK7_SY80 @ SV119 ) ) )
| ~ ! [SY250: $i] :
~ ( triangle @ ( sK6_E1 @ SV119 ) @ ( sK7_SY80 @ SV119 ) @ SY250 ) )
= $false )
| ( ( ! [SY251: $i,SY252: $i] :
~ ( path @ SY251 @ SY252 @ SV119 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV119 )
= ( number_of_in @ triangles @ SV119 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[701]) ).
thf(723,plain,
! [SV143: $i,SV138: $i] :
( ( ( ( SV138 = SV143 )
| ~ ( vertex @ SV138 )
| ~ ( vertex @ SV143 )
| ~ ( ~ ~ ( ~ ( ( SV138
!= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
!= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
!= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
!= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV138
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
| ~ ( ( SV138
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) ) )
| ~ ~ ( ~ ( ( SV143
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
| ~ ( ( SV143
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV143 @ SV138 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(724,plain,
! [SV120: $i] :
( ( ~ ( ~ ( ! [SY253: $i,SY254: $i] :
~ ( path @ SV120 @ SY253 @ SY254 )
| ( vertex @ SV120 ) )
| ~ ! [SY255: $i] :
( ! [SY256: $i] :
~ ( path @ SV120 @ SY255 @ SY256 )
| ( vertex @ SY255 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[703]) ).
thf(725,plain,
! [SV120: $i] :
( ( ! [SY257: $i,SY258: $i] :
( ~ ( path @ SV120 @ SY257 @ SY258 )
| ~ ( ~ ~ ( ( SV120
!= ( tail_of @ ( sK11_E @ SY258 @ SY257 @ SV120 ) ) )
| ~ ( edge @ ( sK11_E @ SY258 @ SY257 @ SV120 ) ) )
| ~ ~ ( ~ ( ( SY257
!= ( head_of @ ( sK11_E @ SY258 @ SY257 @ SV120 ) ) )
| ( SY258
!= ( path_cons @ ( sK11_E @ SY258 @ SY257 @ SV120 ) @ empty ) )
| ! [SY259: $i] :
( ( SY258
!= ( path_cons @ ( sK11_E @ SY258 @ SY257 @ SV120 ) @ SY259 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY258 @ SY257 @ SV120 ) ) @ SY257 @ SY259 ) ) )
| ~ ~ ( ~ ( ( SY257
= ( head_of @ ( sK11_E @ SY258 @ SY257 @ SV120 ) ) )
| ~ ( ( SY258
!= ( path_cons @ ( sK11_E @ SY258 @ SY257 @ SV120 ) @ ( sK13_SY84 @ SY258 @ SY257 @ SV120 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY258 @ SY257 @ SV120 ) ) @ SY257 @ ( sK13_SY84 @ SY258 @ SY257 @ SV120 ) ) ) )
| ~ ( ( SY258
= ( path_cons @ ( sK11_E @ SY258 @ SY257 @ SV120 ) @ empty ) )
| ~ ( ( SY258
!= ( path_cons @ ( sK11_E @ SY258 @ SY257 @ SV120 ) @ ( sK12_SY85 @ SY258 @ SY257 @ SV120 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY258 @ SY257 @ SV120 ) ) @ SY257 @ ( sK12_SY85 @ SY258 @ SY257 @ SV120 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[704]) ).
thf(726,plain,
! [SV132: $i,SV121: $i] :
( ( ~ ~ ( ~ ! [SY327: $i,SY328: $i] :
( ~ ( on_path @ SY328 @ SY327 )
| ~ ( path @ SV121 @ SV132 @ SY327 )
| ( edge @ SY328 ) )
| ~ ! [SY329: $i,SY330: $i] :
( ~ ( on_path @ SY330 @ SY329 )
| ~ ( path @ SV121 @ SV132 @ SY329 )
| ( in_path @ ( head_of @ SY330 ) @ SY329 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[705]) ).
thf(727,plain,
! [SV132: $i,SV121: $i] :
( ( ~ ! [SY331: $i,SY332: $i] :
( ~ ( on_path @ SY332 @ SY331 )
| ~ ( path @ SV121 @ SV132 @ SY331 )
| ( in_path @ ( tail_of @ SY332 ) @ SY331 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[705]) ).
thf(728,plain,
! [SV139: $i,SV133: $i,SV122: $i] :
( ( ( ~ ( vertex @ SV122 )
| ~ ( vertex @ SV133 )
| ~ ( ~ ! [SY348: $i] :
( ( SV122
!= ( tail_of @ SY348 ) )
| ~ ( edge @ SY348 )
| ( SV133
!= ( head_of @ SY348 ) )
| ( SV139
!= ( path_cons @ SY348 @ empty ) ) )
| ~ ! [SY349: $i] :
( ( SV122
!= ( tail_of @ SY349 ) )
| ~ ( edge @ SY349 )
| ! [SY350: $i] :
( ( SV139
!= ( path_cons @ SY349 @ SY350 ) )
| ~ ( path @ ( head_of @ SY349 ) @ SV133 @ SY350 ) ) ) ) )
= $true )
| ( ( path @ SV122 @ SV133 @ SV139 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[706]) ).
thf(729,plain,
! [SV123: $i,SV144: $i,SV140: $i] :
( ( ( ~ ( path @ SV140 @ SV144 @ SV123 ) )
= $true )
| ( ( ~ ( ~ ! [SY274: $i,SY275: $i] :
( ~ ( on_path @ SY274 @ SV123 )
| ~ ( on_path @ SY275 @ SV123 )
| ! [SY276: $i] :
( ~ ( precedes @ SY276 @ SY275 @ SV123 )
| ~ ( sequential @ SY274 @ SY276 ) )
| ( precedes @ SY274 @ SY275 @ SV123 ) )
| ~ ! [SY277: $i,SY278: $i] :
( ~ ( on_path @ SY277 @ SV123 )
| ~ ( on_path @ SY278 @ SV123 )
| ~ ( sequential @ SY277 @ SY278 )
| ( precedes @ SY277 @ SY278 @ SV123 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(730,plain,
! [SV124: $i,SV145: $i,SV141: $i] :
( ( ( ~ ( path @ SV141 @ SV145 @ SV124 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY281: $i] :
( ! [SY282: $i] :
~ ( precedes @ SY281 @ SY282 @ SV124 )
| ( on_path @ SY281 @ SV124 ) )
| ~ ! [SY283: $i,SY284: $i] :
( ~ ( precedes @ SY283 @ SY284 @ SV124 )
| ( on_path @ SY284 @ SV124 ) ) )
| ~ ~ ( ~ ! [SY285: $i,SY286: $i] :
( ~ ( precedes @ SY285 @ SY286 @ SV124 )
| ! [SY287: $i] :
( ~ ( precedes @ SY287 @ SY286 @ SV124 )
| ~ ( sequential @ SY285 @ SY287 ) )
| ~ ( sequential @ SY285 @ SY286 ) )
| ~ ! [SY288: $i,SY289: $i] :
( ~ ( precedes @ SY288 @ SY289 @ SV124 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY289 @ SY288 @ SV124 ) @ SY289 @ SV124 )
| ~ ( sequential @ SY288 @ ( sK9_E3 @ SY289 @ SY288 @ SV124 ) ) )
| ( sequential @ SY288 @ SY289 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[708]) ).
thf(731,plain,
! [SV134: $i,SV125: $i,SV142: $i] :
( ( ~ ! [SY353: $i] :
( ! [SY354: $i] :
( ~ ( precedes @ SV142 @ SY353 @ SY354 )
| ~ ( shortest_path @ SV125 @ SV134 @ SY354 ) )
| ! [SY355: $i] :
( ( ( tail_of @ SY355 )
!= ( tail_of @ SV142 ) )
| ( ( head_of @ SY355 )
!= ( head_of @ SY353 ) ) ) )
| ~ ! [SY356: $i,SY357: $i] :
( ~ ( precedes @ SV142 @ SY356 @ SY357 )
| ~ ( shortest_path @ SV125 @ SV134 @ SY357 )
| ~ ( precedes @ SY356 @ SV142 @ SY357 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[709]) ).
thf(732,plain,
! [SV146: $i] :
( ( ~ ( edge @ SV146 )
| ( vertex @ ( head_of @ SV146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[710]) ).
thf(733,plain,
! [SV147: $i] :
( ( ~ ( edge @ SV147 )
| ( vertex @ ( tail_of @ SV147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[711]) ).
thf(734,plain,
! [SV126: $i] :
( ( ! [SY297: $i,SY298: $i] :
( ~ ( ~ ( path @ SV126 @ SY297 @ ( sK8_P @ SY298 @ SY297 @ SV126 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY298 ) @ ( length_of @ ( sK8_P @ SY298 @ SY297 @ SV126 ) ) ) )
| ( SV126 = SY297 )
| ~ ( path @ SV126 @ SY297 @ SY298 )
| ( shortest_path @ SV126 @ SY297 @ SY298 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[712]) ).
thf(735,plain,
! [SV126: $i] :
( ( ~ ( ~ ! [SY299: $i,SY300: $i] :
( ~ ( shortest_path @ SV126 @ SY299 @ SY300 )
| ! [SY301: $i] :
( ~ ( path @ SV126 @ SY299 @ SY301 )
| ( less_or_equal @ ( length_of @ SY300 ) @ ( length_of @ SY301 ) ) ) )
| ~ ~ ( ~ ! [SY302: $i] :
( ! [SY303: $i] :
~ ( shortest_path @ SV126 @ SY302 @ SY303 )
| ( SV126 != SY302 ) )
| ~ ! [SY304: $i,SY305: $i] :
( ~ ( shortest_path @ SV126 @ SY304 @ SY305 )
| ( path @ SV126 @ SY304 @ SY305 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[713]) ).
thf(736,plain,
! [SV148: $i] :
( ( ! [SY358: $i] :
( ( SV148 = SY358 )
| ~ ( edge @ SV148 )
| ~ ( edge @ SY358 )
| ( ( head_of @ SV148 )
!= ( tail_of @ SY358 ) )
| ( sequential @ SV148 @ SY358 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[714]) ).
thf(737,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[715]) ).
thf(738,plain,
! [SV127: $i] :
( ( ! [SY306: $i,SY307: $i] :
( ~ ( edge @ SV127 )
| ~ ( edge @ SY306 )
| ~ ( edge @ SY307 )
| ~ ( sequential @ SV127 @ SY306 )
| ~ ( sequential @ SY306 @ SY307 )
| ~ ( sequential @ SY307 @ SV127 )
| ( triangle @ SV127 @ SY306 @ SY307 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[716]) ).
thf(739,plain,
! [SV127: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY308: $i,SY309: $i] :
~ ( triangle @ SV127 @ SY308 @ SY309 )
| ( edge @ SV127 ) )
| ~ ! [SY310: $i] :
( ! [SY311: $i] :
~ ( triangle @ SV127 @ SY310 @ SY311 )
| ( edge @ SY310 ) ) )
| ~ ! [SY312: $i,SY313: $i] :
( ~ ( triangle @ SV127 @ SY312 @ SY313 )
| ( edge @ SY313 ) ) )
| ~ ! [SY314: $i] :
( ! [SY315: $i] :
~ ( triangle @ SV127 @ SY314 @ SY315 )
| ( sequential @ SV127 @ SY314 ) ) )
| ~ ! [SY316: $i,SY317: $i] :
( ~ ( triangle @ SV127 @ SY316 @ SY317 )
| ( sequential @ SY316 @ SY317 ) ) )
| ~ ! [SY318: $i,SY319: $i] :
( ~ ( triangle @ SV127 @ SY318 @ SY319 )
| ( sequential @ SY319 @ SV127 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[717]) ).
thf(740,plain,
! [SV135: $i,SV128: $i] :
( ( ~ ! [SY343: $i,SY344: $i] :
( ~ ( in_path @ SY344 @ SY343 )
| ~ ( path @ SV128 @ SV135 @ SY343 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY344 @ SY343 @ SV135 @ SV128 ) @ SY343 )
| ~ ( ( SY344
= ( head_of @ ( sK10_E @ SY344 @ SY343 @ SV135 @ SV128 ) ) )
| ( SY344
= ( tail_of @ ( sK10_E @ SY344 @ SY343 @ SV135 @ SV128 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[718]) ).
thf(741,plain,
! [SV135: $i,SV128: $i] :
( ( ~ ! [SY345: $i,SY346: $i] :
( ~ ( in_path @ SY346 @ SY345 )
| ~ ( path @ SV128 @ SV135 @ SY345 )
| ( vertex @ SY346 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[718]) ).
thf(742,plain,
! [SV136: $i,SV129: $i,SV116: $i] :
( ( ( path @ SV116 @ SV129 @ SV136 )
= $false )
| ( ( ( length_of @ SV136 )
= ( number_of_in @ edges @ SV136 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[720]) ).
thf(743,plain,
! [SV137: $i,SV130: $i,SV117: $i] :
( ( ( path @ SV117 @ SV130 @ SV137 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV137 )
= ( minus @ ( length_of @ SV137 ) @ n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[721]) ).
thf(744,plain,
! [SV119: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV119 ) @ SV119 )
| ~ ( on_path @ ( sK7_SY80 @ SV119 ) @ SV119 ) )
| ~ ( sequential @ ( sK6_E1 @ SV119 ) @ ( sK7_SY80 @ SV119 ) ) ) )
= $false )
| ( ( ! [SY251: $i,SY252: $i] :
~ ( path @ SY251 @ SY252 @ SV119 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV119 )
= ( number_of_in @ triangles @ SV119 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[722]) ).
thf(745,plain,
! [SV119: $i] :
( ( ( ~ ! [SY250: $i] :
~ ( triangle @ ( sK6_E1 @ SV119 ) @ ( sK7_SY80 @ SV119 ) @ SY250 ) )
= $false )
| ( ( ! [SY251: $i,SY252: $i] :
~ ( path @ SY251 @ SY252 @ SV119 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV119 )
= ( number_of_in @ triangles @ SV119 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[722]) ).
thf(746,plain,
! [SV143: $i,SV138: $i] :
( ( ( ( SV138 = SV143 )
| ~ ( vertex @ SV138 )
| ~ ( vertex @ SV143 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV138
!= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
!= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
!= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
!= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV138
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
| ~ ( ( SV138
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) ) )
| ~ ~ ( ~ ( ( SV143
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
| ~ ( ( SV143
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV143 @ SV138 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[723]) ).
thf(747,plain,
! [SV120: $i] :
( ( ~ ( ! [SY253: $i,SY254: $i] :
~ ( path @ SV120 @ SY253 @ SY254 )
| ( vertex @ SV120 ) )
| ~ ! [SY255: $i] :
( ! [SY256: $i] :
~ ( path @ SV120 @ SY255 @ SY256 )
| ( vertex @ SY255 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[724]) ).
thf(748,plain,
! [SV149: $i,SV120: $i] :
( ( ! [SY359: $i] :
( ~ ( path @ SV120 @ SV149 @ SY359 )
| ~ ( ~ ~ ( ( SV120
!= ( tail_of @ ( sK11_E @ SY359 @ SV149 @ SV120 ) ) )
| ~ ( edge @ ( sK11_E @ SY359 @ SV149 @ SV120 ) ) )
| ~ ~ ( ~ ( ( SV149
!= ( head_of @ ( sK11_E @ SY359 @ SV149 @ SV120 ) ) )
| ( SY359
!= ( path_cons @ ( sK11_E @ SY359 @ SV149 @ SV120 ) @ empty ) )
| ! [SY360: $i] :
( ( SY359
!= ( path_cons @ ( sK11_E @ SY359 @ SV149 @ SV120 ) @ SY360 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY359 @ SV149 @ SV120 ) ) @ SV149 @ SY360 ) ) )
| ~ ~ ( ~ ( ( SV149
= ( head_of @ ( sK11_E @ SY359 @ SV149 @ SV120 ) ) )
| ~ ( ( SY359
!= ( path_cons @ ( sK11_E @ SY359 @ SV149 @ SV120 ) @ ( sK13_SY84 @ SY359 @ SV149 @ SV120 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY359 @ SV149 @ SV120 ) ) @ SV149 @ ( sK13_SY84 @ SY359 @ SV149 @ SV120 ) ) ) )
| ~ ( ( SY359
= ( path_cons @ ( sK11_E @ SY359 @ SV149 @ SV120 ) @ empty ) )
| ~ ( ( SY359
!= ( path_cons @ ( sK11_E @ SY359 @ SV149 @ SV120 ) @ ( sK12_SY85 @ SY359 @ SV149 @ SV120 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY359 @ SV149 @ SV120 ) ) @ SV149 @ ( sK12_SY85 @ SY359 @ SV149 @ SV120 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(749,plain,
! [SV132: $i,SV121: $i] :
( ( ~ ( ~ ! [SY327: $i,SY328: $i] :
( ~ ( on_path @ SY328 @ SY327 )
| ~ ( path @ SV121 @ SV132 @ SY327 )
| ( edge @ SY328 ) )
| ~ ! [SY329: $i,SY330: $i] :
( ~ ( on_path @ SY330 @ SY329 )
| ~ ( path @ SV121 @ SV132 @ SY329 )
| ( in_path @ ( head_of @ SY330 ) @ SY329 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[726]) ).
thf(750,plain,
! [SV132: $i,SV121: $i] :
( ( ! [SY331: $i,SY332: $i] :
( ~ ( on_path @ SY332 @ SY331 )
| ~ ( path @ SV121 @ SV132 @ SY331 )
| ( in_path @ ( tail_of @ SY332 ) @ SY331 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[727]) ).
thf(751,plain,
! [SV139: $i,SV133: $i,SV122: $i] :
( ( ( ~ ( vertex @ SV122 )
| ~ ( vertex @ SV133 ) )
= $true )
| ( ( ~ ( ~ ! [SY348: $i] :
( ( SV122
!= ( tail_of @ SY348 ) )
| ~ ( edge @ SY348 )
| ( SV133
!= ( head_of @ SY348 ) )
| ( SV139
!= ( path_cons @ SY348 @ empty ) ) )
| ~ ! [SY349: $i] :
( ( SV122
!= ( tail_of @ SY349 ) )
| ~ ( edge @ SY349 )
| ! [SY350: $i] :
( ( SV139
!= ( path_cons @ SY349 @ SY350 ) )
| ~ ( path @ ( head_of @ SY349 ) @ SV133 @ SY350 ) ) ) ) )
= $true )
| ( ( path @ SV122 @ SV133 @ SV139 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[728]) ).
thf(752,plain,
! [SV123: $i,SV144: $i,SV140: $i] :
( ( ( path @ SV140 @ SV144 @ SV123 )
= $false )
| ( ( ~ ( ~ ! [SY274: $i,SY275: $i] :
( ~ ( on_path @ SY274 @ SV123 )
| ~ ( on_path @ SY275 @ SV123 )
| ! [SY276: $i] :
( ~ ( precedes @ SY276 @ SY275 @ SV123 )
| ~ ( sequential @ SY274 @ SY276 ) )
| ( precedes @ SY274 @ SY275 @ SV123 ) )
| ~ ! [SY277: $i,SY278: $i] :
( ~ ( on_path @ SY277 @ SV123 )
| ~ ( on_path @ SY278 @ SV123 )
| ~ ( sequential @ SY277 @ SY278 )
| ( precedes @ SY277 @ SY278 @ SV123 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[729]) ).
thf(753,plain,
! [SV124: $i,SV145: $i,SV141: $i] :
( ( ( path @ SV141 @ SV145 @ SV124 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY281: $i] :
( ! [SY282: $i] :
~ ( precedes @ SY281 @ SY282 @ SV124 )
| ( on_path @ SY281 @ SV124 ) )
| ~ ! [SY283: $i,SY284: $i] :
( ~ ( precedes @ SY283 @ SY284 @ SV124 )
| ( on_path @ SY284 @ SV124 ) ) )
| ~ ~ ( ~ ! [SY285: $i,SY286: $i] :
( ~ ( precedes @ SY285 @ SY286 @ SV124 )
| ! [SY287: $i] :
( ~ ( precedes @ SY287 @ SY286 @ SV124 )
| ~ ( sequential @ SY285 @ SY287 ) )
| ~ ( sequential @ SY285 @ SY286 ) )
| ~ ! [SY288: $i,SY289: $i] :
( ~ ( precedes @ SY288 @ SY289 @ SV124 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY289 @ SY288 @ SV124 ) @ SY289 @ SV124 )
| ~ ( sequential @ SY288 @ ( sK9_E3 @ SY289 @ SY288 @ SV124 ) ) )
| ( sequential @ SY288 @ SY289 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[730]) ).
thf(754,plain,
! [SV134: $i,SV125: $i,SV142: $i] :
( ( ~ ! [SY353: $i] :
( ! [SY354: $i] :
( ~ ( precedes @ SV142 @ SY353 @ SY354 )
| ~ ( shortest_path @ SV125 @ SV134 @ SY354 ) )
| ! [SY355: $i] :
( ( ( tail_of @ SY355 )
!= ( tail_of @ SV142 ) )
| ( ( head_of @ SY355 )
!= ( head_of @ SY353 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[731]) ).
thf(755,plain,
! [SV134: $i,SV125: $i,SV142: $i] :
( ( ~ ! [SY356: $i,SY357: $i] :
( ~ ( precedes @ SV142 @ SY356 @ SY357 )
| ~ ( shortest_path @ SV125 @ SV134 @ SY357 )
| ~ ( precedes @ SY356 @ SV142 @ SY357 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[731]) ).
thf(756,plain,
! [SV146: $i] :
( ( ( ~ ( edge @ SV146 ) )
= $true )
| ( ( vertex @ ( head_of @ SV146 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[732]) ).
thf(757,plain,
! [SV147: $i] :
( ( ( ~ ( edge @ SV147 ) )
= $true )
| ( ( vertex @ ( tail_of @ SV147 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[733]) ).
thf(758,plain,
! [SV150: $i,SV126: $i] :
( ( ! [SY361: $i] :
( ~ ( ~ ( path @ SV126 @ SV150 @ ( sK8_P @ SY361 @ SV150 @ SV126 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY361 ) @ ( length_of @ ( sK8_P @ SY361 @ SV150 @ SV126 ) ) ) )
| ( SV126 = SV150 )
| ~ ( path @ SV126 @ SV150 @ SY361 )
| ( shortest_path @ SV126 @ SV150 @ SY361 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[734]) ).
thf(759,plain,
! [SV126: $i] :
( ( ~ ! [SY299: $i,SY300: $i] :
( ~ ( shortest_path @ SV126 @ SY299 @ SY300 )
| ! [SY301: $i] :
( ~ ( path @ SV126 @ SY299 @ SY301 )
| ( less_or_equal @ ( length_of @ SY300 ) @ ( length_of @ SY301 ) ) ) )
| ~ ~ ( ~ ! [SY302: $i] :
( ! [SY303: $i] :
~ ( shortest_path @ SV126 @ SY302 @ SY303 )
| ( SV126 != SY302 ) )
| ~ ! [SY304: $i,SY305: $i] :
( ~ ( shortest_path @ SV126 @ SY304 @ SY305 )
| ( path @ SV126 @ SY304 @ SY305 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[735]) ).
thf(760,plain,
! [SV151: $i,SV148: $i] :
( ( ( SV148 = SV151 )
| ~ ( edge @ SV148 )
| ~ ( edge @ SV151 )
| ( ( head_of @ SV148 )
!= ( tail_of @ SV151 ) )
| ( sequential @ SV148 @ SV151 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[736]) ).
thf(761,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[737]) ).
thf(762,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[737]) ).
thf(763,plain,
! [SV152: $i,SV127: $i] :
( ( ! [SY362: $i] :
( ~ ( edge @ SV127 )
| ~ ( edge @ SV152 )
| ~ ( edge @ SY362 )
| ~ ( sequential @ SV127 @ SV152 )
| ~ ( sequential @ SV152 @ SY362 )
| ~ ( sequential @ SY362 @ SV127 )
| ( triangle @ SV127 @ SV152 @ SY362 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[738]) ).
thf(764,plain,
! [SV127: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY308: $i,SY309: $i] :
~ ( triangle @ SV127 @ SY308 @ SY309 )
| ( edge @ SV127 ) )
| ~ ! [SY310: $i] :
( ! [SY311: $i] :
~ ( triangle @ SV127 @ SY310 @ SY311 )
| ( edge @ SY310 ) ) )
| ~ ! [SY312: $i,SY313: $i] :
( ~ ( triangle @ SV127 @ SY312 @ SY313 )
| ( edge @ SY313 ) ) )
| ~ ! [SY314: $i] :
( ! [SY315: $i] :
~ ( triangle @ SV127 @ SY314 @ SY315 )
| ( sequential @ SV127 @ SY314 ) ) )
| ~ ! [SY316: $i,SY317: $i] :
( ~ ( triangle @ SV127 @ SY316 @ SY317 )
| ( sequential @ SY316 @ SY317 ) ) )
| ~ ! [SY318: $i,SY319: $i] :
( ~ ( triangle @ SV127 @ SY318 @ SY319 )
| ( sequential @ SY319 @ SV127 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[739]) ).
thf(765,plain,
! [SV135: $i,SV128: $i] :
( ( ! [SY343: $i,SY344: $i] :
( ~ ( in_path @ SY344 @ SY343 )
| ~ ( path @ SV128 @ SV135 @ SY343 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY344 @ SY343 @ SV135 @ SV128 ) @ SY343 )
| ~ ( ( SY344
= ( head_of @ ( sK10_E @ SY344 @ SY343 @ SV135 @ SV128 ) ) )
| ( SY344
= ( tail_of @ ( sK10_E @ SY344 @ SY343 @ SV135 @ SV128 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[740]) ).
thf(766,plain,
! [SV135: $i,SV128: $i] :
( ( ! [SY345: $i,SY346: $i] :
( ~ ( in_path @ SY346 @ SY345 )
| ~ ( path @ SV128 @ SV135 @ SY345 )
| ( vertex @ SY346 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[741]) ).
thf(767,plain,
! [SV119: $i] :
( ( ( ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV119 ) @ SV119 )
| ~ ( on_path @ ( sK7_SY80 @ SV119 ) @ SV119 ) )
| ~ ( sequential @ ( sK6_E1 @ SV119 ) @ ( sK7_SY80 @ SV119 ) ) ) )
= $true )
| ( ( ! [SY251: $i,SY252: $i] :
~ ( path @ SY251 @ SY252 @ SV119 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV119 )
= ( number_of_in @ triangles @ SV119 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[744]) ).
thf(768,plain,
! [SV119: $i] :
( ( ( ! [SY250: $i] :
~ ( triangle @ ( sK6_E1 @ SV119 ) @ ( sK7_SY80 @ SV119 ) @ SY250 ) )
= $true )
| ( ( ! [SY251: $i,SY252: $i] :
~ ( path @ SY251 @ SY252 @ SV119 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV119 )
= ( number_of_in @ triangles @ SV119 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[745]) ).
thf(769,plain,
! [SV143: $i,SV138: $i] :
( ( ( SV138 = SV143 )
= $true )
| ( ( ~ ( vertex @ SV138 )
| ~ ( vertex @ SV143 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV138
!= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
!= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
!= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
!= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV138
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
| ~ ( ( SV138
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) ) )
| ~ ~ ( ~ ( ( SV143
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
| ~ ( ( SV143
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV143 @ SV138 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[746]) ).
thf(770,plain,
! [SV120: $i] :
( ( ~ ( ! [SY253: $i,SY254: $i] :
~ ( path @ SV120 @ SY253 @ SY254 )
| ( vertex @ SV120 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[747]) ).
thf(771,plain,
! [SV120: $i] :
( ( ~ ! [SY255: $i] :
( ! [SY256: $i] :
~ ( path @ SV120 @ SY255 @ SY256 )
| ( vertex @ SY255 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[747]) ).
thf(772,plain,
! [SV153: $i,SV149: $i,SV120: $i] :
( ( ~ ( path @ SV120 @ SV149 @ SV153 )
| ~ ( ~ ~ ( ( SV120
!= ( tail_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( edge @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
| ~ ~ ( ~ ( ( SV149
!= ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
| ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ empty ) )
| ! [SY363: $i] :
( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ SY363 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ SY363 ) ) )
| ~ ~ ( ~ ( ( SV149
= ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ ( sK13_SY84 @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ ( sK13_SY84 @ SV153 @ SV149 @ SV120 ) ) ) )
| ~ ( ( SV153
= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ empty ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ ( sK12_SY85 @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ ( sK12_SY85 @ SV153 @ SV149 @ SV120 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[748]) ).
thf(773,plain,
! [SV132: $i,SV121: $i] :
( ( ~ ! [SY327: $i,SY328: $i] :
( ~ ( on_path @ SY328 @ SY327 )
| ~ ( path @ SV121 @ SV132 @ SY327 )
| ( edge @ SY328 ) )
| ~ ! [SY329: $i,SY330: $i] :
( ~ ( on_path @ SY330 @ SY329 )
| ~ ( path @ SV121 @ SV132 @ SY329 )
| ( in_path @ ( head_of @ SY330 ) @ SY329 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[749]) ).
thf(774,plain,
! [SV132: $i,SV121: $i,SV154: $i] :
( ( ! [SY364: $i] :
( ~ ( on_path @ SY364 @ SV154 )
| ~ ( path @ SV121 @ SV132 @ SV154 )
| ( in_path @ ( tail_of @ SY364 ) @ SV154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[750]) ).
thf(775,plain,
! [SV139: $i,SV133: $i,SV122: $i] :
( ( ( ~ ( vertex @ SV122 ) )
= $true )
| ( ( ~ ( vertex @ SV133 ) )
= $true )
| ( ( ~ ( ~ ! [SY348: $i] :
( ( SV122
!= ( tail_of @ SY348 ) )
| ~ ( edge @ SY348 )
| ( SV133
!= ( head_of @ SY348 ) )
| ( SV139
!= ( path_cons @ SY348 @ empty ) ) )
| ~ ! [SY349: $i] :
( ( SV122
!= ( tail_of @ SY349 ) )
| ~ ( edge @ SY349 )
| ! [SY350: $i] :
( ( SV139
!= ( path_cons @ SY349 @ SY350 ) )
| ~ ( path @ ( head_of @ SY349 ) @ SV133 @ SY350 ) ) ) ) )
= $true )
| ( ( path @ SV122 @ SV133 @ SV139 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[751]) ).
thf(776,plain,
! [SV144: $i,SV140: $i,SV123: $i] :
( ( ( ~ ! [SY274: $i,SY275: $i] :
( ~ ( on_path @ SY274 @ SV123 )
| ~ ( on_path @ SY275 @ SV123 )
| ! [SY276: $i] :
( ~ ( precedes @ SY276 @ SY275 @ SV123 )
| ~ ( sequential @ SY274 @ SY276 ) )
| ( precedes @ SY274 @ SY275 @ SV123 ) )
| ~ ! [SY277: $i,SY278: $i] :
( ~ ( on_path @ SY277 @ SV123 )
| ~ ( on_path @ SY278 @ SV123 )
| ~ ( sequential @ SY277 @ SY278 )
| ( precedes @ SY277 @ SY278 @ SV123 ) ) )
= $false )
| ( ( path @ SV140 @ SV144 @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[752]) ).
thf(777,plain,
! [SV145: $i,SV141: $i,SV124: $i] :
( ( ( ~ ~ ( ~ ! [SY281: $i] :
( ! [SY282: $i] :
~ ( precedes @ SY281 @ SY282 @ SV124 )
| ( on_path @ SY281 @ SV124 ) )
| ~ ! [SY283: $i,SY284: $i] :
( ~ ( precedes @ SY283 @ SY284 @ SV124 )
| ( on_path @ SY284 @ SV124 ) ) )
| ~ ~ ( ~ ! [SY285: $i,SY286: $i] :
( ~ ( precedes @ SY285 @ SY286 @ SV124 )
| ! [SY287: $i] :
( ~ ( precedes @ SY287 @ SY286 @ SV124 )
| ~ ( sequential @ SY285 @ SY287 ) )
| ~ ( sequential @ SY285 @ SY286 ) )
| ~ ! [SY288: $i,SY289: $i] :
( ~ ( precedes @ SY288 @ SY289 @ SV124 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY289 @ SY288 @ SV124 ) @ SY289 @ SV124 )
| ~ ( sequential @ SY288 @ ( sK9_E3 @ SY289 @ SY288 @ SV124 ) ) )
| ( sequential @ SY288 @ SY289 ) ) ) )
= $false )
| ( ( path @ SV141 @ SV145 @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[753]) ).
thf(778,plain,
! [SV134: $i,SV125: $i,SV142: $i] :
( ( ! [SY353: $i] :
( ! [SY354: $i] :
( ~ ( precedes @ SV142 @ SY353 @ SY354 )
| ~ ( shortest_path @ SV125 @ SV134 @ SY354 ) )
| ! [SY355: $i] :
( ( ( tail_of @ SY355 )
!= ( tail_of @ SV142 ) )
| ( ( head_of @ SY355 )
!= ( head_of @ SY353 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[754]) ).
thf(779,plain,
! [SV134: $i,SV125: $i,SV142: $i] :
( ( ! [SY356: $i,SY357: $i] :
( ~ ( precedes @ SV142 @ SY356 @ SY357 )
| ~ ( shortest_path @ SV125 @ SV134 @ SY357 )
| ~ ( precedes @ SY356 @ SV142 @ SY357 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[755]) ).
thf(780,plain,
! [SV146: $i] :
( ( ( edge @ SV146 )
= $false )
| ( ( vertex @ ( head_of @ SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[756]) ).
thf(781,plain,
! [SV147: $i] :
( ( ( edge @ SV147 )
= $false )
| ( ( vertex @ ( tail_of @ SV147 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[757]) ).
thf(782,plain,
! [SV155: $i,SV150: $i,SV126: $i] :
( ( ~ ( ~ ( path @ SV126 @ SV150 @ ( sK8_P @ SV155 @ SV150 @ SV126 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SV155 ) @ ( length_of @ ( sK8_P @ SV155 @ SV150 @ SV126 ) ) ) )
| ( SV126 = SV150 )
| ~ ( path @ SV126 @ SV150 @ SV155 )
| ( shortest_path @ SV126 @ SV150 @ SV155 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[758]) ).
thf(783,plain,
! [SV126: $i] :
( ( ~ ! [SY299: $i,SY300: $i] :
( ~ ( shortest_path @ SV126 @ SY299 @ SY300 )
| ! [SY301: $i] :
( ~ ( path @ SV126 @ SY299 @ SY301 )
| ( less_or_equal @ ( length_of @ SY300 ) @ ( length_of @ SY301 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[759]) ).
thf(784,plain,
! [SV126: $i] :
( ( ~ ~ ( ~ ! [SY302: $i] :
( ! [SY303: $i] :
~ ( shortest_path @ SV126 @ SY302 @ SY303 )
| ( SV126 != SY302 ) )
| ~ ! [SY304: $i,SY305: $i] :
( ~ ( shortest_path @ SV126 @ SY304 @ SY305 )
| ( path @ SV126 @ SY304 @ SY305 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[759]) ).
thf(785,plain,
! [SV151: $i,SV148: $i] :
( ( ( ( SV148 = SV151 )
| ~ ( edge @ SV148 )
| ~ ( edge @ SV151 )
| ( ( head_of @ SV148 )
!= ( tail_of @ SV151 ) ) )
= $true )
| ( ( sequential @ SV148 @ SV151 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[760]) ).
thf(786,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[761]) ).
thf(787,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[762]) ).
thf(788,plain,
! [SV156: $i,SV152: $i,SV127: $i] :
( ( ~ ( edge @ SV127 )
| ~ ( edge @ SV152 )
| ~ ( edge @ SV156 )
| ~ ( sequential @ SV127 @ SV152 )
| ~ ( sequential @ SV152 @ SV156 )
| ~ ( sequential @ SV156 @ SV127 )
| ( triangle @ SV127 @ SV152 @ SV156 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[763]) ).
thf(789,plain,
! [SV127: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY308: $i,SY309: $i] :
~ ( triangle @ SV127 @ SY308 @ SY309 )
| ( edge @ SV127 ) )
| ~ ! [SY310: $i] :
( ! [SY311: $i] :
~ ( triangle @ SV127 @ SY310 @ SY311 )
| ( edge @ SY310 ) ) )
| ~ ! [SY312: $i,SY313: $i] :
( ~ ( triangle @ SV127 @ SY312 @ SY313 )
| ( edge @ SY313 ) ) )
| ~ ! [SY314: $i] :
( ! [SY315: $i] :
~ ( triangle @ SV127 @ SY314 @ SY315 )
| ( sequential @ SV127 @ SY314 ) ) )
| ~ ! [SY316: $i,SY317: $i] :
( ~ ( triangle @ SV127 @ SY316 @ SY317 )
| ( sequential @ SY316 @ SY317 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[764]) ).
thf(790,plain,
! [SV127: $i] :
( ( ~ ! [SY318: $i,SY319: $i] :
( ~ ( triangle @ SV127 @ SY318 @ SY319 )
| ( sequential @ SY319 @ SV127 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[764]) ).
thf(791,plain,
! [SV135: $i,SV128: $i,SV157: $i] :
( ( ! [SY365: $i] :
( ~ ( in_path @ SY365 @ SV157 )
| ~ ( path @ SV128 @ SV135 @ SV157 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY365 @ SV157 @ SV135 @ SV128 ) @ SV157 )
| ~ ( ( SY365
= ( head_of @ ( sK10_E @ SY365 @ SV157 @ SV135 @ SV128 ) ) )
| ( SY365
= ( tail_of @ ( sK10_E @ SY365 @ SV157 @ SV135 @ SV128 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[765]) ).
thf(792,plain,
! [SV135: $i,SV128: $i,SV158: $i] :
( ( ! [SY366: $i] :
( ~ ( in_path @ SY366 @ SV158 )
| ~ ( path @ SV128 @ SV135 @ SV158 )
| ( vertex @ SY366 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[766]) ).
thf(793,plain,
! [SV119: $i] :
( ( ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV119 ) @ SV119 )
| ~ ( on_path @ ( sK7_SY80 @ SV119 ) @ SV119 ) )
| ~ ( sequential @ ( sK6_E1 @ SV119 ) @ ( sK7_SY80 @ SV119 ) ) )
= $false )
| ( ( ! [SY251: $i,SY252: $i] :
~ ( path @ SY251 @ SY252 @ SV119 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV119 )
= ( number_of_in @ triangles @ SV119 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[767]) ).
thf(794,plain,
! [SV159: $i,SV119: $i] :
( ( ( ~ ( triangle @ ( sK6_E1 @ SV119 ) @ ( sK7_SY80 @ SV119 ) @ SV159 ) )
= $true )
| ( ( ! [SY251: $i,SY252: $i] :
~ ( path @ SY251 @ SY252 @ SV119 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV119 )
= ( number_of_in @ triangles @ SV119 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[768]) ).
thf(795,plain,
! [SV143: $i,SV138: $i] :
( ( ( ~ ( vertex @ SV138 ) )
= $true )
| ( ( ~ ( vertex @ SV143 ) )
= $true )
| ( ( SV138 = SV143 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV138
!= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
!= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
!= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
!= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV138
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
| ~ ( ( SV138
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) ) )
| ~ ~ ( ~ ( ( SV143
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
| ~ ( ( SV143
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV143 @ SV138 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[769]) ).
thf(796,plain,
! [SV120: $i] :
( ( ! [SY253: $i,SY254: $i] :
~ ( path @ SV120 @ SY253 @ SY254 )
| ( vertex @ SV120 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[770]) ).
thf(797,plain,
! [SV120: $i] :
( ( ! [SY255: $i] :
( ! [SY256: $i] :
~ ( path @ SV120 @ SY255 @ SY256 )
| ( vertex @ SY255 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[771]) ).
thf(798,plain,
! [SV153: $i,SV149: $i,SV120: $i] :
( ( ( ~ ( path @ SV120 @ SV149 @ SV153 ) )
= $true )
| ( ( ~ ( ~ ~ ( ( SV120
!= ( tail_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( edge @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
| ~ ~ ( ~ ( ( SV149
!= ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
| ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ empty ) )
| ! [SY363: $i] :
( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ SY363 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ SY363 ) ) )
| ~ ~ ( ~ ( ( SV149
= ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ ( sK13_SY84 @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ ( sK13_SY84 @ SV153 @ SV149 @ SV120 ) ) ) )
| ~ ( ( SV153
= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ empty ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ ( sK12_SY85 @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ ( sK12_SY85 @ SV153 @ SV149 @ SV120 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[772]) ).
thf(799,plain,
! [SV132: $i,SV121: $i] :
( ( ~ ! [SY327: $i,SY328: $i] :
( ~ ( on_path @ SY328 @ SY327 )
| ~ ( path @ SV121 @ SV132 @ SY327 )
| ( edge @ SY328 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[773]) ).
thf(800,plain,
! [SV132: $i,SV121: $i] :
( ( ~ ! [SY329: $i,SY330: $i] :
( ~ ( on_path @ SY330 @ SY329 )
| ~ ( path @ SV121 @ SV132 @ SY329 )
| ( in_path @ ( head_of @ SY330 ) @ SY329 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[773]) ).
thf(801,plain,
! [SV132: $i,SV121: $i,SV154: $i,SV160: $i] :
( ( ~ ( on_path @ SV160 @ SV154 )
| ~ ( path @ SV121 @ SV132 @ SV154 )
| ( in_path @ ( tail_of @ SV160 ) @ SV154 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[774]) ).
thf(802,plain,
! [SV139: $i,SV133: $i,SV122: $i] :
( ( ( vertex @ SV122 )
= $false )
| ( ( ~ ( vertex @ SV133 ) )
= $true )
| ( ( ~ ( ~ ! [SY348: $i] :
( ( SV122
!= ( tail_of @ SY348 ) )
| ~ ( edge @ SY348 )
| ( SV133
!= ( head_of @ SY348 ) )
| ( SV139
!= ( path_cons @ SY348 @ empty ) ) )
| ~ ! [SY349: $i] :
( ( SV122
!= ( tail_of @ SY349 ) )
| ~ ( edge @ SY349 )
| ! [SY350: $i] :
( ( SV139
!= ( path_cons @ SY349 @ SY350 ) )
| ~ ( path @ ( head_of @ SY349 ) @ SV133 @ SY350 ) ) ) ) )
= $true )
| ( ( path @ SV122 @ SV133 @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[775]) ).
thf(803,plain,
! [SV144: $i,SV140: $i,SV123: $i] :
( ( ( ~ ! [SY274: $i,SY275: $i] :
( ~ ( on_path @ SY274 @ SV123 )
| ~ ( on_path @ SY275 @ SV123 )
| ! [SY276: $i] :
( ~ ( precedes @ SY276 @ SY275 @ SV123 )
| ~ ( sequential @ SY274 @ SY276 ) )
| ( precedes @ SY274 @ SY275 @ SV123 ) ) )
= $false )
| ( ( path @ SV140 @ SV144 @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[776]) ).
thf(804,plain,
! [SV144: $i,SV140: $i,SV123: $i] :
( ( ( ~ ! [SY277: $i,SY278: $i] :
( ~ ( on_path @ SY277 @ SV123 )
| ~ ( on_path @ SY278 @ SV123 )
| ~ ( sequential @ SY277 @ SY278 )
| ( precedes @ SY277 @ SY278 @ SV123 ) ) )
= $false )
| ( ( path @ SV140 @ SV144 @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[776]) ).
thf(805,plain,
! [SV145: $i,SV141: $i,SV124: $i] :
( ( ( ~ ~ ( ~ ! [SY281: $i] :
( ! [SY282: $i] :
~ ( precedes @ SY281 @ SY282 @ SV124 )
| ( on_path @ SY281 @ SV124 ) )
| ~ ! [SY283: $i,SY284: $i] :
( ~ ( precedes @ SY283 @ SY284 @ SV124 )
| ( on_path @ SY284 @ SV124 ) ) ) )
= $false )
| ( ( path @ SV141 @ SV145 @ SV124 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[777]) ).
thf(806,plain,
! [SV145: $i,SV141: $i,SV124: $i] :
( ( ( ~ ~ ( ~ ! [SY285: $i,SY286: $i] :
( ~ ( precedes @ SY285 @ SY286 @ SV124 )
| ! [SY287: $i] :
( ~ ( precedes @ SY287 @ SY286 @ SV124 )
| ~ ( sequential @ SY285 @ SY287 ) )
| ~ ( sequential @ SY285 @ SY286 ) )
| ~ ! [SY288: $i,SY289: $i] :
( ~ ( precedes @ SY288 @ SY289 @ SV124 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY289 @ SY288 @ SV124 ) @ SY289 @ SV124 )
| ~ ( sequential @ SY288 @ ( sK9_E3 @ SY289 @ SY288 @ SV124 ) ) )
| ( sequential @ SY288 @ SY289 ) ) ) )
= $false )
| ( ( path @ SV141 @ SV145 @ SV124 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[777]) ).
thf(807,plain,
! [SV134: $i,SV125: $i,SV161: $i,SV142: $i] :
( ( ! [SY367: $i] :
( ~ ( precedes @ SV142 @ SV161 @ SY367 )
| ~ ( shortest_path @ SV125 @ SV134 @ SY367 ) )
| ! [SY368: $i] :
( ( ( tail_of @ SY368 )
!= ( tail_of @ SV142 ) )
| ( ( head_of @ SY368 )
!= ( head_of @ SV161 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[778]) ).
thf(808,plain,
! [SV134: $i,SV125: $i,SV162: $i,SV142: $i] :
( ( ! [SY369: $i] :
( ~ ( precedes @ SV142 @ SV162 @ SY369 )
| ~ ( shortest_path @ SV125 @ SV134 @ SY369 )
| ~ ( precedes @ SV162 @ SV142 @ SY369 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[779]) ).
thf(809,plain,
! [SV155: $i,SV150: $i,SV126: $i] :
( ( ( ~ ( ~ ( path @ SV126 @ SV150 @ ( sK8_P @ SV155 @ SV150 @ SV126 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SV155 ) @ ( length_of @ ( sK8_P @ SV155 @ SV150 @ SV126 ) ) ) )
| ( SV126 = SV150 )
| ~ ( path @ SV126 @ SV150 @ SV155 ) )
= $true )
| ( ( shortest_path @ SV126 @ SV150 @ SV155 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[782]) ).
thf(810,plain,
! [SV126: $i] :
( ( ! [SY299: $i,SY300: $i] :
( ~ ( shortest_path @ SV126 @ SY299 @ SY300 )
| ! [SY301: $i] :
( ~ ( path @ SV126 @ SY299 @ SY301 )
| ( less_or_equal @ ( length_of @ SY300 ) @ ( length_of @ SY301 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[783]) ).
thf(811,plain,
! [SV126: $i] :
( ( ~ ( ~ ! [SY302: $i] :
( ! [SY303: $i] :
~ ( shortest_path @ SV126 @ SY302 @ SY303 )
| ( SV126 != SY302 ) )
| ~ ! [SY304: $i,SY305: $i] :
( ~ ( shortest_path @ SV126 @ SY304 @ SY305 )
| ( path @ SV126 @ SY304 @ SY305 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[784]) ).
thf(812,plain,
! [SV151: $i,SV148: $i] :
( ( ( ( SV148 = SV151 )
| ~ ( edge @ SV148 )
| ~ ( edge @ SV151 ) )
= $true )
| ( ( ( ( head_of @ SV148 )
!= ( tail_of @ SV151 ) ) )
= $true )
| ( ( sequential @ SV148 @ SV151 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[785]) ).
thf(813,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[786]) ).
thf(814,plain,
! [SV163: $i] :
( ( ! [SY370: $i] :
( ~ ( sequential @ SV163 @ SY370 )
| ( ( head_of @ SV163 )
= ( tail_of @ SY370 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[787]) ).
thf(815,plain,
! [SV156: $i,SV152: $i,SV127: $i] :
( ( ( ~ ( edge @ SV127 )
| ~ ( edge @ SV152 )
| ~ ( edge @ SV156 )
| ~ ( sequential @ SV127 @ SV152 )
| ~ ( sequential @ SV152 @ SV156 )
| ~ ( sequential @ SV156 @ SV127 ) )
= $true )
| ( ( triangle @ SV127 @ SV152 @ SV156 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[788]) ).
thf(816,plain,
! [SV127: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY308: $i,SY309: $i] :
~ ( triangle @ SV127 @ SY308 @ SY309 )
| ( edge @ SV127 ) )
| ~ ! [SY310: $i] :
( ! [SY311: $i] :
~ ( triangle @ SV127 @ SY310 @ SY311 )
| ( edge @ SY310 ) ) )
| ~ ! [SY312: $i,SY313: $i] :
( ~ ( triangle @ SV127 @ SY312 @ SY313 )
| ( edge @ SY313 ) ) )
| ~ ! [SY314: $i] :
( ! [SY315: $i] :
~ ( triangle @ SV127 @ SY314 @ SY315 )
| ( sequential @ SV127 @ SY314 ) ) )
| ~ ! [SY316: $i,SY317: $i] :
( ~ ( triangle @ SV127 @ SY316 @ SY317 )
| ( sequential @ SY316 @ SY317 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[789]) ).
thf(817,plain,
! [SV127: $i] :
( ( ! [SY318: $i,SY319: $i] :
( ~ ( triangle @ SV127 @ SY318 @ SY319 )
| ( sequential @ SY319 @ SV127 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[790]) ).
thf(818,plain,
! [SV135: $i,SV128: $i,SV157: $i,SV164: $i] :
( ( ~ ( in_path @ SV164 @ SV157 )
| ~ ( path @ SV128 @ SV135 @ SV157 )
| ~ ( ~ ( on_path @ ( sK10_E @ SV164 @ SV157 @ SV135 @ SV128 ) @ SV157 )
| ~ ( ( SV164
= ( head_of @ ( sK10_E @ SV164 @ SV157 @ SV135 @ SV128 ) ) )
| ( SV164
= ( tail_of @ ( sK10_E @ SV164 @ SV157 @ SV135 @ SV128 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[791]) ).
thf(819,plain,
! [SV135: $i,SV128: $i,SV158: $i,SV165: $i] :
( ( ~ ( in_path @ SV165 @ SV158 )
| ~ ( path @ SV128 @ SV135 @ SV158 )
| ( vertex @ SV165 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[792]) ).
thf(820,plain,
! [SV119: $i] :
( ( ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV119 ) @ SV119 )
| ~ ( on_path @ ( sK7_SY80 @ SV119 ) @ SV119 ) ) )
= $false )
| ( ( ! [SY251: $i,SY252: $i] :
~ ( path @ SY251 @ SY252 @ SV119 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV119 )
= ( number_of_in @ triangles @ SV119 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[793]) ).
thf(821,plain,
! [SV119: $i] :
( ( ( ~ ( sequential @ ( sK6_E1 @ SV119 ) @ ( sK7_SY80 @ SV119 ) ) )
= $false )
| ( ( ! [SY251: $i,SY252: $i] :
~ ( path @ SY251 @ SY252 @ SV119 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV119 )
= ( number_of_in @ triangles @ SV119 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[793]) ).
thf(822,plain,
! [SV159: $i,SV119: $i] :
( ( ( triangle @ ( sK6_E1 @ SV119 ) @ ( sK7_SY80 @ SV119 ) @ SV159 )
= $false )
| ( ( ! [SY251: $i,SY252: $i] :
~ ( path @ SY251 @ SY252 @ SV119 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV119 )
= ( number_of_in @ triangles @ SV119 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[794]) ).
thf(823,plain,
! [SV143: $i,SV138: $i] :
( ( ( vertex @ SV138 )
= $false )
| ( ( ~ ( vertex @ SV143 ) )
= $true )
| ( ( SV138 = SV143 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV138
!= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
!= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
!= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
!= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV138
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
| ~ ( ( SV138
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) ) )
| ~ ~ ( ~ ( ( SV143
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
| ~ ( ( SV143
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV143 @ SV138 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[795]) ).
thf(824,plain,
! [SV120: $i] :
( ( ( ! [SY253: $i,SY254: $i] :
~ ( path @ SV120 @ SY253 @ SY254 ) )
= $true )
| ( ( vertex @ SV120 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[796]) ).
thf(825,plain,
! [SV166: $i,SV120: $i] :
( ( ! [SY371: $i] :
~ ( path @ SV120 @ SV166 @ SY371 )
| ( vertex @ SV166 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(826,plain,
! [SV153: $i,SV149: $i,SV120: $i] :
( ( ( path @ SV120 @ SV149 @ SV153 )
= $false )
| ( ( ~ ( ~ ~ ( ( SV120
!= ( tail_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( edge @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
| ~ ~ ( ~ ( ( SV149
!= ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
| ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ empty ) )
| ! [SY363: $i] :
( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ SY363 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ SY363 ) ) )
| ~ ~ ( ~ ( ( SV149
= ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ ( sK13_SY84 @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ ( sK13_SY84 @ SV153 @ SV149 @ SV120 ) ) ) )
| ~ ( ( SV153
= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ empty ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ ( sK12_SY85 @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ ( sK12_SY85 @ SV153 @ SV149 @ SV120 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[798]) ).
thf(827,plain,
! [SV132: $i,SV121: $i] :
( ( ! [SY327: $i,SY328: $i] :
( ~ ( on_path @ SY328 @ SY327 )
| ~ ( path @ SV121 @ SV132 @ SY327 )
| ( edge @ SY328 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[799]) ).
thf(828,plain,
! [SV132: $i,SV121: $i] :
( ( ! [SY329: $i,SY330: $i] :
( ~ ( on_path @ SY330 @ SY329 )
| ~ ( path @ SV121 @ SV132 @ SY329 )
| ( in_path @ ( head_of @ SY330 ) @ SY329 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[800]) ).
thf(829,plain,
! [SV132: $i,SV121: $i,SV154: $i,SV160: $i] :
( ( ( ~ ( on_path @ SV160 @ SV154 )
| ~ ( path @ SV121 @ SV132 @ SV154 ) )
= $true )
| ( ( in_path @ ( tail_of @ SV160 ) @ SV154 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[801]) ).
thf(830,plain,
! [SV139: $i,SV122: $i,SV133: $i] :
( ( ( vertex @ SV133 )
= $false )
| ( ( vertex @ SV122 )
= $false )
| ( ( ~ ( ~ ! [SY348: $i] :
( ( SV122
!= ( tail_of @ SY348 ) )
| ~ ( edge @ SY348 )
| ( SV133
!= ( head_of @ SY348 ) )
| ( SV139
!= ( path_cons @ SY348 @ empty ) ) )
| ~ ! [SY349: $i] :
( ( SV122
!= ( tail_of @ SY349 ) )
| ~ ( edge @ SY349 )
| ! [SY350: $i] :
( ( SV139
!= ( path_cons @ SY349 @ SY350 ) )
| ~ ( path @ ( head_of @ SY349 ) @ SV133 @ SY350 ) ) ) ) )
= $true )
| ( ( path @ SV122 @ SV133 @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[802]) ).
thf(831,plain,
! [SV144: $i,SV140: $i,SV123: $i] :
( ( ( ! [SY274: $i,SY275: $i] :
( ~ ( on_path @ SY274 @ SV123 )
| ~ ( on_path @ SY275 @ SV123 )
| ! [SY276: $i] :
( ~ ( precedes @ SY276 @ SY275 @ SV123 )
| ~ ( sequential @ SY274 @ SY276 ) )
| ( precedes @ SY274 @ SY275 @ SV123 ) ) )
= $true )
| ( ( path @ SV140 @ SV144 @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[803]) ).
thf(832,plain,
! [SV144: $i,SV140: $i,SV123: $i] :
( ( ( ! [SY277: $i,SY278: $i] :
( ~ ( on_path @ SY277 @ SV123 )
| ~ ( on_path @ SY278 @ SV123 )
| ~ ( sequential @ SY277 @ SY278 )
| ( precedes @ SY277 @ SY278 @ SV123 ) ) )
= $true )
| ( ( path @ SV140 @ SV144 @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[804]) ).
thf(833,plain,
! [SV145: $i,SV141: $i,SV124: $i] :
( ( ( ~ ( ~ ! [SY281: $i] :
( ! [SY282: $i] :
~ ( precedes @ SY281 @ SY282 @ SV124 )
| ( on_path @ SY281 @ SV124 ) )
| ~ ! [SY283: $i,SY284: $i] :
( ~ ( precedes @ SY283 @ SY284 @ SV124 )
| ( on_path @ SY284 @ SV124 ) ) ) )
= $true )
| ( ( path @ SV141 @ SV145 @ SV124 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[805]) ).
thf(834,plain,
! [SV145: $i,SV141: $i,SV124: $i] :
( ( ( ~ ( ~ ! [SY285: $i,SY286: $i] :
( ~ ( precedes @ SY285 @ SY286 @ SV124 )
| ! [SY287: $i] :
( ~ ( precedes @ SY287 @ SY286 @ SV124 )
| ~ ( sequential @ SY285 @ SY287 ) )
| ~ ( sequential @ SY285 @ SY286 ) )
| ~ ! [SY288: $i,SY289: $i] :
( ~ ( precedes @ SY288 @ SY289 @ SV124 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY289 @ SY288 @ SV124 ) @ SY289 @ SV124 )
| ~ ( sequential @ SY288 @ ( sK9_E3 @ SY289 @ SY288 @ SV124 ) ) )
| ( sequential @ SY288 @ SY289 ) ) ) )
= $true )
| ( ( path @ SV141 @ SV145 @ SV124 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[806]) ).
thf(835,plain,
! [SV134: $i,SV125: $i,SV161: $i,SV142: $i] :
( ( ( ! [SY367: $i] :
( ~ ( precedes @ SV142 @ SV161 @ SY367 )
| ~ ( shortest_path @ SV125 @ SV134 @ SY367 ) ) )
= $true )
| ( ( ! [SY368: $i] :
( ( ( tail_of @ SY368 )
!= ( tail_of @ SV142 ) )
| ( ( head_of @ SY368 )
!= ( head_of @ SV161 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[807]) ).
thf(836,plain,
! [SV134: $i,SV125: $i,SV167: $i,SV162: $i,SV142: $i] :
( ( ~ ( precedes @ SV142 @ SV162 @ SV167 )
| ~ ( shortest_path @ SV125 @ SV134 @ SV167 )
| ~ ( precedes @ SV162 @ SV142 @ SV167 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(837,plain,
! [SV155: $i,SV150: $i,SV126: $i] :
( ( ( ~ ( ~ ( path @ SV126 @ SV150 @ ( sK8_P @ SV155 @ SV150 @ SV126 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SV155 ) @ ( length_of @ ( sK8_P @ SV155 @ SV150 @ SV126 ) ) ) ) )
= $true )
| ( ( ( SV126 = SV150 )
| ~ ( path @ SV126 @ SV150 @ SV155 ) )
= $true )
| ( ( shortest_path @ SV126 @ SV150 @ SV155 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[809]) ).
thf(838,plain,
! [SV168: $i,SV126: $i] :
( ( ! [SY372: $i] :
( ~ ( shortest_path @ SV126 @ SV168 @ SY372 )
| ! [SY373: $i] :
( ~ ( path @ SV126 @ SV168 @ SY373 )
| ( less_or_equal @ ( length_of @ SY372 ) @ ( length_of @ SY373 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[810]) ).
thf(839,plain,
! [SV126: $i] :
( ( ~ ! [SY302: $i] :
( ! [SY303: $i] :
~ ( shortest_path @ SV126 @ SY302 @ SY303 )
| ( SV126 != SY302 ) )
| ~ ! [SY304: $i,SY305: $i] :
( ~ ( shortest_path @ SV126 @ SY304 @ SY305 )
| ( path @ SV126 @ SY304 @ SY305 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[811]) ).
thf(840,plain,
! [SV151: $i,SV148: $i] :
( ( ( SV148 = SV151 )
= $true )
| ( ( ~ ( edge @ SV148 )
| ~ ( edge @ SV151 ) )
= $true )
| ( ( ( ( head_of @ SV148 )
!= ( tail_of @ SV151 ) ) )
= $true )
| ( ( sequential @ SV148 @ SV151 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[812]) ).
thf(841,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[813]) ).
thf(842,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[813]) ).
thf(843,plain,
! [SV169: $i,SV163: $i] :
( ( ~ ( sequential @ SV163 @ SV169 )
| ( ( head_of @ SV163 )
= ( tail_of @ SV169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[814]) ).
thf(844,plain,
! [SV156: $i,SV152: $i,SV127: $i] :
( ( ( ~ ( edge @ SV127 )
| ~ ( edge @ SV152 )
| ~ ( edge @ SV156 )
| ~ ( sequential @ SV127 @ SV152 )
| ~ ( sequential @ SV152 @ SV156 ) )
= $true )
| ( ( ~ ( sequential @ SV156 @ SV127 ) )
= $true )
| ( ( triangle @ SV127 @ SV152 @ SV156 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[815]) ).
thf(845,plain,
! [SV127: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY308: $i,SY309: $i] :
~ ( triangle @ SV127 @ SY308 @ SY309 )
| ( edge @ SV127 ) )
| ~ ! [SY310: $i] :
( ! [SY311: $i] :
~ ( triangle @ SV127 @ SY310 @ SY311 )
| ( edge @ SY310 ) ) )
| ~ ! [SY312: $i,SY313: $i] :
( ~ ( triangle @ SV127 @ SY312 @ SY313 )
| ( edge @ SY313 ) ) )
| ~ ! [SY314: $i] :
( ! [SY315: $i] :
~ ( triangle @ SV127 @ SY314 @ SY315 )
| ( sequential @ SV127 @ SY314 ) ) )
| ~ ! [SY316: $i,SY317: $i] :
( ~ ( triangle @ SV127 @ SY316 @ SY317 )
| ( sequential @ SY316 @ SY317 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[816]) ).
thf(846,plain,
! [SV170: $i,SV127: $i] :
( ( ! [SY374: $i] :
( ~ ( triangle @ SV127 @ SV170 @ SY374 )
| ( sequential @ SY374 @ SV127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[817]) ).
thf(847,plain,
! [SV135: $i,SV128: $i,SV157: $i,SV164: $i] :
( ( ( ~ ( in_path @ SV164 @ SV157 )
| ~ ( path @ SV128 @ SV135 @ SV157 ) )
= $true )
| ( ( ~ ( ~ ( on_path @ ( sK10_E @ SV164 @ SV157 @ SV135 @ SV128 ) @ SV157 )
| ~ ( ( SV164
= ( head_of @ ( sK10_E @ SV164 @ SV157 @ SV135 @ SV128 ) ) )
| ( SV164
= ( tail_of @ ( sK10_E @ SV164 @ SV157 @ SV135 @ SV128 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[818]) ).
thf(848,plain,
! [SV135: $i,SV128: $i,SV158: $i,SV165: $i] :
( ( ( ~ ( in_path @ SV165 @ SV158 )
| ~ ( path @ SV128 @ SV135 @ SV158 ) )
= $true )
| ( ( vertex @ SV165 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[819]) ).
thf(849,plain,
! [SV119: $i] :
( ( ( ~ ( ~ ( on_path @ ( sK6_E1 @ SV119 ) @ SV119 )
| ~ ( on_path @ ( sK7_SY80 @ SV119 ) @ SV119 ) ) )
= $true )
| ( ( ! [SY251: $i,SY252: $i] :
~ ( path @ SY251 @ SY252 @ SV119 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV119 )
= ( number_of_in @ triangles @ SV119 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[820]) ).
thf(850,plain,
! [SV119: $i] :
( ( ( sequential @ ( sK6_E1 @ SV119 ) @ ( sK7_SY80 @ SV119 ) )
= $true )
| ( ( ! [SY251: $i,SY252: $i] :
~ ( path @ SY251 @ SY252 @ SV119 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV119 )
= ( number_of_in @ triangles @ SV119 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[821]) ).
thf(851,plain,
! [SV159: $i,SV119: $i,SV171: $i] :
( ( ( ! [SY375: $i] :
~ ( path @ SV171 @ SY375 @ SV119 ) )
= $true )
| ( ( triangle @ ( sK6_E1 @ SV119 ) @ ( sK7_SY80 @ SV119 ) @ SV159 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV119 )
= ( number_of_in @ triangles @ SV119 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[822]) ).
thf(852,plain,
! [SV138: $i,SV143: $i] :
( ( ( vertex @ SV143 )
= $false )
| ( ( vertex @ SV138 )
= $false )
| ( ( SV138 = SV143 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV138
!= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
!= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
!= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
!= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV138
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
| ~ ( ( SV138
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) ) )
| ~ ~ ( ~ ( ( SV143
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
| ~ ( ( SV143
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV143 @ SV138 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[823]) ).
thf(853,plain,
! [SV172: $i,SV120: $i] :
( ( ( ! [SY376: $i] :
~ ( path @ SV120 @ SV172 @ SY376 ) )
= $true )
| ( ( vertex @ SV120 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[824]) ).
thf(854,plain,
! [SV166: $i,SV120: $i] :
( ( ( ! [SY371: $i] :
~ ( path @ SV120 @ SV166 @ SY371 ) )
= $true )
| ( ( vertex @ SV166 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[825]) ).
thf(855,plain,
! [SV149: $i,SV153: $i,SV120: $i] :
( ( ( ~ ~ ( ( SV120
!= ( tail_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( edge @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
| ~ ~ ( ~ ( ( SV149
!= ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
| ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ empty ) )
| ! [SY363: $i] :
( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ SY363 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ SY363 ) ) )
| ~ ~ ( ~ ( ( SV149
= ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ ( sK13_SY84 @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ ( sK13_SY84 @ SV153 @ SV149 @ SV120 ) ) ) )
| ~ ( ( SV153
= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ empty ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ ( sK12_SY85 @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ ( sK12_SY85 @ SV153 @ SV149 @ SV120 ) ) ) ) ) ) )
= $false )
| ( ( path @ SV120 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[826]) ).
thf(856,plain,
! [SV132: $i,SV121: $i,SV173: $i] :
( ( ! [SY377: $i] :
( ~ ( on_path @ SY377 @ SV173 )
| ~ ( path @ SV121 @ SV132 @ SV173 )
| ( edge @ SY377 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(857,plain,
! [SV132: $i,SV121: $i,SV174: $i] :
( ( ! [SY378: $i] :
( ~ ( on_path @ SY378 @ SV174 )
| ~ ( path @ SV121 @ SV132 @ SV174 )
| ( in_path @ ( head_of @ SY378 ) @ SV174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(858,plain,
! [SV132: $i,SV121: $i,SV154: $i,SV160: $i] :
( ( ( ~ ( on_path @ SV160 @ SV154 ) )
= $true )
| ( ( ~ ( path @ SV121 @ SV132 @ SV154 ) )
= $true )
| ( ( in_path @ ( tail_of @ SV160 ) @ SV154 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[829]) ).
thf(859,plain,
! [SV139: $i,SV133: $i,SV122: $i] :
( ( ( ~ ! [SY348: $i] :
( ( SV122
!= ( tail_of @ SY348 ) )
| ~ ( edge @ SY348 )
| ( SV133
!= ( head_of @ SY348 ) )
| ( SV139
!= ( path_cons @ SY348 @ empty ) ) )
| ~ ! [SY349: $i] :
( ( SV122
!= ( tail_of @ SY349 ) )
| ~ ( edge @ SY349 )
| ! [SY350: $i] :
( ( SV139
!= ( path_cons @ SY349 @ SY350 ) )
| ~ ( path @ ( head_of @ SY349 ) @ SV133 @ SY350 ) ) ) )
= $false )
| ( ( vertex @ SV122 )
= $false )
| ( ( vertex @ SV133 )
= $false )
| ( ( path @ SV122 @ SV133 @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[830]) ).
thf(860,plain,
! [SV144: $i,SV140: $i,SV123: $i,SV175: $i] :
( ( ( ! [SY379: $i] :
( ~ ( on_path @ SV175 @ SV123 )
| ~ ( on_path @ SY379 @ SV123 )
| ! [SY380: $i] :
( ~ ( precedes @ SY380 @ SY379 @ SV123 )
| ~ ( sequential @ SV175 @ SY380 ) )
| ( precedes @ SV175 @ SY379 @ SV123 ) ) )
= $true )
| ( ( path @ SV140 @ SV144 @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[831]) ).
thf(861,plain,
! [SV144: $i,SV140: $i,SV123: $i,SV176: $i] :
( ( ( ! [SY381: $i] :
( ~ ( on_path @ SV176 @ SV123 )
| ~ ( on_path @ SY381 @ SV123 )
| ~ ( sequential @ SV176 @ SY381 )
| ( precedes @ SV176 @ SY381 @ SV123 ) ) )
= $true )
| ( ( path @ SV140 @ SV144 @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(862,plain,
! [SV145: $i,SV141: $i,SV124: $i] :
( ( ( ~ ! [SY281: $i] :
( ! [SY282: $i] :
~ ( precedes @ SY281 @ SY282 @ SV124 )
| ( on_path @ SY281 @ SV124 ) )
| ~ ! [SY283: $i,SY284: $i] :
( ~ ( precedes @ SY283 @ SY284 @ SV124 )
| ( on_path @ SY284 @ SV124 ) ) )
= $false )
| ( ( path @ SV141 @ SV145 @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[833]) ).
thf(863,plain,
! [SV145: $i,SV141: $i,SV124: $i] :
( ( ( ~ ! [SY285: $i,SY286: $i] :
( ~ ( precedes @ SY285 @ SY286 @ SV124 )
| ! [SY287: $i] :
( ~ ( precedes @ SY287 @ SY286 @ SV124 )
| ~ ( sequential @ SY285 @ SY287 ) )
| ~ ( sequential @ SY285 @ SY286 ) )
| ~ ! [SY288: $i,SY289: $i] :
( ~ ( precedes @ SY288 @ SY289 @ SV124 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY289 @ SY288 @ SV124 ) @ SY289 @ SV124 )
| ~ ( sequential @ SY288 @ ( sK9_E3 @ SY289 @ SY288 @ SV124 ) ) )
| ( sequential @ SY288 @ SY289 ) ) )
= $false )
| ( ( path @ SV141 @ SV145 @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[834]) ).
thf(864,plain,
! [SV134: $i,SV125: $i,SV177: $i,SV161: $i,SV142: $i] :
( ( ( ~ ( precedes @ SV142 @ SV161 @ SV177 )
| ~ ( shortest_path @ SV125 @ SV134 @ SV177 ) )
= $true )
| ( ( ! [SY368: $i] :
( ( ( tail_of @ SY368 )
!= ( tail_of @ SV142 ) )
| ( ( head_of @ SY368 )
!= ( head_of @ SV161 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(865,plain,
! [SV134: $i,SV125: $i,SV167: $i,SV162: $i,SV142: $i] :
( ( ( ~ ( precedes @ SV142 @ SV162 @ SV167 )
| ~ ( shortest_path @ SV125 @ SV134 @ SV167 ) )
= $true )
| ( ( ~ ( precedes @ SV162 @ SV142 @ SV167 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[836]) ).
thf(866,plain,
! [SV155: $i,SV150: $i,SV126: $i] :
( ( ( ~ ( path @ SV126 @ SV150 @ ( sK8_P @ SV155 @ SV150 @ SV126 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SV155 ) @ ( length_of @ ( sK8_P @ SV155 @ SV150 @ SV126 ) ) ) )
= $false )
| ( ( ( SV126 = SV150 )
| ~ ( path @ SV126 @ SV150 @ SV155 ) )
= $true )
| ( ( shortest_path @ SV126 @ SV150 @ SV155 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[837]) ).
thf(867,plain,
! [SV178: $i,SV168: $i,SV126: $i] :
( ( ~ ( shortest_path @ SV126 @ SV168 @ SV178 )
| ! [SY382: $i] :
( ~ ( path @ SV126 @ SV168 @ SY382 )
| ( less_or_equal @ ( length_of @ SV178 ) @ ( length_of @ SY382 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[838]) ).
thf(868,plain,
! [SV126: $i] :
( ( ~ ! [SY302: $i] :
( ! [SY303: $i] :
~ ( shortest_path @ SV126 @ SY302 @ SY303 )
| ( SV126 != SY302 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[839]) ).
thf(869,plain,
! [SV126: $i] :
( ( ~ ! [SY304: $i,SY305: $i] :
( ~ ( shortest_path @ SV126 @ SY304 @ SY305 )
| ( path @ SV126 @ SY304 @ SY305 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[839]) ).
thf(870,plain,
! [SV151: $i,SV148: $i] :
( ( ( ~ ( edge @ SV148 ) )
= $true )
| ( ( ~ ( edge @ SV151 ) )
= $true )
| ( ( SV148 = SV151 )
= $true )
| ( ( ( ( head_of @ SV148 )
!= ( tail_of @ SV151 ) ) )
= $true )
| ( ( sequential @ SV148 @ SV151 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[840]) ).
thf(871,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[841]) ).
thf(872,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[842]) ).
thf(873,plain,
! [SV169: $i,SV163: $i] :
( ( ( ~ ( sequential @ SV163 @ SV169 ) )
= $true )
| ( ( ( head_of @ SV163 )
= ( tail_of @ SV169 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[843]) ).
thf(874,plain,
! [SV156: $i,SV152: $i,SV127: $i] :
( ( ( ~ ( edge @ SV127 )
| ~ ( edge @ SV152 )
| ~ ( edge @ SV156 )
| ~ ( sequential @ SV127 @ SV152 ) )
= $true )
| ( ( ~ ( sequential @ SV152 @ SV156 ) )
= $true )
| ( ( ~ ( sequential @ SV156 @ SV127 ) )
= $true )
| ( ( triangle @ SV127 @ SV152 @ SV156 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[844]) ).
thf(875,plain,
! [SV127: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY308: $i,SY309: $i] :
~ ( triangle @ SV127 @ SY308 @ SY309 )
| ( edge @ SV127 ) )
| ~ ! [SY310: $i] :
( ! [SY311: $i] :
~ ( triangle @ SV127 @ SY310 @ SY311 )
| ( edge @ SY310 ) ) )
| ~ ! [SY312: $i,SY313: $i] :
( ~ ( triangle @ SV127 @ SY312 @ SY313 )
| ( edge @ SY313 ) ) )
| ~ ! [SY314: $i] :
( ! [SY315: $i] :
~ ( triangle @ SV127 @ SY314 @ SY315 )
| ( sequential @ SV127 @ SY314 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[845]) ).
thf(876,plain,
! [SV127: $i] :
( ( ~ ! [SY316: $i,SY317: $i] :
( ~ ( triangle @ SV127 @ SY316 @ SY317 )
| ( sequential @ SY316 @ SY317 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[845]) ).
thf(877,plain,
! [SV179: $i,SV170: $i,SV127: $i] :
( ( ~ ( triangle @ SV127 @ SV170 @ SV179 )
| ( sequential @ SV179 @ SV127 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[846]) ).
thf(878,plain,
! [SV135: $i,SV128: $i,SV157: $i,SV164: $i] :
( ( ( ~ ( in_path @ SV164 @ SV157 ) )
= $true )
| ( ( ~ ( path @ SV128 @ SV135 @ SV157 ) )
= $true )
| ( ( ~ ( ~ ( on_path @ ( sK10_E @ SV164 @ SV157 @ SV135 @ SV128 ) @ SV157 )
| ~ ( ( SV164
= ( head_of @ ( sK10_E @ SV164 @ SV157 @ SV135 @ SV128 ) ) )
| ( SV164
= ( tail_of @ ( sK10_E @ SV164 @ SV157 @ SV135 @ SV128 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[847]) ).
thf(879,plain,
! [SV135: $i,SV128: $i,SV158: $i,SV165: $i] :
( ( ( ~ ( in_path @ SV165 @ SV158 ) )
= $true )
| ( ( ~ ( path @ SV128 @ SV135 @ SV158 ) )
= $true )
| ( ( vertex @ SV165 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[848]) ).
thf(880,plain,
! [SV119: $i] :
( ( ( ~ ( on_path @ ( sK6_E1 @ SV119 ) @ SV119 )
| ~ ( on_path @ ( sK7_SY80 @ SV119 ) @ SV119 ) )
= $false )
| ( ( ! [SY251: $i,SY252: $i] :
~ ( path @ SY251 @ SY252 @ SV119 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV119 )
= ( number_of_in @ triangles @ SV119 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[849]) ).
thf(881,plain,
! [SV119: $i,SV180: $i] :
( ( ( ! [SY383: $i] :
~ ( path @ SV180 @ SY383 @ SV119 ) )
= $true )
| ( ( sequential @ ( sK6_E1 @ SV119 ) @ ( sK7_SY80 @ SV119 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV119 )
= ( number_of_in @ triangles @ SV119 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[850]) ).
thf(882,plain,
! [SV159: $i,SV119: $i,SV181: $i,SV171: $i] :
( ( ( ~ ( path @ SV171 @ SV181 @ SV119 ) )
= $true )
| ( ( triangle @ ( sK6_E1 @ SV119 ) @ ( sK7_SY80 @ SV119 ) @ SV159 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV119 )
= ( number_of_in @ triangles @ SV119 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[851]) ).
thf(883,plain,
! [SV143: $i,SV138: $i] :
( ( ( ~ ~ ( ~ ( ( SV138
!= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
!= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
!= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
!= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV138
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
| ~ ( ( SV138
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) ) )
| ~ ~ ( ~ ( ( SV143
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
| ~ ( ( SV143
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV143 @ SV138 ) ) )
= $false )
| ( ( SV138 = SV143 )
= $true )
| ( ( vertex @ SV138 )
= $false )
| ( ( vertex @ SV143 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[852]) ).
thf(884,plain,
! [SV182: $i,SV172: $i,SV120: $i] :
( ( ( ~ ( path @ SV120 @ SV172 @ SV182 ) )
= $true )
| ( ( vertex @ SV120 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[853]) ).
thf(885,plain,
! [SV183: $i,SV166: $i,SV120: $i] :
( ( ( ~ ( path @ SV120 @ SV166 @ SV183 ) )
= $true )
| ( ( vertex @ SV166 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[854]) ).
thf(886,plain,
! [SV149: $i,SV153: $i,SV120: $i] :
( ( ( ~ ~ ( ( SV120
!= ( tail_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( edge @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) ) )
= $false )
| ( ( path @ SV120 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[855]) ).
thf(887,plain,
! [SV120: $i,SV153: $i,SV149: $i] :
( ( ( ~ ~ ( ~ ( ( SV149
!= ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
| ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ empty ) )
| ! [SY363: $i] :
( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ SY363 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ SY363 ) ) )
| ~ ~ ( ~ ( ( SV149
= ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ ( sK13_SY84 @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ ( sK13_SY84 @ SV153 @ SV149 @ SV120 ) ) ) )
| ~ ( ( SV153
= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ empty ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ ( sK12_SY85 @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ ( sK12_SY85 @ SV153 @ SV149 @ SV120 ) ) ) ) ) ) )
= $false )
| ( ( path @ SV120 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[855]) ).
thf(888,plain,
! [SV132: $i,SV121: $i,SV173: $i,SV184: $i] :
( ( ~ ( on_path @ SV184 @ SV173 )
| ~ ( path @ SV121 @ SV132 @ SV173 )
| ( edge @ SV184 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[856]) ).
thf(889,plain,
! [SV132: $i,SV121: $i,SV174: $i,SV185: $i] :
( ( ~ ( on_path @ SV185 @ SV174 )
| ~ ( path @ SV121 @ SV132 @ SV174 )
| ( in_path @ ( head_of @ SV185 ) @ SV174 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(890,plain,
! [SV132: $i,SV121: $i,SV154: $i,SV160: $i] :
( ( ( on_path @ SV160 @ SV154 )
= $false )
| ( ( ~ ( path @ SV121 @ SV132 @ SV154 ) )
= $true )
| ( ( in_path @ ( tail_of @ SV160 ) @ SV154 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[858]) ).
thf(891,plain,
! [SV139: $i,SV133: $i,SV122: $i] :
( ( ( ~ ! [SY348: $i] :
( ( SV122
!= ( tail_of @ SY348 ) )
| ~ ( edge @ SY348 )
| ( SV133
!= ( head_of @ SY348 ) )
| ( SV139
!= ( path_cons @ SY348 @ empty ) ) ) )
= $false )
| ( ( vertex @ SV122 )
= $false )
| ( ( vertex @ SV133 )
= $false )
| ( ( path @ SV122 @ SV133 @ SV139 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[859]) ).
thf(892,plain,
! [SV133: $i,SV139: $i,SV122: $i] :
( ( ( ~ ! [SY349: $i] :
( ( SV122
!= ( tail_of @ SY349 ) )
| ~ ( edge @ SY349 )
| ! [SY350: $i] :
( ( SV139
!= ( path_cons @ SY349 @ SY350 ) )
| ~ ( path @ ( head_of @ SY349 ) @ SV133 @ SY350 ) ) ) )
= $false )
| ( ( vertex @ SV122 )
= $false )
| ( ( vertex @ SV133 )
= $false )
| ( ( path @ SV122 @ SV133 @ SV139 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[859]) ).
thf(893,plain,
! [SV144: $i,SV140: $i,SV186: $i,SV123: $i,SV175: $i] :
( ( ( ~ ( on_path @ SV175 @ SV123 )
| ~ ( on_path @ SV186 @ SV123 )
| ! [SY384: $i] :
( ~ ( precedes @ SY384 @ SV186 @ SV123 )
| ~ ( sequential @ SV175 @ SY384 ) )
| ( precedes @ SV175 @ SV186 @ SV123 ) )
= $true )
| ( ( path @ SV140 @ SV144 @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[860]) ).
thf(894,plain,
! [SV144: $i,SV140: $i,SV187: $i,SV123: $i,SV176: $i] :
( ( ( ~ ( on_path @ SV176 @ SV123 )
| ~ ( on_path @ SV187 @ SV123 )
| ~ ( sequential @ SV176 @ SV187 )
| ( precedes @ SV176 @ SV187 @ SV123 ) )
= $true )
| ( ( path @ SV140 @ SV144 @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(895,plain,
! [SV145: $i,SV141: $i,SV124: $i] :
( ( ( ~ ! [SY281: $i] :
( ! [SY282: $i] :
~ ( precedes @ SY281 @ SY282 @ SV124 )
| ( on_path @ SY281 @ SV124 ) ) )
= $false )
| ( ( path @ SV141 @ SV145 @ SV124 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[862]) ).
thf(896,plain,
! [SV145: $i,SV141: $i,SV124: $i] :
( ( ( ~ ! [SY283: $i,SY284: $i] :
( ~ ( precedes @ SY283 @ SY284 @ SV124 )
| ( on_path @ SY284 @ SV124 ) ) )
= $false )
| ( ( path @ SV141 @ SV145 @ SV124 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[862]) ).
thf(897,plain,
! [SV145: $i,SV141: $i,SV124: $i] :
( ( ( ~ ! [SY285: $i,SY286: $i] :
( ~ ( precedes @ SY285 @ SY286 @ SV124 )
| ! [SY287: $i] :
( ~ ( precedes @ SY287 @ SY286 @ SV124 )
| ~ ( sequential @ SY285 @ SY287 ) )
| ~ ( sequential @ SY285 @ SY286 ) ) )
= $false )
| ( ( path @ SV141 @ SV145 @ SV124 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[863]) ).
thf(898,plain,
! [SV145: $i,SV141: $i,SV124: $i] :
( ( ( ~ ! [SY288: $i,SY289: $i] :
( ~ ( precedes @ SY288 @ SY289 @ SV124 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY289 @ SY288 @ SV124 ) @ SY289 @ SV124 )
| ~ ( sequential @ SY288 @ ( sK9_E3 @ SY289 @ SY288 @ SV124 ) ) )
| ( sequential @ SY288 @ SY289 ) ) )
= $false )
| ( ( path @ SV141 @ SV145 @ SV124 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[863]) ).
thf(899,plain,
! [SV134: $i,SV125: $i,SV177: $i,SV161: $i,SV142: $i] :
( ( ( ~ ( precedes @ SV142 @ SV161 @ SV177 ) )
= $true )
| ( ( ~ ( shortest_path @ SV125 @ SV134 @ SV177 ) )
= $true )
| ( ( ! [SY368: $i] :
( ( ( tail_of @ SY368 )
!= ( tail_of @ SV142 ) )
| ( ( head_of @ SY368 )
!= ( head_of @ SV161 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[864]) ).
thf(900,plain,
! [SV134: $i,SV125: $i,SV167: $i,SV162: $i,SV142: $i] :
( ( ( ~ ( precedes @ SV142 @ SV162 @ SV167 ) )
= $true )
| ( ( ~ ( shortest_path @ SV125 @ SV134 @ SV167 ) )
= $true )
| ( ( ~ ( precedes @ SV162 @ SV142 @ SV167 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[865]) ).
thf(901,plain,
! [SV155: $i,SV150: $i,SV126: $i] :
( ( ( ~ ( path @ SV126 @ SV150 @ ( sK8_P @ SV155 @ SV150 @ SV126 ) ) )
= $false )
| ( ( ( SV126 = SV150 )
| ~ ( path @ SV126 @ SV150 @ SV155 ) )
= $true )
| ( ( shortest_path @ SV126 @ SV150 @ SV155 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[866]) ).
thf(902,plain,
! [SV126: $i,SV150: $i,SV155: $i] :
( ( ( ~ ~ ( less_or_equal @ ( length_of @ SV155 ) @ ( length_of @ ( sK8_P @ SV155 @ SV150 @ SV126 ) ) ) )
= $false )
| ( ( ( SV126 = SV150 )
| ~ ( path @ SV126 @ SV150 @ SV155 ) )
= $true )
| ( ( shortest_path @ SV126 @ SV150 @ SV155 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[866]) ).
thf(903,plain,
! [SV178: $i,SV168: $i,SV126: $i] :
( ( ( ~ ( shortest_path @ SV126 @ SV168 @ SV178 ) )
= $true )
| ( ( ! [SY382: $i] :
( ~ ( path @ SV126 @ SV168 @ SY382 )
| ( less_or_equal @ ( length_of @ SV178 ) @ ( length_of @ SY382 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[867]) ).
thf(904,plain,
! [SV126: $i] :
( ( ! [SY302: $i] :
( ! [SY303: $i] :
~ ( shortest_path @ SV126 @ SY302 @ SY303 )
| ( SV126 != SY302 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[868]) ).
thf(905,plain,
! [SV126: $i] :
( ( ! [SY304: $i,SY305: $i] :
( ~ ( shortest_path @ SV126 @ SY304 @ SY305 )
| ( path @ SV126 @ SY304 @ SY305 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[869]) ).
thf(906,plain,
! [SV151: $i,SV148: $i] :
( ( ( edge @ SV148 )
= $false )
| ( ( ~ ( edge @ SV151 ) )
= $true )
| ( ( SV148 = SV151 )
= $true )
| ( ( ( ( head_of @ SV148 )
!= ( tail_of @ SV151 ) ) )
= $true )
| ( ( sequential @ SV148 @ SV151 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[870]) ).
thf(907,plain,
! [SV188: $i] :
( ( ! [SY385: $i] :
( ~ ( sequential @ SV188 @ SY385 )
| ( SV188 != SY385 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[871]) ).
thf(908,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[872]) ).
thf(909,plain,
! [SV169: $i,SV163: $i] :
( ( ( sequential @ SV163 @ SV169 )
= $false )
| ( ( ( head_of @ SV163 )
= ( tail_of @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[873]) ).
thf(910,plain,
! [SV156: $i,SV152: $i,SV127: $i] :
( ( ( ~ ( edge @ SV127 )
| ~ ( edge @ SV152 )
| ~ ( edge @ SV156 ) )
= $true )
| ( ( ~ ( sequential @ SV127 @ SV152 ) )
= $true )
| ( ( ~ ( sequential @ SV152 @ SV156 ) )
= $true )
| ( ( ~ ( sequential @ SV156 @ SV127 ) )
= $true )
| ( ( triangle @ SV127 @ SV152 @ SV156 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[874]) ).
thf(911,plain,
! [SV127: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY308: $i,SY309: $i] :
~ ( triangle @ SV127 @ SY308 @ SY309 )
| ( edge @ SV127 ) )
| ~ ! [SY310: $i] :
( ! [SY311: $i] :
~ ( triangle @ SV127 @ SY310 @ SY311 )
| ( edge @ SY310 ) ) )
| ~ ! [SY312: $i,SY313: $i] :
( ~ ( triangle @ SV127 @ SY312 @ SY313 )
| ( edge @ SY313 ) ) )
| ~ ! [SY314: $i] :
( ! [SY315: $i] :
~ ( triangle @ SV127 @ SY314 @ SY315 )
| ( sequential @ SV127 @ SY314 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[875]) ).
thf(912,plain,
! [SV127: $i] :
( ( ! [SY316: $i,SY317: $i] :
( ~ ( triangle @ SV127 @ SY316 @ SY317 )
| ( sequential @ SY316 @ SY317 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[876]) ).
thf(913,plain,
! [SV179: $i,SV170: $i,SV127: $i] :
( ( ( ~ ( triangle @ SV127 @ SV170 @ SV179 ) )
= $true )
| ( ( sequential @ SV179 @ SV127 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[877]) ).
thf(914,plain,
! [SV135: $i,SV128: $i,SV157: $i,SV164: $i] :
( ( ( in_path @ SV164 @ SV157 )
= $false )
| ( ( ~ ( path @ SV128 @ SV135 @ SV157 ) )
= $true )
| ( ( ~ ( ~ ( on_path @ ( sK10_E @ SV164 @ SV157 @ SV135 @ SV128 ) @ SV157 )
| ~ ( ( SV164
= ( head_of @ ( sK10_E @ SV164 @ SV157 @ SV135 @ SV128 ) ) )
| ( SV164
= ( tail_of @ ( sK10_E @ SV164 @ SV157 @ SV135 @ SV128 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[878]) ).
thf(915,plain,
! [SV135: $i,SV128: $i,SV158: $i,SV165: $i] :
( ( ( in_path @ SV165 @ SV158 )
= $false )
| ( ( ~ ( path @ SV128 @ SV135 @ SV158 ) )
= $true )
| ( ( vertex @ SV165 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[879]) ).
thf(916,plain,
! [SV119: $i] :
( ( ( ~ ( on_path @ ( sK6_E1 @ SV119 ) @ SV119 ) )
= $false )
| ( ( ! [SY251: $i,SY252: $i] :
~ ( path @ SY251 @ SY252 @ SV119 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV119 )
= ( number_of_in @ triangles @ SV119 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[880]) ).
thf(917,plain,
! [SV119: $i] :
( ( ( ~ ( on_path @ ( sK7_SY80 @ SV119 ) @ SV119 ) )
= $false )
| ( ( ! [SY251: $i,SY252: $i] :
~ ( path @ SY251 @ SY252 @ SV119 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV119 )
= ( number_of_in @ triangles @ SV119 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[880]) ).
thf(918,plain,
! [SV119: $i,SV189: $i,SV180: $i] :
( ( ( ~ ( path @ SV180 @ SV189 @ SV119 ) )
= $true )
| ( ( sequential @ ( sK6_E1 @ SV119 ) @ ( sK7_SY80 @ SV119 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV119 )
= ( number_of_in @ triangles @ SV119 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[881]) ).
thf(919,plain,
! [SV159: $i,SV119: $i,SV181: $i,SV171: $i] :
( ( ( path @ SV171 @ SV181 @ SV119 )
= $false )
| ( ( triangle @ ( sK6_E1 @ SV119 ) @ ( sK7_SY80 @ SV119 ) @ SV159 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV119 )
= ( number_of_in @ triangles @ SV119 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[882]) ).
thf(920,plain,
! [SV143: $i,SV138: $i] :
( ( ( ~ ~ ( ~ ( ( SV138
!= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
!= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
!= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
!= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV138
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
| ~ ( ( SV138
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) ) )
| ~ ~ ( ~ ( ( SV143
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
| ~ ( ( SV143
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) ) ) ) ) )
= $false )
| ( ( SV138 = SV143 )
= $true )
| ( ( vertex @ SV138 )
= $false )
| ( ( vertex @ SV143 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[883]) ).
thf(921,plain,
! [SV138: $i,SV143: $i] :
( ( ( ~ ( edge @ ( sK14_E @ SV143 @ SV138 ) ) )
= $false )
| ( ( SV138 = SV143 )
= $true )
| ( ( vertex @ SV138 )
= $false )
| ( ( vertex @ SV143 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[883]) ).
thf(922,plain,
! [SV182: $i,SV172: $i,SV120: $i] :
( ( ( path @ SV120 @ SV172 @ SV182 )
= $false )
| ( ( vertex @ SV120 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[884]) ).
thf(923,plain,
! [SV183: $i,SV166: $i,SV120: $i] :
( ( ( path @ SV120 @ SV166 @ SV183 )
= $false )
| ( ( vertex @ SV166 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[885]) ).
thf(924,plain,
! [SV149: $i,SV153: $i,SV120: $i] :
( ( ( ~ ( ( SV120
!= ( tail_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( edge @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) ) )
= $true )
| ( ( path @ SV120 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[886]) ).
thf(925,plain,
! [SV120: $i,SV153: $i,SV149: $i] :
( ( ( ~ ( ~ ( ( SV149
!= ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
| ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ empty ) )
| ! [SY363: $i] :
( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ SY363 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ SY363 ) ) )
| ~ ~ ( ~ ( ( SV149
= ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ ( sK13_SY84 @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ ( sK13_SY84 @ SV153 @ SV149 @ SV120 ) ) ) )
| ~ ( ( SV153
= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ empty ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ ( sK12_SY85 @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ ( sK12_SY85 @ SV153 @ SV149 @ SV120 ) ) ) ) ) ) )
= $true )
| ( ( path @ SV120 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[887]) ).
thf(926,plain,
! [SV132: $i,SV121: $i,SV173: $i,SV184: $i] :
( ( ( ~ ( on_path @ SV184 @ SV173 )
| ~ ( path @ SV121 @ SV132 @ SV173 ) )
= $true )
| ( ( edge @ SV184 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[888]) ).
thf(927,plain,
! [SV132: $i,SV121: $i,SV174: $i,SV185: $i] :
( ( ( ~ ( on_path @ SV185 @ SV174 )
| ~ ( path @ SV121 @ SV132 @ SV174 ) )
= $true )
| ( ( in_path @ ( head_of @ SV185 ) @ SV174 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[889]) ).
thf(928,plain,
! [SV160: $i,SV154: $i,SV132: $i,SV121: $i] :
( ( ( path @ SV121 @ SV132 @ SV154 )
= $false )
| ( ( on_path @ SV160 @ SV154 )
= $false )
| ( ( in_path @ ( tail_of @ SV160 ) @ SV154 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[890]) ).
thf(929,plain,
! [SV139: $i,SV133: $i,SV122: $i] :
( ( ( ! [SY348: $i] :
( ( SV122
!= ( tail_of @ SY348 ) )
| ~ ( edge @ SY348 )
| ( SV133
!= ( head_of @ SY348 ) )
| ( SV139
!= ( path_cons @ SY348 @ empty ) ) ) )
= $true )
| ( ( vertex @ SV122 )
= $false )
| ( ( vertex @ SV133 )
= $false )
| ( ( path @ SV122 @ SV133 @ SV139 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[891]) ).
thf(930,plain,
! [SV133: $i,SV139: $i,SV122: $i] :
( ( ( ! [SY349: $i] :
( ( SV122
!= ( tail_of @ SY349 ) )
| ~ ( edge @ SY349 )
| ! [SY350: $i] :
( ( SV139
!= ( path_cons @ SY349 @ SY350 ) )
| ~ ( path @ ( head_of @ SY349 ) @ SV133 @ SY350 ) ) ) )
= $true )
| ( ( vertex @ SV122 )
= $false )
| ( ( vertex @ SV133 )
= $false )
| ( ( path @ SV122 @ SV133 @ SV139 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[892]) ).
thf(931,plain,
! [SV144: $i,SV140: $i,SV186: $i,SV123: $i,SV175: $i] :
( ( ( ~ ( on_path @ SV175 @ SV123 )
| ~ ( on_path @ SV186 @ SV123 )
| ! [SY384: $i] :
( ~ ( precedes @ SY384 @ SV186 @ SV123 )
| ~ ( sequential @ SV175 @ SY384 ) ) )
= $true )
| ( ( precedes @ SV175 @ SV186 @ SV123 )
= $true )
| ( ( path @ SV140 @ SV144 @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[893]) ).
thf(932,plain,
! [SV144: $i,SV140: $i,SV187: $i,SV123: $i,SV176: $i] :
( ( ( ~ ( on_path @ SV176 @ SV123 )
| ~ ( on_path @ SV187 @ SV123 )
| ~ ( sequential @ SV176 @ SV187 ) )
= $true )
| ( ( precedes @ SV176 @ SV187 @ SV123 )
= $true )
| ( ( path @ SV140 @ SV144 @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[894]) ).
thf(933,plain,
! [SV145: $i,SV141: $i,SV124: $i] :
( ( ( ! [SY281: $i] :
( ! [SY282: $i] :
~ ( precedes @ SY281 @ SY282 @ SV124 )
| ( on_path @ SY281 @ SV124 ) ) )
= $true )
| ( ( path @ SV141 @ SV145 @ SV124 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[895]) ).
thf(934,plain,
! [SV145: $i,SV141: $i,SV124: $i] :
( ( ( ! [SY283: $i,SY284: $i] :
( ~ ( precedes @ SY283 @ SY284 @ SV124 )
| ( on_path @ SY284 @ SV124 ) ) )
= $true )
| ( ( path @ SV141 @ SV145 @ SV124 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[896]) ).
thf(935,plain,
! [SV145: $i,SV141: $i,SV124: $i] :
( ( ( ! [SY285: $i,SY286: $i] :
( ~ ( precedes @ SY285 @ SY286 @ SV124 )
| ! [SY287: $i] :
( ~ ( precedes @ SY287 @ SY286 @ SV124 )
| ~ ( sequential @ SY285 @ SY287 ) )
| ~ ( sequential @ SY285 @ SY286 ) ) )
= $true )
| ( ( path @ SV141 @ SV145 @ SV124 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[897]) ).
thf(936,plain,
! [SV145: $i,SV141: $i,SV124: $i] :
( ( ( ! [SY288: $i,SY289: $i] :
( ~ ( precedes @ SY288 @ SY289 @ SV124 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY289 @ SY288 @ SV124 ) @ SY289 @ SV124 )
| ~ ( sequential @ SY288 @ ( sK9_E3 @ SY289 @ SY288 @ SV124 ) ) )
| ( sequential @ SY288 @ SY289 ) ) )
= $true )
| ( ( path @ SV141 @ SV145 @ SV124 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[898]) ).
thf(937,plain,
! [SV134: $i,SV125: $i,SV177: $i,SV161: $i,SV142: $i] :
( ( ( precedes @ SV142 @ SV161 @ SV177 )
= $false )
| ( ( ~ ( shortest_path @ SV125 @ SV134 @ SV177 ) )
= $true )
| ( ( ! [SY368: $i] :
( ( ( tail_of @ SY368 )
!= ( tail_of @ SV142 ) )
| ( ( head_of @ SY368 )
!= ( head_of @ SV161 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[899]) ).
thf(938,plain,
! [SV134: $i,SV125: $i,SV167: $i,SV162: $i,SV142: $i] :
( ( ( precedes @ SV142 @ SV162 @ SV167 )
= $false )
| ( ( ~ ( shortest_path @ SV125 @ SV134 @ SV167 ) )
= $true )
| ( ( ~ ( precedes @ SV162 @ SV142 @ SV167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[900]) ).
thf(939,plain,
! [SV155: $i,SV150: $i,SV126: $i] :
( ( ( path @ SV126 @ SV150 @ ( sK8_P @ SV155 @ SV150 @ SV126 ) )
= $true )
| ( ( ( SV126 = SV150 )
| ~ ( path @ SV126 @ SV150 @ SV155 ) )
= $true )
| ( ( shortest_path @ SV126 @ SV150 @ SV155 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[901]) ).
thf(940,plain,
! [SV126: $i,SV150: $i,SV155: $i] :
( ( ( ~ ( less_or_equal @ ( length_of @ SV155 ) @ ( length_of @ ( sK8_P @ SV155 @ SV150 @ SV126 ) ) ) )
= $true )
| ( ( ( SV126 = SV150 )
| ~ ( path @ SV126 @ SV150 @ SV155 ) )
= $true )
| ( ( shortest_path @ SV126 @ SV150 @ SV155 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[902]) ).
thf(941,plain,
! [SV178: $i,SV168: $i,SV126: $i] :
( ( ( shortest_path @ SV126 @ SV168 @ SV178 )
= $false )
| ( ( ! [SY382: $i] :
( ~ ( path @ SV126 @ SV168 @ SY382 )
| ( less_or_equal @ ( length_of @ SV178 ) @ ( length_of @ SY382 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[903]) ).
thf(942,plain,
! [SV190: $i,SV126: $i] :
( ( ! [SY386: $i] :
~ ( shortest_path @ SV126 @ SV190 @ SY386 )
| ( SV126 != SV190 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[904]) ).
thf(943,plain,
! [SV191: $i,SV126: $i] :
( ( ! [SY387: $i] :
( ~ ( shortest_path @ SV126 @ SV191 @ SY387 )
| ( path @ SV126 @ SV191 @ SY387 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[905]) ).
thf(944,plain,
! [SV148: $i,SV151: $i] :
( ( ( edge @ SV151 )
= $false )
| ( ( edge @ SV148 )
= $false )
| ( ( SV148 = SV151 )
= $true )
| ( ( ( ( head_of @ SV148 )
!= ( tail_of @ SV151 ) ) )
= $true )
| ( ( sequential @ SV148 @ SV151 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[906]) ).
thf(945,plain,
! [SV192: $i,SV188: $i] :
( ( ~ ( sequential @ SV188 @ SV192 )
| ( SV188 != SV192 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[907]) ).
thf(946,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[908]) ).
thf(947,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[908]) ).
thf(948,plain,
! [SV156: $i,SV152: $i,SV127: $i] :
( ( ( ~ ( edge @ SV127 )
| ~ ( edge @ SV152 ) )
= $true )
| ( ( ~ ( edge @ SV156 ) )
= $true )
| ( ( ~ ( sequential @ SV127 @ SV152 ) )
= $true )
| ( ( ~ ( sequential @ SV152 @ SV156 ) )
= $true )
| ( ( ~ ( sequential @ SV156 @ SV127 ) )
= $true )
| ( ( triangle @ SV127 @ SV152 @ SV156 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[910]) ).
thf(949,plain,
! [SV127: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( ! [SY308: $i,SY309: $i] :
~ ( triangle @ SV127 @ SY308 @ SY309 )
| ( edge @ SV127 ) )
| ~ ! [SY310: $i] :
( ! [SY311: $i] :
~ ( triangle @ SV127 @ SY310 @ SY311 )
| ( edge @ SY310 ) ) )
| ~ ! [SY312: $i,SY313: $i] :
( ~ ( triangle @ SV127 @ SY312 @ SY313 )
| ( edge @ SY313 ) ) )
| ~ ! [SY314: $i] :
( ! [SY315: $i] :
~ ( triangle @ SV127 @ SY314 @ SY315 )
| ( sequential @ SV127 @ SY314 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[911]) ).
thf(950,plain,
! [SV193: $i,SV127: $i] :
( ( ! [SY388: $i] :
( ~ ( triangle @ SV127 @ SV193 @ SY388 )
| ( sequential @ SV193 @ SY388 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[912]) ).
thf(951,plain,
! [SV179: $i,SV170: $i,SV127: $i] :
( ( ( triangle @ SV127 @ SV170 @ SV179 )
= $false )
| ( ( sequential @ SV179 @ SV127 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[913]) ).
thf(952,plain,
! [SV164: $i,SV157: $i,SV135: $i,SV128: $i] :
( ( ( path @ SV128 @ SV135 @ SV157 )
= $false )
| ( ( in_path @ SV164 @ SV157 )
= $false )
| ( ( ~ ( ~ ( on_path @ ( sK10_E @ SV164 @ SV157 @ SV135 @ SV128 ) @ SV157 )
| ~ ( ( SV164
= ( head_of @ ( sK10_E @ SV164 @ SV157 @ SV135 @ SV128 ) ) )
| ( SV164
= ( tail_of @ ( sK10_E @ SV164 @ SV157 @ SV135 @ SV128 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[914]) ).
thf(953,plain,
! [SV165: $i,SV158: $i,SV135: $i,SV128: $i] :
( ( ( path @ SV128 @ SV135 @ SV158 )
= $false )
| ( ( in_path @ SV165 @ SV158 )
= $false )
| ( ( vertex @ SV165 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[915]) ).
thf(954,plain,
! [SV119: $i] :
( ( ( on_path @ ( sK6_E1 @ SV119 ) @ SV119 )
= $true )
| ( ( ! [SY251: $i,SY252: $i] :
~ ( path @ SY251 @ SY252 @ SV119 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV119 )
= ( number_of_in @ triangles @ SV119 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[916]) ).
thf(955,plain,
! [SV119: $i] :
( ( ( on_path @ ( sK7_SY80 @ SV119 ) @ SV119 )
= $true )
| ( ( ! [SY251: $i,SY252: $i] :
~ ( path @ SY251 @ SY252 @ SV119 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV119 )
= ( number_of_in @ triangles @ SV119 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[917]) ).
thf(956,plain,
! [SV119: $i,SV189: $i,SV180: $i] :
( ( ( path @ SV180 @ SV189 @ SV119 )
= $false )
| ( ( sequential @ ( sK6_E1 @ SV119 ) @ ( sK7_SY80 @ SV119 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV119 )
= ( number_of_in @ triangles @ SV119 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[918]) ).
thf(957,plain,
! [SV143: $i,SV138: $i] :
( ( ( ~ ( ~ ( ( SV138
!= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
!= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
!= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
!= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV138
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
| ~ ( ( SV138
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) ) )
| ~ ~ ( ~ ( ( SV143
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
| ~ ( ( SV143
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) ) ) ) ) )
= $true )
| ( ( SV138 = SV143 )
= $true )
| ( ( vertex @ SV138 )
= $false )
| ( ( vertex @ SV143 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[920]) ).
thf(958,plain,
! [SV138: $i,SV143: $i] :
( ( ( edge @ ( sK14_E @ SV143 @ SV138 ) )
= $true )
| ( ( SV138 = SV143 )
= $true )
| ( ( vertex @ SV138 )
= $false )
| ( ( vertex @ SV143 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[921]) ).
thf(959,plain,
! [SV149: $i,SV153: $i,SV120: $i] :
( ( ( ( SV120
!= ( tail_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( edge @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
= $false )
| ( ( path @ SV120 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[924]) ).
thf(960,plain,
! [SV120: $i,SV153: $i,SV149: $i] :
( ( ( ~ ( ( SV149
!= ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
| ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ empty ) )
| ! [SY363: $i] :
( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ SY363 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ SY363 ) ) )
| ~ ~ ( ~ ( ( SV149
= ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ ( sK13_SY84 @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ ( sK13_SY84 @ SV153 @ SV149 @ SV120 ) ) ) )
| ~ ( ( SV153
= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ empty ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ ( sK12_SY85 @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ ( sK12_SY85 @ SV153 @ SV149 @ SV120 ) ) ) ) ) )
= $false )
| ( ( path @ SV120 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[925]) ).
thf(961,plain,
! [SV132: $i,SV121: $i,SV173: $i,SV184: $i] :
( ( ( ~ ( on_path @ SV184 @ SV173 ) )
= $true )
| ( ( ~ ( path @ SV121 @ SV132 @ SV173 ) )
= $true )
| ( ( edge @ SV184 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[926]) ).
thf(962,plain,
! [SV132: $i,SV121: $i,SV174: $i,SV185: $i] :
( ( ( ~ ( on_path @ SV185 @ SV174 ) )
= $true )
| ( ( ~ ( path @ SV121 @ SV132 @ SV174 ) )
= $true )
| ( ( in_path @ ( head_of @ SV185 ) @ SV174 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[927]) ).
thf(963,plain,
! [SV139: $i,SV133: $i,SV194: $i,SV122: $i] :
( ( ( ( SV122
!= ( tail_of @ SV194 ) )
| ~ ( edge @ SV194 )
| ( SV133
!= ( head_of @ SV194 ) )
| ( SV139
!= ( path_cons @ SV194 @ empty ) ) )
= $true )
| ( ( vertex @ SV122 )
= $false )
| ( ( vertex @ SV133 )
= $false )
| ( ( path @ SV122 @ SV133 @ SV139 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[929]) ).
thf(964,plain,
! [SV133: $i,SV139: $i,SV195: $i,SV122: $i] :
( ( ( ( SV122
!= ( tail_of @ SV195 ) )
| ~ ( edge @ SV195 )
| ! [SY389: $i] :
( ( SV139
!= ( path_cons @ SV195 @ SY389 ) )
| ~ ( path @ ( head_of @ SV195 ) @ SV133 @ SY389 ) ) )
= $true )
| ( ( vertex @ SV122 )
= $false )
| ( ( vertex @ SV133 )
= $false )
| ( ( path @ SV122 @ SV133 @ SV139 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[930]) ).
thf(965,plain,
! [SV144: $i,SV140: $i,SV186: $i,SV123: $i,SV175: $i] :
( ( ( ~ ( on_path @ SV175 @ SV123 )
| ~ ( on_path @ SV186 @ SV123 ) )
= $true )
| ( ( ! [SY384: $i] :
( ~ ( precedes @ SY384 @ SV186 @ SV123 )
| ~ ( sequential @ SV175 @ SY384 ) ) )
= $true )
| ( ( precedes @ SV175 @ SV186 @ SV123 )
= $true )
| ( ( path @ SV140 @ SV144 @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[931]) ).
thf(966,plain,
! [SV144: $i,SV140: $i,SV187: $i,SV123: $i,SV176: $i] :
( ( ( ~ ( on_path @ SV176 @ SV123 )
| ~ ( on_path @ SV187 @ SV123 ) )
= $true )
| ( ( ~ ( sequential @ SV176 @ SV187 ) )
= $true )
| ( ( precedes @ SV176 @ SV187 @ SV123 )
= $true )
| ( ( path @ SV140 @ SV144 @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[932]) ).
thf(967,plain,
! [SV145: $i,SV141: $i,SV124: $i,SV196: $i] :
( ( ( ! [SY390: $i] :
~ ( precedes @ SV196 @ SY390 @ SV124 )
| ( on_path @ SV196 @ SV124 ) )
= $true )
| ( ( path @ SV141 @ SV145 @ SV124 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[933]) ).
thf(968,plain,
! [SV145: $i,SV141: $i,SV124: $i,SV197: $i] :
( ( ( ! [SY391: $i] :
( ~ ( precedes @ SV197 @ SY391 @ SV124 )
| ( on_path @ SY391 @ SV124 ) ) )
= $true )
| ( ( path @ SV141 @ SV145 @ SV124 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[934]) ).
thf(969,plain,
! [SV145: $i,SV141: $i,SV124: $i,SV198: $i] :
( ( ( ! [SY392: $i] :
( ~ ( precedes @ SV198 @ SY392 @ SV124 )
| ! [SY393: $i] :
( ~ ( precedes @ SY393 @ SY392 @ SV124 )
| ~ ( sequential @ SV198 @ SY393 ) )
| ~ ( sequential @ SV198 @ SY392 ) ) )
= $true )
| ( ( path @ SV141 @ SV145 @ SV124 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[935]) ).
thf(970,plain,
! [SV145: $i,SV141: $i,SV124: $i,SV199: $i] :
( ( ( ! [SY394: $i] :
( ~ ( precedes @ SV199 @ SY394 @ SV124 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY394 @ SV199 @ SV124 ) @ SY394 @ SV124 )
| ~ ( sequential @ SV199 @ ( sK9_E3 @ SY394 @ SV199 @ SV124 ) ) )
| ( sequential @ SV199 @ SY394 ) ) )
= $true )
| ( ( path @ SV141 @ SV145 @ SV124 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[936]) ).
thf(971,plain,
! [SV161: $i,SV142: $i,SV177: $i,SV134: $i,SV125: $i] :
( ( ( shortest_path @ SV125 @ SV134 @ SV177 )
= $false )
| ( ( precedes @ SV142 @ SV161 @ SV177 )
= $false )
| ( ( ! [SY368: $i] :
( ( ( tail_of @ SY368 )
!= ( tail_of @ SV142 ) )
| ( ( head_of @ SY368 )
!= ( head_of @ SV161 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[937]) ).
thf(972,plain,
! [SV162: $i,SV142: $i,SV167: $i,SV134: $i,SV125: $i] :
( ( ( shortest_path @ SV125 @ SV134 @ SV167 )
= $false )
| ( ( precedes @ SV142 @ SV162 @ SV167 )
= $false )
| ( ( ~ ( precedes @ SV162 @ SV142 @ SV167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[938]) ).
thf(973,plain,
! [SV155: $i,SV150: $i,SV126: $i] :
( ( ( SV126 = SV150 )
= $true )
| ( ( ~ ( path @ SV126 @ SV150 @ SV155 ) )
= $true )
| ( ( path @ SV126 @ SV150 @ ( sK8_P @ SV155 @ SV150 @ SV126 ) )
= $true )
| ( ( shortest_path @ SV126 @ SV150 @ SV155 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[939]) ).
thf(974,plain,
! [SV126: $i,SV150: $i,SV155: $i] :
( ( ( less_or_equal @ ( length_of @ SV155 ) @ ( length_of @ ( sK8_P @ SV155 @ SV150 @ SV126 ) ) )
= $false )
| ( ( ( SV126 = SV150 )
| ~ ( path @ SV126 @ SV150 @ SV155 ) )
= $true )
| ( ( shortest_path @ SV126 @ SV150 @ SV155 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[940]) ).
thf(975,plain,
! [SV178: $i,SV200: $i,SV168: $i,SV126: $i] :
( ( ( ~ ( path @ SV126 @ SV168 @ SV200 )
| ( less_or_equal @ ( length_of @ SV178 ) @ ( length_of @ SV200 ) ) )
= $true )
| ( ( shortest_path @ SV126 @ SV168 @ SV178 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[941]) ).
thf(976,plain,
! [SV190: $i,SV126: $i] :
( ( ( ! [SY386: $i] :
~ ( shortest_path @ SV126 @ SV190 @ SY386 ) )
= $true )
| ( ( ( SV126 != SV190 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[942]) ).
thf(977,plain,
! [SV201: $i,SV191: $i,SV126: $i] :
( ( ~ ( shortest_path @ SV126 @ SV191 @ SV201 )
| ( path @ SV126 @ SV191 @ SV201 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[943]) ).
thf(978,plain,
! [SV151: $i,SV148: $i] :
( ( ( ( head_of @ SV148 )
= ( tail_of @ SV151 ) )
= $false )
| ( ( SV148 = SV151 )
= $true )
| ( ( edge @ SV148 )
= $false )
| ( ( edge @ SV151 )
= $false )
| ( ( sequential @ SV148 @ SV151 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[944]) ).
thf(979,plain,
! [SV192: $i,SV188: $i] :
( ( ( ~ ( sequential @ SV188 @ SV192 ) )
= $true )
| ( ( ( SV188 != SV192 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[945]) ).
thf(980,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[946]) ).
thf(981,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[947]) ).
thf(982,plain,
! [SV156: $i,SV152: $i,SV127: $i] :
( ( ( ~ ( edge @ SV127 ) )
= $true )
| ( ( ~ ( edge @ SV152 ) )
= $true )
| ( ( ~ ( edge @ SV156 ) )
= $true )
| ( ( ~ ( sequential @ SV127 @ SV152 ) )
= $true )
| ( ( ~ ( sequential @ SV152 @ SV156 ) )
= $true )
| ( ( ~ ( sequential @ SV156 @ SV127 ) )
= $true )
| ( ( triangle @ SV127 @ SV152 @ SV156 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[948]) ).
thf(983,plain,
! [SV127: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( ! [SY308: $i,SY309: $i] :
~ ( triangle @ SV127 @ SY308 @ SY309 )
| ( edge @ SV127 ) )
| ~ ! [SY310: $i] :
( ! [SY311: $i] :
~ ( triangle @ SV127 @ SY310 @ SY311 )
| ( edge @ SY310 ) ) )
| ~ ! [SY312: $i,SY313: $i] :
( ~ ( triangle @ SV127 @ SY312 @ SY313 )
| ( edge @ SY313 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[949]) ).
thf(984,plain,
! [SV127: $i] :
( ( ~ ! [SY314: $i] :
( ! [SY315: $i] :
~ ( triangle @ SV127 @ SY314 @ SY315 )
| ( sequential @ SV127 @ SY314 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[949]) ).
thf(985,plain,
! [SV202: $i,SV193: $i,SV127: $i] :
( ( ~ ( triangle @ SV127 @ SV193 @ SV202 )
| ( sequential @ SV193 @ SV202 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[950]) ).
thf(986,plain,
! [SV128: $i,SV135: $i,SV157: $i,SV164: $i] :
( ( ( ~ ( on_path @ ( sK10_E @ SV164 @ SV157 @ SV135 @ SV128 ) @ SV157 )
| ~ ( ( SV164
= ( head_of @ ( sK10_E @ SV164 @ SV157 @ SV135 @ SV128 ) ) )
| ( SV164
= ( tail_of @ ( sK10_E @ SV164 @ SV157 @ SV135 @ SV128 ) ) ) ) )
= $false )
| ( ( in_path @ SV164 @ SV157 )
= $false )
| ( ( path @ SV128 @ SV135 @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[952]) ).
thf(987,plain,
! [SV119: $i,SV203: $i] :
( ( ( ! [SY395: $i] :
~ ( path @ SV203 @ SY395 @ SV119 ) )
= $true )
| ( ( on_path @ ( sK6_E1 @ SV119 ) @ SV119 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV119 )
= ( number_of_in @ triangles @ SV119 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[954]) ).
thf(988,plain,
! [SV119: $i,SV204: $i] :
( ( ( ! [SY396: $i] :
~ ( path @ SV204 @ SY396 @ SV119 ) )
= $true )
| ( ( on_path @ ( sK7_SY80 @ SV119 ) @ SV119 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV119 )
= ( number_of_in @ triangles @ SV119 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[955]) ).
thf(989,plain,
! [SV143: $i,SV138: $i] :
( ( ( ~ ( ( SV138
!= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
!= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
!= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
!= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV138
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
| ~ ( ( SV138
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) ) )
| ~ ~ ( ~ ( ( SV143
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
| ~ ( ( SV143
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) ) ) ) )
= $false )
| ( ( SV138 = SV143 )
= $true )
| ( ( vertex @ SV138 )
= $false )
| ( ( vertex @ SV143 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[957]) ).
thf(990,plain,
! [SV149: $i,SV153: $i,SV120: $i] :
( ( ( ( SV120
!= ( tail_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) ) )
= $false )
| ( ( path @ SV120 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[959]) ).
thf(991,plain,
! [SV120: $i,SV149: $i,SV153: $i] :
( ( ( ~ ( edge @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
= $false )
| ( ( path @ SV120 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[959]) ).
thf(992,plain,
! [SV120: $i,SV153: $i,SV149: $i] :
( ( ( ~ ( ( SV149
!= ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
| ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ empty ) )
| ! [SY363: $i] :
( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ SY363 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ SY363 ) ) ) )
= $false )
| ( ( path @ SV120 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[960]) ).
thf(993,plain,
! [SV120: $i,SV153: $i,SV149: $i] :
( ( ( ~ ~ ( ~ ( ( SV149
= ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ ( sK13_SY84 @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ ( sK13_SY84 @ SV153 @ SV149 @ SV120 ) ) ) )
| ~ ( ( SV153
= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ empty ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ ( sK12_SY85 @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ ( sK12_SY85 @ SV153 @ SV149 @ SV120 ) ) ) ) ) )
= $false )
| ( ( path @ SV120 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[960]) ).
thf(994,plain,
! [SV132: $i,SV121: $i,SV173: $i,SV184: $i] :
( ( ( on_path @ SV184 @ SV173 )
= $false )
| ( ( ~ ( path @ SV121 @ SV132 @ SV173 ) )
= $true )
| ( ( edge @ SV184 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[961]) ).
thf(995,plain,
! [SV132: $i,SV121: $i,SV174: $i,SV185: $i] :
( ( ( on_path @ SV185 @ SV174 )
= $false )
| ( ( ~ ( path @ SV121 @ SV132 @ SV174 ) )
= $true )
| ( ( in_path @ ( head_of @ SV185 ) @ SV174 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[962]) ).
thf(996,plain,
! [SV139: $i,SV133: $i,SV194: $i,SV122: $i] :
( ( ( ( SV122
!= ( tail_of @ SV194 ) )
| ~ ( edge @ SV194 ) )
= $true )
| ( ( ( SV133
!= ( head_of @ SV194 ) )
| ( SV139
!= ( path_cons @ SV194 @ empty ) ) )
= $true )
| ( ( vertex @ SV122 )
= $false )
| ( ( vertex @ SV133 )
= $false )
| ( ( path @ SV122 @ SV133 @ SV139 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[963]) ).
thf(997,plain,
! [SV133: $i,SV139: $i,SV195: $i,SV122: $i] :
( ( ( ( SV122
!= ( tail_of @ SV195 ) )
| ~ ( edge @ SV195 ) )
= $true )
| ( ( ! [SY389: $i] :
( ( SV139
!= ( path_cons @ SV195 @ SY389 ) )
| ~ ( path @ ( head_of @ SV195 ) @ SV133 @ SY389 ) ) )
= $true )
| ( ( vertex @ SV122 )
= $false )
| ( ( vertex @ SV133 )
= $false )
| ( ( path @ SV122 @ SV133 @ SV139 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[964]) ).
thf(998,plain,
! [SV144: $i,SV140: $i,SV186: $i,SV123: $i,SV175: $i] :
( ( ( ~ ( on_path @ SV175 @ SV123 ) )
= $true )
| ( ( ~ ( on_path @ SV186 @ SV123 ) )
= $true )
| ( ( ! [SY384: $i] :
( ~ ( precedes @ SY384 @ SV186 @ SV123 )
| ~ ( sequential @ SV175 @ SY384 ) ) )
= $true )
| ( ( precedes @ SV175 @ SV186 @ SV123 )
= $true )
| ( ( path @ SV140 @ SV144 @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[965]) ).
thf(999,plain,
! [SV144: $i,SV140: $i,SV187: $i,SV123: $i,SV176: $i] :
( ( ( ~ ( on_path @ SV176 @ SV123 ) )
= $true )
| ( ( ~ ( on_path @ SV187 @ SV123 ) )
= $true )
| ( ( ~ ( sequential @ SV176 @ SV187 ) )
= $true )
| ( ( precedes @ SV176 @ SV187 @ SV123 )
= $true )
| ( ( path @ SV140 @ SV144 @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[966]) ).
thf(1000,plain,
! [SV145: $i,SV141: $i,SV124: $i,SV196: $i] :
( ( ( ! [SY390: $i] :
~ ( precedes @ SV196 @ SY390 @ SV124 ) )
= $true )
| ( ( on_path @ SV196 @ SV124 )
= $true )
| ( ( path @ SV141 @ SV145 @ SV124 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[967]) ).
thf(1001,plain,
! [SV145: $i,SV141: $i,SV124: $i,SV205: $i,SV197: $i] :
( ( ( ~ ( precedes @ SV197 @ SV205 @ SV124 )
| ( on_path @ SV205 @ SV124 ) )
= $true )
| ( ( path @ SV141 @ SV145 @ SV124 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[968]) ).
thf(1002,plain,
! [SV145: $i,SV141: $i,SV124: $i,SV206: $i,SV198: $i] :
( ( ( ~ ( precedes @ SV198 @ SV206 @ SV124 )
| ! [SY397: $i] :
( ~ ( precedes @ SY397 @ SV206 @ SV124 )
| ~ ( sequential @ SV198 @ SY397 ) )
| ~ ( sequential @ SV198 @ SV206 ) )
= $true )
| ( ( path @ SV141 @ SV145 @ SV124 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[969]) ).
thf(1003,plain,
! [SV145: $i,SV141: $i,SV124: $i,SV207: $i,SV199: $i] :
( ( ( ~ ( precedes @ SV199 @ SV207 @ SV124 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SV207 @ SV199 @ SV124 ) @ SV207 @ SV124 )
| ~ ( sequential @ SV199 @ ( sK9_E3 @ SV207 @ SV199 @ SV124 ) ) )
| ( sequential @ SV199 @ SV207 ) )
= $true )
| ( ( path @ SV141 @ SV145 @ SV124 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[970]) ).
thf(1004,plain,
! [SV134: $i,SV125: $i,SV177: $i,SV161: $i,SV142: $i,SV208: $i] :
( ( ( ( ( tail_of @ SV208 )
!= ( tail_of @ SV142 ) )
| ( ( head_of @ SV208 )
!= ( head_of @ SV161 ) ) )
= $true )
| ( ( precedes @ SV142 @ SV161 @ SV177 )
= $false )
| ( ( shortest_path @ SV125 @ SV134 @ SV177 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[971]) ).
thf(1005,plain,
! [SV134: $i,SV125: $i,SV167: $i,SV142: $i,SV162: $i] :
( ( ( precedes @ SV162 @ SV142 @ SV167 )
= $false )
| ( ( precedes @ SV142 @ SV162 @ SV167 )
= $false )
| ( ( shortest_path @ SV125 @ SV134 @ SV167 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[972]) ).
thf(1006,plain,
! [SV155: $i,SV150: $i,SV126: $i] :
( ( ( path @ SV126 @ SV150 @ SV155 )
= $false )
| ( ( SV126 = SV150 )
= $true )
| ( ( path @ SV126 @ SV150 @ ( sK8_P @ SV155 @ SV150 @ SV126 ) )
= $true )
| ( ( shortest_path @ SV126 @ SV150 @ SV155 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[973]) ).
thf(1007,plain,
! [SV155: $i,SV150: $i,SV126: $i] :
( ( ( SV126 = SV150 )
= $true )
| ( ( ~ ( path @ SV126 @ SV150 @ SV155 ) )
= $true )
| ( ( less_or_equal @ ( length_of @ SV155 ) @ ( length_of @ ( sK8_P @ SV155 @ SV150 @ SV126 ) ) )
= $false )
| ( ( shortest_path @ SV126 @ SV150 @ SV155 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[974]) ).
thf(1008,plain,
! [SV178: $i,SV200: $i,SV168: $i,SV126: $i] :
( ( ( ~ ( path @ SV126 @ SV168 @ SV200 ) )
= $true )
| ( ( less_or_equal @ ( length_of @ SV178 ) @ ( length_of @ SV200 ) )
= $true )
| ( ( shortest_path @ SV126 @ SV168 @ SV178 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[975]) ).
thf(1009,plain,
! [SV209: $i,SV190: $i,SV126: $i] :
( ( ( ~ ( shortest_path @ SV126 @ SV190 @ SV209 ) )
= $true )
| ( ( ( SV126 != SV190 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[976]) ).
thf(1010,plain,
! [SV201: $i,SV191: $i,SV126: $i] :
( ( ( ~ ( shortest_path @ SV126 @ SV191 @ SV201 ) )
= $true )
| ( ( path @ SV126 @ SV191 @ SV201 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[977]) ).
thf(1011,plain,
! [SV192: $i,SV188: $i] :
( ( ( sequential @ SV188 @ SV192 )
= $false )
| ( ( ( SV188 != SV192 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[979]) ).
thf(1012,plain,
! [SV210: $i] :
( ( ! [SY398: $i] :
~ ( sequential @ SV210 @ SY398 )
| ( edge @ SV210 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[980]) ).
thf(1013,plain,
! [SV211: $i] :
( ( ! [SY399: $i] :
( ~ ( sequential @ SV211 @ SY399 )
| ( edge @ SY399 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[981]) ).
thf(1014,plain,
! [SV156: $i,SV152: $i,SV127: $i] :
( ( ( edge @ SV127 )
= $false )
| ( ( ~ ( edge @ SV152 ) )
= $true )
| ( ( ~ ( edge @ SV156 ) )
= $true )
| ( ( ~ ( sequential @ SV127 @ SV152 ) )
= $true )
| ( ( ~ ( sequential @ SV152 @ SV156 ) )
= $true )
| ( ( ~ ( sequential @ SV156 @ SV127 ) )
= $true )
| ( ( triangle @ SV127 @ SV152 @ SV156 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[982]) ).
thf(1015,plain,
! [SV127: $i] :
( ( ~ ( ~ ~ ( ~ ( ! [SY308: $i,SY309: $i] :
~ ( triangle @ SV127 @ SY308 @ SY309 )
| ( edge @ SV127 ) )
| ~ ! [SY310: $i] :
( ! [SY311: $i] :
~ ( triangle @ SV127 @ SY310 @ SY311 )
| ( edge @ SY310 ) ) )
| ~ ! [SY312: $i,SY313: $i] :
( ~ ( triangle @ SV127 @ SY312 @ SY313 )
| ( edge @ SY313 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[983]) ).
thf(1016,plain,
! [SV127: $i] :
( ( ! [SY314: $i] :
( ! [SY315: $i] :
~ ( triangle @ SV127 @ SY314 @ SY315 )
| ( sequential @ SV127 @ SY314 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[984]) ).
thf(1017,plain,
! [SV202: $i,SV193: $i,SV127: $i] :
( ( ( ~ ( triangle @ SV127 @ SV193 @ SV202 ) )
= $true )
| ( ( sequential @ SV193 @ SV202 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[985]) ).
thf(1018,plain,
! [SV128: $i,SV135: $i,SV157: $i,SV164: $i] :
( ( ( ~ ( on_path @ ( sK10_E @ SV164 @ SV157 @ SV135 @ SV128 ) @ SV157 ) )
= $false )
| ( ( in_path @ SV164 @ SV157 )
= $false )
| ( ( path @ SV128 @ SV135 @ SV157 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[986]) ).
thf(1019,plain,
! [SV128: $i,SV135: $i,SV157: $i,SV164: $i] :
( ( ( ~ ( ( SV164
= ( head_of @ ( sK10_E @ SV164 @ SV157 @ SV135 @ SV128 ) ) )
| ( SV164
= ( tail_of @ ( sK10_E @ SV164 @ SV157 @ SV135 @ SV128 ) ) ) ) )
= $false )
| ( ( in_path @ SV164 @ SV157 )
= $false )
| ( ( path @ SV128 @ SV135 @ SV157 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[986]) ).
thf(1020,plain,
! [SV119: $i,SV212: $i,SV203: $i] :
( ( ( ~ ( path @ SV203 @ SV212 @ SV119 ) )
= $true )
| ( ( on_path @ ( sK6_E1 @ SV119 ) @ SV119 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV119 )
= ( number_of_in @ triangles @ SV119 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[987]) ).
thf(1021,plain,
! [SV119: $i,SV213: $i,SV204: $i] :
( ( ( ~ ( path @ SV204 @ SV213 @ SV119 ) )
= $true )
| ( ( on_path @ ( sK7_SY80 @ SV119 ) @ SV119 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV119 )
= ( number_of_in @ triangles @ SV119 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[988]) ).
thf(1022,plain,
! [SV143: $i,SV138: $i] :
( ( ( ~ ( ( SV138
!= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
!= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
!= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
!= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) ) )
= $false )
| ( ( SV138 = SV143 )
= $true )
| ( ( vertex @ SV138 )
= $false )
| ( ( vertex @ SV143 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[989]) ).
thf(1023,plain,
! [SV143: $i,SV138: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( SV138
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
| ~ ( ( SV138
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) ) )
| ~ ~ ( ~ ( ( SV143
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
| ~ ( ( SV143
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) ) ) ) )
= $false )
| ( ( SV138 = SV143 )
= $true )
| ( ( vertex @ SV138 )
= $false )
| ( ( vertex @ SV143 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[989]) ).
thf(1024,plain,
! [SV149: $i,SV153: $i,SV120: $i] :
( ( ( SV120
= ( tail_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
= $true )
| ( ( path @ SV120 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[990]) ).
thf(1025,plain,
! [SV120: $i,SV149: $i,SV153: $i] :
( ( ( edge @ ( sK11_E @ SV153 @ SV149 @ SV120 ) )
= $true )
| ( ( path @ SV120 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[991]) ).
thf(1026,plain,
! [SV120: $i,SV153: $i,SV149: $i] :
( ( ( ( SV149
!= ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
| ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ empty ) )
| ! [SY363: $i] :
( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ SY363 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ SY363 ) ) )
= $true )
| ( ( path @ SV120 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[992]) ).
thf(1027,plain,
! [SV120: $i,SV153: $i,SV149: $i] :
( ( ( ~ ( ~ ( ( SV149
= ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ ( sK13_SY84 @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ ( sK13_SY84 @ SV153 @ SV149 @ SV120 ) ) ) )
| ~ ( ( SV153
= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ empty ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ ( sK12_SY85 @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ ( sK12_SY85 @ SV153 @ SV149 @ SV120 ) ) ) ) ) )
= $true )
| ( ( path @ SV120 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[993]) ).
thf(1028,plain,
! [SV184: $i,SV173: $i,SV132: $i,SV121: $i] :
( ( ( path @ SV121 @ SV132 @ SV173 )
= $false )
| ( ( on_path @ SV184 @ SV173 )
= $false )
| ( ( edge @ SV184 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[994]) ).
thf(1029,plain,
! [SV185: $i,SV174: $i,SV132: $i,SV121: $i] :
( ( ( path @ SV121 @ SV132 @ SV174 )
= $false )
| ( ( on_path @ SV185 @ SV174 )
= $false )
| ( ( in_path @ ( head_of @ SV185 ) @ SV174 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[995]) ).
thf(1030,plain,
! [SV139: $i,SV133: $i,SV194: $i,SV122: $i] :
( ( ( ( SV122
!= ( tail_of @ SV194 ) ) )
= $true )
| ( ( ~ ( edge @ SV194 ) )
= $true )
| ( ( ( SV133
!= ( head_of @ SV194 ) )
| ( SV139
!= ( path_cons @ SV194 @ empty ) ) )
= $true )
| ( ( vertex @ SV122 )
= $false )
| ( ( vertex @ SV133 )
= $false )
| ( ( path @ SV122 @ SV133 @ SV139 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[996]) ).
thf(1031,plain,
! [SV133: $i,SV139: $i,SV195: $i,SV122: $i] :
( ( ( ( SV122
!= ( tail_of @ SV195 ) ) )
= $true )
| ( ( ~ ( edge @ SV195 ) )
= $true )
| ( ( ! [SY389: $i] :
( ( SV139
!= ( path_cons @ SV195 @ SY389 ) )
| ~ ( path @ ( head_of @ SV195 ) @ SV133 @ SY389 ) ) )
= $true )
| ( ( vertex @ SV122 )
= $false )
| ( ( vertex @ SV133 )
= $false )
| ( ( path @ SV122 @ SV133 @ SV139 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[997]) ).
thf(1032,plain,
! [SV144: $i,SV140: $i,SV186: $i,SV123: $i,SV175: $i] :
( ( ( on_path @ SV175 @ SV123 )
= $false )
| ( ( ~ ( on_path @ SV186 @ SV123 ) )
= $true )
| ( ( ! [SY384: $i] :
( ~ ( precedes @ SY384 @ SV186 @ SV123 )
| ~ ( sequential @ SV175 @ SY384 ) ) )
= $true )
| ( ( precedes @ SV175 @ SV186 @ SV123 )
= $true )
| ( ( path @ SV140 @ SV144 @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[998]) ).
thf(1033,plain,
! [SV144: $i,SV140: $i,SV187: $i,SV123: $i,SV176: $i] :
( ( ( on_path @ SV176 @ SV123 )
= $false )
| ( ( ~ ( on_path @ SV187 @ SV123 ) )
= $true )
| ( ( ~ ( sequential @ SV176 @ SV187 ) )
= $true )
| ( ( precedes @ SV176 @ SV187 @ SV123 )
= $true )
| ( ( path @ SV140 @ SV144 @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[999]) ).
thf(1034,plain,
! [SV145: $i,SV141: $i,SV124: $i,SV214: $i,SV196: $i] :
( ( ( ~ ( precedes @ SV196 @ SV214 @ SV124 ) )
= $true )
| ( ( on_path @ SV196 @ SV124 )
= $true )
| ( ( path @ SV141 @ SV145 @ SV124 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1000]) ).
thf(1035,plain,
! [SV145: $i,SV141: $i,SV124: $i,SV205: $i,SV197: $i] :
( ( ( ~ ( precedes @ SV197 @ SV205 @ SV124 ) )
= $true )
| ( ( on_path @ SV205 @ SV124 )
= $true )
| ( ( path @ SV141 @ SV145 @ SV124 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1001]) ).
thf(1036,plain,
! [SV145: $i,SV141: $i,SV124: $i,SV206: $i,SV198: $i] :
( ( ( ~ ( precedes @ SV198 @ SV206 @ SV124 ) )
= $true )
| ( ( ! [SY397: $i] :
( ~ ( precedes @ SY397 @ SV206 @ SV124 )
| ~ ( sequential @ SV198 @ SY397 ) )
| ~ ( sequential @ SV198 @ SV206 ) )
= $true )
| ( ( path @ SV141 @ SV145 @ SV124 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1002]) ).
thf(1037,plain,
! [SV145: $i,SV141: $i,SV124: $i,SV207: $i,SV199: $i] :
( ( ( ~ ( precedes @ SV199 @ SV207 @ SV124 ) )
= $true )
| ( ( ~ ( ~ ( precedes @ ( sK9_E3 @ SV207 @ SV199 @ SV124 ) @ SV207 @ SV124 )
| ~ ( sequential @ SV199 @ ( sK9_E3 @ SV207 @ SV199 @ SV124 ) ) )
| ( sequential @ SV199 @ SV207 ) )
= $true )
| ( ( path @ SV141 @ SV145 @ SV124 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1003]) ).
thf(1038,plain,
! [SV134: $i,SV125: $i,SV177: $i,SV161: $i,SV142: $i,SV208: $i] :
( ( ( ( ( tail_of @ SV208 )
!= ( tail_of @ SV142 ) ) )
= $true )
| ( ( ( ( head_of @ SV208 )
!= ( head_of @ SV161 ) ) )
= $true )
| ( ( precedes @ SV142 @ SV161 @ SV177 )
= $false )
| ( ( shortest_path @ SV125 @ SV134 @ SV177 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1004]) ).
thf(1039,plain,
! [SV155: $i,SV150: $i,SV126: $i] :
( ( ( path @ SV126 @ SV150 @ SV155 )
= $false )
| ( ( SV126 = SV150 )
= $true )
| ( ( less_or_equal @ ( length_of @ SV155 ) @ ( length_of @ ( sK8_P @ SV155 @ SV150 @ SV126 ) ) )
= $false )
| ( ( shortest_path @ SV126 @ SV150 @ SV155 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1007]) ).
thf(1040,plain,
! [SV178: $i,SV200: $i,SV168: $i,SV126: $i] :
( ( ( path @ SV126 @ SV168 @ SV200 )
= $false )
| ( ( less_or_equal @ ( length_of @ SV178 ) @ ( length_of @ SV200 ) )
= $true )
| ( ( shortest_path @ SV126 @ SV168 @ SV178 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1008]) ).
thf(1041,plain,
! [SV209: $i,SV190: $i,SV126: $i] :
( ( ( shortest_path @ SV126 @ SV190 @ SV209 )
= $false )
| ( ( ( SV126 != SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1009]) ).
thf(1042,plain,
! [SV201: $i,SV191: $i,SV126: $i] :
( ( ( shortest_path @ SV126 @ SV191 @ SV201 )
= $false )
| ( ( path @ SV126 @ SV191 @ SV201 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1010]) ).
thf(1043,plain,
! [SV192: $i,SV188: $i] :
( ( ( SV188 = SV192 )
= $false )
| ( ( sequential @ SV188 @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1011]) ).
thf(1044,plain,
! [SV210: $i] :
( ( ( ! [SY398: $i] :
~ ( sequential @ SV210 @ SY398 ) )
= $true )
| ( ( edge @ SV210 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1012]) ).
thf(1045,plain,
! [SV215: $i,SV211: $i] :
( ( ~ ( sequential @ SV211 @ SV215 )
| ( edge @ SV215 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1013]) ).
thf(1046,plain,
! [SV156: $i,SV127: $i,SV152: $i] :
( ( ( edge @ SV152 )
= $false )
| ( ( edge @ SV127 )
= $false )
| ( ( ~ ( edge @ SV156 ) )
= $true )
| ( ( ~ ( sequential @ SV127 @ SV152 ) )
= $true )
| ( ( ~ ( sequential @ SV152 @ SV156 ) )
= $true )
| ( ( ~ ( sequential @ SV156 @ SV127 ) )
= $true )
| ( ( triangle @ SV127 @ SV152 @ SV156 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1014]) ).
thf(1047,plain,
! [SV127: $i] :
( ( ~ ~ ( ~ ( ! [SY308: $i,SY309: $i] :
~ ( triangle @ SV127 @ SY308 @ SY309 )
| ( edge @ SV127 ) )
| ~ ! [SY310: $i] :
( ! [SY311: $i] :
~ ( triangle @ SV127 @ SY310 @ SY311 )
| ( edge @ SY310 ) ) )
| ~ ! [SY312: $i,SY313: $i] :
( ~ ( triangle @ SV127 @ SY312 @ SY313 )
| ( edge @ SY313 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1015]) ).
thf(1048,plain,
! [SV216: $i,SV127: $i] :
( ( ! [SY400: $i] :
~ ( triangle @ SV127 @ SV216 @ SY400 )
| ( sequential @ SV127 @ SV216 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1016]) ).
thf(1049,plain,
! [SV202: $i,SV193: $i,SV127: $i] :
( ( ( triangle @ SV127 @ SV193 @ SV202 )
= $false )
| ( ( sequential @ SV193 @ SV202 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1017]) ).
thf(1050,plain,
! [SV128: $i,SV135: $i,SV157: $i,SV164: $i] :
( ( ( on_path @ ( sK10_E @ SV164 @ SV157 @ SV135 @ SV128 ) @ SV157 )
= $true )
| ( ( in_path @ SV164 @ SV157 )
= $false )
| ( ( path @ SV128 @ SV135 @ SV157 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1018]) ).
thf(1051,plain,
! [SV128: $i,SV135: $i,SV157: $i,SV164: $i] :
( ( ( ( SV164
= ( head_of @ ( sK10_E @ SV164 @ SV157 @ SV135 @ SV128 ) ) )
| ( SV164
= ( tail_of @ ( sK10_E @ SV164 @ SV157 @ SV135 @ SV128 ) ) ) )
= $true )
| ( ( in_path @ SV164 @ SV157 )
= $false )
| ( ( path @ SV128 @ SV135 @ SV157 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1019]) ).
thf(1052,plain,
! [SV119: $i,SV212: $i,SV203: $i] :
( ( ( path @ SV203 @ SV212 @ SV119 )
= $false )
| ( ( on_path @ ( sK6_E1 @ SV119 ) @ SV119 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV119 )
= ( number_of_in @ triangles @ SV119 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1020]) ).
thf(1053,plain,
! [SV119: $i,SV213: $i,SV204: $i] :
( ( ( path @ SV204 @ SV213 @ SV119 )
= $false )
| ( ( on_path @ ( sK7_SY80 @ SV119 ) @ SV119 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV119 )
= ( number_of_in @ triangles @ SV119 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1021]) ).
thf(1054,plain,
! [SV143: $i,SV138: $i] :
( ( ( ( SV138
!= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
!= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
!= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
!= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
= $true )
| ( ( SV138 = SV143 )
= $true )
| ( ( vertex @ SV138 )
= $false )
| ( ( vertex @ SV143 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1022]) ).
thf(1055,plain,
! [SV143: $i,SV138: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( SV138
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
| ~ ( ( SV138
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) ) )
| ~ ~ ( ~ ( ( SV143
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
| ~ ( ( SV143
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) ) ) ) )
= $true )
| ( ( SV138 = SV143 )
= $true )
| ( ( vertex @ SV138 )
= $false )
| ( ( vertex @ SV143 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1023]) ).
thf(1056,plain,
! [SV120: $i,SV153: $i,SV149: $i] :
( ( ( ( SV149
!= ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
| ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ empty ) ) )
= $true )
| ( ( ! [SY363: $i] :
( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ SY363 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ SY363 ) ) )
= $true )
| ( ( path @ SV120 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1026]) ).
thf(1057,plain,
! [SV120: $i,SV153: $i,SV149: $i] :
( ( ( ~ ( ( SV149
= ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ ( sK13_SY84 @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ ( sK13_SY84 @ SV153 @ SV149 @ SV120 ) ) ) )
| ~ ( ( SV153
= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ empty ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ ( sK12_SY85 @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ ( sK12_SY85 @ SV153 @ SV149 @ SV120 ) ) ) ) )
= $false )
| ( ( path @ SV120 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1027]) ).
thf(1058,plain,
! [SV139: $i,SV133: $i,SV194: $i,SV122: $i] :
( ( ( SV122
= ( tail_of @ SV194 ) )
= $false )
| ( ( ~ ( edge @ SV194 ) )
= $true )
| ( ( ( SV133
!= ( head_of @ SV194 ) )
| ( SV139
!= ( path_cons @ SV194 @ empty ) ) )
= $true )
| ( ( vertex @ SV122 )
= $false )
| ( ( vertex @ SV133 )
= $false )
| ( ( path @ SV122 @ SV133 @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1030]) ).
thf(1059,plain,
! [SV133: $i,SV139: $i,SV195: $i,SV122: $i] :
( ( ( SV122
= ( tail_of @ SV195 ) )
= $false )
| ( ( ~ ( edge @ SV195 ) )
= $true )
| ( ( ! [SY389: $i] :
( ( SV139
!= ( path_cons @ SV195 @ SY389 ) )
| ~ ( path @ ( head_of @ SV195 ) @ SV133 @ SY389 ) ) )
= $true )
| ( ( vertex @ SV122 )
= $false )
| ( ( vertex @ SV133 )
= $false )
| ( ( path @ SV122 @ SV133 @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1031]) ).
thf(1060,plain,
! [SV144: $i,SV140: $i,SV175: $i,SV123: $i,SV186: $i] :
( ( ( on_path @ SV186 @ SV123 )
= $false )
| ( ( on_path @ SV175 @ SV123 )
= $false )
| ( ( ! [SY384: $i] :
( ~ ( precedes @ SY384 @ SV186 @ SV123 )
| ~ ( sequential @ SV175 @ SY384 ) ) )
= $true )
| ( ( precedes @ SV175 @ SV186 @ SV123 )
= $true )
| ( ( path @ SV140 @ SV144 @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1032]) ).
thf(1061,plain,
! [SV144: $i,SV140: $i,SV176: $i,SV123: $i,SV187: $i] :
( ( ( on_path @ SV187 @ SV123 )
= $false )
| ( ( on_path @ SV176 @ SV123 )
= $false )
| ( ( ~ ( sequential @ SV176 @ SV187 ) )
= $true )
| ( ( precedes @ SV176 @ SV187 @ SV123 )
= $true )
| ( ( path @ SV140 @ SV144 @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1033]) ).
thf(1062,plain,
! [SV145: $i,SV141: $i,SV124: $i,SV214: $i,SV196: $i] :
( ( ( precedes @ SV196 @ SV214 @ SV124 )
= $false )
| ( ( on_path @ SV196 @ SV124 )
= $true )
| ( ( path @ SV141 @ SV145 @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1034]) ).
thf(1063,plain,
! [SV145: $i,SV141: $i,SV124: $i,SV205: $i,SV197: $i] :
( ( ( precedes @ SV197 @ SV205 @ SV124 )
= $false )
| ( ( on_path @ SV205 @ SV124 )
= $true )
| ( ( path @ SV141 @ SV145 @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1035]) ).
thf(1064,plain,
! [SV145: $i,SV141: $i,SV124: $i,SV206: $i,SV198: $i] :
( ( ( precedes @ SV198 @ SV206 @ SV124 )
= $false )
| ( ( ! [SY397: $i] :
( ~ ( precedes @ SY397 @ SV206 @ SV124 )
| ~ ( sequential @ SV198 @ SY397 ) )
| ~ ( sequential @ SV198 @ SV206 ) )
= $true )
| ( ( path @ SV141 @ SV145 @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1036]) ).
thf(1065,plain,
! [SV145: $i,SV141: $i,SV124: $i,SV207: $i,SV199: $i] :
( ( ( precedes @ SV199 @ SV207 @ SV124 )
= $false )
| ( ( ~ ( ~ ( precedes @ ( sK9_E3 @ SV207 @ SV199 @ SV124 ) @ SV207 @ SV124 )
| ~ ( sequential @ SV199 @ ( sK9_E3 @ SV207 @ SV199 @ SV124 ) ) )
| ( sequential @ SV199 @ SV207 ) )
= $true )
| ( ( path @ SV141 @ SV145 @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1037]) ).
thf(1066,plain,
! [SV134: $i,SV125: $i,SV177: $i,SV161: $i,SV142: $i,SV208: $i] :
( ( ( ( tail_of @ SV208 )
= ( tail_of @ SV142 ) )
= $false )
| ( ( ( ( head_of @ SV208 )
!= ( head_of @ SV161 ) ) )
= $true )
| ( ( precedes @ SV142 @ SV161 @ SV177 )
= $false )
| ( ( shortest_path @ SV125 @ SV134 @ SV177 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1038]) ).
thf(1067,plain,
! [SV209: $i,SV190: $i,SV126: $i] :
( ( ( SV126 = SV190 )
= $false )
| ( ( shortest_path @ SV126 @ SV190 @ SV209 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1041]) ).
thf(1068,plain,
! [SV217: $i,SV210: $i] :
( ( ( ~ ( sequential @ SV210 @ SV217 ) )
= $true )
| ( ( edge @ SV210 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1044]) ).
thf(1069,plain,
! [SV215: $i,SV211: $i] :
( ( ( ~ ( sequential @ SV211 @ SV215 ) )
= $true )
| ( ( edge @ SV215 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1045]) ).
thf(1070,plain,
! [SV152: $i,SV127: $i,SV156: $i] :
( ( ( edge @ SV156 )
= $false )
| ( ( edge @ SV127 )
= $false )
| ( ( edge @ SV152 )
= $false )
| ( ( ~ ( sequential @ SV127 @ SV152 ) )
= $true )
| ( ( ~ ( sequential @ SV152 @ SV156 ) )
= $true )
| ( ( ~ ( sequential @ SV156 @ SV127 ) )
= $true )
| ( ( triangle @ SV127 @ SV152 @ SV156 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1046]) ).
thf(1071,plain,
! [SV127: $i] :
( ( ~ ~ ( ~ ( ! [SY308: $i,SY309: $i] :
~ ( triangle @ SV127 @ SY308 @ SY309 )
| ( edge @ SV127 ) )
| ~ ! [SY310: $i] :
( ! [SY311: $i] :
~ ( triangle @ SV127 @ SY310 @ SY311 )
| ( edge @ SY310 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1047]) ).
thf(1072,plain,
! [SV127: $i] :
( ( ~ ! [SY312: $i,SY313: $i] :
( ~ ( triangle @ SV127 @ SY312 @ SY313 )
| ( edge @ SY313 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1047]) ).
thf(1073,plain,
! [SV216: $i,SV127: $i] :
( ( ( ! [SY400: $i] :
~ ( triangle @ SV127 @ SV216 @ SY400 ) )
= $true )
| ( ( sequential @ SV127 @ SV216 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1048]) ).
thf(1074,plain,
! [SV128: $i,SV135: $i,SV157: $i,SV164: $i] :
( ( ( SV164
= ( head_of @ ( sK10_E @ SV164 @ SV157 @ SV135 @ SV128 ) ) )
= $true )
| ( ( SV164
= ( tail_of @ ( sK10_E @ SV164 @ SV157 @ SV135 @ SV128 ) ) )
= $true )
| ( ( in_path @ SV164 @ SV157 )
= $false )
| ( ( path @ SV128 @ SV135 @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1051]) ).
thf(1075,plain,
! [SV143: $i,SV138: $i] :
( ( ( ( SV138
!= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
!= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
= $true )
| ( ( ( SV143
!= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
!= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
= $true )
| ( ( SV138 = SV143 )
= $true )
| ( ( vertex @ SV138 )
= $false )
| ( ( vertex @ SV143 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[1054]) ).
thf(1076,plain,
! [SV143: $i,SV138: $i] :
( ( ( ~ ~ ( ~ ( ( SV138
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
| ~ ( ( SV138
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) ) )
| ~ ~ ( ~ ( ( SV143
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
| ~ ( ( SV143
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) ) ) )
= $false )
| ( ( SV138 = SV143 )
= $true )
| ( ( vertex @ SV138 )
= $false )
| ( ( vertex @ SV143 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1055]) ).
thf(1077,plain,
! [SV120: $i,SV153: $i,SV149: $i] :
( ( ( ( SV149
!= ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) ) )
= $true )
| ( ( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ empty ) ) )
= $true )
| ( ( ! [SY363: $i] :
( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ SY363 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ SY363 ) ) )
= $true )
| ( ( path @ SV120 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1056]) ).
thf(1078,plain,
! [SV120: $i,SV153: $i,SV149: $i] :
( ( ( ~ ( ( SV149
= ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ ( sK13_SY84 @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ ( sK13_SY84 @ SV153 @ SV149 @ SV120 ) ) ) ) )
= $false )
| ( ( path @ SV120 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1057]) ).
thf(1079,plain,
! [SV120: $i,SV149: $i,SV153: $i] :
( ( ( ~ ( ( SV153
= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ empty ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ ( sK12_SY85 @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ ( sK12_SY85 @ SV153 @ SV149 @ SV120 ) ) ) ) )
= $false )
| ( ( path @ SV120 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1057]) ).
thf(1080,plain,
! [SV139: $i,SV133: $i,SV122: $i,SV194: $i] :
( ( ( edge @ SV194 )
= $false )
| ( ( SV122
= ( tail_of @ SV194 ) )
= $false )
| ( ( ( SV133
!= ( head_of @ SV194 ) )
| ( SV139
!= ( path_cons @ SV194 @ empty ) ) )
= $true )
| ( ( vertex @ SV122 )
= $false )
| ( ( vertex @ SV133 )
= $false )
| ( ( path @ SV122 @ SV133 @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1058]) ).
thf(1081,plain,
! [SV133: $i,SV139: $i,SV122: $i,SV195: $i] :
( ( ( edge @ SV195 )
= $false )
| ( ( SV122
= ( tail_of @ SV195 ) )
= $false )
| ( ( ! [SY389: $i] :
( ( SV139
!= ( path_cons @ SV195 @ SY389 ) )
| ~ ( path @ ( head_of @ SV195 ) @ SV133 @ SY389 ) ) )
= $true )
| ( ( vertex @ SV122 )
= $false )
| ( ( vertex @ SV133 )
= $false )
| ( ( path @ SV122 @ SV133 @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1059]) ).
thf(1082,plain,
! [SV144: $i,SV140: $i,SV175: $i,SV123: $i,SV186: $i,SV218: $i] :
( ( ( ~ ( precedes @ SV218 @ SV186 @ SV123 )
| ~ ( sequential @ SV175 @ SV218 ) )
= $true )
| ( ( on_path @ SV175 @ SV123 )
= $false )
| ( ( on_path @ SV186 @ SV123 )
= $false )
| ( ( precedes @ SV175 @ SV186 @ SV123 )
= $true )
| ( ( path @ SV140 @ SV144 @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1060]) ).
thf(1083,plain,
! [SV144: $i,SV140: $i,SV123: $i,SV187: $i,SV176: $i] :
( ( ( sequential @ SV176 @ SV187 )
= $false )
| ( ( on_path @ SV176 @ SV123 )
= $false )
| ( ( on_path @ SV187 @ SV123 )
= $false )
| ( ( precedes @ SV176 @ SV187 @ SV123 )
= $true )
| ( ( path @ SV140 @ SV144 @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1061]) ).
thf(1084,plain,
! [SV145: $i,SV141: $i,SV198: $i,SV124: $i,SV206: $i] :
( ( ( ! [SY397: $i] :
( ~ ( precedes @ SY397 @ SV206 @ SV124 )
| ~ ( sequential @ SV198 @ SY397 ) ) )
= $true )
| ( ( ~ ( sequential @ SV198 @ SV206 ) )
= $true )
| ( ( precedes @ SV198 @ SV206 @ SV124 )
= $false )
| ( ( path @ SV141 @ SV145 @ SV124 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1064]) ).
thf(1085,plain,
! [SV145: $i,SV141: $i,SV124: $i,SV199: $i,SV207: $i] :
( ( ( ~ ( ~ ( precedes @ ( sK9_E3 @ SV207 @ SV199 @ SV124 ) @ SV207 @ SV124 )
| ~ ( sequential @ SV199 @ ( sK9_E3 @ SV207 @ SV199 @ SV124 ) ) ) )
= $true )
| ( ( sequential @ SV199 @ SV207 )
= $true )
| ( ( precedes @ SV199 @ SV207 @ SV124 )
= $false )
| ( ( path @ SV141 @ SV145 @ SV124 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1065]) ).
thf(1086,plain,
! [SV134: $i,SV125: $i,SV177: $i,SV142: $i,SV161: $i,SV208: $i] :
( ( ( ( head_of @ SV208 )
= ( head_of @ SV161 ) )
= $false )
| ( ( ( tail_of @ SV208 )
= ( tail_of @ SV142 ) )
= $false )
| ( ( precedes @ SV142 @ SV161 @ SV177 )
= $false )
| ( ( shortest_path @ SV125 @ SV134 @ SV177 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1066]) ).
thf(1087,plain,
! [SV217: $i,SV210: $i] :
( ( ( sequential @ SV210 @ SV217 )
= $false )
| ( ( edge @ SV210 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1068]) ).
thf(1088,plain,
! [SV215: $i,SV211: $i] :
( ( ( sequential @ SV211 @ SV215 )
= $false )
| ( ( edge @ SV215 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1069]) ).
thf(1089,plain,
! [SV156: $i,SV152: $i,SV127: $i] :
( ( ( sequential @ SV127 @ SV152 )
= $false )
| ( ( edge @ SV152 )
= $false )
| ( ( edge @ SV127 )
= $false )
| ( ( edge @ SV156 )
= $false )
| ( ( ~ ( sequential @ SV152 @ SV156 ) )
= $true )
| ( ( ~ ( sequential @ SV156 @ SV127 ) )
= $true )
| ( ( triangle @ SV127 @ SV152 @ SV156 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1070]) ).
thf(1090,plain,
! [SV127: $i] :
( ( ~ ( ~ ( ! [SY308: $i,SY309: $i] :
~ ( triangle @ SV127 @ SY308 @ SY309 )
| ( edge @ SV127 ) )
| ~ ! [SY310: $i] :
( ! [SY311: $i] :
~ ( triangle @ SV127 @ SY310 @ SY311 )
| ( edge @ SY310 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1071]) ).
thf(1091,plain,
! [SV127: $i] :
( ( ! [SY312: $i,SY313: $i] :
( ~ ( triangle @ SV127 @ SY312 @ SY313 )
| ( edge @ SY313 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1072]) ).
thf(1092,plain,
! [SV219: $i,SV216: $i,SV127: $i] :
( ( ( ~ ( triangle @ SV127 @ SV216 @ SV219 ) )
= $true )
| ( ( sequential @ SV127 @ SV216 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1073]) ).
thf(1093,plain,
! [SV143: $i,SV138: $i] :
( ( ( ( SV138
!= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
= $true )
| ( ( ( SV143
!= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
= $true )
| ( ( ( SV143
!= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
!= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
= $true )
| ( ( SV138 = SV143 )
= $true )
| ( ( vertex @ SV138 )
= $false )
| ( ( vertex @ SV143 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[1075]) ).
thf(1094,plain,
! [SV143: $i,SV138: $i] :
( ( ( ~ ~ ( ~ ( ( SV138
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
| ~ ( ( SV138
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) ) ) )
= $false )
| ( ( SV138 = SV143 )
= $true )
| ( ( vertex @ SV138 )
= $false )
| ( ( vertex @ SV143 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[1076]) ).
thf(1095,plain,
! [SV138: $i,SV143: $i] :
( ( ( ~ ~ ( ~ ( ( SV143
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
| ~ ( ( SV143
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) ) ) )
= $false )
| ( ( SV138 = SV143 )
= $true )
| ( ( vertex @ SV138 )
= $false )
| ( ( vertex @ SV143 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[1076]) ).
thf(1096,plain,
! [SV120: $i,SV153: $i,SV149: $i] :
( ( ( SV149
= ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
= $false )
| ( ( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ empty ) ) )
= $true )
| ( ( ! [SY363: $i] :
( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ SY363 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ SY363 ) ) )
= $true )
| ( ( path @ SV120 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1077]) ).
thf(1097,plain,
! [SV120: $i,SV153: $i,SV149: $i] :
( ( ( ( SV149
= ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ ( sK13_SY84 @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ ( sK13_SY84 @ SV153 @ SV149 @ SV120 ) ) ) )
= $true )
| ( ( path @ SV120 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1078]) ).
thf(1098,plain,
! [SV120: $i,SV149: $i,SV153: $i] :
( ( ( ( SV153
= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ empty ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ ( sK12_SY85 @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ ( sK12_SY85 @ SV153 @ SV149 @ SV120 ) ) ) )
= $true )
| ( ( path @ SV120 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1079]) ).
thf(1099,plain,
! [SV122: $i,SV139: $i,SV194: $i,SV133: $i] :
( ( ( ( SV133
!= ( head_of @ SV194 ) ) )
= $true )
| ( ( ( SV139
!= ( path_cons @ SV194 @ empty ) ) )
= $true )
| ( ( SV122
= ( tail_of @ SV194 ) )
= $false )
| ( ( edge @ SV194 )
= $false )
| ( ( vertex @ SV122 )
= $false )
| ( ( vertex @ SV133 )
= $false )
| ( ( path @ SV122 @ SV133 @ SV139 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1080]) ).
thf(1100,plain,
! [SV122: $i,SV133: $i,SV220: $i,SV195: $i,SV139: $i] :
( ( ( ( SV139
!= ( path_cons @ SV195 @ SV220 ) )
| ~ ( path @ ( head_of @ SV195 ) @ SV133 @ SV220 ) )
= $true )
| ( ( SV122
= ( tail_of @ SV195 ) )
= $false )
| ( ( edge @ SV195 )
= $false )
| ( ( vertex @ SV122 )
= $false )
| ( ( vertex @ SV133 )
= $false )
| ( ( path @ SV122 @ SV133 @ SV139 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1081]) ).
thf(1101,plain,
! [SV144: $i,SV140: $i,SV175: $i,SV123: $i,SV186: $i,SV218: $i] :
( ( ( ~ ( precedes @ SV218 @ SV186 @ SV123 ) )
= $true )
| ( ( ~ ( sequential @ SV175 @ SV218 ) )
= $true )
| ( ( on_path @ SV175 @ SV123 )
= $false )
| ( ( on_path @ SV186 @ SV123 )
= $false )
| ( ( precedes @ SV175 @ SV186 @ SV123 )
= $true )
| ( ( path @ SV140 @ SV144 @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1082]) ).
thf(1102,plain,
! [SV145: $i,SV141: $i,SV198: $i,SV124: $i,SV206: $i,SV221: $i] :
( ( ( ~ ( precedes @ SV221 @ SV206 @ SV124 )
| ~ ( sequential @ SV198 @ SV221 ) )
= $true )
| ( ( ~ ( sequential @ SV198 @ SV206 ) )
= $true )
| ( ( precedes @ SV198 @ SV206 @ SV124 )
= $false )
| ( ( path @ SV141 @ SV145 @ SV124 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1084]) ).
thf(1103,plain,
! [SV145: $i,SV141: $i,SV124: $i,SV199: $i,SV207: $i] :
( ( ( ~ ( precedes @ ( sK9_E3 @ SV207 @ SV199 @ SV124 ) @ SV207 @ SV124 )
| ~ ( sequential @ SV199 @ ( sK9_E3 @ SV207 @ SV199 @ SV124 ) ) )
= $false )
| ( ( sequential @ SV199 @ SV207 )
= $true )
| ( ( precedes @ SV199 @ SV207 @ SV124 )
= $false )
| ( ( path @ SV141 @ SV145 @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1085]) ).
thf(1104,plain,
! [SV127: $i,SV156: $i,SV152: $i] :
( ( ( sequential @ SV152 @ SV156 )
= $false )
| ( ( edge @ SV156 )
= $false )
| ( ( edge @ SV127 )
= $false )
| ( ( edge @ SV152 )
= $false )
| ( ( sequential @ SV127 @ SV152 )
= $false )
| ( ( ~ ( sequential @ SV156 @ SV127 ) )
= $true )
| ( ( triangle @ SV127 @ SV152 @ SV156 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1089]) ).
thf(1105,plain,
! [SV127: $i] :
( ( ~ ( ! [SY308: $i,SY309: $i] :
~ ( triangle @ SV127 @ SY308 @ SY309 )
| ( edge @ SV127 ) )
| ~ ! [SY310: $i] :
( ! [SY311: $i] :
~ ( triangle @ SV127 @ SY310 @ SY311 )
| ( edge @ SY310 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1090]) ).
thf(1106,plain,
! [SV222: $i,SV127: $i] :
( ( ! [SY401: $i] :
( ~ ( triangle @ SV127 @ SV222 @ SY401 )
| ( edge @ SY401 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1091]) ).
thf(1107,plain,
! [SV219: $i,SV216: $i,SV127: $i] :
( ( ( triangle @ SV127 @ SV216 @ SV219 )
= $false )
| ( ( sequential @ SV127 @ SV216 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1092]) ).
thf(1108,plain,
! [SV143: $i,SV138: $i] :
( ( ( SV138
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
= $false )
| ( ( ( SV143
!= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
= $true )
| ( ( ( SV143
!= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
!= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
= $true )
| ( ( SV138 = SV143 )
= $true )
| ( ( vertex @ SV138 )
= $false )
| ( ( vertex @ SV143 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1093]) ).
thf(1109,plain,
! [SV143: $i,SV138: $i] :
( ( ( ~ ( ~ ( ( SV138
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
| ~ ( ( SV138
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) ) ) )
= $true )
| ( ( SV138 = SV143 )
= $true )
| ( ( vertex @ SV138 )
= $false )
| ( ( vertex @ SV143 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1094]) ).
thf(1110,plain,
! [SV138: $i,SV143: $i] :
( ( ( ~ ( ~ ( ( SV143
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
| ~ ( ( SV143
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) ) ) )
= $true )
| ( ( SV138 = SV143 )
= $true )
| ( ( vertex @ SV138 )
= $false )
| ( ( vertex @ SV143 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1095]) ).
thf(1111,plain,
! [SV120: $i,SV149: $i,SV153: $i] :
( ( ( SV153
= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ empty ) )
= $false )
| ( ( SV149
= ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
= $false )
| ( ( ! [SY363: $i] :
( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ SY363 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ SY363 ) ) )
= $true )
| ( ( path @ SV120 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1096]) ).
thf(1112,plain,
! [SV120: $i,SV153: $i,SV149: $i] :
( ( ( SV149
= ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
= $true )
| ( ( ~ ( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ ( sK13_SY84 @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ ( sK13_SY84 @ SV153 @ SV149 @ SV120 ) ) ) )
= $true )
| ( ( path @ SV120 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1097]) ).
thf(1113,plain,
! [SV120: $i,SV149: $i,SV153: $i] :
( ( ( SV153
= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ empty ) )
= $true )
| ( ( ~ ( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ ( sK12_SY85 @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ ( sK12_SY85 @ SV153 @ SV149 @ SV120 ) ) ) )
= $true )
| ( ( path @ SV120 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1098]) ).
thf(1114,plain,
! [SV122: $i,SV139: $i,SV194: $i,SV133: $i] :
( ( ( SV133
= ( head_of @ SV194 ) )
= $false )
| ( ( ( SV139
!= ( path_cons @ SV194 @ empty ) ) )
= $true )
| ( ( SV122
= ( tail_of @ SV194 ) )
= $false )
| ( ( edge @ SV194 )
= $false )
| ( ( vertex @ SV122 )
= $false )
| ( ( vertex @ SV133 )
= $false )
| ( ( path @ SV122 @ SV133 @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1099]) ).
thf(1115,plain,
! [SV122: $i,SV133: $i,SV220: $i,SV195: $i,SV139: $i] :
( ( ( ( SV139
!= ( path_cons @ SV195 @ SV220 ) ) )
= $true )
| ( ( ~ ( path @ ( head_of @ SV195 ) @ SV133 @ SV220 ) )
= $true )
| ( ( SV122
= ( tail_of @ SV195 ) )
= $false )
| ( ( edge @ SV195 )
= $false )
| ( ( vertex @ SV122 )
= $false )
| ( ( vertex @ SV133 )
= $false )
| ( ( path @ SV122 @ SV133 @ SV139 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1100]) ).
thf(1116,plain,
! [SV144: $i,SV140: $i,SV175: $i,SV123: $i,SV186: $i,SV218: $i] :
( ( ( precedes @ SV218 @ SV186 @ SV123 )
= $false )
| ( ( ~ ( sequential @ SV175 @ SV218 ) )
= $true )
| ( ( on_path @ SV175 @ SV123 )
= $false )
| ( ( on_path @ SV186 @ SV123 )
= $false )
| ( ( precedes @ SV175 @ SV186 @ SV123 )
= $true )
| ( ( path @ SV140 @ SV144 @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1101]) ).
thf(1117,plain,
! [SV145: $i,SV141: $i,SV198: $i,SV124: $i,SV206: $i,SV221: $i] :
( ( ( ~ ( precedes @ SV221 @ SV206 @ SV124 ) )
= $true )
| ( ( ~ ( sequential @ SV198 @ SV221 ) )
= $true )
| ( ( ~ ( sequential @ SV198 @ SV206 ) )
= $true )
| ( ( precedes @ SV198 @ SV206 @ SV124 )
= $false )
| ( ( path @ SV141 @ SV145 @ SV124 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1102]) ).
thf(1118,plain,
! [SV145: $i,SV141: $i,SV124: $i,SV199: $i,SV207: $i] :
( ( ( ~ ( precedes @ ( sK9_E3 @ SV207 @ SV199 @ SV124 ) @ SV207 @ SV124 ) )
= $false )
| ( ( sequential @ SV199 @ SV207 )
= $true )
| ( ( precedes @ SV199 @ SV207 @ SV124 )
= $false )
| ( ( path @ SV141 @ SV145 @ SV124 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1103]) ).
thf(1119,plain,
! [SV145: $i,SV141: $i,SV124: $i,SV207: $i,SV199: $i] :
( ( ( ~ ( sequential @ SV199 @ ( sK9_E3 @ SV207 @ SV199 @ SV124 ) ) )
= $false )
| ( ( sequential @ SV199 @ SV207 )
= $true )
| ( ( precedes @ SV199 @ SV207 @ SV124 )
= $false )
| ( ( path @ SV141 @ SV145 @ SV124 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1103]) ).
thf(1120,plain,
! [SV152: $i,SV127: $i,SV156: $i] :
( ( ( sequential @ SV156 @ SV127 )
= $false )
| ( ( sequential @ SV127 @ SV152 )
= $false )
| ( ( edge @ SV152 )
= $false )
| ( ( edge @ SV127 )
= $false )
| ( ( edge @ SV156 )
= $false )
| ( ( sequential @ SV152 @ SV156 )
= $false )
| ( ( triangle @ SV127 @ SV152 @ SV156 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1104]) ).
thf(1121,plain,
! [SV127: $i] :
( ( ~ ( ! [SY308: $i,SY309: $i] :
~ ( triangle @ SV127 @ SY308 @ SY309 )
| ( edge @ SV127 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1105]) ).
thf(1122,plain,
! [SV127: $i] :
( ( ~ ! [SY310: $i] :
( ! [SY311: $i] :
~ ( triangle @ SV127 @ SY310 @ SY311 )
| ( edge @ SY310 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1105]) ).
thf(1123,plain,
! [SV223: $i,SV222: $i,SV127: $i] :
( ( ~ ( triangle @ SV127 @ SV222 @ SV223 )
| ( edge @ SV223 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1106]) ).
thf(1124,plain,
! [SV138: $i,SV143: $i] :
( ( ( SV143
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
= $false )
| ( ( SV138
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
= $false )
| ( ( ( SV143
!= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
!= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
= $true )
| ( ( SV138 = SV143 )
= $true )
| ( ( vertex @ SV138 )
= $false )
| ( ( vertex @ SV143 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1108]) ).
thf(1125,plain,
! [SV143: $i,SV138: $i] :
( ( ( ~ ( ( SV138
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
| ~ ( ( SV138
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) ) )
= $false )
| ( ( SV138 = SV143 )
= $true )
| ( ( vertex @ SV138 )
= $false )
| ( ( vertex @ SV143 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1109]) ).
thf(1126,plain,
! [SV138: $i,SV143: $i] :
( ( ( ~ ( ( SV143
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
| ~ ( ( SV143
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) ) )
= $false )
| ( ( SV138 = SV143 )
= $true )
| ( ( vertex @ SV138 )
= $false )
| ( ( vertex @ SV143 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1110]) ).
thf(1127,plain,
! [SV224: $i,SV120: $i,SV149: $i,SV153: $i] :
( ( ( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ SV224 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ SV224 ) )
= $true )
| ( ( SV149
= ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
= $false )
| ( ( SV153
= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ empty ) )
= $false )
| ( ( path @ SV120 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1111]) ).
thf(1128,plain,
! [SV120: $i,SV149: $i,SV153: $i] :
( ( ( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ ( sK13_SY84 @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ ( sK13_SY84 @ SV153 @ SV149 @ SV120 ) ) )
= $false )
| ( ( SV149
= ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
= $true )
| ( ( path @ SV120 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1112]) ).
thf(1129,plain,
! [SV120: $i,SV149: $i,SV153: $i] :
( ( ( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ ( sK12_SY85 @ SV153 @ SV149 @ SV120 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ ( sK12_SY85 @ SV153 @ SV149 @ SV120 ) ) )
= $false )
| ( ( SV153
= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ empty ) )
= $true )
| ( ( path @ SV120 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1113]) ).
thf(1130,plain,
! [SV122: $i,SV133: $i,SV194: $i,SV139: $i] :
( ( ( SV139
= ( path_cons @ SV194 @ empty ) )
= $false )
| ( ( SV133
= ( head_of @ SV194 ) )
= $false )
| ( ( SV122
= ( tail_of @ SV194 ) )
= $false )
| ( ( edge @ SV194 )
= $false )
| ( ( vertex @ SV122 )
= $false )
| ( ( vertex @ SV133 )
= $false )
| ( ( path @ SV122 @ SV133 @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1114]) ).
thf(1131,plain,
! [SV122: $i,SV133: $i,SV220: $i,SV195: $i,SV139: $i] :
( ( ( SV139
= ( path_cons @ SV195 @ SV220 ) )
= $false )
| ( ( ~ ( path @ ( head_of @ SV195 ) @ SV133 @ SV220 ) )
= $true )
| ( ( SV122
= ( tail_of @ SV195 ) )
= $false )
| ( ( edge @ SV195 )
= $false )
| ( ( vertex @ SV122 )
= $false )
| ( ( vertex @ SV133 )
= $false )
| ( ( path @ SV122 @ SV133 @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1115]) ).
thf(1132,plain,
! [SV144: $i,SV140: $i,SV123: $i,SV186: $i,SV218: $i,SV175: $i] :
( ( ( sequential @ SV175 @ SV218 )
= $false )
| ( ( precedes @ SV218 @ SV186 @ SV123 )
= $false )
| ( ( on_path @ SV175 @ SV123 )
= $false )
| ( ( on_path @ SV186 @ SV123 )
= $false )
| ( ( precedes @ SV175 @ SV186 @ SV123 )
= $true )
| ( ( path @ SV140 @ SV144 @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1116]) ).
thf(1133,plain,
! [SV145: $i,SV141: $i,SV198: $i,SV124: $i,SV206: $i,SV221: $i] :
( ( ( precedes @ SV221 @ SV206 @ SV124 )
= $false )
| ( ( ~ ( sequential @ SV198 @ SV221 ) )
= $true )
| ( ( ~ ( sequential @ SV198 @ SV206 ) )
= $true )
| ( ( precedes @ SV198 @ SV206 @ SV124 )
= $false )
| ( ( path @ SV141 @ SV145 @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1117]) ).
thf(1134,plain,
! [SV145: $i,SV141: $i,SV124: $i,SV199: $i,SV207: $i] :
( ( ( precedes @ ( sK9_E3 @ SV207 @ SV199 @ SV124 ) @ SV207 @ SV124 )
= $true )
| ( ( sequential @ SV199 @ SV207 )
= $true )
| ( ( precedes @ SV199 @ SV207 @ SV124 )
= $false )
| ( ( path @ SV141 @ SV145 @ SV124 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1118]) ).
thf(1135,plain,
! [SV145: $i,SV141: $i,SV124: $i,SV207: $i,SV199: $i] :
( ( ( sequential @ SV199 @ ( sK9_E3 @ SV207 @ SV199 @ SV124 ) )
= $true )
| ( ( sequential @ SV199 @ SV207 )
= $true )
| ( ( precedes @ SV199 @ SV207 @ SV124 )
= $false )
| ( ( path @ SV141 @ SV145 @ SV124 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1119]) ).
thf(1136,plain,
! [SV127: $i] :
( ( ! [SY308: $i,SY309: $i] :
~ ( triangle @ SV127 @ SY308 @ SY309 )
| ( edge @ SV127 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1121]) ).
thf(1137,plain,
! [SV127: $i] :
( ( ! [SY310: $i] :
( ! [SY311: $i] :
~ ( triangle @ SV127 @ SY310 @ SY311 )
| ( edge @ SY310 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1122]) ).
thf(1138,plain,
! [SV223: $i,SV222: $i,SV127: $i] :
( ( ( ~ ( triangle @ SV127 @ SV222 @ SV223 ) )
= $true )
| ( ( edge @ SV223 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1123]) ).
thf(1139,plain,
! [SV138: $i,SV143: $i] :
( ( ( ( SV143
!= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
= $true )
| ( ( ( SV138
!= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
= $true )
| ( ( SV138
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
= $false )
| ( ( SV143
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
= $false )
| ( ( SV138 = SV143 )
= $true )
| ( ( vertex @ SV138 )
= $false )
| ( ( vertex @ SV143 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[1124]) ).
thf(1140,plain,
! [SV143: $i,SV138: $i] :
( ( ( ~ ( ( SV138
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) ) ) )
= $false )
| ( ( SV138 = SV143 )
= $true )
| ( ( vertex @ SV138 )
= $false )
| ( ( vertex @ SV143 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[1125]) ).
thf(1141,plain,
! [SV143: $i,SV138: $i] :
( ( ( ~ ( ( SV138
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) ) )
= $false )
| ( ( SV138 = SV143 )
= $true )
| ( ( vertex @ SV138 )
= $false )
| ( ( vertex @ SV143 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[1125]) ).
thf(1142,plain,
! [SV138: $i,SV143: $i] :
( ( ( ~ ( ( SV143
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) ) ) )
= $false )
| ( ( SV138 = SV143 )
= $true )
| ( ( vertex @ SV138 )
= $false )
| ( ( vertex @ SV143 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[1126]) ).
thf(1143,plain,
! [SV138: $i,SV143: $i] :
( ( ( ~ ( ( SV143
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) ) )
= $false )
| ( ( SV138 = SV143 )
= $true )
| ( ( vertex @ SV138 )
= $false )
| ( ( vertex @ SV143 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[1126]) ).
thf(1144,plain,
! [SV224: $i,SV120: $i,SV149: $i,SV153: $i] :
( ( ( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ SV224 ) ) )
= $true )
| ( ( ~ ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ SV224 ) )
= $true )
| ( ( SV149
= ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
= $false )
| ( ( SV153
= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ empty ) )
= $false )
| ( ( path @ SV120 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1127]) ).
thf(1145,plain,
! [SV120: $i,SV149: $i,SV153: $i] :
( ( ( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ ( sK13_SY84 @ SV153 @ SV149 @ SV120 ) ) ) )
= $false )
| ( ( SV149
= ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
= $true )
| ( ( path @ SV120 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1128]) ).
thf(1146,plain,
! [SV120: $i,SV149: $i,SV153: $i] :
( ( ( ~ ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ ( sK13_SY84 @ SV153 @ SV149 @ SV120 ) ) )
= $false )
| ( ( SV149
= ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
= $true )
| ( ( path @ SV120 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1128]) ).
thf(1147,plain,
! [SV120: $i,SV149: $i,SV153: $i] :
( ( ( ( SV153
!= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ ( sK12_SY85 @ SV153 @ SV149 @ SV120 ) ) ) )
= $false )
| ( ( SV153
= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ empty ) )
= $true )
| ( ( path @ SV120 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1129]) ).
thf(1148,plain,
! [SV120: $i,SV149: $i,SV153: $i] :
( ( ( ~ ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ ( sK12_SY85 @ SV153 @ SV149 @ SV120 ) ) )
= $false )
| ( ( SV153
= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ empty ) )
= $true )
| ( ( path @ SV120 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1129]) ).
thf(1149,plain,
! [SV122: $i,SV139: $i,SV220: $i,SV133: $i,SV195: $i] :
( ( ( path @ ( head_of @ SV195 ) @ SV133 @ SV220 )
= $false )
| ( ( SV139
= ( path_cons @ SV195 @ SV220 ) )
= $false )
| ( ( SV122
= ( tail_of @ SV195 ) )
= $false )
| ( ( edge @ SV195 )
= $false )
| ( ( vertex @ SV122 )
= $false )
| ( ( vertex @ SV133 )
= $false )
| ( ( path @ SV122 @ SV133 @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1131]) ).
thf(1150,plain,
! [SV145: $i,SV141: $i,SV124: $i,SV206: $i,SV221: $i,SV198: $i] :
( ( ( sequential @ SV198 @ SV221 )
= $false )
| ( ( precedes @ SV221 @ SV206 @ SV124 )
= $false )
| ( ( ~ ( sequential @ SV198 @ SV206 ) )
= $true )
| ( ( precedes @ SV198 @ SV206 @ SV124 )
= $false )
| ( ( path @ SV141 @ SV145 @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1133]) ).
thf(1151,plain,
! [SV127: $i] :
( ( ( ! [SY308: $i,SY309: $i] :
~ ( triangle @ SV127 @ SY308 @ SY309 ) )
= $true )
| ( ( edge @ SV127 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1136]) ).
thf(1152,plain,
! [SV225: $i,SV127: $i] :
( ( ! [SY402: $i] :
~ ( triangle @ SV127 @ SV225 @ SY402 )
| ( edge @ SV225 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1137]) ).
thf(1153,plain,
! [SV223: $i,SV222: $i,SV127: $i] :
( ( ( triangle @ SV127 @ SV222 @ SV223 )
= $false )
| ( ( edge @ SV223 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1138]) ).
thf(1154,plain,
! [SV138: $i,SV143: $i] :
( ( ( SV143
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
= $false )
| ( ( ( SV138
!= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
= $true )
| ( ( SV138
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
= $false )
| ( ( SV143
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
= $false )
| ( ( SV138 = SV143 )
= $true )
| ( ( vertex @ SV138 )
= $false )
| ( ( vertex @ SV143 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1139]) ).
thf(1155,plain,
! [SV143: $i,SV138: $i] :
( ( ( ( SV138
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
= $true )
| ( ( SV138 = SV143 )
= $true )
| ( ( vertex @ SV138 )
= $false )
| ( ( vertex @ SV143 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1140]) ).
thf(1156,plain,
! [SV143: $i,SV138: $i] :
( ( ( ( SV138
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
= $true )
| ( ( SV138 = SV143 )
= $true )
| ( ( vertex @ SV138 )
= $false )
| ( ( vertex @ SV143 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1141]) ).
thf(1157,plain,
! [SV138: $i,SV143: $i] :
( ( ( ( SV143
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV143
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
= $true )
| ( ( SV138 = SV143 )
= $true )
| ( ( vertex @ SV138 )
= $false )
| ( ( vertex @ SV143 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1142]) ).
thf(1158,plain,
! [SV138: $i,SV143: $i] :
( ( ( ( SV143
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
| ( SV138
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) ) )
= $true )
| ( ( SV138 = SV143 )
= $true )
| ( ( vertex @ SV138 )
= $false )
| ( ( vertex @ SV143 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1143]) ).
thf(1159,plain,
! [SV224: $i,SV120: $i,SV149: $i,SV153: $i] :
( ( ( SV153
= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ SV224 ) )
= $false )
| ( ( ~ ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ SV224 ) )
= $true )
| ( ( SV149
= ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
= $false )
| ( ( SV153
= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ empty ) )
= $false )
| ( ( path @ SV120 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1144]) ).
thf(1160,plain,
! [SV120: $i,SV149: $i,SV153: $i] :
( ( ( SV153
= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ ( sK13_SY84 @ SV153 @ SV149 @ SV120 ) ) )
= $true )
| ( ( SV149
= ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
= $true )
| ( ( path @ SV120 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1145]) ).
thf(1161,plain,
! [SV120: $i,SV149: $i,SV153: $i] :
( ( ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ ( sK13_SY84 @ SV153 @ SV149 @ SV120 ) )
= $true )
| ( ( SV149
= ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
= $true )
| ( ( path @ SV120 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1146]) ).
thf(1162,plain,
! [SV120: $i,SV149: $i,SV153: $i] :
( ( ( SV153
= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ ( sK12_SY85 @ SV153 @ SV149 @ SV120 ) ) )
= $true )
| ( ( SV153
= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ empty ) )
= $true )
| ( ( path @ SV120 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1147]) ).
thf(1163,plain,
! [SV120: $i,SV149: $i,SV153: $i] :
( ( ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ ( sK12_SY85 @ SV153 @ SV149 @ SV120 ) )
= $true )
| ( ( SV153
= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ empty ) )
= $true )
| ( ( path @ SV120 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1148]) ).
thf(1164,plain,
! [SV145: $i,SV141: $i,SV124: $i,SV221: $i,SV206: $i,SV198: $i] :
( ( ( sequential @ SV198 @ SV206 )
= $false )
| ( ( precedes @ SV221 @ SV206 @ SV124 )
= $false )
| ( ( sequential @ SV198 @ SV221 )
= $false )
| ( ( precedes @ SV198 @ SV206 @ SV124 )
= $false )
| ( ( path @ SV141 @ SV145 @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1150]) ).
thf(1165,plain,
! [SV226: $i,SV127: $i] :
( ( ( ! [SY403: $i] :
~ ( triangle @ SV127 @ SV226 @ SY403 ) )
= $true )
| ( ( edge @ SV127 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1151]) ).
thf(1166,plain,
! [SV225: $i,SV127: $i] :
( ( ( ! [SY402: $i] :
~ ( triangle @ SV127 @ SV225 @ SY402 ) )
= $true )
| ( ( edge @ SV225 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1152]) ).
thf(1167,plain,
! [SV143: $i,SV138: $i] :
( ( ( SV138
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
= $false )
| ( ( SV143
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
= $false )
| ( ( SV138
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
= $false )
| ( ( SV143
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
= $false )
| ( ( SV138 = SV143 )
= $true )
| ( ( vertex @ SV138 )
= $false )
| ( ( vertex @ SV143 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1154]) ).
thf(1168,plain,
! [SV143: $i,SV138: $i] :
( ( ( SV138
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
= $true )
| ( ( SV143
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
= $true )
| ( ( SV138 = SV143 )
= $true )
| ( ( vertex @ SV138 )
= $false )
| ( ( vertex @ SV143 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[1155]) ).
thf(1169,plain,
! [SV143: $i,SV138: $i] :
( ( ( SV138
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
= $true )
| ( ( SV138
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
= $true )
| ( ( SV138 = SV143 )
= $true )
| ( ( vertex @ SV138 )
= $false )
| ( ( vertex @ SV143 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[1156]) ).
thf(1170,plain,
! [SV138: $i,SV143: $i] :
( ( ( SV143
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
= $true )
| ( ( SV143
= ( head_of @ ( sK14_E @ SV143 @ SV138 ) ) )
= $true )
| ( ( SV138 = SV143 )
= $true )
| ( ( vertex @ SV138 )
= $false )
| ( ( vertex @ SV143 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[1157]) ).
thf(1171,plain,
! [SV138: $i,SV143: $i] :
( ( ( SV143
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
= $true )
| ( ( SV138
= ( tail_of @ ( sK14_E @ SV143 @ SV138 ) ) )
= $true )
| ( ( SV138 = SV143 )
= $true )
| ( ( vertex @ SV138 )
= $false )
| ( ( vertex @ SV143 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[1158]) ).
thf(1172,plain,
! [SV224: $i,SV120: $i,SV149: $i,SV153: $i] :
( ( ( path @ ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) @ SV149 @ SV224 )
= $false )
| ( ( SV153
= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ SV224 ) )
= $false )
| ( ( SV149
= ( head_of @ ( sK11_E @ SV153 @ SV149 @ SV120 ) ) )
= $false )
| ( ( SV153
= ( path_cons @ ( sK11_E @ SV153 @ SV149 @ SV120 ) @ empty ) )
= $false )
| ( ( path @ SV120 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1159]) ).
thf(1173,plain,
! [SV227: $i,SV226: $i,SV127: $i] :
( ( ( ~ ( triangle @ SV127 @ SV226 @ SV227 ) )
= $true )
| ( ( edge @ SV127 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1165]) ).
thf(1174,plain,
! [SV228: $i,SV225: $i,SV127: $i] :
( ( ( ~ ( triangle @ SV127 @ SV225 @ SV228 ) )
= $true )
| ( ( edge @ SV225 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1166]) ).
thf(1175,plain,
! [SV227: $i,SV226: $i,SV127: $i] :
( ( ( triangle @ SV127 @ SV226 @ SV227 )
= $false )
| ( ( edge @ SV127 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1173]) ).
thf(1176,plain,
! [SV228: $i,SV225: $i,SV127: $i] :
( ( ( triangle @ SV127 @ SV225 @ SV228 )
= $false )
| ( ( edge @ SV225 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1174]) ).
thf(1177,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[645,1176,1175,1172,1171,1170,1169,1168,1167,1164,1163,1162,1161,1160,1153,1149,1135,1134,1132,1130,1120,1107,1088,1087,1086,1083,1074,1067,1063,1062,1053,1052,1050,1049,1043,1042,1040,1039,1029,1028,1025,1024,1006,1005,978,958,956,953,951,928,923,922,919,909,781,780,743,742,719,682,665,646]) ).
thf(1178,plain,
( ( ! [E: $i] :
( ~ ( edge @ E )
| ( ( head_of @ E )
!= ( tail_of @ E ) ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(1179,plain,
( ( ! [E: $i] :
( ~ ( edge @ E )
| ( vertex @ ( head_of @ E ) ) )
& ! [E: $i] :
( ~ ( edge @ E )
| ( vertex @ ( tail_of @ E ) ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(1180,plain,
( ( ~ complete
| ! [V1: $i,V2: $i] :
( ( V1 = V2 )
| ~ ( vertex @ V1 )
| ~ ( vertex @ V2 )
| ( ( ( V1
!= ( head_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V2
!= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V2
!= ( head_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V1
!= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( ( V1
= ( head_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V2
= ( head_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( ( V1
= ( head_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V1
= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( ( V2
= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V2
= ( head_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( ( V2
= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V1
= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( edge @ ( sK14_E @ V2 @ V1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(1181,plain,
( ( ! [V1: $i,V2: $i,P: $i] :
( ~ ( vertex @ V1 )
| ~ ( vertex @ V2 )
| ( ! [E: $i] :
( ( V1
!= ( tail_of @ E ) )
| ~ ( edge @ E )
| ( V2
!= ( head_of @ E ) )
| ( P
!= ( path_cons @ E @ empty ) ) )
& ! [E: $i] :
( ( V1
!= ( tail_of @ E ) )
| ~ ( edge @ E )
| ! [TP: $i] :
( ( P
!= ( path_cons @ E @ TP ) )
| ~ ( path @ ( head_of @ E ) @ V2 @ TP ) ) ) )
| ( path @ V1 @ V2 @ P ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(1182,plain,
( ( ! [V1: $i] :
( ( ! [V2: $i,P: $i] :
~ ( path @ V1 @ V2 @ P )
| ( vertex @ V1 ) )
& ! [V2: $i] :
( ! [P: $i] :
~ ( path @ V1 @ V2 @ P )
| ( vertex @ V2 ) )
& ! [V2: $i,P: $i] :
( ~ ( path @ V1 @ V2 @ P )
| ( ( V1
= ( tail_of @ ( sK11_E @ P @ V2 @ V1 ) ) )
& ( edge @ ( sK11_E @ P @ V2 @ V1 ) )
& ( ( V2
!= ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) )
| ( P
!= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ empty ) )
| ! [SY83: $i] :
( ( P
!= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ SY83 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) @ V2 @ SY83 ) ) )
& ( ( V2
= ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) )
| ( ( P
= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ ( sK13_SY84 @ P @ V2 @ V1 ) ) )
& ( path @ ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) @ V2 @ ( sK13_SY84 @ P @ V2 @ V1 ) ) ) )
& ( ( P
= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ empty ) )
| ( ( P
= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ ( sK12_SY85 @ P @ V2 @ V1 ) ) )
& ( path @ ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) @ V2 @ ( sK12_SY85 @ P @ V2 @ V1 ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(1183,plain,
( ( ! [V1: $i,V2: $i] :
( ! [P: $i,E: $i] :
( ~ ( on_path @ E @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( edge @ E ) )
& ! [P: $i,E: $i] :
( ~ ( on_path @ E @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( in_path @ ( head_of @ E ) @ P ) )
& ! [P: $i,E: $i] :
( ~ ( on_path @ E @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( in_path @ ( tail_of @ E ) @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(1184,plain,
( ( ! [V1: $i,V2: $i] :
( ! [P: $i,V: $i] :
( ~ ( in_path @ V @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( ( on_path @ ( sK10_E @ V @ P @ V2 @ V1 ) @ P )
& ( ( V
= ( head_of @ ( sK10_E @ V @ P @ V2 @ V1 ) ) )
| ( V
= ( tail_of @ ( sK10_E @ V @ P @ V2 @ V1 ) ) ) ) ) )
& ! [P: $i,V: $i] :
( ~ ( in_path @ V @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( vertex @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(1185,plain,
( ( ! [E1: $i,E2: $i] :
( ( E1 = E2 )
| ~ ( edge @ E1 )
| ~ ( edge @ E2 )
| ( ( head_of @ E1 )
!= ( tail_of @ E2 ) )
| ( sequential @ E1 @ E2 ) )
& ! [E1: $i,E2: $i] :
( ~ ( sequential @ E1 @ E2 )
| ( E1 != E2 ) )
& ! [E1: $i] :
( ! [E2: $i] :
~ ( sequential @ E1 @ E2 )
| ( edge @ E1 ) )
& ! [E1: $i,E2: $i] :
( ~ ( sequential @ E1 @ E2 )
| ( edge @ E2 ) )
& ! [E1: $i,E2: $i] :
( ~ ( sequential @ E1 @ E2 )
| ( ( head_of @ E1 )
= ( tail_of @ E2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(1186,plain,
( ( ! [P: $i] :
( ! [V1: $i,V2: $i] :
~ ( path @ V1 @ V2 @ P )
| ( ! [E1: $i,E2: $i] :
( ~ ( on_path @ E1 @ P )
| ~ ( on_path @ E2 @ P )
| ! [E3: $i] :
( ~ ( precedes @ E3 @ E2 @ P )
| ~ ( sequential @ E1 @ E3 ) )
| ( precedes @ E1 @ E2 @ P ) )
& ! [E1: $i,E2: $i] :
( ~ ( on_path @ E1 @ P )
| ~ ( on_path @ E2 @ P )
| ~ ( sequential @ E1 @ E2 )
| ( precedes @ E1 @ E2 @ P ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(1187,plain,
( ( ! [P: $i] :
( ! [V1: $i,V2: $i] :
~ ( path @ V1 @ V2 @ P )
| ( ! [E1: $i] :
( ! [E2: $i] :
~ ( precedes @ E1 @ E2 @ P )
| ( on_path @ E1 @ P ) )
& ! [E1: $i,E2: $i] :
( ~ ( precedes @ E1 @ E2 @ P )
| ( on_path @ E2 @ P ) )
& ! [E1: $i,E2: $i] :
( ~ ( precedes @ E1 @ E2 @ P )
| ! [E3: $i] :
( ~ ( precedes @ E3 @ E2 @ P )
| ~ ( sequential @ E1 @ E3 ) )
| ~ ( sequential @ E1 @ E2 ) )
& ! [E1: $i,E2: $i] :
( ~ ( precedes @ E1 @ E2 @ P )
| ( ( precedes @ ( sK9_E3 @ E2 @ E1 @ P ) @ E2 @ P )
& ( sequential @ E1 @ ( sK9_E3 @ E2 @ E1 @ P ) ) )
| ( sequential @ E1 @ E2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(1188,plain,
( ( ! [V1: $i] :
( ! [V2: $i,SP: $i] :
( ( ( path @ V1 @ V2 @ ( sK8_P @ SP @ V2 @ V1 ) )
& ~ ( less_or_equal @ ( length_of @ SP ) @ ( length_of @ ( sK8_P @ SP @ V2 @ V1 ) ) ) )
| ( V1 = V2 )
| ~ ( path @ V1 @ V2 @ SP )
| ( shortest_path @ V1 @ V2 @ SP ) )
& ! [V2: $i,SP: $i] :
( ~ ( shortest_path @ V1 @ V2 @ SP )
| ! [P: $i] :
( ~ ( path @ V1 @ V2 @ P )
| ( less_or_equal @ ( length_of @ SP ) @ ( length_of @ P ) ) ) )
& ! [V2: $i] :
( ! [SP: $i] :
~ ( shortest_path @ V1 @ V2 @ SP )
| ( V1 != V2 ) )
& ! [V2: $i,SP: $i] :
( ~ ( shortest_path @ V1 @ V2 @ SP )
| ( path @ V1 @ V2 @ SP ) ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(1189,plain,
( ( ! [V1: $i,V2: $i,E1: $i] :
( ! [E2: $i] :
( ! [P: $i] :
( ~ ( precedes @ E1 @ E2 @ P )
| ~ ( shortest_path @ V1 @ V2 @ P ) )
| ! [E3: $i] :
( ( ( tail_of @ E3 )
!= ( tail_of @ E1 ) )
| ( ( head_of @ E3 )
!= ( head_of @ E2 ) ) ) )
& ! [E2: $i,P: $i] :
( ~ ( precedes @ E1 @ E2 @ P )
| ~ ( shortest_path @ V1 @ V2 @ P )
| ~ ( precedes @ E2 @ E1 @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(1190,plain,
( ( ! [E1: $i] :
( ! [E2: $i,E3: $i] :
( ~ ( edge @ E1 )
| ~ ( edge @ E2 )
| ~ ( edge @ E3 )
| ~ ( sequential @ E1 @ E2 )
| ~ ( sequential @ E2 @ E3 )
| ~ ( sequential @ E3 @ E1 )
| ( triangle @ E1 @ E2 @ E3 ) )
& ( ! [E2: $i,E3: $i] :
~ ( triangle @ E1 @ E2 @ E3 )
| ( edge @ E1 ) )
& ! [E2: $i] :
( ! [E3: $i] :
~ ( triangle @ E1 @ E2 @ E3 )
| ( edge @ E2 ) )
& ! [E2: $i,E3: $i] :
( ~ ( triangle @ E1 @ E2 @ E3 )
| ( edge @ E3 ) )
& ! [E2: $i] :
( ! [E3: $i] :
~ ( triangle @ E1 @ E2 @ E3 )
| ( sequential @ E1 @ E2 ) )
& ! [E2: $i,E3: $i] :
( ~ ( triangle @ E1 @ E2 @ E3 )
| ( sequential @ E2 @ E3 ) )
& ! [E2: $i,E3: $i] :
( ~ ( triangle @ E1 @ E2 @ E3 )
| ( sequential @ E3 @ E1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(1191,plain,
( ( ! [V1: $i,V2: $i,P: $i] :
( ~ ( path @ V1 @ V2 @ P )
| ( ( length_of @ P )
= ( number_of_in @ edges @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(1192,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)],[63]) ).
thf(1193,plain,
( ( ! [P: $i] :
( ( ( on_path @ ( sK6_E1 @ P ) @ P )
& ( on_path @ ( sK7_SY80 @ P ) @ P )
& ( sequential @ ( sK6_E1 @ P ) @ ( sK7_SY80 @ P ) )
& ! [SY82: $i] :
~ ( triangle @ ( sK6_E1 @ P ) @ ( sK7_SY80 @ P ) @ SY82 ) )
| ! [V1: $i,V2: $i] :
~ ( path @ V1 @ V2 @ P )
| ( ( number_of_in @ sequential_pairs @ P )
= ( number_of_in @ triangles @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(1194,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(1195,plain,
( ( precedes @ sK3_SY74 @ sK4_SY77 @ sK5_SY79 )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(1196,plain,
( ( shortest_path @ sK1_V1 @ sK2_SY70 @ sK5_SY79 )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(1197,plain,
( ( sK1_V1 = sK2_SY70 )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(1198,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SX0 ) @ SX0 )
| ~ ( on_path @ ( sK7_SY80 @ SX0 ) @ SX0 ) )
| ~ ( sequential @ ( sK6_E1 @ SX0 ) @ ( sK7_SY80 @ SX0 ) ) )
| ~ ! [SX1: $i] :
~ ( triangle @ ( sK6_E1 @ SX0 ) @ ( sK7_SY80 @ SX0 ) @ SX1 ) )
| ! [SX1: $i,SX2: $i] :
~ ( path @ SX1 @ SX2 @ SX0 )
| ( ( number_of_in @ sequential_pairs @ SX0 )
= ( number_of_in @ triangles @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1193]) ).
thf(1199,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( head_of @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( tail_of @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1179]) ).
thf(1200,plain,
( ( ~ complete
| ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( vertex @ SX0 )
| ~ ( vertex @ SX1 )
| ~ ( ~ ~ ( ~ ( ( SX0
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
| ~ ~ ( ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1180]) ).
thf(1201,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
( ~ ( precedes @ SX2 @ SX3 @ SX4 )
| ~ ( shortest_path @ SX0 @ SX1 @ SX4 ) )
| ! [SX4: $i] :
( ( ( tail_of @ SX4 )
!= ( tail_of @ SX2 ) )
| ( ( head_of @ SX4 )
!= ( head_of @ SX3 ) ) ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( precedes @ SX2 @ SX3 @ SX4 )
| ~ ( shortest_path @ SX0 @ SX1 @ SX4 )
| ~ ( precedes @ SX3 @ SX2 @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1189]) ).
thf(1202,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( on_path @ SX3 @ SX2 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ( edge @ SX3 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( on_path @ SX3 @ SX2 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ( in_path @ ( head_of @ SX3 ) @ SX2 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( on_path @ SX3 @ SX2 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ( in_path @ ( tail_of @ SX3 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1183]) ).
thf(1203,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i,SX2: $i] :
~ ( path @ SX1 @ SX2 @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( on_path @ SX1 @ SX0 )
| ~ ( on_path @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( precedes @ SX3 @ SX2 @ SX0 )
| ~ ( sequential @ SX1 @ SX3 ) )
| ( precedes @ SX1 @ SX2 @ SX0 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( on_path @ SX1 @ SX0 )
| ~ ( on_path @ SX2 @ SX0 )
| ~ ( sequential @ SX1 @ SX2 )
| ( precedes @ SX1 @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1186]) ).
thf(1204,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in_path @ SX3 @ SX2 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ~ ( ~ ( on_path @ ( sK10_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( ( SX3
= ( head_of @ ( sK10_E @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ( SX3
= ( tail_of @ ( sK10_E @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( in_path @ SX3 @ SX2 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ( vertex @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1184]) ).
thf(1205,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( edge @ SX0 )
| ~ ( edge @ SX1 )
| ~ ( edge @ SX2 )
| ~ ( sequential @ SX0 @ SX1 )
| ~ ( sequential @ SX1 @ SX2 )
| ~ ( sequential @ SX2 @ SX0 )
| ( triangle @ SX0 @ SX1 @ SX2 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SX1: $i,SX2: $i] :
~ ( triangle @ SX0 @ SX1 @ SX2 )
| ( edge @ SX0 ) )
| ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( triangle @ SX0 @ SX1 @ SX2 )
| ( edge @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( triangle @ SX0 @ SX1 @ SX2 )
| ( edge @ SX2 ) ) )
| ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( triangle @ SX0 @ SX1 @ SX2 )
| ( sequential @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( triangle @ SX0 @ SX1 @ SX2 )
| ( sequential @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( triangle @ SX0 @ SX1 @ SX2 )
| ( sequential @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1190]) ).
thf(1206,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( path @ SX0 @ SX1 @ ( sK8_P @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SX2 ) @ ( length_of @ ( sK8_P @ SX2 @ SX1 @ SX0 ) ) ) )
| ( SX0 = SX1 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ( shortest_path @ SX0 @ SX1 @ SX2 ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( shortest_path @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( path @ SX0 @ SX1 @ SX3 )
| ( less_or_equal @ ( length_of @ SX2 ) @ ( length_of @ SX3 ) ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( shortest_path @ SX0 @ SX1 @ SX2 )
| ( SX0 != SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( shortest_path @ SX0 @ SX1 @ SX2 )
| ( path @ SX0 @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1188]) ).
thf(1207,plain,
( ( ! [SX0: $i] :
~ ( ~ ~ ( ~ ( ! [SX1: $i,SX2: $i] :
~ ( path @ SX0 @ SX1 @ SX2 )
| ( vertex @ SX0 ) )
| ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( path @ SX0 @ SX1 @ SX2 )
| ( vertex @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( path @ SX0 @ SX1 @ SX2 )
| ~ ( ~ ~ ( ( SX0
!= ( tail_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( edge @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ( SX1
!= ( head_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) )
| ( SX2
!= ( path_cons @ ( sK11_E @ SX2 @ SX1 @ SX0 ) @ empty ) )
| ! [SX3: $i] :
( ( SX2
!= ( path_cons @ ( sK11_E @ SX2 @ SX1 @ SX0 ) @ SX3 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) @ SX1 @ SX3 ) ) )
| ~ ~ ( ~ ( ( SX1
= ( head_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( ( SX2
!= ( path_cons @ ( sK11_E @ SX2 @ SX1 @ SX0 ) @ ( sK13_SY84 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) @ SX1 @ ( sK13_SY84 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX2
= ( path_cons @ ( sK11_E @ SX2 @ SX1 @ SX0 ) @ empty ) )
| ~ ( ( SX2
!= ( path_cons @ ( sK11_E @ SX2 @ SX1 @ SX0 ) @ ( sK12_SY85 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) @ SX1 @ ( sK12_SY85 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1182]) ).
thf(1208,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( vertex @ SX0 )
| ~ ( vertex @ SX1 )
| ~ ( ~ ! [SX3: $i] :
( ( SX0
!= ( tail_of @ SX3 ) )
| ~ ( edge @ SX3 )
| ( SX1
!= ( head_of @ SX3 ) )
| ( SX2
!= ( path_cons @ SX3 @ empty ) ) )
| ~ ! [SX3: $i] :
( ( SX0
!= ( tail_of @ SX3 ) )
| ~ ( edge @ SX3 )
| ! [SX4: $i] :
( ( SX2
!= ( path_cons @ SX3 @ SX4 ) )
| ~ ( path @ ( head_of @ SX3 ) @ SX1 @ SX4 ) ) ) )
| ( path @ SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1181]) ).
thf(1209,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( edge @ SX0 )
| ~ ( edge @ SX1 )
| ( ( head_of @ SX0 )
!= ( tail_of @ SX1 ) )
| ( sequential @ SX0 @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1185]) ).
thf(1210,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i,SX2: $i] :
~ ( path @ SX1 @ SX2 @ SX0 )
| ~ ( ~ ~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( precedes @ SX1 @ SX2 @ SX0 )
| ( on_path @ SX1 @ SX0 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( precedes @ SX1 @ SX2 @ SX0 )
| ( on_path @ SX2 @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( precedes @ SX1 @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( precedes @ SX3 @ SX2 @ SX0 )
| ~ ( sequential @ SX1 @ SX3 ) )
| ~ ( sequential @ SX1 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( precedes @ SX1 @ SX2 @ SX0 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SX2 @ SX1 @ SX0 ) @ SX2 @ SX0 )
| ~ ( sequential @ SX1 @ ( sK9_E3 @ SX2 @ SX1 @ SX0 ) ) )
| ( sequential @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1187]) ).
thf(1211,plain,
! [SV229: $i] :
( ( ~ ( edge @ SV229 )
| ( ( head_of @ SV229 )
!= ( tail_of @ SV229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1178]) ).
thf(1212,plain,
! [SV230: $i] :
( ( ! [SY404: $i,SY405: $i] :
( ~ ( path @ SV230 @ SY404 @ SY405 )
| ( ( length_of @ SY405 )
= ( number_of_in @ edges @ SY405 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1191]) ).
thf(1213,plain,
! [SV231: $i] :
( ( ! [SY406: $i,SY407: $i] :
( ~ ( path @ SV231 @ SY406 @ SY407 )
| ( ( number_of_in @ sequential_pairs @ SY407 )
= ( minus @ ( length_of @ SY407 ) @ n1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1192]) ).
thf(1214,plain,
! [SV232: $i] :
( ( ! [SY408: $i] : ( less_or_equal @ ( number_of_in @ SV232 @ SY408 ) @ ( number_of_in @ SV232 @ graph ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1194]) ).
thf(1215,plain,
! [SV233: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV233 ) @ SV233 )
| ~ ( on_path @ ( sK7_SY80 @ SV233 ) @ SV233 ) )
| ~ ( sequential @ ( sK6_E1 @ SV233 ) @ ( sK7_SY80 @ SV233 ) ) )
| ~ ! [SY409: $i] :
~ ( triangle @ ( sK6_E1 @ SV233 ) @ ( sK7_SY80 @ SV233 ) @ SY409 ) )
| ! [SY410: $i,SY411: $i] :
~ ( path @ SY410 @ SY411 @ SV233 )
| ( ( number_of_in @ sequential_pairs @ SV233 )
= ( number_of_in @ triangles @ SV233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1198]) ).
thf(1216,plain,
( ( ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( head_of @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( tail_of @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1199]) ).
thf(1217,plain,
( ( ( ~ complete )
= $true )
| ( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( vertex @ SX0 )
| ~ ( vertex @ SX1 )
| ~ ( ~ ~ ( ~ ( ( SX0
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
| ~ ~ ( ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1200]) ).
thf(1218,plain,
! [SV234: $i] :
( ( ! [SY412: $i,SY413: $i] :
~ ( ~ ! [SY414: $i] :
( ! [SY415: $i] :
( ~ ( precedes @ SY413 @ SY414 @ SY415 )
| ~ ( shortest_path @ SV234 @ SY412 @ SY415 ) )
| ! [SX4: $i] :
( ( ( tail_of @ SX4 )
!= ( tail_of @ SY413 ) )
| ( ( head_of @ SX4 )
!= ( head_of @ SY414 ) ) ) )
| ~ ! [SY417: $i,SY418: $i] :
( ~ ( precedes @ SY413 @ SY417 @ SY418 )
| ~ ( shortest_path @ SV234 @ SY412 @ SY418 )
| ~ ( precedes @ SY417 @ SY413 @ SY418 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1201]) ).
thf(1219,plain,
! [SV235: $i] :
( ( ! [SY419: $i] :
~ ( ~ ~ ( ~ ! [SY420: $i,SY421: $i] :
( ~ ( on_path @ SY421 @ SY420 )
| ~ ( path @ SV235 @ SY419 @ SY420 )
| ( edge @ SY421 ) )
| ~ ! [SY422: $i,SY423: $i] :
( ~ ( on_path @ SY423 @ SY422 )
| ~ ( path @ SV235 @ SY419 @ SY422 )
| ( in_path @ ( head_of @ SY423 ) @ SY422 ) ) )
| ~ ! [SY424: $i,SY425: $i] :
( ~ ( on_path @ SY425 @ SY424 )
| ~ ( path @ SV235 @ SY419 @ SY424 )
| ( in_path @ ( tail_of @ SY425 ) @ SY424 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1202]) ).
thf(1220,plain,
! [SV236: $i] :
( ( ! [SY426: $i,SY427: $i] :
~ ( path @ SY426 @ SY427 @ SV236 )
| ~ ( ~ ! [SY428: $i,SY429: $i] :
( ~ ( on_path @ SY428 @ SV236 )
| ~ ( on_path @ SY429 @ SV236 )
| ! [SY430: $i] :
( ~ ( precedes @ SY430 @ SY429 @ SV236 )
| ~ ( sequential @ SY428 @ SY430 ) )
| ( precedes @ SY428 @ SY429 @ SV236 ) )
| ~ ! [SY431: $i,SY432: $i] :
( ~ ( on_path @ SY431 @ SV236 )
| ~ ( on_path @ SY432 @ SV236 )
| ~ ( sequential @ SY431 @ SY432 )
| ( precedes @ SY431 @ SY432 @ SV236 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1203]) ).
thf(1221,plain,
! [SV237: $i] :
( ( ! [SY433: $i] :
~ ( ~ ! [SY434: $i,SY435: $i] :
( ~ ( in_path @ SY435 @ SY434 )
| ~ ( path @ SV237 @ SY433 @ SY434 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY435 @ SY434 @ SY433 @ SV237 ) @ SY434 )
| ~ ( ( SY435
= ( head_of @ ( sK10_E @ SY435 @ SY434 @ SY433 @ SV237 ) ) )
| ( SY435
= ( tail_of @ ( sK10_E @ SY435 @ SY434 @ SY433 @ SV237 ) ) ) ) ) )
| ~ ! [SY436: $i,SY437: $i] :
( ~ ( in_path @ SY437 @ SY436 )
| ~ ( path @ SV237 @ SY433 @ SY436 )
| ( vertex @ SY437 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1204]) ).
thf(1222,plain,
! [SV238: $i] :
( ( ~ ( ~ ! [SY438: $i,SY439: $i] :
( ~ ( edge @ SV238 )
| ~ ( edge @ SY438 )
| ~ ( edge @ SY439 )
| ~ ( sequential @ SV238 @ SY438 )
| ~ ( sequential @ SY438 @ SY439 )
| ~ ( sequential @ SY439 @ SV238 )
| ( triangle @ SV238 @ SY438 @ SY439 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY440: $i,SY441: $i] :
~ ( triangle @ SV238 @ SY440 @ SY441 )
| ( edge @ SV238 ) )
| ~ ! [SY442: $i] :
( ! [SY443: $i] :
~ ( triangle @ SV238 @ SY442 @ SY443 )
| ( edge @ SY442 ) ) )
| ~ ! [SY444: $i,SY445: $i] :
( ~ ( triangle @ SV238 @ SY444 @ SY445 )
| ( edge @ SY445 ) ) )
| ~ ! [SY446: $i] :
( ! [SY447: $i] :
~ ( triangle @ SV238 @ SY446 @ SY447 )
| ( sequential @ SV238 @ SY446 ) ) )
| ~ ! [SY448: $i,SY449: $i] :
( ~ ( triangle @ SV238 @ SY448 @ SY449 )
| ( sequential @ SY448 @ SY449 ) ) )
| ~ ! [SY450: $i,SY451: $i] :
( ~ ( triangle @ SV238 @ SY450 @ SY451 )
| ( sequential @ SY451 @ SV238 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1205]) ).
thf(1223,plain,
! [SV239: $i] :
( ( ~ ( ~ ! [SY452: $i,SY453: $i] :
( ~ ( ~ ( path @ SV239 @ SY452 @ ( sK8_P @ SY453 @ SY452 @ SV239 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY453 ) @ ( length_of @ ( sK8_P @ SY453 @ SY452 @ SV239 ) ) ) )
| ( SV239 = SY452 )
| ~ ( path @ SV239 @ SY452 @ SY453 )
| ( shortest_path @ SV239 @ SY452 @ SY453 ) )
| ~ ~ ( ~ ! [SY454: $i,SY455: $i] :
( ~ ( shortest_path @ SV239 @ SY454 @ SY455 )
| ! [SY456: $i] :
( ~ ( path @ SV239 @ SY454 @ SY456 )
| ( less_or_equal @ ( length_of @ SY455 ) @ ( length_of @ SY456 ) ) ) )
| ~ ~ ( ~ ! [SY457: $i] :
( ! [SY458: $i] :
~ ( shortest_path @ SV239 @ SY457 @ SY458 )
| ( SV239 != SY457 ) )
| ~ ! [SY459: $i,SY460: $i] :
( ~ ( shortest_path @ SV239 @ SY459 @ SY460 )
| ( path @ SV239 @ SY459 @ SY460 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1206]) ).
thf(1224,plain,
! [SV240: $i] :
( ( ~ ( ~ ~ ( ~ ( ! [SY461: $i,SY462: $i] :
~ ( path @ SV240 @ SY461 @ SY462 )
| ( vertex @ SV240 ) )
| ~ ! [SY463: $i] :
( ! [SY464: $i] :
~ ( path @ SV240 @ SY463 @ SY464 )
| ( vertex @ SY463 ) ) )
| ~ ! [SY465: $i,SY466: $i] :
( ~ ( path @ SV240 @ SY465 @ SY466 )
| ~ ( ~ ~ ( ( SV240
!= ( tail_of @ ( sK11_E @ SY466 @ SY465 @ SV240 ) ) )
| ~ ( edge @ ( sK11_E @ SY466 @ SY465 @ SV240 ) ) )
| ~ ~ ( ~ ( ( SY465
!= ( head_of @ ( sK11_E @ SY466 @ SY465 @ SV240 ) ) )
| ( SY466
!= ( path_cons @ ( sK11_E @ SY466 @ SY465 @ SV240 ) @ empty ) )
| ! [SY467: $i] :
( ( SY466
!= ( path_cons @ ( sK11_E @ SY466 @ SY465 @ SV240 ) @ SY467 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY466 @ SY465 @ SV240 ) ) @ SY465 @ SY467 ) ) )
| ~ ~ ( ~ ( ( SY465
= ( head_of @ ( sK11_E @ SY466 @ SY465 @ SV240 ) ) )
| ~ ( ( SY466
!= ( path_cons @ ( sK11_E @ SY466 @ SY465 @ SV240 ) @ ( sK13_SY84 @ SY466 @ SY465 @ SV240 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY466 @ SY465 @ SV240 ) ) @ SY465 @ ( sK13_SY84 @ SY466 @ SY465 @ SV240 ) ) ) )
| ~ ( ( SY466
= ( path_cons @ ( sK11_E @ SY466 @ SY465 @ SV240 ) @ empty ) )
| ~ ( ( SY466
!= ( path_cons @ ( sK11_E @ SY466 @ SY465 @ SV240 ) @ ( sK12_SY85 @ SY466 @ SY465 @ SV240 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY466 @ SY465 @ SV240 ) ) @ SY465 @ ( sK12_SY85 @ SY466 @ SY465 @ SV240 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1207]) ).
thf(1225,plain,
! [SV241: $i] :
( ( ! [SY468: $i,SY469: $i] :
( ~ ( vertex @ SV241 )
| ~ ( vertex @ SY468 )
| ~ ( ~ ! [SY470: $i] :
( ( SV241
!= ( tail_of @ SY470 ) )
| ~ ( edge @ SY470 )
| ( SY468
!= ( head_of @ SY470 ) )
| ( SY469
!= ( path_cons @ SY470 @ empty ) ) )
| ~ ! [SY471: $i] :
( ( SV241
!= ( tail_of @ SY471 ) )
| ~ ( edge @ SY471 )
| ! [SX4: $i] :
( ( SY469
!= ( path_cons @ SY471 @ SX4 ) )
| ~ ( path @ ( head_of @ SY471 ) @ SY468 @ SX4 ) ) ) )
| ( path @ SV241 @ SY468 @ SY469 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1208]) ).
thf(1226,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( edge @ SX0 )
| ~ ( edge @ SX1 )
| ( ( head_of @ SX0 )
!= ( tail_of @ SX1 ) )
| ( sequential @ SX0 @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1209]) ).
thf(1227,plain,
! [SV242: $i] :
( ( ! [SY473: $i,SY474: $i] :
~ ( path @ SY473 @ SY474 @ SV242 )
| ~ ( ~ ~ ( ~ ! [SY475: $i] :
( ! [SY476: $i] :
~ ( precedes @ SY475 @ SY476 @ SV242 )
| ( on_path @ SY475 @ SV242 ) )
| ~ ! [SY477: $i,SY478: $i] :
( ~ ( precedes @ SY477 @ SY478 @ SV242 )
| ( on_path @ SY478 @ SV242 ) ) )
| ~ ~ ( ~ ! [SY479: $i,SY480: $i] :
( ~ ( precedes @ SY479 @ SY480 @ SV242 )
| ! [SY481: $i] :
( ~ ( precedes @ SY481 @ SY480 @ SV242 )
| ~ ( sequential @ SY479 @ SY481 ) )
| ~ ( sequential @ SY479 @ SY480 ) )
| ~ ! [SY482: $i,SY483: $i] :
( ~ ( precedes @ SY482 @ SY483 @ SV242 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY483 @ SY482 @ SV242 ) @ SY483 @ SV242 )
| ~ ( sequential @ SY482 @ ( sK9_E3 @ SY483 @ SY482 @ SV242 ) ) )
| ( sequential @ SY482 @ SY483 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1210]) ).
thf(1228,plain,
! [SV229: $i] :
( ( ( ~ ( edge @ SV229 ) )
= $true )
| ( ( ( ( head_of @ SV229 )
!= ( tail_of @ SV229 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1211]) ).
thf(1229,plain,
! [SV243: $i,SV230: $i] :
( ( ! [SY484: $i] :
( ~ ( path @ SV230 @ SV243 @ SY484 )
| ( ( length_of @ SY484 )
= ( number_of_in @ edges @ SY484 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1212]) ).
thf(1230,plain,
! [SV244: $i,SV231: $i] :
( ( ! [SY485: $i] :
( ~ ( path @ SV231 @ SV244 @ SY485 )
| ( ( number_of_in @ sequential_pairs @ SY485 )
= ( minus @ ( length_of @ SY485 ) @ n1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1213]) ).
thf(1231,plain,
! [SV245: $i,SV232: $i] :
( ( less_or_equal @ ( number_of_in @ SV232 @ SV245 ) @ ( number_of_in @ SV232 @ graph ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1214]) ).
thf(1232,plain,
! [SV233: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV233 ) @ SV233 )
| ~ ( on_path @ ( sK7_SY80 @ SV233 ) @ SV233 ) )
| ~ ( sequential @ ( sK6_E1 @ SV233 ) @ ( sK7_SY80 @ SV233 ) ) )
| ~ ! [SY409: $i] :
~ ( triangle @ ( sK6_E1 @ SV233 ) @ ( sK7_SY80 @ SV233 ) @ SY409 ) )
| ! [SY410: $i,SY411: $i] :
~ ( path @ SY410 @ SY411 @ SV233 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV233 )
= ( number_of_in @ triangles @ SV233 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1215]) ).
thf(1233,plain,
( ( ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( head_of @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1216]) ).
thf(1234,plain,
( ( ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( tail_of @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1216]) ).
thf(1235,plain,
( ( complete = $false )
| ( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( vertex @ SX0 )
| ~ ( vertex @ SX1 )
| ~ ( ~ ~ ( ~ ( ( SX0
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
| ~ ~ ( ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1217]) ).
thf(1236,plain,
! [SV246: $i,SV234: $i] :
( ( ! [SY486: $i] :
~ ( ~ ! [SY487: $i] :
( ! [SY488: $i] :
( ~ ( precedes @ SY486 @ SY487 @ SY488 )
| ~ ( shortest_path @ SV234 @ SV246 @ SY488 ) )
| ! [SX4: $i] :
( ( ( tail_of @ SX4 )
!= ( tail_of @ SY486 ) )
| ( ( head_of @ SX4 )
!= ( head_of @ SY487 ) ) ) )
| ~ ! [SY490: $i,SY491: $i] :
( ~ ( precedes @ SY486 @ SY490 @ SY491 )
| ~ ( shortest_path @ SV234 @ SV246 @ SY491 )
| ~ ( precedes @ SY490 @ SY486 @ SY491 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1218]) ).
thf(1237,plain,
! [SV247: $i,SV235: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY492: $i,SY493: $i] :
( ~ ( on_path @ SY493 @ SY492 )
| ~ ( path @ SV235 @ SV247 @ SY492 )
| ( edge @ SY493 ) )
| ~ ! [SY494: $i,SY495: $i] :
( ~ ( on_path @ SY495 @ SY494 )
| ~ ( path @ SV235 @ SV247 @ SY494 )
| ( in_path @ ( head_of @ SY495 ) @ SY494 ) ) )
| ~ ! [SY496: $i,SY497: $i] :
( ~ ( on_path @ SY497 @ SY496 )
| ~ ( path @ SV235 @ SV247 @ SY496 )
| ( in_path @ ( tail_of @ SY497 ) @ SY496 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1219]) ).
thf(1238,plain,
! [SV236: $i] :
( ( ( ! [SY426: $i,SY427: $i] :
~ ( path @ SY426 @ SY427 @ SV236 ) )
= $true )
| ( ( ~ ( ~ ! [SY428: $i,SY429: $i] :
( ~ ( on_path @ SY428 @ SV236 )
| ~ ( on_path @ SY429 @ SV236 )
| ! [SY430: $i] :
( ~ ( precedes @ SY430 @ SY429 @ SV236 )
| ~ ( sequential @ SY428 @ SY430 ) )
| ( precedes @ SY428 @ SY429 @ SV236 ) )
| ~ ! [SY431: $i,SY432: $i] :
( ~ ( on_path @ SY431 @ SV236 )
| ~ ( on_path @ SY432 @ SV236 )
| ~ ( sequential @ SY431 @ SY432 )
| ( precedes @ SY431 @ SY432 @ SV236 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1220]) ).
thf(1239,plain,
! [SV248: $i,SV237: $i] :
( ( ~ ( ~ ! [SY498: $i,SY499: $i] :
( ~ ( in_path @ SY499 @ SY498 )
| ~ ( path @ SV237 @ SV248 @ SY498 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY499 @ SY498 @ SV248 @ SV237 ) @ SY498 )
| ~ ( ( SY499
= ( head_of @ ( sK10_E @ SY499 @ SY498 @ SV248 @ SV237 ) ) )
| ( SY499
= ( tail_of @ ( sK10_E @ SY499 @ SY498 @ SV248 @ SV237 ) ) ) ) ) )
| ~ ! [SY500: $i,SY501: $i] :
( ~ ( in_path @ SY501 @ SY500 )
| ~ ( path @ SV237 @ SV248 @ SY500 )
| ( vertex @ SY501 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1221]) ).
thf(1240,plain,
! [SV238: $i] :
( ( ~ ! [SY438: $i,SY439: $i] :
( ~ ( edge @ SV238 )
| ~ ( edge @ SY438 )
| ~ ( edge @ SY439 )
| ~ ( sequential @ SV238 @ SY438 )
| ~ ( sequential @ SY438 @ SY439 )
| ~ ( sequential @ SY439 @ SV238 )
| ( triangle @ SV238 @ SY438 @ SY439 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY440: $i,SY441: $i] :
~ ( triangle @ SV238 @ SY440 @ SY441 )
| ( edge @ SV238 ) )
| ~ ! [SY442: $i] :
( ! [SY443: $i] :
~ ( triangle @ SV238 @ SY442 @ SY443 )
| ( edge @ SY442 ) ) )
| ~ ! [SY444: $i,SY445: $i] :
( ~ ( triangle @ SV238 @ SY444 @ SY445 )
| ( edge @ SY445 ) ) )
| ~ ! [SY446: $i] :
( ! [SY447: $i] :
~ ( triangle @ SV238 @ SY446 @ SY447 )
| ( sequential @ SV238 @ SY446 ) ) )
| ~ ! [SY448: $i,SY449: $i] :
( ~ ( triangle @ SV238 @ SY448 @ SY449 )
| ( sequential @ SY448 @ SY449 ) ) )
| ~ ! [SY450: $i,SY451: $i] :
( ~ ( triangle @ SV238 @ SY450 @ SY451 )
| ( sequential @ SY451 @ SV238 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1222]) ).
thf(1241,plain,
! [SV239: $i] :
( ( ~ ! [SY452: $i,SY453: $i] :
( ~ ( ~ ( path @ SV239 @ SY452 @ ( sK8_P @ SY453 @ SY452 @ SV239 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY453 ) @ ( length_of @ ( sK8_P @ SY453 @ SY452 @ SV239 ) ) ) )
| ( SV239 = SY452 )
| ~ ( path @ SV239 @ SY452 @ SY453 )
| ( shortest_path @ SV239 @ SY452 @ SY453 ) )
| ~ ~ ( ~ ! [SY454: $i,SY455: $i] :
( ~ ( shortest_path @ SV239 @ SY454 @ SY455 )
| ! [SY456: $i] :
( ~ ( path @ SV239 @ SY454 @ SY456 )
| ( less_or_equal @ ( length_of @ SY455 ) @ ( length_of @ SY456 ) ) ) )
| ~ ~ ( ~ ! [SY457: $i] :
( ! [SY458: $i] :
~ ( shortest_path @ SV239 @ SY457 @ SY458 )
| ( SV239 != SY457 ) )
| ~ ! [SY459: $i,SY460: $i] :
( ~ ( shortest_path @ SV239 @ SY459 @ SY460 )
| ( path @ SV239 @ SY459 @ SY460 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1223]) ).
thf(1242,plain,
! [SV240: $i] :
( ( ~ ~ ( ~ ( ! [SY461: $i,SY462: $i] :
~ ( path @ SV240 @ SY461 @ SY462 )
| ( vertex @ SV240 ) )
| ~ ! [SY463: $i] :
( ! [SY464: $i] :
~ ( path @ SV240 @ SY463 @ SY464 )
| ( vertex @ SY463 ) ) )
| ~ ! [SY465: $i,SY466: $i] :
( ~ ( path @ SV240 @ SY465 @ SY466 )
| ~ ( ~ ~ ( ( SV240
!= ( tail_of @ ( sK11_E @ SY466 @ SY465 @ SV240 ) ) )
| ~ ( edge @ ( sK11_E @ SY466 @ SY465 @ SV240 ) ) )
| ~ ~ ( ~ ( ( SY465
!= ( head_of @ ( sK11_E @ SY466 @ SY465 @ SV240 ) ) )
| ( SY466
!= ( path_cons @ ( sK11_E @ SY466 @ SY465 @ SV240 ) @ empty ) )
| ! [SY467: $i] :
( ( SY466
!= ( path_cons @ ( sK11_E @ SY466 @ SY465 @ SV240 ) @ SY467 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY466 @ SY465 @ SV240 ) ) @ SY465 @ SY467 ) ) )
| ~ ~ ( ~ ( ( SY465
= ( head_of @ ( sK11_E @ SY466 @ SY465 @ SV240 ) ) )
| ~ ( ( SY466
!= ( path_cons @ ( sK11_E @ SY466 @ SY465 @ SV240 ) @ ( sK13_SY84 @ SY466 @ SY465 @ SV240 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY466 @ SY465 @ SV240 ) ) @ SY465 @ ( sK13_SY84 @ SY466 @ SY465 @ SV240 ) ) ) )
| ~ ( ( SY466
= ( path_cons @ ( sK11_E @ SY466 @ SY465 @ SV240 ) @ empty ) )
| ~ ( ( SY466
!= ( path_cons @ ( sK11_E @ SY466 @ SY465 @ SV240 ) @ ( sK12_SY85 @ SY466 @ SY465 @ SV240 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY466 @ SY465 @ SV240 ) ) @ SY465 @ ( sK12_SY85 @ SY466 @ SY465 @ SV240 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1224]) ).
thf(1243,plain,
! [SV249: $i,SV241: $i] :
( ( ! [SY502: $i] :
( ~ ( vertex @ SV241 )
| ~ ( vertex @ SV249 )
| ~ ( ~ ! [SY503: $i] :
( ( SV241
!= ( tail_of @ SY503 ) )
| ~ ( edge @ SY503 )
| ( SV249
!= ( head_of @ SY503 ) )
| ( SY502
!= ( path_cons @ SY503 @ empty ) ) )
| ~ ! [SY504: $i] :
( ( SV241
!= ( tail_of @ SY504 ) )
| ~ ( edge @ SY504 )
| ! [SY505: $i] :
( ( SY502
!= ( path_cons @ SY504 @ SY505 ) )
| ~ ( path @ ( head_of @ SY504 ) @ SV249 @ SY505 ) ) ) )
| ( path @ SV241 @ SV249 @ SY502 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1225]) ).
thf(1244,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( edge @ SX0 )
| ~ ( edge @ SX1 )
| ( ( head_of @ SX0 )
!= ( tail_of @ SX1 ) )
| ( sequential @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1226]) ).
thf(1245,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1226]) ).
thf(1246,plain,
! [SV242: $i] :
( ( ( ! [SY473: $i,SY474: $i] :
~ ( path @ SY473 @ SY474 @ SV242 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY475: $i] :
( ! [SY476: $i] :
~ ( precedes @ SY475 @ SY476 @ SV242 )
| ( on_path @ SY475 @ SV242 ) )
| ~ ! [SY477: $i,SY478: $i] :
( ~ ( precedes @ SY477 @ SY478 @ SV242 )
| ( on_path @ SY478 @ SV242 ) ) )
| ~ ~ ( ~ ! [SY479: $i,SY480: $i] :
( ~ ( precedes @ SY479 @ SY480 @ SV242 )
| ! [SY481: $i] :
( ~ ( precedes @ SY481 @ SY480 @ SV242 )
| ~ ( sequential @ SY479 @ SY481 ) )
| ~ ( sequential @ SY479 @ SY480 ) )
| ~ ! [SY482: $i,SY483: $i] :
( ~ ( precedes @ SY482 @ SY483 @ SV242 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY483 @ SY482 @ SV242 ) @ SY483 @ SV242 )
| ~ ( sequential @ SY482 @ ( sK9_E3 @ SY483 @ SY482 @ SV242 ) ) )
| ( sequential @ SY482 @ SY483 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1227]) ).
thf(1247,plain,
! [SV229: $i] :
( ( ( edge @ SV229 )
= $false )
| ( ( ( ( head_of @ SV229 )
!= ( tail_of @ SV229 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1228]) ).
thf(1248,plain,
! [SV250: $i,SV243: $i,SV230: $i] :
( ( ~ ( path @ SV230 @ SV243 @ SV250 )
| ( ( length_of @ SV250 )
= ( number_of_in @ edges @ SV250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1229]) ).
thf(1249,plain,
! [SV251: $i,SV244: $i,SV231: $i] :
( ( ~ ( path @ SV231 @ SV244 @ SV251 )
| ( ( number_of_in @ sequential_pairs @ SV251 )
= ( minus @ ( length_of @ SV251 ) @ n1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1230]) ).
thf(1250,plain,
! [SV233: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV233 ) @ SV233 )
| ~ ( on_path @ ( sK7_SY80 @ SV233 ) @ SV233 ) )
| ~ ( sequential @ ( sK6_E1 @ SV233 ) @ ( sK7_SY80 @ SV233 ) ) )
| ~ ! [SY409: $i] :
~ ( triangle @ ( sK6_E1 @ SV233 ) @ ( sK7_SY80 @ SV233 ) @ SY409 ) ) )
= $true )
| ( ( ! [SY410: $i,SY411: $i] :
~ ( path @ SY410 @ SY411 @ SV233 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV233 )
= ( number_of_in @ triangles @ SV233 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1232]) ).
thf(1251,plain,
( ( ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( head_of @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1233]) ).
thf(1252,plain,
( ( ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( tail_of @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1234]) ).
thf(1253,plain,
! [SV252: $i] :
( ( ( ! [SY506: $i] :
( ( SV252 = SY506 )
| ~ ( vertex @ SV252 )
| ~ ( vertex @ SY506 )
| ~ ( ~ ~ ( ~ ( ( SV252
!= ( head_of @ ( sK14_E @ SY506 @ SV252 ) ) )
| ( SY506
!= ( tail_of @ ( sK14_E @ SY506 @ SV252 ) ) )
| ( SY506
!= ( head_of @ ( sK14_E @ SY506 @ SV252 ) ) )
| ( SV252
!= ( tail_of @ ( sK14_E @ SY506 @ SV252 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV252
= ( head_of @ ( sK14_E @ SY506 @ SV252 ) ) )
| ( SY506
= ( head_of @ ( sK14_E @ SY506 @ SV252 ) ) ) )
| ~ ( ( SV252
= ( head_of @ ( sK14_E @ SY506 @ SV252 ) ) )
| ( SV252
= ( tail_of @ ( sK14_E @ SY506 @ SV252 ) ) ) ) )
| ~ ~ ( ~ ( ( SY506
= ( tail_of @ ( sK14_E @ SY506 @ SV252 ) ) )
| ( SY506
= ( head_of @ ( sK14_E @ SY506 @ SV252 ) ) ) )
| ~ ( ( SY506
= ( tail_of @ ( sK14_E @ SY506 @ SV252 ) ) )
| ( SV252
= ( tail_of @ ( sK14_E @ SY506 @ SV252 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SY506 @ SV252 ) ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1235]) ).
thf(1254,plain,
! [SV246: $i,SV234: $i,SV253: $i] :
( ( ~ ( ~ ! [SY507: $i] :
( ! [SY508: $i] :
( ~ ( precedes @ SV253 @ SY507 @ SY508 )
| ~ ( shortest_path @ SV234 @ SV246 @ SY508 ) )
| ! [SY509: $i] :
( ( ( tail_of @ SY509 )
!= ( tail_of @ SV253 ) )
| ( ( head_of @ SY509 )
!= ( head_of @ SY507 ) ) ) )
| ~ ! [SY510: $i,SY511: $i] :
( ~ ( precedes @ SV253 @ SY510 @ SY511 )
| ~ ( shortest_path @ SV234 @ SV246 @ SY511 )
| ~ ( precedes @ SY510 @ SV253 @ SY511 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1236]) ).
thf(1255,plain,
! [SV247: $i,SV235: $i] :
( ( ~ ~ ( ~ ! [SY492: $i,SY493: $i] :
( ~ ( on_path @ SY493 @ SY492 )
| ~ ( path @ SV235 @ SV247 @ SY492 )
| ( edge @ SY493 ) )
| ~ ! [SY494: $i,SY495: $i] :
( ~ ( on_path @ SY495 @ SY494 )
| ~ ( path @ SV235 @ SV247 @ SY494 )
| ( in_path @ ( head_of @ SY495 ) @ SY494 ) ) )
| ~ ! [SY496: $i,SY497: $i] :
( ~ ( on_path @ SY497 @ SY496 )
| ~ ( path @ SV235 @ SV247 @ SY496 )
| ( in_path @ ( tail_of @ SY497 ) @ SY496 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1237]) ).
thf(1256,plain,
! [SV236: $i,SV254: $i] :
( ( ( ! [SY512: $i] :
~ ( path @ SV254 @ SY512 @ SV236 ) )
= $true )
| ( ( ~ ( ~ ! [SY428: $i,SY429: $i] :
( ~ ( on_path @ SY428 @ SV236 )
| ~ ( on_path @ SY429 @ SV236 )
| ! [SY430: $i] :
( ~ ( precedes @ SY430 @ SY429 @ SV236 )
| ~ ( sequential @ SY428 @ SY430 ) )
| ( precedes @ SY428 @ SY429 @ SV236 ) )
| ~ ! [SY431: $i,SY432: $i] :
( ~ ( on_path @ SY431 @ SV236 )
| ~ ( on_path @ SY432 @ SV236 )
| ~ ( sequential @ SY431 @ SY432 )
| ( precedes @ SY431 @ SY432 @ SV236 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1238]) ).
thf(1257,plain,
! [SV248: $i,SV237: $i] :
( ( ~ ! [SY498: $i,SY499: $i] :
( ~ ( in_path @ SY499 @ SY498 )
| ~ ( path @ SV237 @ SV248 @ SY498 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY499 @ SY498 @ SV248 @ SV237 ) @ SY498 )
| ~ ( ( SY499
= ( head_of @ ( sK10_E @ SY499 @ SY498 @ SV248 @ SV237 ) ) )
| ( SY499
= ( tail_of @ ( sK10_E @ SY499 @ SY498 @ SV248 @ SV237 ) ) ) ) ) )
| ~ ! [SY500: $i,SY501: $i] :
( ~ ( in_path @ SY501 @ SY500 )
| ~ ( path @ SV237 @ SV248 @ SY500 )
| ( vertex @ SY501 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1239]) ).
thf(1258,plain,
! [SV238: $i] :
( ( ~ ! [SY438: $i,SY439: $i] :
( ~ ( edge @ SV238 )
| ~ ( edge @ SY438 )
| ~ ( edge @ SY439 )
| ~ ( sequential @ SV238 @ SY438 )
| ~ ( sequential @ SY438 @ SY439 )
| ~ ( sequential @ SY439 @ SV238 )
| ( triangle @ SV238 @ SY438 @ SY439 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1240]) ).
thf(1259,plain,
! [SV238: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY440: $i,SY441: $i] :
~ ( triangle @ SV238 @ SY440 @ SY441 )
| ( edge @ SV238 ) )
| ~ ! [SY442: $i] :
( ! [SY443: $i] :
~ ( triangle @ SV238 @ SY442 @ SY443 )
| ( edge @ SY442 ) ) )
| ~ ! [SY444: $i,SY445: $i] :
( ~ ( triangle @ SV238 @ SY444 @ SY445 )
| ( edge @ SY445 ) ) )
| ~ ! [SY446: $i] :
( ! [SY447: $i] :
~ ( triangle @ SV238 @ SY446 @ SY447 )
| ( sequential @ SV238 @ SY446 ) ) )
| ~ ! [SY448: $i,SY449: $i] :
( ~ ( triangle @ SV238 @ SY448 @ SY449 )
| ( sequential @ SY448 @ SY449 ) ) )
| ~ ! [SY450: $i,SY451: $i] :
( ~ ( triangle @ SV238 @ SY450 @ SY451 )
| ( sequential @ SY451 @ SV238 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1240]) ).
thf(1260,plain,
! [SV239: $i] :
( ( ~ ! [SY452: $i,SY453: $i] :
( ~ ( ~ ( path @ SV239 @ SY452 @ ( sK8_P @ SY453 @ SY452 @ SV239 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY453 ) @ ( length_of @ ( sK8_P @ SY453 @ SY452 @ SV239 ) ) ) )
| ( SV239 = SY452 )
| ~ ( path @ SV239 @ SY452 @ SY453 )
| ( shortest_path @ SV239 @ SY452 @ SY453 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1241]) ).
thf(1261,plain,
! [SV239: $i] :
( ( ~ ~ ( ~ ! [SY454: $i,SY455: $i] :
( ~ ( shortest_path @ SV239 @ SY454 @ SY455 )
| ! [SY456: $i] :
( ~ ( path @ SV239 @ SY454 @ SY456 )
| ( less_or_equal @ ( length_of @ SY455 ) @ ( length_of @ SY456 ) ) ) )
| ~ ~ ( ~ ! [SY457: $i] :
( ! [SY458: $i] :
~ ( shortest_path @ SV239 @ SY457 @ SY458 )
| ( SV239 != SY457 ) )
| ~ ! [SY459: $i,SY460: $i] :
( ~ ( shortest_path @ SV239 @ SY459 @ SY460 )
| ( path @ SV239 @ SY459 @ SY460 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1241]) ).
thf(1262,plain,
! [SV240: $i] :
( ( ~ ~ ( ~ ( ! [SY461: $i,SY462: $i] :
~ ( path @ SV240 @ SY461 @ SY462 )
| ( vertex @ SV240 ) )
| ~ ! [SY463: $i] :
( ! [SY464: $i] :
~ ( path @ SV240 @ SY463 @ SY464 )
| ( vertex @ SY463 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1242]) ).
thf(1263,plain,
! [SV240: $i] :
( ( ~ ! [SY465: $i,SY466: $i] :
( ~ ( path @ SV240 @ SY465 @ SY466 )
| ~ ( ~ ~ ( ( SV240
!= ( tail_of @ ( sK11_E @ SY466 @ SY465 @ SV240 ) ) )
| ~ ( edge @ ( sK11_E @ SY466 @ SY465 @ SV240 ) ) )
| ~ ~ ( ~ ( ( SY465
!= ( head_of @ ( sK11_E @ SY466 @ SY465 @ SV240 ) ) )
| ( SY466
!= ( path_cons @ ( sK11_E @ SY466 @ SY465 @ SV240 ) @ empty ) )
| ! [SY467: $i] :
( ( SY466
!= ( path_cons @ ( sK11_E @ SY466 @ SY465 @ SV240 ) @ SY467 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY466 @ SY465 @ SV240 ) ) @ SY465 @ SY467 ) ) )
| ~ ~ ( ~ ( ( SY465
= ( head_of @ ( sK11_E @ SY466 @ SY465 @ SV240 ) ) )
| ~ ( ( SY466
!= ( path_cons @ ( sK11_E @ SY466 @ SY465 @ SV240 ) @ ( sK13_SY84 @ SY466 @ SY465 @ SV240 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY466 @ SY465 @ SV240 ) ) @ SY465 @ ( sK13_SY84 @ SY466 @ SY465 @ SV240 ) ) ) )
| ~ ( ( SY466
= ( path_cons @ ( sK11_E @ SY466 @ SY465 @ SV240 ) @ empty ) )
| ~ ( ( SY466
!= ( path_cons @ ( sK11_E @ SY466 @ SY465 @ SV240 ) @ ( sK12_SY85 @ SY466 @ SY465 @ SV240 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY466 @ SY465 @ SV240 ) ) @ SY465 @ ( sK12_SY85 @ SY466 @ SY465 @ SV240 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1242]) ).
thf(1264,plain,
! [SV255: $i,SV249: $i,SV241: $i] :
( ( ~ ( vertex @ SV241 )
| ~ ( vertex @ SV249 )
| ~ ( ~ ! [SY513: $i] :
( ( SV241
!= ( tail_of @ SY513 ) )
| ~ ( edge @ SY513 )
| ( SV249
!= ( head_of @ SY513 ) )
| ( SV255
!= ( path_cons @ SY513 @ empty ) ) )
| ~ ! [SY514: $i] :
( ( SV241
!= ( tail_of @ SY514 ) )
| ~ ( edge @ SY514 )
| ! [SY515: $i] :
( ( SV255
!= ( path_cons @ SY514 @ SY515 ) )
| ~ ( path @ ( head_of @ SY514 ) @ SV249 @ SY515 ) ) ) )
| ( path @ SV241 @ SV249 @ SV255 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1243]) ).
thf(1265,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( edge @ SX0 )
| ~ ( edge @ SX1 )
| ( ( head_of @ SX0 )
!= ( tail_of @ SX1 ) )
| ( sequential @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1244]) ).
thf(1266,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1245]) ).
thf(1267,plain,
! [SV242: $i,SV256: $i] :
( ( ( ! [SY516: $i] :
~ ( path @ SV256 @ SY516 @ SV242 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY475: $i] :
( ! [SY476: $i] :
~ ( precedes @ SY475 @ SY476 @ SV242 )
| ( on_path @ SY475 @ SV242 ) )
| ~ ! [SY477: $i,SY478: $i] :
( ~ ( precedes @ SY477 @ SY478 @ SV242 )
| ( on_path @ SY478 @ SV242 ) ) )
| ~ ~ ( ~ ! [SY479: $i,SY480: $i] :
( ~ ( precedes @ SY479 @ SY480 @ SV242 )
| ! [SY481: $i] :
( ~ ( precedes @ SY481 @ SY480 @ SV242 )
| ~ ( sequential @ SY479 @ SY481 ) )
| ~ ( sequential @ SY479 @ SY480 ) )
| ~ ! [SY482: $i,SY483: $i] :
( ~ ( precedes @ SY482 @ SY483 @ SV242 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY483 @ SY482 @ SV242 ) @ SY483 @ SV242 )
| ~ ( sequential @ SY482 @ ( sK9_E3 @ SY483 @ SY482 @ SV242 ) ) )
| ( sequential @ SY482 @ SY483 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1246]) ).
thf(1268,plain,
! [SV229: $i] :
( ( ( ( head_of @ SV229 )
= ( tail_of @ SV229 ) )
= $false )
| ( ( edge @ SV229 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1247]) ).
thf(1269,plain,
! [SV250: $i,SV243: $i,SV230: $i] :
( ( ( ~ ( path @ SV230 @ SV243 @ SV250 ) )
= $true )
| ( ( ( length_of @ SV250 )
= ( number_of_in @ edges @ SV250 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1248]) ).
thf(1270,plain,
! [SV251: $i,SV244: $i,SV231: $i] :
( ( ( ~ ( path @ SV231 @ SV244 @ SV251 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV251 )
= ( minus @ ( length_of @ SV251 ) @ n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1249]) ).
thf(1271,plain,
! [SV233: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV233 ) @ SV233 )
| ~ ( on_path @ ( sK7_SY80 @ SV233 ) @ SV233 ) )
| ~ ( sequential @ ( sK6_E1 @ SV233 ) @ ( sK7_SY80 @ SV233 ) ) )
| ~ ! [SY409: $i] :
~ ( triangle @ ( sK6_E1 @ SV233 ) @ ( sK7_SY80 @ SV233 ) @ SY409 ) )
= $false )
| ( ( ! [SY410: $i,SY411: $i] :
~ ( path @ SY410 @ SY411 @ SV233 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV233 )
= ( number_of_in @ triangles @ SV233 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1250]) ).
thf(1272,plain,
! [SV257: $i] :
( ( ~ ( edge @ SV257 )
| ( vertex @ ( head_of @ SV257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1251]) ).
thf(1273,plain,
! [SV258: $i] :
( ( ~ ( edge @ SV258 )
| ( vertex @ ( tail_of @ SV258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1252]) ).
thf(1274,plain,
! [SV259: $i,SV252: $i] :
( ( ( ( SV252 = SV259 )
| ~ ( vertex @ SV252 )
| ~ ( vertex @ SV259 )
| ~ ( ~ ~ ( ~ ( ( SV252
!= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
!= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
!= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
!= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV252
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
| ~ ( ( SV252
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) ) )
| ~ ~ ( ~ ( ( SV259
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
| ~ ( ( SV259
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV259 @ SV252 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1253]) ).
thf(1275,plain,
! [SV246: $i,SV234: $i,SV253: $i] :
( ( ~ ! [SY507: $i] :
( ! [SY508: $i] :
( ~ ( precedes @ SV253 @ SY507 @ SY508 )
| ~ ( shortest_path @ SV234 @ SV246 @ SY508 ) )
| ! [SY509: $i] :
( ( ( tail_of @ SY509 )
!= ( tail_of @ SV253 ) )
| ( ( head_of @ SY509 )
!= ( head_of @ SY507 ) ) ) )
| ~ ! [SY510: $i,SY511: $i] :
( ~ ( precedes @ SV253 @ SY510 @ SY511 )
| ~ ( shortest_path @ SV234 @ SV246 @ SY511 )
| ~ ( precedes @ SY510 @ SV253 @ SY511 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1254]) ).
thf(1276,plain,
! [SV247: $i,SV235: $i] :
( ( ~ ~ ( ~ ! [SY492: $i,SY493: $i] :
( ~ ( on_path @ SY493 @ SY492 )
| ~ ( path @ SV235 @ SV247 @ SY492 )
| ( edge @ SY493 ) )
| ~ ! [SY494: $i,SY495: $i] :
( ~ ( on_path @ SY495 @ SY494 )
| ~ ( path @ SV235 @ SV247 @ SY494 )
| ( in_path @ ( head_of @ SY495 ) @ SY494 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1255]) ).
thf(1277,plain,
! [SV247: $i,SV235: $i] :
( ( ~ ! [SY496: $i,SY497: $i] :
( ~ ( on_path @ SY497 @ SY496 )
| ~ ( path @ SV235 @ SV247 @ SY496 )
| ( in_path @ ( tail_of @ SY497 ) @ SY496 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1255]) ).
thf(1278,plain,
! [SV236: $i,SV260: $i,SV254: $i] :
( ( ( ~ ( path @ SV254 @ SV260 @ SV236 ) )
= $true )
| ( ( ~ ( ~ ! [SY428: $i,SY429: $i] :
( ~ ( on_path @ SY428 @ SV236 )
| ~ ( on_path @ SY429 @ SV236 )
| ! [SY430: $i] :
( ~ ( precedes @ SY430 @ SY429 @ SV236 )
| ~ ( sequential @ SY428 @ SY430 ) )
| ( precedes @ SY428 @ SY429 @ SV236 ) )
| ~ ! [SY431: $i,SY432: $i] :
( ~ ( on_path @ SY431 @ SV236 )
| ~ ( on_path @ SY432 @ SV236 )
| ~ ( sequential @ SY431 @ SY432 )
| ( precedes @ SY431 @ SY432 @ SV236 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1256]) ).
thf(1279,plain,
! [SV248: $i,SV237: $i] :
( ( ~ ! [SY498: $i,SY499: $i] :
( ~ ( in_path @ SY499 @ SY498 )
| ~ ( path @ SV237 @ SV248 @ SY498 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY499 @ SY498 @ SV248 @ SV237 ) @ SY498 )
| ~ ( ( SY499
= ( head_of @ ( sK10_E @ SY499 @ SY498 @ SV248 @ SV237 ) ) )
| ( SY499
= ( tail_of @ ( sK10_E @ SY499 @ SY498 @ SV248 @ SV237 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1257]) ).
thf(1280,plain,
! [SV248: $i,SV237: $i] :
( ( ~ ! [SY500: $i,SY501: $i] :
( ~ ( in_path @ SY501 @ SY500 )
| ~ ( path @ SV237 @ SV248 @ SY500 )
| ( vertex @ SY501 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1257]) ).
thf(1281,plain,
! [SV238: $i] :
( ( ! [SY438: $i,SY439: $i] :
( ~ ( edge @ SV238 )
| ~ ( edge @ SY438 )
| ~ ( edge @ SY439 )
| ~ ( sequential @ SV238 @ SY438 )
| ~ ( sequential @ SY438 @ SY439 )
| ~ ( sequential @ SY439 @ SV238 )
| ( triangle @ SV238 @ SY438 @ SY439 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1258]) ).
thf(1282,plain,
! [SV238: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY440: $i,SY441: $i] :
~ ( triangle @ SV238 @ SY440 @ SY441 )
| ( edge @ SV238 ) )
| ~ ! [SY442: $i] :
( ! [SY443: $i] :
~ ( triangle @ SV238 @ SY442 @ SY443 )
| ( edge @ SY442 ) ) )
| ~ ! [SY444: $i,SY445: $i] :
( ~ ( triangle @ SV238 @ SY444 @ SY445 )
| ( edge @ SY445 ) ) )
| ~ ! [SY446: $i] :
( ! [SY447: $i] :
~ ( triangle @ SV238 @ SY446 @ SY447 )
| ( sequential @ SV238 @ SY446 ) ) )
| ~ ! [SY448: $i,SY449: $i] :
( ~ ( triangle @ SV238 @ SY448 @ SY449 )
| ( sequential @ SY448 @ SY449 ) ) )
| ~ ! [SY450: $i,SY451: $i] :
( ~ ( triangle @ SV238 @ SY450 @ SY451 )
| ( sequential @ SY451 @ SV238 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1259]) ).
thf(1283,plain,
! [SV239: $i] :
( ( ! [SY452: $i,SY453: $i] :
( ~ ( ~ ( path @ SV239 @ SY452 @ ( sK8_P @ SY453 @ SY452 @ SV239 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY453 ) @ ( length_of @ ( sK8_P @ SY453 @ SY452 @ SV239 ) ) ) )
| ( SV239 = SY452 )
| ~ ( path @ SV239 @ SY452 @ SY453 )
| ( shortest_path @ SV239 @ SY452 @ SY453 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1260]) ).
thf(1284,plain,
! [SV239: $i] :
( ( ~ ( ~ ! [SY454: $i,SY455: $i] :
( ~ ( shortest_path @ SV239 @ SY454 @ SY455 )
| ! [SY456: $i] :
( ~ ( path @ SV239 @ SY454 @ SY456 )
| ( less_or_equal @ ( length_of @ SY455 ) @ ( length_of @ SY456 ) ) ) )
| ~ ~ ( ~ ! [SY457: $i] :
( ! [SY458: $i] :
~ ( shortest_path @ SV239 @ SY457 @ SY458 )
| ( SV239 != SY457 ) )
| ~ ! [SY459: $i,SY460: $i] :
( ~ ( shortest_path @ SV239 @ SY459 @ SY460 )
| ( path @ SV239 @ SY459 @ SY460 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1261]) ).
thf(1285,plain,
! [SV240: $i] :
( ( ~ ( ~ ( ! [SY461: $i,SY462: $i] :
~ ( path @ SV240 @ SY461 @ SY462 )
| ( vertex @ SV240 ) )
| ~ ! [SY463: $i] :
( ! [SY464: $i] :
~ ( path @ SV240 @ SY463 @ SY464 )
| ( vertex @ SY463 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1262]) ).
thf(1286,plain,
! [SV240: $i] :
( ( ! [SY465: $i,SY466: $i] :
( ~ ( path @ SV240 @ SY465 @ SY466 )
| ~ ( ~ ~ ( ( SV240
!= ( tail_of @ ( sK11_E @ SY466 @ SY465 @ SV240 ) ) )
| ~ ( edge @ ( sK11_E @ SY466 @ SY465 @ SV240 ) ) )
| ~ ~ ( ~ ( ( SY465
!= ( head_of @ ( sK11_E @ SY466 @ SY465 @ SV240 ) ) )
| ( SY466
!= ( path_cons @ ( sK11_E @ SY466 @ SY465 @ SV240 ) @ empty ) )
| ! [SY467: $i] :
( ( SY466
!= ( path_cons @ ( sK11_E @ SY466 @ SY465 @ SV240 ) @ SY467 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY466 @ SY465 @ SV240 ) ) @ SY465 @ SY467 ) ) )
| ~ ~ ( ~ ( ( SY465
= ( head_of @ ( sK11_E @ SY466 @ SY465 @ SV240 ) ) )
| ~ ( ( SY466
!= ( path_cons @ ( sK11_E @ SY466 @ SY465 @ SV240 ) @ ( sK13_SY84 @ SY466 @ SY465 @ SV240 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY466 @ SY465 @ SV240 ) ) @ SY465 @ ( sK13_SY84 @ SY466 @ SY465 @ SV240 ) ) ) )
| ~ ( ( SY466
= ( path_cons @ ( sK11_E @ SY466 @ SY465 @ SV240 ) @ empty ) )
| ~ ( ( SY466
!= ( path_cons @ ( sK11_E @ SY466 @ SY465 @ SV240 ) @ ( sK12_SY85 @ SY466 @ SY465 @ SV240 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY466 @ SY465 @ SV240 ) ) @ SY465 @ ( sK12_SY85 @ SY466 @ SY465 @ SV240 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1263]) ).
thf(1287,plain,
! [SV255: $i,SV249: $i,SV241: $i] :
( ( ( ~ ( vertex @ SV241 )
| ~ ( vertex @ SV249 )
| ~ ( ~ ! [SY513: $i] :
( ( SV241
!= ( tail_of @ SY513 ) )
| ~ ( edge @ SY513 )
| ( SV249
!= ( head_of @ SY513 ) )
| ( SV255
!= ( path_cons @ SY513 @ empty ) ) )
| ~ ! [SY514: $i] :
( ( SV241
!= ( tail_of @ SY514 ) )
| ~ ( edge @ SY514 )
| ! [SY515: $i] :
( ( SV255
!= ( path_cons @ SY514 @ SY515 ) )
| ~ ( path @ ( head_of @ SY514 ) @ SV249 @ SY515 ) ) ) ) )
= $true )
| ( ( path @ SV241 @ SV249 @ SV255 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1264]) ).
thf(1288,plain,
! [SV261: $i] :
( ( ! [SY517: $i] :
( ( SV261 = SY517 )
| ~ ( edge @ SV261 )
| ~ ( edge @ SY517 )
| ( ( head_of @ SV261 )
!= ( tail_of @ SY517 ) )
| ( sequential @ SV261 @ SY517 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1265]) ).
thf(1289,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1266]) ).
thf(1290,plain,
! [SV242: $i,SV262: $i,SV256: $i] :
( ( ( ~ ( path @ SV256 @ SV262 @ SV242 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY475: $i] :
( ! [SY476: $i] :
~ ( precedes @ SY475 @ SY476 @ SV242 )
| ( on_path @ SY475 @ SV242 ) )
| ~ ! [SY477: $i,SY478: $i] :
( ~ ( precedes @ SY477 @ SY478 @ SV242 )
| ( on_path @ SY478 @ SV242 ) ) )
| ~ ~ ( ~ ! [SY479: $i,SY480: $i] :
( ~ ( precedes @ SY479 @ SY480 @ SV242 )
| ! [SY481: $i] :
( ~ ( precedes @ SY481 @ SY480 @ SV242 )
| ~ ( sequential @ SY479 @ SY481 ) )
| ~ ( sequential @ SY479 @ SY480 ) )
| ~ ! [SY482: $i,SY483: $i] :
( ~ ( precedes @ SY482 @ SY483 @ SV242 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY483 @ SY482 @ SV242 ) @ SY483 @ SV242 )
| ~ ( sequential @ SY482 @ ( sK9_E3 @ SY483 @ SY482 @ SV242 ) ) )
| ( sequential @ SY482 @ SY483 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1267]) ).
thf(1291,plain,
! [SV250: $i,SV243: $i,SV230: $i] :
( ( ( path @ SV230 @ SV243 @ SV250 )
= $false )
| ( ( ( length_of @ SV250 )
= ( number_of_in @ edges @ SV250 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1269]) ).
thf(1292,plain,
! [SV251: $i,SV244: $i,SV231: $i] :
( ( ( path @ SV231 @ SV244 @ SV251 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV251 )
= ( minus @ ( length_of @ SV251 ) @ n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1270]) ).
thf(1293,plain,
! [SV233: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV233 ) @ SV233 )
| ~ ( on_path @ ( sK7_SY80 @ SV233 ) @ SV233 ) )
| ~ ( sequential @ ( sK6_E1 @ SV233 ) @ ( sK7_SY80 @ SV233 ) ) ) )
= $false )
| ( ( ! [SY410: $i,SY411: $i] :
~ ( path @ SY410 @ SY411 @ SV233 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV233 )
= ( number_of_in @ triangles @ SV233 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1271]) ).
thf(1294,plain,
! [SV233: $i] :
( ( ( ~ ! [SY409: $i] :
~ ( triangle @ ( sK6_E1 @ SV233 ) @ ( sK7_SY80 @ SV233 ) @ SY409 ) )
= $false )
| ( ( ! [SY410: $i,SY411: $i] :
~ ( path @ SY410 @ SY411 @ SV233 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV233 )
= ( number_of_in @ triangles @ SV233 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1271]) ).
thf(1295,plain,
! [SV257: $i] :
( ( ( ~ ( edge @ SV257 ) )
= $true )
| ( ( vertex @ ( head_of @ SV257 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1272]) ).
thf(1296,plain,
! [SV258: $i] :
( ( ( ~ ( edge @ SV258 ) )
= $true )
| ( ( vertex @ ( tail_of @ SV258 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1273]) ).
thf(1297,plain,
! [SV259: $i,SV252: $i] :
( ( ( ( SV252 = SV259 )
| ~ ( vertex @ SV252 )
| ~ ( vertex @ SV259 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV252
!= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
!= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
!= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
!= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV252
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
| ~ ( ( SV252
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) ) )
| ~ ~ ( ~ ( ( SV259
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
| ~ ( ( SV259
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV259 @ SV252 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[1274]) ).
thf(1298,plain,
! [SV246: $i,SV234: $i,SV253: $i] :
( ( ~ ! [SY507: $i] :
( ! [SY508: $i] :
( ~ ( precedes @ SV253 @ SY507 @ SY508 )
| ~ ( shortest_path @ SV234 @ SV246 @ SY508 ) )
| ! [SY509: $i] :
( ( ( tail_of @ SY509 )
!= ( tail_of @ SV253 ) )
| ( ( head_of @ SY509 )
!= ( head_of @ SY507 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1275]) ).
thf(1299,plain,
! [SV246: $i,SV234: $i,SV253: $i] :
( ( ~ ! [SY510: $i,SY511: $i] :
( ~ ( precedes @ SV253 @ SY510 @ SY511 )
| ~ ( shortest_path @ SV234 @ SV246 @ SY511 )
| ~ ( precedes @ SY510 @ SV253 @ SY511 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1275]) ).
thf(1300,plain,
! [SV247: $i,SV235: $i] :
( ( ~ ( ~ ! [SY492: $i,SY493: $i] :
( ~ ( on_path @ SY493 @ SY492 )
| ~ ( path @ SV235 @ SV247 @ SY492 )
| ( edge @ SY493 ) )
| ~ ! [SY494: $i,SY495: $i] :
( ~ ( on_path @ SY495 @ SY494 )
| ~ ( path @ SV235 @ SV247 @ SY494 )
| ( in_path @ ( head_of @ SY495 ) @ SY494 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1276]) ).
thf(1301,plain,
! [SV247: $i,SV235: $i] :
( ( ! [SY496: $i,SY497: $i] :
( ~ ( on_path @ SY497 @ SY496 )
| ~ ( path @ SV235 @ SV247 @ SY496 )
| ( in_path @ ( tail_of @ SY497 ) @ SY496 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1277]) ).
thf(1302,plain,
! [SV236: $i,SV260: $i,SV254: $i] :
( ( ( path @ SV254 @ SV260 @ SV236 )
= $false )
| ( ( ~ ( ~ ! [SY428: $i,SY429: $i] :
( ~ ( on_path @ SY428 @ SV236 )
| ~ ( on_path @ SY429 @ SV236 )
| ! [SY430: $i] :
( ~ ( precedes @ SY430 @ SY429 @ SV236 )
| ~ ( sequential @ SY428 @ SY430 ) )
| ( precedes @ SY428 @ SY429 @ SV236 ) )
| ~ ! [SY431: $i,SY432: $i] :
( ~ ( on_path @ SY431 @ SV236 )
| ~ ( on_path @ SY432 @ SV236 )
| ~ ( sequential @ SY431 @ SY432 )
| ( precedes @ SY431 @ SY432 @ SV236 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1278]) ).
thf(1303,plain,
! [SV248: $i,SV237: $i] :
( ( ! [SY498: $i,SY499: $i] :
( ~ ( in_path @ SY499 @ SY498 )
| ~ ( path @ SV237 @ SV248 @ SY498 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY499 @ SY498 @ SV248 @ SV237 ) @ SY498 )
| ~ ( ( SY499
= ( head_of @ ( sK10_E @ SY499 @ SY498 @ SV248 @ SV237 ) ) )
| ( SY499
= ( tail_of @ ( sK10_E @ SY499 @ SY498 @ SV248 @ SV237 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1279]) ).
thf(1304,plain,
! [SV248: $i,SV237: $i] :
( ( ! [SY500: $i,SY501: $i] :
( ~ ( in_path @ SY501 @ SY500 )
| ~ ( path @ SV237 @ SV248 @ SY500 )
| ( vertex @ SY501 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1280]) ).
thf(1305,plain,
! [SV263: $i,SV238: $i] :
( ( ! [SY518: $i] :
( ~ ( edge @ SV238 )
| ~ ( edge @ SV263 )
| ~ ( edge @ SY518 )
| ~ ( sequential @ SV238 @ SV263 )
| ~ ( sequential @ SV263 @ SY518 )
| ~ ( sequential @ SY518 @ SV238 )
| ( triangle @ SV238 @ SV263 @ SY518 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1281]) ).
thf(1306,plain,
! [SV238: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY440: $i,SY441: $i] :
~ ( triangle @ SV238 @ SY440 @ SY441 )
| ( edge @ SV238 ) )
| ~ ! [SY442: $i] :
( ! [SY443: $i] :
~ ( triangle @ SV238 @ SY442 @ SY443 )
| ( edge @ SY442 ) ) )
| ~ ! [SY444: $i,SY445: $i] :
( ~ ( triangle @ SV238 @ SY444 @ SY445 )
| ( edge @ SY445 ) ) )
| ~ ! [SY446: $i] :
( ! [SY447: $i] :
~ ( triangle @ SV238 @ SY446 @ SY447 )
| ( sequential @ SV238 @ SY446 ) ) )
| ~ ! [SY448: $i,SY449: $i] :
( ~ ( triangle @ SV238 @ SY448 @ SY449 )
| ( sequential @ SY448 @ SY449 ) ) )
| ~ ! [SY450: $i,SY451: $i] :
( ~ ( triangle @ SV238 @ SY450 @ SY451 )
| ( sequential @ SY451 @ SV238 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1282]) ).
thf(1307,plain,
! [SV264: $i,SV239: $i] :
( ( ! [SY519: $i] :
( ~ ( ~ ( path @ SV239 @ SV264 @ ( sK8_P @ SY519 @ SV264 @ SV239 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY519 ) @ ( length_of @ ( sK8_P @ SY519 @ SV264 @ SV239 ) ) ) )
| ( SV239 = SV264 )
| ~ ( path @ SV239 @ SV264 @ SY519 )
| ( shortest_path @ SV239 @ SV264 @ SY519 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1283]) ).
thf(1308,plain,
! [SV239: $i] :
( ( ~ ! [SY454: $i,SY455: $i] :
( ~ ( shortest_path @ SV239 @ SY454 @ SY455 )
| ! [SY456: $i] :
( ~ ( path @ SV239 @ SY454 @ SY456 )
| ( less_or_equal @ ( length_of @ SY455 ) @ ( length_of @ SY456 ) ) ) )
| ~ ~ ( ~ ! [SY457: $i] :
( ! [SY458: $i] :
~ ( shortest_path @ SV239 @ SY457 @ SY458 )
| ( SV239 != SY457 ) )
| ~ ! [SY459: $i,SY460: $i] :
( ~ ( shortest_path @ SV239 @ SY459 @ SY460 )
| ( path @ SV239 @ SY459 @ SY460 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1284]) ).
thf(1309,plain,
! [SV240: $i] :
( ( ~ ( ! [SY461: $i,SY462: $i] :
~ ( path @ SV240 @ SY461 @ SY462 )
| ( vertex @ SV240 ) )
| ~ ! [SY463: $i] :
( ! [SY464: $i] :
~ ( path @ SV240 @ SY463 @ SY464 )
| ( vertex @ SY463 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1285]) ).
thf(1310,plain,
! [SV265: $i,SV240: $i] :
( ( ! [SY520: $i] :
( ~ ( path @ SV240 @ SV265 @ SY520 )
| ~ ( ~ ~ ( ( SV240
!= ( tail_of @ ( sK11_E @ SY520 @ SV265 @ SV240 ) ) )
| ~ ( edge @ ( sK11_E @ SY520 @ SV265 @ SV240 ) ) )
| ~ ~ ( ~ ( ( SV265
!= ( head_of @ ( sK11_E @ SY520 @ SV265 @ SV240 ) ) )
| ( SY520
!= ( path_cons @ ( sK11_E @ SY520 @ SV265 @ SV240 ) @ empty ) )
| ! [SY521: $i] :
( ( SY520
!= ( path_cons @ ( sK11_E @ SY520 @ SV265 @ SV240 ) @ SY521 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY520 @ SV265 @ SV240 ) ) @ SV265 @ SY521 ) ) )
| ~ ~ ( ~ ( ( SV265
= ( head_of @ ( sK11_E @ SY520 @ SV265 @ SV240 ) ) )
| ~ ( ( SY520
!= ( path_cons @ ( sK11_E @ SY520 @ SV265 @ SV240 ) @ ( sK13_SY84 @ SY520 @ SV265 @ SV240 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY520 @ SV265 @ SV240 ) ) @ SV265 @ ( sK13_SY84 @ SY520 @ SV265 @ SV240 ) ) ) )
| ~ ( ( SY520
= ( path_cons @ ( sK11_E @ SY520 @ SV265 @ SV240 ) @ empty ) )
| ~ ( ( SY520
!= ( path_cons @ ( sK11_E @ SY520 @ SV265 @ SV240 ) @ ( sK12_SY85 @ SY520 @ SV265 @ SV240 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY520 @ SV265 @ SV240 ) ) @ SV265 @ ( sK12_SY85 @ SY520 @ SV265 @ SV240 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1286]) ).
thf(1311,plain,
! [SV255: $i,SV249: $i,SV241: $i] :
( ( ( ~ ( vertex @ SV241 )
| ~ ( vertex @ SV249 ) )
= $true )
| ( ( ~ ( ~ ! [SY513: $i] :
( ( SV241
!= ( tail_of @ SY513 ) )
| ~ ( edge @ SY513 )
| ( SV249
!= ( head_of @ SY513 ) )
| ( SV255
!= ( path_cons @ SY513 @ empty ) ) )
| ~ ! [SY514: $i] :
( ( SV241
!= ( tail_of @ SY514 ) )
| ~ ( edge @ SY514 )
| ! [SY515: $i] :
( ( SV255
!= ( path_cons @ SY514 @ SY515 ) )
| ~ ( path @ ( head_of @ SY514 ) @ SV249 @ SY515 ) ) ) ) )
= $true )
| ( ( path @ SV241 @ SV249 @ SV255 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1287]) ).
thf(1312,plain,
! [SV266: $i,SV261: $i] :
( ( ( SV261 = SV266 )
| ~ ( edge @ SV261 )
| ~ ( edge @ SV266 )
| ( ( head_of @ SV261 )
!= ( tail_of @ SV266 ) )
| ( sequential @ SV261 @ SV266 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1288]) ).
thf(1313,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1289]) ).
thf(1314,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1289]) ).
thf(1315,plain,
! [SV242: $i,SV262: $i,SV256: $i] :
( ( ( path @ SV256 @ SV262 @ SV242 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY475: $i] :
( ! [SY476: $i] :
~ ( precedes @ SY475 @ SY476 @ SV242 )
| ( on_path @ SY475 @ SV242 ) )
| ~ ! [SY477: $i,SY478: $i] :
( ~ ( precedes @ SY477 @ SY478 @ SV242 )
| ( on_path @ SY478 @ SV242 ) ) )
| ~ ~ ( ~ ! [SY479: $i,SY480: $i] :
( ~ ( precedes @ SY479 @ SY480 @ SV242 )
| ! [SY481: $i] :
( ~ ( precedes @ SY481 @ SY480 @ SV242 )
| ~ ( sequential @ SY479 @ SY481 ) )
| ~ ( sequential @ SY479 @ SY480 ) )
| ~ ! [SY482: $i,SY483: $i] :
( ~ ( precedes @ SY482 @ SY483 @ SV242 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY483 @ SY482 @ SV242 ) @ SY483 @ SV242 )
| ~ ( sequential @ SY482 @ ( sK9_E3 @ SY483 @ SY482 @ SV242 ) ) )
| ( sequential @ SY482 @ SY483 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1290]) ).
thf(1316,plain,
! [SV233: $i] :
( ( ( ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV233 ) @ SV233 )
| ~ ( on_path @ ( sK7_SY80 @ SV233 ) @ SV233 ) )
| ~ ( sequential @ ( sK6_E1 @ SV233 ) @ ( sK7_SY80 @ SV233 ) ) ) )
= $true )
| ( ( ! [SY410: $i,SY411: $i] :
~ ( path @ SY410 @ SY411 @ SV233 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV233 )
= ( number_of_in @ triangles @ SV233 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1293]) ).
thf(1317,plain,
! [SV233: $i] :
( ( ( ! [SY409: $i] :
~ ( triangle @ ( sK6_E1 @ SV233 ) @ ( sK7_SY80 @ SV233 ) @ SY409 ) )
= $true )
| ( ( ! [SY410: $i,SY411: $i] :
~ ( path @ SY410 @ SY411 @ SV233 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV233 )
= ( number_of_in @ triangles @ SV233 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1294]) ).
thf(1318,plain,
! [SV257: $i] :
( ( ( edge @ SV257 )
= $false )
| ( ( vertex @ ( head_of @ SV257 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1295]) ).
thf(1319,plain,
! [SV258: $i] :
( ( ( edge @ SV258 )
= $false )
| ( ( vertex @ ( tail_of @ SV258 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1296]) ).
thf(1320,plain,
! [SV259: $i,SV252: $i] :
( ( ( SV252 = SV259 )
= $true )
| ( ( ~ ( vertex @ SV252 )
| ~ ( vertex @ SV259 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV252
!= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
!= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
!= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
!= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV252
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
| ~ ( ( SV252
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) ) )
| ~ ~ ( ~ ( ( SV259
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
| ~ ( ( SV259
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV259 @ SV252 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[1297]) ).
thf(1321,plain,
! [SV246: $i,SV234: $i,SV253: $i] :
( ( ! [SY507: $i] :
( ! [SY508: $i] :
( ~ ( precedes @ SV253 @ SY507 @ SY508 )
| ~ ( shortest_path @ SV234 @ SV246 @ SY508 ) )
| ! [SY509: $i] :
( ( ( tail_of @ SY509 )
!= ( tail_of @ SV253 ) )
| ( ( head_of @ SY509 )
!= ( head_of @ SY507 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1298]) ).
thf(1322,plain,
! [SV246: $i,SV234: $i,SV253: $i] :
( ( ! [SY510: $i,SY511: $i] :
( ~ ( precedes @ SV253 @ SY510 @ SY511 )
| ~ ( shortest_path @ SV234 @ SV246 @ SY511 )
| ~ ( precedes @ SY510 @ SV253 @ SY511 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1299]) ).
thf(1323,plain,
! [SV247: $i,SV235: $i] :
( ( ~ ! [SY492: $i,SY493: $i] :
( ~ ( on_path @ SY493 @ SY492 )
| ~ ( path @ SV235 @ SV247 @ SY492 )
| ( edge @ SY493 ) )
| ~ ! [SY494: $i,SY495: $i] :
( ~ ( on_path @ SY495 @ SY494 )
| ~ ( path @ SV235 @ SV247 @ SY494 )
| ( in_path @ ( head_of @ SY495 ) @ SY494 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1300]) ).
thf(1324,plain,
! [SV247: $i,SV235: $i,SV267: $i] :
( ( ! [SY522: $i] :
( ~ ( on_path @ SY522 @ SV267 )
| ~ ( path @ SV235 @ SV247 @ SV267 )
| ( in_path @ ( tail_of @ SY522 ) @ SV267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1301]) ).
thf(1325,plain,
! [SV260: $i,SV254: $i,SV236: $i] :
( ( ( ~ ! [SY428: $i,SY429: $i] :
( ~ ( on_path @ SY428 @ SV236 )
| ~ ( on_path @ SY429 @ SV236 )
| ! [SY430: $i] :
( ~ ( precedes @ SY430 @ SY429 @ SV236 )
| ~ ( sequential @ SY428 @ SY430 ) )
| ( precedes @ SY428 @ SY429 @ SV236 ) )
| ~ ! [SY431: $i,SY432: $i] :
( ~ ( on_path @ SY431 @ SV236 )
| ~ ( on_path @ SY432 @ SV236 )
| ~ ( sequential @ SY431 @ SY432 )
| ( precedes @ SY431 @ SY432 @ SV236 ) ) )
= $false )
| ( ( path @ SV254 @ SV260 @ SV236 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1302]) ).
thf(1326,plain,
! [SV248: $i,SV237: $i,SV268: $i] :
( ( ! [SY523: $i] :
( ~ ( in_path @ SY523 @ SV268 )
| ~ ( path @ SV237 @ SV248 @ SV268 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY523 @ SV268 @ SV248 @ SV237 ) @ SV268 )
| ~ ( ( SY523
= ( head_of @ ( sK10_E @ SY523 @ SV268 @ SV248 @ SV237 ) ) )
| ( SY523
= ( tail_of @ ( sK10_E @ SY523 @ SV268 @ SV248 @ SV237 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1303]) ).
thf(1327,plain,
! [SV248: $i,SV237: $i,SV269: $i] :
( ( ! [SY524: $i] :
( ~ ( in_path @ SY524 @ SV269 )
| ~ ( path @ SV237 @ SV248 @ SV269 )
| ( vertex @ SY524 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1304]) ).
thf(1328,plain,
! [SV270: $i,SV263: $i,SV238: $i] :
( ( ~ ( edge @ SV238 )
| ~ ( edge @ SV263 )
| ~ ( edge @ SV270 )
| ~ ( sequential @ SV238 @ SV263 )
| ~ ( sequential @ SV263 @ SV270 )
| ~ ( sequential @ SV270 @ SV238 )
| ( triangle @ SV238 @ SV263 @ SV270 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1305]) ).
thf(1329,plain,
! [SV238: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY440: $i,SY441: $i] :
~ ( triangle @ SV238 @ SY440 @ SY441 )
| ( edge @ SV238 ) )
| ~ ! [SY442: $i] :
( ! [SY443: $i] :
~ ( triangle @ SV238 @ SY442 @ SY443 )
| ( edge @ SY442 ) ) )
| ~ ! [SY444: $i,SY445: $i] :
( ~ ( triangle @ SV238 @ SY444 @ SY445 )
| ( edge @ SY445 ) ) )
| ~ ! [SY446: $i] :
( ! [SY447: $i] :
~ ( triangle @ SV238 @ SY446 @ SY447 )
| ( sequential @ SV238 @ SY446 ) ) )
| ~ ! [SY448: $i,SY449: $i] :
( ~ ( triangle @ SV238 @ SY448 @ SY449 )
| ( sequential @ SY448 @ SY449 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1306]) ).
thf(1330,plain,
! [SV238: $i] :
( ( ~ ! [SY450: $i,SY451: $i] :
( ~ ( triangle @ SV238 @ SY450 @ SY451 )
| ( sequential @ SY451 @ SV238 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1306]) ).
thf(1331,plain,
! [SV271: $i,SV264: $i,SV239: $i] :
( ( ~ ( ~ ( path @ SV239 @ SV264 @ ( sK8_P @ SV271 @ SV264 @ SV239 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SV271 ) @ ( length_of @ ( sK8_P @ SV271 @ SV264 @ SV239 ) ) ) )
| ( SV239 = SV264 )
| ~ ( path @ SV239 @ SV264 @ SV271 )
| ( shortest_path @ SV239 @ SV264 @ SV271 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1307]) ).
thf(1332,plain,
! [SV239: $i] :
( ( ~ ! [SY454: $i,SY455: $i] :
( ~ ( shortest_path @ SV239 @ SY454 @ SY455 )
| ! [SY456: $i] :
( ~ ( path @ SV239 @ SY454 @ SY456 )
| ( less_or_equal @ ( length_of @ SY455 ) @ ( length_of @ SY456 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1308]) ).
thf(1333,plain,
! [SV239: $i] :
( ( ~ ~ ( ~ ! [SY457: $i] :
( ! [SY458: $i] :
~ ( shortest_path @ SV239 @ SY457 @ SY458 )
| ( SV239 != SY457 ) )
| ~ ! [SY459: $i,SY460: $i] :
( ~ ( shortest_path @ SV239 @ SY459 @ SY460 )
| ( path @ SV239 @ SY459 @ SY460 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1308]) ).
thf(1334,plain,
! [SV240: $i] :
( ( ~ ( ! [SY461: $i,SY462: $i] :
~ ( path @ SV240 @ SY461 @ SY462 )
| ( vertex @ SV240 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1309]) ).
thf(1335,plain,
! [SV240: $i] :
( ( ~ ! [SY463: $i] :
( ! [SY464: $i] :
~ ( path @ SV240 @ SY463 @ SY464 )
| ( vertex @ SY463 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1309]) ).
thf(1336,plain,
! [SV272: $i,SV265: $i,SV240: $i] :
( ( ~ ( path @ SV240 @ SV265 @ SV272 )
| ~ ( ~ ~ ( ( SV240
!= ( tail_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( edge @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
| ~ ~ ( ~ ( ( SV265
!= ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
| ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ empty ) )
| ! [SY525: $i] :
( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ SY525 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ SY525 ) ) )
| ~ ~ ( ~ ( ( SV265
= ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ ( sK13_SY84 @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ ( sK13_SY84 @ SV272 @ SV265 @ SV240 ) ) ) )
| ~ ( ( SV272
= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ empty ) )
| ~ ( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ ( sK12_SY85 @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ ( sK12_SY85 @ SV272 @ SV265 @ SV240 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1310]) ).
thf(1337,plain,
! [SV255: $i,SV249: $i,SV241: $i] :
( ( ( ~ ( vertex @ SV241 ) )
= $true )
| ( ( ~ ( vertex @ SV249 ) )
= $true )
| ( ( ~ ( ~ ! [SY513: $i] :
( ( SV241
!= ( tail_of @ SY513 ) )
| ~ ( edge @ SY513 )
| ( SV249
!= ( head_of @ SY513 ) )
| ( SV255
!= ( path_cons @ SY513 @ empty ) ) )
| ~ ! [SY514: $i] :
( ( SV241
!= ( tail_of @ SY514 ) )
| ~ ( edge @ SY514 )
| ! [SY515: $i] :
( ( SV255
!= ( path_cons @ SY514 @ SY515 ) )
| ~ ( path @ ( head_of @ SY514 ) @ SV249 @ SY515 ) ) ) ) )
= $true )
| ( ( path @ SV241 @ SV249 @ SV255 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1311]) ).
thf(1338,plain,
! [SV266: $i,SV261: $i] :
( ( ( ( SV261 = SV266 )
| ~ ( edge @ SV261 )
| ~ ( edge @ SV266 )
| ( ( head_of @ SV261 )
!= ( tail_of @ SV266 ) ) )
= $true )
| ( ( sequential @ SV261 @ SV266 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1312]) ).
thf(1339,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1313]) ).
thf(1340,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1314]) ).
thf(1341,plain,
! [SV262: $i,SV256: $i,SV242: $i] :
( ( ( ~ ~ ( ~ ! [SY475: $i] :
( ! [SY476: $i] :
~ ( precedes @ SY475 @ SY476 @ SV242 )
| ( on_path @ SY475 @ SV242 ) )
| ~ ! [SY477: $i,SY478: $i] :
( ~ ( precedes @ SY477 @ SY478 @ SV242 )
| ( on_path @ SY478 @ SV242 ) ) )
| ~ ~ ( ~ ! [SY479: $i,SY480: $i] :
( ~ ( precedes @ SY479 @ SY480 @ SV242 )
| ! [SY481: $i] :
( ~ ( precedes @ SY481 @ SY480 @ SV242 )
| ~ ( sequential @ SY479 @ SY481 ) )
| ~ ( sequential @ SY479 @ SY480 ) )
| ~ ! [SY482: $i,SY483: $i] :
( ~ ( precedes @ SY482 @ SY483 @ SV242 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY483 @ SY482 @ SV242 ) @ SY483 @ SV242 )
| ~ ( sequential @ SY482 @ ( sK9_E3 @ SY483 @ SY482 @ SV242 ) ) )
| ( sequential @ SY482 @ SY483 ) ) ) )
= $false )
| ( ( path @ SV256 @ SV262 @ SV242 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1315]) ).
thf(1342,plain,
! [SV233: $i] :
( ( ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV233 ) @ SV233 )
| ~ ( on_path @ ( sK7_SY80 @ SV233 ) @ SV233 ) )
| ~ ( sequential @ ( sK6_E1 @ SV233 ) @ ( sK7_SY80 @ SV233 ) ) )
= $false )
| ( ( ! [SY410: $i,SY411: $i] :
~ ( path @ SY410 @ SY411 @ SV233 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV233 )
= ( number_of_in @ triangles @ SV233 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1316]) ).
thf(1343,plain,
! [SV273: $i,SV233: $i] :
( ( ( ~ ( triangle @ ( sK6_E1 @ SV233 ) @ ( sK7_SY80 @ SV233 ) @ SV273 ) )
= $true )
| ( ( ! [SY410: $i,SY411: $i] :
~ ( path @ SY410 @ SY411 @ SV233 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV233 )
= ( number_of_in @ triangles @ SV233 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1317]) ).
thf(1344,plain,
! [SV259: $i,SV252: $i] :
( ( ( ~ ( vertex @ SV252 ) )
= $true )
| ( ( ~ ( vertex @ SV259 ) )
= $true )
| ( ( SV252 = SV259 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV252
!= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
!= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
!= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
!= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV252
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
| ~ ( ( SV252
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) ) )
| ~ ~ ( ~ ( ( SV259
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
| ~ ( ( SV259
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV259 @ SV252 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[1320]) ).
thf(1345,plain,
! [SV246: $i,SV234: $i,SV274: $i,SV253: $i] :
( ( ! [SY526: $i] :
( ~ ( precedes @ SV253 @ SV274 @ SY526 )
| ~ ( shortest_path @ SV234 @ SV246 @ SY526 ) )
| ! [SY527: $i] :
( ( ( tail_of @ SY527 )
!= ( tail_of @ SV253 ) )
| ( ( head_of @ SY527 )
!= ( head_of @ SV274 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1321]) ).
thf(1346,plain,
! [SV246: $i,SV234: $i,SV275: $i,SV253: $i] :
( ( ! [SY528: $i] :
( ~ ( precedes @ SV253 @ SV275 @ SY528 )
| ~ ( shortest_path @ SV234 @ SV246 @ SY528 )
| ~ ( precedes @ SV275 @ SV253 @ SY528 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1322]) ).
thf(1347,plain,
! [SV247: $i,SV235: $i] :
( ( ~ ! [SY492: $i,SY493: $i] :
( ~ ( on_path @ SY493 @ SY492 )
| ~ ( path @ SV235 @ SV247 @ SY492 )
| ( edge @ SY493 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1323]) ).
thf(1348,plain,
! [SV247: $i,SV235: $i] :
( ( ~ ! [SY494: $i,SY495: $i] :
( ~ ( on_path @ SY495 @ SY494 )
| ~ ( path @ SV235 @ SV247 @ SY494 )
| ( in_path @ ( head_of @ SY495 ) @ SY494 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1323]) ).
thf(1349,plain,
! [SV247: $i,SV235: $i,SV267: $i,SV276: $i] :
( ( ~ ( on_path @ SV276 @ SV267 )
| ~ ( path @ SV235 @ SV247 @ SV267 )
| ( in_path @ ( tail_of @ SV276 ) @ SV267 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1324]) ).
thf(1350,plain,
! [SV260: $i,SV254: $i,SV236: $i] :
( ( ( ~ ! [SY428: $i,SY429: $i] :
( ~ ( on_path @ SY428 @ SV236 )
| ~ ( on_path @ SY429 @ SV236 )
| ! [SY430: $i] :
( ~ ( precedes @ SY430 @ SY429 @ SV236 )
| ~ ( sequential @ SY428 @ SY430 ) )
| ( precedes @ SY428 @ SY429 @ SV236 ) ) )
= $false )
| ( ( path @ SV254 @ SV260 @ SV236 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1325]) ).
thf(1351,plain,
! [SV260: $i,SV254: $i,SV236: $i] :
( ( ( ~ ! [SY431: $i,SY432: $i] :
( ~ ( on_path @ SY431 @ SV236 )
| ~ ( on_path @ SY432 @ SV236 )
| ~ ( sequential @ SY431 @ SY432 )
| ( precedes @ SY431 @ SY432 @ SV236 ) ) )
= $false )
| ( ( path @ SV254 @ SV260 @ SV236 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1325]) ).
thf(1352,plain,
! [SV248: $i,SV237: $i,SV268: $i,SV277: $i] :
( ( ~ ( in_path @ SV277 @ SV268 )
| ~ ( path @ SV237 @ SV248 @ SV268 )
| ~ ( ~ ( on_path @ ( sK10_E @ SV277 @ SV268 @ SV248 @ SV237 ) @ SV268 )
| ~ ( ( SV277
= ( head_of @ ( sK10_E @ SV277 @ SV268 @ SV248 @ SV237 ) ) )
| ( SV277
= ( tail_of @ ( sK10_E @ SV277 @ SV268 @ SV248 @ SV237 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1326]) ).
thf(1353,plain,
! [SV248: $i,SV237: $i,SV269: $i,SV278: $i] :
( ( ~ ( in_path @ SV278 @ SV269 )
| ~ ( path @ SV237 @ SV248 @ SV269 )
| ( vertex @ SV278 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1327]) ).
thf(1354,plain,
! [SV270: $i,SV263: $i,SV238: $i] :
( ( ( ~ ( edge @ SV238 )
| ~ ( edge @ SV263 )
| ~ ( edge @ SV270 )
| ~ ( sequential @ SV238 @ SV263 )
| ~ ( sequential @ SV263 @ SV270 )
| ~ ( sequential @ SV270 @ SV238 ) )
= $true )
| ( ( triangle @ SV238 @ SV263 @ SV270 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1328]) ).
thf(1355,plain,
! [SV238: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY440: $i,SY441: $i] :
~ ( triangle @ SV238 @ SY440 @ SY441 )
| ( edge @ SV238 ) )
| ~ ! [SY442: $i] :
( ! [SY443: $i] :
~ ( triangle @ SV238 @ SY442 @ SY443 )
| ( edge @ SY442 ) ) )
| ~ ! [SY444: $i,SY445: $i] :
( ~ ( triangle @ SV238 @ SY444 @ SY445 )
| ( edge @ SY445 ) ) )
| ~ ! [SY446: $i] :
( ! [SY447: $i] :
~ ( triangle @ SV238 @ SY446 @ SY447 )
| ( sequential @ SV238 @ SY446 ) ) )
| ~ ! [SY448: $i,SY449: $i] :
( ~ ( triangle @ SV238 @ SY448 @ SY449 )
| ( sequential @ SY448 @ SY449 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1329]) ).
thf(1356,plain,
! [SV238: $i] :
( ( ! [SY450: $i,SY451: $i] :
( ~ ( triangle @ SV238 @ SY450 @ SY451 )
| ( sequential @ SY451 @ SV238 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1330]) ).
thf(1357,plain,
! [SV271: $i,SV264: $i,SV239: $i] :
( ( ( ~ ( ~ ( path @ SV239 @ SV264 @ ( sK8_P @ SV271 @ SV264 @ SV239 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SV271 ) @ ( length_of @ ( sK8_P @ SV271 @ SV264 @ SV239 ) ) ) )
| ( SV239 = SV264 )
| ~ ( path @ SV239 @ SV264 @ SV271 ) )
= $true )
| ( ( shortest_path @ SV239 @ SV264 @ SV271 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1331]) ).
thf(1358,plain,
! [SV239: $i] :
( ( ! [SY454: $i,SY455: $i] :
( ~ ( shortest_path @ SV239 @ SY454 @ SY455 )
| ! [SY456: $i] :
( ~ ( path @ SV239 @ SY454 @ SY456 )
| ( less_or_equal @ ( length_of @ SY455 ) @ ( length_of @ SY456 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1332]) ).
thf(1359,plain,
! [SV239: $i] :
( ( ~ ( ~ ! [SY457: $i] :
( ! [SY458: $i] :
~ ( shortest_path @ SV239 @ SY457 @ SY458 )
| ( SV239 != SY457 ) )
| ~ ! [SY459: $i,SY460: $i] :
( ~ ( shortest_path @ SV239 @ SY459 @ SY460 )
| ( path @ SV239 @ SY459 @ SY460 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1333]) ).
thf(1360,plain,
! [SV240: $i] :
( ( ! [SY461: $i,SY462: $i] :
~ ( path @ SV240 @ SY461 @ SY462 )
| ( vertex @ SV240 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1334]) ).
thf(1361,plain,
! [SV240: $i] :
( ( ! [SY463: $i] :
( ! [SY464: $i] :
~ ( path @ SV240 @ SY463 @ SY464 )
| ( vertex @ SY463 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1335]) ).
thf(1362,plain,
! [SV272: $i,SV265: $i,SV240: $i] :
( ( ( ~ ( path @ SV240 @ SV265 @ SV272 ) )
= $true )
| ( ( ~ ( ~ ~ ( ( SV240
!= ( tail_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( edge @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
| ~ ~ ( ~ ( ( SV265
!= ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
| ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ empty ) )
| ! [SY525: $i] :
( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ SY525 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ SY525 ) ) )
| ~ ~ ( ~ ( ( SV265
= ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ ( sK13_SY84 @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ ( sK13_SY84 @ SV272 @ SV265 @ SV240 ) ) ) )
| ~ ( ( SV272
= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ empty ) )
| ~ ( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ ( sK12_SY85 @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ ( sK12_SY85 @ SV272 @ SV265 @ SV240 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1336]) ).
thf(1363,plain,
! [SV255: $i,SV249: $i,SV241: $i] :
( ( ( vertex @ SV241 )
= $false )
| ( ( ~ ( vertex @ SV249 ) )
= $true )
| ( ( ~ ( ~ ! [SY513: $i] :
( ( SV241
!= ( tail_of @ SY513 ) )
| ~ ( edge @ SY513 )
| ( SV249
!= ( head_of @ SY513 ) )
| ( SV255
!= ( path_cons @ SY513 @ empty ) ) )
| ~ ! [SY514: $i] :
( ( SV241
!= ( tail_of @ SY514 ) )
| ~ ( edge @ SY514 )
| ! [SY515: $i] :
( ( SV255
!= ( path_cons @ SY514 @ SY515 ) )
| ~ ( path @ ( head_of @ SY514 ) @ SV249 @ SY515 ) ) ) ) )
= $true )
| ( ( path @ SV241 @ SV249 @ SV255 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1337]) ).
thf(1364,plain,
! [SV266: $i,SV261: $i] :
( ( ( ( SV261 = SV266 )
| ~ ( edge @ SV261 )
| ~ ( edge @ SV266 ) )
= $true )
| ( ( ( ( head_of @ SV261 )
!= ( tail_of @ SV266 ) ) )
= $true )
| ( ( sequential @ SV261 @ SV266 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1338]) ).
thf(1365,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1339]) ).
thf(1366,plain,
! [SV279: $i] :
( ( ! [SY529: $i] :
( ~ ( sequential @ SV279 @ SY529 )
| ( ( head_of @ SV279 )
= ( tail_of @ SY529 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1340]) ).
thf(1367,plain,
! [SV262: $i,SV256: $i,SV242: $i] :
( ( ( ~ ~ ( ~ ! [SY475: $i] :
( ! [SY476: $i] :
~ ( precedes @ SY475 @ SY476 @ SV242 )
| ( on_path @ SY475 @ SV242 ) )
| ~ ! [SY477: $i,SY478: $i] :
( ~ ( precedes @ SY477 @ SY478 @ SV242 )
| ( on_path @ SY478 @ SV242 ) ) ) )
= $false )
| ( ( path @ SV256 @ SV262 @ SV242 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1341]) ).
thf(1368,plain,
! [SV262: $i,SV256: $i,SV242: $i] :
( ( ( ~ ~ ( ~ ! [SY479: $i,SY480: $i] :
( ~ ( precedes @ SY479 @ SY480 @ SV242 )
| ! [SY481: $i] :
( ~ ( precedes @ SY481 @ SY480 @ SV242 )
| ~ ( sequential @ SY479 @ SY481 ) )
| ~ ( sequential @ SY479 @ SY480 ) )
| ~ ! [SY482: $i,SY483: $i] :
( ~ ( precedes @ SY482 @ SY483 @ SV242 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY483 @ SY482 @ SV242 ) @ SY483 @ SV242 )
| ~ ( sequential @ SY482 @ ( sK9_E3 @ SY483 @ SY482 @ SV242 ) ) )
| ( sequential @ SY482 @ SY483 ) ) ) )
= $false )
| ( ( path @ SV256 @ SV262 @ SV242 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1341]) ).
thf(1369,plain,
! [SV233: $i] :
( ( ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV233 ) @ SV233 )
| ~ ( on_path @ ( sK7_SY80 @ SV233 ) @ SV233 ) ) )
= $false )
| ( ( ! [SY410: $i,SY411: $i] :
~ ( path @ SY410 @ SY411 @ SV233 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV233 )
= ( number_of_in @ triangles @ SV233 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1342]) ).
thf(1370,plain,
! [SV233: $i] :
( ( ( ~ ( sequential @ ( sK6_E1 @ SV233 ) @ ( sK7_SY80 @ SV233 ) ) )
= $false )
| ( ( ! [SY410: $i,SY411: $i] :
~ ( path @ SY410 @ SY411 @ SV233 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV233 )
= ( number_of_in @ triangles @ SV233 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1342]) ).
thf(1371,plain,
! [SV273: $i,SV233: $i] :
( ( ( triangle @ ( sK6_E1 @ SV233 ) @ ( sK7_SY80 @ SV233 ) @ SV273 )
= $false )
| ( ( ! [SY410: $i,SY411: $i] :
~ ( path @ SY410 @ SY411 @ SV233 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV233 )
= ( number_of_in @ triangles @ SV233 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1343]) ).
thf(1372,plain,
! [SV259: $i,SV252: $i] :
( ( ( vertex @ SV252 )
= $false )
| ( ( ~ ( vertex @ SV259 ) )
= $true )
| ( ( SV252 = SV259 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV252
!= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
!= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
!= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
!= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV252
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
| ~ ( ( SV252
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) ) )
| ~ ~ ( ~ ( ( SV259
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
| ~ ( ( SV259
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV259 @ SV252 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1344]) ).
thf(1373,plain,
! [SV246: $i,SV234: $i,SV274: $i,SV253: $i] :
( ( ( ! [SY526: $i] :
( ~ ( precedes @ SV253 @ SV274 @ SY526 )
| ~ ( shortest_path @ SV234 @ SV246 @ SY526 ) ) )
= $true )
| ( ( ! [SY527: $i] :
( ( ( tail_of @ SY527 )
!= ( tail_of @ SV253 ) )
| ( ( head_of @ SY527 )
!= ( head_of @ SV274 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1345]) ).
thf(1374,plain,
! [SV246: $i,SV234: $i,SV280: $i,SV275: $i,SV253: $i] :
( ( ~ ( precedes @ SV253 @ SV275 @ SV280 )
| ~ ( shortest_path @ SV234 @ SV246 @ SV280 )
| ~ ( precedes @ SV275 @ SV253 @ SV280 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1346]) ).
thf(1375,plain,
! [SV247: $i,SV235: $i] :
( ( ! [SY492: $i,SY493: $i] :
( ~ ( on_path @ SY493 @ SY492 )
| ~ ( path @ SV235 @ SV247 @ SY492 )
| ( edge @ SY493 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1347]) ).
thf(1376,plain,
! [SV247: $i,SV235: $i] :
( ( ! [SY494: $i,SY495: $i] :
( ~ ( on_path @ SY495 @ SY494 )
| ~ ( path @ SV235 @ SV247 @ SY494 )
| ( in_path @ ( head_of @ SY495 ) @ SY494 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1348]) ).
thf(1377,plain,
! [SV247: $i,SV235: $i,SV267: $i,SV276: $i] :
( ( ( ~ ( on_path @ SV276 @ SV267 )
| ~ ( path @ SV235 @ SV247 @ SV267 ) )
= $true )
| ( ( in_path @ ( tail_of @ SV276 ) @ SV267 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1349]) ).
thf(1378,plain,
! [SV260: $i,SV254: $i,SV236: $i] :
( ( ( ! [SY428: $i,SY429: $i] :
( ~ ( on_path @ SY428 @ SV236 )
| ~ ( on_path @ SY429 @ SV236 )
| ! [SY430: $i] :
( ~ ( precedes @ SY430 @ SY429 @ SV236 )
| ~ ( sequential @ SY428 @ SY430 ) )
| ( precedes @ SY428 @ SY429 @ SV236 ) ) )
= $true )
| ( ( path @ SV254 @ SV260 @ SV236 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1350]) ).
thf(1379,plain,
! [SV260: $i,SV254: $i,SV236: $i] :
( ( ( ! [SY431: $i,SY432: $i] :
( ~ ( on_path @ SY431 @ SV236 )
| ~ ( on_path @ SY432 @ SV236 )
| ~ ( sequential @ SY431 @ SY432 )
| ( precedes @ SY431 @ SY432 @ SV236 ) ) )
= $true )
| ( ( path @ SV254 @ SV260 @ SV236 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1351]) ).
thf(1380,plain,
! [SV248: $i,SV237: $i,SV268: $i,SV277: $i] :
( ( ( ~ ( in_path @ SV277 @ SV268 )
| ~ ( path @ SV237 @ SV248 @ SV268 ) )
= $true )
| ( ( ~ ( ~ ( on_path @ ( sK10_E @ SV277 @ SV268 @ SV248 @ SV237 ) @ SV268 )
| ~ ( ( SV277
= ( head_of @ ( sK10_E @ SV277 @ SV268 @ SV248 @ SV237 ) ) )
| ( SV277
= ( tail_of @ ( sK10_E @ SV277 @ SV268 @ SV248 @ SV237 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1352]) ).
thf(1381,plain,
! [SV248: $i,SV237: $i,SV269: $i,SV278: $i] :
( ( ( ~ ( in_path @ SV278 @ SV269 )
| ~ ( path @ SV237 @ SV248 @ SV269 ) )
= $true )
| ( ( vertex @ SV278 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1353]) ).
thf(1382,plain,
! [SV270: $i,SV263: $i,SV238: $i] :
( ( ( ~ ( edge @ SV238 )
| ~ ( edge @ SV263 )
| ~ ( edge @ SV270 )
| ~ ( sequential @ SV238 @ SV263 )
| ~ ( sequential @ SV263 @ SV270 ) )
= $true )
| ( ( ~ ( sequential @ SV270 @ SV238 ) )
= $true )
| ( ( triangle @ SV238 @ SV263 @ SV270 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1354]) ).
thf(1383,plain,
! [SV238: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY440: $i,SY441: $i] :
~ ( triangle @ SV238 @ SY440 @ SY441 )
| ( edge @ SV238 ) )
| ~ ! [SY442: $i] :
( ! [SY443: $i] :
~ ( triangle @ SV238 @ SY442 @ SY443 )
| ( edge @ SY442 ) ) )
| ~ ! [SY444: $i,SY445: $i] :
( ~ ( triangle @ SV238 @ SY444 @ SY445 )
| ( edge @ SY445 ) ) )
| ~ ! [SY446: $i] :
( ! [SY447: $i] :
~ ( triangle @ SV238 @ SY446 @ SY447 )
| ( sequential @ SV238 @ SY446 ) ) )
| ~ ! [SY448: $i,SY449: $i] :
( ~ ( triangle @ SV238 @ SY448 @ SY449 )
| ( sequential @ SY448 @ SY449 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1355]) ).
thf(1384,plain,
! [SV281: $i,SV238: $i] :
( ( ! [SY530: $i] :
( ~ ( triangle @ SV238 @ SV281 @ SY530 )
| ( sequential @ SY530 @ SV238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1356]) ).
thf(1385,plain,
! [SV271: $i,SV264: $i,SV239: $i] :
( ( ( ~ ( ~ ( path @ SV239 @ SV264 @ ( sK8_P @ SV271 @ SV264 @ SV239 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SV271 ) @ ( length_of @ ( sK8_P @ SV271 @ SV264 @ SV239 ) ) ) ) )
= $true )
| ( ( ( SV239 = SV264 )
| ~ ( path @ SV239 @ SV264 @ SV271 ) )
= $true )
| ( ( shortest_path @ SV239 @ SV264 @ SV271 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1357]) ).
thf(1386,plain,
! [SV282: $i,SV239: $i] :
( ( ! [SY531: $i] :
( ~ ( shortest_path @ SV239 @ SV282 @ SY531 )
| ! [SY532: $i] :
( ~ ( path @ SV239 @ SV282 @ SY532 )
| ( less_or_equal @ ( length_of @ SY531 ) @ ( length_of @ SY532 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1358]) ).
thf(1387,plain,
! [SV239: $i] :
( ( ~ ! [SY457: $i] :
( ! [SY458: $i] :
~ ( shortest_path @ SV239 @ SY457 @ SY458 )
| ( SV239 != SY457 ) )
| ~ ! [SY459: $i,SY460: $i] :
( ~ ( shortest_path @ SV239 @ SY459 @ SY460 )
| ( path @ SV239 @ SY459 @ SY460 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1359]) ).
thf(1388,plain,
! [SV240: $i] :
( ( ( ! [SY461: $i,SY462: $i] :
~ ( path @ SV240 @ SY461 @ SY462 ) )
= $true )
| ( ( vertex @ SV240 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1360]) ).
thf(1389,plain,
! [SV283: $i,SV240: $i] :
( ( ! [SY533: $i] :
~ ( path @ SV240 @ SV283 @ SY533 )
| ( vertex @ SV283 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1361]) ).
thf(1390,plain,
! [SV272: $i,SV265: $i,SV240: $i] :
( ( ( path @ SV240 @ SV265 @ SV272 )
= $false )
| ( ( ~ ( ~ ~ ( ( SV240
!= ( tail_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( edge @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
| ~ ~ ( ~ ( ( SV265
!= ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
| ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ empty ) )
| ! [SY525: $i] :
( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ SY525 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ SY525 ) ) )
| ~ ~ ( ~ ( ( SV265
= ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ ( sK13_SY84 @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ ( sK13_SY84 @ SV272 @ SV265 @ SV240 ) ) ) )
| ~ ( ( SV272
= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ empty ) )
| ~ ( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ ( sK12_SY85 @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ ( sK12_SY85 @ SV272 @ SV265 @ SV240 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1362]) ).
thf(1391,plain,
! [SV255: $i,SV241: $i,SV249: $i] :
( ( ( vertex @ SV249 )
= $false )
| ( ( vertex @ SV241 )
= $false )
| ( ( ~ ( ~ ! [SY513: $i] :
( ( SV241
!= ( tail_of @ SY513 ) )
| ~ ( edge @ SY513 )
| ( SV249
!= ( head_of @ SY513 ) )
| ( SV255
!= ( path_cons @ SY513 @ empty ) ) )
| ~ ! [SY514: $i] :
( ( SV241
!= ( tail_of @ SY514 ) )
| ~ ( edge @ SY514 )
| ! [SY515: $i] :
( ( SV255
!= ( path_cons @ SY514 @ SY515 ) )
| ~ ( path @ ( head_of @ SY514 ) @ SV249 @ SY515 ) ) ) ) )
= $true )
| ( ( path @ SV241 @ SV249 @ SV255 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1363]) ).
thf(1392,plain,
! [SV266: $i,SV261: $i] :
( ( ( SV261 = SV266 )
= $true )
| ( ( ~ ( edge @ SV261 )
| ~ ( edge @ SV266 ) )
= $true )
| ( ( ( ( head_of @ SV261 )
!= ( tail_of @ SV266 ) ) )
= $true )
| ( ( sequential @ SV261 @ SV266 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1364]) ).
thf(1393,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1365]) ).
thf(1394,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1365]) ).
thf(1395,plain,
! [SV284: $i,SV279: $i] :
( ( ~ ( sequential @ SV279 @ SV284 )
| ( ( head_of @ SV279 )
= ( tail_of @ SV284 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1366]) ).
thf(1396,plain,
! [SV262: $i,SV256: $i,SV242: $i] :
( ( ( ~ ( ~ ! [SY475: $i] :
( ! [SY476: $i] :
~ ( precedes @ SY475 @ SY476 @ SV242 )
| ( on_path @ SY475 @ SV242 ) )
| ~ ! [SY477: $i,SY478: $i] :
( ~ ( precedes @ SY477 @ SY478 @ SV242 )
| ( on_path @ SY478 @ SV242 ) ) ) )
= $true )
| ( ( path @ SV256 @ SV262 @ SV242 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1367]) ).
thf(1397,plain,
! [SV262: $i,SV256: $i,SV242: $i] :
( ( ( ~ ( ~ ! [SY479: $i,SY480: $i] :
( ~ ( precedes @ SY479 @ SY480 @ SV242 )
| ! [SY481: $i] :
( ~ ( precedes @ SY481 @ SY480 @ SV242 )
| ~ ( sequential @ SY479 @ SY481 ) )
| ~ ( sequential @ SY479 @ SY480 ) )
| ~ ! [SY482: $i,SY483: $i] :
( ~ ( precedes @ SY482 @ SY483 @ SV242 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY483 @ SY482 @ SV242 ) @ SY483 @ SV242 )
| ~ ( sequential @ SY482 @ ( sK9_E3 @ SY483 @ SY482 @ SV242 ) ) )
| ( sequential @ SY482 @ SY483 ) ) ) )
= $true )
| ( ( path @ SV256 @ SV262 @ SV242 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1368]) ).
thf(1398,plain,
! [SV233: $i] :
( ( ( ~ ( ~ ( on_path @ ( sK6_E1 @ SV233 ) @ SV233 )
| ~ ( on_path @ ( sK7_SY80 @ SV233 ) @ SV233 ) ) )
= $true )
| ( ( ! [SY410: $i,SY411: $i] :
~ ( path @ SY410 @ SY411 @ SV233 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV233 )
= ( number_of_in @ triangles @ SV233 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1369]) ).
thf(1399,plain,
! [SV233: $i] :
( ( ( sequential @ ( sK6_E1 @ SV233 ) @ ( sK7_SY80 @ SV233 ) )
= $true )
| ( ( ! [SY410: $i,SY411: $i] :
~ ( path @ SY410 @ SY411 @ SV233 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV233 )
= ( number_of_in @ triangles @ SV233 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1370]) ).
thf(1400,plain,
! [SV273: $i,SV233: $i,SV285: $i] :
( ( ( ! [SY534: $i] :
~ ( path @ SV285 @ SY534 @ SV233 ) )
= $true )
| ( ( triangle @ ( sK6_E1 @ SV233 ) @ ( sK7_SY80 @ SV233 ) @ SV273 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV233 )
= ( number_of_in @ triangles @ SV233 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1371]) ).
thf(1401,plain,
! [SV252: $i,SV259: $i] :
( ( ( vertex @ SV259 )
= $false )
| ( ( vertex @ SV252 )
= $false )
| ( ( SV252 = SV259 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV252
!= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
!= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
!= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
!= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV252
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
| ~ ( ( SV252
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) ) )
| ~ ~ ( ~ ( ( SV259
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
| ~ ( ( SV259
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV259 @ SV252 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1372]) ).
thf(1402,plain,
! [SV246: $i,SV234: $i,SV286: $i,SV274: $i,SV253: $i] :
( ( ( ~ ( precedes @ SV253 @ SV274 @ SV286 )
| ~ ( shortest_path @ SV234 @ SV246 @ SV286 ) )
= $true )
| ( ( ! [SY527: $i] :
( ( ( tail_of @ SY527 )
!= ( tail_of @ SV253 ) )
| ( ( head_of @ SY527 )
!= ( head_of @ SV274 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1373]) ).
thf(1403,plain,
! [SV246: $i,SV234: $i,SV280: $i,SV275: $i,SV253: $i] :
( ( ( ~ ( precedes @ SV253 @ SV275 @ SV280 )
| ~ ( shortest_path @ SV234 @ SV246 @ SV280 ) )
= $true )
| ( ( ~ ( precedes @ SV275 @ SV253 @ SV280 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1374]) ).
thf(1404,plain,
! [SV247: $i,SV235: $i,SV287: $i] :
( ( ! [SY535: $i] :
( ~ ( on_path @ SY535 @ SV287 )
| ~ ( path @ SV235 @ SV247 @ SV287 )
| ( edge @ SY535 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1375]) ).
thf(1405,plain,
! [SV247: $i,SV235: $i,SV288: $i] :
( ( ! [SY536: $i] :
( ~ ( on_path @ SY536 @ SV288 )
| ~ ( path @ SV235 @ SV247 @ SV288 )
| ( in_path @ ( head_of @ SY536 ) @ SV288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1376]) ).
thf(1406,plain,
! [SV247: $i,SV235: $i,SV267: $i,SV276: $i] :
( ( ( ~ ( on_path @ SV276 @ SV267 ) )
= $true )
| ( ( ~ ( path @ SV235 @ SV247 @ SV267 ) )
= $true )
| ( ( in_path @ ( tail_of @ SV276 ) @ SV267 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1377]) ).
thf(1407,plain,
! [SV260: $i,SV254: $i,SV236: $i,SV289: $i] :
( ( ( ! [SY537: $i] :
( ~ ( on_path @ SV289 @ SV236 )
| ~ ( on_path @ SY537 @ SV236 )
| ! [SY538: $i] :
( ~ ( precedes @ SY538 @ SY537 @ SV236 )
| ~ ( sequential @ SV289 @ SY538 ) )
| ( precedes @ SV289 @ SY537 @ SV236 ) ) )
= $true )
| ( ( path @ SV254 @ SV260 @ SV236 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1378]) ).
thf(1408,plain,
! [SV260: $i,SV254: $i,SV236: $i,SV290: $i] :
( ( ( ! [SY539: $i] :
( ~ ( on_path @ SV290 @ SV236 )
| ~ ( on_path @ SY539 @ SV236 )
| ~ ( sequential @ SV290 @ SY539 )
| ( precedes @ SV290 @ SY539 @ SV236 ) ) )
= $true )
| ( ( path @ SV254 @ SV260 @ SV236 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1379]) ).
thf(1409,plain,
! [SV248: $i,SV237: $i,SV268: $i,SV277: $i] :
( ( ( ~ ( in_path @ SV277 @ SV268 ) )
= $true )
| ( ( ~ ( path @ SV237 @ SV248 @ SV268 ) )
= $true )
| ( ( ~ ( ~ ( on_path @ ( sK10_E @ SV277 @ SV268 @ SV248 @ SV237 ) @ SV268 )
| ~ ( ( SV277
= ( head_of @ ( sK10_E @ SV277 @ SV268 @ SV248 @ SV237 ) ) )
| ( SV277
= ( tail_of @ ( sK10_E @ SV277 @ SV268 @ SV248 @ SV237 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1380]) ).
thf(1410,plain,
! [SV248: $i,SV237: $i,SV269: $i,SV278: $i] :
( ( ( ~ ( in_path @ SV278 @ SV269 ) )
= $true )
| ( ( ~ ( path @ SV237 @ SV248 @ SV269 ) )
= $true )
| ( ( vertex @ SV278 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1381]) ).
thf(1411,plain,
! [SV270: $i,SV263: $i,SV238: $i] :
( ( ( ~ ( edge @ SV238 )
| ~ ( edge @ SV263 )
| ~ ( edge @ SV270 )
| ~ ( sequential @ SV238 @ SV263 ) )
= $true )
| ( ( ~ ( sequential @ SV263 @ SV270 ) )
= $true )
| ( ( ~ ( sequential @ SV270 @ SV238 ) )
= $true )
| ( ( triangle @ SV238 @ SV263 @ SV270 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1382]) ).
thf(1412,plain,
! [SV238: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY440: $i,SY441: $i] :
~ ( triangle @ SV238 @ SY440 @ SY441 )
| ( edge @ SV238 ) )
| ~ ! [SY442: $i] :
( ! [SY443: $i] :
~ ( triangle @ SV238 @ SY442 @ SY443 )
| ( edge @ SY442 ) ) )
| ~ ! [SY444: $i,SY445: $i] :
( ~ ( triangle @ SV238 @ SY444 @ SY445 )
| ( edge @ SY445 ) ) )
| ~ ! [SY446: $i] :
( ! [SY447: $i] :
~ ( triangle @ SV238 @ SY446 @ SY447 )
| ( sequential @ SV238 @ SY446 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1383]) ).
thf(1413,plain,
! [SV238: $i] :
( ( ~ ! [SY448: $i,SY449: $i] :
( ~ ( triangle @ SV238 @ SY448 @ SY449 )
| ( sequential @ SY448 @ SY449 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1383]) ).
thf(1414,plain,
! [SV291: $i,SV281: $i,SV238: $i] :
( ( ~ ( triangle @ SV238 @ SV281 @ SV291 )
| ( sequential @ SV291 @ SV238 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1384]) ).
thf(1415,plain,
! [SV271: $i,SV264: $i,SV239: $i] :
( ( ( ~ ( path @ SV239 @ SV264 @ ( sK8_P @ SV271 @ SV264 @ SV239 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SV271 ) @ ( length_of @ ( sK8_P @ SV271 @ SV264 @ SV239 ) ) ) )
= $false )
| ( ( ( SV239 = SV264 )
| ~ ( path @ SV239 @ SV264 @ SV271 ) )
= $true )
| ( ( shortest_path @ SV239 @ SV264 @ SV271 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1385]) ).
thf(1416,plain,
! [SV292: $i,SV282: $i,SV239: $i] :
( ( ~ ( shortest_path @ SV239 @ SV282 @ SV292 )
| ! [SY540: $i] :
( ~ ( path @ SV239 @ SV282 @ SY540 )
| ( less_or_equal @ ( length_of @ SV292 ) @ ( length_of @ SY540 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1386]) ).
thf(1417,plain,
! [SV239: $i] :
( ( ~ ! [SY457: $i] :
( ! [SY458: $i] :
~ ( shortest_path @ SV239 @ SY457 @ SY458 )
| ( SV239 != SY457 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1387]) ).
thf(1418,plain,
! [SV239: $i] :
( ( ~ ! [SY459: $i,SY460: $i] :
( ~ ( shortest_path @ SV239 @ SY459 @ SY460 )
| ( path @ SV239 @ SY459 @ SY460 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1387]) ).
thf(1419,plain,
! [SV293: $i,SV240: $i] :
( ( ( ! [SY541: $i] :
~ ( path @ SV240 @ SV293 @ SY541 ) )
= $true )
| ( ( vertex @ SV240 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1388]) ).
thf(1420,plain,
! [SV283: $i,SV240: $i] :
( ( ( ! [SY533: $i] :
~ ( path @ SV240 @ SV283 @ SY533 ) )
= $true )
| ( ( vertex @ SV283 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1389]) ).
thf(1421,plain,
! [SV265: $i,SV272: $i,SV240: $i] :
( ( ( ~ ~ ( ( SV240
!= ( tail_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( edge @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
| ~ ~ ( ~ ( ( SV265
!= ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
| ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ empty ) )
| ! [SY525: $i] :
( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ SY525 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ SY525 ) ) )
| ~ ~ ( ~ ( ( SV265
= ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ ( sK13_SY84 @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ ( sK13_SY84 @ SV272 @ SV265 @ SV240 ) ) ) )
| ~ ( ( SV272
= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ empty ) )
| ~ ( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ ( sK12_SY85 @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ ( sK12_SY85 @ SV272 @ SV265 @ SV240 ) ) ) ) ) ) )
= $false )
| ( ( path @ SV240 @ SV265 @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1390]) ).
thf(1422,plain,
! [SV255: $i,SV249: $i,SV241: $i] :
( ( ( ~ ! [SY513: $i] :
( ( SV241
!= ( tail_of @ SY513 ) )
| ~ ( edge @ SY513 )
| ( SV249
!= ( head_of @ SY513 ) )
| ( SV255
!= ( path_cons @ SY513 @ empty ) ) )
| ~ ! [SY514: $i] :
( ( SV241
!= ( tail_of @ SY514 ) )
| ~ ( edge @ SY514 )
| ! [SY515: $i] :
( ( SV255
!= ( path_cons @ SY514 @ SY515 ) )
| ~ ( path @ ( head_of @ SY514 ) @ SV249 @ SY515 ) ) ) )
= $false )
| ( ( vertex @ SV241 )
= $false )
| ( ( vertex @ SV249 )
= $false )
| ( ( path @ SV241 @ SV249 @ SV255 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1391]) ).
thf(1423,plain,
! [SV266: $i,SV261: $i] :
( ( ( ~ ( edge @ SV261 ) )
= $true )
| ( ( ~ ( edge @ SV266 ) )
= $true )
| ( ( SV261 = SV266 )
= $true )
| ( ( ( ( head_of @ SV261 )
!= ( tail_of @ SV266 ) ) )
= $true )
| ( ( sequential @ SV261 @ SV266 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1392]) ).
thf(1424,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1393]) ).
thf(1425,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1394]) ).
thf(1426,plain,
! [SV284: $i,SV279: $i] :
( ( ( ~ ( sequential @ SV279 @ SV284 ) )
= $true )
| ( ( ( head_of @ SV279 )
= ( tail_of @ SV284 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1395]) ).
thf(1427,plain,
! [SV262: $i,SV256: $i,SV242: $i] :
( ( ( ~ ! [SY475: $i] :
( ! [SY476: $i] :
~ ( precedes @ SY475 @ SY476 @ SV242 )
| ( on_path @ SY475 @ SV242 ) )
| ~ ! [SY477: $i,SY478: $i] :
( ~ ( precedes @ SY477 @ SY478 @ SV242 )
| ( on_path @ SY478 @ SV242 ) ) )
= $false )
| ( ( path @ SV256 @ SV262 @ SV242 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1396]) ).
thf(1428,plain,
! [SV262: $i,SV256: $i,SV242: $i] :
( ( ( ~ ! [SY479: $i,SY480: $i] :
( ~ ( precedes @ SY479 @ SY480 @ SV242 )
| ! [SY481: $i] :
( ~ ( precedes @ SY481 @ SY480 @ SV242 )
| ~ ( sequential @ SY479 @ SY481 ) )
| ~ ( sequential @ SY479 @ SY480 ) )
| ~ ! [SY482: $i,SY483: $i] :
( ~ ( precedes @ SY482 @ SY483 @ SV242 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY483 @ SY482 @ SV242 ) @ SY483 @ SV242 )
| ~ ( sequential @ SY482 @ ( sK9_E3 @ SY483 @ SY482 @ SV242 ) ) )
| ( sequential @ SY482 @ SY483 ) ) )
= $false )
| ( ( path @ SV256 @ SV262 @ SV242 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1397]) ).
thf(1429,plain,
! [SV233: $i] :
( ( ( ~ ( on_path @ ( sK6_E1 @ SV233 ) @ SV233 )
| ~ ( on_path @ ( sK7_SY80 @ SV233 ) @ SV233 ) )
= $false )
| ( ( ! [SY410: $i,SY411: $i] :
~ ( path @ SY410 @ SY411 @ SV233 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV233 )
= ( number_of_in @ triangles @ SV233 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1398]) ).
thf(1430,plain,
! [SV233: $i,SV294: $i] :
( ( ( ! [SY542: $i] :
~ ( path @ SV294 @ SY542 @ SV233 ) )
= $true )
| ( ( sequential @ ( sK6_E1 @ SV233 ) @ ( sK7_SY80 @ SV233 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV233 )
= ( number_of_in @ triangles @ SV233 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1399]) ).
thf(1431,plain,
! [SV273: $i,SV233: $i,SV295: $i,SV285: $i] :
( ( ( ~ ( path @ SV285 @ SV295 @ SV233 ) )
= $true )
| ( ( triangle @ ( sK6_E1 @ SV233 ) @ ( sK7_SY80 @ SV233 ) @ SV273 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV233 )
= ( number_of_in @ triangles @ SV233 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1400]) ).
thf(1432,plain,
! [SV259: $i,SV252: $i] :
( ( ( ~ ~ ( ~ ( ( SV252
!= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
!= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
!= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
!= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV252
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
| ~ ( ( SV252
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) ) )
| ~ ~ ( ~ ( ( SV259
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
| ~ ( ( SV259
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV259 @ SV252 ) ) )
= $false )
| ( ( SV252 = SV259 )
= $true )
| ( ( vertex @ SV252 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1401]) ).
thf(1433,plain,
! [SV246: $i,SV234: $i,SV286: $i,SV274: $i,SV253: $i] :
( ( ( ~ ( precedes @ SV253 @ SV274 @ SV286 ) )
= $true )
| ( ( ~ ( shortest_path @ SV234 @ SV246 @ SV286 ) )
= $true )
| ( ( ! [SY527: $i] :
( ( ( tail_of @ SY527 )
!= ( tail_of @ SV253 ) )
| ( ( head_of @ SY527 )
!= ( head_of @ SV274 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1402]) ).
thf(1434,plain,
! [SV246: $i,SV234: $i,SV280: $i,SV275: $i,SV253: $i] :
( ( ( ~ ( precedes @ SV253 @ SV275 @ SV280 ) )
= $true )
| ( ( ~ ( shortest_path @ SV234 @ SV246 @ SV280 ) )
= $true )
| ( ( ~ ( precedes @ SV275 @ SV253 @ SV280 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1403]) ).
thf(1435,plain,
! [SV247: $i,SV235: $i,SV287: $i,SV296: $i] :
( ( ~ ( on_path @ SV296 @ SV287 )
| ~ ( path @ SV235 @ SV247 @ SV287 )
| ( edge @ SV296 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1404]) ).
thf(1436,plain,
! [SV247: $i,SV235: $i,SV288: $i,SV297: $i] :
( ( ~ ( on_path @ SV297 @ SV288 )
| ~ ( path @ SV235 @ SV247 @ SV288 )
| ( in_path @ ( head_of @ SV297 ) @ SV288 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1405]) ).
thf(1437,plain,
! [SV247: $i,SV235: $i,SV267: $i,SV276: $i] :
( ( ( on_path @ SV276 @ SV267 )
= $false )
| ( ( ~ ( path @ SV235 @ SV247 @ SV267 ) )
= $true )
| ( ( in_path @ ( tail_of @ SV276 ) @ SV267 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1406]) ).
thf(1438,plain,
! [SV260: $i,SV254: $i,SV298: $i,SV236: $i,SV289: $i] :
( ( ( ~ ( on_path @ SV289 @ SV236 )
| ~ ( on_path @ SV298 @ SV236 )
| ! [SY543: $i] :
( ~ ( precedes @ SY543 @ SV298 @ SV236 )
| ~ ( sequential @ SV289 @ SY543 ) )
| ( precedes @ SV289 @ SV298 @ SV236 ) )
= $true )
| ( ( path @ SV254 @ SV260 @ SV236 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1407]) ).
thf(1439,plain,
! [SV260: $i,SV254: $i,SV299: $i,SV236: $i,SV290: $i] :
( ( ( ~ ( on_path @ SV290 @ SV236 )
| ~ ( on_path @ SV299 @ SV236 )
| ~ ( sequential @ SV290 @ SV299 )
| ( precedes @ SV290 @ SV299 @ SV236 ) )
= $true )
| ( ( path @ SV254 @ SV260 @ SV236 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1408]) ).
thf(1440,plain,
! [SV248: $i,SV237: $i,SV268: $i,SV277: $i] :
( ( ( in_path @ SV277 @ SV268 )
= $false )
| ( ( ~ ( path @ SV237 @ SV248 @ SV268 ) )
= $true )
| ( ( ~ ( ~ ( on_path @ ( sK10_E @ SV277 @ SV268 @ SV248 @ SV237 ) @ SV268 )
| ~ ( ( SV277
= ( head_of @ ( sK10_E @ SV277 @ SV268 @ SV248 @ SV237 ) ) )
| ( SV277
= ( tail_of @ ( sK10_E @ SV277 @ SV268 @ SV248 @ SV237 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1409]) ).
thf(1441,plain,
! [SV248: $i,SV237: $i,SV269: $i,SV278: $i] :
( ( ( in_path @ SV278 @ SV269 )
= $false )
| ( ( ~ ( path @ SV237 @ SV248 @ SV269 ) )
= $true )
| ( ( vertex @ SV278 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1410]) ).
thf(1442,plain,
! [SV270: $i,SV263: $i,SV238: $i] :
( ( ( ~ ( edge @ SV238 )
| ~ ( edge @ SV263 )
| ~ ( edge @ SV270 ) )
= $true )
| ( ( ~ ( sequential @ SV238 @ SV263 ) )
= $true )
| ( ( ~ ( sequential @ SV263 @ SV270 ) )
= $true )
| ( ( ~ ( sequential @ SV270 @ SV238 ) )
= $true )
| ( ( triangle @ SV238 @ SV263 @ SV270 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1411]) ).
thf(1443,plain,
! [SV238: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY440: $i,SY441: $i] :
~ ( triangle @ SV238 @ SY440 @ SY441 )
| ( edge @ SV238 ) )
| ~ ! [SY442: $i] :
( ! [SY443: $i] :
~ ( triangle @ SV238 @ SY442 @ SY443 )
| ( edge @ SY442 ) ) )
| ~ ! [SY444: $i,SY445: $i] :
( ~ ( triangle @ SV238 @ SY444 @ SY445 )
| ( edge @ SY445 ) ) )
| ~ ! [SY446: $i] :
( ! [SY447: $i] :
~ ( triangle @ SV238 @ SY446 @ SY447 )
| ( sequential @ SV238 @ SY446 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1412]) ).
thf(1444,plain,
! [SV238: $i] :
( ( ! [SY448: $i,SY449: $i] :
( ~ ( triangle @ SV238 @ SY448 @ SY449 )
| ( sequential @ SY448 @ SY449 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1413]) ).
thf(1445,plain,
! [SV291: $i,SV281: $i,SV238: $i] :
( ( ( ~ ( triangle @ SV238 @ SV281 @ SV291 ) )
= $true )
| ( ( sequential @ SV291 @ SV238 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1414]) ).
thf(1446,plain,
! [SV271: $i,SV264: $i,SV239: $i] :
( ( ( ~ ( path @ SV239 @ SV264 @ ( sK8_P @ SV271 @ SV264 @ SV239 ) ) )
= $false )
| ( ( ( SV239 = SV264 )
| ~ ( path @ SV239 @ SV264 @ SV271 ) )
= $true )
| ( ( shortest_path @ SV239 @ SV264 @ SV271 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1415]) ).
thf(1447,plain,
! [SV239: $i,SV264: $i,SV271: $i] :
( ( ( ~ ~ ( less_or_equal @ ( length_of @ SV271 ) @ ( length_of @ ( sK8_P @ SV271 @ SV264 @ SV239 ) ) ) )
= $false )
| ( ( ( SV239 = SV264 )
| ~ ( path @ SV239 @ SV264 @ SV271 ) )
= $true )
| ( ( shortest_path @ SV239 @ SV264 @ SV271 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1415]) ).
thf(1448,plain,
! [SV292: $i,SV282: $i,SV239: $i] :
( ( ( ~ ( shortest_path @ SV239 @ SV282 @ SV292 ) )
= $true )
| ( ( ! [SY540: $i] :
( ~ ( path @ SV239 @ SV282 @ SY540 )
| ( less_or_equal @ ( length_of @ SV292 ) @ ( length_of @ SY540 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1416]) ).
thf(1449,plain,
! [SV239: $i] :
( ( ! [SY457: $i] :
( ! [SY458: $i] :
~ ( shortest_path @ SV239 @ SY457 @ SY458 )
| ( SV239 != SY457 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1417]) ).
thf(1450,plain,
! [SV239: $i] :
( ( ! [SY459: $i,SY460: $i] :
( ~ ( shortest_path @ SV239 @ SY459 @ SY460 )
| ( path @ SV239 @ SY459 @ SY460 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1418]) ).
thf(1451,plain,
! [SV300: $i,SV293: $i,SV240: $i] :
( ( ( ~ ( path @ SV240 @ SV293 @ SV300 ) )
= $true )
| ( ( vertex @ SV240 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1419]) ).
thf(1452,plain,
! [SV301: $i,SV283: $i,SV240: $i] :
( ( ( ~ ( path @ SV240 @ SV283 @ SV301 ) )
= $true )
| ( ( vertex @ SV283 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1420]) ).
thf(1453,plain,
! [SV265: $i,SV272: $i,SV240: $i] :
( ( ( ~ ~ ( ( SV240
!= ( tail_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( edge @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) ) )
= $false )
| ( ( path @ SV240 @ SV265 @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1421]) ).
thf(1454,plain,
! [SV240: $i,SV272: $i,SV265: $i] :
( ( ( ~ ~ ( ~ ( ( SV265
!= ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
| ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ empty ) )
| ! [SY525: $i] :
( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ SY525 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ SY525 ) ) )
| ~ ~ ( ~ ( ( SV265
= ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ ( sK13_SY84 @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ ( sK13_SY84 @ SV272 @ SV265 @ SV240 ) ) ) )
| ~ ( ( SV272
= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ empty ) )
| ~ ( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ ( sK12_SY85 @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ ( sK12_SY85 @ SV272 @ SV265 @ SV240 ) ) ) ) ) ) )
= $false )
| ( ( path @ SV240 @ SV265 @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1421]) ).
thf(1455,plain,
! [SV255: $i,SV249: $i,SV241: $i] :
( ( ( ~ ! [SY513: $i] :
( ( SV241
!= ( tail_of @ SY513 ) )
| ~ ( edge @ SY513 )
| ( SV249
!= ( head_of @ SY513 ) )
| ( SV255
!= ( path_cons @ SY513 @ empty ) ) ) )
= $false )
| ( ( vertex @ SV241 )
= $false )
| ( ( vertex @ SV249 )
= $false )
| ( ( path @ SV241 @ SV249 @ SV255 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1422]) ).
thf(1456,plain,
! [SV249: $i,SV255: $i,SV241: $i] :
( ( ( ~ ! [SY514: $i] :
( ( SV241
!= ( tail_of @ SY514 ) )
| ~ ( edge @ SY514 )
| ! [SY515: $i] :
( ( SV255
!= ( path_cons @ SY514 @ SY515 ) )
| ~ ( path @ ( head_of @ SY514 ) @ SV249 @ SY515 ) ) ) )
= $false )
| ( ( vertex @ SV241 )
= $false )
| ( ( vertex @ SV249 )
= $false )
| ( ( path @ SV241 @ SV249 @ SV255 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1422]) ).
thf(1457,plain,
! [SV266: $i,SV261: $i] :
( ( ( edge @ SV261 )
= $false )
| ( ( ~ ( edge @ SV266 ) )
= $true )
| ( ( SV261 = SV266 )
= $true )
| ( ( ( ( head_of @ SV261 )
!= ( tail_of @ SV266 ) ) )
= $true )
| ( ( sequential @ SV261 @ SV266 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1423]) ).
thf(1458,plain,
! [SV302: $i] :
( ( ! [SY544: $i] :
( ~ ( sequential @ SV302 @ SY544 )
| ( SV302 != SY544 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1424]) ).
thf(1459,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1425]) ).
thf(1460,plain,
! [SV284: $i,SV279: $i] :
( ( ( sequential @ SV279 @ SV284 )
= $false )
| ( ( ( head_of @ SV279 )
= ( tail_of @ SV284 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1426]) ).
thf(1461,plain,
! [SV262: $i,SV256: $i,SV242: $i] :
( ( ( ~ ! [SY475: $i] :
( ! [SY476: $i] :
~ ( precedes @ SY475 @ SY476 @ SV242 )
| ( on_path @ SY475 @ SV242 ) ) )
= $false )
| ( ( path @ SV256 @ SV262 @ SV242 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1427]) ).
thf(1462,plain,
! [SV262: $i,SV256: $i,SV242: $i] :
( ( ( ~ ! [SY477: $i,SY478: $i] :
( ~ ( precedes @ SY477 @ SY478 @ SV242 )
| ( on_path @ SY478 @ SV242 ) ) )
= $false )
| ( ( path @ SV256 @ SV262 @ SV242 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1427]) ).
thf(1463,plain,
! [SV262: $i,SV256: $i,SV242: $i] :
( ( ( ~ ! [SY479: $i,SY480: $i] :
( ~ ( precedes @ SY479 @ SY480 @ SV242 )
| ! [SY481: $i] :
( ~ ( precedes @ SY481 @ SY480 @ SV242 )
| ~ ( sequential @ SY479 @ SY481 ) )
| ~ ( sequential @ SY479 @ SY480 ) ) )
= $false )
| ( ( path @ SV256 @ SV262 @ SV242 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1428]) ).
thf(1464,plain,
! [SV262: $i,SV256: $i,SV242: $i] :
( ( ( ~ ! [SY482: $i,SY483: $i] :
( ~ ( precedes @ SY482 @ SY483 @ SV242 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY483 @ SY482 @ SV242 ) @ SY483 @ SV242 )
| ~ ( sequential @ SY482 @ ( sK9_E3 @ SY483 @ SY482 @ SV242 ) ) )
| ( sequential @ SY482 @ SY483 ) ) )
= $false )
| ( ( path @ SV256 @ SV262 @ SV242 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1428]) ).
thf(1465,plain,
! [SV233: $i] :
( ( ( ~ ( on_path @ ( sK6_E1 @ SV233 ) @ SV233 ) )
= $false )
| ( ( ! [SY410: $i,SY411: $i] :
~ ( path @ SY410 @ SY411 @ SV233 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV233 )
= ( number_of_in @ triangles @ SV233 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1429]) ).
thf(1466,plain,
! [SV233: $i] :
( ( ( ~ ( on_path @ ( sK7_SY80 @ SV233 ) @ SV233 ) )
= $false )
| ( ( ! [SY410: $i,SY411: $i] :
~ ( path @ SY410 @ SY411 @ SV233 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV233 )
= ( number_of_in @ triangles @ SV233 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1429]) ).
thf(1467,plain,
! [SV233: $i,SV303: $i,SV294: $i] :
( ( ( ~ ( path @ SV294 @ SV303 @ SV233 ) )
= $true )
| ( ( sequential @ ( sK6_E1 @ SV233 ) @ ( sK7_SY80 @ SV233 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV233 )
= ( number_of_in @ triangles @ SV233 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1430]) ).
thf(1468,plain,
! [SV273: $i,SV233: $i,SV295: $i,SV285: $i] :
( ( ( path @ SV285 @ SV295 @ SV233 )
= $false )
| ( ( triangle @ ( sK6_E1 @ SV233 ) @ ( sK7_SY80 @ SV233 ) @ SV273 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV233 )
= ( number_of_in @ triangles @ SV233 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1431]) ).
thf(1469,plain,
! [SV259: $i,SV252: $i] :
( ( ( ~ ~ ( ~ ( ( SV252
!= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
!= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
!= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
!= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV252
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
| ~ ( ( SV252
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) ) )
| ~ ~ ( ~ ( ( SV259
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
| ~ ( ( SV259
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) ) ) ) ) )
= $false )
| ( ( SV252 = SV259 )
= $true )
| ( ( vertex @ SV252 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[1432]) ).
thf(1470,plain,
! [SV252: $i,SV259: $i] :
( ( ( ~ ( edge @ ( sK14_E @ SV259 @ SV252 ) ) )
= $false )
| ( ( SV252 = SV259 )
= $true )
| ( ( vertex @ SV252 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[1432]) ).
thf(1471,plain,
! [SV246: $i,SV234: $i,SV286: $i,SV274: $i,SV253: $i] :
( ( ( precedes @ SV253 @ SV274 @ SV286 )
= $false )
| ( ( ~ ( shortest_path @ SV234 @ SV246 @ SV286 ) )
= $true )
| ( ( ! [SY527: $i] :
( ( ( tail_of @ SY527 )
!= ( tail_of @ SV253 ) )
| ( ( head_of @ SY527 )
!= ( head_of @ SV274 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1433]) ).
thf(1472,plain,
! [SV246: $i,SV234: $i,SV280: $i,SV275: $i,SV253: $i] :
( ( ( precedes @ SV253 @ SV275 @ SV280 )
= $false )
| ( ( ~ ( shortest_path @ SV234 @ SV246 @ SV280 ) )
= $true )
| ( ( ~ ( precedes @ SV275 @ SV253 @ SV280 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1434]) ).
thf(1473,plain,
! [SV247: $i,SV235: $i,SV287: $i,SV296: $i] :
( ( ( ~ ( on_path @ SV296 @ SV287 )
| ~ ( path @ SV235 @ SV247 @ SV287 ) )
= $true )
| ( ( edge @ SV296 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1435]) ).
thf(1474,plain,
! [SV247: $i,SV235: $i,SV288: $i,SV297: $i] :
( ( ( ~ ( on_path @ SV297 @ SV288 )
| ~ ( path @ SV235 @ SV247 @ SV288 ) )
= $true )
| ( ( in_path @ ( head_of @ SV297 ) @ SV288 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1436]) ).
thf(1475,plain,
! [SV276: $i,SV267: $i,SV247: $i,SV235: $i] :
( ( ( path @ SV235 @ SV247 @ SV267 )
= $false )
| ( ( on_path @ SV276 @ SV267 )
= $false )
| ( ( in_path @ ( tail_of @ SV276 ) @ SV267 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1437]) ).
thf(1476,plain,
! [SV260: $i,SV254: $i,SV298: $i,SV236: $i,SV289: $i] :
( ( ( ~ ( on_path @ SV289 @ SV236 )
| ~ ( on_path @ SV298 @ SV236 )
| ! [SY543: $i] :
( ~ ( precedes @ SY543 @ SV298 @ SV236 )
| ~ ( sequential @ SV289 @ SY543 ) ) )
= $true )
| ( ( precedes @ SV289 @ SV298 @ SV236 )
= $true )
| ( ( path @ SV254 @ SV260 @ SV236 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1438]) ).
thf(1477,plain,
! [SV260: $i,SV254: $i,SV299: $i,SV236: $i,SV290: $i] :
( ( ( ~ ( on_path @ SV290 @ SV236 )
| ~ ( on_path @ SV299 @ SV236 )
| ~ ( sequential @ SV290 @ SV299 ) )
= $true )
| ( ( precedes @ SV290 @ SV299 @ SV236 )
= $true )
| ( ( path @ SV254 @ SV260 @ SV236 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1439]) ).
thf(1478,plain,
! [SV277: $i,SV268: $i,SV248: $i,SV237: $i] :
( ( ( path @ SV237 @ SV248 @ SV268 )
= $false )
| ( ( in_path @ SV277 @ SV268 )
= $false )
| ( ( ~ ( ~ ( on_path @ ( sK10_E @ SV277 @ SV268 @ SV248 @ SV237 ) @ SV268 )
| ~ ( ( SV277
= ( head_of @ ( sK10_E @ SV277 @ SV268 @ SV248 @ SV237 ) ) )
| ( SV277
= ( tail_of @ ( sK10_E @ SV277 @ SV268 @ SV248 @ SV237 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1440]) ).
thf(1479,plain,
! [SV278: $i,SV269: $i,SV248: $i,SV237: $i] :
( ( ( path @ SV237 @ SV248 @ SV269 )
= $false )
| ( ( in_path @ SV278 @ SV269 )
= $false )
| ( ( vertex @ SV278 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1441]) ).
thf(1480,plain,
! [SV270: $i,SV263: $i,SV238: $i] :
( ( ( ~ ( edge @ SV238 )
| ~ ( edge @ SV263 ) )
= $true )
| ( ( ~ ( edge @ SV270 ) )
= $true )
| ( ( ~ ( sequential @ SV238 @ SV263 ) )
= $true )
| ( ( ~ ( sequential @ SV263 @ SV270 ) )
= $true )
| ( ( ~ ( sequential @ SV270 @ SV238 ) )
= $true )
| ( ( triangle @ SV238 @ SV263 @ SV270 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1442]) ).
thf(1481,plain,
! [SV238: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( ! [SY440: $i,SY441: $i] :
~ ( triangle @ SV238 @ SY440 @ SY441 )
| ( edge @ SV238 ) )
| ~ ! [SY442: $i] :
( ! [SY443: $i] :
~ ( triangle @ SV238 @ SY442 @ SY443 )
| ( edge @ SY442 ) ) )
| ~ ! [SY444: $i,SY445: $i] :
( ~ ( triangle @ SV238 @ SY444 @ SY445 )
| ( edge @ SY445 ) ) )
| ~ ! [SY446: $i] :
( ! [SY447: $i] :
~ ( triangle @ SV238 @ SY446 @ SY447 )
| ( sequential @ SV238 @ SY446 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1443]) ).
thf(1482,plain,
! [SV304: $i,SV238: $i] :
( ( ! [SY545: $i] :
( ~ ( triangle @ SV238 @ SV304 @ SY545 )
| ( sequential @ SV304 @ SY545 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1444]) ).
thf(1483,plain,
! [SV291: $i,SV281: $i,SV238: $i] :
( ( ( triangle @ SV238 @ SV281 @ SV291 )
= $false )
| ( ( sequential @ SV291 @ SV238 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1445]) ).
thf(1484,plain,
! [SV271: $i,SV264: $i,SV239: $i] :
( ( ( path @ SV239 @ SV264 @ ( sK8_P @ SV271 @ SV264 @ SV239 ) )
= $true )
| ( ( ( SV239 = SV264 )
| ~ ( path @ SV239 @ SV264 @ SV271 ) )
= $true )
| ( ( shortest_path @ SV239 @ SV264 @ SV271 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1446]) ).
thf(1485,plain,
! [SV239: $i,SV264: $i,SV271: $i] :
( ( ( ~ ( less_or_equal @ ( length_of @ SV271 ) @ ( length_of @ ( sK8_P @ SV271 @ SV264 @ SV239 ) ) ) )
= $true )
| ( ( ( SV239 = SV264 )
| ~ ( path @ SV239 @ SV264 @ SV271 ) )
= $true )
| ( ( shortest_path @ SV239 @ SV264 @ SV271 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1447]) ).
thf(1486,plain,
! [SV292: $i,SV282: $i,SV239: $i] :
( ( ( shortest_path @ SV239 @ SV282 @ SV292 )
= $false )
| ( ( ! [SY540: $i] :
( ~ ( path @ SV239 @ SV282 @ SY540 )
| ( less_or_equal @ ( length_of @ SV292 ) @ ( length_of @ SY540 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1448]) ).
thf(1487,plain,
! [SV305: $i,SV239: $i] :
( ( ! [SY546: $i] :
~ ( shortest_path @ SV239 @ SV305 @ SY546 )
| ( SV239 != SV305 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1449]) ).
thf(1488,plain,
! [SV306: $i,SV239: $i] :
( ( ! [SY547: $i] :
( ~ ( shortest_path @ SV239 @ SV306 @ SY547 )
| ( path @ SV239 @ SV306 @ SY547 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1450]) ).
thf(1489,plain,
! [SV300: $i,SV293: $i,SV240: $i] :
( ( ( path @ SV240 @ SV293 @ SV300 )
= $false )
| ( ( vertex @ SV240 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1451]) ).
thf(1490,plain,
! [SV301: $i,SV283: $i,SV240: $i] :
( ( ( path @ SV240 @ SV283 @ SV301 )
= $false )
| ( ( vertex @ SV283 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1452]) ).
thf(1491,plain,
! [SV265: $i,SV272: $i,SV240: $i] :
( ( ( ~ ( ( SV240
!= ( tail_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( edge @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) ) )
= $true )
| ( ( path @ SV240 @ SV265 @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1453]) ).
thf(1492,plain,
! [SV240: $i,SV272: $i,SV265: $i] :
( ( ( ~ ( ~ ( ( SV265
!= ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
| ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ empty ) )
| ! [SY525: $i] :
( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ SY525 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ SY525 ) ) )
| ~ ~ ( ~ ( ( SV265
= ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ ( sK13_SY84 @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ ( sK13_SY84 @ SV272 @ SV265 @ SV240 ) ) ) )
| ~ ( ( SV272
= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ empty ) )
| ~ ( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ ( sK12_SY85 @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ ( sK12_SY85 @ SV272 @ SV265 @ SV240 ) ) ) ) ) ) )
= $true )
| ( ( path @ SV240 @ SV265 @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1454]) ).
thf(1493,plain,
! [SV255: $i,SV249: $i,SV241: $i] :
( ( ( ! [SY513: $i] :
( ( SV241
!= ( tail_of @ SY513 ) )
| ~ ( edge @ SY513 )
| ( SV249
!= ( head_of @ SY513 ) )
| ( SV255
!= ( path_cons @ SY513 @ empty ) ) ) )
= $true )
| ( ( vertex @ SV241 )
= $false )
| ( ( vertex @ SV249 )
= $false )
| ( ( path @ SV241 @ SV249 @ SV255 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1455]) ).
thf(1494,plain,
! [SV249: $i,SV255: $i,SV241: $i] :
( ( ( ! [SY514: $i] :
( ( SV241
!= ( tail_of @ SY514 ) )
| ~ ( edge @ SY514 )
| ! [SY515: $i] :
( ( SV255
!= ( path_cons @ SY514 @ SY515 ) )
| ~ ( path @ ( head_of @ SY514 ) @ SV249 @ SY515 ) ) ) )
= $true )
| ( ( vertex @ SV241 )
= $false )
| ( ( vertex @ SV249 )
= $false )
| ( ( path @ SV241 @ SV249 @ SV255 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1456]) ).
thf(1495,plain,
! [SV261: $i,SV266: $i] :
( ( ( edge @ SV266 )
= $false )
| ( ( edge @ SV261 )
= $false )
| ( ( SV261 = SV266 )
= $true )
| ( ( ( ( head_of @ SV261 )
!= ( tail_of @ SV266 ) ) )
= $true )
| ( ( sequential @ SV261 @ SV266 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1457]) ).
thf(1496,plain,
! [SV307: $i,SV302: $i] :
( ( ~ ( sequential @ SV302 @ SV307 )
| ( SV302 != SV307 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1458]) ).
thf(1497,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1459]) ).
thf(1498,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1459]) ).
thf(1499,plain,
! [SV262: $i,SV256: $i,SV242: $i] :
( ( ( ! [SY475: $i] :
( ! [SY476: $i] :
~ ( precedes @ SY475 @ SY476 @ SV242 )
| ( on_path @ SY475 @ SV242 ) ) )
= $true )
| ( ( path @ SV256 @ SV262 @ SV242 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1461]) ).
thf(1500,plain,
! [SV262: $i,SV256: $i,SV242: $i] :
( ( ( ! [SY477: $i,SY478: $i] :
( ~ ( precedes @ SY477 @ SY478 @ SV242 )
| ( on_path @ SY478 @ SV242 ) ) )
= $true )
| ( ( path @ SV256 @ SV262 @ SV242 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1462]) ).
thf(1501,plain,
! [SV262: $i,SV256: $i,SV242: $i] :
( ( ( ! [SY479: $i,SY480: $i] :
( ~ ( precedes @ SY479 @ SY480 @ SV242 )
| ! [SY481: $i] :
( ~ ( precedes @ SY481 @ SY480 @ SV242 )
| ~ ( sequential @ SY479 @ SY481 ) )
| ~ ( sequential @ SY479 @ SY480 ) ) )
= $true )
| ( ( path @ SV256 @ SV262 @ SV242 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1463]) ).
thf(1502,plain,
! [SV262: $i,SV256: $i,SV242: $i] :
( ( ( ! [SY482: $i,SY483: $i] :
( ~ ( precedes @ SY482 @ SY483 @ SV242 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY483 @ SY482 @ SV242 ) @ SY483 @ SV242 )
| ~ ( sequential @ SY482 @ ( sK9_E3 @ SY483 @ SY482 @ SV242 ) ) )
| ( sequential @ SY482 @ SY483 ) ) )
= $true )
| ( ( path @ SV256 @ SV262 @ SV242 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1464]) ).
thf(1503,plain,
! [SV233: $i] :
( ( ( on_path @ ( sK6_E1 @ SV233 ) @ SV233 )
= $true )
| ( ( ! [SY410: $i,SY411: $i] :
~ ( path @ SY410 @ SY411 @ SV233 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV233 )
= ( number_of_in @ triangles @ SV233 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1465]) ).
thf(1504,plain,
! [SV233: $i] :
( ( ( on_path @ ( sK7_SY80 @ SV233 ) @ SV233 )
= $true )
| ( ( ! [SY410: $i,SY411: $i] :
~ ( path @ SY410 @ SY411 @ SV233 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV233 )
= ( number_of_in @ triangles @ SV233 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1466]) ).
thf(1505,plain,
! [SV233: $i,SV303: $i,SV294: $i] :
( ( ( path @ SV294 @ SV303 @ SV233 )
= $false )
| ( ( sequential @ ( sK6_E1 @ SV233 ) @ ( sK7_SY80 @ SV233 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV233 )
= ( number_of_in @ triangles @ SV233 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1467]) ).
thf(1506,plain,
! [SV259: $i,SV252: $i] :
( ( ( ~ ( ~ ( ( SV252
!= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
!= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
!= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
!= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV252
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
| ~ ( ( SV252
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) ) )
| ~ ~ ( ~ ( ( SV259
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
| ~ ( ( SV259
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) ) ) ) ) )
= $true )
| ( ( SV252 = SV259 )
= $true )
| ( ( vertex @ SV252 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1469]) ).
thf(1507,plain,
! [SV252: $i,SV259: $i] :
( ( ( edge @ ( sK14_E @ SV259 @ SV252 ) )
= $true )
| ( ( SV252 = SV259 )
= $true )
| ( ( vertex @ SV252 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1470]) ).
thf(1508,plain,
! [SV274: $i,SV253: $i,SV286: $i,SV246: $i,SV234: $i] :
( ( ( shortest_path @ SV234 @ SV246 @ SV286 )
= $false )
| ( ( precedes @ SV253 @ SV274 @ SV286 )
= $false )
| ( ( ! [SY527: $i] :
( ( ( tail_of @ SY527 )
!= ( tail_of @ SV253 ) )
| ( ( head_of @ SY527 )
!= ( head_of @ SV274 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1471]) ).
thf(1509,plain,
! [SV275: $i,SV253: $i,SV280: $i,SV246: $i,SV234: $i] :
( ( ( shortest_path @ SV234 @ SV246 @ SV280 )
= $false )
| ( ( precedes @ SV253 @ SV275 @ SV280 )
= $false )
| ( ( ~ ( precedes @ SV275 @ SV253 @ SV280 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1472]) ).
thf(1510,plain,
! [SV247: $i,SV235: $i,SV287: $i,SV296: $i] :
( ( ( ~ ( on_path @ SV296 @ SV287 ) )
= $true )
| ( ( ~ ( path @ SV235 @ SV247 @ SV287 ) )
= $true )
| ( ( edge @ SV296 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1473]) ).
thf(1511,plain,
! [SV247: $i,SV235: $i,SV288: $i,SV297: $i] :
( ( ( ~ ( on_path @ SV297 @ SV288 ) )
= $true )
| ( ( ~ ( path @ SV235 @ SV247 @ SV288 ) )
= $true )
| ( ( in_path @ ( head_of @ SV297 ) @ SV288 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1474]) ).
thf(1512,plain,
! [SV260: $i,SV254: $i,SV298: $i,SV236: $i,SV289: $i] :
( ( ( ~ ( on_path @ SV289 @ SV236 )
| ~ ( on_path @ SV298 @ SV236 ) )
= $true )
| ( ( ! [SY543: $i] :
( ~ ( precedes @ SY543 @ SV298 @ SV236 )
| ~ ( sequential @ SV289 @ SY543 ) ) )
= $true )
| ( ( precedes @ SV289 @ SV298 @ SV236 )
= $true )
| ( ( path @ SV254 @ SV260 @ SV236 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1476]) ).
thf(1513,plain,
! [SV260: $i,SV254: $i,SV299: $i,SV236: $i,SV290: $i] :
( ( ( ~ ( on_path @ SV290 @ SV236 )
| ~ ( on_path @ SV299 @ SV236 ) )
= $true )
| ( ( ~ ( sequential @ SV290 @ SV299 ) )
= $true )
| ( ( precedes @ SV290 @ SV299 @ SV236 )
= $true )
| ( ( path @ SV254 @ SV260 @ SV236 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1477]) ).
thf(1514,plain,
! [SV237: $i,SV248: $i,SV268: $i,SV277: $i] :
( ( ( ~ ( on_path @ ( sK10_E @ SV277 @ SV268 @ SV248 @ SV237 ) @ SV268 )
| ~ ( ( SV277
= ( head_of @ ( sK10_E @ SV277 @ SV268 @ SV248 @ SV237 ) ) )
| ( SV277
= ( tail_of @ ( sK10_E @ SV277 @ SV268 @ SV248 @ SV237 ) ) ) ) )
= $false )
| ( ( in_path @ SV277 @ SV268 )
= $false )
| ( ( path @ SV237 @ SV248 @ SV268 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1478]) ).
thf(1515,plain,
! [SV270: $i,SV263: $i,SV238: $i] :
( ( ( ~ ( edge @ SV238 ) )
= $true )
| ( ( ~ ( edge @ SV263 ) )
= $true )
| ( ( ~ ( edge @ SV270 ) )
= $true )
| ( ( ~ ( sequential @ SV238 @ SV263 ) )
= $true )
| ( ( ~ ( sequential @ SV263 @ SV270 ) )
= $true )
| ( ( ~ ( sequential @ SV270 @ SV238 ) )
= $true )
| ( ( triangle @ SV238 @ SV263 @ SV270 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1480]) ).
thf(1516,plain,
! [SV238: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( ! [SY440: $i,SY441: $i] :
~ ( triangle @ SV238 @ SY440 @ SY441 )
| ( edge @ SV238 ) )
| ~ ! [SY442: $i] :
( ! [SY443: $i] :
~ ( triangle @ SV238 @ SY442 @ SY443 )
| ( edge @ SY442 ) ) )
| ~ ! [SY444: $i,SY445: $i] :
( ~ ( triangle @ SV238 @ SY444 @ SY445 )
| ( edge @ SY445 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1481]) ).
thf(1517,plain,
! [SV238: $i] :
( ( ~ ! [SY446: $i] :
( ! [SY447: $i] :
~ ( triangle @ SV238 @ SY446 @ SY447 )
| ( sequential @ SV238 @ SY446 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1481]) ).
thf(1518,plain,
! [SV308: $i,SV304: $i,SV238: $i] :
( ( ~ ( triangle @ SV238 @ SV304 @ SV308 )
| ( sequential @ SV304 @ SV308 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1482]) ).
thf(1519,plain,
! [SV271: $i,SV264: $i,SV239: $i] :
( ( ( SV239 = SV264 )
= $true )
| ( ( ~ ( path @ SV239 @ SV264 @ SV271 ) )
= $true )
| ( ( path @ SV239 @ SV264 @ ( sK8_P @ SV271 @ SV264 @ SV239 ) )
= $true )
| ( ( shortest_path @ SV239 @ SV264 @ SV271 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1484]) ).
thf(1520,plain,
! [SV239: $i,SV264: $i,SV271: $i] :
( ( ( less_or_equal @ ( length_of @ SV271 ) @ ( length_of @ ( sK8_P @ SV271 @ SV264 @ SV239 ) ) )
= $false )
| ( ( ( SV239 = SV264 )
| ~ ( path @ SV239 @ SV264 @ SV271 ) )
= $true )
| ( ( shortest_path @ SV239 @ SV264 @ SV271 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1485]) ).
thf(1521,plain,
! [SV292: $i,SV309: $i,SV282: $i,SV239: $i] :
( ( ( ~ ( path @ SV239 @ SV282 @ SV309 )
| ( less_or_equal @ ( length_of @ SV292 ) @ ( length_of @ SV309 ) ) )
= $true )
| ( ( shortest_path @ SV239 @ SV282 @ SV292 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1486]) ).
thf(1522,plain,
! [SV305: $i,SV239: $i] :
( ( ( ! [SY546: $i] :
~ ( shortest_path @ SV239 @ SV305 @ SY546 ) )
= $true )
| ( ( ( SV239 != SV305 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1487]) ).
thf(1523,plain,
! [SV310: $i,SV306: $i,SV239: $i] :
( ( ~ ( shortest_path @ SV239 @ SV306 @ SV310 )
| ( path @ SV239 @ SV306 @ SV310 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1488]) ).
thf(1524,plain,
! [SV265: $i,SV272: $i,SV240: $i] :
( ( ( ( SV240
!= ( tail_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( edge @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
= $false )
| ( ( path @ SV240 @ SV265 @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1491]) ).
thf(1525,plain,
! [SV240: $i,SV272: $i,SV265: $i] :
( ( ( ~ ( ( SV265
!= ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
| ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ empty ) )
| ! [SY525: $i] :
( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ SY525 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ SY525 ) ) )
| ~ ~ ( ~ ( ( SV265
= ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ ( sK13_SY84 @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ ( sK13_SY84 @ SV272 @ SV265 @ SV240 ) ) ) )
| ~ ( ( SV272
= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ empty ) )
| ~ ( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ ( sK12_SY85 @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ ( sK12_SY85 @ SV272 @ SV265 @ SV240 ) ) ) ) ) )
= $false )
| ( ( path @ SV240 @ SV265 @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1492]) ).
thf(1526,plain,
! [SV255: $i,SV249: $i,SV311: $i,SV241: $i] :
( ( ( ( SV241
!= ( tail_of @ SV311 ) )
| ~ ( edge @ SV311 )
| ( SV249
!= ( head_of @ SV311 ) )
| ( SV255
!= ( path_cons @ SV311 @ empty ) ) )
= $true )
| ( ( vertex @ SV241 )
= $false )
| ( ( vertex @ SV249 )
= $false )
| ( ( path @ SV241 @ SV249 @ SV255 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1493]) ).
thf(1527,plain,
! [SV249: $i,SV255: $i,SV312: $i,SV241: $i] :
( ( ( ( SV241
!= ( tail_of @ SV312 ) )
| ~ ( edge @ SV312 )
| ! [SY548: $i] :
( ( SV255
!= ( path_cons @ SV312 @ SY548 ) )
| ~ ( path @ ( head_of @ SV312 ) @ SV249 @ SY548 ) ) )
= $true )
| ( ( vertex @ SV241 )
= $false )
| ( ( vertex @ SV249 )
= $false )
| ( ( path @ SV241 @ SV249 @ SV255 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1494]) ).
thf(1528,plain,
! [SV266: $i,SV261: $i] :
( ( ( ( head_of @ SV261 )
= ( tail_of @ SV266 ) )
= $false )
| ( ( SV261 = SV266 )
= $true )
| ( ( edge @ SV261 )
= $false )
| ( ( edge @ SV266 )
= $false )
| ( ( sequential @ SV261 @ SV266 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1495]) ).
thf(1529,plain,
! [SV307: $i,SV302: $i] :
( ( ( ~ ( sequential @ SV302 @ SV307 ) )
= $true )
| ( ( ( SV302 != SV307 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1496]) ).
thf(1530,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1497]) ).
thf(1531,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1498]) ).
thf(1532,plain,
! [SV262: $i,SV256: $i,SV242: $i,SV313: $i] :
( ( ( ! [SY549: $i] :
~ ( precedes @ SV313 @ SY549 @ SV242 )
| ( on_path @ SV313 @ SV242 ) )
= $true )
| ( ( path @ SV256 @ SV262 @ SV242 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1499]) ).
thf(1533,plain,
! [SV262: $i,SV256: $i,SV242: $i,SV314: $i] :
( ( ( ! [SY550: $i] :
( ~ ( precedes @ SV314 @ SY550 @ SV242 )
| ( on_path @ SY550 @ SV242 ) ) )
= $true )
| ( ( path @ SV256 @ SV262 @ SV242 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1500]) ).
thf(1534,plain,
! [SV262: $i,SV256: $i,SV242: $i,SV315: $i] :
( ( ( ! [SY551: $i] :
( ~ ( precedes @ SV315 @ SY551 @ SV242 )
| ! [SY552: $i] :
( ~ ( precedes @ SY552 @ SY551 @ SV242 )
| ~ ( sequential @ SV315 @ SY552 ) )
| ~ ( sequential @ SV315 @ SY551 ) ) )
= $true )
| ( ( path @ SV256 @ SV262 @ SV242 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1501]) ).
thf(1535,plain,
! [SV262: $i,SV256: $i,SV242: $i,SV316: $i] :
( ( ( ! [SY553: $i] :
( ~ ( precedes @ SV316 @ SY553 @ SV242 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY553 @ SV316 @ SV242 ) @ SY553 @ SV242 )
| ~ ( sequential @ SV316 @ ( sK9_E3 @ SY553 @ SV316 @ SV242 ) ) )
| ( sequential @ SV316 @ SY553 ) ) )
= $true )
| ( ( path @ SV256 @ SV262 @ SV242 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1502]) ).
thf(1536,plain,
! [SV233: $i,SV317: $i] :
( ( ( ! [SY554: $i] :
~ ( path @ SV317 @ SY554 @ SV233 ) )
= $true )
| ( ( on_path @ ( sK6_E1 @ SV233 ) @ SV233 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV233 )
= ( number_of_in @ triangles @ SV233 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1503]) ).
thf(1537,plain,
! [SV233: $i,SV318: $i] :
( ( ( ! [SY555: $i] :
~ ( path @ SV318 @ SY555 @ SV233 ) )
= $true )
| ( ( on_path @ ( sK7_SY80 @ SV233 ) @ SV233 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV233 )
= ( number_of_in @ triangles @ SV233 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1504]) ).
thf(1538,plain,
! [SV259: $i,SV252: $i] :
( ( ( ~ ( ( SV252
!= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
!= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
!= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
!= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV252
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
| ~ ( ( SV252
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) ) )
| ~ ~ ( ~ ( ( SV259
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
| ~ ( ( SV259
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) ) ) ) )
= $false )
| ( ( SV252 = SV259 )
= $true )
| ( ( vertex @ SV252 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1506]) ).
thf(1539,plain,
! [SV246: $i,SV234: $i,SV286: $i,SV274: $i,SV253: $i,SV319: $i] :
( ( ( ( ( tail_of @ SV319 )
!= ( tail_of @ SV253 ) )
| ( ( head_of @ SV319 )
!= ( head_of @ SV274 ) ) )
= $true )
| ( ( precedes @ SV253 @ SV274 @ SV286 )
= $false )
| ( ( shortest_path @ SV234 @ SV246 @ SV286 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1508]) ).
thf(1540,plain,
! [SV246: $i,SV234: $i,SV280: $i,SV253: $i,SV275: $i] :
( ( ( precedes @ SV275 @ SV253 @ SV280 )
= $false )
| ( ( precedes @ SV253 @ SV275 @ SV280 )
= $false )
| ( ( shortest_path @ SV234 @ SV246 @ SV280 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1509]) ).
thf(1541,plain,
! [SV247: $i,SV235: $i,SV287: $i,SV296: $i] :
( ( ( on_path @ SV296 @ SV287 )
= $false )
| ( ( ~ ( path @ SV235 @ SV247 @ SV287 ) )
= $true )
| ( ( edge @ SV296 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1510]) ).
thf(1542,plain,
! [SV247: $i,SV235: $i,SV288: $i,SV297: $i] :
( ( ( on_path @ SV297 @ SV288 )
= $false )
| ( ( ~ ( path @ SV235 @ SV247 @ SV288 ) )
= $true )
| ( ( in_path @ ( head_of @ SV297 ) @ SV288 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1511]) ).
thf(1543,plain,
! [SV260: $i,SV254: $i,SV298: $i,SV236: $i,SV289: $i] :
( ( ( ~ ( on_path @ SV289 @ SV236 ) )
= $true )
| ( ( ~ ( on_path @ SV298 @ SV236 ) )
= $true )
| ( ( ! [SY543: $i] :
( ~ ( precedes @ SY543 @ SV298 @ SV236 )
| ~ ( sequential @ SV289 @ SY543 ) ) )
= $true )
| ( ( precedes @ SV289 @ SV298 @ SV236 )
= $true )
| ( ( path @ SV254 @ SV260 @ SV236 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1512]) ).
thf(1544,plain,
! [SV260: $i,SV254: $i,SV299: $i,SV236: $i,SV290: $i] :
( ( ( ~ ( on_path @ SV290 @ SV236 ) )
= $true )
| ( ( ~ ( on_path @ SV299 @ SV236 ) )
= $true )
| ( ( ~ ( sequential @ SV290 @ SV299 ) )
= $true )
| ( ( precedes @ SV290 @ SV299 @ SV236 )
= $true )
| ( ( path @ SV254 @ SV260 @ SV236 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1513]) ).
thf(1545,plain,
! [SV237: $i,SV248: $i,SV268: $i,SV277: $i] :
( ( ( ~ ( on_path @ ( sK10_E @ SV277 @ SV268 @ SV248 @ SV237 ) @ SV268 ) )
= $false )
| ( ( in_path @ SV277 @ SV268 )
= $false )
| ( ( path @ SV237 @ SV248 @ SV268 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1514]) ).
thf(1546,plain,
! [SV237: $i,SV248: $i,SV268: $i,SV277: $i] :
( ( ( ~ ( ( SV277
= ( head_of @ ( sK10_E @ SV277 @ SV268 @ SV248 @ SV237 ) ) )
| ( SV277
= ( tail_of @ ( sK10_E @ SV277 @ SV268 @ SV248 @ SV237 ) ) ) ) )
= $false )
| ( ( in_path @ SV277 @ SV268 )
= $false )
| ( ( path @ SV237 @ SV248 @ SV268 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1514]) ).
thf(1547,plain,
! [SV270: $i,SV263: $i,SV238: $i] :
( ( ( edge @ SV238 )
= $false )
| ( ( ~ ( edge @ SV263 ) )
= $true )
| ( ( ~ ( edge @ SV270 ) )
= $true )
| ( ( ~ ( sequential @ SV238 @ SV263 ) )
= $true )
| ( ( ~ ( sequential @ SV263 @ SV270 ) )
= $true )
| ( ( ~ ( sequential @ SV270 @ SV238 ) )
= $true )
| ( ( triangle @ SV238 @ SV263 @ SV270 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1515]) ).
thf(1548,plain,
! [SV238: $i] :
( ( ~ ( ~ ~ ( ~ ( ! [SY440: $i,SY441: $i] :
~ ( triangle @ SV238 @ SY440 @ SY441 )
| ( edge @ SV238 ) )
| ~ ! [SY442: $i] :
( ! [SY443: $i] :
~ ( triangle @ SV238 @ SY442 @ SY443 )
| ( edge @ SY442 ) ) )
| ~ ! [SY444: $i,SY445: $i] :
( ~ ( triangle @ SV238 @ SY444 @ SY445 )
| ( edge @ SY445 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1516]) ).
thf(1549,plain,
! [SV238: $i] :
( ( ! [SY446: $i] :
( ! [SY447: $i] :
~ ( triangle @ SV238 @ SY446 @ SY447 )
| ( sequential @ SV238 @ SY446 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1517]) ).
thf(1550,plain,
! [SV308: $i,SV304: $i,SV238: $i] :
( ( ( ~ ( triangle @ SV238 @ SV304 @ SV308 ) )
= $true )
| ( ( sequential @ SV304 @ SV308 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1518]) ).
thf(1551,plain,
! [SV271: $i,SV264: $i,SV239: $i] :
( ( ( path @ SV239 @ SV264 @ SV271 )
= $false )
| ( ( SV239 = SV264 )
= $true )
| ( ( path @ SV239 @ SV264 @ ( sK8_P @ SV271 @ SV264 @ SV239 ) )
= $true )
| ( ( shortest_path @ SV239 @ SV264 @ SV271 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1519]) ).
thf(1552,plain,
! [SV271: $i,SV264: $i,SV239: $i] :
( ( ( SV239 = SV264 )
= $true )
| ( ( ~ ( path @ SV239 @ SV264 @ SV271 ) )
= $true )
| ( ( less_or_equal @ ( length_of @ SV271 ) @ ( length_of @ ( sK8_P @ SV271 @ SV264 @ SV239 ) ) )
= $false )
| ( ( shortest_path @ SV239 @ SV264 @ SV271 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1520]) ).
thf(1553,plain,
! [SV292: $i,SV309: $i,SV282: $i,SV239: $i] :
( ( ( ~ ( path @ SV239 @ SV282 @ SV309 ) )
= $true )
| ( ( less_or_equal @ ( length_of @ SV292 ) @ ( length_of @ SV309 ) )
= $true )
| ( ( shortest_path @ SV239 @ SV282 @ SV292 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1521]) ).
thf(1554,plain,
! [SV320: $i,SV305: $i,SV239: $i] :
( ( ( ~ ( shortest_path @ SV239 @ SV305 @ SV320 ) )
= $true )
| ( ( ( SV239 != SV305 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1522]) ).
thf(1555,plain,
! [SV310: $i,SV306: $i,SV239: $i] :
( ( ( ~ ( shortest_path @ SV239 @ SV306 @ SV310 ) )
= $true )
| ( ( path @ SV239 @ SV306 @ SV310 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1523]) ).
thf(1556,plain,
! [SV265: $i,SV272: $i,SV240: $i] :
( ( ( ( SV240
!= ( tail_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) ) )
= $false )
| ( ( path @ SV240 @ SV265 @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1524]) ).
thf(1557,plain,
! [SV240: $i,SV265: $i,SV272: $i] :
( ( ( ~ ( edge @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
= $false )
| ( ( path @ SV240 @ SV265 @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1524]) ).
thf(1558,plain,
! [SV240: $i,SV272: $i,SV265: $i] :
( ( ( ~ ( ( SV265
!= ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
| ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ empty ) )
| ! [SY525: $i] :
( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ SY525 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ SY525 ) ) ) )
= $false )
| ( ( path @ SV240 @ SV265 @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1525]) ).
thf(1559,plain,
! [SV240: $i,SV272: $i,SV265: $i] :
( ( ( ~ ~ ( ~ ( ( SV265
= ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ ( sK13_SY84 @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ ( sK13_SY84 @ SV272 @ SV265 @ SV240 ) ) ) )
| ~ ( ( SV272
= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ empty ) )
| ~ ( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ ( sK12_SY85 @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ ( sK12_SY85 @ SV272 @ SV265 @ SV240 ) ) ) ) ) )
= $false )
| ( ( path @ SV240 @ SV265 @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1525]) ).
thf(1560,plain,
! [SV255: $i,SV249: $i,SV311: $i,SV241: $i] :
( ( ( ( SV241
!= ( tail_of @ SV311 ) )
| ~ ( edge @ SV311 ) )
= $true )
| ( ( ( SV249
!= ( head_of @ SV311 ) )
| ( SV255
!= ( path_cons @ SV311 @ empty ) ) )
= $true )
| ( ( vertex @ SV241 )
= $false )
| ( ( vertex @ SV249 )
= $false )
| ( ( path @ SV241 @ SV249 @ SV255 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1526]) ).
thf(1561,plain,
! [SV249: $i,SV255: $i,SV312: $i,SV241: $i] :
( ( ( ( SV241
!= ( tail_of @ SV312 ) )
| ~ ( edge @ SV312 ) )
= $true )
| ( ( ! [SY548: $i] :
( ( SV255
!= ( path_cons @ SV312 @ SY548 ) )
| ~ ( path @ ( head_of @ SV312 ) @ SV249 @ SY548 ) ) )
= $true )
| ( ( vertex @ SV241 )
= $false )
| ( ( vertex @ SV249 )
= $false )
| ( ( path @ SV241 @ SV249 @ SV255 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1527]) ).
thf(1562,plain,
! [SV307: $i,SV302: $i] :
( ( ( sequential @ SV302 @ SV307 )
= $false )
| ( ( ( SV302 != SV307 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1529]) ).
thf(1563,plain,
! [SV321: $i] :
( ( ! [SY556: $i] :
~ ( sequential @ SV321 @ SY556 )
| ( edge @ SV321 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1530]) ).
thf(1564,plain,
! [SV322: $i] :
( ( ! [SY557: $i] :
( ~ ( sequential @ SV322 @ SY557 )
| ( edge @ SY557 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1531]) ).
thf(1565,plain,
! [SV262: $i,SV256: $i,SV242: $i,SV313: $i] :
( ( ( ! [SY549: $i] :
~ ( precedes @ SV313 @ SY549 @ SV242 ) )
= $true )
| ( ( on_path @ SV313 @ SV242 )
= $true )
| ( ( path @ SV256 @ SV262 @ SV242 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1532]) ).
thf(1566,plain,
! [SV262: $i,SV256: $i,SV242: $i,SV323: $i,SV314: $i] :
( ( ( ~ ( precedes @ SV314 @ SV323 @ SV242 )
| ( on_path @ SV323 @ SV242 ) )
= $true )
| ( ( path @ SV256 @ SV262 @ SV242 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1533]) ).
thf(1567,plain,
! [SV262: $i,SV256: $i,SV242: $i,SV324: $i,SV315: $i] :
( ( ( ~ ( precedes @ SV315 @ SV324 @ SV242 )
| ! [SY558: $i] :
( ~ ( precedes @ SY558 @ SV324 @ SV242 )
| ~ ( sequential @ SV315 @ SY558 ) )
| ~ ( sequential @ SV315 @ SV324 ) )
= $true )
| ( ( path @ SV256 @ SV262 @ SV242 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1534]) ).
thf(1568,plain,
! [SV262: $i,SV256: $i,SV242: $i,SV325: $i,SV316: $i] :
( ( ( ~ ( precedes @ SV316 @ SV325 @ SV242 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SV325 @ SV316 @ SV242 ) @ SV325 @ SV242 )
| ~ ( sequential @ SV316 @ ( sK9_E3 @ SV325 @ SV316 @ SV242 ) ) )
| ( sequential @ SV316 @ SV325 ) )
= $true )
| ( ( path @ SV256 @ SV262 @ SV242 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1535]) ).
thf(1569,plain,
! [SV233: $i,SV326: $i,SV317: $i] :
( ( ( ~ ( path @ SV317 @ SV326 @ SV233 ) )
= $true )
| ( ( on_path @ ( sK6_E1 @ SV233 ) @ SV233 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV233 )
= ( number_of_in @ triangles @ SV233 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1536]) ).
thf(1570,plain,
! [SV233: $i,SV327: $i,SV318: $i] :
( ( ( ~ ( path @ SV318 @ SV327 @ SV233 ) )
= $true )
| ( ( on_path @ ( sK7_SY80 @ SV233 ) @ SV233 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV233 )
= ( number_of_in @ triangles @ SV233 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1537]) ).
thf(1571,plain,
! [SV259: $i,SV252: $i] :
( ( ( ~ ( ( SV252
!= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
!= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
!= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
!= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) ) )
= $false )
| ( ( SV252 = SV259 )
= $true )
| ( ( vertex @ SV252 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[1538]) ).
thf(1572,plain,
! [SV259: $i,SV252: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( SV252
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
| ~ ( ( SV252
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) ) )
| ~ ~ ( ~ ( ( SV259
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
| ~ ( ( SV259
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) ) ) ) )
= $false )
| ( ( SV252 = SV259 )
= $true )
| ( ( vertex @ SV252 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[1538]) ).
thf(1573,plain,
! [SV246: $i,SV234: $i,SV286: $i,SV274: $i,SV253: $i,SV319: $i] :
( ( ( ( ( tail_of @ SV319 )
!= ( tail_of @ SV253 ) ) )
= $true )
| ( ( ( ( head_of @ SV319 )
!= ( head_of @ SV274 ) ) )
= $true )
| ( ( precedes @ SV253 @ SV274 @ SV286 )
= $false )
| ( ( shortest_path @ SV234 @ SV246 @ SV286 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1539]) ).
thf(1574,plain,
! [SV296: $i,SV287: $i,SV247: $i,SV235: $i] :
( ( ( path @ SV235 @ SV247 @ SV287 )
= $false )
| ( ( on_path @ SV296 @ SV287 )
= $false )
| ( ( edge @ SV296 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1541]) ).
thf(1575,plain,
! [SV297: $i,SV288: $i,SV247: $i,SV235: $i] :
( ( ( path @ SV235 @ SV247 @ SV288 )
= $false )
| ( ( on_path @ SV297 @ SV288 )
= $false )
| ( ( in_path @ ( head_of @ SV297 ) @ SV288 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1542]) ).
thf(1576,plain,
! [SV260: $i,SV254: $i,SV298: $i,SV236: $i,SV289: $i] :
( ( ( on_path @ SV289 @ SV236 )
= $false )
| ( ( ~ ( on_path @ SV298 @ SV236 ) )
= $true )
| ( ( ! [SY543: $i] :
( ~ ( precedes @ SY543 @ SV298 @ SV236 )
| ~ ( sequential @ SV289 @ SY543 ) ) )
= $true )
| ( ( precedes @ SV289 @ SV298 @ SV236 )
= $true )
| ( ( path @ SV254 @ SV260 @ SV236 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1543]) ).
thf(1577,plain,
! [SV260: $i,SV254: $i,SV299: $i,SV236: $i,SV290: $i] :
( ( ( on_path @ SV290 @ SV236 )
= $false )
| ( ( ~ ( on_path @ SV299 @ SV236 ) )
= $true )
| ( ( ~ ( sequential @ SV290 @ SV299 ) )
= $true )
| ( ( precedes @ SV290 @ SV299 @ SV236 )
= $true )
| ( ( path @ SV254 @ SV260 @ SV236 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1544]) ).
thf(1578,plain,
! [SV237: $i,SV248: $i,SV268: $i,SV277: $i] :
( ( ( on_path @ ( sK10_E @ SV277 @ SV268 @ SV248 @ SV237 ) @ SV268 )
= $true )
| ( ( in_path @ SV277 @ SV268 )
= $false )
| ( ( path @ SV237 @ SV248 @ SV268 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1545]) ).
thf(1579,plain,
! [SV237: $i,SV248: $i,SV268: $i,SV277: $i] :
( ( ( ( SV277
= ( head_of @ ( sK10_E @ SV277 @ SV268 @ SV248 @ SV237 ) ) )
| ( SV277
= ( tail_of @ ( sK10_E @ SV277 @ SV268 @ SV248 @ SV237 ) ) ) )
= $true )
| ( ( in_path @ SV277 @ SV268 )
= $false )
| ( ( path @ SV237 @ SV248 @ SV268 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1546]) ).
thf(1580,plain,
! [SV270: $i,SV238: $i,SV263: $i] :
( ( ( edge @ SV263 )
= $false )
| ( ( edge @ SV238 )
= $false )
| ( ( ~ ( edge @ SV270 ) )
= $true )
| ( ( ~ ( sequential @ SV238 @ SV263 ) )
= $true )
| ( ( ~ ( sequential @ SV263 @ SV270 ) )
= $true )
| ( ( ~ ( sequential @ SV270 @ SV238 ) )
= $true )
| ( ( triangle @ SV238 @ SV263 @ SV270 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1547]) ).
thf(1581,plain,
! [SV238: $i] :
( ( ~ ~ ( ~ ( ! [SY440: $i,SY441: $i] :
~ ( triangle @ SV238 @ SY440 @ SY441 )
| ( edge @ SV238 ) )
| ~ ! [SY442: $i] :
( ! [SY443: $i] :
~ ( triangle @ SV238 @ SY442 @ SY443 )
| ( edge @ SY442 ) ) )
| ~ ! [SY444: $i,SY445: $i] :
( ~ ( triangle @ SV238 @ SY444 @ SY445 )
| ( edge @ SY445 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1548]) ).
thf(1582,plain,
! [SV328: $i,SV238: $i] :
( ( ! [SY559: $i] :
~ ( triangle @ SV238 @ SV328 @ SY559 )
| ( sequential @ SV238 @ SV328 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1549]) ).
thf(1583,plain,
! [SV308: $i,SV304: $i,SV238: $i] :
( ( ( triangle @ SV238 @ SV304 @ SV308 )
= $false )
| ( ( sequential @ SV304 @ SV308 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1550]) ).
thf(1584,plain,
! [SV271: $i,SV264: $i,SV239: $i] :
( ( ( path @ SV239 @ SV264 @ SV271 )
= $false )
| ( ( SV239 = SV264 )
= $true )
| ( ( less_or_equal @ ( length_of @ SV271 ) @ ( length_of @ ( sK8_P @ SV271 @ SV264 @ SV239 ) ) )
= $false )
| ( ( shortest_path @ SV239 @ SV264 @ SV271 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1552]) ).
thf(1585,plain,
! [SV292: $i,SV309: $i,SV282: $i,SV239: $i] :
( ( ( path @ SV239 @ SV282 @ SV309 )
= $false )
| ( ( less_or_equal @ ( length_of @ SV292 ) @ ( length_of @ SV309 ) )
= $true )
| ( ( shortest_path @ SV239 @ SV282 @ SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1553]) ).
thf(1586,plain,
! [SV320: $i,SV305: $i,SV239: $i] :
( ( ( shortest_path @ SV239 @ SV305 @ SV320 )
= $false )
| ( ( ( SV239 != SV305 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1554]) ).
thf(1587,plain,
! [SV310: $i,SV306: $i,SV239: $i] :
( ( ( shortest_path @ SV239 @ SV306 @ SV310 )
= $false )
| ( ( path @ SV239 @ SV306 @ SV310 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1555]) ).
thf(1588,plain,
! [SV265: $i,SV272: $i,SV240: $i] :
( ( ( SV240
= ( tail_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
= $true )
| ( ( path @ SV240 @ SV265 @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1556]) ).
thf(1589,plain,
! [SV240: $i,SV265: $i,SV272: $i] :
( ( ( edge @ ( sK11_E @ SV272 @ SV265 @ SV240 ) )
= $true )
| ( ( path @ SV240 @ SV265 @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1557]) ).
thf(1590,plain,
! [SV240: $i,SV272: $i,SV265: $i] :
( ( ( ( SV265
!= ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
| ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ empty ) )
| ! [SY525: $i] :
( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ SY525 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ SY525 ) ) )
= $true )
| ( ( path @ SV240 @ SV265 @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1558]) ).
thf(1591,plain,
! [SV240: $i,SV272: $i,SV265: $i] :
( ( ( ~ ( ~ ( ( SV265
= ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ ( sK13_SY84 @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ ( sK13_SY84 @ SV272 @ SV265 @ SV240 ) ) ) )
| ~ ( ( SV272
= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ empty ) )
| ~ ( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ ( sK12_SY85 @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ ( sK12_SY85 @ SV272 @ SV265 @ SV240 ) ) ) ) ) )
= $true )
| ( ( path @ SV240 @ SV265 @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1559]) ).
thf(1592,plain,
! [SV255: $i,SV249: $i,SV311: $i,SV241: $i] :
( ( ( ( SV241
!= ( tail_of @ SV311 ) ) )
= $true )
| ( ( ~ ( edge @ SV311 ) )
= $true )
| ( ( ( SV249
!= ( head_of @ SV311 ) )
| ( SV255
!= ( path_cons @ SV311 @ empty ) ) )
= $true )
| ( ( vertex @ SV241 )
= $false )
| ( ( vertex @ SV249 )
= $false )
| ( ( path @ SV241 @ SV249 @ SV255 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1560]) ).
thf(1593,plain,
! [SV249: $i,SV255: $i,SV312: $i,SV241: $i] :
( ( ( ( SV241
!= ( tail_of @ SV312 ) ) )
= $true )
| ( ( ~ ( edge @ SV312 ) )
= $true )
| ( ( ! [SY548: $i] :
( ( SV255
!= ( path_cons @ SV312 @ SY548 ) )
| ~ ( path @ ( head_of @ SV312 ) @ SV249 @ SY548 ) ) )
= $true )
| ( ( vertex @ SV241 )
= $false )
| ( ( vertex @ SV249 )
= $false )
| ( ( path @ SV241 @ SV249 @ SV255 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1561]) ).
thf(1594,plain,
! [SV307: $i,SV302: $i] :
( ( ( SV302 = SV307 )
= $false )
| ( ( sequential @ SV302 @ SV307 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1562]) ).
thf(1595,plain,
! [SV321: $i] :
( ( ( ! [SY556: $i] :
~ ( sequential @ SV321 @ SY556 ) )
= $true )
| ( ( edge @ SV321 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1563]) ).
thf(1596,plain,
! [SV329: $i,SV322: $i] :
( ( ~ ( sequential @ SV322 @ SV329 )
| ( edge @ SV329 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1564]) ).
thf(1597,plain,
! [SV262: $i,SV256: $i,SV242: $i,SV330: $i,SV313: $i] :
( ( ( ~ ( precedes @ SV313 @ SV330 @ SV242 ) )
= $true )
| ( ( on_path @ SV313 @ SV242 )
= $true )
| ( ( path @ SV256 @ SV262 @ SV242 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1565]) ).
thf(1598,plain,
! [SV262: $i,SV256: $i,SV242: $i,SV323: $i,SV314: $i] :
( ( ( ~ ( precedes @ SV314 @ SV323 @ SV242 ) )
= $true )
| ( ( on_path @ SV323 @ SV242 )
= $true )
| ( ( path @ SV256 @ SV262 @ SV242 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1566]) ).
thf(1599,plain,
! [SV262: $i,SV256: $i,SV242: $i,SV324: $i,SV315: $i] :
( ( ( ~ ( precedes @ SV315 @ SV324 @ SV242 ) )
= $true )
| ( ( ! [SY558: $i] :
( ~ ( precedes @ SY558 @ SV324 @ SV242 )
| ~ ( sequential @ SV315 @ SY558 ) )
| ~ ( sequential @ SV315 @ SV324 ) )
= $true )
| ( ( path @ SV256 @ SV262 @ SV242 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1567]) ).
thf(1600,plain,
! [SV262: $i,SV256: $i,SV242: $i,SV325: $i,SV316: $i] :
( ( ( ~ ( precedes @ SV316 @ SV325 @ SV242 ) )
= $true )
| ( ( ~ ( ~ ( precedes @ ( sK9_E3 @ SV325 @ SV316 @ SV242 ) @ SV325 @ SV242 )
| ~ ( sequential @ SV316 @ ( sK9_E3 @ SV325 @ SV316 @ SV242 ) ) )
| ( sequential @ SV316 @ SV325 ) )
= $true )
| ( ( path @ SV256 @ SV262 @ SV242 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1568]) ).
thf(1601,plain,
! [SV233: $i,SV326: $i,SV317: $i] :
( ( ( path @ SV317 @ SV326 @ SV233 )
= $false )
| ( ( on_path @ ( sK6_E1 @ SV233 ) @ SV233 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV233 )
= ( number_of_in @ triangles @ SV233 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1569]) ).
thf(1602,plain,
! [SV233: $i,SV327: $i,SV318: $i] :
( ( ( path @ SV318 @ SV327 @ SV233 )
= $false )
| ( ( on_path @ ( sK7_SY80 @ SV233 ) @ SV233 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV233 )
= ( number_of_in @ triangles @ SV233 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1570]) ).
thf(1603,plain,
! [SV259: $i,SV252: $i] :
( ( ( ( SV252
!= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
!= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
!= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
!= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
= $true )
| ( ( SV252 = SV259 )
= $true )
| ( ( vertex @ SV252 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1571]) ).
thf(1604,plain,
! [SV259: $i,SV252: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( SV252
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
| ~ ( ( SV252
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) ) )
| ~ ~ ( ~ ( ( SV259
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
| ~ ( ( SV259
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) ) ) ) )
= $true )
| ( ( SV252 = SV259 )
= $true )
| ( ( vertex @ SV252 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1572]) ).
thf(1605,plain,
! [SV246: $i,SV234: $i,SV286: $i,SV274: $i,SV253: $i,SV319: $i] :
( ( ( ( tail_of @ SV319 )
= ( tail_of @ SV253 ) )
= $false )
| ( ( ( ( head_of @ SV319 )
!= ( head_of @ SV274 ) ) )
= $true )
| ( ( precedes @ SV253 @ SV274 @ SV286 )
= $false )
| ( ( shortest_path @ SV234 @ SV246 @ SV286 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1573]) ).
thf(1606,plain,
! [SV260: $i,SV254: $i,SV289: $i,SV236: $i,SV298: $i] :
( ( ( on_path @ SV298 @ SV236 )
= $false )
| ( ( on_path @ SV289 @ SV236 )
= $false )
| ( ( ! [SY543: $i] :
( ~ ( precedes @ SY543 @ SV298 @ SV236 )
| ~ ( sequential @ SV289 @ SY543 ) ) )
= $true )
| ( ( precedes @ SV289 @ SV298 @ SV236 )
= $true )
| ( ( path @ SV254 @ SV260 @ SV236 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1576]) ).
thf(1607,plain,
! [SV260: $i,SV254: $i,SV290: $i,SV236: $i,SV299: $i] :
( ( ( on_path @ SV299 @ SV236 )
= $false )
| ( ( on_path @ SV290 @ SV236 )
= $false )
| ( ( ~ ( sequential @ SV290 @ SV299 ) )
= $true )
| ( ( precedes @ SV290 @ SV299 @ SV236 )
= $true )
| ( ( path @ SV254 @ SV260 @ SV236 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1577]) ).
thf(1608,plain,
! [SV237: $i,SV248: $i,SV268: $i,SV277: $i] :
( ( ( SV277
= ( head_of @ ( sK10_E @ SV277 @ SV268 @ SV248 @ SV237 ) ) )
= $true )
| ( ( SV277
= ( tail_of @ ( sK10_E @ SV277 @ SV268 @ SV248 @ SV237 ) ) )
= $true )
| ( ( in_path @ SV277 @ SV268 )
= $false )
| ( ( path @ SV237 @ SV248 @ SV268 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1579]) ).
thf(1609,plain,
! [SV263: $i,SV238: $i,SV270: $i] :
( ( ( edge @ SV270 )
= $false )
| ( ( edge @ SV238 )
= $false )
| ( ( edge @ SV263 )
= $false )
| ( ( ~ ( sequential @ SV238 @ SV263 ) )
= $true )
| ( ( ~ ( sequential @ SV263 @ SV270 ) )
= $true )
| ( ( ~ ( sequential @ SV270 @ SV238 ) )
= $true )
| ( ( triangle @ SV238 @ SV263 @ SV270 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1580]) ).
thf(1610,plain,
! [SV238: $i] :
( ( ~ ~ ( ~ ( ! [SY440: $i,SY441: $i] :
~ ( triangle @ SV238 @ SY440 @ SY441 )
| ( edge @ SV238 ) )
| ~ ! [SY442: $i] :
( ! [SY443: $i] :
~ ( triangle @ SV238 @ SY442 @ SY443 )
| ( edge @ SY442 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1581]) ).
thf(1611,plain,
! [SV238: $i] :
( ( ~ ! [SY444: $i,SY445: $i] :
( ~ ( triangle @ SV238 @ SY444 @ SY445 )
| ( edge @ SY445 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1581]) ).
thf(1612,plain,
! [SV328: $i,SV238: $i] :
( ( ( ! [SY559: $i] :
~ ( triangle @ SV238 @ SV328 @ SY559 ) )
= $true )
| ( ( sequential @ SV238 @ SV328 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1582]) ).
thf(1613,plain,
! [SV320: $i,SV305: $i,SV239: $i] :
( ( ( SV239 = SV305 )
= $false )
| ( ( shortest_path @ SV239 @ SV305 @ SV320 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1586]) ).
thf(1614,plain,
! [SV240: $i,SV272: $i,SV265: $i] :
( ( ( ( SV265
!= ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
| ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ empty ) ) )
= $true )
| ( ( ! [SY525: $i] :
( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ SY525 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ SY525 ) ) )
= $true )
| ( ( path @ SV240 @ SV265 @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1590]) ).
thf(1615,plain,
! [SV240: $i,SV272: $i,SV265: $i] :
( ( ( ~ ( ( SV265
= ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ ( sK13_SY84 @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ ( sK13_SY84 @ SV272 @ SV265 @ SV240 ) ) ) )
| ~ ( ( SV272
= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ empty ) )
| ~ ( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ ( sK12_SY85 @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ ( sK12_SY85 @ SV272 @ SV265 @ SV240 ) ) ) ) )
= $false )
| ( ( path @ SV240 @ SV265 @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1591]) ).
thf(1616,plain,
! [SV255: $i,SV249: $i,SV311: $i,SV241: $i] :
( ( ( SV241
= ( tail_of @ SV311 ) )
= $false )
| ( ( ~ ( edge @ SV311 ) )
= $true )
| ( ( ( SV249
!= ( head_of @ SV311 ) )
| ( SV255
!= ( path_cons @ SV311 @ empty ) ) )
= $true )
| ( ( vertex @ SV241 )
= $false )
| ( ( vertex @ SV249 )
= $false )
| ( ( path @ SV241 @ SV249 @ SV255 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1592]) ).
thf(1617,plain,
! [SV249: $i,SV255: $i,SV312: $i,SV241: $i] :
( ( ( SV241
= ( tail_of @ SV312 ) )
= $false )
| ( ( ~ ( edge @ SV312 ) )
= $true )
| ( ( ! [SY548: $i] :
( ( SV255
!= ( path_cons @ SV312 @ SY548 ) )
| ~ ( path @ ( head_of @ SV312 ) @ SV249 @ SY548 ) ) )
= $true )
| ( ( vertex @ SV241 )
= $false )
| ( ( vertex @ SV249 )
= $false )
| ( ( path @ SV241 @ SV249 @ SV255 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1593]) ).
thf(1618,plain,
! [SV331: $i,SV321: $i] :
( ( ( ~ ( sequential @ SV321 @ SV331 ) )
= $true )
| ( ( edge @ SV321 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1595]) ).
thf(1619,plain,
! [SV329: $i,SV322: $i] :
( ( ( ~ ( sequential @ SV322 @ SV329 ) )
= $true )
| ( ( edge @ SV329 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1596]) ).
thf(1620,plain,
! [SV262: $i,SV256: $i,SV242: $i,SV330: $i,SV313: $i] :
( ( ( precedes @ SV313 @ SV330 @ SV242 )
= $false )
| ( ( on_path @ SV313 @ SV242 )
= $true )
| ( ( path @ SV256 @ SV262 @ SV242 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1597]) ).
thf(1621,plain,
! [SV262: $i,SV256: $i,SV242: $i,SV323: $i,SV314: $i] :
( ( ( precedes @ SV314 @ SV323 @ SV242 )
= $false )
| ( ( on_path @ SV323 @ SV242 )
= $true )
| ( ( path @ SV256 @ SV262 @ SV242 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1598]) ).
thf(1622,plain,
! [SV262: $i,SV256: $i,SV242: $i,SV324: $i,SV315: $i] :
( ( ( precedes @ SV315 @ SV324 @ SV242 )
= $false )
| ( ( ! [SY558: $i] :
( ~ ( precedes @ SY558 @ SV324 @ SV242 )
| ~ ( sequential @ SV315 @ SY558 ) )
| ~ ( sequential @ SV315 @ SV324 ) )
= $true )
| ( ( path @ SV256 @ SV262 @ SV242 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1599]) ).
thf(1623,plain,
! [SV262: $i,SV256: $i,SV242: $i,SV325: $i,SV316: $i] :
( ( ( precedes @ SV316 @ SV325 @ SV242 )
= $false )
| ( ( ~ ( ~ ( precedes @ ( sK9_E3 @ SV325 @ SV316 @ SV242 ) @ SV325 @ SV242 )
| ~ ( sequential @ SV316 @ ( sK9_E3 @ SV325 @ SV316 @ SV242 ) ) )
| ( sequential @ SV316 @ SV325 ) )
= $true )
| ( ( path @ SV256 @ SV262 @ SV242 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1600]) ).
thf(1624,plain,
! [SV259: $i,SV252: $i] :
( ( ( ( SV252
!= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
!= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
= $true )
| ( ( ( SV259
!= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
!= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
= $true )
| ( ( SV252 = SV259 )
= $true )
| ( ( vertex @ SV252 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[1603]) ).
thf(1625,plain,
! [SV259: $i,SV252: $i] :
( ( ( ~ ~ ( ~ ( ( SV252
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
| ~ ( ( SV252
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) ) )
| ~ ~ ( ~ ( ( SV259
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
| ~ ( ( SV259
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) ) ) )
= $false )
| ( ( SV252 = SV259 )
= $true )
| ( ( vertex @ SV252 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1604]) ).
thf(1626,plain,
! [SV246: $i,SV234: $i,SV286: $i,SV253: $i,SV274: $i,SV319: $i] :
( ( ( ( head_of @ SV319 )
= ( head_of @ SV274 ) )
= $false )
| ( ( ( tail_of @ SV319 )
= ( tail_of @ SV253 ) )
= $false )
| ( ( precedes @ SV253 @ SV274 @ SV286 )
= $false )
| ( ( shortest_path @ SV234 @ SV246 @ SV286 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1605]) ).
thf(1627,plain,
! [SV260: $i,SV254: $i,SV289: $i,SV236: $i,SV298: $i,SV332: $i] :
( ( ( ~ ( precedes @ SV332 @ SV298 @ SV236 )
| ~ ( sequential @ SV289 @ SV332 ) )
= $true )
| ( ( on_path @ SV289 @ SV236 )
= $false )
| ( ( on_path @ SV298 @ SV236 )
= $false )
| ( ( precedes @ SV289 @ SV298 @ SV236 )
= $true )
| ( ( path @ SV254 @ SV260 @ SV236 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1606]) ).
thf(1628,plain,
! [SV260: $i,SV254: $i,SV236: $i,SV299: $i,SV290: $i] :
( ( ( sequential @ SV290 @ SV299 )
= $false )
| ( ( on_path @ SV290 @ SV236 )
= $false )
| ( ( on_path @ SV299 @ SV236 )
= $false )
| ( ( precedes @ SV290 @ SV299 @ SV236 )
= $true )
| ( ( path @ SV254 @ SV260 @ SV236 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1607]) ).
thf(1629,plain,
! [SV270: $i,SV263: $i,SV238: $i] :
( ( ( sequential @ SV238 @ SV263 )
= $false )
| ( ( edge @ SV263 )
= $false )
| ( ( edge @ SV238 )
= $false )
| ( ( edge @ SV270 )
= $false )
| ( ( ~ ( sequential @ SV263 @ SV270 ) )
= $true )
| ( ( ~ ( sequential @ SV270 @ SV238 ) )
= $true )
| ( ( triangle @ SV238 @ SV263 @ SV270 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1609]) ).
thf(1630,plain,
! [SV238: $i] :
( ( ~ ( ~ ( ! [SY440: $i,SY441: $i] :
~ ( triangle @ SV238 @ SY440 @ SY441 )
| ( edge @ SV238 ) )
| ~ ! [SY442: $i] :
( ! [SY443: $i] :
~ ( triangle @ SV238 @ SY442 @ SY443 )
| ( edge @ SY442 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1610]) ).
thf(1631,plain,
! [SV238: $i] :
( ( ! [SY444: $i,SY445: $i] :
( ~ ( triangle @ SV238 @ SY444 @ SY445 )
| ( edge @ SY445 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1611]) ).
thf(1632,plain,
! [SV333: $i,SV328: $i,SV238: $i] :
( ( ( ~ ( triangle @ SV238 @ SV328 @ SV333 ) )
= $true )
| ( ( sequential @ SV238 @ SV328 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1612]) ).
thf(1633,plain,
! [SV240: $i,SV272: $i,SV265: $i] :
( ( ( ( SV265
!= ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) ) )
= $true )
| ( ( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ empty ) ) )
= $true )
| ( ( ! [SY525: $i] :
( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ SY525 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ SY525 ) ) )
= $true )
| ( ( path @ SV240 @ SV265 @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1614]) ).
thf(1634,plain,
! [SV240: $i,SV272: $i,SV265: $i] :
( ( ( ~ ( ( SV265
= ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ ( sK13_SY84 @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ ( sK13_SY84 @ SV272 @ SV265 @ SV240 ) ) ) ) )
= $false )
| ( ( path @ SV240 @ SV265 @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1615]) ).
thf(1635,plain,
! [SV240: $i,SV265: $i,SV272: $i] :
( ( ( ~ ( ( SV272
= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ empty ) )
| ~ ( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ ( sK12_SY85 @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ ( sK12_SY85 @ SV272 @ SV265 @ SV240 ) ) ) ) )
= $false )
| ( ( path @ SV240 @ SV265 @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1615]) ).
thf(1636,plain,
! [SV255: $i,SV249: $i,SV241: $i,SV311: $i] :
( ( ( edge @ SV311 )
= $false )
| ( ( SV241
= ( tail_of @ SV311 ) )
= $false )
| ( ( ( SV249
!= ( head_of @ SV311 ) )
| ( SV255
!= ( path_cons @ SV311 @ empty ) ) )
= $true )
| ( ( vertex @ SV241 )
= $false )
| ( ( vertex @ SV249 )
= $false )
| ( ( path @ SV241 @ SV249 @ SV255 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1616]) ).
thf(1637,plain,
! [SV249: $i,SV255: $i,SV241: $i,SV312: $i] :
( ( ( edge @ SV312 )
= $false )
| ( ( SV241
= ( tail_of @ SV312 ) )
= $false )
| ( ( ! [SY548: $i] :
( ( SV255
!= ( path_cons @ SV312 @ SY548 ) )
| ~ ( path @ ( head_of @ SV312 ) @ SV249 @ SY548 ) ) )
= $true )
| ( ( vertex @ SV241 )
= $false )
| ( ( vertex @ SV249 )
= $false )
| ( ( path @ SV241 @ SV249 @ SV255 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1617]) ).
thf(1638,plain,
! [SV331: $i,SV321: $i] :
( ( ( sequential @ SV321 @ SV331 )
= $false )
| ( ( edge @ SV321 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1618]) ).
thf(1639,plain,
! [SV329: $i,SV322: $i] :
( ( ( sequential @ SV322 @ SV329 )
= $false )
| ( ( edge @ SV329 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1619]) ).
thf(1640,plain,
! [SV262: $i,SV256: $i,SV315: $i,SV242: $i,SV324: $i] :
( ( ( ! [SY558: $i] :
( ~ ( precedes @ SY558 @ SV324 @ SV242 )
| ~ ( sequential @ SV315 @ SY558 ) ) )
= $true )
| ( ( ~ ( sequential @ SV315 @ SV324 ) )
= $true )
| ( ( precedes @ SV315 @ SV324 @ SV242 )
= $false )
| ( ( path @ SV256 @ SV262 @ SV242 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1622]) ).
thf(1641,plain,
! [SV262: $i,SV256: $i,SV242: $i,SV316: $i,SV325: $i] :
( ( ( ~ ( ~ ( precedes @ ( sK9_E3 @ SV325 @ SV316 @ SV242 ) @ SV325 @ SV242 )
| ~ ( sequential @ SV316 @ ( sK9_E3 @ SV325 @ SV316 @ SV242 ) ) ) )
= $true )
| ( ( sequential @ SV316 @ SV325 )
= $true )
| ( ( precedes @ SV316 @ SV325 @ SV242 )
= $false )
| ( ( path @ SV256 @ SV262 @ SV242 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1623]) ).
thf(1642,plain,
! [SV259: $i,SV252: $i] :
( ( ( ( SV252
!= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
= $true )
| ( ( ( SV259
!= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
= $true )
| ( ( ( SV259
!= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
!= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
= $true )
| ( ( SV252 = SV259 )
= $true )
| ( ( vertex @ SV252 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[1624]) ).
thf(1643,plain,
! [SV259: $i,SV252: $i] :
( ( ( ~ ~ ( ~ ( ( SV252
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
| ~ ( ( SV252
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) ) ) )
= $false )
| ( ( SV252 = SV259 )
= $true )
| ( ( vertex @ SV252 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[1625]) ).
thf(1644,plain,
! [SV252: $i,SV259: $i] :
( ( ( ~ ~ ( ~ ( ( SV259
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
| ~ ( ( SV259
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) ) ) )
= $false )
| ( ( SV252 = SV259 )
= $true )
| ( ( vertex @ SV252 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[1625]) ).
thf(1645,plain,
! [SV260: $i,SV254: $i,SV289: $i,SV236: $i,SV298: $i,SV332: $i] :
( ( ( ~ ( precedes @ SV332 @ SV298 @ SV236 ) )
= $true )
| ( ( ~ ( sequential @ SV289 @ SV332 ) )
= $true )
| ( ( on_path @ SV289 @ SV236 )
= $false )
| ( ( on_path @ SV298 @ SV236 )
= $false )
| ( ( precedes @ SV289 @ SV298 @ SV236 )
= $true )
| ( ( path @ SV254 @ SV260 @ SV236 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1627]) ).
thf(1646,plain,
! [SV238: $i,SV270: $i,SV263: $i] :
( ( ( sequential @ SV263 @ SV270 )
= $false )
| ( ( edge @ SV270 )
= $false )
| ( ( edge @ SV238 )
= $false )
| ( ( edge @ SV263 )
= $false )
| ( ( sequential @ SV238 @ SV263 )
= $false )
| ( ( ~ ( sequential @ SV270 @ SV238 ) )
= $true )
| ( ( triangle @ SV238 @ SV263 @ SV270 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1629]) ).
thf(1647,plain,
! [SV238: $i] :
( ( ~ ( ! [SY440: $i,SY441: $i] :
~ ( triangle @ SV238 @ SY440 @ SY441 )
| ( edge @ SV238 ) )
| ~ ! [SY442: $i] :
( ! [SY443: $i] :
~ ( triangle @ SV238 @ SY442 @ SY443 )
| ( edge @ SY442 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1630]) ).
thf(1648,plain,
! [SV334: $i,SV238: $i] :
( ( ! [SY560: $i] :
( ~ ( triangle @ SV238 @ SV334 @ SY560 )
| ( edge @ SY560 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1631]) ).
thf(1649,plain,
! [SV333: $i,SV328: $i,SV238: $i] :
( ( ( triangle @ SV238 @ SV328 @ SV333 )
= $false )
| ( ( sequential @ SV238 @ SV328 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1632]) ).
thf(1650,plain,
! [SV240: $i,SV272: $i,SV265: $i] :
( ( ( SV265
= ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
= $false )
| ( ( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ empty ) ) )
= $true )
| ( ( ! [SY525: $i] :
( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ SY525 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ SY525 ) ) )
= $true )
| ( ( path @ SV240 @ SV265 @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1633]) ).
thf(1651,plain,
! [SV240: $i,SV272: $i,SV265: $i] :
( ( ( ( SV265
= ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ ( sK13_SY84 @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ ( sK13_SY84 @ SV272 @ SV265 @ SV240 ) ) ) )
= $true )
| ( ( path @ SV240 @ SV265 @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1634]) ).
thf(1652,plain,
! [SV240: $i,SV265: $i,SV272: $i] :
( ( ( ( SV272
= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ empty ) )
| ~ ( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ ( sK12_SY85 @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ ( sK12_SY85 @ SV272 @ SV265 @ SV240 ) ) ) )
= $true )
| ( ( path @ SV240 @ SV265 @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1635]) ).
thf(1653,plain,
! [SV241: $i,SV255: $i,SV311: $i,SV249: $i] :
( ( ( ( SV249
!= ( head_of @ SV311 ) ) )
= $true )
| ( ( ( SV255
!= ( path_cons @ SV311 @ empty ) ) )
= $true )
| ( ( SV241
= ( tail_of @ SV311 ) )
= $false )
| ( ( edge @ SV311 )
= $false )
| ( ( vertex @ SV241 )
= $false )
| ( ( vertex @ SV249 )
= $false )
| ( ( path @ SV241 @ SV249 @ SV255 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1636]) ).
thf(1654,plain,
! [SV241: $i,SV249: $i,SV335: $i,SV312: $i,SV255: $i] :
( ( ( ( SV255
!= ( path_cons @ SV312 @ SV335 ) )
| ~ ( path @ ( head_of @ SV312 ) @ SV249 @ SV335 ) )
= $true )
| ( ( SV241
= ( tail_of @ SV312 ) )
= $false )
| ( ( edge @ SV312 )
= $false )
| ( ( vertex @ SV241 )
= $false )
| ( ( vertex @ SV249 )
= $false )
| ( ( path @ SV241 @ SV249 @ SV255 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1637]) ).
thf(1655,plain,
! [SV262: $i,SV256: $i,SV315: $i,SV242: $i,SV324: $i,SV336: $i] :
( ( ( ~ ( precedes @ SV336 @ SV324 @ SV242 )
| ~ ( sequential @ SV315 @ SV336 ) )
= $true )
| ( ( ~ ( sequential @ SV315 @ SV324 ) )
= $true )
| ( ( precedes @ SV315 @ SV324 @ SV242 )
= $false )
| ( ( path @ SV256 @ SV262 @ SV242 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1640]) ).
thf(1656,plain,
! [SV262: $i,SV256: $i,SV242: $i,SV316: $i,SV325: $i] :
( ( ( ~ ( precedes @ ( sK9_E3 @ SV325 @ SV316 @ SV242 ) @ SV325 @ SV242 )
| ~ ( sequential @ SV316 @ ( sK9_E3 @ SV325 @ SV316 @ SV242 ) ) )
= $false )
| ( ( sequential @ SV316 @ SV325 )
= $true )
| ( ( precedes @ SV316 @ SV325 @ SV242 )
= $false )
| ( ( path @ SV256 @ SV262 @ SV242 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1641]) ).
thf(1657,plain,
! [SV259: $i,SV252: $i] :
( ( ( SV252
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
= $false )
| ( ( ( SV259
!= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
= $true )
| ( ( ( SV259
!= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
!= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
= $true )
| ( ( SV252 = SV259 )
= $true )
| ( ( vertex @ SV252 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1642]) ).
thf(1658,plain,
! [SV259: $i,SV252: $i] :
( ( ( ~ ( ~ ( ( SV252
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
| ~ ( ( SV252
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) ) ) )
= $true )
| ( ( SV252 = SV259 )
= $true )
| ( ( vertex @ SV252 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1643]) ).
thf(1659,plain,
! [SV252: $i,SV259: $i] :
( ( ( ~ ( ~ ( ( SV259
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
| ~ ( ( SV259
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) ) ) )
= $true )
| ( ( SV252 = SV259 )
= $true )
| ( ( vertex @ SV252 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1644]) ).
thf(1660,plain,
! [SV260: $i,SV254: $i,SV289: $i,SV236: $i,SV298: $i,SV332: $i] :
( ( ( precedes @ SV332 @ SV298 @ SV236 )
= $false )
| ( ( ~ ( sequential @ SV289 @ SV332 ) )
= $true )
| ( ( on_path @ SV289 @ SV236 )
= $false )
| ( ( on_path @ SV298 @ SV236 )
= $false )
| ( ( precedes @ SV289 @ SV298 @ SV236 )
= $true )
| ( ( path @ SV254 @ SV260 @ SV236 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1645]) ).
thf(1661,plain,
! [SV263: $i,SV238: $i,SV270: $i] :
( ( ( sequential @ SV270 @ SV238 )
= $false )
| ( ( sequential @ SV238 @ SV263 )
= $false )
| ( ( edge @ SV263 )
= $false )
| ( ( edge @ SV238 )
= $false )
| ( ( edge @ SV270 )
= $false )
| ( ( sequential @ SV263 @ SV270 )
= $false )
| ( ( triangle @ SV238 @ SV263 @ SV270 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1646]) ).
thf(1662,plain,
! [SV238: $i] :
( ( ~ ( ! [SY440: $i,SY441: $i] :
~ ( triangle @ SV238 @ SY440 @ SY441 )
| ( edge @ SV238 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1647]) ).
thf(1663,plain,
! [SV238: $i] :
( ( ~ ! [SY442: $i] :
( ! [SY443: $i] :
~ ( triangle @ SV238 @ SY442 @ SY443 )
| ( edge @ SY442 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1647]) ).
thf(1664,plain,
! [SV337: $i,SV334: $i,SV238: $i] :
( ( ~ ( triangle @ SV238 @ SV334 @ SV337 )
| ( edge @ SV337 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1648]) ).
thf(1665,plain,
! [SV240: $i,SV265: $i,SV272: $i] :
( ( ( SV272
= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ empty ) )
= $false )
| ( ( SV265
= ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
= $false )
| ( ( ! [SY525: $i] :
( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ SY525 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ SY525 ) ) )
= $true )
| ( ( path @ SV240 @ SV265 @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1650]) ).
thf(1666,plain,
! [SV240: $i,SV272: $i,SV265: $i] :
( ( ( SV265
= ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
= $true )
| ( ( ~ ( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ ( sK13_SY84 @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ ( sK13_SY84 @ SV272 @ SV265 @ SV240 ) ) ) )
= $true )
| ( ( path @ SV240 @ SV265 @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1651]) ).
thf(1667,plain,
! [SV240: $i,SV265: $i,SV272: $i] :
( ( ( SV272
= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ empty ) )
= $true )
| ( ( ~ ( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ ( sK12_SY85 @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ ( sK12_SY85 @ SV272 @ SV265 @ SV240 ) ) ) )
= $true )
| ( ( path @ SV240 @ SV265 @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1652]) ).
thf(1668,plain,
! [SV241: $i,SV255: $i,SV311: $i,SV249: $i] :
( ( ( SV249
= ( head_of @ SV311 ) )
= $false )
| ( ( ( SV255
!= ( path_cons @ SV311 @ empty ) ) )
= $true )
| ( ( SV241
= ( tail_of @ SV311 ) )
= $false )
| ( ( edge @ SV311 )
= $false )
| ( ( vertex @ SV241 )
= $false )
| ( ( vertex @ SV249 )
= $false )
| ( ( path @ SV241 @ SV249 @ SV255 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1653]) ).
thf(1669,plain,
! [SV241: $i,SV249: $i,SV335: $i,SV312: $i,SV255: $i] :
( ( ( ( SV255
!= ( path_cons @ SV312 @ SV335 ) ) )
= $true )
| ( ( ~ ( path @ ( head_of @ SV312 ) @ SV249 @ SV335 ) )
= $true )
| ( ( SV241
= ( tail_of @ SV312 ) )
= $false )
| ( ( edge @ SV312 )
= $false )
| ( ( vertex @ SV241 )
= $false )
| ( ( vertex @ SV249 )
= $false )
| ( ( path @ SV241 @ SV249 @ SV255 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1654]) ).
thf(1670,plain,
! [SV262: $i,SV256: $i,SV315: $i,SV242: $i,SV324: $i,SV336: $i] :
( ( ( ~ ( precedes @ SV336 @ SV324 @ SV242 ) )
= $true )
| ( ( ~ ( sequential @ SV315 @ SV336 ) )
= $true )
| ( ( ~ ( sequential @ SV315 @ SV324 ) )
= $true )
| ( ( precedes @ SV315 @ SV324 @ SV242 )
= $false )
| ( ( path @ SV256 @ SV262 @ SV242 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1655]) ).
thf(1671,plain,
! [SV262: $i,SV256: $i,SV242: $i,SV316: $i,SV325: $i] :
( ( ( ~ ( precedes @ ( sK9_E3 @ SV325 @ SV316 @ SV242 ) @ SV325 @ SV242 ) )
= $false )
| ( ( sequential @ SV316 @ SV325 )
= $true )
| ( ( precedes @ SV316 @ SV325 @ SV242 )
= $false )
| ( ( path @ SV256 @ SV262 @ SV242 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1656]) ).
thf(1672,plain,
! [SV262: $i,SV256: $i,SV242: $i,SV325: $i,SV316: $i] :
( ( ( ~ ( sequential @ SV316 @ ( sK9_E3 @ SV325 @ SV316 @ SV242 ) ) )
= $false )
| ( ( sequential @ SV316 @ SV325 )
= $true )
| ( ( precedes @ SV316 @ SV325 @ SV242 )
= $false )
| ( ( path @ SV256 @ SV262 @ SV242 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1656]) ).
thf(1673,plain,
! [SV252: $i,SV259: $i] :
( ( ( SV259
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
= $false )
| ( ( SV252
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
= $false )
| ( ( ( SV259
!= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
!= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
= $true )
| ( ( SV252 = SV259 )
= $true )
| ( ( vertex @ SV252 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1657]) ).
thf(1674,plain,
! [SV259: $i,SV252: $i] :
( ( ( ~ ( ( SV252
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
| ~ ( ( SV252
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) ) )
= $false )
| ( ( SV252 = SV259 )
= $true )
| ( ( vertex @ SV252 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1658]) ).
thf(1675,plain,
! [SV252: $i,SV259: $i] :
( ( ( ~ ( ( SV259
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
| ~ ( ( SV259
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) ) )
= $false )
| ( ( SV252 = SV259 )
= $true )
| ( ( vertex @ SV252 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1659]) ).
thf(1676,plain,
! [SV260: $i,SV254: $i,SV236: $i,SV298: $i,SV332: $i,SV289: $i] :
( ( ( sequential @ SV289 @ SV332 )
= $false )
| ( ( precedes @ SV332 @ SV298 @ SV236 )
= $false )
| ( ( on_path @ SV289 @ SV236 )
= $false )
| ( ( on_path @ SV298 @ SV236 )
= $false )
| ( ( precedes @ SV289 @ SV298 @ SV236 )
= $true )
| ( ( path @ SV254 @ SV260 @ SV236 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1660]) ).
thf(1677,plain,
! [SV238: $i] :
( ( ! [SY440: $i,SY441: $i] :
~ ( triangle @ SV238 @ SY440 @ SY441 )
| ( edge @ SV238 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1662]) ).
thf(1678,plain,
! [SV238: $i] :
( ( ! [SY442: $i] :
( ! [SY443: $i] :
~ ( triangle @ SV238 @ SY442 @ SY443 )
| ( edge @ SY442 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1663]) ).
thf(1679,plain,
! [SV337: $i,SV334: $i,SV238: $i] :
( ( ( ~ ( triangle @ SV238 @ SV334 @ SV337 ) )
= $true )
| ( ( edge @ SV337 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1664]) ).
thf(1680,plain,
! [SV338: $i,SV240: $i,SV265: $i,SV272: $i] :
( ( ( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ SV338 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ SV338 ) )
= $true )
| ( ( SV265
= ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
= $false )
| ( ( SV272
= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ empty ) )
= $false )
| ( ( path @ SV240 @ SV265 @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1665]) ).
thf(1681,plain,
! [SV240: $i,SV265: $i,SV272: $i] :
( ( ( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ ( sK13_SY84 @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ ( sK13_SY84 @ SV272 @ SV265 @ SV240 ) ) )
= $false )
| ( ( SV265
= ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
= $true )
| ( ( path @ SV240 @ SV265 @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1666]) ).
thf(1682,plain,
! [SV240: $i,SV265: $i,SV272: $i] :
( ( ( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ ( sK12_SY85 @ SV272 @ SV265 @ SV240 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ ( sK12_SY85 @ SV272 @ SV265 @ SV240 ) ) )
= $false )
| ( ( SV272
= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ empty ) )
= $true )
| ( ( path @ SV240 @ SV265 @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1667]) ).
thf(1683,plain,
! [SV241: $i,SV249: $i,SV311: $i,SV255: $i] :
( ( ( SV255
= ( path_cons @ SV311 @ empty ) )
= $false )
| ( ( SV249
= ( head_of @ SV311 ) )
= $false )
| ( ( SV241
= ( tail_of @ SV311 ) )
= $false )
| ( ( edge @ SV311 )
= $false )
| ( ( vertex @ SV241 )
= $false )
| ( ( vertex @ SV249 )
= $false )
| ( ( path @ SV241 @ SV249 @ SV255 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1668]) ).
thf(1684,plain,
! [SV241: $i,SV249: $i,SV335: $i,SV312: $i,SV255: $i] :
( ( ( SV255
= ( path_cons @ SV312 @ SV335 ) )
= $false )
| ( ( ~ ( path @ ( head_of @ SV312 ) @ SV249 @ SV335 ) )
= $true )
| ( ( SV241
= ( tail_of @ SV312 ) )
= $false )
| ( ( edge @ SV312 )
= $false )
| ( ( vertex @ SV241 )
= $false )
| ( ( vertex @ SV249 )
= $false )
| ( ( path @ SV241 @ SV249 @ SV255 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1669]) ).
thf(1685,plain,
! [SV262: $i,SV256: $i,SV315: $i,SV242: $i,SV324: $i,SV336: $i] :
( ( ( precedes @ SV336 @ SV324 @ SV242 )
= $false )
| ( ( ~ ( sequential @ SV315 @ SV336 ) )
= $true )
| ( ( ~ ( sequential @ SV315 @ SV324 ) )
= $true )
| ( ( precedes @ SV315 @ SV324 @ SV242 )
= $false )
| ( ( path @ SV256 @ SV262 @ SV242 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1670]) ).
thf(1686,plain,
! [SV262: $i,SV256: $i,SV242: $i,SV316: $i,SV325: $i] :
( ( ( precedes @ ( sK9_E3 @ SV325 @ SV316 @ SV242 ) @ SV325 @ SV242 )
= $true )
| ( ( sequential @ SV316 @ SV325 )
= $true )
| ( ( precedes @ SV316 @ SV325 @ SV242 )
= $false )
| ( ( path @ SV256 @ SV262 @ SV242 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1671]) ).
thf(1687,plain,
! [SV262: $i,SV256: $i,SV242: $i,SV325: $i,SV316: $i] :
( ( ( sequential @ SV316 @ ( sK9_E3 @ SV325 @ SV316 @ SV242 ) )
= $true )
| ( ( sequential @ SV316 @ SV325 )
= $true )
| ( ( precedes @ SV316 @ SV325 @ SV242 )
= $false )
| ( ( path @ SV256 @ SV262 @ SV242 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1672]) ).
thf(1688,plain,
! [SV252: $i,SV259: $i] :
( ( ( ( SV259
!= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
= $true )
| ( ( ( SV252
!= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
= $true )
| ( ( SV252
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
= $false )
| ( ( SV259
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
= $false )
| ( ( SV252 = SV259 )
= $true )
| ( ( vertex @ SV252 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[1673]) ).
thf(1689,plain,
! [SV259: $i,SV252: $i] :
( ( ( ~ ( ( SV252
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) ) ) )
= $false )
| ( ( SV252 = SV259 )
= $true )
| ( ( vertex @ SV252 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[1674]) ).
thf(1690,plain,
! [SV259: $i,SV252: $i] :
( ( ( ~ ( ( SV252
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) ) )
= $false )
| ( ( SV252 = SV259 )
= $true )
| ( ( vertex @ SV252 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[1674]) ).
thf(1691,plain,
! [SV252: $i,SV259: $i] :
( ( ( ~ ( ( SV259
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) ) ) )
= $false )
| ( ( SV252 = SV259 )
= $true )
| ( ( vertex @ SV252 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[1675]) ).
thf(1692,plain,
! [SV252: $i,SV259: $i] :
( ( ( ~ ( ( SV259
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) ) )
= $false )
| ( ( SV252 = SV259 )
= $true )
| ( ( vertex @ SV252 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[1675]) ).
thf(1693,plain,
! [SV238: $i] :
( ( ( ! [SY440: $i,SY441: $i] :
~ ( triangle @ SV238 @ SY440 @ SY441 ) )
= $true )
| ( ( edge @ SV238 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1677]) ).
thf(1694,plain,
! [SV339: $i,SV238: $i] :
( ( ! [SY561: $i] :
~ ( triangle @ SV238 @ SV339 @ SY561 )
| ( edge @ SV339 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1678]) ).
thf(1695,plain,
! [SV337: $i,SV334: $i,SV238: $i] :
( ( ( triangle @ SV238 @ SV334 @ SV337 )
= $false )
| ( ( edge @ SV337 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1679]) ).
thf(1696,plain,
! [SV338: $i,SV240: $i,SV265: $i,SV272: $i] :
( ( ( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ SV338 ) ) )
= $true )
| ( ( ~ ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ SV338 ) )
= $true )
| ( ( SV265
= ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
= $false )
| ( ( SV272
= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ empty ) )
= $false )
| ( ( path @ SV240 @ SV265 @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1680]) ).
thf(1697,plain,
! [SV240: $i,SV265: $i,SV272: $i] :
( ( ( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ ( sK13_SY84 @ SV272 @ SV265 @ SV240 ) ) ) )
= $false )
| ( ( SV265
= ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
= $true )
| ( ( path @ SV240 @ SV265 @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1681]) ).
thf(1698,plain,
! [SV240: $i,SV265: $i,SV272: $i] :
( ( ( ~ ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ ( sK13_SY84 @ SV272 @ SV265 @ SV240 ) ) )
= $false )
| ( ( SV265
= ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
= $true )
| ( ( path @ SV240 @ SV265 @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1681]) ).
thf(1699,plain,
! [SV240: $i,SV265: $i,SV272: $i] :
( ( ( ( SV272
!= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ ( sK12_SY85 @ SV272 @ SV265 @ SV240 ) ) ) )
= $false )
| ( ( SV272
= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ empty ) )
= $true )
| ( ( path @ SV240 @ SV265 @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1682]) ).
thf(1700,plain,
! [SV240: $i,SV265: $i,SV272: $i] :
( ( ( ~ ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ ( sK12_SY85 @ SV272 @ SV265 @ SV240 ) ) )
= $false )
| ( ( SV272
= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ empty ) )
= $true )
| ( ( path @ SV240 @ SV265 @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1682]) ).
thf(1701,plain,
! [SV241: $i,SV255: $i,SV335: $i,SV249: $i,SV312: $i] :
( ( ( path @ ( head_of @ SV312 ) @ SV249 @ SV335 )
= $false )
| ( ( SV255
= ( path_cons @ SV312 @ SV335 ) )
= $false )
| ( ( SV241
= ( tail_of @ SV312 ) )
= $false )
| ( ( edge @ SV312 )
= $false )
| ( ( vertex @ SV241 )
= $false )
| ( ( vertex @ SV249 )
= $false )
| ( ( path @ SV241 @ SV249 @ SV255 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1684]) ).
thf(1702,plain,
! [SV262: $i,SV256: $i,SV242: $i,SV324: $i,SV336: $i,SV315: $i] :
( ( ( sequential @ SV315 @ SV336 )
= $false )
| ( ( precedes @ SV336 @ SV324 @ SV242 )
= $false )
| ( ( ~ ( sequential @ SV315 @ SV324 ) )
= $true )
| ( ( precedes @ SV315 @ SV324 @ SV242 )
= $false )
| ( ( path @ SV256 @ SV262 @ SV242 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1685]) ).
thf(1703,plain,
! [SV252: $i,SV259: $i] :
( ( ( SV259
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
= $false )
| ( ( ( SV252
!= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
= $true )
| ( ( SV252
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
= $false )
| ( ( SV259
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
= $false )
| ( ( SV252 = SV259 )
= $true )
| ( ( vertex @ SV252 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1688]) ).
thf(1704,plain,
! [SV259: $i,SV252: $i] :
( ( ( ( SV252
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
= $true )
| ( ( SV252 = SV259 )
= $true )
| ( ( vertex @ SV252 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1689]) ).
thf(1705,plain,
! [SV259: $i,SV252: $i] :
( ( ( ( SV252
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
= $true )
| ( ( SV252 = SV259 )
= $true )
| ( ( vertex @ SV252 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1690]) ).
thf(1706,plain,
! [SV252: $i,SV259: $i] :
( ( ( ( SV259
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV259
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
= $true )
| ( ( SV252 = SV259 )
= $true )
| ( ( vertex @ SV252 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1691]) ).
thf(1707,plain,
! [SV252: $i,SV259: $i] :
( ( ( ( SV259
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
| ( SV252
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) ) )
= $true )
| ( ( SV252 = SV259 )
= $true )
| ( ( vertex @ SV252 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1692]) ).
thf(1708,plain,
! [SV340: $i,SV238: $i] :
( ( ( ! [SY562: $i] :
~ ( triangle @ SV238 @ SV340 @ SY562 ) )
= $true )
| ( ( edge @ SV238 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1693]) ).
thf(1709,plain,
! [SV339: $i,SV238: $i] :
( ( ( ! [SY561: $i] :
~ ( triangle @ SV238 @ SV339 @ SY561 ) )
= $true )
| ( ( edge @ SV339 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1694]) ).
thf(1710,plain,
! [SV338: $i,SV240: $i,SV265: $i,SV272: $i] :
( ( ( SV272
= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ SV338 ) )
= $false )
| ( ( ~ ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ SV338 ) )
= $true )
| ( ( SV265
= ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
= $false )
| ( ( SV272
= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ empty ) )
= $false )
| ( ( path @ SV240 @ SV265 @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1696]) ).
thf(1711,plain,
! [SV240: $i,SV265: $i,SV272: $i] :
( ( ( SV272
= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ ( sK13_SY84 @ SV272 @ SV265 @ SV240 ) ) )
= $true )
| ( ( SV265
= ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
= $true )
| ( ( path @ SV240 @ SV265 @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1697]) ).
thf(1712,plain,
! [SV240: $i,SV265: $i,SV272: $i] :
( ( ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ ( sK13_SY84 @ SV272 @ SV265 @ SV240 ) )
= $true )
| ( ( SV265
= ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
= $true )
| ( ( path @ SV240 @ SV265 @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1698]) ).
thf(1713,plain,
! [SV240: $i,SV265: $i,SV272: $i] :
( ( ( SV272
= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ ( sK12_SY85 @ SV272 @ SV265 @ SV240 ) ) )
= $true )
| ( ( SV272
= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ empty ) )
= $true )
| ( ( path @ SV240 @ SV265 @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1699]) ).
thf(1714,plain,
! [SV240: $i,SV265: $i,SV272: $i] :
( ( ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ ( sK12_SY85 @ SV272 @ SV265 @ SV240 ) )
= $true )
| ( ( SV272
= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ empty ) )
= $true )
| ( ( path @ SV240 @ SV265 @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1700]) ).
thf(1715,plain,
! [SV262: $i,SV256: $i,SV242: $i,SV336: $i,SV324: $i,SV315: $i] :
( ( ( sequential @ SV315 @ SV324 )
= $false )
| ( ( precedes @ SV336 @ SV324 @ SV242 )
= $false )
| ( ( sequential @ SV315 @ SV336 )
= $false )
| ( ( precedes @ SV315 @ SV324 @ SV242 )
= $false )
| ( ( path @ SV256 @ SV262 @ SV242 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1702]) ).
thf(1716,plain,
! [SV259: $i,SV252: $i] :
( ( ( SV252
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
= $false )
| ( ( SV259
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
= $false )
| ( ( SV252
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
= $false )
| ( ( SV259
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
= $false )
| ( ( SV252 = SV259 )
= $true )
| ( ( vertex @ SV252 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1703]) ).
thf(1717,plain,
! [SV259: $i,SV252: $i] :
( ( ( SV252
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
= $true )
| ( ( SV259
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
= $true )
| ( ( SV252 = SV259 )
= $true )
| ( ( vertex @ SV252 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[1704]) ).
thf(1718,plain,
! [SV259: $i,SV252: $i] :
( ( ( SV252
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
= $true )
| ( ( SV252
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
= $true )
| ( ( SV252 = SV259 )
= $true )
| ( ( vertex @ SV252 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[1705]) ).
thf(1719,plain,
! [SV252: $i,SV259: $i] :
( ( ( SV259
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
= $true )
| ( ( SV259
= ( head_of @ ( sK14_E @ SV259 @ SV252 ) ) )
= $true )
| ( ( SV252 = SV259 )
= $true )
| ( ( vertex @ SV252 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[1706]) ).
thf(1720,plain,
! [SV252: $i,SV259: $i] :
( ( ( SV259
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
= $true )
| ( ( SV252
= ( tail_of @ ( sK14_E @ SV259 @ SV252 ) ) )
= $true )
| ( ( SV252 = SV259 )
= $true )
| ( ( vertex @ SV252 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[1707]) ).
thf(1721,plain,
! [SV341: $i,SV340: $i,SV238: $i] :
( ( ( ~ ( triangle @ SV238 @ SV340 @ SV341 ) )
= $true )
| ( ( edge @ SV238 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1708]) ).
thf(1722,plain,
! [SV342: $i,SV339: $i,SV238: $i] :
( ( ( ~ ( triangle @ SV238 @ SV339 @ SV342 ) )
= $true )
| ( ( edge @ SV339 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1709]) ).
thf(1723,plain,
! [SV338: $i,SV240: $i,SV265: $i,SV272: $i] :
( ( ( path @ ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) @ SV265 @ SV338 )
= $false )
| ( ( SV272
= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ SV338 ) )
= $false )
| ( ( SV265
= ( head_of @ ( sK11_E @ SV272 @ SV265 @ SV240 ) ) )
= $false )
| ( ( SV272
= ( path_cons @ ( sK11_E @ SV272 @ SV265 @ SV240 ) @ empty ) )
= $false )
| ( ( path @ SV240 @ SV265 @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1710]) ).
thf(1724,plain,
! [SV341: $i,SV340: $i,SV238: $i] :
( ( ( triangle @ SV238 @ SV340 @ SV341 )
= $false )
| ( ( edge @ SV238 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1721]) ).
thf(1725,plain,
! [SV342: $i,SV339: $i,SV238: $i] :
( ( ( triangle @ SV238 @ SV339 @ SV342 )
= $false )
| ( ( edge @ SV339 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1722]) ).
thf(1726,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[1195,1725,1724,1723,1720,1719,1718,1717,1716,1715,1714,1713,1712,1711,1701,1695,1687,1686,1683,1676,1661,1649,1639,1638,1628,1626,1621,1620,1613,1608,1602,1601,1594,1589,1588,1587,1585,1584,1583,1578,1575,1574,1551,1540,1528,1507,1505,1490,1489,1483,1479,1475,1468,1460,1319,1318,1292,1291,1268,1231,1197,1196]) ).
thf(1727,plain,
( ( ! [E: $i] :
( ~ ( edge @ E )
| ( ( head_of @ E )
!= ( tail_of @ E ) ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(1728,plain,
( ( ! [E: $i] :
( ~ ( edge @ E )
| ( vertex @ ( head_of @ E ) ) )
& ! [E: $i] :
( ~ ( edge @ E )
| ( vertex @ ( tail_of @ E ) ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(1729,plain,
( ( ~ complete
| ! [V1: $i,V2: $i] :
( ( V1 = V2 )
| ~ ( vertex @ V1 )
| ~ ( vertex @ V2 )
| ( ( ( V1
!= ( head_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V2
!= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V2
!= ( head_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V1
!= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( ( V1
= ( head_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V2
= ( head_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( ( V1
= ( head_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V1
= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( ( V2
= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V2
= ( head_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( ( V2
= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V1
= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( edge @ ( sK14_E @ V2 @ V1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(1730,plain,
( ( ! [V1: $i,V2: $i,P: $i] :
( ~ ( vertex @ V1 )
| ~ ( vertex @ V2 )
| ( ! [E: $i] :
( ( V1
!= ( tail_of @ E ) )
| ~ ( edge @ E )
| ( V2
!= ( head_of @ E ) )
| ( P
!= ( path_cons @ E @ empty ) ) )
& ! [E: $i] :
( ( V1
!= ( tail_of @ E ) )
| ~ ( edge @ E )
| ! [TP: $i] :
( ( P
!= ( path_cons @ E @ TP ) )
| ~ ( path @ ( head_of @ E ) @ V2 @ TP ) ) ) )
| ( path @ V1 @ V2 @ P ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(1731,plain,
( ( ! [V1: $i] :
( ( ! [V2: $i,P: $i] :
~ ( path @ V1 @ V2 @ P )
| ( vertex @ V1 ) )
& ! [V2: $i] :
( ! [P: $i] :
~ ( path @ V1 @ V2 @ P )
| ( vertex @ V2 ) )
& ! [V2: $i,P: $i] :
( ~ ( path @ V1 @ V2 @ P )
| ( ( V1
= ( tail_of @ ( sK11_E @ P @ V2 @ V1 ) ) )
& ( edge @ ( sK11_E @ P @ V2 @ V1 ) )
& ( ( V2
!= ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) )
| ( P
!= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ empty ) )
| ! [SY83: $i] :
( ( P
!= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ SY83 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) @ V2 @ SY83 ) ) )
& ( ( V2
= ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) )
| ( ( P
= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ ( sK13_SY84 @ P @ V2 @ V1 ) ) )
& ( path @ ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) @ V2 @ ( sK13_SY84 @ P @ V2 @ V1 ) ) ) )
& ( ( P
= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ empty ) )
| ( ( P
= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ ( sK12_SY85 @ P @ V2 @ V1 ) ) )
& ( path @ ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) @ V2 @ ( sK12_SY85 @ P @ V2 @ V1 ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(1732,plain,
( ( ! [V1: $i,V2: $i] :
( ! [P: $i,E: $i] :
( ~ ( on_path @ E @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( edge @ E ) )
& ! [P: $i,E: $i] :
( ~ ( on_path @ E @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( in_path @ ( head_of @ E ) @ P ) )
& ! [P: $i,E: $i] :
( ~ ( on_path @ E @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( in_path @ ( tail_of @ E ) @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(1733,plain,
( ( ! [V1: $i,V2: $i] :
( ! [P: $i,V: $i] :
( ~ ( in_path @ V @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( ( on_path @ ( sK10_E @ V @ P @ V2 @ V1 ) @ P )
& ( ( V
= ( head_of @ ( sK10_E @ V @ P @ V2 @ V1 ) ) )
| ( V
= ( tail_of @ ( sK10_E @ V @ P @ V2 @ V1 ) ) ) ) ) )
& ! [P: $i,V: $i] :
( ~ ( in_path @ V @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( vertex @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(1734,plain,
( ( ! [E1: $i,E2: $i] :
( ( E1 = E2 )
| ~ ( edge @ E1 )
| ~ ( edge @ E2 )
| ( ( head_of @ E1 )
!= ( tail_of @ E2 ) )
| ( sequential @ E1 @ E2 ) )
& ! [E1: $i,E2: $i] :
( ~ ( sequential @ E1 @ E2 )
| ( E1 != E2 ) )
& ! [E1: $i] :
( ! [E2: $i] :
~ ( sequential @ E1 @ E2 )
| ( edge @ E1 ) )
& ! [E1: $i,E2: $i] :
( ~ ( sequential @ E1 @ E2 )
| ( edge @ E2 ) )
& ! [E1: $i,E2: $i] :
( ~ ( sequential @ E1 @ E2 )
| ( ( head_of @ E1 )
= ( tail_of @ E2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(1735,plain,
( ( ! [P: $i] :
( ! [V1: $i,V2: $i] :
~ ( path @ V1 @ V2 @ P )
| ( ! [E1: $i,E2: $i] :
( ~ ( on_path @ E1 @ P )
| ~ ( on_path @ E2 @ P )
| ! [E3: $i] :
( ~ ( precedes @ E3 @ E2 @ P )
| ~ ( sequential @ E1 @ E3 ) )
| ( precedes @ E1 @ E2 @ P ) )
& ! [E1: $i,E2: $i] :
( ~ ( on_path @ E1 @ P )
| ~ ( on_path @ E2 @ P )
| ~ ( sequential @ E1 @ E2 )
| ( precedes @ E1 @ E2 @ P ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(1736,plain,
( ( ! [P: $i] :
( ! [V1: $i,V2: $i] :
~ ( path @ V1 @ V2 @ P )
| ( ! [E1: $i] :
( ! [E2: $i] :
~ ( precedes @ E1 @ E2 @ P )
| ( on_path @ E1 @ P ) )
& ! [E1: $i,E2: $i] :
( ~ ( precedes @ E1 @ E2 @ P )
| ( on_path @ E2 @ P ) )
& ! [E1: $i,E2: $i] :
( ~ ( precedes @ E1 @ E2 @ P )
| ! [E3: $i] :
( ~ ( precedes @ E3 @ E2 @ P )
| ~ ( sequential @ E1 @ E3 ) )
| ~ ( sequential @ E1 @ E2 ) )
& ! [E1: $i,E2: $i] :
( ~ ( precedes @ E1 @ E2 @ P )
| ( ( precedes @ ( sK9_E3 @ E2 @ E1 @ P ) @ E2 @ P )
& ( sequential @ E1 @ ( sK9_E3 @ E2 @ E1 @ P ) ) )
| ( sequential @ E1 @ E2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(1737,plain,
( ( ! [V1: $i] :
( ! [V2: $i,SP: $i] :
( ( ( path @ V1 @ V2 @ ( sK8_P @ SP @ V2 @ V1 ) )
& ~ ( less_or_equal @ ( length_of @ SP ) @ ( length_of @ ( sK8_P @ SP @ V2 @ V1 ) ) ) )
| ( V1 = V2 )
| ~ ( path @ V1 @ V2 @ SP )
| ( shortest_path @ V1 @ V2 @ SP ) )
& ! [V2: $i,SP: $i] :
( ~ ( shortest_path @ V1 @ V2 @ SP )
| ! [P: $i] :
( ~ ( path @ V1 @ V2 @ P )
| ( less_or_equal @ ( length_of @ SP ) @ ( length_of @ P ) ) ) )
& ! [V2: $i] :
( ! [SP: $i] :
~ ( shortest_path @ V1 @ V2 @ SP )
| ( V1 != V2 ) )
& ! [V2: $i,SP: $i] :
( ~ ( shortest_path @ V1 @ V2 @ SP )
| ( path @ V1 @ V2 @ SP ) ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(1738,plain,
( ( ! [V1: $i,V2: $i,E1: $i] :
( ! [E2: $i] :
( ! [P: $i] :
( ~ ( precedes @ E1 @ E2 @ P )
| ~ ( shortest_path @ V1 @ V2 @ P ) )
| ! [E3: $i] :
( ( ( tail_of @ E3 )
!= ( tail_of @ E1 ) )
| ( ( head_of @ E3 )
!= ( head_of @ E2 ) ) ) )
& ! [E2: $i,P: $i] :
( ~ ( precedes @ E1 @ E2 @ P )
| ~ ( shortest_path @ V1 @ V2 @ P )
| ~ ( precedes @ E2 @ E1 @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(1739,plain,
( ( ! [E1: $i] :
( ! [E2: $i,E3: $i] :
( ~ ( edge @ E1 )
| ~ ( edge @ E2 )
| ~ ( edge @ E3 )
| ~ ( sequential @ E1 @ E2 )
| ~ ( sequential @ E2 @ E3 )
| ~ ( sequential @ E3 @ E1 )
| ( triangle @ E1 @ E2 @ E3 ) )
& ( ! [E2: $i,E3: $i] :
~ ( triangle @ E1 @ E2 @ E3 )
| ( edge @ E1 ) )
& ! [E2: $i] :
( ! [E3: $i] :
~ ( triangle @ E1 @ E2 @ E3 )
| ( edge @ E2 ) )
& ! [E2: $i,E3: $i] :
( ~ ( triangle @ E1 @ E2 @ E3 )
| ( edge @ E3 ) )
& ! [E2: $i] :
( ! [E3: $i] :
~ ( triangle @ E1 @ E2 @ E3 )
| ( sequential @ E1 @ E2 ) )
& ! [E2: $i,E3: $i] :
( ~ ( triangle @ E1 @ E2 @ E3 )
| ( sequential @ E2 @ E3 ) )
& ! [E2: $i,E3: $i] :
( ~ ( triangle @ E1 @ E2 @ E3 )
| ( sequential @ E3 @ E1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(1740,plain,
( ( ! [V1: $i,V2: $i,P: $i] :
( ~ ( path @ V1 @ V2 @ P )
| ( ( length_of @ P )
= ( number_of_in @ edges @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(1741,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)],[63]) ).
thf(1742,plain,
( ( ! [P: $i] :
( ( ( on_path @ ( sK6_E1 @ P ) @ P )
& ( on_path @ ( sK7_SY80 @ P ) @ P )
& ( sequential @ ( sK6_E1 @ P ) @ ( sK7_SY80 @ P ) )
& ! [SY82: $i] :
~ ( triangle @ ( sK6_E1 @ P ) @ ( sK7_SY80 @ P ) @ SY82 ) )
| ! [V1: $i,V2: $i] :
~ ( path @ V1 @ V2 @ P )
| ( ( number_of_in @ sequential_pairs @ P )
= ( number_of_in @ triangles @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(1743,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(1744,plain,
( ( precedes @ sK3_SY74 @ sK4_SY77 @ sK5_SY79 )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(1745,plain,
( ( shortest_path @ sK1_V1 @ sK2_SY70 @ sK5_SY79 )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(1746,plain,
( ( ~ ( edge @ sK3_SY74 ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(1747,plain,
( ( ! [SX0: $i] :
~ ( ~ ~ ( ~ ( ! [SX1: $i,SX2: $i] :
~ ( path @ SX0 @ SX1 @ SX2 )
| ( vertex @ SX0 ) )
| ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( path @ SX0 @ SX1 @ SX2 )
| ( vertex @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( path @ SX0 @ SX1 @ SX2 )
| ~ ( ~ ~ ( ( SX0
!= ( tail_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( edge @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ( SX1
!= ( head_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) )
| ( SX2
!= ( path_cons @ ( sK11_E @ SX2 @ SX1 @ SX0 ) @ empty ) )
| ! [SX3: $i] :
( ( SX2
!= ( path_cons @ ( sK11_E @ SX2 @ SX1 @ SX0 ) @ SX3 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) @ SX1 @ SX3 ) ) )
| ~ ~ ( ~ ( ( SX1
= ( head_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( ( SX2
!= ( path_cons @ ( sK11_E @ SX2 @ SX1 @ SX0 ) @ ( sK13_SY84 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) @ SX1 @ ( sK13_SY84 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX2
= ( path_cons @ ( sK11_E @ SX2 @ SX1 @ SX0 ) @ empty ) )
| ~ ( ( SX2
!= ( path_cons @ ( sK11_E @ SX2 @ SX1 @ SX0 ) @ ( sK12_SY85 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) @ SX1 @ ( sK12_SY85 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1731]) ).
thf(1748,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( vertex @ SX0 )
| ~ ( vertex @ SX1 )
| ~ ( ~ ! [SX3: $i] :
( ( SX0
!= ( tail_of @ SX3 ) )
| ~ ( edge @ SX3 )
| ( SX1
!= ( head_of @ SX3 ) )
| ( SX2
!= ( path_cons @ SX3 @ empty ) ) )
| ~ ! [SX3: $i] :
( ( SX0
!= ( tail_of @ SX3 ) )
| ~ ( edge @ SX3 )
| ! [SX4: $i] :
( ( SX2
!= ( path_cons @ SX3 @ SX4 ) )
| ~ ( path @ ( head_of @ SX3 ) @ SX1 @ SX4 ) ) ) )
| ( path @ SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1730]) ).
thf(1749,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( edge @ SX0 )
| ~ ( edge @ SX1 )
| ( ( head_of @ SX0 )
!= ( tail_of @ SX1 ) )
| ( sequential @ SX0 @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1734]) ).
thf(1750,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
( ~ ( precedes @ SX2 @ SX3 @ SX4 )
| ~ ( shortest_path @ SX0 @ SX1 @ SX4 ) )
| ! [SX4: $i] :
( ( ( tail_of @ SX4 )
!= ( tail_of @ SX2 ) )
| ( ( head_of @ SX4 )
!= ( head_of @ SX3 ) ) ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( precedes @ SX2 @ SX3 @ SX4 )
| ~ ( shortest_path @ SX0 @ SX1 @ SX4 )
| ~ ( precedes @ SX3 @ SX2 @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1738]) ).
thf(1751,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( on_path @ SX3 @ SX2 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ( edge @ SX3 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( on_path @ SX3 @ SX2 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ( in_path @ ( head_of @ SX3 ) @ SX2 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( on_path @ SX3 @ SX2 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ( in_path @ ( tail_of @ SX3 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1732]) ).
thf(1752,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( head_of @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( tail_of @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1728]) ).
thf(1753,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SX0 ) @ SX0 )
| ~ ( on_path @ ( sK7_SY80 @ SX0 ) @ SX0 ) )
| ~ ( sequential @ ( sK6_E1 @ SX0 ) @ ( sK7_SY80 @ SX0 ) ) )
| ~ ! [SX1: $i] :
~ ( triangle @ ( sK6_E1 @ SX0 ) @ ( sK7_SY80 @ SX0 ) @ SX1 ) )
| ! [SX1: $i,SX2: $i] :
~ ( path @ SX1 @ SX2 @ SX0 )
| ( ( number_of_in @ sequential_pairs @ SX0 )
= ( number_of_in @ triangles @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1742]) ).
thf(1754,plain,
( ( ~ complete
| ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( vertex @ SX0 )
| ~ ( vertex @ SX1 )
| ~ ( ~ ~ ( ~ ( ( SX0
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
| ~ ~ ( ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1729]) ).
thf(1755,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( edge @ SX0 )
| ~ ( edge @ SX1 )
| ~ ( edge @ SX2 )
| ~ ( sequential @ SX0 @ SX1 )
| ~ ( sequential @ SX1 @ SX2 )
| ~ ( sequential @ SX2 @ SX0 )
| ( triangle @ SX0 @ SX1 @ SX2 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SX1: $i,SX2: $i] :
~ ( triangle @ SX0 @ SX1 @ SX2 )
| ( edge @ SX0 ) )
| ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( triangle @ SX0 @ SX1 @ SX2 )
| ( edge @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( triangle @ SX0 @ SX1 @ SX2 )
| ( edge @ SX2 ) ) )
| ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( triangle @ SX0 @ SX1 @ SX2 )
| ( sequential @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( triangle @ SX0 @ SX1 @ SX2 )
| ( sequential @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( triangle @ SX0 @ SX1 @ SX2 )
| ( sequential @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1739]) ).
thf(1756,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i,SX2: $i] :
~ ( path @ SX1 @ SX2 @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( on_path @ SX1 @ SX0 )
| ~ ( on_path @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( precedes @ SX3 @ SX2 @ SX0 )
| ~ ( sequential @ SX1 @ SX3 ) )
| ( precedes @ SX1 @ SX2 @ SX0 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( on_path @ SX1 @ SX0 )
| ~ ( on_path @ SX2 @ SX0 )
| ~ ( sequential @ SX1 @ SX2 )
| ( precedes @ SX1 @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1735]) ).
thf(1757,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i,SX2: $i] :
~ ( path @ SX1 @ SX2 @ SX0 )
| ~ ( ~ ~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( precedes @ SX1 @ SX2 @ SX0 )
| ( on_path @ SX1 @ SX0 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( precedes @ SX1 @ SX2 @ SX0 )
| ( on_path @ SX2 @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( precedes @ SX1 @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( precedes @ SX3 @ SX2 @ SX0 )
| ~ ( sequential @ SX1 @ SX3 ) )
| ~ ( sequential @ SX1 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( precedes @ SX1 @ SX2 @ SX0 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SX2 @ SX1 @ SX0 ) @ SX2 @ SX0 )
| ~ ( sequential @ SX1 @ ( sK9_E3 @ SX2 @ SX1 @ SX0 ) ) )
| ( sequential @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1736]) ).
thf(1758,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in_path @ SX3 @ SX2 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ~ ( ~ ( on_path @ ( sK10_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( ( SX3
= ( head_of @ ( sK10_E @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ( SX3
= ( tail_of @ ( sK10_E @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( in_path @ SX3 @ SX2 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ( vertex @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1733]) ).
thf(1759,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( path @ SX0 @ SX1 @ ( sK8_P @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SX2 ) @ ( length_of @ ( sK8_P @ SX2 @ SX1 @ SX0 ) ) ) )
| ( SX0 = SX1 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ( shortest_path @ SX0 @ SX1 @ SX2 ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( shortest_path @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( path @ SX0 @ SX1 @ SX3 )
| ( less_or_equal @ ( length_of @ SX2 ) @ ( length_of @ SX3 ) ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( shortest_path @ SX0 @ SX1 @ SX2 )
| ( SX0 != SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( shortest_path @ SX0 @ SX1 @ SX2 )
| ( path @ SX0 @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1737]) ).
thf(1760,plain,
! [SV343: $i] :
( ( ~ ( edge @ SV343 )
| ( ( head_of @ SV343 )
!= ( tail_of @ SV343 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1727]) ).
thf(1761,plain,
! [SV344: $i] :
( ( ! [SY563: $i,SY564: $i] :
( ~ ( path @ SV344 @ SY563 @ SY564 )
| ( ( length_of @ SY564 )
= ( number_of_in @ edges @ SY564 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1740]) ).
thf(1762,plain,
! [SV345: $i] :
( ( ! [SY565: $i,SY566: $i] :
( ~ ( path @ SV345 @ SY565 @ SY566 )
| ( ( number_of_in @ sequential_pairs @ SY566 )
= ( minus @ ( length_of @ SY566 ) @ n1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1741]) ).
thf(1763,plain,
! [SV346: $i] :
( ( ! [SY567: $i] : ( less_or_equal @ ( number_of_in @ SV346 @ SY567 ) @ ( number_of_in @ SV346 @ graph ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1743]) ).
thf(1764,plain,
( ( edge @ sK3_SY74 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1746]) ).
thf(1765,plain,
! [SV347: $i] :
( ( ~ ( ~ ~ ( ~ ( ! [SY568: $i,SY569: $i] :
~ ( path @ SV347 @ SY568 @ SY569 )
| ( vertex @ SV347 ) )
| ~ ! [SY570: $i] :
( ! [SY571: $i] :
~ ( path @ SV347 @ SY570 @ SY571 )
| ( vertex @ SY570 ) ) )
| ~ ! [SY572: $i,SY573: $i] :
( ~ ( path @ SV347 @ SY572 @ SY573 )
| ~ ( ~ ~ ( ( SV347
!= ( tail_of @ ( sK11_E @ SY573 @ SY572 @ SV347 ) ) )
| ~ ( edge @ ( sK11_E @ SY573 @ SY572 @ SV347 ) ) )
| ~ ~ ( ~ ( ( SY572
!= ( head_of @ ( sK11_E @ SY573 @ SY572 @ SV347 ) ) )
| ( SY573
!= ( path_cons @ ( sK11_E @ SY573 @ SY572 @ SV347 ) @ empty ) )
| ! [SY574: $i] :
( ( SY573
!= ( path_cons @ ( sK11_E @ SY573 @ SY572 @ SV347 ) @ SY574 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY573 @ SY572 @ SV347 ) ) @ SY572 @ SY574 ) ) )
| ~ ~ ( ~ ( ( SY572
= ( head_of @ ( sK11_E @ SY573 @ SY572 @ SV347 ) ) )
| ~ ( ( SY573
!= ( path_cons @ ( sK11_E @ SY573 @ SY572 @ SV347 ) @ ( sK13_SY84 @ SY573 @ SY572 @ SV347 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY573 @ SY572 @ SV347 ) ) @ SY572 @ ( sK13_SY84 @ SY573 @ SY572 @ SV347 ) ) ) )
| ~ ( ( SY573
= ( path_cons @ ( sK11_E @ SY573 @ SY572 @ SV347 ) @ empty ) )
| ~ ( ( SY573
!= ( path_cons @ ( sK11_E @ SY573 @ SY572 @ SV347 ) @ ( sK12_SY85 @ SY573 @ SY572 @ SV347 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY573 @ SY572 @ SV347 ) ) @ SY572 @ ( sK12_SY85 @ SY573 @ SY572 @ SV347 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1747]) ).
thf(1766,plain,
! [SV348: $i] :
( ( ! [SY575: $i,SY576: $i] :
( ~ ( vertex @ SV348 )
| ~ ( vertex @ SY575 )
| ~ ( ~ ! [SY577: $i] :
( ( SV348
!= ( tail_of @ SY577 ) )
| ~ ( edge @ SY577 )
| ( SY575
!= ( head_of @ SY577 ) )
| ( SY576
!= ( path_cons @ SY577 @ empty ) ) )
| ~ ! [SY578: $i] :
( ( SV348
!= ( tail_of @ SY578 ) )
| ~ ( edge @ SY578 )
| ! [SX4: $i] :
( ( SY576
!= ( path_cons @ SY578 @ SX4 ) )
| ~ ( path @ ( head_of @ SY578 ) @ SY575 @ SX4 ) ) ) )
| ( path @ SV348 @ SY575 @ SY576 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1748]) ).
thf(1767,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( edge @ SX0 )
| ~ ( edge @ SX1 )
| ( ( head_of @ SX0 )
!= ( tail_of @ SX1 ) )
| ( sequential @ SX0 @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1749]) ).
thf(1768,plain,
! [SV349: $i] :
( ( ! [SY580: $i,SY581: $i] :
~ ( ~ ! [SY582: $i] :
( ! [SY583: $i] :
( ~ ( precedes @ SY581 @ SY582 @ SY583 )
| ~ ( shortest_path @ SV349 @ SY580 @ SY583 ) )
| ! [SX4: $i] :
( ( ( tail_of @ SX4 )
!= ( tail_of @ SY581 ) )
| ( ( head_of @ SX4 )
!= ( head_of @ SY582 ) ) ) )
| ~ ! [SY585: $i,SY586: $i] :
( ~ ( precedes @ SY581 @ SY585 @ SY586 )
| ~ ( shortest_path @ SV349 @ SY580 @ SY586 )
| ~ ( precedes @ SY585 @ SY581 @ SY586 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1750]) ).
thf(1769,plain,
! [SV350: $i] :
( ( ! [SY587: $i] :
~ ( ~ ~ ( ~ ! [SY588: $i,SY589: $i] :
( ~ ( on_path @ SY589 @ SY588 )
| ~ ( path @ SV350 @ SY587 @ SY588 )
| ( edge @ SY589 ) )
| ~ ! [SY590: $i,SY591: $i] :
( ~ ( on_path @ SY591 @ SY590 )
| ~ ( path @ SV350 @ SY587 @ SY590 )
| ( in_path @ ( head_of @ SY591 ) @ SY590 ) ) )
| ~ ! [SY592: $i,SY593: $i] :
( ~ ( on_path @ SY593 @ SY592 )
| ~ ( path @ SV350 @ SY587 @ SY592 )
| ( in_path @ ( tail_of @ SY593 ) @ SY592 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1751]) ).
thf(1770,plain,
( ( ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( head_of @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( tail_of @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1752]) ).
thf(1771,plain,
! [SV351: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV351 ) @ SV351 )
| ~ ( on_path @ ( sK7_SY80 @ SV351 ) @ SV351 ) )
| ~ ( sequential @ ( sK6_E1 @ SV351 ) @ ( sK7_SY80 @ SV351 ) ) )
| ~ ! [SY594: $i] :
~ ( triangle @ ( sK6_E1 @ SV351 ) @ ( sK7_SY80 @ SV351 ) @ SY594 ) )
| ! [SY595: $i,SY596: $i] :
~ ( path @ SY595 @ SY596 @ SV351 )
| ( ( number_of_in @ sequential_pairs @ SV351 )
= ( number_of_in @ triangles @ SV351 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1753]) ).
thf(1772,plain,
( ( ( ~ complete )
= $true )
| ( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( vertex @ SX0 )
| ~ ( vertex @ SX1 )
| ~ ( ~ ~ ( ~ ( ( SX0
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
| ~ ~ ( ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1754]) ).
thf(1773,plain,
! [SV352: $i] :
( ( ~ ( ~ ! [SY597: $i,SY598: $i] :
( ~ ( edge @ SV352 )
| ~ ( edge @ SY597 )
| ~ ( edge @ SY598 )
| ~ ( sequential @ SV352 @ SY597 )
| ~ ( sequential @ SY597 @ SY598 )
| ~ ( sequential @ SY598 @ SV352 )
| ( triangle @ SV352 @ SY597 @ SY598 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY599: $i,SY600: $i] :
~ ( triangle @ SV352 @ SY599 @ SY600 )
| ( edge @ SV352 ) )
| ~ ! [SY601: $i] :
( ! [SY602: $i] :
~ ( triangle @ SV352 @ SY601 @ SY602 )
| ( edge @ SY601 ) ) )
| ~ ! [SY603: $i,SY604: $i] :
( ~ ( triangle @ SV352 @ SY603 @ SY604 )
| ( edge @ SY604 ) ) )
| ~ ! [SY605: $i] :
( ! [SY606: $i] :
~ ( triangle @ SV352 @ SY605 @ SY606 )
| ( sequential @ SV352 @ SY605 ) ) )
| ~ ! [SY607: $i,SY608: $i] :
( ~ ( triangle @ SV352 @ SY607 @ SY608 )
| ( sequential @ SY607 @ SY608 ) ) )
| ~ ! [SY609: $i,SY610: $i] :
( ~ ( triangle @ SV352 @ SY609 @ SY610 )
| ( sequential @ SY610 @ SV352 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1755]) ).
thf(1774,plain,
! [SV353: $i] :
( ( ! [SY611: $i,SY612: $i] :
~ ( path @ SY611 @ SY612 @ SV353 )
| ~ ( ~ ! [SY613: $i,SY614: $i] :
( ~ ( on_path @ SY613 @ SV353 )
| ~ ( on_path @ SY614 @ SV353 )
| ! [SY615: $i] :
( ~ ( precedes @ SY615 @ SY614 @ SV353 )
| ~ ( sequential @ SY613 @ SY615 ) )
| ( precedes @ SY613 @ SY614 @ SV353 ) )
| ~ ! [SY616: $i,SY617: $i] :
( ~ ( on_path @ SY616 @ SV353 )
| ~ ( on_path @ SY617 @ SV353 )
| ~ ( sequential @ SY616 @ SY617 )
| ( precedes @ SY616 @ SY617 @ SV353 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1756]) ).
thf(1775,plain,
! [SV354: $i] :
( ( ! [SY618: $i,SY619: $i] :
~ ( path @ SY618 @ SY619 @ SV354 )
| ~ ( ~ ~ ( ~ ! [SY620: $i] :
( ! [SY621: $i] :
~ ( precedes @ SY620 @ SY621 @ SV354 )
| ( on_path @ SY620 @ SV354 ) )
| ~ ! [SY622: $i,SY623: $i] :
( ~ ( precedes @ SY622 @ SY623 @ SV354 )
| ( on_path @ SY623 @ SV354 ) ) )
| ~ ~ ( ~ ! [SY624: $i,SY625: $i] :
( ~ ( precedes @ SY624 @ SY625 @ SV354 )
| ! [SY626: $i] :
( ~ ( precedes @ SY626 @ SY625 @ SV354 )
| ~ ( sequential @ SY624 @ SY626 ) )
| ~ ( sequential @ SY624 @ SY625 ) )
| ~ ! [SY627: $i,SY628: $i] :
( ~ ( precedes @ SY627 @ SY628 @ SV354 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY628 @ SY627 @ SV354 ) @ SY628 @ SV354 )
| ~ ( sequential @ SY627 @ ( sK9_E3 @ SY628 @ SY627 @ SV354 ) ) )
| ( sequential @ SY627 @ SY628 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1757]) ).
thf(1776,plain,
! [SV355: $i] :
( ( ! [SY629: $i] :
~ ( ~ ! [SY630: $i,SY631: $i] :
( ~ ( in_path @ SY631 @ SY630 )
| ~ ( path @ SV355 @ SY629 @ SY630 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY631 @ SY630 @ SY629 @ SV355 ) @ SY630 )
| ~ ( ( SY631
= ( head_of @ ( sK10_E @ SY631 @ SY630 @ SY629 @ SV355 ) ) )
| ( SY631
= ( tail_of @ ( sK10_E @ SY631 @ SY630 @ SY629 @ SV355 ) ) ) ) ) )
| ~ ! [SY632: $i,SY633: $i] :
( ~ ( in_path @ SY633 @ SY632 )
| ~ ( path @ SV355 @ SY629 @ SY632 )
| ( vertex @ SY633 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1758]) ).
thf(1777,plain,
! [SV356: $i] :
( ( ~ ( ~ ! [SY634: $i,SY635: $i] :
( ~ ( ~ ( path @ SV356 @ SY634 @ ( sK8_P @ SY635 @ SY634 @ SV356 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY635 ) @ ( length_of @ ( sK8_P @ SY635 @ SY634 @ SV356 ) ) ) )
| ( SV356 = SY634 )
| ~ ( path @ SV356 @ SY634 @ SY635 )
| ( shortest_path @ SV356 @ SY634 @ SY635 ) )
| ~ ~ ( ~ ! [SY636: $i,SY637: $i] :
( ~ ( shortest_path @ SV356 @ SY636 @ SY637 )
| ! [SY638: $i] :
( ~ ( path @ SV356 @ SY636 @ SY638 )
| ( less_or_equal @ ( length_of @ SY637 ) @ ( length_of @ SY638 ) ) ) )
| ~ ~ ( ~ ! [SY639: $i] :
( ! [SY640: $i] :
~ ( shortest_path @ SV356 @ SY639 @ SY640 )
| ( SV356 != SY639 ) )
| ~ ! [SY641: $i,SY642: $i] :
( ~ ( shortest_path @ SV356 @ SY641 @ SY642 )
| ( path @ SV356 @ SY641 @ SY642 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1759]) ).
thf(1778,plain,
! [SV343: $i] :
( ( ( ~ ( edge @ SV343 ) )
= $true )
| ( ( ( ( head_of @ SV343 )
!= ( tail_of @ SV343 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1760]) ).
thf(1779,plain,
! [SV357: $i,SV344: $i] :
( ( ! [SY643: $i] :
( ~ ( path @ SV344 @ SV357 @ SY643 )
| ( ( length_of @ SY643 )
= ( number_of_in @ edges @ SY643 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1761]) ).
thf(1780,plain,
! [SV358: $i,SV345: $i] :
( ( ! [SY644: $i] :
( ~ ( path @ SV345 @ SV358 @ SY644 )
| ( ( number_of_in @ sequential_pairs @ SY644 )
= ( minus @ ( length_of @ SY644 ) @ n1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1762]) ).
thf(1781,plain,
! [SV359: $i,SV346: $i] :
( ( less_or_equal @ ( number_of_in @ SV346 @ SV359 ) @ ( number_of_in @ SV346 @ graph ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1763]) ).
thf(1782,plain,
! [SV347: $i] :
( ( ~ ~ ( ~ ( ! [SY568: $i,SY569: $i] :
~ ( path @ SV347 @ SY568 @ SY569 )
| ( vertex @ SV347 ) )
| ~ ! [SY570: $i] :
( ! [SY571: $i] :
~ ( path @ SV347 @ SY570 @ SY571 )
| ( vertex @ SY570 ) ) )
| ~ ! [SY572: $i,SY573: $i] :
( ~ ( path @ SV347 @ SY572 @ SY573 )
| ~ ( ~ ~ ( ( SV347
!= ( tail_of @ ( sK11_E @ SY573 @ SY572 @ SV347 ) ) )
| ~ ( edge @ ( sK11_E @ SY573 @ SY572 @ SV347 ) ) )
| ~ ~ ( ~ ( ( SY572
!= ( head_of @ ( sK11_E @ SY573 @ SY572 @ SV347 ) ) )
| ( SY573
!= ( path_cons @ ( sK11_E @ SY573 @ SY572 @ SV347 ) @ empty ) )
| ! [SY574: $i] :
( ( SY573
!= ( path_cons @ ( sK11_E @ SY573 @ SY572 @ SV347 ) @ SY574 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY573 @ SY572 @ SV347 ) ) @ SY572 @ SY574 ) ) )
| ~ ~ ( ~ ( ( SY572
= ( head_of @ ( sK11_E @ SY573 @ SY572 @ SV347 ) ) )
| ~ ( ( SY573
!= ( path_cons @ ( sK11_E @ SY573 @ SY572 @ SV347 ) @ ( sK13_SY84 @ SY573 @ SY572 @ SV347 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY573 @ SY572 @ SV347 ) ) @ SY572 @ ( sK13_SY84 @ SY573 @ SY572 @ SV347 ) ) ) )
| ~ ( ( SY573
= ( path_cons @ ( sK11_E @ SY573 @ SY572 @ SV347 ) @ empty ) )
| ~ ( ( SY573
!= ( path_cons @ ( sK11_E @ SY573 @ SY572 @ SV347 ) @ ( sK12_SY85 @ SY573 @ SY572 @ SV347 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY573 @ SY572 @ SV347 ) ) @ SY572 @ ( sK12_SY85 @ SY573 @ SY572 @ SV347 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1765]) ).
thf(1783,plain,
! [SV360: $i,SV348: $i] :
( ( ! [SY645: $i] :
( ~ ( vertex @ SV348 )
| ~ ( vertex @ SV360 )
| ~ ( ~ ! [SY646: $i] :
( ( SV348
!= ( tail_of @ SY646 ) )
| ~ ( edge @ SY646 )
| ( SV360
!= ( head_of @ SY646 ) )
| ( SY645
!= ( path_cons @ SY646 @ empty ) ) )
| ~ ! [SY647: $i] :
( ( SV348
!= ( tail_of @ SY647 ) )
| ~ ( edge @ SY647 )
| ! [SY648: $i] :
( ( SY645
!= ( path_cons @ SY647 @ SY648 ) )
| ~ ( path @ ( head_of @ SY647 ) @ SV360 @ SY648 ) ) ) )
| ( path @ SV348 @ SV360 @ SY645 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1766]) ).
thf(1784,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( edge @ SX0 )
| ~ ( edge @ SX1 )
| ( ( head_of @ SX0 )
!= ( tail_of @ SX1 ) )
| ( sequential @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1767]) ).
thf(1785,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1767]) ).
thf(1786,plain,
! [SV361: $i,SV349: $i] :
( ( ! [SY649: $i] :
~ ( ~ ! [SY650: $i] :
( ! [SY651: $i] :
( ~ ( precedes @ SY649 @ SY650 @ SY651 )
| ~ ( shortest_path @ SV349 @ SV361 @ SY651 ) )
| ! [SX4: $i] :
( ( ( tail_of @ SX4 )
!= ( tail_of @ SY649 ) )
| ( ( head_of @ SX4 )
!= ( head_of @ SY650 ) ) ) )
| ~ ! [SY653: $i,SY654: $i] :
( ~ ( precedes @ SY649 @ SY653 @ SY654 )
| ~ ( shortest_path @ SV349 @ SV361 @ SY654 )
| ~ ( precedes @ SY653 @ SY649 @ SY654 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1768]) ).
thf(1787,plain,
! [SV362: $i,SV350: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY655: $i,SY656: $i] :
( ~ ( on_path @ SY656 @ SY655 )
| ~ ( path @ SV350 @ SV362 @ SY655 )
| ( edge @ SY656 ) )
| ~ ! [SY657: $i,SY658: $i] :
( ~ ( on_path @ SY658 @ SY657 )
| ~ ( path @ SV350 @ SV362 @ SY657 )
| ( in_path @ ( head_of @ SY658 ) @ SY657 ) ) )
| ~ ! [SY659: $i,SY660: $i] :
( ~ ( on_path @ SY660 @ SY659 )
| ~ ( path @ SV350 @ SV362 @ SY659 )
| ( in_path @ ( tail_of @ SY660 ) @ SY659 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1769]) ).
thf(1788,plain,
( ( ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( head_of @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1770]) ).
thf(1789,plain,
( ( ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( tail_of @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1770]) ).
thf(1790,plain,
! [SV351: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV351 ) @ SV351 )
| ~ ( on_path @ ( sK7_SY80 @ SV351 ) @ SV351 ) )
| ~ ( sequential @ ( sK6_E1 @ SV351 ) @ ( sK7_SY80 @ SV351 ) ) )
| ~ ! [SY594: $i] :
~ ( triangle @ ( sK6_E1 @ SV351 ) @ ( sK7_SY80 @ SV351 ) @ SY594 ) )
| ! [SY595: $i,SY596: $i] :
~ ( path @ SY595 @ SY596 @ SV351 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV351 )
= ( number_of_in @ triangles @ SV351 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1771]) ).
thf(1791,plain,
( ( complete = $false )
| ( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( vertex @ SX0 )
| ~ ( vertex @ SX1 )
| ~ ( ~ ~ ( ~ ( ( SX0
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
| ~ ~ ( ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1772]) ).
thf(1792,plain,
! [SV352: $i] :
( ( ~ ! [SY597: $i,SY598: $i] :
( ~ ( edge @ SV352 )
| ~ ( edge @ SY597 )
| ~ ( edge @ SY598 )
| ~ ( sequential @ SV352 @ SY597 )
| ~ ( sequential @ SY597 @ SY598 )
| ~ ( sequential @ SY598 @ SV352 )
| ( triangle @ SV352 @ SY597 @ SY598 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY599: $i,SY600: $i] :
~ ( triangle @ SV352 @ SY599 @ SY600 )
| ( edge @ SV352 ) )
| ~ ! [SY601: $i] :
( ! [SY602: $i] :
~ ( triangle @ SV352 @ SY601 @ SY602 )
| ( edge @ SY601 ) ) )
| ~ ! [SY603: $i,SY604: $i] :
( ~ ( triangle @ SV352 @ SY603 @ SY604 )
| ( edge @ SY604 ) ) )
| ~ ! [SY605: $i] :
( ! [SY606: $i] :
~ ( triangle @ SV352 @ SY605 @ SY606 )
| ( sequential @ SV352 @ SY605 ) ) )
| ~ ! [SY607: $i,SY608: $i] :
( ~ ( triangle @ SV352 @ SY607 @ SY608 )
| ( sequential @ SY607 @ SY608 ) ) )
| ~ ! [SY609: $i,SY610: $i] :
( ~ ( triangle @ SV352 @ SY609 @ SY610 )
| ( sequential @ SY610 @ SV352 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1773]) ).
thf(1793,plain,
! [SV353: $i] :
( ( ( ! [SY611: $i,SY612: $i] :
~ ( path @ SY611 @ SY612 @ SV353 ) )
= $true )
| ( ( ~ ( ~ ! [SY613: $i,SY614: $i] :
( ~ ( on_path @ SY613 @ SV353 )
| ~ ( on_path @ SY614 @ SV353 )
| ! [SY615: $i] :
( ~ ( precedes @ SY615 @ SY614 @ SV353 )
| ~ ( sequential @ SY613 @ SY615 ) )
| ( precedes @ SY613 @ SY614 @ SV353 ) )
| ~ ! [SY616: $i,SY617: $i] :
( ~ ( on_path @ SY616 @ SV353 )
| ~ ( on_path @ SY617 @ SV353 )
| ~ ( sequential @ SY616 @ SY617 )
| ( precedes @ SY616 @ SY617 @ SV353 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1774]) ).
thf(1794,plain,
! [SV354: $i] :
( ( ( ! [SY618: $i,SY619: $i] :
~ ( path @ SY618 @ SY619 @ SV354 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY620: $i] :
( ! [SY621: $i] :
~ ( precedes @ SY620 @ SY621 @ SV354 )
| ( on_path @ SY620 @ SV354 ) )
| ~ ! [SY622: $i,SY623: $i] :
( ~ ( precedes @ SY622 @ SY623 @ SV354 )
| ( on_path @ SY623 @ SV354 ) ) )
| ~ ~ ( ~ ! [SY624: $i,SY625: $i] :
( ~ ( precedes @ SY624 @ SY625 @ SV354 )
| ! [SY626: $i] :
( ~ ( precedes @ SY626 @ SY625 @ SV354 )
| ~ ( sequential @ SY624 @ SY626 ) )
| ~ ( sequential @ SY624 @ SY625 ) )
| ~ ! [SY627: $i,SY628: $i] :
( ~ ( precedes @ SY627 @ SY628 @ SV354 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY628 @ SY627 @ SV354 ) @ SY628 @ SV354 )
| ~ ( sequential @ SY627 @ ( sK9_E3 @ SY628 @ SY627 @ SV354 ) ) )
| ( sequential @ SY627 @ SY628 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1775]) ).
thf(1795,plain,
! [SV363: $i,SV355: $i] :
( ( ~ ( ~ ! [SY661: $i,SY662: $i] :
( ~ ( in_path @ SY662 @ SY661 )
| ~ ( path @ SV355 @ SV363 @ SY661 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY662 @ SY661 @ SV363 @ SV355 ) @ SY661 )
| ~ ( ( SY662
= ( head_of @ ( sK10_E @ SY662 @ SY661 @ SV363 @ SV355 ) ) )
| ( SY662
= ( tail_of @ ( sK10_E @ SY662 @ SY661 @ SV363 @ SV355 ) ) ) ) ) )
| ~ ! [SY663: $i,SY664: $i] :
( ~ ( in_path @ SY664 @ SY663 )
| ~ ( path @ SV355 @ SV363 @ SY663 )
| ( vertex @ SY664 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1776]) ).
thf(1796,plain,
! [SV356: $i] :
( ( ~ ! [SY634: $i,SY635: $i] :
( ~ ( ~ ( path @ SV356 @ SY634 @ ( sK8_P @ SY635 @ SY634 @ SV356 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY635 ) @ ( length_of @ ( sK8_P @ SY635 @ SY634 @ SV356 ) ) ) )
| ( SV356 = SY634 )
| ~ ( path @ SV356 @ SY634 @ SY635 )
| ( shortest_path @ SV356 @ SY634 @ SY635 ) )
| ~ ~ ( ~ ! [SY636: $i,SY637: $i] :
( ~ ( shortest_path @ SV356 @ SY636 @ SY637 )
| ! [SY638: $i] :
( ~ ( path @ SV356 @ SY636 @ SY638 )
| ( less_or_equal @ ( length_of @ SY637 ) @ ( length_of @ SY638 ) ) ) )
| ~ ~ ( ~ ! [SY639: $i] :
( ! [SY640: $i] :
~ ( shortest_path @ SV356 @ SY639 @ SY640 )
| ( SV356 != SY639 ) )
| ~ ! [SY641: $i,SY642: $i] :
( ~ ( shortest_path @ SV356 @ SY641 @ SY642 )
| ( path @ SV356 @ SY641 @ SY642 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1777]) ).
thf(1797,plain,
! [SV343: $i] :
( ( ( edge @ SV343 )
= $false )
| ( ( ( ( head_of @ SV343 )
!= ( tail_of @ SV343 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1778]) ).
thf(1798,plain,
! [SV364: $i,SV357: $i,SV344: $i] :
( ( ~ ( path @ SV344 @ SV357 @ SV364 )
| ( ( length_of @ SV364 )
= ( number_of_in @ edges @ SV364 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1779]) ).
thf(1799,plain,
! [SV365: $i,SV358: $i,SV345: $i] :
( ( ~ ( path @ SV345 @ SV358 @ SV365 )
| ( ( number_of_in @ sequential_pairs @ SV365 )
= ( minus @ ( length_of @ SV365 ) @ n1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1780]) ).
thf(1800,plain,
! [SV347: $i] :
( ( ~ ~ ( ~ ( ! [SY568: $i,SY569: $i] :
~ ( path @ SV347 @ SY568 @ SY569 )
| ( vertex @ SV347 ) )
| ~ ! [SY570: $i] :
( ! [SY571: $i] :
~ ( path @ SV347 @ SY570 @ SY571 )
| ( vertex @ SY570 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1782]) ).
thf(1801,plain,
! [SV347: $i] :
( ( ~ ! [SY572: $i,SY573: $i] :
( ~ ( path @ SV347 @ SY572 @ SY573 )
| ~ ( ~ ~ ( ( SV347
!= ( tail_of @ ( sK11_E @ SY573 @ SY572 @ SV347 ) ) )
| ~ ( edge @ ( sK11_E @ SY573 @ SY572 @ SV347 ) ) )
| ~ ~ ( ~ ( ( SY572
!= ( head_of @ ( sK11_E @ SY573 @ SY572 @ SV347 ) ) )
| ( SY573
!= ( path_cons @ ( sK11_E @ SY573 @ SY572 @ SV347 ) @ empty ) )
| ! [SY574: $i] :
( ( SY573
!= ( path_cons @ ( sK11_E @ SY573 @ SY572 @ SV347 ) @ SY574 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY573 @ SY572 @ SV347 ) ) @ SY572 @ SY574 ) ) )
| ~ ~ ( ~ ( ( SY572
= ( head_of @ ( sK11_E @ SY573 @ SY572 @ SV347 ) ) )
| ~ ( ( SY573
!= ( path_cons @ ( sK11_E @ SY573 @ SY572 @ SV347 ) @ ( sK13_SY84 @ SY573 @ SY572 @ SV347 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY573 @ SY572 @ SV347 ) ) @ SY572 @ ( sK13_SY84 @ SY573 @ SY572 @ SV347 ) ) ) )
| ~ ( ( SY573
= ( path_cons @ ( sK11_E @ SY573 @ SY572 @ SV347 ) @ empty ) )
| ~ ( ( SY573
!= ( path_cons @ ( sK11_E @ SY573 @ SY572 @ SV347 ) @ ( sK12_SY85 @ SY573 @ SY572 @ SV347 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY573 @ SY572 @ SV347 ) ) @ SY572 @ ( sK12_SY85 @ SY573 @ SY572 @ SV347 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1782]) ).
thf(1802,plain,
! [SV366: $i,SV360: $i,SV348: $i] :
( ( ~ ( vertex @ SV348 )
| ~ ( vertex @ SV360 )
| ~ ( ~ ! [SY665: $i] :
( ( SV348
!= ( tail_of @ SY665 ) )
| ~ ( edge @ SY665 )
| ( SV360
!= ( head_of @ SY665 ) )
| ( SV366
!= ( path_cons @ SY665 @ empty ) ) )
| ~ ! [SY666: $i] :
( ( SV348
!= ( tail_of @ SY666 ) )
| ~ ( edge @ SY666 )
| ! [SY667: $i] :
( ( SV366
!= ( path_cons @ SY666 @ SY667 ) )
| ~ ( path @ ( head_of @ SY666 ) @ SV360 @ SY667 ) ) ) )
| ( path @ SV348 @ SV360 @ SV366 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1783]) ).
thf(1803,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( edge @ SX0 )
| ~ ( edge @ SX1 )
| ( ( head_of @ SX0 )
!= ( tail_of @ SX1 ) )
| ( sequential @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1784]) ).
thf(1804,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1785]) ).
thf(1805,plain,
! [SV361: $i,SV349: $i,SV367: $i] :
( ( ~ ( ~ ! [SY668: $i] :
( ! [SY669: $i] :
( ~ ( precedes @ SV367 @ SY668 @ SY669 )
| ~ ( shortest_path @ SV349 @ SV361 @ SY669 ) )
| ! [SY670: $i] :
( ( ( tail_of @ SY670 )
!= ( tail_of @ SV367 ) )
| ( ( head_of @ SY670 )
!= ( head_of @ SY668 ) ) ) )
| ~ ! [SY671: $i,SY672: $i] :
( ~ ( precedes @ SV367 @ SY671 @ SY672 )
| ~ ( shortest_path @ SV349 @ SV361 @ SY672 )
| ~ ( precedes @ SY671 @ SV367 @ SY672 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1786]) ).
thf(1806,plain,
! [SV362: $i,SV350: $i] :
( ( ~ ~ ( ~ ! [SY655: $i,SY656: $i] :
( ~ ( on_path @ SY656 @ SY655 )
| ~ ( path @ SV350 @ SV362 @ SY655 )
| ( edge @ SY656 ) )
| ~ ! [SY657: $i,SY658: $i] :
( ~ ( on_path @ SY658 @ SY657 )
| ~ ( path @ SV350 @ SV362 @ SY657 )
| ( in_path @ ( head_of @ SY658 ) @ SY657 ) ) )
| ~ ! [SY659: $i,SY660: $i] :
( ~ ( on_path @ SY660 @ SY659 )
| ~ ( path @ SV350 @ SV362 @ SY659 )
| ( in_path @ ( tail_of @ SY660 ) @ SY659 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1787]) ).
thf(1807,plain,
( ( ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( head_of @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1788]) ).
thf(1808,plain,
( ( ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( tail_of @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1789]) ).
thf(1809,plain,
! [SV351: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV351 ) @ SV351 )
| ~ ( on_path @ ( sK7_SY80 @ SV351 ) @ SV351 ) )
| ~ ( sequential @ ( sK6_E1 @ SV351 ) @ ( sK7_SY80 @ SV351 ) ) )
| ~ ! [SY594: $i] :
~ ( triangle @ ( sK6_E1 @ SV351 ) @ ( sK7_SY80 @ SV351 ) @ SY594 ) ) )
= $true )
| ( ( ! [SY595: $i,SY596: $i] :
~ ( path @ SY595 @ SY596 @ SV351 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV351 )
= ( number_of_in @ triangles @ SV351 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1790]) ).
thf(1810,plain,
! [SV368: $i] :
( ( ( ! [SY673: $i] :
( ( SV368 = SY673 )
| ~ ( vertex @ SV368 )
| ~ ( vertex @ SY673 )
| ~ ( ~ ~ ( ~ ( ( SV368
!= ( head_of @ ( sK14_E @ SY673 @ SV368 ) ) )
| ( SY673
!= ( tail_of @ ( sK14_E @ SY673 @ SV368 ) ) )
| ( SY673
!= ( head_of @ ( sK14_E @ SY673 @ SV368 ) ) )
| ( SV368
!= ( tail_of @ ( sK14_E @ SY673 @ SV368 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV368
= ( head_of @ ( sK14_E @ SY673 @ SV368 ) ) )
| ( SY673
= ( head_of @ ( sK14_E @ SY673 @ SV368 ) ) ) )
| ~ ( ( SV368
= ( head_of @ ( sK14_E @ SY673 @ SV368 ) ) )
| ( SV368
= ( tail_of @ ( sK14_E @ SY673 @ SV368 ) ) ) ) )
| ~ ~ ( ~ ( ( SY673
= ( tail_of @ ( sK14_E @ SY673 @ SV368 ) ) )
| ( SY673
= ( head_of @ ( sK14_E @ SY673 @ SV368 ) ) ) )
| ~ ( ( SY673
= ( tail_of @ ( sK14_E @ SY673 @ SV368 ) ) )
| ( SV368
= ( tail_of @ ( sK14_E @ SY673 @ SV368 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SY673 @ SV368 ) ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1791]) ).
thf(1811,plain,
! [SV352: $i] :
( ( ~ ! [SY597: $i,SY598: $i] :
( ~ ( edge @ SV352 )
| ~ ( edge @ SY597 )
| ~ ( edge @ SY598 )
| ~ ( sequential @ SV352 @ SY597 )
| ~ ( sequential @ SY597 @ SY598 )
| ~ ( sequential @ SY598 @ SV352 )
| ( triangle @ SV352 @ SY597 @ SY598 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1792]) ).
thf(1812,plain,
! [SV352: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY599: $i,SY600: $i] :
~ ( triangle @ SV352 @ SY599 @ SY600 )
| ( edge @ SV352 ) )
| ~ ! [SY601: $i] :
( ! [SY602: $i] :
~ ( triangle @ SV352 @ SY601 @ SY602 )
| ( edge @ SY601 ) ) )
| ~ ! [SY603: $i,SY604: $i] :
( ~ ( triangle @ SV352 @ SY603 @ SY604 )
| ( edge @ SY604 ) ) )
| ~ ! [SY605: $i] :
( ! [SY606: $i] :
~ ( triangle @ SV352 @ SY605 @ SY606 )
| ( sequential @ SV352 @ SY605 ) ) )
| ~ ! [SY607: $i,SY608: $i] :
( ~ ( triangle @ SV352 @ SY607 @ SY608 )
| ( sequential @ SY607 @ SY608 ) ) )
| ~ ! [SY609: $i,SY610: $i] :
( ~ ( triangle @ SV352 @ SY609 @ SY610 )
| ( sequential @ SY610 @ SV352 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1792]) ).
thf(1813,plain,
! [SV353: $i,SV369: $i] :
( ( ( ! [SY674: $i] :
~ ( path @ SV369 @ SY674 @ SV353 ) )
= $true )
| ( ( ~ ( ~ ! [SY613: $i,SY614: $i] :
( ~ ( on_path @ SY613 @ SV353 )
| ~ ( on_path @ SY614 @ SV353 )
| ! [SY615: $i] :
( ~ ( precedes @ SY615 @ SY614 @ SV353 )
| ~ ( sequential @ SY613 @ SY615 ) )
| ( precedes @ SY613 @ SY614 @ SV353 ) )
| ~ ! [SY616: $i,SY617: $i] :
( ~ ( on_path @ SY616 @ SV353 )
| ~ ( on_path @ SY617 @ SV353 )
| ~ ( sequential @ SY616 @ SY617 )
| ( precedes @ SY616 @ SY617 @ SV353 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1793]) ).
thf(1814,plain,
! [SV354: $i,SV370: $i] :
( ( ( ! [SY675: $i] :
~ ( path @ SV370 @ SY675 @ SV354 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY620: $i] :
( ! [SY621: $i] :
~ ( precedes @ SY620 @ SY621 @ SV354 )
| ( on_path @ SY620 @ SV354 ) )
| ~ ! [SY622: $i,SY623: $i] :
( ~ ( precedes @ SY622 @ SY623 @ SV354 )
| ( on_path @ SY623 @ SV354 ) ) )
| ~ ~ ( ~ ! [SY624: $i,SY625: $i] :
( ~ ( precedes @ SY624 @ SY625 @ SV354 )
| ! [SY626: $i] :
( ~ ( precedes @ SY626 @ SY625 @ SV354 )
| ~ ( sequential @ SY624 @ SY626 ) )
| ~ ( sequential @ SY624 @ SY625 ) )
| ~ ! [SY627: $i,SY628: $i] :
( ~ ( precedes @ SY627 @ SY628 @ SV354 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY628 @ SY627 @ SV354 ) @ SY628 @ SV354 )
| ~ ( sequential @ SY627 @ ( sK9_E3 @ SY628 @ SY627 @ SV354 ) ) )
| ( sequential @ SY627 @ SY628 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1794]) ).
thf(1815,plain,
! [SV363: $i,SV355: $i] :
( ( ~ ! [SY661: $i,SY662: $i] :
( ~ ( in_path @ SY662 @ SY661 )
| ~ ( path @ SV355 @ SV363 @ SY661 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY662 @ SY661 @ SV363 @ SV355 ) @ SY661 )
| ~ ( ( SY662
= ( head_of @ ( sK10_E @ SY662 @ SY661 @ SV363 @ SV355 ) ) )
| ( SY662
= ( tail_of @ ( sK10_E @ SY662 @ SY661 @ SV363 @ SV355 ) ) ) ) ) )
| ~ ! [SY663: $i,SY664: $i] :
( ~ ( in_path @ SY664 @ SY663 )
| ~ ( path @ SV355 @ SV363 @ SY663 )
| ( vertex @ SY664 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1795]) ).
thf(1816,plain,
! [SV356: $i] :
( ( ~ ! [SY634: $i,SY635: $i] :
( ~ ( ~ ( path @ SV356 @ SY634 @ ( sK8_P @ SY635 @ SY634 @ SV356 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY635 ) @ ( length_of @ ( sK8_P @ SY635 @ SY634 @ SV356 ) ) ) )
| ( SV356 = SY634 )
| ~ ( path @ SV356 @ SY634 @ SY635 )
| ( shortest_path @ SV356 @ SY634 @ SY635 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1796]) ).
thf(1817,plain,
! [SV356: $i] :
( ( ~ ~ ( ~ ! [SY636: $i,SY637: $i] :
( ~ ( shortest_path @ SV356 @ SY636 @ SY637 )
| ! [SY638: $i] :
( ~ ( path @ SV356 @ SY636 @ SY638 )
| ( less_or_equal @ ( length_of @ SY637 ) @ ( length_of @ SY638 ) ) ) )
| ~ ~ ( ~ ! [SY639: $i] :
( ! [SY640: $i] :
~ ( shortest_path @ SV356 @ SY639 @ SY640 )
| ( SV356 != SY639 ) )
| ~ ! [SY641: $i,SY642: $i] :
( ~ ( shortest_path @ SV356 @ SY641 @ SY642 )
| ( path @ SV356 @ SY641 @ SY642 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1796]) ).
thf(1818,plain,
! [SV343: $i] :
( ( ( ( head_of @ SV343 )
= ( tail_of @ SV343 ) )
= $false )
| ( ( edge @ SV343 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1797]) ).
thf(1819,plain,
! [SV364: $i,SV357: $i,SV344: $i] :
( ( ( ~ ( path @ SV344 @ SV357 @ SV364 ) )
= $true )
| ( ( ( length_of @ SV364 )
= ( number_of_in @ edges @ SV364 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1798]) ).
thf(1820,plain,
! [SV365: $i,SV358: $i,SV345: $i] :
( ( ( ~ ( path @ SV345 @ SV358 @ SV365 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV365 )
= ( minus @ ( length_of @ SV365 ) @ n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1799]) ).
thf(1821,plain,
! [SV347: $i] :
( ( ~ ( ~ ( ! [SY568: $i,SY569: $i] :
~ ( path @ SV347 @ SY568 @ SY569 )
| ( vertex @ SV347 ) )
| ~ ! [SY570: $i] :
( ! [SY571: $i] :
~ ( path @ SV347 @ SY570 @ SY571 )
| ( vertex @ SY570 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1800]) ).
thf(1822,plain,
! [SV347: $i] :
( ( ! [SY572: $i,SY573: $i] :
( ~ ( path @ SV347 @ SY572 @ SY573 )
| ~ ( ~ ~ ( ( SV347
!= ( tail_of @ ( sK11_E @ SY573 @ SY572 @ SV347 ) ) )
| ~ ( edge @ ( sK11_E @ SY573 @ SY572 @ SV347 ) ) )
| ~ ~ ( ~ ( ( SY572
!= ( head_of @ ( sK11_E @ SY573 @ SY572 @ SV347 ) ) )
| ( SY573
!= ( path_cons @ ( sK11_E @ SY573 @ SY572 @ SV347 ) @ empty ) )
| ! [SY574: $i] :
( ( SY573
!= ( path_cons @ ( sK11_E @ SY573 @ SY572 @ SV347 ) @ SY574 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY573 @ SY572 @ SV347 ) ) @ SY572 @ SY574 ) ) )
| ~ ~ ( ~ ( ( SY572
= ( head_of @ ( sK11_E @ SY573 @ SY572 @ SV347 ) ) )
| ~ ( ( SY573
!= ( path_cons @ ( sK11_E @ SY573 @ SY572 @ SV347 ) @ ( sK13_SY84 @ SY573 @ SY572 @ SV347 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY573 @ SY572 @ SV347 ) ) @ SY572 @ ( sK13_SY84 @ SY573 @ SY572 @ SV347 ) ) ) )
| ~ ( ( SY573
= ( path_cons @ ( sK11_E @ SY573 @ SY572 @ SV347 ) @ empty ) )
| ~ ( ( SY573
!= ( path_cons @ ( sK11_E @ SY573 @ SY572 @ SV347 ) @ ( sK12_SY85 @ SY573 @ SY572 @ SV347 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY573 @ SY572 @ SV347 ) ) @ SY572 @ ( sK12_SY85 @ SY573 @ SY572 @ SV347 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1801]) ).
thf(1823,plain,
! [SV366: $i,SV360: $i,SV348: $i] :
( ( ( ~ ( vertex @ SV348 )
| ~ ( vertex @ SV360 )
| ~ ( ~ ! [SY665: $i] :
( ( SV348
!= ( tail_of @ SY665 ) )
| ~ ( edge @ SY665 )
| ( SV360
!= ( head_of @ SY665 ) )
| ( SV366
!= ( path_cons @ SY665 @ empty ) ) )
| ~ ! [SY666: $i] :
( ( SV348
!= ( tail_of @ SY666 ) )
| ~ ( edge @ SY666 )
| ! [SY667: $i] :
( ( SV366
!= ( path_cons @ SY666 @ SY667 ) )
| ~ ( path @ ( head_of @ SY666 ) @ SV360 @ SY667 ) ) ) ) )
= $true )
| ( ( path @ SV348 @ SV360 @ SV366 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1802]) ).
thf(1824,plain,
! [SV371: $i] :
( ( ! [SY676: $i] :
( ( SV371 = SY676 )
| ~ ( edge @ SV371 )
| ~ ( edge @ SY676 )
| ( ( head_of @ SV371 )
!= ( tail_of @ SY676 ) )
| ( sequential @ SV371 @ SY676 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1803]) ).
thf(1825,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1804]) ).
thf(1826,plain,
! [SV361: $i,SV349: $i,SV367: $i] :
( ( ~ ! [SY668: $i] :
( ! [SY669: $i] :
( ~ ( precedes @ SV367 @ SY668 @ SY669 )
| ~ ( shortest_path @ SV349 @ SV361 @ SY669 ) )
| ! [SY670: $i] :
( ( ( tail_of @ SY670 )
!= ( tail_of @ SV367 ) )
| ( ( head_of @ SY670 )
!= ( head_of @ SY668 ) ) ) )
| ~ ! [SY671: $i,SY672: $i] :
( ~ ( precedes @ SV367 @ SY671 @ SY672 )
| ~ ( shortest_path @ SV349 @ SV361 @ SY672 )
| ~ ( precedes @ SY671 @ SV367 @ SY672 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1805]) ).
thf(1827,plain,
! [SV362: $i,SV350: $i] :
( ( ~ ~ ( ~ ! [SY655: $i,SY656: $i] :
( ~ ( on_path @ SY656 @ SY655 )
| ~ ( path @ SV350 @ SV362 @ SY655 )
| ( edge @ SY656 ) )
| ~ ! [SY657: $i,SY658: $i] :
( ~ ( on_path @ SY658 @ SY657 )
| ~ ( path @ SV350 @ SV362 @ SY657 )
| ( in_path @ ( head_of @ SY658 ) @ SY657 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1806]) ).
thf(1828,plain,
! [SV362: $i,SV350: $i] :
( ( ~ ! [SY659: $i,SY660: $i] :
( ~ ( on_path @ SY660 @ SY659 )
| ~ ( path @ SV350 @ SV362 @ SY659 )
| ( in_path @ ( tail_of @ SY660 ) @ SY659 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1806]) ).
thf(1829,plain,
! [SV372: $i] :
( ( ~ ( edge @ SV372 )
| ( vertex @ ( head_of @ SV372 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1807]) ).
thf(1830,plain,
! [SV373: $i] :
( ( ~ ( edge @ SV373 )
| ( vertex @ ( tail_of @ SV373 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1808]) ).
thf(1831,plain,
! [SV351: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV351 ) @ SV351 )
| ~ ( on_path @ ( sK7_SY80 @ SV351 ) @ SV351 ) )
| ~ ( sequential @ ( sK6_E1 @ SV351 ) @ ( sK7_SY80 @ SV351 ) ) )
| ~ ! [SY594: $i] :
~ ( triangle @ ( sK6_E1 @ SV351 ) @ ( sK7_SY80 @ SV351 ) @ SY594 ) )
= $false )
| ( ( ! [SY595: $i,SY596: $i] :
~ ( path @ SY595 @ SY596 @ SV351 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV351 )
= ( number_of_in @ triangles @ SV351 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1809]) ).
thf(1832,plain,
! [SV374: $i,SV368: $i] :
( ( ( ( SV368 = SV374 )
| ~ ( vertex @ SV368 )
| ~ ( vertex @ SV374 )
| ~ ( ~ ~ ( ~ ( ( SV368
!= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
!= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
!= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
!= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV368
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
| ~ ( ( SV368
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) ) )
| ~ ~ ( ~ ( ( SV374
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
| ~ ( ( SV374
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV374 @ SV368 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1810]) ).
thf(1833,plain,
! [SV352: $i] :
( ( ! [SY597: $i,SY598: $i] :
( ~ ( edge @ SV352 )
| ~ ( edge @ SY597 )
| ~ ( edge @ SY598 )
| ~ ( sequential @ SV352 @ SY597 )
| ~ ( sequential @ SY597 @ SY598 )
| ~ ( sequential @ SY598 @ SV352 )
| ( triangle @ SV352 @ SY597 @ SY598 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1811]) ).
thf(1834,plain,
! [SV352: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY599: $i,SY600: $i] :
~ ( triangle @ SV352 @ SY599 @ SY600 )
| ( edge @ SV352 ) )
| ~ ! [SY601: $i] :
( ! [SY602: $i] :
~ ( triangle @ SV352 @ SY601 @ SY602 )
| ( edge @ SY601 ) ) )
| ~ ! [SY603: $i,SY604: $i] :
( ~ ( triangle @ SV352 @ SY603 @ SY604 )
| ( edge @ SY604 ) ) )
| ~ ! [SY605: $i] :
( ! [SY606: $i] :
~ ( triangle @ SV352 @ SY605 @ SY606 )
| ( sequential @ SV352 @ SY605 ) ) )
| ~ ! [SY607: $i,SY608: $i] :
( ~ ( triangle @ SV352 @ SY607 @ SY608 )
| ( sequential @ SY607 @ SY608 ) ) )
| ~ ! [SY609: $i,SY610: $i] :
( ~ ( triangle @ SV352 @ SY609 @ SY610 )
| ( sequential @ SY610 @ SV352 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1812]) ).
thf(1835,plain,
! [SV353: $i,SV375: $i,SV369: $i] :
( ( ( ~ ( path @ SV369 @ SV375 @ SV353 ) )
= $true )
| ( ( ~ ( ~ ! [SY613: $i,SY614: $i] :
( ~ ( on_path @ SY613 @ SV353 )
| ~ ( on_path @ SY614 @ SV353 )
| ! [SY615: $i] :
( ~ ( precedes @ SY615 @ SY614 @ SV353 )
| ~ ( sequential @ SY613 @ SY615 ) )
| ( precedes @ SY613 @ SY614 @ SV353 ) )
| ~ ! [SY616: $i,SY617: $i] :
( ~ ( on_path @ SY616 @ SV353 )
| ~ ( on_path @ SY617 @ SV353 )
| ~ ( sequential @ SY616 @ SY617 )
| ( precedes @ SY616 @ SY617 @ SV353 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1813]) ).
thf(1836,plain,
! [SV354: $i,SV376: $i,SV370: $i] :
( ( ( ~ ( path @ SV370 @ SV376 @ SV354 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY620: $i] :
( ! [SY621: $i] :
~ ( precedes @ SY620 @ SY621 @ SV354 )
| ( on_path @ SY620 @ SV354 ) )
| ~ ! [SY622: $i,SY623: $i] :
( ~ ( precedes @ SY622 @ SY623 @ SV354 )
| ( on_path @ SY623 @ SV354 ) ) )
| ~ ~ ( ~ ! [SY624: $i,SY625: $i] :
( ~ ( precedes @ SY624 @ SY625 @ SV354 )
| ! [SY626: $i] :
( ~ ( precedes @ SY626 @ SY625 @ SV354 )
| ~ ( sequential @ SY624 @ SY626 ) )
| ~ ( sequential @ SY624 @ SY625 ) )
| ~ ! [SY627: $i,SY628: $i] :
( ~ ( precedes @ SY627 @ SY628 @ SV354 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY628 @ SY627 @ SV354 ) @ SY628 @ SV354 )
| ~ ( sequential @ SY627 @ ( sK9_E3 @ SY628 @ SY627 @ SV354 ) ) )
| ( sequential @ SY627 @ SY628 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1814]) ).
thf(1837,plain,
! [SV363: $i,SV355: $i] :
( ( ~ ! [SY661: $i,SY662: $i] :
( ~ ( in_path @ SY662 @ SY661 )
| ~ ( path @ SV355 @ SV363 @ SY661 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY662 @ SY661 @ SV363 @ SV355 ) @ SY661 )
| ~ ( ( SY662
= ( head_of @ ( sK10_E @ SY662 @ SY661 @ SV363 @ SV355 ) ) )
| ( SY662
= ( tail_of @ ( sK10_E @ SY662 @ SY661 @ SV363 @ SV355 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1815]) ).
thf(1838,plain,
! [SV363: $i,SV355: $i] :
( ( ~ ! [SY663: $i,SY664: $i] :
( ~ ( in_path @ SY664 @ SY663 )
| ~ ( path @ SV355 @ SV363 @ SY663 )
| ( vertex @ SY664 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1815]) ).
thf(1839,plain,
! [SV356: $i] :
( ( ! [SY634: $i,SY635: $i] :
( ~ ( ~ ( path @ SV356 @ SY634 @ ( sK8_P @ SY635 @ SY634 @ SV356 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY635 ) @ ( length_of @ ( sK8_P @ SY635 @ SY634 @ SV356 ) ) ) )
| ( SV356 = SY634 )
| ~ ( path @ SV356 @ SY634 @ SY635 )
| ( shortest_path @ SV356 @ SY634 @ SY635 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1816]) ).
thf(1840,plain,
! [SV356: $i] :
( ( ~ ( ~ ! [SY636: $i,SY637: $i] :
( ~ ( shortest_path @ SV356 @ SY636 @ SY637 )
| ! [SY638: $i] :
( ~ ( path @ SV356 @ SY636 @ SY638 )
| ( less_or_equal @ ( length_of @ SY637 ) @ ( length_of @ SY638 ) ) ) )
| ~ ~ ( ~ ! [SY639: $i] :
( ! [SY640: $i] :
~ ( shortest_path @ SV356 @ SY639 @ SY640 )
| ( SV356 != SY639 ) )
| ~ ! [SY641: $i,SY642: $i] :
( ~ ( shortest_path @ SV356 @ SY641 @ SY642 )
| ( path @ SV356 @ SY641 @ SY642 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1817]) ).
thf(1841,plain,
! [SV364: $i,SV357: $i,SV344: $i] :
( ( ( path @ SV344 @ SV357 @ SV364 )
= $false )
| ( ( ( length_of @ SV364 )
= ( number_of_in @ edges @ SV364 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1819]) ).
thf(1842,plain,
! [SV365: $i,SV358: $i,SV345: $i] :
( ( ( path @ SV345 @ SV358 @ SV365 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV365 )
= ( minus @ ( length_of @ SV365 ) @ n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1820]) ).
thf(1843,plain,
! [SV347: $i] :
( ( ~ ( ! [SY568: $i,SY569: $i] :
~ ( path @ SV347 @ SY568 @ SY569 )
| ( vertex @ SV347 ) )
| ~ ! [SY570: $i] :
( ! [SY571: $i] :
~ ( path @ SV347 @ SY570 @ SY571 )
| ( vertex @ SY570 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1821]) ).
thf(1844,plain,
! [SV377: $i,SV347: $i] :
( ( ! [SY677: $i] :
( ~ ( path @ SV347 @ SV377 @ SY677 )
| ~ ( ~ ~ ( ( SV347
!= ( tail_of @ ( sK11_E @ SY677 @ SV377 @ SV347 ) ) )
| ~ ( edge @ ( sK11_E @ SY677 @ SV377 @ SV347 ) ) )
| ~ ~ ( ~ ( ( SV377
!= ( head_of @ ( sK11_E @ SY677 @ SV377 @ SV347 ) ) )
| ( SY677
!= ( path_cons @ ( sK11_E @ SY677 @ SV377 @ SV347 ) @ empty ) )
| ! [SY678: $i] :
( ( SY677
!= ( path_cons @ ( sK11_E @ SY677 @ SV377 @ SV347 ) @ SY678 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY677 @ SV377 @ SV347 ) ) @ SV377 @ SY678 ) ) )
| ~ ~ ( ~ ( ( SV377
= ( head_of @ ( sK11_E @ SY677 @ SV377 @ SV347 ) ) )
| ~ ( ( SY677
!= ( path_cons @ ( sK11_E @ SY677 @ SV377 @ SV347 ) @ ( sK13_SY84 @ SY677 @ SV377 @ SV347 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY677 @ SV377 @ SV347 ) ) @ SV377 @ ( sK13_SY84 @ SY677 @ SV377 @ SV347 ) ) ) )
| ~ ( ( SY677
= ( path_cons @ ( sK11_E @ SY677 @ SV377 @ SV347 ) @ empty ) )
| ~ ( ( SY677
!= ( path_cons @ ( sK11_E @ SY677 @ SV377 @ SV347 ) @ ( sK12_SY85 @ SY677 @ SV377 @ SV347 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY677 @ SV377 @ SV347 ) ) @ SV377 @ ( sK12_SY85 @ SY677 @ SV377 @ SV347 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1822]) ).
thf(1845,plain,
! [SV366: $i,SV360: $i,SV348: $i] :
( ( ( ~ ( vertex @ SV348 )
| ~ ( vertex @ SV360 ) )
= $true )
| ( ( ~ ( ~ ! [SY665: $i] :
( ( SV348
!= ( tail_of @ SY665 ) )
| ~ ( edge @ SY665 )
| ( SV360
!= ( head_of @ SY665 ) )
| ( SV366
!= ( path_cons @ SY665 @ empty ) ) )
| ~ ! [SY666: $i] :
( ( SV348
!= ( tail_of @ SY666 ) )
| ~ ( edge @ SY666 )
| ! [SY667: $i] :
( ( SV366
!= ( path_cons @ SY666 @ SY667 ) )
| ~ ( path @ ( head_of @ SY666 ) @ SV360 @ SY667 ) ) ) ) )
= $true )
| ( ( path @ SV348 @ SV360 @ SV366 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1823]) ).
thf(1846,plain,
! [SV378: $i,SV371: $i] :
( ( ( SV371 = SV378 )
| ~ ( edge @ SV371 )
| ~ ( edge @ SV378 )
| ( ( head_of @ SV371 )
!= ( tail_of @ SV378 ) )
| ( sequential @ SV371 @ SV378 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1824]) ).
thf(1847,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1825]) ).
thf(1848,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1825]) ).
thf(1849,plain,
! [SV361: $i,SV349: $i,SV367: $i] :
( ( ~ ! [SY668: $i] :
( ! [SY669: $i] :
( ~ ( precedes @ SV367 @ SY668 @ SY669 )
| ~ ( shortest_path @ SV349 @ SV361 @ SY669 ) )
| ! [SY670: $i] :
( ( ( tail_of @ SY670 )
!= ( tail_of @ SV367 ) )
| ( ( head_of @ SY670 )
!= ( head_of @ SY668 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1826]) ).
thf(1850,plain,
! [SV361: $i,SV349: $i,SV367: $i] :
( ( ~ ! [SY671: $i,SY672: $i] :
( ~ ( precedes @ SV367 @ SY671 @ SY672 )
| ~ ( shortest_path @ SV349 @ SV361 @ SY672 )
| ~ ( precedes @ SY671 @ SV367 @ SY672 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1826]) ).
thf(1851,plain,
! [SV362: $i,SV350: $i] :
( ( ~ ( ~ ! [SY655: $i,SY656: $i] :
( ~ ( on_path @ SY656 @ SY655 )
| ~ ( path @ SV350 @ SV362 @ SY655 )
| ( edge @ SY656 ) )
| ~ ! [SY657: $i,SY658: $i] :
( ~ ( on_path @ SY658 @ SY657 )
| ~ ( path @ SV350 @ SV362 @ SY657 )
| ( in_path @ ( head_of @ SY658 ) @ SY657 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1827]) ).
thf(1852,plain,
! [SV362: $i,SV350: $i] :
( ( ! [SY659: $i,SY660: $i] :
( ~ ( on_path @ SY660 @ SY659 )
| ~ ( path @ SV350 @ SV362 @ SY659 )
| ( in_path @ ( tail_of @ SY660 ) @ SY659 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1828]) ).
thf(1853,plain,
! [SV372: $i] :
( ( ( ~ ( edge @ SV372 ) )
= $true )
| ( ( vertex @ ( head_of @ SV372 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1829]) ).
thf(1854,plain,
! [SV373: $i] :
( ( ( ~ ( edge @ SV373 ) )
= $true )
| ( ( vertex @ ( tail_of @ SV373 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1830]) ).
thf(1855,plain,
! [SV351: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV351 ) @ SV351 )
| ~ ( on_path @ ( sK7_SY80 @ SV351 ) @ SV351 ) )
| ~ ( sequential @ ( sK6_E1 @ SV351 ) @ ( sK7_SY80 @ SV351 ) ) ) )
= $false )
| ( ( ! [SY595: $i,SY596: $i] :
~ ( path @ SY595 @ SY596 @ SV351 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV351 )
= ( number_of_in @ triangles @ SV351 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1831]) ).
thf(1856,plain,
! [SV351: $i] :
( ( ( ~ ! [SY594: $i] :
~ ( triangle @ ( sK6_E1 @ SV351 ) @ ( sK7_SY80 @ SV351 ) @ SY594 ) )
= $false )
| ( ( ! [SY595: $i,SY596: $i] :
~ ( path @ SY595 @ SY596 @ SV351 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV351 )
= ( number_of_in @ triangles @ SV351 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1831]) ).
thf(1857,plain,
! [SV374: $i,SV368: $i] :
( ( ( ( SV368 = SV374 )
| ~ ( vertex @ SV368 )
| ~ ( vertex @ SV374 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV368
!= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
!= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
!= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
!= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV368
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
| ~ ( ( SV368
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) ) )
| ~ ~ ( ~ ( ( SV374
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
| ~ ( ( SV374
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV374 @ SV368 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[1832]) ).
thf(1858,plain,
! [SV379: $i,SV352: $i] :
( ( ! [SY679: $i] :
( ~ ( edge @ SV352 )
| ~ ( edge @ SV379 )
| ~ ( edge @ SY679 )
| ~ ( sequential @ SV352 @ SV379 )
| ~ ( sequential @ SV379 @ SY679 )
| ~ ( sequential @ SY679 @ SV352 )
| ( triangle @ SV352 @ SV379 @ SY679 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1833]) ).
thf(1859,plain,
! [SV352: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY599: $i,SY600: $i] :
~ ( triangle @ SV352 @ SY599 @ SY600 )
| ( edge @ SV352 ) )
| ~ ! [SY601: $i] :
( ! [SY602: $i] :
~ ( triangle @ SV352 @ SY601 @ SY602 )
| ( edge @ SY601 ) ) )
| ~ ! [SY603: $i,SY604: $i] :
( ~ ( triangle @ SV352 @ SY603 @ SY604 )
| ( edge @ SY604 ) ) )
| ~ ! [SY605: $i] :
( ! [SY606: $i] :
~ ( triangle @ SV352 @ SY605 @ SY606 )
| ( sequential @ SV352 @ SY605 ) ) )
| ~ ! [SY607: $i,SY608: $i] :
( ~ ( triangle @ SV352 @ SY607 @ SY608 )
| ( sequential @ SY607 @ SY608 ) ) )
| ~ ! [SY609: $i,SY610: $i] :
( ~ ( triangle @ SV352 @ SY609 @ SY610 )
| ( sequential @ SY610 @ SV352 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1834]) ).
thf(1860,plain,
! [SV353: $i,SV375: $i,SV369: $i] :
( ( ( path @ SV369 @ SV375 @ SV353 )
= $false )
| ( ( ~ ( ~ ! [SY613: $i,SY614: $i] :
( ~ ( on_path @ SY613 @ SV353 )
| ~ ( on_path @ SY614 @ SV353 )
| ! [SY615: $i] :
( ~ ( precedes @ SY615 @ SY614 @ SV353 )
| ~ ( sequential @ SY613 @ SY615 ) )
| ( precedes @ SY613 @ SY614 @ SV353 ) )
| ~ ! [SY616: $i,SY617: $i] :
( ~ ( on_path @ SY616 @ SV353 )
| ~ ( on_path @ SY617 @ SV353 )
| ~ ( sequential @ SY616 @ SY617 )
| ( precedes @ SY616 @ SY617 @ SV353 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1835]) ).
thf(1861,plain,
! [SV354: $i,SV376: $i,SV370: $i] :
( ( ( path @ SV370 @ SV376 @ SV354 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY620: $i] :
( ! [SY621: $i] :
~ ( precedes @ SY620 @ SY621 @ SV354 )
| ( on_path @ SY620 @ SV354 ) )
| ~ ! [SY622: $i,SY623: $i] :
( ~ ( precedes @ SY622 @ SY623 @ SV354 )
| ( on_path @ SY623 @ SV354 ) ) )
| ~ ~ ( ~ ! [SY624: $i,SY625: $i] :
( ~ ( precedes @ SY624 @ SY625 @ SV354 )
| ! [SY626: $i] :
( ~ ( precedes @ SY626 @ SY625 @ SV354 )
| ~ ( sequential @ SY624 @ SY626 ) )
| ~ ( sequential @ SY624 @ SY625 ) )
| ~ ! [SY627: $i,SY628: $i] :
( ~ ( precedes @ SY627 @ SY628 @ SV354 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY628 @ SY627 @ SV354 ) @ SY628 @ SV354 )
| ~ ( sequential @ SY627 @ ( sK9_E3 @ SY628 @ SY627 @ SV354 ) ) )
| ( sequential @ SY627 @ SY628 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1836]) ).
thf(1862,plain,
! [SV363: $i,SV355: $i] :
( ( ! [SY661: $i,SY662: $i] :
( ~ ( in_path @ SY662 @ SY661 )
| ~ ( path @ SV355 @ SV363 @ SY661 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY662 @ SY661 @ SV363 @ SV355 ) @ SY661 )
| ~ ( ( SY662
= ( head_of @ ( sK10_E @ SY662 @ SY661 @ SV363 @ SV355 ) ) )
| ( SY662
= ( tail_of @ ( sK10_E @ SY662 @ SY661 @ SV363 @ SV355 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1837]) ).
thf(1863,plain,
! [SV363: $i,SV355: $i] :
( ( ! [SY663: $i,SY664: $i] :
( ~ ( in_path @ SY664 @ SY663 )
| ~ ( path @ SV355 @ SV363 @ SY663 )
| ( vertex @ SY664 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1838]) ).
thf(1864,plain,
! [SV380: $i,SV356: $i] :
( ( ! [SY680: $i] :
( ~ ( ~ ( path @ SV356 @ SV380 @ ( sK8_P @ SY680 @ SV380 @ SV356 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY680 ) @ ( length_of @ ( sK8_P @ SY680 @ SV380 @ SV356 ) ) ) )
| ( SV356 = SV380 )
| ~ ( path @ SV356 @ SV380 @ SY680 )
| ( shortest_path @ SV356 @ SV380 @ SY680 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1839]) ).
thf(1865,plain,
! [SV356: $i] :
( ( ~ ! [SY636: $i,SY637: $i] :
( ~ ( shortest_path @ SV356 @ SY636 @ SY637 )
| ! [SY638: $i] :
( ~ ( path @ SV356 @ SY636 @ SY638 )
| ( less_or_equal @ ( length_of @ SY637 ) @ ( length_of @ SY638 ) ) ) )
| ~ ~ ( ~ ! [SY639: $i] :
( ! [SY640: $i] :
~ ( shortest_path @ SV356 @ SY639 @ SY640 )
| ( SV356 != SY639 ) )
| ~ ! [SY641: $i,SY642: $i] :
( ~ ( shortest_path @ SV356 @ SY641 @ SY642 )
| ( path @ SV356 @ SY641 @ SY642 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1840]) ).
thf(1866,plain,
! [SV347: $i] :
( ( ~ ( ! [SY568: $i,SY569: $i] :
~ ( path @ SV347 @ SY568 @ SY569 )
| ( vertex @ SV347 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1843]) ).
thf(1867,plain,
! [SV347: $i] :
( ( ~ ! [SY570: $i] :
( ! [SY571: $i] :
~ ( path @ SV347 @ SY570 @ SY571 )
| ( vertex @ SY570 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1843]) ).
thf(1868,plain,
! [SV381: $i,SV377: $i,SV347: $i] :
( ( ~ ( path @ SV347 @ SV377 @ SV381 )
| ~ ( ~ ~ ( ( SV347
!= ( tail_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( edge @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
| ~ ~ ( ~ ( ( SV377
!= ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
| ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ empty ) )
| ! [SY681: $i] :
( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ SY681 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ SY681 ) ) )
| ~ ~ ( ~ ( ( SV377
= ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ ( sK13_SY84 @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ ( sK13_SY84 @ SV381 @ SV377 @ SV347 ) ) ) )
| ~ ( ( SV381
= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ empty ) )
| ~ ( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ ( sK12_SY85 @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ ( sK12_SY85 @ SV381 @ SV377 @ SV347 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1844]) ).
thf(1869,plain,
! [SV366: $i,SV360: $i,SV348: $i] :
( ( ( ~ ( vertex @ SV348 ) )
= $true )
| ( ( ~ ( vertex @ SV360 ) )
= $true )
| ( ( ~ ( ~ ! [SY665: $i] :
( ( SV348
!= ( tail_of @ SY665 ) )
| ~ ( edge @ SY665 )
| ( SV360
!= ( head_of @ SY665 ) )
| ( SV366
!= ( path_cons @ SY665 @ empty ) ) )
| ~ ! [SY666: $i] :
( ( SV348
!= ( tail_of @ SY666 ) )
| ~ ( edge @ SY666 )
| ! [SY667: $i] :
( ( SV366
!= ( path_cons @ SY666 @ SY667 ) )
| ~ ( path @ ( head_of @ SY666 ) @ SV360 @ SY667 ) ) ) ) )
= $true )
| ( ( path @ SV348 @ SV360 @ SV366 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1845]) ).
thf(1870,plain,
! [SV378: $i,SV371: $i] :
( ( ( ( SV371 = SV378 )
| ~ ( edge @ SV371 )
| ~ ( edge @ SV378 )
| ( ( head_of @ SV371 )
!= ( tail_of @ SV378 ) ) )
= $true )
| ( ( sequential @ SV371 @ SV378 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1846]) ).
thf(1871,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1847]) ).
thf(1872,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1848]) ).
thf(1873,plain,
! [SV361: $i,SV349: $i,SV367: $i] :
( ( ! [SY668: $i] :
( ! [SY669: $i] :
( ~ ( precedes @ SV367 @ SY668 @ SY669 )
| ~ ( shortest_path @ SV349 @ SV361 @ SY669 ) )
| ! [SY670: $i] :
( ( ( tail_of @ SY670 )
!= ( tail_of @ SV367 ) )
| ( ( head_of @ SY670 )
!= ( head_of @ SY668 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1849]) ).
thf(1874,plain,
! [SV361: $i,SV349: $i,SV367: $i] :
( ( ! [SY671: $i,SY672: $i] :
( ~ ( precedes @ SV367 @ SY671 @ SY672 )
| ~ ( shortest_path @ SV349 @ SV361 @ SY672 )
| ~ ( precedes @ SY671 @ SV367 @ SY672 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1850]) ).
thf(1875,plain,
! [SV362: $i,SV350: $i] :
( ( ~ ! [SY655: $i,SY656: $i] :
( ~ ( on_path @ SY656 @ SY655 )
| ~ ( path @ SV350 @ SV362 @ SY655 )
| ( edge @ SY656 ) )
| ~ ! [SY657: $i,SY658: $i] :
( ~ ( on_path @ SY658 @ SY657 )
| ~ ( path @ SV350 @ SV362 @ SY657 )
| ( in_path @ ( head_of @ SY658 ) @ SY657 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1851]) ).
thf(1876,plain,
! [SV362: $i,SV350: $i,SV382: $i] :
( ( ! [SY682: $i] :
( ~ ( on_path @ SY682 @ SV382 )
| ~ ( path @ SV350 @ SV362 @ SV382 )
| ( in_path @ ( tail_of @ SY682 ) @ SV382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1852]) ).
thf(1877,plain,
! [SV372: $i] :
( ( ( edge @ SV372 )
= $false )
| ( ( vertex @ ( head_of @ SV372 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1853]) ).
thf(1878,plain,
! [SV373: $i] :
( ( ( edge @ SV373 )
= $false )
| ( ( vertex @ ( tail_of @ SV373 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1854]) ).
thf(1879,plain,
! [SV351: $i] :
( ( ( ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV351 ) @ SV351 )
| ~ ( on_path @ ( sK7_SY80 @ SV351 ) @ SV351 ) )
| ~ ( sequential @ ( sK6_E1 @ SV351 ) @ ( sK7_SY80 @ SV351 ) ) ) )
= $true )
| ( ( ! [SY595: $i,SY596: $i] :
~ ( path @ SY595 @ SY596 @ SV351 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV351 )
= ( number_of_in @ triangles @ SV351 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1855]) ).
thf(1880,plain,
! [SV351: $i] :
( ( ( ! [SY594: $i] :
~ ( triangle @ ( sK6_E1 @ SV351 ) @ ( sK7_SY80 @ SV351 ) @ SY594 ) )
= $true )
| ( ( ! [SY595: $i,SY596: $i] :
~ ( path @ SY595 @ SY596 @ SV351 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV351 )
= ( number_of_in @ triangles @ SV351 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1856]) ).
thf(1881,plain,
! [SV374: $i,SV368: $i] :
( ( ( SV368 = SV374 )
= $true )
| ( ( ~ ( vertex @ SV368 )
| ~ ( vertex @ SV374 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV368
!= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
!= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
!= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
!= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV368
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
| ~ ( ( SV368
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) ) )
| ~ ~ ( ~ ( ( SV374
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
| ~ ( ( SV374
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV374 @ SV368 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[1857]) ).
thf(1882,plain,
! [SV383: $i,SV379: $i,SV352: $i] :
( ( ~ ( edge @ SV352 )
| ~ ( edge @ SV379 )
| ~ ( edge @ SV383 )
| ~ ( sequential @ SV352 @ SV379 )
| ~ ( sequential @ SV379 @ SV383 )
| ~ ( sequential @ SV383 @ SV352 )
| ( triangle @ SV352 @ SV379 @ SV383 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1858]) ).
thf(1883,plain,
! [SV352: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY599: $i,SY600: $i] :
~ ( triangle @ SV352 @ SY599 @ SY600 )
| ( edge @ SV352 ) )
| ~ ! [SY601: $i] :
( ! [SY602: $i] :
~ ( triangle @ SV352 @ SY601 @ SY602 )
| ( edge @ SY601 ) ) )
| ~ ! [SY603: $i,SY604: $i] :
( ~ ( triangle @ SV352 @ SY603 @ SY604 )
| ( edge @ SY604 ) ) )
| ~ ! [SY605: $i] :
( ! [SY606: $i] :
~ ( triangle @ SV352 @ SY605 @ SY606 )
| ( sequential @ SV352 @ SY605 ) ) )
| ~ ! [SY607: $i,SY608: $i] :
( ~ ( triangle @ SV352 @ SY607 @ SY608 )
| ( sequential @ SY607 @ SY608 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1859]) ).
thf(1884,plain,
! [SV352: $i] :
( ( ~ ! [SY609: $i,SY610: $i] :
( ~ ( triangle @ SV352 @ SY609 @ SY610 )
| ( sequential @ SY610 @ SV352 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1859]) ).
thf(1885,plain,
! [SV375: $i,SV369: $i,SV353: $i] :
( ( ( ~ ! [SY613: $i,SY614: $i] :
( ~ ( on_path @ SY613 @ SV353 )
| ~ ( on_path @ SY614 @ SV353 )
| ! [SY615: $i] :
( ~ ( precedes @ SY615 @ SY614 @ SV353 )
| ~ ( sequential @ SY613 @ SY615 ) )
| ( precedes @ SY613 @ SY614 @ SV353 ) )
| ~ ! [SY616: $i,SY617: $i] :
( ~ ( on_path @ SY616 @ SV353 )
| ~ ( on_path @ SY617 @ SV353 )
| ~ ( sequential @ SY616 @ SY617 )
| ( precedes @ SY616 @ SY617 @ SV353 ) ) )
= $false )
| ( ( path @ SV369 @ SV375 @ SV353 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1860]) ).
thf(1886,plain,
! [SV376: $i,SV370: $i,SV354: $i] :
( ( ( ~ ~ ( ~ ! [SY620: $i] :
( ! [SY621: $i] :
~ ( precedes @ SY620 @ SY621 @ SV354 )
| ( on_path @ SY620 @ SV354 ) )
| ~ ! [SY622: $i,SY623: $i] :
( ~ ( precedes @ SY622 @ SY623 @ SV354 )
| ( on_path @ SY623 @ SV354 ) ) )
| ~ ~ ( ~ ! [SY624: $i,SY625: $i] :
( ~ ( precedes @ SY624 @ SY625 @ SV354 )
| ! [SY626: $i] :
( ~ ( precedes @ SY626 @ SY625 @ SV354 )
| ~ ( sequential @ SY624 @ SY626 ) )
| ~ ( sequential @ SY624 @ SY625 ) )
| ~ ! [SY627: $i,SY628: $i] :
( ~ ( precedes @ SY627 @ SY628 @ SV354 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY628 @ SY627 @ SV354 ) @ SY628 @ SV354 )
| ~ ( sequential @ SY627 @ ( sK9_E3 @ SY628 @ SY627 @ SV354 ) ) )
| ( sequential @ SY627 @ SY628 ) ) ) )
= $false )
| ( ( path @ SV370 @ SV376 @ SV354 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1861]) ).
thf(1887,plain,
! [SV363: $i,SV355: $i,SV384: $i] :
( ( ! [SY683: $i] :
( ~ ( in_path @ SY683 @ SV384 )
| ~ ( path @ SV355 @ SV363 @ SV384 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY683 @ SV384 @ SV363 @ SV355 ) @ SV384 )
| ~ ( ( SY683
= ( head_of @ ( sK10_E @ SY683 @ SV384 @ SV363 @ SV355 ) ) )
| ( SY683
= ( tail_of @ ( sK10_E @ SY683 @ SV384 @ SV363 @ SV355 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1862]) ).
thf(1888,plain,
! [SV363: $i,SV355: $i,SV385: $i] :
( ( ! [SY684: $i] :
( ~ ( in_path @ SY684 @ SV385 )
| ~ ( path @ SV355 @ SV363 @ SV385 )
| ( vertex @ SY684 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1863]) ).
thf(1889,plain,
! [SV386: $i,SV380: $i,SV356: $i] :
( ( ~ ( ~ ( path @ SV356 @ SV380 @ ( sK8_P @ SV386 @ SV380 @ SV356 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SV386 ) @ ( length_of @ ( sK8_P @ SV386 @ SV380 @ SV356 ) ) ) )
| ( SV356 = SV380 )
| ~ ( path @ SV356 @ SV380 @ SV386 )
| ( shortest_path @ SV356 @ SV380 @ SV386 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1864]) ).
thf(1890,plain,
! [SV356: $i] :
( ( ~ ! [SY636: $i,SY637: $i] :
( ~ ( shortest_path @ SV356 @ SY636 @ SY637 )
| ! [SY638: $i] :
( ~ ( path @ SV356 @ SY636 @ SY638 )
| ( less_or_equal @ ( length_of @ SY637 ) @ ( length_of @ SY638 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1865]) ).
thf(1891,plain,
! [SV356: $i] :
( ( ~ ~ ( ~ ! [SY639: $i] :
( ! [SY640: $i] :
~ ( shortest_path @ SV356 @ SY639 @ SY640 )
| ( SV356 != SY639 ) )
| ~ ! [SY641: $i,SY642: $i] :
( ~ ( shortest_path @ SV356 @ SY641 @ SY642 )
| ( path @ SV356 @ SY641 @ SY642 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1865]) ).
thf(1892,plain,
! [SV347: $i] :
( ( ! [SY568: $i,SY569: $i] :
~ ( path @ SV347 @ SY568 @ SY569 )
| ( vertex @ SV347 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1866]) ).
thf(1893,plain,
! [SV347: $i] :
( ( ! [SY570: $i] :
( ! [SY571: $i] :
~ ( path @ SV347 @ SY570 @ SY571 )
| ( vertex @ SY570 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1867]) ).
thf(1894,plain,
! [SV381: $i,SV377: $i,SV347: $i] :
( ( ( ~ ( path @ SV347 @ SV377 @ SV381 ) )
= $true )
| ( ( ~ ( ~ ~ ( ( SV347
!= ( tail_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( edge @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
| ~ ~ ( ~ ( ( SV377
!= ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
| ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ empty ) )
| ! [SY681: $i] :
( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ SY681 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ SY681 ) ) )
| ~ ~ ( ~ ( ( SV377
= ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ ( sK13_SY84 @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ ( sK13_SY84 @ SV381 @ SV377 @ SV347 ) ) ) )
| ~ ( ( SV381
= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ empty ) )
| ~ ( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ ( sK12_SY85 @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ ( sK12_SY85 @ SV381 @ SV377 @ SV347 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1868]) ).
thf(1895,plain,
! [SV366: $i,SV360: $i,SV348: $i] :
( ( ( vertex @ SV348 )
= $false )
| ( ( ~ ( vertex @ SV360 ) )
= $true )
| ( ( ~ ( ~ ! [SY665: $i] :
( ( SV348
!= ( tail_of @ SY665 ) )
| ~ ( edge @ SY665 )
| ( SV360
!= ( head_of @ SY665 ) )
| ( SV366
!= ( path_cons @ SY665 @ empty ) ) )
| ~ ! [SY666: $i] :
( ( SV348
!= ( tail_of @ SY666 ) )
| ~ ( edge @ SY666 )
| ! [SY667: $i] :
( ( SV366
!= ( path_cons @ SY666 @ SY667 ) )
| ~ ( path @ ( head_of @ SY666 ) @ SV360 @ SY667 ) ) ) ) )
= $true )
| ( ( path @ SV348 @ SV360 @ SV366 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1869]) ).
thf(1896,plain,
! [SV378: $i,SV371: $i] :
( ( ( ( SV371 = SV378 )
| ~ ( edge @ SV371 )
| ~ ( edge @ SV378 ) )
= $true )
| ( ( ( ( head_of @ SV371 )
!= ( tail_of @ SV378 ) ) )
= $true )
| ( ( sequential @ SV371 @ SV378 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1870]) ).
thf(1897,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1871]) ).
thf(1898,plain,
! [SV387: $i] :
( ( ! [SY685: $i] :
( ~ ( sequential @ SV387 @ SY685 )
| ( ( head_of @ SV387 )
= ( tail_of @ SY685 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1872]) ).
thf(1899,plain,
! [SV361: $i,SV349: $i,SV388: $i,SV367: $i] :
( ( ! [SY686: $i] :
( ~ ( precedes @ SV367 @ SV388 @ SY686 )
| ~ ( shortest_path @ SV349 @ SV361 @ SY686 ) )
| ! [SY687: $i] :
( ( ( tail_of @ SY687 )
!= ( tail_of @ SV367 ) )
| ( ( head_of @ SY687 )
!= ( head_of @ SV388 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1873]) ).
thf(1900,plain,
! [SV361: $i,SV349: $i,SV389: $i,SV367: $i] :
( ( ! [SY688: $i] :
( ~ ( precedes @ SV367 @ SV389 @ SY688 )
| ~ ( shortest_path @ SV349 @ SV361 @ SY688 )
| ~ ( precedes @ SV389 @ SV367 @ SY688 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1874]) ).
thf(1901,plain,
! [SV362: $i,SV350: $i] :
( ( ~ ! [SY655: $i,SY656: $i] :
( ~ ( on_path @ SY656 @ SY655 )
| ~ ( path @ SV350 @ SV362 @ SY655 )
| ( edge @ SY656 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1875]) ).
thf(1902,plain,
! [SV362: $i,SV350: $i] :
( ( ~ ! [SY657: $i,SY658: $i] :
( ~ ( on_path @ SY658 @ SY657 )
| ~ ( path @ SV350 @ SV362 @ SY657 )
| ( in_path @ ( head_of @ SY658 ) @ SY657 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1875]) ).
thf(1903,plain,
! [SV362: $i,SV350: $i,SV382: $i,SV390: $i] :
( ( ~ ( on_path @ SV390 @ SV382 )
| ~ ( path @ SV350 @ SV362 @ SV382 )
| ( in_path @ ( tail_of @ SV390 ) @ SV382 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1876]) ).
thf(1904,plain,
! [SV351: $i] :
( ( ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV351 ) @ SV351 )
| ~ ( on_path @ ( sK7_SY80 @ SV351 ) @ SV351 ) )
| ~ ( sequential @ ( sK6_E1 @ SV351 ) @ ( sK7_SY80 @ SV351 ) ) )
= $false )
| ( ( ! [SY595: $i,SY596: $i] :
~ ( path @ SY595 @ SY596 @ SV351 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV351 )
= ( number_of_in @ triangles @ SV351 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1879]) ).
thf(1905,plain,
! [SV391: $i,SV351: $i] :
( ( ( ~ ( triangle @ ( sK6_E1 @ SV351 ) @ ( sK7_SY80 @ SV351 ) @ SV391 ) )
= $true )
| ( ( ! [SY595: $i,SY596: $i] :
~ ( path @ SY595 @ SY596 @ SV351 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV351 )
= ( number_of_in @ triangles @ SV351 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1880]) ).
thf(1906,plain,
! [SV374: $i,SV368: $i] :
( ( ( ~ ( vertex @ SV368 ) )
= $true )
| ( ( ~ ( vertex @ SV374 ) )
= $true )
| ( ( SV368 = SV374 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV368
!= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
!= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
!= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
!= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV368
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
| ~ ( ( SV368
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) ) )
| ~ ~ ( ~ ( ( SV374
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
| ~ ( ( SV374
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV374 @ SV368 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[1881]) ).
thf(1907,plain,
! [SV383: $i,SV379: $i,SV352: $i] :
( ( ( ~ ( edge @ SV352 )
| ~ ( edge @ SV379 )
| ~ ( edge @ SV383 )
| ~ ( sequential @ SV352 @ SV379 )
| ~ ( sequential @ SV379 @ SV383 )
| ~ ( sequential @ SV383 @ SV352 ) )
= $true )
| ( ( triangle @ SV352 @ SV379 @ SV383 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1882]) ).
thf(1908,plain,
! [SV352: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY599: $i,SY600: $i] :
~ ( triangle @ SV352 @ SY599 @ SY600 )
| ( edge @ SV352 ) )
| ~ ! [SY601: $i] :
( ! [SY602: $i] :
~ ( triangle @ SV352 @ SY601 @ SY602 )
| ( edge @ SY601 ) ) )
| ~ ! [SY603: $i,SY604: $i] :
( ~ ( triangle @ SV352 @ SY603 @ SY604 )
| ( edge @ SY604 ) ) )
| ~ ! [SY605: $i] :
( ! [SY606: $i] :
~ ( triangle @ SV352 @ SY605 @ SY606 )
| ( sequential @ SV352 @ SY605 ) ) )
| ~ ! [SY607: $i,SY608: $i] :
( ~ ( triangle @ SV352 @ SY607 @ SY608 )
| ( sequential @ SY607 @ SY608 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1883]) ).
thf(1909,plain,
! [SV352: $i] :
( ( ! [SY609: $i,SY610: $i] :
( ~ ( triangle @ SV352 @ SY609 @ SY610 )
| ( sequential @ SY610 @ SV352 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1884]) ).
thf(1910,plain,
! [SV375: $i,SV369: $i,SV353: $i] :
( ( ( ~ ! [SY613: $i,SY614: $i] :
( ~ ( on_path @ SY613 @ SV353 )
| ~ ( on_path @ SY614 @ SV353 )
| ! [SY615: $i] :
( ~ ( precedes @ SY615 @ SY614 @ SV353 )
| ~ ( sequential @ SY613 @ SY615 ) )
| ( precedes @ SY613 @ SY614 @ SV353 ) ) )
= $false )
| ( ( path @ SV369 @ SV375 @ SV353 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1885]) ).
thf(1911,plain,
! [SV375: $i,SV369: $i,SV353: $i] :
( ( ( ~ ! [SY616: $i,SY617: $i] :
( ~ ( on_path @ SY616 @ SV353 )
| ~ ( on_path @ SY617 @ SV353 )
| ~ ( sequential @ SY616 @ SY617 )
| ( precedes @ SY616 @ SY617 @ SV353 ) ) )
= $false )
| ( ( path @ SV369 @ SV375 @ SV353 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1885]) ).
thf(1912,plain,
! [SV376: $i,SV370: $i,SV354: $i] :
( ( ( ~ ~ ( ~ ! [SY620: $i] :
( ! [SY621: $i] :
~ ( precedes @ SY620 @ SY621 @ SV354 )
| ( on_path @ SY620 @ SV354 ) )
| ~ ! [SY622: $i,SY623: $i] :
( ~ ( precedes @ SY622 @ SY623 @ SV354 )
| ( on_path @ SY623 @ SV354 ) ) ) )
= $false )
| ( ( path @ SV370 @ SV376 @ SV354 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1886]) ).
thf(1913,plain,
! [SV376: $i,SV370: $i,SV354: $i] :
( ( ( ~ ~ ( ~ ! [SY624: $i,SY625: $i] :
( ~ ( precedes @ SY624 @ SY625 @ SV354 )
| ! [SY626: $i] :
( ~ ( precedes @ SY626 @ SY625 @ SV354 )
| ~ ( sequential @ SY624 @ SY626 ) )
| ~ ( sequential @ SY624 @ SY625 ) )
| ~ ! [SY627: $i,SY628: $i] :
( ~ ( precedes @ SY627 @ SY628 @ SV354 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY628 @ SY627 @ SV354 ) @ SY628 @ SV354 )
| ~ ( sequential @ SY627 @ ( sK9_E3 @ SY628 @ SY627 @ SV354 ) ) )
| ( sequential @ SY627 @ SY628 ) ) ) )
= $false )
| ( ( path @ SV370 @ SV376 @ SV354 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1886]) ).
thf(1914,plain,
! [SV363: $i,SV355: $i,SV384: $i,SV392: $i] :
( ( ~ ( in_path @ SV392 @ SV384 )
| ~ ( path @ SV355 @ SV363 @ SV384 )
| ~ ( ~ ( on_path @ ( sK10_E @ SV392 @ SV384 @ SV363 @ SV355 ) @ SV384 )
| ~ ( ( SV392
= ( head_of @ ( sK10_E @ SV392 @ SV384 @ SV363 @ SV355 ) ) )
| ( SV392
= ( tail_of @ ( sK10_E @ SV392 @ SV384 @ SV363 @ SV355 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1887]) ).
thf(1915,plain,
! [SV363: $i,SV355: $i,SV385: $i,SV393: $i] :
( ( ~ ( in_path @ SV393 @ SV385 )
| ~ ( path @ SV355 @ SV363 @ SV385 )
| ( vertex @ SV393 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1888]) ).
thf(1916,plain,
! [SV386: $i,SV380: $i,SV356: $i] :
( ( ( ~ ( ~ ( path @ SV356 @ SV380 @ ( sK8_P @ SV386 @ SV380 @ SV356 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SV386 ) @ ( length_of @ ( sK8_P @ SV386 @ SV380 @ SV356 ) ) ) )
| ( SV356 = SV380 )
| ~ ( path @ SV356 @ SV380 @ SV386 ) )
= $true )
| ( ( shortest_path @ SV356 @ SV380 @ SV386 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1889]) ).
thf(1917,plain,
! [SV356: $i] :
( ( ! [SY636: $i,SY637: $i] :
( ~ ( shortest_path @ SV356 @ SY636 @ SY637 )
| ! [SY638: $i] :
( ~ ( path @ SV356 @ SY636 @ SY638 )
| ( less_or_equal @ ( length_of @ SY637 ) @ ( length_of @ SY638 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1890]) ).
thf(1918,plain,
! [SV356: $i] :
( ( ~ ( ~ ! [SY639: $i] :
( ! [SY640: $i] :
~ ( shortest_path @ SV356 @ SY639 @ SY640 )
| ( SV356 != SY639 ) )
| ~ ! [SY641: $i,SY642: $i] :
( ~ ( shortest_path @ SV356 @ SY641 @ SY642 )
| ( path @ SV356 @ SY641 @ SY642 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1891]) ).
thf(1919,plain,
! [SV347: $i] :
( ( ( ! [SY568: $i,SY569: $i] :
~ ( path @ SV347 @ SY568 @ SY569 ) )
= $true )
| ( ( vertex @ SV347 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1892]) ).
thf(1920,plain,
! [SV394: $i,SV347: $i] :
( ( ! [SY689: $i] :
~ ( path @ SV347 @ SV394 @ SY689 )
| ( vertex @ SV394 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1893]) ).
thf(1921,plain,
! [SV381: $i,SV377: $i,SV347: $i] :
( ( ( path @ SV347 @ SV377 @ SV381 )
= $false )
| ( ( ~ ( ~ ~ ( ( SV347
!= ( tail_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( edge @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
| ~ ~ ( ~ ( ( SV377
!= ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
| ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ empty ) )
| ! [SY681: $i] :
( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ SY681 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ SY681 ) ) )
| ~ ~ ( ~ ( ( SV377
= ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ ( sK13_SY84 @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ ( sK13_SY84 @ SV381 @ SV377 @ SV347 ) ) ) )
| ~ ( ( SV381
= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ empty ) )
| ~ ( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ ( sK12_SY85 @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ ( sK12_SY85 @ SV381 @ SV377 @ SV347 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1894]) ).
thf(1922,plain,
! [SV366: $i,SV348: $i,SV360: $i] :
( ( ( vertex @ SV360 )
= $false )
| ( ( vertex @ SV348 )
= $false )
| ( ( ~ ( ~ ! [SY665: $i] :
( ( SV348
!= ( tail_of @ SY665 ) )
| ~ ( edge @ SY665 )
| ( SV360
!= ( head_of @ SY665 ) )
| ( SV366
!= ( path_cons @ SY665 @ empty ) ) )
| ~ ! [SY666: $i] :
( ( SV348
!= ( tail_of @ SY666 ) )
| ~ ( edge @ SY666 )
| ! [SY667: $i] :
( ( SV366
!= ( path_cons @ SY666 @ SY667 ) )
| ~ ( path @ ( head_of @ SY666 ) @ SV360 @ SY667 ) ) ) ) )
= $true )
| ( ( path @ SV348 @ SV360 @ SV366 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1895]) ).
thf(1923,plain,
! [SV378: $i,SV371: $i] :
( ( ( SV371 = SV378 )
= $true )
| ( ( ~ ( edge @ SV371 )
| ~ ( edge @ SV378 ) )
= $true )
| ( ( ( ( head_of @ SV371 )
!= ( tail_of @ SV378 ) ) )
= $true )
| ( ( sequential @ SV371 @ SV378 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1896]) ).
thf(1924,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1897]) ).
thf(1925,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1897]) ).
thf(1926,plain,
! [SV395: $i,SV387: $i] :
( ( ~ ( sequential @ SV387 @ SV395 )
| ( ( head_of @ SV387 )
= ( tail_of @ SV395 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1898]) ).
thf(1927,plain,
! [SV361: $i,SV349: $i,SV388: $i,SV367: $i] :
( ( ( ! [SY686: $i] :
( ~ ( precedes @ SV367 @ SV388 @ SY686 )
| ~ ( shortest_path @ SV349 @ SV361 @ SY686 ) ) )
= $true )
| ( ( ! [SY687: $i] :
( ( ( tail_of @ SY687 )
!= ( tail_of @ SV367 ) )
| ( ( head_of @ SY687 )
!= ( head_of @ SV388 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1899]) ).
thf(1928,plain,
! [SV361: $i,SV349: $i,SV396: $i,SV389: $i,SV367: $i] :
( ( ~ ( precedes @ SV367 @ SV389 @ SV396 )
| ~ ( shortest_path @ SV349 @ SV361 @ SV396 )
| ~ ( precedes @ SV389 @ SV367 @ SV396 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1900]) ).
thf(1929,plain,
! [SV362: $i,SV350: $i] :
( ( ! [SY655: $i,SY656: $i] :
( ~ ( on_path @ SY656 @ SY655 )
| ~ ( path @ SV350 @ SV362 @ SY655 )
| ( edge @ SY656 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1901]) ).
thf(1930,plain,
! [SV362: $i,SV350: $i] :
( ( ! [SY657: $i,SY658: $i] :
( ~ ( on_path @ SY658 @ SY657 )
| ~ ( path @ SV350 @ SV362 @ SY657 )
| ( in_path @ ( head_of @ SY658 ) @ SY657 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1902]) ).
thf(1931,plain,
! [SV362: $i,SV350: $i,SV382: $i,SV390: $i] :
( ( ( ~ ( on_path @ SV390 @ SV382 )
| ~ ( path @ SV350 @ SV362 @ SV382 ) )
= $true )
| ( ( in_path @ ( tail_of @ SV390 ) @ SV382 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1903]) ).
thf(1932,plain,
! [SV351: $i] :
( ( ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV351 ) @ SV351 )
| ~ ( on_path @ ( sK7_SY80 @ SV351 ) @ SV351 ) ) )
= $false )
| ( ( ! [SY595: $i,SY596: $i] :
~ ( path @ SY595 @ SY596 @ SV351 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV351 )
= ( number_of_in @ triangles @ SV351 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1904]) ).
thf(1933,plain,
! [SV351: $i] :
( ( ( ~ ( sequential @ ( sK6_E1 @ SV351 ) @ ( sK7_SY80 @ SV351 ) ) )
= $false )
| ( ( ! [SY595: $i,SY596: $i] :
~ ( path @ SY595 @ SY596 @ SV351 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV351 )
= ( number_of_in @ triangles @ SV351 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1904]) ).
thf(1934,plain,
! [SV391: $i,SV351: $i] :
( ( ( triangle @ ( sK6_E1 @ SV351 ) @ ( sK7_SY80 @ SV351 ) @ SV391 )
= $false )
| ( ( ! [SY595: $i,SY596: $i] :
~ ( path @ SY595 @ SY596 @ SV351 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV351 )
= ( number_of_in @ triangles @ SV351 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1905]) ).
thf(1935,plain,
! [SV374: $i,SV368: $i] :
( ( ( vertex @ SV368 )
= $false )
| ( ( ~ ( vertex @ SV374 ) )
= $true )
| ( ( SV368 = SV374 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV368
!= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
!= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
!= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
!= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV368
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
| ~ ( ( SV368
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) ) )
| ~ ~ ( ~ ( ( SV374
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
| ~ ( ( SV374
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV374 @ SV368 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1906]) ).
thf(1936,plain,
! [SV383: $i,SV379: $i,SV352: $i] :
( ( ( ~ ( edge @ SV352 )
| ~ ( edge @ SV379 )
| ~ ( edge @ SV383 )
| ~ ( sequential @ SV352 @ SV379 )
| ~ ( sequential @ SV379 @ SV383 ) )
= $true )
| ( ( ~ ( sequential @ SV383 @ SV352 ) )
= $true )
| ( ( triangle @ SV352 @ SV379 @ SV383 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1907]) ).
thf(1937,plain,
! [SV352: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY599: $i,SY600: $i] :
~ ( triangle @ SV352 @ SY599 @ SY600 )
| ( edge @ SV352 ) )
| ~ ! [SY601: $i] :
( ! [SY602: $i] :
~ ( triangle @ SV352 @ SY601 @ SY602 )
| ( edge @ SY601 ) ) )
| ~ ! [SY603: $i,SY604: $i] :
( ~ ( triangle @ SV352 @ SY603 @ SY604 )
| ( edge @ SY604 ) ) )
| ~ ! [SY605: $i] :
( ! [SY606: $i] :
~ ( triangle @ SV352 @ SY605 @ SY606 )
| ( sequential @ SV352 @ SY605 ) ) )
| ~ ! [SY607: $i,SY608: $i] :
( ~ ( triangle @ SV352 @ SY607 @ SY608 )
| ( sequential @ SY607 @ SY608 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1908]) ).
thf(1938,plain,
! [SV397: $i,SV352: $i] :
( ( ! [SY690: $i] :
( ~ ( triangle @ SV352 @ SV397 @ SY690 )
| ( sequential @ SY690 @ SV352 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1909]) ).
thf(1939,plain,
! [SV375: $i,SV369: $i,SV353: $i] :
( ( ( ! [SY613: $i,SY614: $i] :
( ~ ( on_path @ SY613 @ SV353 )
| ~ ( on_path @ SY614 @ SV353 )
| ! [SY615: $i] :
( ~ ( precedes @ SY615 @ SY614 @ SV353 )
| ~ ( sequential @ SY613 @ SY615 ) )
| ( precedes @ SY613 @ SY614 @ SV353 ) ) )
= $true )
| ( ( path @ SV369 @ SV375 @ SV353 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1910]) ).
thf(1940,plain,
! [SV375: $i,SV369: $i,SV353: $i] :
( ( ( ! [SY616: $i,SY617: $i] :
( ~ ( on_path @ SY616 @ SV353 )
| ~ ( on_path @ SY617 @ SV353 )
| ~ ( sequential @ SY616 @ SY617 )
| ( precedes @ SY616 @ SY617 @ SV353 ) ) )
= $true )
| ( ( path @ SV369 @ SV375 @ SV353 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1911]) ).
thf(1941,plain,
! [SV376: $i,SV370: $i,SV354: $i] :
( ( ( ~ ( ~ ! [SY620: $i] :
( ! [SY621: $i] :
~ ( precedes @ SY620 @ SY621 @ SV354 )
| ( on_path @ SY620 @ SV354 ) )
| ~ ! [SY622: $i,SY623: $i] :
( ~ ( precedes @ SY622 @ SY623 @ SV354 )
| ( on_path @ SY623 @ SV354 ) ) ) )
= $true )
| ( ( path @ SV370 @ SV376 @ SV354 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1912]) ).
thf(1942,plain,
! [SV376: $i,SV370: $i,SV354: $i] :
( ( ( ~ ( ~ ! [SY624: $i,SY625: $i] :
( ~ ( precedes @ SY624 @ SY625 @ SV354 )
| ! [SY626: $i] :
( ~ ( precedes @ SY626 @ SY625 @ SV354 )
| ~ ( sequential @ SY624 @ SY626 ) )
| ~ ( sequential @ SY624 @ SY625 ) )
| ~ ! [SY627: $i,SY628: $i] :
( ~ ( precedes @ SY627 @ SY628 @ SV354 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY628 @ SY627 @ SV354 ) @ SY628 @ SV354 )
| ~ ( sequential @ SY627 @ ( sK9_E3 @ SY628 @ SY627 @ SV354 ) ) )
| ( sequential @ SY627 @ SY628 ) ) ) )
= $true )
| ( ( path @ SV370 @ SV376 @ SV354 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1913]) ).
thf(1943,plain,
! [SV363: $i,SV355: $i,SV384: $i,SV392: $i] :
( ( ( ~ ( in_path @ SV392 @ SV384 )
| ~ ( path @ SV355 @ SV363 @ SV384 ) )
= $true )
| ( ( ~ ( ~ ( on_path @ ( sK10_E @ SV392 @ SV384 @ SV363 @ SV355 ) @ SV384 )
| ~ ( ( SV392
= ( head_of @ ( sK10_E @ SV392 @ SV384 @ SV363 @ SV355 ) ) )
| ( SV392
= ( tail_of @ ( sK10_E @ SV392 @ SV384 @ SV363 @ SV355 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1914]) ).
thf(1944,plain,
! [SV363: $i,SV355: $i,SV385: $i,SV393: $i] :
( ( ( ~ ( in_path @ SV393 @ SV385 )
| ~ ( path @ SV355 @ SV363 @ SV385 ) )
= $true )
| ( ( vertex @ SV393 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1915]) ).
thf(1945,plain,
! [SV386: $i,SV380: $i,SV356: $i] :
( ( ( ~ ( ~ ( path @ SV356 @ SV380 @ ( sK8_P @ SV386 @ SV380 @ SV356 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SV386 ) @ ( length_of @ ( sK8_P @ SV386 @ SV380 @ SV356 ) ) ) ) )
= $true )
| ( ( ( SV356 = SV380 )
| ~ ( path @ SV356 @ SV380 @ SV386 ) )
= $true )
| ( ( shortest_path @ SV356 @ SV380 @ SV386 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1916]) ).
thf(1946,plain,
! [SV398: $i,SV356: $i] :
( ( ! [SY691: $i] :
( ~ ( shortest_path @ SV356 @ SV398 @ SY691 )
| ! [SY692: $i] :
( ~ ( path @ SV356 @ SV398 @ SY692 )
| ( less_or_equal @ ( length_of @ SY691 ) @ ( length_of @ SY692 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1917]) ).
thf(1947,plain,
! [SV356: $i] :
( ( ~ ! [SY639: $i] :
( ! [SY640: $i] :
~ ( shortest_path @ SV356 @ SY639 @ SY640 )
| ( SV356 != SY639 ) )
| ~ ! [SY641: $i,SY642: $i] :
( ~ ( shortest_path @ SV356 @ SY641 @ SY642 )
| ( path @ SV356 @ SY641 @ SY642 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1918]) ).
thf(1948,plain,
! [SV399: $i,SV347: $i] :
( ( ( ! [SY693: $i] :
~ ( path @ SV347 @ SV399 @ SY693 ) )
= $true )
| ( ( vertex @ SV347 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1919]) ).
thf(1949,plain,
! [SV394: $i,SV347: $i] :
( ( ( ! [SY689: $i] :
~ ( path @ SV347 @ SV394 @ SY689 ) )
= $true )
| ( ( vertex @ SV394 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1920]) ).
thf(1950,plain,
! [SV377: $i,SV381: $i,SV347: $i] :
( ( ( ~ ~ ( ( SV347
!= ( tail_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( edge @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
| ~ ~ ( ~ ( ( SV377
!= ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
| ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ empty ) )
| ! [SY681: $i] :
( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ SY681 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ SY681 ) ) )
| ~ ~ ( ~ ( ( SV377
= ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ ( sK13_SY84 @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ ( sK13_SY84 @ SV381 @ SV377 @ SV347 ) ) ) )
| ~ ( ( SV381
= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ empty ) )
| ~ ( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ ( sK12_SY85 @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ ( sK12_SY85 @ SV381 @ SV377 @ SV347 ) ) ) ) ) ) )
= $false )
| ( ( path @ SV347 @ SV377 @ SV381 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1921]) ).
thf(1951,plain,
! [SV366: $i,SV360: $i,SV348: $i] :
( ( ( ~ ! [SY665: $i] :
( ( SV348
!= ( tail_of @ SY665 ) )
| ~ ( edge @ SY665 )
| ( SV360
!= ( head_of @ SY665 ) )
| ( SV366
!= ( path_cons @ SY665 @ empty ) ) )
| ~ ! [SY666: $i] :
( ( SV348
!= ( tail_of @ SY666 ) )
| ~ ( edge @ SY666 )
| ! [SY667: $i] :
( ( SV366
!= ( path_cons @ SY666 @ SY667 ) )
| ~ ( path @ ( head_of @ SY666 ) @ SV360 @ SY667 ) ) ) )
= $false )
| ( ( vertex @ SV348 )
= $false )
| ( ( vertex @ SV360 )
= $false )
| ( ( path @ SV348 @ SV360 @ SV366 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1922]) ).
thf(1952,plain,
! [SV378: $i,SV371: $i] :
( ( ( ~ ( edge @ SV371 ) )
= $true )
| ( ( ~ ( edge @ SV378 ) )
= $true )
| ( ( SV371 = SV378 )
= $true )
| ( ( ( ( head_of @ SV371 )
!= ( tail_of @ SV378 ) ) )
= $true )
| ( ( sequential @ SV371 @ SV378 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1923]) ).
thf(1953,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1924]) ).
thf(1954,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1925]) ).
thf(1955,plain,
! [SV395: $i,SV387: $i] :
( ( ( ~ ( sequential @ SV387 @ SV395 ) )
= $true )
| ( ( ( head_of @ SV387 )
= ( tail_of @ SV395 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1926]) ).
thf(1956,plain,
! [SV361: $i,SV349: $i,SV400: $i,SV388: $i,SV367: $i] :
( ( ( ~ ( precedes @ SV367 @ SV388 @ SV400 )
| ~ ( shortest_path @ SV349 @ SV361 @ SV400 ) )
= $true )
| ( ( ! [SY687: $i] :
( ( ( tail_of @ SY687 )
!= ( tail_of @ SV367 ) )
| ( ( head_of @ SY687 )
!= ( head_of @ SV388 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1927]) ).
thf(1957,plain,
! [SV361: $i,SV349: $i,SV396: $i,SV389: $i,SV367: $i] :
( ( ( ~ ( precedes @ SV367 @ SV389 @ SV396 )
| ~ ( shortest_path @ SV349 @ SV361 @ SV396 ) )
= $true )
| ( ( ~ ( precedes @ SV389 @ SV367 @ SV396 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1928]) ).
thf(1958,plain,
! [SV362: $i,SV350: $i,SV401: $i] :
( ( ! [SY694: $i] :
( ~ ( on_path @ SY694 @ SV401 )
| ~ ( path @ SV350 @ SV362 @ SV401 )
| ( edge @ SY694 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1929]) ).
thf(1959,plain,
! [SV362: $i,SV350: $i,SV402: $i] :
( ( ! [SY695: $i] :
( ~ ( on_path @ SY695 @ SV402 )
| ~ ( path @ SV350 @ SV362 @ SV402 )
| ( in_path @ ( head_of @ SY695 ) @ SV402 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1930]) ).
thf(1960,plain,
! [SV362: $i,SV350: $i,SV382: $i,SV390: $i] :
( ( ( ~ ( on_path @ SV390 @ SV382 ) )
= $true )
| ( ( ~ ( path @ SV350 @ SV362 @ SV382 ) )
= $true )
| ( ( in_path @ ( tail_of @ SV390 ) @ SV382 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1931]) ).
thf(1961,plain,
! [SV351: $i] :
( ( ( ~ ( ~ ( on_path @ ( sK6_E1 @ SV351 ) @ SV351 )
| ~ ( on_path @ ( sK7_SY80 @ SV351 ) @ SV351 ) ) )
= $true )
| ( ( ! [SY595: $i,SY596: $i] :
~ ( path @ SY595 @ SY596 @ SV351 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV351 )
= ( number_of_in @ triangles @ SV351 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1932]) ).
thf(1962,plain,
! [SV351: $i] :
( ( ( sequential @ ( sK6_E1 @ SV351 ) @ ( sK7_SY80 @ SV351 ) )
= $true )
| ( ( ! [SY595: $i,SY596: $i] :
~ ( path @ SY595 @ SY596 @ SV351 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV351 )
= ( number_of_in @ triangles @ SV351 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1933]) ).
thf(1963,plain,
! [SV391: $i,SV351: $i,SV403: $i] :
( ( ( ! [SY696: $i] :
~ ( path @ SV403 @ SY696 @ SV351 ) )
= $true )
| ( ( triangle @ ( sK6_E1 @ SV351 ) @ ( sK7_SY80 @ SV351 ) @ SV391 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV351 )
= ( number_of_in @ triangles @ SV351 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1934]) ).
thf(1964,plain,
! [SV368: $i,SV374: $i] :
( ( ( vertex @ SV374 )
= $false )
| ( ( vertex @ SV368 )
= $false )
| ( ( SV368 = SV374 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV368
!= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
!= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
!= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
!= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV368
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
| ~ ( ( SV368
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) ) )
| ~ ~ ( ~ ( ( SV374
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
| ~ ( ( SV374
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV374 @ SV368 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1935]) ).
thf(1965,plain,
! [SV383: $i,SV379: $i,SV352: $i] :
( ( ( ~ ( edge @ SV352 )
| ~ ( edge @ SV379 )
| ~ ( edge @ SV383 )
| ~ ( sequential @ SV352 @ SV379 ) )
= $true )
| ( ( ~ ( sequential @ SV379 @ SV383 ) )
= $true )
| ( ( ~ ( sequential @ SV383 @ SV352 ) )
= $true )
| ( ( triangle @ SV352 @ SV379 @ SV383 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1936]) ).
thf(1966,plain,
! [SV352: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY599: $i,SY600: $i] :
~ ( triangle @ SV352 @ SY599 @ SY600 )
| ( edge @ SV352 ) )
| ~ ! [SY601: $i] :
( ! [SY602: $i] :
~ ( triangle @ SV352 @ SY601 @ SY602 )
| ( edge @ SY601 ) ) )
| ~ ! [SY603: $i,SY604: $i] :
( ~ ( triangle @ SV352 @ SY603 @ SY604 )
| ( edge @ SY604 ) ) )
| ~ ! [SY605: $i] :
( ! [SY606: $i] :
~ ( triangle @ SV352 @ SY605 @ SY606 )
| ( sequential @ SV352 @ SY605 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1937]) ).
thf(1967,plain,
! [SV352: $i] :
( ( ~ ! [SY607: $i,SY608: $i] :
( ~ ( triangle @ SV352 @ SY607 @ SY608 )
| ( sequential @ SY607 @ SY608 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1937]) ).
thf(1968,plain,
! [SV404: $i,SV397: $i,SV352: $i] :
( ( ~ ( triangle @ SV352 @ SV397 @ SV404 )
| ( sequential @ SV404 @ SV352 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1938]) ).
thf(1969,plain,
! [SV375: $i,SV369: $i,SV353: $i,SV405: $i] :
( ( ( ! [SY697: $i] :
( ~ ( on_path @ SV405 @ SV353 )
| ~ ( on_path @ SY697 @ SV353 )
| ! [SY698: $i] :
( ~ ( precedes @ SY698 @ SY697 @ SV353 )
| ~ ( sequential @ SV405 @ SY698 ) )
| ( precedes @ SV405 @ SY697 @ SV353 ) ) )
= $true )
| ( ( path @ SV369 @ SV375 @ SV353 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1939]) ).
thf(1970,plain,
! [SV375: $i,SV369: $i,SV353: $i,SV406: $i] :
( ( ( ! [SY699: $i] :
( ~ ( on_path @ SV406 @ SV353 )
| ~ ( on_path @ SY699 @ SV353 )
| ~ ( sequential @ SV406 @ SY699 )
| ( precedes @ SV406 @ SY699 @ SV353 ) ) )
= $true )
| ( ( path @ SV369 @ SV375 @ SV353 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1940]) ).
thf(1971,plain,
! [SV376: $i,SV370: $i,SV354: $i] :
( ( ( ~ ! [SY620: $i] :
( ! [SY621: $i] :
~ ( precedes @ SY620 @ SY621 @ SV354 )
| ( on_path @ SY620 @ SV354 ) )
| ~ ! [SY622: $i,SY623: $i] :
( ~ ( precedes @ SY622 @ SY623 @ SV354 )
| ( on_path @ SY623 @ SV354 ) ) )
= $false )
| ( ( path @ SV370 @ SV376 @ SV354 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1941]) ).
thf(1972,plain,
! [SV376: $i,SV370: $i,SV354: $i] :
( ( ( ~ ! [SY624: $i,SY625: $i] :
( ~ ( precedes @ SY624 @ SY625 @ SV354 )
| ! [SY626: $i] :
( ~ ( precedes @ SY626 @ SY625 @ SV354 )
| ~ ( sequential @ SY624 @ SY626 ) )
| ~ ( sequential @ SY624 @ SY625 ) )
| ~ ! [SY627: $i,SY628: $i] :
( ~ ( precedes @ SY627 @ SY628 @ SV354 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY628 @ SY627 @ SV354 ) @ SY628 @ SV354 )
| ~ ( sequential @ SY627 @ ( sK9_E3 @ SY628 @ SY627 @ SV354 ) ) )
| ( sequential @ SY627 @ SY628 ) ) )
= $false )
| ( ( path @ SV370 @ SV376 @ SV354 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1942]) ).
thf(1973,plain,
! [SV363: $i,SV355: $i,SV384: $i,SV392: $i] :
( ( ( ~ ( in_path @ SV392 @ SV384 ) )
= $true )
| ( ( ~ ( path @ SV355 @ SV363 @ SV384 ) )
= $true )
| ( ( ~ ( ~ ( on_path @ ( sK10_E @ SV392 @ SV384 @ SV363 @ SV355 ) @ SV384 )
| ~ ( ( SV392
= ( head_of @ ( sK10_E @ SV392 @ SV384 @ SV363 @ SV355 ) ) )
| ( SV392
= ( tail_of @ ( sK10_E @ SV392 @ SV384 @ SV363 @ SV355 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1943]) ).
thf(1974,plain,
! [SV363: $i,SV355: $i,SV385: $i,SV393: $i] :
( ( ( ~ ( in_path @ SV393 @ SV385 ) )
= $true )
| ( ( ~ ( path @ SV355 @ SV363 @ SV385 ) )
= $true )
| ( ( vertex @ SV393 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1944]) ).
thf(1975,plain,
! [SV386: $i,SV380: $i,SV356: $i] :
( ( ( ~ ( path @ SV356 @ SV380 @ ( sK8_P @ SV386 @ SV380 @ SV356 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SV386 ) @ ( length_of @ ( sK8_P @ SV386 @ SV380 @ SV356 ) ) ) )
= $false )
| ( ( ( SV356 = SV380 )
| ~ ( path @ SV356 @ SV380 @ SV386 ) )
= $true )
| ( ( shortest_path @ SV356 @ SV380 @ SV386 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1945]) ).
thf(1976,plain,
! [SV407: $i,SV398: $i,SV356: $i] :
( ( ~ ( shortest_path @ SV356 @ SV398 @ SV407 )
| ! [SY700: $i] :
( ~ ( path @ SV356 @ SV398 @ SY700 )
| ( less_or_equal @ ( length_of @ SV407 ) @ ( length_of @ SY700 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1946]) ).
thf(1977,plain,
! [SV356: $i] :
( ( ~ ! [SY639: $i] :
( ! [SY640: $i] :
~ ( shortest_path @ SV356 @ SY639 @ SY640 )
| ( SV356 != SY639 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1947]) ).
thf(1978,plain,
! [SV356: $i] :
( ( ~ ! [SY641: $i,SY642: $i] :
( ~ ( shortest_path @ SV356 @ SY641 @ SY642 )
| ( path @ SV356 @ SY641 @ SY642 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1947]) ).
thf(1979,plain,
! [SV408: $i,SV399: $i,SV347: $i] :
( ( ( ~ ( path @ SV347 @ SV399 @ SV408 ) )
= $true )
| ( ( vertex @ SV347 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1948]) ).
thf(1980,plain,
! [SV409: $i,SV394: $i,SV347: $i] :
( ( ( ~ ( path @ SV347 @ SV394 @ SV409 ) )
= $true )
| ( ( vertex @ SV394 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1949]) ).
thf(1981,plain,
! [SV377: $i,SV381: $i,SV347: $i] :
( ( ( ~ ~ ( ( SV347
!= ( tail_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( edge @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) ) )
= $false )
| ( ( path @ SV347 @ SV377 @ SV381 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1950]) ).
thf(1982,plain,
! [SV347: $i,SV381: $i,SV377: $i] :
( ( ( ~ ~ ( ~ ( ( SV377
!= ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
| ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ empty ) )
| ! [SY681: $i] :
( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ SY681 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ SY681 ) ) )
| ~ ~ ( ~ ( ( SV377
= ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ ( sK13_SY84 @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ ( sK13_SY84 @ SV381 @ SV377 @ SV347 ) ) ) )
| ~ ( ( SV381
= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ empty ) )
| ~ ( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ ( sK12_SY85 @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ ( sK12_SY85 @ SV381 @ SV377 @ SV347 ) ) ) ) ) ) )
= $false )
| ( ( path @ SV347 @ SV377 @ SV381 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1950]) ).
thf(1983,plain,
! [SV366: $i,SV360: $i,SV348: $i] :
( ( ( ~ ! [SY665: $i] :
( ( SV348
!= ( tail_of @ SY665 ) )
| ~ ( edge @ SY665 )
| ( SV360
!= ( head_of @ SY665 ) )
| ( SV366
!= ( path_cons @ SY665 @ empty ) ) ) )
= $false )
| ( ( vertex @ SV348 )
= $false )
| ( ( vertex @ SV360 )
= $false )
| ( ( path @ SV348 @ SV360 @ SV366 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1951]) ).
thf(1984,plain,
! [SV360: $i,SV366: $i,SV348: $i] :
( ( ( ~ ! [SY666: $i] :
( ( SV348
!= ( tail_of @ SY666 ) )
| ~ ( edge @ SY666 )
| ! [SY667: $i] :
( ( SV366
!= ( path_cons @ SY666 @ SY667 ) )
| ~ ( path @ ( head_of @ SY666 ) @ SV360 @ SY667 ) ) ) )
= $false )
| ( ( vertex @ SV348 )
= $false )
| ( ( vertex @ SV360 )
= $false )
| ( ( path @ SV348 @ SV360 @ SV366 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1951]) ).
thf(1985,plain,
! [SV378: $i,SV371: $i] :
( ( ( edge @ SV371 )
= $false )
| ( ( ~ ( edge @ SV378 ) )
= $true )
| ( ( SV371 = SV378 )
= $true )
| ( ( ( ( head_of @ SV371 )
!= ( tail_of @ SV378 ) ) )
= $true )
| ( ( sequential @ SV371 @ SV378 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1952]) ).
thf(1986,plain,
! [SV410: $i] :
( ( ! [SY701: $i] :
( ~ ( sequential @ SV410 @ SY701 )
| ( SV410 != SY701 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1953]) ).
thf(1987,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1954]) ).
thf(1988,plain,
! [SV395: $i,SV387: $i] :
( ( ( sequential @ SV387 @ SV395 )
= $false )
| ( ( ( head_of @ SV387 )
= ( tail_of @ SV395 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1955]) ).
thf(1989,plain,
! [SV361: $i,SV349: $i,SV400: $i,SV388: $i,SV367: $i] :
( ( ( ~ ( precedes @ SV367 @ SV388 @ SV400 ) )
= $true )
| ( ( ~ ( shortest_path @ SV349 @ SV361 @ SV400 ) )
= $true )
| ( ( ! [SY687: $i] :
( ( ( tail_of @ SY687 )
!= ( tail_of @ SV367 ) )
| ( ( head_of @ SY687 )
!= ( head_of @ SV388 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1956]) ).
thf(1990,plain,
! [SV361: $i,SV349: $i,SV396: $i,SV389: $i,SV367: $i] :
( ( ( ~ ( precedes @ SV367 @ SV389 @ SV396 ) )
= $true )
| ( ( ~ ( shortest_path @ SV349 @ SV361 @ SV396 ) )
= $true )
| ( ( ~ ( precedes @ SV389 @ SV367 @ SV396 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1957]) ).
thf(1991,plain,
! [SV362: $i,SV350: $i,SV401: $i,SV411: $i] :
( ( ~ ( on_path @ SV411 @ SV401 )
| ~ ( path @ SV350 @ SV362 @ SV401 )
| ( edge @ SV411 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1958]) ).
thf(1992,plain,
! [SV362: $i,SV350: $i,SV402: $i,SV412: $i] :
( ( ~ ( on_path @ SV412 @ SV402 )
| ~ ( path @ SV350 @ SV362 @ SV402 )
| ( in_path @ ( head_of @ SV412 ) @ SV402 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1959]) ).
thf(1993,plain,
! [SV362: $i,SV350: $i,SV382: $i,SV390: $i] :
( ( ( on_path @ SV390 @ SV382 )
= $false )
| ( ( ~ ( path @ SV350 @ SV362 @ SV382 ) )
= $true )
| ( ( in_path @ ( tail_of @ SV390 ) @ SV382 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1960]) ).
thf(1994,plain,
! [SV351: $i] :
( ( ( ~ ( on_path @ ( sK6_E1 @ SV351 ) @ SV351 )
| ~ ( on_path @ ( sK7_SY80 @ SV351 ) @ SV351 ) )
= $false )
| ( ( ! [SY595: $i,SY596: $i] :
~ ( path @ SY595 @ SY596 @ SV351 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV351 )
= ( number_of_in @ triangles @ SV351 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1961]) ).
thf(1995,plain,
! [SV351: $i,SV413: $i] :
( ( ( ! [SY702: $i] :
~ ( path @ SV413 @ SY702 @ SV351 ) )
= $true )
| ( ( sequential @ ( sK6_E1 @ SV351 ) @ ( sK7_SY80 @ SV351 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV351 )
= ( number_of_in @ triangles @ SV351 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1962]) ).
thf(1996,plain,
! [SV391: $i,SV351: $i,SV414: $i,SV403: $i] :
( ( ( ~ ( path @ SV403 @ SV414 @ SV351 ) )
= $true )
| ( ( triangle @ ( sK6_E1 @ SV351 ) @ ( sK7_SY80 @ SV351 ) @ SV391 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV351 )
= ( number_of_in @ triangles @ SV351 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1963]) ).
thf(1997,plain,
! [SV374: $i,SV368: $i] :
( ( ( ~ ~ ( ~ ( ( SV368
!= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
!= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
!= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
!= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV368
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
| ~ ( ( SV368
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) ) )
| ~ ~ ( ~ ( ( SV374
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
| ~ ( ( SV374
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV374 @ SV368 ) ) )
= $false )
| ( ( SV368 = SV374 )
= $true )
| ( ( vertex @ SV368 )
= $false )
| ( ( vertex @ SV374 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1964]) ).
thf(1998,plain,
! [SV383: $i,SV379: $i,SV352: $i] :
( ( ( ~ ( edge @ SV352 )
| ~ ( edge @ SV379 )
| ~ ( edge @ SV383 ) )
= $true )
| ( ( ~ ( sequential @ SV352 @ SV379 ) )
= $true )
| ( ( ~ ( sequential @ SV379 @ SV383 ) )
= $true )
| ( ( ~ ( sequential @ SV383 @ SV352 ) )
= $true )
| ( ( triangle @ SV352 @ SV379 @ SV383 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1965]) ).
thf(1999,plain,
! [SV352: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY599: $i,SY600: $i] :
~ ( triangle @ SV352 @ SY599 @ SY600 )
| ( edge @ SV352 ) )
| ~ ! [SY601: $i] :
( ! [SY602: $i] :
~ ( triangle @ SV352 @ SY601 @ SY602 )
| ( edge @ SY601 ) ) )
| ~ ! [SY603: $i,SY604: $i] :
( ~ ( triangle @ SV352 @ SY603 @ SY604 )
| ( edge @ SY604 ) ) )
| ~ ! [SY605: $i] :
( ! [SY606: $i] :
~ ( triangle @ SV352 @ SY605 @ SY606 )
| ( sequential @ SV352 @ SY605 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1966]) ).
thf(2000,plain,
! [SV352: $i] :
( ( ! [SY607: $i,SY608: $i] :
( ~ ( triangle @ SV352 @ SY607 @ SY608 )
| ( sequential @ SY607 @ SY608 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1967]) ).
thf(2001,plain,
! [SV404: $i,SV397: $i,SV352: $i] :
( ( ( ~ ( triangle @ SV352 @ SV397 @ SV404 ) )
= $true )
| ( ( sequential @ SV404 @ SV352 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1968]) ).
thf(2002,plain,
! [SV375: $i,SV369: $i,SV415: $i,SV353: $i,SV405: $i] :
( ( ( ~ ( on_path @ SV405 @ SV353 )
| ~ ( on_path @ SV415 @ SV353 )
| ! [SY703: $i] :
( ~ ( precedes @ SY703 @ SV415 @ SV353 )
| ~ ( sequential @ SV405 @ SY703 ) )
| ( precedes @ SV405 @ SV415 @ SV353 ) )
= $true )
| ( ( path @ SV369 @ SV375 @ SV353 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1969]) ).
thf(2003,plain,
! [SV375: $i,SV369: $i,SV416: $i,SV353: $i,SV406: $i] :
( ( ( ~ ( on_path @ SV406 @ SV353 )
| ~ ( on_path @ SV416 @ SV353 )
| ~ ( sequential @ SV406 @ SV416 )
| ( precedes @ SV406 @ SV416 @ SV353 ) )
= $true )
| ( ( path @ SV369 @ SV375 @ SV353 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1970]) ).
thf(2004,plain,
! [SV376: $i,SV370: $i,SV354: $i] :
( ( ( ~ ! [SY620: $i] :
( ! [SY621: $i] :
~ ( precedes @ SY620 @ SY621 @ SV354 )
| ( on_path @ SY620 @ SV354 ) ) )
= $false )
| ( ( path @ SV370 @ SV376 @ SV354 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1971]) ).
thf(2005,plain,
! [SV376: $i,SV370: $i,SV354: $i] :
( ( ( ~ ! [SY622: $i,SY623: $i] :
( ~ ( precedes @ SY622 @ SY623 @ SV354 )
| ( on_path @ SY623 @ SV354 ) ) )
= $false )
| ( ( path @ SV370 @ SV376 @ SV354 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1971]) ).
thf(2006,plain,
! [SV376: $i,SV370: $i,SV354: $i] :
( ( ( ~ ! [SY624: $i,SY625: $i] :
( ~ ( precedes @ SY624 @ SY625 @ SV354 )
| ! [SY626: $i] :
( ~ ( precedes @ SY626 @ SY625 @ SV354 )
| ~ ( sequential @ SY624 @ SY626 ) )
| ~ ( sequential @ SY624 @ SY625 ) ) )
= $false )
| ( ( path @ SV370 @ SV376 @ SV354 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1972]) ).
thf(2007,plain,
! [SV376: $i,SV370: $i,SV354: $i] :
( ( ( ~ ! [SY627: $i,SY628: $i] :
( ~ ( precedes @ SY627 @ SY628 @ SV354 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY628 @ SY627 @ SV354 ) @ SY628 @ SV354 )
| ~ ( sequential @ SY627 @ ( sK9_E3 @ SY628 @ SY627 @ SV354 ) ) )
| ( sequential @ SY627 @ SY628 ) ) )
= $false )
| ( ( path @ SV370 @ SV376 @ SV354 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1972]) ).
thf(2008,plain,
! [SV363: $i,SV355: $i,SV384: $i,SV392: $i] :
( ( ( in_path @ SV392 @ SV384 )
= $false )
| ( ( ~ ( path @ SV355 @ SV363 @ SV384 ) )
= $true )
| ( ( ~ ( ~ ( on_path @ ( sK10_E @ SV392 @ SV384 @ SV363 @ SV355 ) @ SV384 )
| ~ ( ( SV392
= ( head_of @ ( sK10_E @ SV392 @ SV384 @ SV363 @ SV355 ) ) )
| ( SV392
= ( tail_of @ ( sK10_E @ SV392 @ SV384 @ SV363 @ SV355 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1973]) ).
thf(2009,plain,
! [SV363: $i,SV355: $i,SV385: $i,SV393: $i] :
( ( ( in_path @ SV393 @ SV385 )
= $false )
| ( ( ~ ( path @ SV355 @ SV363 @ SV385 ) )
= $true )
| ( ( vertex @ SV393 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1974]) ).
thf(2010,plain,
! [SV386: $i,SV380: $i,SV356: $i] :
( ( ( ~ ( path @ SV356 @ SV380 @ ( sK8_P @ SV386 @ SV380 @ SV356 ) ) )
= $false )
| ( ( ( SV356 = SV380 )
| ~ ( path @ SV356 @ SV380 @ SV386 ) )
= $true )
| ( ( shortest_path @ SV356 @ SV380 @ SV386 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1975]) ).
thf(2011,plain,
! [SV356: $i,SV380: $i,SV386: $i] :
( ( ( ~ ~ ( less_or_equal @ ( length_of @ SV386 ) @ ( length_of @ ( sK8_P @ SV386 @ SV380 @ SV356 ) ) ) )
= $false )
| ( ( ( SV356 = SV380 )
| ~ ( path @ SV356 @ SV380 @ SV386 ) )
= $true )
| ( ( shortest_path @ SV356 @ SV380 @ SV386 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1975]) ).
thf(2012,plain,
! [SV407: $i,SV398: $i,SV356: $i] :
( ( ( ~ ( shortest_path @ SV356 @ SV398 @ SV407 ) )
= $true )
| ( ( ! [SY700: $i] :
( ~ ( path @ SV356 @ SV398 @ SY700 )
| ( less_or_equal @ ( length_of @ SV407 ) @ ( length_of @ SY700 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1976]) ).
thf(2013,plain,
! [SV356: $i] :
( ( ! [SY639: $i] :
( ! [SY640: $i] :
~ ( shortest_path @ SV356 @ SY639 @ SY640 )
| ( SV356 != SY639 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1977]) ).
thf(2014,plain,
! [SV356: $i] :
( ( ! [SY641: $i,SY642: $i] :
( ~ ( shortest_path @ SV356 @ SY641 @ SY642 )
| ( path @ SV356 @ SY641 @ SY642 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1978]) ).
thf(2015,plain,
! [SV408: $i,SV399: $i,SV347: $i] :
( ( ( path @ SV347 @ SV399 @ SV408 )
= $false )
| ( ( vertex @ SV347 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1979]) ).
thf(2016,plain,
! [SV409: $i,SV394: $i,SV347: $i] :
( ( ( path @ SV347 @ SV394 @ SV409 )
= $false )
| ( ( vertex @ SV394 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1980]) ).
thf(2017,plain,
! [SV377: $i,SV381: $i,SV347: $i] :
( ( ( ~ ( ( SV347
!= ( tail_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( edge @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) ) )
= $true )
| ( ( path @ SV347 @ SV377 @ SV381 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1981]) ).
thf(2018,plain,
! [SV347: $i,SV381: $i,SV377: $i] :
( ( ( ~ ( ~ ( ( SV377
!= ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
| ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ empty ) )
| ! [SY681: $i] :
( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ SY681 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ SY681 ) ) )
| ~ ~ ( ~ ( ( SV377
= ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ ( sK13_SY84 @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ ( sK13_SY84 @ SV381 @ SV377 @ SV347 ) ) ) )
| ~ ( ( SV381
= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ empty ) )
| ~ ( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ ( sK12_SY85 @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ ( sK12_SY85 @ SV381 @ SV377 @ SV347 ) ) ) ) ) ) )
= $true )
| ( ( path @ SV347 @ SV377 @ SV381 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1982]) ).
thf(2019,plain,
! [SV366: $i,SV360: $i,SV348: $i] :
( ( ( ! [SY665: $i] :
( ( SV348
!= ( tail_of @ SY665 ) )
| ~ ( edge @ SY665 )
| ( SV360
!= ( head_of @ SY665 ) )
| ( SV366
!= ( path_cons @ SY665 @ empty ) ) ) )
= $true )
| ( ( vertex @ SV348 )
= $false )
| ( ( vertex @ SV360 )
= $false )
| ( ( path @ SV348 @ SV360 @ SV366 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1983]) ).
thf(2020,plain,
! [SV360: $i,SV366: $i,SV348: $i] :
( ( ( ! [SY666: $i] :
( ( SV348
!= ( tail_of @ SY666 ) )
| ~ ( edge @ SY666 )
| ! [SY667: $i] :
( ( SV366
!= ( path_cons @ SY666 @ SY667 ) )
| ~ ( path @ ( head_of @ SY666 ) @ SV360 @ SY667 ) ) ) )
= $true )
| ( ( vertex @ SV348 )
= $false )
| ( ( vertex @ SV360 )
= $false )
| ( ( path @ SV348 @ SV360 @ SV366 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1984]) ).
thf(2021,plain,
! [SV371: $i,SV378: $i] :
( ( ( edge @ SV378 )
= $false )
| ( ( edge @ SV371 )
= $false )
| ( ( SV371 = SV378 )
= $true )
| ( ( ( ( head_of @ SV371 )
!= ( tail_of @ SV378 ) ) )
= $true )
| ( ( sequential @ SV371 @ SV378 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1985]) ).
thf(2022,plain,
! [SV417: $i,SV410: $i] :
( ( ~ ( sequential @ SV410 @ SV417 )
| ( SV410 != SV417 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1986]) ).
thf(2023,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1987]) ).
thf(2024,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1987]) ).
thf(2025,plain,
! [SV361: $i,SV349: $i,SV400: $i,SV388: $i,SV367: $i] :
( ( ( precedes @ SV367 @ SV388 @ SV400 )
= $false )
| ( ( ~ ( shortest_path @ SV349 @ SV361 @ SV400 ) )
= $true )
| ( ( ! [SY687: $i] :
( ( ( tail_of @ SY687 )
!= ( tail_of @ SV367 ) )
| ( ( head_of @ SY687 )
!= ( head_of @ SV388 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1989]) ).
thf(2026,plain,
! [SV361: $i,SV349: $i,SV396: $i,SV389: $i,SV367: $i] :
( ( ( precedes @ SV367 @ SV389 @ SV396 )
= $false )
| ( ( ~ ( shortest_path @ SV349 @ SV361 @ SV396 ) )
= $true )
| ( ( ~ ( precedes @ SV389 @ SV367 @ SV396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1990]) ).
thf(2027,plain,
! [SV362: $i,SV350: $i,SV401: $i,SV411: $i] :
( ( ( ~ ( on_path @ SV411 @ SV401 )
| ~ ( path @ SV350 @ SV362 @ SV401 ) )
= $true )
| ( ( edge @ SV411 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1991]) ).
thf(2028,plain,
! [SV362: $i,SV350: $i,SV402: $i,SV412: $i] :
( ( ( ~ ( on_path @ SV412 @ SV402 )
| ~ ( path @ SV350 @ SV362 @ SV402 ) )
= $true )
| ( ( in_path @ ( head_of @ SV412 ) @ SV402 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1992]) ).
thf(2029,plain,
! [SV390: $i,SV382: $i,SV362: $i,SV350: $i] :
( ( ( path @ SV350 @ SV362 @ SV382 )
= $false )
| ( ( on_path @ SV390 @ SV382 )
= $false )
| ( ( in_path @ ( tail_of @ SV390 ) @ SV382 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1993]) ).
thf(2030,plain,
! [SV351: $i] :
( ( ( ~ ( on_path @ ( sK6_E1 @ SV351 ) @ SV351 ) )
= $false )
| ( ( ! [SY595: $i,SY596: $i] :
~ ( path @ SY595 @ SY596 @ SV351 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV351 )
= ( number_of_in @ triangles @ SV351 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1994]) ).
thf(2031,plain,
! [SV351: $i] :
( ( ( ~ ( on_path @ ( sK7_SY80 @ SV351 ) @ SV351 ) )
= $false )
| ( ( ! [SY595: $i,SY596: $i] :
~ ( path @ SY595 @ SY596 @ SV351 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV351 )
= ( number_of_in @ triangles @ SV351 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1994]) ).
thf(2032,plain,
! [SV351: $i,SV418: $i,SV413: $i] :
( ( ( ~ ( path @ SV413 @ SV418 @ SV351 ) )
= $true )
| ( ( sequential @ ( sK6_E1 @ SV351 ) @ ( sK7_SY80 @ SV351 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV351 )
= ( number_of_in @ triangles @ SV351 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1995]) ).
thf(2033,plain,
! [SV391: $i,SV351: $i,SV414: $i,SV403: $i] :
( ( ( path @ SV403 @ SV414 @ SV351 )
= $false )
| ( ( triangle @ ( sK6_E1 @ SV351 ) @ ( sK7_SY80 @ SV351 ) @ SV391 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV351 )
= ( number_of_in @ triangles @ SV351 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1996]) ).
thf(2034,plain,
! [SV374: $i,SV368: $i] :
( ( ( ~ ~ ( ~ ( ( SV368
!= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
!= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
!= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
!= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV368
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
| ~ ( ( SV368
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) ) )
| ~ ~ ( ~ ( ( SV374
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
| ~ ( ( SV374
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) ) ) ) ) )
= $false )
| ( ( SV368 = SV374 )
= $true )
| ( ( vertex @ SV368 )
= $false )
| ( ( vertex @ SV374 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[1997]) ).
thf(2035,plain,
! [SV368: $i,SV374: $i] :
( ( ( ~ ( edge @ ( sK14_E @ SV374 @ SV368 ) ) )
= $false )
| ( ( SV368 = SV374 )
= $true )
| ( ( vertex @ SV368 )
= $false )
| ( ( vertex @ SV374 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[1997]) ).
thf(2036,plain,
! [SV383: $i,SV379: $i,SV352: $i] :
( ( ( ~ ( edge @ SV352 )
| ~ ( edge @ SV379 ) )
= $true )
| ( ( ~ ( edge @ SV383 ) )
= $true )
| ( ( ~ ( sequential @ SV352 @ SV379 ) )
= $true )
| ( ( ~ ( sequential @ SV379 @ SV383 ) )
= $true )
| ( ( ~ ( sequential @ SV383 @ SV352 ) )
= $true )
| ( ( triangle @ SV352 @ SV379 @ SV383 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1998]) ).
thf(2037,plain,
! [SV352: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( ! [SY599: $i,SY600: $i] :
~ ( triangle @ SV352 @ SY599 @ SY600 )
| ( edge @ SV352 ) )
| ~ ! [SY601: $i] :
( ! [SY602: $i] :
~ ( triangle @ SV352 @ SY601 @ SY602 )
| ( edge @ SY601 ) ) )
| ~ ! [SY603: $i,SY604: $i] :
( ~ ( triangle @ SV352 @ SY603 @ SY604 )
| ( edge @ SY604 ) ) )
| ~ ! [SY605: $i] :
( ! [SY606: $i] :
~ ( triangle @ SV352 @ SY605 @ SY606 )
| ( sequential @ SV352 @ SY605 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1999]) ).
thf(2038,plain,
! [SV419: $i,SV352: $i] :
( ( ! [SY704: $i] :
( ~ ( triangle @ SV352 @ SV419 @ SY704 )
| ( sequential @ SV419 @ SY704 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2000]) ).
thf(2039,plain,
! [SV404: $i,SV397: $i,SV352: $i] :
( ( ( triangle @ SV352 @ SV397 @ SV404 )
= $false )
| ( ( sequential @ SV404 @ SV352 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2001]) ).
thf(2040,plain,
! [SV375: $i,SV369: $i,SV415: $i,SV353: $i,SV405: $i] :
( ( ( ~ ( on_path @ SV405 @ SV353 )
| ~ ( on_path @ SV415 @ SV353 )
| ! [SY703: $i] :
( ~ ( precedes @ SY703 @ SV415 @ SV353 )
| ~ ( sequential @ SV405 @ SY703 ) ) )
= $true )
| ( ( precedes @ SV405 @ SV415 @ SV353 )
= $true )
| ( ( path @ SV369 @ SV375 @ SV353 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2002]) ).
thf(2041,plain,
! [SV375: $i,SV369: $i,SV416: $i,SV353: $i,SV406: $i] :
( ( ( ~ ( on_path @ SV406 @ SV353 )
| ~ ( on_path @ SV416 @ SV353 )
| ~ ( sequential @ SV406 @ SV416 ) )
= $true )
| ( ( precedes @ SV406 @ SV416 @ SV353 )
= $true )
| ( ( path @ SV369 @ SV375 @ SV353 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2003]) ).
thf(2042,plain,
! [SV376: $i,SV370: $i,SV354: $i] :
( ( ( ! [SY620: $i] :
( ! [SY621: $i] :
~ ( precedes @ SY620 @ SY621 @ SV354 )
| ( on_path @ SY620 @ SV354 ) ) )
= $true )
| ( ( path @ SV370 @ SV376 @ SV354 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2004]) ).
thf(2043,plain,
! [SV376: $i,SV370: $i,SV354: $i] :
( ( ( ! [SY622: $i,SY623: $i] :
( ~ ( precedes @ SY622 @ SY623 @ SV354 )
| ( on_path @ SY623 @ SV354 ) ) )
= $true )
| ( ( path @ SV370 @ SV376 @ SV354 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2005]) ).
thf(2044,plain,
! [SV376: $i,SV370: $i,SV354: $i] :
( ( ( ! [SY624: $i,SY625: $i] :
( ~ ( precedes @ SY624 @ SY625 @ SV354 )
| ! [SY626: $i] :
( ~ ( precedes @ SY626 @ SY625 @ SV354 )
| ~ ( sequential @ SY624 @ SY626 ) )
| ~ ( sequential @ SY624 @ SY625 ) ) )
= $true )
| ( ( path @ SV370 @ SV376 @ SV354 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2006]) ).
thf(2045,plain,
! [SV376: $i,SV370: $i,SV354: $i] :
( ( ( ! [SY627: $i,SY628: $i] :
( ~ ( precedes @ SY627 @ SY628 @ SV354 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY628 @ SY627 @ SV354 ) @ SY628 @ SV354 )
| ~ ( sequential @ SY627 @ ( sK9_E3 @ SY628 @ SY627 @ SV354 ) ) )
| ( sequential @ SY627 @ SY628 ) ) )
= $true )
| ( ( path @ SV370 @ SV376 @ SV354 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2007]) ).
thf(2046,plain,
! [SV392: $i,SV384: $i,SV363: $i,SV355: $i] :
( ( ( path @ SV355 @ SV363 @ SV384 )
= $false )
| ( ( in_path @ SV392 @ SV384 )
= $false )
| ( ( ~ ( ~ ( on_path @ ( sK10_E @ SV392 @ SV384 @ SV363 @ SV355 ) @ SV384 )
| ~ ( ( SV392
= ( head_of @ ( sK10_E @ SV392 @ SV384 @ SV363 @ SV355 ) ) )
| ( SV392
= ( tail_of @ ( sK10_E @ SV392 @ SV384 @ SV363 @ SV355 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2008]) ).
thf(2047,plain,
! [SV393: $i,SV385: $i,SV363: $i,SV355: $i] :
( ( ( path @ SV355 @ SV363 @ SV385 )
= $false )
| ( ( in_path @ SV393 @ SV385 )
= $false )
| ( ( vertex @ SV393 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2009]) ).
thf(2048,plain,
! [SV386: $i,SV380: $i,SV356: $i] :
( ( ( path @ SV356 @ SV380 @ ( sK8_P @ SV386 @ SV380 @ SV356 ) )
= $true )
| ( ( ( SV356 = SV380 )
| ~ ( path @ SV356 @ SV380 @ SV386 ) )
= $true )
| ( ( shortest_path @ SV356 @ SV380 @ SV386 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2010]) ).
thf(2049,plain,
! [SV356: $i,SV380: $i,SV386: $i] :
( ( ( ~ ( less_or_equal @ ( length_of @ SV386 ) @ ( length_of @ ( sK8_P @ SV386 @ SV380 @ SV356 ) ) ) )
= $true )
| ( ( ( SV356 = SV380 )
| ~ ( path @ SV356 @ SV380 @ SV386 ) )
= $true )
| ( ( shortest_path @ SV356 @ SV380 @ SV386 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2011]) ).
thf(2050,plain,
! [SV407: $i,SV398: $i,SV356: $i] :
( ( ( shortest_path @ SV356 @ SV398 @ SV407 )
= $false )
| ( ( ! [SY700: $i] :
( ~ ( path @ SV356 @ SV398 @ SY700 )
| ( less_or_equal @ ( length_of @ SV407 ) @ ( length_of @ SY700 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2012]) ).
thf(2051,plain,
! [SV420: $i,SV356: $i] :
( ( ! [SY705: $i] :
~ ( shortest_path @ SV356 @ SV420 @ SY705 )
| ( SV356 != SV420 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2013]) ).
thf(2052,plain,
! [SV421: $i,SV356: $i] :
( ( ! [SY706: $i] :
( ~ ( shortest_path @ SV356 @ SV421 @ SY706 )
| ( path @ SV356 @ SV421 @ SY706 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2014]) ).
thf(2053,plain,
! [SV377: $i,SV381: $i,SV347: $i] :
( ( ( ( SV347
!= ( tail_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( edge @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
= $false )
| ( ( path @ SV347 @ SV377 @ SV381 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2017]) ).
thf(2054,plain,
! [SV347: $i,SV381: $i,SV377: $i] :
( ( ( ~ ( ( SV377
!= ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
| ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ empty ) )
| ! [SY681: $i] :
( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ SY681 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ SY681 ) ) )
| ~ ~ ( ~ ( ( SV377
= ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ ( sK13_SY84 @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ ( sK13_SY84 @ SV381 @ SV377 @ SV347 ) ) ) )
| ~ ( ( SV381
= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ empty ) )
| ~ ( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ ( sK12_SY85 @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ ( sK12_SY85 @ SV381 @ SV377 @ SV347 ) ) ) ) ) )
= $false )
| ( ( path @ SV347 @ SV377 @ SV381 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2018]) ).
thf(2055,plain,
! [SV366: $i,SV360: $i,SV422: $i,SV348: $i] :
( ( ( ( SV348
!= ( tail_of @ SV422 ) )
| ~ ( edge @ SV422 )
| ( SV360
!= ( head_of @ SV422 ) )
| ( SV366
!= ( path_cons @ SV422 @ empty ) ) )
= $true )
| ( ( vertex @ SV348 )
= $false )
| ( ( vertex @ SV360 )
= $false )
| ( ( path @ SV348 @ SV360 @ SV366 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2019]) ).
thf(2056,plain,
! [SV360: $i,SV366: $i,SV423: $i,SV348: $i] :
( ( ( ( SV348
!= ( tail_of @ SV423 ) )
| ~ ( edge @ SV423 )
| ! [SY707: $i] :
( ( SV366
!= ( path_cons @ SV423 @ SY707 ) )
| ~ ( path @ ( head_of @ SV423 ) @ SV360 @ SY707 ) ) )
= $true )
| ( ( vertex @ SV348 )
= $false )
| ( ( vertex @ SV360 )
= $false )
| ( ( path @ SV348 @ SV360 @ SV366 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2020]) ).
thf(2057,plain,
! [SV378: $i,SV371: $i] :
( ( ( ( head_of @ SV371 )
= ( tail_of @ SV378 ) )
= $false )
| ( ( SV371 = SV378 )
= $true )
| ( ( edge @ SV371 )
= $false )
| ( ( edge @ SV378 )
= $false )
| ( ( sequential @ SV371 @ SV378 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2021]) ).
thf(2058,plain,
! [SV417: $i,SV410: $i] :
( ( ( ~ ( sequential @ SV410 @ SV417 ) )
= $true )
| ( ( ( SV410 != SV417 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2022]) ).
thf(2059,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2023]) ).
thf(2060,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2024]) ).
thf(2061,plain,
! [SV388: $i,SV367: $i,SV400: $i,SV361: $i,SV349: $i] :
( ( ( shortest_path @ SV349 @ SV361 @ SV400 )
= $false )
| ( ( precedes @ SV367 @ SV388 @ SV400 )
= $false )
| ( ( ! [SY687: $i] :
( ( ( tail_of @ SY687 )
!= ( tail_of @ SV367 ) )
| ( ( head_of @ SY687 )
!= ( head_of @ SV388 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2025]) ).
thf(2062,plain,
! [SV389: $i,SV367: $i,SV396: $i,SV361: $i,SV349: $i] :
( ( ( shortest_path @ SV349 @ SV361 @ SV396 )
= $false )
| ( ( precedes @ SV367 @ SV389 @ SV396 )
= $false )
| ( ( ~ ( precedes @ SV389 @ SV367 @ SV396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2026]) ).
thf(2063,plain,
! [SV362: $i,SV350: $i,SV401: $i,SV411: $i] :
( ( ( ~ ( on_path @ SV411 @ SV401 ) )
= $true )
| ( ( ~ ( path @ SV350 @ SV362 @ SV401 ) )
= $true )
| ( ( edge @ SV411 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2027]) ).
thf(2064,plain,
! [SV362: $i,SV350: $i,SV402: $i,SV412: $i] :
( ( ( ~ ( on_path @ SV412 @ SV402 ) )
= $true )
| ( ( ~ ( path @ SV350 @ SV362 @ SV402 ) )
= $true )
| ( ( in_path @ ( head_of @ SV412 ) @ SV402 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2028]) ).
thf(2065,plain,
! [SV351: $i] :
( ( ( on_path @ ( sK6_E1 @ SV351 ) @ SV351 )
= $true )
| ( ( ! [SY595: $i,SY596: $i] :
~ ( path @ SY595 @ SY596 @ SV351 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV351 )
= ( number_of_in @ triangles @ SV351 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2030]) ).
thf(2066,plain,
! [SV351: $i] :
( ( ( on_path @ ( sK7_SY80 @ SV351 ) @ SV351 )
= $true )
| ( ( ! [SY595: $i,SY596: $i] :
~ ( path @ SY595 @ SY596 @ SV351 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV351 )
= ( number_of_in @ triangles @ SV351 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2031]) ).
thf(2067,plain,
! [SV351: $i,SV418: $i,SV413: $i] :
( ( ( path @ SV413 @ SV418 @ SV351 )
= $false )
| ( ( sequential @ ( sK6_E1 @ SV351 ) @ ( sK7_SY80 @ SV351 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV351 )
= ( number_of_in @ triangles @ SV351 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2032]) ).
thf(2068,plain,
! [SV374: $i,SV368: $i] :
( ( ( ~ ( ~ ( ( SV368
!= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
!= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
!= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
!= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV368
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
| ~ ( ( SV368
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) ) )
| ~ ~ ( ~ ( ( SV374
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
| ~ ( ( SV374
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) ) ) ) ) )
= $true )
| ( ( SV368 = SV374 )
= $true )
| ( ( vertex @ SV368 )
= $false )
| ( ( vertex @ SV374 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[2034]) ).
thf(2069,plain,
! [SV368: $i,SV374: $i] :
( ( ( edge @ ( sK14_E @ SV374 @ SV368 ) )
= $true )
| ( ( SV368 = SV374 )
= $true )
| ( ( vertex @ SV368 )
= $false )
| ( ( vertex @ SV374 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[2035]) ).
thf(2070,plain,
! [SV383: $i,SV379: $i,SV352: $i] :
( ( ( ~ ( edge @ SV352 ) )
= $true )
| ( ( ~ ( edge @ SV379 ) )
= $true )
| ( ( ~ ( edge @ SV383 ) )
= $true )
| ( ( ~ ( sequential @ SV352 @ SV379 ) )
= $true )
| ( ( ~ ( sequential @ SV379 @ SV383 ) )
= $true )
| ( ( ~ ( sequential @ SV383 @ SV352 ) )
= $true )
| ( ( triangle @ SV352 @ SV379 @ SV383 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2036]) ).
thf(2071,plain,
! [SV352: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( ! [SY599: $i,SY600: $i] :
~ ( triangle @ SV352 @ SY599 @ SY600 )
| ( edge @ SV352 ) )
| ~ ! [SY601: $i] :
( ! [SY602: $i] :
~ ( triangle @ SV352 @ SY601 @ SY602 )
| ( edge @ SY601 ) ) )
| ~ ! [SY603: $i,SY604: $i] :
( ~ ( triangle @ SV352 @ SY603 @ SY604 )
| ( edge @ SY604 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2037]) ).
thf(2072,plain,
! [SV352: $i] :
( ( ~ ! [SY605: $i] :
( ! [SY606: $i] :
~ ( triangle @ SV352 @ SY605 @ SY606 )
| ( sequential @ SV352 @ SY605 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2037]) ).
thf(2073,plain,
! [SV424: $i,SV419: $i,SV352: $i] :
( ( ~ ( triangle @ SV352 @ SV419 @ SV424 )
| ( sequential @ SV419 @ SV424 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2038]) ).
thf(2074,plain,
! [SV375: $i,SV369: $i,SV415: $i,SV353: $i,SV405: $i] :
( ( ( ~ ( on_path @ SV405 @ SV353 )
| ~ ( on_path @ SV415 @ SV353 ) )
= $true )
| ( ( ! [SY703: $i] :
( ~ ( precedes @ SY703 @ SV415 @ SV353 )
| ~ ( sequential @ SV405 @ SY703 ) ) )
= $true )
| ( ( precedes @ SV405 @ SV415 @ SV353 )
= $true )
| ( ( path @ SV369 @ SV375 @ SV353 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2040]) ).
thf(2075,plain,
! [SV375: $i,SV369: $i,SV416: $i,SV353: $i,SV406: $i] :
( ( ( ~ ( on_path @ SV406 @ SV353 )
| ~ ( on_path @ SV416 @ SV353 ) )
= $true )
| ( ( ~ ( sequential @ SV406 @ SV416 ) )
= $true )
| ( ( precedes @ SV406 @ SV416 @ SV353 )
= $true )
| ( ( path @ SV369 @ SV375 @ SV353 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2041]) ).
thf(2076,plain,
! [SV376: $i,SV370: $i,SV354: $i,SV425: $i] :
( ( ( ! [SY708: $i] :
~ ( precedes @ SV425 @ SY708 @ SV354 )
| ( on_path @ SV425 @ SV354 ) )
= $true )
| ( ( path @ SV370 @ SV376 @ SV354 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2042]) ).
thf(2077,plain,
! [SV376: $i,SV370: $i,SV354: $i,SV426: $i] :
( ( ( ! [SY709: $i] :
( ~ ( precedes @ SV426 @ SY709 @ SV354 )
| ( on_path @ SY709 @ SV354 ) ) )
= $true )
| ( ( path @ SV370 @ SV376 @ SV354 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2043]) ).
thf(2078,plain,
! [SV376: $i,SV370: $i,SV354: $i,SV427: $i] :
( ( ( ! [SY710: $i] :
( ~ ( precedes @ SV427 @ SY710 @ SV354 )
| ! [SY711: $i] :
( ~ ( precedes @ SY711 @ SY710 @ SV354 )
| ~ ( sequential @ SV427 @ SY711 ) )
| ~ ( sequential @ SV427 @ SY710 ) ) )
= $true )
| ( ( path @ SV370 @ SV376 @ SV354 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2044]) ).
thf(2079,plain,
! [SV376: $i,SV370: $i,SV354: $i,SV428: $i] :
( ( ( ! [SY712: $i] :
( ~ ( precedes @ SV428 @ SY712 @ SV354 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY712 @ SV428 @ SV354 ) @ SY712 @ SV354 )
| ~ ( sequential @ SV428 @ ( sK9_E3 @ SY712 @ SV428 @ SV354 ) ) )
| ( sequential @ SV428 @ SY712 ) ) )
= $true )
| ( ( path @ SV370 @ SV376 @ SV354 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2045]) ).
thf(2080,plain,
! [SV355: $i,SV363: $i,SV384: $i,SV392: $i] :
( ( ( ~ ( on_path @ ( sK10_E @ SV392 @ SV384 @ SV363 @ SV355 ) @ SV384 )
| ~ ( ( SV392
= ( head_of @ ( sK10_E @ SV392 @ SV384 @ SV363 @ SV355 ) ) )
| ( SV392
= ( tail_of @ ( sK10_E @ SV392 @ SV384 @ SV363 @ SV355 ) ) ) ) )
= $false )
| ( ( in_path @ SV392 @ SV384 )
= $false )
| ( ( path @ SV355 @ SV363 @ SV384 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2046]) ).
thf(2081,plain,
! [SV386: $i,SV380: $i,SV356: $i] :
( ( ( SV356 = SV380 )
= $true )
| ( ( ~ ( path @ SV356 @ SV380 @ SV386 ) )
= $true )
| ( ( path @ SV356 @ SV380 @ ( sK8_P @ SV386 @ SV380 @ SV356 ) )
= $true )
| ( ( shortest_path @ SV356 @ SV380 @ SV386 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2048]) ).
thf(2082,plain,
! [SV356: $i,SV380: $i,SV386: $i] :
( ( ( less_or_equal @ ( length_of @ SV386 ) @ ( length_of @ ( sK8_P @ SV386 @ SV380 @ SV356 ) ) )
= $false )
| ( ( ( SV356 = SV380 )
| ~ ( path @ SV356 @ SV380 @ SV386 ) )
= $true )
| ( ( shortest_path @ SV356 @ SV380 @ SV386 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2049]) ).
thf(2083,plain,
! [SV407: $i,SV429: $i,SV398: $i,SV356: $i] :
( ( ( ~ ( path @ SV356 @ SV398 @ SV429 )
| ( less_or_equal @ ( length_of @ SV407 ) @ ( length_of @ SV429 ) ) )
= $true )
| ( ( shortest_path @ SV356 @ SV398 @ SV407 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2050]) ).
thf(2084,plain,
! [SV420: $i,SV356: $i] :
( ( ( ! [SY705: $i] :
~ ( shortest_path @ SV356 @ SV420 @ SY705 ) )
= $true )
| ( ( ( SV356 != SV420 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2051]) ).
thf(2085,plain,
! [SV430: $i,SV421: $i,SV356: $i] :
( ( ~ ( shortest_path @ SV356 @ SV421 @ SV430 )
| ( path @ SV356 @ SV421 @ SV430 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2052]) ).
thf(2086,plain,
! [SV377: $i,SV381: $i,SV347: $i] :
( ( ( ( SV347
!= ( tail_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) ) )
= $false )
| ( ( path @ SV347 @ SV377 @ SV381 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2053]) ).
thf(2087,plain,
! [SV347: $i,SV377: $i,SV381: $i] :
( ( ( ~ ( edge @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
= $false )
| ( ( path @ SV347 @ SV377 @ SV381 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2053]) ).
thf(2088,plain,
! [SV347: $i,SV381: $i,SV377: $i] :
( ( ( ~ ( ( SV377
!= ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
| ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ empty ) )
| ! [SY681: $i] :
( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ SY681 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ SY681 ) ) ) )
= $false )
| ( ( path @ SV347 @ SV377 @ SV381 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2054]) ).
thf(2089,plain,
! [SV347: $i,SV381: $i,SV377: $i] :
( ( ( ~ ~ ( ~ ( ( SV377
= ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ ( sK13_SY84 @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ ( sK13_SY84 @ SV381 @ SV377 @ SV347 ) ) ) )
| ~ ( ( SV381
= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ empty ) )
| ~ ( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ ( sK12_SY85 @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ ( sK12_SY85 @ SV381 @ SV377 @ SV347 ) ) ) ) ) )
= $false )
| ( ( path @ SV347 @ SV377 @ SV381 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2054]) ).
thf(2090,plain,
! [SV366: $i,SV360: $i,SV422: $i,SV348: $i] :
( ( ( ( SV348
!= ( tail_of @ SV422 ) )
| ~ ( edge @ SV422 ) )
= $true )
| ( ( ( SV360
!= ( head_of @ SV422 ) )
| ( SV366
!= ( path_cons @ SV422 @ empty ) ) )
= $true )
| ( ( vertex @ SV348 )
= $false )
| ( ( vertex @ SV360 )
= $false )
| ( ( path @ SV348 @ SV360 @ SV366 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2055]) ).
thf(2091,plain,
! [SV360: $i,SV366: $i,SV423: $i,SV348: $i] :
( ( ( ( SV348
!= ( tail_of @ SV423 ) )
| ~ ( edge @ SV423 ) )
= $true )
| ( ( ! [SY707: $i] :
( ( SV366
!= ( path_cons @ SV423 @ SY707 ) )
| ~ ( path @ ( head_of @ SV423 ) @ SV360 @ SY707 ) ) )
= $true )
| ( ( vertex @ SV348 )
= $false )
| ( ( vertex @ SV360 )
= $false )
| ( ( path @ SV348 @ SV360 @ SV366 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2056]) ).
thf(2092,plain,
! [SV417: $i,SV410: $i] :
( ( ( sequential @ SV410 @ SV417 )
= $false )
| ( ( ( SV410 != SV417 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2058]) ).
thf(2093,plain,
! [SV431: $i] :
( ( ! [SY713: $i] :
~ ( sequential @ SV431 @ SY713 )
| ( edge @ SV431 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2059]) ).
thf(2094,plain,
! [SV432: $i] :
( ( ! [SY714: $i] :
( ~ ( sequential @ SV432 @ SY714 )
| ( edge @ SY714 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2060]) ).
thf(2095,plain,
! [SV361: $i,SV349: $i,SV400: $i,SV388: $i,SV367: $i,SV433: $i] :
( ( ( ( ( tail_of @ SV433 )
!= ( tail_of @ SV367 ) )
| ( ( head_of @ SV433 )
!= ( head_of @ SV388 ) ) )
= $true )
| ( ( precedes @ SV367 @ SV388 @ SV400 )
= $false )
| ( ( shortest_path @ SV349 @ SV361 @ SV400 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2061]) ).
thf(2096,plain,
! [SV361: $i,SV349: $i,SV396: $i,SV367: $i,SV389: $i] :
( ( ( precedes @ SV389 @ SV367 @ SV396 )
= $false )
| ( ( precedes @ SV367 @ SV389 @ SV396 )
= $false )
| ( ( shortest_path @ SV349 @ SV361 @ SV396 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2062]) ).
thf(2097,plain,
! [SV362: $i,SV350: $i,SV401: $i,SV411: $i] :
( ( ( on_path @ SV411 @ SV401 )
= $false )
| ( ( ~ ( path @ SV350 @ SV362 @ SV401 ) )
= $true )
| ( ( edge @ SV411 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2063]) ).
thf(2098,plain,
! [SV362: $i,SV350: $i,SV402: $i,SV412: $i] :
( ( ( on_path @ SV412 @ SV402 )
= $false )
| ( ( ~ ( path @ SV350 @ SV362 @ SV402 ) )
= $true )
| ( ( in_path @ ( head_of @ SV412 ) @ SV402 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2064]) ).
thf(2099,plain,
! [SV351: $i,SV434: $i] :
( ( ( ! [SY715: $i] :
~ ( path @ SV434 @ SY715 @ SV351 ) )
= $true )
| ( ( on_path @ ( sK6_E1 @ SV351 ) @ SV351 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV351 )
= ( number_of_in @ triangles @ SV351 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2065]) ).
thf(2100,plain,
! [SV351: $i,SV435: $i] :
( ( ( ! [SY716: $i] :
~ ( path @ SV435 @ SY716 @ SV351 ) )
= $true )
| ( ( on_path @ ( sK7_SY80 @ SV351 ) @ SV351 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV351 )
= ( number_of_in @ triangles @ SV351 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2066]) ).
thf(2101,plain,
! [SV374: $i,SV368: $i] :
( ( ( ~ ( ( SV368
!= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
!= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
!= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
!= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV368
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
| ~ ( ( SV368
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) ) )
| ~ ~ ( ~ ( ( SV374
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
| ~ ( ( SV374
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) ) ) ) )
= $false )
| ( ( SV368 = SV374 )
= $true )
| ( ( vertex @ SV368 )
= $false )
| ( ( vertex @ SV374 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[2068]) ).
thf(2102,plain,
! [SV383: $i,SV379: $i,SV352: $i] :
( ( ( edge @ SV352 )
= $false )
| ( ( ~ ( edge @ SV379 ) )
= $true )
| ( ( ~ ( edge @ SV383 ) )
= $true )
| ( ( ~ ( sequential @ SV352 @ SV379 ) )
= $true )
| ( ( ~ ( sequential @ SV379 @ SV383 ) )
= $true )
| ( ( ~ ( sequential @ SV383 @ SV352 ) )
= $true )
| ( ( triangle @ SV352 @ SV379 @ SV383 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2070]) ).
thf(2103,plain,
! [SV352: $i] :
( ( ~ ( ~ ~ ( ~ ( ! [SY599: $i,SY600: $i] :
~ ( triangle @ SV352 @ SY599 @ SY600 )
| ( edge @ SV352 ) )
| ~ ! [SY601: $i] :
( ! [SY602: $i] :
~ ( triangle @ SV352 @ SY601 @ SY602 )
| ( edge @ SY601 ) ) )
| ~ ! [SY603: $i,SY604: $i] :
( ~ ( triangle @ SV352 @ SY603 @ SY604 )
| ( edge @ SY604 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2071]) ).
thf(2104,plain,
! [SV352: $i] :
( ( ! [SY605: $i] :
( ! [SY606: $i] :
~ ( triangle @ SV352 @ SY605 @ SY606 )
| ( sequential @ SV352 @ SY605 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2072]) ).
thf(2105,plain,
! [SV424: $i,SV419: $i,SV352: $i] :
( ( ( ~ ( triangle @ SV352 @ SV419 @ SV424 ) )
= $true )
| ( ( sequential @ SV419 @ SV424 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2073]) ).
thf(2106,plain,
! [SV375: $i,SV369: $i,SV415: $i,SV353: $i,SV405: $i] :
( ( ( ~ ( on_path @ SV405 @ SV353 ) )
= $true )
| ( ( ~ ( on_path @ SV415 @ SV353 ) )
= $true )
| ( ( ! [SY703: $i] :
( ~ ( precedes @ SY703 @ SV415 @ SV353 )
| ~ ( sequential @ SV405 @ SY703 ) ) )
= $true )
| ( ( precedes @ SV405 @ SV415 @ SV353 )
= $true )
| ( ( path @ SV369 @ SV375 @ SV353 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2074]) ).
thf(2107,plain,
! [SV375: $i,SV369: $i,SV416: $i,SV353: $i,SV406: $i] :
( ( ( ~ ( on_path @ SV406 @ SV353 ) )
= $true )
| ( ( ~ ( on_path @ SV416 @ SV353 ) )
= $true )
| ( ( ~ ( sequential @ SV406 @ SV416 ) )
= $true )
| ( ( precedes @ SV406 @ SV416 @ SV353 )
= $true )
| ( ( path @ SV369 @ SV375 @ SV353 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2075]) ).
thf(2108,plain,
! [SV376: $i,SV370: $i,SV354: $i,SV425: $i] :
( ( ( ! [SY708: $i] :
~ ( precedes @ SV425 @ SY708 @ SV354 ) )
= $true )
| ( ( on_path @ SV425 @ SV354 )
= $true )
| ( ( path @ SV370 @ SV376 @ SV354 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2076]) ).
thf(2109,plain,
! [SV376: $i,SV370: $i,SV354: $i,SV436: $i,SV426: $i] :
( ( ( ~ ( precedes @ SV426 @ SV436 @ SV354 )
| ( on_path @ SV436 @ SV354 ) )
= $true )
| ( ( path @ SV370 @ SV376 @ SV354 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2077]) ).
thf(2110,plain,
! [SV376: $i,SV370: $i,SV354: $i,SV437: $i,SV427: $i] :
( ( ( ~ ( precedes @ SV427 @ SV437 @ SV354 )
| ! [SY717: $i] :
( ~ ( precedes @ SY717 @ SV437 @ SV354 )
| ~ ( sequential @ SV427 @ SY717 ) )
| ~ ( sequential @ SV427 @ SV437 ) )
= $true )
| ( ( path @ SV370 @ SV376 @ SV354 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2078]) ).
thf(2111,plain,
! [SV376: $i,SV370: $i,SV354: $i,SV438: $i,SV428: $i] :
( ( ( ~ ( precedes @ SV428 @ SV438 @ SV354 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SV438 @ SV428 @ SV354 ) @ SV438 @ SV354 )
| ~ ( sequential @ SV428 @ ( sK9_E3 @ SV438 @ SV428 @ SV354 ) ) )
| ( sequential @ SV428 @ SV438 ) )
= $true )
| ( ( path @ SV370 @ SV376 @ SV354 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2079]) ).
thf(2112,plain,
! [SV355: $i,SV363: $i,SV384: $i,SV392: $i] :
( ( ( ~ ( on_path @ ( sK10_E @ SV392 @ SV384 @ SV363 @ SV355 ) @ SV384 ) )
= $false )
| ( ( in_path @ SV392 @ SV384 )
= $false )
| ( ( path @ SV355 @ SV363 @ SV384 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2080]) ).
thf(2113,plain,
! [SV355: $i,SV363: $i,SV384: $i,SV392: $i] :
( ( ( ~ ( ( SV392
= ( head_of @ ( sK10_E @ SV392 @ SV384 @ SV363 @ SV355 ) ) )
| ( SV392
= ( tail_of @ ( sK10_E @ SV392 @ SV384 @ SV363 @ SV355 ) ) ) ) )
= $false )
| ( ( in_path @ SV392 @ SV384 )
= $false )
| ( ( path @ SV355 @ SV363 @ SV384 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2080]) ).
thf(2114,plain,
! [SV386: $i,SV380: $i,SV356: $i] :
( ( ( path @ SV356 @ SV380 @ SV386 )
= $false )
| ( ( SV356 = SV380 )
= $true )
| ( ( path @ SV356 @ SV380 @ ( sK8_P @ SV386 @ SV380 @ SV356 ) )
= $true )
| ( ( shortest_path @ SV356 @ SV380 @ SV386 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2081]) ).
thf(2115,plain,
! [SV386: $i,SV380: $i,SV356: $i] :
( ( ( SV356 = SV380 )
= $true )
| ( ( ~ ( path @ SV356 @ SV380 @ SV386 ) )
= $true )
| ( ( less_or_equal @ ( length_of @ SV386 ) @ ( length_of @ ( sK8_P @ SV386 @ SV380 @ SV356 ) ) )
= $false )
| ( ( shortest_path @ SV356 @ SV380 @ SV386 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2082]) ).
thf(2116,plain,
! [SV407: $i,SV429: $i,SV398: $i,SV356: $i] :
( ( ( ~ ( path @ SV356 @ SV398 @ SV429 ) )
= $true )
| ( ( less_or_equal @ ( length_of @ SV407 ) @ ( length_of @ SV429 ) )
= $true )
| ( ( shortest_path @ SV356 @ SV398 @ SV407 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2083]) ).
thf(2117,plain,
! [SV439: $i,SV420: $i,SV356: $i] :
( ( ( ~ ( shortest_path @ SV356 @ SV420 @ SV439 ) )
= $true )
| ( ( ( SV356 != SV420 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2084]) ).
thf(2118,plain,
! [SV430: $i,SV421: $i,SV356: $i] :
( ( ( ~ ( shortest_path @ SV356 @ SV421 @ SV430 ) )
= $true )
| ( ( path @ SV356 @ SV421 @ SV430 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2085]) ).
thf(2119,plain,
! [SV377: $i,SV381: $i,SV347: $i] :
( ( ( SV347
= ( tail_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
= $true )
| ( ( path @ SV347 @ SV377 @ SV381 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2086]) ).
thf(2120,plain,
! [SV347: $i,SV377: $i,SV381: $i] :
( ( ( edge @ ( sK11_E @ SV381 @ SV377 @ SV347 ) )
= $true )
| ( ( path @ SV347 @ SV377 @ SV381 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2087]) ).
thf(2121,plain,
! [SV347: $i,SV381: $i,SV377: $i] :
( ( ( ( SV377
!= ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
| ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ empty ) )
| ! [SY681: $i] :
( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ SY681 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ SY681 ) ) )
= $true )
| ( ( path @ SV347 @ SV377 @ SV381 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2088]) ).
thf(2122,plain,
! [SV347: $i,SV381: $i,SV377: $i] :
( ( ( ~ ( ~ ( ( SV377
= ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ ( sK13_SY84 @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ ( sK13_SY84 @ SV381 @ SV377 @ SV347 ) ) ) )
| ~ ( ( SV381
= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ empty ) )
| ~ ( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ ( sK12_SY85 @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ ( sK12_SY85 @ SV381 @ SV377 @ SV347 ) ) ) ) ) )
= $true )
| ( ( path @ SV347 @ SV377 @ SV381 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2089]) ).
thf(2123,plain,
! [SV366: $i,SV360: $i,SV422: $i,SV348: $i] :
( ( ( ( SV348
!= ( tail_of @ SV422 ) ) )
= $true )
| ( ( ~ ( edge @ SV422 ) )
= $true )
| ( ( ( SV360
!= ( head_of @ SV422 ) )
| ( SV366
!= ( path_cons @ SV422 @ empty ) ) )
= $true )
| ( ( vertex @ SV348 )
= $false )
| ( ( vertex @ SV360 )
= $false )
| ( ( path @ SV348 @ SV360 @ SV366 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2090]) ).
thf(2124,plain,
! [SV360: $i,SV366: $i,SV423: $i,SV348: $i] :
( ( ( ( SV348
!= ( tail_of @ SV423 ) ) )
= $true )
| ( ( ~ ( edge @ SV423 ) )
= $true )
| ( ( ! [SY707: $i] :
( ( SV366
!= ( path_cons @ SV423 @ SY707 ) )
| ~ ( path @ ( head_of @ SV423 ) @ SV360 @ SY707 ) ) )
= $true )
| ( ( vertex @ SV348 )
= $false )
| ( ( vertex @ SV360 )
= $false )
| ( ( path @ SV348 @ SV360 @ SV366 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2091]) ).
thf(2125,plain,
! [SV417: $i,SV410: $i] :
( ( ( SV410 = SV417 )
= $false )
| ( ( sequential @ SV410 @ SV417 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2092]) ).
thf(2126,plain,
! [SV431: $i] :
( ( ( ! [SY713: $i] :
~ ( sequential @ SV431 @ SY713 ) )
= $true )
| ( ( edge @ SV431 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2093]) ).
thf(2127,plain,
! [SV440: $i,SV432: $i] :
( ( ~ ( sequential @ SV432 @ SV440 )
| ( edge @ SV440 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2094]) ).
thf(2128,plain,
! [SV361: $i,SV349: $i,SV400: $i,SV388: $i,SV367: $i,SV433: $i] :
( ( ( ( ( tail_of @ SV433 )
!= ( tail_of @ SV367 ) ) )
= $true )
| ( ( ( ( head_of @ SV433 )
!= ( head_of @ SV388 ) ) )
= $true )
| ( ( precedes @ SV367 @ SV388 @ SV400 )
= $false )
| ( ( shortest_path @ SV349 @ SV361 @ SV400 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2095]) ).
thf(2129,plain,
! [SV411: $i,SV401: $i,SV362: $i,SV350: $i] :
( ( ( path @ SV350 @ SV362 @ SV401 )
= $false )
| ( ( on_path @ SV411 @ SV401 )
= $false )
| ( ( edge @ SV411 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2097]) ).
thf(2130,plain,
! [SV412: $i,SV402: $i,SV362: $i,SV350: $i] :
( ( ( path @ SV350 @ SV362 @ SV402 )
= $false )
| ( ( on_path @ SV412 @ SV402 )
= $false )
| ( ( in_path @ ( head_of @ SV412 ) @ SV402 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2098]) ).
thf(2131,plain,
! [SV351: $i,SV441: $i,SV434: $i] :
( ( ( ~ ( path @ SV434 @ SV441 @ SV351 ) )
= $true )
| ( ( on_path @ ( sK6_E1 @ SV351 ) @ SV351 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV351 )
= ( number_of_in @ triangles @ SV351 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2099]) ).
thf(2132,plain,
! [SV351: $i,SV442: $i,SV435: $i] :
( ( ( ~ ( path @ SV435 @ SV442 @ SV351 ) )
= $true )
| ( ( on_path @ ( sK7_SY80 @ SV351 ) @ SV351 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV351 )
= ( number_of_in @ triangles @ SV351 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2100]) ).
thf(2133,plain,
! [SV374: $i,SV368: $i] :
( ( ( ~ ( ( SV368
!= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
!= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
!= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
!= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) ) )
= $false )
| ( ( SV368 = SV374 )
= $true )
| ( ( vertex @ SV368 )
= $false )
| ( ( vertex @ SV374 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[2101]) ).
thf(2134,plain,
! [SV374: $i,SV368: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( SV368
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
| ~ ( ( SV368
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) ) )
| ~ ~ ( ~ ( ( SV374
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
| ~ ( ( SV374
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) ) ) ) )
= $false )
| ( ( SV368 = SV374 )
= $true )
| ( ( vertex @ SV368 )
= $false )
| ( ( vertex @ SV374 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[2101]) ).
thf(2135,plain,
! [SV383: $i,SV352: $i,SV379: $i] :
( ( ( edge @ SV379 )
= $false )
| ( ( edge @ SV352 )
= $false )
| ( ( ~ ( edge @ SV383 ) )
= $true )
| ( ( ~ ( sequential @ SV352 @ SV379 ) )
= $true )
| ( ( ~ ( sequential @ SV379 @ SV383 ) )
= $true )
| ( ( ~ ( sequential @ SV383 @ SV352 ) )
= $true )
| ( ( triangle @ SV352 @ SV379 @ SV383 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2102]) ).
thf(2136,plain,
! [SV352: $i] :
( ( ~ ~ ( ~ ( ! [SY599: $i,SY600: $i] :
~ ( triangle @ SV352 @ SY599 @ SY600 )
| ( edge @ SV352 ) )
| ~ ! [SY601: $i] :
( ! [SY602: $i] :
~ ( triangle @ SV352 @ SY601 @ SY602 )
| ( edge @ SY601 ) ) )
| ~ ! [SY603: $i,SY604: $i] :
( ~ ( triangle @ SV352 @ SY603 @ SY604 )
| ( edge @ SY604 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2103]) ).
thf(2137,plain,
! [SV443: $i,SV352: $i] :
( ( ! [SY718: $i] :
~ ( triangle @ SV352 @ SV443 @ SY718 )
| ( sequential @ SV352 @ SV443 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2104]) ).
thf(2138,plain,
! [SV424: $i,SV419: $i,SV352: $i] :
( ( ( triangle @ SV352 @ SV419 @ SV424 )
= $false )
| ( ( sequential @ SV419 @ SV424 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2105]) ).
thf(2139,plain,
! [SV375: $i,SV369: $i,SV415: $i,SV353: $i,SV405: $i] :
( ( ( on_path @ SV405 @ SV353 )
= $false )
| ( ( ~ ( on_path @ SV415 @ SV353 ) )
= $true )
| ( ( ! [SY703: $i] :
( ~ ( precedes @ SY703 @ SV415 @ SV353 )
| ~ ( sequential @ SV405 @ SY703 ) ) )
= $true )
| ( ( precedes @ SV405 @ SV415 @ SV353 )
= $true )
| ( ( path @ SV369 @ SV375 @ SV353 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2106]) ).
thf(2140,plain,
! [SV375: $i,SV369: $i,SV416: $i,SV353: $i,SV406: $i] :
( ( ( on_path @ SV406 @ SV353 )
= $false )
| ( ( ~ ( on_path @ SV416 @ SV353 ) )
= $true )
| ( ( ~ ( sequential @ SV406 @ SV416 ) )
= $true )
| ( ( precedes @ SV406 @ SV416 @ SV353 )
= $true )
| ( ( path @ SV369 @ SV375 @ SV353 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2107]) ).
thf(2141,plain,
! [SV376: $i,SV370: $i,SV354: $i,SV444: $i,SV425: $i] :
( ( ( ~ ( precedes @ SV425 @ SV444 @ SV354 ) )
= $true )
| ( ( on_path @ SV425 @ SV354 )
= $true )
| ( ( path @ SV370 @ SV376 @ SV354 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2108]) ).
thf(2142,plain,
! [SV376: $i,SV370: $i,SV354: $i,SV436: $i,SV426: $i] :
( ( ( ~ ( precedes @ SV426 @ SV436 @ SV354 ) )
= $true )
| ( ( on_path @ SV436 @ SV354 )
= $true )
| ( ( path @ SV370 @ SV376 @ SV354 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2109]) ).
thf(2143,plain,
! [SV376: $i,SV370: $i,SV354: $i,SV437: $i,SV427: $i] :
( ( ( ~ ( precedes @ SV427 @ SV437 @ SV354 ) )
= $true )
| ( ( ! [SY717: $i] :
( ~ ( precedes @ SY717 @ SV437 @ SV354 )
| ~ ( sequential @ SV427 @ SY717 ) )
| ~ ( sequential @ SV427 @ SV437 ) )
= $true )
| ( ( path @ SV370 @ SV376 @ SV354 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2110]) ).
thf(2144,plain,
! [SV376: $i,SV370: $i,SV354: $i,SV438: $i,SV428: $i] :
( ( ( ~ ( precedes @ SV428 @ SV438 @ SV354 ) )
= $true )
| ( ( ~ ( ~ ( precedes @ ( sK9_E3 @ SV438 @ SV428 @ SV354 ) @ SV438 @ SV354 )
| ~ ( sequential @ SV428 @ ( sK9_E3 @ SV438 @ SV428 @ SV354 ) ) )
| ( sequential @ SV428 @ SV438 ) )
= $true )
| ( ( path @ SV370 @ SV376 @ SV354 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2111]) ).
thf(2145,plain,
! [SV355: $i,SV363: $i,SV384: $i,SV392: $i] :
( ( ( on_path @ ( sK10_E @ SV392 @ SV384 @ SV363 @ SV355 ) @ SV384 )
= $true )
| ( ( in_path @ SV392 @ SV384 )
= $false )
| ( ( path @ SV355 @ SV363 @ SV384 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2112]) ).
thf(2146,plain,
! [SV355: $i,SV363: $i,SV384: $i,SV392: $i] :
( ( ( ( SV392
= ( head_of @ ( sK10_E @ SV392 @ SV384 @ SV363 @ SV355 ) ) )
| ( SV392
= ( tail_of @ ( sK10_E @ SV392 @ SV384 @ SV363 @ SV355 ) ) ) )
= $true )
| ( ( in_path @ SV392 @ SV384 )
= $false )
| ( ( path @ SV355 @ SV363 @ SV384 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2113]) ).
thf(2147,plain,
! [SV386: $i,SV380: $i,SV356: $i] :
( ( ( path @ SV356 @ SV380 @ SV386 )
= $false )
| ( ( SV356 = SV380 )
= $true )
| ( ( less_or_equal @ ( length_of @ SV386 ) @ ( length_of @ ( sK8_P @ SV386 @ SV380 @ SV356 ) ) )
= $false )
| ( ( shortest_path @ SV356 @ SV380 @ SV386 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2115]) ).
thf(2148,plain,
! [SV407: $i,SV429: $i,SV398: $i,SV356: $i] :
( ( ( path @ SV356 @ SV398 @ SV429 )
= $false )
| ( ( less_or_equal @ ( length_of @ SV407 ) @ ( length_of @ SV429 ) )
= $true )
| ( ( shortest_path @ SV356 @ SV398 @ SV407 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2116]) ).
thf(2149,plain,
! [SV439: $i,SV420: $i,SV356: $i] :
( ( ( shortest_path @ SV356 @ SV420 @ SV439 )
= $false )
| ( ( ( SV356 != SV420 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2117]) ).
thf(2150,plain,
! [SV430: $i,SV421: $i,SV356: $i] :
( ( ( shortest_path @ SV356 @ SV421 @ SV430 )
= $false )
| ( ( path @ SV356 @ SV421 @ SV430 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2118]) ).
thf(2151,plain,
! [SV347: $i,SV381: $i,SV377: $i] :
( ( ( ( SV377
!= ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
| ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ empty ) ) )
= $true )
| ( ( ! [SY681: $i] :
( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ SY681 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ SY681 ) ) )
= $true )
| ( ( path @ SV347 @ SV377 @ SV381 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2121]) ).
thf(2152,plain,
! [SV347: $i,SV381: $i,SV377: $i] :
( ( ( ~ ( ( SV377
= ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ ( sK13_SY84 @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ ( sK13_SY84 @ SV381 @ SV377 @ SV347 ) ) ) )
| ~ ( ( SV381
= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ empty ) )
| ~ ( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ ( sK12_SY85 @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ ( sK12_SY85 @ SV381 @ SV377 @ SV347 ) ) ) ) )
= $false )
| ( ( path @ SV347 @ SV377 @ SV381 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2122]) ).
thf(2153,plain,
! [SV366: $i,SV360: $i,SV422: $i,SV348: $i] :
( ( ( SV348
= ( tail_of @ SV422 ) )
= $false )
| ( ( ~ ( edge @ SV422 ) )
= $true )
| ( ( ( SV360
!= ( head_of @ SV422 ) )
| ( SV366
!= ( path_cons @ SV422 @ empty ) ) )
= $true )
| ( ( vertex @ SV348 )
= $false )
| ( ( vertex @ SV360 )
= $false )
| ( ( path @ SV348 @ SV360 @ SV366 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2123]) ).
thf(2154,plain,
! [SV360: $i,SV366: $i,SV423: $i,SV348: $i] :
( ( ( SV348
= ( tail_of @ SV423 ) )
= $false )
| ( ( ~ ( edge @ SV423 ) )
= $true )
| ( ( ! [SY707: $i] :
( ( SV366
!= ( path_cons @ SV423 @ SY707 ) )
| ~ ( path @ ( head_of @ SV423 ) @ SV360 @ SY707 ) ) )
= $true )
| ( ( vertex @ SV348 )
= $false )
| ( ( vertex @ SV360 )
= $false )
| ( ( path @ SV348 @ SV360 @ SV366 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2124]) ).
thf(2155,plain,
! [SV445: $i,SV431: $i] :
( ( ( ~ ( sequential @ SV431 @ SV445 ) )
= $true )
| ( ( edge @ SV431 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2126]) ).
thf(2156,plain,
! [SV440: $i,SV432: $i] :
( ( ( ~ ( sequential @ SV432 @ SV440 ) )
= $true )
| ( ( edge @ SV440 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2127]) ).
thf(2157,plain,
! [SV361: $i,SV349: $i,SV400: $i,SV388: $i,SV367: $i,SV433: $i] :
( ( ( ( tail_of @ SV433 )
= ( tail_of @ SV367 ) )
= $false )
| ( ( ( ( head_of @ SV433 )
!= ( head_of @ SV388 ) ) )
= $true )
| ( ( precedes @ SV367 @ SV388 @ SV400 )
= $false )
| ( ( shortest_path @ SV349 @ SV361 @ SV400 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2128]) ).
thf(2158,plain,
! [SV351: $i,SV441: $i,SV434: $i] :
( ( ( path @ SV434 @ SV441 @ SV351 )
= $false )
| ( ( on_path @ ( sK6_E1 @ SV351 ) @ SV351 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV351 )
= ( number_of_in @ triangles @ SV351 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2131]) ).
thf(2159,plain,
! [SV351: $i,SV442: $i,SV435: $i] :
( ( ( path @ SV435 @ SV442 @ SV351 )
= $false )
| ( ( on_path @ ( sK7_SY80 @ SV351 ) @ SV351 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV351 )
= ( number_of_in @ triangles @ SV351 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2132]) ).
thf(2160,plain,
! [SV374: $i,SV368: $i] :
( ( ( ( SV368
!= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
!= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
!= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
!= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
= $true )
| ( ( SV368 = SV374 )
= $true )
| ( ( vertex @ SV368 )
= $false )
| ( ( vertex @ SV374 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[2133]) ).
thf(2161,plain,
! [SV374: $i,SV368: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( SV368
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
| ~ ( ( SV368
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) ) )
| ~ ~ ( ~ ( ( SV374
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
| ~ ( ( SV374
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) ) ) ) )
= $true )
| ( ( SV368 = SV374 )
= $true )
| ( ( vertex @ SV368 )
= $false )
| ( ( vertex @ SV374 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[2134]) ).
thf(2162,plain,
! [SV379: $i,SV352: $i,SV383: $i] :
( ( ( edge @ SV383 )
= $false )
| ( ( edge @ SV352 )
= $false )
| ( ( edge @ SV379 )
= $false )
| ( ( ~ ( sequential @ SV352 @ SV379 ) )
= $true )
| ( ( ~ ( sequential @ SV379 @ SV383 ) )
= $true )
| ( ( ~ ( sequential @ SV383 @ SV352 ) )
= $true )
| ( ( triangle @ SV352 @ SV379 @ SV383 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2135]) ).
thf(2163,plain,
! [SV352: $i] :
( ( ~ ~ ( ~ ( ! [SY599: $i,SY600: $i] :
~ ( triangle @ SV352 @ SY599 @ SY600 )
| ( edge @ SV352 ) )
| ~ ! [SY601: $i] :
( ! [SY602: $i] :
~ ( triangle @ SV352 @ SY601 @ SY602 )
| ( edge @ SY601 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2136]) ).
thf(2164,plain,
! [SV352: $i] :
( ( ~ ! [SY603: $i,SY604: $i] :
( ~ ( triangle @ SV352 @ SY603 @ SY604 )
| ( edge @ SY604 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2136]) ).
thf(2165,plain,
! [SV443: $i,SV352: $i] :
( ( ( ! [SY718: $i] :
~ ( triangle @ SV352 @ SV443 @ SY718 ) )
= $true )
| ( ( sequential @ SV352 @ SV443 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2137]) ).
thf(2166,plain,
! [SV375: $i,SV369: $i,SV405: $i,SV353: $i,SV415: $i] :
( ( ( on_path @ SV415 @ SV353 )
= $false )
| ( ( on_path @ SV405 @ SV353 )
= $false )
| ( ( ! [SY703: $i] :
( ~ ( precedes @ SY703 @ SV415 @ SV353 )
| ~ ( sequential @ SV405 @ SY703 ) ) )
= $true )
| ( ( precedes @ SV405 @ SV415 @ SV353 )
= $true )
| ( ( path @ SV369 @ SV375 @ SV353 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2139]) ).
thf(2167,plain,
! [SV375: $i,SV369: $i,SV406: $i,SV353: $i,SV416: $i] :
( ( ( on_path @ SV416 @ SV353 )
= $false )
| ( ( on_path @ SV406 @ SV353 )
= $false )
| ( ( ~ ( sequential @ SV406 @ SV416 ) )
= $true )
| ( ( precedes @ SV406 @ SV416 @ SV353 )
= $true )
| ( ( path @ SV369 @ SV375 @ SV353 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2140]) ).
thf(2168,plain,
! [SV376: $i,SV370: $i,SV354: $i,SV444: $i,SV425: $i] :
( ( ( precedes @ SV425 @ SV444 @ SV354 )
= $false )
| ( ( on_path @ SV425 @ SV354 )
= $true )
| ( ( path @ SV370 @ SV376 @ SV354 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2141]) ).
thf(2169,plain,
! [SV376: $i,SV370: $i,SV354: $i,SV436: $i,SV426: $i] :
( ( ( precedes @ SV426 @ SV436 @ SV354 )
= $false )
| ( ( on_path @ SV436 @ SV354 )
= $true )
| ( ( path @ SV370 @ SV376 @ SV354 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2142]) ).
thf(2170,plain,
! [SV376: $i,SV370: $i,SV354: $i,SV437: $i,SV427: $i] :
( ( ( precedes @ SV427 @ SV437 @ SV354 )
= $false )
| ( ( ! [SY717: $i] :
( ~ ( precedes @ SY717 @ SV437 @ SV354 )
| ~ ( sequential @ SV427 @ SY717 ) )
| ~ ( sequential @ SV427 @ SV437 ) )
= $true )
| ( ( path @ SV370 @ SV376 @ SV354 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2143]) ).
thf(2171,plain,
! [SV376: $i,SV370: $i,SV354: $i,SV438: $i,SV428: $i] :
( ( ( precedes @ SV428 @ SV438 @ SV354 )
= $false )
| ( ( ~ ( ~ ( precedes @ ( sK9_E3 @ SV438 @ SV428 @ SV354 ) @ SV438 @ SV354 )
| ~ ( sequential @ SV428 @ ( sK9_E3 @ SV438 @ SV428 @ SV354 ) ) )
| ( sequential @ SV428 @ SV438 ) )
= $true )
| ( ( path @ SV370 @ SV376 @ SV354 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2144]) ).
thf(2172,plain,
! [SV355: $i,SV363: $i,SV384: $i,SV392: $i] :
( ( ( SV392
= ( head_of @ ( sK10_E @ SV392 @ SV384 @ SV363 @ SV355 ) ) )
= $true )
| ( ( SV392
= ( tail_of @ ( sK10_E @ SV392 @ SV384 @ SV363 @ SV355 ) ) )
= $true )
| ( ( in_path @ SV392 @ SV384 )
= $false )
| ( ( path @ SV355 @ SV363 @ SV384 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2146]) ).
thf(2173,plain,
! [SV439: $i,SV420: $i,SV356: $i] :
( ( ( SV356 = SV420 )
= $false )
| ( ( shortest_path @ SV356 @ SV420 @ SV439 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2149]) ).
thf(2174,plain,
! [SV347: $i,SV381: $i,SV377: $i] :
( ( ( ( SV377
!= ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) ) )
= $true )
| ( ( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ empty ) ) )
= $true )
| ( ( ! [SY681: $i] :
( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ SY681 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ SY681 ) ) )
= $true )
| ( ( path @ SV347 @ SV377 @ SV381 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2151]) ).
thf(2175,plain,
! [SV347: $i,SV381: $i,SV377: $i] :
( ( ( ~ ( ( SV377
= ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ ( sK13_SY84 @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ ( sK13_SY84 @ SV381 @ SV377 @ SV347 ) ) ) ) )
= $false )
| ( ( path @ SV347 @ SV377 @ SV381 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2152]) ).
thf(2176,plain,
! [SV347: $i,SV377: $i,SV381: $i] :
( ( ( ~ ( ( SV381
= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ empty ) )
| ~ ( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ ( sK12_SY85 @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ ( sK12_SY85 @ SV381 @ SV377 @ SV347 ) ) ) ) )
= $false )
| ( ( path @ SV347 @ SV377 @ SV381 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2152]) ).
thf(2177,plain,
! [SV366: $i,SV360: $i,SV348: $i,SV422: $i] :
( ( ( edge @ SV422 )
= $false )
| ( ( SV348
= ( tail_of @ SV422 ) )
= $false )
| ( ( ( SV360
!= ( head_of @ SV422 ) )
| ( SV366
!= ( path_cons @ SV422 @ empty ) ) )
= $true )
| ( ( vertex @ SV348 )
= $false )
| ( ( vertex @ SV360 )
= $false )
| ( ( path @ SV348 @ SV360 @ SV366 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2153]) ).
thf(2178,plain,
! [SV360: $i,SV366: $i,SV348: $i,SV423: $i] :
( ( ( edge @ SV423 )
= $false )
| ( ( SV348
= ( tail_of @ SV423 ) )
= $false )
| ( ( ! [SY707: $i] :
( ( SV366
!= ( path_cons @ SV423 @ SY707 ) )
| ~ ( path @ ( head_of @ SV423 ) @ SV360 @ SY707 ) ) )
= $true )
| ( ( vertex @ SV348 )
= $false )
| ( ( vertex @ SV360 )
= $false )
| ( ( path @ SV348 @ SV360 @ SV366 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2154]) ).
thf(2179,plain,
! [SV445: $i,SV431: $i] :
( ( ( sequential @ SV431 @ SV445 )
= $false )
| ( ( edge @ SV431 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2155]) ).
thf(2180,plain,
! [SV440: $i,SV432: $i] :
( ( ( sequential @ SV432 @ SV440 )
= $false )
| ( ( edge @ SV440 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2156]) ).
thf(2181,plain,
! [SV361: $i,SV349: $i,SV400: $i,SV367: $i,SV388: $i,SV433: $i] :
( ( ( ( head_of @ SV433 )
= ( head_of @ SV388 ) )
= $false )
| ( ( ( tail_of @ SV433 )
= ( tail_of @ SV367 ) )
= $false )
| ( ( precedes @ SV367 @ SV388 @ SV400 )
= $false )
| ( ( shortest_path @ SV349 @ SV361 @ SV400 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2157]) ).
thf(2182,plain,
! [SV374: $i,SV368: $i] :
( ( ( ( SV368
!= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
!= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
= $true )
| ( ( ( SV374
!= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
!= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
= $true )
| ( ( SV368 = SV374 )
= $true )
| ( ( vertex @ SV368 )
= $false )
| ( ( vertex @ SV374 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[2160]) ).
thf(2183,plain,
! [SV374: $i,SV368: $i] :
( ( ( ~ ~ ( ~ ( ( SV368
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
| ~ ( ( SV368
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) ) )
| ~ ~ ( ~ ( ( SV374
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
| ~ ( ( SV374
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) ) ) )
= $false )
| ( ( SV368 = SV374 )
= $true )
| ( ( vertex @ SV368 )
= $false )
| ( ( vertex @ SV374 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[2161]) ).
thf(2184,plain,
! [SV383: $i,SV379: $i,SV352: $i] :
( ( ( sequential @ SV352 @ SV379 )
= $false )
| ( ( edge @ SV379 )
= $false )
| ( ( edge @ SV352 )
= $false )
| ( ( edge @ SV383 )
= $false )
| ( ( ~ ( sequential @ SV379 @ SV383 ) )
= $true )
| ( ( ~ ( sequential @ SV383 @ SV352 ) )
= $true )
| ( ( triangle @ SV352 @ SV379 @ SV383 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2162]) ).
thf(2185,plain,
! [SV352: $i] :
( ( ~ ( ~ ( ! [SY599: $i,SY600: $i] :
~ ( triangle @ SV352 @ SY599 @ SY600 )
| ( edge @ SV352 ) )
| ~ ! [SY601: $i] :
( ! [SY602: $i] :
~ ( triangle @ SV352 @ SY601 @ SY602 )
| ( edge @ SY601 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2163]) ).
thf(2186,plain,
! [SV352: $i] :
( ( ! [SY603: $i,SY604: $i] :
( ~ ( triangle @ SV352 @ SY603 @ SY604 )
| ( edge @ SY604 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2164]) ).
thf(2187,plain,
! [SV446: $i,SV443: $i,SV352: $i] :
( ( ( ~ ( triangle @ SV352 @ SV443 @ SV446 ) )
= $true )
| ( ( sequential @ SV352 @ SV443 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2165]) ).
thf(2188,plain,
! [SV375: $i,SV369: $i,SV405: $i,SV353: $i,SV415: $i,SV447: $i] :
( ( ( ~ ( precedes @ SV447 @ SV415 @ SV353 )
| ~ ( sequential @ SV405 @ SV447 ) )
= $true )
| ( ( on_path @ SV405 @ SV353 )
= $false )
| ( ( on_path @ SV415 @ SV353 )
= $false )
| ( ( precedes @ SV405 @ SV415 @ SV353 )
= $true )
| ( ( path @ SV369 @ SV375 @ SV353 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2166]) ).
thf(2189,plain,
! [SV375: $i,SV369: $i,SV353: $i,SV416: $i,SV406: $i] :
( ( ( sequential @ SV406 @ SV416 )
= $false )
| ( ( on_path @ SV406 @ SV353 )
= $false )
| ( ( on_path @ SV416 @ SV353 )
= $false )
| ( ( precedes @ SV406 @ SV416 @ SV353 )
= $true )
| ( ( path @ SV369 @ SV375 @ SV353 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2167]) ).
thf(2190,plain,
! [SV376: $i,SV370: $i,SV427: $i,SV354: $i,SV437: $i] :
( ( ( ! [SY717: $i] :
( ~ ( precedes @ SY717 @ SV437 @ SV354 )
| ~ ( sequential @ SV427 @ SY717 ) ) )
= $true )
| ( ( ~ ( sequential @ SV427 @ SV437 ) )
= $true )
| ( ( precedes @ SV427 @ SV437 @ SV354 )
= $false )
| ( ( path @ SV370 @ SV376 @ SV354 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2170]) ).
thf(2191,plain,
! [SV376: $i,SV370: $i,SV354: $i,SV428: $i,SV438: $i] :
( ( ( ~ ( ~ ( precedes @ ( sK9_E3 @ SV438 @ SV428 @ SV354 ) @ SV438 @ SV354 )
| ~ ( sequential @ SV428 @ ( sK9_E3 @ SV438 @ SV428 @ SV354 ) ) ) )
= $true )
| ( ( sequential @ SV428 @ SV438 )
= $true )
| ( ( precedes @ SV428 @ SV438 @ SV354 )
= $false )
| ( ( path @ SV370 @ SV376 @ SV354 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2171]) ).
thf(2192,plain,
! [SV347: $i,SV381: $i,SV377: $i] :
( ( ( SV377
= ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
= $false )
| ( ( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ empty ) ) )
= $true )
| ( ( ! [SY681: $i] :
( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ SY681 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ SY681 ) ) )
= $true )
| ( ( path @ SV347 @ SV377 @ SV381 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2174]) ).
thf(2193,plain,
! [SV347: $i,SV381: $i,SV377: $i] :
( ( ( ( SV377
= ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ ( sK13_SY84 @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ ( sK13_SY84 @ SV381 @ SV377 @ SV347 ) ) ) )
= $true )
| ( ( path @ SV347 @ SV377 @ SV381 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2175]) ).
thf(2194,plain,
! [SV347: $i,SV377: $i,SV381: $i] :
( ( ( ( SV381
= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ empty ) )
| ~ ( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ ( sK12_SY85 @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ ( sK12_SY85 @ SV381 @ SV377 @ SV347 ) ) ) )
= $true )
| ( ( path @ SV347 @ SV377 @ SV381 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2176]) ).
thf(2195,plain,
! [SV348: $i,SV366: $i,SV422: $i,SV360: $i] :
( ( ( ( SV360
!= ( head_of @ SV422 ) ) )
= $true )
| ( ( ( SV366
!= ( path_cons @ SV422 @ empty ) ) )
= $true )
| ( ( SV348
= ( tail_of @ SV422 ) )
= $false )
| ( ( edge @ SV422 )
= $false )
| ( ( vertex @ SV348 )
= $false )
| ( ( vertex @ SV360 )
= $false )
| ( ( path @ SV348 @ SV360 @ SV366 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2177]) ).
thf(2196,plain,
! [SV348: $i,SV360: $i,SV448: $i,SV423: $i,SV366: $i] :
( ( ( ( SV366
!= ( path_cons @ SV423 @ SV448 ) )
| ~ ( path @ ( head_of @ SV423 ) @ SV360 @ SV448 ) )
= $true )
| ( ( SV348
= ( tail_of @ SV423 ) )
= $false )
| ( ( edge @ SV423 )
= $false )
| ( ( vertex @ SV348 )
= $false )
| ( ( vertex @ SV360 )
= $false )
| ( ( path @ SV348 @ SV360 @ SV366 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2178]) ).
thf(2197,plain,
! [SV374: $i,SV368: $i] :
( ( ( ( SV368
!= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
= $true )
| ( ( ( SV374
!= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
= $true )
| ( ( ( SV374
!= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
!= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
= $true )
| ( ( SV368 = SV374 )
= $true )
| ( ( vertex @ SV368 )
= $false )
| ( ( vertex @ SV374 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[2182]) ).
thf(2198,plain,
! [SV374: $i,SV368: $i] :
( ( ( ~ ~ ( ~ ( ( SV368
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
| ~ ( ( SV368
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) ) ) )
= $false )
| ( ( SV368 = SV374 )
= $true )
| ( ( vertex @ SV368 )
= $false )
| ( ( vertex @ SV374 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[2183]) ).
thf(2199,plain,
! [SV368: $i,SV374: $i] :
( ( ( ~ ~ ( ~ ( ( SV374
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
| ~ ( ( SV374
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) ) ) )
= $false )
| ( ( SV368 = SV374 )
= $true )
| ( ( vertex @ SV368 )
= $false )
| ( ( vertex @ SV374 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[2183]) ).
thf(2200,plain,
! [SV352: $i,SV383: $i,SV379: $i] :
( ( ( sequential @ SV379 @ SV383 )
= $false )
| ( ( edge @ SV383 )
= $false )
| ( ( edge @ SV352 )
= $false )
| ( ( edge @ SV379 )
= $false )
| ( ( sequential @ SV352 @ SV379 )
= $false )
| ( ( ~ ( sequential @ SV383 @ SV352 ) )
= $true )
| ( ( triangle @ SV352 @ SV379 @ SV383 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2184]) ).
thf(2201,plain,
! [SV352: $i] :
( ( ~ ( ! [SY599: $i,SY600: $i] :
~ ( triangle @ SV352 @ SY599 @ SY600 )
| ( edge @ SV352 ) )
| ~ ! [SY601: $i] :
( ! [SY602: $i] :
~ ( triangle @ SV352 @ SY601 @ SY602 )
| ( edge @ SY601 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2185]) ).
thf(2202,plain,
! [SV449: $i,SV352: $i] :
( ( ! [SY719: $i] :
( ~ ( triangle @ SV352 @ SV449 @ SY719 )
| ( edge @ SY719 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2186]) ).
thf(2203,plain,
! [SV446: $i,SV443: $i,SV352: $i] :
( ( ( triangle @ SV352 @ SV443 @ SV446 )
= $false )
| ( ( sequential @ SV352 @ SV443 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2187]) ).
thf(2204,plain,
! [SV375: $i,SV369: $i,SV405: $i,SV353: $i,SV415: $i,SV447: $i] :
( ( ( ~ ( precedes @ SV447 @ SV415 @ SV353 ) )
= $true )
| ( ( ~ ( sequential @ SV405 @ SV447 ) )
= $true )
| ( ( on_path @ SV405 @ SV353 )
= $false )
| ( ( on_path @ SV415 @ SV353 )
= $false )
| ( ( precedes @ SV405 @ SV415 @ SV353 )
= $true )
| ( ( path @ SV369 @ SV375 @ SV353 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2188]) ).
thf(2205,plain,
! [SV376: $i,SV370: $i,SV427: $i,SV354: $i,SV437: $i,SV450: $i] :
( ( ( ~ ( precedes @ SV450 @ SV437 @ SV354 )
| ~ ( sequential @ SV427 @ SV450 ) )
= $true )
| ( ( ~ ( sequential @ SV427 @ SV437 ) )
= $true )
| ( ( precedes @ SV427 @ SV437 @ SV354 )
= $false )
| ( ( path @ SV370 @ SV376 @ SV354 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2190]) ).
thf(2206,plain,
! [SV376: $i,SV370: $i,SV354: $i,SV428: $i,SV438: $i] :
( ( ( ~ ( precedes @ ( sK9_E3 @ SV438 @ SV428 @ SV354 ) @ SV438 @ SV354 )
| ~ ( sequential @ SV428 @ ( sK9_E3 @ SV438 @ SV428 @ SV354 ) ) )
= $false )
| ( ( sequential @ SV428 @ SV438 )
= $true )
| ( ( precedes @ SV428 @ SV438 @ SV354 )
= $false )
| ( ( path @ SV370 @ SV376 @ SV354 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2191]) ).
thf(2207,plain,
! [SV347: $i,SV377: $i,SV381: $i] :
( ( ( SV381
= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ empty ) )
= $false )
| ( ( SV377
= ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
= $false )
| ( ( ! [SY681: $i] :
( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ SY681 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ SY681 ) ) )
= $true )
| ( ( path @ SV347 @ SV377 @ SV381 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2192]) ).
thf(2208,plain,
! [SV347: $i,SV381: $i,SV377: $i] :
( ( ( SV377
= ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
= $true )
| ( ( ~ ( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ ( sK13_SY84 @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ ( sK13_SY84 @ SV381 @ SV377 @ SV347 ) ) ) )
= $true )
| ( ( path @ SV347 @ SV377 @ SV381 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2193]) ).
thf(2209,plain,
! [SV347: $i,SV377: $i,SV381: $i] :
( ( ( SV381
= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ empty ) )
= $true )
| ( ( ~ ( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ ( sK12_SY85 @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ ( sK12_SY85 @ SV381 @ SV377 @ SV347 ) ) ) )
= $true )
| ( ( path @ SV347 @ SV377 @ SV381 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2194]) ).
thf(2210,plain,
! [SV348: $i,SV366: $i,SV422: $i,SV360: $i] :
( ( ( SV360
= ( head_of @ SV422 ) )
= $false )
| ( ( ( SV366
!= ( path_cons @ SV422 @ empty ) ) )
= $true )
| ( ( SV348
= ( tail_of @ SV422 ) )
= $false )
| ( ( edge @ SV422 )
= $false )
| ( ( vertex @ SV348 )
= $false )
| ( ( vertex @ SV360 )
= $false )
| ( ( path @ SV348 @ SV360 @ SV366 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2195]) ).
thf(2211,plain,
! [SV348: $i,SV360: $i,SV448: $i,SV423: $i,SV366: $i] :
( ( ( ( SV366
!= ( path_cons @ SV423 @ SV448 ) ) )
= $true )
| ( ( ~ ( path @ ( head_of @ SV423 ) @ SV360 @ SV448 ) )
= $true )
| ( ( SV348
= ( tail_of @ SV423 ) )
= $false )
| ( ( edge @ SV423 )
= $false )
| ( ( vertex @ SV348 )
= $false )
| ( ( vertex @ SV360 )
= $false )
| ( ( path @ SV348 @ SV360 @ SV366 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2196]) ).
thf(2212,plain,
! [SV374: $i,SV368: $i] :
( ( ( SV368
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
= $false )
| ( ( ( SV374
!= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
= $true )
| ( ( ( SV374
!= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
!= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
= $true )
| ( ( SV368 = SV374 )
= $true )
| ( ( vertex @ SV368 )
= $false )
| ( ( vertex @ SV374 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[2197]) ).
thf(2213,plain,
! [SV374: $i,SV368: $i] :
( ( ( ~ ( ~ ( ( SV368
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
| ~ ( ( SV368
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) ) ) )
= $true )
| ( ( SV368 = SV374 )
= $true )
| ( ( vertex @ SV368 )
= $false )
| ( ( vertex @ SV374 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[2198]) ).
thf(2214,plain,
! [SV368: $i,SV374: $i] :
( ( ( ~ ( ~ ( ( SV374
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
| ~ ( ( SV374
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) ) ) )
= $true )
| ( ( SV368 = SV374 )
= $true )
| ( ( vertex @ SV368 )
= $false )
| ( ( vertex @ SV374 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[2199]) ).
thf(2215,plain,
! [SV379: $i,SV352: $i,SV383: $i] :
( ( ( sequential @ SV383 @ SV352 )
= $false )
| ( ( sequential @ SV352 @ SV379 )
= $false )
| ( ( edge @ SV379 )
= $false )
| ( ( edge @ SV352 )
= $false )
| ( ( edge @ SV383 )
= $false )
| ( ( sequential @ SV379 @ SV383 )
= $false )
| ( ( triangle @ SV352 @ SV379 @ SV383 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2200]) ).
thf(2216,plain,
! [SV352: $i] :
( ( ~ ( ! [SY599: $i,SY600: $i] :
~ ( triangle @ SV352 @ SY599 @ SY600 )
| ( edge @ SV352 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2201]) ).
thf(2217,plain,
! [SV352: $i] :
( ( ~ ! [SY601: $i] :
( ! [SY602: $i] :
~ ( triangle @ SV352 @ SY601 @ SY602 )
| ( edge @ SY601 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2201]) ).
thf(2218,plain,
! [SV451: $i,SV449: $i,SV352: $i] :
( ( ~ ( triangle @ SV352 @ SV449 @ SV451 )
| ( edge @ SV451 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2202]) ).
thf(2219,plain,
! [SV375: $i,SV369: $i,SV405: $i,SV353: $i,SV415: $i,SV447: $i] :
( ( ( precedes @ SV447 @ SV415 @ SV353 )
= $false )
| ( ( ~ ( sequential @ SV405 @ SV447 ) )
= $true )
| ( ( on_path @ SV405 @ SV353 )
= $false )
| ( ( on_path @ SV415 @ SV353 )
= $false )
| ( ( precedes @ SV405 @ SV415 @ SV353 )
= $true )
| ( ( path @ SV369 @ SV375 @ SV353 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2204]) ).
thf(2220,plain,
! [SV376: $i,SV370: $i,SV427: $i,SV354: $i,SV437: $i,SV450: $i] :
( ( ( ~ ( precedes @ SV450 @ SV437 @ SV354 ) )
= $true )
| ( ( ~ ( sequential @ SV427 @ SV450 ) )
= $true )
| ( ( ~ ( sequential @ SV427 @ SV437 ) )
= $true )
| ( ( precedes @ SV427 @ SV437 @ SV354 )
= $false )
| ( ( path @ SV370 @ SV376 @ SV354 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2205]) ).
thf(2221,plain,
! [SV376: $i,SV370: $i,SV354: $i,SV428: $i,SV438: $i] :
( ( ( ~ ( precedes @ ( sK9_E3 @ SV438 @ SV428 @ SV354 ) @ SV438 @ SV354 ) )
= $false )
| ( ( sequential @ SV428 @ SV438 )
= $true )
| ( ( precedes @ SV428 @ SV438 @ SV354 )
= $false )
| ( ( path @ SV370 @ SV376 @ SV354 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2206]) ).
thf(2222,plain,
! [SV376: $i,SV370: $i,SV354: $i,SV438: $i,SV428: $i] :
( ( ( ~ ( sequential @ SV428 @ ( sK9_E3 @ SV438 @ SV428 @ SV354 ) ) )
= $false )
| ( ( sequential @ SV428 @ SV438 )
= $true )
| ( ( precedes @ SV428 @ SV438 @ SV354 )
= $false )
| ( ( path @ SV370 @ SV376 @ SV354 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2206]) ).
thf(2223,plain,
! [SV452: $i,SV347: $i,SV377: $i,SV381: $i] :
( ( ( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ SV452 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ SV452 ) )
= $true )
| ( ( SV377
= ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
= $false )
| ( ( SV381
= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ empty ) )
= $false )
| ( ( path @ SV347 @ SV377 @ SV381 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2207]) ).
thf(2224,plain,
! [SV347: $i,SV377: $i,SV381: $i] :
( ( ( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ ( sK13_SY84 @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ ( sK13_SY84 @ SV381 @ SV377 @ SV347 ) ) )
= $false )
| ( ( SV377
= ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
= $true )
| ( ( path @ SV347 @ SV377 @ SV381 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2208]) ).
thf(2225,plain,
! [SV347: $i,SV377: $i,SV381: $i] :
( ( ( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ ( sK12_SY85 @ SV381 @ SV377 @ SV347 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ ( sK12_SY85 @ SV381 @ SV377 @ SV347 ) ) )
= $false )
| ( ( SV381
= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ empty ) )
= $true )
| ( ( path @ SV347 @ SV377 @ SV381 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2209]) ).
thf(2226,plain,
! [SV348: $i,SV360: $i,SV422: $i,SV366: $i] :
( ( ( SV366
= ( path_cons @ SV422 @ empty ) )
= $false )
| ( ( SV360
= ( head_of @ SV422 ) )
= $false )
| ( ( SV348
= ( tail_of @ SV422 ) )
= $false )
| ( ( edge @ SV422 )
= $false )
| ( ( vertex @ SV348 )
= $false )
| ( ( vertex @ SV360 )
= $false )
| ( ( path @ SV348 @ SV360 @ SV366 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2210]) ).
thf(2227,plain,
! [SV348: $i,SV360: $i,SV448: $i,SV423: $i,SV366: $i] :
( ( ( SV366
= ( path_cons @ SV423 @ SV448 ) )
= $false )
| ( ( ~ ( path @ ( head_of @ SV423 ) @ SV360 @ SV448 ) )
= $true )
| ( ( SV348
= ( tail_of @ SV423 ) )
= $false )
| ( ( edge @ SV423 )
= $false )
| ( ( vertex @ SV348 )
= $false )
| ( ( vertex @ SV360 )
= $false )
| ( ( path @ SV348 @ SV360 @ SV366 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2211]) ).
thf(2228,plain,
! [SV368: $i,SV374: $i] :
( ( ( SV374
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
= $false )
| ( ( SV368
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
= $false )
| ( ( ( SV374
!= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
!= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
= $true )
| ( ( SV368 = SV374 )
= $true )
| ( ( vertex @ SV368 )
= $false )
| ( ( vertex @ SV374 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[2212]) ).
thf(2229,plain,
! [SV374: $i,SV368: $i] :
( ( ( ~ ( ( SV368
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
| ~ ( ( SV368
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) ) )
= $false )
| ( ( SV368 = SV374 )
= $true )
| ( ( vertex @ SV368 )
= $false )
| ( ( vertex @ SV374 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[2213]) ).
thf(2230,plain,
! [SV368: $i,SV374: $i] :
( ( ( ~ ( ( SV374
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
| ~ ( ( SV374
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) ) )
= $false )
| ( ( SV368 = SV374 )
= $true )
| ( ( vertex @ SV368 )
= $false )
| ( ( vertex @ SV374 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[2214]) ).
thf(2231,plain,
! [SV352: $i] :
( ( ! [SY599: $i,SY600: $i] :
~ ( triangle @ SV352 @ SY599 @ SY600 )
| ( edge @ SV352 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2216]) ).
thf(2232,plain,
! [SV352: $i] :
( ( ! [SY601: $i] :
( ! [SY602: $i] :
~ ( triangle @ SV352 @ SY601 @ SY602 )
| ( edge @ SY601 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2217]) ).
thf(2233,plain,
! [SV451: $i,SV449: $i,SV352: $i] :
( ( ( ~ ( triangle @ SV352 @ SV449 @ SV451 ) )
= $true )
| ( ( edge @ SV451 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2218]) ).
thf(2234,plain,
! [SV375: $i,SV369: $i,SV353: $i,SV415: $i,SV447: $i,SV405: $i] :
( ( ( sequential @ SV405 @ SV447 )
= $false )
| ( ( precedes @ SV447 @ SV415 @ SV353 )
= $false )
| ( ( on_path @ SV405 @ SV353 )
= $false )
| ( ( on_path @ SV415 @ SV353 )
= $false )
| ( ( precedes @ SV405 @ SV415 @ SV353 )
= $true )
| ( ( path @ SV369 @ SV375 @ SV353 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2219]) ).
thf(2235,plain,
! [SV376: $i,SV370: $i,SV427: $i,SV354: $i,SV437: $i,SV450: $i] :
( ( ( precedes @ SV450 @ SV437 @ SV354 )
= $false )
| ( ( ~ ( sequential @ SV427 @ SV450 ) )
= $true )
| ( ( ~ ( sequential @ SV427 @ SV437 ) )
= $true )
| ( ( precedes @ SV427 @ SV437 @ SV354 )
= $false )
| ( ( path @ SV370 @ SV376 @ SV354 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2220]) ).
thf(2236,plain,
! [SV376: $i,SV370: $i,SV354: $i,SV428: $i,SV438: $i] :
( ( ( precedes @ ( sK9_E3 @ SV438 @ SV428 @ SV354 ) @ SV438 @ SV354 )
= $true )
| ( ( sequential @ SV428 @ SV438 )
= $true )
| ( ( precedes @ SV428 @ SV438 @ SV354 )
= $false )
| ( ( path @ SV370 @ SV376 @ SV354 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2221]) ).
thf(2237,plain,
! [SV376: $i,SV370: $i,SV354: $i,SV438: $i,SV428: $i] :
( ( ( sequential @ SV428 @ ( sK9_E3 @ SV438 @ SV428 @ SV354 ) )
= $true )
| ( ( sequential @ SV428 @ SV438 )
= $true )
| ( ( precedes @ SV428 @ SV438 @ SV354 )
= $false )
| ( ( path @ SV370 @ SV376 @ SV354 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2222]) ).
thf(2238,plain,
! [SV452: $i,SV347: $i,SV377: $i,SV381: $i] :
( ( ( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ SV452 ) ) )
= $true )
| ( ( ~ ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ SV452 ) )
= $true )
| ( ( SV377
= ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
= $false )
| ( ( SV381
= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ empty ) )
= $false )
| ( ( path @ SV347 @ SV377 @ SV381 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2223]) ).
thf(2239,plain,
! [SV347: $i,SV377: $i,SV381: $i] :
( ( ( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ ( sK13_SY84 @ SV381 @ SV377 @ SV347 ) ) ) )
= $false )
| ( ( SV377
= ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
= $true )
| ( ( path @ SV347 @ SV377 @ SV381 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2224]) ).
thf(2240,plain,
! [SV347: $i,SV377: $i,SV381: $i] :
( ( ( ~ ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ ( sK13_SY84 @ SV381 @ SV377 @ SV347 ) ) )
= $false )
| ( ( SV377
= ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
= $true )
| ( ( path @ SV347 @ SV377 @ SV381 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2224]) ).
thf(2241,plain,
! [SV347: $i,SV377: $i,SV381: $i] :
( ( ( ( SV381
!= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ ( sK12_SY85 @ SV381 @ SV377 @ SV347 ) ) ) )
= $false )
| ( ( SV381
= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ empty ) )
= $true )
| ( ( path @ SV347 @ SV377 @ SV381 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2225]) ).
thf(2242,plain,
! [SV347: $i,SV377: $i,SV381: $i] :
( ( ( ~ ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ ( sK12_SY85 @ SV381 @ SV377 @ SV347 ) ) )
= $false )
| ( ( SV381
= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ empty ) )
= $true )
| ( ( path @ SV347 @ SV377 @ SV381 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2225]) ).
thf(2243,plain,
! [SV348: $i,SV366: $i,SV448: $i,SV360: $i,SV423: $i] :
( ( ( path @ ( head_of @ SV423 ) @ SV360 @ SV448 )
= $false )
| ( ( SV366
= ( path_cons @ SV423 @ SV448 ) )
= $false )
| ( ( SV348
= ( tail_of @ SV423 ) )
= $false )
| ( ( edge @ SV423 )
= $false )
| ( ( vertex @ SV348 )
= $false )
| ( ( vertex @ SV360 )
= $false )
| ( ( path @ SV348 @ SV360 @ SV366 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2227]) ).
thf(2244,plain,
! [SV368: $i,SV374: $i] :
( ( ( ( SV374
!= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
= $true )
| ( ( ( SV368
!= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
= $true )
| ( ( SV368
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
= $false )
| ( ( SV374
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
= $false )
| ( ( SV368 = SV374 )
= $true )
| ( ( vertex @ SV368 )
= $false )
| ( ( vertex @ SV374 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[2228]) ).
thf(2245,plain,
! [SV374: $i,SV368: $i] :
( ( ( ~ ( ( SV368
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) ) ) )
= $false )
| ( ( SV368 = SV374 )
= $true )
| ( ( vertex @ SV368 )
= $false )
| ( ( vertex @ SV374 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[2229]) ).
thf(2246,plain,
! [SV374: $i,SV368: $i] :
( ( ( ~ ( ( SV368
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) ) )
= $false )
| ( ( SV368 = SV374 )
= $true )
| ( ( vertex @ SV368 )
= $false )
| ( ( vertex @ SV374 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[2229]) ).
thf(2247,plain,
! [SV368: $i,SV374: $i] :
( ( ( ~ ( ( SV374
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) ) ) )
= $false )
| ( ( SV368 = SV374 )
= $true )
| ( ( vertex @ SV368 )
= $false )
| ( ( vertex @ SV374 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[2230]) ).
thf(2248,plain,
! [SV368: $i,SV374: $i] :
( ( ( ~ ( ( SV374
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) ) )
= $false )
| ( ( SV368 = SV374 )
= $true )
| ( ( vertex @ SV368 )
= $false )
| ( ( vertex @ SV374 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[2230]) ).
thf(2249,plain,
! [SV352: $i] :
( ( ( ! [SY599: $i,SY600: $i] :
~ ( triangle @ SV352 @ SY599 @ SY600 ) )
= $true )
| ( ( edge @ SV352 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2231]) ).
thf(2250,plain,
! [SV453: $i,SV352: $i] :
( ( ! [SY720: $i] :
~ ( triangle @ SV352 @ SV453 @ SY720 )
| ( edge @ SV453 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2232]) ).
thf(2251,plain,
! [SV451: $i,SV449: $i,SV352: $i] :
( ( ( triangle @ SV352 @ SV449 @ SV451 )
= $false )
| ( ( edge @ SV451 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2233]) ).
thf(2252,plain,
! [SV376: $i,SV370: $i,SV354: $i,SV437: $i,SV450: $i,SV427: $i] :
( ( ( sequential @ SV427 @ SV450 )
= $false )
| ( ( precedes @ SV450 @ SV437 @ SV354 )
= $false )
| ( ( ~ ( sequential @ SV427 @ SV437 ) )
= $true )
| ( ( precedes @ SV427 @ SV437 @ SV354 )
= $false )
| ( ( path @ SV370 @ SV376 @ SV354 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2235]) ).
thf(2253,plain,
! [SV452: $i,SV347: $i,SV377: $i,SV381: $i] :
( ( ( SV381
= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ SV452 ) )
= $false )
| ( ( ~ ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ SV452 ) )
= $true )
| ( ( SV377
= ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
= $false )
| ( ( SV381
= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ empty ) )
= $false )
| ( ( path @ SV347 @ SV377 @ SV381 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2238]) ).
thf(2254,plain,
! [SV347: $i,SV377: $i,SV381: $i] :
( ( ( SV381
= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ ( sK13_SY84 @ SV381 @ SV377 @ SV347 ) ) )
= $true )
| ( ( SV377
= ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
= $true )
| ( ( path @ SV347 @ SV377 @ SV381 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2239]) ).
thf(2255,plain,
! [SV347: $i,SV377: $i,SV381: $i] :
( ( ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ ( sK13_SY84 @ SV381 @ SV377 @ SV347 ) )
= $true )
| ( ( SV377
= ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
= $true )
| ( ( path @ SV347 @ SV377 @ SV381 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2240]) ).
thf(2256,plain,
! [SV347: $i,SV377: $i,SV381: $i] :
( ( ( SV381
= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ ( sK12_SY85 @ SV381 @ SV377 @ SV347 ) ) )
= $true )
| ( ( SV381
= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ empty ) )
= $true )
| ( ( path @ SV347 @ SV377 @ SV381 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2241]) ).
thf(2257,plain,
! [SV347: $i,SV377: $i,SV381: $i] :
( ( ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ ( sK12_SY85 @ SV381 @ SV377 @ SV347 ) )
= $true )
| ( ( SV381
= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ empty ) )
= $true )
| ( ( path @ SV347 @ SV377 @ SV381 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2242]) ).
thf(2258,plain,
! [SV368: $i,SV374: $i] :
( ( ( SV374
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
= $false )
| ( ( ( SV368
!= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
= $true )
| ( ( SV368
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
= $false )
| ( ( SV374
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
= $false )
| ( ( SV368 = SV374 )
= $true )
| ( ( vertex @ SV368 )
= $false )
| ( ( vertex @ SV374 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[2244]) ).
thf(2259,plain,
! [SV374: $i,SV368: $i] :
( ( ( ( SV368
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
= $true )
| ( ( SV368 = SV374 )
= $true )
| ( ( vertex @ SV368 )
= $false )
| ( ( vertex @ SV374 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[2245]) ).
thf(2260,plain,
! [SV374: $i,SV368: $i] :
( ( ( ( SV368
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
= $true )
| ( ( SV368 = SV374 )
= $true )
| ( ( vertex @ SV368 )
= $false )
| ( ( vertex @ SV374 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[2246]) ).
thf(2261,plain,
! [SV368: $i,SV374: $i] :
( ( ( ( SV374
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV374
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
= $true )
| ( ( SV368 = SV374 )
= $true )
| ( ( vertex @ SV368 )
= $false )
| ( ( vertex @ SV374 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[2247]) ).
thf(2262,plain,
! [SV368: $i,SV374: $i] :
( ( ( ( SV374
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
| ( SV368
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) ) )
= $true )
| ( ( SV368 = SV374 )
= $true )
| ( ( vertex @ SV368 )
= $false )
| ( ( vertex @ SV374 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[2248]) ).
thf(2263,plain,
! [SV454: $i,SV352: $i] :
( ( ( ! [SY721: $i] :
~ ( triangle @ SV352 @ SV454 @ SY721 ) )
= $true )
| ( ( edge @ SV352 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2249]) ).
thf(2264,plain,
! [SV453: $i,SV352: $i] :
( ( ( ! [SY720: $i] :
~ ( triangle @ SV352 @ SV453 @ SY720 ) )
= $true )
| ( ( edge @ SV453 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2250]) ).
thf(2265,plain,
! [SV376: $i,SV370: $i,SV354: $i,SV450: $i,SV437: $i,SV427: $i] :
( ( ( sequential @ SV427 @ SV437 )
= $false )
| ( ( precedes @ SV450 @ SV437 @ SV354 )
= $false )
| ( ( sequential @ SV427 @ SV450 )
= $false )
| ( ( precedes @ SV427 @ SV437 @ SV354 )
= $false )
| ( ( path @ SV370 @ SV376 @ SV354 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2252]) ).
thf(2266,plain,
! [SV452: $i,SV347: $i,SV377: $i,SV381: $i] :
( ( ( path @ ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) @ SV377 @ SV452 )
= $false )
| ( ( SV381
= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ SV452 ) )
= $false )
| ( ( SV377
= ( head_of @ ( sK11_E @ SV381 @ SV377 @ SV347 ) ) )
= $false )
| ( ( SV381
= ( path_cons @ ( sK11_E @ SV381 @ SV377 @ SV347 ) @ empty ) )
= $false )
| ( ( path @ SV347 @ SV377 @ SV381 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2253]) ).
thf(2267,plain,
! [SV374: $i,SV368: $i] :
( ( ( SV368
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
= $false )
| ( ( SV374
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
= $false )
| ( ( SV368
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
= $false )
| ( ( SV374
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
= $false )
| ( ( SV368 = SV374 )
= $true )
| ( ( vertex @ SV368 )
= $false )
| ( ( vertex @ SV374 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[2258]) ).
thf(2268,plain,
! [SV374: $i,SV368: $i] :
( ( ( SV368
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
= $true )
| ( ( SV374
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
= $true )
| ( ( SV368 = SV374 )
= $true )
| ( ( vertex @ SV368 )
= $false )
| ( ( vertex @ SV374 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[2259]) ).
thf(2269,plain,
! [SV374: $i,SV368: $i] :
( ( ( SV368
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
= $true )
| ( ( SV368
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
= $true )
| ( ( SV368 = SV374 )
= $true )
| ( ( vertex @ SV368 )
= $false )
| ( ( vertex @ SV374 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[2260]) ).
thf(2270,plain,
! [SV368: $i,SV374: $i] :
( ( ( SV374
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
= $true )
| ( ( SV374
= ( head_of @ ( sK14_E @ SV374 @ SV368 ) ) )
= $true )
| ( ( SV368 = SV374 )
= $true )
| ( ( vertex @ SV368 )
= $false )
| ( ( vertex @ SV374 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[2261]) ).
thf(2271,plain,
! [SV368: $i,SV374: $i] :
( ( ( SV374
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
= $true )
| ( ( SV368
= ( tail_of @ ( sK14_E @ SV374 @ SV368 ) ) )
= $true )
| ( ( SV368 = SV374 )
= $true )
| ( ( vertex @ SV368 )
= $false )
| ( ( vertex @ SV374 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[2262]) ).
thf(2272,plain,
! [SV455: $i,SV454: $i,SV352: $i] :
( ( ( ~ ( triangle @ SV352 @ SV454 @ SV455 ) )
= $true )
| ( ( edge @ SV352 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2263]) ).
thf(2273,plain,
! [SV456: $i,SV453: $i,SV352: $i] :
( ( ( ~ ( triangle @ SV352 @ SV453 @ SV456 ) )
= $true )
| ( ( edge @ SV453 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2264]) ).
thf(2274,plain,
! [SV455: $i,SV454: $i,SV352: $i] :
( ( ( triangle @ SV352 @ SV454 @ SV455 )
= $false )
| ( ( edge @ SV352 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2272]) ).
thf(2275,plain,
! [SV456: $i,SV453: $i,SV352: $i] :
( ( ( triangle @ SV352 @ SV453 @ SV456 )
= $false )
| ( ( edge @ SV453 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2273]) ).
thf(2276,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[1744,2275,2274,2271,2270,2269,2268,2267,2266,2265,2257,2256,2255,2254,2251,2243,2237,2236,2234,2226,2215,2203,2189,2181,2180,2179,2173,2172,2169,2168,2159,2158,2150,2148,2147,2145,2138,2130,2129,2125,2120,2119,2114,2096,2069,2067,2057,2047,2039,2033,2029,2016,2015,1988,1878,1877,1842,1841,1818,1781,1764,1745]) ).
thf(2277,plain,
( ( ! [E: $i] :
( ~ ( edge @ E )
| ( ( head_of @ E )
!= ( tail_of @ E ) ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(2278,plain,
( ( ! [E: $i] :
( ~ ( edge @ E )
| ( vertex @ ( head_of @ E ) ) )
& ! [E: $i] :
( ~ ( edge @ E )
| ( vertex @ ( tail_of @ E ) ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(2279,plain,
( ( ~ complete
| ! [V1: $i,V2: $i] :
( ( V1 = V2 )
| ~ ( vertex @ V1 )
| ~ ( vertex @ V2 )
| ( ( ( V1
!= ( head_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V2
!= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V2
!= ( head_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V1
!= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( ( V1
= ( head_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V2
= ( head_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( ( V1
= ( head_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V1
= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( ( V2
= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V2
= ( head_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( ( V2
= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V1
= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( edge @ ( sK14_E @ V2 @ V1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(2280,plain,
( ( ! [V1: $i,V2: $i,P: $i] :
( ~ ( vertex @ V1 )
| ~ ( vertex @ V2 )
| ( ! [E: $i] :
( ( V1
!= ( tail_of @ E ) )
| ~ ( edge @ E )
| ( V2
!= ( head_of @ E ) )
| ( P
!= ( path_cons @ E @ empty ) ) )
& ! [E: $i] :
( ( V1
!= ( tail_of @ E ) )
| ~ ( edge @ E )
| ! [TP: $i] :
( ( P
!= ( path_cons @ E @ TP ) )
| ~ ( path @ ( head_of @ E ) @ V2 @ TP ) ) ) )
| ( path @ V1 @ V2 @ P ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(2281,plain,
( ( ! [V1: $i] :
( ( ! [V2: $i,P: $i] :
~ ( path @ V1 @ V2 @ P )
| ( vertex @ V1 ) )
& ! [V2: $i] :
( ! [P: $i] :
~ ( path @ V1 @ V2 @ P )
| ( vertex @ V2 ) )
& ! [V2: $i,P: $i] :
( ~ ( path @ V1 @ V2 @ P )
| ( ( V1
= ( tail_of @ ( sK11_E @ P @ V2 @ V1 ) ) )
& ( edge @ ( sK11_E @ P @ V2 @ V1 ) )
& ( ( V2
!= ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) )
| ( P
!= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ empty ) )
| ! [SY83: $i] :
( ( P
!= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ SY83 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) @ V2 @ SY83 ) ) )
& ( ( V2
= ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) )
| ( ( P
= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ ( sK13_SY84 @ P @ V2 @ V1 ) ) )
& ( path @ ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) @ V2 @ ( sK13_SY84 @ P @ V2 @ V1 ) ) ) )
& ( ( P
= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ empty ) )
| ( ( P
= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ ( sK12_SY85 @ P @ V2 @ V1 ) ) )
& ( path @ ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) @ V2 @ ( sK12_SY85 @ P @ V2 @ V1 ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(2282,plain,
( ( ! [V1: $i,V2: $i] :
( ! [P: $i,E: $i] :
( ~ ( on_path @ E @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( edge @ E ) )
& ! [P: $i,E: $i] :
( ~ ( on_path @ E @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( in_path @ ( head_of @ E ) @ P ) )
& ! [P: $i,E: $i] :
( ~ ( on_path @ E @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( in_path @ ( tail_of @ E ) @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(2283,plain,
( ( ! [V1: $i,V2: $i] :
( ! [P: $i,V: $i] :
( ~ ( in_path @ V @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( ( on_path @ ( sK10_E @ V @ P @ V2 @ V1 ) @ P )
& ( ( V
= ( head_of @ ( sK10_E @ V @ P @ V2 @ V1 ) ) )
| ( V
= ( tail_of @ ( sK10_E @ V @ P @ V2 @ V1 ) ) ) ) ) )
& ! [P: $i,V: $i] :
( ~ ( in_path @ V @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( vertex @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(2284,plain,
( ( ! [E1: $i,E2: $i] :
( ( E1 = E2 )
| ~ ( edge @ E1 )
| ~ ( edge @ E2 )
| ( ( head_of @ E1 )
!= ( tail_of @ E2 ) )
| ( sequential @ E1 @ E2 ) )
& ! [E1: $i,E2: $i] :
( ~ ( sequential @ E1 @ E2 )
| ( E1 != E2 ) )
& ! [E1: $i] :
( ! [E2: $i] :
~ ( sequential @ E1 @ E2 )
| ( edge @ E1 ) )
& ! [E1: $i,E2: $i] :
( ~ ( sequential @ E1 @ E2 )
| ( edge @ E2 ) )
& ! [E1: $i,E2: $i] :
( ~ ( sequential @ E1 @ E2 )
| ( ( head_of @ E1 )
= ( tail_of @ E2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(2285,plain,
( ( ! [P: $i] :
( ! [V1: $i,V2: $i] :
~ ( path @ V1 @ V2 @ P )
| ( ! [E1: $i,E2: $i] :
( ~ ( on_path @ E1 @ P )
| ~ ( on_path @ E2 @ P )
| ! [E3: $i] :
( ~ ( precedes @ E3 @ E2 @ P )
| ~ ( sequential @ E1 @ E3 ) )
| ( precedes @ E1 @ E2 @ P ) )
& ! [E1: $i,E2: $i] :
( ~ ( on_path @ E1 @ P )
| ~ ( on_path @ E2 @ P )
| ~ ( sequential @ E1 @ E2 )
| ( precedes @ E1 @ E2 @ P ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(2286,plain,
( ( ! [P: $i] :
( ! [V1: $i,V2: $i] :
~ ( path @ V1 @ V2 @ P )
| ( ! [E1: $i] :
( ! [E2: $i] :
~ ( precedes @ E1 @ E2 @ P )
| ( on_path @ E1 @ P ) )
& ! [E1: $i,E2: $i] :
( ~ ( precedes @ E1 @ E2 @ P )
| ( on_path @ E2 @ P ) )
& ! [E1: $i,E2: $i] :
( ~ ( precedes @ E1 @ E2 @ P )
| ! [E3: $i] :
( ~ ( precedes @ E3 @ E2 @ P )
| ~ ( sequential @ E1 @ E3 ) )
| ~ ( sequential @ E1 @ E2 ) )
& ! [E1: $i,E2: $i] :
( ~ ( precedes @ E1 @ E2 @ P )
| ( ( precedes @ ( sK9_E3 @ E2 @ E1 @ P ) @ E2 @ P )
& ( sequential @ E1 @ ( sK9_E3 @ E2 @ E1 @ P ) ) )
| ( sequential @ E1 @ E2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(2287,plain,
( ( ! [V1: $i] :
( ! [V2: $i,SP: $i] :
( ( ( path @ V1 @ V2 @ ( sK8_P @ SP @ V2 @ V1 ) )
& ~ ( less_or_equal @ ( length_of @ SP ) @ ( length_of @ ( sK8_P @ SP @ V2 @ V1 ) ) ) )
| ( V1 = V2 )
| ~ ( path @ V1 @ V2 @ SP )
| ( shortest_path @ V1 @ V2 @ SP ) )
& ! [V2: $i,SP: $i] :
( ~ ( shortest_path @ V1 @ V2 @ SP )
| ! [P: $i] :
( ~ ( path @ V1 @ V2 @ P )
| ( less_or_equal @ ( length_of @ SP ) @ ( length_of @ P ) ) ) )
& ! [V2: $i] :
( ! [SP: $i] :
~ ( shortest_path @ V1 @ V2 @ SP )
| ( V1 != V2 ) )
& ! [V2: $i,SP: $i] :
( ~ ( shortest_path @ V1 @ V2 @ SP )
| ( path @ V1 @ V2 @ SP ) ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(2288,plain,
( ( ! [V1: $i,V2: $i,E1: $i] :
( ! [E2: $i] :
( ! [P: $i] :
( ~ ( precedes @ E1 @ E2 @ P )
| ~ ( shortest_path @ V1 @ V2 @ P ) )
| ! [E3: $i] :
( ( ( tail_of @ E3 )
!= ( tail_of @ E1 ) )
| ( ( head_of @ E3 )
!= ( head_of @ E2 ) ) ) )
& ! [E2: $i,P: $i] :
( ~ ( precedes @ E1 @ E2 @ P )
| ~ ( shortest_path @ V1 @ V2 @ P )
| ~ ( precedes @ E2 @ E1 @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(2289,plain,
( ( ! [E1: $i] :
( ! [E2: $i,E3: $i] :
( ~ ( edge @ E1 )
| ~ ( edge @ E2 )
| ~ ( edge @ E3 )
| ~ ( sequential @ E1 @ E2 )
| ~ ( sequential @ E2 @ E3 )
| ~ ( sequential @ E3 @ E1 )
| ( triangle @ E1 @ E2 @ E3 ) )
& ( ! [E2: $i,E3: $i] :
~ ( triangle @ E1 @ E2 @ E3 )
| ( edge @ E1 ) )
& ! [E2: $i] :
( ! [E3: $i] :
~ ( triangle @ E1 @ E2 @ E3 )
| ( edge @ E2 ) )
& ! [E2: $i,E3: $i] :
( ~ ( triangle @ E1 @ E2 @ E3 )
| ( edge @ E3 ) )
& ! [E2: $i] :
( ! [E3: $i] :
~ ( triangle @ E1 @ E2 @ E3 )
| ( sequential @ E1 @ E2 ) )
& ! [E2: $i,E3: $i] :
( ~ ( triangle @ E1 @ E2 @ E3 )
| ( sequential @ E2 @ E3 ) )
& ! [E2: $i,E3: $i] :
( ~ ( triangle @ E1 @ E2 @ E3 )
| ( sequential @ E3 @ E1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(2290,plain,
( ( ! [V1: $i,V2: $i,P: $i] :
( ~ ( path @ V1 @ V2 @ P )
| ( ( length_of @ P )
= ( number_of_in @ edges @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(2291,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)],[63]) ).
thf(2292,plain,
( ( ! [P: $i] :
( ( ( on_path @ ( sK6_E1 @ P ) @ P )
& ( on_path @ ( sK7_SY80 @ P ) @ P )
& ( sequential @ ( sK6_E1 @ P ) @ ( sK7_SY80 @ P ) )
& ! [SY82: $i] :
~ ( triangle @ ( sK6_E1 @ P ) @ ( sK7_SY80 @ P ) @ SY82 ) )
| ! [V1: $i,V2: $i] :
~ ( path @ V1 @ V2 @ P )
| ( ( number_of_in @ sequential_pairs @ P )
= ( number_of_in @ triangles @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(2293,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(2294,plain,
( ( precedes @ sK3_SY74 @ sK4_SY77 @ sK5_SY79 )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(2295,plain,
( ( shortest_path @ sK1_V1 @ sK2_SY70 @ sK5_SY79 )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(2296,plain,
( ( ~ ( edge @ sK4_SY77 ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(2297,plain,
( ( ~ complete
| ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( vertex @ SX0 )
| ~ ( vertex @ SX1 )
| ~ ( ~ ~ ( ~ ( ( SX0
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
| ~ ~ ( ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2279]) ).
thf(2298,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( head_of @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( tail_of @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2278]) ).
thf(2299,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i,SX2: $i] :
~ ( path @ SX1 @ SX2 @ SX0 )
| ~ ( ~ ~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( precedes @ SX1 @ SX2 @ SX0 )
| ( on_path @ SX1 @ SX0 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( precedes @ SX1 @ SX2 @ SX0 )
| ( on_path @ SX2 @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( precedes @ SX1 @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( precedes @ SX3 @ SX2 @ SX0 )
| ~ ( sequential @ SX1 @ SX3 ) )
| ~ ( sequential @ SX1 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( precedes @ SX1 @ SX2 @ SX0 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SX2 @ SX1 @ SX0 ) @ SX2 @ SX0 )
| ~ ( sequential @ SX1 @ ( sK9_E3 @ SX2 @ SX1 @ SX0 ) ) )
| ( sequential @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2286]) ).
thf(2300,plain,
( ( ! [SX0: $i] :
~ ( ~ ~ ( ~ ( ! [SX1: $i,SX2: $i] :
~ ( path @ SX0 @ SX1 @ SX2 )
| ( vertex @ SX0 ) )
| ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( path @ SX0 @ SX1 @ SX2 )
| ( vertex @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( path @ SX0 @ SX1 @ SX2 )
| ~ ( ~ ~ ( ( SX0
!= ( tail_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( edge @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ( SX1
!= ( head_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) )
| ( SX2
!= ( path_cons @ ( sK11_E @ SX2 @ SX1 @ SX0 ) @ empty ) )
| ! [SX3: $i] :
( ( SX2
!= ( path_cons @ ( sK11_E @ SX2 @ SX1 @ SX0 ) @ SX3 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) @ SX1 @ SX3 ) ) )
| ~ ~ ( ~ ( ( SX1
= ( head_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( ( SX2
!= ( path_cons @ ( sK11_E @ SX2 @ SX1 @ SX0 ) @ ( sK13_SY84 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) @ SX1 @ ( sK13_SY84 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX2
= ( path_cons @ ( sK11_E @ SX2 @ SX1 @ SX0 ) @ empty ) )
| ~ ( ( SX2
!= ( path_cons @ ( sK11_E @ SX2 @ SX1 @ SX0 ) @ ( sK12_SY85 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) @ SX1 @ ( sK12_SY85 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2281]) ).
thf(2301,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in_path @ SX3 @ SX2 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ~ ( ~ ( on_path @ ( sK10_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( ( SX3
= ( head_of @ ( sK10_E @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ( SX3
= ( tail_of @ ( sK10_E @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( in_path @ SX3 @ SX2 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ( vertex @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2283]) ).
thf(2302,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SX0 ) @ SX0 )
| ~ ( on_path @ ( sK7_SY80 @ SX0 ) @ SX0 ) )
| ~ ( sequential @ ( sK6_E1 @ SX0 ) @ ( sK7_SY80 @ SX0 ) ) )
| ~ ! [SX1: $i] :
~ ( triangle @ ( sK6_E1 @ SX0 ) @ ( sK7_SY80 @ SX0 ) @ SX1 ) )
| ! [SX1: $i,SX2: $i] :
~ ( path @ SX1 @ SX2 @ SX0 )
| ( ( number_of_in @ sequential_pairs @ SX0 )
= ( number_of_in @ triangles @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2292]) ).
thf(2303,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( on_path @ SX3 @ SX2 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ( edge @ SX3 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( on_path @ SX3 @ SX2 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ( in_path @ ( head_of @ SX3 ) @ SX2 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( on_path @ SX3 @ SX2 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ( in_path @ ( tail_of @ SX3 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2282]) ).
thf(2304,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( edge @ SX0 )
| ~ ( edge @ SX1 )
| ~ ( edge @ SX2 )
| ~ ( sequential @ SX0 @ SX1 )
| ~ ( sequential @ SX1 @ SX2 )
| ~ ( sequential @ SX2 @ SX0 )
| ( triangle @ SX0 @ SX1 @ SX2 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SX1: $i,SX2: $i] :
~ ( triangle @ SX0 @ SX1 @ SX2 )
| ( edge @ SX0 ) )
| ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( triangle @ SX0 @ SX1 @ SX2 )
| ( edge @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( triangle @ SX0 @ SX1 @ SX2 )
| ( edge @ SX2 ) ) )
| ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( triangle @ SX0 @ SX1 @ SX2 )
| ( sequential @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( triangle @ SX0 @ SX1 @ SX2 )
| ( sequential @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( triangle @ SX0 @ SX1 @ SX2 )
| ( sequential @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2289]) ).
thf(2305,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( path @ SX0 @ SX1 @ ( sK8_P @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SX2 ) @ ( length_of @ ( sK8_P @ SX2 @ SX1 @ SX0 ) ) ) )
| ( SX0 = SX1 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ( shortest_path @ SX0 @ SX1 @ SX2 ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( shortest_path @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( path @ SX0 @ SX1 @ SX3 )
| ( less_or_equal @ ( length_of @ SX2 ) @ ( length_of @ SX3 ) ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( shortest_path @ SX0 @ SX1 @ SX2 )
| ( SX0 != SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( shortest_path @ SX0 @ SX1 @ SX2 )
| ( path @ SX0 @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2287]) ).
thf(2306,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( vertex @ SX0 )
| ~ ( vertex @ SX1 )
| ~ ( ~ ! [SX3: $i] :
( ( SX0
!= ( tail_of @ SX3 ) )
| ~ ( edge @ SX3 )
| ( SX1
!= ( head_of @ SX3 ) )
| ( SX2
!= ( path_cons @ SX3 @ empty ) ) )
| ~ ! [SX3: $i] :
( ( SX0
!= ( tail_of @ SX3 ) )
| ~ ( edge @ SX3 )
| ! [SX4: $i] :
( ( SX2
!= ( path_cons @ SX3 @ SX4 ) )
| ~ ( path @ ( head_of @ SX3 ) @ SX1 @ SX4 ) ) ) )
| ( path @ SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2280]) ).
thf(2307,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
( ~ ( precedes @ SX2 @ SX3 @ SX4 )
| ~ ( shortest_path @ SX0 @ SX1 @ SX4 ) )
| ! [SX4: $i] :
( ( ( tail_of @ SX4 )
!= ( tail_of @ SX2 ) )
| ( ( head_of @ SX4 )
!= ( head_of @ SX3 ) ) ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( precedes @ SX2 @ SX3 @ SX4 )
| ~ ( shortest_path @ SX0 @ SX1 @ SX4 )
| ~ ( precedes @ SX3 @ SX2 @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2288]) ).
thf(2308,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( edge @ SX0 )
| ~ ( edge @ SX1 )
| ( ( head_of @ SX0 )
!= ( tail_of @ SX1 ) )
| ( sequential @ SX0 @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2284]) ).
thf(2309,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i,SX2: $i] :
~ ( path @ SX1 @ SX2 @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( on_path @ SX1 @ SX0 )
| ~ ( on_path @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( precedes @ SX3 @ SX2 @ SX0 )
| ~ ( sequential @ SX1 @ SX3 ) )
| ( precedes @ SX1 @ SX2 @ SX0 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( on_path @ SX1 @ SX0 )
| ~ ( on_path @ SX2 @ SX0 )
| ~ ( sequential @ SX1 @ SX2 )
| ( precedes @ SX1 @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2285]) ).
thf(2310,plain,
! [SV457: $i] :
( ( ~ ( edge @ SV457 )
| ( ( head_of @ SV457 )
!= ( tail_of @ SV457 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2277]) ).
thf(2311,plain,
! [SV458: $i] :
( ( ! [SY722: $i,SY723: $i] :
( ~ ( path @ SV458 @ SY722 @ SY723 )
| ( ( length_of @ SY723 )
= ( number_of_in @ edges @ SY723 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2290]) ).
thf(2312,plain,
! [SV459: $i] :
( ( ! [SY724: $i,SY725: $i] :
( ~ ( path @ SV459 @ SY724 @ SY725 )
| ( ( number_of_in @ sequential_pairs @ SY725 )
= ( minus @ ( length_of @ SY725 ) @ n1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2291]) ).
thf(2313,plain,
! [SV460: $i] :
( ( ! [SY726: $i] : ( less_or_equal @ ( number_of_in @ SV460 @ SY726 ) @ ( number_of_in @ SV460 @ graph ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2293]) ).
thf(2314,plain,
( ( edge @ sK4_SY77 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2296]) ).
thf(2315,plain,
( ( ( ~ complete )
= $true )
| ( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( vertex @ SX0 )
| ~ ( vertex @ SX1 )
| ~ ( ~ ~ ( ~ ( ( SX0
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
| ~ ~ ( ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2297]) ).
thf(2316,plain,
( ( ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( head_of @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( tail_of @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2298]) ).
thf(2317,plain,
! [SV461: $i] :
( ( ! [SY727: $i,SY728: $i] :
~ ( path @ SY727 @ SY728 @ SV461 )
| ~ ( ~ ~ ( ~ ! [SY729: $i] :
( ! [SY730: $i] :
~ ( precedes @ SY729 @ SY730 @ SV461 )
| ( on_path @ SY729 @ SV461 ) )
| ~ ! [SY731: $i,SY732: $i] :
( ~ ( precedes @ SY731 @ SY732 @ SV461 )
| ( on_path @ SY732 @ SV461 ) ) )
| ~ ~ ( ~ ! [SY733: $i,SY734: $i] :
( ~ ( precedes @ SY733 @ SY734 @ SV461 )
| ! [SY735: $i] :
( ~ ( precedes @ SY735 @ SY734 @ SV461 )
| ~ ( sequential @ SY733 @ SY735 ) )
| ~ ( sequential @ SY733 @ SY734 ) )
| ~ ! [SY736: $i,SY737: $i] :
( ~ ( precedes @ SY736 @ SY737 @ SV461 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY737 @ SY736 @ SV461 ) @ SY737 @ SV461 )
| ~ ( sequential @ SY736 @ ( sK9_E3 @ SY737 @ SY736 @ SV461 ) ) )
| ( sequential @ SY736 @ SY737 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2299]) ).
thf(2318,plain,
! [SV462: $i] :
( ( ~ ( ~ ~ ( ~ ( ! [SY738: $i,SY739: $i] :
~ ( path @ SV462 @ SY738 @ SY739 )
| ( vertex @ SV462 ) )
| ~ ! [SY740: $i] :
( ! [SY741: $i] :
~ ( path @ SV462 @ SY740 @ SY741 )
| ( vertex @ SY740 ) ) )
| ~ ! [SY742: $i,SY743: $i] :
( ~ ( path @ SV462 @ SY742 @ SY743 )
| ~ ( ~ ~ ( ( SV462
!= ( tail_of @ ( sK11_E @ SY743 @ SY742 @ SV462 ) ) )
| ~ ( edge @ ( sK11_E @ SY743 @ SY742 @ SV462 ) ) )
| ~ ~ ( ~ ( ( SY742
!= ( head_of @ ( sK11_E @ SY743 @ SY742 @ SV462 ) ) )
| ( SY743
!= ( path_cons @ ( sK11_E @ SY743 @ SY742 @ SV462 ) @ empty ) )
| ! [SY744: $i] :
( ( SY743
!= ( path_cons @ ( sK11_E @ SY743 @ SY742 @ SV462 ) @ SY744 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY743 @ SY742 @ SV462 ) ) @ SY742 @ SY744 ) ) )
| ~ ~ ( ~ ( ( SY742
= ( head_of @ ( sK11_E @ SY743 @ SY742 @ SV462 ) ) )
| ~ ( ( SY743
!= ( path_cons @ ( sK11_E @ SY743 @ SY742 @ SV462 ) @ ( sK13_SY84 @ SY743 @ SY742 @ SV462 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY743 @ SY742 @ SV462 ) ) @ SY742 @ ( sK13_SY84 @ SY743 @ SY742 @ SV462 ) ) ) )
| ~ ( ( SY743
= ( path_cons @ ( sK11_E @ SY743 @ SY742 @ SV462 ) @ empty ) )
| ~ ( ( SY743
!= ( path_cons @ ( sK11_E @ SY743 @ SY742 @ SV462 ) @ ( sK12_SY85 @ SY743 @ SY742 @ SV462 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY743 @ SY742 @ SV462 ) ) @ SY742 @ ( sK12_SY85 @ SY743 @ SY742 @ SV462 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2300]) ).
thf(2319,plain,
! [SV463: $i] :
( ( ! [SY745: $i] :
~ ( ~ ! [SY746: $i,SY747: $i] :
( ~ ( in_path @ SY747 @ SY746 )
| ~ ( path @ SV463 @ SY745 @ SY746 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY747 @ SY746 @ SY745 @ SV463 ) @ SY746 )
| ~ ( ( SY747
= ( head_of @ ( sK10_E @ SY747 @ SY746 @ SY745 @ SV463 ) ) )
| ( SY747
= ( tail_of @ ( sK10_E @ SY747 @ SY746 @ SY745 @ SV463 ) ) ) ) ) )
| ~ ! [SY748: $i,SY749: $i] :
( ~ ( in_path @ SY749 @ SY748 )
| ~ ( path @ SV463 @ SY745 @ SY748 )
| ( vertex @ SY749 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2301]) ).
thf(2320,plain,
! [SV464: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV464 ) @ SV464 )
| ~ ( on_path @ ( sK7_SY80 @ SV464 ) @ SV464 ) )
| ~ ( sequential @ ( sK6_E1 @ SV464 ) @ ( sK7_SY80 @ SV464 ) ) )
| ~ ! [SY750: $i] :
~ ( triangle @ ( sK6_E1 @ SV464 ) @ ( sK7_SY80 @ SV464 ) @ SY750 ) )
| ! [SY751: $i,SY752: $i] :
~ ( path @ SY751 @ SY752 @ SV464 )
| ( ( number_of_in @ sequential_pairs @ SV464 )
= ( number_of_in @ triangles @ SV464 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2302]) ).
thf(2321,plain,
! [SV465: $i] :
( ( ! [SY753: $i] :
~ ( ~ ~ ( ~ ! [SY754: $i,SY755: $i] :
( ~ ( on_path @ SY755 @ SY754 )
| ~ ( path @ SV465 @ SY753 @ SY754 )
| ( edge @ SY755 ) )
| ~ ! [SY756: $i,SY757: $i] :
( ~ ( on_path @ SY757 @ SY756 )
| ~ ( path @ SV465 @ SY753 @ SY756 )
| ( in_path @ ( head_of @ SY757 ) @ SY756 ) ) )
| ~ ! [SY758: $i,SY759: $i] :
( ~ ( on_path @ SY759 @ SY758 )
| ~ ( path @ SV465 @ SY753 @ SY758 )
| ( in_path @ ( tail_of @ SY759 ) @ SY758 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2303]) ).
thf(2322,plain,
! [SV466: $i] :
( ( ~ ( ~ ! [SY760: $i,SY761: $i] :
( ~ ( edge @ SV466 )
| ~ ( edge @ SY760 )
| ~ ( edge @ SY761 )
| ~ ( sequential @ SV466 @ SY760 )
| ~ ( sequential @ SY760 @ SY761 )
| ~ ( sequential @ SY761 @ SV466 )
| ( triangle @ SV466 @ SY760 @ SY761 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY762: $i,SY763: $i] :
~ ( triangle @ SV466 @ SY762 @ SY763 )
| ( edge @ SV466 ) )
| ~ ! [SY764: $i] :
( ! [SY765: $i] :
~ ( triangle @ SV466 @ SY764 @ SY765 )
| ( edge @ SY764 ) ) )
| ~ ! [SY766: $i,SY767: $i] :
( ~ ( triangle @ SV466 @ SY766 @ SY767 )
| ( edge @ SY767 ) ) )
| ~ ! [SY768: $i] :
( ! [SY769: $i] :
~ ( triangle @ SV466 @ SY768 @ SY769 )
| ( sequential @ SV466 @ SY768 ) ) )
| ~ ! [SY770: $i,SY771: $i] :
( ~ ( triangle @ SV466 @ SY770 @ SY771 )
| ( sequential @ SY770 @ SY771 ) ) )
| ~ ! [SY772: $i,SY773: $i] :
( ~ ( triangle @ SV466 @ SY772 @ SY773 )
| ( sequential @ SY773 @ SV466 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2304]) ).
thf(2323,plain,
! [SV467: $i] :
( ( ~ ( ~ ! [SY774: $i,SY775: $i] :
( ~ ( ~ ( path @ SV467 @ SY774 @ ( sK8_P @ SY775 @ SY774 @ SV467 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY775 ) @ ( length_of @ ( sK8_P @ SY775 @ SY774 @ SV467 ) ) ) )
| ( SV467 = SY774 )
| ~ ( path @ SV467 @ SY774 @ SY775 )
| ( shortest_path @ SV467 @ SY774 @ SY775 ) )
| ~ ~ ( ~ ! [SY776: $i,SY777: $i] :
( ~ ( shortest_path @ SV467 @ SY776 @ SY777 )
| ! [SY778: $i] :
( ~ ( path @ SV467 @ SY776 @ SY778 )
| ( less_or_equal @ ( length_of @ SY777 ) @ ( length_of @ SY778 ) ) ) )
| ~ ~ ( ~ ! [SY779: $i] :
( ! [SY780: $i] :
~ ( shortest_path @ SV467 @ SY779 @ SY780 )
| ( SV467 != SY779 ) )
| ~ ! [SY781: $i,SY782: $i] :
( ~ ( shortest_path @ SV467 @ SY781 @ SY782 )
| ( path @ SV467 @ SY781 @ SY782 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2305]) ).
thf(2324,plain,
! [SV468: $i] :
( ( ! [SY783: $i,SY784: $i] :
( ~ ( vertex @ SV468 )
| ~ ( vertex @ SY783 )
| ~ ( ~ ! [SY785: $i] :
( ( SV468
!= ( tail_of @ SY785 ) )
| ~ ( edge @ SY785 )
| ( SY783
!= ( head_of @ SY785 ) )
| ( SY784
!= ( path_cons @ SY785 @ empty ) ) )
| ~ ! [SY786: $i] :
( ( SV468
!= ( tail_of @ SY786 ) )
| ~ ( edge @ SY786 )
| ! [SX4: $i] :
( ( SY784
!= ( path_cons @ SY786 @ SX4 ) )
| ~ ( path @ ( head_of @ SY786 ) @ SY783 @ SX4 ) ) ) )
| ( path @ SV468 @ SY783 @ SY784 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2306]) ).
thf(2325,plain,
! [SV469: $i] :
( ( ! [SY788: $i,SY789: $i] :
~ ( ~ ! [SY790: $i] :
( ! [SY791: $i] :
( ~ ( precedes @ SY789 @ SY790 @ SY791 )
| ~ ( shortest_path @ SV469 @ SY788 @ SY791 ) )
| ! [SX4: $i] :
( ( ( tail_of @ SX4 )
!= ( tail_of @ SY789 ) )
| ( ( head_of @ SX4 )
!= ( head_of @ SY790 ) ) ) )
| ~ ! [SY793: $i,SY794: $i] :
( ~ ( precedes @ SY789 @ SY793 @ SY794 )
| ~ ( shortest_path @ SV469 @ SY788 @ SY794 )
| ~ ( precedes @ SY793 @ SY789 @ SY794 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2307]) ).
thf(2326,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( edge @ SX0 )
| ~ ( edge @ SX1 )
| ( ( head_of @ SX0 )
!= ( tail_of @ SX1 ) )
| ( sequential @ SX0 @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2308]) ).
thf(2327,plain,
! [SV470: $i] :
( ( ! [SY795: $i,SY796: $i] :
~ ( path @ SY795 @ SY796 @ SV470 )
| ~ ( ~ ! [SY797: $i,SY798: $i] :
( ~ ( on_path @ SY797 @ SV470 )
| ~ ( on_path @ SY798 @ SV470 )
| ! [SY799: $i] :
( ~ ( precedes @ SY799 @ SY798 @ SV470 )
| ~ ( sequential @ SY797 @ SY799 ) )
| ( precedes @ SY797 @ SY798 @ SV470 ) )
| ~ ! [SY800: $i,SY801: $i] :
( ~ ( on_path @ SY800 @ SV470 )
| ~ ( on_path @ SY801 @ SV470 )
| ~ ( sequential @ SY800 @ SY801 )
| ( precedes @ SY800 @ SY801 @ SV470 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2309]) ).
thf(2328,plain,
! [SV457: $i] :
( ( ( ~ ( edge @ SV457 ) )
= $true )
| ( ( ( ( head_of @ SV457 )
!= ( tail_of @ SV457 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2310]) ).
thf(2329,plain,
! [SV471: $i,SV458: $i] :
( ( ! [SY802: $i] :
( ~ ( path @ SV458 @ SV471 @ SY802 )
| ( ( length_of @ SY802 )
= ( number_of_in @ edges @ SY802 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2311]) ).
thf(2330,plain,
! [SV472: $i,SV459: $i] :
( ( ! [SY803: $i] :
( ~ ( path @ SV459 @ SV472 @ SY803 )
| ( ( number_of_in @ sequential_pairs @ SY803 )
= ( minus @ ( length_of @ SY803 ) @ n1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2312]) ).
thf(2331,plain,
! [SV473: $i,SV460: $i] :
( ( less_or_equal @ ( number_of_in @ SV460 @ SV473 ) @ ( number_of_in @ SV460 @ graph ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2313]) ).
thf(2332,plain,
( ( complete = $false )
| ( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( vertex @ SX0 )
| ~ ( vertex @ SX1 )
| ~ ( ~ ~ ( ~ ( ( SX0
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
| ~ ~ ( ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2315]) ).
thf(2333,plain,
( ( ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( head_of @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2316]) ).
thf(2334,plain,
( ( ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( tail_of @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2316]) ).
thf(2335,plain,
! [SV461: $i] :
( ( ( ! [SY727: $i,SY728: $i] :
~ ( path @ SY727 @ SY728 @ SV461 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY729: $i] :
( ! [SY730: $i] :
~ ( precedes @ SY729 @ SY730 @ SV461 )
| ( on_path @ SY729 @ SV461 ) )
| ~ ! [SY731: $i,SY732: $i] :
( ~ ( precedes @ SY731 @ SY732 @ SV461 )
| ( on_path @ SY732 @ SV461 ) ) )
| ~ ~ ( ~ ! [SY733: $i,SY734: $i] :
( ~ ( precedes @ SY733 @ SY734 @ SV461 )
| ! [SY735: $i] :
( ~ ( precedes @ SY735 @ SY734 @ SV461 )
| ~ ( sequential @ SY733 @ SY735 ) )
| ~ ( sequential @ SY733 @ SY734 ) )
| ~ ! [SY736: $i,SY737: $i] :
( ~ ( precedes @ SY736 @ SY737 @ SV461 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY737 @ SY736 @ SV461 ) @ SY737 @ SV461 )
| ~ ( sequential @ SY736 @ ( sK9_E3 @ SY737 @ SY736 @ SV461 ) ) )
| ( sequential @ SY736 @ SY737 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2317]) ).
thf(2336,plain,
! [SV462: $i] :
( ( ~ ~ ( ~ ( ! [SY738: $i,SY739: $i] :
~ ( path @ SV462 @ SY738 @ SY739 )
| ( vertex @ SV462 ) )
| ~ ! [SY740: $i] :
( ! [SY741: $i] :
~ ( path @ SV462 @ SY740 @ SY741 )
| ( vertex @ SY740 ) ) )
| ~ ! [SY742: $i,SY743: $i] :
( ~ ( path @ SV462 @ SY742 @ SY743 )
| ~ ( ~ ~ ( ( SV462
!= ( tail_of @ ( sK11_E @ SY743 @ SY742 @ SV462 ) ) )
| ~ ( edge @ ( sK11_E @ SY743 @ SY742 @ SV462 ) ) )
| ~ ~ ( ~ ( ( SY742
!= ( head_of @ ( sK11_E @ SY743 @ SY742 @ SV462 ) ) )
| ( SY743
!= ( path_cons @ ( sK11_E @ SY743 @ SY742 @ SV462 ) @ empty ) )
| ! [SY744: $i] :
( ( SY743
!= ( path_cons @ ( sK11_E @ SY743 @ SY742 @ SV462 ) @ SY744 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY743 @ SY742 @ SV462 ) ) @ SY742 @ SY744 ) ) )
| ~ ~ ( ~ ( ( SY742
= ( head_of @ ( sK11_E @ SY743 @ SY742 @ SV462 ) ) )
| ~ ( ( SY743
!= ( path_cons @ ( sK11_E @ SY743 @ SY742 @ SV462 ) @ ( sK13_SY84 @ SY743 @ SY742 @ SV462 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY743 @ SY742 @ SV462 ) ) @ SY742 @ ( sK13_SY84 @ SY743 @ SY742 @ SV462 ) ) ) )
| ~ ( ( SY743
= ( path_cons @ ( sK11_E @ SY743 @ SY742 @ SV462 ) @ empty ) )
| ~ ( ( SY743
!= ( path_cons @ ( sK11_E @ SY743 @ SY742 @ SV462 ) @ ( sK12_SY85 @ SY743 @ SY742 @ SV462 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY743 @ SY742 @ SV462 ) ) @ SY742 @ ( sK12_SY85 @ SY743 @ SY742 @ SV462 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2318]) ).
thf(2337,plain,
! [SV474: $i,SV463: $i] :
( ( ~ ( ~ ! [SY804: $i,SY805: $i] :
( ~ ( in_path @ SY805 @ SY804 )
| ~ ( path @ SV463 @ SV474 @ SY804 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY805 @ SY804 @ SV474 @ SV463 ) @ SY804 )
| ~ ( ( SY805
= ( head_of @ ( sK10_E @ SY805 @ SY804 @ SV474 @ SV463 ) ) )
| ( SY805
= ( tail_of @ ( sK10_E @ SY805 @ SY804 @ SV474 @ SV463 ) ) ) ) ) )
| ~ ! [SY806: $i,SY807: $i] :
( ~ ( in_path @ SY807 @ SY806 )
| ~ ( path @ SV463 @ SV474 @ SY806 )
| ( vertex @ SY807 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2319]) ).
thf(2338,plain,
! [SV464: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV464 ) @ SV464 )
| ~ ( on_path @ ( sK7_SY80 @ SV464 ) @ SV464 ) )
| ~ ( sequential @ ( sK6_E1 @ SV464 ) @ ( sK7_SY80 @ SV464 ) ) )
| ~ ! [SY750: $i] :
~ ( triangle @ ( sK6_E1 @ SV464 ) @ ( sK7_SY80 @ SV464 ) @ SY750 ) )
| ! [SY751: $i,SY752: $i] :
~ ( path @ SY751 @ SY752 @ SV464 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV464 )
= ( number_of_in @ triangles @ SV464 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2320]) ).
thf(2339,plain,
! [SV475: $i,SV465: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY808: $i,SY809: $i] :
( ~ ( on_path @ SY809 @ SY808 )
| ~ ( path @ SV465 @ SV475 @ SY808 )
| ( edge @ SY809 ) )
| ~ ! [SY810: $i,SY811: $i] :
( ~ ( on_path @ SY811 @ SY810 )
| ~ ( path @ SV465 @ SV475 @ SY810 )
| ( in_path @ ( head_of @ SY811 ) @ SY810 ) ) )
| ~ ! [SY812: $i,SY813: $i] :
( ~ ( on_path @ SY813 @ SY812 )
| ~ ( path @ SV465 @ SV475 @ SY812 )
| ( in_path @ ( tail_of @ SY813 ) @ SY812 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2321]) ).
thf(2340,plain,
! [SV466: $i] :
( ( ~ ! [SY760: $i,SY761: $i] :
( ~ ( edge @ SV466 )
| ~ ( edge @ SY760 )
| ~ ( edge @ SY761 )
| ~ ( sequential @ SV466 @ SY760 )
| ~ ( sequential @ SY760 @ SY761 )
| ~ ( sequential @ SY761 @ SV466 )
| ( triangle @ SV466 @ SY760 @ SY761 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY762: $i,SY763: $i] :
~ ( triangle @ SV466 @ SY762 @ SY763 )
| ( edge @ SV466 ) )
| ~ ! [SY764: $i] :
( ! [SY765: $i] :
~ ( triangle @ SV466 @ SY764 @ SY765 )
| ( edge @ SY764 ) ) )
| ~ ! [SY766: $i,SY767: $i] :
( ~ ( triangle @ SV466 @ SY766 @ SY767 )
| ( edge @ SY767 ) ) )
| ~ ! [SY768: $i] :
( ! [SY769: $i] :
~ ( triangle @ SV466 @ SY768 @ SY769 )
| ( sequential @ SV466 @ SY768 ) ) )
| ~ ! [SY770: $i,SY771: $i] :
( ~ ( triangle @ SV466 @ SY770 @ SY771 )
| ( sequential @ SY770 @ SY771 ) ) )
| ~ ! [SY772: $i,SY773: $i] :
( ~ ( triangle @ SV466 @ SY772 @ SY773 )
| ( sequential @ SY773 @ SV466 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2322]) ).
thf(2341,plain,
! [SV467: $i] :
( ( ~ ! [SY774: $i,SY775: $i] :
( ~ ( ~ ( path @ SV467 @ SY774 @ ( sK8_P @ SY775 @ SY774 @ SV467 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY775 ) @ ( length_of @ ( sK8_P @ SY775 @ SY774 @ SV467 ) ) ) )
| ( SV467 = SY774 )
| ~ ( path @ SV467 @ SY774 @ SY775 )
| ( shortest_path @ SV467 @ SY774 @ SY775 ) )
| ~ ~ ( ~ ! [SY776: $i,SY777: $i] :
( ~ ( shortest_path @ SV467 @ SY776 @ SY777 )
| ! [SY778: $i] :
( ~ ( path @ SV467 @ SY776 @ SY778 )
| ( less_or_equal @ ( length_of @ SY777 ) @ ( length_of @ SY778 ) ) ) )
| ~ ~ ( ~ ! [SY779: $i] :
( ! [SY780: $i] :
~ ( shortest_path @ SV467 @ SY779 @ SY780 )
| ( SV467 != SY779 ) )
| ~ ! [SY781: $i,SY782: $i] :
( ~ ( shortest_path @ SV467 @ SY781 @ SY782 )
| ( path @ SV467 @ SY781 @ SY782 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2323]) ).
thf(2342,plain,
! [SV476: $i,SV468: $i] :
( ( ! [SY814: $i] :
( ~ ( vertex @ SV468 )
| ~ ( vertex @ SV476 )
| ~ ( ~ ! [SY815: $i] :
( ( SV468
!= ( tail_of @ SY815 ) )
| ~ ( edge @ SY815 )
| ( SV476
!= ( head_of @ SY815 ) )
| ( SY814
!= ( path_cons @ SY815 @ empty ) ) )
| ~ ! [SY816: $i] :
( ( SV468
!= ( tail_of @ SY816 ) )
| ~ ( edge @ SY816 )
| ! [SY817: $i] :
( ( SY814
!= ( path_cons @ SY816 @ SY817 ) )
| ~ ( path @ ( head_of @ SY816 ) @ SV476 @ SY817 ) ) ) )
| ( path @ SV468 @ SV476 @ SY814 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2324]) ).
thf(2343,plain,
! [SV477: $i,SV469: $i] :
( ( ! [SY818: $i] :
~ ( ~ ! [SY819: $i] :
( ! [SY820: $i] :
( ~ ( precedes @ SY818 @ SY819 @ SY820 )
| ~ ( shortest_path @ SV469 @ SV477 @ SY820 ) )
| ! [SX4: $i] :
( ( ( tail_of @ SX4 )
!= ( tail_of @ SY818 ) )
| ( ( head_of @ SX4 )
!= ( head_of @ SY819 ) ) ) )
| ~ ! [SY822: $i,SY823: $i] :
( ~ ( precedes @ SY818 @ SY822 @ SY823 )
| ~ ( shortest_path @ SV469 @ SV477 @ SY823 )
| ~ ( precedes @ SY822 @ SY818 @ SY823 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2325]) ).
thf(2344,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( edge @ SX0 )
| ~ ( edge @ SX1 )
| ( ( head_of @ SX0 )
!= ( tail_of @ SX1 ) )
| ( sequential @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2326]) ).
thf(2345,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2326]) ).
thf(2346,plain,
! [SV470: $i] :
( ( ( ! [SY795: $i,SY796: $i] :
~ ( path @ SY795 @ SY796 @ SV470 ) )
= $true )
| ( ( ~ ( ~ ! [SY797: $i,SY798: $i] :
( ~ ( on_path @ SY797 @ SV470 )
| ~ ( on_path @ SY798 @ SV470 )
| ! [SY799: $i] :
( ~ ( precedes @ SY799 @ SY798 @ SV470 )
| ~ ( sequential @ SY797 @ SY799 ) )
| ( precedes @ SY797 @ SY798 @ SV470 ) )
| ~ ! [SY800: $i,SY801: $i] :
( ~ ( on_path @ SY800 @ SV470 )
| ~ ( on_path @ SY801 @ SV470 )
| ~ ( sequential @ SY800 @ SY801 )
| ( precedes @ SY800 @ SY801 @ SV470 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2327]) ).
thf(2347,plain,
! [SV457: $i] :
( ( ( edge @ SV457 )
= $false )
| ( ( ( ( head_of @ SV457 )
!= ( tail_of @ SV457 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2328]) ).
thf(2348,plain,
! [SV478: $i,SV471: $i,SV458: $i] :
( ( ~ ( path @ SV458 @ SV471 @ SV478 )
| ( ( length_of @ SV478 )
= ( number_of_in @ edges @ SV478 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2329]) ).
thf(2349,plain,
! [SV479: $i,SV472: $i,SV459: $i] :
( ( ~ ( path @ SV459 @ SV472 @ SV479 )
| ( ( number_of_in @ sequential_pairs @ SV479 )
= ( minus @ ( length_of @ SV479 ) @ n1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2330]) ).
thf(2350,plain,
! [SV480: $i] :
( ( ( ! [SY824: $i] :
( ( SV480 = SY824 )
| ~ ( vertex @ SV480 )
| ~ ( vertex @ SY824 )
| ~ ( ~ ~ ( ~ ( ( SV480
!= ( head_of @ ( sK14_E @ SY824 @ SV480 ) ) )
| ( SY824
!= ( tail_of @ ( sK14_E @ SY824 @ SV480 ) ) )
| ( SY824
!= ( head_of @ ( sK14_E @ SY824 @ SV480 ) ) )
| ( SV480
!= ( tail_of @ ( sK14_E @ SY824 @ SV480 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV480
= ( head_of @ ( sK14_E @ SY824 @ SV480 ) ) )
| ( SY824
= ( head_of @ ( sK14_E @ SY824 @ SV480 ) ) ) )
| ~ ( ( SV480
= ( head_of @ ( sK14_E @ SY824 @ SV480 ) ) )
| ( SV480
= ( tail_of @ ( sK14_E @ SY824 @ SV480 ) ) ) ) )
| ~ ~ ( ~ ( ( SY824
= ( tail_of @ ( sK14_E @ SY824 @ SV480 ) ) )
| ( SY824
= ( head_of @ ( sK14_E @ SY824 @ SV480 ) ) ) )
| ~ ( ( SY824
= ( tail_of @ ( sK14_E @ SY824 @ SV480 ) ) )
| ( SV480
= ( tail_of @ ( sK14_E @ SY824 @ SV480 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SY824 @ SV480 ) ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2332]) ).
thf(2351,plain,
( ( ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( head_of @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2333]) ).
thf(2352,plain,
( ( ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( tail_of @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2334]) ).
thf(2353,plain,
! [SV461: $i,SV481: $i] :
( ( ( ! [SY825: $i] :
~ ( path @ SV481 @ SY825 @ SV461 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY729: $i] :
( ! [SY730: $i] :
~ ( precedes @ SY729 @ SY730 @ SV461 )
| ( on_path @ SY729 @ SV461 ) )
| ~ ! [SY731: $i,SY732: $i] :
( ~ ( precedes @ SY731 @ SY732 @ SV461 )
| ( on_path @ SY732 @ SV461 ) ) )
| ~ ~ ( ~ ! [SY733: $i,SY734: $i] :
( ~ ( precedes @ SY733 @ SY734 @ SV461 )
| ! [SY735: $i] :
( ~ ( precedes @ SY735 @ SY734 @ SV461 )
| ~ ( sequential @ SY733 @ SY735 ) )
| ~ ( sequential @ SY733 @ SY734 ) )
| ~ ! [SY736: $i,SY737: $i] :
( ~ ( precedes @ SY736 @ SY737 @ SV461 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY737 @ SY736 @ SV461 ) @ SY737 @ SV461 )
| ~ ( sequential @ SY736 @ ( sK9_E3 @ SY737 @ SY736 @ SV461 ) ) )
| ( sequential @ SY736 @ SY737 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2335]) ).
thf(2354,plain,
! [SV462: $i] :
( ( ~ ~ ( ~ ( ! [SY738: $i,SY739: $i] :
~ ( path @ SV462 @ SY738 @ SY739 )
| ( vertex @ SV462 ) )
| ~ ! [SY740: $i] :
( ! [SY741: $i] :
~ ( path @ SV462 @ SY740 @ SY741 )
| ( vertex @ SY740 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2336]) ).
thf(2355,plain,
! [SV462: $i] :
( ( ~ ! [SY742: $i,SY743: $i] :
( ~ ( path @ SV462 @ SY742 @ SY743 )
| ~ ( ~ ~ ( ( SV462
!= ( tail_of @ ( sK11_E @ SY743 @ SY742 @ SV462 ) ) )
| ~ ( edge @ ( sK11_E @ SY743 @ SY742 @ SV462 ) ) )
| ~ ~ ( ~ ( ( SY742
!= ( head_of @ ( sK11_E @ SY743 @ SY742 @ SV462 ) ) )
| ( SY743
!= ( path_cons @ ( sK11_E @ SY743 @ SY742 @ SV462 ) @ empty ) )
| ! [SY744: $i] :
( ( SY743
!= ( path_cons @ ( sK11_E @ SY743 @ SY742 @ SV462 ) @ SY744 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY743 @ SY742 @ SV462 ) ) @ SY742 @ SY744 ) ) )
| ~ ~ ( ~ ( ( SY742
= ( head_of @ ( sK11_E @ SY743 @ SY742 @ SV462 ) ) )
| ~ ( ( SY743
!= ( path_cons @ ( sK11_E @ SY743 @ SY742 @ SV462 ) @ ( sK13_SY84 @ SY743 @ SY742 @ SV462 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY743 @ SY742 @ SV462 ) ) @ SY742 @ ( sK13_SY84 @ SY743 @ SY742 @ SV462 ) ) ) )
| ~ ( ( SY743
= ( path_cons @ ( sK11_E @ SY743 @ SY742 @ SV462 ) @ empty ) )
| ~ ( ( SY743
!= ( path_cons @ ( sK11_E @ SY743 @ SY742 @ SV462 ) @ ( sK12_SY85 @ SY743 @ SY742 @ SV462 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY743 @ SY742 @ SV462 ) ) @ SY742 @ ( sK12_SY85 @ SY743 @ SY742 @ SV462 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2336]) ).
thf(2356,plain,
! [SV474: $i,SV463: $i] :
( ( ~ ! [SY804: $i,SY805: $i] :
( ~ ( in_path @ SY805 @ SY804 )
| ~ ( path @ SV463 @ SV474 @ SY804 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY805 @ SY804 @ SV474 @ SV463 ) @ SY804 )
| ~ ( ( SY805
= ( head_of @ ( sK10_E @ SY805 @ SY804 @ SV474 @ SV463 ) ) )
| ( SY805
= ( tail_of @ ( sK10_E @ SY805 @ SY804 @ SV474 @ SV463 ) ) ) ) ) )
| ~ ! [SY806: $i,SY807: $i] :
( ~ ( in_path @ SY807 @ SY806 )
| ~ ( path @ SV463 @ SV474 @ SY806 )
| ( vertex @ SY807 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2337]) ).
thf(2357,plain,
! [SV464: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV464 ) @ SV464 )
| ~ ( on_path @ ( sK7_SY80 @ SV464 ) @ SV464 ) )
| ~ ( sequential @ ( sK6_E1 @ SV464 ) @ ( sK7_SY80 @ SV464 ) ) )
| ~ ! [SY750: $i] :
~ ( triangle @ ( sK6_E1 @ SV464 ) @ ( sK7_SY80 @ SV464 ) @ SY750 ) ) )
= $true )
| ( ( ! [SY751: $i,SY752: $i] :
~ ( path @ SY751 @ SY752 @ SV464 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV464 )
= ( number_of_in @ triangles @ SV464 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2338]) ).
thf(2358,plain,
! [SV475: $i,SV465: $i] :
( ( ~ ~ ( ~ ! [SY808: $i,SY809: $i] :
( ~ ( on_path @ SY809 @ SY808 )
| ~ ( path @ SV465 @ SV475 @ SY808 )
| ( edge @ SY809 ) )
| ~ ! [SY810: $i,SY811: $i] :
( ~ ( on_path @ SY811 @ SY810 )
| ~ ( path @ SV465 @ SV475 @ SY810 )
| ( in_path @ ( head_of @ SY811 ) @ SY810 ) ) )
| ~ ! [SY812: $i,SY813: $i] :
( ~ ( on_path @ SY813 @ SY812 )
| ~ ( path @ SV465 @ SV475 @ SY812 )
| ( in_path @ ( tail_of @ SY813 ) @ SY812 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2339]) ).
thf(2359,plain,
! [SV466: $i] :
( ( ~ ! [SY760: $i,SY761: $i] :
( ~ ( edge @ SV466 )
| ~ ( edge @ SY760 )
| ~ ( edge @ SY761 )
| ~ ( sequential @ SV466 @ SY760 )
| ~ ( sequential @ SY760 @ SY761 )
| ~ ( sequential @ SY761 @ SV466 )
| ( triangle @ SV466 @ SY760 @ SY761 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2340]) ).
thf(2360,plain,
! [SV466: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY762: $i,SY763: $i] :
~ ( triangle @ SV466 @ SY762 @ SY763 )
| ( edge @ SV466 ) )
| ~ ! [SY764: $i] :
( ! [SY765: $i] :
~ ( triangle @ SV466 @ SY764 @ SY765 )
| ( edge @ SY764 ) ) )
| ~ ! [SY766: $i,SY767: $i] :
( ~ ( triangle @ SV466 @ SY766 @ SY767 )
| ( edge @ SY767 ) ) )
| ~ ! [SY768: $i] :
( ! [SY769: $i] :
~ ( triangle @ SV466 @ SY768 @ SY769 )
| ( sequential @ SV466 @ SY768 ) ) )
| ~ ! [SY770: $i,SY771: $i] :
( ~ ( triangle @ SV466 @ SY770 @ SY771 )
| ( sequential @ SY770 @ SY771 ) ) )
| ~ ! [SY772: $i,SY773: $i] :
( ~ ( triangle @ SV466 @ SY772 @ SY773 )
| ( sequential @ SY773 @ SV466 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2340]) ).
thf(2361,plain,
! [SV467: $i] :
( ( ~ ! [SY774: $i,SY775: $i] :
( ~ ( ~ ( path @ SV467 @ SY774 @ ( sK8_P @ SY775 @ SY774 @ SV467 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY775 ) @ ( length_of @ ( sK8_P @ SY775 @ SY774 @ SV467 ) ) ) )
| ( SV467 = SY774 )
| ~ ( path @ SV467 @ SY774 @ SY775 )
| ( shortest_path @ SV467 @ SY774 @ SY775 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2341]) ).
thf(2362,plain,
! [SV467: $i] :
( ( ~ ~ ( ~ ! [SY776: $i,SY777: $i] :
( ~ ( shortest_path @ SV467 @ SY776 @ SY777 )
| ! [SY778: $i] :
( ~ ( path @ SV467 @ SY776 @ SY778 )
| ( less_or_equal @ ( length_of @ SY777 ) @ ( length_of @ SY778 ) ) ) )
| ~ ~ ( ~ ! [SY779: $i] :
( ! [SY780: $i] :
~ ( shortest_path @ SV467 @ SY779 @ SY780 )
| ( SV467 != SY779 ) )
| ~ ! [SY781: $i,SY782: $i] :
( ~ ( shortest_path @ SV467 @ SY781 @ SY782 )
| ( path @ SV467 @ SY781 @ SY782 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2341]) ).
thf(2363,plain,
! [SV482: $i,SV476: $i,SV468: $i] :
( ( ~ ( vertex @ SV468 )
| ~ ( vertex @ SV476 )
| ~ ( ~ ! [SY826: $i] :
( ( SV468
!= ( tail_of @ SY826 ) )
| ~ ( edge @ SY826 )
| ( SV476
!= ( head_of @ SY826 ) )
| ( SV482
!= ( path_cons @ SY826 @ empty ) ) )
| ~ ! [SY827: $i] :
( ( SV468
!= ( tail_of @ SY827 ) )
| ~ ( edge @ SY827 )
| ! [SY828: $i] :
( ( SV482
!= ( path_cons @ SY827 @ SY828 ) )
| ~ ( path @ ( head_of @ SY827 ) @ SV476 @ SY828 ) ) ) )
| ( path @ SV468 @ SV476 @ SV482 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2342]) ).
thf(2364,plain,
! [SV477: $i,SV469: $i,SV483: $i] :
( ( ~ ( ~ ! [SY829: $i] :
( ! [SY830: $i] :
( ~ ( precedes @ SV483 @ SY829 @ SY830 )
| ~ ( shortest_path @ SV469 @ SV477 @ SY830 ) )
| ! [SY831: $i] :
( ( ( tail_of @ SY831 )
!= ( tail_of @ SV483 ) )
| ( ( head_of @ SY831 )
!= ( head_of @ SY829 ) ) ) )
| ~ ! [SY832: $i,SY833: $i] :
( ~ ( precedes @ SV483 @ SY832 @ SY833 )
| ~ ( shortest_path @ SV469 @ SV477 @ SY833 )
| ~ ( precedes @ SY832 @ SV483 @ SY833 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2343]) ).
thf(2365,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( edge @ SX0 )
| ~ ( edge @ SX1 )
| ( ( head_of @ SX0 )
!= ( tail_of @ SX1 ) )
| ( sequential @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2344]) ).
thf(2366,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2345]) ).
thf(2367,plain,
! [SV470: $i,SV484: $i] :
( ( ( ! [SY834: $i] :
~ ( path @ SV484 @ SY834 @ SV470 ) )
= $true )
| ( ( ~ ( ~ ! [SY797: $i,SY798: $i] :
( ~ ( on_path @ SY797 @ SV470 )
| ~ ( on_path @ SY798 @ SV470 )
| ! [SY799: $i] :
( ~ ( precedes @ SY799 @ SY798 @ SV470 )
| ~ ( sequential @ SY797 @ SY799 ) )
| ( precedes @ SY797 @ SY798 @ SV470 ) )
| ~ ! [SY800: $i,SY801: $i] :
( ~ ( on_path @ SY800 @ SV470 )
| ~ ( on_path @ SY801 @ SV470 )
| ~ ( sequential @ SY800 @ SY801 )
| ( precedes @ SY800 @ SY801 @ SV470 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2346]) ).
thf(2368,plain,
! [SV457: $i] :
( ( ( ( head_of @ SV457 )
= ( tail_of @ SV457 ) )
= $false )
| ( ( edge @ SV457 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2347]) ).
thf(2369,plain,
! [SV478: $i,SV471: $i,SV458: $i] :
( ( ( ~ ( path @ SV458 @ SV471 @ SV478 ) )
= $true )
| ( ( ( length_of @ SV478 )
= ( number_of_in @ edges @ SV478 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2348]) ).
thf(2370,plain,
! [SV479: $i,SV472: $i,SV459: $i] :
( ( ( ~ ( path @ SV459 @ SV472 @ SV479 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV479 )
= ( minus @ ( length_of @ SV479 ) @ n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2349]) ).
thf(2371,plain,
! [SV485: $i,SV480: $i] :
( ( ( ( SV480 = SV485 )
| ~ ( vertex @ SV480 )
| ~ ( vertex @ SV485 )
| ~ ( ~ ~ ( ~ ( ( SV480
!= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
!= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
!= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
!= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV480
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
| ~ ( ( SV480
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) ) )
| ~ ~ ( ~ ( ( SV485
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
| ~ ( ( SV485
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV485 @ SV480 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2350]) ).
thf(2372,plain,
! [SV486: $i] :
( ( ~ ( edge @ SV486 )
| ( vertex @ ( head_of @ SV486 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2351]) ).
thf(2373,plain,
! [SV487: $i] :
( ( ~ ( edge @ SV487 )
| ( vertex @ ( tail_of @ SV487 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2352]) ).
thf(2374,plain,
! [SV461: $i,SV488: $i,SV481: $i] :
( ( ( ~ ( path @ SV481 @ SV488 @ SV461 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY729: $i] :
( ! [SY730: $i] :
~ ( precedes @ SY729 @ SY730 @ SV461 )
| ( on_path @ SY729 @ SV461 ) )
| ~ ! [SY731: $i,SY732: $i] :
( ~ ( precedes @ SY731 @ SY732 @ SV461 )
| ( on_path @ SY732 @ SV461 ) ) )
| ~ ~ ( ~ ! [SY733: $i,SY734: $i] :
( ~ ( precedes @ SY733 @ SY734 @ SV461 )
| ! [SY735: $i] :
( ~ ( precedes @ SY735 @ SY734 @ SV461 )
| ~ ( sequential @ SY733 @ SY735 ) )
| ~ ( sequential @ SY733 @ SY734 ) )
| ~ ! [SY736: $i,SY737: $i] :
( ~ ( precedes @ SY736 @ SY737 @ SV461 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY737 @ SY736 @ SV461 ) @ SY737 @ SV461 )
| ~ ( sequential @ SY736 @ ( sK9_E3 @ SY737 @ SY736 @ SV461 ) ) )
| ( sequential @ SY736 @ SY737 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2353]) ).
thf(2375,plain,
! [SV462: $i] :
( ( ~ ( ~ ( ! [SY738: $i,SY739: $i] :
~ ( path @ SV462 @ SY738 @ SY739 )
| ( vertex @ SV462 ) )
| ~ ! [SY740: $i] :
( ! [SY741: $i] :
~ ( path @ SV462 @ SY740 @ SY741 )
| ( vertex @ SY740 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2354]) ).
thf(2376,plain,
! [SV462: $i] :
( ( ! [SY742: $i,SY743: $i] :
( ~ ( path @ SV462 @ SY742 @ SY743 )
| ~ ( ~ ~ ( ( SV462
!= ( tail_of @ ( sK11_E @ SY743 @ SY742 @ SV462 ) ) )
| ~ ( edge @ ( sK11_E @ SY743 @ SY742 @ SV462 ) ) )
| ~ ~ ( ~ ( ( SY742
!= ( head_of @ ( sK11_E @ SY743 @ SY742 @ SV462 ) ) )
| ( SY743
!= ( path_cons @ ( sK11_E @ SY743 @ SY742 @ SV462 ) @ empty ) )
| ! [SY744: $i] :
( ( SY743
!= ( path_cons @ ( sK11_E @ SY743 @ SY742 @ SV462 ) @ SY744 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY743 @ SY742 @ SV462 ) ) @ SY742 @ SY744 ) ) )
| ~ ~ ( ~ ( ( SY742
= ( head_of @ ( sK11_E @ SY743 @ SY742 @ SV462 ) ) )
| ~ ( ( SY743
!= ( path_cons @ ( sK11_E @ SY743 @ SY742 @ SV462 ) @ ( sK13_SY84 @ SY743 @ SY742 @ SV462 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY743 @ SY742 @ SV462 ) ) @ SY742 @ ( sK13_SY84 @ SY743 @ SY742 @ SV462 ) ) ) )
| ~ ( ( SY743
= ( path_cons @ ( sK11_E @ SY743 @ SY742 @ SV462 ) @ empty ) )
| ~ ( ( SY743
!= ( path_cons @ ( sK11_E @ SY743 @ SY742 @ SV462 ) @ ( sK12_SY85 @ SY743 @ SY742 @ SV462 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY743 @ SY742 @ SV462 ) ) @ SY742 @ ( sK12_SY85 @ SY743 @ SY742 @ SV462 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2355]) ).
thf(2377,plain,
! [SV474: $i,SV463: $i] :
( ( ~ ! [SY804: $i,SY805: $i] :
( ~ ( in_path @ SY805 @ SY804 )
| ~ ( path @ SV463 @ SV474 @ SY804 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY805 @ SY804 @ SV474 @ SV463 ) @ SY804 )
| ~ ( ( SY805
= ( head_of @ ( sK10_E @ SY805 @ SY804 @ SV474 @ SV463 ) ) )
| ( SY805
= ( tail_of @ ( sK10_E @ SY805 @ SY804 @ SV474 @ SV463 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2356]) ).
thf(2378,plain,
! [SV474: $i,SV463: $i] :
( ( ~ ! [SY806: $i,SY807: $i] :
( ~ ( in_path @ SY807 @ SY806 )
| ~ ( path @ SV463 @ SV474 @ SY806 )
| ( vertex @ SY807 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2356]) ).
thf(2379,plain,
! [SV464: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV464 ) @ SV464 )
| ~ ( on_path @ ( sK7_SY80 @ SV464 ) @ SV464 ) )
| ~ ( sequential @ ( sK6_E1 @ SV464 ) @ ( sK7_SY80 @ SV464 ) ) )
| ~ ! [SY750: $i] :
~ ( triangle @ ( sK6_E1 @ SV464 ) @ ( sK7_SY80 @ SV464 ) @ SY750 ) )
= $false )
| ( ( ! [SY751: $i,SY752: $i] :
~ ( path @ SY751 @ SY752 @ SV464 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV464 )
= ( number_of_in @ triangles @ SV464 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2357]) ).
thf(2380,plain,
! [SV475: $i,SV465: $i] :
( ( ~ ~ ( ~ ! [SY808: $i,SY809: $i] :
( ~ ( on_path @ SY809 @ SY808 )
| ~ ( path @ SV465 @ SV475 @ SY808 )
| ( edge @ SY809 ) )
| ~ ! [SY810: $i,SY811: $i] :
( ~ ( on_path @ SY811 @ SY810 )
| ~ ( path @ SV465 @ SV475 @ SY810 )
| ( in_path @ ( head_of @ SY811 ) @ SY810 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2358]) ).
thf(2381,plain,
! [SV475: $i,SV465: $i] :
( ( ~ ! [SY812: $i,SY813: $i] :
( ~ ( on_path @ SY813 @ SY812 )
| ~ ( path @ SV465 @ SV475 @ SY812 )
| ( in_path @ ( tail_of @ SY813 ) @ SY812 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2358]) ).
thf(2382,plain,
! [SV466: $i] :
( ( ! [SY760: $i,SY761: $i] :
( ~ ( edge @ SV466 )
| ~ ( edge @ SY760 )
| ~ ( edge @ SY761 )
| ~ ( sequential @ SV466 @ SY760 )
| ~ ( sequential @ SY760 @ SY761 )
| ~ ( sequential @ SY761 @ SV466 )
| ( triangle @ SV466 @ SY760 @ SY761 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2359]) ).
thf(2383,plain,
! [SV466: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY762: $i,SY763: $i] :
~ ( triangle @ SV466 @ SY762 @ SY763 )
| ( edge @ SV466 ) )
| ~ ! [SY764: $i] :
( ! [SY765: $i] :
~ ( triangle @ SV466 @ SY764 @ SY765 )
| ( edge @ SY764 ) ) )
| ~ ! [SY766: $i,SY767: $i] :
( ~ ( triangle @ SV466 @ SY766 @ SY767 )
| ( edge @ SY767 ) ) )
| ~ ! [SY768: $i] :
( ! [SY769: $i] :
~ ( triangle @ SV466 @ SY768 @ SY769 )
| ( sequential @ SV466 @ SY768 ) ) )
| ~ ! [SY770: $i,SY771: $i] :
( ~ ( triangle @ SV466 @ SY770 @ SY771 )
| ( sequential @ SY770 @ SY771 ) ) )
| ~ ! [SY772: $i,SY773: $i] :
( ~ ( triangle @ SV466 @ SY772 @ SY773 )
| ( sequential @ SY773 @ SV466 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2360]) ).
thf(2384,plain,
! [SV467: $i] :
( ( ! [SY774: $i,SY775: $i] :
( ~ ( ~ ( path @ SV467 @ SY774 @ ( sK8_P @ SY775 @ SY774 @ SV467 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY775 ) @ ( length_of @ ( sK8_P @ SY775 @ SY774 @ SV467 ) ) ) )
| ( SV467 = SY774 )
| ~ ( path @ SV467 @ SY774 @ SY775 )
| ( shortest_path @ SV467 @ SY774 @ SY775 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2361]) ).
thf(2385,plain,
! [SV467: $i] :
( ( ~ ( ~ ! [SY776: $i,SY777: $i] :
( ~ ( shortest_path @ SV467 @ SY776 @ SY777 )
| ! [SY778: $i] :
( ~ ( path @ SV467 @ SY776 @ SY778 )
| ( less_or_equal @ ( length_of @ SY777 ) @ ( length_of @ SY778 ) ) ) )
| ~ ~ ( ~ ! [SY779: $i] :
( ! [SY780: $i] :
~ ( shortest_path @ SV467 @ SY779 @ SY780 )
| ( SV467 != SY779 ) )
| ~ ! [SY781: $i,SY782: $i] :
( ~ ( shortest_path @ SV467 @ SY781 @ SY782 )
| ( path @ SV467 @ SY781 @ SY782 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2362]) ).
thf(2386,plain,
! [SV482: $i,SV476: $i,SV468: $i] :
( ( ( ~ ( vertex @ SV468 )
| ~ ( vertex @ SV476 )
| ~ ( ~ ! [SY826: $i] :
( ( SV468
!= ( tail_of @ SY826 ) )
| ~ ( edge @ SY826 )
| ( SV476
!= ( head_of @ SY826 ) )
| ( SV482
!= ( path_cons @ SY826 @ empty ) ) )
| ~ ! [SY827: $i] :
( ( SV468
!= ( tail_of @ SY827 ) )
| ~ ( edge @ SY827 )
| ! [SY828: $i] :
( ( SV482
!= ( path_cons @ SY827 @ SY828 ) )
| ~ ( path @ ( head_of @ SY827 ) @ SV476 @ SY828 ) ) ) ) )
= $true )
| ( ( path @ SV468 @ SV476 @ SV482 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2363]) ).
thf(2387,plain,
! [SV477: $i,SV469: $i,SV483: $i] :
( ( ~ ! [SY829: $i] :
( ! [SY830: $i] :
( ~ ( precedes @ SV483 @ SY829 @ SY830 )
| ~ ( shortest_path @ SV469 @ SV477 @ SY830 ) )
| ! [SY831: $i] :
( ( ( tail_of @ SY831 )
!= ( tail_of @ SV483 ) )
| ( ( head_of @ SY831 )
!= ( head_of @ SY829 ) ) ) )
| ~ ! [SY832: $i,SY833: $i] :
( ~ ( precedes @ SV483 @ SY832 @ SY833 )
| ~ ( shortest_path @ SV469 @ SV477 @ SY833 )
| ~ ( precedes @ SY832 @ SV483 @ SY833 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2364]) ).
thf(2388,plain,
! [SV489: $i] :
( ( ! [SY835: $i] :
( ( SV489 = SY835 )
| ~ ( edge @ SV489 )
| ~ ( edge @ SY835 )
| ( ( head_of @ SV489 )
!= ( tail_of @ SY835 ) )
| ( sequential @ SV489 @ SY835 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2365]) ).
thf(2389,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2366]) ).
thf(2390,plain,
! [SV470: $i,SV490: $i,SV484: $i] :
( ( ( ~ ( path @ SV484 @ SV490 @ SV470 ) )
= $true )
| ( ( ~ ( ~ ! [SY797: $i,SY798: $i] :
( ~ ( on_path @ SY797 @ SV470 )
| ~ ( on_path @ SY798 @ SV470 )
| ! [SY799: $i] :
( ~ ( precedes @ SY799 @ SY798 @ SV470 )
| ~ ( sequential @ SY797 @ SY799 ) )
| ( precedes @ SY797 @ SY798 @ SV470 ) )
| ~ ! [SY800: $i,SY801: $i] :
( ~ ( on_path @ SY800 @ SV470 )
| ~ ( on_path @ SY801 @ SV470 )
| ~ ( sequential @ SY800 @ SY801 )
| ( precedes @ SY800 @ SY801 @ SV470 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2367]) ).
thf(2391,plain,
! [SV478: $i,SV471: $i,SV458: $i] :
( ( ( path @ SV458 @ SV471 @ SV478 )
= $false )
| ( ( ( length_of @ SV478 )
= ( number_of_in @ edges @ SV478 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2369]) ).
thf(2392,plain,
! [SV479: $i,SV472: $i,SV459: $i] :
( ( ( path @ SV459 @ SV472 @ SV479 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV479 )
= ( minus @ ( length_of @ SV479 ) @ n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2370]) ).
thf(2393,plain,
! [SV485: $i,SV480: $i] :
( ( ( ( SV480 = SV485 )
| ~ ( vertex @ SV480 )
| ~ ( vertex @ SV485 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV480
!= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
!= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
!= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
!= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV480
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
| ~ ( ( SV480
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) ) )
| ~ ~ ( ~ ( ( SV485
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
| ~ ( ( SV485
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV485 @ SV480 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[2371]) ).
thf(2394,plain,
! [SV486: $i] :
( ( ( ~ ( edge @ SV486 ) )
= $true )
| ( ( vertex @ ( head_of @ SV486 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2372]) ).
thf(2395,plain,
! [SV487: $i] :
( ( ( ~ ( edge @ SV487 ) )
= $true )
| ( ( vertex @ ( tail_of @ SV487 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2373]) ).
thf(2396,plain,
! [SV461: $i,SV488: $i,SV481: $i] :
( ( ( path @ SV481 @ SV488 @ SV461 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY729: $i] :
( ! [SY730: $i] :
~ ( precedes @ SY729 @ SY730 @ SV461 )
| ( on_path @ SY729 @ SV461 ) )
| ~ ! [SY731: $i,SY732: $i] :
( ~ ( precedes @ SY731 @ SY732 @ SV461 )
| ( on_path @ SY732 @ SV461 ) ) )
| ~ ~ ( ~ ! [SY733: $i,SY734: $i] :
( ~ ( precedes @ SY733 @ SY734 @ SV461 )
| ! [SY735: $i] :
( ~ ( precedes @ SY735 @ SY734 @ SV461 )
| ~ ( sequential @ SY733 @ SY735 ) )
| ~ ( sequential @ SY733 @ SY734 ) )
| ~ ! [SY736: $i,SY737: $i] :
( ~ ( precedes @ SY736 @ SY737 @ SV461 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY737 @ SY736 @ SV461 ) @ SY737 @ SV461 )
| ~ ( sequential @ SY736 @ ( sK9_E3 @ SY737 @ SY736 @ SV461 ) ) )
| ( sequential @ SY736 @ SY737 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2374]) ).
thf(2397,plain,
! [SV462: $i] :
( ( ~ ( ! [SY738: $i,SY739: $i] :
~ ( path @ SV462 @ SY738 @ SY739 )
| ( vertex @ SV462 ) )
| ~ ! [SY740: $i] :
( ! [SY741: $i] :
~ ( path @ SV462 @ SY740 @ SY741 )
| ( vertex @ SY740 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2375]) ).
thf(2398,plain,
! [SV491: $i,SV462: $i] :
( ( ! [SY836: $i] :
( ~ ( path @ SV462 @ SV491 @ SY836 )
| ~ ( ~ ~ ( ( SV462
!= ( tail_of @ ( sK11_E @ SY836 @ SV491 @ SV462 ) ) )
| ~ ( edge @ ( sK11_E @ SY836 @ SV491 @ SV462 ) ) )
| ~ ~ ( ~ ( ( SV491
!= ( head_of @ ( sK11_E @ SY836 @ SV491 @ SV462 ) ) )
| ( SY836
!= ( path_cons @ ( sK11_E @ SY836 @ SV491 @ SV462 ) @ empty ) )
| ! [SY837: $i] :
( ( SY836
!= ( path_cons @ ( sK11_E @ SY836 @ SV491 @ SV462 ) @ SY837 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY836 @ SV491 @ SV462 ) ) @ SV491 @ SY837 ) ) )
| ~ ~ ( ~ ( ( SV491
= ( head_of @ ( sK11_E @ SY836 @ SV491 @ SV462 ) ) )
| ~ ( ( SY836
!= ( path_cons @ ( sK11_E @ SY836 @ SV491 @ SV462 ) @ ( sK13_SY84 @ SY836 @ SV491 @ SV462 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY836 @ SV491 @ SV462 ) ) @ SV491 @ ( sK13_SY84 @ SY836 @ SV491 @ SV462 ) ) ) )
| ~ ( ( SY836
= ( path_cons @ ( sK11_E @ SY836 @ SV491 @ SV462 ) @ empty ) )
| ~ ( ( SY836
!= ( path_cons @ ( sK11_E @ SY836 @ SV491 @ SV462 ) @ ( sK12_SY85 @ SY836 @ SV491 @ SV462 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY836 @ SV491 @ SV462 ) ) @ SV491 @ ( sK12_SY85 @ SY836 @ SV491 @ SV462 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2376]) ).
thf(2399,plain,
! [SV474: $i,SV463: $i] :
( ( ! [SY804: $i,SY805: $i] :
( ~ ( in_path @ SY805 @ SY804 )
| ~ ( path @ SV463 @ SV474 @ SY804 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY805 @ SY804 @ SV474 @ SV463 ) @ SY804 )
| ~ ( ( SY805
= ( head_of @ ( sK10_E @ SY805 @ SY804 @ SV474 @ SV463 ) ) )
| ( SY805
= ( tail_of @ ( sK10_E @ SY805 @ SY804 @ SV474 @ SV463 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2377]) ).
thf(2400,plain,
! [SV474: $i,SV463: $i] :
( ( ! [SY806: $i,SY807: $i] :
( ~ ( in_path @ SY807 @ SY806 )
| ~ ( path @ SV463 @ SV474 @ SY806 )
| ( vertex @ SY807 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2378]) ).
thf(2401,plain,
! [SV464: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV464 ) @ SV464 )
| ~ ( on_path @ ( sK7_SY80 @ SV464 ) @ SV464 ) )
| ~ ( sequential @ ( sK6_E1 @ SV464 ) @ ( sK7_SY80 @ SV464 ) ) ) )
= $false )
| ( ( ! [SY751: $i,SY752: $i] :
~ ( path @ SY751 @ SY752 @ SV464 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV464 )
= ( number_of_in @ triangles @ SV464 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2379]) ).
thf(2402,plain,
! [SV464: $i] :
( ( ( ~ ! [SY750: $i] :
~ ( triangle @ ( sK6_E1 @ SV464 ) @ ( sK7_SY80 @ SV464 ) @ SY750 ) )
= $false )
| ( ( ! [SY751: $i,SY752: $i] :
~ ( path @ SY751 @ SY752 @ SV464 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV464 )
= ( number_of_in @ triangles @ SV464 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2379]) ).
thf(2403,plain,
! [SV475: $i,SV465: $i] :
( ( ~ ( ~ ! [SY808: $i,SY809: $i] :
( ~ ( on_path @ SY809 @ SY808 )
| ~ ( path @ SV465 @ SV475 @ SY808 )
| ( edge @ SY809 ) )
| ~ ! [SY810: $i,SY811: $i] :
( ~ ( on_path @ SY811 @ SY810 )
| ~ ( path @ SV465 @ SV475 @ SY810 )
| ( in_path @ ( head_of @ SY811 ) @ SY810 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2380]) ).
thf(2404,plain,
! [SV475: $i,SV465: $i] :
( ( ! [SY812: $i,SY813: $i] :
( ~ ( on_path @ SY813 @ SY812 )
| ~ ( path @ SV465 @ SV475 @ SY812 )
| ( in_path @ ( tail_of @ SY813 ) @ SY812 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2381]) ).
thf(2405,plain,
! [SV492: $i,SV466: $i] :
( ( ! [SY838: $i] :
( ~ ( edge @ SV466 )
| ~ ( edge @ SV492 )
| ~ ( edge @ SY838 )
| ~ ( sequential @ SV466 @ SV492 )
| ~ ( sequential @ SV492 @ SY838 )
| ~ ( sequential @ SY838 @ SV466 )
| ( triangle @ SV466 @ SV492 @ SY838 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2382]) ).
thf(2406,plain,
! [SV466: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY762: $i,SY763: $i] :
~ ( triangle @ SV466 @ SY762 @ SY763 )
| ( edge @ SV466 ) )
| ~ ! [SY764: $i] :
( ! [SY765: $i] :
~ ( triangle @ SV466 @ SY764 @ SY765 )
| ( edge @ SY764 ) ) )
| ~ ! [SY766: $i,SY767: $i] :
( ~ ( triangle @ SV466 @ SY766 @ SY767 )
| ( edge @ SY767 ) ) )
| ~ ! [SY768: $i] :
( ! [SY769: $i] :
~ ( triangle @ SV466 @ SY768 @ SY769 )
| ( sequential @ SV466 @ SY768 ) ) )
| ~ ! [SY770: $i,SY771: $i] :
( ~ ( triangle @ SV466 @ SY770 @ SY771 )
| ( sequential @ SY770 @ SY771 ) ) )
| ~ ! [SY772: $i,SY773: $i] :
( ~ ( triangle @ SV466 @ SY772 @ SY773 )
| ( sequential @ SY773 @ SV466 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2383]) ).
thf(2407,plain,
! [SV493: $i,SV467: $i] :
( ( ! [SY839: $i] :
( ~ ( ~ ( path @ SV467 @ SV493 @ ( sK8_P @ SY839 @ SV493 @ SV467 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY839 ) @ ( length_of @ ( sK8_P @ SY839 @ SV493 @ SV467 ) ) ) )
| ( SV467 = SV493 )
| ~ ( path @ SV467 @ SV493 @ SY839 )
| ( shortest_path @ SV467 @ SV493 @ SY839 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2384]) ).
thf(2408,plain,
! [SV467: $i] :
( ( ~ ! [SY776: $i,SY777: $i] :
( ~ ( shortest_path @ SV467 @ SY776 @ SY777 )
| ! [SY778: $i] :
( ~ ( path @ SV467 @ SY776 @ SY778 )
| ( less_or_equal @ ( length_of @ SY777 ) @ ( length_of @ SY778 ) ) ) )
| ~ ~ ( ~ ! [SY779: $i] :
( ! [SY780: $i] :
~ ( shortest_path @ SV467 @ SY779 @ SY780 )
| ( SV467 != SY779 ) )
| ~ ! [SY781: $i,SY782: $i] :
( ~ ( shortest_path @ SV467 @ SY781 @ SY782 )
| ( path @ SV467 @ SY781 @ SY782 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2385]) ).
thf(2409,plain,
! [SV482: $i,SV476: $i,SV468: $i] :
( ( ( ~ ( vertex @ SV468 )
| ~ ( vertex @ SV476 ) )
= $true )
| ( ( ~ ( ~ ! [SY826: $i] :
( ( SV468
!= ( tail_of @ SY826 ) )
| ~ ( edge @ SY826 )
| ( SV476
!= ( head_of @ SY826 ) )
| ( SV482
!= ( path_cons @ SY826 @ empty ) ) )
| ~ ! [SY827: $i] :
( ( SV468
!= ( tail_of @ SY827 ) )
| ~ ( edge @ SY827 )
| ! [SY828: $i] :
( ( SV482
!= ( path_cons @ SY827 @ SY828 ) )
| ~ ( path @ ( head_of @ SY827 ) @ SV476 @ SY828 ) ) ) ) )
= $true )
| ( ( path @ SV468 @ SV476 @ SV482 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2386]) ).
thf(2410,plain,
! [SV477: $i,SV469: $i,SV483: $i] :
( ( ~ ! [SY829: $i] :
( ! [SY830: $i] :
( ~ ( precedes @ SV483 @ SY829 @ SY830 )
| ~ ( shortest_path @ SV469 @ SV477 @ SY830 ) )
| ! [SY831: $i] :
( ( ( tail_of @ SY831 )
!= ( tail_of @ SV483 ) )
| ( ( head_of @ SY831 )
!= ( head_of @ SY829 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2387]) ).
thf(2411,plain,
! [SV477: $i,SV469: $i,SV483: $i] :
( ( ~ ! [SY832: $i,SY833: $i] :
( ~ ( precedes @ SV483 @ SY832 @ SY833 )
| ~ ( shortest_path @ SV469 @ SV477 @ SY833 )
| ~ ( precedes @ SY832 @ SV483 @ SY833 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2387]) ).
thf(2412,plain,
! [SV494: $i,SV489: $i] :
( ( ( SV489 = SV494 )
| ~ ( edge @ SV489 )
| ~ ( edge @ SV494 )
| ( ( head_of @ SV489 )
!= ( tail_of @ SV494 ) )
| ( sequential @ SV489 @ SV494 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2388]) ).
thf(2413,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2389]) ).
thf(2414,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2389]) ).
thf(2415,plain,
! [SV470: $i,SV490: $i,SV484: $i] :
( ( ( path @ SV484 @ SV490 @ SV470 )
= $false )
| ( ( ~ ( ~ ! [SY797: $i,SY798: $i] :
( ~ ( on_path @ SY797 @ SV470 )
| ~ ( on_path @ SY798 @ SV470 )
| ! [SY799: $i] :
( ~ ( precedes @ SY799 @ SY798 @ SV470 )
| ~ ( sequential @ SY797 @ SY799 ) )
| ( precedes @ SY797 @ SY798 @ SV470 ) )
| ~ ! [SY800: $i,SY801: $i] :
( ~ ( on_path @ SY800 @ SV470 )
| ~ ( on_path @ SY801 @ SV470 )
| ~ ( sequential @ SY800 @ SY801 )
| ( precedes @ SY800 @ SY801 @ SV470 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2390]) ).
thf(2416,plain,
! [SV485: $i,SV480: $i] :
( ( ( SV480 = SV485 )
= $true )
| ( ( ~ ( vertex @ SV480 )
| ~ ( vertex @ SV485 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV480
!= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
!= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
!= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
!= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV480
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
| ~ ( ( SV480
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) ) )
| ~ ~ ( ~ ( ( SV485
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
| ~ ( ( SV485
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV485 @ SV480 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[2393]) ).
thf(2417,plain,
! [SV486: $i] :
( ( ( edge @ SV486 )
= $false )
| ( ( vertex @ ( head_of @ SV486 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2394]) ).
thf(2418,plain,
! [SV487: $i] :
( ( ( edge @ SV487 )
= $false )
| ( ( vertex @ ( tail_of @ SV487 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2395]) ).
thf(2419,plain,
! [SV488: $i,SV481: $i,SV461: $i] :
( ( ( ~ ~ ( ~ ! [SY729: $i] :
( ! [SY730: $i] :
~ ( precedes @ SY729 @ SY730 @ SV461 )
| ( on_path @ SY729 @ SV461 ) )
| ~ ! [SY731: $i,SY732: $i] :
( ~ ( precedes @ SY731 @ SY732 @ SV461 )
| ( on_path @ SY732 @ SV461 ) ) )
| ~ ~ ( ~ ! [SY733: $i,SY734: $i] :
( ~ ( precedes @ SY733 @ SY734 @ SV461 )
| ! [SY735: $i] :
( ~ ( precedes @ SY735 @ SY734 @ SV461 )
| ~ ( sequential @ SY733 @ SY735 ) )
| ~ ( sequential @ SY733 @ SY734 ) )
| ~ ! [SY736: $i,SY737: $i] :
( ~ ( precedes @ SY736 @ SY737 @ SV461 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY737 @ SY736 @ SV461 ) @ SY737 @ SV461 )
| ~ ( sequential @ SY736 @ ( sK9_E3 @ SY737 @ SY736 @ SV461 ) ) )
| ( sequential @ SY736 @ SY737 ) ) ) )
= $false )
| ( ( path @ SV481 @ SV488 @ SV461 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2396]) ).
thf(2420,plain,
! [SV462: $i] :
( ( ~ ( ! [SY738: $i,SY739: $i] :
~ ( path @ SV462 @ SY738 @ SY739 )
| ( vertex @ SV462 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2397]) ).
thf(2421,plain,
! [SV462: $i] :
( ( ~ ! [SY740: $i] :
( ! [SY741: $i] :
~ ( path @ SV462 @ SY740 @ SY741 )
| ( vertex @ SY740 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2397]) ).
thf(2422,plain,
! [SV495: $i,SV491: $i,SV462: $i] :
( ( ~ ( path @ SV462 @ SV491 @ SV495 )
| ~ ( ~ ~ ( ( SV462
!= ( tail_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( edge @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
| ~ ~ ( ~ ( ( SV491
!= ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
| ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ empty ) )
| ! [SY840: $i] :
( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ SY840 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ SY840 ) ) )
| ~ ~ ( ~ ( ( SV491
= ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ ( sK13_SY84 @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ ( sK13_SY84 @ SV495 @ SV491 @ SV462 ) ) ) )
| ~ ( ( SV495
= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ empty ) )
| ~ ( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ ( sK12_SY85 @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ ( sK12_SY85 @ SV495 @ SV491 @ SV462 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2398]) ).
thf(2423,plain,
! [SV474: $i,SV463: $i,SV496: $i] :
( ( ! [SY841: $i] :
( ~ ( in_path @ SY841 @ SV496 )
| ~ ( path @ SV463 @ SV474 @ SV496 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY841 @ SV496 @ SV474 @ SV463 ) @ SV496 )
| ~ ( ( SY841
= ( head_of @ ( sK10_E @ SY841 @ SV496 @ SV474 @ SV463 ) ) )
| ( SY841
= ( tail_of @ ( sK10_E @ SY841 @ SV496 @ SV474 @ SV463 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2399]) ).
thf(2424,plain,
! [SV474: $i,SV463: $i,SV497: $i] :
( ( ! [SY842: $i] :
( ~ ( in_path @ SY842 @ SV497 )
| ~ ( path @ SV463 @ SV474 @ SV497 )
| ( vertex @ SY842 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2400]) ).
thf(2425,plain,
! [SV464: $i] :
( ( ( ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV464 ) @ SV464 )
| ~ ( on_path @ ( sK7_SY80 @ SV464 ) @ SV464 ) )
| ~ ( sequential @ ( sK6_E1 @ SV464 ) @ ( sK7_SY80 @ SV464 ) ) ) )
= $true )
| ( ( ! [SY751: $i,SY752: $i] :
~ ( path @ SY751 @ SY752 @ SV464 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV464 )
= ( number_of_in @ triangles @ SV464 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2401]) ).
thf(2426,plain,
! [SV464: $i] :
( ( ( ! [SY750: $i] :
~ ( triangle @ ( sK6_E1 @ SV464 ) @ ( sK7_SY80 @ SV464 ) @ SY750 ) )
= $true )
| ( ( ! [SY751: $i,SY752: $i] :
~ ( path @ SY751 @ SY752 @ SV464 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV464 )
= ( number_of_in @ triangles @ SV464 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2402]) ).
thf(2427,plain,
! [SV475: $i,SV465: $i] :
( ( ~ ! [SY808: $i,SY809: $i] :
( ~ ( on_path @ SY809 @ SY808 )
| ~ ( path @ SV465 @ SV475 @ SY808 )
| ( edge @ SY809 ) )
| ~ ! [SY810: $i,SY811: $i] :
( ~ ( on_path @ SY811 @ SY810 )
| ~ ( path @ SV465 @ SV475 @ SY810 )
| ( in_path @ ( head_of @ SY811 ) @ SY810 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2403]) ).
thf(2428,plain,
! [SV475: $i,SV465: $i,SV498: $i] :
( ( ! [SY843: $i] :
( ~ ( on_path @ SY843 @ SV498 )
| ~ ( path @ SV465 @ SV475 @ SV498 )
| ( in_path @ ( tail_of @ SY843 ) @ SV498 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2404]) ).
thf(2429,plain,
! [SV499: $i,SV492: $i,SV466: $i] :
( ( ~ ( edge @ SV466 )
| ~ ( edge @ SV492 )
| ~ ( edge @ SV499 )
| ~ ( sequential @ SV466 @ SV492 )
| ~ ( sequential @ SV492 @ SV499 )
| ~ ( sequential @ SV499 @ SV466 )
| ( triangle @ SV466 @ SV492 @ SV499 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2405]) ).
thf(2430,plain,
! [SV466: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY762: $i,SY763: $i] :
~ ( triangle @ SV466 @ SY762 @ SY763 )
| ( edge @ SV466 ) )
| ~ ! [SY764: $i] :
( ! [SY765: $i] :
~ ( triangle @ SV466 @ SY764 @ SY765 )
| ( edge @ SY764 ) ) )
| ~ ! [SY766: $i,SY767: $i] :
( ~ ( triangle @ SV466 @ SY766 @ SY767 )
| ( edge @ SY767 ) ) )
| ~ ! [SY768: $i] :
( ! [SY769: $i] :
~ ( triangle @ SV466 @ SY768 @ SY769 )
| ( sequential @ SV466 @ SY768 ) ) )
| ~ ! [SY770: $i,SY771: $i] :
( ~ ( triangle @ SV466 @ SY770 @ SY771 )
| ( sequential @ SY770 @ SY771 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2406]) ).
thf(2431,plain,
! [SV466: $i] :
( ( ~ ! [SY772: $i,SY773: $i] :
( ~ ( triangle @ SV466 @ SY772 @ SY773 )
| ( sequential @ SY773 @ SV466 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2406]) ).
thf(2432,plain,
! [SV500: $i,SV493: $i,SV467: $i] :
( ( ~ ( ~ ( path @ SV467 @ SV493 @ ( sK8_P @ SV500 @ SV493 @ SV467 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SV500 ) @ ( length_of @ ( sK8_P @ SV500 @ SV493 @ SV467 ) ) ) )
| ( SV467 = SV493 )
| ~ ( path @ SV467 @ SV493 @ SV500 )
| ( shortest_path @ SV467 @ SV493 @ SV500 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2407]) ).
thf(2433,plain,
! [SV467: $i] :
( ( ~ ! [SY776: $i,SY777: $i] :
( ~ ( shortest_path @ SV467 @ SY776 @ SY777 )
| ! [SY778: $i] :
( ~ ( path @ SV467 @ SY776 @ SY778 )
| ( less_or_equal @ ( length_of @ SY777 ) @ ( length_of @ SY778 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2408]) ).
thf(2434,plain,
! [SV467: $i] :
( ( ~ ~ ( ~ ! [SY779: $i] :
( ! [SY780: $i] :
~ ( shortest_path @ SV467 @ SY779 @ SY780 )
| ( SV467 != SY779 ) )
| ~ ! [SY781: $i,SY782: $i] :
( ~ ( shortest_path @ SV467 @ SY781 @ SY782 )
| ( path @ SV467 @ SY781 @ SY782 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2408]) ).
thf(2435,plain,
! [SV482: $i,SV476: $i,SV468: $i] :
( ( ( ~ ( vertex @ SV468 ) )
= $true )
| ( ( ~ ( vertex @ SV476 ) )
= $true )
| ( ( ~ ( ~ ! [SY826: $i] :
( ( SV468
!= ( tail_of @ SY826 ) )
| ~ ( edge @ SY826 )
| ( SV476
!= ( head_of @ SY826 ) )
| ( SV482
!= ( path_cons @ SY826 @ empty ) ) )
| ~ ! [SY827: $i] :
( ( SV468
!= ( tail_of @ SY827 ) )
| ~ ( edge @ SY827 )
| ! [SY828: $i] :
( ( SV482
!= ( path_cons @ SY827 @ SY828 ) )
| ~ ( path @ ( head_of @ SY827 ) @ SV476 @ SY828 ) ) ) ) )
= $true )
| ( ( path @ SV468 @ SV476 @ SV482 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2409]) ).
thf(2436,plain,
! [SV477: $i,SV469: $i,SV483: $i] :
( ( ! [SY829: $i] :
( ! [SY830: $i] :
( ~ ( precedes @ SV483 @ SY829 @ SY830 )
| ~ ( shortest_path @ SV469 @ SV477 @ SY830 ) )
| ! [SY831: $i] :
( ( ( tail_of @ SY831 )
!= ( tail_of @ SV483 ) )
| ( ( head_of @ SY831 )
!= ( head_of @ SY829 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2410]) ).
thf(2437,plain,
! [SV477: $i,SV469: $i,SV483: $i] :
( ( ! [SY832: $i,SY833: $i] :
( ~ ( precedes @ SV483 @ SY832 @ SY833 )
| ~ ( shortest_path @ SV469 @ SV477 @ SY833 )
| ~ ( precedes @ SY832 @ SV483 @ SY833 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2411]) ).
thf(2438,plain,
! [SV494: $i,SV489: $i] :
( ( ( ( SV489 = SV494 )
| ~ ( edge @ SV489 )
| ~ ( edge @ SV494 )
| ( ( head_of @ SV489 )
!= ( tail_of @ SV494 ) ) )
= $true )
| ( ( sequential @ SV489 @ SV494 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2412]) ).
thf(2439,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2413]) ).
thf(2440,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2414]) ).
thf(2441,plain,
! [SV490: $i,SV484: $i,SV470: $i] :
( ( ( ~ ! [SY797: $i,SY798: $i] :
( ~ ( on_path @ SY797 @ SV470 )
| ~ ( on_path @ SY798 @ SV470 )
| ! [SY799: $i] :
( ~ ( precedes @ SY799 @ SY798 @ SV470 )
| ~ ( sequential @ SY797 @ SY799 ) )
| ( precedes @ SY797 @ SY798 @ SV470 ) )
| ~ ! [SY800: $i,SY801: $i] :
( ~ ( on_path @ SY800 @ SV470 )
| ~ ( on_path @ SY801 @ SV470 )
| ~ ( sequential @ SY800 @ SY801 )
| ( precedes @ SY800 @ SY801 @ SV470 ) ) )
= $false )
| ( ( path @ SV484 @ SV490 @ SV470 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2415]) ).
thf(2442,plain,
! [SV485: $i,SV480: $i] :
( ( ( ~ ( vertex @ SV480 ) )
= $true )
| ( ( ~ ( vertex @ SV485 ) )
= $true )
| ( ( SV480 = SV485 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV480
!= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
!= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
!= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
!= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV480
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
| ~ ( ( SV480
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) ) )
| ~ ~ ( ~ ( ( SV485
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
| ~ ( ( SV485
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV485 @ SV480 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[2416]) ).
thf(2443,plain,
! [SV488: $i,SV481: $i,SV461: $i] :
( ( ( ~ ~ ( ~ ! [SY729: $i] :
( ! [SY730: $i] :
~ ( precedes @ SY729 @ SY730 @ SV461 )
| ( on_path @ SY729 @ SV461 ) )
| ~ ! [SY731: $i,SY732: $i] :
( ~ ( precedes @ SY731 @ SY732 @ SV461 )
| ( on_path @ SY732 @ SV461 ) ) ) )
= $false )
| ( ( path @ SV481 @ SV488 @ SV461 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2419]) ).
thf(2444,plain,
! [SV488: $i,SV481: $i,SV461: $i] :
( ( ( ~ ~ ( ~ ! [SY733: $i,SY734: $i] :
( ~ ( precedes @ SY733 @ SY734 @ SV461 )
| ! [SY735: $i] :
( ~ ( precedes @ SY735 @ SY734 @ SV461 )
| ~ ( sequential @ SY733 @ SY735 ) )
| ~ ( sequential @ SY733 @ SY734 ) )
| ~ ! [SY736: $i,SY737: $i] :
( ~ ( precedes @ SY736 @ SY737 @ SV461 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY737 @ SY736 @ SV461 ) @ SY737 @ SV461 )
| ~ ( sequential @ SY736 @ ( sK9_E3 @ SY737 @ SY736 @ SV461 ) ) )
| ( sequential @ SY736 @ SY737 ) ) ) )
= $false )
| ( ( path @ SV481 @ SV488 @ SV461 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2419]) ).
thf(2445,plain,
! [SV462: $i] :
( ( ! [SY738: $i,SY739: $i] :
~ ( path @ SV462 @ SY738 @ SY739 )
| ( vertex @ SV462 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2420]) ).
thf(2446,plain,
! [SV462: $i] :
( ( ! [SY740: $i] :
( ! [SY741: $i] :
~ ( path @ SV462 @ SY740 @ SY741 )
| ( vertex @ SY740 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2421]) ).
thf(2447,plain,
! [SV495: $i,SV491: $i,SV462: $i] :
( ( ( ~ ( path @ SV462 @ SV491 @ SV495 ) )
= $true )
| ( ( ~ ( ~ ~ ( ( SV462
!= ( tail_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( edge @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
| ~ ~ ( ~ ( ( SV491
!= ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
| ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ empty ) )
| ! [SY840: $i] :
( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ SY840 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ SY840 ) ) )
| ~ ~ ( ~ ( ( SV491
= ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ ( sK13_SY84 @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ ( sK13_SY84 @ SV495 @ SV491 @ SV462 ) ) ) )
| ~ ( ( SV495
= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ empty ) )
| ~ ( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ ( sK12_SY85 @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ ( sK12_SY85 @ SV495 @ SV491 @ SV462 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2422]) ).
thf(2448,plain,
! [SV474: $i,SV463: $i,SV496: $i,SV501: $i] :
( ( ~ ( in_path @ SV501 @ SV496 )
| ~ ( path @ SV463 @ SV474 @ SV496 )
| ~ ( ~ ( on_path @ ( sK10_E @ SV501 @ SV496 @ SV474 @ SV463 ) @ SV496 )
| ~ ( ( SV501
= ( head_of @ ( sK10_E @ SV501 @ SV496 @ SV474 @ SV463 ) ) )
| ( SV501
= ( tail_of @ ( sK10_E @ SV501 @ SV496 @ SV474 @ SV463 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2423]) ).
thf(2449,plain,
! [SV474: $i,SV463: $i,SV497: $i,SV502: $i] :
( ( ~ ( in_path @ SV502 @ SV497 )
| ~ ( path @ SV463 @ SV474 @ SV497 )
| ( vertex @ SV502 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2424]) ).
thf(2450,plain,
! [SV464: $i] :
( ( ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV464 ) @ SV464 )
| ~ ( on_path @ ( sK7_SY80 @ SV464 ) @ SV464 ) )
| ~ ( sequential @ ( sK6_E1 @ SV464 ) @ ( sK7_SY80 @ SV464 ) ) )
= $false )
| ( ( ! [SY751: $i,SY752: $i] :
~ ( path @ SY751 @ SY752 @ SV464 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV464 )
= ( number_of_in @ triangles @ SV464 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2425]) ).
thf(2451,plain,
! [SV503: $i,SV464: $i] :
( ( ( ~ ( triangle @ ( sK6_E1 @ SV464 ) @ ( sK7_SY80 @ SV464 ) @ SV503 ) )
= $true )
| ( ( ! [SY751: $i,SY752: $i] :
~ ( path @ SY751 @ SY752 @ SV464 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV464 )
= ( number_of_in @ triangles @ SV464 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2426]) ).
thf(2452,plain,
! [SV475: $i,SV465: $i] :
( ( ~ ! [SY808: $i,SY809: $i] :
( ~ ( on_path @ SY809 @ SY808 )
| ~ ( path @ SV465 @ SV475 @ SY808 )
| ( edge @ SY809 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2427]) ).
thf(2453,plain,
! [SV475: $i,SV465: $i] :
( ( ~ ! [SY810: $i,SY811: $i] :
( ~ ( on_path @ SY811 @ SY810 )
| ~ ( path @ SV465 @ SV475 @ SY810 )
| ( in_path @ ( head_of @ SY811 ) @ SY810 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2427]) ).
thf(2454,plain,
! [SV475: $i,SV465: $i,SV498: $i,SV504: $i] :
( ( ~ ( on_path @ SV504 @ SV498 )
| ~ ( path @ SV465 @ SV475 @ SV498 )
| ( in_path @ ( tail_of @ SV504 ) @ SV498 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2428]) ).
thf(2455,plain,
! [SV499: $i,SV492: $i,SV466: $i] :
( ( ( ~ ( edge @ SV466 )
| ~ ( edge @ SV492 )
| ~ ( edge @ SV499 )
| ~ ( sequential @ SV466 @ SV492 )
| ~ ( sequential @ SV492 @ SV499 )
| ~ ( sequential @ SV499 @ SV466 ) )
= $true )
| ( ( triangle @ SV466 @ SV492 @ SV499 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2429]) ).
thf(2456,plain,
! [SV466: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY762: $i,SY763: $i] :
~ ( triangle @ SV466 @ SY762 @ SY763 )
| ( edge @ SV466 ) )
| ~ ! [SY764: $i] :
( ! [SY765: $i] :
~ ( triangle @ SV466 @ SY764 @ SY765 )
| ( edge @ SY764 ) ) )
| ~ ! [SY766: $i,SY767: $i] :
( ~ ( triangle @ SV466 @ SY766 @ SY767 )
| ( edge @ SY767 ) ) )
| ~ ! [SY768: $i] :
( ! [SY769: $i] :
~ ( triangle @ SV466 @ SY768 @ SY769 )
| ( sequential @ SV466 @ SY768 ) ) )
| ~ ! [SY770: $i,SY771: $i] :
( ~ ( triangle @ SV466 @ SY770 @ SY771 )
| ( sequential @ SY770 @ SY771 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2430]) ).
thf(2457,plain,
! [SV466: $i] :
( ( ! [SY772: $i,SY773: $i] :
( ~ ( triangle @ SV466 @ SY772 @ SY773 )
| ( sequential @ SY773 @ SV466 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2431]) ).
thf(2458,plain,
! [SV500: $i,SV493: $i,SV467: $i] :
( ( ( ~ ( ~ ( path @ SV467 @ SV493 @ ( sK8_P @ SV500 @ SV493 @ SV467 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SV500 ) @ ( length_of @ ( sK8_P @ SV500 @ SV493 @ SV467 ) ) ) )
| ( SV467 = SV493 )
| ~ ( path @ SV467 @ SV493 @ SV500 ) )
= $true )
| ( ( shortest_path @ SV467 @ SV493 @ SV500 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2432]) ).
thf(2459,plain,
! [SV467: $i] :
( ( ! [SY776: $i,SY777: $i] :
( ~ ( shortest_path @ SV467 @ SY776 @ SY777 )
| ! [SY778: $i] :
( ~ ( path @ SV467 @ SY776 @ SY778 )
| ( less_or_equal @ ( length_of @ SY777 ) @ ( length_of @ SY778 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2433]) ).
thf(2460,plain,
! [SV467: $i] :
( ( ~ ( ~ ! [SY779: $i] :
( ! [SY780: $i] :
~ ( shortest_path @ SV467 @ SY779 @ SY780 )
| ( SV467 != SY779 ) )
| ~ ! [SY781: $i,SY782: $i] :
( ~ ( shortest_path @ SV467 @ SY781 @ SY782 )
| ( path @ SV467 @ SY781 @ SY782 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2434]) ).
thf(2461,plain,
! [SV482: $i,SV476: $i,SV468: $i] :
( ( ( vertex @ SV468 )
= $false )
| ( ( ~ ( vertex @ SV476 ) )
= $true )
| ( ( ~ ( ~ ! [SY826: $i] :
( ( SV468
!= ( tail_of @ SY826 ) )
| ~ ( edge @ SY826 )
| ( SV476
!= ( head_of @ SY826 ) )
| ( SV482
!= ( path_cons @ SY826 @ empty ) ) )
| ~ ! [SY827: $i] :
( ( SV468
!= ( tail_of @ SY827 ) )
| ~ ( edge @ SY827 )
| ! [SY828: $i] :
( ( SV482
!= ( path_cons @ SY827 @ SY828 ) )
| ~ ( path @ ( head_of @ SY827 ) @ SV476 @ SY828 ) ) ) ) )
= $true )
| ( ( path @ SV468 @ SV476 @ SV482 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2435]) ).
thf(2462,plain,
! [SV477: $i,SV469: $i,SV505: $i,SV483: $i] :
( ( ! [SY844: $i] :
( ~ ( precedes @ SV483 @ SV505 @ SY844 )
| ~ ( shortest_path @ SV469 @ SV477 @ SY844 ) )
| ! [SY845: $i] :
( ( ( tail_of @ SY845 )
!= ( tail_of @ SV483 ) )
| ( ( head_of @ SY845 )
!= ( head_of @ SV505 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2436]) ).
thf(2463,plain,
! [SV477: $i,SV469: $i,SV506: $i,SV483: $i] :
( ( ! [SY846: $i] :
( ~ ( precedes @ SV483 @ SV506 @ SY846 )
| ~ ( shortest_path @ SV469 @ SV477 @ SY846 )
| ~ ( precedes @ SV506 @ SV483 @ SY846 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2437]) ).
thf(2464,plain,
! [SV494: $i,SV489: $i] :
( ( ( ( SV489 = SV494 )
| ~ ( edge @ SV489 )
| ~ ( edge @ SV494 ) )
= $true )
| ( ( ( ( head_of @ SV489 )
!= ( tail_of @ SV494 ) ) )
= $true )
| ( ( sequential @ SV489 @ SV494 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2438]) ).
thf(2465,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2439]) ).
thf(2466,plain,
! [SV507: $i] :
( ( ! [SY847: $i] :
( ~ ( sequential @ SV507 @ SY847 )
| ( ( head_of @ SV507 )
= ( tail_of @ SY847 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2440]) ).
thf(2467,plain,
! [SV490: $i,SV484: $i,SV470: $i] :
( ( ( ~ ! [SY797: $i,SY798: $i] :
( ~ ( on_path @ SY797 @ SV470 )
| ~ ( on_path @ SY798 @ SV470 )
| ! [SY799: $i] :
( ~ ( precedes @ SY799 @ SY798 @ SV470 )
| ~ ( sequential @ SY797 @ SY799 ) )
| ( precedes @ SY797 @ SY798 @ SV470 ) ) )
= $false )
| ( ( path @ SV484 @ SV490 @ SV470 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2441]) ).
thf(2468,plain,
! [SV490: $i,SV484: $i,SV470: $i] :
( ( ( ~ ! [SY800: $i,SY801: $i] :
( ~ ( on_path @ SY800 @ SV470 )
| ~ ( on_path @ SY801 @ SV470 )
| ~ ( sequential @ SY800 @ SY801 )
| ( precedes @ SY800 @ SY801 @ SV470 ) ) )
= $false )
| ( ( path @ SV484 @ SV490 @ SV470 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2441]) ).
thf(2469,plain,
! [SV485: $i,SV480: $i] :
( ( ( vertex @ SV480 )
= $false )
| ( ( ~ ( vertex @ SV485 ) )
= $true )
| ( ( SV480 = SV485 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV480
!= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
!= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
!= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
!= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV480
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
| ~ ( ( SV480
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) ) )
| ~ ~ ( ~ ( ( SV485
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
| ~ ( ( SV485
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV485 @ SV480 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[2442]) ).
thf(2470,plain,
! [SV488: $i,SV481: $i,SV461: $i] :
( ( ( ~ ( ~ ! [SY729: $i] :
( ! [SY730: $i] :
~ ( precedes @ SY729 @ SY730 @ SV461 )
| ( on_path @ SY729 @ SV461 ) )
| ~ ! [SY731: $i,SY732: $i] :
( ~ ( precedes @ SY731 @ SY732 @ SV461 )
| ( on_path @ SY732 @ SV461 ) ) ) )
= $true )
| ( ( path @ SV481 @ SV488 @ SV461 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2443]) ).
thf(2471,plain,
! [SV488: $i,SV481: $i,SV461: $i] :
( ( ( ~ ( ~ ! [SY733: $i,SY734: $i] :
( ~ ( precedes @ SY733 @ SY734 @ SV461 )
| ! [SY735: $i] :
( ~ ( precedes @ SY735 @ SY734 @ SV461 )
| ~ ( sequential @ SY733 @ SY735 ) )
| ~ ( sequential @ SY733 @ SY734 ) )
| ~ ! [SY736: $i,SY737: $i] :
( ~ ( precedes @ SY736 @ SY737 @ SV461 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY737 @ SY736 @ SV461 ) @ SY737 @ SV461 )
| ~ ( sequential @ SY736 @ ( sK9_E3 @ SY737 @ SY736 @ SV461 ) ) )
| ( sequential @ SY736 @ SY737 ) ) ) )
= $true )
| ( ( path @ SV481 @ SV488 @ SV461 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2444]) ).
thf(2472,plain,
! [SV462: $i] :
( ( ( ! [SY738: $i,SY739: $i] :
~ ( path @ SV462 @ SY738 @ SY739 ) )
= $true )
| ( ( vertex @ SV462 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2445]) ).
thf(2473,plain,
! [SV508: $i,SV462: $i] :
( ( ! [SY848: $i] :
~ ( path @ SV462 @ SV508 @ SY848 )
| ( vertex @ SV508 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2446]) ).
thf(2474,plain,
! [SV495: $i,SV491: $i,SV462: $i] :
( ( ( path @ SV462 @ SV491 @ SV495 )
= $false )
| ( ( ~ ( ~ ~ ( ( SV462
!= ( tail_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( edge @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
| ~ ~ ( ~ ( ( SV491
!= ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
| ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ empty ) )
| ! [SY840: $i] :
( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ SY840 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ SY840 ) ) )
| ~ ~ ( ~ ( ( SV491
= ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ ( sK13_SY84 @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ ( sK13_SY84 @ SV495 @ SV491 @ SV462 ) ) ) )
| ~ ( ( SV495
= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ empty ) )
| ~ ( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ ( sK12_SY85 @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ ( sK12_SY85 @ SV495 @ SV491 @ SV462 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2447]) ).
thf(2475,plain,
! [SV474: $i,SV463: $i,SV496: $i,SV501: $i] :
( ( ( ~ ( in_path @ SV501 @ SV496 )
| ~ ( path @ SV463 @ SV474 @ SV496 ) )
= $true )
| ( ( ~ ( ~ ( on_path @ ( sK10_E @ SV501 @ SV496 @ SV474 @ SV463 ) @ SV496 )
| ~ ( ( SV501
= ( head_of @ ( sK10_E @ SV501 @ SV496 @ SV474 @ SV463 ) ) )
| ( SV501
= ( tail_of @ ( sK10_E @ SV501 @ SV496 @ SV474 @ SV463 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2448]) ).
thf(2476,plain,
! [SV474: $i,SV463: $i,SV497: $i,SV502: $i] :
( ( ( ~ ( in_path @ SV502 @ SV497 )
| ~ ( path @ SV463 @ SV474 @ SV497 ) )
= $true )
| ( ( vertex @ SV502 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2449]) ).
thf(2477,plain,
! [SV464: $i] :
( ( ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV464 ) @ SV464 )
| ~ ( on_path @ ( sK7_SY80 @ SV464 ) @ SV464 ) ) )
= $false )
| ( ( ! [SY751: $i,SY752: $i] :
~ ( path @ SY751 @ SY752 @ SV464 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV464 )
= ( number_of_in @ triangles @ SV464 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2450]) ).
thf(2478,plain,
! [SV464: $i] :
( ( ( ~ ( sequential @ ( sK6_E1 @ SV464 ) @ ( sK7_SY80 @ SV464 ) ) )
= $false )
| ( ( ! [SY751: $i,SY752: $i] :
~ ( path @ SY751 @ SY752 @ SV464 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV464 )
= ( number_of_in @ triangles @ SV464 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2450]) ).
thf(2479,plain,
! [SV503: $i,SV464: $i] :
( ( ( triangle @ ( sK6_E1 @ SV464 ) @ ( sK7_SY80 @ SV464 ) @ SV503 )
= $false )
| ( ( ! [SY751: $i,SY752: $i] :
~ ( path @ SY751 @ SY752 @ SV464 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV464 )
= ( number_of_in @ triangles @ SV464 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2451]) ).
thf(2480,plain,
! [SV475: $i,SV465: $i] :
( ( ! [SY808: $i,SY809: $i] :
( ~ ( on_path @ SY809 @ SY808 )
| ~ ( path @ SV465 @ SV475 @ SY808 )
| ( edge @ SY809 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2452]) ).
thf(2481,plain,
! [SV475: $i,SV465: $i] :
( ( ! [SY810: $i,SY811: $i] :
( ~ ( on_path @ SY811 @ SY810 )
| ~ ( path @ SV465 @ SV475 @ SY810 )
| ( in_path @ ( head_of @ SY811 ) @ SY810 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2453]) ).
thf(2482,plain,
! [SV475: $i,SV465: $i,SV498: $i,SV504: $i] :
( ( ( ~ ( on_path @ SV504 @ SV498 )
| ~ ( path @ SV465 @ SV475 @ SV498 ) )
= $true )
| ( ( in_path @ ( tail_of @ SV504 ) @ SV498 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2454]) ).
thf(2483,plain,
! [SV499: $i,SV492: $i,SV466: $i] :
( ( ( ~ ( edge @ SV466 )
| ~ ( edge @ SV492 )
| ~ ( edge @ SV499 )
| ~ ( sequential @ SV466 @ SV492 )
| ~ ( sequential @ SV492 @ SV499 ) )
= $true )
| ( ( ~ ( sequential @ SV499 @ SV466 ) )
= $true )
| ( ( triangle @ SV466 @ SV492 @ SV499 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2455]) ).
thf(2484,plain,
! [SV466: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY762: $i,SY763: $i] :
~ ( triangle @ SV466 @ SY762 @ SY763 )
| ( edge @ SV466 ) )
| ~ ! [SY764: $i] :
( ! [SY765: $i] :
~ ( triangle @ SV466 @ SY764 @ SY765 )
| ( edge @ SY764 ) ) )
| ~ ! [SY766: $i,SY767: $i] :
( ~ ( triangle @ SV466 @ SY766 @ SY767 )
| ( edge @ SY767 ) ) )
| ~ ! [SY768: $i] :
( ! [SY769: $i] :
~ ( triangle @ SV466 @ SY768 @ SY769 )
| ( sequential @ SV466 @ SY768 ) ) )
| ~ ! [SY770: $i,SY771: $i] :
( ~ ( triangle @ SV466 @ SY770 @ SY771 )
| ( sequential @ SY770 @ SY771 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2456]) ).
thf(2485,plain,
! [SV509: $i,SV466: $i] :
( ( ! [SY849: $i] :
( ~ ( triangle @ SV466 @ SV509 @ SY849 )
| ( sequential @ SY849 @ SV466 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2457]) ).
thf(2486,plain,
! [SV500: $i,SV493: $i,SV467: $i] :
( ( ( ~ ( ~ ( path @ SV467 @ SV493 @ ( sK8_P @ SV500 @ SV493 @ SV467 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SV500 ) @ ( length_of @ ( sK8_P @ SV500 @ SV493 @ SV467 ) ) ) ) )
= $true )
| ( ( ( SV467 = SV493 )
| ~ ( path @ SV467 @ SV493 @ SV500 ) )
= $true )
| ( ( shortest_path @ SV467 @ SV493 @ SV500 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2458]) ).
thf(2487,plain,
! [SV510: $i,SV467: $i] :
( ( ! [SY850: $i] :
( ~ ( shortest_path @ SV467 @ SV510 @ SY850 )
| ! [SY851: $i] :
( ~ ( path @ SV467 @ SV510 @ SY851 )
| ( less_or_equal @ ( length_of @ SY850 ) @ ( length_of @ SY851 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2459]) ).
thf(2488,plain,
! [SV467: $i] :
( ( ~ ! [SY779: $i] :
( ! [SY780: $i] :
~ ( shortest_path @ SV467 @ SY779 @ SY780 )
| ( SV467 != SY779 ) )
| ~ ! [SY781: $i,SY782: $i] :
( ~ ( shortest_path @ SV467 @ SY781 @ SY782 )
| ( path @ SV467 @ SY781 @ SY782 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2460]) ).
thf(2489,plain,
! [SV482: $i,SV468: $i,SV476: $i] :
( ( ( vertex @ SV476 )
= $false )
| ( ( vertex @ SV468 )
= $false )
| ( ( ~ ( ~ ! [SY826: $i] :
( ( SV468
!= ( tail_of @ SY826 ) )
| ~ ( edge @ SY826 )
| ( SV476
!= ( head_of @ SY826 ) )
| ( SV482
!= ( path_cons @ SY826 @ empty ) ) )
| ~ ! [SY827: $i] :
( ( SV468
!= ( tail_of @ SY827 ) )
| ~ ( edge @ SY827 )
| ! [SY828: $i] :
( ( SV482
!= ( path_cons @ SY827 @ SY828 ) )
| ~ ( path @ ( head_of @ SY827 ) @ SV476 @ SY828 ) ) ) ) )
= $true )
| ( ( path @ SV468 @ SV476 @ SV482 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2461]) ).
thf(2490,plain,
! [SV477: $i,SV469: $i,SV505: $i,SV483: $i] :
( ( ( ! [SY844: $i] :
( ~ ( precedes @ SV483 @ SV505 @ SY844 )
| ~ ( shortest_path @ SV469 @ SV477 @ SY844 ) ) )
= $true )
| ( ( ! [SY845: $i] :
( ( ( tail_of @ SY845 )
!= ( tail_of @ SV483 ) )
| ( ( head_of @ SY845 )
!= ( head_of @ SV505 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2462]) ).
thf(2491,plain,
! [SV477: $i,SV469: $i,SV511: $i,SV506: $i,SV483: $i] :
( ( ~ ( precedes @ SV483 @ SV506 @ SV511 )
| ~ ( shortest_path @ SV469 @ SV477 @ SV511 )
| ~ ( precedes @ SV506 @ SV483 @ SV511 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2463]) ).
thf(2492,plain,
! [SV494: $i,SV489: $i] :
( ( ( SV489 = SV494 )
= $true )
| ( ( ~ ( edge @ SV489 )
| ~ ( edge @ SV494 ) )
= $true )
| ( ( ( ( head_of @ SV489 )
!= ( tail_of @ SV494 ) ) )
= $true )
| ( ( sequential @ SV489 @ SV494 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2464]) ).
thf(2493,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2465]) ).
thf(2494,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2465]) ).
thf(2495,plain,
! [SV512: $i,SV507: $i] :
( ( ~ ( sequential @ SV507 @ SV512 )
| ( ( head_of @ SV507 )
= ( tail_of @ SV512 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2466]) ).
thf(2496,plain,
! [SV490: $i,SV484: $i,SV470: $i] :
( ( ( ! [SY797: $i,SY798: $i] :
( ~ ( on_path @ SY797 @ SV470 )
| ~ ( on_path @ SY798 @ SV470 )
| ! [SY799: $i] :
( ~ ( precedes @ SY799 @ SY798 @ SV470 )
| ~ ( sequential @ SY797 @ SY799 ) )
| ( precedes @ SY797 @ SY798 @ SV470 ) ) )
= $true )
| ( ( path @ SV484 @ SV490 @ SV470 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2467]) ).
thf(2497,plain,
! [SV490: $i,SV484: $i,SV470: $i] :
( ( ( ! [SY800: $i,SY801: $i] :
( ~ ( on_path @ SY800 @ SV470 )
| ~ ( on_path @ SY801 @ SV470 )
| ~ ( sequential @ SY800 @ SY801 )
| ( precedes @ SY800 @ SY801 @ SV470 ) ) )
= $true )
| ( ( path @ SV484 @ SV490 @ SV470 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2468]) ).
thf(2498,plain,
! [SV480: $i,SV485: $i] :
( ( ( vertex @ SV485 )
= $false )
| ( ( vertex @ SV480 )
= $false )
| ( ( SV480 = SV485 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV480
!= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
!= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
!= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
!= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV480
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
| ~ ( ( SV480
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) ) )
| ~ ~ ( ~ ( ( SV485
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
| ~ ( ( SV485
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV485 @ SV480 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[2469]) ).
thf(2499,plain,
! [SV488: $i,SV481: $i,SV461: $i] :
( ( ( ~ ! [SY729: $i] :
( ! [SY730: $i] :
~ ( precedes @ SY729 @ SY730 @ SV461 )
| ( on_path @ SY729 @ SV461 ) )
| ~ ! [SY731: $i,SY732: $i] :
( ~ ( precedes @ SY731 @ SY732 @ SV461 )
| ( on_path @ SY732 @ SV461 ) ) )
= $false )
| ( ( path @ SV481 @ SV488 @ SV461 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2470]) ).
thf(2500,plain,
! [SV488: $i,SV481: $i,SV461: $i] :
( ( ( ~ ! [SY733: $i,SY734: $i] :
( ~ ( precedes @ SY733 @ SY734 @ SV461 )
| ! [SY735: $i] :
( ~ ( precedes @ SY735 @ SY734 @ SV461 )
| ~ ( sequential @ SY733 @ SY735 ) )
| ~ ( sequential @ SY733 @ SY734 ) )
| ~ ! [SY736: $i,SY737: $i] :
( ~ ( precedes @ SY736 @ SY737 @ SV461 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY737 @ SY736 @ SV461 ) @ SY737 @ SV461 )
| ~ ( sequential @ SY736 @ ( sK9_E3 @ SY737 @ SY736 @ SV461 ) ) )
| ( sequential @ SY736 @ SY737 ) ) )
= $false )
| ( ( path @ SV481 @ SV488 @ SV461 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2471]) ).
thf(2501,plain,
! [SV513: $i,SV462: $i] :
( ( ( ! [SY852: $i] :
~ ( path @ SV462 @ SV513 @ SY852 ) )
= $true )
| ( ( vertex @ SV462 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2472]) ).
thf(2502,plain,
! [SV508: $i,SV462: $i] :
( ( ( ! [SY848: $i] :
~ ( path @ SV462 @ SV508 @ SY848 ) )
= $true )
| ( ( vertex @ SV508 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2473]) ).
thf(2503,plain,
! [SV491: $i,SV495: $i,SV462: $i] :
( ( ( ~ ~ ( ( SV462
!= ( tail_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( edge @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
| ~ ~ ( ~ ( ( SV491
!= ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
| ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ empty ) )
| ! [SY840: $i] :
( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ SY840 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ SY840 ) ) )
| ~ ~ ( ~ ( ( SV491
= ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ ( sK13_SY84 @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ ( sK13_SY84 @ SV495 @ SV491 @ SV462 ) ) ) )
| ~ ( ( SV495
= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ empty ) )
| ~ ( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ ( sK12_SY85 @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ ( sK12_SY85 @ SV495 @ SV491 @ SV462 ) ) ) ) ) ) )
= $false )
| ( ( path @ SV462 @ SV491 @ SV495 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2474]) ).
thf(2504,plain,
! [SV474: $i,SV463: $i,SV496: $i,SV501: $i] :
( ( ( ~ ( in_path @ SV501 @ SV496 ) )
= $true )
| ( ( ~ ( path @ SV463 @ SV474 @ SV496 ) )
= $true )
| ( ( ~ ( ~ ( on_path @ ( sK10_E @ SV501 @ SV496 @ SV474 @ SV463 ) @ SV496 )
| ~ ( ( SV501
= ( head_of @ ( sK10_E @ SV501 @ SV496 @ SV474 @ SV463 ) ) )
| ( SV501
= ( tail_of @ ( sK10_E @ SV501 @ SV496 @ SV474 @ SV463 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2475]) ).
thf(2505,plain,
! [SV474: $i,SV463: $i,SV497: $i,SV502: $i] :
( ( ( ~ ( in_path @ SV502 @ SV497 ) )
= $true )
| ( ( ~ ( path @ SV463 @ SV474 @ SV497 ) )
= $true )
| ( ( vertex @ SV502 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2476]) ).
thf(2506,plain,
! [SV464: $i] :
( ( ( ~ ( ~ ( on_path @ ( sK6_E1 @ SV464 ) @ SV464 )
| ~ ( on_path @ ( sK7_SY80 @ SV464 ) @ SV464 ) ) )
= $true )
| ( ( ! [SY751: $i,SY752: $i] :
~ ( path @ SY751 @ SY752 @ SV464 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV464 )
= ( number_of_in @ triangles @ SV464 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2477]) ).
thf(2507,plain,
! [SV464: $i] :
( ( ( sequential @ ( sK6_E1 @ SV464 ) @ ( sK7_SY80 @ SV464 ) )
= $true )
| ( ( ! [SY751: $i,SY752: $i] :
~ ( path @ SY751 @ SY752 @ SV464 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV464 )
= ( number_of_in @ triangles @ SV464 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2478]) ).
thf(2508,plain,
! [SV503: $i,SV464: $i,SV514: $i] :
( ( ( ! [SY853: $i] :
~ ( path @ SV514 @ SY853 @ SV464 ) )
= $true )
| ( ( triangle @ ( sK6_E1 @ SV464 ) @ ( sK7_SY80 @ SV464 ) @ SV503 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV464 )
= ( number_of_in @ triangles @ SV464 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2479]) ).
thf(2509,plain,
! [SV475: $i,SV465: $i,SV515: $i] :
( ( ! [SY854: $i] :
( ~ ( on_path @ SY854 @ SV515 )
| ~ ( path @ SV465 @ SV475 @ SV515 )
| ( edge @ SY854 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2480]) ).
thf(2510,plain,
! [SV475: $i,SV465: $i,SV516: $i] :
( ( ! [SY855: $i] :
( ~ ( on_path @ SY855 @ SV516 )
| ~ ( path @ SV465 @ SV475 @ SV516 )
| ( in_path @ ( head_of @ SY855 ) @ SV516 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2481]) ).
thf(2511,plain,
! [SV475: $i,SV465: $i,SV498: $i,SV504: $i] :
( ( ( ~ ( on_path @ SV504 @ SV498 ) )
= $true )
| ( ( ~ ( path @ SV465 @ SV475 @ SV498 ) )
= $true )
| ( ( in_path @ ( tail_of @ SV504 ) @ SV498 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2482]) ).
thf(2512,plain,
! [SV499: $i,SV492: $i,SV466: $i] :
( ( ( ~ ( edge @ SV466 )
| ~ ( edge @ SV492 )
| ~ ( edge @ SV499 )
| ~ ( sequential @ SV466 @ SV492 ) )
= $true )
| ( ( ~ ( sequential @ SV492 @ SV499 ) )
= $true )
| ( ( ~ ( sequential @ SV499 @ SV466 ) )
= $true )
| ( ( triangle @ SV466 @ SV492 @ SV499 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2483]) ).
thf(2513,plain,
! [SV466: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY762: $i,SY763: $i] :
~ ( triangle @ SV466 @ SY762 @ SY763 )
| ( edge @ SV466 ) )
| ~ ! [SY764: $i] :
( ! [SY765: $i] :
~ ( triangle @ SV466 @ SY764 @ SY765 )
| ( edge @ SY764 ) ) )
| ~ ! [SY766: $i,SY767: $i] :
( ~ ( triangle @ SV466 @ SY766 @ SY767 )
| ( edge @ SY767 ) ) )
| ~ ! [SY768: $i] :
( ! [SY769: $i] :
~ ( triangle @ SV466 @ SY768 @ SY769 )
| ( sequential @ SV466 @ SY768 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2484]) ).
thf(2514,plain,
! [SV466: $i] :
( ( ~ ! [SY770: $i,SY771: $i] :
( ~ ( triangle @ SV466 @ SY770 @ SY771 )
| ( sequential @ SY770 @ SY771 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2484]) ).
thf(2515,plain,
! [SV517: $i,SV509: $i,SV466: $i] :
( ( ~ ( triangle @ SV466 @ SV509 @ SV517 )
| ( sequential @ SV517 @ SV466 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2485]) ).
thf(2516,plain,
! [SV500: $i,SV493: $i,SV467: $i] :
( ( ( ~ ( path @ SV467 @ SV493 @ ( sK8_P @ SV500 @ SV493 @ SV467 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SV500 ) @ ( length_of @ ( sK8_P @ SV500 @ SV493 @ SV467 ) ) ) )
= $false )
| ( ( ( SV467 = SV493 )
| ~ ( path @ SV467 @ SV493 @ SV500 ) )
= $true )
| ( ( shortest_path @ SV467 @ SV493 @ SV500 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2486]) ).
thf(2517,plain,
! [SV518: $i,SV510: $i,SV467: $i] :
( ( ~ ( shortest_path @ SV467 @ SV510 @ SV518 )
| ! [SY856: $i] :
( ~ ( path @ SV467 @ SV510 @ SY856 )
| ( less_or_equal @ ( length_of @ SV518 ) @ ( length_of @ SY856 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2487]) ).
thf(2518,plain,
! [SV467: $i] :
( ( ~ ! [SY779: $i] :
( ! [SY780: $i] :
~ ( shortest_path @ SV467 @ SY779 @ SY780 )
| ( SV467 != SY779 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2488]) ).
thf(2519,plain,
! [SV467: $i] :
( ( ~ ! [SY781: $i,SY782: $i] :
( ~ ( shortest_path @ SV467 @ SY781 @ SY782 )
| ( path @ SV467 @ SY781 @ SY782 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2488]) ).
thf(2520,plain,
! [SV482: $i,SV476: $i,SV468: $i] :
( ( ( ~ ! [SY826: $i] :
( ( SV468
!= ( tail_of @ SY826 ) )
| ~ ( edge @ SY826 )
| ( SV476
!= ( head_of @ SY826 ) )
| ( SV482
!= ( path_cons @ SY826 @ empty ) ) )
| ~ ! [SY827: $i] :
( ( SV468
!= ( tail_of @ SY827 ) )
| ~ ( edge @ SY827 )
| ! [SY828: $i] :
( ( SV482
!= ( path_cons @ SY827 @ SY828 ) )
| ~ ( path @ ( head_of @ SY827 ) @ SV476 @ SY828 ) ) ) )
= $false )
| ( ( vertex @ SV468 )
= $false )
| ( ( vertex @ SV476 )
= $false )
| ( ( path @ SV468 @ SV476 @ SV482 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2489]) ).
thf(2521,plain,
! [SV477: $i,SV469: $i,SV519: $i,SV505: $i,SV483: $i] :
( ( ( ~ ( precedes @ SV483 @ SV505 @ SV519 )
| ~ ( shortest_path @ SV469 @ SV477 @ SV519 ) )
= $true )
| ( ( ! [SY845: $i] :
( ( ( tail_of @ SY845 )
!= ( tail_of @ SV483 ) )
| ( ( head_of @ SY845 )
!= ( head_of @ SV505 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2490]) ).
thf(2522,plain,
! [SV477: $i,SV469: $i,SV511: $i,SV506: $i,SV483: $i] :
( ( ( ~ ( precedes @ SV483 @ SV506 @ SV511 )
| ~ ( shortest_path @ SV469 @ SV477 @ SV511 ) )
= $true )
| ( ( ~ ( precedes @ SV506 @ SV483 @ SV511 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2491]) ).
thf(2523,plain,
! [SV494: $i,SV489: $i] :
( ( ( ~ ( edge @ SV489 ) )
= $true )
| ( ( ~ ( edge @ SV494 ) )
= $true )
| ( ( SV489 = SV494 )
= $true )
| ( ( ( ( head_of @ SV489 )
!= ( tail_of @ SV494 ) ) )
= $true )
| ( ( sequential @ SV489 @ SV494 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2492]) ).
thf(2524,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2493]) ).
thf(2525,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2494]) ).
thf(2526,plain,
! [SV512: $i,SV507: $i] :
( ( ( ~ ( sequential @ SV507 @ SV512 ) )
= $true )
| ( ( ( head_of @ SV507 )
= ( tail_of @ SV512 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2495]) ).
thf(2527,plain,
! [SV490: $i,SV484: $i,SV470: $i,SV520: $i] :
( ( ( ! [SY857: $i] :
( ~ ( on_path @ SV520 @ SV470 )
| ~ ( on_path @ SY857 @ SV470 )
| ! [SY858: $i] :
( ~ ( precedes @ SY858 @ SY857 @ SV470 )
| ~ ( sequential @ SV520 @ SY858 ) )
| ( precedes @ SV520 @ SY857 @ SV470 ) ) )
= $true )
| ( ( path @ SV484 @ SV490 @ SV470 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2496]) ).
thf(2528,plain,
! [SV490: $i,SV484: $i,SV470: $i,SV521: $i] :
( ( ( ! [SY859: $i] :
( ~ ( on_path @ SV521 @ SV470 )
| ~ ( on_path @ SY859 @ SV470 )
| ~ ( sequential @ SV521 @ SY859 )
| ( precedes @ SV521 @ SY859 @ SV470 ) ) )
= $true )
| ( ( path @ SV484 @ SV490 @ SV470 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2497]) ).
thf(2529,plain,
! [SV485: $i,SV480: $i] :
( ( ( ~ ~ ( ~ ( ( SV480
!= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
!= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
!= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
!= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV480
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
| ~ ( ( SV480
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) ) )
| ~ ~ ( ~ ( ( SV485
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
| ~ ( ( SV485
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV485 @ SV480 ) ) )
= $false )
| ( ( SV480 = SV485 )
= $true )
| ( ( vertex @ SV480 )
= $false )
| ( ( vertex @ SV485 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[2498]) ).
thf(2530,plain,
! [SV488: $i,SV481: $i,SV461: $i] :
( ( ( ~ ! [SY729: $i] :
( ! [SY730: $i] :
~ ( precedes @ SY729 @ SY730 @ SV461 )
| ( on_path @ SY729 @ SV461 ) ) )
= $false )
| ( ( path @ SV481 @ SV488 @ SV461 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2499]) ).
thf(2531,plain,
! [SV488: $i,SV481: $i,SV461: $i] :
( ( ( ~ ! [SY731: $i,SY732: $i] :
( ~ ( precedes @ SY731 @ SY732 @ SV461 )
| ( on_path @ SY732 @ SV461 ) ) )
= $false )
| ( ( path @ SV481 @ SV488 @ SV461 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2499]) ).
thf(2532,plain,
! [SV488: $i,SV481: $i,SV461: $i] :
( ( ( ~ ! [SY733: $i,SY734: $i] :
( ~ ( precedes @ SY733 @ SY734 @ SV461 )
| ! [SY735: $i] :
( ~ ( precedes @ SY735 @ SY734 @ SV461 )
| ~ ( sequential @ SY733 @ SY735 ) )
| ~ ( sequential @ SY733 @ SY734 ) ) )
= $false )
| ( ( path @ SV481 @ SV488 @ SV461 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2500]) ).
thf(2533,plain,
! [SV488: $i,SV481: $i,SV461: $i] :
( ( ( ~ ! [SY736: $i,SY737: $i] :
( ~ ( precedes @ SY736 @ SY737 @ SV461 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY737 @ SY736 @ SV461 ) @ SY737 @ SV461 )
| ~ ( sequential @ SY736 @ ( sK9_E3 @ SY737 @ SY736 @ SV461 ) ) )
| ( sequential @ SY736 @ SY737 ) ) )
= $false )
| ( ( path @ SV481 @ SV488 @ SV461 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2500]) ).
thf(2534,plain,
! [SV522: $i,SV513: $i,SV462: $i] :
( ( ( ~ ( path @ SV462 @ SV513 @ SV522 ) )
= $true )
| ( ( vertex @ SV462 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2501]) ).
thf(2535,plain,
! [SV523: $i,SV508: $i,SV462: $i] :
( ( ( ~ ( path @ SV462 @ SV508 @ SV523 ) )
= $true )
| ( ( vertex @ SV508 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2502]) ).
thf(2536,plain,
! [SV491: $i,SV495: $i,SV462: $i] :
( ( ( ~ ~ ( ( SV462
!= ( tail_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( edge @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) ) )
= $false )
| ( ( path @ SV462 @ SV491 @ SV495 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2503]) ).
thf(2537,plain,
! [SV462: $i,SV495: $i,SV491: $i] :
( ( ( ~ ~ ( ~ ( ( SV491
!= ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
| ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ empty ) )
| ! [SY840: $i] :
( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ SY840 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ SY840 ) ) )
| ~ ~ ( ~ ( ( SV491
= ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ ( sK13_SY84 @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ ( sK13_SY84 @ SV495 @ SV491 @ SV462 ) ) ) )
| ~ ( ( SV495
= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ empty ) )
| ~ ( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ ( sK12_SY85 @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ ( sK12_SY85 @ SV495 @ SV491 @ SV462 ) ) ) ) ) ) )
= $false )
| ( ( path @ SV462 @ SV491 @ SV495 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2503]) ).
thf(2538,plain,
! [SV474: $i,SV463: $i,SV496: $i,SV501: $i] :
( ( ( in_path @ SV501 @ SV496 )
= $false )
| ( ( ~ ( path @ SV463 @ SV474 @ SV496 ) )
= $true )
| ( ( ~ ( ~ ( on_path @ ( sK10_E @ SV501 @ SV496 @ SV474 @ SV463 ) @ SV496 )
| ~ ( ( SV501
= ( head_of @ ( sK10_E @ SV501 @ SV496 @ SV474 @ SV463 ) ) )
| ( SV501
= ( tail_of @ ( sK10_E @ SV501 @ SV496 @ SV474 @ SV463 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2504]) ).
thf(2539,plain,
! [SV474: $i,SV463: $i,SV497: $i,SV502: $i] :
( ( ( in_path @ SV502 @ SV497 )
= $false )
| ( ( ~ ( path @ SV463 @ SV474 @ SV497 ) )
= $true )
| ( ( vertex @ SV502 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2505]) ).
thf(2540,plain,
! [SV464: $i] :
( ( ( ~ ( on_path @ ( sK6_E1 @ SV464 ) @ SV464 )
| ~ ( on_path @ ( sK7_SY80 @ SV464 ) @ SV464 ) )
= $false )
| ( ( ! [SY751: $i,SY752: $i] :
~ ( path @ SY751 @ SY752 @ SV464 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV464 )
= ( number_of_in @ triangles @ SV464 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2506]) ).
thf(2541,plain,
! [SV464: $i,SV524: $i] :
( ( ( ! [SY860: $i] :
~ ( path @ SV524 @ SY860 @ SV464 ) )
= $true )
| ( ( sequential @ ( sK6_E1 @ SV464 ) @ ( sK7_SY80 @ SV464 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV464 )
= ( number_of_in @ triangles @ SV464 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2507]) ).
thf(2542,plain,
! [SV503: $i,SV464: $i,SV525: $i,SV514: $i] :
( ( ( ~ ( path @ SV514 @ SV525 @ SV464 ) )
= $true )
| ( ( triangle @ ( sK6_E1 @ SV464 ) @ ( sK7_SY80 @ SV464 ) @ SV503 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV464 )
= ( number_of_in @ triangles @ SV464 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2508]) ).
thf(2543,plain,
! [SV475: $i,SV465: $i,SV515: $i,SV526: $i] :
( ( ~ ( on_path @ SV526 @ SV515 )
| ~ ( path @ SV465 @ SV475 @ SV515 )
| ( edge @ SV526 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2509]) ).
thf(2544,plain,
! [SV475: $i,SV465: $i,SV516: $i,SV527: $i] :
( ( ~ ( on_path @ SV527 @ SV516 )
| ~ ( path @ SV465 @ SV475 @ SV516 )
| ( in_path @ ( head_of @ SV527 ) @ SV516 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2510]) ).
thf(2545,plain,
! [SV475: $i,SV465: $i,SV498: $i,SV504: $i] :
( ( ( on_path @ SV504 @ SV498 )
= $false )
| ( ( ~ ( path @ SV465 @ SV475 @ SV498 ) )
= $true )
| ( ( in_path @ ( tail_of @ SV504 ) @ SV498 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2511]) ).
thf(2546,plain,
! [SV499: $i,SV492: $i,SV466: $i] :
( ( ( ~ ( edge @ SV466 )
| ~ ( edge @ SV492 )
| ~ ( edge @ SV499 ) )
= $true )
| ( ( ~ ( sequential @ SV466 @ SV492 ) )
= $true )
| ( ( ~ ( sequential @ SV492 @ SV499 ) )
= $true )
| ( ( ~ ( sequential @ SV499 @ SV466 ) )
= $true )
| ( ( triangle @ SV466 @ SV492 @ SV499 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2512]) ).
thf(2547,plain,
! [SV466: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY762: $i,SY763: $i] :
~ ( triangle @ SV466 @ SY762 @ SY763 )
| ( edge @ SV466 ) )
| ~ ! [SY764: $i] :
( ! [SY765: $i] :
~ ( triangle @ SV466 @ SY764 @ SY765 )
| ( edge @ SY764 ) ) )
| ~ ! [SY766: $i,SY767: $i] :
( ~ ( triangle @ SV466 @ SY766 @ SY767 )
| ( edge @ SY767 ) ) )
| ~ ! [SY768: $i] :
( ! [SY769: $i] :
~ ( triangle @ SV466 @ SY768 @ SY769 )
| ( sequential @ SV466 @ SY768 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2513]) ).
thf(2548,plain,
! [SV466: $i] :
( ( ! [SY770: $i,SY771: $i] :
( ~ ( triangle @ SV466 @ SY770 @ SY771 )
| ( sequential @ SY770 @ SY771 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2514]) ).
thf(2549,plain,
! [SV517: $i,SV509: $i,SV466: $i] :
( ( ( ~ ( triangle @ SV466 @ SV509 @ SV517 ) )
= $true )
| ( ( sequential @ SV517 @ SV466 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2515]) ).
thf(2550,plain,
! [SV500: $i,SV493: $i,SV467: $i] :
( ( ( ~ ( path @ SV467 @ SV493 @ ( sK8_P @ SV500 @ SV493 @ SV467 ) ) )
= $false )
| ( ( ( SV467 = SV493 )
| ~ ( path @ SV467 @ SV493 @ SV500 ) )
= $true )
| ( ( shortest_path @ SV467 @ SV493 @ SV500 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2516]) ).
thf(2551,plain,
! [SV467: $i,SV493: $i,SV500: $i] :
( ( ( ~ ~ ( less_or_equal @ ( length_of @ SV500 ) @ ( length_of @ ( sK8_P @ SV500 @ SV493 @ SV467 ) ) ) )
= $false )
| ( ( ( SV467 = SV493 )
| ~ ( path @ SV467 @ SV493 @ SV500 ) )
= $true )
| ( ( shortest_path @ SV467 @ SV493 @ SV500 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2516]) ).
thf(2552,plain,
! [SV518: $i,SV510: $i,SV467: $i] :
( ( ( ~ ( shortest_path @ SV467 @ SV510 @ SV518 ) )
= $true )
| ( ( ! [SY856: $i] :
( ~ ( path @ SV467 @ SV510 @ SY856 )
| ( less_or_equal @ ( length_of @ SV518 ) @ ( length_of @ SY856 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2517]) ).
thf(2553,plain,
! [SV467: $i] :
( ( ! [SY779: $i] :
( ! [SY780: $i] :
~ ( shortest_path @ SV467 @ SY779 @ SY780 )
| ( SV467 != SY779 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2518]) ).
thf(2554,plain,
! [SV467: $i] :
( ( ! [SY781: $i,SY782: $i] :
( ~ ( shortest_path @ SV467 @ SY781 @ SY782 )
| ( path @ SV467 @ SY781 @ SY782 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2519]) ).
thf(2555,plain,
! [SV482: $i,SV476: $i,SV468: $i] :
( ( ( ~ ! [SY826: $i] :
( ( SV468
!= ( tail_of @ SY826 ) )
| ~ ( edge @ SY826 )
| ( SV476
!= ( head_of @ SY826 ) )
| ( SV482
!= ( path_cons @ SY826 @ empty ) ) ) )
= $false )
| ( ( vertex @ SV468 )
= $false )
| ( ( vertex @ SV476 )
= $false )
| ( ( path @ SV468 @ SV476 @ SV482 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2520]) ).
thf(2556,plain,
! [SV476: $i,SV482: $i,SV468: $i] :
( ( ( ~ ! [SY827: $i] :
( ( SV468
!= ( tail_of @ SY827 ) )
| ~ ( edge @ SY827 )
| ! [SY828: $i] :
( ( SV482
!= ( path_cons @ SY827 @ SY828 ) )
| ~ ( path @ ( head_of @ SY827 ) @ SV476 @ SY828 ) ) ) )
= $false )
| ( ( vertex @ SV468 )
= $false )
| ( ( vertex @ SV476 )
= $false )
| ( ( path @ SV468 @ SV476 @ SV482 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2520]) ).
thf(2557,plain,
! [SV477: $i,SV469: $i,SV519: $i,SV505: $i,SV483: $i] :
( ( ( ~ ( precedes @ SV483 @ SV505 @ SV519 ) )
= $true )
| ( ( ~ ( shortest_path @ SV469 @ SV477 @ SV519 ) )
= $true )
| ( ( ! [SY845: $i] :
( ( ( tail_of @ SY845 )
!= ( tail_of @ SV483 ) )
| ( ( head_of @ SY845 )
!= ( head_of @ SV505 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2521]) ).
thf(2558,plain,
! [SV477: $i,SV469: $i,SV511: $i,SV506: $i,SV483: $i] :
( ( ( ~ ( precedes @ SV483 @ SV506 @ SV511 ) )
= $true )
| ( ( ~ ( shortest_path @ SV469 @ SV477 @ SV511 ) )
= $true )
| ( ( ~ ( precedes @ SV506 @ SV483 @ SV511 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2522]) ).
thf(2559,plain,
! [SV494: $i,SV489: $i] :
( ( ( edge @ SV489 )
= $false )
| ( ( ~ ( edge @ SV494 ) )
= $true )
| ( ( SV489 = SV494 )
= $true )
| ( ( ( ( head_of @ SV489 )
!= ( tail_of @ SV494 ) ) )
= $true )
| ( ( sequential @ SV489 @ SV494 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2523]) ).
thf(2560,plain,
! [SV528: $i] :
( ( ! [SY861: $i] :
( ~ ( sequential @ SV528 @ SY861 )
| ( SV528 != SY861 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2524]) ).
thf(2561,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2525]) ).
thf(2562,plain,
! [SV512: $i,SV507: $i] :
( ( ( sequential @ SV507 @ SV512 )
= $false )
| ( ( ( head_of @ SV507 )
= ( tail_of @ SV512 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2526]) ).
thf(2563,plain,
! [SV490: $i,SV484: $i,SV529: $i,SV470: $i,SV520: $i] :
( ( ( ~ ( on_path @ SV520 @ SV470 )
| ~ ( on_path @ SV529 @ SV470 )
| ! [SY862: $i] :
( ~ ( precedes @ SY862 @ SV529 @ SV470 )
| ~ ( sequential @ SV520 @ SY862 ) )
| ( precedes @ SV520 @ SV529 @ SV470 ) )
= $true )
| ( ( path @ SV484 @ SV490 @ SV470 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2527]) ).
thf(2564,plain,
! [SV490: $i,SV484: $i,SV530: $i,SV470: $i,SV521: $i] :
( ( ( ~ ( on_path @ SV521 @ SV470 )
| ~ ( on_path @ SV530 @ SV470 )
| ~ ( sequential @ SV521 @ SV530 )
| ( precedes @ SV521 @ SV530 @ SV470 ) )
= $true )
| ( ( path @ SV484 @ SV490 @ SV470 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2528]) ).
thf(2565,plain,
! [SV485: $i,SV480: $i] :
( ( ( ~ ~ ( ~ ( ( SV480
!= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
!= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
!= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
!= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV480
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
| ~ ( ( SV480
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) ) )
| ~ ~ ( ~ ( ( SV485
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
| ~ ( ( SV485
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) ) ) ) ) )
= $false )
| ( ( SV480 = SV485 )
= $true )
| ( ( vertex @ SV480 )
= $false )
| ( ( vertex @ SV485 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[2529]) ).
thf(2566,plain,
! [SV480: $i,SV485: $i] :
( ( ( ~ ( edge @ ( sK14_E @ SV485 @ SV480 ) ) )
= $false )
| ( ( SV480 = SV485 )
= $true )
| ( ( vertex @ SV480 )
= $false )
| ( ( vertex @ SV485 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[2529]) ).
thf(2567,plain,
! [SV488: $i,SV481: $i,SV461: $i] :
( ( ( ! [SY729: $i] :
( ! [SY730: $i] :
~ ( precedes @ SY729 @ SY730 @ SV461 )
| ( on_path @ SY729 @ SV461 ) ) )
= $true )
| ( ( path @ SV481 @ SV488 @ SV461 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2530]) ).
thf(2568,plain,
! [SV488: $i,SV481: $i,SV461: $i] :
( ( ( ! [SY731: $i,SY732: $i] :
( ~ ( precedes @ SY731 @ SY732 @ SV461 )
| ( on_path @ SY732 @ SV461 ) ) )
= $true )
| ( ( path @ SV481 @ SV488 @ SV461 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2531]) ).
thf(2569,plain,
! [SV488: $i,SV481: $i,SV461: $i] :
( ( ( ! [SY733: $i,SY734: $i] :
( ~ ( precedes @ SY733 @ SY734 @ SV461 )
| ! [SY735: $i] :
( ~ ( precedes @ SY735 @ SY734 @ SV461 )
| ~ ( sequential @ SY733 @ SY735 ) )
| ~ ( sequential @ SY733 @ SY734 ) ) )
= $true )
| ( ( path @ SV481 @ SV488 @ SV461 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2532]) ).
thf(2570,plain,
! [SV488: $i,SV481: $i,SV461: $i] :
( ( ( ! [SY736: $i,SY737: $i] :
( ~ ( precedes @ SY736 @ SY737 @ SV461 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY737 @ SY736 @ SV461 ) @ SY737 @ SV461 )
| ~ ( sequential @ SY736 @ ( sK9_E3 @ SY737 @ SY736 @ SV461 ) ) )
| ( sequential @ SY736 @ SY737 ) ) )
= $true )
| ( ( path @ SV481 @ SV488 @ SV461 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2533]) ).
thf(2571,plain,
! [SV522: $i,SV513: $i,SV462: $i] :
( ( ( path @ SV462 @ SV513 @ SV522 )
= $false )
| ( ( vertex @ SV462 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2534]) ).
thf(2572,plain,
! [SV523: $i,SV508: $i,SV462: $i] :
( ( ( path @ SV462 @ SV508 @ SV523 )
= $false )
| ( ( vertex @ SV508 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2535]) ).
thf(2573,plain,
! [SV491: $i,SV495: $i,SV462: $i] :
( ( ( ~ ( ( SV462
!= ( tail_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( edge @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) ) )
= $true )
| ( ( path @ SV462 @ SV491 @ SV495 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2536]) ).
thf(2574,plain,
! [SV462: $i,SV495: $i,SV491: $i] :
( ( ( ~ ( ~ ( ( SV491
!= ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
| ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ empty ) )
| ! [SY840: $i] :
( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ SY840 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ SY840 ) ) )
| ~ ~ ( ~ ( ( SV491
= ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ ( sK13_SY84 @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ ( sK13_SY84 @ SV495 @ SV491 @ SV462 ) ) ) )
| ~ ( ( SV495
= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ empty ) )
| ~ ( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ ( sK12_SY85 @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ ( sK12_SY85 @ SV495 @ SV491 @ SV462 ) ) ) ) ) ) )
= $true )
| ( ( path @ SV462 @ SV491 @ SV495 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2537]) ).
thf(2575,plain,
! [SV501: $i,SV496: $i,SV474: $i,SV463: $i] :
( ( ( path @ SV463 @ SV474 @ SV496 )
= $false )
| ( ( in_path @ SV501 @ SV496 )
= $false )
| ( ( ~ ( ~ ( on_path @ ( sK10_E @ SV501 @ SV496 @ SV474 @ SV463 ) @ SV496 )
| ~ ( ( SV501
= ( head_of @ ( sK10_E @ SV501 @ SV496 @ SV474 @ SV463 ) ) )
| ( SV501
= ( tail_of @ ( sK10_E @ SV501 @ SV496 @ SV474 @ SV463 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2538]) ).
thf(2576,plain,
! [SV502: $i,SV497: $i,SV474: $i,SV463: $i] :
( ( ( path @ SV463 @ SV474 @ SV497 )
= $false )
| ( ( in_path @ SV502 @ SV497 )
= $false )
| ( ( vertex @ SV502 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2539]) ).
thf(2577,plain,
! [SV464: $i] :
( ( ( ~ ( on_path @ ( sK6_E1 @ SV464 ) @ SV464 ) )
= $false )
| ( ( ! [SY751: $i,SY752: $i] :
~ ( path @ SY751 @ SY752 @ SV464 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV464 )
= ( number_of_in @ triangles @ SV464 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2540]) ).
thf(2578,plain,
! [SV464: $i] :
( ( ( ~ ( on_path @ ( sK7_SY80 @ SV464 ) @ SV464 ) )
= $false )
| ( ( ! [SY751: $i,SY752: $i] :
~ ( path @ SY751 @ SY752 @ SV464 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV464 )
= ( number_of_in @ triangles @ SV464 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2540]) ).
thf(2579,plain,
! [SV464: $i,SV531: $i,SV524: $i] :
( ( ( ~ ( path @ SV524 @ SV531 @ SV464 ) )
= $true )
| ( ( sequential @ ( sK6_E1 @ SV464 ) @ ( sK7_SY80 @ SV464 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV464 )
= ( number_of_in @ triangles @ SV464 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2541]) ).
thf(2580,plain,
! [SV503: $i,SV464: $i,SV525: $i,SV514: $i] :
( ( ( path @ SV514 @ SV525 @ SV464 )
= $false )
| ( ( triangle @ ( sK6_E1 @ SV464 ) @ ( sK7_SY80 @ SV464 ) @ SV503 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV464 )
= ( number_of_in @ triangles @ SV464 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2542]) ).
thf(2581,plain,
! [SV475: $i,SV465: $i,SV515: $i,SV526: $i] :
( ( ( ~ ( on_path @ SV526 @ SV515 )
| ~ ( path @ SV465 @ SV475 @ SV515 ) )
= $true )
| ( ( edge @ SV526 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2543]) ).
thf(2582,plain,
! [SV475: $i,SV465: $i,SV516: $i,SV527: $i] :
( ( ( ~ ( on_path @ SV527 @ SV516 )
| ~ ( path @ SV465 @ SV475 @ SV516 ) )
= $true )
| ( ( in_path @ ( head_of @ SV527 ) @ SV516 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2544]) ).
thf(2583,plain,
! [SV504: $i,SV498: $i,SV475: $i,SV465: $i] :
( ( ( path @ SV465 @ SV475 @ SV498 )
= $false )
| ( ( on_path @ SV504 @ SV498 )
= $false )
| ( ( in_path @ ( tail_of @ SV504 ) @ SV498 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2545]) ).
thf(2584,plain,
! [SV499: $i,SV492: $i,SV466: $i] :
( ( ( ~ ( edge @ SV466 )
| ~ ( edge @ SV492 ) )
= $true )
| ( ( ~ ( edge @ SV499 ) )
= $true )
| ( ( ~ ( sequential @ SV466 @ SV492 ) )
= $true )
| ( ( ~ ( sequential @ SV492 @ SV499 ) )
= $true )
| ( ( ~ ( sequential @ SV499 @ SV466 ) )
= $true )
| ( ( triangle @ SV466 @ SV492 @ SV499 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2546]) ).
thf(2585,plain,
! [SV466: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( ! [SY762: $i,SY763: $i] :
~ ( triangle @ SV466 @ SY762 @ SY763 )
| ( edge @ SV466 ) )
| ~ ! [SY764: $i] :
( ! [SY765: $i] :
~ ( triangle @ SV466 @ SY764 @ SY765 )
| ( edge @ SY764 ) ) )
| ~ ! [SY766: $i,SY767: $i] :
( ~ ( triangle @ SV466 @ SY766 @ SY767 )
| ( edge @ SY767 ) ) )
| ~ ! [SY768: $i] :
( ! [SY769: $i] :
~ ( triangle @ SV466 @ SY768 @ SY769 )
| ( sequential @ SV466 @ SY768 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2547]) ).
thf(2586,plain,
! [SV532: $i,SV466: $i] :
( ( ! [SY863: $i] :
( ~ ( triangle @ SV466 @ SV532 @ SY863 )
| ( sequential @ SV532 @ SY863 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2548]) ).
thf(2587,plain,
! [SV517: $i,SV509: $i,SV466: $i] :
( ( ( triangle @ SV466 @ SV509 @ SV517 )
= $false )
| ( ( sequential @ SV517 @ SV466 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2549]) ).
thf(2588,plain,
! [SV500: $i,SV493: $i,SV467: $i] :
( ( ( path @ SV467 @ SV493 @ ( sK8_P @ SV500 @ SV493 @ SV467 ) )
= $true )
| ( ( ( SV467 = SV493 )
| ~ ( path @ SV467 @ SV493 @ SV500 ) )
= $true )
| ( ( shortest_path @ SV467 @ SV493 @ SV500 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2550]) ).
thf(2589,plain,
! [SV467: $i,SV493: $i,SV500: $i] :
( ( ( ~ ( less_or_equal @ ( length_of @ SV500 ) @ ( length_of @ ( sK8_P @ SV500 @ SV493 @ SV467 ) ) ) )
= $true )
| ( ( ( SV467 = SV493 )
| ~ ( path @ SV467 @ SV493 @ SV500 ) )
= $true )
| ( ( shortest_path @ SV467 @ SV493 @ SV500 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2551]) ).
thf(2590,plain,
! [SV518: $i,SV510: $i,SV467: $i] :
( ( ( shortest_path @ SV467 @ SV510 @ SV518 )
= $false )
| ( ( ! [SY856: $i] :
( ~ ( path @ SV467 @ SV510 @ SY856 )
| ( less_or_equal @ ( length_of @ SV518 ) @ ( length_of @ SY856 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2552]) ).
thf(2591,plain,
! [SV533: $i,SV467: $i] :
( ( ! [SY864: $i] :
~ ( shortest_path @ SV467 @ SV533 @ SY864 )
| ( SV467 != SV533 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2553]) ).
thf(2592,plain,
! [SV534: $i,SV467: $i] :
( ( ! [SY865: $i] :
( ~ ( shortest_path @ SV467 @ SV534 @ SY865 )
| ( path @ SV467 @ SV534 @ SY865 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2554]) ).
thf(2593,plain,
! [SV482: $i,SV476: $i,SV468: $i] :
( ( ( ! [SY826: $i] :
( ( SV468
!= ( tail_of @ SY826 ) )
| ~ ( edge @ SY826 )
| ( SV476
!= ( head_of @ SY826 ) )
| ( SV482
!= ( path_cons @ SY826 @ empty ) ) ) )
= $true )
| ( ( vertex @ SV468 )
= $false )
| ( ( vertex @ SV476 )
= $false )
| ( ( path @ SV468 @ SV476 @ SV482 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2555]) ).
thf(2594,plain,
! [SV476: $i,SV482: $i,SV468: $i] :
( ( ( ! [SY827: $i] :
( ( SV468
!= ( tail_of @ SY827 ) )
| ~ ( edge @ SY827 )
| ! [SY828: $i] :
( ( SV482
!= ( path_cons @ SY827 @ SY828 ) )
| ~ ( path @ ( head_of @ SY827 ) @ SV476 @ SY828 ) ) ) )
= $true )
| ( ( vertex @ SV468 )
= $false )
| ( ( vertex @ SV476 )
= $false )
| ( ( path @ SV468 @ SV476 @ SV482 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2556]) ).
thf(2595,plain,
! [SV477: $i,SV469: $i,SV519: $i,SV505: $i,SV483: $i] :
( ( ( precedes @ SV483 @ SV505 @ SV519 )
= $false )
| ( ( ~ ( shortest_path @ SV469 @ SV477 @ SV519 ) )
= $true )
| ( ( ! [SY845: $i] :
( ( ( tail_of @ SY845 )
!= ( tail_of @ SV483 ) )
| ( ( head_of @ SY845 )
!= ( head_of @ SV505 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2557]) ).
thf(2596,plain,
! [SV477: $i,SV469: $i,SV511: $i,SV506: $i,SV483: $i] :
( ( ( precedes @ SV483 @ SV506 @ SV511 )
= $false )
| ( ( ~ ( shortest_path @ SV469 @ SV477 @ SV511 ) )
= $true )
| ( ( ~ ( precedes @ SV506 @ SV483 @ SV511 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2558]) ).
thf(2597,plain,
! [SV489: $i,SV494: $i] :
( ( ( edge @ SV494 )
= $false )
| ( ( edge @ SV489 )
= $false )
| ( ( SV489 = SV494 )
= $true )
| ( ( ( ( head_of @ SV489 )
!= ( tail_of @ SV494 ) ) )
= $true )
| ( ( sequential @ SV489 @ SV494 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2559]) ).
thf(2598,plain,
! [SV535: $i,SV528: $i] :
( ( ~ ( sequential @ SV528 @ SV535 )
| ( SV528 != SV535 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2560]) ).
thf(2599,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2561]) ).
thf(2600,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2561]) ).
thf(2601,plain,
! [SV490: $i,SV484: $i,SV529: $i,SV470: $i,SV520: $i] :
( ( ( ~ ( on_path @ SV520 @ SV470 )
| ~ ( on_path @ SV529 @ SV470 )
| ! [SY862: $i] :
( ~ ( precedes @ SY862 @ SV529 @ SV470 )
| ~ ( sequential @ SV520 @ SY862 ) ) )
= $true )
| ( ( precedes @ SV520 @ SV529 @ SV470 )
= $true )
| ( ( path @ SV484 @ SV490 @ SV470 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2563]) ).
thf(2602,plain,
! [SV490: $i,SV484: $i,SV530: $i,SV470: $i,SV521: $i] :
( ( ( ~ ( on_path @ SV521 @ SV470 )
| ~ ( on_path @ SV530 @ SV470 )
| ~ ( sequential @ SV521 @ SV530 ) )
= $true )
| ( ( precedes @ SV521 @ SV530 @ SV470 )
= $true )
| ( ( path @ SV484 @ SV490 @ SV470 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2564]) ).
thf(2603,plain,
! [SV485: $i,SV480: $i] :
( ( ( ~ ( ~ ( ( SV480
!= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
!= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
!= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
!= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV480
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
| ~ ( ( SV480
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) ) )
| ~ ~ ( ~ ( ( SV485
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
| ~ ( ( SV485
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) ) ) ) ) )
= $true )
| ( ( SV480 = SV485 )
= $true )
| ( ( vertex @ SV480 )
= $false )
| ( ( vertex @ SV485 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[2565]) ).
thf(2604,plain,
! [SV480: $i,SV485: $i] :
( ( ( edge @ ( sK14_E @ SV485 @ SV480 ) )
= $true )
| ( ( SV480 = SV485 )
= $true )
| ( ( vertex @ SV480 )
= $false )
| ( ( vertex @ SV485 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[2566]) ).
thf(2605,plain,
! [SV488: $i,SV481: $i,SV461: $i,SV536: $i] :
( ( ( ! [SY866: $i] :
~ ( precedes @ SV536 @ SY866 @ SV461 )
| ( on_path @ SV536 @ SV461 ) )
= $true )
| ( ( path @ SV481 @ SV488 @ SV461 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2567]) ).
thf(2606,plain,
! [SV488: $i,SV481: $i,SV461: $i,SV537: $i] :
( ( ( ! [SY867: $i] :
( ~ ( precedes @ SV537 @ SY867 @ SV461 )
| ( on_path @ SY867 @ SV461 ) ) )
= $true )
| ( ( path @ SV481 @ SV488 @ SV461 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2568]) ).
thf(2607,plain,
! [SV488: $i,SV481: $i,SV461: $i,SV538: $i] :
( ( ( ! [SY868: $i] :
( ~ ( precedes @ SV538 @ SY868 @ SV461 )
| ! [SY869: $i] :
( ~ ( precedes @ SY869 @ SY868 @ SV461 )
| ~ ( sequential @ SV538 @ SY869 ) )
| ~ ( sequential @ SV538 @ SY868 ) ) )
= $true )
| ( ( path @ SV481 @ SV488 @ SV461 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2569]) ).
thf(2608,plain,
! [SV488: $i,SV481: $i,SV461: $i,SV539: $i] :
( ( ( ! [SY870: $i] :
( ~ ( precedes @ SV539 @ SY870 @ SV461 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY870 @ SV539 @ SV461 ) @ SY870 @ SV461 )
| ~ ( sequential @ SV539 @ ( sK9_E3 @ SY870 @ SV539 @ SV461 ) ) )
| ( sequential @ SV539 @ SY870 ) ) )
= $true )
| ( ( path @ SV481 @ SV488 @ SV461 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2570]) ).
thf(2609,plain,
! [SV491: $i,SV495: $i,SV462: $i] :
( ( ( ( SV462
!= ( tail_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( edge @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
= $false )
| ( ( path @ SV462 @ SV491 @ SV495 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2573]) ).
thf(2610,plain,
! [SV462: $i,SV495: $i,SV491: $i] :
( ( ( ~ ( ( SV491
!= ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
| ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ empty ) )
| ! [SY840: $i] :
( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ SY840 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ SY840 ) ) )
| ~ ~ ( ~ ( ( SV491
= ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ ( sK13_SY84 @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ ( sK13_SY84 @ SV495 @ SV491 @ SV462 ) ) ) )
| ~ ( ( SV495
= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ empty ) )
| ~ ( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ ( sK12_SY85 @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ ( sK12_SY85 @ SV495 @ SV491 @ SV462 ) ) ) ) ) )
= $false )
| ( ( path @ SV462 @ SV491 @ SV495 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2574]) ).
thf(2611,plain,
! [SV463: $i,SV474: $i,SV496: $i,SV501: $i] :
( ( ( ~ ( on_path @ ( sK10_E @ SV501 @ SV496 @ SV474 @ SV463 ) @ SV496 )
| ~ ( ( SV501
= ( head_of @ ( sK10_E @ SV501 @ SV496 @ SV474 @ SV463 ) ) )
| ( SV501
= ( tail_of @ ( sK10_E @ SV501 @ SV496 @ SV474 @ SV463 ) ) ) ) )
= $false )
| ( ( in_path @ SV501 @ SV496 )
= $false )
| ( ( path @ SV463 @ SV474 @ SV496 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2575]) ).
thf(2612,plain,
! [SV464: $i] :
( ( ( on_path @ ( sK6_E1 @ SV464 ) @ SV464 )
= $true )
| ( ( ! [SY751: $i,SY752: $i] :
~ ( path @ SY751 @ SY752 @ SV464 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV464 )
= ( number_of_in @ triangles @ SV464 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2577]) ).
thf(2613,plain,
! [SV464: $i] :
( ( ( on_path @ ( sK7_SY80 @ SV464 ) @ SV464 )
= $true )
| ( ( ! [SY751: $i,SY752: $i] :
~ ( path @ SY751 @ SY752 @ SV464 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV464 )
= ( number_of_in @ triangles @ SV464 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2578]) ).
thf(2614,plain,
! [SV464: $i,SV531: $i,SV524: $i] :
( ( ( path @ SV524 @ SV531 @ SV464 )
= $false )
| ( ( sequential @ ( sK6_E1 @ SV464 ) @ ( sK7_SY80 @ SV464 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV464 )
= ( number_of_in @ triangles @ SV464 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2579]) ).
thf(2615,plain,
! [SV475: $i,SV465: $i,SV515: $i,SV526: $i] :
( ( ( ~ ( on_path @ SV526 @ SV515 ) )
= $true )
| ( ( ~ ( path @ SV465 @ SV475 @ SV515 ) )
= $true )
| ( ( edge @ SV526 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2581]) ).
thf(2616,plain,
! [SV475: $i,SV465: $i,SV516: $i,SV527: $i] :
( ( ( ~ ( on_path @ SV527 @ SV516 ) )
= $true )
| ( ( ~ ( path @ SV465 @ SV475 @ SV516 ) )
= $true )
| ( ( in_path @ ( head_of @ SV527 ) @ SV516 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2582]) ).
thf(2617,plain,
! [SV499: $i,SV492: $i,SV466: $i] :
( ( ( ~ ( edge @ SV466 ) )
= $true )
| ( ( ~ ( edge @ SV492 ) )
= $true )
| ( ( ~ ( edge @ SV499 ) )
= $true )
| ( ( ~ ( sequential @ SV466 @ SV492 ) )
= $true )
| ( ( ~ ( sequential @ SV492 @ SV499 ) )
= $true )
| ( ( ~ ( sequential @ SV499 @ SV466 ) )
= $true )
| ( ( triangle @ SV466 @ SV492 @ SV499 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2584]) ).
thf(2618,plain,
! [SV466: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( ! [SY762: $i,SY763: $i] :
~ ( triangle @ SV466 @ SY762 @ SY763 )
| ( edge @ SV466 ) )
| ~ ! [SY764: $i] :
( ! [SY765: $i] :
~ ( triangle @ SV466 @ SY764 @ SY765 )
| ( edge @ SY764 ) ) )
| ~ ! [SY766: $i,SY767: $i] :
( ~ ( triangle @ SV466 @ SY766 @ SY767 )
| ( edge @ SY767 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2585]) ).
thf(2619,plain,
! [SV466: $i] :
( ( ~ ! [SY768: $i] :
( ! [SY769: $i] :
~ ( triangle @ SV466 @ SY768 @ SY769 )
| ( sequential @ SV466 @ SY768 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2585]) ).
thf(2620,plain,
! [SV540: $i,SV532: $i,SV466: $i] :
( ( ~ ( triangle @ SV466 @ SV532 @ SV540 )
| ( sequential @ SV532 @ SV540 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2586]) ).
thf(2621,plain,
! [SV500: $i,SV493: $i,SV467: $i] :
( ( ( SV467 = SV493 )
= $true )
| ( ( ~ ( path @ SV467 @ SV493 @ SV500 ) )
= $true )
| ( ( path @ SV467 @ SV493 @ ( sK8_P @ SV500 @ SV493 @ SV467 ) )
= $true )
| ( ( shortest_path @ SV467 @ SV493 @ SV500 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2588]) ).
thf(2622,plain,
! [SV467: $i,SV493: $i,SV500: $i] :
( ( ( less_or_equal @ ( length_of @ SV500 ) @ ( length_of @ ( sK8_P @ SV500 @ SV493 @ SV467 ) ) )
= $false )
| ( ( ( SV467 = SV493 )
| ~ ( path @ SV467 @ SV493 @ SV500 ) )
= $true )
| ( ( shortest_path @ SV467 @ SV493 @ SV500 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2589]) ).
thf(2623,plain,
! [SV518: $i,SV541: $i,SV510: $i,SV467: $i] :
( ( ( ~ ( path @ SV467 @ SV510 @ SV541 )
| ( less_or_equal @ ( length_of @ SV518 ) @ ( length_of @ SV541 ) ) )
= $true )
| ( ( shortest_path @ SV467 @ SV510 @ SV518 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2590]) ).
thf(2624,plain,
! [SV533: $i,SV467: $i] :
( ( ( ! [SY864: $i] :
~ ( shortest_path @ SV467 @ SV533 @ SY864 ) )
= $true )
| ( ( ( SV467 != SV533 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2591]) ).
thf(2625,plain,
! [SV542: $i,SV534: $i,SV467: $i] :
( ( ~ ( shortest_path @ SV467 @ SV534 @ SV542 )
| ( path @ SV467 @ SV534 @ SV542 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2592]) ).
thf(2626,plain,
! [SV482: $i,SV476: $i,SV543: $i,SV468: $i] :
( ( ( ( SV468
!= ( tail_of @ SV543 ) )
| ~ ( edge @ SV543 )
| ( SV476
!= ( head_of @ SV543 ) )
| ( SV482
!= ( path_cons @ SV543 @ empty ) ) )
= $true )
| ( ( vertex @ SV468 )
= $false )
| ( ( vertex @ SV476 )
= $false )
| ( ( path @ SV468 @ SV476 @ SV482 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2593]) ).
thf(2627,plain,
! [SV476: $i,SV482: $i,SV544: $i,SV468: $i] :
( ( ( ( SV468
!= ( tail_of @ SV544 ) )
| ~ ( edge @ SV544 )
| ! [SY871: $i] :
( ( SV482
!= ( path_cons @ SV544 @ SY871 ) )
| ~ ( path @ ( head_of @ SV544 ) @ SV476 @ SY871 ) ) )
= $true )
| ( ( vertex @ SV468 )
= $false )
| ( ( vertex @ SV476 )
= $false )
| ( ( path @ SV468 @ SV476 @ SV482 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2594]) ).
thf(2628,plain,
! [SV505: $i,SV483: $i,SV519: $i,SV477: $i,SV469: $i] :
( ( ( shortest_path @ SV469 @ SV477 @ SV519 )
= $false )
| ( ( precedes @ SV483 @ SV505 @ SV519 )
= $false )
| ( ( ! [SY845: $i] :
( ( ( tail_of @ SY845 )
!= ( tail_of @ SV483 ) )
| ( ( head_of @ SY845 )
!= ( head_of @ SV505 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2595]) ).
thf(2629,plain,
! [SV506: $i,SV483: $i,SV511: $i,SV477: $i,SV469: $i] :
( ( ( shortest_path @ SV469 @ SV477 @ SV511 )
= $false )
| ( ( precedes @ SV483 @ SV506 @ SV511 )
= $false )
| ( ( ~ ( precedes @ SV506 @ SV483 @ SV511 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2596]) ).
thf(2630,plain,
! [SV494: $i,SV489: $i] :
( ( ( ( head_of @ SV489 )
= ( tail_of @ SV494 ) )
= $false )
| ( ( SV489 = SV494 )
= $true )
| ( ( edge @ SV489 )
= $false )
| ( ( edge @ SV494 )
= $false )
| ( ( sequential @ SV489 @ SV494 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2597]) ).
thf(2631,plain,
! [SV535: $i,SV528: $i] :
( ( ( ~ ( sequential @ SV528 @ SV535 ) )
= $true )
| ( ( ( SV528 != SV535 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2598]) ).
thf(2632,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2599]) ).
thf(2633,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2600]) ).
thf(2634,plain,
! [SV490: $i,SV484: $i,SV529: $i,SV470: $i,SV520: $i] :
( ( ( ~ ( on_path @ SV520 @ SV470 )
| ~ ( on_path @ SV529 @ SV470 ) )
= $true )
| ( ( ! [SY862: $i] :
( ~ ( precedes @ SY862 @ SV529 @ SV470 )
| ~ ( sequential @ SV520 @ SY862 ) ) )
= $true )
| ( ( precedes @ SV520 @ SV529 @ SV470 )
= $true )
| ( ( path @ SV484 @ SV490 @ SV470 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2601]) ).
thf(2635,plain,
! [SV490: $i,SV484: $i,SV530: $i,SV470: $i,SV521: $i] :
( ( ( ~ ( on_path @ SV521 @ SV470 )
| ~ ( on_path @ SV530 @ SV470 ) )
= $true )
| ( ( ~ ( sequential @ SV521 @ SV530 ) )
= $true )
| ( ( precedes @ SV521 @ SV530 @ SV470 )
= $true )
| ( ( path @ SV484 @ SV490 @ SV470 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2602]) ).
thf(2636,plain,
! [SV485: $i,SV480: $i] :
( ( ( ~ ( ( SV480
!= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
!= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
!= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
!= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV480
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
| ~ ( ( SV480
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) ) )
| ~ ~ ( ~ ( ( SV485
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
| ~ ( ( SV485
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) ) ) ) )
= $false )
| ( ( SV480 = SV485 )
= $true )
| ( ( vertex @ SV480 )
= $false )
| ( ( vertex @ SV485 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[2603]) ).
thf(2637,plain,
! [SV488: $i,SV481: $i,SV461: $i,SV536: $i] :
( ( ( ! [SY866: $i] :
~ ( precedes @ SV536 @ SY866 @ SV461 ) )
= $true )
| ( ( on_path @ SV536 @ SV461 )
= $true )
| ( ( path @ SV481 @ SV488 @ SV461 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2605]) ).
thf(2638,plain,
! [SV488: $i,SV481: $i,SV461: $i,SV545: $i,SV537: $i] :
( ( ( ~ ( precedes @ SV537 @ SV545 @ SV461 )
| ( on_path @ SV545 @ SV461 ) )
= $true )
| ( ( path @ SV481 @ SV488 @ SV461 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2606]) ).
thf(2639,plain,
! [SV488: $i,SV481: $i,SV461: $i,SV546: $i,SV538: $i] :
( ( ( ~ ( precedes @ SV538 @ SV546 @ SV461 )
| ! [SY872: $i] :
( ~ ( precedes @ SY872 @ SV546 @ SV461 )
| ~ ( sequential @ SV538 @ SY872 ) )
| ~ ( sequential @ SV538 @ SV546 ) )
= $true )
| ( ( path @ SV481 @ SV488 @ SV461 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2607]) ).
thf(2640,plain,
! [SV488: $i,SV481: $i,SV461: $i,SV547: $i,SV539: $i] :
( ( ( ~ ( precedes @ SV539 @ SV547 @ SV461 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SV547 @ SV539 @ SV461 ) @ SV547 @ SV461 )
| ~ ( sequential @ SV539 @ ( sK9_E3 @ SV547 @ SV539 @ SV461 ) ) )
| ( sequential @ SV539 @ SV547 ) )
= $true )
| ( ( path @ SV481 @ SV488 @ SV461 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2608]) ).
thf(2641,plain,
! [SV491: $i,SV495: $i,SV462: $i] :
( ( ( ( SV462
!= ( tail_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) ) )
= $false )
| ( ( path @ SV462 @ SV491 @ SV495 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2609]) ).
thf(2642,plain,
! [SV462: $i,SV491: $i,SV495: $i] :
( ( ( ~ ( edge @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
= $false )
| ( ( path @ SV462 @ SV491 @ SV495 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2609]) ).
thf(2643,plain,
! [SV462: $i,SV495: $i,SV491: $i] :
( ( ( ~ ( ( SV491
!= ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
| ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ empty ) )
| ! [SY840: $i] :
( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ SY840 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ SY840 ) ) ) )
= $false )
| ( ( path @ SV462 @ SV491 @ SV495 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2610]) ).
thf(2644,plain,
! [SV462: $i,SV495: $i,SV491: $i] :
( ( ( ~ ~ ( ~ ( ( SV491
= ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ ( sK13_SY84 @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ ( sK13_SY84 @ SV495 @ SV491 @ SV462 ) ) ) )
| ~ ( ( SV495
= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ empty ) )
| ~ ( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ ( sK12_SY85 @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ ( sK12_SY85 @ SV495 @ SV491 @ SV462 ) ) ) ) ) )
= $false )
| ( ( path @ SV462 @ SV491 @ SV495 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2610]) ).
thf(2645,plain,
! [SV463: $i,SV474: $i,SV496: $i,SV501: $i] :
( ( ( ~ ( on_path @ ( sK10_E @ SV501 @ SV496 @ SV474 @ SV463 ) @ SV496 ) )
= $false )
| ( ( in_path @ SV501 @ SV496 )
= $false )
| ( ( path @ SV463 @ SV474 @ SV496 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2611]) ).
thf(2646,plain,
! [SV463: $i,SV474: $i,SV496: $i,SV501: $i] :
( ( ( ~ ( ( SV501
= ( head_of @ ( sK10_E @ SV501 @ SV496 @ SV474 @ SV463 ) ) )
| ( SV501
= ( tail_of @ ( sK10_E @ SV501 @ SV496 @ SV474 @ SV463 ) ) ) ) )
= $false )
| ( ( in_path @ SV501 @ SV496 )
= $false )
| ( ( path @ SV463 @ SV474 @ SV496 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2611]) ).
thf(2647,plain,
! [SV464: $i,SV548: $i] :
( ( ( ! [SY873: $i] :
~ ( path @ SV548 @ SY873 @ SV464 ) )
= $true )
| ( ( on_path @ ( sK6_E1 @ SV464 ) @ SV464 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV464 )
= ( number_of_in @ triangles @ SV464 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2612]) ).
thf(2648,plain,
! [SV464: $i,SV549: $i] :
( ( ( ! [SY874: $i] :
~ ( path @ SV549 @ SY874 @ SV464 ) )
= $true )
| ( ( on_path @ ( sK7_SY80 @ SV464 ) @ SV464 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV464 )
= ( number_of_in @ triangles @ SV464 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2613]) ).
thf(2649,plain,
! [SV475: $i,SV465: $i,SV515: $i,SV526: $i] :
( ( ( on_path @ SV526 @ SV515 )
= $false )
| ( ( ~ ( path @ SV465 @ SV475 @ SV515 ) )
= $true )
| ( ( edge @ SV526 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2615]) ).
thf(2650,plain,
! [SV475: $i,SV465: $i,SV516: $i,SV527: $i] :
( ( ( on_path @ SV527 @ SV516 )
= $false )
| ( ( ~ ( path @ SV465 @ SV475 @ SV516 ) )
= $true )
| ( ( in_path @ ( head_of @ SV527 ) @ SV516 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2616]) ).
thf(2651,plain,
! [SV499: $i,SV492: $i,SV466: $i] :
( ( ( edge @ SV466 )
= $false )
| ( ( ~ ( edge @ SV492 ) )
= $true )
| ( ( ~ ( edge @ SV499 ) )
= $true )
| ( ( ~ ( sequential @ SV466 @ SV492 ) )
= $true )
| ( ( ~ ( sequential @ SV492 @ SV499 ) )
= $true )
| ( ( ~ ( sequential @ SV499 @ SV466 ) )
= $true )
| ( ( triangle @ SV466 @ SV492 @ SV499 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2617]) ).
thf(2652,plain,
! [SV466: $i] :
( ( ~ ( ~ ~ ( ~ ( ! [SY762: $i,SY763: $i] :
~ ( triangle @ SV466 @ SY762 @ SY763 )
| ( edge @ SV466 ) )
| ~ ! [SY764: $i] :
( ! [SY765: $i] :
~ ( triangle @ SV466 @ SY764 @ SY765 )
| ( edge @ SY764 ) ) )
| ~ ! [SY766: $i,SY767: $i] :
( ~ ( triangle @ SV466 @ SY766 @ SY767 )
| ( edge @ SY767 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2618]) ).
thf(2653,plain,
! [SV466: $i] :
( ( ! [SY768: $i] :
( ! [SY769: $i] :
~ ( triangle @ SV466 @ SY768 @ SY769 )
| ( sequential @ SV466 @ SY768 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2619]) ).
thf(2654,plain,
! [SV540: $i,SV532: $i,SV466: $i] :
( ( ( ~ ( triangle @ SV466 @ SV532 @ SV540 ) )
= $true )
| ( ( sequential @ SV532 @ SV540 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2620]) ).
thf(2655,plain,
! [SV500: $i,SV493: $i,SV467: $i] :
( ( ( path @ SV467 @ SV493 @ SV500 )
= $false )
| ( ( SV467 = SV493 )
= $true )
| ( ( path @ SV467 @ SV493 @ ( sK8_P @ SV500 @ SV493 @ SV467 ) )
= $true )
| ( ( shortest_path @ SV467 @ SV493 @ SV500 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2621]) ).
thf(2656,plain,
! [SV500: $i,SV493: $i,SV467: $i] :
( ( ( SV467 = SV493 )
= $true )
| ( ( ~ ( path @ SV467 @ SV493 @ SV500 ) )
= $true )
| ( ( less_or_equal @ ( length_of @ SV500 ) @ ( length_of @ ( sK8_P @ SV500 @ SV493 @ SV467 ) ) )
= $false )
| ( ( shortest_path @ SV467 @ SV493 @ SV500 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2622]) ).
thf(2657,plain,
! [SV518: $i,SV541: $i,SV510: $i,SV467: $i] :
( ( ( ~ ( path @ SV467 @ SV510 @ SV541 ) )
= $true )
| ( ( less_or_equal @ ( length_of @ SV518 ) @ ( length_of @ SV541 ) )
= $true )
| ( ( shortest_path @ SV467 @ SV510 @ SV518 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2623]) ).
thf(2658,plain,
! [SV550: $i,SV533: $i,SV467: $i] :
( ( ( ~ ( shortest_path @ SV467 @ SV533 @ SV550 ) )
= $true )
| ( ( ( SV467 != SV533 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2624]) ).
thf(2659,plain,
! [SV542: $i,SV534: $i,SV467: $i] :
( ( ( ~ ( shortest_path @ SV467 @ SV534 @ SV542 ) )
= $true )
| ( ( path @ SV467 @ SV534 @ SV542 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2625]) ).
thf(2660,plain,
! [SV482: $i,SV476: $i,SV543: $i,SV468: $i] :
( ( ( ( SV468
!= ( tail_of @ SV543 ) )
| ~ ( edge @ SV543 ) )
= $true )
| ( ( ( SV476
!= ( head_of @ SV543 ) )
| ( SV482
!= ( path_cons @ SV543 @ empty ) ) )
= $true )
| ( ( vertex @ SV468 )
= $false )
| ( ( vertex @ SV476 )
= $false )
| ( ( path @ SV468 @ SV476 @ SV482 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2626]) ).
thf(2661,plain,
! [SV476: $i,SV482: $i,SV544: $i,SV468: $i] :
( ( ( ( SV468
!= ( tail_of @ SV544 ) )
| ~ ( edge @ SV544 ) )
= $true )
| ( ( ! [SY871: $i] :
( ( SV482
!= ( path_cons @ SV544 @ SY871 ) )
| ~ ( path @ ( head_of @ SV544 ) @ SV476 @ SY871 ) ) )
= $true )
| ( ( vertex @ SV468 )
= $false )
| ( ( vertex @ SV476 )
= $false )
| ( ( path @ SV468 @ SV476 @ SV482 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2627]) ).
thf(2662,plain,
! [SV477: $i,SV469: $i,SV519: $i,SV505: $i,SV483: $i,SV551: $i] :
( ( ( ( ( tail_of @ SV551 )
!= ( tail_of @ SV483 ) )
| ( ( head_of @ SV551 )
!= ( head_of @ SV505 ) ) )
= $true )
| ( ( precedes @ SV483 @ SV505 @ SV519 )
= $false )
| ( ( shortest_path @ SV469 @ SV477 @ SV519 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2628]) ).
thf(2663,plain,
! [SV477: $i,SV469: $i,SV511: $i,SV483: $i,SV506: $i] :
( ( ( precedes @ SV506 @ SV483 @ SV511 )
= $false )
| ( ( precedes @ SV483 @ SV506 @ SV511 )
= $false )
| ( ( shortest_path @ SV469 @ SV477 @ SV511 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2629]) ).
thf(2664,plain,
! [SV535: $i,SV528: $i] :
( ( ( sequential @ SV528 @ SV535 )
= $false )
| ( ( ( SV528 != SV535 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2631]) ).
thf(2665,plain,
! [SV552: $i] :
( ( ! [SY875: $i] :
~ ( sequential @ SV552 @ SY875 )
| ( edge @ SV552 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2632]) ).
thf(2666,plain,
! [SV553: $i] :
( ( ! [SY876: $i] :
( ~ ( sequential @ SV553 @ SY876 )
| ( edge @ SY876 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2633]) ).
thf(2667,plain,
! [SV490: $i,SV484: $i,SV529: $i,SV470: $i,SV520: $i] :
( ( ( ~ ( on_path @ SV520 @ SV470 ) )
= $true )
| ( ( ~ ( on_path @ SV529 @ SV470 ) )
= $true )
| ( ( ! [SY862: $i] :
( ~ ( precedes @ SY862 @ SV529 @ SV470 )
| ~ ( sequential @ SV520 @ SY862 ) ) )
= $true )
| ( ( precedes @ SV520 @ SV529 @ SV470 )
= $true )
| ( ( path @ SV484 @ SV490 @ SV470 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2634]) ).
thf(2668,plain,
! [SV490: $i,SV484: $i,SV530: $i,SV470: $i,SV521: $i] :
( ( ( ~ ( on_path @ SV521 @ SV470 ) )
= $true )
| ( ( ~ ( on_path @ SV530 @ SV470 ) )
= $true )
| ( ( ~ ( sequential @ SV521 @ SV530 ) )
= $true )
| ( ( precedes @ SV521 @ SV530 @ SV470 )
= $true )
| ( ( path @ SV484 @ SV490 @ SV470 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2635]) ).
thf(2669,plain,
! [SV485: $i,SV480: $i] :
( ( ( ~ ( ( SV480
!= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
!= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
!= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
!= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) ) )
= $false )
| ( ( SV480 = SV485 )
= $true )
| ( ( vertex @ SV480 )
= $false )
| ( ( vertex @ SV485 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[2636]) ).
thf(2670,plain,
! [SV485: $i,SV480: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( SV480
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
| ~ ( ( SV480
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) ) )
| ~ ~ ( ~ ( ( SV485
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
| ~ ( ( SV485
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) ) ) ) )
= $false )
| ( ( SV480 = SV485 )
= $true )
| ( ( vertex @ SV480 )
= $false )
| ( ( vertex @ SV485 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[2636]) ).
thf(2671,plain,
! [SV488: $i,SV481: $i,SV461: $i,SV554: $i,SV536: $i] :
( ( ( ~ ( precedes @ SV536 @ SV554 @ SV461 ) )
= $true )
| ( ( on_path @ SV536 @ SV461 )
= $true )
| ( ( path @ SV481 @ SV488 @ SV461 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2637]) ).
thf(2672,plain,
! [SV488: $i,SV481: $i,SV461: $i,SV545: $i,SV537: $i] :
( ( ( ~ ( precedes @ SV537 @ SV545 @ SV461 ) )
= $true )
| ( ( on_path @ SV545 @ SV461 )
= $true )
| ( ( path @ SV481 @ SV488 @ SV461 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2638]) ).
thf(2673,plain,
! [SV488: $i,SV481: $i,SV461: $i,SV546: $i,SV538: $i] :
( ( ( ~ ( precedes @ SV538 @ SV546 @ SV461 ) )
= $true )
| ( ( ! [SY872: $i] :
( ~ ( precedes @ SY872 @ SV546 @ SV461 )
| ~ ( sequential @ SV538 @ SY872 ) )
| ~ ( sequential @ SV538 @ SV546 ) )
= $true )
| ( ( path @ SV481 @ SV488 @ SV461 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2639]) ).
thf(2674,plain,
! [SV488: $i,SV481: $i,SV461: $i,SV547: $i,SV539: $i] :
( ( ( ~ ( precedes @ SV539 @ SV547 @ SV461 ) )
= $true )
| ( ( ~ ( ~ ( precedes @ ( sK9_E3 @ SV547 @ SV539 @ SV461 ) @ SV547 @ SV461 )
| ~ ( sequential @ SV539 @ ( sK9_E3 @ SV547 @ SV539 @ SV461 ) ) )
| ( sequential @ SV539 @ SV547 ) )
= $true )
| ( ( path @ SV481 @ SV488 @ SV461 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2640]) ).
thf(2675,plain,
! [SV491: $i,SV495: $i,SV462: $i] :
( ( ( SV462
= ( tail_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
= $true )
| ( ( path @ SV462 @ SV491 @ SV495 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2641]) ).
thf(2676,plain,
! [SV462: $i,SV491: $i,SV495: $i] :
( ( ( edge @ ( sK11_E @ SV495 @ SV491 @ SV462 ) )
= $true )
| ( ( path @ SV462 @ SV491 @ SV495 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2642]) ).
thf(2677,plain,
! [SV462: $i,SV495: $i,SV491: $i] :
( ( ( ( SV491
!= ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
| ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ empty ) )
| ! [SY840: $i] :
( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ SY840 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ SY840 ) ) )
= $true )
| ( ( path @ SV462 @ SV491 @ SV495 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2643]) ).
thf(2678,plain,
! [SV462: $i,SV495: $i,SV491: $i] :
( ( ( ~ ( ~ ( ( SV491
= ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ ( sK13_SY84 @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ ( sK13_SY84 @ SV495 @ SV491 @ SV462 ) ) ) )
| ~ ( ( SV495
= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ empty ) )
| ~ ( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ ( sK12_SY85 @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ ( sK12_SY85 @ SV495 @ SV491 @ SV462 ) ) ) ) ) )
= $true )
| ( ( path @ SV462 @ SV491 @ SV495 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2644]) ).
thf(2679,plain,
! [SV463: $i,SV474: $i,SV496: $i,SV501: $i] :
( ( ( on_path @ ( sK10_E @ SV501 @ SV496 @ SV474 @ SV463 ) @ SV496 )
= $true )
| ( ( in_path @ SV501 @ SV496 )
= $false )
| ( ( path @ SV463 @ SV474 @ SV496 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2645]) ).
thf(2680,plain,
! [SV463: $i,SV474: $i,SV496: $i,SV501: $i] :
( ( ( ( SV501
= ( head_of @ ( sK10_E @ SV501 @ SV496 @ SV474 @ SV463 ) ) )
| ( SV501
= ( tail_of @ ( sK10_E @ SV501 @ SV496 @ SV474 @ SV463 ) ) ) )
= $true )
| ( ( in_path @ SV501 @ SV496 )
= $false )
| ( ( path @ SV463 @ SV474 @ SV496 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2646]) ).
thf(2681,plain,
! [SV464: $i,SV555: $i,SV548: $i] :
( ( ( ~ ( path @ SV548 @ SV555 @ SV464 ) )
= $true )
| ( ( on_path @ ( sK6_E1 @ SV464 ) @ SV464 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV464 )
= ( number_of_in @ triangles @ SV464 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2647]) ).
thf(2682,plain,
! [SV464: $i,SV556: $i,SV549: $i] :
( ( ( ~ ( path @ SV549 @ SV556 @ SV464 ) )
= $true )
| ( ( on_path @ ( sK7_SY80 @ SV464 ) @ SV464 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV464 )
= ( number_of_in @ triangles @ SV464 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2648]) ).
thf(2683,plain,
! [SV526: $i,SV515: $i,SV475: $i,SV465: $i] :
( ( ( path @ SV465 @ SV475 @ SV515 )
= $false )
| ( ( on_path @ SV526 @ SV515 )
= $false )
| ( ( edge @ SV526 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2649]) ).
thf(2684,plain,
! [SV527: $i,SV516: $i,SV475: $i,SV465: $i] :
( ( ( path @ SV465 @ SV475 @ SV516 )
= $false )
| ( ( on_path @ SV527 @ SV516 )
= $false )
| ( ( in_path @ ( head_of @ SV527 ) @ SV516 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2650]) ).
thf(2685,plain,
! [SV499: $i,SV466: $i,SV492: $i] :
( ( ( edge @ SV492 )
= $false )
| ( ( edge @ SV466 )
= $false )
| ( ( ~ ( edge @ SV499 ) )
= $true )
| ( ( ~ ( sequential @ SV466 @ SV492 ) )
= $true )
| ( ( ~ ( sequential @ SV492 @ SV499 ) )
= $true )
| ( ( ~ ( sequential @ SV499 @ SV466 ) )
= $true )
| ( ( triangle @ SV466 @ SV492 @ SV499 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2651]) ).
thf(2686,plain,
! [SV466: $i] :
( ( ~ ~ ( ~ ( ! [SY762: $i,SY763: $i] :
~ ( triangle @ SV466 @ SY762 @ SY763 )
| ( edge @ SV466 ) )
| ~ ! [SY764: $i] :
( ! [SY765: $i] :
~ ( triangle @ SV466 @ SY764 @ SY765 )
| ( edge @ SY764 ) ) )
| ~ ! [SY766: $i,SY767: $i] :
( ~ ( triangle @ SV466 @ SY766 @ SY767 )
| ( edge @ SY767 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2652]) ).
thf(2687,plain,
! [SV557: $i,SV466: $i] :
( ( ! [SY877: $i] :
~ ( triangle @ SV466 @ SV557 @ SY877 )
| ( sequential @ SV466 @ SV557 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2653]) ).
thf(2688,plain,
! [SV540: $i,SV532: $i,SV466: $i] :
( ( ( triangle @ SV466 @ SV532 @ SV540 )
= $false )
| ( ( sequential @ SV532 @ SV540 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2654]) ).
thf(2689,plain,
! [SV500: $i,SV493: $i,SV467: $i] :
( ( ( path @ SV467 @ SV493 @ SV500 )
= $false )
| ( ( SV467 = SV493 )
= $true )
| ( ( less_or_equal @ ( length_of @ SV500 ) @ ( length_of @ ( sK8_P @ SV500 @ SV493 @ SV467 ) ) )
= $false )
| ( ( shortest_path @ SV467 @ SV493 @ SV500 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2656]) ).
thf(2690,plain,
! [SV518: $i,SV541: $i,SV510: $i,SV467: $i] :
( ( ( path @ SV467 @ SV510 @ SV541 )
= $false )
| ( ( less_or_equal @ ( length_of @ SV518 ) @ ( length_of @ SV541 ) )
= $true )
| ( ( shortest_path @ SV467 @ SV510 @ SV518 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2657]) ).
thf(2691,plain,
! [SV550: $i,SV533: $i,SV467: $i] :
( ( ( shortest_path @ SV467 @ SV533 @ SV550 )
= $false )
| ( ( ( SV467 != SV533 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2658]) ).
thf(2692,plain,
! [SV542: $i,SV534: $i,SV467: $i] :
( ( ( shortest_path @ SV467 @ SV534 @ SV542 )
= $false )
| ( ( path @ SV467 @ SV534 @ SV542 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2659]) ).
thf(2693,plain,
! [SV482: $i,SV476: $i,SV543: $i,SV468: $i] :
( ( ( ( SV468
!= ( tail_of @ SV543 ) ) )
= $true )
| ( ( ~ ( edge @ SV543 ) )
= $true )
| ( ( ( SV476
!= ( head_of @ SV543 ) )
| ( SV482
!= ( path_cons @ SV543 @ empty ) ) )
= $true )
| ( ( vertex @ SV468 )
= $false )
| ( ( vertex @ SV476 )
= $false )
| ( ( path @ SV468 @ SV476 @ SV482 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2660]) ).
thf(2694,plain,
! [SV476: $i,SV482: $i,SV544: $i,SV468: $i] :
( ( ( ( SV468
!= ( tail_of @ SV544 ) ) )
= $true )
| ( ( ~ ( edge @ SV544 ) )
= $true )
| ( ( ! [SY871: $i] :
( ( SV482
!= ( path_cons @ SV544 @ SY871 ) )
| ~ ( path @ ( head_of @ SV544 ) @ SV476 @ SY871 ) ) )
= $true )
| ( ( vertex @ SV468 )
= $false )
| ( ( vertex @ SV476 )
= $false )
| ( ( path @ SV468 @ SV476 @ SV482 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2661]) ).
thf(2695,plain,
! [SV477: $i,SV469: $i,SV519: $i,SV505: $i,SV483: $i,SV551: $i] :
( ( ( ( ( tail_of @ SV551 )
!= ( tail_of @ SV483 ) ) )
= $true )
| ( ( ( ( head_of @ SV551 )
!= ( head_of @ SV505 ) ) )
= $true )
| ( ( precedes @ SV483 @ SV505 @ SV519 )
= $false )
| ( ( shortest_path @ SV469 @ SV477 @ SV519 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2662]) ).
thf(2696,plain,
! [SV535: $i,SV528: $i] :
( ( ( SV528 = SV535 )
= $false )
| ( ( sequential @ SV528 @ SV535 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2664]) ).
thf(2697,plain,
! [SV552: $i] :
( ( ( ! [SY875: $i] :
~ ( sequential @ SV552 @ SY875 ) )
= $true )
| ( ( edge @ SV552 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2665]) ).
thf(2698,plain,
! [SV558: $i,SV553: $i] :
( ( ~ ( sequential @ SV553 @ SV558 )
| ( edge @ SV558 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2666]) ).
thf(2699,plain,
! [SV490: $i,SV484: $i,SV529: $i,SV470: $i,SV520: $i] :
( ( ( on_path @ SV520 @ SV470 )
= $false )
| ( ( ~ ( on_path @ SV529 @ SV470 ) )
= $true )
| ( ( ! [SY862: $i] :
( ~ ( precedes @ SY862 @ SV529 @ SV470 )
| ~ ( sequential @ SV520 @ SY862 ) ) )
= $true )
| ( ( precedes @ SV520 @ SV529 @ SV470 )
= $true )
| ( ( path @ SV484 @ SV490 @ SV470 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2667]) ).
thf(2700,plain,
! [SV490: $i,SV484: $i,SV530: $i,SV470: $i,SV521: $i] :
( ( ( on_path @ SV521 @ SV470 )
= $false )
| ( ( ~ ( on_path @ SV530 @ SV470 ) )
= $true )
| ( ( ~ ( sequential @ SV521 @ SV530 ) )
= $true )
| ( ( precedes @ SV521 @ SV530 @ SV470 )
= $true )
| ( ( path @ SV484 @ SV490 @ SV470 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2668]) ).
thf(2701,plain,
! [SV485: $i,SV480: $i] :
( ( ( ( SV480
!= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
!= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
!= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
!= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
= $true )
| ( ( SV480 = SV485 )
= $true )
| ( ( vertex @ SV480 )
= $false )
| ( ( vertex @ SV485 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[2669]) ).
thf(2702,plain,
! [SV485: $i,SV480: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( SV480
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
| ~ ( ( SV480
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) ) )
| ~ ~ ( ~ ( ( SV485
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
| ~ ( ( SV485
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) ) ) ) )
= $true )
| ( ( SV480 = SV485 )
= $true )
| ( ( vertex @ SV480 )
= $false )
| ( ( vertex @ SV485 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[2670]) ).
thf(2703,plain,
! [SV488: $i,SV481: $i,SV461: $i,SV554: $i,SV536: $i] :
( ( ( precedes @ SV536 @ SV554 @ SV461 )
= $false )
| ( ( on_path @ SV536 @ SV461 )
= $true )
| ( ( path @ SV481 @ SV488 @ SV461 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2671]) ).
thf(2704,plain,
! [SV488: $i,SV481: $i,SV461: $i,SV545: $i,SV537: $i] :
( ( ( precedes @ SV537 @ SV545 @ SV461 )
= $false )
| ( ( on_path @ SV545 @ SV461 )
= $true )
| ( ( path @ SV481 @ SV488 @ SV461 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2672]) ).
thf(2705,plain,
! [SV488: $i,SV481: $i,SV461: $i,SV546: $i,SV538: $i] :
( ( ( precedes @ SV538 @ SV546 @ SV461 )
= $false )
| ( ( ! [SY872: $i] :
( ~ ( precedes @ SY872 @ SV546 @ SV461 )
| ~ ( sequential @ SV538 @ SY872 ) )
| ~ ( sequential @ SV538 @ SV546 ) )
= $true )
| ( ( path @ SV481 @ SV488 @ SV461 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2673]) ).
thf(2706,plain,
! [SV488: $i,SV481: $i,SV461: $i,SV547: $i,SV539: $i] :
( ( ( precedes @ SV539 @ SV547 @ SV461 )
= $false )
| ( ( ~ ( ~ ( precedes @ ( sK9_E3 @ SV547 @ SV539 @ SV461 ) @ SV547 @ SV461 )
| ~ ( sequential @ SV539 @ ( sK9_E3 @ SV547 @ SV539 @ SV461 ) ) )
| ( sequential @ SV539 @ SV547 ) )
= $true )
| ( ( path @ SV481 @ SV488 @ SV461 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2674]) ).
thf(2707,plain,
! [SV462: $i,SV495: $i,SV491: $i] :
( ( ( ( SV491
!= ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
| ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ empty ) ) )
= $true )
| ( ( ! [SY840: $i] :
( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ SY840 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ SY840 ) ) )
= $true )
| ( ( path @ SV462 @ SV491 @ SV495 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2677]) ).
thf(2708,plain,
! [SV462: $i,SV495: $i,SV491: $i] :
( ( ( ~ ( ( SV491
= ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ ( sK13_SY84 @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ ( sK13_SY84 @ SV495 @ SV491 @ SV462 ) ) ) )
| ~ ( ( SV495
= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ empty ) )
| ~ ( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ ( sK12_SY85 @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ ( sK12_SY85 @ SV495 @ SV491 @ SV462 ) ) ) ) )
= $false )
| ( ( path @ SV462 @ SV491 @ SV495 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2678]) ).
thf(2709,plain,
! [SV463: $i,SV474: $i,SV496: $i,SV501: $i] :
( ( ( SV501
= ( head_of @ ( sK10_E @ SV501 @ SV496 @ SV474 @ SV463 ) ) )
= $true )
| ( ( SV501
= ( tail_of @ ( sK10_E @ SV501 @ SV496 @ SV474 @ SV463 ) ) )
= $true )
| ( ( in_path @ SV501 @ SV496 )
= $false )
| ( ( path @ SV463 @ SV474 @ SV496 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2680]) ).
thf(2710,plain,
! [SV464: $i,SV555: $i,SV548: $i] :
( ( ( path @ SV548 @ SV555 @ SV464 )
= $false )
| ( ( on_path @ ( sK6_E1 @ SV464 ) @ SV464 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV464 )
= ( number_of_in @ triangles @ SV464 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2681]) ).
thf(2711,plain,
! [SV464: $i,SV556: $i,SV549: $i] :
( ( ( path @ SV549 @ SV556 @ SV464 )
= $false )
| ( ( on_path @ ( sK7_SY80 @ SV464 ) @ SV464 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV464 )
= ( number_of_in @ triangles @ SV464 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2682]) ).
thf(2712,plain,
! [SV492: $i,SV466: $i,SV499: $i] :
( ( ( edge @ SV499 )
= $false )
| ( ( edge @ SV466 )
= $false )
| ( ( edge @ SV492 )
= $false )
| ( ( ~ ( sequential @ SV466 @ SV492 ) )
= $true )
| ( ( ~ ( sequential @ SV492 @ SV499 ) )
= $true )
| ( ( ~ ( sequential @ SV499 @ SV466 ) )
= $true )
| ( ( triangle @ SV466 @ SV492 @ SV499 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2685]) ).
thf(2713,plain,
! [SV466: $i] :
( ( ~ ~ ( ~ ( ! [SY762: $i,SY763: $i] :
~ ( triangle @ SV466 @ SY762 @ SY763 )
| ( edge @ SV466 ) )
| ~ ! [SY764: $i] :
( ! [SY765: $i] :
~ ( triangle @ SV466 @ SY764 @ SY765 )
| ( edge @ SY764 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2686]) ).
thf(2714,plain,
! [SV466: $i] :
( ( ~ ! [SY766: $i,SY767: $i] :
( ~ ( triangle @ SV466 @ SY766 @ SY767 )
| ( edge @ SY767 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2686]) ).
thf(2715,plain,
! [SV557: $i,SV466: $i] :
( ( ( ! [SY877: $i] :
~ ( triangle @ SV466 @ SV557 @ SY877 ) )
= $true )
| ( ( sequential @ SV466 @ SV557 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2687]) ).
thf(2716,plain,
! [SV550: $i,SV533: $i,SV467: $i] :
( ( ( SV467 = SV533 )
= $false )
| ( ( shortest_path @ SV467 @ SV533 @ SV550 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2691]) ).
thf(2717,plain,
! [SV482: $i,SV476: $i,SV543: $i,SV468: $i] :
( ( ( SV468
= ( tail_of @ SV543 ) )
= $false )
| ( ( ~ ( edge @ SV543 ) )
= $true )
| ( ( ( SV476
!= ( head_of @ SV543 ) )
| ( SV482
!= ( path_cons @ SV543 @ empty ) ) )
= $true )
| ( ( vertex @ SV468 )
= $false )
| ( ( vertex @ SV476 )
= $false )
| ( ( path @ SV468 @ SV476 @ SV482 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2693]) ).
thf(2718,plain,
! [SV476: $i,SV482: $i,SV544: $i,SV468: $i] :
( ( ( SV468
= ( tail_of @ SV544 ) )
= $false )
| ( ( ~ ( edge @ SV544 ) )
= $true )
| ( ( ! [SY871: $i] :
( ( SV482
!= ( path_cons @ SV544 @ SY871 ) )
| ~ ( path @ ( head_of @ SV544 ) @ SV476 @ SY871 ) ) )
= $true )
| ( ( vertex @ SV468 )
= $false )
| ( ( vertex @ SV476 )
= $false )
| ( ( path @ SV468 @ SV476 @ SV482 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2694]) ).
thf(2719,plain,
! [SV477: $i,SV469: $i,SV519: $i,SV505: $i,SV483: $i,SV551: $i] :
( ( ( ( tail_of @ SV551 )
= ( tail_of @ SV483 ) )
= $false )
| ( ( ( ( head_of @ SV551 )
!= ( head_of @ SV505 ) ) )
= $true )
| ( ( precedes @ SV483 @ SV505 @ SV519 )
= $false )
| ( ( shortest_path @ SV469 @ SV477 @ SV519 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2695]) ).
thf(2720,plain,
! [SV559: $i,SV552: $i] :
( ( ( ~ ( sequential @ SV552 @ SV559 ) )
= $true )
| ( ( edge @ SV552 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2697]) ).
thf(2721,plain,
! [SV558: $i,SV553: $i] :
( ( ( ~ ( sequential @ SV553 @ SV558 ) )
= $true )
| ( ( edge @ SV558 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2698]) ).
thf(2722,plain,
! [SV490: $i,SV484: $i,SV520: $i,SV470: $i,SV529: $i] :
( ( ( on_path @ SV529 @ SV470 )
= $false )
| ( ( on_path @ SV520 @ SV470 )
= $false )
| ( ( ! [SY862: $i] :
( ~ ( precedes @ SY862 @ SV529 @ SV470 )
| ~ ( sequential @ SV520 @ SY862 ) ) )
= $true )
| ( ( precedes @ SV520 @ SV529 @ SV470 )
= $true )
| ( ( path @ SV484 @ SV490 @ SV470 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2699]) ).
thf(2723,plain,
! [SV490: $i,SV484: $i,SV521: $i,SV470: $i,SV530: $i] :
( ( ( on_path @ SV530 @ SV470 )
= $false )
| ( ( on_path @ SV521 @ SV470 )
= $false )
| ( ( ~ ( sequential @ SV521 @ SV530 ) )
= $true )
| ( ( precedes @ SV521 @ SV530 @ SV470 )
= $true )
| ( ( path @ SV484 @ SV490 @ SV470 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2700]) ).
thf(2724,plain,
! [SV485: $i,SV480: $i] :
( ( ( ( SV480
!= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
!= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
= $true )
| ( ( ( SV485
!= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
!= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
= $true )
| ( ( SV480 = SV485 )
= $true )
| ( ( vertex @ SV480 )
= $false )
| ( ( vertex @ SV485 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[2701]) ).
thf(2725,plain,
! [SV485: $i,SV480: $i] :
( ( ( ~ ~ ( ~ ( ( SV480
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
| ~ ( ( SV480
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) ) )
| ~ ~ ( ~ ( ( SV485
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
| ~ ( ( SV485
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) ) ) )
= $false )
| ( ( SV480 = SV485 )
= $true )
| ( ( vertex @ SV480 )
= $false )
| ( ( vertex @ SV485 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[2702]) ).
thf(2726,plain,
! [SV488: $i,SV481: $i,SV538: $i,SV461: $i,SV546: $i] :
( ( ( ! [SY872: $i] :
( ~ ( precedes @ SY872 @ SV546 @ SV461 )
| ~ ( sequential @ SV538 @ SY872 ) ) )
= $true )
| ( ( ~ ( sequential @ SV538 @ SV546 ) )
= $true )
| ( ( precedes @ SV538 @ SV546 @ SV461 )
= $false )
| ( ( path @ SV481 @ SV488 @ SV461 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2705]) ).
thf(2727,plain,
! [SV488: $i,SV481: $i,SV461: $i,SV539: $i,SV547: $i] :
( ( ( ~ ( ~ ( precedes @ ( sK9_E3 @ SV547 @ SV539 @ SV461 ) @ SV547 @ SV461 )
| ~ ( sequential @ SV539 @ ( sK9_E3 @ SV547 @ SV539 @ SV461 ) ) ) )
= $true )
| ( ( sequential @ SV539 @ SV547 )
= $true )
| ( ( precedes @ SV539 @ SV547 @ SV461 )
= $false )
| ( ( path @ SV481 @ SV488 @ SV461 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2706]) ).
thf(2728,plain,
! [SV462: $i,SV495: $i,SV491: $i] :
( ( ( ( SV491
!= ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) ) )
= $true )
| ( ( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ empty ) ) )
= $true )
| ( ( ! [SY840: $i] :
( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ SY840 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ SY840 ) ) )
= $true )
| ( ( path @ SV462 @ SV491 @ SV495 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2707]) ).
thf(2729,plain,
! [SV462: $i,SV495: $i,SV491: $i] :
( ( ( ~ ( ( SV491
= ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ ( sK13_SY84 @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ ( sK13_SY84 @ SV495 @ SV491 @ SV462 ) ) ) ) )
= $false )
| ( ( path @ SV462 @ SV491 @ SV495 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2708]) ).
thf(2730,plain,
! [SV462: $i,SV491: $i,SV495: $i] :
( ( ( ~ ( ( SV495
= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ empty ) )
| ~ ( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ ( sK12_SY85 @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ ( sK12_SY85 @ SV495 @ SV491 @ SV462 ) ) ) ) )
= $false )
| ( ( path @ SV462 @ SV491 @ SV495 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2708]) ).
thf(2731,plain,
! [SV499: $i,SV492: $i,SV466: $i] :
( ( ( sequential @ SV466 @ SV492 )
= $false )
| ( ( edge @ SV492 )
= $false )
| ( ( edge @ SV466 )
= $false )
| ( ( edge @ SV499 )
= $false )
| ( ( ~ ( sequential @ SV492 @ SV499 ) )
= $true )
| ( ( ~ ( sequential @ SV499 @ SV466 ) )
= $true )
| ( ( triangle @ SV466 @ SV492 @ SV499 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2712]) ).
thf(2732,plain,
! [SV466: $i] :
( ( ~ ( ~ ( ! [SY762: $i,SY763: $i] :
~ ( triangle @ SV466 @ SY762 @ SY763 )
| ( edge @ SV466 ) )
| ~ ! [SY764: $i] :
( ! [SY765: $i] :
~ ( triangle @ SV466 @ SY764 @ SY765 )
| ( edge @ SY764 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2713]) ).
thf(2733,plain,
! [SV466: $i] :
( ( ! [SY766: $i,SY767: $i] :
( ~ ( triangle @ SV466 @ SY766 @ SY767 )
| ( edge @ SY767 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2714]) ).
thf(2734,plain,
! [SV560: $i,SV557: $i,SV466: $i] :
( ( ( ~ ( triangle @ SV466 @ SV557 @ SV560 ) )
= $true )
| ( ( sequential @ SV466 @ SV557 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2715]) ).
thf(2735,plain,
! [SV482: $i,SV476: $i,SV468: $i,SV543: $i] :
( ( ( edge @ SV543 )
= $false )
| ( ( SV468
= ( tail_of @ SV543 ) )
= $false )
| ( ( ( SV476
!= ( head_of @ SV543 ) )
| ( SV482
!= ( path_cons @ SV543 @ empty ) ) )
= $true )
| ( ( vertex @ SV468 )
= $false )
| ( ( vertex @ SV476 )
= $false )
| ( ( path @ SV468 @ SV476 @ SV482 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2717]) ).
thf(2736,plain,
! [SV476: $i,SV482: $i,SV468: $i,SV544: $i] :
( ( ( edge @ SV544 )
= $false )
| ( ( SV468
= ( tail_of @ SV544 ) )
= $false )
| ( ( ! [SY871: $i] :
( ( SV482
!= ( path_cons @ SV544 @ SY871 ) )
| ~ ( path @ ( head_of @ SV544 ) @ SV476 @ SY871 ) ) )
= $true )
| ( ( vertex @ SV468 )
= $false )
| ( ( vertex @ SV476 )
= $false )
| ( ( path @ SV468 @ SV476 @ SV482 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2718]) ).
thf(2737,plain,
! [SV477: $i,SV469: $i,SV519: $i,SV483: $i,SV505: $i,SV551: $i] :
( ( ( ( head_of @ SV551 )
= ( head_of @ SV505 ) )
= $false )
| ( ( ( tail_of @ SV551 )
= ( tail_of @ SV483 ) )
= $false )
| ( ( precedes @ SV483 @ SV505 @ SV519 )
= $false )
| ( ( shortest_path @ SV469 @ SV477 @ SV519 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2719]) ).
thf(2738,plain,
! [SV559: $i,SV552: $i] :
( ( ( sequential @ SV552 @ SV559 )
= $false )
| ( ( edge @ SV552 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2720]) ).
thf(2739,plain,
! [SV558: $i,SV553: $i] :
( ( ( sequential @ SV553 @ SV558 )
= $false )
| ( ( edge @ SV558 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2721]) ).
thf(2740,plain,
! [SV490: $i,SV484: $i,SV520: $i,SV470: $i,SV529: $i,SV561: $i] :
( ( ( ~ ( precedes @ SV561 @ SV529 @ SV470 )
| ~ ( sequential @ SV520 @ SV561 ) )
= $true )
| ( ( on_path @ SV520 @ SV470 )
= $false )
| ( ( on_path @ SV529 @ SV470 )
= $false )
| ( ( precedes @ SV520 @ SV529 @ SV470 )
= $true )
| ( ( path @ SV484 @ SV490 @ SV470 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2722]) ).
thf(2741,plain,
! [SV490: $i,SV484: $i,SV470: $i,SV530: $i,SV521: $i] :
( ( ( sequential @ SV521 @ SV530 )
= $false )
| ( ( on_path @ SV521 @ SV470 )
= $false )
| ( ( on_path @ SV530 @ SV470 )
= $false )
| ( ( precedes @ SV521 @ SV530 @ SV470 )
= $true )
| ( ( path @ SV484 @ SV490 @ SV470 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2723]) ).
thf(2742,plain,
! [SV485: $i,SV480: $i] :
( ( ( ( SV480
!= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
= $true )
| ( ( ( SV485
!= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
= $true )
| ( ( ( SV485
!= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
!= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
= $true )
| ( ( SV480 = SV485 )
= $true )
| ( ( vertex @ SV480 )
= $false )
| ( ( vertex @ SV485 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[2724]) ).
thf(2743,plain,
! [SV485: $i,SV480: $i] :
( ( ( ~ ~ ( ~ ( ( SV480
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
| ~ ( ( SV480
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) ) ) )
= $false )
| ( ( SV480 = SV485 )
= $true )
| ( ( vertex @ SV480 )
= $false )
| ( ( vertex @ SV485 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[2725]) ).
thf(2744,plain,
! [SV480: $i,SV485: $i] :
( ( ( ~ ~ ( ~ ( ( SV485
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
| ~ ( ( SV485
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) ) ) )
= $false )
| ( ( SV480 = SV485 )
= $true )
| ( ( vertex @ SV480 )
= $false )
| ( ( vertex @ SV485 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[2725]) ).
thf(2745,plain,
! [SV488: $i,SV481: $i,SV538: $i,SV461: $i,SV546: $i,SV562: $i] :
( ( ( ~ ( precedes @ SV562 @ SV546 @ SV461 )
| ~ ( sequential @ SV538 @ SV562 ) )
= $true )
| ( ( ~ ( sequential @ SV538 @ SV546 ) )
= $true )
| ( ( precedes @ SV538 @ SV546 @ SV461 )
= $false )
| ( ( path @ SV481 @ SV488 @ SV461 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2726]) ).
thf(2746,plain,
! [SV488: $i,SV481: $i,SV461: $i,SV539: $i,SV547: $i] :
( ( ( ~ ( precedes @ ( sK9_E3 @ SV547 @ SV539 @ SV461 ) @ SV547 @ SV461 )
| ~ ( sequential @ SV539 @ ( sK9_E3 @ SV547 @ SV539 @ SV461 ) ) )
= $false )
| ( ( sequential @ SV539 @ SV547 )
= $true )
| ( ( precedes @ SV539 @ SV547 @ SV461 )
= $false )
| ( ( path @ SV481 @ SV488 @ SV461 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2727]) ).
thf(2747,plain,
! [SV462: $i,SV495: $i,SV491: $i] :
( ( ( SV491
= ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
= $false )
| ( ( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ empty ) ) )
= $true )
| ( ( ! [SY840: $i] :
( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ SY840 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ SY840 ) ) )
= $true )
| ( ( path @ SV462 @ SV491 @ SV495 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2728]) ).
thf(2748,plain,
! [SV462: $i,SV495: $i,SV491: $i] :
( ( ( ( SV491
= ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ ( sK13_SY84 @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ ( sK13_SY84 @ SV495 @ SV491 @ SV462 ) ) ) )
= $true )
| ( ( path @ SV462 @ SV491 @ SV495 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2729]) ).
thf(2749,plain,
! [SV462: $i,SV491: $i,SV495: $i] :
( ( ( ( SV495
= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ empty ) )
| ~ ( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ ( sK12_SY85 @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ ( sK12_SY85 @ SV495 @ SV491 @ SV462 ) ) ) )
= $true )
| ( ( path @ SV462 @ SV491 @ SV495 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2730]) ).
thf(2750,plain,
! [SV466: $i,SV499: $i,SV492: $i] :
( ( ( sequential @ SV492 @ SV499 )
= $false )
| ( ( edge @ SV499 )
= $false )
| ( ( edge @ SV466 )
= $false )
| ( ( edge @ SV492 )
= $false )
| ( ( sequential @ SV466 @ SV492 )
= $false )
| ( ( ~ ( sequential @ SV499 @ SV466 ) )
= $true )
| ( ( triangle @ SV466 @ SV492 @ SV499 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2731]) ).
thf(2751,plain,
! [SV466: $i] :
( ( ~ ( ! [SY762: $i,SY763: $i] :
~ ( triangle @ SV466 @ SY762 @ SY763 )
| ( edge @ SV466 ) )
| ~ ! [SY764: $i] :
( ! [SY765: $i] :
~ ( triangle @ SV466 @ SY764 @ SY765 )
| ( edge @ SY764 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2732]) ).
thf(2752,plain,
! [SV563: $i,SV466: $i] :
( ( ! [SY878: $i] :
( ~ ( triangle @ SV466 @ SV563 @ SY878 )
| ( edge @ SY878 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2733]) ).
thf(2753,plain,
! [SV560: $i,SV557: $i,SV466: $i] :
( ( ( triangle @ SV466 @ SV557 @ SV560 )
= $false )
| ( ( sequential @ SV466 @ SV557 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2734]) ).
thf(2754,plain,
! [SV468: $i,SV482: $i,SV543: $i,SV476: $i] :
( ( ( ( SV476
!= ( head_of @ SV543 ) ) )
= $true )
| ( ( ( SV482
!= ( path_cons @ SV543 @ empty ) ) )
= $true )
| ( ( SV468
= ( tail_of @ SV543 ) )
= $false )
| ( ( edge @ SV543 )
= $false )
| ( ( vertex @ SV468 )
= $false )
| ( ( vertex @ SV476 )
= $false )
| ( ( path @ SV468 @ SV476 @ SV482 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2735]) ).
thf(2755,plain,
! [SV468: $i,SV476: $i,SV564: $i,SV544: $i,SV482: $i] :
( ( ( ( SV482
!= ( path_cons @ SV544 @ SV564 ) )
| ~ ( path @ ( head_of @ SV544 ) @ SV476 @ SV564 ) )
= $true )
| ( ( SV468
= ( tail_of @ SV544 ) )
= $false )
| ( ( edge @ SV544 )
= $false )
| ( ( vertex @ SV468 )
= $false )
| ( ( vertex @ SV476 )
= $false )
| ( ( path @ SV468 @ SV476 @ SV482 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2736]) ).
thf(2756,plain,
! [SV490: $i,SV484: $i,SV520: $i,SV470: $i,SV529: $i,SV561: $i] :
( ( ( ~ ( precedes @ SV561 @ SV529 @ SV470 ) )
= $true )
| ( ( ~ ( sequential @ SV520 @ SV561 ) )
= $true )
| ( ( on_path @ SV520 @ SV470 )
= $false )
| ( ( on_path @ SV529 @ SV470 )
= $false )
| ( ( precedes @ SV520 @ SV529 @ SV470 )
= $true )
| ( ( path @ SV484 @ SV490 @ SV470 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2740]) ).
thf(2757,plain,
! [SV485: $i,SV480: $i] :
( ( ( SV480
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
= $false )
| ( ( ( SV485
!= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
= $true )
| ( ( ( SV485
!= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
!= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
= $true )
| ( ( SV480 = SV485 )
= $true )
| ( ( vertex @ SV480 )
= $false )
| ( ( vertex @ SV485 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[2742]) ).
thf(2758,plain,
! [SV485: $i,SV480: $i] :
( ( ( ~ ( ~ ( ( SV480
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
| ~ ( ( SV480
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) ) ) )
= $true )
| ( ( SV480 = SV485 )
= $true )
| ( ( vertex @ SV480 )
= $false )
| ( ( vertex @ SV485 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[2743]) ).
thf(2759,plain,
! [SV480: $i,SV485: $i] :
( ( ( ~ ( ~ ( ( SV485
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
| ~ ( ( SV485
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) ) ) )
= $true )
| ( ( SV480 = SV485 )
= $true )
| ( ( vertex @ SV480 )
= $false )
| ( ( vertex @ SV485 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[2744]) ).
thf(2760,plain,
! [SV488: $i,SV481: $i,SV538: $i,SV461: $i,SV546: $i,SV562: $i] :
( ( ( ~ ( precedes @ SV562 @ SV546 @ SV461 ) )
= $true )
| ( ( ~ ( sequential @ SV538 @ SV562 ) )
= $true )
| ( ( ~ ( sequential @ SV538 @ SV546 ) )
= $true )
| ( ( precedes @ SV538 @ SV546 @ SV461 )
= $false )
| ( ( path @ SV481 @ SV488 @ SV461 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2745]) ).
thf(2761,plain,
! [SV488: $i,SV481: $i,SV461: $i,SV539: $i,SV547: $i] :
( ( ( ~ ( precedes @ ( sK9_E3 @ SV547 @ SV539 @ SV461 ) @ SV547 @ SV461 ) )
= $false )
| ( ( sequential @ SV539 @ SV547 )
= $true )
| ( ( precedes @ SV539 @ SV547 @ SV461 )
= $false )
| ( ( path @ SV481 @ SV488 @ SV461 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2746]) ).
thf(2762,plain,
! [SV488: $i,SV481: $i,SV461: $i,SV547: $i,SV539: $i] :
( ( ( ~ ( sequential @ SV539 @ ( sK9_E3 @ SV547 @ SV539 @ SV461 ) ) )
= $false )
| ( ( sequential @ SV539 @ SV547 )
= $true )
| ( ( precedes @ SV539 @ SV547 @ SV461 )
= $false )
| ( ( path @ SV481 @ SV488 @ SV461 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2746]) ).
thf(2763,plain,
! [SV462: $i,SV491: $i,SV495: $i] :
( ( ( SV495
= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ empty ) )
= $false )
| ( ( SV491
= ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
= $false )
| ( ( ! [SY840: $i] :
( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ SY840 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ SY840 ) ) )
= $true )
| ( ( path @ SV462 @ SV491 @ SV495 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2747]) ).
thf(2764,plain,
! [SV462: $i,SV495: $i,SV491: $i] :
( ( ( SV491
= ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
= $true )
| ( ( ~ ( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ ( sK13_SY84 @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ ( sK13_SY84 @ SV495 @ SV491 @ SV462 ) ) ) )
= $true )
| ( ( path @ SV462 @ SV491 @ SV495 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2748]) ).
thf(2765,plain,
! [SV462: $i,SV491: $i,SV495: $i] :
( ( ( SV495
= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ empty ) )
= $true )
| ( ( ~ ( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ ( sK12_SY85 @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ ( sK12_SY85 @ SV495 @ SV491 @ SV462 ) ) ) )
= $true )
| ( ( path @ SV462 @ SV491 @ SV495 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2749]) ).
thf(2766,plain,
! [SV492: $i,SV466: $i,SV499: $i] :
( ( ( sequential @ SV499 @ SV466 )
= $false )
| ( ( sequential @ SV466 @ SV492 )
= $false )
| ( ( edge @ SV492 )
= $false )
| ( ( edge @ SV466 )
= $false )
| ( ( edge @ SV499 )
= $false )
| ( ( sequential @ SV492 @ SV499 )
= $false )
| ( ( triangle @ SV466 @ SV492 @ SV499 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2750]) ).
thf(2767,plain,
! [SV466: $i] :
( ( ~ ( ! [SY762: $i,SY763: $i] :
~ ( triangle @ SV466 @ SY762 @ SY763 )
| ( edge @ SV466 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2751]) ).
thf(2768,plain,
! [SV466: $i] :
( ( ~ ! [SY764: $i] :
( ! [SY765: $i] :
~ ( triangle @ SV466 @ SY764 @ SY765 )
| ( edge @ SY764 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2751]) ).
thf(2769,plain,
! [SV565: $i,SV563: $i,SV466: $i] :
( ( ~ ( triangle @ SV466 @ SV563 @ SV565 )
| ( edge @ SV565 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2752]) ).
thf(2770,plain,
! [SV468: $i,SV482: $i,SV543: $i,SV476: $i] :
( ( ( SV476
= ( head_of @ SV543 ) )
= $false )
| ( ( ( SV482
!= ( path_cons @ SV543 @ empty ) ) )
= $true )
| ( ( SV468
= ( tail_of @ SV543 ) )
= $false )
| ( ( edge @ SV543 )
= $false )
| ( ( vertex @ SV468 )
= $false )
| ( ( vertex @ SV476 )
= $false )
| ( ( path @ SV468 @ SV476 @ SV482 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2754]) ).
thf(2771,plain,
! [SV468: $i,SV476: $i,SV564: $i,SV544: $i,SV482: $i] :
( ( ( ( SV482
!= ( path_cons @ SV544 @ SV564 ) ) )
= $true )
| ( ( ~ ( path @ ( head_of @ SV544 ) @ SV476 @ SV564 ) )
= $true )
| ( ( SV468
= ( tail_of @ SV544 ) )
= $false )
| ( ( edge @ SV544 )
= $false )
| ( ( vertex @ SV468 )
= $false )
| ( ( vertex @ SV476 )
= $false )
| ( ( path @ SV468 @ SV476 @ SV482 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2755]) ).
thf(2772,plain,
! [SV490: $i,SV484: $i,SV520: $i,SV470: $i,SV529: $i,SV561: $i] :
( ( ( precedes @ SV561 @ SV529 @ SV470 )
= $false )
| ( ( ~ ( sequential @ SV520 @ SV561 ) )
= $true )
| ( ( on_path @ SV520 @ SV470 )
= $false )
| ( ( on_path @ SV529 @ SV470 )
= $false )
| ( ( precedes @ SV520 @ SV529 @ SV470 )
= $true )
| ( ( path @ SV484 @ SV490 @ SV470 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2756]) ).
thf(2773,plain,
! [SV480: $i,SV485: $i] :
( ( ( SV485
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
= $false )
| ( ( SV480
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
= $false )
| ( ( ( SV485
!= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
!= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
= $true )
| ( ( SV480 = SV485 )
= $true )
| ( ( vertex @ SV480 )
= $false )
| ( ( vertex @ SV485 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[2757]) ).
thf(2774,plain,
! [SV485: $i,SV480: $i] :
( ( ( ~ ( ( SV480
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
| ~ ( ( SV480
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) ) )
= $false )
| ( ( SV480 = SV485 )
= $true )
| ( ( vertex @ SV480 )
= $false )
| ( ( vertex @ SV485 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[2758]) ).
thf(2775,plain,
! [SV480: $i,SV485: $i] :
( ( ( ~ ( ( SV485
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
| ~ ( ( SV485
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) ) )
= $false )
| ( ( SV480 = SV485 )
= $true )
| ( ( vertex @ SV480 )
= $false )
| ( ( vertex @ SV485 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[2759]) ).
thf(2776,plain,
! [SV488: $i,SV481: $i,SV538: $i,SV461: $i,SV546: $i,SV562: $i] :
( ( ( precedes @ SV562 @ SV546 @ SV461 )
= $false )
| ( ( ~ ( sequential @ SV538 @ SV562 ) )
= $true )
| ( ( ~ ( sequential @ SV538 @ SV546 ) )
= $true )
| ( ( precedes @ SV538 @ SV546 @ SV461 )
= $false )
| ( ( path @ SV481 @ SV488 @ SV461 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2760]) ).
thf(2777,plain,
! [SV488: $i,SV481: $i,SV461: $i,SV539: $i,SV547: $i] :
( ( ( precedes @ ( sK9_E3 @ SV547 @ SV539 @ SV461 ) @ SV547 @ SV461 )
= $true )
| ( ( sequential @ SV539 @ SV547 )
= $true )
| ( ( precedes @ SV539 @ SV547 @ SV461 )
= $false )
| ( ( path @ SV481 @ SV488 @ SV461 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2761]) ).
thf(2778,plain,
! [SV488: $i,SV481: $i,SV461: $i,SV547: $i,SV539: $i] :
( ( ( sequential @ SV539 @ ( sK9_E3 @ SV547 @ SV539 @ SV461 ) )
= $true )
| ( ( sequential @ SV539 @ SV547 )
= $true )
| ( ( precedes @ SV539 @ SV547 @ SV461 )
= $false )
| ( ( path @ SV481 @ SV488 @ SV461 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2762]) ).
thf(2779,plain,
! [SV566: $i,SV462: $i,SV491: $i,SV495: $i] :
( ( ( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ SV566 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ SV566 ) )
= $true )
| ( ( SV491
= ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
= $false )
| ( ( SV495
= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ empty ) )
= $false )
| ( ( path @ SV462 @ SV491 @ SV495 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2763]) ).
thf(2780,plain,
! [SV462: $i,SV491: $i,SV495: $i] :
( ( ( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ ( sK13_SY84 @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ ( sK13_SY84 @ SV495 @ SV491 @ SV462 ) ) )
= $false )
| ( ( SV491
= ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
= $true )
| ( ( path @ SV462 @ SV491 @ SV495 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2764]) ).
thf(2781,plain,
! [SV462: $i,SV491: $i,SV495: $i] :
( ( ( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ ( sK12_SY85 @ SV495 @ SV491 @ SV462 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ ( sK12_SY85 @ SV495 @ SV491 @ SV462 ) ) )
= $false )
| ( ( SV495
= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ empty ) )
= $true )
| ( ( path @ SV462 @ SV491 @ SV495 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2765]) ).
thf(2782,plain,
! [SV466: $i] :
( ( ! [SY762: $i,SY763: $i] :
~ ( triangle @ SV466 @ SY762 @ SY763 )
| ( edge @ SV466 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2767]) ).
thf(2783,plain,
! [SV466: $i] :
( ( ! [SY764: $i] :
( ! [SY765: $i] :
~ ( triangle @ SV466 @ SY764 @ SY765 )
| ( edge @ SY764 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2768]) ).
thf(2784,plain,
! [SV565: $i,SV563: $i,SV466: $i] :
( ( ( ~ ( triangle @ SV466 @ SV563 @ SV565 ) )
= $true )
| ( ( edge @ SV565 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2769]) ).
thf(2785,plain,
! [SV468: $i,SV476: $i,SV543: $i,SV482: $i] :
( ( ( SV482
= ( path_cons @ SV543 @ empty ) )
= $false )
| ( ( SV476
= ( head_of @ SV543 ) )
= $false )
| ( ( SV468
= ( tail_of @ SV543 ) )
= $false )
| ( ( edge @ SV543 )
= $false )
| ( ( vertex @ SV468 )
= $false )
| ( ( vertex @ SV476 )
= $false )
| ( ( path @ SV468 @ SV476 @ SV482 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2770]) ).
thf(2786,plain,
! [SV468: $i,SV476: $i,SV564: $i,SV544: $i,SV482: $i] :
( ( ( SV482
= ( path_cons @ SV544 @ SV564 ) )
= $false )
| ( ( ~ ( path @ ( head_of @ SV544 ) @ SV476 @ SV564 ) )
= $true )
| ( ( SV468
= ( tail_of @ SV544 ) )
= $false )
| ( ( edge @ SV544 )
= $false )
| ( ( vertex @ SV468 )
= $false )
| ( ( vertex @ SV476 )
= $false )
| ( ( path @ SV468 @ SV476 @ SV482 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2771]) ).
thf(2787,plain,
! [SV490: $i,SV484: $i,SV470: $i,SV529: $i,SV561: $i,SV520: $i] :
( ( ( sequential @ SV520 @ SV561 )
= $false )
| ( ( precedes @ SV561 @ SV529 @ SV470 )
= $false )
| ( ( on_path @ SV520 @ SV470 )
= $false )
| ( ( on_path @ SV529 @ SV470 )
= $false )
| ( ( precedes @ SV520 @ SV529 @ SV470 )
= $true )
| ( ( path @ SV484 @ SV490 @ SV470 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2772]) ).
thf(2788,plain,
! [SV480: $i,SV485: $i] :
( ( ( ( SV485
!= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
= $true )
| ( ( ( SV480
!= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
= $true )
| ( ( SV480
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
= $false )
| ( ( SV485
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
= $false )
| ( ( SV480 = SV485 )
= $true )
| ( ( vertex @ SV480 )
= $false )
| ( ( vertex @ SV485 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[2773]) ).
thf(2789,plain,
! [SV485: $i,SV480: $i] :
( ( ( ~ ( ( SV480
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) ) ) )
= $false )
| ( ( SV480 = SV485 )
= $true )
| ( ( vertex @ SV480 )
= $false )
| ( ( vertex @ SV485 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[2774]) ).
thf(2790,plain,
! [SV485: $i,SV480: $i] :
( ( ( ~ ( ( SV480
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) ) )
= $false )
| ( ( SV480 = SV485 )
= $true )
| ( ( vertex @ SV480 )
= $false )
| ( ( vertex @ SV485 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[2774]) ).
thf(2791,plain,
! [SV480: $i,SV485: $i] :
( ( ( ~ ( ( SV485
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) ) ) )
= $false )
| ( ( SV480 = SV485 )
= $true )
| ( ( vertex @ SV480 )
= $false )
| ( ( vertex @ SV485 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[2775]) ).
thf(2792,plain,
! [SV480: $i,SV485: $i] :
( ( ( ~ ( ( SV485
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) ) )
= $false )
| ( ( SV480 = SV485 )
= $true )
| ( ( vertex @ SV480 )
= $false )
| ( ( vertex @ SV485 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[2775]) ).
thf(2793,plain,
! [SV488: $i,SV481: $i,SV461: $i,SV546: $i,SV562: $i,SV538: $i] :
( ( ( sequential @ SV538 @ SV562 )
= $false )
| ( ( precedes @ SV562 @ SV546 @ SV461 )
= $false )
| ( ( ~ ( sequential @ SV538 @ SV546 ) )
= $true )
| ( ( precedes @ SV538 @ SV546 @ SV461 )
= $false )
| ( ( path @ SV481 @ SV488 @ SV461 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2776]) ).
thf(2794,plain,
! [SV566: $i,SV462: $i,SV491: $i,SV495: $i] :
( ( ( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ SV566 ) ) )
= $true )
| ( ( ~ ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ SV566 ) )
= $true )
| ( ( SV491
= ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
= $false )
| ( ( SV495
= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ empty ) )
= $false )
| ( ( path @ SV462 @ SV491 @ SV495 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2779]) ).
thf(2795,plain,
! [SV462: $i,SV491: $i,SV495: $i] :
( ( ( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ ( sK13_SY84 @ SV495 @ SV491 @ SV462 ) ) ) )
= $false )
| ( ( SV491
= ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
= $true )
| ( ( path @ SV462 @ SV491 @ SV495 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2780]) ).
thf(2796,plain,
! [SV462: $i,SV491: $i,SV495: $i] :
( ( ( ~ ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ ( sK13_SY84 @ SV495 @ SV491 @ SV462 ) ) )
= $false )
| ( ( SV491
= ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
= $true )
| ( ( path @ SV462 @ SV491 @ SV495 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2780]) ).
thf(2797,plain,
! [SV462: $i,SV491: $i,SV495: $i] :
( ( ( ( SV495
!= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ ( sK12_SY85 @ SV495 @ SV491 @ SV462 ) ) ) )
= $false )
| ( ( SV495
= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ empty ) )
= $true )
| ( ( path @ SV462 @ SV491 @ SV495 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2781]) ).
thf(2798,plain,
! [SV462: $i,SV491: $i,SV495: $i] :
( ( ( ~ ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ ( sK12_SY85 @ SV495 @ SV491 @ SV462 ) ) )
= $false )
| ( ( SV495
= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ empty ) )
= $true )
| ( ( path @ SV462 @ SV491 @ SV495 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2781]) ).
thf(2799,plain,
! [SV466: $i] :
( ( ( ! [SY762: $i,SY763: $i] :
~ ( triangle @ SV466 @ SY762 @ SY763 ) )
= $true )
| ( ( edge @ SV466 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2782]) ).
thf(2800,plain,
! [SV567: $i,SV466: $i] :
( ( ! [SY879: $i] :
~ ( triangle @ SV466 @ SV567 @ SY879 )
| ( edge @ SV567 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2783]) ).
thf(2801,plain,
! [SV565: $i,SV563: $i,SV466: $i] :
( ( ( triangle @ SV466 @ SV563 @ SV565 )
= $false )
| ( ( edge @ SV565 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2784]) ).
thf(2802,plain,
! [SV468: $i,SV482: $i,SV564: $i,SV476: $i,SV544: $i] :
( ( ( path @ ( head_of @ SV544 ) @ SV476 @ SV564 )
= $false )
| ( ( SV482
= ( path_cons @ SV544 @ SV564 ) )
= $false )
| ( ( SV468
= ( tail_of @ SV544 ) )
= $false )
| ( ( edge @ SV544 )
= $false )
| ( ( vertex @ SV468 )
= $false )
| ( ( vertex @ SV476 )
= $false )
| ( ( path @ SV468 @ SV476 @ SV482 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2786]) ).
thf(2803,plain,
! [SV480: $i,SV485: $i] :
( ( ( SV485
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
= $false )
| ( ( ( SV480
!= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
= $true )
| ( ( SV480
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
= $false )
| ( ( SV485
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
= $false )
| ( ( SV480 = SV485 )
= $true )
| ( ( vertex @ SV480 )
= $false )
| ( ( vertex @ SV485 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[2788]) ).
thf(2804,plain,
! [SV485: $i,SV480: $i] :
( ( ( ( SV480
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
= $true )
| ( ( SV480 = SV485 )
= $true )
| ( ( vertex @ SV480 )
= $false )
| ( ( vertex @ SV485 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[2789]) ).
thf(2805,plain,
! [SV485: $i,SV480: $i] :
( ( ( ( SV480
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
= $true )
| ( ( SV480 = SV485 )
= $true )
| ( ( vertex @ SV480 )
= $false )
| ( ( vertex @ SV485 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[2790]) ).
thf(2806,plain,
! [SV480: $i,SV485: $i] :
( ( ( ( SV485
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV485
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
= $true )
| ( ( SV480 = SV485 )
= $true )
| ( ( vertex @ SV480 )
= $false )
| ( ( vertex @ SV485 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[2791]) ).
thf(2807,plain,
! [SV480: $i,SV485: $i] :
( ( ( ( SV485
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
| ( SV480
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) ) )
= $true )
| ( ( SV480 = SV485 )
= $true )
| ( ( vertex @ SV480 )
= $false )
| ( ( vertex @ SV485 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[2792]) ).
thf(2808,plain,
! [SV488: $i,SV481: $i,SV461: $i,SV562: $i,SV546: $i,SV538: $i] :
( ( ( sequential @ SV538 @ SV546 )
= $false )
| ( ( precedes @ SV562 @ SV546 @ SV461 )
= $false )
| ( ( sequential @ SV538 @ SV562 )
= $false )
| ( ( precedes @ SV538 @ SV546 @ SV461 )
= $false )
| ( ( path @ SV481 @ SV488 @ SV461 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2793]) ).
thf(2809,plain,
! [SV566: $i,SV462: $i,SV491: $i,SV495: $i] :
( ( ( SV495
= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ SV566 ) )
= $false )
| ( ( ~ ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ SV566 ) )
= $true )
| ( ( SV491
= ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
= $false )
| ( ( SV495
= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ empty ) )
= $false )
| ( ( path @ SV462 @ SV491 @ SV495 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2794]) ).
thf(2810,plain,
! [SV462: $i,SV491: $i,SV495: $i] :
( ( ( SV495
= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ ( sK13_SY84 @ SV495 @ SV491 @ SV462 ) ) )
= $true )
| ( ( SV491
= ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
= $true )
| ( ( path @ SV462 @ SV491 @ SV495 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2795]) ).
thf(2811,plain,
! [SV462: $i,SV491: $i,SV495: $i] :
( ( ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ ( sK13_SY84 @ SV495 @ SV491 @ SV462 ) )
= $true )
| ( ( SV491
= ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
= $true )
| ( ( path @ SV462 @ SV491 @ SV495 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2796]) ).
thf(2812,plain,
! [SV462: $i,SV491: $i,SV495: $i] :
( ( ( SV495
= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ ( sK12_SY85 @ SV495 @ SV491 @ SV462 ) ) )
= $true )
| ( ( SV495
= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ empty ) )
= $true )
| ( ( path @ SV462 @ SV491 @ SV495 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2797]) ).
thf(2813,plain,
! [SV462: $i,SV491: $i,SV495: $i] :
( ( ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ ( sK12_SY85 @ SV495 @ SV491 @ SV462 ) )
= $true )
| ( ( SV495
= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ empty ) )
= $true )
| ( ( path @ SV462 @ SV491 @ SV495 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2798]) ).
thf(2814,plain,
! [SV568: $i,SV466: $i] :
( ( ( ! [SY880: $i] :
~ ( triangle @ SV466 @ SV568 @ SY880 ) )
= $true )
| ( ( edge @ SV466 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2799]) ).
thf(2815,plain,
! [SV567: $i,SV466: $i] :
( ( ( ! [SY879: $i] :
~ ( triangle @ SV466 @ SV567 @ SY879 ) )
= $true )
| ( ( edge @ SV567 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2800]) ).
thf(2816,plain,
! [SV485: $i,SV480: $i] :
( ( ( SV480
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
= $false )
| ( ( SV485
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
= $false )
| ( ( SV480
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
= $false )
| ( ( SV485
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
= $false )
| ( ( SV480 = SV485 )
= $true )
| ( ( vertex @ SV480 )
= $false )
| ( ( vertex @ SV485 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[2803]) ).
thf(2817,plain,
! [SV485: $i,SV480: $i] :
( ( ( SV480
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
= $true )
| ( ( SV485
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
= $true )
| ( ( SV480 = SV485 )
= $true )
| ( ( vertex @ SV480 )
= $false )
| ( ( vertex @ SV485 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[2804]) ).
thf(2818,plain,
! [SV485: $i,SV480: $i] :
( ( ( SV480
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
= $true )
| ( ( SV480
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
= $true )
| ( ( SV480 = SV485 )
= $true )
| ( ( vertex @ SV480 )
= $false )
| ( ( vertex @ SV485 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[2805]) ).
thf(2819,plain,
! [SV480: $i,SV485: $i] :
( ( ( SV485
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
= $true )
| ( ( SV485
= ( head_of @ ( sK14_E @ SV485 @ SV480 ) ) )
= $true )
| ( ( SV480 = SV485 )
= $true )
| ( ( vertex @ SV480 )
= $false )
| ( ( vertex @ SV485 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[2806]) ).
thf(2820,plain,
! [SV480: $i,SV485: $i] :
( ( ( SV485
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
= $true )
| ( ( SV480
= ( tail_of @ ( sK14_E @ SV485 @ SV480 ) ) )
= $true )
| ( ( SV480 = SV485 )
= $true )
| ( ( vertex @ SV480 )
= $false )
| ( ( vertex @ SV485 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[2807]) ).
thf(2821,plain,
! [SV566: $i,SV462: $i,SV491: $i,SV495: $i] :
( ( ( path @ ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) @ SV491 @ SV566 )
= $false )
| ( ( SV495
= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ SV566 ) )
= $false )
| ( ( SV491
= ( head_of @ ( sK11_E @ SV495 @ SV491 @ SV462 ) ) )
= $false )
| ( ( SV495
= ( path_cons @ ( sK11_E @ SV495 @ SV491 @ SV462 ) @ empty ) )
= $false )
| ( ( path @ SV462 @ SV491 @ SV495 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2809]) ).
thf(2822,plain,
! [SV569: $i,SV568: $i,SV466: $i] :
( ( ( ~ ( triangle @ SV466 @ SV568 @ SV569 ) )
= $true )
| ( ( edge @ SV466 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2814]) ).
thf(2823,plain,
! [SV570: $i,SV567: $i,SV466: $i] :
( ( ( ~ ( triangle @ SV466 @ SV567 @ SV570 ) )
= $true )
| ( ( edge @ SV567 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2815]) ).
thf(2824,plain,
! [SV569: $i,SV568: $i,SV466: $i] :
( ( ( triangle @ SV466 @ SV568 @ SV569 )
= $false )
| ( ( edge @ SV466 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2822]) ).
thf(2825,plain,
! [SV570: $i,SV567: $i,SV466: $i] :
( ( ( triangle @ SV466 @ SV567 @ SV570 )
= $false )
| ( ( edge @ SV567 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2823]) ).
thf(2826,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[2294,2825,2824,2821,2820,2819,2818,2817,2816,2813,2812,2811,2810,2808,2802,2801,2787,2785,2778,2777,2766,2753,2741,2739,2738,2737,2716,2711,2710,2709,2704,2703,2696,2692,2690,2689,2688,2684,2683,2679,2676,2675,2663,2655,2630,2614,2604,2587,2583,2580,2576,2572,2571,2562,2418,2417,2392,2391,2368,2331,2314,2295]) ).
thf(2827,plain,
( ( ! [E: $i] :
( ~ ( edge @ E )
| ( ( head_of @ E )
!= ( tail_of @ E ) ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(2828,plain,
( ( ! [E: $i] :
( ~ ( edge @ E )
| ( vertex @ ( head_of @ E ) ) )
& ! [E: $i] :
( ~ ( edge @ E )
| ( vertex @ ( tail_of @ E ) ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(2829,plain,
( ( ~ complete
| ! [V1: $i,V2: $i] :
( ( V1 = V2 )
| ~ ( vertex @ V1 )
| ~ ( vertex @ V2 )
| ( ( ( V1
!= ( head_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V2
!= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V2
!= ( head_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V1
!= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( ( V1
= ( head_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V2
= ( head_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( ( V1
= ( head_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V1
= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( ( V2
= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V2
= ( head_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( ( V2
= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V1
= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( edge @ ( sK14_E @ V2 @ V1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(2830,plain,
( ( ! [V1: $i,V2: $i,P: $i] :
( ~ ( vertex @ V1 )
| ~ ( vertex @ V2 )
| ( ! [E: $i] :
( ( V1
!= ( tail_of @ E ) )
| ~ ( edge @ E )
| ( V2
!= ( head_of @ E ) )
| ( P
!= ( path_cons @ E @ empty ) ) )
& ! [E: $i] :
( ( V1
!= ( tail_of @ E ) )
| ~ ( edge @ E )
| ! [TP: $i] :
( ( P
!= ( path_cons @ E @ TP ) )
| ~ ( path @ ( head_of @ E ) @ V2 @ TP ) ) ) )
| ( path @ V1 @ V2 @ P ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(2831,plain,
( ( ! [V1: $i] :
( ( ! [V2: $i,P: $i] :
~ ( path @ V1 @ V2 @ P )
| ( vertex @ V1 ) )
& ! [V2: $i] :
( ! [P: $i] :
~ ( path @ V1 @ V2 @ P )
| ( vertex @ V2 ) )
& ! [V2: $i,P: $i] :
( ~ ( path @ V1 @ V2 @ P )
| ( ( V1
= ( tail_of @ ( sK11_E @ P @ V2 @ V1 ) ) )
& ( edge @ ( sK11_E @ P @ V2 @ V1 ) )
& ( ( V2
!= ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) )
| ( P
!= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ empty ) )
| ! [SY83: $i] :
( ( P
!= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ SY83 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) @ V2 @ SY83 ) ) )
& ( ( V2
= ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) )
| ( ( P
= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ ( sK13_SY84 @ P @ V2 @ V1 ) ) )
& ( path @ ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) @ V2 @ ( sK13_SY84 @ P @ V2 @ V1 ) ) ) )
& ( ( P
= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ empty ) )
| ( ( P
= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ ( sK12_SY85 @ P @ V2 @ V1 ) ) )
& ( path @ ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) @ V2 @ ( sK12_SY85 @ P @ V2 @ V1 ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(2832,plain,
( ( ! [V1: $i,V2: $i] :
( ! [P: $i,E: $i] :
( ~ ( on_path @ E @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( edge @ E ) )
& ! [P: $i,E: $i] :
( ~ ( on_path @ E @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( in_path @ ( head_of @ E ) @ P ) )
& ! [P: $i,E: $i] :
( ~ ( on_path @ E @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( in_path @ ( tail_of @ E ) @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(2833,plain,
( ( ! [V1: $i,V2: $i] :
( ! [P: $i,V: $i] :
( ~ ( in_path @ V @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( ( on_path @ ( sK10_E @ V @ P @ V2 @ V1 ) @ P )
& ( ( V
= ( head_of @ ( sK10_E @ V @ P @ V2 @ V1 ) ) )
| ( V
= ( tail_of @ ( sK10_E @ V @ P @ V2 @ V1 ) ) ) ) ) )
& ! [P: $i,V: $i] :
( ~ ( in_path @ V @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( vertex @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(2834,plain,
( ( ! [E1: $i,E2: $i] :
( ( E1 = E2 )
| ~ ( edge @ E1 )
| ~ ( edge @ E2 )
| ( ( head_of @ E1 )
!= ( tail_of @ E2 ) )
| ( sequential @ E1 @ E2 ) )
& ! [E1: $i,E2: $i] :
( ~ ( sequential @ E1 @ E2 )
| ( E1 != E2 ) )
& ! [E1: $i] :
( ! [E2: $i] :
~ ( sequential @ E1 @ E2 )
| ( edge @ E1 ) )
& ! [E1: $i,E2: $i] :
( ~ ( sequential @ E1 @ E2 )
| ( edge @ E2 ) )
& ! [E1: $i,E2: $i] :
( ~ ( sequential @ E1 @ E2 )
| ( ( head_of @ E1 )
= ( tail_of @ E2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(2835,plain,
( ( ! [P: $i] :
( ! [V1: $i,V2: $i] :
~ ( path @ V1 @ V2 @ P )
| ( ! [E1: $i,E2: $i] :
( ~ ( on_path @ E1 @ P )
| ~ ( on_path @ E2 @ P )
| ! [E3: $i] :
( ~ ( precedes @ E3 @ E2 @ P )
| ~ ( sequential @ E1 @ E3 ) )
| ( precedes @ E1 @ E2 @ P ) )
& ! [E1: $i,E2: $i] :
( ~ ( on_path @ E1 @ P )
| ~ ( on_path @ E2 @ P )
| ~ ( sequential @ E1 @ E2 )
| ( precedes @ E1 @ E2 @ P ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(2836,plain,
( ( ! [P: $i] :
( ! [V1: $i,V2: $i] :
~ ( path @ V1 @ V2 @ P )
| ( ! [E1: $i] :
( ! [E2: $i] :
~ ( precedes @ E1 @ E2 @ P )
| ( on_path @ E1 @ P ) )
& ! [E1: $i,E2: $i] :
( ~ ( precedes @ E1 @ E2 @ P )
| ( on_path @ E2 @ P ) )
& ! [E1: $i,E2: $i] :
( ~ ( precedes @ E1 @ E2 @ P )
| ! [E3: $i] :
( ~ ( precedes @ E3 @ E2 @ P )
| ~ ( sequential @ E1 @ E3 ) )
| ~ ( sequential @ E1 @ E2 ) )
& ! [E1: $i,E2: $i] :
( ~ ( precedes @ E1 @ E2 @ P )
| ( ( precedes @ ( sK9_E3 @ E2 @ E1 @ P ) @ E2 @ P )
& ( sequential @ E1 @ ( sK9_E3 @ E2 @ E1 @ P ) ) )
| ( sequential @ E1 @ E2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(2837,plain,
( ( ! [V1: $i] :
( ! [V2: $i,SP: $i] :
( ( ( path @ V1 @ V2 @ ( sK8_P @ SP @ V2 @ V1 ) )
& ~ ( less_or_equal @ ( length_of @ SP ) @ ( length_of @ ( sK8_P @ SP @ V2 @ V1 ) ) ) )
| ( V1 = V2 )
| ~ ( path @ V1 @ V2 @ SP )
| ( shortest_path @ V1 @ V2 @ SP ) )
& ! [V2: $i,SP: $i] :
( ~ ( shortest_path @ V1 @ V2 @ SP )
| ! [P: $i] :
( ~ ( path @ V1 @ V2 @ P )
| ( less_or_equal @ ( length_of @ SP ) @ ( length_of @ P ) ) ) )
& ! [V2: $i] :
( ! [SP: $i] :
~ ( shortest_path @ V1 @ V2 @ SP )
| ( V1 != V2 ) )
& ! [V2: $i,SP: $i] :
( ~ ( shortest_path @ V1 @ V2 @ SP )
| ( path @ V1 @ V2 @ SP ) ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(2838,plain,
( ( ! [V1: $i,V2: $i,E1: $i] :
( ! [E2: $i] :
( ! [P: $i] :
( ~ ( precedes @ E1 @ E2 @ P )
| ~ ( shortest_path @ V1 @ V2 @ P ) )
| ! [E3: $i] :
( ( ( tail_of @ E3 )
!= ( tail_of @ E1 ) )
| ( ( head_of @ E3 )
!= ( head_of @ E2 ) ) ) )
& ! [E2: $i,P: $i] :
( ~ ( precedes @ E1 @ E2 @ P )
| ~ ( shortest_path @ V1 @ V2 @ P )
| ~ ( precedes @ E2 @ E1 @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(2839,plain,
( ( ! [E1: $i] :
( ! [E2: $i,E3: $i] :
( ~ ( edge @ E1 )
| ~ ( edge @ E2 )
| ~ ( edge @ E3 )
| ~ ( sequential @ E1 @ E2 )
| ~ ( sequential @ E2 @ E3 )
| ~ ( sequential @ E3 @ E1 )
| ( triangle @ E1 @ E2 @ E3 ) )
& ( ! [E2: $i,E3: $i] :
~ ( triangle @ E1 @ E2 @ E3 )
| ( edge @ E1 ) )
& ! [E2: $i] :
( ! [E3: $i] :
~ ( triangle @ E1 @ E2 @ E3 )
| ( edge @ E2 ) )
& ! [E2: $i,E3: $i] :
( ~ ( triangle @ E1 @ E2 @ E3 )
| ( edge @ E3 ) )
& ! [E2: $i] :
( ! [E3: $i] :
~ ( triangle @ E1 @ E2 @ E3 )
| ( sequential @ E1 @ E2 ) )
& ! [E2: $i,E3: $i] :
( ~ ( triangle @ E1 @ E2 @ E3 )
| ( sequential @ E2 @ E3 ) )
& ! [E2: $i,E3: $i] :
( ~ ( triangle @ E1 @ E2 @ E3 )
| ( sequential @ E3 @ E1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(2840,plain,
( ( ! [V1: $i,V2: $i,P: $i] :
( ~ ( path @ V1 @ V2 @ P )
| ( ( length_of @ P )
= ( number_of_in @ edges @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(2841,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)],[63]) ).
thf(2842,plain,
( ( ! [P: $i] :
( ( ( on_path @ ( sK6_E1 @ P ) @ P )
& ( on_path @ ( sK7_SY80 @ P ) @ P )
& ( sequential @ ( sK6_E1 @ P ) @ ( sK7_SY80 @ P ) )
& ! [SY82: $i] :
~ ( triangle @ ( sK6_E1 @ P ) @ ( sK7_SY80 @ P ) @ SY82 ) )
| ! [V1: $i,V2: $i] :
~ ( path @ V1 @ V2 @ P )
| ( ( number_of_in @ sequential_pairs @ P )
= ( number_of_in @ triangles @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(2843,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(2844,plain,
( ( precedes @ sK3_SY74 @ sK4_SY77 @ sK5_SY79 )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(2845,plain,
( ( shortest_path @ sK1_V1 @ sK2_SY70 @ sK5_SY79 )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(2846,plain,
( ( sK3_SY74 = sK4_SY77 )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(2847,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( on_path @ SX3 @ SX2 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ( edge @ SX3 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( on_path @ SX3 @ SX2 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ( in_path @ ( head_of @ SX3 ) @ SX2 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( on_path @ SX3 @ SX2 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ( in_path @ ( tail_of @ SX3 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2832]) ).
thf(2848,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( vertex @ SX0 )
| ~ ( vertex @ SX1 )
| ~ ( ~ ! [SX3: $i] :
( ( SX0
!= ( tail_of @ SX3 ) )
| ~ ( edge @ SX3 )
| ( SX1
!= ( head_of @ SX3 ) )
| ( SX2
!= ( path_cons @ SX3 @ empty ) ) )
| ~ ! [SX3: $i] :
( ( SX0
!= ( tail_of @ SX3 ) )
| ~ ( edge @ SX3 )
| ! [SX4: $i] :
( ( SX2
!= ( path_cons @ SX3 @ SX4 ) )
| ~ ( path @ ( head_of @ SX3 ) @ SX1 @ SX4 ) ) ) )
| ( path @ SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2830]) ).
thf(2849,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
( ~ ( precedes @ SX2 @ SX3 @ SX4 )
| ~ ( shortest_path @ SX0 @ SX1 @ SX4 ) )
| ! [SX4: $i] :
( ( ( tail_of @ SX4 )
!= ( tail_of @ SX2 ) )
| ( ( head_of @ SX4 )
!= ( head_of @ SX3 ) ) ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( precedes @ SX2 @ SX3 @ SX4 )
| ~ ( shortest_path @ SX0 @ SX1 @ SX4 )
| ~ ( precedes @ SX3 @ SX2 @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2838]) ).
thf(2850,plain,
( ( ~ complete
| ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( vertex @ SX0 )
| ~ ( vertex @ SX1 )
| ~ ( ~ ~ ( ~ ( ( SX0
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
| ~ ~ ( ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2829]) ).
thf(2851,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( head_of @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( tail_of @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2828]) ).
thf(2852,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i,SX2: $i] :
~ ( path @ SX1 @ SX2 @ SX0 )
| ~ ( ~ ~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( precedes @ SX1 @ SX2 @ SX0 )
| ( on_path @ SX1 @ SX0 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( precedes @ SX1 @ SX2 @ SX0 )
| ( on_path @ SX2 @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( precedes @ SX1 @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( precedes @ SX3 @ SX2 @ SX0 )
| ~ ( sequential @ SX1 @ SX3 ) )
| ~ ( sequential @ SX1 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( precedes @ SX1 @ SX2 @ SX0 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SX2 @ SX1 @ SX0 ) @ SX2 @ SX0 )
| ~ ( sequential @ SX1 @ ( sK9_E3 @ SX2 @ SX1 @ SX0 ) ) )
| ( sequential @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2836]) ).
thf(2853,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in_path @ SX3 @ SX2 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ~ ( ~ ( on_path @ ( sK10_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( ( SX3
= ( head_of @ ( sK10_E @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ( SX3
= ( tail_of @ ( sK10_E @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( in_path @ SX3 @ SX2 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ( vertex @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2833]) ).
thf(2854,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i,SX2: $i] :
~ ( path @ SX1 @ SX2 @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( on_path @ SX1 @ SX0 )
| ~ ( on_path @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( precedes @ SX3 @ SX2 @ SX0 )
| ~ ( sequential @ SX1 @ SX3 ) )
| ( precedes @ SX1 @ SX2 @ SX0 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( on_path @ SX1 @ SX0 )
| ~ ( on_path @ SX2 @ SX0 )
| ~ ( sequential @ SX1 @ SX2 )
| ( precedes @ SX1 @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2835]) ).
thf(2855,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( edge @ SX0 )
| ~ ( edge @ SX1 )
| ~ ( edge @ SX2 )
| ~ ( sequential @ SX0 @ SX1 )
| ~ ( sequential @ SX1 @ SX2 )
| ~ ( sequential @ SX2 @ SX0 )
| ( triangle @ SX0 @ SX1 @ SX2 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SX1: $i,SX2: $i] :
~ ( triangle @ SX0 @ SX1 @ SX2 )
| ( edge @ SX0 ) )
| ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( triangle @ SX0 @ SX1 @ SX2 )
| ( edge @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( triangle @ SX0 @ SX1 @ SX2 )
| ( edge @ SX2 ) ) )
| ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( triangle @ SX0 @ SX1 @ SX2 )
| ( sequential @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( triangle @ SX0 @ SX1 @ SX2 )
| ( sequential @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( triangle @ SX0 @ SX1 @ SX2 )
| ( sequential @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2839]) ).
thf(2856,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( edge @ SX0 )
| ~ ( edge @ SX1 )
| ( ( head_of @ SX0 )
!= ( tail_of @ SX1 ) )
| ( sequential @ SX0 @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2834]) ).
thf(2857,plain,
( ( ! [SX0: $i] :
~ ( ~ ~ ( ~ ( ! [SX1: $i,SX2: $i] :
~ ( path @ SX0 @ SX1 @ SX2 )
| ( vertex @ SX0 ) )
| ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( path @ SX0 @ SX1 @ SX2 )
| ( vertex @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( path @ SX0 @ SX1 @ SX2 )
| ~ ( ~ ~ ( ( SX0
!= ( tail_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( edge @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ( SX1
!= ( head_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) )
| ( SX2
!= ( path_cons @ ( sK11_E @ SX2 @ SX1 @ SX0 ) @ empty ) )
| ! [SX3: $i] :
( ( SX2
!= ( path_cons @ ( sK11_E @ SX2 @ SX1 @ SX0 ) @ SX3 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) @ SX1 @ SX3 ) ) )
| ~ ~ ( ~ ( ( SX1
= ( head_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( ( SX2
!= ( path_cons @ ( sK11_E @ SX2 @ SX1 @ SX0 ) @ ( sK13_SY84 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) @ SX1 @ ( sK13_SY84 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX2
= ( path_cons @ ( sK11_E @ SX2 @ SX1 @ SX0 ) @ empty ) )
| ~ ( ( SX2
!= ( path_cons @ ( sK11_E @ SX2 @ SX1 @ SX0 ) @ ( sK12_SY85 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) @ SX1 @ ( sK12_SY85 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2831]) ).
thf(2858,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( path @ SX0 @ SX1 @ ( sK8_P @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SX2 ) @ ( length_of @ ( sK8_P @ SX2 @ SX1 @ SX0 ) ) ) )
| ( SX0 = SX1 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ( shortest_path @ SX0 @ SX1 @ SX2 ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( shortest_path @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( path @ SX0 @ SX1 @ SX3 )
| ( less_or_equal @ ( length_of @ SX2 ) @ ( length_of @ SX3 ) ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( shortest_path @ SX0 @ SX1 @ SX2 )
| ( SX0 != SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( shortest_path @ SX0 @ SX1 @ SX2 )
| ( path @ SX0 @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2837]) ).
thf(2859,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SX0 ) @ SX0 )
| ~ ( on_path @ ( sK7_SY80 @ SX0 ) @ SX0 ) )
| ~ ( sequential @ ( sK6_E1 @ SX0 ) @ ( sK7_SY80 @ SX0 ) ) )
| ~ ! [SX1: $i] :
~ ( triangle @ ( sK6_E1 @ SX0 ) @ ( sK7_SY80 @ SX0 ) @ SX1 ) )
| ! [SX1: $i,SX2: $i] :
~ ( path @ SX1 @ SX2 @ SX0 )
| ( ( number_of_in @ sequential_pairs @ SX0 )
= ( number_of_in @ triangles @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2842]) ).
thf(2860,plain,
! [SV571: $i] :
( ( ~ ( edge @ SV571 )
| ( ( head_of @ SV571 )
!= ( tail_of @ SV571 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2827]) ).
thf(2861,plain,
! [SV572: $i] :
( ( ! [SY881: $i,SY882: $i] :
( ~ ( path @ SV572 @ SY881 @ SY882 )
| ( ( length_of @ SY882 )
= ( number_of_in @ edges @ SY882 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2840]) ).
thf(2862,plain,
! [SV573: $i] :
( ( ! [SY883: $i,SY884: $i] :
( ~ ( path @ SV573 @ SY883 @ SY884 )
| ( ( number_of_in @ sequential_pairs @ SY884 )
= ( minus @ ( length_of @ SY884 ) @ n1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2841]) ).
thf(2863,plain,
! [SV574: $i] :
( ( ! [SY885: $i] : ( less_or_equal @ ( number_of_in @ SV574 @ SY885 ) @ ( number_of_in @ SV574 @ graph ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2843]) ).
thf(2864,plain,
! [SV575: $i] :
( ( ! [SY886: $i] :
~ ( ~ ~ ( ~ ! [SY887: $i,SY888: $i] :
( ~ ( on_path @ SY888 @ SY887 )
| ~ ( path @ SV575 @ SY886 @ SY887 )
| ( edge @ SY888 ) )
| ~ ! [SY889: $i,SY890: $i] :
( ~ ( on_path @ SY890 @ SY889 )
| ~ ( path @ SV575 @ SY886 @ SY889 )
| ( in_path @ ( head_of @ SY890 ) @ SY889 ) ) )
| ~ ! [SY891: $i,SY892: $i] :
( ~ ( on_path @ SY892 @ SY891 )
| ~ ( path @ SV575 @ SY886 @ SY891 )
| ( in_path @ ( tail_of @ SY892 ) @ SY891 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2847]) ).
thf(2865,plain,
! [SV576: $i] :
( ( ! [SY893: $i,SY894: $i] :
( ~ ( vertex @ SV576 )
| ~ ( vertex @ SY893 )
| ~ ( ~ ! [SY895: $i] :
( ( SV576
!= ( tail_of @ SY895 ) )
| ~ ( edge @ SY895 )
| ( SY893
!= ( head_of @ SY895 ) )
| ( SY894
!= ( path_cons @ SY895 @ empty ) ) )
| ~ ! [SY896: $i] :
( ( SV576
!= ( tail_of @ SY896 ) )
| ~ ( edge @ SY896 )
| ! [SX4: $i] :
( ( SY894
!= ( path_cons @ SY896 @ SX4 ) )
| ~ ( path @ ( head_of @ SY896 ) @ SY893 @ SX4 ) ) ) )
| ( path @ SV576 @ SY893 @ SY894 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2848]) ).
thf(2866,plain,
! [SV577: $i] :
( ( ! [SY898: $i,SY899: $i] :
~ ( ~ ! [SY900: $i] :
( ! [SY901: $i] :
( ~ ( precedes @ SY899 @ SY900 @ SY901 )
| ~ ( shortest_path @ SV577 @ SY898 @ SY901 ) )
| ! [SX4: $i] :
( ( ( tail_of @ SX4 )
!= ( tail_of @ SY899 ) )
| ( ( head_of @ SX4 )
!= ( head_of @ SY900 ) ) ) )
| ~ ! [SY903: $i,SY904: $i] :
( ~ ( precedes @ SY899 @ SY903 @ SY904 )
| ~ ( shortest_path @ SV577 @ SY898 @ SY904 )
| ~ ( precedes @ SY903 @ SY899 @ SY904 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2849]) ).
thf(2867,plain,
( ( ( ~ complete )
= $true )
| ( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( vertex @ SX0 )
| ~ ( vertex @ SX1 )
| ~ ( ~ ~ ( ~ ( ( SX0
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
| ~ ~ ( ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2850]) ).
thf(2868,plain,
( ( ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( head_of @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( tail_of @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2851]) ).
thf(2869,plain,
! [SV578: $i] :
( ( ! [SY905: $i,SY906: $i] :
~ ( path @ SY905 @ SY906 @ SV578 )
| ~ ( ~ ~ ( ~ ! [SY907: $i] :
( ! [SY908: $i] :
~ ( precedes @ SY907 @ SY908 @ SV578 )
| ( on_path @ SY907 @ SV578 ) )
| ~ ! [SY909: $i,SY910: $i] :
( ~ ( precedes @ SY909 @ SY910 @ SV578 )
| ( on_path @ SY910 @ SV578 ) ) )
| ~ ~ ( ~ ! [SY911: $i,SY912: $i] :
( ~ ( precedes @ SY911 @ SY912 @ SV578 )
| ! [SY913: $i] :
( ~ ( precedes @ SY913 @ SY912 @ SV578 )
| ~ ( sequential @ SY911 @ SY913 ) )
| ~ ( sequential @ SY911 @ SY912 ) )
| ~ ! [SY914: $i,SY915: $i] :
( ~ ( precedes @ SY914 @ SY915 @ SV578 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY915 @ SY914 @ SV578 ) @ SY915 @ SV578 )
| ~ ( sequential @ SY914 @ ( sK9_E3 @ SY915 @ SY914 @ SV578 ) ) )
| ( sequential @ SY914 @ SY915 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2852]) ).
thf(2870,plain,
! [SV579: $i] :
( ( ! [SY916: $i] :
~ ( ~ ! [SY917: $i,SY918: $i] :
( ~ ( in_path @ SY918 @ SY917 )
| ~ ( path @ SV579 @ SY916 @ SY917 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY918 @ SY917 @ SY916 @ SV579 ) @ SY917 )
| ~ ( ( SY918
= ( head_of @ ( sK10_E @ SY918 @ SY917 @ SY916 @ SV579 ) ) )
| ( SY918
= ( tail_of @ ( sK10_E @ SY918 @ SY917 @ SY916 @ SV579 ) ) ) ) ) )
| ~ ! [SY919: $i,SY920: $i] :
( ~ ( in_path @ SY920 @ SY919 )
| ~ ( path @ SV579 @ SY916 @ SY919 )
| ( vertex @ SY920 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2853]) ).
thf(2871,plain,
! [SV580: $i] :
( ( ! [SY921: $i,SY922: $i] :
~ ( path @ SY921 @ SY922 @ SV580 )
| ~ ( ~ ! [SY923: $i,SY924: $i] :
( ~ ( on_path @ SY923 @ SV580 )
| ~ ( on_path @ SY924 @ SV580 )
| ! [SY925: $i] :
( ~ ( precedes @ SY925 @ SY924 @ SV580 )
| ~ ( sequential @ SY923 @ SY925 ) )
| ( precedes @ SY923 @ SY924 @ SV580 ) )
| ~ ! [SY926: $i,SY927: $i] :
( ~ ( on_path @ SY926 @ SV580 )
| ~ ( on_path @ SY927 @ SV580 )
| ~ ( sequential @ SY926 @ SY927 )
| ( precedes @ SY926 @ SY927 @ SV580 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2854]) ).
thf(2872,plain,
! [SV581: $i] :
( ( ~ ( ~ ! [SY928: $i,SY929: $i] :
( ~ ( edge @ SV581 )
| ~ ( edge @ SY928 )
| ~ ( edge @ SY929 )
| ~ ( sequential @ SV581 @ SY928 )
| ~ ( sequential @ SY928 @ SY929 )
| ~ ( sequential @ SY929 @ SV581 )
| ( triangle @ SV581 @ SY928 @ SY929 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY930: $i,SY931: $i] :
~ ( triangle @ SV581 @ SY930 @ SY931 )
| ( edge @ SV581 ) )
| ~ ! [SY932: $i] :
( ! [SY933: $i] :
~ ( triangle @ SV581 @ SY932 @ SY933 )
| ( edge @ SY932 ) ) )
| ~ ! [SY934: $i,SY935: $i] :
( ~ ( triangle @ SV581 @ SY934 @ SY935 )
| ( edge @ SY935 ) ) )
| ~ ! [SY936: $i] :
( ! [SY937: $i] :
~ ( triangle @ SV581 @ SY936 @ SY937 )
| ( sequential @ SV581 @ SY936 ) ) )
| ~ ! [SY938: $i,SY939: $i] :
( ~ ( triangle @ SV581 @ SY938 @ SY939 )
| ( sequential @ SY938 @ SY939 ) ) )
| ~ ! [SY940: $i,SY941: $i] :
( ~ ( triangle @ SV581 @ SY940 @ SY941 )
| ( sequential @ SY941 @ SV581 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2855]) ).
thf(2873,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( edge @ SX0 )
| ~ ( edge @ SX1 )
| ( ( head_of @ SX0 )
!= ( tail_of @ SX1 ) )
| ( sequential @ SX0 @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2856]) ).
thf(2874,plain,
! [SV582: $i] :
( ( ~ ( ~ ~ ( ~ ( ! [SY942: $i,SY943: $i] :
~ ( path @ SV582 @ SY942 @ SY943 )
| ( vertex @ SV582 ) )
| ~ ! [SY944: $i] :
( ! [SY945: $i] :
~ ( path @ SV582 @ SY944 @ SY945 )
| ( vertex @ SY944 ) ) )
| ~ ! [SY946: $i,SY947: $i] :
( ~ ( path @ SV582 @ SY946 @ SY947 )
| ~ ( ~ ~ ( ( SV582
!= ( tail_of @ ( sK11_E @ SY947 @ SY946 @ SV582 ) ) )
| ~ ( edge @ ( sK11_E @ SY947 @ SY946 @ SV582 ) ) )
| ~ ~ ( ~ ( ( SY946
!= ( head_of @ ( sK11_E @ SY947 @ SY946 @ SV582 ) ) )
| ( SY947
!= ( path_cons @ ( sK11_E @ SY947 @ SY946 @ SV582 ) @ empty ) )
| ! [SY948: $i] :
( ( SY947
!= ( path_cons @ ( sK11_E @ SY947 @ SY946 @ SV582 ) @ SY948 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY947 @ SY946 @ SV582 ) ) @ SY946 @ SY948 ) ) )
| ~ ~ ( ~ ( ( SY946
= ( head_of @ ( sK11_E @ SY947 @ SY946 @ SV582 ) ) )
| ~ ( ( SY947
!= ( path_cons @ ( sK11_E @ SY947 @ SY946 @ SV582 ) @ ( sK13_SY84 @ SY947 @ SY946 @ SV582 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY947 @ SY946 @ SV582 ) ) @ SY946 @ ( sK13_SY84 @ SY947 @ SY946 @ SV582 ) ) ) )
| ~ ( ( SY947
= ( path_cons @ ( sK11_E @ SY947 @ SY946 @ SV582 ) @ empty ) )
| ~ ( ( SY947
!= ( path_cons @ ( sK11_E @ SY947 @ SY946 @ SV582 ) @ ( sK12_SY85 @ SY947 @ SY946 @ SV582 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY947 @ SY946 @ SV582 ) ) @ SY946 @ ( sK12_SY85 @ SY947 @ SY946 @ SV582 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2857]) ).
thf(2875,plain,
! [SV583: $i] :
( ( ~ ( ~ ! [SY949: $i,SY950: $i] :
( ~ ( ~ ( path @ SV583 @ SY949 @ ( sK8_P @ SY950 @ SY949 @ SV583 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY950 ) @ ( length_of @ ( sK8_P @ SY950 @ SY949 @ SV583 ) ) ) )
| ( SV583 = SY949 )
| ~ ( path @ SV583 @ SY949 @ SY950 )
| ( shortest_path @ SV583 @ SY949 @ SY950 ) )
| ~ ~ ( ~ ! [SY951: $i,SY952: $i] :
( ~ ( shortest_path @ SV583 @ SY951 @ SY952 )
| ! [SY953: $i] :
( ~ ( path @ SV583 @ SY951 @ SY953 )
| ( less_or_equal @ ( length_of @ SY952 ) @ ( length_of @ SY953 ) ) ) )
| ~ ~ ( ~ ! [SY954: $i] :
( ! [SY955: $i] :
~ ( shortest_path @ SV583 @ SY954 @ SY955 )
| ( SV583 != SY954 ) )
| ~ ! [SY956: $i,SY957: $i] :
( ~ ( shortest_path @ SV583 @ SY956 @ SY957 )
| ( path @ SV583 @ SY956 @ SY957 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2858]) ).
thf(2876,plain,
! [SV584: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV584 ) @ SV584 )
| ~ ( on_path @ ( sK7_SY80 @ SV584 ) @ SV584 ) )
| ~ ( sequential @ ( sK6_E1 @ SV584 ) @ ( sK7_SY80 @ SV584 ) ) )
| ~ ! [SY958: $i] :
~ ( triangle @ ( sK6_E1 @ SV584 ) @ ( sK7_SY80 @ SV584 ) @ SY958 ) )
| ! [SY959: $i,SY960: $i] :
~ ( path @ SY959 @ SY960 @ SV584 )
| ( ( number_of_in @ sequential_pairs @ SV584 )
= ( number_of_in @ triangles @ SV584 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2859]) ).
thf(2877,plain,
! [SV571: $i] :
( ( ( ~ ( edge @ SV571 ) )
= $true )
| ( ( ( ( head_of @ SV571 )
!= ( tail_of @ SV571 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2860]) ).
thf(2878,plain,
! [SV585: $i,SV572: $i] :
( ( ! [SY961: $i] :
( ~ ( path @ SV572 @ SV585 @ SY961 )
| ( ( length_of @ SY961 )
= ( number_of_in @ edges @ SY961 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2861]) ).
thf(2879,plain,
! [SV586: $i,SV573: $i] :
( ( ! [SY962: $i] :
( ~ ( path @ SV573 @ SV586 @ SY962 )
| ( ( number_of_in @ sequential_pairs @ SY962 )
= ( minus @ ( length_of @ SY962 ) @ n1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2862]) ).
thf(2880,plain,
! [SV587: $i,SV574: $i] :
( ( less_or_equal @ ( number_of_in @ SV574 @ SV587 ) @ ( number_of_in @ SV574 @ graph ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2863]) ).
thf(2881,plain,
! [SV588: $i,SV575: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY963: $i,SY964: $i] :
( ~ ( on_path @ SY964 @ SY963 )
| ~ ( path @ SV575 @ SV588 @ SY963 )
| ( edge @ SY964 ) )
| ~ ! [SY965: $i,SY966: $i] :
( ~ ( on_path @ SY966 @ SY965 )
| ~ ( path @ SV575 @ SV588 @ SY965 )
| ( in_path @ ( head_of @ SY966 ) @ SY965 ) ) )
| ~ ! [SY967: $i,SY968: $i] :
( ~ ( on_path @ SY968 @ SY967 )
| ~ ( path @ SV575 @ SV588 @ SY967 )
| ( in_path @ ( tail_of @ SY968 ) @ SY967 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2864]) ).
thf(2882,plain,
! [SV589: $i,SV576: $i] :
( ( ! [SY969: $i] :
( ~ ( vertex @ SV576 )
| ~ ( vertex @ SV589 )
| ~ ( ~ ! [SY970: $i] :
( ( SV576
!= ( tail_of @ SY970 ) )
| ~ ( edge @ SY970 )
| ( SV589
!= ( head_of @ SY970 ) )
| ( SY969
!= ( path_cons @ SY970 @ empty ) ) )
| ~ ! [SY971: $i] :
( ( SV576
!= ( tail_of @ SY971 ) )
| ~ ( edge @ SY971 )
| ! [SY972: $i] :
( ( SY969
!= ( path_cons @ SY971 @ SY972 ) )
| ~ ( path @ ( head_of @ SY971 ) @ SV589 @ SY972 ) ) ) )
| ( path @ SV576 @ SV589 @ SY969 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2865]) ).
thf(2883,plain,
! [SV590: $i,SV577: $i] :
( ( ! [SY973: $i] :
~ ( ~ ! [SY974: $i] :
( ! [SY975: $i] :
( ~ ( precedes @ SY973 @ SY974 @ SY975 )
| ~ ( shortest_path @ SV577 @ SV590 @ SY975 ) )
| ! [SX4: $i] :
( ( ( tail_of @ SX4 )
!= ( tail_of @ SY973 ) )
| ( ( head_of @ SX4 )
!= ( head_of @ SY974 ) ) ) )
| ~ ! [SY977: $i,SY978: $i] :
( ~ ( precedes @ SY973 @ SY977 @ SY978 )
| ~ ( shortest_path @ SV577 @ SV590 @ SY978 )
| ~ ( precedes @ SY977 @ SY973 @ SY978 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2866]) ).
thf(2884,plain,
( ( complete = $false )
| ( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( vertex @ SX0 )
| ~ ( vertex @ SX1 )
| ~ ( ~ ~ ( ~ ( ( SX0
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
| ~ ~ ( ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2867]) ).
thf(2885,plain,
( ( ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( head_of @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2868]) ).
thf(2886,plain,
( ( ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( tail_of @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2868]) ).
thf(2887,plain,
! [SV578: $i] :
( ( ( ! [SY905: $i,SY906: $i] :
~ ( path @ SY905 @ SY906 @ SV578 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY907: $i] :
( ! [SY908: $i] :
~ ( precedes @ SY907 @ SY908 @ SV578 )
| ( on_path @ SY907 @ SV578 ) )
| ~ ! [SY909: $i,SY910: $i] :
( ~ ( precedes @ SY909 @ SY910 @ SV578 )
| ( on_path @ SY910 @ SV578 ) ) )
| ~ ~ ( ~ ! [SY911: $i,SY912: $i] :
( ~ ( precedes @ SY911 @ SY912 @ SV578 )
| ! [SY913: $i] :
( ~ ( precedes @ SY913 @ SY912 @ SV578 )
| ~ ( sequential @ SY911 @ SY913 ) )
| ~ ( sequential @ SY911 @ SY912 ) )
| ~ ! [SY914: $i,SY915: $i] :
( ~ ( precedes @ SY914 @ SY915 @ SV578 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY915 @ SY914 @ SV578 ) @ SY915 @ SV578 )
| ~ ( sequential @ SY914 @ ( sK9_E3 @ SY915 @ SY914 @ SV578 ) ) )
| ( sequential @ SY914 @ SY915 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2869]) ).
thf(2888,plain,
! [SV591: $i,SV579: $i] :
( ( ~ ( ~ ! [SY979: $i,SY980: $i] :
( ~ ( in_path @ SY980 @ SY979 )
| ~ ( path @ SV579 @ SV591 @ SY979 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY980 @ SY979 @ SV591 @ SV579 ) @ SY979 )
| ~ ( ( SY980
= ( head_of @ ( sK10_E @ SY980 @ SY979 @ SV591 @ SV579 ) ) )
| ( SY980
= ( tail_of @ ( sK10_E @ SY980 @ SY979 @ SV591 @ SV579 ) ) ) ) ) )
| ~ ! [SY981: $i,SY982: $i] :
( ~ ( in_path @ SY982 @ SY981 )
| ~ ( path @ SV579 @ SV591 @ SY981 )
| ( vertex @ SY982 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2870]) ).
thf(2889,plain,
! [SV580: $i] :
( ( ( ! [SY921: $i,SY922: $i] :
~ ( path @ SY921 @ SY922 @ SV580 ) )
= $true )
| ( ( ~ ( ~ ! [SY923: $i,SY924: $i] :
( ~ ( on_path @ SY923 @ SV580 )
| ~ ( on_path @ SY924 @ SV580 )
| ! [SY925: $i] :
( ~ ( precedes @ SY925 @ SY924 @ SV580 )
| ~ ( sequential @ SY923 @ SY925 ) )
| ( precedes @ SY923 @ SY924 @ SV580 ) )
| ~ ! [SY926: $i,SY927: $i] :
( ~ ( on_path @ SY926 @ SV580 )
| ~ ( on_path @ SY927 @ SV580 )
| ~ ( sequential @ SY926 @ SY927 )
| ( precedes @ SY926 @ SY927 @ SV580 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2871]) ).
thf(2890,plain,
! [SV581: $i] :
( ( ~ ! [SY928: $i,SY929: $i] :
( ~ ( edge @ SV581 )
| ~ ( edge @ SY928 )
| ~ ( edge @ SY929 )
| ~ ( sequential @ SV581 @ SY928 )
| ~ ( sequential @ SY928 @ SY929 )
| ~ ( sequential @ SY929 @ SV581 )
| ( triangle @ SV581 @ SY928 @ SY929 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY930: $i,SY931: $i] :
~ ( triangle @ SV581 @ SY930 @ SY931 )
| ( edge @ SV581 ) )
| ~ ! [SY932: $i] :
( ! [SY933: $i] :
~ ( triangle @ SV581 @ SY932 @ SY933 )
| ( edge @ SY932 ) ) )
| ~ ! [SY934: $i,SY935: $i] :
( ~ ( triangle @ SV581 @ SY934 @ SY935 )
| ( edge @ SY935 ) ) )
| ~ ! [SY936: $i] :
( ! [SY937: $i] :
~ ( triangle @ SV581 @ SY936 @ SY937 )
| ( sequential @ SV581 @ SY936 ) ) )
| ~ ! [SY938: $i,SY939: $i] :
( ~ ( triangle @ SV581 @ SY938 @ SY939 )
| ( sequential @ SY938 @ SY939 ) ) )
| ~ ! [SY940: $i,SY941: $i] :
( ~ ( triangle @ SV581 @ SY940 @ SY941 )
| ( sequential @ SY941 @ SV581 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2872]) ).
thf(2891,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( edge @ SX0 )
| ~ ( edge @ SX1 )
| ( ( head_of @ SX0 )
!= ( tail_of @ SX1 ) )
| ( sequential @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2873]) ).
thf(2892,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2873]) ).
thf(2893,plain,
! [SV582: $i] :
( ( ~ ~ ( ~ ( ! [SY942: $i,SY943: $i] :
~ ( path @ SV582 @ SY942 @ SY943 )
| ( vertex @ SV582 ) )
| ~ ! [SY944: $i] :
( ! [SY945: $i] :
~ ( path @ SV582 @ SY944 @ SY945 )
| ( vertex @ SY944 ) ) )
| ~ ! [SY946: $i,SY947: $i] :
( ~ ( path @ SV582 @ SY946 @ SY947 )
| ~ ( ~ ~ ( ( SV582
!= ( tail_of @ ( sK11_E @ SY947 @ SY946 @ SV582 ) ) )
| ~ ( edge @ ( sK11_E @ SY947 @ SY946 @ SV582 ) ) )
| ~ ~ ( ~ ( ( SY946
!= ( head_of @ ( sK11_E @ SY947 @ SY946 @ SV582 ) ) )
| ( SY947
!= ( path_cons @ ( sK11_E @ SY947 @ SY946 @ SV582 ) @ empty ) )
| ! [SY948: $i] :
( ( SY947
!= ( path_cons @ ( sK11_E @ SY947 @ SY946 @ SV582 ) @ SY948 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY947 @ SY946 @ SV582 ) ) @ SY946 @ SY948 ) ) )
| ~ ~ ( ~ ( ( SY946
= ( head_of @ ( sK11_E @ SY947 @ SY946 @ SV582 ) ) )
| ~ ( ( SY947
!= ( path_cons @ ( sK11_E @ SY947 @ SY946 @ SV582 ) @ ( sK13_SY84 @ SY947 @ SY946 @ SV582 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY947 @ SY946 @ SV582 ) ) @ SY946 @ ( sK13_SY84 @ SY947 @ SY946 @ SV582 ) ) ) )
| ~ ( ( SY947
= ( path_cons @ ( sK11_E @ SY947 @ SY946 @ SV582 ) @ empty ) )
| ~ ( ( SY947
!= ( path_cons @ ( sK11_E @ SY947 @ SY946 @ SV582 ) @ ( sK12_SY85 @ SY947 @ SY946 @ SV582 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY947 @ SY946 @ SV582 ) ) @ SY946 @ ( sK12_SY85 @ SY947 @ SY946 @ SV582 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2874]) ).
thf(2894,plain,
! [SV583: $i] :
( ( ~ ! [SY949: $i,SY950: $i] :
( ~ ( ~ ( path @ SV583 @ SY949 @ ( sK8_P @ SY950 @ SY949 @ SV583 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY950 ) @ ( length_of @ ( sK8_P @ SY950 @ SY949 @ SV583 ) ) ) )
| ( SV583 = SY949 )
| ~ ( path @ SV583 @ SY949 @ SY950 )
| ( shortest_path @ SV583 @ SY949 @ SY950 ) )
| ~ ~ ( ~ ! [SY951: $i,SY952: $i] :
( ~ ( shortest_path @ SV583 @ SY951 @ SY952 )
| ! [SY953: $i] :
( ~ ( path @ SV583 @ SY951 @ SY953 )
| ( less_or_equal @ ( length_of @ SY952 ) @ ( length_of @ SY953 ) ) ) )
| ~ ~ ( ~ ! [SY954: $i] :
( ! [SY955: $i] :
~ ( shortest_path @ SV583 @ SY954 @ SY955 )
| ( SV583 != SY954 ) )
| ~ ! [SY956: $i,SY957: $i] :
( ~ ( shortest_path @ SV583 @ SY956 @ SY957 )
| ( path @ SV583 @ SY956 @ SY957 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2875]) ).
thf(2895,plain,
! [SV584: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV584 ) @ SV584 )
| ~ ( on_path @ ( sK7_SY80 @ SV584 ) @ SV584 ) )
| ~ ( sequential @ ( sK6_E1 @ SV584 ) @ ( sK7_SY80 @ SV584 ) ) )
| ~ ! [SY958: $i] :
~ ( triangle @ ( sK6_E1 @ SV584 ) @ ( sK7_SY80 @ SV584 ) @ SY958 ) )
| ! [SY959: $i,SY960: $i] :
~ ( path @ SY959 @ SY960 @ SV584 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV584 )
= ( number_of_in @ triangles @ SV584 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2876]) ).
thf(2896,plain,
! [SV571: $i] :
( ( ( edge @ SV571 )
= $false )
| ( ( ( ( head_of @ SV571 )
!= ( tail_of @ SV571 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2877]) ).
thf(2897,plain,
! [SV592: $i,SV585: $i,SV572: $i] :
( ( ~ ( path @ SV572 @ SV585 @ SV592 )
| ( ( length_of @ SV592 )
= ( number_of_in @ edges @ SV592 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2878]) ).
thf(2898,plain,
! [SV593: $i,SV586: $i,SV573: $i] :
( ( ~ ( path @ SV573 @ SV586 @ SV593 )
| ( ( number_of_in @ sequential_pairs @ SV593 )
= ( minus @ ( length_of @ SV593 ) @ n1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2879]) ).
thf(2899,plain,
! [SV588: $i,SV575: $i] :
( ( ~ ~ ( ~ ! [SY963: $i,SY964: $i] :
( ~ ( on_path @ SY964 @ SY963 )
| ~ ( path @ SV575 @ SV588 @ SY963 )
| ( edge @ SY964 ) )
| ~ ! [SY965: $i,SY966: $i] :
( ~ ( on_path @ SY966 @ SY965 )
| ~ ( path @ SV575 @ SV588 @ SY965 )
| ( in_path @ ( head_of @ SY966 ) @ SY965 ) ) )
| ~ ! [SY967: $i,SY968: $i] :
( ~ ( on_path @ SY968 @ SY967 )
| ~ ( path @ SV575 @ SV588 @ SY967 )
| ( in_path @ ( tail_of @ SY968 ) @ SY967 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2881]) ).
thf(2900,plain,
! [SV594: $i,SV589: $i,SV576: $i] :
( ( ~ ( vertex @ SV576 )
| ~ ( vertex @ SV589 )
| ~ ( ~ ! [SY983: $i] :
( ( SV576
!= ( tail_of @ SY983 ) )
| ~ ( edge @ SY983 )
| ( SV589
!= ( head_of @ SY983 ) )
| ( SV594
!= ( path_cons @ SY983 @ empty ) ) )
| ~ ! [SY984: $i] :
( ( SV576
!= ( tail_of @ SY984 ) )
| ~ ( edge @ SY984 )
| ! [SY985: $i] :
( ( SV594
!= ( path_cons @ SY984 @ SY985 ) )
| ~ ( path @ ( head_of @ SY984 ) @ SV589 @ SY985 ) ) ) )
| ( path @ SV576 @ SV589 @ SV594 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2882]) ).
thf(2901,plain,
! [SV590: $i,SV577: $i,SV595: $i] :
( ( ~ ( ~ ! [SY986: $i] :
( ! [SY987: $i] :
( ~ ( precedes @ SV595 @ SY986 @ SY987 )
| ~ ( shortest_path @ SV577 @ SV590 @ SY987 ) )
| ! [SY988: $i] :
( ( ( tail_of @ SY988 )
!= ( tail_of @ SV595 ) )
| ( ( head_of @ SY988 )
!= ( head_of @ SY986 ) ) ) )
| ~ ! [SY989: $i,SY990: $i] :
( ~ ( precedes @ SV595 @ SY989 @ SY990 )
| ~ ( shortest_path @ SV577 @ SV590 @ SY990 )
| ~ ( precedes @ SY989 @ SV595 @ SY990 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2883]) ).
thf(2902,plain,
! [SV596: $i] :
( ( ( ! [SY991: $i] :
( ( SV596 = SY991 )
| ~ ( vertex @ SV596 )
| ~ ( vertex @ SY991 )
| ~ ( ~ ~ ( ~ ( ( SV596
!= ( head_of @ ( sK14_E @ SY991 @ SV596 ) ) )
| ( SY991
!= ( tail_of @ ( sK14_E @ SY991 @ SV596 ) ) )
| ( SY991
!= ( head_of @ ( sK14_E @ SY991 @ SV596 ) ) )
| ( SV596
!= ( tail_of @ ( sK14_E @ SY991 @ SV596 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV596
= ( head_of @ ( sK14_E @ SY991 @ SV596 ) ) )
| ( SY991
= ( head_of @ ( sK14_E @ SY991 @ SV596 ) ) ) )
| ~ ( ( SV596
= ( head_of @ ( sK14_E @ SY991 @ SV596 ) ) )
| ( SV596
= ( tail_of @ ( sK14_E @ SY991 @ SV596 ) ) ) ) )
| ~ ~ ( ~ ( ( SY991
= ( tail_of @ ( sK14_E @ SY991 @ SV596 ) ) )
| ( SY991
= ( head_of @ ( sK14_E @ SY991 @ SV596 ) ) ) )
| ~ ( ( SY991
= ( tail_of @ ( sK14_E @ SY991 @ SV596 ) ) )
| ( SV596
= ( tail_of @ ( sK14_E @ SY991 @ SV596 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SY991 @ SV596 ) ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2884]) ).
thf(2903,plain,
( ( ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( head_of @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2885]) ).
thf(2904,plain,
( ( ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( tail_of @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2886]) ).
thf(2905,plain,
! [SV578: $i,SV597: $i] :
( ( ( ! [SY992: $i] :
~ ( path @ SV597 @ SY992 @ SV578 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY907: $i] :
( ! [SY908: $i] :
~ ( precedes @ SY907 @ SY908 @ SV578 )
| ( on_path @ SY907 @ SV578 ) )
| ~ ! [SY909: $i,SY910: $i] :
( ~ ( precedes @ SY909 @ SY910 @ SV578 )
| ( on_path @ SY910 @ SV578 ) ) )
| ~ ~ ( ~ ! [SY911: $i,SY912: $i] :
( ~ ( precedes @ SY911 @ SY912 @ SV578 )
| ! [SY913: $i] :
( ~ ( precedes @ SY913 @ SY912 @ SV578 )
| ~ ( sequential @ SY911 @ SY913 ) )
| ~ ( sequential @ SY911 @ SY912 ) )
| ~ ! [SY914: $i,SY915: $i] :
( ~ ( precedes @ SY914 @ SY915 @ SV578 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY915 @ SY914 @ SV578 ) @ SY915 @ SV578 )
| ~ ( sequential @ SY914 @ ( sK9_E3 @ SY915 @ SY914 @ SV578 ) ) )
| ( sequential @ SY914 @ SY915 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2887]) ).
thf(2906,plain,
! [SV591: $i,SV579: $i] :
( ( ~ ! [SY979: $i,SY980: $i] :
( ~ ( in_path @ SY980 @ SY979 )
| ~ ( path @ SV579 @ SV591 @ SY979 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY980 @ SY979 @ SV591 @ SV579 ) @ SY979 )
| ~ ( ( SY980
= ( head_of @ ( sK10_E @ SY980 @ SY979 @ SV591 @ SV579 ) ) )
| ( SY980
= ( tail_of @ ( sK10_E @ SY980 @ SY979 @ SV591 @ SV579 ) ) ) ) ) )
| ~ ! [SY981: $i,SY982: $i] :
( ~ ( in_path @ SY982 @ SY981 )
| ~ ( path @ SV579 @ SV591 @ SY981 )
| ( vertex @ SY982 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2888]) ).
thf(2907,plain,
! [SV580: $i,SV598: $i] :
( ( ( ! [SY993: $i] :
~ ( path @ SV598 @ SY993 @ SV580 ) )
= $true )
| ( ( ~ ( ~ ! [SY923: $i,SY924: $i] :
( ~ ( on_path @ SY923 @ SV580 )
| ~ ( on_path @ SY924 @ SV580 )
| ! [SY925: $i] :
( ~ ( precedes @ SY925 @ SY924 @ SV580 )
| ~ ( sequential @ SY923 @ SY925 ) )
| ( precedes @ SY923 @ SY924 @ SV580 ) )
| ~ ! [SY926: $i,SY927: $i] :
( ~ ( on_path @ SY926 @ SV580 )
| ~ ( on_path @ SY927 @ SV580 )
| ~ ( sequential @ SY926 @ SY927 )
| ( precedes @ SY926 @ SY927 @ SV580 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2889]) ).
thf(2908,plain,
! [SV581: $i] :
( ( ~ ! [SY928: $i,SY929: $i] :
( ~ ( edge @ SV581 )
| ~ ( edge @ SY928 )
| ~ ( edge @ SY929 )
| ~ ( sequential @ SV581 @ SY928 )
| ~ ( sequential @ SY928 @ SY929 )
| ~ ( sequential @ SY929 @ SV581 )
| ( triangle @ SV581 @ SY928 @ SY929 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2890]) ).
thf(2909,plain,
! [SV581: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY930: $i,SY931: $i] :
~ ( triangle @ SV581 @ SY930 @ SY931 )
| ( edge @ SV581 ) )
| ~ ! [SY932: $i] :
( ! [SY933: $i] :
~ ( triangle @ SV581 @ SY932 @ SY933 )
| ( edge @ SY932 ) ) )
| ~ ! [SY934: $i,SY935: $i] :
( ~ ( triangle @ SV581 @ SY934 @ SY935 )
| ( edge @ SY935 ) ) )
| ~ ! [SY936: $i] :
( ! [SY937: $i] :
~ ( triangle @ SV581 @ SY936 @ SY937 )
| ( sequential @ SV581 @ SY936 ) ) )
| ~ ! [SY938: $i,SY939: $i] :
( ~ ( triangle @ SV581 @ SY938 @ SY939 )
| ( sequential @ SY938 @ SY939 ) ) )
| ~ ! [SY940: $i,SY941: $i] :
( ~ ( triangle @ SV581 @ SY940 @ SY941 )
| ( sequential @ SY941 @ SV581 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2890]) ).
thf(2910,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( edge @ SX0 )
| ~ ( edge @ SX1 )
| ( ( head_of @ SX0 )
!= ( tail_of @ SX1 ) )
| ( sequential @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2891]) ).
thf(2911,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2892]) ).
thf(2912,plain,
! [SV582: $i] :
( ( ~ ~ ( ~ ( ! [SY942: $i,SY943: $i] :
~ ( path @ SV582 @ SY942 @ SY943 )
| ( vertex @ SV582 ) )
| ~ ! [SY944: $i] :
( ! [SY945: $i] :
~ ( path @ SV582 @ SY944 @ SY945 )
| ( vertex @ SY944 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2893]) ).
thf(2913,plain,
! [SV582: $i] :
( ( ~ ! [SY946: $i,SY947: $i] :
( ~ ( path @ SV582 @ SY946 @ SY947 )
| ~ ( ~ ~ ( ( SV582
!= ( tail_of @ ( sK11_E @ SY947 @ SY946 @ SV582 ) ) )
| ~ ( edge @ ( sK11_E @ SY947 @ SY946 @ SV582 ) ) )
| ~ ~ ( ~ ( ( SY946
!= ( head_of @ ( sK11_E @ SY947 @ SY946 @ SV582 ) ) )
| ( SY947
!= ( path_cons @ ( sK11_E @ SY947 @ SY946 @ SV582 ) @ empty ) )
| ! [SY948: $i] :
( ( SY947
!= ( path_cons @ ( sK11_E @ SY947 @ SY946 @ SV582 ) @ SY948 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY947 @ SY946 @ SV582 ) ) @ SY946 @ SY948 ) ) )
| ~ ~ ( ~ ( ( SY946
= ( head_of @ ( sK11_E @ SY947 @ SY946 @ SV582 ) ) )
| ~ ( ( SY947
!= ( path_cons @ ( sK11_E @ SY947 @ SY946 @ SV582 ) @ ( sK13_SY84 @ SY947 @ SY946 @ SV582 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY947 @ SY946 @ SV582 ) ) @ SY946 @ ( sK13_SY84 @ SY947 @ SY946 @ SV582 ) ) ) )
| ~ ( ( SY947
= ( path_cons @ ( sK11_E @ SY947 @ SY946 @ SV582 ) @ empty ) )
| ~ ( ( SY947
!= ( path_cons @ ( sK11_E @ SY947 @ SY946 @ SV582 ) @ ( sK12_SY85 @ SY947 @ SY946 @ SV582 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY947 @ SY946 @ SV582 ) ) @ SY946 @ ( sK12_SY85 @ SY947 @ SY946 @ SV582 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2893]) ).
thf(2914,plain,
! [SV583: $i] :
( ( ~ ! [SY949: $i,SY950: $i] :
( ~ ( ~ ( path @ SV583 @ SY949 @ ( sK8_P @ SY950 @ SY949 @ SV583 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY950 ) @ ( length_of @ ( sK8_P @ SY950 @ SY949 @ SV583 ) ) ) )
| ( SV583 = SY949 )
| ~ ( path @ SV583 @ SY949 @ SY950 )
| ( shortest_path @ SV583 @ SY949 @ SY950 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2894]) ).
thf(2915,plain,
! [SV583: $i] :
( ( ~ ~ ( ~ ! [SY951: $i,SY952: $i] :
( ~ ( shortest_path @ SV583 @ SY951 @ SY952 )
| ! [SY953: $i] :
( ~ ( path @ SV583 @ SY951 @ SY953 )
| ( less_or_equal @ ( length_of @ SY952 ) @ ( length_of @ SY953 ) ) ) )
| ~ ~ ( ~ ! [SY954: $i] :
( ! [SY955: $i] :
~ ( shortest_path @ SV583 @ SY954 @ SY955 )
| ( SV583 != SY954 ) )
| ~ ! [SY956: $i,SY957: $i] :
( ~ ( shortest_path @ SV583 @ SY956 @ SY957 )
| ( path @ SV583 @ SY956 @ SY957 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2894]) ).
thf(2916,plain,
! [SV584: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV584 ) @ SV584 )
| ~ ( on_path @ ( sK7_SY80 @ SV584 ) @ SV584 ) )
| ~ ( sequential @ ( sK6_E1 @ SV584 ) @ ( sK7_SY80 @ SV584 ) ) )
| ~ ! [SY958: $i] :
~ ( triangle @ ( sK6_E1 @ SV584 ) @ ( sK7_SY80 @ SV584 ) @ SY958 ) ) )
= $true )
| ( ( ! [SY959: $i,SY960: $i] :
~ ( path @ SY959 @ SY960 @ SV584 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV584 )
= ( number_of_in @ triangles @ SV584 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2895]) ).
thf(2917,plain,
! [SV571: $i] :
( ( ( ( head_of @ SV571 )
= ( tail_of @ SV571 ) )
= $false )
| ( ( edge @ SV571 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2896]) ).
thf(2918,plain,
! [SV592: $i,SV585: $i,SV572: $i] :
( ( ( ~ ( path @ SV572 @ SV585 @ SV592 ) )
= $true )
| ( ( ( length_of @ SV592 )
= ( number_of_in @ edges @ SV592 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2897]) ).
thf(2919,plain,
! [SV593: $i,SV586: $i,SV573: $i] :
( ( ( ~ ( path @ SV573 @ SV586 @ SV593 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV593 )
= ( minus @ ( length_of @ SV593 ) @ n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2898]) ).
thf(2920,plain,
! [SV588: $i,SV575: $i] :
( ( ~ ~ ( ~ ! [SY963: $i,SY964: $i] :
( ~ ( on_path @ SY964 @ SY963 )
| ~ ( path @ SV575 @ SV588 @ SY963 )
| ( edge @ SY964 ) )
| ~ ! [SY965: $i,SY966: $i] :
( ~ ( on_path @ SY966 @ SY965 )
| ~ ( path @ SV575 @ SV588 @ SY965 )
| ( in_path @ ( head_of @ SY966 ) @ SY965 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2899]) ).
thf(2921,plain,
! [SV588: $i,SV575: $i] :
( ( ~ ! [SY967: $i,SY968: $i] :
( ~ ( on_path @ SY968 @ SY967 )
| ~ ( path @ SV575 @ SV588 @ SY967 )
| ( in_path @ ( tail_of @ SY968 ) @ SY967 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2899]) ).
thf(2922,plain,
! [SV594: $i,SV589: $i,SV576: $i] :
( ( ( ~ ( vertex @ SV576 )
| ~ ( vertex @ SV589 )
| ~ ( ~ ! [SY983: $i] :
( ( SV576
!= ( tail_of @ SY983 ) )
| ~ ( edge @ SY983 )
| ( SV589
!= ( head_of @ SY983 ) )
| ( SV594
!= ( path_cons @ SY983 @ empty ) ) )
| ~ ! [SY984: $i] :
( ( SV576
!= ( tail_of @ SY984 ) )
| ~ ( edge @ SY984 )
| ! [SY985: $i] :
( ( SV594
!= ( path_cons @ SY984 @ SY985 ) )
| ~ ( path @ ( head_of @ SY984 ) @ SV589 @ SY985 ) ) ) ) )
= $true )
| ( ( path @ SV576 @ SV589 @ SV594 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2900]) ).
thf(2923,plain,
! [SV590: $i,SV577: $i,SV595: $i] :
( ( ~ ! [SY986: $i] :
( ! [SY987: $i] :
( ~ ( precedes @ SV595 @ SY986 @ SY987 )
| ~ ( shortest_path @ SV577 @ SV590 @ SY987 ) )
| ! [SY988: $i] :
( ( ( tail_of @ SY988 )
!= ( tail_of @ SV595 ) )
| ( ( head_of @ SY988 )
!= ( head_of @ SY986 ) ) ) )
| ~ ! [SY989: $i,SY990: $i] :
( ~ ( precedes @ SV595 @ SY989 @ SY990 )
| ~ ( shortest_path @ SV577 @ SV590 @ SY990 )
| ~ ( precedes @ SY989 @ SV595 @ SY990 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2901]) ).
thf(2924,plain,
! [SV599: $i,SV596: $i] :
( ( ( ( SV596 = SV599 )
| ~ ( vertex @ SV596 )
| ~ ( vertex @ SV599 )
| ~ ( ~ ~ ( ~ ( ( SV596
!= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
!= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
!= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
!= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV596
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
| ~ ( ( SV596
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) ) )
| ~ ~ ( ~ ( ( SV599
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
| ~ ( ( SV599
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV599 @ SV596 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2902]) ).
thf(2925,plain,
! [SV600: $i] :
( ( ~ ( edge @ SV600 )
| ( vertex @ ( head_of @ SV600 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2903]) ).
thf(2926,plain,
! [SV601: $i] :
( ( ~ ( edge @ SV601 )
| ( vertex @ ( tail_of @ SV601 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2904]) ).
thf(2927,plain,
! [SV578: $i,SV602: $i,SV597: $i] :
( ( ( ~ ( path @ SV597 @ SV602 @ SV578 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY907: $i] :
( ! [SY908: $i] :
~ ( precedes @ SY907 @ SY908 @ SV578 )
| ( on_path @ SY907 @ SV578 ) )
| ~ ! [SY909: $i,SY910: $i] :
( ~ ( precedes @ SY909 @ SY910 @ SV578 )
| ( on_path @ SY910 @ SV578 ) ) )
| ~ ~ ( ~ ! [SY911: $i,SY912: $i] :
( ~ ( precedes @ SY911 @ SY912 @ SV578 )
| ! [SY913: $i] :
( ~ ( precedes @ SY913 @ SY912 @ SV578 )
| ~ ( sequential @ SY911 @ SY913 ) )
| ~ ( sequential @ SY911 @ SY912 ) )
| ~ ! [SY914: $i,SY915: $i] :
( ~ ( precedes @ SY914 @ SY915 @ SV578 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY915 @ SY914 @ SV578 ) @ SY915 @ SV578 )
| ~ ( sequential @ SY914 @ ( sK9_E3 @ SY915 @ SY914 @ SV578 ) ) )
| ( sequential @ SY914 @ SY915 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2905]) ).
thf(2928,plain,
! [SV591: $i,SV579: $i] :
( ( ~ ! [SY979: $i,SY980: $i] :
( ~ ( in_path @ SY980 @ SY979 )
| ~ ( path @ SV579 @ SV591 @ SY979 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY980 @ SY979 @ SV591 @ SV579 ) @ SY979 )
| ~ ( ( SY980
= ( head_of @ ( sK10_E @ SY980 @ SY979 @ SV591 @ SV579 ) ) )
| ( SY980
= ( tail_of @ ( sK10_E @ SY980 @ SY979 @ SV591 @ SV579 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2906]) ).
thf(2929,plain,
! [SV591: $i,SV579: $i] :
( ( ~ ! [SY981: $i,SY982: $i] :
( ~ ( in_path @ SY982 @ SY981 )
| ~ ( path @ SV579 @ SV591 @ SY981 )
| ( vertex @ SY982 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2906]) ).
thf(2930,plain,
! [SV580: $i,SV603: $i,SV598: $i] :
( ( ( ~ ( path @ SV598 @ SV603 @ SV580 ) )
= $true )
| ( ( ~ ( ~ ! [SY923: $i,SY924: $i] :
( ~ ( on_path @ SY923 @ SV580 )
| ~ ( on_path @ SY924 @ SV580 )
| ! [SY925: $i] :
( ~ ( precedes @ SY925 @ SY924 @ SV580 )
| ~ ( sequential @ SY923 @ SY925 ) )
| ( precedes @ SY923 @ SY924 @ SV580 ) )
| ~ ! [SY926: $i,SY927: $i] :
( ~ ( on_path @ SY926 @ SV580 )
| ~ ( on_path @ SY927 @ SV580 )
| ~ ( sequential @ SY926 @ SY927 )
| ( precedes @ SY926 @ SY927 @ SV580 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2907]) ).
thf(2931,plain,
! [SV581: $i] :
( ( ! [SY928: $i,SY929: $i] :
( ~ ( edge @ SV581 )
| ~ ( edge @ SY928 )
| ~ ( edge @ SY929 )
| ~ ( sequential @ SV581 @ SY928 )
| ~ ( sequential @ SY928 @ SY929 )
| ~ ( sequential @ SY929 @ SV581 )
| ( triangle @ SV581 @ SY928 @ SY929 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2908]) ).
thf(2932,plain,
! [SV581: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY930: $i,SY931: $i] :
~ ( triangle @ SV581 @ SY930 @ SY931 )
| ( edge @ SV581 ) )
| ~ ! [SY932: $i] :
( ! [SY933: $i] :
~ ( triangle @ SV581 @ SY932 @ SY933 )
| ( edge @ SY932 ) ) )
| ~ ! [SY934: $i,SY935: $i] :
( ~ ( triangle @ SV581 @ SY934 @ SY935 )
| ( edge @ SY935 ) ) )
| ~ ! [SY936: $i] :
( ! [SY937: $i] :
~ ( triangle @ SV581 @ SY936 @ SY937 )
| ( sequential @ SV581 @ SY936 ) ) )
| ~ ! [SY938: $i,SY939: $i] :
( ~ ( triangle @ SV581 @ SY938 @ SY939 )
| ( sequential @ SY938 @ SY939 ) ) )
| ~ ! [SY940: $i,SY941: $i] :
( ~ ( triangle @ SV581 @ SY940 @ SY941 )
| ( sequential @ SY941 @ SV581 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2909]) ).
thf(2933,plain,
! [SV604: $i] :
( ( ! [SY994: $i] :
( ( SV604 = SY994 )
| ~ ( edge @ SV604 )
| ~ ( edge @ SY994 )
| ( ( head_of @ SV604 )
!= ( tail_of @ SY994 ) )
| ( sequential @ SV604 @ SY994 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2910]) ).
thf(2934,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2911]) ).
thf(2935,plain,
! [SV582: $i] :
( ( ~ ( ~ ( ! [SY942: $i,SY943: $i] :
~ ( path @ SV582 @ SY942 @ SY943 )
| ( vertex @ SV582 ) )
| ~ ! [SY944: $i] :
( ! [SY945: $i] :
~ ( path @ SV582 @ SY944 @ SY945 )
| ( vertex @ SY944 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2912]) ).
thf(2936,plain,
! [SV582: $i] :
( ( ! [SY946: $i,SY947: $i] :
( ~ ( path @ SV582 @ SY946 @ SY947 )
| ~ ( ~ ~ ( ( SV582
!= ( tail_of @ ( sK11_E @ SY947 @ SY946 @ SV582 ) ) )
| ~ ( edge @ ( sK11_E @ SY947 @ SY946 @ SV582 ) ) )
| ~ ~ ( ~ ( ( SY946
!= ( head_of @ ( sK11_E @ SY947 @ SY946 @ SV582 ) ) )
| ( SY947
!= ( path_cons @ ( sK11_E @ SY947 @ SY946 @ SV582 ) @ empty ) )
| ! [SY948: $i] :
( ( SY947
!= ( path_cons @ ( sK11_E @ SY947 @ SY946 @ SV582 ) @ SY948 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY947 @ SY946 @ SV582 ) ) @ SY946 @ SY948 ) ) )
| ~ ~ ( ~ ( ( SY946
= ( head_of @ ( sK11_E @ SY947 @ SY946 @ SV582 ) ) )
| ~ ( ( SY947
!= ( path_cons @ ( sK11_E @ SY947 @ SY946 @ SV582 ) @ ( sK13_SY84 @ SY947 @ SY946 @ SV582 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY947 @ SY946 @ SV582 ) ) @ SY946 @ ( sK13_SY84 @ SY947 @ SY946 @ SV582 ) ) ) )
| ~ ( ( SY947
= ( path_cons @ ( sK11_E @ SY947 @ SY946 @ SV582 ) @ empty ) )
| ~ ( ( SY947
!= ( path_cons @ ( sK11_E @ SY947 @ SY946 @ SV582 ) @ ( sK12_SY85 @ SY947 @ SY946 @ SV582 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY947 @ SY946 @ SV582 ) ) @ SY946 @ ( sK12_SY85 @ SY947 @ SY946 @ SV582 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2913]) ).
thf(2937,plain,
! [SV583: $i] :
( ( ! [SY949: $i,SY950: $i] :
( ~ ( ~ ( path @ SV583 @ SY949 @ ( sK8_P @ SY950 @ SY949 @ SV583 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY950 ) @ ( length_of @ ( sK8_P @ SY950 @ SY949 @ SV583 ) ) ) )
| ( SV583 = SY949 )
| ~ ( path @ SV583 @ SY949 @ SY950 )
| ( shortest_path @ SV583 @ SY949 @ SY950 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2914]) ).
thf(2938,plain,
! [SV583: $i] :
( ( ~ ( ~ ! [SY951: $i,SY952: $i] :
( ~ ( shortest_path @ SV583 @ SY951 @ SY952 )
| ! [SY953: $i] :
( ~ ( path @ SV583 @ SY951 @ SY953 )
| ( less_or_equal @ ( length_of @ SY952 ) @ ( length_of @ SY953 ) ) ) )
| ~ ~ ( ~ ! [SY954: $i] :
( ! [SY955: $i] :
~ ( shortest_path @ SV583 @ SY954 @ SY955 )
| ( SV583 != SY954 ) )
| ~ ! [SY956: $i,SY957: $i] :
( ~ ( shortest_path @ SV583 @ SY956 @ SY957 )
| ( path @ SV583 @ SY956 @ SY957 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2915]) ).
thf(2939,plain,
! [SV584: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV584 ) @ SV584 )
| ~ ( on_path @ ( sK7_SY80 @ SV584 ) @ SV584 ) )
| ~ ( sequential @ ( sK6_E1 @ SV584 ) @ ( sK7_SY80 @ SV584 ) ) )
| ~ ! [SY958: $i] :
~ ( triangle @ ( sK6_E1 @ SV584 ) @ ( sK7_SY80 @ SV584 ) @ SY958 ) )
= $false )
| ( ( ! [SY959: $i,SY960: $i] :
~ ( path @ SY959 @ SY960 @ SV584 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV584 )
= ( number_of_in @ triangles @ SV584 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2916]) ).
thf(2940,plain,
! [SV592: $i,SV585: $i,SV572: $i] :
( ( ( path @ SV572 @ SV585 @ SV592 )
= $false )
| ( ( ( length_of @ SV592 )
= ( number_of_in @ edges @ SV592 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2918]) ).
thf(2941,plain,
! [SV593: $i,SV586: $i,SV573: $i] :
( ( ( path @ SV573 @ SV586 @ SV593 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV593 )
= ( minus @ ( length_of @ SV593 ) @ n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2919]) ).
thf(2942,plain,
! [SV588: $i,SV575: $i] :
( ( ~ ( ~ ! [SY963: $i,SY964: $i] :
( ~ ( on_path @ SY964 @ SY963 )
| ~ ( path @ SV575 @ SV588 @ SY963 )
| ( edge @ SY964 ) )
| ~ ! [SY965: $i,SY966: $i] :
( ~ ( on_path @ SY966 @ SY965 )
| ~ ( path @ SV575 @ SV588 @ SY965 )
| ( in_path @ ( head_of @ SY966 ) @ SY965 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2920]) ).
thf(2943,plain,
! [SV588: $i,SV575: $i] :
( ( ! [SY967: $i,SY968: $i] :
( ~ ( on_path @ SY968 @ SY967 )
| ~ ( path @ SV575 @ SV588 @ SY967 )
| ( in_path @ ( tail_of @ SY968 ) @ SY967 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2921]) ).
thf(2944,plain,
! [SV594: $i,SV589: $i,SV576: $i] :
( ( ( ~ ( vertex @ SV576 )
| ~ ( vertex @ SV589 ) )
= $true )
| ( ( ~ ( ~ ! [SY983: $i] :
( ( SV576
!= ( tail_of @ SY983 ) )
| ~ ( edge @ SY983 )
| ( SV589
!= ( head_of @ SY983 ) )
| ( SV594
!= ( path_cons @ SY983 @ empty ) ) )
| ~ ! [SY984: $i] :
( ( SV576
!= ( tail_of @ SY984 ) )
| ~ ( edge @ SY984 )
| ! [SY985: $i] :
( ( SV594
!= ( path_cons @ SY984 @ SY985 ) )
| ~ ( path @ ( head_of @ SY984 ) @ SV589 @ SY985 ) ) ) ) )
= $true )
| ( ( path @ SV576 @ SV589 @ SV594 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2922]) ).
thf(2945,plain,
! [SV590: $i,SV577: $i,SV595: $i] :
( ( ~ ! [SY986: $i] :
( ! [SY987: $i] :
( ~ ( precedes @ SV595 @ SY986 @ SY987 )
| ~ ( shortest_path @ SV577 @ SV590 @ SY987 ) )
| ! [SY988: $i] :
( ( ( tail_of @ SY988 )
!= ( tail_of @ SV595 ) )
| ( ( head_of @ SY988 )
!= ( head_of @ SY986 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2923]) ).
thf(2946,plain,
! [SV590: $i,SV577: $i,SV595: $i] :
( ( ~ ! [SY989: $i,SY990: $i] :
( ~ ( precedes @ SV595 @ SY989 @ SY990 )
| ~ ( shortest_path @ SV577 @ SV590 @ SY990 )
| ~ ( precedes @ SY989 @ SV595 @ SY990 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2923]) ).
thf(2947,plain,
! [SV599: $i,SV596: $i] :
( ( ( ( SV596 = SV599 )
| ~ ( vertex @ SV596 )
| ~ ( vertex @ SV599 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV596
!= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
!= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
!= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
!= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV596
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
| ~ ( ( SV596
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) ) )
| ~ ~ ( ~ ( ( SV599
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
| ~ ( ( SV599
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV599 @ SV596 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[2924]) ).
thf(2948,plain,
! [SV600: $i] :
( ( ( ~ ( edge @ SV600 ) )
= $true )
| ( ( vertex @ ( head_of @ SV600 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2925]) ).
thf(2949,plain,
! [SV601: $i] :
( ( ( ~ ( edge @ SV601 ) )
= $true )
| ( ( vertex @ ( tail_of @ SV601 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2926]) ).
thf(2950,plain,
! [SV578: $i,SV602: $i,SV597: $i] :
( ( ( path @ SV597 @ SV602 @ SV578 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY907: $i] :
( ! [SY908: $i] :
~ ( precedes @ SY907 @ SY908 @ SV578 )
| ( on_path @ SY907 @ SV578 ) )
| ~ ! [SY909: $i,SY910: $i] :
( ~ ( precedes @ SY909 @ SY910 @ SV578 )
| ( on_path @ SY910 @ SV578 ) ) )
| ~ ~ ( ~ ! [SY911: $i,SY912: $i] :
( ~ ( precedes @ SY911 @ SY912 @ SV578 )
| ! [SY913: $i] :
( ~ ( precedes @ SY913 @ SY912 @ SV578 )
| ~ ( sequential @ SY911 @ SY913 ) )
| ~ ( sequential @ SY911 @ SY912 ) )
| ~ ! [SY914: $i,SY915: $i] :
( ~ ( precedes @ SY914 @ SY915 @ SV578 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY915 @ SY914 @ SV578 ) @ SY915 @ SV578 )
| ~ ( sequential @ SY914 @ ( sK9_E3 @ SY915 @ SY914 @ SV578 ) ) )
| ( sequential @ SY914 @ SY915 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2927]) ).
thf(2951,plain,
! [SV591: $i,SV579: $i] :
( ( ! [SY979: $i,SY980: $i] :
( ~ ( in_path @ SY980 @ SY979 )
| ~ ( path @ SV579 @ SV591 @ SY979 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY980 @ SY979 @ SV591 @ SV579 ) @ SY979 )
| ~ ( ( SY980
= ( head_of @ ( sK10_E @ SY980 @ SY979 @ SV591 @ SV579 ) ) )
| ( SY980
= ( tail_of @ ( sK10_E @ SY980 @ SY979 @ SV591 @ SV579 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2928]) ).
thf(2952,plain,
! [SV591: $i,SV579: $i] :
( ( ! [SY981: $i,SY982: $i] :
( ~ ( in_path @ SY982 @ SY981 )
| ~ ( path @ SV579 @ SV591 @ SY981 )
| ( vertex @ SY982 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2929]) ).
thf(2953,plain,
! [SV580: $i,SV603: $i,SV598: $i] :
( ( ( path @ SV598 @ SV603 @ SV580 )
= $false )
| ( ( ~ ( ~ ! [SY923: $i,SY924: $i] :
( ~ ( on_path @ SY923 @ SV580 )
| ~ ( on_path @ SY924 @ SV580 )
| ! [SY925: $i] :
( ~ ( precedes @ SY925 @ SY924 @ SV580 )
| ~ ( sequential @ SY923 @ SY925 ) )
| ( precedes @ SY923 @ SY924 @ SV580 ) )
| ~ ! [SY926: $i,SY927: $i] :
( ~ ( on_path @ SY926 @ SV580 )
| ~ ( on_path @ SY927 @ SV580 )
| ~ ( sequential @ SY926 @ SY927 )
| ( precedes @ SY926 @ SY927 @ SV580 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2930]) ).
thf(2954,plain,
! [SV605: $i,SV581: $i] :
( ( ! [SY995: $i] :
( ~ ( edge @ SV581 )
| ~ ( edge @ SV605 )
| ~ ( edge @ SY995 )
| ~ ( sequential @ SV581 @ SV605 )
| ~ ( sequential @ SV605 @ SY995 )
| ~ ( sequential @ SY995 @ SV581 )
| ( triangle @ SV581 @ SV605 @ SY995 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2931]) ).
thf(2955,plain,
! [SV581: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY930: $i,SY931: $i] :
~ ( triangle @ SV581 @ SY930 @ SY931 )
| ( edge @ SV581 ) )
| ~ ! [SY932: $i] :
( ! [SY933: $i] :
~ ( triangle @ SV581 @ SY932 @ SY933 )
| ( edge @ SY932 ) ) )
| ~ ! [SY934: $i,SY935: $i] :
( ~ ( triangle @ SV581 @ SY934 @ SY935 )
| ( edge @ SY935 ) ) )
| ~ ! [SY936: $i] :
( ! [SY937: $i] :
~ ( triangle @ SV581 @ SY936 @ SY937 )
| ( sequential @ SV581 @ SY936 ) ) )
| ~ ! [SY938: $i,SY939: $i] :
( ~ ( triangle @ SV581 @ SY938 @ SY939 )
| ( sequential @ SY938 @ SY939 ) ) )
| ~ ! [SY940: $i,SY941: $i] :
( ~ ( triangle @ SV581 @ SY940 @ SY941 )
| ( sequential @ SY941 @ SV581 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2932]) ).
thf(2956,plain,
! [SV606: $i,SV604: $i] :
( ( ( SV604 = SV606 )
| ~ ( edge @ SV604 )
| ~ ( edge @ SV606 )
| ( ( head_of @ SV604 )
!= ( tail_of @ SV606 ) )
| ( sequential @ SV604 @ SV606 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2933]) ).
thf(2957,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2934]) ).
thf(2958,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2934]) ).
thf(2959,plain,
! [SV582: $i] :
( ( ~ ( ! [SY942: $i,SY943: $i] :
~ ( path @ SV582 @ SY942 @ SY943 )
| ( vertex @ SV582 ) )
| ~ ! [SY944: $i] :
( ! [SY945: $i] :
~ ( path @ SV582 @ SY944 @ SY945 )
| ( vertex @ SY944 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2935]) ).
thf(2960,plain,
! [SV607: $i,SV582: $i] :
( ( ! [SY996: $i] :
( ~ ( path @ SV582 @ SV607 @ SY996 )
| ~ ( ~ ~ ( ( SV582
!= ( tail_of @ ( sK11_E @ SY996 @ SV607 @ SV582 ) ) )
| ~ ( edge @ ( sK11_E @ SY996 @ SV607 @ SV582 ) ) )
| ~ ~ ( ~ ( ( SV607
!= ( head_of @ ( sK11_E @ SY996 @ SV607 @ SV582 ) ) )
| ( SY996
!= ( path_cons @ ( sK11_E @ SY996 @ SV607 @ SV582 ) @ empty ) )
| ! [SY997: $i] :
( ( SY996
!= ( path_cons @ ( sK11_E @ SY996 @ SV607 @ SV582 ) @ SY997 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY996 @ SV607 @ SV582 ) ) @ SV607 @ SY997 ) ) )
| ~ ~ ( ~ ( ( SV607
= ( head_of @ ( sK11_E @ SY996 @ SV607 @ SV582 ) ) )
| ~ ( ( SY996
!= ( path_cons @ ( sK11_E @ SY996 @ SV607 @ SV582 ) @ ( sK13_SY84 @ SY996 @ SV607 @ SV582 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY996 @ SV607 @ SV582 ) ) @ SV607 @ ( sK13_SY84 @ SY996 @ SV607 @ SV582 ) ) ) )
| ~ ( ( SY996
= ( path_cons @ ( sK11_E @ SY996 @ SV607 @ SV582 ) @ empty ) )
| ~ ( ( SY996
!= ( path_cons @ ( sK11_E @ SY996 @ SV607 @ SV582 ) @ ( sK12_SY85 @ SY996 @ SV607 @ SV582 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY996 @ SV607 @ SV582 ) ) @ SV607 @ ( sK12_SY85 @ SY996 @ SV607 @ SV582 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2936]) ).
thf(2961,plain,
! [SV608: $i,SV583: $i] :
( ( ! [SY998: $i] :
( ~ ( ~ ( path @ SV583 @ SV608 @ ( sK8_P @ SY998 @ SV608 @ SV583 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY998 ) @ ( length_of @ ( sK8_P @ SY998 @ SV608 @ SV583 ) ) ) )
| ( SV583 = SV608 )
| ~ ( path @ SV583 @ SV608 @ SY998 )
| ( shortest_path @ SV583 @ SV608 @ SY998 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2937]) ).
thf(2962,plain,
! [SV583: $i] :
( ( ~ ! [SY951: $i,SY952: $i] :
( ~ ( shortest_path @ SV583 @ SY951 @ SY952 )
| ! [SY953: $i] :
( ~ ( path @ SV583 @ SY951 @ SY953 )
| ( less_or_equal @ ( length_of @ SY952 ) @ ( length_of @ SY953 ) ) ) )
| ~ ~ ( ~ ! [SY954: $i] :
( ! [SY955: $i] :
~ ( shortest_path @ SV583 @ SY954 @ SY955 )
| ( SV583 != SY954 ) )
| ~ ! [SY956: $i,SY957: $i] :
( ~ ( shortest_path @ SV583 @ SY956 @ SY957 )
| ( path @ SV583 @ SY956 @ SY957 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2938]) ).
thf(2963,plain,
! [SV584: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV584 ) @ SV584 )
| ~ ( on_path @ ( sK7_SY80 @ SV584 ) @ SV584 ) )
| ~ ( sequential @ ( sK6_E1 @ SV584 ) @ ( sK7_SY80 @ SV584 ) ) ) )
= $false )
| ( ( ! [SY959: $i,SY960: $i] :
~ ( path @ SY959 @ SY960 @ SV584 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV584 )
= ( number_of_in @ triangles @ SV584 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2939]) ).
thf(2964,plain,
! [SV584: $i] :
( ( ( ~ ! [SY958: $i] :
~ ( triangle @ ( sK6_E1 @ SV584 ) @ ( sK7_SY80 @ SV584 ) @ SY958 ) )
= $false )
| ( ( ! [SY959: $i,SY960: $i] :
~ ( path @ SY959 @ SY960 @ SV584 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV584 )
= ( number_of_in @ triangles @ SV584 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2939]) ).
thf(2965,plain,
! [SV588: $i,SV575: $i] :
( ( ~ ! [SY963: $i,SY964: $i] :
( ~ ( on_path @ SY964 @ SY963 )
| ~ ( path @ SV575 @ SV588 @ SY963 )
| ( edge @ SY964 ) )
| ~ ! [SY965: $i,SY966: $i] :
( ~ ( on_path @ SY966 @ SY965 )
| ~ ( path @ SV575 @ SV588 @ SY965 )
| ( in_path @ ( head_of @ SY966 ) @ SY965 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2942]) ).
thf(2966,plain,
! [SV588: $i,SV575: $i,SV609: $i] :
( ( ! [SY999: $i] :
( ~ ( on_path @ SY999 @ SV609 )
| ~ ( path @ SV575 @ SV588 @ SV609 )
| ( in_path @ ( tail_of @ SY999 ) @ SV609 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2943]) ).
thf(2967,plain,
! [SV594: $i,SV589: $i,SV576: $i] :
( ( ( ~ ( vertex @ SV576 ) )
= $true )
| ( ( ~ ( vertex @ SV589 ) )
= $true )
| ( ( ~ ( ~ ! [SY983: $i] :
( ( SV576
!= ( tail_of @ SY983 ) )
| ~ ( edge @ SY983 )
| ( SV589
!= ( head_of @ SY983 ) )
| ( SV594
!= ( path_cons @ SY983 @ empty ) ) )
| ~ ! [SY984: $i] :
( ( SV576
!= ( tail_of @ SY984 ) )
| ~ ( edge @ SY984 )
| ! [SY985: $i] :
( ( SV594
!= ( path_cons @ SY984 @ SY985 ) )
| ~ ( path @ ( head_of @ SY984 ) @ SV589 @ SY985 ) ) ) ) )
= $true )
| ( ( path @ SV576 @ SV589 @ SV594 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2944]) ).
thf(2968,plain,
! [SV590: $i,SV577: $i,SV595: $i] :
( ( ! [SY986: $i] :
( ! [SY987: $i] :
( ~ ( precedes @ SV595 @ SY986 @ SY987 )
| ~ ( shortest_path @ SV577 @ SV590 @ SY987 ) )
| ! [SY988: $i] :
( ( ( tail_of @ SY988 )
!= ( tail_of @ SV595 ) )
| ( ( head_of @ SY988 )
!= ( head_of @ SY986 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2945]) ).
thf(2969,plain,
! [SV590: $i,SV577: $i,SV595: $i] :
( ( ! [SY989: $i,SY990: $i] :
( ~ ( precedes @ SV595 @ SY989 @ SY990 )
| ~ ( shortest_path @ SV577 @ SV590 @ SY990 )
| ~ ( precedes @ SY989 @ SV595 @ SY990 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2946]) ).
thf(2970,plain,
! [SV599: $i,SV596: $i] :
( ( ( SV596 = SV599 )
= $true )
| ( ( ~ ( vertex @ SV596 )
| ~ ( vertex @ SV599 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV596
!= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
!= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
!= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
!= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV596
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
| ~ ( ( SV596
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) ) )
| ~ ~ ( ~ ( ( SV599
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
| ~ ( ( SV599
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV599 @ SV596 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[2947]) ).
thf(2971,plain,
! [SV600: $i] :
( ( ( edge @ SV600 )
= $false )
| ( ( vertex @ ( head_of @ SV600 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2948]) ).
thf(2972,plain,
! [SV601: $i] :
( ( ( edge @ SV601 )
= $false )
| ( ( vertex @ ( tail_of @ SV601 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2949]) ).
thf(2973,plain,
! [SV602: $i,SV597: $i,SV578: $i] :
( ( ( ~ ~ ( ~ ! [SY907: $i] :
( ! [SY908: $i] :
~ ( precedes @ SY907 @ SY908 @ SV578 )
| ( on_path @ SY907 @ SV578 ) )
| ~ ! [SY909: $i,SY910: $i] :
( ~ ( precedes @ SY909 @ SY910 @ SV578 )
| ( on_path @ SY910 @ SV578 ) ) )
| ~ ~ ( ~ ! [SY911: $i,SY912: $i] :
( ~ ( precedes @ SY911 @ SY912 @ SV578 )
| ! [SY913: $i] :
( ~ ( precedes @ SY913 @ SY912 @ SV578 )
| ~ ( sequential @ SY911 @ SY913 ) )
| ~ ( sequential @ SY911 @ SY912 ) )
| ~ ! [SY914: $i,SY915: $i] :
( ~ ( precedes @ SY914 @ SY915 @ SV578 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY915 @ SY914 @ SV578 ) @ SY915 @ SV578 )
| ~ ( sequential @ SY914 @ ( sK9_E3 @ SY915 @ SY914 @ SV578 ) ) )
| ( sequential @ SY914 @ SY915 ) ) ) )
= $false )
| ( ( path @ SV597 @ SV602 @ SV578 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2950]) ).
thf(2974,plain,
! [SV591: $i,SV579: $i,SV610: $i] :
( ( ! [SY1000: $i] :
( ~ ( in_path @ SY1000 @ SV610 )
| ~ ( path @ SV579 @ SV591 @ SV610 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY1000 @ SV610 @ SV591 @ SV579 ) @ SV610 )
| ~ ( ( SY1000
= ( head_of @ ( sK10_E @ SY1000 @ SV610 @ SV591 @ SV579 ) ) )
| ( SY1000
= ( tail_of @ ( sK10_E @ SY1000 @ SV610 @ SV591 @ SV579 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2951]) ).
thf(2975,plain,
! [SV591: $i,SV579: $i,SV611: $i] :
( ( ! [SY1001: $i] :
( ~ ( in_path @ SY1001 @ SV611 )
| ~ ( path @ SV579 @ SV591 @ SV611 )
| ( vertex @ SY1001 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2952]) ).
thf(2976,plain,
! [SV603: $i,SV598: $i,SV580: $i] :
( ( ( ~ ! [SY923: $i,SY924: $i] :
( ~ ( on_path @ SY923 @ SV580 )
| ~ ( on_path @ SY924 @ SV580 )
| ! [SY925: $i] :
( ~ ( precedes @ SY925 @ SY924 @ SV580 )
| ~ ( sequential @ SY923 @ SY925 ) )
| ( precedes @ SY923 @ SY924 @ SV580 ) )
| ~ ! [SY926: $i,SY927: $i] :
( ~ ( on_path @ SY926 @ SV580 )
| ~ ( on_path @ SY927 @ SV580 )
| ~ ( sequential @ SY926 @ SY927 )
| ( precedes @ SY926 @ SY927 @ SV580 ) ) )
= $false )
| ( ( path @ SV598 @ SV603 @ SV580 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2953]) ).
thf(2977,plain,
! [SV612: $i,SV605: $i,SV581: $i] :
( ( ~ ( edge @ SV581 )
| ~ ( edge @ SV605 )
| ~ ( edge @ SV612 )
| ~ ( sequential @ SV581 @ SV605 )
| ~ ( sequential @ SV605 @ SV612 )
| ~ ( sequential @ SV612 @ SV581 )
| ( triangle @ SV581 @ SV605 @ SV612 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2954]) ).
thf(2978,plain,
! [SV581: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY930: $i,SY931: $i] :
~ ( triangle @ SV581 @ SY930 @ SY931 )
| ( edge @ SV581 ) )
| ~ ! [SY932: $i] :
( ! [SY933: $i] :
~ ( triangle @ SV581 @ SY932 @ SY933 )
| ( edge @ SY932 ) ) )
| ~ ! [SY934: $i,SY935: $i] :
( ~ ( triangle @ SV581 @ SY934 @ SY935 )
| ( edge @ SY935 ) ) )
| ~ ! [SY936: $i] :
( ! [SY937: $i] :
~ ( triangle @ SV581 @ SY936 @ SY937 )
| ( sequential @ SV581 @ SY936 ) ) )
| ~ ! [SY938: $i,SY939: $i] :
( ~ ( triangle @ SV581 @ SY938 @ SY939 )
| ( sequential @ SY938 @ SY939 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2955]) ).
thf(2979,plain,
! [SV581: $i] :
( ( ~ ! [SY940: $i,SY941: $i] :
( ~ ( triangle @ SV581 @ SY940 @ SY941 )
| ( sequential @ SY941 @ SV581 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2955]) ).
thf(2980,plain,
! [SV606: $i,SV604: $i] :
( ( ( ( SV604 = SV606 )
| ~ ( edge @ SV604 )
| ~ ( edge @ SV606 )
| ( ( head_of @ SV604 )
!= ( tail_of @ SV606 ) ) )
= $true )
| ( ( sequential @ SV604 @ SV606 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2956]) ).
thf(2981,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2957]) ).
thf(2982,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2958]) ).
thf(2983,plain,
! [SV582: $i] :
( ( ~ ( ! [SY942: $i,SY943: $i] :
~ ( path @ SV582 @ SY942 @ SY943 )
| ( vertex @ SV582 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2959]) ).
thf(2984,plain,
! [SV582: $i] :
( ( ~ ! [SY944: $i] :
( ! [SY945: $i] :
~ ( path @ SV582 @ SY944 @ SY945 )
| ( vertex @ SY944 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2959]) ).
thf(2985,plain,
! [SV613: $i,SV607: $i,SV582: $i] :
( ( ~ ( path @ SV582 @ SV607 @ SV613 )
| ~ ( ~ ~ ( ( SV582
!= ( tail_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( edge @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
| ~ ~ ( ~ ( ( SV607
!= ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
| ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ empty ) )
| ! [SY1002: $i] :
( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ SY1002 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ SY1002 ) ) )
| ~ ~ ( ~ ( ( SV607
= ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ ( sK13_SY84 @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ ( sK13_SY84 @ SV613 @ SV607 @ SV582 ) ) ) )
| ~ ( ( SV613
= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ empty ) )
| ~ ( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ ( sK12_SY85 @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ ( sK12_SY85 @ SV613 @ SV607 @ SV582 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2960]) ).
thf(2986,plain,
! [SV614: $i,SV608: $i,SV583: $i] :
( ( ~ ( ~ ( path @ SV583 @ SV608 @ ( sK8_P @ SV614 @ SV608 @ SV583 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SV614 ) @ ( length_of @ ( sK8_P @ SV614 @ SV608 @ SV583 ) ) ) )
| ( SV583 = SV608 )
| ~ ( path @ SV583 @ SV608 @ SV614 )
| ( shortest_path @ SV583 @ SV608 @ SV614 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2961]) ).
thf(2987,plain,
! [SV583: $i] :
( ( ~ ! [SY951: $i,SY952: $i] :
( ~ ( shortest_path @ SV583 @ SY951 @ SY952 )
| ! [SY953: $i] :
( ~ ( path @ SV583 @ SY951 @ SY953 )
| ( less_or_equal @ ( length_of @ SY952 ) @ ( length_of @ SY953 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2962]) ).
thf(2988,plain,
! [SV583: $i] :
( ( ~ ~ ( ~ ! [SY954: $i] :
( ! [SY955: $i] :
~ ( shortest_path @ SV583 @ SY954 @ SY955 )
| ( SV583 != SY954 ) )
| ~ ! [SY956: $i,SY957: $i] :
( ~ ( shortest_path @ SV583 @ SY956 @ SY957 )
| ( path @ SV583 @ SY956 @ SY957 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2962]) ).
thf(2989,plain,
! [SV584: $i] :
( ( ( ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV584 ) @ SV584 )
| ~ ( on_path @ ( sK7_SY80 @ SV584 ) @ SV584 ) )
| ~ ( sequential @ ( sK6_E1 @ SV584 ) @ ( sK7_SY80 @ SV584 ) ) ) )
= $true )
| ( ( ! [SY959: $i,SY960: $i] :
~ ( path @ SY959 @ SY960 @ SV584 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV584 )
= ( number_of_in @ triangles @ SV584 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2963]) ).
thf(2990,plain,
! [SV584: $i] :
( ( ( ! [SY958: $i] :
~ ( triangle @ ( sK6_E1 @ SV584 ) @ ( sK7_SY80 @ SV584 ) @ SY958 ) )
= $true )
| ( ( ! [SY959: $i,SY960: $i] :
~ ( path @ SY959 @ SY960 @ SV584 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV584 )
= ( number_of_in @ triangles @ SV584 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2964]) ).
thf(2991,plain,
! [SV588: $i,SV575: $i] :
( ( ~ ! [SY963: $i,SY964: $i] :
( ~ ( on_path @ SY964 @ SY963 )
| ~ ( path @ SV575 @ SV588 @ SY963 )
| ( edge @ SY964 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2965]) ).
thf(2992,plain,
! [SV588: $i,SV575: $i] :
( ( ~ ! [SY965: $i,SY966: $i] :
( ~ ( on_path @ SY966 @ SY965 )
| ~ ( path @ SV575 @ SV588 @ SY965 )
| ( in_path @ ( head_of @ SY966 ) @ SY965 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2965]) ).
thf(2993,plain,
! [SV588: $i,SV575: $i,SV609: $i,SV615: $i] :
( ( ~ ( on_path @ SV615 @ SV609 )
| ~ ( path @ SV575 @ SV588 @ SV609 )
| ( in_path @ ( tail_of @ SV615 ) @ SV609 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2966]) ).
thf(2994,plain,
! [SV594: $i,SV589: $i,SV576: $i] :
( ( ( vertex @ SV576 )
= $false )
| ( ( ~ ( vertex @ SV589 ) )
= $true )
| ( ( ~ ( ~ ! [SY983: $i] :
( ( SV576
!= ( tail_of @ SY983 ) )
| ~ ( edge @ SY983 )
| ( SV589
!= ( head_of @ SY983 ) )
| ( SV594
!= ( path_cons @ SY983 @ empty ) ) )
| ~ ! [SY984: $i] :
( ( SV576
!= ( tail_of @ SY984 ) )
| ~ ( edge @ SY984 )
| ! [SY985: $i] :
( ( SV594
!= ( path_cons @ SY984 @ SY985 ) )
| ~ ( path @ ( head_of @ SY984 ) @ SV589 @ SY985 ) ) ) ) )
= $true )
| ( ( path @ SV576 @ SV589 @ SV594 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2967]) ).
thf(2995,plain,
! [SV590: $i,SV577: $i,SV616: $i,SV595: $i] :
( ( ! [SY1003: $i] :
( ~ ( precedes @ SV595 @ SV616 @ SY1003 )
| ~ ( shortest_path @ SV577 @ SV590 @ SY1003 ) )
| ! [SY1004: $i] :
( ( ( tail_of @ SY1004 )
!= ( tail_of @ SV595 ) )
| ( ( head_of @ SY1004 )
!= ( head_of @ SV616 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2968]) ).
thf(2996,plain,
! [SV590: $i,SV577: $i,SV617: $i,SV595: $i] :
( ( ! [SY1005: $i] :
( ~ ( precedes @ SV595 @ SV617 @ SY1005 )
| ~ ( shortest_path @ SV577 @ SV590 @ SY1005 )
| ~ ( precedes @ SV617 @ SV595 @ SY1005 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2969]) ).
thf(2997,plain,
! [SV599: $i,SV596: $i] :
( ( ( ~ ( vertex @ SV596 ) )
= $true )
| ( ( ~ ( vertex @ SV599 ) )
= $true )
| ( ( SV596 = SV599 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV596
!= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
!= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
!= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
!= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV596
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
| ~ ( ( SV596
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) ) )
| ~ ~ ( ~ ( ( SV599
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
| ~ ( ( SV599
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV599 @ SV596 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[2970]) ).
thf(2998,plain,
! [SV602: $i,SV597: $i,SV578: $i] :
( ( ( ~ ~ ( ~ ! [SY907: $i] :
( ! [SY908: $i] :
~ ( precedes @ SY907 @ SY908 @ SV578 )
| ( on_path @ SY907 @ SV578 ) )
| ~ ! [SY909: $i,SY910: $i] :
( ~ ( precedes @ SY909 @ SY910 @ SV578 )
| ( on_path @ SY910 @ SV578 ) ) ) )
= $false )
| ( ( path @ SV597 @ SV602 @ SV578 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2973]) ).
thf(2999,plain,
! [SV602: $i,SV597: $i,SV578: $i] :
( ( ( ~ ~ ( ~ ! [SY911: $i,SY912: $i] :
( ~ ( precedes @ SY911 @ SY912 @ SV578 )
| ! [SY913: $i] :
( ~ ( precedes @ SY913 @ SY912 @ SV578 )
| ~ ( sequential @ SY911 @ SY913 ) )
| ~ ( sequential @ SY911 @ SY912 ) )
| ~ ! [SY914: $i,SY915: $i] :
( ~ ( precedes @ SY914 @ SY915 @ SV578 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY915 @ SY914 @ SV578 ) @ SY915 @ SV578 )
| ~ ( sequential @ SY914 @ ( sK9_E3 @ SY915 @ SY914 @ SV578 ) ) )
| ( sequential @ SY914 @ SY915 ) ) ) )
= $false )
| ( ( path @ SV597 @ SV602 @ SV578 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2973]) ).
thf(3000,plain,
! [SV591: $i,SV579: $i,SV610: $i,SV618: $i] :
( ( ~ ( in_path @ SV618 @ SV610 )
| ~ ( path @ SV579 @ SV591 @ SV610 )
| ~ ( ~ ( on_path @ ( sK10_E @ SV618 @ SV610 @ SV591 @ SV579 ) @ SV610 )
| ~ ( ( SV618
= ( head_of @ ( sK10_E @ SV618 @ SV610 @ SV591 @ SV579 ) ) )
| ( SV618
= ( tail_of @ ( sK10_E @ SV618 @ SV610 @ SV591 @ SV579 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2974]) ).
thf(3001,plain,
! [SV591: $i,SV579: $i,SV611: $i,SV619: $i] :
( ( ~ ( in_path @ SV619 @ SV611 )
| ~ ( path @ SV579 @ SV591 @ SV611 )
| ( vertex @ SV619 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2975]) ).
thf(3002,plain,
! [SV603: $i,SV598: $i,SV580: $i] :
( ( ( ~ ! [SY923: $i,SY924: $i] :
( ~ ( on_path @ SY923 @ SV580 )
| ~ ( on_path @ SY924 @ SV580 )
| ! [SY925: $i] :
( ~ ( precedes @ SY925 @ SY924 @ SV580 )
| ~ ( sequential @ SY923 @ SY925 ) )
| ( precedes @ SY923 @ SY924 @ SV580 ) ) )
= $false )
| ( ( path @ SV598 @ SV603 @ SV580 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2976]) ).
thf(3003,plain,
! [SV603: $i,SV598: $i,SV580: $i] :
( ( ( ~ ! [SY926: $i,SY927: $i] :
( ~ ( on_path @ SY926 @ SV580 )
| ~ ( on_path @ SY927 @ SV580 )
| ~ ( sequential @ SY926 @ SY927 )
| ( precedes @ SY926 @ SY927 @ SV580 ) ) )
= $false )
| ( ( path @ SV598 @ SV603 @ SV580 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2976]) ).
thf(3004,plain,
! [SV612: $i,SV605: $i,SV581: $i] :
( ( ( ~ ( edge @ SV581 )
| ~ ( edge @ SV605 )
| ~ ( edge @ SV612 )
| ~ ( sequential @ SV581 @ SV605 )
| ~ ( sequential @ SV605 @ SV612 )
| ~ ( sequential @ SV612 @ SV581 ) )
= $true )
| ( ( triangle @ SV581 @ SV605 @ SV612 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2977]) ).
thf(3005,plain,
! [SV581: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY930: $i,SY931: $i] :
~ ( triangle @ SV581 @ SY930 @ SY931 )
| ( edge @ SV581 ) )
| ~ ! [SY932: $i] :
( ! [SY933: $i] :
~ ( triangle @ SV581 @ SY932 @ SY933 )
| ( edge @ SY932 ) ) )
| ~ ! [SY934: $i,SY935: $i] :
( ~ ( triangle @ SV581 @ SY934 @ SY935 )
| ( edge @ SY935 ) ) )
| ~ ! [SY936: $i] :
( ! [SY937: $i] :
~ ( triangle @ SV581 @ SY936 @ SY937 )
| ( sequential @ SV581 @ SY936 ) ) )
| ~ ! [SY938: $i,SY939: $i] :
( ~ ( triangle @ SV581 @ SY938 @ SY939 )
| ( sequential @ SY938 @ SY939 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2978]) ).
thf(3006,plain,
! [SV581: $i] :
( ( ! [SY940: $i,SY941: $i] :
( ~ ( triangle @ SV581 @ SY940 @ SY941 )
| ( sequential @ SY941 @ SV581 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2979]) ).
thf(3007,plain,
! [SV606: $i,SV604: $i] :
( ( ( ( SV604 = SV606 )
| ~ ( edge @ SV604 )
| ~ ( edge @ SV606 ) )
= $true )
| ( ( ( ( head_of @ SV604 )
!= ( tail_of @ SV606 ) ) )
= $true )
| ( ( sequential @ SV604 @ SV606 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2980]) ).
thf(3008,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2981]) ).
thf(3009,plain,
! [SV620: $i] :
( ( ! [SY1006: $i] :
( ~ ( sequential @ SV620 @ SY1006 )
| ( ( head_of @ SV620 )
= ( tail_of @ SY1006 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2982]) ).
thf(3010,plain,
! [SV582: $i] :
( ( ! [SY942: $i,SY943: $i] :
~ ( path @ SV582 @ SY942 @ SY943 )
| ( vertex @ SV582 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2983]) ).
thf(3011,plain,
! [SV582: $i] :
( ( ! [SY944: $i] :
( ! [SY945: $i] :
~ ( path @ SV582 @ SY944 @ SY945 )
| ( vertex @ SY944 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2984]) ).
thf(3012,plain,
! [SV613: $i,SV607: $i,SV582: $i] :
( ( ( ~ ( path @ SV582 @ SV607 @ SV613 ) )
= $true )
| ( ( ~ ( ~ ~ ( ( SV582
!= ( tail_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( edge @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
| ~ ~ ( ~ ( ( SV607
!= ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
| ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ empty ) )
| ! [SY1002: $i] :
( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ SY1002 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ SY1002 ) ) )
| ~ ~ ( ~ ( ( SV607
= ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ ( sK13_SY84 @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ ( sK13_SY84 @ SV613 @ SV607 @ SV582 ) ) ) )
| ~ ( ( SV613
= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ empty ) )
| ~ ( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ ( sK12_SY85 @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ ( sK12_SY85 @ SV613 @ SV607 @ SV582 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2985]) ).
thf(3013,plain,
! [SV614: $i,SV608: $i,SV583: $i] :
( ( ( ~ ( ~ ( path @ SV583 @ SV608 @ ( sK8_P @ SV614 @ SV608 @ SV583 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SV614 ) @ ( length_of @ ( sK8_P @ SV614 @ SV608 @ SV583 ) ) ) )
| ( SV583 = SV608 )
| ~ ( path @ SV583 @ SV608 @ SV614 ) )
= $true )
| ( ( shortest_path @ SV583 @ SV608 @ SV614 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2986]) ).
thf(3014,plain,
! [SV583: $i] :
( ( ! [SY951: $i,SY952: $i] :
( ~ ( shortest_path @ SV583 @ SY951 @ SY952 )
| ! [SY953: $i] :
( ~ ( path @ SV583 @ SY951 @ SY953 )
| ( less_or_equal @ ( length_of @ SY952 ) @ ( length_of @ SY953 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2987]) ).
thf(3015,plain,
! [SV583: $i] :
( ( ~ ( ~ ! [SY954: $i] :
( ! [SY955: $i] :
~ ( shortest_path @ SV583 @ SY954 @ SY955 )
| ( SV583 != SY954 ) )
| ~ ! [SY956: $i,SY957: $i] :
( ~ ( shortest_path @ SV583 @ SY956 @ SY957 )
| ( path @ SV583 @ SY956 @ SY957 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2988]) ).
thf(3016,plain,
! [SV584: $i] :
( ( ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV584 ) @ SV584 )
| ~ ( on_path @ ( sK7_SY80 @ SV584 ) @ SV584 ) )
| ~ ( sequential @ ( sK6_E1 @ SV584 ) @ ( sK7_SY80 @ SV584 ) ) )
= $false )
| ( ( ! [SY959: $i,SY960: $i] :
~ ( path @ SY959 @ SY960 @ SV584 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV584 )
= ( number_of_in @ triangles @ SV584 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2989]) ).
thf(3017,plain,
! [SV621: $i,SV584: $i] :
( ( ( ~ ( triangle @ ( sK6_E1 @ SV584 ) @ ( sK7_SY80 @ SV584 ) @ SV621 ) )
= $true )
| ( ( ! [SY959: $i,SY960: $i] :
~ ( path @ SY959 @ SY960 @ SV584 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV584 )
= ( number_of_in @ triangles @ SV584 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2990]) ).
thf(3018,plain,
! [SV588: $i,SV575: $i] :
( ( ! [SY963: $i,SY964: $i] :
( ~ ( on_path @ SY964 @ SY963 )
| ~ ( path @ SV575 @ SV588 @ SY963 )
| ( edge @ SY964 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2991]) ).
thf(3019,plain,
! [SV588: $i,SV575: $i] :
( ( ! [SY965: $i,SY966: $i] :
( ~ ( on_path @ SY966 @ SY965 )
| ~ ( path @ SV575 @ SV588 @ SY965 )
| ( in_path @ ( head_of @ SY966 ) @ SY965 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2992]) ).
thf(3020,plain,
! [SV588: $i,SV575: $i,SV609: $i,SV615: $i] :
( ( ( ~ ( on_path @ SV615 @ SV609 )
| ~ ( path @ SV575 @ SV588 @ SV609 ) )
= $true )
| ( ( in_path @ ( tail_of @ SV615 ) @ SV609 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2993]) ).
thf(3021,plain,
! [SV594: $i,SV576: $i,SV589: $i] :
( ( ( vertex @ SV589 )
= $false )
| ( ( vertex @ SV576 )
= $false )
| ( ( ~ ( ~ ! [SY983: $i] :
( ( SV576
!= ( tail_of @ SY983 ) )
| ~ ( edge @ SY983 )
| ( SV589
!= ( head_of @ SY983 ) )
| ( SV594
!= ( path_cons @ SY983 @ empty ) ) )
| ~ ! [SY984: $i] :
( ( SV576
!= ( tail_of @ SY984 ) )
| ~ ( edge @ SY984 )
| ! [SY985: $i] :
( ( SV594
!= ( path_cons @ SY984 @ SY985 ) )
| ~ ( path @ ( head_of @ SY984 ) @ SV589 @ SY985 ) ) ) ) )
= $true )
| ( ( path @ SV576 @ SV589 @ SV594 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2994]) ).
thf(3022,plain,
! [SV590: $i,SV577: $i,SV616: $i,SV595: $i] :
( ( ( ! [SY1003: $i] :
( ~ ( precedes @ SV595 @ SV616 @ SY1003 )
| ~ ( shortest_path @ SV577 @ SV590 @ SY1003 ) ) )
= $true )
| ( ( ! [SY1004: $i] :
( ( ( tail_of @ SY1004 )
!= ( tail_of @ SV595 ) )
| ( ( head_of @ SY1004 )
!= ( head_of @ SV616 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2995]) ).
thf(3023,plain,
! [SV590: $i,SV577: $i,SV622: $i,SV617: $i,SV595: $i] :
( ( ~ ( precedes @ SV595 @ SV617 @ SV622 )
| ~ ( shortest_path @ SV577 @ SV590 @ SV622 )
| ~ ( precedes @ SV617 @ SV595 @ SV622 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2996]) ).
thf(3024,plain,
! [SV599: $i,SV596: $i] :
( ( ( vertex @ SV596 )
= $false )
| ( ( ~ ( vertex @ SV599 ) )
= $true )
| ( ( SV596 = SV599 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV596
!= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
!= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
!= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
!= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV596
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
| ~ ( ( SV596
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) ) )
| ~ ~ ( ~ ( ( SV599
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
| ~ ( ( SV599
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV599 @ SV596 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[2997]) ).
thf(3025,plain,
! [SV602: $i,SV597: $i,SV578: $i] :
( ( ( ~ ( ~ ! [SY907: $i] :
( ! [SY908: $i] :
~ ( precedes @ SY907 @ SY908 @ SV578 )
| ( on_path @ SY907 @ SV578 ) )
| ~ ! [SY909: $i,SY910: $i] :
( ~ ( precedes @ SY909 @ SY910 @ SV578 )
| ( on_path @ SY910 @ SV578 ) ) ) )
= $true )
| ( ( path @ SV597 @ SV602 @ SV578 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2998]) ).
thf(3026,plain,
! [SV602: $i,SV597: $i,SV578: $i] :
( ( ( ~ ( ~ ! [SY911: $i,SY912: $i] :
( ~ ( precedes @ SY911 @ SY912 @ SV578 )
| ! [SY913: $i] :
( ~ ( precedes @ SY913 @ SY912 @ SV578 )
| ~ ( sequential @ SY911 @ SY913 ) )
| ~ ( sequential @ SY911 @ SY912 ) )
| ~ ! [SY914: $i,SY915: $i] :
( ~ ( precedes @ SY914 @ SY915 @ SV578 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY915 @ SY914 @ SV578 ) @ SY915 @ SV578 )
| ~ ( sequential @ SY914 @ ( sK9_E3 @ SY915 @ SY914 @ SV578 ) ) )
| ( sequential @ SY914 @ SY915 ) ) ) )
= $true )
| ( ( path @ SV597 @ SV602 @ SV578 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2999]) ).
thf(3027,plain,
! [SV591: $i,SV579: $i,SV610: $i,SV618: $i] :
( ( ( ~ ( in_path @ SV618 @ SV610 )
| ~ ( path @ SV579 @ SV591 @ SV610 ) )
= $true )
| ( ( ~ ( ~ ( on_path @ ( sK10_E @ SV618 @ SV610 @ SV591 @ SV579 ) @ SV610 )
| ~ ( ( SV618
= ( head_of @ ( sK10_E @ SV618 @ SV610 @ SV591 @ SV579 ) ) )
| ( SV618
= ( tail_of @ ( sK10_E @ SV618 @ SV610 @ SV591 @ SV579 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3000]) ).
thf(3028,plain,
! [SV591: $i,SV579: $i,SV611: $i,SV619: $i] :
( ( ( ~ ( in_path @ SV619 @ SV611 )
| ~ ( path @ SV579 @ SV591 @ SV611 ) )
= $true )
| ( ( vertex @ SV619 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3001]) ).
thf(3029,plain,
! [SV603: $i,SV598: $i,SV580: $i] :
( ( ( ! [SY923: $i,SY924: $i] :
( ~ ( on_path @ SY923 @ SV580 )
| ~ ( on_path @ SY924 @ SV580 )
| ! [SY925: $i] :
( ~ ( precedes @ SY925 @ SY924 @ SV580 )
| ~ ( sequential @ SY923 @ SY925 ) )
| ( precedes @ SY923 @ SY924 @ SV580 ) ) )
= $true )
| ( ( path @ SV598 @ SV603 @ SV580 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3002]) ).
thf(3030,plain,
! [SV603: $i,SV598: $i,SV580: $i] :
( ( ( ! [SY926: $i,SY927: $i] :
( ~ ( on_path @ SY926 @ SV580 )
| ~ ( on_path @ SY927 @ SV580 )
| ~ ( sequential @ SY926 @ SY927 )
| ( precedes @ SY926 @ SY927 @ SV580 ) ) )
= $true )
| ( ( path @ SV598 @ SV603 @ SV580 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3003]) ).
thf(3031,plain,
! [SV612: $i,SV605: $i,SV581: $i] :
( ( ( ~ ( edge @ SV581 )
| ~ ( edge @ SV605 )
| ~ ( edge @ SV612 )
| ~ ( sequential @ SV581 @ SV605 )
| ~ ( sequential @ SV605 @ SV612 ) )
= $true )
| ( ( ~ ( sequential @ SV612 @ SV581 ) )
= $true )
| ( ( triangle @ SV581 @ SV605 @ SV612 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3004]) ).
thf(3032,plain,
! [SV581: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY930: $i,SY931: $i] :
~ ( triangle @ SV581 @ SY930 @ SY931 )
| ( edge @ SV581 ) )
| ~ ! [SY932: $i] :
( ! [SY933: $i] :
~ ( triangle @ SV581 @ SY932 @ SY933 )
| ( edge @ SY932 ) ) )
| ~ ! [SY934: $i,SY935: $i] :
( ~ ( triangle @ SV581 @ SY934 @ SY935 )
| ( edge @ SY935 ) ) )
| ~ ! [SY936: $i] :
( ! [SY937: $i] :
~ ( triangle @ SV581 @ SY936 @ SY937 )
| ( sequential @ SV581 @ SY936 ) ) )
| ~ ! [SY938: $i,SY939: $i] :
( ~ ( triangle @ SV581 @ SY938 @ SY939 )
| ( sequential @ SY938 @ SY939 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3005]) ).
thf(3033,plain,
! [SV623: $i,SV581: $i] :
( ( ! [SY1007: $i] :
( ~ ( triangle @ SV581 @ SV623 @ SY1007 )
| ( sequential @ SY1007 @ SV581 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3006]) ).
thf(3034,plain,
! [SV606: $i,SV604: $i] :
( ( ( SV604 = SV606 )
= $true )
| ( ( ~ ( edge @ SV604 )
| ~ ( edge @ SV606 ) )
= $true )
| ( ( ( ( head_of @ SV604 )
!= ( tail_of @ SV606 ) ) )
= $true )
| ( ( sequential @ SV604 @ SV606 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3007]) ).
thf(3035,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3008]) ).
thf(3036,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3008]) ).
thf(3037,plain,
! [SV624: $i,SV620: $i] :
( ( ~ ( sequential @ SV620 @ SV624 )
| ( ( head_of @ SV620 )
= ( tail_of @ SV624 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3009]) ).
thf(3038,plain,
! [SV582: $i] :
( ( ( ! [SY942: $i,SY943: $i] :
~ ( path @ SV582 @ SY942 @ SY943 ) )
= $true )
| ( ( vertex @ SV582 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3010]) ).
thf(3039,plain,
! [SV625: $i,SV582: $i] :
( ( ! [SY1008: $i] :
~ ( path @ SV582 @ SV625 @ SY1008 )
| ( vertex @ SV625 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3011]) ).
thf(3040,plain,
! [SV613: $i,SV607: $i,SV582: $i] :
( ( ( path @ SV582 @ SV607 @ SV613 )
= $false )
| ( ( ~ ( ~ ~ ( ( SV582
!= ( tail_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( edge @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
| ~ ~ ( ~ ( ( SV607
!= ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
| ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ empty ) )
| ! [SY1002: $i] :
( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ SY1002 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ SY1002 ) ) )
| ~ ~ ( ~ ( ( SV607
= ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ ( sK13_SY84 @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ ( sK13_SY84 @ SV613 @ SV607 @ SV582 ) ) ) )
| ~ ( ( SV613
= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ empty ) )
| ~ ( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ ( sK12_SY85 @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ ( sK12_SY85 @ SV613 @ SV607 @ SV582 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3012]) ).
thf(3041,plain,
! [SV614: $i,SV608: $i,SV583: $i] :
( ( ( ~ ( ~ ( path @ SV583 @ SV608 @ ( sK8_P @ SV614 @ SV608 @ SV583 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SV614 ) @ ( length_of @ ( sK8_P @ SV614 @ SV608 @ SV583 ) ) ) ) )
= $true )
| ( ( ( SV583 = SV608 )
| ~ ( path @ SV583 @ SV608 @ SV614 ) )
= $true )
| ( ( shortest_path @ SV583 @ SV608 @ SV614 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3013]) ).
thf(3042,plain,
! [SV626: $i,SV583: $i] :
( ( ! [SY1009: $i] :
( ~ ( shortest_path @ SV583 @ SV626 @ SY1009 )
| ! [SY1010: $i] :
( ~ ( path @ SV583 @ SV626 @ SY1010 )
| ( less_or_equal @ ( length_of @ SY1009 ) @ ( length_of @ SY1010 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3014]) ).
thf(3043,plain,
! [SV583: $i] :
( ( ~ ! [SY954: $i] :
( ! [SY955: $i] :
~ ( shortest_path @ SV583 @ SY954 @ SY955 )
| ( SV583 != SY954 ) )
| ~ ! [SY956: $i,SY957: $i] :
( ~ ( shortest_path @ SV583 @ SY956 @ SY957 )
| ( path @ SV583 @ SY956 @ SY957 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3015]) ).
thf(3044,plain,
! [SV584: $i] :
( ( ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV584 ) @ SV584 )
| ~ ( on_path @ ( sK7_SY80 @ SV584 ) @ SV584 ) ) )
= $false )
| ( ( ! [SY959: $i,SY960: $i] :
~ ( path @ SY959 @ SY960 @ SV584 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV584 )
= ( number_of_in @ triangles @ SV584 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3016]) ).
thf(3045,plain,
! [SV584: $i] :
( ( ( ~ ( sequential @ ( sK6_E1 @ SV584 ) @ ( sK7_SY80 @ SV584 ) ) )
= $false )
| ( ( ! [SY959: $i,SY960: $i] :
~ ( path @ SY959 @ SY960 @ SV584 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV584 )
= ( number_of_in @ triangles @ SV584 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3016]) ).
thf(3046,plain,
! [SV621: $i,SV584: $i] :
( ( ( triangle @ ( sK6_E1 @ SV584 ) @ ( sK7_SY80 @ SV584 ) @ SV621 )
= $false )
| ( ( ! [SY959: $i,SY960: $i] :
~ ( path @ SY959 @ SY960 @ SV584 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV584 )
= ( number_of_in @ triangles @ SV584 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3017]) ).
thf(3047,plain,
! [SV588: $i,SV575: $i,SV627: $i] :
( ( ! [SY1011: $i] :
( ~ ( on_path @ SY1011 @ SV627 )
| ~ ( path @ SV575 @ SV588 @ SV627 )
| ( edge @ SY1011 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3018]) ).
thf(3048,plain,
! [SV588: $i,SV575: $i,SV628: $i] :
( ( ! [SY1012: $i] :
( ~ ( on_path @ SY1012 @ SV628 )
| ~ ( path @ SV575 @ SV588 @ SV628 )
| ( in_path @ ( head_of @ SY1012 ) @ SV628 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3019]) ).
thf(3049,plain,
! [SV588: $i,SV575: $i,SV609: $i,SV615: $i] :
( ( ( ~ ( on_path @ SV615 @ SV609 ) )
= $true )
| ( ( ~ ( path @ SV575 @ SV588 @ SV609 ) )
= $true )
| ( ( in_path @ ( tail_of @ SV615 ) @ SV609 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3020]) ).
thf(3050,plain,
! [SV594: $i,SV589: $i,SV576: $i] :
( ( ( ~ ! [SY983: $i] :
( ( SV576
!= ( tail_of @ SY983 ) )
| ~ ( edge @ SY983 )
| ( SV589
!= ( head_of @ SY983 ) )
| ( SV594
!= ( path_cons @ SY983 @ empty ) ) )
| ~ ! [SY984: $i] :
( ( SV576
!= ( tail_of @ SY984 ) )
| ~ ( edge @ SY984 )
| ! [SY985: $i] :
( ( SV594
!= ( path_cons @ SY984 @ SY985 ) )
| ~ ( path @ ( head_of @ SY984 ) @ SV589 @ SY985 ) ) ) )
= $false )
| ( ( vertex @ SV576 )
= $false )
| ( ( vertex @ SV589 )
= $false )
| ( ( path @ SV576 @ SV589 @ SV594 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3021]) ).
thf(3051,plain,
! [SV590: $i,SV577: $i,SV629: $i,SV616: $i,SV595: $i] :
( ( ( ~ ( precedes @ SV595 @ SV616 @ SV629 )
| ~ ( shortest_path @ SV577 @ SV590 @ SV629 ) )
= $true )
| ( ( ! [SY1004: $i] :
( ( ( tail_of @ SY1004 )
!= ( tail_of @ SV595 ) )
| ( ( head_of @ SY1004 )
!= ( head_of @ SV616 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3022]) ).
thf(3052,plain,
! [SV590: $i,SV577: $i,SV622: $i,SV617: $i,SV595: $i] :
( ( ( ~ ( precedes @ SV595 @ SV617 @ SV622 )
| ~ ( shortest_path @ SV577 @ SV590 @ SV622 ) )
= $true )
| ( ( ~ ( precedes @ SV617 @ SV595 @ SV622 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3023]) ).
thf(3053,plain,
! [SV596: $i,SV599: $i] :
( ( ( vertex @ SV599 )
= $false )
| ( ( vertex @ SV596 )
= $false )
| ( ( SV596 = SV599 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV596
!= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
!= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
!= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
!= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV596
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
| ~ ( ( SV596
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) ) )
| ~ ~ ( ~ ( ( SV599
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
| ~ ( ( SV599
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV599 @ SV596 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[3024]) ).
thf(3054,plain,
! [SV602: $i,SV597: $i,SV578: $i] :
( ( ( ~ ! [SY907: $i] :
( ! [SY908: $i] :
~ ( precedes @ SY907 @ SY908 @ SV578 )
| ( on_path @ SY907 @ SV578 ) )
| ~ ! [SY909: $i,SY910: $i] :
( ~ ( precedes @ SY909 @ SY910 @ SV578 )
| ( on_path @ SY910 @ SV578 ) ) )
= $false )
| ( ( path @ SV597 @ SV602 @ SV578 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3025]) ).
thf(3055,plain,
! [SV602: $i,SV597: $i,SV578: $i] :
( ( ( ~ ! [SY911: $i,SY912: $i] :
( ~ ( precedes @ SY911 @ SY912 @ SV578 )
| ! [SY913: $i] :
( ~ ( precedes @ SY913 @ SY912 @ SV578 )
| ~ ( sequential @ SY911 @ SY913 ) )
| ~ ( sequential @ SY911 @ SY912 ) )
| ~ ! [SY914: $i,SY915: $i] :
( ~ ( precedes @ SY914 @ SY915 @ SV578 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY915 @ SY914 @ SV578 ) @ SY915 @ SV578 )
| ~ ( sequential @ SY914 @ ( sK9_E3 @ SY915 @ SY914 @ SV578 ) ) )
| ( sequential @ SY914 @ SY915 ) ) )
= $false )
| ( ( path @ SV597 @ SV602 @ SV578 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3026]) ).
thf(3056,plain,
! [SV591: $i,SV579: $i,SV610: $i,SV618: $i] :
( ( ( ~ ( in_path @ SV618 @ SV610 ) )
= $true )
| ( ( ~ ( path @ SV579 @ SV591 @ SV610 ) )
= $true )
| ( ( ~ ( ~ ( on_path @ ( sK10_E @ SV618 @ SV610 @ SV591 @ SV579 ) @ SV610 )
| ~ ( ( SV618
= ( head_of @ ( sK10_E @ SV618 @ SV610 @ SV591 @ SV579 ) ) )
| ( SV618
= ( tail_of @ ( sK10_E @ SV618 @ SV610 @ SV591 @ SV579 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3027]) ).
thf(3057,plain,
! [SV591: $i,SV579: $i,SV611: $i,SV619: $i] :
( ( ( ~ ( in_path @ SV619 @ SV611 ) )
= $true )
| ( ( ~ ( path @ SV579 @ SV591 @ SV611 ) )
= $true )
| ( ( vertex @ SV619 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3028]) ).
thf(3058,plain,
! [SV603: $i,SV598: $i,SV580: $i,SV630: $i] :
( ( ( ! [SY1013: $i] :
( ~ ( on_path @ SV630 @ SV580 )
| ~ ( on_path @ SY1013 @ SV580 )
| ! [SY1014: $i] :
( ~ ( precedes @ SY1014 @ SY1013 @ SV580 )
| ~ ( sequential @ SV630 @ SY1014 ) )
| ( precedes @ SV630 @ SY1013 @ SV580 ) ) )
= $true )
| ( ( path @ SV598 @ SV603 @ SV580 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3029]) ).
thf(3059,plain,
! [SV603: $i,SV598: $i,SV580: $i,SV631: $i] :
( ( ( ! [SY1015: $i] :
( ~ ( on_path @ SV631 @ SV580 )
| ~ ( on_path @ SY1015 @ SV580 )
| ~ ( sequential @ SV631 @ SY1015 )
| ( precedes @ SV631 @ SY1015 @ SV580 ) ) )
= $true )
| ( ( path @ SV598 @ SV603 @ SV580 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3030]) ).
thf(3060,plain,
! [SV612: $i,SV605: $i,SV581: $i] :
( ( ( ~ ( edge @ SV581 )
| ~ ( edge @ SV605 )
| ~ ( edge @ SV612 )
| ~ ( sequential @ SV581 @ SV605 ) )
= $true )
| ( ( ~ ( sequential @ SV605 @ SV612 ) )
= $true )
| ( ( ~ ( sequential @ SV612 @ SV581 ) )
= $true )
| ( ( triangle @ SV581 @ SV605 @ SV612 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3031]) ).
thf(3061,plain,
! [SV581: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY930: $i,SY931: $i] :
~ ( triangle @ SV581 @ SY930 @ SY931 )
| ( edge @ SV581 ) )
| ~ ! [SY932: $i] :
( ! [SY933: $i] :
~ ( triangle @ SV581 @ SY932 @ SY933 )
| ( edge @ SY932 ) ) )
| ~ ! [SY934: $i,SY935: $i] :
( ~ ( triangle @ SV581 @ SY934 @ SY935 )
| ( edge @ SY935 ) ) )
| ~ ! [SY936: $i] :
( ! [SY937: $i] :
~ ( triangle @ SV581 @ SY936 @ SY937 )
| ( sequential @ SV581 @ SY936 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3032]) ).
thf(3062,plain,
! [SV581: $i] :
( ( ~ ! [SY938: $i,SY939: $i] :
( ~ ( triangle @ SV581 @ SY938 @ SY939 )
| ( sequential @ SY938 @ SY939 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3032]) ).
thf(3063,plain,
! [SV632: $i,SV623: $i,SV581: $i] :
( ( ~ ( triangle @ SV581 @ SV623 @ SV632 )
| ( sequential @ SV632 @ SV581 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3033]) ).
thf(3064,plain,
! [SV606: $i,SV604: $i] :
( ( ( ~ ( edge @ SV604 ) )
= $true )
| ( ( ~ ( edge @ SV606 ) )
= $true )
| ( ( SV604 = SV606 )
= $true )
| ( ( ( ( head_of @ SV604 )
!= ( tail_of @ SV606 ) ) )
= $true )
| ( ( sequential @ SV604 @ SV606 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3034]) ).
thf(3065,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3035]) ).
thf(3066,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3036]) ).
thf(3067,plain,
! [SV624: $i,SV620: $i] :
( ( ( ~ ( sequential @ SV620 @ SV624 ) )
= $true )
| ( ( ( head_of @ SV620 )
= ( tail_of @ SV624 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3037]) ).
thf(3068,plain,
! [SV633: $i,SV582: $i] :
( ( ( ! [SY1016: $i] :
~ ( path @ SV582 @ SV633 @ SY1016 ) )
= $true )
| ( ( vertex @ SV582 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3038]) ).
thf(3069,plain,
! [SV625: $i,SV582: $i] :
( ( ( ! [SY1008: $i] :
~ ( path @ SV582 @ SV625 @ SY1008 ) )
= $true )
| ( ( vertex @ SV625 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3039]) ).
thf(3070,plain,
! [SV607: $i,SV613: $i,SV582: $i] :
( ( ( ~ ~ ( ( SV582
!= ( tail_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( edge @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
| ~ ~ ( ~ ( ( SV607
!= ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
| ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ empty ) )
| ! [SY1002: $i] :
( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ SY1002 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ SY1002 ) ) )
| ~ ~ ( ~ ( ( SV607
= ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ ( sK13_SY84 @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ ( sK13_SY84 @ SV613 @ SV607 @ SV582 ) ) ) )
| ~ ( ( SV613
= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ empty ) )
| ~ ( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ ( sK12_SY85 @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ ( sK12_SY85 @ SV613 @ SV607 @ SV582 ) ) ) ) ) ) )
= $false )
| ( ( path @ SV582 @ SV607 @ SV613 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3040]) ).
thf(3071,plain,
! [SV614: $i,SV608: $i,SV583: $i] :
( ( ( ~ ( path @ SV583 @ SV608 @ ( sK8_P @ SV614 @ SV608 @ SV583 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SV614 ) @ ( length_of @ ( sK8_P @ SV614 @ SV608 @ SV583 ) ) ) )
= $false )
| ( ( ( SV583 = SV608 )
| ~ ( path @ SV583 @ SV608 @ SV614 ) )
= $true )
| ( ( shortest_path @ SV583 @ SV608 @ SV614 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3041]) ).
thf(3072,plain,
! [SV634: $i,SV626: $i,SV583: $i] :
( ( ~ ( shortest_path @ SV583 @ SV626 @ SV634 )
| ! [SY1017: $i] :
( ~ ( path @ SV583 @ SV626 @ SY1017 )
| ( less_or_equal @ ( length_of @ SV634 ) @ ( length_of @ SY1017 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3042]) ).
thf(3073,plain,
! [SV583: $i] :
( ( ~ ! [SY954: $i] :
( ! [SY955: $i] :
~ ( shortest_path @ SV583 @ SY954 @ SY955 )
| ( SV583 != SY954 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3043]) ).
thf(3074,plain,
! [SV583: $i] :
( ( ~ ! [SY956: $i,SY957: $i] :
( ~ ( shortest_path @ SV583 @ SY956 @ SY957 )
| ( path @ SV583 @ SY956 @ SY957 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3043]) ).
thf(3075,plain,
! [SV584: $i] :
( ( ( ~ ( ~ ( on_path @ ( sK6_E1 @ SV584 ) @ SV584 )
| ~ ( on_path @ ( sK7_SY80 @ SV584 ) @ SV584 ) ) )
= $true )
| ( ( ! [SY959: $i,SY960: $i] :
~ ( path @ SY959 @ SY960 @ SV584 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV584 )
= ( number_of_in @ triangles @ SV584 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3044]) ).
thf(3076,plain,
! [SV584: $i] :
( ( ( sequential @ ( sK6_E1 @ SV584 ) @ ( sK7_SY80 @ SV584 ) )
= $true )
| ( ( ! [SY959: $i,SY960: $i] :
~ ( path @ SY959 @ SY960 @ SV584 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV584 )
= ( number_of_in @ triangles @ SV584 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3045]) ).
thf(3077,plain,
! [SV621: $i,SV584: $i,SV635: $i] :
( ( ( ! [SY1018: $i] :
~ ( path @ SV635 @ SY1018 @ SV584 ) )
= $true )
| ( ( triangle @ ( sK6_E1 @ SV584 ) @ ( sK7_SY80 @ SV584 ) @ SV621 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV584 )
= ( number_of_in @ triangles @ SV584 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3046]) ).
thf(3078,plain,
! [SV588: $i,SV575: $i,SV627: $i,SV636: $i] :
( ( ~ ( on_path @ SV636 @ SV627 )
| ~ ( path @ SV575 @ SV588 @ SV627 )
| ( edge @ SV636 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3047]) ).
thf(3079,plain,
! [SV588: $i,SV575: $i,SV628: $i,SV637: $i] :
( ( ~ ( on_path @ SV637 @ SV628 )
| ~ ( path @ SV575 @ SV588 @ SV628 )
| ( in_path @ ( head_of @ SV637 ) @ SV628 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3048]) ).
thf(3080,plain,
! [SV588: $i,SV575: $i,SV609: $i,SV615: $i] :
( ( ( on_path @ SV615 @ SV609 )
= $false )
| ( ( ~ ( path @ SV575 @ SV588 @ SV609 ) )
= $true )
| ( ( in_path @ ( tail_of @ SV615 ) @ SV609 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3049]) ).
thf(3081,plain,
! [SV594: $i,SV589: $i,SV576: $i] :
( ( ( ~ ! [SY983: $i] :
( ( SV576
!= ( tail_of @ SY983 ) )
| ~ ( edge @ SY983 )
| ( SV589
!= ( head_of @ SY983 ) )
| ( SV594
!= ( path_cons @ SY983 @ empty ) ) ) )
= $false )
| ( ( vertex @ SV576 )
= $false )
| ( ( vertex @ SV589 )
= $false )
| ( ( path @ SV576 @ SV589 @ SV594 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3050]) ).
thf(3082,plain,
! [SV589: $i,SV594: $i,SV576: $i] :
( ( ( ~ ! [SY984: $i] :
( ( SV576
!= ( tail_of @ SY984 ) )
| ~ ( edge @ SY984 )
| ! [SY985: $i] :
( ( SV594
!= ( path_cons @ SY984 @ SY985 ) )
| ~ ( path @ ( head_of @ SY984 ) @ SV589 @ SY985 ) ) ) )
= $false )
| ( ( vertex @ SV576 )
= $false )
| ( ( vertex @ SV589 )
= $false )
| ( ( path @ SV576 @ SV589 @ SV594 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3050]) ).
thf(3083,plain,
! [SV590: $i,SV577: $i,SV629: $i,SV616: $i,SV595: $i] :
( ( ( ~ ( precedes @ SV595 @ SV616 @ SV629 ) )
= $true )
| ( ( ~ ( shortest_path @ SV577 @ SV590 @ SV629 ) )
= $true )
| ( ( ! [SY1004: $i] :
( ( ( tail_of @ SY1004 )
!= ( tail_of @ SV595 ) )
| ( ( head_of @ SY1004 )
!= ( head_of @ SV616 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3051]) ).
thf(3084,plain,
! [SV590: $i,SV577: $i,SV622: $i,SV617: $i,SV595: $i] :
( ( ( ~ ( precedes @ SV595 @ SV617 @ SV622 ) )
= $true )
| ( ( ~ ( shortest_path @ SV577 @ SV590 @ SV622 ) )
= $true )
| ( ( ~ ( precedes @ SV617 @ SV595 @ SV622 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3052]) ).
thf(3085,plain,
! [SV599: $i,SV596: $i] :
( ( ( ~ ~ ( ~ ( ( SV596
!= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
!= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
!= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
!= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV596
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
| ~ ( ( SV596
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) ) )
| ~ ~ ( ~ ( ( SV599
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
| ~ ( ( SV599
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV599 @ SV596 ) ) )
= $false )
| ( ( SV596 = SV599 )
= $true )
| ( ( vertex @ SV596 )
= $false )
| ( ( vertex @ SV599 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[3053]) ).
thf(3086,plain,
! [SV602: $i,SV597: $i,SV578: $i] :
( ( ( ~ ! [SY907: $i] :
( ! [SY908: $i] :
~ ( precedes @ SY907 @ SY908 @ SV578 )
| ( on_path @ SY907 @ SV578 ) ) )
= $false )
| ( ( path @ SV597 @ SV602 @ SV578 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3054]) ).
thf(3087,plain,
! [SV602: $i,SV597: $i,SV578: $i] :
( ( ( ~ ! [SY909: $i,SY910: $i] :
( ~ ( precedes @ SY909 @ SY910 @ SV578 )
| ( on_path @ SY910 @ SV578 ) ) )
= $false )
| ( ( path @ SV597 @ SV602 @ SV578 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3054]) ).
thf(3088,plain,
! [SV602: $i,SV597: $i,SV578: $i] :
( ( ( ~ ! [SY911: $i,SY912: $i] :
( ~ ( precedes @ SY911 @ SY912 @ SV578 )
| ! [SY913: $i] :
( ~ ( precedes @ SY913 @ SY912 @ SV578 )
| ~ ( sequential @ SY911 @ SY913 ) )
| ~ ( sequential @ SY911 @ SY912 ) ) )
= $false )
| ( ( path @ SV597 @ SV602 @ SV578 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3055]) ).
thf(3089,plain,
! [SV602: $i,SV597: $i,SV578: $i] :
( ( ( ~ ! [SY914: $i,SY915: $i] :
( ~ ( precedes @ SY914 @ SY915 @ SV578 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY915 @ SY914 @ SV578 ) @ SY915 @ SV578 )
| ~ ( sequential @ SY914 @ ( sK9_E3 @ SY915 @ SY914 @ SV578 ) ) )
| ( sequential @ SY914 @ SY915 ) ) )
= $false )
| ( ( path @ SV597 @ SV602 @ SV578 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3055]) ).
thf(3090,plain,
! [SV591: $i,SV579: $i,SV610: $i,SV618: $i] :
( ( ( in_path @ SV618 @ SV610 )
= $false )
| ( ( ~ ( path @ SV579 @ SV591 @ SV610 ) )
= $true )
| ( ( ~ ( ~ ( on_path @ ( sK10_E @ SV618 @ SV610 @ SV591 @ SV579 ) @ SV610 )
| ~ ( ( SV618
= ( head_of @ ( sK10_E @ SV618 @ SV610 @ SV591 @ SV579 ) ) )
| ( SV618
= ( tail_of @ ( sK10_E @ SV618 @ SV610 @ SV591 @ SV579 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3056]) ).
thf(3091,plain,
! [SV591: $i,SV579: $i,SV611: $i,SV619: $i] :
( ( ( in_path @ SV619 @ SV611 )
= $false )
| ( ( ~ ( path @ SV579 @ SV591 @ SV611 ) )
= $true )
| ( ( vertex @ SV619 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3057]) ).
thf(3092,plain,
! [SV603: $i,SV598: $i,SV638: $i,SV580: $i,SV630: $i] :
( ( ( ~ ( on_path @ SV630 @ SV580 )
| ~ ( on_path @ SV638 @ SV580 )
| ! [SY1019: $i] :
( ~ ( precedes @ SY1019 @ SV638 @ SV580 )
| ~ ( sequential @ SV630 @ SY1019 ) )
| ( precedes @ SV630 @ SV638 @ SV580 ) )
= $true )
| ( ( path @ SV598 @ SV603 @ SV580 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3058]) ).
thf(3093,plain,
! [SV603: $i,SV598: $i,SV639: $i,SV580: $i,SV631: $i] :
( ( ( ~ ( on_path @ SV631 @ SV580 )
| ~ ( on_path @ SV639 @ SV580 )
| ~ ( sequential @ SV631 @ SV639 )
| ( precedes @ SV631 @ SV639 @ SV580 ) )
= $true )
| ( ( path @ SV598 @ SV603 @ SV580 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3059]) ).
thf(3094,plain,
! [SV612: $i,SV605: $i,SV581: $i] :
( ( ( ~ ( edge @ SV581 )
| ~ ( edge @ SV605 )
| ~ ( edge @ SV612 ) )
= $true )
| ( ( ~ ( sequential @ SV581 @ SV605 ) )
= $true )
| ( ( ~ ( sequential @ SV605 @ SV612 ) )
= $true )
| ( ( ~ ( sequential @ SV612 @ SV581 ) )
= $true )
| ( ( triangle @ SV581 @ SV605 @ SV612 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3060]) ).
thf(3095,plain,
! [SV581: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY930: $i,SY931: $i] :
~ ( triangle @ SV581 @ SY930 @ SY931 )
| ( edge @ SV581 ) )
| ~ ! [SY932: $i] :
( ! [SY933: $i] :
~ ( triangle @ SV581 @ SY932 @ SY933 )
| ( edge @ SY932 ) ) )
| ~ ! [SY934: $i,SY935: $i] :
( ~ ( triangle @ SV581 @ SY934 @ SY935 )
| ( edge @ SY935 ) ) )
| ~ ! [SY936: $i] :
( ! [SY937: $i] :
~ ( triangle @ SV581 @ SY936 @ SY937 )
| ( sequential @ SV581 @ SY936 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3061]) ).
thf(3096,plain,
! [SV581: $i] :
( ( ! [SY938: $i,SY939: $i] :
( ~ ( triangle @ SV581 @ SY938 @ SY939 )
| ( sequential @ SY938 @ SY939 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3062]) ).
thf(3097,plain,
! [SV632: $i,SV623: $i,SV581: $i] :
( ( ( ~ ( triangle @ SV581 @ SV623 @ SV632 ) )
= $true )
| ( ( sequential @ SV632 @ SV581 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3063]) ).
thf(3098,plain,
! [SV606: $i,SV604: $i] :
( ( ( edge @ SV604 )
= $false )
| ( ( ~ ( edge @ SV606 ) )
= $true )
| ( ( SV604 = SV606 )
= $true )
| ( ( ( ( head_of @ SV604 )
!= ( tail_of @ SV606 ) ) )
= $true )
| ( ( sequential @ SV604 @ SV606 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3064]) ).
thf(3099,plain,
! [SV640: $i] :
( ( ! [SY1020: $i] :
( ~ ( sequential @ SV640 @ SY1020 )
| ( SV640 != SY1020 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3065]) ).
thf(3100,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3066]) ).
thf(3101,plain,
! [SV624: $i,SV620: $i] :
( ( ( sequential @ SV620 @ SV624 )
= $false )
| ( ( ( head_of @ SV620 )
= ( tail_of @ SV624 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3067]) ).
thf(3102,plain,
! [SV641: $i,SV633: $i,SV582: $i] :
( ( ( ~ ( path @ SV582 @ SV633 @ SV641 ) )
= $true )
| ( ( vertex @ SV582 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3068]) ).
thf(3103,plain,
! [SV642: $i,SV625: $i,SV582: $i] :
( ( ( ~ ( path @ SV582 @ SV625 @ SV642 ) )
= $true )
| ( ( vertex @ SV625 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3069]) ).
thf(3104,plain,
! [SV607: $i,SV613: $i,SV582: $i] :
( ( ( ~ ~ ( ( SV582
!= ( tail_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( edge @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) ) )
= $false )
| ( ( path @ SV582 @ SV607 @ SV613 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3070]) ).
thf(3105,plain,
! [SV582: $i,SV613: $i,SV607: $i] :
( ( ( ~ ~ ( ~ ( ( SV607
!= ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
| ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ empty ) )
| ! [SY1002: $i] :
( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ SY1002 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ SY1002 ) ) )
| ~ ~ ( ~ ( ( SV607
= ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ ( sK13_SY84 @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ ( sK13_SY84 @ SV613 @ SV607 @ SV582 ) ) ) )
| ~ ( ( SV613
= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ empty ) )
| ~ ( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ ( sK12_SY85 @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ ( sK12_SY85 @ SV613 @ SV607 @ SV582 ) ) ) ) ) ) )
= $false )
| ( ( path @ SV582 @ SV607 @ SV613 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3070]) ).
thf(3106,plain,
! [SV614: $i,SV608: $i,SV583: $i] :
( ( ( ~ ( path @ SV583 @ SV608 @ ( sK8_P @ SV614 @ SV608 @ SV583 ) ) )
= $false )
| ( ( ( SV583 = SV608 )
| ~ ( path @ SV583 @ SV608 @ SV614 ) )
= $true )
| ( ( shortest_path @ SV583 @ SV608 @ SV614 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3071]) ).
thf(3107,plain,
! [SV583: $i,SV608: $i,SV614: $i] :
( ( ( ~ ~ ( less_or_equal @ ( length_of @ SV614 ) @ ( length_of @ ( sK8_P @ SV614 @ SV608 @ SV583 ) ) ) )
= $false )
| ( ( ( SV583 = SV608 )
| ~ ( path @ SV583 @ SV608 @ SV614 ) )
= $true )
| ( ( shortest_path @ SV583 @ SV608 @ SV614 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3071]) ).
thf(3108,plain,
! [SV634: $i,SV626: $i,SV583: $i] :
( ( ( ~ ( shortest_path @ SV583 @ SV626 @ SV634 ) )
= $true )
| ( ( ! [SY1017: $i] :
( ~ ( path @ SV583 @ SV626 @ SY1017 )
| ( less_or_equal @ ( length_of @ SV634 ) @ ( length_of @ SY1017 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3072]) ).
thf(3109,plain,
! [SV583: $i] :
( ( ! [SY954: $i] :
( ! [SY955: $i] :
~ ( shortest_path @ SV583 @ SY954 @ SY955 )
| ( SV583 != SY954 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3073]) ).
thf(3110,plain,
! [SV583: $i] :
( ( ! [SY956: $i,SY957: $i] :
( ~ ( shortest_path @ SV583 @ SY956 @ SY957 )
| ( path @ SV583 @ SY956 @ SY957 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3074]) ).
thf(3111,plain,
! [SV584: $i] :
( ( ( ~ ( on_path @ ( sK6_E1 @ SV584 ) @ SV584 )
| ~ ( on_path @ ( sK7_SY80 @ SV584 ) @ SV584 ) )
= $false )
| ( ( ! [SY959: $i,SY960: $i] :
~ ( path @ SY959 @ SY960 @ SV584 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV584 )
= ( number_of_in @ triangles @ SV584 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3075]) ).
thf(3112,plain,
! [SV584: $i,SV643: $i] :
( ( ( ! [SY1021: $i] :
~ ( path @ SV643 @ SY1021 @ SV584 ) )
= $true )
| ( ( sequential @ ( sK6_E1 @ SV584 ) @ ( sK7_SY80 @ SV584 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV584 )
= ( number_of_in @ triangles @ SV584 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3076]) ).
thf(3113,plain,
! [SV621: $i,SV584: $i,SV644: $i,SV635: $i] :
( ( ( ~ ( path @ SV635 @ SV644 @ SV584 ) )
= $true )
| ( ( triangle @ ( sK6_E1 @ SV584 ) @ ( sK7_SY80 @ SV584 ) @ SV621 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV584 )
= ( number_of_in @ triangles @ SV584 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3077]) ).
thf(3114,plain,
! [SV588: $i,SV575: $i,SV627: $i,SV636: $i] :
( ( ( ~ ( on_path @ SV636 @ SV627 )
| ~ ( path @ SV575 @ SV588 @ SV627 ) )
= $true )
| ( ( edge @ SV636 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3078]) ).
thf(3115,plain,
! [SV588: $i,SV575: $i,SV628: $i,SV637: $i] :
( ( ( ~ ( on_path @ SV637 @ SV628 )
| ~ ( path @ SV575 @ SV588 @ SV628 ) )
= $true )
| ( ( in_path @ ( head_of @ SV637 ) @ SV628 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3079]) ).
thf(3116,plain,
! [SV615: $i,SV609: $i,SV588: $i,SV575: $i] :
( ( ( path @ SV575 @ SV588 @ SV609 )
= $false )
| ( ( on_path @ SV615 @ SV609 )
= $false )
| ( ( in_path @ ( tail_of @ SV615 ) @ SV609 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3080]) ).
thf(3117,plain,
! [SV594: $i,SV589: $i,SV576: $i] :
( ( ( ! [SY983: $i] :
( ( SV576
!= ( tail_of @ SY983 ) )
| ~ ( edge @ SY983 )
| ( SV589
!= ( head_of @ SY983 ) )
| ( SV594
!= ( path_cons @ SY983 @ empty ) ) ) )
= $true )
| ( ( vertex @ SV576 )
= $false )
| ( ( vertex @ SV589 )
= $false )
| ( ( path @ SV576 @ SV589 @ SV594 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3081]) ).
thf(3118,plain,
! [SV589: $i,SV594: $i,SV576: $i] :
( ( ( ! [SY984: $i] :
( ( SV576
!= ( tail_of @ SY984 ) )
| ~ ( edge @ SY984 )
| ! [SY985: $i] :
( ( SV594
!= ( path_cons @ SY984 @ SY985 ) )
| ~ ( path @ ( head_of @ SY984 ) @ SV589 @ SY985 ) ) ) )
= $true )
| ( ( vertex @ SV576 )
= $false )
| ( ( vertex @ SV589 )
= $false )
| ( ( path @ SV576 @ SV589 @ SV594 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3082]) ).
thf(3119,plain,
! [SV590: $i,SV577: $i,SV629: $i,SV616: $i,SV595: $i] :
( ( ( precedes @ SV595 @ SV616 @ SV629 )
= $false )
| ( ( ~ ( shortest_path @ SV577 @ SV590 @ SV629 ) )
= $true )
| ( ( ! [SY1004: $i] :
( ( ( tail_of @ SY1004 )
!= ( tail_of @ SV595 ) )
| ( ( head_of @ SY1004 )
!= ( head_of @ SV616 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3083]) ).
thf(3120,plain,
! [SV590: $i,SV577: $i,SV622: $i,SV617: $i,SV595: $i] :
( ( ( precedes @ SV595 @ SV617 @ SV622 )
= $false )
| ( ( ~ ( shortest_path @ SV577 @ SV590 @ SV622 ) )
= $true )
| ( ( ~ ( precedes @ SV617 @ SV595 @ SV622 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3084]) ).
thf(3121,plain,
! [SV599: $i,SV596: $i] :
( ( ( ~ ~ ( ~ ( ( SV596
!= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
!= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
!= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
!= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV596
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
| ~ ( ( SV596
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) ) )
| ~ ~ ( ~ ( ( SV599
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
| ~ ( ( SV599
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) ) ) ) ) )
= $false )
| ( ( SV596 = SV599 )
= $true )
| ( ( vertex @ SV596 )
= $false )
| ( ( vertex @ SV599 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[3085]) ).
thf(3122,plain,
! [SV596: $i,SV599: $i] :
( ( ( ~ ( edge @ ( sK14_E @ SV599 @ SV596 ) ) )
= $false )
| ( ( SV596 = SV599 )
= $true )
| ( ( vertex @ SV596 )
= $false )
| ( ( vertex @ SV599 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[3085]) ).
thf(3123,plain,
! [SV602: $i,SV597: $i,SV578: $i] :
( ( ( ! [SY907: $i] :
( ! [SY908: $i] :
~ ( precedes @ SY907 @ SY908 @ SV578 )
| ( on_path @ SY907 @ SV578 ) ) )
= $true )
| ( ( path @ SV597 @ SV602 @ SV578 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3086]) ).
thf(3124,plain,
! [SV602: $i,SV597: $i,SV578: $i] :
( ( ( ! [SY909: $i,SY910: $i] :
( ~ ( precedes @ SY909 @ SY910 @ SV578 )
| ( on_path @ SY910 @ SV578 ) ) )
= $true )
| ( ( path @ SV597 @ SV602 @ SV578 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3087]) ).
thf(3125,plain,
! [SV602: $i,SV597: $i,SV578: $i] :
( ( ( ! [SY911: $i,SY912: $i] :
( ~ ( precedes @ SY911 @ SY912 @ SV578 )
| ! [SY913: $i] :
( ~ ( precedes @ SY913 @ SY912 @ SV578 )
| ~ ( sequential @ SY911 @ SY913 ) )
| ~ ( sequential @ SY911 @ SY912 ) ) )
= $true )
| ( ( path @ SV597 @ SV602 @ SV578 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3088]) ).
thf(3126,plain,
! [SV602: $i,SV597: $i,SV578: $i] :
( ( ( ! [SY914: $i,SY915: $i] :
( ~ ( precedes @ SY914 @ SY915 @ SV578 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY915 @ SY914 @ SV578 ) @ SY915 @ SV578 )
| ~ ( sequential @ SY914 @ ( sK9_E3 @ SY915 @ SY914 @ SV578 ) ) )
| ( sequential @ SY914 @ SY915 ) ) )
= $true )
| ( ( path @ SV597 @ SV602 @ SV578 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3089]) ).
thf(3127,plain,
! [SV618: $i,SV610: $i,SV591: $i,SV579: $i] :
( ( ( path @ SV579 @ SV591 @ SV610 )
= $false )
| ( ( in_path @ SV618 @ SV610 )
= $false )
| ( ( ~ ( ~ ( on_path @ ( sK10_E @ SV618 @ SV610 @ SV591 @ SV579 ) @ SV610 )
| ~ ( ( SV618
= ( head_of @ ( sK10_E @ SV618 @ SV610 @ SV591 @ SV579 ) ) )
| ( SV618
= ( tail_of @ ( sK10_E @ SV618 @ SV610 @ SV591 @ SV579 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3090]) ).
thf(3128,plain,
! [SV619: $i,SV611: $i,SV591: $i,SV579: $i] :
( ( ( path @ SV579 @ SV591 @ SV611 )
= $false )
| ( ( in_path @ SV619 @ SV611 )
= $false )
| ( ( vertex @ SV619 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3091]) ).
thf(3129,plain,
! [SV603: $i,SV598: $i,SV638: $i,SV580: $i,SV630: $i] :
( ( ( ~ ( on_path @ SV630 @ SV580 )
| ~ ( on_path @ SV638 @ SV580 )
| ! [SY1019: $i] :
( ~ ( precedes @ SY1019 @ SV638 @ SV580 )
| ~ ( sequential @ SV630 @ SY1019 ) ) )
= $true )
| ( ( precedes @ SV630 @ SV638 @ SV580 )
= $true )
| ( ( path @ SV598 @ SV603 @ SV580 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3092]) ).
thf(3130,plain,
! [SV603: $i,SV598: $i,SV639: $i,SV580: $i,SV631: $i] :
( ( ( ~ ( on_path @ SV631 @ SV580 )
| ~ ( on_path @ SV639 @ SV580 )
| ~ ( sequential @ SV631 @ SV639 ) )
= $true )
| ( ( precedes @ SV631 @ SV639 @ SV580 )
= $true )
| ( ( path @ SV598 @ SV603 @ SV580 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3093]) ).
thf(3131,plain,
! [SV612: $i,SV605: $i,SV581: $i] :
( ( ( ~ ( edge @ SV581 )
| ~ ( edge @ SV605 ) )
= $true )
| ( ( ~ ( edge @ SV612 ) )
= $true )
| ( ( ~ ( sequential @ SV581 @ SV605 ) )
= $true )
| ( ( ~ ( sequential @ SV605 @ SV612 ) )
= $true )
| ( ( ~ ( sequential @ SV612 @ SV581 ) )
= $true )
| ( ( triangle @ SV581 @ SV605 @ SV612 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3094]) ).
thf(3132,plain,
! [SV581: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( ! [SY930: $i,SY931: $i] :
~ ( triangle @ SV581 @ SY930 @ SY931 )
| ( edge @ SV581 ) )
| ~ ! [SY932: $i] :
( ! [SY933: $i] :
~ ( triangle @ SV581 @ SY932 @ SY933 )
| ( edge @ SY932 ) ) )
| ~ ! [SY934: $i,SY935: $i] :
( ~ ( triangle @ SV581 @ SY934 @ SY935 )
| ( edge @ SY935 ) ) )
| ~ ! [SY936: $i] :
( ! [SY937: $i] :
~ ( triangle @ SV581 @ SY936 @ SY937 )
| ( sequential @ SV581 @ SY936 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3095]) ).
thf(3133,plain,
! [SV645: $i,SV581: $i] :
( ( ! [SY1022: $i] :
( ~ ( triangle @ SV581 @ SV645 @ SY1022 )
| ( sequential @ SV645 @ SY1022 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3096]) ).
thf(3134,plain,
! [SV632: $i,SV623: $i,SV581: $i] :
( ( ( triangle @ SV581 @ SV623 @ SV632 )
= $false )
| ( ( sequential @ SV632 @ SV581 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3097]) ).
thf(3135,plain,
! [SV604: $i,SV606: $i] :
( ( ( edge @ SV606 )
= $false )
| ( ( edge @ SV604 )
= $false )
| ( ( SV604 = SV606 )
= $true )
| ( ( ( ( head_of @ SV604 )
!= ( tail_of @ SV606 ) ) )
= $true )
| ( ( sequential @ SV604 @ SV606 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3098]) ).
thf(3136,plain,
! [SV646: $i,SV640: $i] :
( ( ~ ( sequential @ SV640 @ SV646 )
| ( SV640 != SV646 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3099]) ).
thf(3137,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3100]) ).
thf(3138,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3100]) ).
thf(3139,plain,
! [SV641: $i,SV633: $i,SV582: $i] :
( ( ( path @ SV582 @ SV633 @ SV641 )
= $false )
| ( ( vertex @ SV582 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3102]) ).
thf(3140,plain,
! [SV642: $i,SV625: $i,SV582: $i] :
( ( ( path @ SV582 @ SV625 @ SV642 )
= $false )
| ( ( vertex @ SV625 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3103]) ).
thf(3141,plain,
! [SV607: $i,SV613: $i,SV582: $i] :
( ( ( ~ ( ( SV582
!= ( tail_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( edge @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) ) )
= $true )
| ( ( path @ SV582 @ SV607 @ SV613 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3104]) ).
thf(3142,plain,
! [SV582: $i,SV613: $i,SV607: $i] :
( ( ( ~ ( ~ ( ( SV607
!= ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
| ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ empty ) )
| ! [SY1002: $i] :
( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ SY1002 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ SY1002 ) ) )
| ~ ~ ( ~ ( ( SV607
= ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ ( sK13_SY84 @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ ( sK13_SY84 @ SV613 @ SV607 @ SV582 ) ) ) )
| ~ ( ( SV613
= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ empty ) )
| ~ ( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ ( sK12_SY85 @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ ( sK12_SY85 @ SV613 @ SV607 @ SV582 ) ) ) ) ) ) )
= $true )
| ( ( path @ SV582 @ SV607 @ SV613 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3105]) ).
thf(3143,plain,
! [SV614: $i,SV608: $i,SV583: $i] :
( ( ( path @ SV583 @ SV608 @ ( sK8_P @ SV614 @ SV608 @ SV583 ) )
= $true )
| ( ( ( SV583 = SV608 )
| ~ ( path @ SV583 @ SV608 @ SV614 ) )
= $true )
| ( ( shortest_path @ SV583 @ SV608 @ SV614 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3106]) ).
thf(3144,plain,
! [SV583: $i,SV608: $i,SV614: $i] :
( ( ( ~ ( less_or_equal @ ( length_of @ SV614 ) @ ( length_of @ ( sK8_P @ SV614 @ SV608 @ SV583 ) ) ) )
= $true )
| ( ( ( SV583 = SV608 )
| ~ ( path @ SV583 @ SV608 @ SV614 ) )
= $true )
| ( ( shortest_path @ SV583 @ SV608 @ SV614 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3107]) ).
thf(3145,plain,
! [SV634: $i,SV626: $i,SV583: $i] :
( ( ( shortest_path @ SV583 @ SV626 @ SV634 )
= $false )
| ( ( ! [SY1017: $i] :
( ~ ( path @ SV583 @ SV626 @ SY1017 )
| ( less_or_equal @ ( length_of @ SV634 ) @ ( length_of @ SY1017 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3108]) ).
thf(3146,plain,
! [SV647: $i,SV583: $i] :
( ( ! [SY1023: $i] :
~ ( shortest_path @ SV583 @ SV647 @ SY1023 )
| ( SV583 != SV647 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3109]) ).
thf(3147,plain,
! [SV648: $i,SV583: $i] :
( ( ! [SY1024: $i] :
( ~ ( shortest_path @ SV583 @ SV648 @ SY1024 )
| ( path @ SV583 @ SV648 @ SY1024 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3110]) ).
thf(3148,plain,
! [SV584: $i] :
( ( ( ~ ( on_path @ ( sK6_E1 @ SV584 ) @ SV584 ) )
= $false )
| ( ( ! [SY959: $i,SY960: $i] :
~ ( path @ SY959 @ SY960 @ SV584 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV584 )
= ( number_of_in @ triangles @ SV584 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3111]) ).
thf(3149,plain,
! [SV584: $i] :
( ( ( ~ ( on_path @ ( sK7_SY80 @ SV584 ) @ SV584 ) )
= $false )
| ( ( ! [SY959: $i,SY960: $i] :
~ ( path @ SY959 @ SY960 @ SV584 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV584 )
= ( number_of_in @ triangles @ SV584 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3111]) ).
thf(3150,plain,
! [SV584: $i,SV649: $i,SV643: $i] :
( ( ( ~ ( path @ SV643 @ SV649 @ SV584 ) )
= $true )
| ( ( sequential @ ( sK6_E1 @ SV584 ) @ ( sK7_SY80 @ SV584 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV584 )
= ( number_of_in @ triangles @ SV584 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3112]) ).
thf(3151,plain,
! [SV621: $i,SV584: $i,SV644: $i,SV635: $i] :
( ( ( path @ SV635 @ SV644 @ SV584 )
= $false )
| ( ( triangle @ ( sK6_E1 @ SV584 ) @ ( sK7_SY80 @ SV584 ) @ SV621 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV584 )
= ( number_of_in @ triangles @ SV584 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3113]) ).
thf(3152,plain,
! [SV588: $i,SV575: $i,SV627: $i,SV636: $i] :
( ( ( ~ ( on_path @ SV636 @ SV627 ) )
= $true )
| ( ( ~ ( path @ SV575 @ SV588 @ SV627 ) )
= $true )
| ( ( edge @ SV636 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3114]) ).
thf(3153,plain,
! [SV588: $i,SV575: $i,SV628: $i,SV637: $i] :
( ( ( ~ ( on_path @ SV637 @ SV628 ) )
= $true )
| ( ( ~ ( path @ SV575 @ SV588 @ SV628 ) )
= $true )
| ( ( in_path @ ( head_of @ SV637 ) @ SV628 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3115]) ).
thf(3154,plain,
! [SV594: $i,SV589: $i,SV650: $i,SV576: $i] :
( ( ( ( SV576
!= ( tail_of @ SV650 ) )
| ~ ( edge @ SV650 )
| ( SV589
!= ( head_of @ SV650 ) )
| ( SV594
!= ( path_cons @ SV650 @ empty ) ) )
= $true )
| ( ( vertex @ SV576 )
= $false )
| ( ( vertex @ SV589 )
= $false )
| ( ( path @ SV576 @ SV589 @ SV594 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3117]) ).
thf(3155,plain,
! [SV589: $i,SV594: $i,SV651: $i,SV576: $i] :
( ( ( ( SV576
!= ( tail_of @ SV651 ) )
| ~ ( edge @ SV651 )
| ! [SY1025: $i] :
( ( SV594
!= ( path_cons @ SV651 @ SY1025 ) )
| ~ ( path @ ( head_of @ SV651 ) @ SV589 @ SY1025 ) ) )
= $true )
| ( ( vertex @ SV576 )
= $false )
| ( ( vertex @ SV589 )
= $false )
| ( ( path @ SV576 @ SV589 @ SV594 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3118]) ).
thf(3156,plain,
! [SV616: $i,SV595: $i,SV629: $i,SV590: $i,SV577: $i] :
( ( ( shortest_path @ SV577 @ SV590 @ SV629 )
= $false )
| ( ( precedes @ SV595 @ SV616 @ SV629 )
= $false )
| ( ( ! [SY1004: $i] :
( ( ( tail_of @ SY1004 )
!= ( tail_of @ SV595 ) )
| ( ( head_of @ SY1004 )
!= ( head_of @ SV616 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3119]) ).
thf(3157,plain,
! [SV617: $i,SV595: $i,SV622: $i,SV590: $i,SV577: $i] :
( ( ( shortest_path @ SV577 @ SV590 @ SV622 )
= $false )
| ( ( precedes @ SV595 @ SV617 @ SV622 )
= $false )
| ( ( ~ ( precedes @ SV617 @ SV595 @ SV622 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3120]) ).
thf(3158,plain,
! [SV599: $i,SV596: $i] :
( ( ( ~ ( ~ ( ( SV596
!= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
!= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
!= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
!= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV596
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
| ~ ( ( SV596
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) ) )
| ~ ~ ( ~ ( ( SV599
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
| ~ ( ( SV599
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) ) ) ) ) )
= $true )
| ( ( SV596 = SV599 )
= $true )
| ( ( vertex @ SV596 )
= $false )
| ( ( vertex @ SV599 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[3121]) ).
thf(3159,plain,
! [SV596: $i,SV599: $i] :
( ( ( edge @ ( sK14_E @ SV599 @ SV596 ) )
= $true )
| ( ( SV596 = SV599 )
= $true )
| ( ( vertex @ SV596 )
= $false )
| ( ( vertex @ SV599 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[3122]) ).
thf(3160,plain,
! [SV602: $i,SV597: $i,SV578: $i,SV652: $i] :
( ( ( ! [SY1026: $i] :
~ ( precedes @ SV652 @ SY1026 @ SV578 )
| ( on_path @ SV652 @ SV578 ) )
= $true )
| ( ( path @ SV597 @ SV602 @ SV578 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3123]) ).
thf(3161,plain,
! [SV602: $i,SV597: $i,SV578: $i,SV653: $i] :
( ( ( ! [SY1027: $i] :
( ~ ( precedes @ SV653 @ SY1027 @ SV578 )
| ( on_path @ SY1027 @ SV578 ) ) )
= $true )
| ( ( path @ SV597 @ SV602 @ SV578 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3124]) ).
thf(3162,plain,
! [SV602: $i,SV597: $i,SV578: $i,SV654: $i] :
( ( ( ! [SY1028: $i] :
( ~ ( precedes @ SV654 @ SY1028 @ SV578 )
| ! [SY1029: $i] :
( ~ ( precedes @ SY1029 @ SY1028 @ SV578 )
| ~ ( sequential @ SV654 @ SY1029 ) )
| ~ ( sequential @ SV654 @ SY1028 ) ) )
= $true )
| ( ( path @ SV597 @ SV602 @ SV578 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3125]) ).
thf(3163,plain,
! [SV602: $i,SV597: $i,SV578: $i,SV655: $i] :
( ( ( ! [SY1030: $i] :
( ~ ( precedes @ SV655 @ SY1030 @ SV578 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY1030 @ SV655 @ SV578 ) @ SY1030 @ SV578 )
| ~ ( sequential @ SV655 @ ( sK9_E3 @ SY1030 @ SV655 @ SV578 ) ) )
| ( sequential @ SV655 @ SY1030 ) ) )
= $true )
| ( ( path @ SV597 @ SV602 @ SV578 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3126]) ).
thf(3164,plain,
! [SV579: $i,SV591: $i,SV610: $i,SV618: $i] :
( ( ( ~ ( on_path @ ( sK10_E @ SV618 @ SV610 @ SV591 @ SV579 ) @ SV610 )
| ~ ( ( SV618
= ( head_of @ ( sK10_E @ SV618 @ SV610 @ SV591 @ SV579 ) ) )
| ( SV618
= ( tail_of @ ( sK10_E @ SV618 @ SV610 @ SV591 @ SV579 ) ) ) ) )
= $false )
| ( ( in_path @ SV618 @ SV610 )
= $false )
| ( ( path @ SV579 @ SV591 @ SV610 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3127]) ).
thf(3165,plain,
! [SV603: $i,SV598: $i,SV638: $i,SV580: $i,SV630: $i] :
( ( ( ~ ( on_path @ SV630 @ SV580 )
| ~ ( on_path @ SV638 @ SV580 ) )
= $true )
| ( ( ! [SY1019: $i] :
( ~ ( precedes @ SY1019 @ SV638 @ SV580 )
| ~ ( sequential @ SV630 @ SY1019 ) ) )
= $true )
| ( ( precedes @ SV630 @ SV638 @ SV580 )
= $true )
| ( ( path @ SV598 @ SV603 @ SV580 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3129]) ).
thf(3166,plain,
! [SV603: $i,SV598: $i,SV639: $i,SV580: $i,SV631: $i] :
( ( ( ~ ( on_path @ SV631 @ SV580 )
| ~ ( on_path @ SV639 @ SV580 ) )
= $true )
| ( ( ~ ( sequential @ SV631 @ SV639 ) )
= $true )
| ( ( precedes @ SV631 @ SV639 @ SV580 )
= $true )
| ( ( path @ SV598 @ SV603 @ SV580 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3130]) ).
thf(3167,plain,
! [SV612: $i,SV605: $i,SV581: $i] :
( ( ( ~ ( edge @ SV581 ) )
= $true )
| ( ( ~ ( edge @ SV605 ) )
= $true )
| ( ( ~ ( edge @ SV612 ) )
= $true )
| ( ( ~ ( sequential @ SV581 @ SV605 ) )
= $true )
| ( ( ~ ( sequential @ SV605 @ SV612 ) )
= $true )
| ( ( ~ ( sequential @ SV612 @ SV581 ) )
= $true )
| ( ( triangle @ SV581 @ SV605 @ SV612 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3131]) ).
thf(3168,plain,
! [SV581: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( ! [SY930: $i,SY931: $i] :
~ ( triangle @ SV581 @ SY930 @ SY931 )
| ( edge @ SV581 ) )
| ~ ! [SY932: $i] :
( ! [SY933: $i] :
~ ( triangle @ SV581 @ SY932 @ SY933 )
| ( edge @ SY932 ) ) )
| ~ ! [SY934: $i,SY935: $i] :
( ~ ( triangle @ SV581 @ SY934 @ SY935 )
| ( edge @ SY935 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3132]) ).
thf(3169,plain,
! [SV581: $i] :
( ( ~ ! [SY936: $i] :
( ! [SY937: $i] :
~ ( triangle @ SV581 @ SY936 @ SY937 )
| ( sequential @ SV581 @ SY936 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3132]) ).
thf(3170,plain,
! [SV656: $i,SV645: $i,SV581: $i] :
( ( ~ ( triangle @ SV581 @ SV645 @ SV656 )
| ( sequential @ SV645 @ SV656 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3133]) ).
thf(3171,plain,
! [SV606: $i,SV604: $i] :
( ( ( ( head_of @ SV604 )
= ( tail_of @ SV606 ) )
= $false )
| ( ( SV604 = SV606 )
= $true )
| ( ( edge @ SV604 )
= $false )
| ( ( edge @ SV606 )
= $false )
| ( ( sequential @ SV604 @ SV606 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3135]) ).
thf(3172,plain,
! [SV646: $i,SV640: $i] :
( ( ( ~ ( sequential @ SV640 @ SV646 ) )
= $true )
| ( ( ( SV640 != SV646 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3136]) ).
thf(3173,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3137]) ).
thf(3174,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3138]) ).
thf(3175,plain,
! [SV607: $i,SV613: $i,SV582: $i] :
( ( ( ( SV582
!= ( tail_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( edge @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
= $false )
| ( ( path @ SV582 @ SV607 @ SV613 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3141]) ).
thf(3176,plain,
! [SV582: $i,SV613: $i,SV607: $i] :
( ( ( ~ ( ( SV607
!= ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
| ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ empty ) )
| ! [SY1002: $i] :
( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ SY1002 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ SY1002 ) ) )
| ~ ~ ( ~ ( ( SV607
= ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ ( sK13_SY84 @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ ( sK13_SY84 @ SV613 @ SV607 @ SV582 ) ) ) )
| ~ ( ( SV613
= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ empty ) )
| ~ ( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ ( sK12_SY85 @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ ( sK12_SY85 @ SV613 @ SV607 @ SV582 ) ) ) ) ) )
= $false )
| ( ( path @ SV582 @ SV607 @ SV613 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3142]) ).
thf(3177,plain,
! [SV614: $i,SV608: $i,SV583: $i] :
( ( ( SV583 = SV608 )
= $true )
| ( ( ~ ( path @ SV583 @ SV608 @ SV614 ) )
= $true )
| ( ( path @ SV583 @ SV608 @ ( sK8_P @ SV614 @ SV608 @ SV583 ) )
= $true )
| ( ( shortest_path @ SV583 @ SV608 @ SV614 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3143]) ).
thf(3178,plain,
! [SV583: $i,SV608: $i,SV614: $i] :
( ( ( less_or_equal @ ( length_of @ SV614 ) @ ( length_of @ ( sK8_P @ SV614 @ SV608 @ SV583 ) ) )
= $false )
| ( ( ( SV583 = SV608 )
| ~ ( path @ SV583 @ SV608 @ SV614 ) )
= $true )
| ( ( shortest_path @ SV583 @ SV608 @ SV614 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3144]) ).
thf(3179,plain,
! [SV634: $i,SV657: $i,SV626: $i,SV583: $i] :
( ( ( ~ ( path @ SV583 @ SV626 @ SV657 )
| ( less_or_equal @ ( length_of @ SV634 ) @ ( length_of @ SV657 ) ) )
= $true )
| ( ( shortest_path @ SV583 @ SV626 @ SV634 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3145]) ).
thf(3180,plain,
! [SV647: $i,SV583: $i] :
( ( ( ! [SY1023: $i] :
~ ( shortest_path @ SV583 @ SV647 @ SY1023 ) )
= $true )
| ( ( ( SV583 != SV647 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3146]) ).
thf(3181,plain,
! [SV658: $i,SV648: $i,SV583: $i] :
( ( ~ ( shortest_path @ SV583 @ SV648 @ SV658 )
| ( path @ SV583 @ SV648 @ SV658 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3147]) ).
thf(3182,plain,
! [SV584: $i] :
( ( ( on_path @ ( sK6_E1 @ SV584 ) @ SV584 )
= $true )
| ( ( ! [SY959: $i,SY960: $i] :
~ ( path @ SY959 @ SY960 @ SV584 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV584 )
= ( number_of_in @ triangles @ SV584 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3148]) ).
thf(3183,plain,
! [SV584: $i] :
( ( ( on_path @ ( sK7_SY80 @ SV584 ) @ SV584 )
= $true )
| ( ( ! [SY959: $i,SY960: $i] :
~ ( path @ SY959 @ SY960 @ SV584 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV584 )
= ( number_of_in @ triangles @ SV584 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3149]) ).
thf(3184,plain,
! [SV584: $i,SV649: $i,SV643: $i] :
( ( ( path @ SV643 @ SV649 @ SV584 )
= $false )
| ( ( sequential @ ( sK6_E1 @ SV584 ) @ ( sK7_SY80 @ SV584 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV584 )
= ( number_of_in @ triangles @ SV584 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3150]) ).
thf(3185,plain,
! [SV588: $i,SV575: $i,SV627: $i,SV636: $i] :
( ( ( on_path @ SV636 @ SV627 )
= $false )
| ( ( ~ ( path @ SV575 @ SV588 @ SV627 ) )
= $true )
| ( ( edge @ SV636 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3152]) ).
thf(3186,plain,
! [SV588: $i,SV575: $i,SV628: $i,SV637: $i] :
( ( ( on_path @ SV637 @ SV628 )
= $false )
| ( ( ~ ( path @ SV575 @ SV588 @ SV628 ) )
= $true )
| ( ( in_path @ ( head_of @ SV637 ) @ SV628 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3153]) ).
thf(3187,plain,
! [SV594: $i,SV589: $i,SV650: $i,SV576: $i] :
( ( ( ( SV576
!= ( tail_of @ SV650 ) )
| ~ ( edge @ SV650 ) )
= $true )
| ( ( ( SV589
!= ( head_of @ SV650 ) )
| ( SV594
!= ( path_cons @ SV650 @ empty ) ) )
= $true )
| ( ( vertex @ SV576 )
= $false )
| ( ( vertex @ SV589 )
= $false )
| ( ( path @ SV576 @ SV589 @ SV594 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3154]) ).
thf(3188,plain,
! [SV589: $i,SV594: $i,SV651: $i,SV576: $i] :
( ( ( ( SV576
!= ( tail_of @ SV651 ) )
| ~ ( edge @ SV651 ) )
= $true )
| ( ( ! [SY1025: $i] :
( ( SV594
!= ( path_cons @ SV651 @ SY1025 ) )
| ~ ( path @ ( head_of @ SV651 ) @ SV589 @ SY1025 ) ) )
= $true )
| ( ( vertex @ SV576 )
= $false )
| ( ( vertex @ SV589 )
= $false )
| ( ( path @ SV576 @ SV589 @ SV594 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3155]) ).
thf(3189,plain,
! [SV590: $i,SV577: $i,SV629: $i,SV616: $i,SV595: $i,SV659: $i] :
( ( ( ( ( tail_of @ SV659 )
!= ( tail_of @ SV595 ) )
| ( ( head_of @ SV659 )
!= ( head_of @ SV616 ) ) )
= $true )
| ( ( precedes @ SV595 @ SV616 @ SV629 )
= $false )
| ( ( shortest_path @ SV577 @ SV590 @ SV629 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3156]) ).
thf(3190,plain,
! [SV590: $i,SV577: $i,SV622: $i,SV595: $i,SV617: $i] :
( ( ( precedes @ SV617 @ SV595 @ SV622 )
= $false )
| ( ( precedes @ SV595 @ SV617 @ SV622 )
= $false )
| ( ( shortest_path @ SV577 @ SV590 @ SV622 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3157]) ).
thf(3191,plain,
! [SV599: $i,SV596: $i] :
( ( ( ~ ( ( SV596
!= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
!= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
!= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
!= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV596
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
| ~ ( ( SV596
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) ) )
| ~ ~ ( ~ ( ( SV599
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
| ~ ( ( SV599
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) ) ) ) )
= $false )
| ( ( SV596 = SV599 )
= $true )
| ( ( vertex @ SV596 )
= $false )
| ( ( vertex @ SV599 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[3158]) ).
thf(3192,plain,
! [SV602: $i,SV597: $i,SV578: $i,SV652: $i] :
( ( ( ! [SY1026: $i] :
~ ( precedes @ SV652 @ SY1026 @ SV578 ) )
= $true )
| ( ( on_path @ SV652 @ SV578 )
= $true )
| ( ( path @ SV597 @ SV602 @ SV578 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3160]) ).
thf(3193,plain,
! [SV602: $i,SV597: $i,SV578: $i,SV660: $i,SV653: $i] :
( ( ( ~ ( precedes @ SV653 @ SV660 @ SV578 )
| ( on_path @ SV660 @ SV578 ) )
= $true )
| ( ( path @ SV597 @ SV602 @ SV578 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3161]) ).
thf(3194,plain,
! [SV602: $i,SV597: $i,SV578: $i,SV661: $i,SV654: $i] :
( ( ( ~ ( precedes @ SV654 @ SV661 @ SV578 )
| ! [SY1031: $i] :
( ~ ( precedes @ SY1031 @ SV661 @ SV578 )
| ~ ( sequential @ SV654 @ SY1031 ) )
| ~ ( sequential @ SV654 @ SV661 ) )
= $true )
| ( ( path @ SV597 @ SV602 @ SV578 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3162]) ).
thf(3195,plain,
! [SV602: $i,SV597: $i,SV578: $i,SV662: $i,SV655: $i] :
( ( ( ~ ( precedes @ SV655 @ SV662 @ SV578 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SV662 @ SV655 @ SV578 ) @ SV662 @ SV578 )
| ~ ( sequential @ SV655 @ ( sK9_E3 @ SV662 @ SV655 @ SV578 ) ) )
| ( sequential @ SV655 @ SV662 ) )
= $true )
| ( ( path @ SV597 @ SV602 @ SV578 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3163]) ).
thf(3196,plain,
! [SV579: $i,SV591: $i,SV610: $i,SV618: $i] :
( ( ( ~ ( on_path @ ( sK10_E @ SV618 @ SV610 @ SV591 @ SV579 ) @ SV610 ) )
= $false )
| ( ( in_path @ SV618 @ SV610 )
= $false )
| ( ( path @ SV579 @ SV591 @ SV610 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3164]) ).
thf(3197,plain,
! [SV579: $i,SV591: $i,SV610: $i,SV618: $i] :
( ( ( ~ ( ( SV618
= ( head_of @ ( sK10_E @ SV618 @ SV610 @ SV591 @ SV579 ) ) )
| ( SV618
= ( tail_of @ ( sK10_E @ SV618 @ SV610 @ SV591 @ SV579 ) ) ) ) )
= $false )
| ( ( in_path @ SV618 @ SV610 )
= $false )
| ( ( path @ SV579 @ SV591 @ SV610 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3164]) ).
thf(3198,plain,
! [SV603: $i,SV598: $i,SV638: $i,SV580: $i,SV630: $i] :
( ( ( ~ ( on_path @ SV630 @ SV580 ) )
= $true )
| ( ( ~ ( on_path @ SV638 @ SV580 ) )
= $true )
| ( ( ! [SY1019: $i] :
( ~ ( precedes @ SY1019 @ SV638 @ SV580 )
| ~ ( sequential @ SV630 @ SY1019 ) ) )
= $true )
| ( ( precedes @ SV630 @ SV638 @ SV580 )
= $true )
| ( ( path @ SV598 @ SV603 @ SV580 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3165]) ).
thf(3199,plain,
! [SV603: $i,SV598: $i,SV639: $i,SV580: $i,SV631: $i] :
( ( ( ~ ( on_path @ SV631 @ SV580 ) )
= $true )
| ( ( ~ ( on_path @ SV639 @ SV580 ) )
= $true )
| ( ( ~ ( sequential @ SV631 @ SV639 ) )
= $true )
| ( ( precedes @ SV631 @ SV639 @ SV580 )
= $true )
| ( ( path @ SV598 @ SV603 @ SV580 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3166]) ).
thf(3200,plain,
! [SV612: $i,SV605: $i,SV581: $i] :
( ( ( edge @ SV581 )
= $false )
| ( ( ~ ( edge @ SV605 ) )
= $true )
| ( ( ~ ( edge @ SV612 ) )
= $true )
| ( ( ~ ( sequential @ SV581 @ SV605 ) )
= $true )
| ( ( ~ ( sequential @ SV605 @ SV612 ) )
= $true )
| ( ( ~ ( sequential @ SV612 @ SV581 ) )
= $true )
| ( ( triangle @ SV581 @ SV605 @ SV612 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3167]) ).
thf(3201,plain,
! [SV581: $i] :
( ( ~ ( ~ ~ ( ~ ( ! [SY930: $i,SY931: $i] :
~ ( triangle @ SV581 @ SY930 @ SY931 )
| ( edge @ SV581 ) )
| ~ ! [SY932: $i] :
( ! [SY933: $i] :
~ ( triangle @ SV581 @ SY932 @ SY933 )
| ( edge @ SY932 ) ) )
| ~ ! [SY934: $i,SY935: $i] :
( ~ ( triangle @ SV581 @ SY934 @ SY935 )
| ( edge @ SY935 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3168]) ).
thf(3202,plain,
! [SV581: $i] :
( ( ! [SY936: $i] :
( ! [SY937: $i] :
~ ( triangle @ SV581 @ SY936 @ SY937 )
| ( sequential @ SV581 @ SY936 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3169]) ).
thf(3203,plain,
! [SV656: $i,SV645: $i,SV581: $i] :
( ( ( ~ ( triangle @ SV581 @ SV645 @ SV656 ) )
= $true )
| ( ( sequential @ SV645 @ SV656 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3170]) ).
thf(3204,plain,
! [SV646: $i,SV640: $i] :
( ( ( sequential @ SV640 @ SV646 )
= $false )
| ( ( ( SV640 != SV646 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3172]) ).
thf(3205,plain,
! [SV663: $i] :
( ( ! [SY1032: $i] :
~ ( sequential @ SV663 @ SY1032 )
| ( edge @ SV663 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3173]) ).
thf(3206,plain,
! [SV664: $i] :
( ( ! [SY1033: $i] :
( ~ ( sequential @ SV664 @ SY1033 )
| ( edge @ SY1033 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3174]) ).
thf(3207,plain,
! [SV607: $i,SV613: $i,SV582: $i] :
( ( ( ( SV582
!= ( tail_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) ) )
= $false )
| ( ( path @ SV582 @ SV607 @ SV613 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3175]) ).
thf(3208,plain,
! [SV582: $i,SV607: $i,SV613: $i] :
( ( ( ~ ( edge @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
= $false )
| ( ( path @ SV582 @ SV607 @ SV613 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3175]) ).
thf(3209,plain,
! [SV582: $i,SV613: $i,SV607: $i] :
( ( ( ~ ( ( SV607
!= ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
| ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ empty ) )
| ! [SY1002: $i] :
( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ SY1002 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ SY1002 ) ) ) )
= $false )
| ( ( path @ SV582 @ SV607 @ SV613 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3176]) ).
thf(3210,plain,
! [SV582: $i,SV613: $i,SV607: $i] :
( ( ( ~ ~ ( ~ ( ( SV607
= ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ ( sK13_SY84 @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ ( sK13_SY84 @ SV613 @ SV607 @ SV582 ) ) ) )
| ~ ( ( SV613
= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ empty ) )
| ~ ( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ ( sK12_SY85 @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ ( sK12_SY85 @ SV613 @ SV607 @ SV582 ) ) ) ) ) )
= $false )
| ( ( path @ SV582 @ SV607 @ SV613 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3176]) ).
thf(3211,plain,
! [SV614: $i,SV608: $i,SV583: $i] :
( ( ( path @ SV583 @ SV608 @ SV614 )
= $false )
| ( ( SV583 = SV608 )
= $true )
| ( ( path @ SV583 @ SV608 @ ( sK8_P @ SV614 @ SV608 @ SV583 ) )
= $true )
| ( ( shortest_path @ SV583 @ SV608 @ SV614 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3177]) ).
thf(3212,plain,
! [SV614: $i,SV608: $i,SV583: $i] :
( ( ( SV583 = SV608 )
= $true )
| ( ( ~ ( path @ SV583 @ SV608 @ SV614 ) )
= $true )
| ( ( less_or_equal @ ( length_of @ SV614 ) @ ( length_of @ ( sK8_P @ SV614 @ SV608 @ SV583 ) ) )
= $false )
| ( ( shortest_path @ SV583 @ SV608 @ SV614 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3178]) ).
thf(3213,plain,
! [SV634: $i,SV657: $i,SV626: $i,SV583: $i] :
( ( ( ~ ( path @ SV583 @ SV626 @ SV657 ) )
= $true )
| ( ( less_or_equal @ ( length_of @ SV634 ) @ ( length_of @ SV657 ) )
= $true )
| ( ( shortest_path @ SV583 @ SV626 @ SV634 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3179]) ).
thf(3214,plain,
! [SV665: $i,SV647: $i,SV583: $i] :
( ( ( ~ ( shortest_path @ SV583 @ SV647 @ SV665 ) )
= $true )
| ( ( ( SV583 != SV647 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3180]) ).
thf(3215,plain,
! [SV658: $i,SV648: $i,SV583: $i] :
( ( ( ~ ( shortest_path @ SV583 @ SV648 @ SV658 ) )
= $true )
| ( ( path @ SV583 @ SV648 @ SV658 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3181]) ).
thf(3216,plain,
! [SV584: $i,SV666: $i] :
( ( ( ! [SY1034: $i] :
~ ( path @ SV666 @ SY1034 @ SV584 ) )
= $true )
| ( ( on_path @ ( sK6_E1 @ SV584 ) @ SV584 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV584 )
= ( number_of_in @ triangles @ SV584 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3182]) ).
thf(3217,plain,
! [SV584: $i,SV667: $i] :
( ( ( ! [SY1035: $i] :
~ ( path @ SV667 @ SY1035 @ SV584 ) )
= $true )
| ( ( on_path @ ( sK7_SY80 @ SV584 ) @ SV584 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV584 )
= ( number_of_in @ triangles @ SV584 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3183]) ).
thf(3218,plain,
! [SV636: $i,SV627: $i,SV588: $i,SV575: $i] :
( ( ( path @ SV575 @ SV588 @ SV627 )
= $false )
| ( ( on_path @ SV636 @ SV627 )
= $false )
| ( ( edge @ SV636 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3185]) ).
thf(3219,plain,
! [SV637: $i,SV628: $i,SV588: $i,SV575: $i] :
( ( ( path @ SV575 @ SV588 @ SV628 )
= $false )
| ( ( on_path @ SV637 @ SV628 )
= $false )
| ( ( in_path @ ( head_of @ SV637 ) @ SV628 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3186]) ).
thf(3220,plain,
! [SV594: $i,SV589: $i,SV650: $i,SV576: $i] :
( ( ( ( SV576
!= ( tail_of @ SV650 ) ) )
= $true )
| ( ( ~ ( edge @ SV650 ) )
= $true )
| ( ( ( SV589
!= ( head_of @ SV650 ) )
| ( SV594
!= ( path_cons @ SV650 @ empty ) ) )
= $true )
| ( ( vertex @ SV576 )
= $false )
| ( ( vertex @ SV589 )
= $false )
| ( ( path @ SV576 @ SV589 @ SV594 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3187]) ).
thf(3221,plain,
! [SV589: $i,SV594: $i,SV651: $i,SV576: $i] :
( ( ( ( SV576
!= ( tail_of @ SV651 ) ) )
= $true )
| ( ( ~ ( edge @ SV651 ) )
= $true )
| ( ( ! [SY1025: $i] :
( ( SV594
!= ( path_cons @ SV651 @ SY1025 ) )
| ~ ( path @ ( head_of @ SV651 ) @ SV589 @ SY1025 ) ) )
= $true )
| ( ( vertex @ SV576 )
= $false )
| ( ( vertex @ SV589 )
= $false )
| ( ( path @ SV576 @ SV589 @ SV594 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3188]) ).
thf(3222,plain,
! [SV590: $i,SV577: $i,SV629: $i,SV616: $i,SV595: $i,SV659: $i] :
( ( ( ( ( tail_of @ SV659 )
!= ( tail_of @ SV595 ) ) )
= $true )
| ( ( ( ( head_of @ SV659 )
!= ( head_of @ SV616 ) ) )
= $true )
| ( ( precedes @ SV595 @ SV616 @ SV629 )
= $false )
| ( ( shortest_path @ SV577 @ SV590 @ SV629 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3189]) ).
thf(3223,plain,
! [SV599: $i,SV596: $i] :
( ( ( ~ ( ( SV596
!= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
!= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
!= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
!= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) ) )
= $false )
| ( ( SV596 = SV599 )
= $true )
| ( ( vertex @ SV596 )
= $false )
| ( ( vertex @ SV599 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[3191]) ).
thf(3224,plain,
! [SV599: $i,SV596: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( SV596
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
| ~ ( ( SV596
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) ) )
| ~ ~ ( ~ ( ( SV599
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
| ~ ( ( SV599
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) ) ) ) )
= $false )
| ( ( SV596 = SV599 )
= $true )
| ( ( vertex @ SV596 )
= $false )
| ( ( vertex @ SV599 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[3191]) ).
thf(3225,plain,
! [SV602: $i,SV597: $i,SV578: $i,SV668: $i,SV652: $i] :
( ( ( ~ ( precedes @ SV652 @ SV668 @ SV578 ) )
= $true )
| ( ( on_path @ SV652 @ SV578 )
= $true )
| ( ( path @ SV597 @ SV602 @ SV578 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3192]) ).
thf(3226,plain,
! [SV602: $i,SV597: $i,SV578: $i,SV660: $i,SV653: $i] :
( ( ( ~ ( precedes @ SV653 @ SV660 @ SV578 ) )
= $true )
| ( ( on_path @ SV660 @ SV578 )
= $true )
| ( ( path @ SV597 @ SV602 @ SV578 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3193]) ).
thf(3227,plain,
! [SV602: $i,SV597: $i,SV578: $i,SV661: $i,SV654: $i] :
( ( ( ~ ( precedes @ SV654 @ SV661 @ SV578 ) )
= $true )
| ( ( ! [SY1031: $i] :
( ~ ( precedes @ SY1031 @ SV661 @ SV578 )
| ~ ( sequential @ SV654 @ SY1031 ) )
| ~ ( sequential @ SV654 @ SV661 ) )
= $true )
| ( ( path @ SV597 @ SV602 @ SV578 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3194]) ).
thf(3228,plain,
! [SV602: $i,SV597: $i,SV578: $i,SV662: $i,SV655: $i] :
( ( ( ~ ( precedes @ SV655 @ SV662 @ SV578 ) )
= $true )
| ( ( ~ ( ~ ( precedes @ ( sK9_E3 @ SV662 @ SV655 @ SV578 ) @ SV662 @ SV578 )
| ~ ( sequential @ SV655 @ ( sK9_E3 @ SV662 @ SV655 @ SV578 ) ) )
| ( sequential @ SV655 @ SV662 ) )
= $true )
| ( ( path @ SV597 @ SV602 @ SV578 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3195]) ).
thf(3229,plain,
! [SV579: $i,SV591: $i,SV610: $i,SV618: $i] :
( ( ( on_path @ ( sK10_E @ SV618 @ SV610 @ SV591 @ SV579 ) @ SV610 )
= $true )
| ( ( in_path @ SV618 @ SV610 )
= $false )
| ( ( path @ SV579 @ SV591 @ SV610 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3196]) ).
thf(3230,plain,
! [SV579: $i,SV591: $i,SV610: $i,SV618: $i] :
( ( ( ( SV618
= ( head_of @ ( sK10_E @ SV618 @ SV610 @ SV591 @ SV579 ) ) )
| ( SV618
= ( tail_of @ ( sK10_E @ SV618 @ SV610 @ SV591 @ SV579 ) ) ) )
= $true )
| ( ( in_path @ SV618 @ SV610 )
= $false )
| ( ( path @ SV579 @ SV591 @ SV610 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3197]) ).
thf(3231,plain,
! [SV603: $i,SV598: $i,SV638: $i,SV580: $i,SV630: $i] :
( ( ( on_path @ SV630 @ SV580 )
= $false )
| ( ( ~ ( on_path @ SV638 @ SV580 ) )
= $true )
| ( ( ! [SY1019: $i] :
( ~ ( precedes @ SY1019 @ SV638 @ SV580 )
| ~ ( sequential @ SV630 @ SY1019 ) ) )
= $true )
| ( ( precedes @ SV630 @ SV638 @ SV580 )
= $true )
| ( ( path @ SV598 @ SV603 @ SV580 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3198]) ).
thf(3232,plain,
! [SV603: $i,SV598: $i,SV639: $i,SV580: $i,SV631: $i] :
( ( ( on_path @ SV631 @ SV580 )
= $false )
| ( ( ~ ( on_path @ SV639 @ SV580 ) )
= $true )
| ( ( ~ ( sequential @ SV631 @ SV639 ) )
= $true )
| ( ( precedes @ SV631 @ SV639 @ SV580 )
= $true )
| ( ( path @ SV598 @ SV603 @ SV580 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3199]) ).
thf(3233,plain,
! [SV612: $i,SV581: $i,SV605: $i] :
( ( ( edge @ SV605 )
= $false )
| ( ( edge @ SV581 )
= $false )
| ( ( ~ ( edge @ SV612 ) )
= $true )
| ( ( ~ ( sequential @ SV581 @ SV605 ) )
= $true )
| ( ( ~ ( sequential @ SV605 @ SV612 ) )
= $true )
| ( ( ~ ( sequential @ SV612 @ SV581 ) )
= $true )
| ( ( triangle @ SV581 @ SV605 @ SV612 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3200]) ).
thf(3234,plain,
! [SV581: $i] :
( ( ~ ~ ( ~ ( ! [SY930: $i,SY931: $i] :
~ ( triangle @ SV581 @ SY930 @ SY931 )
| ( edge @ SV581 ) )
| ~ ! [SY932: $i] :
( ! [SY933: $i] :
~ ( triangle @ SV581 @ SY932 @ SY933 )
| ( edge @ SY932 ) ) )
| ~ ! [SY934: $i,SY935: $i] :
( ~ ( triangle @ SV581 @ SY934 @ SY935 )
| ( edge @ SY935 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3201]) ).
thf(3235,plain,
! [SV669: $i,SV581: $i] :
( ( ! [SY1036: $i] :
~ ( triangle @ SV581 @ SV669 @ SY1036 )
| ( sequential @ SV581 @ SV669 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3202]) ).
thf(3236,plain,
! [SV656: $i,SV645: $i,SV581: $i] :
( ( ( triangle @ SV581 @ SV645 @ SV656 )
= $false )
| ( ( sequential @ SV645 @ SV656 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3203]) ).
thf(3237,plain,
! [SV646: $i,SV640: $i] :
( ( ( SV640 = SV646 )
= $false )
| ( ( sequential @ SV640 @ SV646 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3204]) ).
thf(3238,plain,
! [SV663: $i] :
( ( ( ! [SY1032: $i] :
~ ( sequential @ SV663 @ SY1032 ) )
= $true )
| ( ( edge @ SV663 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3205]) ).
thf(3239,plain,
! [SV670: $i,SV664: $i] :
( ( ~ ( sequential @ SV664 @ SV670 )
| ( edge @ SV670 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3206]) ).
thf(3240,plain,
! [SV607: $i,SV613: $i,SV582: $i] :
( ( ( SV582
= ( tail_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
= $true )
| ( ( path @ SV582 @ SV607 @ SV613 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3207]) ).
thf(3241,plain,
! [SV582: $i,SV607: $i,SV613: $i] :
( ( ( edge @ ( sK11_E @ SV613 @ SV607 @ SV582 ) )
= $true )
| ( ( path @ SV582 @ SV607 @ SV613 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3208]) ).
thf(3242,plain,
! [SV582: $i,SV613: $i,SV607: $i] :
( ( ( ( SV607
!= ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
| ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ empty ) )
| ! [SY1002: $i] :
( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ SY1002 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ SY1002 ) ) )
= $true )
| ( ( path @ SV582 @ SV607 @ SV613 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3209]) ).
thf(3243,plain,
! [SV582: $i,SV613: $i,SV607: $i] :
( ( ( ~ ( ~ ( ( SV607
= ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ ( sK13_SY84 @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ ( sK13_SY84 @ SV613 @ SV607 @ SV582 ) ) ) )
| ~ ( ( SV613
= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ empty ) )
| ~ ( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ ( sK12_SY85 @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ ( sK12_SY85 @ SV613 @ SV607 @ SV582 ) ) ) ) ) )
= $true )
| ( ( path @ SV582 @ SV607 @ SV613 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3210]) ).
thf(3244,plain,
! [SV614: $i,SV608: $i,SV583: $i] :
( ( ( path @ SV583 @ SV608 @ SV614 )
= $false )
| ( ( SV583 = SV608 )
= $true )
| ( ( less_or_equal @ ( length_of @ SV614 ) @ ( length_of @ ( sK8_P @ SV614 @ SV608 @ SV583 ) ) )
= $false )
| ( ( shortest_path @ SV583 @ SV608 @ SV614 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3212]) ).
thf(3245,plain,
! [SV634: $i,SV657: $i,SV626: $i,SV583: $i] :
( ( ( path @ SV583 @ SV626 @ SV657 )
= $false )
| ( ( less_or_equal @ ( length_of @ SV634 ) @ ( length_of @ SV657 ) )
= $true )
| ( ( shortest_path @ SV583 @ SV626 @ SV634 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3213]) ).
thf(3246,plain,
! [SV665: $i,SV647: $i,SV583: $i] :
( ( ( shortest_path @ SV583 @ SV647 @ SV665 )
= $false )
| ( ( ( SV583 != SV647 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3214]) ).
thf(3247,plain,
! [SV658: $i,SV648: $i,SV583: $i] :
( ( ( shortest_path @ SV583 @ SV648 @ SV658 )
= $false )
| ( ( path @ SV583 @ SV648 @ SV658 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3215]) ).
thf(3248,plain,
! [SV584: $i,SV671: $i,SV666: $i] :
( ( ( ~ ( path @ SV666 @ SV671 @ SV584 ) )
= $true )
| ( ( on_path @ ( sK6_E1 @ SV584 ) @ SV584 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV584 )
= ( number_of_in @ triangles @ SV584 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3216]) ).
thf(3249,plain,
! [SV584: $i,SV672: $i,SV667: $i] :
( ( ( ~ ( path @ SV667 @ SV672 @ SV584 ) )
= $true )
| ( ( on_path @ ( sK7_SY80 @ SV584 ) @ SV584 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV584 )
= ( number_of_in @ triangles @ SV584 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3217]) ).
thf(3250,plain,
! [SV594: $i,SV589: $i,SV650: $i,SV576: $i] :
( ( ( SV576
= ( tail_of @ SV650 ) )
= $false )
| ( ( ~ ( edge @ SV650 ) )
= $true )
| ( ( ( SV589
!= ( head_of @ SV650 ) )
| ( SV594
!= ( path_cons @ SV650 @ empty ) ) )
= $true )
| ( ( vertex @ SV576 )
= $false )
| ( ( vertex @ SV589 )
= $false )
| ( ( path @ SV576 @ SV589 @ SV594 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3220]) ).
thf(3251,plain,
! [SV589: $i,SV594: $i,SV651: $i,SV576: $i] :
( ( ( SV576
= ( tail_of @ SV651 ) )
= $false )
| ( ( ~ ( edge @ SV651 ) )
= $true )
| ( ( ! [SY1025: $i] :
( ( SV594
!= ( path_cons @ SV651 @ SY1025 ) )
| ~ ( path @ ( head_of @ SV651 ) @ SV589 @ SY1025 ) ) )
= $true )
| ( ( vertex @ SV576 )
= $false )
| ( ( vertex @ SV589 )
= $false )
| ( ( path @ SV576 @ SV589 @ SV594 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3221]) ).
thf(3252,plain,
! [SV590: $i,SV577: $i,SV629: $i,SV616: $i,SV595: $i,SV659: $i] :
( ( ( ( tail_of @ SV659 )
= ( tail_of @ SV595 ) )
= $false )
| ( ( ( ( head_of @ SV659 )
!= ( head_of @ SV616 ) ) )
= $true )
| ( ( precedes @ SV595 @ SV616 @ SV629 )
= $false )
| ( ( shortest_path @ SV577 @ SV590 @ SV629 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3222]) ).
thf(3253,plain,
! [SV599: $i,SV596: $i] :
( ( ( ( SV596
!= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
!= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
!= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
!= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
= $true )
| ( ( SV596 = SV599 )
= $true )
| ( ( vertex @ SV596 )
= $false )
| ( ( vertex @ SV599 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[3223]) ).
thf(3254,plain,
! [SV599: $i,SV596: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( SV596
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
| ~ ( ( SV596
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) ) )
| ~ ~ ( ~ ( ( SV599
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
| ~ ( ( SV599
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) ) ) ) )
= $true )
| ( ( SV596 = SV599 )
= $true )
| ( ( vertex @ SV596 )
= $false )
| ( ( vertex @ SV599 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[3224]) ).
thf(3255,plain,
! [SV602: $i,SV597: $i,SV578: $i,SV668: $i,SV652: $i] :
( ( ( precedes @ SV652 @ SV668 @ SV578 )
= $false )
| ( ( on_path @ SV652 @ SV578 )
= $true )
| ( ( path @ SV597 @ SV602 @ SV578 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3225]) ).
thf(3256,plain,
! [SV602: $i,SV597: $i,SV578: $i,SV660: $i,SV653: $i] :
( ( ( precedes @ SV653 @ SV660 @ SV578 )
= $false )
| ( ( on_path @ SV660 @ SV578 )
= $true )
| ( ( path @ SV597 @ SV602 @ SV578 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3226]) ).
thf(3257,plain,
! [SV602: $i,SV597: $i,SV578: $i,SV661: $i,SV654: $i] :
( ( ( precedes @ SV654 @ SV661 @ SV578 )
= $false )
| ( ( ! [SY1031: $i] :
( ~ ( precedes @ SY1031 @ SV661 @ SV578 )
| ~ ( sequential @ SV654 @ SY1031 ) )
| ~ ( sequential @ SV654 @ SV661 ) )
= $true )
| ( ( path @ SV597 @ SV602 @ SV578 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3227]) ).
thf(3258,plain,
! [SV602: $i,SV597: $i,SV578: $i,SV662: $i,SV655: $i] :
( ( ( precedes @ SV655 @ SV662 @ SV578 )
= $false )
| ( ( ~ ( ~ ( precedes @ ( sK9_E3 @ SV662 @ SV655 @ SV578 ) @ SV662 @ SV578 )
| ~ ( sequential @ SV655 @ ( sK9_E3 @ SV662 @ SV655 @ SV578 ) ) )
| ( sequential @ SV655 @ SV662 ) )
= $true )
| ( ( path @ SV597 @ SV602 @ SV578 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3228]) ).
thf(3259,plain,
! [SV579: $i,SV591: $i,SV610: $i,SV618: $i] :
( ( ( SV618
= ( head_of @ ( sK10_E @ SV618 @ SV610 @ SV591 @ SV579 ) ) )
= $true )
| ( ( SV618
= ( tail_of @ ( sK10_E @ SV618 @ SV610 @ SV591 @ SV579 ) ) )
= $true )
| ( ( in_path @ SV618 @ SV610 )
= $false )
| ( ( path @ SV579 @ SV591 @ SV610 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3230]) ).
thf(3260,plain,
! [SV603: $i,SV598: $i,SV630: $i,SV580: $i,SV638: $i] :
( ( ( on_path @ SV638 @ SV580 )
= $false )
| ( ( on_path @ SV630 @ SV580 )
= $false )
| ( ( ! [SY1019: $i] :
( ~ ( precedes @ SY1019 @ SV638 @ SV580 )
| ~ ( sequential @ SV630 @ SY1019 ) ) )
= $true )
| ( ( precedes @ SV630 @ SV638 @ SV580 )
= $true )
| ( ( path @ SV598 @ SV603 @ SV580 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3231]) ).
thf(3261,plain,
! [SV603: $i,SV598: $i,SV631: $i,SV580: $i,SV639: $i] :
( ( ( on_path @ SV639 @ SV580 )
= $false )
| ( ( on_path @ SV631 @ SV580 )
= $false )
| ( ( ~ ( sequential @ SV631 @ SV639 ) )
= $true )
| ( ( precedes @ SV631 @ SV639 @ SV580 )
= $true )
| ( ( path @ SV598 @ SV603 @ SV580 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3232]) ).
thf(3262,plain,
! [SV605: $i,SV581: $i,SV612: $i] :
( ( ( edge @ SV612 )
= $false )
| ( ( edge @ SV581 )
= $false )
| ( ( edge @ SV605 )
= $false )
| ( ( ~ ( sequential @ SV581 @ SV605 ) )
= $true )
| ( ( ~ ( sequential @ SV605 @ SV612 ) )
= $true )
| ( ( ~ ( sequential @ SV612 @ SV581 ) )
= $true )
| ( ( triangle @ SV581 @ SV605 @ SV612 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3233]) ).
thf(3263,plain,
! [SV581: $i] :
( ( ~ ~ ( ~ ( ! [SY930: $i,SY931: $i] :
~ ( triangle @ SV581 @ SY930 @ SY931 )
| ( edge @ SV581 ) )
| ~ ! [SY932: $i] :
( ! [SY933: $i] :
~ ( triangle @ SV581 @ SY932 @ SY933 )
| ( edge @ SY932 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3234]) ).
thf(3264,plain,
! [SV581: $i] :
( ( ~ ! [SY934: $i,SY935: $i] :
( ~ ( triangle @ SV581 @ SY934 @ SY935 )
| ( edge @ SY935 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3234]) ).
thf(3265,plain,
! [SV669: $i,SV581: $i] :
( ( ( ! [SY1036: $i] :
~ ( triangle @ SV581 @ SV669 @ SY1036 ) )
= $true )
| ( ( sequential @ SV581 @ SV669 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3235]) ).
thf(3266,plain,
! [SV673: $i,SV663: $i] :
( ( ( ~ ( sequential @ SV663 @ SV673 ) )
= $true )
| ( ( edge @ SV663 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3238]) ).
thf(3267,plain,
! [SV670: $i,SV664: $i] :
( ( ( ~ ( sequential @ SV664 @ SV670 ) )
= $true )
| ( ( edge @ SV670 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3239]) ).
thf(3268,plain,
! [SV582: $i,SV613: $i,SV607: $i] :
( ( ( ( SV607
!= ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
| ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ empty ) ) )
= $true )
| ( ( ! [SY1002: $i] :
( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ SY1002 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ SY1002 ) ) )
= $true )
| ( ( path @ SV582 @ SV607 @ SV613 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3242]) ).
thf(3269,plain,
! [SV582: $i,SV613: $i,SV607: $i] :
( ( ( ~ ( ( SV607
= ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ ( sK13_SY84 @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ ( sK13_SY84 @ SV613 @ SV607 @ SV582 ) ) ) )
| ~ ( ( SV613
= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ empty ) )
| ~ ( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ ( sK12_SY85 @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ ( sK12_SY85 @ SV613 @ SV607 @ SV582 ) ) ) ) )
= $false )
| ( ( path @ SV582 @ SV607 @ SV613 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3243]) ).
thf(3270,plain,
! [SV665: $i,SV647: $i,SV583: $i] :
( ( ( SV583 = SV647 )
= $false )
| ( ( shortest_path @ SV583 @ SV647 @ SV665 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3246]) ).
thf(3271,plain,
! [SV584: $i,SV671: $i,SV666: $i] :
( ( ( path @ SV666 @ SV671 @ SV584 )
= $false )
| ( ( on_path @ ( sK6_E1 @ SV584 ) @ SV584 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV584 )
= ( number_of_in @ triangles @ SV584 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3248]) ).
thf(3272,plain,
! [SV584: $i,SV672: $i,SV667: $i] :
( ( ( path @ SV667 @ SV672 @ SV584 )
= $false )
| ( ( on_path @ ( sK7_SY80 @ SV584 ) @ SV584 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV584 )
= ( number_of_in @ triangles @ SV584 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3249]) ).
thf(3273,plain,
! [SV594: $i,SV589: $i,SV576: $i,SV650: $i] :
( ( ( edge @ SV650 )
= $false )
| ( ( SV576
= ( tail_of @ SV650 ) )
= $false )
| ( ( ( SV589
!= ( head_of @ SV650 ) )
| ( SV594
!= ( path_cons @ SV650 @ empty ) ) )
= $true )
| ( ( vertex @ SV576 )
= $false )
| ( ( vertex @ SV589 )
= $false )
| ( ( path @ SV576 @ SV589 @ SV594 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3250]) ).
thf(3274,plain,
! [SV589: $i,SV594: $i,SV576: $i,SV651: $i] :
( ( ( edge @ SV651 )
= $false )
| ( ( SV576
= ( tail_of @ SV651 ) )
= $false )
| ( ( ! [SY1025: $i] :
( ( SV594
!= ( path_cons @ SV651 @ SY1025 ) )
| ~ ( path @ ( head_of @ SV651 ) @ SV589 @ SY1025 ) ) )
= $true )
| ( ( vertex @ SV576 )
= $false )
| ( ( vertex @ SV589 )
= $false )
| ( ( path @ SV576 @ SV589 @ SV594 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3251]) ).
thf(3275,plain,
! [SV590: $i,SV577: $i,SV629: $i,SV595: $i,SV616: $i,SV659: $i] :
( ( ( ( head_of @ SV659 )
= ( head_of @ SV616 ) )
= $false )
| ( ( ( tail_of @ SV659 )
= ( tail_of @ SV595 ) )
= $false )
| ( ( precedes @ SV595 @ SV616 @ SV629 )
= $false )
| ( ( shortest_path @ SV577 @ SV590 @ SV629 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3252]) ).
thf(3276,plain,
! [SV599: $i,SV596: $i] :
( ( ( ( SV596
!= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
!= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
= $true )
| ( ( ( SV599
!= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
!= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
= $true )
| ( ( SV596 = SV599 )
= $true )
| ( ( vertex @ SV596 )
= $false )
| ( ( vertex @ SV599 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[3253]) ).
thf(3277,plain,
! [SV599: $i,SV596: $i] :
( ( ( ~ ~ ( ~ ( ( SV596
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
| ~ ( ( SV596
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) ) )
| ~ ~ ( ~ ( ( SV599
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
| ~ ( ( SV599
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) ) ) )
= $false )
| ( ( SV596 = SV599 )
= $true )
| ( ( vertex @ SV596 )
= $false )
| ( ( vertex @ SV599 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[3254]) ).
thf(3278,plain,
! [SV602: $i,SV597: $i,SV654: $i,SV578: $i,SV661: $i] :
( ( ( ! [SY1031: $i] :
( ~ ( precedes @ SY1031 @ SV661 @ SV578 )
| ~ ( sequential @ SV654 @ SY1031 ) ) )
= $true )
| ( ( ~ ( sequential @ SV654 @ SV661 ) )
= $true )
| ( ( precedes @ SV654 @ SV661 @ SV578 )
= $false )
| ( ( path @ SV597 @ SV602 @ SV578 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3257]) ).
thf(3279,plain,
! [SV602: $i,SV597: $i,SV578: $i,SV655: $i,SV662: $i] :
( ( ( ~ ( ~ ( precedes @ ( sK9_E3 @ SV662 @ SV655 @ SV578 ) @ SV662 @ SV578 )
| ~ ( sequential @ SV655 @ ( sK9_E3 @ SV662 @ SV655 @ SV578 ) ) ) )
= $true )
| ( ( sequential @ SV655 @ SV662 )
= $true )
| ( ( precedes @ SV655 @ SV662 @ SV578 )
= $false )
| ( ( path @ SV597 @ SV602 @ SV578 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3258]) ).
thf(3280,plain,
! [SV603: $i,SV598: $i,SV630: $i,SV580: $i,SV638: $i,SV674: $i] :
( ( ( ~ ( precedes @ SV674 @ SV638 @ SV580 )
| ~ ( sequential @ SV630 @ SV674 ) )
= $true )
| ( ( on_path @ SV630 @ SV580 )
= $false )
| ( ( on_path @ SV638 @ SV580 )
= $false )
| ( ( precedes @ SV630 @ SV638 @ SV580 )
= $true )
| ( ( path @ SV598 @ SV603 @ SV580 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3260]) ).
thf(3281,plain,
! [SV603: $i,SV598: $i,SV580: $i,SV639: $i,SV631: $i] :
( ( ( sequential @ SV631 @ SV639 )
= $false )
| ( ( on_path @ SV631 @ SV580 )
= $false )
| ( ( on_path @ SV639 @ SV580 )
= $false )
| ( ( precedes @ SV631 @ SV639 @ SV580 )
= $true )
| ( ( path @ SV598 @ SV603 @ SV580 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3261]) ).
thf(3282,plain,
! [SV612: $i,SV605: $i,SV581: $i] :
( ( ( sequential @ SV581 @ SV605 )
= $false )
| ( ( edge @ SV605 )
= $false )
| ( ( edge @ SV581 )
= $false )
| ( ( edge @ SV612 )
= $false )
| ( ( ~ ( sequential @ SV605 @ SV612 ) )
= $true )
| ( ( ~ ( sequential @ SV612 @ SV581 ) )
= $true )
| ( ( triangle @ SV581 @ SV605 @ SV612 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3262]) ).
thf(3283,plain,
! [SV581: $i] :
( ( ~ ( ~ ( ! [SY930: $i,SY931: $i] :
~ ( triangle @ SV581 @ SY930 @ SY931 )
| ( edge @ SV581 ) )
| ~ ! [SY932: $i] :
( ! [SY933: $i] :
~ ( triangle @ SV581 @ SY932 @ SY933 )
| ( edge @ SY932 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3263]) ).
thf(3284,plain,
! [SV581: $i] :
( ( ! [SY934: $i,SY935: $i] :
( ~ ( triangle @ SV581 @ SY934 @ SY935 )
| ( edge @ SY935 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3264]) ).
thf(3285,plain,
! [SV675: $i,SV669: $i,SV581: $i] :
( ( ( ~ ( triangle @ SV581 @ SV669 @ SV675 ) )
= $true )
| ( ( sequential @ SV581 @ SV669 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3265]) ).
thf(3286,plain,
! [SV673: $i,SV663: $i] :
( ( ( sequential @ SV663 @ SV673 )
= $false )
| ( ( edge @ SV663 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3266]) ).
thf(3287,plain,
! [SV670: $i,SV664: $i] :
( ( ( sequential @ SV664 @ SV670 )
= $false )
| ( ( edge @ SV670 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3267]) ).
thf(3288,plain,
! [SV582: $i,SV613: $i,SV607: $i] :
( ( ( ( SV607
!= ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) ) )
= $true )
| ( ( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ empty ) ) )
= $true )
| ( ( ! [SY1002: $i] :
( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ SY1002 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ SY1002 ) ) )
= $true )
| ( ( path @ SV582 @ SV607 @ SV613 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3268]) ).
thf(3289,plain,
! [SV582: $i,SV613: $i,SV607: $i] :
( ( ( ~ ( ( SV607
= ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ ( sK13_SY84 @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ ( sK13_SY84 @ SV613 @ SV607 @ SV582 ) ) ) ) )
= $false )
| ( ( path @ SV582 @ SV607 @ SV613 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3269]) ).
thf(3290,plain,
! [SV582: $i,SV607: $i,SV613: $i] :
( ( ( ~ ( ( SV613
= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ empty ) )
| ~ ( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ ( sK12_SY85 @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ ( sK12_SY85 @ SV613 @ SV607 @ SV582 ) ) ) ) )
= $false )
| ( ( path @ SV582 @ SV607 @ SV613 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3269]) ).
thf(3291,plain,
! [SV576: $i,SV594: $i,SV650: $i,SV589: $i] :
( ( ( ( SV589
!= ( head_of @ SV650 ) ) )
= $true )
| ( ( ( SV594
!= ( path_cons @ SV650 @ empty ) ) )
= $true )
| ( ( SV576
= ( tail_of @ SV650 ) )
= $false )
| ( ( edge @ SV650 )
= $false )
| ( ( vertex @ SV576 )
= $false )
| ( ( vertex @ SV589 )
= $false )
| ( ( path @ SV576 @ SV589 @ SV594 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3273]) ).
thf(3292,plain,
! [SV576: $i,SV589: $i,SV676: $i,SV651: $i,SV594: $i] :
( ( ( ( SV594
!= ( path_cons @ SV651 @ SV676 ) )
| ~ ( path @ ( head_of @ SV651 ) @ SV589 @ SV676 ) )
= $true )
| ( ( SV576
= ( tail_of @ SV651 ) )
= $false )
| ( ( edge @ SV651 )
= $false )
| ( ( vertex @ SV576 )
= $false )
| ( ( vertex @ SV589 )
= $false )
| ( ( path @ SV576 @ SV589 @ SV594 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3274]) ).
thf(3293,plain,
! [SV599: $i,SV596: $i] :
( ( ( ( SV596
!= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
= $true )
| ( ( ( SV599
!= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
= $true )
| ( ( ( SV599
!= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
!= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
= $true )
| ( ( SV596 = SV599 )
= $true )
| ( ( vertex @ SV596 )
= $false )
| ( ( vertex @ SV599 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[3276]) ).
thf(3294,plain,
! [SV599: $i,SV596: $i] :
( ( ( ~ ~ ( ~ ( ( SV596
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
| ~ ( ( SV596
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) ) ) )
= $false )
| ( ( SV596 = SV599 )
= $true )
| ( ( vertex @ SV596 )
= $false )
| ( ( vertex @ SV599 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[3277]) ).
thf(3295,plain,
! [SV596: $i,SV599: $i] :
( ( ( ~ ~ ( ~ ( ( SV599
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
| ~ ( ( SV599
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) ) ) )
= $false )
| ( ( SV596 = SV599 )
= $true )
| ( ( vertex @ SV596 )
= $false )
| ( ( vertex @ SV599 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[3277]) ).
thf(3296,plain,
! [SV602: $i,SV597: $i,SV654: $i,SV578: $i,SV661: $i,SV677: $i] :
( ( ( ~ ( precedes @ SV677 @ SV661 @ SV578 )
| ~ ( sequential @ SV654 @ SV677 ) )
= $true )
| ( ( ~ ( sequential @ SV654 @ SV661 ) )
= $true )
| ( ( precedes @ SV654 @ SV661 @ SV578 )
= $false )
| ( ( path @ SV597 @ SV602 @ SV578 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3278]) ).
thf(3297,plain,
! [SV602: $i,SV597: $i,SV578: $i,SV655: $i,SV662: $i] :
( ( ( ~ ( precedes @ ( sK9_E3 @ SV662 @ SV655 @ SV578 ) @ SV662 @ SV578 )
| ~ ( sequential @ SV655 @ ( sK9_E3 @ SV662 @ SV655 @ SV578 ) ) )
= $false )
| ( ( sequential @ SV655 @ SV662 )
= $true )
| ( ( precedes @ SV655 @ SV662 @ SV578 )
= $false )
| ( ( path @ SV597 @ SV602 @ SV578 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3279]) ).
thf(3298,plain,
! [SV603: $i,SV598: $i,SV630: $i,SV580: $i,SV638: $i,SV674: $i] :
( ( ( ~ ( precedes @ SV674 @ SV638 @ SV580 ) )
= $true )
| ( ( ~ ( sequential @ SV630 @ SV674 ) )
= $true )
| ( ( on_path @ SV630 @ SV580 )
= $false )
| ( ( on_path @ SV638 @ SV580 )
= $false )
| ( ( precedes @ SV630 @ SV638 @ SV580 )
= $true )
| ( ( path @ SV598 @ SV603 @ SV580 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3280]) ).
thf(3299,plain,
! [SV581: $i,SV612: $i,SV605: $i] :
( ( ( sequential @ SV605 @ SV612 )
= $false )
| ( ( edge @ SV612 )
= $false )
| ( ( edge @ SV581 )
= $false )
| ( ( edge @ SV605 )
= $false )
| ( ( sequential @ SV581 @ SV605 )
= $false )
| ( ( ~ ( sequential @ SV612 @ SV581 ) )
= $true )
| ( ( triangle @ SV581 @ SV605 @ SV612 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3282]) ).
thf(3300,plain,
! [SV581: $i] :
( ( ~ ( ! [SY930: $i,SY931: $i] :
~ ( triangle @ SV581 @ SY930 @ SY931 )
| ( edge @ SV581 ) )
| ~ ! [SY932: $i] :
( ! [SY933: $i] :
~ ( triangle @ SV581 @ SY932 @ SY933 )
| ( edge @ SY932 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3283]) ).
thf(3301,plain,
! [SV678: $i,SV581: $i] :
( ( ! [SY1037: $i] :
( ~ ( triangle @ SV581 @ SV678 @ SY1037 )
| ( edge @ SY1037 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3284]) ).
thf(3302,plain,
! [SV675: $i,SV669: $i,SV581: $i] :
( ( ( triangle @ SV581 @ SV669 @ SV675 )
= $false )
| ( ( sequential @ SV581 @ SV669 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3285]) ).
thf(3303,plain,
! [SV582: $i,SV613: $i,SV607: $i] :
( ( ( SV607
= ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
= $false )
| ( ( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ empty ) ) )
= $true )
| ( ( ! [SY1002: $i] :
( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ SY1002 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ SY1002 ) ) )
= $true )
| ( ( path @ SV582 @ SV607 @ SV613 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3288]) ).
thf(3304,plain,
! [SV582: $i,SV613: $i,SV607: $i] :
( ( ( ( SV607
= ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ ( sK13_SY84 @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ ( sK13_SY84 @ SV613 @ SV607 @ SV582 ) ) ) )
= $true )
| ( ( path @ SV582 @ SV607 @ SV613 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3289]) ).
thf(3305,plain,
! [SV582: $i,SV607: $i,SV613: $i] :
( ( ( ( SV613
= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ empty ) )
| ~ ( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ ( sK12_SY85 @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ ( sK12_SY85 @ SV613 @ SV607 @ SV582 ) ) ) )
= $true )
| ( ( path @ SV582 @ SV607 @ SV613 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3290]) ).
thf(3306,plain,
! [SV576: $i,SV594: $i,SV650: $i,SV589: $i] :
( ( ( SV589
= ( head_of @ SV650 ) )
= $false )
| ( ( ( SV594
!= ( path_cons @ SV650 @ empty ) ) )
= $true )
| ( ( SV576
= ( tail_of @ SV650 ) )
= $false )
| ( ( edge @ SV650 )
= $false )
| ( ( vertex @ SV576 )
= $false )
| ( ( vertex @ SV589 )
= $false )
| ( ( path @ SV576 @ SV589 @ SV594 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3291]) ).
thf(3307,plain,
! [SV576: $i,SV589: $i,SV676: $i,SV651: $i,SV594: $i] :
( ( ( ( SV594
!= ( path_cons @ SV651 @ SV676 ) ) )
= $true )
| ( ( ~ ( path @ ( head_of @ SV651 ) @ SV589 @ SV676 ) )
= $true )
| ( ( SV576
= ( tail_of @ SV651 ) )
= $false )
| ( ( edge @ SV651 )
= $false )
| ( ( vertex @ SV576 )
= $false )
| ( ( vertex @ SV589 )
= $false )
| ( ( path @ SV576 @ SV589 @ SV594 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3292]) ).
thf(3308,plain,
! [SV599: $i,SV596: $i] :
( ( ( SV596
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
= $false )
| ( ( ( SV599
!= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
= $true )
| ( ( ( SV599
!= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
!= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
= $true )
| ( ( SV596 = SV599 )
= $true )
| ( ( vertex @ SV596 )
= $false )
| ( ( vertex @ SV599 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[3293]) ).
thf(3309,plain,
! [SV599: $i,SV596: $i] :
( ( ( ~ ( ~ ( ( SV596
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
| ~ ( ( SV596
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) ) ) )
= $true )
| ( ( SV596 = SV599 )
= $true )
| ( ( vertex @ SV596 )
= $false )
| ( ( vertex @ SV599 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[3294]) ).
thf(3310,plain,
! [SV596: $i,SV599: $i] :
( ( ( ~ ( ~ ( ( SV599
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
| ~ ( ( SV599
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) ) ) )
= $true )
| ( ( SV596 = SV599 )
= $true )
| ( ( vertex @ SV596 )
= $false )
| ( ( vertex @ SV599 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[3295]) ).
thf(3311,plain,
! [SV602: $i,SV597: $i,SV654: $i,SV578: $i,SV661: $i,SV677: $i] :
( ( ( ~ ( precedes @ SV677 @ SV661 @ SV578 ) )
= $true )
| ( ( ~ ( sequential @ SV654 @ SV677 ) )
= $true )
| ( ( ~ ( sequential @ SV654 @ SV661 ) )
= $true )
| ( ( precedes @ SV654 @ SV661 @ SV578 )
= $false )
| ( ( path @ SV597 @ SV602 @ SV578 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3296]) ).
thf(3312,plain,
! [SV602: $i,SV597: $i,SV578: $i,SV655: $i,SV662: $i] :
( ( ( ~ ( precedes @ ( sK9_E3 @ SV662 @ SV655 @ SV578 ) @ SV662 @ SV578 ) )
= $false )
| ( ( sequential @ SV655 @ SV662 )
= $true )
| ( ( precedes @ SV655 @ SV662 @ SV578 )
= $false )
| ( ( path @ SV597 @ SV602 @ SV578 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3297]) ).
thf(3313,plain,
! [SV602: $i,SV597: $i,SV578: $i,SV662: $i,SV655: $i] :
( ( ( ~ ( sequential @ SV655 @ ( sK9_E3 @ SV662 @ SV655 @ SV578 ) ) )
= $false )
| ( ( sequential @ SV655 @ SV662 )
= $true )
| ( ( precedes @ SV655 @ SV662 @ SV578 )
= $false )
| ( ( path @ SV597 @ SV602 @ SV578 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3297]) ).
thf(3314,plain,
! [SV603: $i,SV598: $i,SV630: $i,SV580: $i,SV638: $i,SV674: $i] :
( ( ( precedes @ SV674 @ SV638 @ SV580 )
= $false )
| ( ( ~ ( sequential @ SV630 @ SV674 ) )
= $true )
| ( ( on_path @ SV630 @ SV580 )
= $false )
| ( ( on_path @ SV638 @ SV580 )
= $false )
| ( ( precedes @ SV630 @ SV638 @ SV580 )
= $true )
| ( ( path @ SV598 @ SV603 @ SV580 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3298]) ).
thf(3315,plain,
! [SV605: $i,SV581: $i,SV612: $i] :
( ( ( sequential @ SV612 @ SV581 )
= $false )
| ( ( sequential @ SV581 @ SV605 )
= $false )
| ( ( edge @ SV605 )
= $false )
| ( ( edge @ SV581 )
= $false )
| ( ( edge @ SV612 )
= $false )
| ( ( sequential @ SV605 @ SV612 )
= $false )
| ( ( triangle @ SV581 @ SV605 @ SV612 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3299]) ).
thf(3316,plain,
! [SV581: $i] :
( ( ~ ( ! [SY930: $i,SY931: $i] :
~ ( triangle @ SV581 @ SY930 @ SY931 )
| ( edge @ SV581 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3300]) ).
thf(3317,plain,
! [SV581: $i] :
( ( ~ ! [SY932: $i] :
( ! [SY933: $i] :
~ ( triangle @ SV581 @ SY932 @ SY933 )
| ( edge @ SY932 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3300]) ).
thf(3318,plain,
! [SV679: $i,SV678: $i,SV581: $i] :
( ( ~ ( triangle @ SV581 @ SV678 @ SV679 )
| ( edge @ SV679 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3301]) ).
thf(3319,plain,
! [SV582: $i,SV607: $i,SV613: $i] :
( ( ( SV613
= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ empty ) )
= $false )
| ( ( SV607
= ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
= $false )
| ( ( ! [SY1002: $i] :
( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ SY1002 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ SY1002 ) ) )
= $true )
| ( ( path @ SV582 @ SV607 @ SV613 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3303]) ).
thf(3320,plain,
! [SV582: $i,SV613: $i,SV607: $i] :
( ( ( SV607
= ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
= $true )
| ( ( ~ ( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ ( sK13_SY84 @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ ( sK13_SY84 @ SV613 @ SV607 @ SV582 ) ) ) )
= $true )
| ( ( path @ SV582 @ SV607 @ SV613 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3304]) ).
thf(3321,plain,
! [SV582: $i,SV607: $i,SV613: $i] :
( ( ( SV613
= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ empty ) )
= $true )
| ( ( ~ ( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ ( sK12_SY85 @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ ( sK12_SY85 @ SV613 @ SV607 @ SV582 ) ) ) )
= $true )
| ( ( path @ SV582 @ SV607 @ SV613 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3305]) ).
thf(3322,plain,
! [SV576: $i,SV589: $i,SV650: $i,SV594: $i] :
( ( ( SV594
= ( path_cons @ SV650 @ empty ) )
= $false )
| ( ( SV589
= ( head_of @ SV650 ) )
= $false )
| ( ( SV576
= ( tail_of @ SV650 ) )
= $false )
| ( ( edge @ SV650 )
= $false )
| ( ( vertex @ SV576 )
= $false )
| ( ( vertex @ SV589 )
= $false )
| ( ( path @ SV576 @ SV589 @ SV594 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3306]) ).
thf(3323,plain,
! [SV576: $i,SV589: $i,SV676: $i,SV651: $i,SV594: $i] :
( ( ( SV594
= ( path_cons @ SV651 @ SV676 ) )
= $false )
| ( ( ~ ( path @ ( head_of @ SV651 ) @ SV589 @ SV676 ) )
= $true )
| ( ( SV576
= ( tail_of @ SV651 ) )
= $false )
| ( ( edge @ SV651 )
= $false )
| ( ( vertex @ SV576 )
= $false )
| ( ( vertex @ SV589 )
= $false )
| ( ( path @ SV576 @ SV589 @ SV594 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3307]) ).
thf(3324,plain,
! [SV596: $i,SV599: $i] :
( ( ( SV599
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
= $false )
| ( ( SV596
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
= $false )
| ( ( ( SV599
!= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
!= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
= $true )
| ( ( SV596 = SV599 )
= $true )
| ( ( vertex @ SV596 )
= $false )
| ( ( vertex @ SV599 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[3308]) ).
thf(3325,plain,
! [SV599: $i,SV596: $i] :
( ( ( ~ ( ( SV596
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
| ~ ( ( SV596
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) ) )
= $false )
| ( ( SV596 = SV599 )
= $true )
| ( ( vertex @ SV596 )
= $false )
| ( ( vertex @ SV599 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[3309]) ).
thf(3326,plain,
! [SV596: $i,SV599: $i] :
( ( ( ~ ( ( SV599
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
| ~ ( ( SV599
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) ) )
= $false )
| ( ( SV596 = SV599 )
= $true )
| ( ( vertex @ SV596 )
= $false )
| ( ( vertex @ SV599 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[3310]) ).
thf(3327,plain,
! [SV602: $i,SV597: $i,SV654: $i,SV578: $i,SV661: $i,SV677: $i] :
( ( ( precedes @ SV677 @ SV661 @ SV578 )
= $false )
| ( ( ~ ( sequential @ SV654 @ SV677 ) )
= $true )
| ( ( ~ ( sequential @ SV654 @ SV661 ) )
= $true )
| ( ( precedes @ SV654 @ SV661 @ SV578 )
= $false )
| ( ( path @ SV597 @ SV602 @ SV578 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3311]) ).
thf(3328,plain,
! [SV602: $i,SV597: $i,SV578: $i,SV655: $i,SV662: $i] :
( ( ( precedes @ ( sK9_E3 @ SV662 @ SV655 @ SV578 ) @ SV662 @ SV578 )
= $true )
| ( ( sequential @ SV655 @ SV662 )
= $true )
| ( ( precedes @ SV655 @ SV662 @ SV578 )
= $false )
| ( ( path @ SV597 @ SV602 @ SV578 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3312]) ).
thf(3329,plain,
! [SV602: $i,SV597: $i,SV578: $i,SV662: $i,SV655: $i] :
( ( ( sequential @ SV655 @ ( sK9_E3 @ SV662 @ SV655 @ SV578 ) )
= $true )
| ( ( sequential @ SV655 @ SV662 )
= $true )
| ( ( precedes @ SV655 @ SV662 @ SV578 )
= $false )
| ( ( path @ SV597 @ SV602 @ SV578 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3313]) ).
thf(3330,plain,
! [SV603: $i,SV598: $i,SV580: $i,SV638: $i,SV674: $i,SV630: $i] :
( ( ( sequential @ SV630 @ SV674 )
= $false )
| ( ( precedes @ SV674 @ SV638 @ SV580 )
= $false )
| ( ( on_path @ SV630 @ SV580 )
= $false )
| ( ( on_path @ SV638 @ SV580 )
= $false )
| ( ( precedes @ SV630 @ SV638 @ SV580 )
= $true )
| ( ( path @ SV598 @ SV603 @ SV580 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3314]) ).
thf(3331,plain,
! [SV581: $i] :
( ( ! [SY930: $i,SY931: $i] :
~ ( triangle @ SV581 @ SY930 @ SY931 )
| ( edge @ SV581 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3316]) ).
thf(3332,plain,
! [SV581: $i] :
( ( ! [SY932: $i] :
( ! [SY933: $i] :
~ ( triangle @ SV581 @ SY932 @ SY933 )
| ( edge @ SY932 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3317]) ).
thf(3333,plain,
! [SV679: $i,SV678: $i,SV581: $i] :
( ( ( ~ ( triangle @ SV581 @ SV678 @ SV679 ) )
= $true )
| ( ( edge @ SV679 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3318]) ).
thf(3334,plain,
! [SV680: $i,SV582: $i,SV607: $i,SV613: $i] :
( ( ( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ SV680 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ SV680 ) )
= $true )
| ( ( SV607
= ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
= $false )
| ( ( SV613
= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ empty ) )
= $false )
| ( ( path @ SV582 @ SV607 @ SV613 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3319]) ).
thf(3335,plain,
! [SV582: $i,SV607: $i,SV613: $i] :
( ( ( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ ( sK13_SY84 @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ ( sK13_SY84 @ SV613 @ SV607 @ SV582 ) ) )
= $false )
| ( ( SV607
= ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
= $true )
| ( ( path @ SV582 @ SV607 @ SV613 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3320]) ).
thf(3336,plain,
! [SV582: $i,SV607: $i,SV613: $i] :
( ( ( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ ( sK12_SY85 @ SV613 @ SV607 @ SV582 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ ( sK12_SY85 @ SV613 @ SV607 @ SV582 ) ) )
= $false )
| ( ( SV613
= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ empty ) )
= $true )
| ( ( path @ SV582 @ SV607 @ SV613 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3321]) ).
thf(3337,plain,
! [SV576: $i,SV594: $i,SV676: $i,SV589: $i,SV651: $i] :
( ( ( path @ ( head_of @ SV651 ) @ SV589 @ SV676 )
= $false )
| ( ( SV594
= ( path_cons @ SV651 @ SV676 ) )
= $false )
| ( ( SV576
= ( tail_of @ SV651 ) )
= $false )
| ( ( edge @ SV651 )
= $false )
| ( ( vertex @ SV576 )
= $false )
| ( ( vertex @ SV589 )
= $false )
| ( ( path @ SV576 @ SV589 @ SV594 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3323]) ).
thf(3338,plain,
! [SV596: $i,SV599: $i] :
( ( ( ( SV599
!= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
= $true )
| ( ( ( SV596
!= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
= $true )
| ( ( SV596
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
= $false )
| ( ( SV599
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
= $false )
| ( ( SV596 = SV599 )
= $true )
| ( ( vertex @ SV596 )
= $false )
| ( ( vertex @ SV599 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[3324]) ).
thf(3339,plain,
! [SV599: $i,SV596: $i] :
( ( ( ~ ( ( SV596
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) ) ) )
= $false )
| ( ( SV596 = SV599 )
= $true )
| ( ( vertex @ SV596 )
= $false )
| ( ( vertex @ SV599 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[3325]) ).
thf(3340,plain,
! [SV599: $i,SV596: $i] :
( ( ( ~ ( ( SV596
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) ) )
= $false )
| ( ( SV596 = SV599 )
= $true )
| ( ( vertex @ SV596 )
= $false )
| ( ( vertex @ SV599 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[3325]) ).
thf(3341,plain,
! [SV596: $i,SV599: $i] :
( ( ( ~ ( ( SV599
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) ) ) )
= $false )
| ( ( SV596 = SV599 )
= $true )
| ( ( vertex @ SV596 )
= $false )
| ( ( vertex @ SV599 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[3326]) ).
thf(3342,plain,
! [SV596: $i,SV599: $i] :
( ( ( ~ ( ( SV599
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) ) )
= $false )
| ( ( SV596 = SV599 )
= $true )
| ( ( vertex @ SV596 )
= $false )
| ( ( vertex @ SV599 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[3326]) ).
thf(3343,plain,
! [SV602: $i,SV597: $i,SV578: $i,SV661: $i,SV677: $i,SV654: $i] :
( ( ( sequential @ SV654 @ SV677 )
= $false )
| ( ( precedes @ SV677 @ SV661 @ SV578 )
= $false )
| ( ( ~ ( sequential @ SV654 @ SV661 ) )
= $true )
| ( ( precedes @ SV654 @ SV661 @ SV578 )
= $false )
| ( ( path @ SV597 @ SV602 @ SV578 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3327]) ).
thf(3344,plain,
! [SV581: $i] :
( ( ( ! [SY930: $i,SY931: $i] :
~ ( triangle @ SV581 @ SY930 @ SY931 ) )
= $true )
| ( ( edge @ SV581 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3331]) ).
thf(3345,plain,
! [SV681: $i,SV581: $i] :
( ( ! [SY1038: $i] :
~ ( triangle @ SV581 @ SV681 @ SY1038 )
| ( edge @ SV681 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3332]) ).
thf(3346,plain,
! [SV679: $i,SV678: $i,SV581: $i] :
( ( ( triangle @ SV581 @ SV678 @ SV679 )
= $false )
| ( ( edge @ SV679 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3333]) ).
thf(3347,plain,
! [SV680: $i,SV582: $i,SV607: $i,SV613: $i] :
( ( ( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ SV680 ) ) )
= $true )
| ( ( ~ ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ SV680 ) )
= $true )
| ( ( SV607
= ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
= $false )
| ( ( SV613
= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ empty ) )
= $false )
| ( ( path @ SV582 @ SV607 @ SV613 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3334]) ).
thf(3348,plain,
! [SV582: $i,SV607: $i,SV613: $i] :
( ( ( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ ( sK13_SY84 @ SV613 @ SV607 @ SV582 ) ) ) )
= $false )
| ( ( SV607
= ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
= $true )
| ( ( path @ SV582 @ SV607 @ SV613 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3335]) ).
thf(3349,plain,
! [SV582: $i,SV607: $i,SV613: $i] :
( ( ( ~ ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ ( sK13_SY84 @ SV613 @ SV607 @ SV582 ) ) )
= $false )
| ( ( SV607
= ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
= $true )
| ( ( path @ SV582 @ SV607 @ SV613 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3335]) ).
thf(3350,plain,
! [SV582: $i,SV607: $i,SV613: $i] :
( ( ( ( SV613
!= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ ( sK12_SY85 @ SV613 @ SV607 @ SV582 ) ) ) )
= $false )
| ( ( SV613
= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ empty ) )
= $true )
| ( ( path @ SV582 @ SV607 @ SV613 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3336]) ).
thf(3351,plain,
! [SV582: $i,SV607: $i,SV613: $i] :
( ( ( ~ ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ ( sK12_SY85 @ SV613 @ SV607 @ SV582 ) ) )
= $false )
| ( ( SV613
= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ empty ) )
= $true )
| ( ( path @ SV582 @ SV607 @ SV613 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3336]) ).
thf(3352,plain,
! [SV596: $i,SV599: $i] :
( ( ( SV599
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
= $false )
| ( ( ( SV596
!= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
= $true )
| ( ( SV596
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
= $false )
| ( ( SV599
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
= $false )
| ( ( SV596 = SV599 )
= $true )
| ( ( vertex @ SV596 )
= $false )
| ( ( vertex @ SV599 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[3338]) ).
thf(3353,plain,
! [SV599: $i,SV596: $i] :
( ( ( ( SV596
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
= $true )
| ( ( SV596 = SV599 )
= $true )
| ( ( vertex @ SV596 )
= $false )
| ( ( vertex @ SV599 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[3339]) ).
thf(3354,plain,
! [SV599: $i,SV596: $i] :
( ( ( ( SV596
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
= $true )
| ( ( SV596 = SV599 )
= $true )
| ( ( vertex @ SV596 )
= $false )
| ( ( vertex @ SV599 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[3340]) ).
thf(3355,plain,
! [SV596: $i,SV599: $i] :
( ( ( ( SV599
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV599
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
= $true )
| ( ( SV596 = SV599 )
= $true )
| ( ( vertex @ SV596 )
= $false )
| ( ( vertex @ SV599 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[3341]) ).
thf(3356,plain,
! [SV596: $i,SV599: $i] :
( ( ( ( SV599
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
| ( SV596
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) ) )
= $true )
| ( ( SV596 = SV599 )
= $true )
| ( ( vertex @ SV596 )
= $false )
| ( ( vertex @ SV599 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[3342]) ).
thf(3357,plain,
! [SV602: $i,SV597: $i,SV578: $i,SV677: $i,SV661: $i,SV654: $i] :
( ( ( sequential @ SV654 @ SV661 )
= $false )
| ( ( precedes @ SV677 @ SV661 @ SV578 )
= $false )
| ( ( sequential @ SV654 @ SV677 )
= $false )
| ( ( precedes @ SV654 @ SV661 @ SV578 )
= $false )
| ( ( path @ SV597 @ SV602 @ SV578 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3343]) ).
thf(3358,plain,
! [SV682: $i,SV581: $i] :
( ( ( ! [SY1039: $i] :
~ ( triangle @ SV581 @ SV682 @ SY1039 ) )
= $true )
| ( ( edge @ SV581 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3344]) ).
thf(3359,plain,
! [SV681: $i,SV581: $i] :
( ( ( ! [SY1038: $i] :
~ ( triangle @ SV581 @ SV681 @ SY1038 ) )
= $true )
| ( ( edge @ SV681 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3345]) ).
thf(3360,plain,
! [SV680: $i,SV582: $i,SV607: $i,SV613: $i] :
( ( ( SV613
= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ SV680 ) )
= $false )
| ( ( ~ ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ SV680 ) )
= $true )
| ( ( SV607
= ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
= $false )
| ( ( SV613
= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ empty ) )
= $false )
| ( ( path @ SV582 @ SV607 @ SV613 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3347]) ).
thf(3361,plain,
! [SV582: $i,SV607: $i,SV613: $i] :
( ( ( SV613
= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ ( sK13_SY84 @ SV613 @ SV607 @ SV582 ) ) )
= $true )
| ( ( SV607
= ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
= $true )
| ( ( path @ SV582 @ SV607 @ SV613 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3348]) ).
thf(3362,plain,
! [SV582: $i,SV607: $i,SV613: $i] :
( ( ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ ( sK13_SY84 @ SV613 @ SV607 @ SV582 ) )
= $true )
| ( ( SV607
= ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
= $true )
| ( ( path @ SV582 @ SV607 @ SV613 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3349]) ).
thf(3363,plain,
! [SV582: $i,SV607: $i,SV613: $i] :
( ( ( SV613
= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ ( sK12_SY85 @ SV613 @ SV607 @ SV582 ) ) )
= $true )
| ( ( SV613
= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ empty ) )
= $true )
| ( ( path @ SV582 @ SV607 @ SV613 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3350]) ).
thf(3364,plain,
! [SV582: $i,SV607: $i,SV613: $i] :
( ( ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ ( sK12_SY85 @ SV613 @ SV607 @ SV582 ) )
= $true )
| ( ( SV613
= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ empty ) )
= $true )
| ( ( path @ SV582 @ SV607 @ SV613 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3351]) ).
thf(3365,plain,
! [SV599: $i,SV596: $i] :
( ( ( SV596
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
= $false )
| ( ( SV599
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
= $false )
| ( ( SV596
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
= $false )
| ( ( SV599
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
= $false )
| ( ( SV596 = SV599 )
= $true )
| ( ( vertex @ SV596 )
= $false )
| ( ( vertex @ SV599 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[3352]) ).
thf(3366,plain,
! [SV599: $i,SV596: $i] :
( ( ( SV596
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
= $true )
| ( ( SV599
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
= $true )
| ( ( SV596 = SV599 )
= $true )
| ( ( vertex @ SV596 )
= $false )
| ( ( vertex @ SV599 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[3353]) ).
thf(3367,plain,
! [SV599: $i,SV596: $i] :
( ( ( SV596
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
= $true )
| ( ( SV596
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
= $true )
| ( ( SV596 = SV599 )
= $true )
| ( ( vertex @ SV596 )
= $false )
| ( ( vertex @ SV599 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[3354]) ).
thf(3368,plain,
! [SV596: $i,SV599: $i] :
( ( ( SV599
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
= $true )
| ( ( SV599
= ( head_of @ ( sK14_E @ SV599 @ SV596 ) ) )
= $true )
| ( ( SV596 = SV599 )
= $true )
| ( ( vertex @ SV596 )
= $false )
| ( ( vertex @ SV599 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[3355]) ).
thf(3369,plain,
! [SV596: $i,SV599: $i] :
( ( ( SV599
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
= $true )
| ( ( SV596
= ( tail_of @ ( sK14_E @ SV599 @ SV596 ) ) )
= $true )
| ( ( SV596 = SV599 )
= $true )
| ( ( vertex @ SV596 )
= $false )
| ( ( vertex @ SV599 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[3356]) ).
thf(3370,plain,
! [SV683: $i,SV682: $i,SV581: $i] :
( ( ( ~ ( triangle @ SV581 @ SV682 @ SV683 ) )
= $true )
| ( ( edge @ SV581 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3358]) ).
thf(3371,plain,
! [SV684: $i,SV681: $i,SV581: $i] :
( ( ( ~ ( triangle @ SV581 @ SV681 @ SV684 ) )
= $true )
| ( ( edge @ SV681 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3359]) ).
thf(3372,plain,
! [SV680: $i,SV582: $i,SV607: $i,SV613: $i] :
( ( ( path @ ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) @ SV607 @ SV680 )
= $false )
| ( ( SV613
= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ SV680 ) )
= $false )
| ( ( SV607
= ( head_of @ ( sK11_E @ SV613 @ SV607 @ SV582 ) ) )
= $false )
| ( ( SV613
= ( path_cons @ ( sK11_E @ SV613 @ SV607 @ SV582 ) @ empty ) )
= $false )
| ( ( path @ SV582 @ SV607 @ SV613 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3360]) ).
thf(3373,plain,
! [SV683: $i,SV682: $i,SV581: $i] :
( ( ( triangle @ SV581 @ SV682 @ SV683 )
= $false )
| ( ( edge @ SV581 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3370]) ).
thf(3374,plain,
! [SV684: $i,SV681: $i,SV581: $i] :
( ( ( triangle @ SV581 @ SV681 @ SV684 )
= $false )
| ( ( edge @ SV681 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3371]) ).
thf(3375,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[2844,3374,3373,3372,3369,3368,3367,3366,3365,3364,3363,3362,3361,3357,3346,3337,3330,3329,3328,3322,3315,3302,3287,3286,3281,3275,3272,3271,3270,3259,3256,3255,3247,3245,3244,3241,3240,3237,3236,3229,3219,3218,3211,3190,3184,3171,3159,3151,3140,3139,3134,3128,3116,3101,2972,2971,2941,2940,2917,2880,2846,2845]) ).
thf(3376,plain,
( ( ! [E: $i] :
( ~ ( edge @ E )
| ( ( head_of @ E )
!= ( tail_of @ E ) ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(3377,plain,
( ( ! [E: $i] :
( ~ ( edge @ E )
| ( vertex @ ( head_of @ E ) ) )
& ! [E: $i] :
( ~ ( edge @ E )
| ( vertex @ ( tail_of @ E ) ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(3378,plain,
( ( ~ complete
| ! [V1: $i,V2: $i] :
( ( V1 = V2 )
| ~ ( vertex @ V1 )
| ~ ( vertex @ V2 )
| ( ( ( V1
!= ( head_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V2
!= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V2
!= ( head_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V1
!= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( ( V1
= ( head_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V2
= ( head_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( ( V1
= ( head_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V1
= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( ( V2
= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V2
= ( head_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( ( V2
= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V1
= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( edge @ ( sK14_E @ V2 @ V1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(3379,plain,
( ( ! [V1: $i,V2: $i,P: $i] :
( ~ ( vertex @ V1 )
| ~ ( vertex @ V2 )
| ( ! [E: $i] :
( ( V1
!= ( tail_of @ E ) )
| ~ ( edge @ E )
| ( V2
!= ( head_of @ E ) )
| ( P
!= ( path_cons @ E @ empty ) ) )
& ! [E: $i] :
( ( V1
!= ( tail_of @ E ) )
| ~ ( edge @ E )
| ! [TP: $i] :
( ( P
!= ( path_cons @ E @ TP ) )
| ~ ( path @ ( head_of @ E ) @ V2 @ TP ) ) ) )
| ( path @ V1 @ V2 @ P ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(3380,plain,
( ( ! [V1: $i] :
( ( ! [V2: $i,P: $i] :
~ ( path @ V1 @ V2 @ P )
| ( vertex @ V1 ) )
& ! [V2: $i] :
( ! [P: $i] :
~ ( path @ V1 @ V2 @ P )
| ( vertex @ V2 ) )
& ! [V2: $i,P: $i] :
( ~ ( path @ V1 @ V2 @ P )
| ( ( V1
= ( tail_of @ ( sK11_E @ P @ V2 @ V1 ) ) )
& ( edge @ ( sK11_E @ P @ V2 @ V1 ) )
& ( ( V2
!= ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) )
| ( P
!= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ empty ) )
| ! [SY83: $i] :
( ( P
!= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ SY83 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) @ V2 @ SY83 ) ) )
& ( ( V2
= ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) )
| ( ( P
= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ ( sK13_SY84 @ P @ V2 @ V1 ) ) )
& ( path @ ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) @ V2 @ ( sK13_SY84 @ P @ V2 @ V1 ) ) ) )
& ( ( P
= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ empty ) )
| ( ( P
= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ ( sK12_SY85 @ P @ V2 @ V1 ) ) )
& ( path @ ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) @ V2 @ ( sK12_SY85 @ P @ V2 @ V1 ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(3381,plain,
( ( ! [V1: $i,V2: $i] :
( ! [P: $i,E: $i] :
( ~ ( on_path @ E @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( edge @ E ) )
& ! [P: $i,E: $i] :
( ~ ( on_path @ E @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( in_path @ ( head_of @ E ) @ P ) )
& ! [P: $i,E: $i] :
( ~ ( on_path @ E @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( in_path @ ( tail_of @ E ) @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(3382,plain,
( ( ! [V1: $i,V2: $i] :
( ! [P: $i,V: $i] :
( ~ ( in_path @ V @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( ( on_path @ ( sK10_E @ V @ P @ V2 @ V1 ) @ P )
& ( ( V
= ( head_of @ ( sK10_E @ V @ P @ V2 @ V1 ) ) )
| ( V
= ( tail_of @ ( sK10_E @ V @ P @ V2 @ V1 ) ) ) ) ) )
& ! [P: $i,V: $i] :
( ~ ( in_path @ V @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( vertex @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(3383,plain,
( ( ! [E1: $i,E2: $i] :
( ( E1 = E2 )
| ~ ( edge @ E1 )
| ~ ( edge @ E2 )
| ( ( head_of @ E1 )
!= ( tail_of @ E2 ) )
| ( sequential @ E1 @ E2 ) )
& ! [E1: $i,E2: $i] :
( ~ ( sequential @ E1 @ E2 )
| ( E1 != E2 ) )
& ! [E1: $i] :
( ! [E2: $i] :
~ ( sequential @ E1 @ E2 )
| ( edge @ E1 ) )
& ! [E1: $i,E2: $i] :
( ~ ( sequential @ E1 @ E2 )
| ( edge @ E2 ) )
& ! [E1: $i,E2: $i] :
( ~ ( sequential @ E1 @ E2 )
| ( ( head_of @ E1 )
= ( tail_of @ E2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(3384,plain,
( ( ! [P: $i] :
( ! [V1: $i,V2: $i] :
~ ( path @ V1 @ V2 @ P )
| ( ! [E1: $i,E2: $i] :
( ~ ( on_path @ E1 @ P )
| ~ ( on_path @ E2 @ P )
| ! [E3: $i] :
( ~ ( precedes @ E3 @ E2 @ P )
| ~ ( sequential @ E1 @ E3 ) )
| ( precedes @ E1 @ E2 @ P ) )
& ! [E1: $i,E2: $i] :
( ~ ( on_path @ E1 @ P )
| ~ ( on_path @ E2 @ P )
| ~ ( sequential @ E1 @ E2 )
| ( precedes @ E1 @ E2 @ P ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(3385,plain,
( ( ! [P: $i] :
( ! [V1: $i,V2: $i] :
~ ( path @ V1 @ V2 @ P )
| ( ! [E1: $i] :
( ! [E2: $i] :
~ ( precedes @ E1 @ E2 @ P )
| ( on_path @ E1 @ P ) )
& ! [E1: $i,E2: $i] :
( ~ ( precedes @ E1 @ E2 @ P )
| ( on_path @ E2 @ P ) )
& ! [E1: $i,E2: $i] :
( ~ ( precedes @ E1 @ E2 @ P )
| ! [E3: $i] :
( ~ ( precedes @ E3 @ E2 @ P )
| ~ ( sequential @ E1 @ E3 ) )
| ~ ( sequential @ E1 @ E2 ) )
& ! [E1: $i,E2: $i] :
( ~ ( precedes @ E1 @ E2 @ P )
| ( ( precedes @ ( sK9_E3 @ E2 @ E1 @ P ) @ E2 @ P )
& ( sequential @ E1 @ ( sK9_E3 @ E2 @ E1 @ P ) ) )
| ( sequential @ E1 @ E2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(3386,plain,
( ( ! [V1: $i] :
( ! [V2: $i,SP: $i] :
( ( ( path @ V1 @ V2 @ ( sK8_P @ SP @ V2 @ V1 ) )
& ~ ( less_or_equal @ ( length_of @ SP ) @ ( length_of @ ( sK8_P @ SP @ V2 @ V1 ) ) ) )
| ( V1 = V2 )
| ~ ( path @ V1 @ V2 @ SP )
| ( shortest_path @ V1 @ V2 @ SP ) )
& ! [V2: $i,SP: $i] :
( ~ ( shortest_path @ V1 @ V2 @ SP )
| ! [P: $i] :
( ~ ( path @ V1 @ V2 @ P )
| ( less_or_equal @ ( length_of @ SP ) @ ( length_of @ P ) ) ) )
& ! [V2: $i] :
( ! [SP: $i] :
~ ( shortest_path @ V1 @ V2 @ SP )
| ( V1 != V2 ) )
& ! [V2: $i,SP: $i] :
( ~ ( shortest_path @ V1 @ V2 @ SP )
| ( path @ V1 @ V2 @ SP ) ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(3387,plain,
( ( ! [V1: $i,V2: $i,E1: $i] :
( ! [E2: $i] :
( ! [P: $i] :
( ~ ( precedes @ E1 @ E2 @ P )
| ~ ( shortest_path @ V1 @ V2 @ P ) )
| ! [E3: $i] :
( ( ( tail_of @ E3 )
!= ( tail_of @ E1 ) )
| ( ( head_of @ E3 )
!= ( head_of @ E2 ) ) ) )
& ! [E2: $i,P: $i] :
( ~ ( precedes @ E1 @ E2 @ P )
| ~ ( shortest_path @ V1 @ V2 @ P )
| ~ ( precedes @ E2 @ E1 @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(3388,plain,
( ( ! [E1: $i] :
( ! [E2: $i,E3: $i] :
( ~ ( edge @ E1 )
| ~ ( edge @ E2 )
| ~ ( edge @ E3 )
| ~ ( sequential @ E1 @ E2 )
| ~ ( sequential @ E2 @ E3 )
| ~ ( sequential @ E3 @ E1 )
| ( triangle @ E1 @ E2 @ E3 ) )
& ( ! [E2: $i,E3: $i] :
~ ( triangle @ E1 @ E2 @ E3 )
| ( edge @ E1 ) )
& ! [E2: $i] :
( ! [E3: $i] :
~ ( triangle @ E1 @ E2 @ E3 )
| ( edge @ E2 ) )
& ! [E2: $i,E3: $i] :
( ~ ( triangle @ E1 @ E2 @ E3 )
| ( edge @ E3 ) )
& ! [E2: $i] :
( ! [E3: $i] :
~ ( triangle @ E1 @ E2 @ E3 )
| ( sequential @ E1 @ E2 ) )
& ! [E2: $i,E3: $i] :
( ~ ( triangle @ E1 @ E2 @ E3 )
| ( sequential @ E2 @ E3 ) )
& ! [E2: $i,E3: $i] :
( ~ ( triangle @ E1 @ E2 @ E3 )
| ( sequential @ E3 @ E1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(3389,plain,
( ( ! [V1: $i,V2: $i,P: $i] :
( ~ ( path @ V1 @ V2 @ P )
| ( ( length_of @ P )
= ( number_of_in @ edges @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(3390,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)],[63]) ).
thf(3391,plain,
( ( ! [P: $i] :
( ( ( on_path @ ( sK6_E1 @ P ) @ P )
& ( on_path @ ( sK7_SY80 @ P ) @ P )
& ( sequential @ ( sK6_E1 @ P ) @ ( sK7_SY80 @ P ) )
& ! [SY82: $i] :
~ ( triangle @ ( sK6_E1 @ P ) @ ( sK7_SY80 @ P ) @ SY82 ) )
| ! [V1: $i,V2: $i] :
~ ( path @ V1 @ V2 @ P )
| ( ( number_of_in @ sequential_pairs @ P )
= ( number_of_in @ triangles @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(3392,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(3393,plain,
( ( precedes @ sK3_SY74 @ sK4_SY77 @ sK5_SY79 )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(3394,plain,
( ( shortest_path @ sK1_V1 @ sK2_SY70 @ sK5_SY79 )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(3395,plain,
( ( ~ ( path @ sK1_V1 @ sK2_SY70 @ sK5_SY79 ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(3396,plain,
( ( ~ complete
| ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( vertex @ SX0 )
| ~ ( vertex @ SX1 )
| ~ ( ~ ~ ( ~ ( ( SX0
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
| ~ ~ ( ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3378]) ).
thf(3397,plain,
( ( ! [SX0: $i] :
~ ( ~ ~ ( ~ ( ! [SX1: $i,SX2: $i] :
~ ( path @ SX0 @ SX1 @ SX2 )
| ( vertex @ SX0 ) )
| ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( path @ SX0 @ SX1 @ SX2 )
| ( vertex @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( path @ SX0 @ SX1 @ SX2 )
| ~ ( ~ ~ ( ( SX0
!= ( tail_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( edge @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ( SX1
!= ( head_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) )
| ( SX2
!= ( path_cons @ ( sK11_E @ SX2 @ SX1 @ SX0 ) @ empty ) )
| ! [SX3: $i] :
( ( SX2
!= ( path_cons @ ( sK11_E @ SX2 @ SX1 @ SX0 ) @ SX3 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) @ SX1 @ SX3 ) ) )
| ~ ~ ( ~ ( ( SX1
= ( head_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( ( SX2
!= ( path_cons @ ( sK11_E @ SX2 @ SX1 @ SX0 ) @ ( sK13_SY84 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) @ SX1 @ ( sK13_SY84 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX2
= ( path_cons @ ( sK11_E @ SX2 @ SX1 @ SX0 ) @ empty ) )
| ~ ( ( SX2
!= ( path_cons @ ( sK11_E @ SX2 @ SX1 @ SX0 ) @ ( sK12_SY85 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) @ SX1 @ ( sK12_SY85 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3380]) ).
thf(3398,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( vertex @ SX0 )
| ~ ( vertex @ SX1 )
| ~ ( ~ ! [SX3: $i] :
( ( SX0
!= ( tail_of @ SX3 ) )
| ~ ( edge @ SX3 )
| ( SX1
!= ( head_of @ SX3 ) )
| ( SX2
!= ( path_cons @ SX3 @ empty ) ) )
| ~ ! [SX3: $i] :
( ( SX0
!= ( tail_of @ SX3 ) )
| ~ ( edge @ SX3 )
| ! [SX4: $i] :
( ( SX2
!= ( path_cons @ SX3 @ SX4 ) )
| ~ ( path @ ( head_of @ SX3 ) @ SX1 @ SX4 ) ) ) )
| ( path @ SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3379]) ).
thf(3399,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( path @ SX0 @ SX1 @ ( sK8_P @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SX2 ) @ ( length_of @ ( sK8_P @ SX2 @ SX1 @ SX0 ) ) ) )
| ( SX0 = SX1 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ( shortest_path @ SX0 @ SX1 @ SX2 ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( shortest_path @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( path @ SX0 @ SX1 @ SX3 )
| ( less_or_equal @ ( length_of @ SX2 ) @ ( length_of @ SX3 ) ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( shortest_path @ SX0 @ SX1 @ SX2 )
| ( SX0 != SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( shortest_path @ SX0 @ SX1 @ SX2 )
| ( path @ SX0 @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3386]) ).
thf(3400,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SX0 ) @ SX0 )
| ~ ( on_path @ ( sK7_SY80 @ SX0 ) @ SX0 ) )
| ~ ( sequential @ ( sK6_E1 @ SX0 ) @ ( sK7_SY80 @ SX0 ) ) )
| ~ ! [SX1: $i] :
~ ( triangle @ ( sK6_E1 @ SX0 ) @ ( sK7_SY80 @ SX0 ) @ SX1 ) )
| ! [SX1: $i,SX2: $i] :
~ ( path @ SX1 @ SX2 @ SX0 )
| ( ( number_of_in @ sequential_pairs @ SX0 )
= ( number_of_in @ triangles @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3391]) ).
thf(3401,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( on_path @ SX3 @ SX2 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ( edge @ SX3 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( on_path @ SX3 @ SX2 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ( in_path @ ( head_of @ SX3 ) @ SX2 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( on_path @ SX3 @ SX2 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ( in_path @ ( tail_of @ SX3 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3381]) ).
thf(3402,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( edge @ SX0 )
| ~ ( edge @ SX1 )
| ( ( head_of @ SX0 )
!= ( tail_of @ SX1 ) )
| ( sequential @ SX0 @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3383]) ).
thf(3403,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i,SX2: $i] :
~ ( path @ SX1 @ SX2 @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( on_path @ SX1 @ SX0 )
| ~ ( on_path @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( precedes @ SX3 @ SX2 @ SX0 )
| ~ ( sequential @ SX1 @ SX3 ) )
| ( precedes @ SX1 @ SX2 @ SX0 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( on_path @ SX1 @ SX0 )
| ~ ( on_path @ SX2 @ SX0 )
| ~ ( sequential @ SX1 @ SX2 )
| ( precedes @ SX1 @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3384]) ).
thf(3404,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in_path @ SX3 @ SX2 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ~ ( ~ ( on_path @ ( sK10_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( ( SX3
= ( head_of @ ( sK10_E @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ( SX3
= ( tail_of @ ( sK10_E @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( in_path @ SX3 @ SX2 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ( vertex @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3382]) ).
thf(3405,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( edge @ SX0 )
| ~ ( edge @ SX1 )
| ~ ( edge @ SX2 )
| ~ ( sequential @ SX0 @ SX1 )
| ~ ( sequential @ SX1 @ SX2 )
| ~ ( sequential @ SX2 @ SX0 )
| ( triangle @ SX0 @ SX1 @ SX2 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SX1: $i,SX2: $i] :
~ ( triangle @ SX0 @ SX1 @ SX2 )
| ( edge @ SX0 ) )
| ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( triangle @ SX0 @ SX1 @ SX2 )
| ( edge @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( triangle @ SX0 @ SX1 @ SX2 )
| ( edge @ SX2 ) ) )
| ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( triangle @ SX0 @ SX1 @ SX2 )
| ( sequential @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( triangle @ SX0 @ SX1 @ SX2 )
| ( sequential @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( triangle @ SX0 @ SX1 @ SX2 )
| ( sequential @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3388]) ).
thf(3406,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i,SX2: $i] :
~ ( path @ SX1 @ SX2 @ SX0 )
| ~ ( ~ ~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( precedes @ SX1 @ SX2 @ SX0 )
| ( on_path @ SX1 @ SX0 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( precedes @ SX1 @ SX2 @ SX0 )
| ( on_path @ SX2 @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( precedes @ SX1 @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( precedes @ SX3 @ SX2 @ SX0 )
| ~ ( sequential @ SX1 @ SX3 ) )
| ~ ( sequential @ SX1 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( precedes @ SX1 @ SX2 @ SX0 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SX2 @ SX1 @ SX0 ) @ SX2 @ SX0 )
| ~ ( sequential @ SX1 @ ( sK9_E3 @ SX2 @ SX1 @ SX0 ) ) )
| ( sequential @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3385]) ).
thf(3407,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( head_of @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( tail_of @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3377]) ).
thf(3408,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
( ~ ( precedes @ SX2 @ SX3 @ SX4 )
| ~ ( shortest_path @ SX0 @ SX1 @ SX4 ) )
| ! [SX4: $i] :
( ( ( tail_of @ SX4 )
!= ( tail_of @ SX2 ) )
| ( ( head_of @ SX4 )
!= ( head_of @ SX3 ) ) ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( precedes @ SX2 @ SX3 @ SX4 )
| ~ ( shortest_path @ SX0 @ SX1 @ SX4 )
| ~ ( precedes @ SX3 @ SX2 @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3387]) ).
thf(3409,plain,
! [SV685: $i] :
( ( ~ ( edge @ SV685 )
| ( ( head_of @ SV685 )
!= ( tail_of @ SV685 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3376]) ).
thf(3410,plain,
! [SV686: $i] :
( ( ! [SY1040: $i,SY1041: $i] :
( ~ ( path @ SV686 @ SY1040 @ SY1041 )
| ( ( length_of @ SY1041 )
= ( number_of_in @ edges @ SY1041 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3389]) ).
thf(3411,plain,
! [SV687: $i] :
( ( ! [SY1042: $i,SY1043: $i] :
( ~ ( path @ SV687 @ SY1042 @ SY1043 )
| ( ( number_of_in @ sequential_pairs @ SY1043 )
= ( minus @ ( length_of @ SY1043 ) @ n1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3390]) ).
thf(3412,plain,
! [SV688: $i] :
( ( ! [SY1044: $i] : ( less_or_equal @ ( number_of_in @ SV688 @ SY1044 ) @ ( number_of_in @ SV688 @ graph ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3392]) ).
thf(3413,plain,
( ( path @ sK1_V1 @ sK2_SY70 @ sK5_SY79 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3395]) ).
thf(3414,plain,
( ( ( ~ complete )
= $true )
| ( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( vertex @ SX0 )
| ~ ( vertex @ SX1 )
| ~ ( ~ ~ ( ~ ( ( SX0
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
| ~ ~ ( ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3396]) ).
thf(3415,plain,
! [SV689: $i] :
( ( ~ ( ~ ~ ( ~ ( ! [SY1045: $i,SY1046: $i] :
~ ( path @ SV689 @ SY1045 @ SY1046 )
| ( vertex @ SV689 ) )
| ~ ! [SY1047: $i] :
( ! [SY1048: $i] :
~ ( path @ SV689 @ SY1047 @ SY1048 )
| ( vertex @ SY1047 ) ) )
| ~ ! [SY1049: $i,SY1050: $i] :
( ~ ( path @ SV689 @ SY1049 @ SY1050 )
| ~ ( ~ ~ ( ( SV689
!= ( tail_of @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) ) )
| ~ ( edge @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) ) )
| ~ ~ ( ~ ( ( SY1049
!= ( head_of @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) ) )
| ( SY1050
!= ( path_cons @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) @ empty ) )
| ! [SY1051: $i] :
( ( SY1050
!= ( path_cons @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) @ SY1051 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) ) @ SY1049 @ SY1051 ) ) )
| ~ ~ ( ~ ( ( SY1049
= ( head_of @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) ) )
| ~ ( ( SY1050
!= ( path_cons @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) @ ( sK13_SY84 @ SY1050 @ SY1049 @ SV689 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) ) @ SY1049 @ ( sK13_SY84 @ SY1050 @ SY1049 @ SV689 ) ) ) )
| ~ ( ( SY1050
= ( path_cons @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) @ empty ) )
| ~ ( ( SY1050
!= ( path_cons @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) @ ( sK12_SY85 @ SY1050 @ SY1049 @ SV689 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) ) @ SY1049 @ ( sK12_SY85 @ SY1050 @ SY1049 @ SV689 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3397]) ).
thf(3416,plain,
! [SV690: $i] :
( ( ! [SY1052: $i,SY1053: $i] :
( ~ ( vertex @ SV690 )
| ~ ( vertex @ SY1052 )
| ~ ( ~ ! [SY1054: $i] :
( ( SV690
!= ( tail_of @ SY1054 ) )
| ~ ( edge @ SY1054 )
| ( SY1052
!= ( head_of @ SY1054 ) )
| ( SY1053
!= ( path_cons @ SY1054 @ empty ) ) )
| ~ ! [SY1055: $i] :
( ( SV690
!= ( tail_of @ SY1055 ) )
| ~ ( edge @ SY1055 )
| ! [SX4: $i] :
( ( SY1053
!= ( path_cons @ SY1055 @ SX4 ) )
| ~ ( path @ ( head_of @ SY1055 ) @ SY1052 @ SX4 ) ) ) )
| ( path @ SV690 @ SY1052 @ SY1053 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3398]) ).
thf(3417,plain,
! [SV691: $i] :
( ( ~ ( ~ ! [SY1057: $i,SY1058: $i] :
( ~ ( ~ ( path @ SV691 @ SY1057 @ ( sK8_P @ SY1058 @ SY1057 @ SV691 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY1058 ) @ ( length_of @ ( sK8_P @ SY1058 @ SY1057 @ SV691 ) ) ) )
| ( SV691 = SY1057 )
| ~ ( path @ SV691 @ SY1057 @ SY1058 )
| ( shortest_path @ SV691 @ SY1057 @ SY1058 ) )
| ~ ~ ( ~ ! [SY1059: $i,SY1060: $i] :
( ~ ( shortest_path @ SV691 @ SY1059 @ SY1060 )
| ! [SY1061: $i] :
( ~ ( path @ SV691 @ SY1059 @ SY1061 )
| ( less_or_equal @ ( length_of @ SY1060 ) @ ( length_of @ SY1061 ) ) ) )
| ~ ~ ( ~ ! [SY1062: $i] :
( ! [SY1063: $i] :
~ ( shortest_path @ SV691 @ SY1062 @ SY1063 )
| ( SV691 != SY1062 ) )
| ~ ! [SY1064: $i,SY1065: $i] :
( ~ ( shortest_path @ SV691 @ SY1064 @ SY1065 )
| ( path @ SV691 @ SY1064 @ SY1065 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3399]) ).
thf(3418,plain,
! [SV692: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV692 ) @ SV692 )
| ~ ( on_path @ ( sK7_SY80 @ SV692 ) @ SV692 ) )
| ~ ( sequential @ ( sK6_E1 @ SV692 ) @ ( sK7_SY80 @ SV692 ) ) )
| ~ ! [SY1066: $i] :
~ ( triangle @ ( sK6_E1 @ SV692 ) @ ( sK7_SY80 @ SV692 ) @ SY1066 ) )
| ! [SY1067: $i,SY1068: $i] :
~ ( path @ SY1067 @ SY1068 @ SV692 )
| ( ( number_of_in @ sequential_pairs @ SV692 )
= ( number_of_in @ triangles @ SV692 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3400]) ).
thf(3419,plain,
! [SV693: $i] :
( ( ! [SY1069: $i] :
~ ( ~ ~ ( ~ ! [SY1070: $i,SY1071: $i] :
( ~ ( on_path @ SY1071 @ SY1070 )
| ~ ( path @ SV693 @ SY1069 @ SY1070 )
| ( edge @ SY1071 ) )
| ~ ! [SY1072: $i,SY1073: $i] :
( ~ ( on_path @ SY1073 @ SY1072 )
| ~ ( path @ SV693 @ SY1069 @ SY1072 )
| ( in_path @ ( head_of @ SY1073 ) @ SY1072 ) ) )
| ~ ! [SY1074: $i,SY1075: $i] :
( ~ ( on_path @ SY1075 @ SY1074 )
| ~ ( path @ SV693 @ SY1069 @ SY1074 )
| ( in_path @ ( tail_of @ SY1075 ) @ SY1074 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3401]) ).
thf(3420,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( edge @ SX0 )
| ~ ( edge @ SX1 )
| ( ( head_of @ SX0 )
!= ( tail_of @ SX1 ) )
| ( sequential @ SX0 @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3402]) ).
thf(3421,plain,
! [SV694: $i] :
( ( ! [SY1076: $i,SY1077: $i] :
~ ( path @ SY1076 @ SY1077 @ SV694 )
| ~ ( ~ ! [SY1078: $i,SY1079: $i] :
( ~ ( on_path @ SY1078 @ SV694 )
| ~ ( on_path @ SY1079 @ SV694 )
| ! [SY1080: $i] :
( ~ ( precedes @ SY1080 @ SY1079 @ SV694 )
| ~ ( sequential @ SY1078 @ SY1080 ) )
| ( precedes @ SY1078 @ SY1079 @ SV694 ) )
| ~ ! [SY1081: $i,SY1082: $i] :
( ~ ( on_path @ SY1081 @ SV694 )
| ~ ( on_path @ SY1082 @ SV694 )
| ~ ( sequential @ SY1081 @ SY1082 )
| ( precedes @ SY1081 @ SY1082 @ SV694 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3403]) ).
thf(3422,plain,
! [SV695: $i] :
( ( ! [SY1083: $i] :
~ ( ~ ! [SY1084: $i,SY1085: $i] :
( ~ ( in_path @ SY1085 @ SY1084 )
| ~ ( path @ SV695 @ SY1083 @ SY1084 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY1085 @ SY1084 @ SY1083 @ SV695 ) @ SY1084 )
| ~ ( ( SY1085
= ( head_of @ ( sK10_E @ SY1085 @ SY1084 @ SY1083 @ SV695 ) ) )
| ( SY1085
= ( tail_of @ ( sK10_E @ SY1085 @ SY1084 @ SY1083 @ SV695 ) ) ) ) ) )
| ~ ! [SY1086: $i,SY1087: $i] :
( ~ ( in_path @ SY1087 @ SY1086 )
| ~ ( path @ SV695 @ SY1083 @ SY1086 )
| ( vertex @ SY1087 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3404]) ).
thf(3423,plain,
! [SV696: $i] :
( ( ~ ( ~ ! [SY1088: $i,SY1089: $i] :
( ~ ( edge @ SV696 )
| ~ ( edge @ SY1088 )
| ~ ( edge @ SY1089 )
| ~ ( sequential @ SV696 @ SY1088 )
| ~ ( sequential @ SY1088 @ SY1089 )
| ~ ( sequential @ SY1089 @ SV696 )
| ( triangle @ SV696 @ SY1088 @ SY1089 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY1090: $i,SY1091: $i] :
~ ( triangle @ SV696 @ SY1090 @ SY1091 )
| ( edge @ SV696 ) )
| ~ ! [SY1092: $i] :
( ! [SY1093: $i] :
~ ( triangle @ SV696 @ SY1092 @ SY1093 )
| ( edge @ SY1092 ) ) )
| ~ ! [SY1094: $i,SY1095: $i] :
( ~ ( triangle @ SV696 @ SY1094 @ SY1095 )
| ( edge @ SY1095 ) ) )
| ~ ! [SY1096: $i] :
( ! [SY1097: $i] :
~ ( triangle @ SV696 @ SY1096 @ SY1097 )
| ( sequential @ SV696 @ SY1096 ) ) )
| ~ ! [SY1098: $i,SY1099: $i] :
( ~ ( triangle @ SV696 @ SY1098 @ SY1099 )
| ( sequential @ SY1098 @ SY1099 ) ) )
| ~ ! [SY1100: $i,SY1101: $i] :
( ~ ( triangle @ SV696 @ SY1100 @ SY1101 )
| ( sequential @ SY1101 @ SV696 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3405]) ).
thf(3424,plain,
! [SV697: $i] :
( ( ! [SY1102: $i,SY1103: $i] :
~ ( path @ SY1102 @ SY1103 @ SV697 )
| ~ ( ~ ~ ( ~ ! [SY1104: $i] :
( ! [SY1105: $i] :
~ ( precedes @ SY1104 @ SY1105 @ SV697 )
| ( on_path @ SY1104 @ SV697 ) )
| ~ ! [SY1106: $i,SY1107: $i] :
( ~ ( precedes @ SY1106 @ SY1107 @ SV697 )
| ( on_path @ SY1107 @ SV697 ) ) )
| ~ ~ ( ~ ! [SY1108: $i,SY1109: $i] :
( ~ ( precedes @ SY1108 @ SY1109 @ SV697 )
| ! [SY1110: $i] :
( ~ ( precedes @ SY1110 @ SY1109 @ SV697 )
| ~ ( sequential @ SY1108 @ SY1110 ) )
| ~ ( sequential @ SY1108 @ SY1109 ) )
| ~ ! [SY1111: $i,SY1112: $i] :
( ~ ( precedes @ SY1111 @ SY1112 @ SV697 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY1112 @ SY1111 @ SV697 ) @ SY1112 @ SV697 )
| ~ ( sequential @ SY1111 @ ( sK9_E3 @ SY1112 @ SY1111 @ SV697 ) ) )
| ( sequential @ SY1111 @ SY1112 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3406]) ).
thf(3425,plain,
( ( ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( head_of @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( tail_of @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3407]) ).
thf(3426,plain,
! [SV698: $i] :
( ( ! [SY1113: $i,SY1114: $i] :
~ ( ~ ! [SY1115: $i] :
( ! [SY1116: $i] :
( ~ ( precedes @ SY1114 @ SY1115 @ SY1116 )
| ~ ( shortest_path @ SV698 @ SY1113 @ SY1116 ) )
| ! [SX4: $i] :
( ( ( tail_of @ SX4 )
!= ( tail_of @ SY1114 ) )
| ( ( head_of @ SX4 )
!= ( head_of @ SY1115 ) ) ) )
| ~ ! [SY1118: $i,SY1119: $i] :
( ~ ( precedes @ SY1114 @ SY1118 @ SY1119 )
| ~ ( shortest_path @ SV698 @ SY1113 @ SY1119 )
| ~ ( precedes @ SY1118 @ SY1114 @ SY1119 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3408]) ).
thf(3427,plain,
! [SV685: $i] :
( ( ( ~ ( edge @ SV685 ) )
= $true )
| ( ( ( ( head_of @ SV685 )
!= ( tail_of @ SV685 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3409]) ).
thf(3428,plain,
! [SV699: $i,SV686: $i] :
( ( ! [SY1120: $i] :
( ~ ( path @ SV686 @ SV699 @ SY1120 )
| ( ( length_of @ SY1120 )
= ( number_of_in @ edges @ SY1120 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3410]) ).
thf(3429,plain,
! [SV700: $i,SV687: $i] :
( ( ! [SY1121: $i] :
( ~ ( path @ SV687 @ SV700 @ SY1121 )
| ( ( number_of_in @ sequential_pairs @ SY1121 )
= ( minus @ ( length_of @ SY1121 ) @ n1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3411]) ).
thf(3430,plain,
! [SV701: $i,SV688: $i] :
( ( less_or_equal @ ( number_of_in @ SV688 @ SV701 ) @ ( number_of_in @ SV688 @ graph ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3412]) ).
thf(3431,plain,
( ( complete = $false )
| ( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( vertex @ SX0 )
| ~ ( vertex @ SX1 )
| ~ ( ~ ~ ( ~ ( ( SX0
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
| ~ ~ ( ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3414]) ).
thf(3432,plain,
! [SV689: $i] :
( ( ~ ~ ( ~ ( ! [SY1045: $i,SY1046: $i] :
~ ( path @ SV689 @ SY1045 @ SY1046 )
| ( vertex @ SV689 ) )
| ~ ! [SY1047: $i] :
( ! [SY1048: $i] :
~ ( path @ SV689 @ SY1047 @ SY1048 )
| ( vertex @ SY1047 ) ) )
| ~ ! [SY1049: $i,SY1050: $i] :
( ~ ( path @ SV689 @ SY1049 @ SY1050 )
| ~ ( ~ ~ ( ( SV689
!= ( tail_of @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) ) )
| ~ ( edge @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) ) )
| ~ ~ ( ~ ( ( SY1049
!= ( head_of @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) ) )
| ( SY1050
!= ( path_cons @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) @ empty ) )
| ! [SY1051: $i] :
( ( SY1050
!= ( path_cons @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) @ SY1051 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) ) @ SY1049 @ SY1051 ) ) )
| ~ ~ ( ~ ( ( SY1049
= ( head_of @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) ) )
| ~ ( ( SY1050
!= ( path_cons @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) @ ( sK13_SY84 @ SY1050 @ SY1049 @ SV689 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) ) @ SY1049 @ ( sK13_SY84 @ SY1050 @ SY1049 @ SV689 ) ) ) )
| ~ ( ( SY1050
= ( path_cons @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) @ empty ) )
| ~ ( ( SY1050
!= ( path_cons @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) @ ( sK12_SY85 @ SY1050 @ SY1049 @ SV689 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) ) @ SY1049 @ ( sK12_SY85 @ SY1050 @ SY1049 @ SV689 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3415]) ).
thf(3433,plain,
! [SV702: $i,SV690: $i] :
( ( ! [SY1122: $i] :
( ~ ( vertex @ SV690 )
| ~ ( vertex @ SV702 )
| ~ ( ~ ! [SY1123: $i] :
( ( SV690
!= ( tail_of @ SY1123 ) )
| ~ ( edge @ SY1123 )
| ( SV702
!= ( head_of @ SY1123 ) )
| ( SY1122
!= ( path_cons @ SY1123 @ empty ) ) )
| ~ ! [SY1124: $i] :
( ( SV690
!= ( tail_of @ SY1124 ) )
| ~ ( edge @ SY1124 )
| ! [SY1125: $i] :
( ( SY1122
!= ( path_cons @ SY1124 @ SY1125 ) )
| ~ ( path @ ( head_of @ SY1124 ) @ SV702 @ SY1125 ) ) ) )
| ( path @ SV690 @ SV702 @ SY1122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3416]) ).
thf(3434,plain,
! [SV691: $i] :
( ( ~ ! [SY1057: $i,SY1058: $i] :
( ~ ( ~ ( path @ SV691 @ SY1057 @ ( sK8_P @ SY1058 @ SY1057 @ SV691 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY1058 ) @ ( length_of @ ( sK8_P @ SY1058 @ SY1057 @ SV691 ) ) ) )
| ( SV691 = SY1057 )
| ~ ( path @ SV691 @ SY1057 @ SY1058 )
| ( shortest_path @ SV691 @ SY1057 @ SY1058 ) )
| ~ ~ ( ~ ! [SY1059: $i,SY1060: $i] :
( ~ ( shortest_path @ SV691 @ SY1059 @ SY1060 )
| ! [SY1061: $i] :
( ~ ( path @ SV691 @ SY1059 @ SY1061 )
| ( less_or_equal @ ( length_of @ SY1060 ) @ ( length_of @ SY1061 ) ) ) )
| ~ ~ ( ~ ! [SY1062: $i] :
( ! [SY1063: $i] :
~ ( shortest_path @ SV691 @ SY1062 @ SY1063 )
| ( SV691 != SY1062 ) )
| ~ ! [SY1064: $i,SY1065: $i] :
( ~ ( shortest_path @ SV691 @ SY1064 @ SY1065 )
| ( path @ SV691 @ SY1064 @ SY1065 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3417]) ).
thf(3435,plain,
! [SV692: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV692 ) @ SV692 )
| ~ ( on_path @ ( sK7_SY80 @ SV692 ) @ SV692 ) )
| ~ ( sequential @ ( sK6_E1 @ SV692 ) @ ( sK7_SY80 @ SV692 ) ) )
| ~ ! [SY1066: $i] :
~ ( triangle @ ( sK6_E1 @ SV692 ) @ ( sK7_SY80 @ SV692 ) @ SY1066 ) )
| ! [SY1067: $i,SY1068: $i] :
~ ( path @ SY1067 @ SY1068 @ SV692 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV692 )
= ( number_of_in @ triangles @ SV692 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3418]) ).
thf(3436,plain,
! [SV703: $i,SV693: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY1126: $i,SY1127: $i] :
( ~ ( on_path @ SY1127 @ SY1126 )
| ~ ( path @ SV693 @ SV703 @ SY1126 )
| ( edge @ SY1127 ) )
| ~ ! [SY1128: $i,SY1129: $i] :
( ~ ( on_path @ SY1129 @ SY1128 )
| ~ ( path @ SV693 @ SV703 @ SY1128 )
| ( in_path @ ( head_of @ SY1129 ) @ SY1128 ) ) )
| ~ ! [SY1130: $i,SY1131: $i] :
( ~ ( on_path @ SY1131 @ SY1130 )
| ~ ( path @ SV693 @ SV703 @ SY1130 )
| ( in_path @ ( tail_of @ SY1131 ) @ SY1130 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3419]) ).
thf(3437,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( edge @ SX0 )
| ~ ( edge @ SX1 )
| ( ( head_of @ SX0 )
!= ( tail_of @ SX1 ) )
| ( sequential @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3420]) ).
thf(3438,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3420]) ).
thf(3439,plain,
! [SV694: $i] :
( ( ( ! [SY1076: $i,SY1077: $i] :
~ ( path @ SY1076 @ SY1077 @ SV694 ) )
= $true )
| ( ( ~ ( ~ ! [SY1078: $i,SY1079: $i] :
( ~ ( on_path @ SY1078 @ SV694 )
| ~ ( on_path @ SY1079 @ SV694 )
| ! [SY1080: $i] :
( ~ ( precedes @ SY1080 @ SY1079 @ SV694 )
| ~ ( sequential @ SY1078 @ SY1080 ) )
| ( precedes @ SY1078 @ SY1079 @ SV694 ) )
| ~ ! [SY1081: $i,SY1082: $i] :
( ~ ( on_path @ SY1081 @ SV694 )
| ~ ( on_path @ SY1082 @ SV694 )
| ~ ( sequential @ SY1081 @ SY1082 )
| ( precedes @ SY1081 @ SY1082 @ SV694 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3421]) ).
thf(3440,plain,
! [SV704: $i,SV695: $i] :
( ( ~ ( ~ ! [SY1132: $i,SY1133: $i] :
( ~ ( in_path @ SY1133 @ SY1132 )
| ~ ( path @ SV695 @ SV704 @ SY1132 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY1133 @ SY1132 @ SV704 @ SV695 ) @ SY1132 )
| ~ ( ( SY1133
= ( head_of @ ( sK10_E @ SY1133 @ SY1132 @ SV704 @ SV695 ) ) )
| ( SY1133
= ( tail_of @ ( sK10_E @ SY1133 @ SY1132 @ SV704 @ SV695 ) ) ) ) ) )
| ~ ! [SY1134: $i,SY1135: $i] :
( ~ ( in_path @ SY1135 @ SY1134 )
| ~ ( path @ SV695 @ SV704 @ SY1134 )
| ( vertex @ SY1135 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3422]) ).
thf(3441,plain,
! [SV696: $i] :
( ( ~ ! [SY1088: $i,SY1089: $i] :
( ~ ( edge @ SV696 )
| ~ ( edge @ SY1088 )
| ~ ( edge @ SY1089 )
| ~ ( sequential @ SV696 @ SY1088 )
| ~ ( sequential @ SY1088 @ SY1089 )
| ~ ( sequential @ SY1089 @ SV696 )
| ( triangle @ SV696 @ SY1088 @ SY1089 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY1090: $i,SY1091: $i] :
~ ( triangle @ SV696 @ SY1090 @ SY1091 )
| ( edge @ SV696 ) )
| ~ ! [SY1092: $i] :
( ! [SY1093: $i] :
~ ( triangle @ SV696 @ SY1092 @ SY1093 )
| ( edge @ SY1092 ) ) )
| ~ ! [SY1094: $i,SY1095: $i] :
( ~ ( triangle @ SV696 @ SY1094 @ SY1095 )
| ( edge @ SY1095 ) ) )
| ~ ! [SY1096: $i] :
( ! [SY1097: $i] :
~ ( triangle @ SV696 @ SY1096 @ SY1097 )
| ( sequential @ SV696 @ SY1096 ) ) )
| ~ ! [SY1098: $i,SY1099: $i] :
( ~ ( triangle @ SV696 @ SY1098 @ SY1099 )
| ( sequential @ SY1098 @ SY1099 ) ) )
| ~ ! [SY1100: $i,SY1101: $i] :
( ~ ( triangle @ SV696 @ SY1100 @ SY1101 )
| ( sequential @ SY1101 @ SV696 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3423]) ).
thf(3442,plain,
! [SV697: $i] :
( ( ( ! [SY1102: $i,SY1103: $i] :
~ ( path @ SY1102 @ SY1103 @ SV697 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY1104: $i] :
( ! [SY1105: $i] :
~ ( precedes @ SY1104 @ SY1105 @ SV697 )
| ( on_path @ SY1104 @ SV697 ) )
| ~ ! [SY1106: $i,SY1107: $i] :
( ~ ( precedes @ SY1106 @ SY1107 @ SV697 )
| ( on_path @ SY1107 @ SV697 ) ) )
| ~ ~ ( ~ ! [SY1108: $i,SY1109: $i] :
( ~ ( precedes @ SY1108 @ SY1109 @ SV697 )
| ! [SY1110: $i] :
( ~ ( precedes @ SY1110 @ SY1109 @ SV697 )
| ~ ( sequential @ SY1108 @ SY1110 ) )
| ~ ( sequential @ SY1108 @ SY1109 ) )
| ~ ! [SY1111: $i,SY1112: $i] :
( ~ ( precedes @ SY1111 @ SY1112 @ SV697 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY1112 @ SY1111 @ SV697 ) @ SY1112 @ SV697 )
| ~ ( sequential @ SY1111 @ ( sK9_E3 @ SY1112 @ SY1111 @ SV697 ) ) )
| ( sequential @ SY1111 @ SY1112 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3424]) ).
thf(3443,plain,
( ( ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( head_of @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3425]) ).
thf(3444,plain,
( ( ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( tail_of @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3425]) ).
thf(3445,plain,
! [SV705: $i,SV698: $i] :
( ( ! [SY1136: $i] :
~ ( ~ ! [SY1137: $i] :
( ! [SY1138: $i] :
( ~ ( precedes @ SY1136 @ SY1137 @ SY1138 )
| ~ ( shortest_path @ SV698 @ SV705 @ SY1138 ) )
| ! [SX4: $i] :
( ( ( tail_of @ SX4 )
!= ( tail_of @ SY1136 ) )
| ( ( head_of @ SX4 )
!= ( head_of @ SY1137 ) ) ) )
| ~ ! [SY1140: $i,SY1141: $i] :
( ~ ( precedes @ SY1136 @ SY1140 @ SY1141 )
| ~ ( shortest_path @ SV698 @ SV705 @ SY1141 )
| ~ ( precedes @ SY1140 @ SY1136 @ SY1141 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3426]) ).
thf(3446,plain,
! [SV685: $i] :
( ( ( edge @ SV685 )
= $false )
| ( ( ( ( head_of @ SV685 )
!= ( tail_of @ SV685 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3427]) ).
thf(3447,plain,
! [SV706: $i,SV699: $i,SV686: $i] :
( ( ~ ( path @ SV686 @ SV699 @ SV706 )
| ( ( length_of @ SV706 )
= ( number_of_in @ edges @ SV706 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3428]) ).
thf(3448,plain,
! [SV707: $i,SV700: $i,SV687: $i] :
( ( ~ ( path @ SV687 @ SV700 @ SV707 )
| ( ( number_of_in @ sequential_pairs @ SV707 )
= ( minus @ ( length_of @ SV707 ) @ n1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3429]) ).
thf(3449,plain,
! [SV708: $i] :
( ( ( ! [SY1142: $i] :
( ( SV708 = SY1142 )
| ~ ( vertex @ SV708 )
| ~ ( vertex @ SY1142 )
| ~ ( ~ ~ ( ~ ( ( SV708
!= ( head_of @ ( sK14_E @ SY1142 @ SV708 ) ) )
| ( SY1142
!= ( tail_of @ ( sK14_E @ SY1142 @ SV708 ) ) )
| ( SY1142
!= ( head_of @ ( sK14_E @ SY1142 @ SV708 ) ) )
| ( SV708
!= ( tail_of @ ( sK14_E @ SY1142 @ SV708 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV708
= ( head_of @ ( sK14_E @ SY1142 @ SV708 ) ) )
| ( SY1142
= ( head_of @ ( sK14_E @ SY1142 @ SV708 ) ) ) )
| ~ ( ( SV708
= ( head_of @ ( sK14_E @ SY1142 @ SV708 ) ) )
| ( SV708
= ( tail_of @ ( sK14_E @ SY1142 @ SV708 ) ) ) ) )
| ~ ~ ( ~ ( ( SY1142
= ( tail_of @ ( sK14_E @ SY1142 @ SV708 ) ) )
| ( SY1142
= ( head_of @ ( sK14_E @ SY1142 @ SV708 ) ) ) )
| ~ ( ( SY1142
= ( tail_of @ ( sK14_E @ SY1142 @ SV708 ) ) )
| ( SV708
= ( tail_of @ ( sK14_E @ SY1142 @ SV708 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SY1142 @ SV708 ) ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3431]) ).
thf(3450,plain,
! [SV689: $i] :
( ( ~ ~ ( ~ ( ! [SY1045: $i,SY1046: $i] :
~ ( path @ SV689 @ SY1045 @ SY1046 )
| ( vertex @ SV689 ) )
| ~ ! [SY1047: $i] :
( ! [SY1048: $i] :
~ ( path @ SV689 @ SY1047 @ SY1048 )
| ( vertex @ SY1047 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3432]) ).
thf(3451,plain,
! [SV689: $i] :
( ( ~ ! [SY1049: $i,SY1050: $i] :
( ~ ( path @ SV689 @ SY1049 @ SY1050 )
| ~ ( ~ ~ ( ( SV689
!= ( tail_of @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) ) )
| ~ ( edge @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) ) )
| ~ ~ ( ~ ( ( SY1049
!= ( head_of @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) ) )
| ( SY1050
!= ( path_cons @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) @ empty ) )
| ! [SY1051: $i] :
( ( SY1050
!= ( path_cons @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) @ SY1051 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) ) @ SY1049 @ SY1051 ) ) )
| ~ ~ ( ~ ( ( SY1049
= ( head_of @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) ) )
| ~ ( ( SY1050
!= ( path_cons @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) @ ( sK13_SY84 @ SY1050 @ SY1049 @ SV689 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) ) @ SY1049 @ ( sK13_SY84 @ SY1050 @ SY1049 @ SV689 ) ) ) )
| ~ ( ( SY1050
= ( path_cons @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) @ empty ) )
| ~ ( ( SY1050
!= ( path_cons @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) @ ( sK12_SY85 @ SY1050 @ SY1049 @ SV689 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) ) @ SY1049 @ ( sK12_SY85 @ SY1050 @ SY1049 @ SV689 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3432]) ).
thf(3452,plain,
! [SV709: $i,SV702: $i,SV690: $i] :
( ( ~ ( vertex @ SV690 )
| ~ ( vertex @ SV702 )
| ~ ( ~ ! [SY1143: $i] :
( ( SV690
!= ( tail_of @ SY1143 ) )
| ~ ( edge @ SY1143 )
| ( SV702
!= ( head_of @ SY1143 ) )
| ( SV709
!= ( path_cons @ SY1143 @ empty ) ) )
| ~ ! [SY1144: $i] :
( ( SV690
!= ( tail_of @ SY1144 ) )
| ~ ( edge @ SY1144 )
| ! [SY1145: $i] :
( ( SV709
!= ( path_cons @ SY1144 @ SY1145 ) )
| ~ ( path @ ( head_of @ SY1144 ) @ SV702 @ SY1145 ) ) ) )
| ( path @ SV690 @ SV702 @ SV709 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3433]) ).
thf(3453,plain,
! [SV691: $i] :
( ( ~ ! [SY1057: $i,SY1058: $i] :
( ~ ( ~ ( path @ SV691 @ SY1057 @ ( sK8_P @ SY1058 @ SY1057 @ SV691 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY1058 ) @ ( length_of @ ( sK8_P @ SY1058 @ SY1057 @ SV691 ) ) ) )
| ( SV691 = SY1057 )
| ~ ( path @ SV691 @ SY1057 @ SY1058 )
| ( shortest_path @ SV691 @ SY1057 @ SY1058 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3434]) ).
thf(3454,plain,
! [SV691: $i] :
( ( ~ ~ ( ~ ! [SY1059: $i,SY1060: $i] :
( ~ ( shortest_path @ SV691 @ SY1059 @ SY1060 )
| ! [SY1061: $i] :
( ~ ( path @ SV691 @ SY1059 @ SY1061 )
| ( less_or_equal @ ( length_of @ SY1060 ) @ ( length_of @ SY1061 ) ) ) )
| ~ ~ ( ~ ! [SY1062: $i] :
( ! [SY1063: $i] :
~ ( shortest_path @ SV691 @ SY1062 @ SY1063 )
| ( SV691 != SY1062 ) )
| ~ ! [SY1064: $i,SY1065: $i] :
( ~ ( shortest_path @ SV691 @ SY1064 @ SY1065 )
| ( path @ SV691 @ SY1064 @ SY1065 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3434]) ).
thf(3455,plain,
! [SV692: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV692 ) @ SV692 )
| ~ ( on_path @ ( sK7_SY80 @ SV692 ) @ SV692 ) )
| ~ ( sequential @ ( sK6_E1 @ SV692 ) @ ( sK7_SY80 @ SV692 ) ) )
| ~ ! [SY1066: $i] :
~ ( triangle @ ( sK6_E1 @ SV692 ) @ ( sK7_SY80 @ SV692 ) @ SY1066 ) ) )
= $true )
| ( ( ! [SY1067: $i,SY1068: $i] :
~ ( path @ SY1067 @ SY1068 @ SV692 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV692 )
= ( number_of_in @ triangles @ SV692 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3435]) ).
thf(3456,plain,
! [SV703: $i,SV693: $i] :
( ( ~ ~ ( ~ ! [SY1126: $i,SY1127: $i] :
( ~ ( on_path @ SY1127 @ SY1126 )
| ~ ( path @ SV693 @ SV703 @ SY1126 )
| ( edge @ SY1127 ) )
| ~ ! [SY1128: $i,SY1129: $i] :
( ~ ( on_path @ SY1129 @ SY1128 )
| ~ ( path @ SV693 @ SV703 @ SY1128 )
| ( in_path @ ( head_of @ SY1129 ) @ SY1128 ) ) )
| ~ ! [SY1130: $i,SY1131: $i] :
( ~ ( on_path @ SY1131 @ SY1130 )
| ~ ( path @ SV693 @ SV703 @ SY1130 )
| ( in_path @ ( tail_of @ SY1131 ) @ SY1130 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3436]) ).
thf(3457,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( edge @ SX0 )
| ~ ( edge @ SX1 )
| ( ( head_of @ SX0 )
!= ( tail_of @ SX1 ) )
| ( sequential @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3437]) ).
thf(3458,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3438]) ).
thf(3459,plain,
! [SV694: $i,SV710: $i] :
( ( ( ! [SY1146: $i] :
~ ( path @ SV710 @ SY1146 @ SV694 ) )
= $true )
| ( ( ~ ( ~ ! [SY1078: $i,SY1079: $i] :
( ~ ( on_path @ SY1078 @ SV694 )
| ~ ( on_path @ SY1079 @ SV694 )
| ! [SY1080: $i] :
( ~ ( precedes @ SY1080 @ SY1079 @ SV694 )
| ~ ( sequential @ SY1078 @ SY1080 ) )
| ( precedes @ SY1078 @ SY1079 @ SV694 ) )
| ~ ! [SY1081: $i,SY1082: $i] :
( ~ ( on_path @ SY1081 @ SV694 )
| ~ ( on_path @ SY1082 @ SV694 )
| ~ ( sequential @ SY1081 @ SY1082 )
| ( precedes @ SY1081 @ SY1082 @ SV694 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3439]) ).
thf(3460,plain,
! [SV704: $i,SV695: $i] :
( ( ~ ! [SY1132: $i,SY1133: $i] :
( ~ ( in_path @ SY1133 @ SY1132 )
| ~ ( path @ SV695 @ SV704 @ SY1132 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY1133 @ SY1132 @ SV704 @ SV695 ) @ SY1132 )
| ~ ( ( SY1133
= ( head_of @ ( sK10_E @ SY1133 @ SY1132 @ SV704 @ SV695 ) ) )
| ( SY1133
= ( tail_of @ ( sK10_E @ SY1133 @ SY1132 @ SV704 @ SV695 ) ) ) ) ) )
| ~ ! [SY1134: $i,SY1135: $i] :
( ~ ( in_path @ SY1135 @ SY1134 )
| ~ ( path @ SV695 @ SV704 @ SY1134 )
| ( vertex @ SY1135 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3440]) ).
thf(3461,plain,
! [SV696: $i] :
( ( ~ ! [SY1088: $i,SY1089: $i] :
( ~ ( edge @ SV696 )
| ~ ( edge @ SY1088 )
| ~ ( edge @ SY1089 )
| ~ ( sequential @ SV696 @ SY1088 )
| ~ ( sequential @ SY1088 @ SY1089 )
| ~ ( sequential @ SY1089 @ SV696 )
| ( triangle @ SV696 @ SY1088 @ SY1089 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3441]) ).
thf(3462,plain,
! [SV696: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY1090: $i,SY1091: $i] :
~ ( triangle @ SV696 @ SY1090 @ SY1091 )
| ( edge @ SV696 ) )
| ~ ! [SY1092: $i] :
( ! [SY1093: $i] :
~ ( triangle @ SV696 @ SY1092 @ SY1093 )
| ( edge @ SY1092 ) ) )
| ~ ! [SY1094: $i,SY1095: $i] :
( ~ ( triangle @ SV696 @ SY1094 @ SY1095 )
| ( edge @ SY1095 ) ) )
| ~ ! [SY1096: $i] :
( ! [SY1097: $i] :
~ ( triangle @ SV696 @ SY1096 @ SY1097 )
| ( sequential @ SV696 @ SY1096 ) ) )
| ~ ! [SY1098: $i,SY1099: $i] :
( ~ ( triangle @ SV696 @ SY1098 @ SY1099 )
| ( sequential @ SY1098 @ SY1099 ) ) )
| ~ ! [SY1100: $i,SY1101: $i] :
( ~ ( triangle @ SV696 @ SY1100 @ SY1101 )
| ( sequential @ SY1101 @ SV696 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3441]) ).
thf(3463,plain,
! [SV697: $i,SV711: $i] :
( ( ( ! [SY1147: $i] :
~ ( path @ SV711 @ SY1147 @ SV697 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY1104: $i] :
( ! [SY1105: $i] :
~ ( precedes @ SY1104 @ SY1105 @ SV697 )
| ( on_path @ SY1104 @ SV697 ) )
| ~ ! [SY1106: $i,SY1107: $i] :
( ~ ( precedes @ SY1106 @ SY1107 @ SV697 )
| ( on_path @ SY1107 @ SV697 ) ) )
| ~ ~ ( ~ ! [SY1108: $i,SY1109: $i] :
( ~ ( precedes @ SY1108 @ SY1109 @ SV697 )
| ! [SY1110: $i] :
( ~ ( precedes @ SY1110 @ SY1109 @ SV697 )
| ~ ( sequential @ SY1108 @ SY1110 ) )
| ~ ( sequential @ SY1108 @ SY1109 ) )
| ~ ! [SY1111: $i,SY1112: $i] :
( ~ ( precedes @ SY1111 @ SY1112 @ SV697 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY1112 @ SY1111 @ SV697 ) @ SY1112 @ SV697 )
| ~ ( sequential @ SY1111 @ ( sK9_E3 @ SY1112 @ SY1111 @ SV697 ) ) )
| ( sequential @ SY1111 @ SY1112 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3442]) ).
thf(3464,plain,
( ( ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( head_of @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3443]) ).
thf(3465,plain,
( ( ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( tail_of @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3444]) ).
thf(3466,plain,
! [SV705: $i,SV698: $i,SV712: $i] :
( ( ~ ( ~ ! [SY1148: $i] :
( ! [SY1149: $i] :
( ~ ( precedes @ SV712 @ SY1148 @ SY1149 )
| ~ ( shortest_path @ SV698 @ SV705 @ SY1149 ) )
| ! [SY1150: $i] :
( ( ( tail_of @ SY1150 )
!= ( tail_of @ SV712 ) )
| ( ( head_of @ SY1150 )
!= ( head_of @ SY1148 ) ) ) )
| ~ ! [SY1151: $i,SY1152: $i] :
( ~ ( precedes @ SV712 @ SY1151 @ SY1152 )
| ~ ( shortest_path @ SV698 @ SV705 @ SY1152 )
| ~ ( precedes @ SY1151 @ SV712 @ SY1152 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3445]) ).
thf(3467,plain,
! [SV685: $i] :
( ( ( ( head_of @ SV685 )
= ( tail_of @ SV685 ) )
= $false )
| ( ( edge @ SV685 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3446]) ).
thf(3468,plain,
! [SV706: $i,SV699: $i,SV686: $i] :
( ( ( ~ ( path @ SV686 @ SV699 @ SV706 ) )
= $true )
| ( ( ( length_of @ SV706 )
= ( number_of_in @ edges @ SV706 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3447]) ).
thf(3469,plain,
! [SV707: $i,SV700: $i,SV687: $i] :
( ( ( ~ ( path @ SV687 @ SV700 @ SV707 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV707 )
= ( minus @ ( length_of @ SV707 ) @ n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3448]) ).
thf(3470,plain,
! [SV713: $i,SV708: $i] :
( ( ( ( SV708 = SV713 )
| ~ ( vertex @ SV708 )
| ~ ( vertex @ SV713 )
| ~ ( ~ ~ ( ~ ( ( SV708
!= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
!= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
!= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
!= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV708
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
| ~ ( ( SV708
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) ) )
| ~ ~ ( ~ ( ( SV713
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
| ~ ( ( SV713
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV713 @ SV708 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3449]) ).
thf(3471,plain,
! [SV689: $i] :
( ( ~ ( ~ ( ! [SY1045: $i,SY1046: $i] :
~ ( path @ SV689 @ SY1045 @ SY1046 )
| ( vertex @ SV689 ) )
| ~ ! [SY1047: $i] :
( ! [SY1048: $i] :
~ ( path @ SV689 @ SY1047 @ SY1048 )
| ( vertex @ SY1047 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3450]) ).
thf(3472,plain,
! [SV689: $i] :
( ( ! [SY1049: $i,SY1050: $i] :
( ~ ( path @ SV689 @ SY1049 @ SY1050 )
| ~ ( ~ ~ ( ( SV689
!= ( tail_of @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) ) )
| ~ ( edge @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) ) )
| ~ ~ ( ~ ( ( SY1049
!= ( head_of @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) ) )
| ( SY1050
!= ( path_cons @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) @ empty ) )
| ! [SY1051: $i] :
( ( SY1050
!= ( path_cons @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) @ SY1051 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) ) @ SY1049 @ SY1051 ) ) )
| ~ ~ ( ~ ( ( SY1049
= ( head_of @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) ) )
| ~ ( ( SY1050
!= ( path_cons @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) @ ( sK13_SY84 @ SY1050 @ SY1049 @ SV689 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) ) @ SY1049 @ ( sK13_SY84 @ SY1050 @ SY1049 @ SV689 ) ) ) )
| ~ ( ( SY1050
= ( path_cons @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) @ empty ) )
| ~ ( ( SY1050
!= ( path_cons @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) @ ( sK12_SY85 @ SY1050 @ SY1049 @ SV689 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY1050 @ SY1049 @ SV689 ) ) @ SY1049 @ ( sK12_SY85 @ SY1050 @ SY1049 @ SV689 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3451]) ).
thf(3473,plain,
! [SV709: $i,SV702: $i,SV690: $i] :
( ( ( ~ ( vertex @ SV690 )
| ~ ( vertex @ SV702 )
| ~ ( ~ ! [SY1143: $i] :
( ( SV690
!= ( tail_of @ SY1143 ) )
| ~ ( edge @ SY1143 )
| ( SV702
!= ( head_of @ SY1143 ) )
| ( SV709
!= ( path_cons @ SY1143 @ empty ) ) )
| ~ ! [SY1144: $i] :
( ( SV690
!= ( tail_of @ SY1144 ) )
| ~ ( edge @ SY1144 )
| ! [SY1145: $i] :
( ( SV709
!= ( path_cons @ SY1144 @ SY1145 ) )
| ~ ( path @ ( head_of @ SY1144 ) @ SV702 @ SY1145 ) ) ) ) )
= $true )
| ( ( path @ SV690 @ SV702 @ SV709 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3452]) ).
thf(3474,plain,
! [SV691: $i] :
( ( ! [SY1057: $i,SY1058: $i] :
( ~ ( ~ ( path @ SV691 @ SY1057 @ ( sK8_P @ SY1058 @ SY1057 @ SV691 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY1058 ) @ ( length_of @ ( sK8_P @ SY1058 @ SY1057 @ SV691 ) ) ) )
| ( SV691 = SY1057 )
| ~ ( path @ SV691 @ SY1057 @ SY1058 )
| ( shortest_path @ SV691 @ SY1057 @ SY1058 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3453]) ).
thf(3475,plain,
! [SV691: $i] :
( ( ~ ( ~ ! [SY1059: $i,SY1060: $i] :
( ~ ( shortest_path @ SV691 @ SY1059 @ SY1060 )
| ! [SY1061: $i] :
( ~ ( path @ SV691 @ SY1059 @ SY1061 )
| ( less_or_equal @ ( length_of @ SY1060 ) @ ( length_of @ SY1061 ) ) ) )
| ~ ~ ( ~ ! [SY1062: $i] :
( ! [SY1063: $i] :
~ ( shortest_path @ SV691 @ SY1062 @ SY1063 )
| ( SV691 != SY1062 ) )
| ~ ! [SY1064: $i,SY1065: $i] :
( ~ ( shortest_path @ SV691 @ SY1064 @ SY1065 )
| ( path @ SV691 @ SY1064 @ SY1065 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3454]) ).
thf(3476,plain,
! [SV692: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV692 ) @ SV692 )
| ~ ( on_path @ ( sK7_SY80 @ SV692 ) @ SV692 ) )
| ~ ( sequential @ ( sK6_E1 @ SV692 ) @ ( sK7_SY80 @ SV692 ) ) )
| ~ ! [SY1066: $i] :
~ ( triangle @ ( sK6_E1 @ SV692 ) @ ( sK7_SY80 @ SV692 ) @ SY1066 ) )
= $false )
| ( ( ! [SY1067: $i,SY1068: $i] :
~ ( path @ SY1067 @ SY1068 @ SV692 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV692 )
= ( number_of_in @ triangles @ SV692 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3455]) ).
thf(3477,plain,
! [SV703: $i,SV693: $i] :
( ( ~ ~ ( ~ ! [SY1126: $i,SY1127: $i] :
( ~ ( on_path @ SY1127 @ SY1126 )
| ~ ( path @ SV693 @ SV703 @ SY1126 )
| ( edge @ SY1127 ) )
| ~ ! [SY1128: $i,SY1129: $i] :
( ~ ( on_path @ SY1129 @ SY1128 )
| ~ ( path @ SV693 @ SV703 @ SY1128 )
| ( in_path @ ( head_of @ SY1129 ) @ SY1128 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3456]) ).
thf(3478,plain,
! [SV703: $i,SV693: $i] :
( ( ~ ! [SY1130: $i,SY1131: $i] :
( ~ ( on_path @ SY1131 @ SY1130 )
| ~ ( path @ SV693 @ SV703 @ SY1130 )
| ( in_path @ ( tail_of @ SY1131 ) @ SY1130 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3456]) ).
thf(3479,plain,
! [SV714: $i] :
( ( ! [SY1153: $i] :
( ( SV714 = SY1153 )
| ~ ( edge @ SV714 )
| ~ ( edge @ SY1153 )
| ( ( head_of @ SV714 )
!= ( tail_of @ SY1153 ) )
| ( sequential @ SV714 @ SY1153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3457]) ).
thf(3480,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3458]) ).
thf(3481,plain,
! [SV694: $i,SV715: $i,SV710: $i] :
( ( ( ~ ( path @ SV710 @ SV715 @ SV694 ) )
= $true )
| ( ( ~ ( ~ ! [SY1078: $i,SY1079: $i] :
( ~ ( on_path @ SY1078 @ SV694 )
| ~ ( on_path @ SY1079 @ SV694 )
| ! [SY1080: $i] :
( ~ ( precedes @ SY1080 @ SY1079 @ SV694 )
| ~ ( sequential @ SY1078 @ SY1080 ) )
| ( precedes @ SY1078 @ SY1079 @ SV694 ) )
| ~ ! [SY1081: $i,SY1082: $i] :
( ~ ( on_path @ SY1081 @ SV694 )
| ~ ( on_path @ SY1082 @ SV694 )
| ~ ( sequential @ SY1081 @ SY1082 )
| ( precedes @ SY1081 @ SY1082 @ SV694 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3459]) ).
thf(3482,plain,
! [SV704: $i,SV695: $i] :
( ( ~ ! [SY1132: $i,SY1133: $i] :
( ~ ( in_path @ SY1133 @ SY1132 )
| ~ ( path @ SV695 @ SV704 @ SY1132 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY1133 @ SY1132 @ SV704 @ SV695 ) @ SY1132 )
| ~ ( ( SY1133
= ( head_of @ ( sK10_E @ SY1133 @ SY1132 @ SV704 @ SV695 ) ) )
| ( SY1133
= ( tail_of @ ( sK10_E @ SY1133 @ SY1132 @ SV704 @ SV695 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3460]) ).
thf(3483,plain,
! [SV704: $i,SV695: $i] :
( ( ~ ! [SY1134: $i,SY1135: $i] :
( ~ ( in_path @ SY1135 @ SY1134 )
| ~ ( path @ SV695 @ SV704 @ SY1134 )
| ( vertex @ SY1135 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3460]) ).
thf(3484,plain,
! [SV696: $i] :
( ( ! [SY1088: $i,SY1089: $i] :
( ~ ( edge @ SV696 )
| ~ ( edge @ SY1088 )
| ~ ( edge @ SY1089 )
| ~ ( sequential @ SV696 @ SY1088 )
| ~ ( sequential @ SY1088 @ SY1089 )
| ~ ( sequential @ SY1089 @ SV696 )
| ( triangle @ SV696 @ SY1088 @ SY1089 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3461]) ).
thf(3485,plain,
! [SV696: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY1090: $i,SY1091: $i] :
~ ( triangle @ SV696 @ SY1090 @ SY1091 )
| ( edge @ SV696 ) )
| ~ ! [SY1092: $i] :
( ! [SY1093: $i] :
~ ( triangle @ SV696 @ SY1092 @ SY1093 )
| ( edge @ SY1092 ) ) )
| ~ ! [SY1094: $i,SY1095: $i] :
( ~ ( triangle @ SV696 @ SY1094 @ SY1095 )
| ( edge @ SY1095 ) ) )
| ~ ! [SY1096: $i] :
( ! [SY1097: $i] :
~ ( triangle @ SV696 @ SY1096 @ SY1097 )
| ( sequential @ SV696 @ SY1096 ) ) )
| ~ ! [SY1098: $i,SY1099: $i] :
( ~ ( triangle @ SV696 @ SY1098 @ SY1099 )
| ( sequential @ SY1098 @ SY1099 ) ) )
| ~ ! [SY1100: $i,SY1101: $i] :
( ~ ( triangle @ SV696 @ SY1100 @ SY1101 )
| ( sequential @ SY1101 @ SV696 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3462]) ).
thf(3486,plain,
! [SV697: $i,SV716: $i,SV711: $i] :
( ( ( ~ ( path @ SV711 @ SV716 @ SV697 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY1104: $i] :
( ! [SY1105: $i] :
~ ( precedes @ SY1104 @ SY1105 @ SV697 )
| ( on_path @ SY1104 @ SV697 ) )
| ~ ! [SY1106: $i,SY1107: $i] :
( ~ ( precedes @ SY1106 @ SY1107 @ SV697 )
| ( on_path @ SY1107 @ SV697 ) ) )
| ~ ~ ( ~ ! [SY1108: $i,SY1109: $i] :
( ~ ( precedes @ SY1108 @ SY1109 @ SV697 )
| ! [SY1110: $i] :
( ~ ( precedes @ SY1110 @ SY1109 @ SV697 )
| ~ ( sequential @ SY1108 @ SY1110 ) )
| ~ ( sequential @ SY1108 @ SY1109 ) )
| ~ ! [SY1111: $i,SY1112: $i] :
( ~ ( precedes @ SY1111 @ SY1112 @ SV697 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY1112 @ SY1111 @ SV697 ) @ SY1112 @ SV697 )
| ~ ( sequential @ SY1111 @ ( sK9_E3 @ SY1112 @ SY1111 @ SV697 ) ) )
| ( sequential @ SY1111 @ SY1112 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3463]) ).
thf(3487,plain,
! [SV717: $i] :
( ( ~ ( edge @ SV717 )
| ( vertex @ ( head_of @ SV717 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3464]) ).
thf(3488,plain,
! [SV718: $i] :
( ( ~ ( edge @ SV718 )
| ( vertex @ ( tail_of @ SV718 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3465]) ).
thf(3489,plain,
! [SV705: $i,SV698: $i,SV712: $i] :
( ( ~ ! [SY1148: $i] :
( ! [SY1149: $i] :
( ~ ( precedes @ SV712 @ SY1148 @ SY1149 )
| ~ ( shortest_path @ SV698 @ SV705 @ SY1149 ) )
| ! [SY1150: $i] :
( ( ( tail_of @ SY1150 )
!= ( tail_of @ SV712 ) )
| ( ( head_of @ SY1150 )
!= ( head_of @ SY1148 ) ) ) )
| ~ ! [SY1151: $i,SY1152: $i] :
( ~ ( precedes @ SV712 @ SY1151 @ SY1152 )
| ~ ( shortest_path @ SV698 @ SV705 @ SY1152 )
| ~ ( precedes @ SY1151 @ SV712 @ SY1152 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3466]) ).
thf(3490,plain,
! [SV706: $i,SV699: $i,SV686: $i] :
( ( ( path @ SV686 @ SV699 @ SV706 )
= $false )
| ( ( ( length_of @ SV706 )
= ( number_of_in @ edges @ SV706 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3468]) ).
thf(3491,plain,
! [SV707: $i,SV700: $i,SV687: $i] :
( ( ( path @ SV687 @ SV700 @ SV707 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV707 )
= ( minus @ ( length_of @ SV707 ) @ n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3469]) ).
thf(3492,plain,
! [SV713: $i,SV708: $i] :
( ( ( ( SV708 = SV713 )
| ~ ( vertex @ SV708 )
| ~ ( vertex @ SV713 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV708
!= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
!= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
!= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
!= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV708
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
| ~ ( ( SV708
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) ) )
| ~ ~ ( ~ ( ( SV713
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
| ~ ( ( SV713
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV713 @ SV708 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[3470]) ).
thf(3493,plain,
! [SV689: $i] :
( ( ~ ( ! [SY1045: $i,SY1046: $i] :
~ ( path @ SV689 @ SY1045 @ SY1046 )
| ( vertex @ SV689 ) )
| ~ ! [SY1047: $i] :
( ! [SY1048: $i] :
~ ( path @ SV689 @ SY1047 @ SY1048 )
| ( vertex @ SY1047 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3471]) ).
thf(3494,plain,
! [SV719: $i,SV689: $i] :
( ( ! [SY1154: $i] :
( ~ ( path @ SV689 @ SV719 @ SY1154 )
| ~ ( ~ ~ ( ( SV689
!= ( tail_of @ ( sK11_E @ SY1154 @ SV719 @ SV689 ) ) )
| ~ ( edge @ ( sK11_E @ SY1154 @ SV719 @ SV689 ) ) )
| ~ ~ ( ~ ( ( SV719
!= ( head_of @ ( sK11_E @ SY1154 @ SV719 @ SV689 ) ) )
| ( SY1154
!= ( path_cons @ ( sK11_E @ SY1154 @ SV719 @ SV689 ) @ empty ) )
| ! [SY1155: $i] :
( ( SY1154
!= ( path_cons @ ( sK11_E @ SY1154 @ SV719 @ SV689 ) @ SY1155 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY1154 @ SV719 @ SV689 ) ) @ SV719 @ SY1155 ) ) )
| ~ ~ ( ~ ( ( SV719
= ( head_of @ ( sK11_E @ SY1154 @ SV719 @ SV689 ) ) )
| ~ ( ( SY1154
!= ( path_cons @ ( sK11_E @ SY1154 @ SV719 @ SV689 ) @ ( sK13_SY84 @ SY1154 @ SV719 @ SV689 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY1154 @ SV719 @ SV689 ) ) @ SV719 @ ( sK13_SY84 @ SY1154 @ SV719 @ SV689 ) ) ) )
| ~ ( ( SY1154
= ( path_cons @ ( sK11_E @ SY1154 @ SV719 @ SV689 ) @ empty ) )
| ~ ( ( SY1154
!= ( path_cons @ ( sK11_E @ SY1154 @ SV719 @ SV689 ) @ ( sK12_SY85 @ SY1154 @ SV719 @ SV689 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY1154 @ SV719 @ SV689 ) ) @ SV719 @ ( sK12_SY85 @ SY1154 @ SV719 @ SV689 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3472]) ).
thf(3495,plain,
! [SV709: $i,SV702: $i,SV690: $i] :
( ( ( ~ ( vertex @ SV690 )
| ~ ( vertex @ SV702 ) )
= $true )
| ( ( ~ ( ~ ! [SY1143: $i] :
( ( SV690
!= ( tail_of @ SY1143 ) )
| ~ ( edge @ SY1143 )
| ( SV702
!= ( head_of @ SY1143 ) )
| ( SV709
!= ( path_cons @ SY1143 @ empty ) ) )
| ~ ! [SY1144: $i] :
( ( SV690
!= ( tail_of @ SY1144 ) )
| ~ ( edge @ SY1144 )
| ! [SY1145: $i] :
( ( SV709
!= ( path_cons @ SY1144 @ SY1145 ) )
| ~ ( path @ ( head_of @ SY1144 ) @ SV702 @ SY1145 ) ) ) ) )
= $true )
| ( ( path @ SV690 @ SV702 @ SV709 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3473]) ).
thf(3496,plain,
! [SV720: $i,SV691: $i] :
( ( ! [SY1156: $i] :
( ~ ( ~ ( path @ SV691 @ SV720 @ ( sK8_P @ SY1156 @ SV720 @ SV691 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY1156 ) @ ( length_of @ ( sK8_P @ SY1156 @ SV720 @ SV691 ) ) ) )
| ( SV691 = SV720 )
| ~ ( path @ SV691 @ SV720 @ SY1156 )
| ( shortest_path @ SV691 @ SV720 @ SY1156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3474]) ).
thf(3497,plain,
! [SV691: $i] :
( ( ~ ! [SY1059: $i,SY1060: $i] :
( ~ ( shortest_path @ SV691 @ SY1059 @ SY1060 )
| ! [SY1061: $i] :
( ~ ( path @ SV691 @ SY1059 @ SY1061 )
| ( less_or_equal @ ( length_of @ SY1060 ) @ ( length_of @ SY1061 ) ) ) )
| ~ ~ ( ~ ! [SY1062: $i] :
( ! [SY1063: $i] :
~ ( shortest_path @ SV691 @ SY1062 @ SY1063 )
| ( SV691 != SY1062 ) )
| ~ ! [SY1064: $i,SY1065: $i] :
( ~ ( shortest_path @ SV691 @ SY1064 @ SY1065 )
| ( path @ SV691 @ SY1064 @ SY1065 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3475]) ).
thf(3498,plain,
! [SV692: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV692 ) @ SV692 )
| ~ ( on_path @ ( sK7_SY80 @ SV692 ) @ SV692 ) )
| ~ ( sequential @ ( sK6_E1 @ SV692 ) @ ( sK7_SY80 @ SV692 ) ) ) )
= $false )
| ( ( ! [SY1067: $i,SY1068: $i] :
~ ( path @ SY1067 @ SY1068 @ SV692 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV692 )
= ( number_of_in @ triangles @ SV692 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3476]) ).
thf(3499,plain,
! [SV692: $i] :
( ( ( ~ ! [SY1066: $i] :
~ ( triangle @ ( sK6_E1 @ SV692 ) @ ( sK7_SY80 @ SV692 ) @ SY1066 ) )
= $false )
| ( ( ! [SY1067: $i,SY1068: $i] :
~ ( path @ SY1067 @ SY1068 @ SV692 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV692 )
= ( number_of_in @ triangles @ SV692 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3476]) ).
thf(3500,plain,
! [SV703: $i,SV693: $i] :
( ( ~ ( ~ ! [SY1126: $i,SY1127: $i] :
( ~ ( on_path @ SY1127 @ SY1126 )
| ~ ( path @ SV693 @ SV703 @ SY1126 )
| ( edge @ SY1127 ) )
| ~ ! [SY1128: $i,SY1129: $i] :
( ~ ( on_path @ SY1129 @ SY1128 )
| ~ ( path @ SV693 @ SV703 @ SY1128 )
| ( in_path @ ( head_of @ SY1129 ) @ SY1128 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3477]) ).
thf(3501,plain,
! [SV703: $i,SV693: $i] :
( ( ! [SY1130: $i,SY1131: $i] :
( ~ ( on_path @ SY1131 @ SY1130 )
| ~ ( path @ SV693 @ SV703 @ SY1130 )
| ( in_path @ ( tail_of @ SY1131 ) @ SY1130 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3478]) ).
thf(3502,plain,
! [SV721: $i,SV714: $i] :
( ( ( SV714 = SV721 )
| ~ ( edge @ SV714 )
| ~ ( edge @ SV721 )
| ( ( head_of @ SV714 )
!= ( tail_of @ SV721 ) )
| ( sequential @ SV714 @ SV721 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3479]) ).
thf(3503,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3480]) ).
thf(3504,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3480]) ).
thf(3505,plain,
! [SV694: $i,SV715: $i,SV710: $i] :
( ( ( path @ SV710 @ SV715 @ SV694 )
= $false )
| ( ( ~ ( ~ ! [SY1078: $i,SY1079: $i] :
( ~ ( on_path @ SY1078 @ SV694 )
| ~ ( on_path @ SY1079 @ SV694 )
| ! [SY1080: $i] :
( ~ ( precedes @ SY1080 @ SY1079 @ SV694 )
| ~ ( sequential @ SY1078 @ SY1080 ) )
| ( precedes @ SY1078 @ SY1079 @ SV694 ) )
| ~ ! [SY1081: $i,SY1082: $i] :
( ~ ( on_path @ SY1081 @ SV694 )
| ~ ( on_path @ SY1082 @ SV694 )
| ~ ( sequential @ SY1081 @ SY1082 )
| ( precedes @ SY1081 @ SY1082 @ SV694 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3481]) ).
thf(3506,plain,
! [SV704: $i,SV695: $i] :
( ( ! [SY1132: $i,SY1133: $i] :
( ~ ( in_path @ SY1133 @ SY1132 )
| ~ ( path @ SV695 @ SV704 @ SY1132 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY1133 @ SY1132 @ SV704 @ SV695 ) @ SY1132 )
| ~ ( ( SY1133
= ( head_of @ ( sK10_E @ SY1133 @ SY1132 @ SV704 @ SV695 ) ) )
| ( SY1133
= ( tail_of @ ( sK10_E @ SY1133 @ SY1132 @ SV704 @ SV695 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3482]) ).
thf(3507,plain,
! [SV704: $i,SV695: $i] :
( ( ! [SY1134: $i,SY1135: $i] :
( ~ ( in_path @ SY1135 @ SY1134 )
| ~ ( path @ SV695 @ SV704 @ SY1134 )
| ( vertex @ SY1135 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3483]) ).
thf(3508,plain,
! [SV722: $i,SV696: $i] :
( ( ! [SY1157: $i] :
( ~ ( edge @ SV696 )
| ~ ( edge @ SV722 )
| ~ ( edge @ SY1157 )
| ~ ( sequential @ SV696 @ SV722 )
| ~ ( sequential @ SV722 @ SY1157 )
| ~ ( sequential @ SY1157 @ SV696 )
| ( triangle @ SV696 @ SV722 @ SY1157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3484]) ).
thf(3509,plain,
! [SV696: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY1090: $i,SY1091: $i] :
~ ( triangle @ SV696 @ SY1090 @ SY1091 )
| ( edge @ SV696 ) )
| ~ ! [SY1092: $i] :
( ! [SY1093: $i] :
~ ( triangle @ SV696 @ SY1092 @ SY1093 )
| ( edge @ SY1092 ) ) )
| ~ ! [SY1094: $i,SY1095: $i] :
( ~ ( triangle @ SV696 @ SY1094 @ SY1095 )
| ( edge @ SY1095 ) ) )
| ~ ! [SY1096: $i] :
( ! [SY1097: $i] :
~ ( triangle @ SV696 @ SY1096 @ SY1097 )
| ( sequential @ SV696 @ SY1096 ) ) )
| ~ ! [SY1098: $i,SY1099: $i] :
( ~ ( triangle @ SV696 @ SY1098 @ SY1099 )
| ( sequential @ SY1098 @ SY1099 ) ) )
| ~ ! [SY1100: $i,SY1101: $i] :
( ~ ( triangle @ SV696 @ SY1100 @ SY1101 )
| ( sequential @ SY1101 @ SV696 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3485]) ).
thf(3510,plain,
! [SV697: $i,SV716: $i,SV711: $i] :
( ( ( path @ SV711 @ SV716 @ SV697 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY1104: $i] :
( ! [SY1105: $i] :
~ ( precedes @ SY1104 @ SY1105 @ SV697 )
| ( on_path @ SY1104 @ SV697 ) )
| ~ ! [SY1106: $i,SY1107: $i] :
( ~ ( precedes @ SY1106 @ SY1107 @ SV697 )
| ( on_path @ SY1107 @ SV697 ) ) )
| ~ ~ ( ~ ! [SY1108: $i,SY1109: $i] :
( ~ ( precedes @ SY1108 @ SY1109 @ SV697 )
| ! [SY1110: $i] :
( ~ ( precedes @ SY1110 @ SY1109 @ SV697 )
| ~ ( sequential @ SY1108 @ SY1110 ) )
| ~ ( sequential @ SY1108 @ SY1109 ) )
| ~ ! [SY1111: $i,SY1112: $i] :
( ~ ( precedes @ SY1111 @ SY1112 @ SV697 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY1112 @ SY1111 @ SV697 ) @ SY1112 @ SV697 )
| ~ ( sequential @ SY1111 @ ( sK9_E3 @ SY1112 @ SY1111 @ SV697 ) ) )
| ( sequential @ SY1111 @ SY1112 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3486]) ).
thf(3511,plain,
! [SV717: $i] :
( ( ( ~ ( edge @ SV717 ) )
= $true )
| ( ( vertex @ ( head_of @ SV717 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3487]) ).
thf(3512,plain,
! [SV718: $i] :
( ( ( ~ ( edge @ SV718 ) )
= $true )
| ( ( vertex @ ( tail_of @ SV718 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3488]) ).
thf(3513,plain,
! [SV705: $i,SV698: $i,SV712: $i] :
( ( ~ ! [SY1148: $i] :
( ! [SY1149: $i] :
( ~ ( precedes @ SV712 @ SY1148 @ SY1149 )
| ~ ( shortest_path @ SV698 @ SV705 @ SY1149 ) )
| ! [SY1150: $i] :
( ( ( tail_of @ SY1150 )
!= ( tail_of @ SV712 ) )
| ( ( head_of @ SY1150 )
!= ( head_of @ SY1148 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3489]) ).
thf(3514,plain,
! [SV705: $i,SV698: $i,SV712: $i] :
( ( ~ ! [SY1151: $i,SY1152: $i] :
( ~ ( precedes @ SV712 @ SY1151 @ SY1152 )
| ~ ( shortest_path @ SV698 @ SV705 @ SY1152 )
| ~ ( precedes @ SY1151 @ SV712 @ SY1152 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3489]) ).
thf(3515,plain,
! [SV713: $i,SV708: $i] :
( ( ( SV708 = SV713 )
= $true )
| ( ( ~ ( vertex @ SV708 )
| ~ ( vertex @ SV713 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV708
!= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
!= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
!= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
!= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV708
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
| ~ ( ( SV708
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) ) )
| ~ ~ ( ~ ( ( SV713
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
| ~ ( ( SV713
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV713 @ SV708 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[3492]) ).
thf(3516,plain,
! [SV689: $i] :
( ( ~ ( ! [SY1045: $i,SY1046: $i] :
~ ( path @ SV689 @ SY1045 @ SY1046 )
| ( vertex @ SV689 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3493]) ).
thf(3517,plain,
! [SV689: $i] :
( ( ~ ! [SY1047: $i] :
( ! [SY1048: $i] :
~ ( path @ SV689 @ SY1047 @ SY1048 )
| ( vertex @ SY1047 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3493]) ).
thf(3518,plain,
! [SV723: $i,SV719: $i,SV689: $i] :
( ( ~ ( path @ SV689 @ SV719 @ SV723 )
| ~ ( ~ ~ ( ( SV689
!= ( tail_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( edge @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
| ~ ~ ( ~ ( ( SV719
!= ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
| ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ empty ) )
| ! [SY1158: $i] :
( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ SY1158 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ SY1158 ) ) )
| ~ ~ ( ~ ( ( SV719
= ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ ( sK13_SY84 @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ ( sK13_SY84 @ SV723 @ SV719 @ SV689 ) ) ) )
| ~ ( ( SV723
= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ empty ) )
| ~ ( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ ( sK12_SY85 @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ ( sK12_SY85 @ SV723 @ SV719 @ SV689 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3494]) ).
thf(3519,plain,
! [SV709: $i,SV702: $i,SV690: $i] :
( ( ( ~ ( vertex @ SV690 ) )
= $true )
| ( ( ~ ( vertex @ SV702 ) )
= $true )
| ( ( ~ ( ~ ! [SY1143: $i] :
( ( SV690
!= ( tail_of @ SY1143 ) )
| ~ ( edge @ SY1143 )
| ( SV702
!= ( head_of @ SY1143 ) )
| ( SV709
!= ( path_cons @ SY1143 @ empty ) ) )
| ~ ! [SY1144: $i] :
( ( SV690
!= ( tail_of @ SY1144 ) )
| ~ ( edge @ SY1144 )
| ! [SY1145: $i] :
( ( SV709
!= ( path_cons @ SY1144 @ SY1145 ) )
| ~ ( path @ ( head_of @ SY1144 ) @ SV702 @ SY1145 ) ) ) ) )
= $true )
| ( ( path @ SV690 @ SV702 @ SV709 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3495]) ).
thf(3520,plain,
! [SV724: $i,SV720: $i,SV691: $i] :
( ( ~ ( ~ ( path @ SV691 @ SV720 @ ( sK8_P @ SV724 @ SV720 @ SV691 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SV724 ) @ ( length_of @ ( sK8_P @ SV724 @ SV720 @ SV691 ) ) ) )
| ( SV691 = SV720 )
| ~ ( path @ SV691 @ SV720 @ SV724 )
| ( shortest_path @ SV691 @ SV720 @ SV724 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3496]) ).
thf(3521,plain,
! [SV691: $i] :
( ( ~ ! [SY1059: $i,SY1060: $i] :
( ~ ( shortest_path @ SV691 @ SY1059 @ SY1060 )
| ! [SY1061: $i] :
( ~ ( path @ SV691 @ SY1059 @ SY1061 )
| ( less_or_equal @ ( length_of @ SY1060 ) @ ( length_of @ SY1061 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3497]) ).
thf(3522,plain,
! [SV691: $i] :
( ( ~ ~ ( ~ ! [SY1062: $i] :
( ! [SY1063: $i] :
~ ( shortest_path @ SV691 @ SY1062 @ SY1063 )
| ( SV691 != SY1062 ) )
| ~ ! [SY1064: $i,SY1065: $i] :
( ~ ( shortest_path @ SV691 @ SY1064 @ SY1065 )
| ( path @ SV691 @ SY1064 @ SY1065 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3497]) ).
thf(3523,plain,
! [SV692: $i] :
( ( ( ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV692 ) @ SV692 )
| ~ ( on_path @ ( sK7_SY80 @ SV692 ) @ SV692 ) )
| ~ ( sequential @ ( sK6_E1 @ SV692 ) @ ( sK7_SY80 @ SV692 ) ) ) )
= $true )
| ( ( ! [SY1067: $i,SY1068: $i] :
~ ( path @ SY1067 @ SY1068 @ SV692 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV692 )
= ( number_of_in @ triangles @ SV692 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3498]) ).
thf(3524,plain,
! [SV692: $i] :
( ( ( ! [SY1066: $i] :
~ ( triangle @ ( sK6_E1 @ SV692 ) @ ( sK7_SY80 @ SV692 ) @ SY1066 ) )
= $true )
| ( ( ! [SY1067: $i,SY1068: $i] :
~ ( path @ SY1067 @ SY1068 @ SV692 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV692 )
= ( number_of_in @ triangles @ SV692 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3499]) ).
thf(3525,plain,
! [SV703: $i,SV693: $i] :
( ( ~ ! [SY1126: $i,SY1127: $i] :
( ~ ( on_path @ SY1127 @ SY1126 )
| ~ ( path @ SV693 @ SV703 @ SY1126 )
| ( edge @ SY1127 ) )
| ~ ! [SY1128: $i,SY1129: $i] :
( ~ ( on_path @ SY1129 @ SY1128 )
| ~ ( path @ SV693 @ SV703 @ SY1128 )
| ( in_path @ ( head_of @ SY1129 ) @ SY1128 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3500]) ).
thf(3526,plain,
! [SV703: $i,SV693: $i,SV725: $i] :
( ( ! [SY1159: $i] :
( ~ ( on_path @ SY1159 @ SV725 )
| ~ ( path @ SV693 @ SV703 @ SV725 )
| ( in_path @ ( tail_of @ SY1159 ) @ SV725 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3501]) ).
thf(3527,plain,
! [SV721: $i,SV714: $i] :
( ( ( ( SV714 = SV721 )
| ~ ( edge @ SV714 )
| ~ ( edge @ SV721 )
| ( ( head_of @ SV714 )
!= ( tail_of @ SV721 ) ) )
= $true )
| ( ( sequential @ SV714 @ SV721 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3502]) ).
thf(3528,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3503]) ).
thf(3529,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3504]) ).
thf(3530,plain,
! [SV715: $i,SV710: $i,SV694: $i] :
( ( ( ~ ! [SY1078: $i,SY1079: $i] :
( ~ ( on_path @ SY1078 @ SV694 )
| ~ ( on_path @ SY1079 @ SV694 )
| ! [SY1080: $i] :
( ~ ( precedes @ SY1080 @ SY1079 @ SV694 )
| ~ ( sequential @ SY1078 @ SY1080 ) )
| ( precedes @ SY1078 @ SY1079 @ SV694 ) )
| ~ ! [SY1081: $i,SY1082: $i] :
( ~ ( on_path @ SY1081 @ SV694 )
| ~ ( on_path @ SY1082 @ SV694 )
| ~ ( sequential @ SY1081 @ SY1082 )
| ( precedes @ SY1081 @ SY1082 @ SV694 ) ) )
= $false )
| ( ( path @ SV710 @ SV715 @ SV694 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3505]) ).
thf(3531,plain,
! [SV704: $i,SV695: $i,SV726: $i] :
( ( ! [SY1160: $i] :
( ~ ( in_path @ SY1160 @ SV726 )
| ~ ( path @ SV695 @ SV704 @ SV726 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY1160 @ SV726 @ SV704 @ SV695 ) @ SV726 )
| ~ ( ( SY1160
= ( head_of @ ( sK10_E @ SY1160 @ SV726 @ SV704 @ SV695 ) ) )
| ( SY1160
= ( tail_of @ ( sK10_E @ SY1160 @ SV726 @ SV704 @ SV695 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3506]) ).
thf(3532,plain,
! [SV704: $i,SV695: $i,SV727: $i] :
( ( ! [SY1161: $i] :
( ~ ( in_path @ SY1161 @ SV727 )
| ~ ( path @ SV695 @ SV704 @ SV727 )
| ( vertex @ SY1161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3507]) ).
thf(3533,plain,
! [SV728: $i,SV722: $i,SV696: $i] :
( ( ~ ( edge @ SV696 )
| ~ ( edge @ SV722 )
| ~ ( edge @ SV728 )
| ~ ( sequential @ SV696 @ SV722 )
| ~ ( sequential @ SV722 @ SV728 )
| ~ ( sequential @ SV728 @ SV696 )
| ( triangle @ SV696 @ SV722 @ SV728 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3508]) ).
thf(3534,plain,
! [SV696: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY1090: $i,SY1091: $i] :
~ ( triangle @ SV696 @ SY1090 @ SY1091 )
| ( edge @ SV696 ) )
| ~ ! [SY1092: $i] :
( ! [SY1093: $i] :
~ ( triangle @ SV696 @ SY1092 @ SY1093 )
| ( edge @ SY1092 ) ) )
| ~ ! [SY1094: $i,SY1095: $i] :
( ~ ( triangle @ SV696 @ SY1094 @ SY1095 )
| ( edge @ SY1095 ) ) )
| ~ ! [SY1096: $i] :
( ! [SY1097: $i] :
~ ( triangle @ SV696 @ SY1096 @ SY1097 )
| ( sequential @ SV696 @ SY1096 ) ) )
| ~ ! [SY1098: $i,SY1099: $i] :
( ~ ( triangle @ SV696 @ SY1098 @ SY1099 )
| ( sequential @ SY1098 @ SY1099 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3509]) ).
thf(3535,plain,
! [SV696: $i] :
( ( ~ ! [SY1100: $i,SY1101: $i] :
( ~ ( triangle @ SV696 @ SY1100 @ SY1101 )
| ( sequential @ SY1101 @ SV696 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3509]) ).
thf(3536,plain,
! [SV716: $i,SV711: $i,SV697: $i] :
( ( ( ~ ~ ( ~ ! [SY1104: $i] :
( ! [SY1105: $i] :
~ ( precedes @ SY1104 @ SY1105 @ SV697 )
| ( on_path @ SY1104 @ SV697 ) )
| ~ ! [SY1106: $i,SY1107: $i] :
( ~ ( precedes @ SY1106 @ SY1107 @ SV697 )
| ( on_path @ SY1107 @ SV697 ) ) )
| ~ ~ ( ~ ! [SY1108: $i,SY1109: $i] :
( ~ ( precedes @ SY1108 @ SY1109 @ SV697 )
| ! [SY1110: $i] :
( ~ ( precedes @ SY1110 @ SY1109 @ SV697 )
| ~ ( sequential @ SY1108 @ SY1110 ) )
| ~ ( sequential @ SY1108 @ SY1109 ) )
| ~ ! [SY1111: $i,SY1112: $i] :
( ~ ( precedes @ SY1111 @ SY1112 @ SV697 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY1112 @ SY1111 @ SV697 ) @ SY1112 @ SV697 )
| ~ ( sequential @ SY1111 @ ( sK9_E3 @ SY1112 @ SY1111 @ SV697 ) ) )
| ( sequential @ SY1111 @ SY1112 ) ) ) )
= $false )
| ( ( path @ SV711 @ SV716 @ SV697 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3510]) ).
thf(3537,plain,
! [SV717: $i] :
( ( ( edge @ SV717 )
= $false )
| ( ( vertex @ ( head_of @ SV717 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3511]) ).
thf(3538,plain,
! [SV718: $i] :
( ( ( edge @ SV718 )
= $false )
| ( ( vertex @ ( tail_of @ SV718 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3512]) ).
thf(3539,plain,
! [SV705: $i,SV698: $i,SV712: $i] :
( ( ! [SY1148: $i] :
( ! [SY1149: $i] :
( ~ ( precedes @ SV712 @ SY1148 @ SY1149 )
| ~ ( shortest_path @ SV698 @ SV705 @ SY1149 ) )
| ! [SY1150: $i] :
( ( ( tail_of @ SY1150 )
!= ( tail_of @ SV712 ) )
| ( ( head_of @ SY1150 )
!= ( head_of @ SY1148 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3513]) ).
thf(3540,plain,
! [SV705: $i,SV698: $i,SV712: $i] :
( ( ! [SY1151: $i,SY1152: $i] :
( ~ ( precedes @ SV712 @ SY1151 @ SY1152 )
| ~ ( shortest_path @ SV698 @ SV705 @ SY1152 )
| ~ ( precedes @ SY1151 @ SV712 @ SY1152 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3514]) ).
thf(3541,plain,
! [SV713: $i,SV708: $i] :
( ( ( ~ ( vertex @ SV708 ) )
= $true )
| ( ( ~ ( vertex @ SV713 ) )
= $true )
| ( ( SV708 = SV713 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV708
!= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
!= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
!= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
!= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV708
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
| ~ ( ( SV708
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) ) )
| ~ ~ ( ~ ( ( SV713
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
| ~ ( ( SV713
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV713 @ SV708 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[3515]) ).
thf(3542,plain,
! [SV689: $i] :
( ( ! [SY1045: $i,SY1046: $i] :
~ ( path @ SV689 @ SY1045 @ SY1046 )
| ( vertex @ SV689 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3516]) ).
thf(3543,plain,
! [SV689: $i] :
( ( ! [SY1047: $i] :
( ! [SY1048: $i] :
~ ( path @ SV689 @ SY1047 @ SY1048 )
| ( vertex @ SY1047 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3517]) ).
thf(3544,plain,
! [SV723: $i,SV719: $i,SV689: $i] :
( ( ( ~ ( path @ SV689 @ SV719 @ SV723 ) )
= $true )
| ( ( ~ ( ~ ~ ( ( SV689
!= ( tail_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( edge @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
| ~ ~ ( ~ ( ( SV719
!= ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
| ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ empty ) )
| ! [SY1158: $i] :
( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ SY1158 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ SY1158 ) ) )
| ~ ~ ( ~ ( ( SV719
= ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ ( sK13_SY84 @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ ( sK13_SY84 @ SV723 @ SV719 @ SV689 ) ) ) )
| ~ ( ( SV723
= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ empty ) )
| ~ ( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ ( sK12_SY85 @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ ( sK12_SY85 @ SV723 @ SV719 @ SV689 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3518]) ).
thf(3545,plain,
! [SV709: $i,SV702: $i,SV690: $i] :
( ( ( vertex @ SV690 )
= $false )
| ( ( ~ ( vertex @ SV702 ) )
= $true )
| ( ( ~ ( ~ ! [SY1143: $i] :
( ( SV690
!= ( tail_of @ SY1143 ) )
| ~ ( edge @ SY1143 )
| ( SV702
!= ( head_of @ SY1143 ) )
| ( SV709
!= ( path_cons @ SY1143 @ empty ) ) )
| ~ ! [SY1144: $i] :
( ( SV690
!= ( tail_of @ SY1144 ) )
| ~ ( edge @ SY1144 )
| ! [SY1145: $i] :
( ( SV709
!= ( path_cons @ SY1144 @ SY1145 ) )
| ~ ( path @ ( head_of @ SY1144 ) @ SV702 @ SY1145 ) ) ) ) )
= $true )
| ( ( path @ SV690 @ SV702 @ SV709 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3519]) ).
thf(3546,plain,
! [SV724: $i,SV720: $i,SV691: $i] :
( ( ( ~ ( ~ ( path @ SV691 @ SV720 @ ( sK8_P @ SV724 @ SV720 @ SV691 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SV724 ) @ ( length_of @ ( sK8_P @ SV724 @ SV720 @ SV691 ) ) ) )
| ( SV691 = SV720 )
| ~ ( path @ SV691 @ SV720 @ SV724 ) )
= $true )
| ( ( shortest_path @ SV691 @ SV720 @ SV724 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3520]) ).
thf(3547,plain,
! [SV691: $i] :
( ( ! [SY1059: $i,SY1060: $i] :
( ~ ( shortest_path @ SV691 @ SY1059 @ SY1060 )
| ! [SY1061: $i] :
( ~ ( path @ SV691 @ SY1059 @ SY1061 )
| ( less_or_equal @ ( length_of @ SY1060 ) @ ( length_of @ SY1061 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3521]) ).
thf(3548,plain,
! [SV691: $i] :
( ( ~ ( ~ ! [SY1062: $i] :
( ! [SY1063: $i] :
~ ( shortest_path @ SV691 @ SY1062 @ SY1063 )
| ( SV691 != SY1062 ) )
| ~ ! [SY1064: $i,SY1065: $i] :
( ~ ( shortest_path @ SV691 @ SY1064 @ SY1065 )
| ( path @ SV691 @ SY1064 @ SY1065 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3522]) ).
thf(3549,plain,
! [SV692: $i] :
( ( ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV692 ) @ SV692 )
| ~ ( on_path @ ( sK7_SY80 @ SV692 ) @ SV692 ) )
| ~ ( sequential @ ( sK6_E1 @ SV692 ) @ ( sK7_SY80 @ SV692 ) ) )
= $false )
| ( ( ! [SY1067: $i,SY1068: $i] :
~ ( path @ SY1067 @ SY1068 @ SV692 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV692 )
= ( number_of_in @ triangles @ SV692 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3523]) ).
thf(3550,plain,
! [SV729: $i,SV692: $i] :
( ( ( ~ ( triangle @ ( sK6_E1 @ SV692 ) @ ( sK7_SY80 @ SV692 ) @ SV729 ) )
= $true )
| ( ( ! [SY1067: $i,SY1068: $i] :
~ ( path @ SY1067 @ SY1068 @ SV692 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV692 )
= ( number_of_in @ triangles @ SV692 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3524]) ).
thf(3551,plain,
! [SV703: $i,SV693: $i] :
( ( ~ ! [SY1126: $i,SY1127: $i] :
( ~ ( on_path @ SY1127 @ SY1126 )
| ~ ( path @ SV693 @ SV703 @ SY1126 )
| ( edge @ SY1127 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3525]) ).
thf(3552,plain,
! [SV703: $i,SV693: $i] :
( ( ~ ! [SY1128: $i,SY1129: $i] :
( ~ ( on_path @ SY1129 @ SY1128 )
| ~ ( path @ SV693 @ SV703 @ SY1128 )
| ( in_path @ ( head_of @ SY1129 ) @ SY1128 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3525]) ).
thf(3553,plain,
! [SV703: $i,SV693: $i,SV725: $i,SV730: $i] :
( ( ~ ( on_path @ SV730 @ SV725 )
| ~ ( path @ SV693 @ SV703 @ SV725 )
| ( in_path @ ( tail_of @ SV730 ) @ SV725 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3526]) ).
thf(3554,plain,
! [SV721: $i,SV714: $i] :
( ( ( ( SV714 = SV721 )
| ~ ( edge @ SV714 )
| ~ ( edge @ SV721 ) )
= $true )
| ( ( ( ( head_of @ SV714 )
!= ( tail_of @ SV721 ) ) )
= $true )
| ( ( sequential @ SV714 @ SV721 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3527]) ).
thf(3555,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3528]) ).
thf(3556,plain,
! [SV731: $i] :
( ( ! [SY1162: $i] :
( ~ ( sequential @ SV731 @ SY1162 )
| ( ( head_of @ SV731 )
= ( tail_of @ SY1162 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3529]) ).
thf(3557,plain,
! [SV715: $i,SV710: $i,SV694: $i] :
( ( ( ~ ! [SY1078: $i,SY1079: $i] :
( ~ ( on_path @ SY1078 @ SV694 )
| ~ ( on_path @ SY1079 @ SV694 )
| ! [SY1080: $i] :
( ~ ( precedes @ SY1080 @ SY1079 @ SV694 )
| ~ ( sequential @ SY1078 @ SY1080 ) )
| ( precedes @ SY1078 @ SY1079 @ SV694 ) ) )
= $false )
| ( ( path @ SV710 @ SV715 @ SV694 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3530]) ).
thf(3558,plain,
! [SV715: $i,SV710: $i,SV694: $i] :
( ( ( ~ ! [SY1081: $i,SY1082: $i] :
( ~ ( on_path @ SY1081 @ SV694 )
| ~ ( on_path @ SY1082 @ SV694 )
| ~ ( sequential @ SY1081 @ SY1082 )
| ( precedes @ SY1081 @ SY1082 @ SV694 ) ) )
= $false )
| ( ( path @ SV710 @ SV715 @ SV694 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3530]) ).
thf(3559,plain,
! [SV704: $i,SV695: $i,SV726: $i,SV732: $i] :
( ( ~ ( in_path @ SV732 @ SV726 )
| ~ ( path @ SV695 @ SV704 @ SV726 )
| ~ ( ~ ( on_path @ ( sK10_E @ SV732 @ SV726 @ SV704 @ SV695 ) @ SV726 )
| ~ ( ( SV732
= ( head_of @ ( sK10_E @ SV732 @ SV726 @ SV704 @ SV695 ) ) )
| ( SV732
= ( tail_of @ ( sK10_E @ SV732 @ SV726 @ SV704 @ SV695 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3531]) ).
thf(3560,plain,
! [SV704: $i,SV695: $i,SV727: $i,SV733: $i] :
( ( ~ ( in_path @ SV733 @ SV727 )
| ~ ( path @ SV695 @ SV704 @ SV727 )
| ( vertex @ SV733 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3532]) ).
thf(3561,plain,
! [SV728: $i,SV722: $i,SV696: $i] :
( ( ( ~ ( edge @ SV696 )
| ~ ( edge @ SV722 )
| ~ ( edge @ SV728 )
| ~ ( sequential @ SV696 @ SV722 )
| ~ ( sequential @ SV722 @ SV728 )
| ~ ( sequential @ SV728 @ SV696 ) )
= $true )
| ( ( triangle @ SV696 @ SV722 @ SV728 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3533]) ).
thf(3562,plain,
! [SV696: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY1090: $i,SY1091: $i] :
~ ( triangle @ SV696 @ SY1090 @ SY1091 )
| ( edge @ SV696 ) )
| ~ ! [SY1092: $i] :
( ! [SY1093: $i] :
~ ( triangle @ SV696 @ SY1092 @ SY1093 )
| ( edge @ SY1092 ) ) )
| ~ ! [SY1094: $i,SY1095: $i] :
( ~ ( triangle @ SV696 @ SY1094 @ SY1095 )
| ( edge @ SY1095 ) ) )
| ~ ! [SY1096: $i] :
( ! [SY1097: $i] :
~ ( triangle @ SV696 @ SY1096 @ SY1097 )
| ( sequential @ SV696 @ SY1096 ) ) )
| ~ ! [SY1098: $i,SY1099: $i] :
( ~ ( triangle @ SV696 @ SY1098 @ SY1099 )
| ( sequential @ SY1098 @ SY1099 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3534]) ).
thf(3563,plain,
! [SV696: $i] :
( ( ! [SY1100: $i,SY1101: $i] :
( ~ ( triangle @ SV696 @ SY1100 @ SY1101 )
| ( sequential @ SY1101 @ SV696 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3535]) ).
thf(3564,plain,
! [SV716: $i,SV711: $i,SV697: $i] :
( ( ( ~ ~ ( ~ ! [SY1104: $i] :
( ! [SY1105: $i] :
~ ( precedes @ SY1104 @ SY1105 @ SV697 )
| ( on_path @ SY1104 @ SV697 ) )
| ~ ! [SY1106: $i,SY1107: $i] :
( ~ ( precedes @ SY1106 @ SY1107 @ SV697 )
| ( on_path @ SY1107 @ SV697 ) ) ) )
= $false )
| ( ( path @ SV711 @ SV716 @ SV697 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3536]) ).
thf(3565,plain,
! [SV716: $i,SV711: $i,SV697: $i] :
( ( ( ~ ~ ( ~ ! [SY1108: $i,SY1109: $i] :
( ~ ( precedes @ SY1108 @ SY1109 @ SV697 )
| ! [SY1110: $i] :
( ~ ( precedes @ SY1110 @ SY1109 @ SV697 )
| ~ ( sequential @ SY1108 @ SY1110 ) )
| ~ ( sequential @ SY1108 @ SY1109 ) )
| ~ ! [SY1111: $i,SY1112: $i] :
( ~ ( precedes @ SY1111 @ SY1112 @ SV697 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY1112 @ SY1111 @ SV697 ) @ SY1112 @ SV697 )
| ~ ( sequential @ SY1111 @ ( sK9_E3 @ SY1112 @ SY1111 @ SV697 ) ) )
| ( sequential @ SY1111 @ SY1112 ) ) ) )
= $false )
| ( ( path @ SV711 @ SV716 @ SV697 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3536]) ).
thf(3566,plain,
! [SV705: $i,SV698: $i,SV734: $i,SV712: $i] :
( ( ! [SY1163: $i] :
( ~ ( precedes @ SV712 @ SV734 @ SY1163 )
| ~ ( shortest_path @ SV698 @ SV705 @ SY1163 ) )
| ! [SY1164: $i] :
( ( ( tail_of @ SY1164 )
!= ( tail_of @ SV712 ) )
| ( ( head_of @ SY1164 )
!= ( head_of @ SV734 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3539]) ).
thf(3567,plain,
! [SV705: $i,SV698: $i,SV735: $i,SV712: $i] :
( ( ! [SY1165: $i] :
( ~ ( precedes @ SV712 @ SV735 @ SY1165 )
| ~ ( shortest_path @ SV698 @ SV705 @ SY1165 )
| ~ ( precedes @ SV735 @ SV712 @ SY1165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3540]) ).
thf(3568,plain,
! [SV713: $i,SV708: $i] :
( ( ( vertex @ SV708 )
= $false )
| ( ( ~ ( vertex @ SV713 ) )
= $true )
| ( ( SV708 = SV713 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV708
!= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
!= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
!= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
!= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV708
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
| ~ ( ( SV708
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) ) )
| ~ ~ ( ~ ( ( SV713
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
| ~ ( ( SV713
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV713 @ SV708 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[3541]) ).
thf(3569,plain,
! [SV689: $i] :
( ( ( ! [SY1045: $i,SY1046: $i] :
~ ( path @ SV689 @ SY1045 @ SY1046 ) )
= $true )
| ( ( vertex @ SV689 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3542]) ).
thf(3570,plain,
! [SV736: $i,SV689: $i] :
( ( ! [SY1166: $i] :
~ ( path @ SV689 @ SV736 @ SY1166 )
| ( vertex @ SV736 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3543]) ).
thf(3571,plain,
! [SV723: $i,SV719: $i,SV689: $i] :
( ( ( path @ SV689 @ SV719 @ SV723 )
= $false )
| ( ( ~ ( ~ ~ ( ( SV689
!= ( tail_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( edge @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
| ~ ~ ( ~ ( ( SV719
!= ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
| ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ empty ) )
| ! [SY1158: $i] :
( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ SY1158 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ SY1158 ) ) )
| ~ ~ ( ~ ( ( SV719
= ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ ( sK13_SY84 @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ ( sK13_SY84 @ SV723 @ SV719 @ SV689 ) ) ) )
| ~ ( ( SV723
= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ empty ) )
| ~ ( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ ( sK12_SY85 @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ ( sK12_SY85 @ SV723 @ SV719 @ SV689 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3544]) ).
thf(3572,plain,
! [SV709: $i,SV690: $i,SV702: $i] :
( ( ( vertex @ SV702 )
= $false )
| ( ( vertex @ SV690 )
= $false )
| ( ( ~ ( ~ ! [SY1143: $i] :
( ( SV690
!= ( tail_of @ SY1143 ) )
| ~ ( edge @ SY1143 )
| ( SV702
!= ( head_of @ SY1143 ) )
| ( SV709
!= ( path_cons @ SY1143 @ empty ) ) )
| ~ ! [SY1144: $i] :
( ( SV690
!= ( tail_of @ SY1144 ) )
| ~ ( edge @ SY1144 )
| ! [SY1145: $i] :
( ( SV709
!= ( path_cons @ SY1144 @ SY1145 ) )
| ~ ( path @ ( head_of @ SY1144 ) @ SV702 @ SY1145 ) ) ) ) )
= $true )
| ( ( path @ SV690 @ SV702 @ SV709 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3545]) ).
thf(3573,plain,
! [SV724: $i,SV720: $i,SV691: $i] :
( ( ( ~ ( ~ ( path @ SV691 @ SV720 @ ( sK8_P @ SV724 @ SV720 @ SV691 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SV724 ) @ ( length_of @ ( sK8_P @ SV724 @ SV720 @ SV691 ) ) ) ) )
= $true )
| ( ( ( SV691 = SV720 )
| ~ ( path @ SV691 @ SV720 @ SV724 ) )
= $true )
| ( ( shortest_path @ SV691 @ SV720 @ SV724 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3546]) ).
thf(3574,plain,
! [SV737: $i,SV691: $i] :
( ( ! [SY1167: $i] :
( ~ ( shortest_path @ SV691 @ SV737 @ SY1167 )
| ! [SY1168: $i] :
( ~ ( path @ SV691 @ SV737 @ SY1168 )
| ( less_or_equal @ ( length_of @ SY1167 ) @ ( length_of @ SY1168 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3547]) ).
thf(3575,plain,
! [SV691: $i] :
( ( ~ ! [SY1062: $i] :
( ! [SY1063: $i] :
~ ( shortest_path @ SV691 @ SY1062 @ SY1063 )
| ( SV691 != SY1062 ) )
| ~ ! [SY1064: $i,SY1065: $i] :
( ~ ( shortest_path @ SV691 @ SY1064 @ SY1065 )
| ( path @ SV691 @ SY1064 @ SY1065 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3548]) ).
thf(3576,plain,
! [SV692: $i] :
( ( ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV692 ) @ SV692 )
| ~ ( on_path @ ( sK7_SY80 @ SV692 ) @ SV692 ) ) )
= $false )
| ( ( ! [SY1067: $i,SY1068: $i] :
~ ( path @ SY1067 @ SY1068 @ SV692 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV692 )
= ( number_of_in @ triangles @ SV692 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3549]) ).
thf(3577,plain,
! [SV692: $i] :
( ( ( ~ ( sequential @ ( sK6_E1 @ SV692 ) @ ( sK7_SY80 @ SV692 ) ) )
= $false )
| ( ( ! [SY1067: $i,SY1068: $i] :
~ ( path @ SY1067 @ SY1068 @ SV692 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV692 )
= ( number_of_in @ triangles @ SV692 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3549]) ).
thf(3578,plain,
! [SV729: $i,SV692: $i] :
( ( ( triangle @ ( sK6_E1 @ SV692 ) @ ( sK7_SY80 @ SV692 ) @ SV729 )
= $false )
| ( ( ! [SY1067: $i,SY1068: $i] :
~ ( path @ SY1067 @ SY1068 @ SV692 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV692 )
= ( number_of_in @ triangles @ SV692 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3550]) ).
thf(3579,plain,
! [SV703: $i,SV693: $i] :
( ( ! [SY1126: $i,SY1127: $i] :
( ~ ( on_path @ SY1127 @ SY1126 )
| ~ ( path @ SV693 @ SV703 @ SY1126 )
| ( edge @ SY1127 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3551]) ).
thf(3580,plain,
! [SV703: $i,SV693: $i] :
( ( ! [SY1128: $i,SY1129: $i] :
( ~ ( on_path @ SY1129 @ SY1128 )
| ~ ( path @ SV693 @ SV703 @ SY1128 )
| ( in_path @ ( head_of @ SY1129 ) @ SY1128 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3552]) ).
thf(3581,plain,
! [SV703: $i,SV693: $i,SV725: $i,SV730: $i] :
( ( ( ~ ( on_path @ SV730 @ SV725 )
| ~ ( path @ SV693 @ SV703 @ SV725 ) )
= $true )
| ( ( in_path @ ( tail_of @ SV730 ) @ SV725 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3553]) ).
thf(3582,plain,
! [SV721: $i,SV714: $i] :
( ( ( SV714 = SV721 )
= $true )
| ( ( ~ ( edge @ SV714 )
| ~ ( edge @ SV721 ) )
= $true )
| ( ( ( ( head_of @ SV714 )
!= ( tail_of @ SV721 ) ) )
= $true )
| ( ( sequential @ SV714 @ SV721 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3554]) ).
thf(3583,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3555]) ).
thf(3584,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3555]) ).
thf(3585,plain,
! [SV738: $i,SV731: $i] :
( ( ~ ( sequential @ SV731 @ SV738 )
| ( ( head_of @ SV731 )
= ( tail_of @ SV738 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3556]) ).
thf(3586,plain,
! [SV715: $i,SV710: $i,SV694: $i] :
( ( ( ! [SY1078: $i,SY1079: $i] :
( ~ ( on_path @ SY1078 @ SV694 )
| ~ ( on_path @ SY1079 @ SV694 )
| ! [SY1080: $i] :
( ~ ( precedes @ SY1080 @ SY1079 @ SV694 )
| ~ ( sequential @ SY1078 @ SY1080 ) )
| ( precedes @ SY1078 @ SY1079 @ SV694 ) ) )
= $true )
| ( ( path @ SV710 @ SV715 @ SV694 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3557]) ).
thf(3587,plain,
! [SV715: $i,SV710: $i,SV694: $i] :
( ( ( ! [SY1081: $i,SY1082: $i] :
( ~ ( on_path @ SY1081 @ SV694 )
| ~ ( on_path @ SY1082 @ SV694 )
| ~ ( sequential @ SY1081 @ SY1082 )
| ( precedes @ SY1081 @ SY1082 @ SV694 ) ) )
= $true )
| ( ( path @ SV710 @ SV715 @ SV694 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3558]) ).
thf(3588,plain,
! [SV704: $i,SV695: $i,SV726: $i,SV732: $i] :
( ( ( ~ ( in_path @ SV732 @ SV726 )
| ~ ( path @ SV695 @ SV704 @ SV726 ) )
= $true )
| ( ( ~ ( ~ ( on_path @ ( sK10_E @ SV732 @ SV726 @ SV704 @ SV695 ) @ SV726 )
| ~ ( ( SV732
= ( head_of @ ( sK10_E @ SV732 @ SV726 @ SV704 @ SV695 ) ) )
| ( SV732
= ( tail_of @ ( sK10_E @ SV732 @ SV726 @ SV704 @ SV695 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3559]) ).
thf(3589,plain,
! [SV704: $i,SV695: $i,SV727: $i,SV733: $i] :
( ( ( ~ ( in_path @ SV733 @ SV727 )
| ~ ( path @ SV695 @ SV704 @ SV727 ) )
= $true )
| ( ( vertex @ SV733 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3560]) ).
thf(3590,plain,
! [SV728: $i,SV722: $i,SV696: $i] :
( ( ( ~ ( edge @ SV696 )
| ~ ( edge @ SV722 )
| ~ ( edge @ SV728 )
| ~ ( sequential @ SV696 @ SV722 )
| ~ ( sequential @ SV722 @ SV728 ) )
= $true )
| ( ( ~ ( sequential @ SV728 @ SV696 ) )
= $true )
| ( ( triangle @ SV696 @ SV722 @ SV728 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3561]) ).
thf(3591,plain,
! [SV696: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY1090: $i,SY1091: $i] :
~ ( triangle @ SV696 @ SY1090 @ SY1091 )
| ( edge @ SV696 ) )
| ~ ! [SY1092: $i] :
( ! [SY1093: $i] :
~ ( triangle @ SV696 @ SY1092 @ SY1093 )
| ( edge @ SY1092 ) ) )
| ~ ! [SY1094: $i,SY1095: $i] :
( ~ ( triangle @ SV696 @ SY1094 @ SY1095 )
| ( edge @ SY1095 ) ) )
| ~ ! [SY1096: $i] :
( ! [SY1097: $i] :
~ ( triangle @ SV696 @ SY1096 @ SY1097 )
| ( sequential @ SV696 @ SY1096 ) ) )
| ~ ! [SY1098: $i,SY1099: $i] :
( ~ ( triangle @ SV696 @ SY1098 @ SY1099 )
| ( sequential @ SY1098 @ SY1099 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3562]) ).
thf(3592,plain,
! [SV739: $i,SV696: $i] :
( ( ! [SY1169: $i] :
( ~ ( triangle @ SV696 @ SV739 @ SY1169 )
| ( sequential @ SY1169 @ SV696 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3563]) ).
thf(3593,plain,
! [SV716: $i,SV711: $i,SV697: $i] :
( ( ( ~ ( ~ ! [SY1104: $i] :
( ! [SY1105: $i] :
~ ( precedes @ SY1104 @ SY1105 @ SV697 )
| ( on_path @ SY1104 @ SV697 ) )
| ~ ! [SY1106: $i,SY1107: $i] :
( ~ ( precedes @ SY1106 @ SY1107 @ SV697 )
| ( on_path @ SY1107 @ SV697 ) ) ) )
= $true )
| ( ( path @ SV711 @ SV716 @ SV697 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3564]) ).
thf(3594,plain,
! [SV716: $i,SV711: $i,SV697: $i] :
( ( ( ~ ( ~ ! [SY1108: $i,SY1109: $i] :
( ~ ( precedes @ SY1108 @ SY1109 @ SV697 )
| ! [SY1110: $i] :
( ~ ( precedes @ SY1110 @ SY1109 @ SV697 )
| ~ ( sequential @ SY1108 @ SY1110 ) )
| ~ ( sequential @ SY1108 @ SY1109 ) )
| ~ ! [SY1111: $i,SY1112: $i] :
( ~ ( precedes @ SY1111 @ SY1112 @ SV697 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY1112 @ SY1111 @ SV697 ) @ SY1112 @ SV697 )
| ~ ( sequential @ SY1111 @ ( sK9_E3 @ SY1112 @ SY1111 @ SV697 ) ) )
| ( sequential @ SY1111 @ SY1112 ) ) ) )
= $true )
| ( ( path @ SV711 @ SV716 @ SV697 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3565]) ).
thf(3595,plain,
! [SV705: $i,SV698: $i,SV734: $i,SV712: $i] :
( ( ( ! [SY1163: $i] :
( ~ ( precedes @ SV712 @ SV734 @ SY1163 )
| ~ ( shortest_path @ SV698 @ SV705 @ SY1163 ) ) )
= $true )
| ( ( ! [SY1164: $i] :
( ( ( tail_of @ SY1164 )
!= ( tail_of @ SV712 ) )
| ( ( head_of @ SY1164 )
!= ( head_of @ SV734 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3566]) ).
thf(3596,plain,
! [SV705: $i,SV698: $i,SV740: $i,SV735: $i,SV712: $i] :
( ( ~ ( precedes @ SV712 @ SV735 @ SV740 )
| ~ ( shortest_path @ SV698 @ SV705 @ SV740 )
| ~ ( precedes @ SV735 @ SV712 @ SV740 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3567]) ).
thf(3597,plain,
! [SV708: $i,SV713: $i] :
( ( ( vertex @ SV713 )
= $false )
| ( ( vertex @ SV708 )
= $false )
| ( ( SV708 = SV713 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV708
!= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
!= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
!= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
!= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV708
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
| ~ ( ( SV708
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) ) )
| ~ ~ ( ~ ( ( SV713
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
| ~ ( ( SV713
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV713 @ SV708 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[3568]) ).
thf(3598,plain,
! [SV741: $i,SV689: $i] :
( ( ( ! [SY1170: $i] :
~ ( path @ SV689 @ SV741 @ SY1170 ) )
= $true )
| ( ( vertex @ SV689 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3569]) ).
thf(3599,plain,
! [SV736: $i,SV689: $i] :
( ( ( ! [SY1166: $i] :
~ ( path @ SV689 @ SV736 @ SY1166 ) )
= $true )
| ( ( vertex @ SV736 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3570]) ).
thf(3600,plain,
! [SV719: $i,SV723: $i,SV689: $i] :
( ( ( ~ ~ ( ( SV689
!= ( tail_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( edge @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
| ~ ~ ( ~ ( ( SV719
!= ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
| ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ empty ) )
| ! [SY1158: $i] :
( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ SY1158 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ SY1158 ) ) )
| ~ ~ ( ~ ( ( SV719
= ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ ( sK13_SY84 @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ ( sK13_SY84 @ SV723 @ SV719 @ SV689 ) ) ) )
| ~ ( ( SV723
= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ empty ) )
| ~ ( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ ( sK12_SY85 @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ ( sK12_SY85 @ SV723 @ SV719 @ SV689 ) ) ) ) ) ) )
= $false )
| ( ( path @ SV689 @ SV719 @ SV723 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3571]) ).
thf(3601,plain,
! [SV709: $i,SV702: $i,SV690: $i] :
( ( ( ~ ! [SY1143: $i] :
( ( SV690
!= ( tail_of @ SY1143 ) )
| ~ ( edge @ SY1143 )
| ( SV702
!= ( head_of @ SY1143 ) )
| ( SV709
!= ( path_cons @ SY1143 @ empty ) ) )
| ~ ! [SY1144: $i] :
( ( SV690
!= ( tail_of @ SY1144 ) )
| ~ ( edge @ SY1144 )
| ! [SY1145: $i] :
( ( SV709
!= ( path_cons @ SY1144 @ SY1145 ) )
| ~ ( path @ ( head_of @ SY1144 ) @ SV702 @ SY1145 ) ) ) )
= $false )
| ( ( vertex @ SV690 )
= $false )
| ( ( vertex @ SV702 )
= $false )
| ( ( path @ SV690 @ SV702 @ SV709 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3572]) ).
thf(3602,plain,
! [SV724: $i,SV720: $i,SV691: $i] :
( ( ( ~ ( path @ SV691 @ SV720 @ ( sK8_P @ SV724 @ SV720 @ SV691 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SV724 ) @ ( length_of @ ( sK8_P @ SV724 @ SV720 @ SV691 ) ) ) )
= $false )
| ( ( ( SV691 = SV720 )
| ~ ( path @ SV691 @ SV720 @ SV724 ) )
= $true )
| ( ( shortest_path @ SV691 @ SV720 @ SV724 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3573]) ).
thf(3603,plain,
! [SV742: $i,SV737: $i,SV691: $i] :
( ( ~ ( shortest_path @ SV691 @ SV737 @ SV742 )
| ! [SY1171: $i] :
( ~ ( path @ SV691 @ SV737 @ SY1171 )
| ( less_or_equal @ ( length_of @ SV742 ) @ ( length_of @ SY1171 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3574]) ).
thf(3604,plain,
! [SV691: $i] :
( ( ~ ! [SY1062: $i] :
( ! [SY1063: $i] :
~ ( shortest_path @ SV691 @ SY1062 @ SY1063 )
| ( SV691 != SY1062 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3575]) ).
thf(3605,plain,
! [SV691: $i] :
( ( ~ ! [SY1064: $i,SY1065: $i] :
( ~ ( shortest_path @ SV691 @ SY1064 @ SY1065 )
| ( path @ SV691 @ SY1064 @ SY1065 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3575]) ).
thf(3606,plain,
! [SV692: $i] :
( ( ( ~ ( ~ ( on_path @ ( sK6_E1 @ SV692 ) @ SV692 )
| ~ ( on_path @ ( sK7_SY80 @ SV692 ) @ SV692 ) ) )
= $true )
| ( ( ! [SY1067: $i,SY1068: $i] :
~ ( path @ SY1067 @ SY1068 @ SV692 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV692 )
= ( number_of_in @ triangles @ SV692 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3576]) ).
thf(3607,plain,
! [SV692: $i] :
( ( ( sequential @ ( sK6_E1 @ SV692 ) @ ( sK7_SY80 @ SV692 ) )
= $true )
| ( ( ! [SY1067: $i,SY1068: $i] :
~ ( path @ SY1067 @ SY1068 @ SV692 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV692 )
= ( number_of_in @ triangles @ SV692 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3577]) ).
thf(3608,plain,
! [SV729: $i,SV692: $i,SV743: $i] :
( ( ( ! [SY1172: $i] :
~ ( path @ SV743 @ SY1172 @ SV692 ) )
= $true )
| ( ( triangle @ ( sK6_E1 @ SV692 ) @ ( sK7_SY80 @ SV692 ) @ SV729 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV692 )
= ( number_of_in @ triangles @ SV692 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3578]) ).
thf(3609,plain,
! [SV703: $i,SV693: $i,SV744: $i] :
( ( ! [SY1173: $i] :
( ~ ( on_path @ SY1173 @ SV744 )
| ~ ( path @ SV693 @ SV703 @ SV744 )
| ( edge @ SY1173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3579]) ).
thf(3610,plain,
! [SV703: $i,SV693: $i,SV745: $i] :
( ( ! [SY1174: $i] :
( ~ ( on_path @ SY1174 @ SV745 )
| ~ ( path @ SV693 @ SV703 @ SV745 )
| ( in_path @ ( head_of @ SY1174 ) @ SV745 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3580]) ).
thf(3611,plain,
! [SV703: $i,SV693: $i,SV725: $i,SV730: $i] :
( ( ( ~ ( on_path @ SV730 @ SV725 ) )
= $true )
| ( ( ~ ( path @ SV693 @ SV703 @ SV725 ) )
= $true )
| ( ( in_path @ ( tail_of @ SV730 ) @ SV725 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3581]) ).
thf(3612,plain,
! [SV721: $i,SV714: $i] :
( ( ( ~ ( edge @ SV714 ) )
= $true )
| ( ( ~ ( edge @ SV721 ) )
= $true )
| ( ( SV714 = SV721 )
= $true )
| ( ( ( ( head_of @ SV714 )
!= ( tail_of @ SV721 ) ) )
= $true )
| ( ( sequential @ SV714 @ SV721 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3582]) ).
thf(3613,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3583]) ).
thf(3614,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3584]) ).
thf(3615,plain,
! [SV738: $i,SV731: $i] :
( ( ( ~ ( sequential @ SV731 @ SV738 ) )
= $true )
| ( ( ( head_of @ SV731 )
= ( tail_of @ SV738 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3585]) ).
thf(3616,plain,
! [SV715: $i,SV710: $i,SV694: $i,SV746: $i] :
( ( ( ! [SY1175: $i] :
( ~ ( on_path @ SV746 @ SV694 )
| ~ ( on_path @ SY1175 @ SV694 )
| ! [SY1176: $i] :
( ~ ( precedes @ SY1176 @ SY1175 @ SV694 )
| ~ ( sequential @ SV746 @ SY1176 ) )
| ( precedes @ SV746 @ SY1175 @ SV694 ) ) )
= $true )
| ( ( path @ SV710 @ SV715 @ SV694 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3586]) ).
thf(3617,plain,
! [SV715: $i,SV710: $i,SV694: $i,SV747: $i] :
( ( ( ! [SY1177: $i] :
( ~ ( on_path @ SV747 @ SV694 )
| ~ ( on_path @ SY1177 @ SV694 )
| ~ ( sequential @ SV747 @ SY1177 )
| ( precedes @ SV747 @ SY1177 @ SV694 ) ) )
= $true )
| ( ( path @ SV710 @ SV715 @ SV694 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3587]) ).
thf(3618,plain,
! [SV704: $i,SV695: $i,SV726: $i,SV732: $i] :
( ( ( ~ ( in_path @ SV732 @ SV726 ) )
= $true )
| ( ( ~ ( path @ SV695 @ SV704 @ SV726 ) )
= $true )
| ( ( ~ ( ~ ( on_path @ ( sK10_E @ SV732 @ SV726 @ SV704 @ SV695 ) @ SV726 )
| ~ ( ( SV732
= ( head_of @ ( sK10_E @ SV732 @ SV726 @ SV704 @ SV695 ) ) )
| ( SV732
= ( tail_of @ ( sK10_E @ SV732 @ SV726 @ SV704 @ SV695 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3588]) ).
thf(3619,plain,
! [SV704: $i,SV695: $i,SV727: $i,SV733: $i] :
( ( ( ~ ( in_path @ SV733 @ SV727 ) )
= $true )
| ( ( ~ ( path @ SV695 @ SV704 @ SV727 ) )
= $true )
| ( ( vertex @ SV733 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3589]) ).
thf(3620,plain,
! [SV728: $i,SV722: $i,SV696: $i] :
( ( ( ~ ( edge @ SV696 )
| ~ ( edge @ SV722 )
| ~ ( edge @ SV728 )
| ~ ( sequential @ SV696 @ SV722 ) )
= $true )
| ( ( ~ ( sequential @ SV722 @ SV728 ) )
= $true )
| ( ( ~ ( sequential @ SV728 @ SV696 ) )
= $true )
| ( ( triangle @ SV696 @ SV722 @ SV728 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3590]) ).
thf(3621,plain,
! [SV696: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY1090: $i,SY1091: $i] :
~ ( triangle @ SV696 @ SY1090 @ SY1091 )
| ( edge @ SV696 ) )
| ~ ! [SY1092: $i] :
( ! [SY1093: $i] :
~ ( triangle @ SV696 @ SY1092 @ SY1093 )
| ( edge @ SY1092 ) ) )
| ~ ! [SY1094: $i,SY1095: $i] :
( ~ ( triangle @ SV696 @ SY1094 @ SY1095 )
| ( edge @ SY1095 ) ) )
| ~ ! [SY1096: $i] :
( ! [SY1097: $i] :
~ ( triangle @ SV696 @ SY1096 @ SY1097 )
| ( sequential @ SV696 @ SY1096 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3591]) ).
thf(3622,plain,
! [SV696: $i] :
( ( ~ ! [SY1098: $i,SY1099: $i] :
( ~ ( triangle @ SV696 @ SY1098 @ SY1099 )
| ( sequential @ SY1098 @ SY1099 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3591]) ).
thf(3623,plain,
! [SV748: $i,SV739: $i,SV696: $i] :
( ( ~ ( triangle @ SV696 @ SV739 @ SV748 )
| ( sequential @ SV748 @ SV696 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3592]) ).
thf(3624,plain,
! [SV716: $i,SV711: $i,SV697: $i] :
( ( ( ~ ! [SY1104: $i] :
( ! [SY1105: $i] :
~ ( precedes @ SY1104 @ SY1105 @ SV697 )
| ( on_path @ SY1104 @ SV697 ) )
| ~ ! [SY1106: $i,SY1107: $i] :
( ~ ( precedes @ SY1106 @ SY1107 @ SV697 )
| ( on_path @ SY1107 @ SV697 ) ) )
= $false )
| ( ( path @ SV711 @ SV716 @ SV697 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3593]) ).
thf(3625,plain,
! [SV716: $i,SV711: $i,SV697: $i] :
( ( ( ~ ! [SY1108: $i,SY1109: $i] :
( ~ ( precedes @ SY1108 @ SY1109 @ SV697 )
| ! [SY1110: $i] :
( ~ ( precedes @ SY1110 @ SY1109 @ SV697 )
| ~ ( sequential @ SY1108 @ SY1110 ) )
| ~ ( sequential @ SY1108 @ SY1109 ) )
| ~ ! [SY1111: $i,SY1112: $i] :
( ~ ( precedes @ SY1111 @ SY1112 @ SV697 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY1112 @ SY1111 @ SV697 ) @ SY1112 @ SV697 )
| ~ ( sequential @ SY1111 @ ( sK9_E3 @ SY1112 @ SY1111 @ SV697 ) ) )
| ( sequential @ SY1111 @ SY1112 ) ) )
= $false )
| ( ( path @ SV711 @ SV716 @ SV697 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3594]) ).
thf(3626,plain,
! [SV705: $i,SV698: $i,SV749: $i,SV734: $i,SV712: $i] :
( ( ( ~ ( precedes @ SV712 @ SV734 @ SV749 )
| ~ ( shortest_path @ SV698 @ SV705 @ SV749 ) )
= $true )
| ( ( ! [SY1164: $i] :
( ( ( tail_of @ SY1164 )
!= ( tail_of @ SV712 ) )
| ( ( head_of @ SY1164 )
!= ( head_of @ SV734 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3595]) ).
thf(3627,plain,
! [SV705: $i,SV698: $i,SV740: $i,SV735: $i,SV712: $i] :
( ( ( ~ ( precedes @ SV712 @ SV735 @ SV740 )
| ~ ( shortest_path @ SV698 @ SV705 @ SV740 ) )
= $true )
| ( ( ~ ( precedes @ SV735 @ SV712 @ SV740 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3596]) ).
thf(3628,plain,
! [SV713: $i,SV708: $i] :
( ( ( ~ ~ ( ~ ( ( SV708
!= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
!= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
!= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
!= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV708
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
| ~ ( ( SV708
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) ) )
| ~ ~ ( ~ ( ( SV713
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
| ~ ( ( SV713
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV713 @ SV708 ) ) )
= $false )
| ( ( SV708 = SV713 )
= $true )
| ( ( vertex @ SV708 )
= $false )
| ( ( vertex @ SV713 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[3597]) ).
thf(3629,plain,
! [SV750: $i,SV741: $i,SV689: $i] :
( ( ( ~ ( path @ SV689 @ SV741 @ SV750 ) )
= $true )
| ( ( vertex @ SV689 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3598]) ).
thf(3630,plain,
! [SV751: $i,SV736: $i,SV689: $i] :
( ( ( ~ ( path @ SV689 @ SV736 @ SV751 ) )
= $true )
| ( ( vertex @ SV736 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3599]) ).
thf(3631,plain,
! [SV719: $i,SV723: $i,SV689: $i] :
( ( ( ~ ~ ( ( SV689
!= ( tail_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( edge @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) ) )
= $false )
| ( ( path @ SV689 @ SV719 @ SV723 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3600]) ).
thf(3632,plain,
! [SV689: $i,SV723: $i,SV719: $i] :
( ( ( ~ ~ ( ~ ( ( SV719
!= ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
| ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ empty ) )
| ! [SY1158: $i] :
( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ SY1158 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ SY1158 ) ) )
| ~ ~ ( ~ ( ( SV719
= ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ ( sK13_SY84 @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ ( sK13_SY84 @ SV723 @ SV719 @ SV689 ) ) ) )
| ~ ( ( SV723
= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ empty ) )
| ~ ( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ ( sK12_SY85 @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ ( sK12_SY85 @ SV723 @ SV719 @ SV689 ) ) ) ) ) ) )
= $false )
| ( ( path @ SV689 @ SV719 @ SV723 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3600]) ).
thf(3633,plain,
! [SV709: $i,SV702: $i,SV690: $i] :
( ( ( ~ ! [SY1143: $i] :
( ( SV690
!= ( tail_of @ SY1143 ) )
| ~ ( edge @ SY1143 )
| ( SV702
!= ( head_of @ SY1143 ) )
| ( SV709
!= ( path_cons @ SY1143 @ empty ) ) ) )
= $false )
| ( ( vertex @ SV690 )
= $false )
| ( ( vertex @ SV702 )
= $false )
| ( ( path @ SV690 @ SV702 @ SV709 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3601]) ).
thf(3634,plain,
! [SV702: $i,SV709: $i,SV690: $i] :
( ( ( ~ ! [SY1144: $i] :
( ( SV690
!= ( tail_of @ SY1144 ) )
| ~ ( edge @ SY1144 )
| ! [SY1145: $i] :
( ( SV709
!= ( path_cons @ SY1144 @ SY1145 ) )
| ~ ( path @ ( head_of @ SY1144 ) @ SV702 @ SY1145 ) ) ) )
= $false )
| ( ( vertex @ SV690 )
= $false )
| ( ( vertex @ SV702 )
= $false )
| ( ( path @ SV690 @ SV702 @ SV709 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3601]) ).
thf(3635,plain,
! [SV724: $i,SV720: $i,SV691: $i] :
( ( ( ~ ( path @ SV691 @ SV720 @ ( sK8_P @ SV724 @ SV720 @ SV691 ) ) )
= $false )
| ( ( ( SV691 = SV720 )
| ~ ( path @ SV691 @ SV720 @ SV724 ) )
= $true )
| ( ( shortest_path @ SV691 @ SV720 @ SV724 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3602]) ).
thf(3636,plain,
! [SV691: $i,SV720: $i,SV724: $i] :
( ( ( ~ ~ ( less_or_equal @ ( length_of @ SV724 ) @ ( length_of @ ( sK8_P @ SV724 @ SV720 @ SV691 ) ) ) )
= $false )
| ( ( ( SV691 = SV720 )
| ~ ( path @ SV691 @ SV720 @ SV724 ) )
= $true )
| ( ( shortest_path @ SV691 @ SV720 @ SV724 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3602]) ).
thf(3637,plain,
! [SV742: $i,SV737: $i,SV691: $i] :
( ( ( ~ ( shortest_path @ SV691 @ SV737 @ SV742 ) )
= $true )
| ( ( ! [SY1171: $i] :
( ~ ( path @ SV691 @ SV737 @ SY1171 )
| ( less_or_equal @ ( length_of @ SV742 ) @ ( length_of @ SY1171 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3603]) ).
thf(3638,plain,
! [SV691: $i] :
( ( ! [SY1062: $i] :
( ! [SY1063: $i] :
~ ( shortest_path @ SV691 @ SY1062 @ SY1063 )
| ( SV691 != SY1062 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3604]) ).
thf(3639,plain,
! [SV691: $i] :
( ( ! [SY1064: $i,SY1065: $i] :
( ~ ( shortest_path @ SV691 @ SY1064 @ SY1065 )
| ( path @ SV691 @ SY1064 @ SY1065 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3605]) ).
thf(3640,plain,
! [SV692: $i] :
( ( ( ~ ( on_path @ ( sK6_E1 @ SV692 ) @ SV692 )
| ~ ( on_path @ ( sK7_SY80 @ SV692 ) @ SV692 ) )
= $false )
| ( ( ! [SY1067: $i,SY1068: $i] :
~ ( path @ SY1067 @ SY1068 @ SV692 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV692 )
= ( number_of_in @ triangles @ SV692 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3606]) ).
thf(3641,plain,
! [SV692: $i,SV752: $i] :
( ( ( ! [SY1178: $i] :
~ ( path @ SV752 @ SY1178 @ SV692 ) )
= $true )
| ( ( sequential @ ( sK6_E1 @ SV692 ) @ ( sK7_SY80 @ SV692 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV692 )
= ( number_of_in @ triangles @ SV692 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3607]) ).
thf(3642,plain,
! [SV729: $i,SV692: $i,SV753: $i,SV743: $i] :
( ( ( ~ ( path @ SV743 @ SV753 @ SV692 ) )
= $true )
| ( ( triangle @ ( sK6_E1 @ SV692 ) @ ( sK7_SY80 @ SV692 ) @ SV729 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV692 )
= ( number_of_in @ triangles @ SV692 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3608]) ).
thf(3643,plain,
! [SV703: $i,SV693: $i,SV744: $i,SV754: $i] :
( ( ~ ( on_path @ SV754 @ SV744 )
| ~ ( path @ SV693 @ SV703 @ SV744 )
| ( edge @ SV754 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3609]) ).
thf(3644,plain,
! [SV703: $i,SV693: $i,SV745: $i,SV755: $i] :
( ( ~ ( on_path @ SV755 @ SV745 )
| ~ ( path @ SV693 @ SV703 @ SV745 )
| ( in_path @ ( head_of @ SV755 ) @ SV745 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3610]) ).
thf(3645,plain,
! [SV703: $i,SV693: $i,SV725: $i,SV730: $i] :
( ( ( on_path @ SV730 @ SV725 )
= $false )
| ( ( ~ ( path @ SV693 @ SV703 @ SV725 ) )
= $true )
| ( ( in_path @ ( tail_of @ SV730 ) @ SV725 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3611]) ).
thf(3646,plain,
! [SV721: $i,SV714: $i] :
( ( ( edge @ SV714 )
= $false )
| ( ( ~ ( edge @ SV721 ) )
= $true )
| ( ( SV714 = SV721 )
= $true )
| ( ( ( ( head_of @ SV714 )
!= ( tail_of @ SV721 ) ) )
= $true )
| ( ( sequential @ SV714 @ SV721 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3612]) ).
thf(3647,plain,
! [SV756: $i] :
( ( ! [SY1179: $i] :
( ~ ( sequential @ SV756 @ SY1179 )
| ( SV756 != SY1179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3613]) ).
thf(3648,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3614]) ).
thf(3649,plain,
! [SV738: $i,SV731: $i] :
( ( ( sequential @ SV731 @ SV738 )
= $false )
| ( ( ( head_of @ SV731 )
= ( tail_of @ SV738 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3615]) ).
thf(3650,plain,
! [SV715: $i,SV710: $i,SV757: $i,SV694: $i,SV746: $i] :
( ( ( ~ ( on_path @ SV746 @ SV694 )
| ~ ( on_path @ SV757 @ SV694 )
| ! [SY1180: $i] :
( ~ ( precedes @ SY1180 @ SV757 @ SV694 )
| ~ ( sequential @ SV746 @ SY1180 ) )
| ( precedes @ SV746 @ SV757 @ SV694 ) )
= $true )
| ( ( path @ SV710 @ SV715 @ SV694 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3616]) ).
thf(3651,plain,
! [SV715: $i,SV710: $i,SV758: $i,SV694: $i,SV747: $i] :
( ( ( ~ ( on_path @ SV747 @ SV694 )
| ~ ( on_path @ SV758 @ SV694 )
| ~ ( sequential @ SV747 @ SV758 )
| ( precedes @ SV747 @ SV758 @ SV694 ) )
= $true )
| ( ( path @ SV710 @ SV715 @ SV694 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3617]) ).
thf(3652,plain,
! [SV704: $i,SV695: $i,SV726: $i,SV732: $i] :
( ( ( in_path @ SV732 @ SV726 )
= $false )
| ( ( ~ ( path @ SV695 @ SV704 @ SV726 ) )
= $true )
| ( ( ~ ( ~ ( on_path @ ( sK10_E @ SV732 @ SV726 @ SV704 @ SV695 ) @ SV726 )
| ~ ( ( SV732
= ( head_of @ ( sK10_E @ SV732 @ SV726 @ SV704 @ SV695 ) ) )
| ( SV732
= ( tail_of @ ( sK10_E @ SV732 @ SV726 @ SV704 @ SV695 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3618]) ).
thf(3653,plain,
! [SV704: $i,SV695: $i,SV727: $i,SV733: $i] :
( ( ( in_path @ SV733 @ SV727 )
= $false )
| ( ( ~ ( path @ SV695 @ SV704 @ SV727 ) )
= $true )
| ( ( vertex @ SV733 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3619]) ).
thf(3654,plain,
! [SV728: $i,SV722: $i,SV696: $i] :
( ( ( ~ ( edge @ SV696 )
| ~ ( edge @ SV722 )
| ~ ( edge @ SV728 ) )
= $true )
| ( ( ~ ( sequential @ SV696 @ SV722 ) )
= $true )
| ( ( ~ ( sequential @ SV722 @ SV728 ) )
= $true )
| ( ( ~ ( sequential @ SV728 @ SV696 ) )
= $true )
| ( ( triangle @ SV696 @ SV722 @ SV728 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3620]) ).
thf(3655,plain,
! [SV696: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY1090: $i,SY1091: $i] :
~ ( triangle @ SV696 @ SY1090 @ SY1091 )
| ( edge @ SV696 ) )
| ~ ! [SY1092: $i] :
( ! [SY1093: $i] :
~ ( triangle @ SV696 @ SY1092 @ SY1093 )
| ( edge @ SY1092 ) ) )
| ~ ! [SY1094: $i,SY1095: $i] :
( ~ ( triangle @ SV696 @ SY1094 @ SY1095 )
| ( edge @ SY1095 ) ) )
| ~ ! [SY1096: $i] :
( ! [SY1097: $i] :
~ ( triangle @ SV696 @ SY1096 @ SY1097 )
| ( sequential @ SV696 @ SY1096 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3621]) ).
thf(3656,plain,
! [SV696: $i] :
( ( ! [SY1098: $i,SY1099: $i] :
( ~ ( triangle @ SV696 @ SY1098 @ SY1099 )
| ( sequential @ SY1098 @ SY1099 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3622]) ).
thf(3657,plain,
! [SV748: $i,SV739: $i,SV696: $i] :
( ( ( ~ ( triangle @ SV696 @ SV739 @ SV748 ) )
= $true )
| ( ( sequential @ SV748 @ SV696 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3623]) ).
thf(3658,plain,
! [SV716: $i,SV711: $i,SV697: $i] :
( ( ( ~ ! [SY1104: $i] :
( ! [SY1105: $i] :
~ ( precedes @ SY1104 @ SY1105 @ SV697 )
| ( on_path @ SY1104 @ SV697 ) ) )
= $false )
| ( ( path @ SV711 @ SV716 @ SV697 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3624]) ).
thf(3659,plain,
! [SV716: $i,SV711: $i,SV697: $i] :
( ( ( ~ ! [SY1106: $i,SY1107: $i] :
( ~ ( precedes @ SY1106 @ SY1107 @ SV697 )
| ( on_path @ SY1107 @ SV697 ) ) )
= $false )
| ( ( path @ SV711 @ SV716 @ SV697 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3624]) ).
thf(3660,plain,
! [SV716: $i,SV711: $i,SV697: $i] :
( ( ( ~ ! [SY1108: $i,SY1109: $i] :
( ~ ( precedes @ SY1108 @ SY1109 @ SV697 )
| ! [SY1110: $i] :
( ~ ( precedes @ SY1110 @ SY1109 @ SV697 )
| ~ ( sequential @ SY1108 @ SY1110 ) )
| ~ ( sequential @ SY1108 @ SY1109 ) ) )
= $false )
| ( ( path @ SV711 @ SV716 @ SV697 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3625]) ).
thf(3661,plain,
! [SV716: $i,SV711: $i,SV697: $i] :
( ( ( ~ ! [SY1111: $i,SY1112: $i] :
( ~ ( precedes @ SY1111 @ SY1112 @ SV697 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY1112 @ SY1111 @ SV697 ) @ SY1112 @ SV697 )
| ~ ( sequential @ SY1111 @ ( sK9_E3 @ SY1112 @ SY1111 @ SV697 ) ) )
| ( sequential @ SY1111 @ SY1112 ) ) )
= $false )
| ( ( path @ SV711 @ SV716 @ SV697 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3625]) ).
thf(3662,plain,
! [SV705: $i,SV698: $i,SV749: $i,SV734: $i,SV712: $i] :
( ( ( ~ ( precedes @ SV712 @ SV734 @ SV749 ) )
= $true )
| ( ( ~ ( shortest_path @ SV698 @ SV705 @ SV749 ) )
= $true )
| ( ( ! [SY1164: $i] :
( ( ( tail_of @ SY1164 )
!= ( tail_of @ SV712 ) )
| ( ( head_of @ SY1164 )
!= ( head_of @ SV734 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3626]) ).
thf(3663,plain,
! [SV705: $i,SV698: $i,SV740: $i,SV735: $i,SV712: $i] :
( ( ( ~ ( precedes @ SV712 @ SV735 @ SV740 ) )
= $true )
| ( ( ~ ( shortest_path @ SV698 @ SV705 @ SV740 ) )
= $true )
| ( ( ~ ( precedes @ SV735 @ SV712 @ SV740 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3627]) ).
thf(3664,plain,
! [SV713: $i,SV708: $i] :
( ( ( ~ ~ ( ~ ( ( SV708
!= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
!= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
!= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
!= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV708
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
| ~ ( ( SV708
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) ) )
| ~ ~ ( ~ ( ( SV713
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
| ~ ( ( SV713
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) ) ) ) ) )
= $false )
| ( ( SV708 = SV713 )
= $true )
| ( ( vertex @ SV708 )
= $false )
| ( ( vertex @ SV713 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[3628]) ).
thf(3665,plain,
! [SV708: $i,SV713: $i] :
( ( ( ~ ( edge @ ( sK14_E @ SV713 @ SV708 ) ) )
= $false )
| ( ( SV708 = SV713 )
= $true )
| ( ( vertex @ SV708 )
= $false )
| ( ( vertex @ SV713 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[3628]) ).
thf(3666,plain,
! [SV750: $i,SV741: $i,SV689: $i] :
( ( ( path @ SV689 @ SV741 @ SV750 )
= $false )
| ( ( vertex @ SV689 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3629]) ).
thf(3667,plain,
! [SV751: $i,SV736: $i,SV689: $i] :
( ( ( path @ SV689 @ SV736 @ SV751 )
= $false )
| ( ( vertex @ SV736 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3630]) ).
thf(3668,plain,
! [SV719: $i,SV723: $i,SV689: $i] :
( ( ( ~ ( ( SV689
!= ( tail_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( edge @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) ) )
= $true )
| ( ( path @ SV689 @ SV719 @ SV723 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3631]) ).
thf(3669,plain,
! [SV689: $i,SV723: $i,SV719: $i] :
( ( ( ~ ( ~ ( ( SV719
!= ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
| ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ empty ) )
| ! [SY1158: $i] :
( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ SY1158 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ SY1158 ) ) )
| ~ ~ ( ~ ( ( SV719
= ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ ( sK13_SY84 @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ ( sK13_SY84 @ SV723 @ SV719 @ SV689 ) ) ) )
| ~ ( ( SV723
= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ empty ) )
| ~ ( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ ( sK12_SY85 @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ ( sK12_SY85 @ SV723 @ SV719 @ SV689 ) ) ) ) ) ) )
= $true )
| ( ( path @ SV689 @ SV719 @ SV723 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3632]) ).
thf(3670,plain,
! [SV709: $i,SV702: $i,SV690: $i] :
( ( ( ! [SY1143: $i] :
( ( SV690
!= ( tail_of @ SY1143 ) )
| ~ ( edge @ SY1143 )
| ( SV702
!= ( head_of @ SY1143 ) )
| ( SV709
!= ( path_cons @ SY1143 @ empty ) ) ) )
= $true )
| ( ( vertex @ SV690 )
= $false )
| ( ( vertex @ SV702 )
= $false )
| ( ( path @ SV690 @ SV702 @ SV709 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3633]) ).
thf(3671,plain,
! [SV702: $i,SV709: $i,SV690: $i] :
( ( ( ! [SY1144: $i] :
( ( SV690
!= ( tail_of @ SY1144 ) )
| ~ ( edge @ SY1144 )
| ! [SY1145: $i] :
( ( SV709
!= ( path_cons @ SY1144 @ SY1145 ) )
| ~ ( path @ ( head_of @ SY1144 ) @ SV702 @ SY1145 ) ) ) )
= $true )
| ( ( vertex @ SV690 )
= $false )
| ( ( vertex @ SV702 )
= $false )
| ( ( path @ SV690 @ SV702 @ SV709 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3634]) ).
thf(3672,plain,
! [SV724: $i,SV720: $i,SV691: $i] :
( ( ( path @ SV691 @ SV720 @ ( sK8_P @ SV724 @ SV720 @ SV691 ) )
= $true )
| ( ( ( SV691 = SV720 )
| ~ ( path @ SV691 @ SV720 @ SV724 ) )
= $true )
| ( ( shortest_path @ SV691 @ SV720 @ SV724 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3635]) ).
thf(3673,plain,
! [SV691: $i,SV720: $i,SV724: $i] :
( ( ( ~ ( less_or_equal @ ( length_of @ SV724 ) @ ( length_of @ ( sK8_P @ SV724 @ SV720 @ SV691 ) ) ) )
= $true )
| ( ( ( SV691 = SV720 )
| ~ ( path @ SV691 @ SV720 @ SV724 ) )
= $true )
| ( ( shortest_path @ SV691 @ SV720 @ SV724 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3636]) ).
thf(3674,plain,
! [SV742: $i,SV737: $i,SV691: $i] :
( ( ( shortest_path @ SV691 @ SV737 @ SV742 )
= $false )
| ( ( ! [SY1171: $i] :
( ~ ( path @ SV691 @ SV737 @ SY1171 )
| ( less_or_equal @ ( length_of @ SV742 ) @ ( length_of @ SY1171 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3637]) ).
thf(3675,plain,
! [SV759: $i,SV691: $i] :
( ( ! [SY1181: $i] :
~ ( shortest_path @ SV691 @ SV759 @ SY1181 )
| ( SV691 != SV759 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3638]) ).
thf(3676,plain,
! [SV760: $i,SV691: $i] :
( ( ! [SY1182: $i] :
( ~ ( shortest_path @ SV691 @ SV760 @ SY1182 )
| ( path @ SV691 @ SV760 @ SY1182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3639]) ).
thf(3677,plain,
! [SV692: $i] :
( ( ( ~ ( on_path @ ( sK6_E1 @ SV692 ) @ SV692 ) )
= $false )
| ( ( ! [SY1067: $i,SY1068: $i] :
~ ( path @ SY1067 @ SY1068 @ SV692 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV692 )
= ( number_of_in @ triangles @ SV692 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3640]) ).
thf(3678,plain,
! [SV692: $i] :
( ( ( ~ ( on_path @ ( sK7_SY80 @ SV692 ) @ SV692 ) )
= $false )
| ( ( ! [SY1067: $i,SY1068: $i] :
~ ( path @ SY1067 @ SY1068 @ SV692 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV692 )
= ( number_of_in @ triangles @ SV692 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3640]) ).
thf(3679,plain,
! [SV692: $i,SV761: $i,SV752: $i] :
( ( ( ~ ( path @ SV752 @ SV761 @ SV692 ) )
= $true )
| ( ( sequential @ ( sK6_E1 @ SV692 ) @ ( sK7_SY80 @ SV692 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV692 )
= ( number_of_in @ triangles @ SV692 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3641]) ).
thf(3680,plain,
! [SV729: $i,SV692: $i,SV753: $i,SV743: $i] :
( ( ( path @ SV743 @ SV753 @ SV692 )
= $false )
| ( ( triangle @ ( sK6_E1 @ SV692 ) @ ( sK7_SY80 @ SV692 ) @ SV729 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV692 )
= ( number_of_in @ triangles @ SV692 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3642]) ).
thf(3681,plain,
! [SV703: $i,SV693: $i,SV744: $i,SV754: $i] :
( ( ( ~ ( on_path @ SV754 @ SV744 )
| ~ ( path @ SV693 @ SV703 @ SV744 ) )
= $true )
| ( ( edge @ SV754 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3643]) ).
thf(3682,plain,
! [SV703: $i,SV693: $i,SV745: $i,SV755: $i] :
( ( ( ~ ( on_path @ SV755 @ SV745 )
| ~ ( path @ SV693 @ SV703 @ SV745 ) )
= $true )
| ( ( in_path @ ( head_of @ SV755 ) @ SV745 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3644]) ).
thf(3683,plain,
! [SV730: $i,SV725: $i,SV703: $i,SV693: $i] :
( ( ( path @ SV693 @ SV703 @ SV725 )
= $false )
| ( ( on_path @ SV730 @ SV725 )
= $false )
| ( ( in_path @ ( tail_of @ SV730 ) @ SV725 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3645]) ).
thf(3684,plain,
! [SV714: $i,SV721: $i] :
( ( ( edge @ SV721 )
= $false )
| ( ( edge @ SV714 )
= $false )
| ( ( SV714 = SV721 )
= $true )
| ( ( ( ( head_of @ SV714 )
!= ( tail_of @ SV721 ) ) )
= $true )
| ( ( sequential @ SV714 @ SV721 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3646]) ).
thf(3685,plain,
! [SV762: $i,SV756: $i] :
( ( ~ ( sequential @ SV756 @ SV762 )
| ( SV756 != SV762 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3647]) ).
thf(3686,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3648]) ).
thf(3687,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3648]) ).
thf(3688,plain,
! [SV715: $i,SV710: $i,SV757: $i,SV694: $i,SV746: $i] :
( ( ( ~ ( on_path @ SV746 @ SV694 )
| ~ ( on_path @ SV757 @ SV694 )
| ! [SY1180: $i] :
( ~ ( precedes @ SY1180 @ SV757 @ SV694 )
| ~ ( sequential @ SV746 @ SY1180 ) ) )
= $true )
| ( ( precedes @ SV746 @ SV757 @ SV694 )
= $true )
| ( ( path @ SV710 @ SV715 @ SV694 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3650]) ).
thf(3689,plain,
! [SV715: $i,SV710: $i,SV758: $i,SV694: $i,SV747: $i] :
( ( ( ~ ( on_path @ SV747 @ SV694 )
| ~ ( on_path @ SV758 @ SV694 )
| ~ ( sequential @ SV747 @ SV758 ) )
= $true )
| ( ( precedes @ SV747 @ SV758 @ SV694 )
= $true )
| ( ( path @ SV710 @ SV715 @ SV694 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3651]) ).
thf(3690,plain,
! [SV732: $i,SV726: $i,SV704: $i,SV695: $i] :
( ( ( path @ SV695 @ SV704 @ SV726 )
= $false )
| ( ( in_path @ SV732 @ SV726 )
= $false )
| ( ( ~ ( ~ ( on_path @ ( sK10_E @ SV732 @ SV726 @ SV704 @ SV695 ) @ SV726 )
| ~ ( ( SV732
= ( head_of @ ( sK10_E @ SV732 @ SV726 @ SV704 @ SV695 ) ) )
| ( SV732
= ( tail_of @ ( sK10_E @ SV732 @ SV726 @ SV704 @ SV695 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3652]) ).
thf(3691,plain,
! [SV733: $i,SV727: $i,SV704: $i,SV695: $i] :
( ( ( path @ SV695 @ SV704 @ SV727 )
= $false )
| ( ( in_path @ SV733 @ SV727 )
= $false )
| ( ( vertex @ SV733 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3653]) ).
thf(3692,plain,
! [SV728: $i,SV722: $i,SV696: $i] :
( ( ( ~ ( edge @ SV696 )
| ~ ( edge @ SV722 ) )
= $true )
| ( ( ~ ( edge @ SV728 ) )
= $true )
| ( ( ~ ( sequential @ SV696 @ SV722 ) )
= $true )
| ( ( ~ ( sequential @ SV722 @ SV728 ) )
= $true )
| ( ( ~ ( sequential @ SV728 @ SV696 ) )
= $true )
| ( ( triangle @ SV696 @ SV722 @ SV728 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3654]) ).
thf(3693,plain,
! [SV696: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( ! [SY1090: $i,SY1091: $i] :
~ ( triangle @ SV696 @ SY1090 @ SY1091 )
| ( edge @ SV696 ) )
| ~ ! [SY1092: $i] :
( ! [SY1093: $i] :
~ ( triangle @ SV696 @ SY1092 @ SY1093 )
| ( edge @ SY1092 ) ) )
| ~ ! [SY1094: $i,SY1095: $i] :
( ~ ( triangle @ SV696 @ SY1094 @ SY1095 )
| ( edge @ SY1095 ) ) )
| ~ ! [SY1096: $i] :
( ! [SY1097: $i] :
~ ( triangle @ SV696 @ SY1096 @ SY1097 )
| ( sequential @ SV696 @ SY1096 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3655]) ).
thf(3694,plain,
! [SV763: $i,SV696: $i] :
( ( ! [SY1183: $i] :
( ~ ( triangle @ SV696 @ SV763 @ SY1183 )
| ( sequential @ SV763 @ SY1183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3656]) ).
thf(3695,plain,
! [SV748: $i,SV739: $i,SV696: $i] :
( ( ( triangle @ SV696 @ SV739 @ SV748 )
= $false )
| ( ( sequential @ SV748 @ SV696 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3657]) ).
thf(3696,plain,
! [SV716: $i,SV711: $i,SV697: $i] :
( ( ( ! [SY1104: $i] :
( ! [SY1105: $i] :
~ ( precedes @ SY1104 @ SY1105 @ SV697 )
| ( on_path @ SY1104 @ SV697 ) ) )
= $true )
| ( ( path @ SV711 @ SV716 @ SV697 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3658]) ).
thf(3697,plain,
! [SV716: $i,SV711: $i,SV697: $i] :
( ( ( ! [SY1106: $i,SY1107: $i] :
( ~ ( precedes @ SY1106 @ SY1107 @ SV697 )
| ( on_path @ SY1107 @ SV697 ) ) )
= $true )
| ( ( path @ SV711 @ SV716 @ SV697 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3659]) ).
thf(3698,plain,
! [SV716: $i,SV711: $i,SV697: $i] :
( ( ( ! [SY1108: $i,SY1109: $i] :
( ~ ( precedes @ SY1108 @ SY1109 @ SV697 )
| ! [SY1110: $i] :
( ~ ( precedes @ SY1110 @ SY1109 @ SV697 )
| ~ ( sequential @ SY1108 @ SY1110 ) )
| ~ ( sequential @ SY1108 @ SY1109 ) ) )
= $true )
| ( ( path @ SV711 @ SV716 @ SV697 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3660]) ).
thf(3699,plain,
! [SV716: $i,SV711: $i,SV697: $i] :
( ( ( ! [SY1111: $i,SY1112: $i] :
( ~ ( precedes @ SY1111 @ SY1112 @ SV697 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY1112 @ SY1111 @ SV697 ) @ SY1112 @ SV697 )
| ~ ( sequential @ SY1111 @ ( sK9_E3 @ SY1112 @ SY1111 @ SV697 ) ) )
| ( sequential @ SY1111 @ SY1112 ) ) )
= $true )
| ( ( path @ SV711 @ SV716 @ SV697 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3661]) ).
thf(3700,plain,
! [SV705: $i,SV698: $i,SV749: $i,SV734: $i,SV712: $i] :
( ( ( precedes @ SV712 @ SV734 @ SV749 )
= $false )
| ( ( ~ ( shortest_path @ SV698 @ SV705 @ SV749 ) )
= $true )
| ( ( ! [SY1164: $i] :
( ( ( tail_of @ SY1164 )
!= ( tail_of @ SV712 ) )
| ( ( head_of @ SY1164 )
!= ( head_of @ SV734 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3662]) ).
thf(3701,plain,
! [SV705: $i,SV698: $i,SV740: $i,SV735: $i,SV712: $i] :
( ( ( precedes @ SV712 @ SV735 @ SV740 )
= $false )
| ( ( ~ ( shortest_path @ SV698 @ SV705 @ SV740 ) )
= $true )
| ( ( ~ ( precedes @ SV735 @ SV712 @ SV740 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3663]) ).
thf(3702,plain,
! [SV713: $i,SV708: $i] :
( ( ( ~ ( ~ ( ( SV708
!= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
!= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
!= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
!= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV708
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
| ~ ( ( SV708
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) ) )
| ~ ~ ( ~ ( ( SV713
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
| ~ ( ( SV713
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) ) ) ) ) )
= $true )
| ( ( SV708 = SV713 )
= $true )
| ( ( vertex @ SV708 )
= $false )
| ( ( vertex @ SV713 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[3664]) ).
thf(3703,plain,
! [SV708: $i,SV713: $i] :
( ( ( edge @ ( sK14_E @ SV713 @ SV708 ) )
= $true )
| ( ( SV708 = SV713 )
= $true )
| ( ( vertex @ SV708 )
= $false )
| ( ( vertex @ SV713 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[3665]) ).
thf(3704,plain,
! [SV719: $i,SV723: $i,SV689: $i] :
( ( ( ( SV689
!= ( tail_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( edge @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
= $false )
| ( ( path @ SV689 @ SV719 @ SV723 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3668]) ).
thf(3705,plain,
! [SV689: $i,SV723: $i,SV719: $i] :
( ( ( ~ ( ( SV719
!= ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
| ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ empty ) )
| ! [SY1158: $i] :
( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ SY1158 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ SY1158 ) ) )
| ~ ~ ( ~ ( ( SV719
= ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ ( sK13_SY84 @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ ( sK13_SY84 @ SV723 @ SV719 @ SV689 ) ) ) )
| ~ ( ( SV723
= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ empty ) )
| ~ ( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ ( sK12_SY85 @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ ( sK12_SY85 @ SV723 @ SV719 @ SV689 ) ) ) ) ) )
= $false )
| ( ( path @ SV689 @ SV719 @ SV723 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3669]) ).
thf(3706,plain,
! [SV709: $i,SV702: $i,SV764: $i,SV690: $i] :
( ( ( ( SV690
!= ( tail_of @ SV764 ) )
| ~ ( edge @ SV764 )
| ( SV702
!= ( head_of @ SV764 ) )
| ( SV709
!= ( path_cons @ SV764 @ empty ) ) )
= $true )
| ( ( vertex @ SV690 )
= $false )
| ( ( vertex @ SV702 )
= $false )
| ( ( path @ SV690 @ SV702 @ SV709 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3670]) ).
thf(3707,plain,
! [SV702: $i,SV709: $i,SV765: $i,SV690: $i] :
( ( ( ( SV690
!= ( tail_of @ SV765 ) )
| ~ ( edge @ SV765 )
| ! [SY1184: $i] :
( ( SV709
!= ( path_cons @ SV765 @ SY1184 ) )
| ~ ( path @ ( head_of @ SV765 ) @ SV702 @ SY1184 ) ) )
= $true )
| ( ( vertex @ SV690 )
= $false )
| ( ( vertex @ SV702 )
= $false )
| ( ( path @ SV690 @ SV702 @ SV709 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3671]) ).
thf(3708,plain,
! [SV724: $i,SV720: $i,SV691: $i] :
( ( ( SV691 = SV720 )
= $true )
| ( ( ~ ( path @ SV691 @ SV720 @ SV724 ) )
= $true )
| ( ( path @ SV691 @ SV720 @ ( sK8_P @ SV724 @ SV720 @ SV691 ) )
= $true )
| ( ( shortest_path @ SV691 @ SV720 @ SV724 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3672]) ).
thf(3709,plain,
! [SV691: $i,SV720: $i,SV724: $i] :
( ( ( less_or_equal @ ( length_of @ SV724 ) @ ( length_of @ ( sK8_P @ SV724 @ SV720 @ SV691 ) ) )
= $false )
| ( ( ( SV691 = SV720 )
| ~ ( path @ SV691 @ SV720 @ SV724 ) )
= $true )
| ( ( shortest_path @ SV691 @ SV720 @ SV724 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3673]) ).
thf(3710,plain,
! [SV742: $i,SV766: $i,SV737: $i,SV691: $i] :
( ( ( ~ ( path @ SV691 @ SV737 @ SV766 )
| ( less_or_equal @ ( length_of @ SV742 ) @ ( length_of @ SV766 ) ) )
= $true )
| ( ( shortest_path @ SV691 @ SV737 @ SV742 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3674]) ).
thf(3711,plain,
! [SV759: $i,SV691: $i] :
( ( ( ! [SY1181: $i] :
~ ( shortest_path @ SV691 @ SV759 @ SY1181 ) )
= $true )
| ( ( ( SV691 != SV759 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3675]) ).
thf(3712,plain,
! [SV767: $i,SV760: $i,SV691: $i] :
( ( ~ ( shortest_path @ SV691 @ SV760 @ SV767 )
| ( path @ SV691 @ SV760 @ SV767 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3676]) ).
thf(3713,plain,
! [SV692: $i] :
( ( ( on_path @ ( sK6_E1 @ SV692 ) @ SV692 )
= $true )
| ( ( ! [SY1067: $i,SY1068: $i] :
~ ( path @ SY1067 @ SY1068 @ SV692 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV692 )
= ( number_of_in @ triangles @ SV692 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3677]) ).
thf(3714,plain,
! [SV692: $i] :
( ( ( on_path @ ( sK7_SY80 @ SV692 ) @ SV692 )
= $true )
| ( ( ! [SY1067: $i,SY1068: $i] :
~ ( path @ SY1067 @ SY1068 @ SV692 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV692 )
= ( number_of_in @ triangles @ SV692 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3678]) ).
thf(3715,plain,
! [SV692: $i,SV761: $i,SV752: $i] :
( ( ( path @ SV752 @ SV761 @ SV692 )
= $false )
| ( ( sequential @ ( sK6_E1 @ SV692 ) @ ( sK7_SY80 @ SV692 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV692 )
= ( number_of_in @ triangles @ SV692 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3679]) ).
thf(3716,plain,
! [SV703: $i,SV693: $i,SV744: $i,SV754: $i] :
( ( ( ~ ( on_path @ SV754 @ SV744 ) )
= $true )
| ( ( ~ ( path @ SV693 @ SV703 @ SV744 ) )
= $true )
| ( ( edge @ SV754 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3681]) ).
thf(3717,plain,
! [SV703: $i,SV693: $i,SV745: $i,SV755: $i] :
( ( ( ~ ( on_path @ SV755 @ SV745 ) )
= $true )
| ( ( ~ ( path @ SV693 @ SV703 @ SV745 ) )
= $true )
| ( ( in_path @ ( head_of @ SV755 ) @ SV745 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3682]) ).
thf(3718,plain,
! [SV721: $i,SV714: $i] :
( ( ( ( head_of @ SV714 )
= ( tail_of @ SV721 ) )
= $false )
| ( ( SV714 = SV721 )
= $true )
| ( ( edge @ SV714 )
= $false )
| ( ( edge @ SV721 )
= $false )
| ( ( sequential @ SV714 @ SV721 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3684]) ).
thf(3719,plain,
! [SV762: $i,SV756: $i] :
( ( ( ~ ( sequential @ SV756 @ SV762 ) )
= $true )
| ( ( ( SV756 != SV762 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3685]) ).
thf(3720,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3686]) ).
thf(3721,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3687]) ).
thf(3722,plain,
! [SV715: $i,SV710: $i,SV757: $i,SV694: $i,SV746: $i] :
( ( ( ~ ( on_path @ SV746 @ SV694 )
| ~ ( on_path @ SV757 @ SV694 ) )
= $true )
| ( ( ! [SY1180: $i] :
( ~ ( precedes @ SY1180 @ SV757 @ SV694 )
| ~ ( sequential @ SV746 @ SY1180 ) ) )
= $true )
| ( ( precedes @ SV746 @ SV757 @ SV694 )
= $true )
| ( ( path @ SV710 @ SV715 @ SV694 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3688]) ).
thf(3723,plain,
! [SV715: $i,SV710: $i,SV758: $i,SV694: $i,SV747: $i] :
( ( ( ~ ( on_path @ SV747 @ SV694 )
| ~ ( on_path @ SV758 @ SV694 ) )
= $true )
| ( ( ~ ( sequential @ SV747 @ SV758 ) )
= $true )
| ( ( precedes @ SV747 @ SV758 @ SV694 )
= $true )
| ( ( path @ SV710 @ SV715 @ SV694 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3689]) ).
thf(3724,plain,
! [SV695: $i,SV704: $i,SV726: $i,SV732: $i] :
( ( ( ~ ( on_path @ ( sK10_E @ SV732 @ SV726 @ SV704 @ SV695 ) @ SV726 )
| ~ ( ( SV732
= ( head_of @ ( sK10_E @ SV732 @ SV726 @ SV704 @ SV695 ) ) )
| ( SV732
= ( tail_of @ ( sK10_E @ SV732 @ SV726 @ SV704 @ SV695 ) ) ) ) )
= $false )
| ( ( in_path @ SV732 @ SV726 )
= $false )
| ( ( path @ SV695 @ SV704 @ SV726 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3690]) ).
thf(3725,plain,
! [SV728: $i,SV722: $i,SV696: $i] :
( ( ( ~ ( edge @ SV696 ) )
= $true )
| ( ( ~ ( edge @ SV722 ) )
= $true )
| ( ( ~ ( edge @ SV728 ) )
= $true )
| ( ( ~ ( sequential @ SV696 @ SV722 ) )
= $true )
| ( ( ~ ( sequential @ SV722 @ SV728 ) )
= $true )
| ( ( ~ ( sequential @ SV728 @ SV696 ) )
= $true )
| ( ( triangle @ SV696 @ SV722 @ SV728 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3692]) ).
thf(3726,plain,
! [SV696: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( ! [SY1090: $i,SY1091: $i] :
~ ( triangle @ SV696 @ SY1090 @ SY1091 )
| ( edge @ SV696 ) )
| ~ ! [SY1092: $i] :
( ! [SY1093: $i] :
~ ( triangle @ SV696 @ SY1092 @ SY1093 )
| ( edge @ SY1092 ) ) )
| ~ ! [SY1094: $i,SY1095: $i] :
( ~ ( triangle @ SV696 @ SY1094 @ SY1095 )
| ( edge @ SY1095 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3693]) ).
thf(3727,plain,
! [SV696: $i] :
( ( ~ ! [SY1096: $i] :
( ! [SY1097: $i] :
~ ( triangle @ SV696 @ SY1096 @ SY1097 )
| ( sequential @ SV696 @ SY1096 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3693]) ).
thf(3728,plain,
! [SV768: $i,SV763: $i,SV696: $i] :
( ( ~ ( triangle @ SV696 @ SV763 @ SV768 )
| ( sequential @ SV763 @ SV768 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3694]) ).
thf(3729,plain,
! [SV716: $i,SV711: $i,SV697: $i,SV769: $i] :
( ( ( ! [SY1185: $i] :
~ ( precedes @ SV769 @ SY1185 @ SV697 )
| ( on_path @ SV769 @ SV697 ) )
= $true )
| ( ( path @ SV711 @ SV716 @ SV697 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3696]) ).
thf(3730,plain,
! [SV716: $i,SV711: $i,SV697: $i,SV770: $i] :
( ( ( ! [SY1186: $i] :
( ~ ( precedes @ SV770 @ SY1186 @ SV697 )
| ( on_path @ SY1186 @ SV697 ) ) )
= $true )
| ( ( path @ SV711 @ SV716 @ SV697 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3697]) ).
thf(3731,plain,
! [SV716: $i,SV711: $i,SV697: $i,SV771: $i] :
( ( ( ! [SY1187: $i] :
( ~ ( precedes @ SV771 @ SY1187 @ SV697 )
| ! [SY1188: $i] :
( ~ ( precedes @ SY1188 @ SY1187 @ SV697 )
| ~ ( sequential @ SV771 @ SY1188 ) )
| ~ ( sequential @ SV771 @ SY1187 ) ) )
= $true )
| ( ( path @ SV711 @ SV716 @ SV697 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3698]) ).
thf(3732,plain,
! [SV716: $i,SV711: $i,SV697: $i,SV772: $i] :
( ( ( ! [SY1189: $i] :
( ~ ( precedes @ SV772 @ SY1189 @ SV697 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY1189 @ SV772 @ SV697 ) @ SY1189 @ SV697 )
| ~ ( sequential @ SV772 @ ( sK9_E3 @ SY1189 @ SV772 @ SV697 ) ) )
| ( sequential @ SV772 @ SY1189 ) ) )
= $true )
| ( ( path @ SV711 @ SV716 @ SV697 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3699]) ).
thf(3733,plain,
! [SV734: $i,SV712: $i,SV749: $i,SV705: $i,SV698: $i] :
( ( ( shortest_path @ SV698 @ SV705 @ SV749 )
= $false )
| ( ( precedes @ SV712 @ SV734 @ SV749 )
= $false )
| ( ( ! [SY1164: $i] :
( ( ( tail_of @ SY1164 )
!= ( tail_of @ SV712 ) )
| ( ( head_of @ SY1164 )
!= ( head_of @ SV734 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3700]) ).
thf(3734,plain,
! [SV735: $i,SV712: $i,SV740: $i,SV705: $i,SV698: $i] :
( ( ( shortest_path @ SV698 @ SV705 @ SV740 )
= $false )
| ( ( precedes @ SV712 @ SV735 @ SV740 )
= $false )
| ( ( ~ ( precedes @ SV735 @ SV712 @ SV740 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3701]) ).
thf(3735,plain,
! [SV713: $i,SV708: $i] :
( ( ( ~ ( ( SV708
!= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
!= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
!= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
!= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV708
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
| ~ ( ( SV708
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) ) )
| ~ ~ ( ~ ( ( SV713
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
| ~ ( ( SV713
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) ) ) ) )
= $false )
| ( ( SV708 = SV713 )
= $true )
| ( ( vertex @ SV708 )
= $false )
| ( ( vertex @ SV713 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[3702]) ).
thf(3736,plain,
! [SV719: $i,SV723: $i,SV689: $i] :
( ( ( ( SV689
!= ( tail_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) ) )
= $false )
| ( ( path @ SV689 @ SV719 @ SV723 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3704]) ).
thf(3737,plain,
! [SV689: $i,SV719: $i,SV723: $i] :
( ( ( ~ ( edge @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
= $false )
| ( ( path @ SV689 @ SV719 @ SV723 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3704]) ).
thf(3738,plain,
! [SV689: $i,SV723: $i,SV719: $i] :
( ( ( ~ ( ( SV719
!= ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
| ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ empty ) )
| ! [SY1158: $i] :
( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ SY1158 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ SY1158 ) ) ) )
= $false )
| ( ( path @ SV689 @ SV719 @ SV723 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3705]) ).
thf(3739,plain,
! [SV689: $i,SV723: $i,SV719: $i] :
( ( ( ~ ~ ( ~ ( ( SV719
= ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ ( sK13_SY84 @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ ( sK13_SY84 @ SV723 @ SV719 @ SV689 ) ) ) )
| ~ ( ( SV723
= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ empty ) )
| ~ ( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ ( sK12_SY85 @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ ( sK12_SY85 @ SV723 @ SV719 @ SV689 ) ) ) ) ) )
= $false )
| ( ( path @ SV689 @ SV719 @ SV723 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3705]) ).
thf(3740,plain,
! [SV709: $i,SV702: $i,SV764: $i,SV690: $i] :
( ( ( ( SV690
!= ( tail_of @ SV764 ) )
| ~ ( edge @ SV764 ) )
= $true )
| ( ( ( SV702
!= ( head_of @ SV764 ) )
| ( SV709
!= ( path_cons @ SV764 @ empty ) ) )
= $true )
| ( ( vertex @ SV690 )
= $false )
| ( ( vertex @ SV702 )
= $false )
| ( ( path @ SV690 @ SV702 @ SV709 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3706]) ).
thf(3741,plain,
! [SV702: $i,SV709: $i,SV765: $i,SV690: $i] :
( ( ( ( SV690
!= ( tail_of @ SV765 ) )
| ~ ( edge @ SV765 ) )
= $true )
| ( ( ! [SY1184: $i] :
( ( SV709
!= ( path_cons @ SV765 @ SY1184 ) )
| ~ ( path @ ( head_of @ SV765 ) @ SV702 @ SY1184 ) ) )
= $true )
| ( ( vertex @ SV690 )
= $false )
| ( ( vertex @ SV702 )
= $false )
| ( ( path @ SV690 @ SV702 @ SV709 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3707]) ).
thf(3742,plain,
! [SV724: $i,SV720: $i,SV691: $i] :
( ( ( path @ SV691 @ SV720 @ SV724 )
= $false )
| ( ( SV691 = SV720 )
= $true )
| ( ( path @ SV691 @ SV720 @ ( sK8_P @ SV724 @ SV720 @ SV691 ) )
= $true )
| ( ( shortest_path @ SV691 @ SV720 @ SV724 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3708]) ).
thf(3743,plain,
! [SV724: $i,SV720: $i,SV691: $i] :
( ( ( SV691 = SV720 )
= $true )
| ( ( ~ ( path @ SV691 @ SV720 @ SV724 ) )
= $true )
| ( ( less_or_equal @ ( length_of @ SV724 ) @ ( length_of @ ( sK8_P @ SV724 @ SV720 @ SV691 ) ) )
= $false )
| ( ( shortest_path @ SV691 @ SV720 @ SV724 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3709]) ).
thf(3744,plain,
! [SV742: $i,SV766: $i,SV737: $i,SV691: $i] :
( ( ( ~ ( path @ SV691 @ SV737 @ SV766 ) )
= $true )
| ( ( less_or_equal @ ( length_of @ SV742 ) @ ( length_of @ SV766 ) )
= $true )
| ( ( shortest_path @ SV691 @ SV737 @ SV742 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3710]) ).
thf(3745,plain,
! [SV773: $i,SV759: $i,SV691: $i] :
( ( ( ~ ( shortest_path @ SV691 @ SV759 @ SV773 ) )
= $true )
| ( ( ( SV691 != SV759 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3711]) ).
thf(3746,plain,
! [SV767: $i,SV760: $i,SV691: $i] :
( ( ( ~ ( shortest_path @ SV691 @ SV760 @ SV767 ) )
= $true )
| ( ( path @ SV691 @ SV760 @ SV767 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3712]) ).
thf(3747,plain,
! [SV692: $i,SV774: $i] :
( ( ( ! [SY1190: $i] :
~ ( path @ SV774 @ SY1190 @ SV692 ) )
= $true )
| ( ( on_path @ ( sK6_E1 @ SV692 ) @ SV692 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV692 )
= ( number_of_in @ triangles @ SV692 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3713]) ).
thf(3748,plain,
! [SV692: $i,SV775: $i] :
( ( ( ! [SY1191: $i] :
~ ( path @ SV775 @ SY1191 @ SV692 ) )
= $true )
| ( ( on_path @ ( sK7_SY80 @ SV692 ) @ SV692 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV692 )
= ( number_of_in @ triangles @ SV692 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3714]) ).
thf(3749,plain,
! [SV703: $i,SV693: $i,SV744: $i,SV754: $i] :
( ( ( on_path @ SV754 @ SV744 )
= $false )
| ( ( ~ ( path @ SV693 @ SV703 @ SV744 ) )
= $true )
| ( ( edge @ SV754 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3716]) ).
thf(3750,plain,
! [SV703: $i,SV693: $i,SV745: $i,SV755: $i] :
( ( ( on_path @ SV755 @ SV745 )
= $false )
| ( ( ~ ( path @ SV693 @ SV703 @ SV745 ) )
= $true )
| ( ( in_path @ ( head_of @ SV755 ) @ SV745 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3717]) ).
thf(3751,plain,
! [SV762: $i,SV756: $i] :
( ( ( sequential @ SV756 @ SV762 )
= $false )
| ( ( ( SV756 != SV762 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3719]) ).
thf(3752,plain,
! [SV776: $i] :
( ( ! [SY1192: $i] :
~ ( sequential @ SV776 @ SY1192 )
| ( edge @ SV776 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3720]) ).
thf(3753,plain,
! [SV777: $i] :
( ( ! [SY1193: $i] :
( ~ ( sequential @ SV777 @ SY1193 )
| ( edge @ SY1193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3721]) ).
thf(3754,plain,
! [SV715: $i,SV710: $i,SV757: $i,SV694: $i,SV746: $i] :
( ( ( ~ ( on_path @ SV746 @ SV694 ) )
= $true )
| ( ( ~ ( on_path @ SV757 @ SV694 ) )
= $true )
| ( ( ! [SY1180: $i] :
( ~ ( precedes @ SY1180 @ SV757 @ SV694 )
| ~ ( sequential @ SV746 @ SY1180 ) ) )
= $true )
| ( ( precedes @ SV746 @ SV757 @ SV694 )
= $true )
| ( ( path @ SV710 @ SV715 @ SV694 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3722]) ).
thf(3755,plain,
! [SV715: $i,SV710: $i,SV758: $i,SV694: $i,SV747: $i] :
( ( ( ~ ( on_path @ SV747 @ SV694 ) )
= $true )
| ( ( ~ ( on_path @ SV758 @ SV694 ) )
= $true )
| ( ( ~ ( sequential @ SV747 @ SV758 ) )
= $true )
| ( ( precedes @ SV747 @ SV758 @ SV694 )
= $true )
| ( ( path @ SV710 @ SV715 @ SV694 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3723]) ).
thf(3756,plain,
! [SV695: $i,SV704: $i,SV726: $i,SV732: $i] :
( ( ( ~ ( on_path @ ( sK10_E @ SV732 @ SV726 @ SV704 @ SV695 ) @ SV726 ) )
= $false )
| ( ( in_path @ SV732 @ SV726 )
= $false )
| ( ( path @ SV695 @ SV704 @ SV726 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3724]) ).
thf(3757,plain,
! [SV695: $i,SV704: $i,SV726: $i,SV732: $i] :
( ( ( ~ ( ( SV732
= ( head_of @ ( sK10_E @ SV732 @ SV726 @ SV704 @ SV695 ) ) )
| ( SV732
= ( tail_of @ ( sK10_E @ SV732 @ SV726 @ SV704 @ SV695 ) ) ) ) )
= $false )
| ( ( in_path @ SV732 @ SV726 )
= $false )
| ( ( path @ SV695 @ SV704 @ SV726 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3724]) ).
thf(3758,plain,
! [SV728: $i,SV722: $i,SV696: $i] :
( ( ( edge @ SV696 )
= $false )
| ( ( ~ ( edge @ SV722 ) )
= $true )
| ( ( ~ ( edge @ SV728 ) )
= $true )
| ( ( ~ ( sequential @ SV696 @ SV722 ) )
= $true )
| ( ( ~ ( sequential @ SV722 @ SV728 ) )
= $true )
| ( ( ~ ( sequential @ SV728 @ SV696 ) )
= $true )
| ( ( triangle @ SV696 @ SV722 @ SV728 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3725]) ).
thf(3759,plain,
! [SV696: $i] :
( ( ~ ( ~ ~ ( ~ ( ! [SY1090: $i,SY1091: $i] :
~ ( triangle @ SV696 @ SY1090 @ SY1091 )
| ( edge @ SV696 ) )
| ~ ! [SY1092: $i] :
( ! [SY1093: $i] :
~ ( triangle @ SV696 @ SY1092 @ SY1093 )
| ( edge @ SY1092 ) ) )
| ~ ! [SY1094: $i,SY1095: $i] :
( ~ ( triangle @ SV696 @ SY1094 @ SY1095 )
| ( edge @ SY1095 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3726]) ).
thf(3760,plain,
! [SV696: $i] :
( ( ! [SY1096: $i] :
( ! [SY1097: $i] :
~ ( triangle @ SV696 @ SY1096 @ SY1097 )
| ( sequential @ SV696 @ SY1096 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3727]) ).
thf(3761,plain,
! [SV768: $i,SV763: $i,SV696: $i] :
( ( ( ~ ( triangle @ SV696 @ SV763 @ SV768 ) )
= $true )
| ( ( sequential @ SV763 @ SV768 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3728]) ).
thf(3762,plain,
! [SV716: $i,SV711: $i,SV697: $i,SV769: $i] :
( ( ( ! [SY1185: $i] :
~ ( precedes @ SV769 @ SY1185 @ SV697 ) )
= $true )
| ( ( on_path @ SV769 @ SV697 )
= $true )
| ( ( path @ SV711 @ SV716 @ SV697 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3729]) ).
thf(3763,plain,
! [SV716: $i,SV711: $i,SV697: $i,SV778: $i,SV770: $i] :
( ( ( ~ ( precedes @ SV770 @ SV778 @ SV697 )
| ( on_path @ SV778 @ SV697 ) )
= $true )
| ( ( path @ SV711 @ SV716 @ SV697 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3730]) ).
thf(3764,plain,
! [SV716: $i,SV711: $i,SV697: $i,SV779: $i,SV771: $i] :
( ( ( ~ ( precedes @ SV771 @ SV779 @ SV697 )
| ! [SY1194: $i] :
( ~ ( precedes @ SY1194 @ SV779 @ SV697 )
| ~ ( sequential @ SV771 @ SY1194 ) )
| ~ ( sequential @ SV771 @ SV779 ) )
= $true )
| ( ( path @ SV711 @ SV716 @ SV697 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3731]) ).
thf(3765,plain,
! [SV716: $i,SV711: $i,SV697: $i,SV780: $i,SV772: $i] :
( ( ( ~ ( precedes @ SV772 @ SV780 @ SV697 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SV780 @ SV772 @ SV697 ) @ SV780 @ SV697 )
| ~ ( sequential @ SV772 @ ( sK9_E3 @ SV780 @ SV772 @ SV697 ) ) )
| ( sequential @ SV772 @ SV780 ) )
= $true )
| ( ( path @ SV711 @ SV716 @ SV697 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3732]) ).
thf(3766,plain,
! [SV705: $i,SV698: $i,SV749: $i,SV734: $i,SV712: $i,SV781: $i] :
( ( ( ( ( tail_of @ SV781 )
!= ( tail_of @ SV712 ) )
| ( ( head_of @ SV781 )
!= ( head_of @ SV734 ) ) )
= $true )
| ( ( precedes @ SV712 @ SV734 @ SV749 )
= $false )
| ( ( shortest_path @ SV698 @ SV705 @ SV749 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3733]) ).
thf(3767,plain,
! [SV705: $i,SV698: $i,SV740: $i,SV712: $i,SV735: $i] :
( ( ( precedes @ SV735 @ SV712 @ SV740 )
= $false )
| ( ( precedes @ SV712 @ SV735 @ SV740 )
= $false )
| ( ( shortest_path @ SV698 @ SV705 @ SV740 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3734]) ).
thf(3768,plain,
! [SV713: $i,SV708: $i] :
( ( ( ~ ( ( SV708
!= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
!= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
!= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
!= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) ) )
= $false )
| ( ( SV708 = SV713 )
= $true )
| ( ( vertex @ SV708 )
= $false )
| ( ( vertex @ SV713 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[3735]) ).
thf(3769,plain,
! [SV713: $i,SV708: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( SV708
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
| ~ ( ( SV708
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) ) )
| ~ ~ ( ~ ( ( SV713
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
| ~ ( ( SV713
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) ) ) ) )
= $false )
| ( ( SV708 = SV713 )
= $true )
| ( ( vertex @ SV708 )
= $false )
| ( ( vertex @ SV713 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[3735]) ).
thf(3770,plain,
! [SV719: $i,SV723: $i,SV689: $i] :
( ( ( SV689
= ( tail_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
= $true )
| ( ( path @ SV689 @ SV719 @ SV723 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3736]) ).
thf(3771,plain,
! [SV689: $i,SV719: $i,SV723: $i] :
( ( ( edge @ ( sK11_E @ SV723 @ SV719 @ SV689 ) )
= $true )
| ( ( path @ SV689 @ SV719 @ SV723 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3737]) ).
thf(3772,plain,
! [SV689: $i,SV723: $i,SV719: $i] :
( ( ( ( SV719
!= ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
| ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ empty ) )
| ! [SY1158: $i] :
( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ SY1158 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ SY1158 ) ) )
= $true )
| ( ( path @ SV689 @ SV719 @ SV723 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3738]) ).
thf(3773,plain,
! [SV689: $i,SV723: $i,SV719: $i] :
( ( ( ~ ( ~ ( ( SV719
= ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ ( sK13_SY84 @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ ( sK13_SY84 @ SV723 @ SV719 @ SV689 ) ) ) )
| ~ ( ( SV723
= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ empty ) )
| ~ ( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ ( sK12_SY85 @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ ( sK12_SY85 @ SV723 @ SV719 @ SV689 ) ) ) ) ) )
= $true )
| ( ( path @ SV689 @ SV719 @ SV723 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3739]) ).
thf(3774,plain,
! [SV709: $i,SV702: $i,SV764: $i,SV690: $i] :
( ( ( ( SV690
!= ( tail_of @ SV764 ) ) )
= $true )
| ( ( ~ ( edge @ SV764 ) )
= $true )
| ( ( ( SV702
!= ( head_of @ SV764 ) )
| ( SV709
!= ( path_cons @ SV764 @ empty ) ) )
= $true )
| ( ( vertex @ SV690 )
= $false )
| ( ( vertex @ SV702 )
= $false )
| ( ( path @ SV690 @ SV702 @ SV709 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3740]) ).
thf(3775,plain,
! [SV702: $i,SV709: $i,SV765: $i,SV690: $i] :
( ( ( ( SV690
!= ( tail_of @ SV765 ) ) )
= $true )
| ( ( ~ ( edge @ SV765 ) )
= $true )
| ( ( ! [SY1184: $i] :
( ( SV709
!= ( path_cons @ SV765 @ SY1184 ) )
| ~ ( path @ ( head_of @ SV765 ) @ SV702 @ SY1184 ) ) )
= $true )
| ( ( vertex @ SV690 )
= $false )
| ( ( vertex @ SV702 )
= $false )
| ( ( path @ SV690 @ SV702 @ SV709 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3741]) ).
thf(3776,plain,
! [SV724: $i,SV720: $i,SV691: $i] :
( ( ( path @ SV691 @ SV720 @ SV724 )
= $false )
| ( ( SV691 = SV720 )
= $true )
| ( ( less_or_equal @ ( length_of @ SV724 ) @ ( length_of @ ( sK8_P @ SV724 @ SV720 @ SV691 ) ) )
= $false )
| ( ( shortest_path @ SV691 @ SV720 @ SV724 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3743]) ).
thf(3777,plain,
! [SV742: $i,SV766: $i,SV737: $i,SV691: $i] :
( ( ( path @ SV691 @ SV737 @ SV766 )
= $false )
| ( ( less_or_equal @ ( length_of @ SV742 ) @ ( length_of @ SV766 ) )
= $true )
| ( ( shortest_path @ SV691 @ SV737 @ SV742 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3744]) ).
thf(3778,plain,
! [SV773: $i,SV759: $i,SV691: $i] :
( ( ( shortest_path @ SV691 @ SV759 @ SV773 )
= $false )
| ( ( ( SV691 != SV759 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3745]) ).
thf(3779,plain,
! [SV767: $i,SV760: $i,SV691: $i] :
( ( ( shortest_path @ SV691 @ SV760 @ SV767 )
= $false )
| ( ( path @ SV691 @ SV760 @ SV767 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3746]) ).
thf(3780,plain,
! [SV692: $i,SV782: $i,SV774: $i] :
( ( ( ~ ( path @ SV774 @ SV782 @ SV692 ) )
= $true )
| ( ( on_path @ ( sK6_E1 @ SV692 ) @ SV692 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV692 )
= ( number_of_in @ triangles @ SV692 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3747]) ).
thf(3781,plain,
! [SV692: $i,SV783: $i,SV775: $i] :
( ( ( ~ ( path @ SV775 @ SV783 @ SV692 ) )
= $true )
| ( ( on_path @ ( sK7_SY80 @ SV692 ) @ SV692 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV692 )
= ( number_of_in @ triangles @ SV692 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3748]) ).
thf(3782,plain,
! [SV754: $i,SV744: $i,SV703: $i,SV693: $i] :
( ( ( path @ SV693 @ SV703 @ SV744 )
= $false )
| ( ( on_path @ SV754 @ SV744 )
= $false )
| ( ( edge @ SV754 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3749]) ).
thf(3783,plain,
! [SV755: $i,SV745: $i,SV703: $i,SV693: $i] :
( ( ( path @ SV693 @ SV703 @ SV745 )
= $false )
| ( ( on_path @ SV755 @ SV745 )
= $false )
| ( ( in_path @ ( head_of @ SV755 ) @ SV745 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3750]) ).
thf(3784,plain,
! [SV762: $i,SV756: $i] :
( ( ( SV756 = SV762 )
= $false )
| ( ( sequential @ SV756 @ SV762 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3751]) ).
thf(3785,plain,
! [SV776: $i] :
( ( ( ! [SY1192: $i] :
~ ( sequential @ SV776 @ SY1192 ) )
= $true )
| ( ( edge @ SV776 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3752]) ).
thf(3786,plain,
! [SV784: $i,SV777: $i] :
( ( ~ ( sequential @ SV777 @ SV784 )
| ( edge @ SV784 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3753]) ).
thf(3787,plain,
! [SV715: $i,SV710: $i,SV757: $i,SV694: $i,SV746: $i] :
( ( ( on_path @ SV746 @ SV694 )
= $false )
| ( ( ~ ( on_path @ SV757 @ SV694 ) )
= $true )
| ( ( ! [SY1180: $i] :
( ~ ( precedes @ SY1180 @ SV757 @ SV694 )
| ~ ( sequential @ SV746 @ SY1180 ) ) )
= $true )
| ( ( precedes @ SV746 @ SV757 @ SV694 )
= $true )
| ( ( path @ SV710 @ SV715 @ SV694 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3754]) ).
thf(3788,plain,
! [SV715: $i,SV710: $i,SV758: $i,SV694: $i,SV747: $i] :
( ( ( on_path @ SV747 @ SV694 )
= $false )
| ( ( ~ ( on_path @ SV758 @ SV694 ) )
= $true )
| ( ( ~ ( sequential @ SV747 @ SV758 ) )
= $true )
| ( ( precedes @ SV747 @ SV758 @ SV694 )
= $true )
| ( ( path @ SV710 @ SV715 @ SV694 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3755]) ).
thf(3789,plain,
! [SV695: $i,SV704: $i,SV726: $i,SV732: $i] :
( ( ( on_path @ ( sK10_E @ SV732 @ SV726 @ SV704 @ SV695 ) @ SV726 )
= $true )
| ( ( in_path @ SV732 @ SV726 )
= $false )
| ( ( path @ SV695 @ SV704 @ SV726 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3756]) ).
thf(3790,plain,
! [SV695: $i,SV704: $i,SV726: $i,SV732: $i] :
( ( ( ( SV732
= ( head_of @ ( sK10_E @ SV732 @ SV726 @ SV704 @ SV695 ) ) )
| ( SV732
= ( tail_of @ ( sK10_E @ SV732 @ SV726 @ SV704 @ SV695 ) ) ) )
= $true )
| ( ( in_path @ SV732 @ SV726 )
= $false )
| ( ( path @ SV695 @ SV704 @ SV726 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3757]) ).
thf(3791,plain,
! [SV728: $i,SV696: $i,SV722: $i] :
( ( ( edge @ SV722 )
= $false )
| ( ( edge @ SV696 )
= $false )
| ( ( ~ ( edge @ SV728 ) )
= $true )
| ( ( ~ ( sequential @ SV696 @ SV722 ) )
= $true )
| ( ( ~ ( sequential @ SV722 @ SV728 ) )
= $true )
| ( ( ~ ( sequential @ SV728 @ SV696 ) )
= $true )
| ( ( triangle @ SV696 @ SV722 @ SV728 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3758]) ).
thf(3792,plain,
! [SV696: $i] :
( ( ~ ~ ( ~ ( ! [SY1090: $i,SY1091: $i] :
~ ( triangle @ SV696 @ SY1090 @ SY1091 )
| ( edge @ SV696 ) )
| ~ ! [SY1092: $i] :
( ! [SY1093: $i] :
~ ( triangle @ SV696 @ SY1092 @ SY1093 )
| ( edge @ SY1092 ) ) )
| ~ ! [SY1094: $i,SY1095: $i] :
( ~ ( triangle @ SV696 @ SY1094 @ SY1095 )
| ( edge @ SY1095 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3759]) ).
thf(3793,plain,
! [SV785: $i,SV696: $i] :
( ( ! [SY1195: $i] :
~ ( triangle @ SV696 @ SV785 @ SY1195 )
| ( sequential @ SV696 @ SV785 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3760]) ).
thf(3794,plain,
! [SV768: $i,SV763: $i,SV696: $i] :
( ( ( triangle @ SV696 @ SV763 @ SV768 )
= $false )
| ( ( sequential @ SV763 @ SV768 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3761]) ).
thf(3795,plain,
! [SV716: $i,SV711: $i,SV697: $i,SV786: $i,SV769: $i] :
( ( ( ~ ( precedes @ SV769 @ SV786 @ SV697 ) )
= $true )
| ( ( on_path @ SV769 @ SV697 )
= $true )
| ( ( path @ SV711 @ SV716 @ SV697 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3762]) ).
thf(3796,plain,
! [SV716: $i,SV711: $i,SV697: $i,SV778: $i,SV770: $i] :
( ( ( ~ ( precedes @ SV770 @ SV778 @ SV697 ) )
= $true )
| ( ( on_path @ SV778 @ SV697 )
= $true )
| ( ( path @ SV711 @ SV716 @ SV697 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3763]) ).
thf(3797,plain,
! [SV716: $i,SV711: $i,SV697: $i,SV779: $i,SV771: $i] :
( ( ( ~ ( precedes @ SV771 @ SV779 @ SV697 ) )
= $true )
| ( ( ! [SY1194: $i] :
( ~ ( precedes @ SY1194 @ SV779 @ SV697 )
| ~ ( sequential @ SV771 @ SY1194 ) )
| ~ ( sequential @ SV771 @ SV779 ) )
= $true )
| ( ( path @ SV711 @ SV716 @ SV697 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3764]) ).
thf(3798,plain,
! [SV716: $i,SV711: $i,SV697: $i,SV780: $i,SV772: $i] :
( ( ( ~ ( precedes @ SV772 @ SV780 @ SV697 ) )
= $true )
| ( ( ~ ( ~ ( precedes @ ( sK9_E3 @ SV780 @ SV772 @ SV697 ) @ SV780 @ SV697 )
| ~ ( sequential @ SV772 @ ( sK9_E3 @ SV780 @ SV772 @ SV697 ) ) )
| ( sequential @ SV772 @ SV780 ) )
= $true )
| ( ( path @ SV711 @ SV716 @ SV697 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3765]) ).
thf(3799,plain,
! [SV705: $i,SV698: $i,SV749: $i,SV734: $i,SV712: $i,SV781: $i] :
( ( ( ( ( tail_of @ SV781 )
!= ( tail_of @ SV712 ) ) )
= $true )
| ( ( ( ( head_of @ SV781 )
!= ( head_of @ SV734 ) ) )
= $true )
| ( ( precedes @ SV712 @ SV734 @ SV749 )
= $false )
| ( ( shortest_path @ SV698 @ SV705 @ SV749 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3766]) ).
thf(3800,plain,
! [SV713: $i,SV708: $i] :
( ( ( ( SV708
!= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
!= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
!= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
!= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
= $true )
| ( ( SV708 = SV713 )
= $true )
| ( ( vertex @ SV708 )
= $false )
| ( ( vertex @ SV713 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[3768]) ).
thf(3801,plain,
! [SV713: $i,SV708: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( SV708
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
| ~ ( ( SV708
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) ) )
| ~ ~ ( ~ ( ( SV713
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
| ~ ( ( SV713
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) ) ) ) )
= $true )
| ( ( SV708 = SV713 )
= $true )
| ( ( vertex @ SV708 )
= $false )
| ( ( vertex @ SV713 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[3769]) ).
thf(3802,plain,
! [SV689: $i,SV723: $i,SV719: $i] :
( ( ( ( SV719
!= ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
| ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ empty ) ) )
= $true )
| ( ( ! [SY1158: $i] :
( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ SY1158 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ SY1158 ) ) )
= $true )
| ( ( path @ SV689 @ SV719 @ SV723 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3772]) ).
thf(3803,plain,
! [SV689: $i,SV723: $i,SV719: $i] :
( ( ( ~ ( ( SV719
= ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ ( sK13_SY84 @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ ( sK13_SY84 @ SV723 @ SV719 @ SV689 ) ) ) )
| ~ ( ( SV723
= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ empty ) )
| ~ ( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ ( sK12_SY85 @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ ( sK12_SY85 @ SV723 @ SV719 @ SV689 ) ) ) ) )
= $false )
| ( ( path @ SV689 @ SV719 @ SV723 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3773]) ).
thf(3804,plain,
! [SV709: $i,SV702: $i,SV764: $i,SV690: $i] :
( ( ( SV690
= ( tail_of @ SV764 ) )
= $false )
| ( ( ~ ( edge @ SV764 ) )
= $true )
| ( ( ( SV702
!= ( head_of @ SV764 ) )
| ( SV709
!= ( path_cons @ SV764 @ empty ) ) )
= $true )
| ( ( vertex @ SV690 )
= $false )
| ( ( vertex @ SV702 )
= $false )
| ( ( path @ SV690 @ SV702 @ SV709 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3774]) ).
thf(3805,plain,
! [SV702: $i,SV709: $i,SV765: $i,SV690: $i] :
( ( ( SV690
= ( tail_of @ SV765 ) )
= $false )
| ( ( ~ ( edge @ SV765 ) )
= $true )
| ( ( ! [SY1184: $i] :
( ( SV709
!= ( path_cons @ SV765 @ SY1184 ) )
| ~ ( path @ ( head_of @ SV765 ) @ SV702 @ SY1184 ) ) )
= $true )
| ( ( vertex @ SV690 )
= $false )
| ( ( vertex @ SV702 )
= $false )
| ( ( path @ SV690 @ SV702 @ SV709 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3775]) ).
thf(3806,plain,
! [SV773: $i,SV759: $i,SV691: $i] :
( ( ( SV691 = SV759 )
= $false )
| ( ( shortest_path @ SV691 @ SV759 @ SV773 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3778]) ).
thf(3807,plain,
! [SV692: $i,SV782: $i,SV774: $i] :
( ( ( path @ SV774 @ SV782 @ SV692 )
= $false )
| ( ( on_path @ ( sK6_E1 @ SV692 ) @ SV692 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV692 )
= ( number_of_in @ triangles @ SV692 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3780]) ).
thf(3808,plain,
! [SV692: $i,SV783: $i,SV775: $i] :
( ( ( path @ SV775 @ SV783 @ SV692 )
= $false )
| ( ( on_path @ ( sK7_SY80 @ SV692 ) @ SV692 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV692 )
= ( number_of_in @ triangles @ SV692 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3781]) ).
thf(3809,plain,
! [SV787: $i,SV776: $i] :
( ( ( ~ ( sequential @ SV776 @ SV787 ) )
= $true )
| ( ( edge @ SV776 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3785]) ).
thf(3810,plain,
! [SV784: $i,SV777: $i] :
( ( ( ~ ( sequential @ SV777 @ SV784 ) )
= $true )
| ( ( edge @ SV784 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3786]) ).
thf(3811,plain,
! [SV715: $i,SV710: $i,SV746: $i,SV694: $i,SV757: $i] :
( ( ( on_path @ SV757 @ SV694 )
= $false )
| ( ( on_path @ SV746 @ SV694 )
= $false )
| ( ( ! [SY1180: $i] :
( ~ ( precedes @ SY1180 @ SV757 @ SV694 )
| ~ ( sequential @ SV746 @ SY1180 ) ) )
= $true )
| ( ( precedes @ SV746 @ SV757 @ SV694 )
= $true )
| ( ( path @ SV710 @ SV715 @ SV694 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3787]) ).
thf(3812,plain,
! [SV715: $i,SV710: $i,SV747: $i,SV694: $i,SV758: $i] :
( ( ( on_path @ SV758 @ SV694 )
= $false )
| ( ( on_path @ SV747 @ SV694 )
= $false )
| ( ( ~ ( sequential @ SV747 @ SV758 ) )
= $true )
| ( ( precedes @ SV747 @ SV758 @ SV694 )
= $true )
| ( ( path @ SV710 @ SV715 @ SV694 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3788]) ).
thf(3813,plain,
! [SV695: $i,SV704: $i,SV726: $i,SV732: $i] :
( ( ( SV732
= ( head_of @ ( sK10_E @ SV732 @ SV726 @ SV704 @ SV695 ) ) )
= $true )
| ( ( SV732
= ( tail_of @ ( sK10_E @ SV732 @ SV726 @ SV704 @ SV695 ) ) )
= $true )
| ( ( in_path @ SV732 @ SV726 )
= $false )
| ( ( path @ SV695 @ SV704 @ SV726 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3790]) ).
thf(3814,plain,
! [SV722: $i,SV696: $i,SV728: $i] :
( ( ( edge @ SV728 )
= $false )
| ( ( edge @ SV696 )
= $false )
| ( ( edge @ SV722 )
= $false )
| ( ( ~ ( sequential @ SV696 @ SV722 ) )
= $true )
| ( ( ~ ( sequential @ SV722 @ SV728 ) )
= $true )
| ( ( ~ ( sequential @ SV728 @ SV696 ) )
= $true )
| ( ( triangle @ SV696 @ SV722 @ SV728 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3791]) ).
thf(3815,plain,
! [SV696: $i] :
( ( ~ ~ ( ~ ( ! [SY1090: $i,SY1091: $i] :
~ ( triangle @ SV696 @ SY1090 @ SY1091 )
| ( edge @ SV696 ) )
| ~ ! [SY1092: $i] :
( ! [SY1093: $i] :
~ ( triangle @ SV696 @ SY1092 @ SY1093 )
| ( edge @ SY1092 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3792]) ).
thf(3816,plain,
! [SV696: $i] :
( ( ~ ! [SY1094: $i,SY1095: $i] :
( ~ ( triangle @ SV696 @ SY1094 @ SY1095 )
| ( edge @ SY1095 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3792]) ).
thf(3817,plain,
! [SV785: $i,SV696: $i] :
( ( ( ! [SY1195: $i] :
~ ( triangle @ SV696 @ SV785 @ SY1195 ) )
= $true )
| ( ( sequential @ SV696 @ SV785 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3793]) ).
thf(3818,plain,
! [SV716: $i,SV711: $i,SV697: $i,SV786: $i,SV769: $i] :
( ( ( precedes @ SV769 @ SV786 @ SV697 )
= $false )
| ( ( on_path @ SV769 @ SV697 )
= $true )
| ( ( path @ SV711 @ SV716 @ SV697 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3795]) ).
thf(3819,plain,
! [SV716: $i,SV711: $i,SV697: $i,SV778: $i,SV770: $i] :
( ( ( precedes @ SV770 @ SV778 @ SV697 )
= $false )
| ( ( on_path @ SV778 @ SV697 )
= $true )
| ( ( path @ SV711 @ SV716 @ SV697 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3796]) ).
thf(3820,plain,
! [SV716: $i,SV711: $i,SV697: $i,SV779: $i,SV771: $i] :
( ( ( precedes @ SV771 @ SV779 @ SV697 )
= $false )
| ( ( ! [SY1194: $i] :
( ~ ( precedes @ SY1194 @ SV779 @ SV697 )
| ~ ( sequential @ SV771 @ SY1194 ) )
| ~ ( sequential @ SV771 @ SV779 ) )
= $true )
| ( ( path @ SV711 @ SV716 @ SV697 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3797]) ).
thf(3821,plain,
! [SV716: $i,SV711: $i,SV697: $i,SV780: $i,SV772: $i] :
( ( ( precedes @ SV772 @ SV780 @ SV697 )
= $false )
| ( ( ~ ( ~ ( precedes @ ( sK9_E3 @ SV780 @ SV772 @ SV697 ) @ SV780 @ SV697 )
| ~ ( sequential @ SV772 @ ( sK9_E3 @ SV780 @ SV772 @ SV697 ) ) )
| ( sequential @ SV772 @ SV780 ) )
= $true )
| ( ( path @ SV711 @ SV716 @ SV697 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3798]) ).
thf(3822,plain,
! [SV705: $i,SV698: $i,SV749: $i,SV734: $i,SV712: $i,SV781: $i] :
( ( ( ( tail_of @ SV781 )
= ( tail_of @ SV712 ) )
= $false )
| ( ( ( ( head_of @ SV781 )
!= ( head_of @ SV734 ) ) )
= $true )
| ( ( precedes @ SV712 @ SV734 @ SV749 )
= $false )
| ( ( shortest_path @ SV698 @ SV705 @ SV749 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3799]) ).
thf(3823,plain,
! [SV713: $i,SV708: $i] :
( ( ( ( SV708
!= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
!= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
= $true )
| ( ( ( SV713
!= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
!= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
= $true )
| ( ( SV708 = SV713 )
= $true )
| ( ( vertex @ SV708 )
= $false )
| ( ( vertex @ SV713 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[3800]) ).
thf(3824,plain,
! [SV713: $i,SV708: $i] :
( ( ( ~ ~ ( ~ ( ( SV708
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
| ~ ( ( SV708
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) ) )
| ~ ~ ( ~ ( ( SV713
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
| ~ ( ( SV713
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) ) ) )
= $false )
| ( ( SV708 = SV713 )
= $true )
| ( ( vertex @ SV708 )
= $false )
| ( ( vertex @ SV713 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[3801]) ).
thf(3825,plain,
! [SV689: $i,SV723: $i,SV719: $i] :
( ( ( ( SV719
!= ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) ) )
= $true )
| ( ( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ empty ) ) )
= $true )
| ( ( ! [SY1158: $i] :
( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ SY1158 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ SY1158 ) ) )
= $true )
| ( ( path @ SV689 @ SV719 @ SV723 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3802]) ).
thf(3826,plain,
! [SV689: $i,SV723: $i,SV719: $i] :
( ( ( ~ ( ( SV719
= ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ ( sK13_SY84 @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ ( sK13_SY84 @ SV723 @ SV719 @ SV689 ) ) ) ) )
= $false )
| ( ( path @ SV689 @ SV719 @ SV723 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3803]) ).
thf(3827,plain,
! [SV689: $i,SV719: $i,SV723: $i] :
( ( ( ~ ( ( SV723
= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ empty ) )
| ~ ( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ ( sK12_SY85 @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ ( sK12_SY85 @ SV723 @ SV719 @ SV689 ) ) ) ) )
= $false )
| ( ( path @ SV689 @ SV719 @ SV723 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3803]) ).
thf(3828,plain,
! [SV709: $i,SV702: $i,SV690: $i,SV764: $i] :
( ( ( edge @ SV764 )
= $false )
| ( ( SV690
= ( tail_of @ SV764 ) )
= $false )
| ( ( ( SV702
!= ( head_of @ SV764 ) )
| ( SV709
!= ( path_cons @ SV764 @ empty ) ) )
= $true )
| ( ( vertex @ SV690 )
= $false )
| ( ( vertex @ SV702 )
= $false )
| ( ( path @ SV690 @ SV702 @ SV709 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3804]) ).
thf(3829,plain,
! [SV702: $i,SV709: $i,SV690: $i,SV765: $i] :
( ( ( edge @ SV765 )
= $false )
| ( ( SV690
= ( tail_of @ SV765 ) )
= $false )
| ( ( ! [SY1184: $i] :
( ( SV709
!= ( path_cons @ SV765 @ SY1184 ) )
| ~ ( path @ ( head_of @ SV765 ) @ SV702 @ SY1184 ) ) )
= $true )
| ( ( vertex @ SV690 )
= $false )
| ( ( vertex @ SV702 )
= $false )
| ( ( path @ SV690 @ SV702 @ SV709 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3805]) ).
thf(3830,plain,
! [SV787: $i,SV776: $i] :
( ( ( sequential @ SV776 @ SV787 )
= $false )
| ( ( edge @ SV776 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3809]) ).
thf(3831,plain,
! [SV784: $i,SV777: $i] :
( ( ( sequential @ SV777 @ SV784 )
= $false )
| ( ( edge @ SV784 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3810]) ).
thf(3832,plain,
! [SV715: $i,SV710: $i,SV746: $i,SV694: $i,SV757: $i,SV788: $i] :
( ( ( ~ ( precedes @ SV788 @ SV757 @ SV694 )
| ~ ( sequential @ SV746 @ SV788 ) )
= $true )
| ( ( on_path @ SV746 @ SV694 )
= $false )
| ( ( on_path @ SV757 @ SV694 )
= $false )
| ( ( precedes @ SV746 @ SV757 @ SV694 )
= $true )
| ( ( path @ SV710 @ SV715 @ SV694 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3811]) ).
thf(3833,plain,
! [SV715: $i,SV710: $i,SV694: $i,SV758: $i,SV747: $i] :
( ( ( sequential @ SV747 @ SV758 )
= $false )
| ( ( on_path @ SV747 @ SV694 )
= $false )
| ( ( on_path @ SV758 @ SV694 )
= $false )
| ( ( precedes @ SV747 @ SV758 @ SV694 )
= $true )
| ( ( path @ SV710 @ SV715 @ SV694 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3812]) ).
thf(3834,plain,
! [SV728: $i,SV722: $i,SV696: $i] :
( ( ( sequential @ SV696 @ SV722 )
= $false )
| ( ( edge @ SV722 )
= $false )
| ( ( edge @ SV696 )
= $false )
| ( ( edge @ SV728 )
= $false )
| ( ( ~ ( sequential @ SV722 @ SV728 ) )
= $true )
| ( ( ~ ( sequential @ SV728 @ SV696 ) )
= $true )
| ( ( triangle @ SV696 @ SV722 @ SV728 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3814]) ).
thf(3835,plain,
! [SV696: $i] :
( ( ~ ( ~ ( ! [SY1090: $i,SY1091: $i] :
~ ( triangle @ SV696 @ SY1090 @ SY1091 )
| ( edge @ SV696 ) )
| ~ ! [SY1092: $i] :
( ! [SY1093: $i] :
~ ( triangle @ SV696 @ SY1092 @ SY1093 )
| ( edge @ SY1092 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3815]) ).
thf(3836,plain,
! [SV696: $i] :
( ( ! [SY1094: $i,SY1095: $i] :
( ~ ( triangle @ SV696 @ SY1094 @ SY1095 )
| ( edge @ SY1095 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3816]) ).
thf(3837,plain,
! [SV789: $i,SV785: $i,SV696: $i] :
( ( ( ~ ( triangle @ SV696 @ SV785 @ SV789 ) )
= $true )
| ( ( sequential @ SV696 @ SV785 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3817]) ).
thf(3838,plain,
! [SV716: $i,SV711: $i,SV771: $i,SV697: $i,SV779: $i] :
( ( ( ! [SY1194: $i] :
( ~ ( precedes @ SY1194 @ SV779 @ SV697 )
| ~ ( sequential @ SV771 @ SY1194 ) ) )
= $true )
| ( ( ~ ( sequential @ SV771 @ SV779 ) )
= $true )
| ( ( precedes @ SV771 @ SV779 @ SV697 )
= $false )
| ( ( path @ SV711 @ SV716 @ SV697 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3820]) ).
thf(3839,plain,
! [SV716: $i,SV711: $i,SV697: $i,SV772: $i,SV780: $i] :
( ( ( ~ ( ~ ( precedes @ ( sK9_E3 @ SV780 @ SV772 @ SV697 ) @ SV780 @ SV697 )
| ~ ( sequential @ SV772 @ ( sK9_E3 @ SV780 @ SV772 @ SV697 ) ) ) )
= $true )
| ( ( sequential @ SV772 @ SV780 )
= $true )
| ( ( precedes @ SV772 @ SV780 @ SV697 )
= $false )
| ( ( path @ SV711 @ SV716 @ SV697 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3821]) ).
thf(3840,plain,
! [SV705: $i,SV698: $i,SV749: $i,SV712: $i,SV734: $i,SV781: $i] :
( ( ( ( head_of @ SV781 )
= ( head_of @ SV734 ) )
= $false )
| ( ( ( tail_of @ SV781 )
= ( tail_of @ SV712 ) )
= $false )
| ( ( precedes @ SV712 @ SV734 @ SV749 )
= $false )
| ( ( shortest_path @ SV698 @ SV705 @ SV749 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3822]) ).
thf(3841,plain,
! [SV713: $i,SV708: $i] :
( ( ( ( SV708
!= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
= $true )
| ( ( ( SV713
!= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
= $true )
| ( ( ( SV713
!= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
!= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
= $true )
| ( ( SV708 = SV713 )
= $true )
| ( ( vertex @ SV708 )
= $false )
| ( ( vertex @ SV713 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[3823]) ).
thf(3842,plain,
! [SV713: $i,SV708: $i] :
( ( ( ~ ~ ( ~ ( ( SV708
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
| ~ ( ( SV708
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) ) ) )
= $false )
| ( ( SV708 = SV713 )
= $true )
| ( ( vertex @ SV708 )
= $false )
| ( ( vertex @ SV713 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[3824]) ).
thf(3843,plain,
! [SV708: $i,SV713: $i] :
( ( ( ~ ~ ( ~ ( ( SV713
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
| ~ ( ( SV713
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) ) ) )
= $false )
| ( ( SV708 = SV713 )
= $true )
| ( ( vertex @ SV708 )
= $false )
| ( ( vertex @ SV713 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[3824]) ).
thf(3844,plain,
! [SV689: $i,SV723: $i,SV719: $i] :
( ( ( SV719
= ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
= $false )
| ( ( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ empty ) ) )
= $true )
| ( ( ! [SY1158: $i] :
( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ SY1158 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ SY1158 ) ) )
= $true )
| ( ( path @ SV689 @ SV719 @ SV723 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3825]) ).
thf(3845,plain,
! [SV689: $i,SV723: $i,SV719: $i] :
( ( ( ( SV719
= ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ ( sK13_SY84 @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ ( sK13_SY84 @ SV723 @ SV719 @ SV689 ) ) ) )
= $true )
| ( ( path @ SV689 @ SV719 @ SV723 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3826]) ).
thf(3846,plain,
! [SV689: $i,SV719: $i,SV723: $i] :
( ( ( ( SV723
= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ empty ) )
| ~ ( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ ( sK12_SY85 @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ ( sK12_SY85 @ SV723 @ SV719 @ SV689 ) ) ) )
= $true )
| ( ( path @ SV689 @ SV719 @ SV723 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3827]) ).
thf(3847,plain,
! [SV690: $i,SV709: $i,SV764: $i,SV702: $i] :
( ( ( ( SV702
!= ( head_of @ SV764 ) ) )
= $true )
| ( ( ( SV709
!= ( path_cons @ SV764 @ empty ) ) )
= $true )
| ( ( SV690
= ( tail_of @ SV764 ) )
= $false )
| ( ( edge @ SV764 )
= $false )
| ( ( vertex @ SV690 )
= $false )
| ( ( vertex @ SV702 )
= $false )
| ( ( path @ SV690 @ SV702 @ SV709 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3828]) ).
thf(3848,plain,
! [SV690: $i,SV702: $i,SV790: $i,SV765: $i,SV709: $i] :
( ( ( ( SV709
!= ( path_cons @ SV765 @ SV790 ) )
| ~ ( path @ ( head_of @ SV765 ) @ SV702 @ SV790 ) )
= $true )
| ( ( SV690
= ( tail_of @ SV765 ) )
= $false )
| ( ( edge @ SV765 )
= $false )
| ( ( vertex @ SV690 )
= $false )
| ( ( vertex @ SV702 )
= $false )
| ( ( path @ SV690 @ SV702 @ SV709 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3829]) ).
thf(3849,plain,
! [SV715: $i,SV710: $i,SV746: $i,SV694: $i,SV757: $i,SV788: $i] :
( ( ( ~ ( precedes @ SV788 @ SV757 @ SV694 ) )
= $true )
| ( ( ~ ( sequential @ SV746 @ SV788 ) )
= $true )
| ( ( on_path @ SV746 @ SV694 )
= $false )
| ( ( on_path @ SV757 @ SV694 )
= $false )
| ( ( precedes @ SV746 @ SV757 @ SV694 )
= $true )
| ( ( path @ SV710 @ SV715 @ SV694 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3832]) ).
thf(3850,plain,
! [SV696: $i,SV728: $i,SV722: $i] :
( ( ( sequential @ SV722 @ SV728 )
= $false )
| ( ( edge @ SV728 )
= $false )
| ( ( edge @ SV696 )
= $false )
| ( ( edge @ SV722 )
= $false )
| ( ( sequential @ SV696 @ SV722 )
= $false )
| ( ( ~ ( sequential @ SV728 @ SV696 ) )
= $true )
| ( ( triangle @ SV696 @ SV722 @ SV728 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3834]) ).
thf(3851,plain,
! [SV696: $i] :
( ( ~ ( ! [SY1090: $i,SY1091: $i] :
~ ( triangle @ SV696 @ SY1090 @ SY1091 )
| ( edge @ SV696 ) )
| ~ ! [SY1092: $i] :
( ! [SY1093: $i] :
~ ( triangle @ SV696 @ SY1092 @ SY1093 )
| ( edge @ SY1092 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3835]) ).
thf(3852,plain,
! [SV791: $i,SV696: $i] :
( ( ! [SY1196: $i] :
( ~ ( triangle @ SV696 @ SV791 @ SY1196 )
| ( edge @ SY1196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3836]) ).
thf(3853,plain,
! [SV789: $i,SV785: $i,SV696: $i] :
( ( ( triangle @ SV696 @ SV785 @ SV789 )
= $false )
| ( ( sequential @ SV696 @ SV785 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3837]) ).
thf(3854,plain,
! [SV716: $i,SV711: $i,SV771: $i,SV697: $i,SV779: $i,SV792: $i] :
( ( ( ~ ( precedes @ SV792 @ SV779 @ SV697 )
| ~ ( sequential @ SV771 @ SV792 ) )
= $true )
| ( ( ~ ( sequential @ SV771 @ SV779 ) )
= $true )
| ( ( precedes @ SV771 @ SV779 @ SV697 )
= $false )
| ( ( path @ SV711 @ SV716 @ SV697 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3838]) ).
thf(3855,plain,
! [SV716: $i,SV711: $i,SV697: $i,SV772: $i,SV780: $i] :
( ( ( ~ ( precedes @ ( sK9_E3 @ SV780 @ SV772 @ SV697 ) @ SV780 @ SV697 )
| ~ ( sequential @ SV772 @ ( sK9_E3 @ SV780 @ SV772 @ SV697 ) ) )
= $false )
| ( ( sequential @ SV772 @ SV780 )
= $true )
| ( ( precedes @ SV772 @ SV780 @ SV697 )
= $false )
| ( ( path @ SV711 @ SV716 @ SV697 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3839]) ).
thf(3856,plain,
! [SV713: $i,SV708: $i] :
( ( ( SV708
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
= $false )
| ( ( ( SV713
!= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
= $true )
| ( ( ( SV713
!= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
!= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
= $true )
| ( ( SV708 = SV713 )
= $true )
| ( ( vertex @ SV708 )
= $false )
| ( ( vertex @ SV713 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[3841]) ).
thf(3857,plain,
! [SV713: $i,SV708: $i] :
( ( ( ~ ( ~ ( ( SV708
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
| ~ ( ( SV708
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) ) ) )
= $true )
| ( ( SV708 = SV713 )
= $true )
| ( ( vertex @ SV708 )
= $false )
| ( ( vertex @ SV713 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[3842]) ).
thf(3858,plain,
! [SV708: $i,SV713: $i] :
( ( ( ~ ( ~ ( ( SV713
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
| ~ ( ( SV713
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) ) ) )
= $true )
| ( ( SV708 = SV713 )
= $true )
| ( ( vertex @ SV708 )
= $false )
| ( ( vertex @ SV713 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[3843]) ).
thf(3859,plain,
! [SV689: $i,SV719: $i,SV723: $i] :
( ( ( SV723
= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ empty ) )
= $false )
| ( ( SV719
= ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
= $false )
| ( ( ! [SY1158: $i] :
( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ SY1158 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ SY1158 ) ) )
= $true )
| ( ( path @ SV689 @ SV719 @ SV723 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3844]) ).
thf(3860,plain,
! [SV689: $i,SV723: $i,SV719: $i] :
( ( ( SV719
= ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
= $true )
| ( ( ~ ( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ ( sK13_SY84 @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ ( sK13_SY84 @ SV723 @ SV719 @ SV689 ) ) ) )
= $true )
| ( ( path @ SV689 @ SV719 @ SV723 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3845]) ).
thf(3861,plain,
! [SV689: $i,SV719: $i,SV723: $i] :
( ( ( SV723
= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ empty ) )
= $true )
| ( ( ~ ( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ ( sK12_SY85 @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ ( sK12_SY85 @ SV723 @ SV719 @ SV689 ) ) ) )
= $true )
| ( ( path @ SV689 @ SV719 @ SV723 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3846]) ).
thf(3862,plain,
! [SV690: $i,SV709: $i,SV764: $i,SV702: $i] :
( ( ( SV702
= ( head_of @ SV764 ) )
= $false )
| ( ( ( SV709
!= ( path_cons @ SV764 @ empty ) ) )
= $true )
| ( ( SV690
= ( tail_of @ SV764 ) )
= $false )
| ( ( edge @ SV764 )
= $false )
| ( ( vertex @ SV690 )
= $false )
| ( ( vertex @ SV702 )
= $false )
| ( ( path @ SV690 @ SV702 @ SV709 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3847]) ).
thf(3863,plain,
! [SV690: $i,SV702: $i,SV790: $i,SV765: $i,SV709: $i] :
( ( ( ( SV709
!= ( path_cons @ SV765 @ SV790 ) ) )
= $true )
| ( ( ~ ( path @ ( head_of @ SV765 ) @ SV702 @ SV790 ) )
= $true )
| ( ( SV690
= ( tail_of @ SV765 ) )
= $false )
| ( ( edge @ SV765 )
= $false )
| ( ( vertex @ SV690 )
= $false )
| ( ( vertex @ SV702 )
= $false )
| ( ( path @ SV690 @ SV702 @ SV709 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3848]) ).
thf(3864,plain,
! [SV715: $i,SV710: $i,SV746: $i,SV694: $i,SV757: $i,SV788: $i] :
( ( ( precedes @ SV788 @ SV757 @ SV694 )
= $false )
| ( ( ~ ( sequential @ SV746 @ SV788 ) )
= $true )
| ( ( on_path @ SV746 @ SV694 )
= $false )
| ( ( on_path @ SV757 @ SV694 )
= $false )
| ( ( precedes @ SV746 @ SV757 @ SV694 )
= $true )
| ( ( path @ SV710 @ SV715 @ SV694 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3849]) ).
thf(3865,plain,
! [SV722: $i,SV696: $i,SV728: $i] :
( ( ( sequential @ SV728 @ SV696 )
= $false )
| ( ( sequential @ SV696 @ SV722 )
= $false )
| ( ( edge @ SV722 )
= $false )
| ( ( edge @ SV696 )
= $false )
| ( ( edge @ SV728 )
= $false )
| ( ( sequential @ SV722 @ SV728 )
= $false )
| ( ( triangle @ SV696 @ SV722 @ SV728 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3850]) ).
thf(3866,plain,
! [SV696: $i] :
( ( ~ ( ! [SY1090: $i,SY1091: $i] :
~ ( triangle @ SV696 @ SY1090 @ SY1091 )
| ( edge @ SV696 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3851]) ).
thf(3867,plain,
! [SV696: $i] :
( ( ~ ! [SY1092: $i] :
( ! [SY1093: $i] :
~ ( triangle @ SV696 @ SY1092 @ SY1093 )
| ( edge @ SY1092 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3851]) ).
thf(3868,plain,
! [SV793: $i,SV791: $i,SV696: $i] :
( ( ~ ( triangle @ SV696 @ SV791 @ SV793 )
| ( edge @ SV793 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3852]) ).
thf(3869,plain,
! [SV716: $i,SV711: $i,SV771: $i,SV697: $i,SV779: $i,SV792: $i] :
( ( ( ~ ( precedes @ SV792 @ SV779 @ SV697 ) )
= $true )
| ( ( ~ ( sequential @ SV771 @ SV792 ) )
= $true )
| ( ( ~ ( sequential @ SV771 @ SV779 ) )
= $true )
| ( ( precedes @ SV771 @ SV779 @ SV697 )
= $false )
| ( ( path @ SV711 @ SV716 @ SV697 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3854]) ).
thf(3870,plain,
! [SV716: $i,SV711: $i,SV697: $i,SV772: $i,SV780: $i] :
( ( ( ~ ( precedes @ ( sK9_E3 @ SV780 @ SV772 @ SV697 ) @ SV780 @ SV697 ) )
= $false )
| ( ( sequential @ SV772 @ SV780 )
= $true )
| ( ( precedes @ SV772 @ SV780 @ SV697 )
= $false )
| ( ( path @ SV711 @ SV716 @ SV697 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3855]) ).
thf(3871,plain,
! [SV716: $i,SV711: $i,SV697: $i,SV780: $i,SV772: $i] :
( ( ( ~ ( sequential @ SV772 @ ( sK9_E3 @ SV780 @ SV772 @ SV697 ) ) )
= $false )
| ( ( sequential @ SV772 @ SV780 )
= $true )
| ( ( precedes @ SV772 @ SV780 @ SV697 )
= $false )
| ( ( path @ SV711 @ SV716 @ SV697 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3855]) ).
thf(3872,plain,
! [SV708: $i,SV713: $i] :
( ( ( SV713
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
= $false )
| ( ( SV708
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
= $false )
| ( ( ( SV713
!= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
!= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
= $true )
| ( ( SV708 = SV713 )
= $true )
| ( ( vertex @ SV708 )
= $false )
| ( ( vertex @ SV713 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[3856]) ).
thf(3873,plain,
! [SV713: $i,SV708: $i] :
( ( ( ~ ( ( SV708
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
| ~ ( ( SV708
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) ) )
= $false )
| ( ( SV708 = SV713 )
= $true )
| ( ( vertex @ SV708 )
= $false )
| ( ( vertex @ SV713 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[3857]) ).
thf(3874,plain,
! [SV708: $i,SV713: $i] :
( ( ( ~ ( ( SV713
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
| ~ ( ( SV713
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) ) )
= $false )
| ( ( SV708 = SV713 )
= $true )
| ( ( vertex @ SV708 )
= $false )
| ( ( vertex @ SV713 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[3858]) ).
thf(3875,plain,
! [SV794: $i,SV689: $i,SV719: $i,SV723: $i] :
( ( ( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ SV794 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ SV794 ) )
= $true )
| ( ( SV719
= ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
= $false )
| ( ( SV723
= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ empty ) )
= $false )
| ( ( path @ SV689 @ SV719 @ SV723 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3859]) ).
thf(3876,plain,
! [SV689: $i,SV719: $i,SV723: $i] :
( ( ( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ ( sK13_SY84 @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ ( sK13_SY84 @ SV723 @ SV719 @ SV689 ) ) )
= $false )
| ( ( SV719
= ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
= $true )
| ( ( path @ SV689 @ SV719 @ SV723 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3860]) ).
thf(3877,plain,
! [SV689: $i,SV719: $i,SV723: $i] :
( ( ( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ ( sK12_SY85 @ SV723 @ SV719 @ SV689 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ ( sK12_SY85 @ SV723 @ SV719 @ SV689 ) ) )
= $false )
| ( ( SV723
= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ empty ) )
= $true )
| ( ( path @ SV689 @ SV719 @ SV723 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3861]) ).
thf(3878,plain,
! [SV690: $i,SV702: $i,SV764: $i,SV709: $i] :
( ( ( SV709
= ( path_cons @ SV764 @ empty ) )
= $false )
| ( ( SV702
= ( head_of @ SV764 ) )
= $false )
| ( ( SV690
= ( tail_of @ SV764 ) )
= $false )
| ( ( edge @ SV764 )
= $false )
| ( ( vertex @ SV690 )
= $false )
| ( ( vertex @ SV702 )
= $false )
| ( ( path @ SV690 @ SV702 @ SV709 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3862]) ).
thf(3879,plain,
! [SV690: $i,SV702: $i,SV790: $i,SV765: $i,SV709: $i] :
( ( ( SV709
= ( path_cons @ SV765 @ SV790 ) )
= $false )
| ( ( ~ ( path @ ( head_of @ SV765 ) @ SV702 @ SV790 ) )
= $true )
| ( ( SV690
= ( tail_of @ SV765 ) )
= $false )
| ( ( edge @ SV765 )
= $false )
| ( ( vertex @ SV690 )
= $false )
| ( ( vertex @ SV702 )
= $false )
| ( ( path @ SV690 @ SV702 @ SV709 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3863]) ).
thf(3880,plain,
! [SV715: $i,SV710: $i,SV694: $i,SV757: $i,SV788: $i,SV746: $i] :
( ( ( sequential @ SV746 @ SV788 )
= $false )
| ( ( precedes @ SV788 @ SV757 @ SV694 )
= $false )
| ( ( on_path @ SV746 @ SV694 )
= $false )
| ( ( on_path @ SV757 @ SV694 )
= $false )
| ( ( precedes @ SV746 @ SV757 @ SV694 )
= $true )
| ( ( path @ SV710 @ SV715 @ SV694 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3864]) ).
thf(3881,plain,
! [SV696: $i] :
( ( ! [SY1090: $i,SY1091: $i] :
~ ( triangle @ SV696 @ SY1090 @ SY1091 )
| ( edge @ SV696 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3866]) ).
thf(3882,plain,
! [SV696: $i] :
( ( ! [SY1092: $i] :
( ! [SY1093: $i] :
~ ( triangle @ SV696 @ SY1092 @ SY1093 )
| ( edge @ SY1092 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3867]) ).
thf(3883,plain,
! [SV793: $i,SV791: $i,SV696: $i] :
( ( ( ~ ( triangle @ SV696 @ SV791 @ SV793 ) )
= $true )
| ( ( edge @ SV793 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3868]) ).
thf(3884,plain,
! [SV716: $i,SV711: $i,SV771: $i,SV697: $i,SV779: $i,SV792: $i] :
( ( ( precedes @ SV792 @ SV779 @ SV697 )
= $false )
| ( ( ~ ( sequential @ SV771 @ SV792 ) )
= $true )
| ( ( ~ ( sequential @ SV771 @ SV779 ) )
= $true )
| ( ( precedes @ SV771 @ SV779 @ SV697 )
= $false )
| ( ( path @ SV711 @ SV716 @ SV697 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3869]) ).
thf(3885,plain,
! [SV716: $i,SV711: $i,SV697: $i,SV772: $i,SV780: $i] :
( ( ( precedes @ ( sK9_E3 @ SV780 @ SV772 @ SV697 ) @ SV780 @ SV697 )
= $true )
| ( ( sequential @ SV772 @ SV780 )
= $true )
| ( ( precedes @ SV772 @ SV780 @ SV697 )
= $false )
| ( ( path @ SV711 @ SV716 @ SV697 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3870]) ).
thf(3886,plain,
! [SV716: $i,SV711: $i,SV697: $i,SV780: $i,SV772: $i] :
( ( ( sequential @ SV772 @ ( sK9_E3 @ SV780 @ SV772 @ SV697 ) )
= $true )
| ( ( sequential @ SV772 @ SV780 )
= $true )
| ( ( precedes @ SV772 @ SV780 @ SV697 )
= $false )
| ( ( path @ SV711 @ SV716 @ SV697 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3871]) ).
thf(3887,plain,
! [SV708: $i,SV713: $i] :
( ( ( ( SV713
!= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
= $true )
| ( ( ( SV708
!= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
= $true )
| ( ( SV708
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
= $false )
| ( ( SV713
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
= $false )
| ( ( SV708 = SV713 )
= $true )
| ( ( vertex @ SV708 )
= $false )
| ( ( vertex @ SV713 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[3872]) ).
thf(3888,plain,
! [SV713: $i,SV708: $i] :
( ( ( ~ ( ( SV708
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) ) ) )
= $false )
| ( ( SV708 = SV713 )
= $true )
| ( ( vertex @ SV708 )
= $false )
| ( ( vertex @ SV713 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[3873]) ).
thf(3889,plain,
! [SV713: $i,SV708: $i] :
( ( ( ~ ( ( SV708
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) ) )
= $false )
| ( ( SV708 = SV713 )
= $true )
| ( ( vertex @ SV708 )
= $false )
| ( ( vertex @ SV713 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[3873]) ).
thf(3890,plain,
! [SV708: $i,SV713: $i] :
( ( ( ~ ( ( SV713
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) ) ) )
= $false )
| ( ( SV708 = SV713 )
= $true )
| ( ( vertex @ SV708 )
= $false )
| ( ( vertex @ SV713 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[3874]) ).
thf(3891,plain,
! [SV708: $i,SV713: $i] :
( ( ( ~ ( ( SV713
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) ) )
= $false )
| ( ( SV708 = SV713 )
= $true )
| ( ( vertex @ SV708 )
= $false )
| ( ( vertex @ SV713 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[3874]) ).
thf(3892,plain,
! [SV794: $i,SV689: $i,SV719: $i,SV723: $i] :
( ( ( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ SV794 ) ) )
= $true )
| ( ( ~ ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ SV794 ) )
= $true )
| ( ( SV719
= ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
= $false )
| ( ( SV723
= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ empty ) )
= $false )
| ( ( path @ SV689 @ SV719 @ SV723 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3875]) ).
thf(3893,plain,
! [SV689: $i,SV719: $i,SV723: $i] :
( ( ( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ ( sK13_SY84 @ SV723 @ SV719 @ SV689 ) ) ) )
= $false )
| ( ( SV719
= ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
= $true )
| ( ( path @ SV689 @ SV719 @ SV723 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3876]) ).
thf(3894,plain,
! [SV689: $i,SV719: $i,SV723: $i] :
( ( ( ~ ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ ( sK13_SY84 @ SV723 @ SV719 @ SV689 ) ) )
= $false )
| ( ( SV719
= ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
= $true )
| ( ( path @ SV689 @ SV719 @ SV723 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3876]) ).
thf(3895,plain,
! [SV689: $i,SV719: $i,SV723: $i] :
( ( ( ( SV723
!= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ ( sK12_SY85 @ SV723 @ SV719 @ SV689 ) ) ) )
= $false )
| ( ( SV723
= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ empty ) )
= $true )
| ( ( path @ SV689 @ SV719 @ SV723 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3877]) ).
thf(3896,plain,
! [SV689: $i,SV719: $i,SV723: $i] :
( ( ( ~ ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ ( sK12_SY85 @ SV723 @ SV719 @ SV689 ) ) )
= $false )
| ( ( SV723
= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ empty ) )
= $true )
| ( ( path @ SV689 @ SV719 @ SV723 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3877]) ).
thf(3897,plain,
! [SV690: $i,SV709: $i,SV790: $i,SV702: $i,SV765: $i] :
( ( ( path @ ( head_of @ SV765 ) @ SV702 @ SV790 )
= $false )
| ( ( SV709
= ( path_cons @ SV765 @ SV790 ) )
= $false )
| ( ( SV690
= ( tail_of @ SV765 ) )
= $false )
| ( ( edge @ SV765 )
= $false )
| ( ( vertex @ SV690 )
= $false )
| ( ( vertex @ SV702 )
= $false )
| ( ( path @ SV690 @ SV702 @ SV709 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3879]) ).
thf(3898,plain,
! [SV696: $i] :
( ( ( ! [SY1090: $i,SY1091: $i] :
~ ( triangle @ SV696 @ SY1090 @ SY1091 ) )
= $true )
| ( ( edge @ SV696 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3881]) ).
thf(3899,plain,
! [SV795: $i,SV696: $i] :
( ( ! [SY1197: $i] :
~ ( triangle @ SV696 @ SV795 @ SY1197 )
| ( edge @ SV795 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3882]) ).
thf(3900,plain,
! [SV793: $i,SV791: $i,SV696: $i] :
( ( ( triangle @ SV696 @ SV791 @ SV793 )
= $false )
| ( ( edge @ SV793 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3883]) ).
thf(3901,plain,
! [SV716: $i,SV711: $i,SV697: $i,SV779: $i,SV792: $i,SV771: $i] :
( ( ( sequential @ SV771 @ SV792 )
= $false )
| ( ( precedes @ SV792 @ SV779 @ SV697 )
= $false )
| ( ( ~ ( sequential @ SV771 @ SV779 ) )
= $true )
| ( ( precedes @ SV771 @ SV779 @ SV697 )
= $false )
| ( ( path @ SV711 @ SV716 @ SV697 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3884]) ).
thf(3902,plain,
! [SV708: $i,SV713: $i] :
( ( ( SV713
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
= $false )
| ( ( ( SV708
!= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
= $true )
| ( ( SV708
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
= $false )
| ( ( SV713
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
= $false )
| ( ( SV708 = SV713 )
= $true )
| ( ( vertex @ SV708 )
= $false )
| ( ( vertex @ SV713 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[3887]) ).
thf(3903,plain,
! [SV713: $i,SV708: $i] :
( ( ( ( SV708
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
= $true )
| ( ( SV708 = SV713 )
= $true )
| ( ( vertex @ SV708 )
= $false )
| ( ( vertex @ SV713 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[3888]) ).
thf(3904,plain,
! [SV713: $i,SV708: $i] :
( ( ( ( SV708
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
= $true )
| ( ( SV708 = SV713 )
= $true )
| ( ( vertex @ SV708 )
= $false )
| ( ( vertex @ SV713 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[3889]) ).
thf(3905,plain,
! [SV708: $i,SV713: $i] :
( ( ( ( SV713
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV713
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
= $true )
| ( ( SV708 = SV713 )
= $true )
| ( ( vertex @ SV708 )
= $false )
| ( ( vertex @ SV713 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[3890]) ).
thf(3906,plain,
! [SV708: $i,SV713: $i] :
( ( ( ( SV713
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
| ( SV708
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) ) )
= $true )
| ( ( SV708 = SV713 )
= $true )
| ( ( vertex @ SV708 )
= $false )
| ( ( vertex @ SV713 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[3891]) ).
thf(3907,plain,
! [SV794: $i,SV689: $i,SV719: $i,SV723: $i] :
( ( ( SV723
= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ SV794 ) )
= $false )
| ( ( ~ ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ SV794 ) )
= $true )
| ( ( SV719
= ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
= $false )
| ( ( SV723
= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ empty ) )
= $false )
| ( ( path @ SV689 @ SV719 @ SV723 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3892]) ).
thf(3908,plain,
! [SV689: $i,SV719: $i,SV723: $i] :
( ( ( SV723
= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ ( sK13_SY84 @ SV723 @ SV719 @ SV689 ) ) )
= $true )
| ( ( SV719
= ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
= $true )
| ( ( path @ SV689 @ SV719 @ SV723 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3893]) ).
thf(3909,plain,
! [SV689: $i,SV719: $i,SV723: $i] :
( ( ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ ( sK13_SY84 @ SV723 @ SV719 @ SV689 ) )
= $true )
| ( ( SV719
= ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
= $true )
| ( ( path @ SV689 @ SV719 @ SV723 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3894]) ).
thf(3910,plain,
! [SV689: $i,SV719: $i,SV723: $i] :
( ( ( SV723
= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ ( sK12_SY85 @ SV723 @ SV719 @ SV689 ) ) )
= $true )
| ( ( SV723
= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ empty ) )
= $true )
| ( ( path @ SV689 @ SV719 @ SV723 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3895]) ).
thf(3911,plain,
! [SV689: $i,SV719: $i,SV723: $i] :
( ( ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ ( sK12_SY85 @ SV723 @ SV719 @ SV689 ) )
= $true )
| ( ( SV723
= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ empty ) )
= $true )
| ( ( path @ SV689 @ SV719 @ SV723 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3896]) ).
thf(3912,plain,
! [SV796: $i,SV696: $i] :
( ( ( ! [SY1198: $i] :
~ ( triangle @ SV696 @ SV796 @ SY1198 ) )
= $true )
| ( ( edge @ SV696 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3898]) ).
thf(3913,plain,
! [SV795: $i,SV696: $i] :
( ( ( ! [SY1197: $i] :
~ ( triangle @ SV696 @ SV795 @ SY1197 ) )
= $true )
| ( ( edge @ SV795 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3899]) ).
thf(3914,plain,
! [SV716: $i,SV711: $i,SV697: $i,SV792: $i,SV779: $i,SV771: $i] :
( ( ( sequential @ SV771 @ SV779 )
= $false )
| ( ( precedes @ SV792 @ SV779 @ SV697 )
= $false )
| ( ( sequential @ SV771 @ SV792 )
= $false )
| ( ( precedes @ SV771 @ SV779 @ SV697 )
= $false )
| ( ( path @ SV711 @ SV716 @ SV697 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3901]) ).
thf(3915,plain,
! [SV713: $i,SV708: $i] :
( ( ( SV708
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
= $false )
| ( ( SV713
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
= $false )
| ( ( SV708
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
= $false )
| ( ( SV713
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
= $false )
| ( ( SV708 = SV713 )
= $true )
| ( ( vertex @ SV708 )
= $false )
| ( ( vertex @ SV713 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[3902]) ).
thf(3916,plain,
! [SV713: $i,SV708: $i] :
( ( ( SV708
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
= $true )
| ( ( SV713
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
= $true )
| ( ( SV708 = SV713 )
= $true )
| ( ( vertex @ SV708 )
= $false )
| ( ( vertex @ SV713 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[3903]) ).
thf(3917,plain,
! [SV713: $i,SV708: $i] :
( ( ( SV708
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
= $true )
| ( ( SV708
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
= $true )
| ( ( SV708 = SV713 )
= $true )
| ( ( vertex @ SV708 )
= $false )
| ( ( vertex @ SV713 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[3904]) ).
thf(3918,plain,
! [SV708: $i,SV713: $i] :
( ( ( SV713
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
= $true )
| ( ( SV713
= ( head_of @ ( sK14_E @ SV713 @ SV708 ) ) )
= $true )
| ( ( SV708 = SV713 )
= $true )
| ( ( vertex @ SV708 )
= $false )
| ( ( vertex @ SV713 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[3905]) ).
thf(3919,plain,
! [SV708: $i,SV713: $i] :
( ( ( SV713
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
= $true )
| ( ( SV708
= ( tail_of @ ( sK14_E @ SV713 @ SV708 ) ) )
= $true )
| ( ( SV708 = SV713 )
= $true )
| ( ( vertex @ SV708 )
= $false )
| ( ( vertex @ SV713 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[3906]) ).
thf(3920,plain,
! [SV794: $i,SV689: $i,SV719: $i,SV723: $i] :
( ( ( path @ ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) @ SV719 @ SV794 )
= $false )
| ( ( SV723
= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ SV794 ) )
= $false )
| ( ( SV719
= ( head_of @ ( sK11_E @ SV723 @ SV719 @ SV689 ) ) )
= $false )
| ( ( SV723
= ( path_cons @ ( sK11_E @ SV723 @ SV719 @ SV689 ) @ empty ) )
= $false )
| ( ( path @ SV689 @ SV719 @ SV723 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3907]) ).
thf(3921,plain,
! [SV797: $i,SV796: $i,SV696: $i] :
( ( ( ~ ( triangle @ SV696 @ SV796 @ SV797 ) )
= $true )
| ( ( edge @ SV696 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3912]) ).
thf(3922,plain,
! [SV798: $i,SV795: $i,SV696: $i] :
( ( ( ~ ( triangle @ SV696 @ SV795 @ SV798 ) )
= $true )
| ( ( edge @ SV795 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3913]) ).
thf(3923,plain,
! [SV797: $i,SV796: $i,SV696: $i] :
( ( ( triangle @ SV696 @ SV796 @ SV797 )
= $false )
| ( ( edge @ SV696 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3921]) ).
thf(3924,plain,
! [SV798: $i,SV795: $i,SV696: $i] :
( ( ( triangle @ SV696 @ SV795 @ SV798 )
= $false )
| ( ( edge @ SV795 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3922]) ).
thf(3925,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[3393,3924,3923,3920,3919,3918,3917,3916,3915,3914,3911,3910,3909,3908,3900,3897,3886,3885,3880,3878,3865,3853,3840,3833,3831,3830,3819,3818,3813,3808,3807,3806,3794,3789,3784,3783,3782,3779,3777,3776,3771,3770,3767,3742,3718,3715,3703,3695,3691,3683,3680,3667,3666,3649,3538,3537,3491,3490,3467,3430,3413,3394]) ).
thf(3926,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[3925,627,1177,1726,2276,2826,3375]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRA003+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.11/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue May 31 02:40:40 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.38
% 0.12/0.38 No.of.Axioms: 17
% 0.12/0.38
% 0.12/0.38 Length.of.Defs: 0
% 0.12/0.38
% 0.12/0.38 Contains.Choice.Funs: false
% 0.18/0.42 .
% 0.18/0.42 (rf:0,axioms:17,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:19,loop_count:0,foatp_calls:0,translation:fof_full)........................................................................................................................................................................................................................................................................................
% 1.81/1.99
% 1.81/1.99 ********************************
% 1.81/1.99 * All subproblems solved! *
% 1.81/1.99 ********************************
% 1.81/1.99 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:19,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:73,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:3925,loop_count:0,foatp_calls:1,translation:fof_full)
% 7.45/7.65
% 7.45/7.65 %**** Beginning of derivation protocol ****
% 7.45/7.65 % SZS output start CNFRefutation
% See solution above
% 7.45/7.67
% 7.45/7.67 %**** End of derivation protocol ****
% 7.45/7.67 %**** no. of clauses in derivation: 3926 ****
% 7.45/7.67 %**** clause counter: 3925 ****
% 7.45/7.67
% 7.45/7.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:19,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:73,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:3925,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------