TSTP Solution File: GRA004+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GRA004+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 : n017.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 07:19:15 EDT 2022
% Result : Theorem 1.24s 1.48s
% Output : CNFRefutation 2.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 56
% Syntax : Number of formulae : 1762 ( 669 unt; 38 typ; 0 def)
% Number of atoms : 17756 (6842 equ; 0 cnn)
% Maximal formula atoms : 9 ( 10 avg)
% Number of connectives : 41283 (8146 ~;7329 |; 299 &;25453 @)
% ( 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 : 41 ( 38 usr; 15 con; 0-4 aty)
% Number of variables : 7307 ( 0 ^7276 !; 31 ?;7307 :)
% 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_E3,type,
sK10_E3: $i > $i > $i > $i ).
thf(tp_sK11_E,type,
sK11_E: $i > $i > $i > $i > $i ).
thf(tp_sK12_E,type,
sK12_E: $i > $i > $i > $i ).
thf(tp_sK13_SY91,type,
sK13_SY91: $i > $i > $i > $i ).
thf(tp_sK14_SY90,type,
sK14_SY90: $i > $i > $i > $i ).
thf(tp_sK15_E,type,
sK15_E: $i > $i > $i ).
thf(tp_sK1_V1,type,
sK1_V1: $i ).
thf(tp_sK2_SY71,type,
sK2_SY71: $i ).
thf(tp_sK3_SY76,type,
sK3_SY76: $i ).
thf(tp_sK4_SY80,type,
sK4_SY80: $i ).
thf(tp_sK5_SY83,type,
sK5_SY83: $i ).
thf(tp_sK6_SY84,type,
sK6_SY84: $i ).
thf(tp_sK7_E1,type,
sK7_E1: $i > $i ).
thf(tp_sK8_SY86,type,
sK8_SY86: $i > $i ).
thf(tp_sK9_P,type,
sK9_P: $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 ) )
=> ( ~ ? [E3: $i] :
( ( ( tail_of @ E3 )
= ( tail_of @ E1 ) )
& ( ( head_of @ E3 )
= ( head_of @ E2 ) ) )
& ( ( head_of @ E2 )
!= ( tail_of @ E1 ) )
& ( ( head_of @ E2 )
!= ( head_of @ E1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',shortest_path_properties_lemma) ).
thf(19,negated_conjecture,
( ( ! [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 ) ) )
& ( ( head_of @ E2 )
!= ( tail_of @ E1 ) )
& ( ( head_of @ E2 )
!= ( head_of @ E1 ) ) ) ) )
= $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 ) )
=> ( ~ ? [E3: $i] :
( ( ( tail_of @ E3 )
= ( tail_of @ E1 ) )
& ( ( head_of @ E3 )
= ( head_of @ E2 ) ) )
& ( ( head_of @ E2 )
!= ( tail_of @ E1 ) )
& ( ( head_of @ E2 )
!= ( head_of @ E1 ) ) ) ) )
= $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,
( ( ! [SY71: $i,SY72: $i,SY73: $i,SY74: $i] :
( ( ( shortest_path @ sK1_V1 @ SY71 @ SY74 )
& ( precedes @ SY72 @ SY73 @ SY74 ) )
=> ( ~ ? [E3: $i] :
( ( ( tail_of @ E3 )
= ( tail_of @ SY72 ) )
& ( ( head_of @ E3 )
= ( head_of @ SY73 ) ) )
& ( ( head_of @ SY73 )
!= ( tail_of @ SY72 ) )
& ( ( head_of @ SY73 )
!= ( head_of @ SY72 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[20]) ).
thf(39,plain,
( ( ! [SY76: $i,SY77: $i,SY78: $i] :
( ( ( shortest_path @ sK1_V1 @ sK2_SY71 @ SY78 )
& ( precedes @ SY76 @ SY77 @ SY78 ) )
=> ( ~ ? [E3: $i] :
( ( ( tail_of @ E3 )
= ( tail_of @ SY76 ) )
& ( ( head_of @ E3 )
= ( head_of @ SY77 ) ) )
& ( ( head_of @ SY77 )
!= ( tail_of @ SY76 ) )
& ( ( head_of @ SY77 )
!= ( head_of @ SY76 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[38]) ).
thf(40,plain,
( ( ! [SY80: $i,SY81: $i] :
( ( ( shortest_path @ sK1_V1 @ sK2_SY71 @ SY81 )
& ( precedes @ sK3_SY76 @ SY80 @ SY81 ) )
=> ( ~ ? [SY82: $i] :
( ( ( tail_of @ SY82 )
= ( tail_of @ sK3_SY76 ) )
& ( ( head_of @ SY82 )
= ( head_of @ SY80 ) ) )
& ( ( head_of @ SY80 )
!= ( tail_of @ sK3_SY76 ) )
& ( ( head_of @ SY80 )
!= ( head_of @ sK3_SY76 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[39]) ).
thf(41,plain,
( ( ! [SY83: $i] :
( ( ( shortest_path @ sK1_V1 @ sK2_SY71 @ SY83 )
& ( precedes @ sK3_SY76 @ sK4_SY80 @ SY83 ) )
=> ( ~ ? [SY84: $i] :
( ( ( tail_of @ SY84 )
= ( tail_of @ sK3_SY76 ) )
& ( ( head_of @ SY84 )
= ( head_of @ sK4_SY80 ) ) )
& ( ( head_of @ sK4_SY80 )
!= ( tail_of @ sK3_SY76 ) )
& ( ( head_of @ sK4_SY80 )
!= ( head_of @ sK3_SY76 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[40]) ).
thf(42,plain,
( ( ( ( shortest_path @ sK1_V1 @ sK2_SY71 @ sK5_SY83 )
& ( precedes @ sK3_SY76 @ sK4_SY80 @ sK5_SY83 ) )
=> ( ~ ? [SY84: $i] :
( ( ( tail_of @ SY84 )
= ( tail_of @ sK3_SY76 ) )
& ( ( head_of @ SY84 )
= ( head_of @ sK4_SY80 ) ) )
& ( ( head_of @ sK4_SY80 )
!= ( tail_of @ sK3_SY76 ) )
& ( ( head_of @ sK4_SY80 )
!= ( head_of @ sK3_SY76 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[41]) ).
thf(43,plain,
( ( shortest_path @ sK1_V1 @ sK2_SY71 @ sK5_SY83 )
= $true ),
inference(standard_cnf,[status(thm)],[42]) ).
thf(44,plain,
( ( precedes @ sK3_SY76 @ sK4_SY80 @ sK5_SY83 )
= $true ),
inference(standard_cnf,[status(thm)],[42]) ).
thf(45,plain,
( ( ~ ? [SY84: $i] :
( ( ( tail_of @ SY84 )
= ( tail_of @ sK3_SY76 ) )
& ( ( head_of @ SY84 )
= ( head_of @ sK4_SY80 ) ) )
& ( ( head_of @ sK4_SY80 )
!= ( tail_of @ sK3_SY76 ) )
& ( ( head_of @ sK4_SY80 )
!= ( head_of @ sK3_SY76 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[42]) ).
thf(46,plain,
( ( ~ ? [SY84: $i] :
( ( ( tail_of @ SY84 )
= ( tail_of @ sK3_SY76 ) )
& ( ( head_of @ SY84 )
= ( head_of @ sK4_SY80 ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[45]) ).
thf(47,plain,
( ( ( ( head_of @ sK4_SY80 )
!= ( tail_of @ sK3_SY76 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[45]) ).
thf(48,plain,
( ( ( ( head_of @ sK4_SY80 )
!= ( head_of @ sK3_SY76 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[45]) ).
thf(49,plain,
( ( ? [SY84: $i] :
( ( ( tail_of @ SY84 )
= ( tail_of @ sK3_SY76 ) )
& ( ( head_of @ SY84 )
= ( head_of @ sK4_SY80 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[46]) ).
thf(50,plain,
( ( ~ ( ( ( head_of @ sK4_SY80 )
!= ( tail_of @ sK3_SY76 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[47]) ).
thf(51,plain,
( ( ~ ( ( ( head_of @ sK4_SY80 )
!= ( head_of @ sK3_SY76 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[48]) ).
thf(52,plain,
( ( ( ( tail_of @ sK6_SY84 )
= ( tail_of @ sK3_SY76 ) )
& ( ( head_of @ sK6_SY84 )
= ( head_of @ sK4_SY80 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[49]) ).
thf(53,plain,
( ( ( head_of @ sK4_SY80 )
= ( tail_of @ sK3_SY76 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[50]) ).
thf(54,plain,
( ( ( head_of @ sK4_SY80 )
= ( head_of @ sK3_SY76 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[51]) ).
thf(55,plain,
( ( ! [P: $i] :
( ( ( on_path @ ( sK7_E1 @ P ) @ P )
& ( on_path @ ( sK8_SY86 @ P ) @ P )
& ( sequential @ ( sK7_E1 @ P ) @ ( sK8_SY86 @ P ) )
& ! [SY88: $i] :
~ ( triangle @ ( sK7_E1 @ P ) @ ( sK8_SY86 @ P ) @ SY88 ) )
| ! [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(56,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(57,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(58,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(59,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(60,plain,
( ( ! [V1: $i] :
( ! [V2: $i,SP: $i] :
( ( ( path @ V1 @ V2 @ ( sK9_P @ SP @ V2 @ V1 ) )
& ~ ( less_or_equal @ ( length_of @ SP ) @ ( length_of @ ( sK9_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(61,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 @ ( sK10_E3 @ E2 @ E1 @ P ) @ E2 @ P )
& ( sequential @ E1 @ ( sK10_E3 @ E2 @ E1 @ P ) ) )
| ( sequential @ E1 @ E2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[28]) ).
thf(62,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(63,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(64,plain,
( ( ! [V1: $i,V2: $i] :
( ! [P: $i,V: $i] :
( ~ ( in_path @ V @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( ( on_path @ ( sK11_E @ V @ P @ V2 @ V1 ) @ P )
& ( ( V
= ( head_of @ ( sK11_E @ V @ P @ V2 @ V1 ) ) )
| ( V
= ( tail_of @ ( sK11_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(65,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(66,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 @ ( sK12_E @ P @ V2 @ V1 ) ) )
& ( edge @ ( sK12_E @ P @ V2 @ V1 ) )
& ( ( V2
!= ( head_of @ ( sK12_E @ P @ V2 @ V1 ) ) )
| ( P
!= ( path_cons @ ( sK12_E @ P @ V2 @ V1 ) @ empty ) )
| ! [SY89: $i] :
( ( P
!= ( path_cons @ ( sK12_E @ P @ V2 @ V1 ) @ SY89 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ P @ V2 @ V1 ) ) @ V2 @ SY89 ) ) )
& ( ( V2
= ( head_of @ ( sK12_E @ P @ V2 @ V1 ) ) )
| ( ( P
= ( path_cons @ ( sK12_E @ P @ V2 @ V1 ) @ ( sK14_SY90 @ P @ V2 @ V1 ) ) )
& ( path @ ( head_of @ ( sK12_E @ P @ V2 @ V1 ) ) @ V2 @ ( sK14_SY90 @ P @ V2 @ V1 ) ) ) )
& ( ( P
= ( path_cons @ ( sK12_E @ P @ V2 @ V1 ) @ empty ) )
| ( ( P
= ( path_cons @ ( sK12_E @ P @ V2 @ V1 ) @ ( sK13_SY91 @ P @ V2 @ V1 ) ) )
& ( path @ ( head_of @ ( sK12_E @ P @ V2 @ V1 ) ) @ V2 @ ( sK13_SY91 @ P @ V2 @ V1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[33]) ).
thf(67,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(68,plain,
( ( ~ complete
| ! [V1: $i,V2: $i] :
( ( V1 = V2 )
| ~ ( vertex @ V1 )
| ~ ( vertex @ V2 )
| ( ( ( V1
!= ( head_of @ ( sK15_E @ V2 @ V1 ) ) )
| ( V2
!= ( tail_of @ ( sK15_E @ V2 @ V1 ) ) )
| ( V2
!= ( head_of @ ( sK15_E @ V2 @ V1 ) ) )
| ( V1
!= ( tail_of @ ( sK15_E @ V2 @ V1 ) ) ) )
& ( ( V1
= ( head_of @ ( sK15_E @ V2 @ V1 ) ) )
| ( V2
= ( head_of @ ( sK15_E @ V2 @ V1 ) ) ) )
& ( ( V1
= ( head_of @ ( sK15_E @ V2 @ V1 ) ) )
| ( V1
= ( tail_of @ ( sK15_E @ V2 @ V1 ) ) ) )
& ( ( V2
= ( tail_of @ ( sK15_E @ V2 @ V1 ) ) )
| ( V2
= ( head_of @ ( sK15_E @ V2 @ V1 ) ) ) )
& ( ( V2
= ( tail_of @ ( sK15_E @ V2 @ V1 ) ) )
| ( V1
= ( tail_of @ ( sK15_E @ V2 @ V1 ) ) ) )
& ( edge @ ( sK15_E @ V2 @ V1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[35]) ).
thf(69,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(70,plain,
( ( ! [E: $i] :
( ~ ( edge @ E )
| ( ( head_of @ E )
!= ( tail_of @ E ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[37]) ).
thf(71,plain,
( ( ! [E: $i] :
( ~ ( edge @ E )
| ( ( head_of @ E )
!= ( tail_of @ E ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(72,plain,
( ( ! [E: $i] :
( ~ ( edge @ E )
| ( vertex @ ( head_of @ E ) ) )
& ! [E: $i] :
( ~ ( edge @ E )
| ( vertex @ ( tail_of @ E ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(73,plain,
( ( ~ complete
| ! [V1: $i,V2: $i] :
( ( V1 = V2 )
| ~ ( vertex @ V1 )
| ~ ( vertex @ V2 )
| ( ( ( V1
!= ( head_of @ ( sK15_E @ V2 @ V1 ) ) )
| ( V2
!= ( tail_of @ ( sK15_E @ V2 @ V1 ) ) )
| ( V2
!= ( head_of @ ( sK15_E @ V2 @ V1 ) ) )
| ( V1
!= ( tail_of @ ( sK15_E @ V2 @ V1 ) ) ) )
& ( ( V1
= ( head_of @ ( sK15_E @ V2 @ V1 ) ) )
| ( V2
= ( head_of @ ( sK15_E @ V2 @ V1 ) ) ) )
& ( ( V1
= ( head_of @ ( sK15_E @ V2 @ V1 ) ) )
| ( V1
= ( tail_of @ ( sK15_E @ V2 @ V1 ) ) ) )
& ( ( V2
= ( tail_of @ ( sK15_E @ V2 @ V1 ) ) )
| ( V2
= ( head_of @ ( sK15_E @ V2 @ V1 ) ) ) )
& ( ( V2
= ( tail_of @ ( sK15_E @ V2 @ V1 ) ) )
| ( V1
= ( tail_of @ ( sK15_E @ V2 @ V1 ) ) ) )
& ( edge @ ( sK15_E @ V2 @ V1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
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(copy,[status(thm)],[67]) ).
thf(75,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 @ ( sK12_E @ P @ V2 @ V1 ) ) )
& ( edge @ ( sK12_E @ P @ V2 @ V1 ) )
& ( ( V2
!= ( head_of @ ( sK12_E @ P @ V2 @ V1 ) ) )
| ( P
!= ( path_cons @ ( sK12_E @ P @ V2 @ V1 ) @ empty ) )
| ! [SY89: $i] :
( ( P
!= ( path_cons @ ( sK12_E @ P @ V2 @ V1 ) @ SY89 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ P @ V2 @ V1 ) ) @ V2 @ SY89 ) ) )
& ( ( V2
= ( head_of @ ( sK12_E @ P @ V2 @ V1 ) ) )
| ( ( P
= ( path_cons @ ( sK12_E @ P @ V2 @ V1 ) @ ( sK14_SY90 @ P @ V2 @ V1 ) ) )
& ( path @ ( head_of @ ( sK12_E @ P @ V2 @ V1 ) ) @ V2 @ ( sK14_SY90 @ P @ V2 @ V1 ) ) ) )
& ( ( P
= ( path_cons @ ( sK12_E @ P @ V2 @ V1 ) @ empty ) )
| ( ( P
= ( path_cons @ ( sK12_E @ P @ V2 @ V1 ) @ ( sK13_SY91 @ P @ V2 @ V1 ) ) )
& ( path @ ( head_of @ ( sK12_E @ P @ V2 @ V1 ) ) @ V2 @ ( sK13_SY91 @ P @ V2 @ V1 ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(76,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)],[65]) ).
thf(77,plain,
( ( ! [V1: $i,V2: $i] :
( ! [P: $i,V: $i] :
( ~ ( in_path @ V @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( ( on_path @ ( sK11_E @ V @ P @ V2 @ V1 ) @ P )
& ( ( V
= ( head_of @ ( sK11_E @ V @ P @ V2 @ V1 ) ) )
| ( V
= ( tail_of @ ( sK11_E @ V @ P @ V2 @ V1 ) ) ) ) ) )
& ! [P: $i,V: $i] :
( ~ ( in_path @ V @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( vertex @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(78,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)],[63]) ).
thf(79,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)],[62]) ).
thf(80,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 @ ( sK10_E3 @ E2 @ E1 @ P ) @ E2 @ P )
& ( sequential @ E1 @ ( sK10_E3 @ E2 @ E1 @ P ) ) )
| ( sequential @ E1 @ E2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(81,plain,
( ( ! [V1: $i] :
( ! [V2: $i,SP: $i] :
( ( ( path @ V1 @ V2 @ ( sK9_P @ SP @ V2 @ V1 ) )
& ~ ( less_or_equal @ ( length_of @ SP ) @ ( length_of @ ( sK9_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)],[60]) ).
thf(82,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)],[59]) ).
thf(83,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)],[58]) ).
thf(84,plain,
( ( ! [V1: $i,V2: $i,P: $i] :
( ~ ( path @ V1 @ V2 @ P )
| ( ( length_of @ P )
= ( number_of_in @ edges @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(85,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)],[56]) ).
thf(86,plain,
( ( ! [P: $i] :
( ( ( on_path @ ( sK7_E1 @ P ) @ P )
& ( on_path @ ( sK8_SY86 @ P ) @ P )
& ( sequential @ ( sK7_E1 @ P ) @ ( sK8_SY86 @ P ) )
& ! [SY88: $i] :
~ ( triangle @ ( sK7_E1 @ P ) @ ( sK8_SY86 @ P ) @ SY88 ) )
| ! [V1: $i,V2: $i] :
~ ( path @ V1 @ V2 @ P )
| ( ( number_of_in @ sequential_pairs @ P )
= ( number_of_in @ triangles @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(87,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(88,plain,
( ( precedes @ sK3_SY76 @ sK4_SY80 @ sK5_SY83 )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(89,plain,
( ( shortest_path @ sK1_V1 @ sK2_SY71 @ sK5_SY83 )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(90,plain,
( ( ( ( tail_of @ sK6_SY84 )
= ( tail_of @ sK3_SY76 ) )
& ( ( head_of @ sK6_SY84 )
= ( head_of @ sK4_SY80 ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(91,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK7_E1 @ SX0 ) @ SX0 )
| ~ ( on_path @ ( sK8_SY86 @ SX0 ) @ SX0 ) )
| ~ ( sequential @ ( sK7_E1 @ SX0 ) @ ( sK8_SY86 @ SX0 ) ) )
| ~ ! [SX1: $i] :
~ ( triangle @ ( sK7_E1 @ SX0 ) @ ( sK8_SY86 @ 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)],[86]) ).
thf(92,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)],[83]) ).
thf(93,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( head_of @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( tail_of @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(94,plain,
( ( ~ complete
| ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( vertex @ SX0 )
| ~ ( vertex @ SX1 )
| ~ ( ~ ~ ( ~ ( ( SX0
!= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX0
!= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SX0
= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX0
= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) ) ) )
| ~ ~ ( ~ ( ( SX1
= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX1
= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) ) ) ) ) )
| ~ ( edge @ ( sK15_E @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(95,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 @ ( sK12_E @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( edge @ ( sK12_E @ SX2 @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ( SX1
!= ( head_of @ ( sK12_E @ SX2 @ SX1 @ SX0 ) ) )
| ( SX2
!= ( path_cons @ ( sK12_E @ SX2 @ SX1 @ SX0 ) @ empty ) )
| ! [SX3: $i] :
( ( SX2
!= ( path_cons @ ( sK12_E @ SX2 @ SX1 @ SX0 ) @ SX3 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SX2 @ SX1 @ SX0 ) ) @ SX1 @ SX3 ) ) )
| ~ ~ ( ~ ( ( SX1
= ( head_of @ ( sK12_E @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( ( SX2
!= ( path_cons @ ( sK12_E @ SX2 @ SX1 @ SX0 ) @ ( sK14_SY90 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SX2 @ SX1 @ SX0 ) ) @ SX1 @ ( sK14_SY90 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX2
= ( path_cons @ ( sK12_E @ SX2 @ SX1 @ SX0 ) @ empty ) )
| ~ ( ( SX2
!= ( path_cons @ ( sK12_E @ SX2 @ SX1 @ SX0 ) @ ( sK13_SY91 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SX2 @ SX1 @ SX0 ) ) @ SX1 @ ( sK13_SY91 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(96,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)],[74]) ).
thf(97,plain,
( ( ~ ( ( ( tail_of @ sK6_SY84 )
!= ( tail_of @ sK3_SY76 ) )
| ( ( head_of @ sK6_SY84 )
!= ( head_of @ sK4_SY80 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(98,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)],[76]) ).
thf(99,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in_path @ SX3 @ SX2 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ~ ( ~ ( on_path @ ( sK11_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( ( SX3
= ( head_of @ ( sK11_E @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ( SX3
= ( tail_of @ ( sK11_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)],[77]) ).
thf(100,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( path @ SX0 @ SX1 @ ( sK9_P @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SX2 ) @ ( length_of @ ( sK9_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)],[81]) ).
thf(101,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)],[78]) ).
thf(102,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)],[79]) ).
thf(103,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)],[82]) ).
thf(104,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 @ ( sK10_E3 @ SX2 @ SX1 @ SX0 ) @ SX2 @ SX0 )
| ~ ( sequential @ SX1 @ ( sK10_E3 @ SX2 @ SX1 @ SX0 ) ) )
| ( sequential @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(105,plain,
! [SV1: $i] :
( ( ~ ( edge @ SV1 )
| ( ( head_of @ SV1 )
!= ( tail_of @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(106,plain,
! [SV2: $i] :
( ( ! [SY92: $i,SY93: $i] :
( ~ ( path @ SV2 @ SY92 @ SY93 )
| ( ( length_of @ SY93 )
= ( number_of_in @ edges @ SY93 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(107,plain,
! [SV3: $i] :
( ( ! [SY94: $i,SY95: $i] :
( ~ ( path @ SV3 @ SY94 @ SY95 )
| ( ( number_of_in @ sequential_pairs @ SY95 )
= ( minus @ ( length_of @ SY95 ) @ n1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(108,plain,
! [SV4: $i] :
( ( ! [SY96: $i] : ( less_or_equal @ ( number_of_in @ SV4 @ SY96 ) @ ( number_of_in @ SV4 @ graph ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(109,plain,
! [SV5: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK7_E1 @ SV5 ) @ SV5 )
| ~ ( on_path @ ( sK8_SY86 @ SV5 ) @ SV5 ) )
| ~ ( sequential @ ( sK7_E1 @ SV5 ) @ ( sK8_SY86 @ SV5 ) ) )
| ~ ! [SY97: $i] :
~ ( triangle @ ( sK7_E1 @ SV5 ) @ ( sK8_SY86 @ SV5 ) @ SY97 ) )
| ! [SY98: $i,SY99: $i] :
~ ( path @ SY98 @ SY99 @ SV5 )
| ( ( number_of_in @ sequential_pairs @ SV5 )
= ( number_of_in @ triangles @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(110,plain,
! [SV6: $i] :
( ( ~ ( ~ ! [SY100: $i,SY101: $i] :
( ~ ( edge @ SV6 )
| ~ ( edge @ SY100 )
| ~ ( edge @ SY101 )
| ~ ( sequential @ SV6 @ SY100 )
| ~ ( sequential @ SY100 @ SY101 )
| ~ ( sequential @ SY101 @ SV6 )
| ( triangle @ SV6 @ SY100 @ SY101 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY102: $i,SY103: $i] :
~ ( triangle @ SV6 @ SY102 @ SY103 )
| ( edge @ SV6 ) )
| ~ ! [SY104: $i] :
( ! [SY105: $i] :
~ ( triangle @ SV6 @ SY104 @ SY105 )
| ( edge @ SY104 ) ) )
| ~ ! [SY106: $i,SY107: $i] :
( ~ ( triangle @ SV6 @ SY106 @ SY107 )
| ( edge @ SY107 ) ) )
| ~ ! [SY108: $i] :
( ! [SY109: $i] :
~ ( triangle @ SV6 @ SY108 @ SY109 )
| ( sequential @ SV6 @ SY108 ) ) )
| ~ ! [SY110: $i,SY111: $i] :
( ~ ( triangle @ SV6 @ SY110 @ SY111 )
| ( sequential @ SY110 @ SY111 ) ) )
| ~ ! [SY112: $i,SY113: $i] :
( ~ ( triangle @ SV6 @ SY112 @ SY113 )
| ( sequential @ SY113 @ SV6 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(111,plain,
( ( ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( head_of @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( tail_of @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(112,plain,
( ( ( ~ complete )
= $true )
| ( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( vertex @ SX0 )
| ~ ( vertex @ SX1 )
| ~ ( ~ ~ ( ~ ( ( SX0
!= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX0
!= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SX0
= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX0
= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) ) ) )
| ~ ~ ( ~ ( ( SX1
= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX1
= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) ) ) ) ) )
| ~ ( edge @ ( sK15_E @ SX1 @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(113,plain,
! [SV7: $i] :
( ( ~ ( ~ ~ ( ~ ( ! [SY114: $i,SY115: $i] :
~ ( path @ SV7 @ SY114 @ SY115 )
| ( vertex @ SV7 ) )
| ~ ! [SY116: $i] :
( ! [SY117: $i] :
~ ( path @ SV7 @ SY116 @ SY117 )
| ( vertex @ SY116 ) ) )
| ~ ! [SY118: $i,SY119: $i] :
( ~ ( path @ SV7 @ SY118 @ SY119 )
| ~ ( ~ ~ ( ( SV7
!= ( tail_of @ ( sK12_E @ SY119 @ SY118 @ SV7 ) ) )
| ~ ( edge @ ( sK12_E @ SY119 @ SY118 @ SV7 ) ) )
| ~ ~ ( ~ ( ( SY118
!= ( head_of @ ( sK12_E @ SY119 @ SY118 @ SV7 ) ) )
| ( SY119
!= ( path_cons @ ( sK12_E @ SY119 @ SY118 @ SV7 ) @ empty ) )
| ! [SY120: $i] :
( ( SY119
!= ( path_cons @ ( sK12_E @ SY119 @ SY118 @ SV7 ) @ SY120 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SY119 @ SY118 @ SV7 ) ) @ SY118 @ SY120 ) ) )
| ~ ~ ( ~ ( ( SY118
= ( head_of @ ( sK12_E @ SY119 @ SY118 @ SV7 ) ) )
| ~ ( ( SY119
!= ( path_cons @ ( sK12_E @ SY119 @ SY118 @ SV7 ) @ ( sK14_SY90 @ SY119 @ SY118 @ SV7 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SY119 @ SY118 @ SV7 ) ) @ SY118 @ ( sK14_SY90 @ SY119 @ SY118 @ SV7 ) ) ) )
| ~ ( ( SY119
= ( path_cons @ ( sK12_E @ SY119 @ SY118 @ SV7 ) @ empty ) )
| ~ ( ( SY119
!= ( path_cons @ ( sK12_E @ SY119 @ SY118 @ SV7 ) @ ( sK13_SY91 @ SY119 @ SY118 @ SV7 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SY119 @ SY118 @ SV7 ) ) @ SY118 @ ( sK13_SY91 @ SY119 @ SY118 @ SV7 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(114,plain,
! [SV8: $i] :
( ( ! [SY121: $i,SY122: $i] :
( ~ ( vertex @ SV8 )
| ~ ( vertex @ SY121 )
| ~ ( ~ ! [SY123: $i] :
( ( SV8
!= ( tail_of @ SY123 ) )
| ~ ( edge @ SY123 )
| ( SY121
!= ( head_of @ SY123 ) )
| ( SY122
!= ( path_cons @ SY123 @ empty ) ) )
| ~ ! [SY124: $i] :
( ( SV8
!= ( tail_of @ SY124 ) )
| ~ ( edge @ SY124 )
| ! [SX4: $i] :
( ( SY122
!= ( path_cons @ SY124 @ SX4 ) )
| ~ ( path @ ( head_of @ SY124 ) @ SY121 @ SX4 ) ) ) )
| ( path @ SV8 @ SY121 @ SY122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(115,plain,
( ( ( ( tail_of @ sK6_SY84 )
!= ( tail_of @ sK3_SY76 ) )
| ( ( head_of @ sK6_SY84 )
!= ( head_of @ sK4_SY80 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(116,plain,
! [SV9: $i] :
( ( ! [SY126: $i] :
~ ( ~ ~ ( ~ ! [SY127: $i,SY128: $i] :
( ~ ( on_path @ SY128 @ SY127 )
| ~ ( path @ SV9 @ SY126 @ SY127 )
| ( edge @ SY128 ) )
| ~ ! [SY129: $i,SY130: $i] :
( ~ ( on_path @ SY130 @ SY129 )
| ~ ( path @ SV9 @ SY126 @ SY129 )
| ( in_path @ ( head_of @ SY130 ) @ SY129 ) ) )
| ~ ! [SY131: $i,SY132: $i] :
( ~ ( on_path @ SY132 @ SY131 )
| ~ ( path @ SV9 @ SY126 @ SY131 )
| ( in_path @ ( tail_of @ SY132 ) @ SY131 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(117,plain,
! [SV10: $i] :
( ( ! [SY133: $i] :
~ ( ~ ! [SY134: $i,SY135: $i] :
( ~ ( in_path @ SY135 @ SY134 )
| ~ ( path @ SV10 @ SY133 @ SY134 )
| ~ ( ~ ( on_path @ ( sK11_E @ SY135 @ SY134 @ SY133 @ SV10 ) @ SY134 )
| ~ ( ( SY135
= ( head_of @ ( sK11_E @ SY135 @ SY134 @ SY133 @ SV10 ) ) )
| ( SY135
= ( tail_of @ ( sK11_E @ SY135 @ SY134 @ SY133 @ SV10 ) ) ) ) ) )
| ~ ! [SY136: $i,SY137: $i] :
( ~ ( in_path @ SY137 @ SY136 )
| ~ ( path @ SV10 @ SY133 @ SY136 )
| ( vertex @ SY137 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(118,plain,
! [SV11: $i] :
( ( ~ ( ~ ! [SY138: $i,SY139: $i] :
( ~ ( ~ ( path @ SV11 @ SY138 @ ( sK9_P @ SY139 @ SY138 @ SV11 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY139 ) @ ( length_of @ ( sK9_P @ SY139 @ SY138 @ SV11 ) ) ) )
| ( SV11 = SY138 )
| ~ ( path @ SV11 @ SY138 @ SY139 )
| ( shortest_path @ SV11 @ SY138 @ SY139 ) )
| ~ ~ ( ~ ! [SY140: $i,SY141: $i] :
( ~ ( shortest_path @ SV11 @ SY140 @ SY141 )
| ! [SY142: $i] :
( ~ ( path @ SV11 @ SY140 @ SY142 )
| ( less_or_equal @ ( length_of @ SY141 ) @ ( length_of @ SY142 ) ) ) )
| ~ ~ ( ~ ! [SY143: $i] :
( ! [SY144: $i] :
~ ( shortest_path @ SV11 @ SY143 @ SY144 )
| ( SV11 != SY143 ) )
| ~ ! [SY145: $i,SY146: $i] :
( ~ ( shortest_path @ SV11 @ SY145 @ SY146 )
| ( path @ SV11 @ SY145 @ SY146 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(119,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)],[101]) ).
thf(120,plain,
! [SV12: $i] :
( ( ! [SY147: $i,SY148: $i] :
~ ( path @ SY147 @ SY148 @ SV12 )
| ~ ( ~ ! [SY149: $i,SY150: $i] :
( ~ ( on_path @ SY149 @ SV12 )
| ~ ( on_path @ SY150 @ SV12 )
| ! [SY151: $i] :
( ~ ( precedes @ SY151 @ SY150 @ SV12 )
| ~ ( sequential @ SY149 @ SY151 ) )
| ( precedes @ SY149 @ SY150 @ SV12 ) )
| ~ ! [SY152: $i,SY153: $i] :
( ~ ( on_path @ SY152 @ SV12 )
| ~ ( on_path @ SY153 @ SV12 )
| ~ ( sequential @ SY152 @ SY153 )
| ( precedes @ SY152 @ SY153 @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(121,plain,
! [SV13: $i] :
( ( ! [SY154: $i,SY155: $i] :
~ ( ~ ! [SY156: $i] :
( ! [SY157: $i] :
( ~ ( precedes @ SY155 @ SY156 @ SY157 )
| ~ ( shortest_path @ SV13 @ SY154 @ SY157 ) )
| ! [SX4: $i] :
( ( ( tail_of @ SX4 )
!= ( tail_of @ SY155 ) )
| ( ( head_of @ SX4 )
!= ( head_of @ SY156 ) ) ) )
| ~ ! [SY159: $i,SY160: $i] :
( ~ ( precedes @ SY155 @ SY159 @ SY160 )
| ~ ( shortest_path @ SV13 @ SY154 @ SY160 )
| ~ ( precedes @ SY159 @ SY155 @ SY160 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(122,plain,
! [SV14: $i] :
( ( ! [SY161: $i,SY162: $i] :
~ ( path @ SY161 @ SY162 @ SV14 )
| ~ ( ~ ~ ( ~ ! [SY163: $i] :
( ! [SY164: $i] :
~ ( precedes @ SY163 @ SY164 @ SV14 )
| ( on_path @ SY163 @ SV14 ) )
| ~ ! [SY165: $i,SY166: $i] :
( ~ ( precedes @ SY165 @ SY166 @ SV14 )
| ( on_path @ SY166 @ SV14 ) ) )
| ~ ~ ( ~ ! [SY167: $i,SY168: $i] :
( ~ ( precedes @ SY167 @ SY168 @ SV14 )
| ! [SY169: $i] :
( ~ ( precedes @ SY169 @ SY168 @ SV14 )
| ~ ( sequential @ SY167 @ SY169 ) )
| ~ ( sequential @ SY167 @ SY168 ) )
| ~ ! [SY170: $i,SY171: $i] :
( ~ ( precedes @ SY170 @ SY171 @ SV14 )
| ~ ( ~ ( precedes @ ( sK10_E3 @ SY171 @ SY170 @ SV14 ) @ SY171 @ SV14 )
| ~ ( sequential @ SY170 @ ( sK10_E3 @ SY171 @ SY170 @ SV14 ) ) )
| ( sequential @ SY170 @ SY171 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(123,plain,
! [SV1: $i] :
( ( ( ~ ( edge @ SV1 ) )
= $true )
| ( ( ( ( head_of @ SV1 )
!= ( tail_of @ SV1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(124,plain,
! [SV15: $i,SV2: $i] :
( ( ! [SY172: $i] :
( ~ ( path @ SV2 @ SV15 @ SY172 )
| ( ( length_of @ SY172 )
= ( number_of_in @ edges @ SY172 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(125,plain,
! [SV16: $i,SV3: $i] :
( ( ! [SY173: $i] :
( ~ ( path @ SV3 @ SV16 @ SY173 )
| ( ( number_of_in @ sequential_pairs @ SY173 )
= ( minus @ ( length_of @ SY173 ) @ n1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(126,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)],[108]) ).
thf(127,plain,
! [SV5: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK7_E1 @ SV5 ) @ SV5 )
| ~ ( on_path @ ( sK8_SY86 @ SV5 ) @ SV5 ) )
| ~ ( sequential @ ( sK7_E1 @ SV5 ) @ ( sK8_SY86 @ SV5 ) ) )
| ~ ! [SY97: $i] :
~ ( triangle @ ( sK7_E1 @ SV5 ) @ ( sK8_SY86 @ SV5 ) @ SY97 ) )
| ! [SY98: $i,SY99: $i] :
~ ( path @ SY98 @ SY99 @ SV5 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV5 )
= ( number_of_in @ triangles @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(128,plain,
! [SV6: $i] :
( ( ~ ! [SY100: $i,SY101: $i] :
( ~ ( edge @ SV6 )
| ~ ( edge @ SY100 )
| ~ ( edge @ SY101 )
| ~ ( sequential @ SV6 @ SY100 )
| ~ ( sequential @ SY100 @ SY101 )
| ~ ( sequential @ SY101 @ SV6 )
| ( triangle @ SV6 @ SY100 @ SY101 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY102: $i,SY103: $i] :
~ ( triangle @ SV6 @ SY102 @ SY103 )
| ( edge @ SV6 ) )
| ~ ! [SY104: $i] :
( ! [SY105: $i] :
~ ( triangle @ SV6 @ SY104 @ SY105 )
| ( edge @ SY104 ) ) )
| ~ ! [SY106: $i,SY107: $i] :
( ~ ( triangle @ SV6 @ SY106 @ SY107 )
| ( edge @ SY107 ) ) )
| ~ ! [SY108: $i] :
( ! [SY109: $i] :
~ ( triangle @ SV6 @ SY108 @ SY109 )
| ( sequential @ SV6 @ SY108 ) ) )
| ~ ! [SY110: $i,SY111: $i] :
( ~ ( triangle @ SV6 @ SY110 @ SY111 )
| ( sequential @ SY110 @ SY111 ) ) )
| ~ ! [SY112: $i,SY113: $i] :
( ~ ( triangle @ SV6 @ SY112 @ SY113 )
| ( sequential @ SY113 @ SV6 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(129,plain,
( ( ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( head_of @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[111]) ).
thf(130,plain,
( ( ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( tail_of @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[111]) ).
thf(131,plain,
( ( complete = $false )
| ( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( vertex @ SX0 )
| ~ ( vertex @ SX1 )
| ~ ( ~ ~ ( ~ ( ( SX0
!= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX0
!= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SX0
= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX0
= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) ) ) )
| ~ ~ ( ~ ( ( SX1
= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX1
= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) ) ) ) ) )
| ~ ( edge @ ( sK15_E @ SX1 @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(132,plain,
! [SV7: $i] :
( ( ~ ~ ( ~ ( ! [SY114: $i,SY115: $i] :
~ ( path @ SV7 @ SY114 @ SY115 )
| ( vertex @ SV7 ) )
| ~ ! [SY116: $i] :
( ! [SY117: $i] :
~ ( path @ SV7 @ SY116 @ SY117 )
| ( vertex @ SY116 ) ) )
| ~ ! [SY118: $i,SY119: $i] :
( ~ ( path @ SV7 @ SY118 @ SY119 )
| ~ ( ~ ~ ( ( SV7
!= ( tail_of @ ( sK12_E @ SY119 @ SY118 @ SV7 ) ) )
| ~ ( edge @ ( sK12_E @ SY119 @ SY118 @ SV7 ) ) )
| ~ ~ ( ~ ( ( SY118
!= ( head_of @ ( sK12_E @ SY119 @ SY118 @ SV7 ) ) )
| ( SY119
!= ( path_cons @ ( sK12_E @ SY119 @ SY118 @ SV7 ) @ empty ) )
| ! [SY120: $i] :
( ( SY119
!= ( path_cons @ ( sK12_E @ SY119 @ SY118 @ SV7 ) @ SY120 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SY119 @ SY118 @ SV7 ) ) @ SY118 @ SY120 ) ) )
| ~ ~ ( ~ ( ( SY118
= ( head_of @ ( sK12_E @ SY119 @ SY118 @ SV7 ) ) )
| ~ ( ( SY119
!= ( path_cons @ ( sK12_E @ SY119 @ SY118 @ SV7 ) @ ( sK14_SY90 @ SY119 @ SY118 @ SV7 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SY119 @ SY118 @ SV7 ) ) @ SY118 @ ( sK14_SY90 @ SY119 @ SY118 @ SV7 ) ) ) )
| ~ ( ( SY119
= ( path_cons @ ( sK12_E @ SY119 @ SY118 @ SV7 ) @ empty ) )
| ~ ( ( SY119
!= ( path_cons @ ( sK12_E @ SY119 @ SY118 @ SV7 ) @ ( sK13_SY91 @ SY119 @ SY118 @ SV7 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SY119 @ SY118 @ SV7 ) ) @ SY118 @ ( sK13_SY91 @ SY119 @ SY118 @ SV7 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(133,plain,
! [SV18: $i,SV8: $i] :
( ( ! [SY174: $i] :
( ~ ( vertex @ SV8 )
| ~ ( vertex @ SV18 )
| ~ ( ~ ! [SY175: $i] :
( ( SV8
!= ( tail_of @ SY175 ) )
| ~ ( edge @ SY175 )
| ( SV18
!= ( head_of @ SY175 ) )
| ( SY174
!= ( path_cons @ SY175 @ empty ) ) )
| ~ ! [SY176: $i] :
( ( SV8
!= ( tail_of @ SY176 ) )
| ~ ( edge @ SY176 )
| ! [SY177: $i] :
( ( SY174
!= ( path_cons @ SY176 @ SY177 ) )
| ~ ( path @ ( head_of @ SY176 ) @ SV18 @ SY177 ) ) ) )
| ( path @ SV8 @ SV18 @ SY174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(134,plain,
( ( ( ( tail_of @ sK6_SY84 )
!= ( tail_of @ sK3_SY76 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[115]) ).
thf(135,plain,
( ( ( ( head_of @ sK6_SY84 )
!= ( head_of @ sK4_SY80 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[115]) ).
thf(136,plain,
! [SV19: $i,SV9: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY178: $i,SY179: $i] :
( ~ ( on_path @ SY179 @ SY178 )
| ~ ( path @ SV9 @ SV19 @ SY178 )
| ( edge @ SY179 ) )
| ~ ! [SY180: $i,SY181: $i] :
( ~ ( on_path @ SY181 @ SY180 )
| ~ ( path @ SV9 @ SV19 @ SY180 )
| ( in_path @ ( head_of @ SY181 ) @ SY180 ) ) )
| ~ ! [SY182: $i,SY183: $i] :
( ~ ( on_path @ SY183 @ SY182 )
| ~ ( path @ SV9 @ SV19 @ SY182 )
| ( in_path @ ( tail_of @ SY183 ) @ SY182 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(137,plain,
! [SV20: $i,SV10: $i] :
( ( ~ ( ~ ! [SY184: $i,SY185: $i] :
( ~ ( in_path @ SY185 @ SY184 )
| ~ ( path @ SV10 @ SV20 @ SY184 )
| ~ ( ~ ( on_path @ ( sK11_E @ SY185 @ SY184 @ SV20 @ SV10 ) @ SY184 )
| ~ ( ( SY185
= ( head_of @ ( sK11_E @ SY185 @ SY184 @ SV20 @ SV10 ) ) )
| ( SY185
= ( tail_of @ ( sK11_E @ SY185 @ SY184 @ SV20 @ SV10 ) ) ) ) ) )
| ~ ! [SY186: $i,SY187: $i] :
( ~ ( in_path @ SY187 @ SY186 )
| ~ ( path @ SV10 @ SV20 @ SY186 )
| ( vertex @ SY187 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(138,plain,
! [SV11: $i] :
( ( ~ ! [SY138: $i,SY139: $i] :
( ~ ( ~ ( path @ SV11 @ SY138 @ ( sK9_P @ SY139 @ SY138 @ SV11 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY139 ) @ ( length_of @ ( sK9_P @ SY139 @ SY138 @ SV11 ) ) ) )
| ( SV11 = SY138 )
| ~ ( path @ SV11 @ SY138 @ SY139 )
| ( shortest_path @ SV11 @ SY138 @ SY139 ) )
| ~ ~ ( ~ ! [SY140: $i,SY141: $i] :
( ~ ( shortest_path @ SV11 @ SY140 @ SY141 )
| ! [SY142: $i] :
( ~ ( path @ SV11 @ SY140 @ SY142 )
| ( less_or_equal @ ( length_of @ SY141 ) @ ( length_of @ SY142 ) ) ) )
| ~ ~ ( ~ ! [SY143: $i] :
( ! [SY144: $i] :
~ ( shortest_path @ SV11 @ SY143 @ SY144 )
| ( SV11 != SY143 ) )
| ~ ! [SY145: $i,SY146: $i] :
( ~ ( shortest_path @ SV11 @ SY145 @ SY146 )
| ( path @ SV11 @ SY145 @ SY146 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(139,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)],[119]) ).
thf(140,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)],[119]) ).
thf(141,plain,
! [SV12: $i] :
( ( ( ! [SY147: $i,SY148: $i] :
~ ( path @ SY147 @ SY148 @ SV12 ) )
= $true )
| ( ( ~ ( ~ ! [SY149: $i,SY150: $i] :
( ~ ( on_path @ SY149 @ SV12 )
| ~ ( on_path @ SY150 @ SV12 )
| ! [SY151: $i] :
( ~ ( precedes @ SY151 @ SY150 @ SV12 )
| ~ ( sequential @ SY149 @ SY151 ) )
| ( precedes @ SY149 @ SY150 @ SV12 ) )
| ~ ! [SY152: $i,SY153: $i] :
( ~ ( on_path @ SY152 @ SV12 )
| ~ ( on_path @ SY153 @ SV12 )
| ~ ( sequential @ SY152 @ SY153 )
| ( precedes @ SY152 @ SY153 @ SV12 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(142,plain,
! [SV21: $i,SV13: $i] :
( ( ! [SY188: $i] :
~ ( ~ ! [SY189: $i] :
( ! [SY190: $i] :
( ~ ( precedes @ SY188 @ SY189 @ SY190 )
| ~ ( shortest_path @ SV13 @ SV21 @ SY190 ) )
| ! [SX4: $i] :
( ( ( tail_of @ SX4 )
!= ( tail_of @ SY188 ) )
| ( ( head_of @ SX4 )
!= ( head_of @ SY189 ) ) ) )
| ~ ! [SY192: $i,SY193: $i] :
( ~ ( precedes @ SY188 @ SY192 @ SY193 )
| ~ ( shortest_path @ SV13 @ SV21 @ SY193 )
| ~ ( precedes @ SY192 @ SY188 @ SY193 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(143,plain,
! [SV14: $i] :
( ( ( ! [SY161: $i,SY162: $i] :
~ ( path @ SY161 @ SY162 @ SV14 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY163: $i] :
( ! [SY164: $i] :
~ ( precedes @ SY163 @ SY164 @ SV14 )
| ( on_path @ SY163 @ SV14 ) )
| ~ ! [SY165: $i,SY166: $i] :
( ~ ( precedes @ SY165 @ SY166 @ SV14 )
| ( on_path @ SY166 @ SV14 ) ) )
| ~ ~ ( ~ ! [SY167: $i,SY168: $i] :
( ~ ( precedes @ SY167 @ SY168 @ SV14 )
| ! [SY169: $i] :
( ~ ( precedes @ SY169 @ SY168 @ SV14 )
| ~ ( sequential @ SY167 @ SY169 ) )
| ~ ( sequential @ SY167 @ SY168 ) )
| ~ ! [SY170: $i,SY171: $i] :
( ~ ( precedes @ SY170 @ SY171 @ SV14 )
| ~ ( ~ ( precedes @ ( sK10_E3 @ SY171 @ SY170 @ SV14 ) @ SY171 @ SV14 )
| ~ ( sequential @ SY170 @ ( sK10_E3 @ SY171 @ SY170 @ SV14 ) ) )
| ( sequential @ SY170 @ SY171 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[122]) ).
thf(144,plain,
! [SV1: $i] :
( ( ( edge @ SV1 )
= $false )
| ( ( ( ( head_of @ SV1 )
!= ( tail_of @ SV1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(145,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)],[124]) ).
thf(146,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)],[125]) ).
thf(147,plain,
! [SV5: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK7_E1 @ SV5 ) @ SV5 )
| ~ ( on_path @ ( sK8_SY86 @ SV5 ) @ SV5 ) )
| ~ ( sequential @ ( sK7_E1 @ SV5 ) @ ( sK8_SY86 @ SV5 ) ) )
| ~ ! [SY97: $i] :
~ ( triangle @ ( sK7_E1 @ SV5 ) @ ( sK8_SY86 @ SV5 ) @ SY97 ) ) )
= $true )
| ( ( ! [SY98: $i,SY99: $i] :
~ ( path @ SY98 @ SY99 @ SV5 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV5 )
= ( number_of_in @ triangles @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(148,plain,
! [SV6: $i] :
( ( ~ ! [SY100: $i,SY101: $i] :
( ~ ( edge @ SV6 )
| ~ ( edge @ SY100 )
| ~ ( edge @ SY101 )
| ~ ( sequential @ SV6 @ SY100 )
| ~ ( sequential @ SY100 @ SY101 )
| ~ ( sequential @ SY101 @ SV6 )
| ( triangle @ SV6 @ SY100 @ SY101 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[128]) ).
thf(149,plain,
! [SV6: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY102: $i,SY103: $i] :
~ ( triangle @ SV6 @ SY102 @ SY103 )
| ( edge @ SV6 ) )
| ~ ! [SY104: $i] :
( ! [SY105: $i] :
~ ( triangle @ SV6 @ SY104 @ SY105 )
| ( edge @ SY104 ) ) )
| ~ ! [SY106: $i,SY107: $i] :
( ~ ( triangle @ SV6 @ SY106 @ SY107 )
| ( edge @ SY107 ) ) )
| ~ ! [SY108: $i] :
( ! [SY109: $i] :
~ ( triangle @ SV6 @ SY108 @ SY109 )
| ( sequential @ SV6 @ SY108 ) ) )
| ~ ! [SY110: $i,SY111: $i] :
( ~ ( triangle @ SV6 @ SY110 @ SY111 )
| ( sequential @ SY110 @ SY111 ) ) )
| ~ ! [SY112: $i,SY113: $i] :
( ~ ( triangle @ SV6 @ SY112 @ SY113 )
| ( sequential @ SY113 @ SV6 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[128]) ).
thf(150,plain,
( ( ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( head_of @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[129]) ).
thf(151,plain,
( ( ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( tail_of @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[130]) ).
thf(152,plain,
! [SV24: $i] :
( ( ( ! [SY194: $i] :
( ( SV24 = SY194 )
| ~ ( vertex @ SV24 )
| ~ ( vertex @ SY194 )
| ~ ( ~ ~ ( ~ ( ( SV24
!= ( head_of @ ( sK15_E @ SY194 @ SV24 ) ) )
| ( SY194
!= ( tail_of @ ( sK15_E @ SY194 @ SV24 ) ) )
| ( SY194
!= ( head_of @ ( sK15_E @ SY194 @ SV24 ) ) )
| ( SV24
!= ( tail_of @ ( sK15_E @ SY194 @ SV24 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV24
= ( head_of @ ( sK15_E @ SY194 @ SV24 ) ) )
| ( SY194
= ( head_of @ ( sK15_E @ SY194 @ SV24 ) ) ) )
| ~ ( ( SV24
= ( head_of @ ( sK15_E @ SY194 @ SV24 ) ) )
| ( SV24
= ( tail_of @ ( sK15_E @ SY194 @ SV24 ) ) ) ) )
| ~ ~ ( ~ ( ( SY194
= ( tail_of @ ( sK15_E @ SY194 @ SV24 ) ) )
| ( SY194
= ( head_of @ ( sK15_E @ SY194 @ SV24 ) ) ) )
| ~ ( ( SY194
= ( tail_of @ ( sK15_E @ SY194 @ SV24 ) ) )
| ( SV24
= ( tail_of @ ( sK15_E @ SY194 @ SV24 ) ) ) ) ) ) )
| ~ ( edge @ ( sK15_E @ SY194 @ SV24 ) ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(153,plain,
! [SV7: $i] :
( ( ~ ~ ( ~ ( ! [SY114: $i,SY115: $i] :
~ ( path @ SV7 @ SY114 @ SY115 )
| ( vertex @ SV7 ) )
| ~ ! [SY116: $i] :
( ! [SY117: $i] :
~ ( path @ SV7 @ SY116 @ SY117 )
| ( vertex @ SY116 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[132]) ).
thf(154,plain,
! [SV7: $i] :
( ( ~ ! [SY118: $i,SY119: $i] :
( ~ ( path @ SV7 @ SY118 @ SY119 )
| ~ ( ~ ~ ( ( SV7
!= ( tail_of @ ( sK12_E @ SY119 @ SY118 @ SV7 ) ) )
| ~ ( edge @ ( sK12_E @ SY119 @ SY118 @ SV7 ) ) )
| ~ ~ ( ~ ( ( SY118
!= ( head_of @ ( sK12_E @ SY119 @ SY118 @ SV7 ) ) )
| ( SY119
!= ( path_cons @ ( sK12_E @ SY119 @ SY118 @ SV7 ) @ empty ) )
| ! [SY120: $i] :
( ( SY119
!= ( path_cons @ ( sK12_E @ SY119 @ SY118 @ SV7 ) @ SY120 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SY119 @ SY118 @ SV7 ) ) @ SY118 @ SY120 ) ) )
| ~ ~ ( ~ ( ( SY118
= ( head_of @ ( sK12_E @ SY119 @ SY118 @ SV7 ) ) )
| ~ ( ( SY119
!= ( path_cons @ ( sK12_E @ SY119 @ SY118 @ SV7 ) @ ( sK14_SY90 @ SY119 @ SY118 @ SV7 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SY119 @ SY118 @ SV7 ) ) @ SY118 @ ( sK14_SY90 @ SY119 @ SY118 @ SV7 ) ) ) )
| ~ ( ( SY119
= ( path_cons @ ( sK12_E @ SY119 @ SY118 @ SV7 ) @ empty ) )
| ~ ( ( SY119
!= ( path_cons @ ( sK12_E @ SY119 @ SY118 @ SV7 ) @ ( sK13_SY91 @ SY119 @ SY118 @ SV7 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SY119 @ SY118 @ SV7 ) ) @ SY118 @ ( sK13_SY91 @ SY119 @ SY118 @ SV7 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[132]) ).
thf(155,plain,
! [SV25: $i,SV18: $i,SV8: $i] :
( ( ~ ( vertex @ SV8 )
| ~ ( vertex @ SV18 )
| ~ ( ~ ! [SY195: $i] :
( ( SV8
!= ( tail_of @ SY195 ) )
| ~ ( edge @ SY195 )
| ( SV18
!= ( head_of @ SY195 ) )
| ( SV25
!= ( path_cons @ SY195 @ empty ) ) )
| ~ ! [SY196: $i] :
( ( SV8
!= ( tail_of @ SY196 ) )
| ~ ( edge @ SY196 )
| ! [SY197: $i] :
( ( SV25
!= ( path_cons @ SY196 @ SY197 ) )
| ~ ( path @ ( head_of @ SY196 ) @ SV18 @ SY197 ) ) ) )
| ( path @ SV8 @ SV18 @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(156,plain,
( ( ( tail_of @ sK6_SY84 )
= ( tail_of @ sK3_SY76 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[134]) ).
thf(157,plain,
( ( ( head_of @ sK6_SY84 )
= ( head_of @ sK4_SY80 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(158,plain,
! [SV19: $i,SV9: $i] :
( ( ~ ~ ( ~ ! [SY178: $i,SY179: $i] :
( ~ ( on_path @ SY179 @ SY178 )
| ~ ( path @ SV9 @ SV19 @ SY178 )
| ( edge @ SY179 ) )
| ~ ! [SY180: $i,SY181: $i] :
( ~ ( on_path @ SY181 @ SY180 )
| ~ ( path @ SV9 @ SV19 @ SY180 )
| ( in_path @ ( head_of @ SY181 ) @ SY180 ) ) )
| ~ ! [SY182: $i,SY183: $i] :
( ~ ( on_path @ SY183 @ SY182 )
| ~ ( path @ SV9 @ SV19 @ SY182 )
| ( in_path @ ( tail_of @ SY183 ) @ SY182 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(159,plain,
! [SV20: $i,SV10: $i] :
( ( ~ ! [SY184: $i,SY185: $i] :
( ~ ( in_path @ SY185 @ SY184 )
| ~ ( path @ SV10 @ SV20 @ SY184 )
| ~ ( ~ ( on_path @ ( sK11_E @ SY185 @ SY184 @ SV20 @ SV10 ) @ SY184 )
| ~ ( ( SY185
= ( head_of @ ( sK11_E @ SY185 @ SY184 @ SV20 @ SV10 ) ) )
| ( SY185
= ( tail_of @ ( sK11_E @ SY185 @ SY184 @ SV20 @ SV10 ) ) ) ) ) )
| ~ ! [SY186: $i,SY187: $i] :
( ~ ( in_path @ SY187 @ SY186 )
| ~ ( path @ SV10 @ SV20 @ SY186 )
| ( vertex @ SY187 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(160,plain,
! [SV11: $i] :
( ( ~ ! [SY138: $i,SY139: $i] :
( ~ ( ~ ( path @ SV11 @ SY138 @ ( sK9_P @ SY139 @ SY138 @ SV11 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY139 ) @ ( length_of @ ( sK9_P @ SY139 @ SY138 @ SV11 ) ) ) )
| ( SV11 = SY138 )
| ~ ( path @ SV11 @ SY138 @ SY139 )
| ( shortest_path @ SV11 @ SY138 @ SY139 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[138]) ).
thf(161,plain,
! [SV11: $i] :
( ( ~ ~ ( ~ ! [SY140: $i,SY141: $i] :
( ~ ( shortest_path @ SV11 @ SY140 @ SY141 )
| ! [SY142: $i] :
( ~ ( path @ SV11 @ SY140 @ SY142 )
| ( less_or_equal @ ( length_of @ SY141 ) @ ( length_of @ SY142 ) ) ) )
| ~ ~ ( ~ ! [SY143: $i] :
( ! [SY144: $i] :
~ ( shortest_path @ SV11 @ SY143 @ SY144 )
| ( SV11 != SY143 ) )
| ~ ! [SY145: $i,SY146: $i] :
( ~ ( shortest_path @ SV11 @ SY145 @ SY146 )
| ( path @ SV11 @ SY145 @ SY146 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[138]) ).
thf(162,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)],[139]) ).
thf(163,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)],[140]) ).
thf(164,plain,
! [SV12: $i,SV26: $i] :
( ( ( ! [SY198: $i] :
~ ( path @ SV26 @ SY198 @ SV12 ) )
= $true )
| ( ( ~ ( ~ ! [SY149: $i,SY150: $i] :
( ~ ( on_path @ SY149 @ SV12 )
| ~ ( on_path @ SY150 @ SV12 )
| ! [SY151: $i] :
( ~ ( precedes @ SY151 @ SY150 @ SV12 )
| ~ ( sequential @ SY149 @ SY151 ) )
| ( precedes @ SY149 @ SY150 @ SV12 ) )
| ~ ! [SY152: $i,SY153: $i] :
( ~ ( on_path @ SY152 @ SV12 )
| ~ ( on_path @ SY153 @ SV12 )
| ~ ( sequential @ SY152 @ SY153 )
| ( precedes @ SY152 @ SY153 @ SV12 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(165,plain,
! [SV21: $i,SV13: $i,SV27: $i] :
( ( ~ ( ~ ! [SY199: $i] :
( ! [SY200: $i] :
( ~ ( precedes @ SV27 @ SY199 @ SY200 )
| ~ ( shortest_path @ SV13 @ SV21 @ SY200 ) )
| ! [SY201: $i] :
( ( ( tail_of @ SY201 )
!= ( tail_of @ SV27 ) )
| ( ( head_of @ SY201 )
!= ( head_of @ SY199 ) ) ) )
| ~ ! [SY202: $i,SY203: $i] :
( ~ ( precedes @ SV27 @ SY202 @ SY203 )
| ~ ( shortest_path @ SV13 @ SV21 @ SY203 )
| ~ ( precedes @ SY202 @ SV27 @ SY203 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(166,plain,
! [SV14: $i,SV28: $i] :
( ( ( ! [SY204: $i] :
~ ( path @ SV28 @ SY204 @ SV14 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY163: $i] :
( ! [SY164: $i] :
~ ( precedes @ SY163 @ SY164 @ SV14 )
| ( on_path @ SY163 @ SV14 ) )
| ~ ! [SY165: $i,SY166: $i] :
( ~ ( precedes @ SY165 @ SY166 @ SV14 )
| ( on_path @ SY166 @ SV14 ) ) )
| ~ ~ ( ~ ! [SY167: $i,SY168: $i] :
( ~ ( precedes @ SY167 @ SY168 @ SV14 )
| ! [SY169: $i] :
( ~ ( precedes @ SY169 @ SY168 @ SV14 )
| ~ ( sequential @ SY167 @ SY169 ) )
| ~ ( sequential @ SY167 @ SY168 ) )
| ~ ! [SY170: $i,SY171: $i] :
( ~ ( precedes @ SY170 @ SY171 @ SV14 )
| ~ ( ~ ( precedes @ ( sK10_E3 @ SY171 @ SY170 @ SV14 ) @ SY171 @ SV14 )
| ~ ( sequential @ SY170 @ ( sK10_E3 @ SY171 @ SY170 @ SV14 ) ) )
| ( sequential @ SY170 @ SY171 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(167,plain,
! [SV1: $i] :
( ( ( ( head_of @ SV1 )
= ( tail_of @ SV1 ) )
= $false )
| ( ( edge @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(168,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)],[145]) ).
thf(169,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)],[146]) ).
thf(170,plain,
! [SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK7_E1 @ SV5 ) @ SV5 )
| ~ ( on_path @ ( sK8_SY86 @ SV5 ) @ SV5 ) )
| ~ ( sequential @ ( sK7_E1 @ SV5 ) @ ( sK8_SY86 @ SV5 ) ) )
| ~ ! [SY97: $i] :
~ ( triangle @ ( sK7_E1 @ SV5 ) @ ( sK8_SY86 @ SV5 ) @ SY97 ) )
= $false )
| ( ( ! [SY98: $i,SY99: $i] :
~ ( path @ SY98 @ SY99 @ SV5 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV5 )
= ( number_of_in @ triangles @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(171,plain,
! [SV6: $i] :
( ( ! [SY100: $i,SY101: $i] :
( ~ ( edge @ SV6 )
| ~ ( edge @ SY100 )
| ~ ( edge @ SY101 )
| ~ ( sequential @ SV6 @ SY100 )
| ~ ( sequential @ SY100 @ SY101 )
| ~ ( sequential @ SY101 @ SV6 )
| ( triangle @ SV6 @ SY100 @ SY101 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[148]) ).
thf(172,plain,
! [SV6: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY102: $i,SY103: $i] :
~ ( triangle @ SV6 @ SY102 @ SY103 )
| ( edge @ SV6 ) )
| ~ ! [SY104: $i] :
( ! [SY105: $i] :
~ ( triangle @ SV6 @ SY104 @ SY105 )
| ( edge @ SY104 ) ) )
| ~ ! [SY106: $i,SY107: $i] :
( ~ ( triangle @ SV6 @ SY106 @ SY107 )
| ( edge @ SY107 ) ) )
| ~ ! [SY108: $i] :
( ! [SY109: $i] :
~ ( triangle @ SV6 @ SY108 @ SY109 )
| ( sequential @ SV6 @ SY108 ) ) )
| ~ ! [SY110: $i,SY111: $i] :
( ~ ( triangle @ SV6 @ SY110 @ SY111 )
| ( sequential @ SY110 @ SY111 ) ) )
| ~ ! [SY112: $i,SY113: $i] :
( ~ ( triangle @ SV6 @ SY112 @ SY113 )
| ( sequential @ SY113 @ SV6 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(173,plain,
! [SV29: $i] :
( ( ~ ( edge @ SV29 )
| ( vertex @ ( head_of @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(174,plain,
! [SV30: $i] :
( ( ~ ( edge @ SV30 )
| ( vertex @ ( tail_of @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(175,plain,
! [SV31: $i,SV24: $i] :
( ( ( ( SV24 = SV31 )
| ~ ( vertex @ SV24 )
| ~ ( vertex @ SV31 )
| ~ ( ~ ~ ( ~ ( ( SV24
!= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
!= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
!= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
!= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV24
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
| ~ ( ( SV24
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) ) )
| ~ ~ ( ~ ( ( SV31
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
| ~ ( ( SV31
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) ) ) ) )
| ~ ( edge @ ( sK15_E @ SV31 @ SV24 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(176,plain,
! [SV7: $i] :
( ( ~ ( ~ ( ! [SY114: $i,SY115: $i] :
~ ( path @ SV7 @ SY114 @ SY115 )
| ( vertex @ SV7 ) )
| ~ ! [SY116: $i] :
( ! [SY117: $i] :
~ ( path @ SV7 @ SY116 @ SY117 )
| ( vertex @ SY116 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[153]) ).
thf(177,plain,
! [SV7: $i] :
( ( ! [SY118: $i,SY119: $i] :
( ~ ( path @ SV7 @ SY118 @ SY119 )
| ~ ( ~ ~ ( ( SV7
!= ( tail_of @ ( sK12_E @ SY119 @ SY118 @ SV7 ) ) )
| ~ ( edge @ ( sK12_E @ SY119 @ SY118 @ SV7 ) ) )
| ~ ~ ( ~ ( ( SY118
!= ( head_of @ ( sK12_E @ SY119 @ SY118 @ SV7 ) ) )
| ( SY119
!= ( path_cons @ ( sK12_E @ SY119 @ SY118 @ SV7 ) @ empty ) )
| ! [SY120: $i] :
( ( SY119
!= ( path_cons @ ( sK12_E @ SY119 @ SY118 @ SV7 ) @ SY120 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SY119 @ SY118 @ SV7 ) ) @ SY118 @ SY120 ) ) )
| ~ ~ ( ~ ( ( SY118
= ( head_of @ ( sK12_E @ SY119 @ SY118 @ SV7 ) ) )
| ~ ( ( SY119
!= ( path_cons @ ( sK12_E @ SY119 @ SY118 @ SV7 ) @ ( sK14_SY90 @ SY119 @ SY118 @ SV7 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SY119 @ SY118 @ SV7 ) ) @ SY118 @ ( sK14_SY90 @ SY119 @ SY118 @ SV7 ) ) ) )
| ~ ( ( SY119
= ( path_cons @ ( sK12_E @ SY119 @ SY118 @ SV7 ) @ empty ) )
| ~ ( ( SY119
!= ( path_cons @ ( sK12_E @ SY119 @ SY118 @ SV7 ) @ ( sK13_SY91 @ SY119 @ SY118 @ SV7 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SY119 @ SY118 @ SV7 ) ) @ SY118 @ ( sK13_SY91 @ SY119 @ SY118 @ SV7 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[154]) ).
thf(178,plain,
! [SV25: $i,SV18: $i,SV8: $i] :
( ( ( ~ ( vertex @ SV8 )
| ~ ( vertex @ SV18 )
| ~ ( ~ ! [SY195: $i] :
( ( SV8
!= ( tail_of @ SY195 ) )
| ~ ( edge @ SY195 )
| ( SV18
!= ( head_of @ SY195 ) )
| ( SV25
!= ( path_cons @ SY195 @ empty ) ) )
| ~ ! [SY196: $i] :
( ( SV8
!= ( tail_of @ SY196 ) )
| ~ ( edge @ SY196 )
| ! [SY197: $i] :
( ( SV25
!= ( path_cons @ SY196 @ SY197 ) )
| ~ ( path @ ( head_of @ SY196 ) @ SV18 @ SY197 ) ) ) ) )
= $true )
| ( ( path @ SV8 @ SV18 @ SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(179,plain,
! [SV19: $i,SV9: $i] :
( ( ~ ~ ( ~ ! [SY178: $i,SY179: $i] :
( ~ ( on_path @ SY179 @ SY178 )
| ~ ( path @ SV9 @ SV19 @ SY178 )
| ( edge @ SY179 ) )
| ~ ! [SY180: $i,SY181: $i] :
( ~ ( on_path @ SY181 @ SY180 )
| ~ ( path @ SV9 @ SV19 @ SY180 )
| ( in_path @ ( head_of @ SY181 ) @ SY180 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[158]) ).
thf(180,plain,
! [SV19: $i,SV9: $i] :
( ( ~ ! [SY182: $i,SY183: $i] :
( ~ ( on_path @ SY183 @ SY182 )
| ~ ( path @ SV9 @ SV19 @ SY182 )
| ( in_path @ ( tail_of @ SY183 ) @ SY182 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[158]) ).
thf(181,plain,
! [SV20: $i,SV10: $i] :
( ( ~ ! [SY184: $i,SY185: $i] :
( ~ ( in_path @ SY185 @ SY184 )
| ~ ( path @ SV10 @ SV20 @ SY184 )
| ~ ( ~ ( on_path @ ( sK11_E @ SY185 @ SY184 @ SV20 @ SV10 ) @ SY184 )
| ~ ( ( SY185
= ( head_of @ ( sK11_E @ SY185 @ SY184 @ SV20 @ SV10 ) ) )
| ( SY185
= ( tail_of @ ( sK11_E @ SY185 @ SY184 @ SV20 @ SV10 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[159]) ).
thf(182,plain,
! [SV20: $i,SV10: $i] :
( ( ~ ! [SY186: $i,SY187: $i] :
( ~ ( in_path @ SY187 @ SY186 )
| ~ ( path @ SV10 @ SV20 @ SY186 )
| ( vertex @ SY187 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[159]) ).
thf(183,plain,
! [SV11: $i] :
( ( ! [SY138: $i,SY139: $i] :
( ~ ( ~ ( path @ SV11 @ SY138 @ ( sK9_P @ SY139 @ SY138 @ SV11 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY139 ) @ ( length_of @ ( sK9_P @ SY139 @ SY138 @ SV11 ) ) ) )
| ( SV11 = SY138 )
| ~ ( path @ SV11 @ SY138 @ SY139 )
| ( shortest_path @ SV11 @ SY138 @ SY139 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[160]) ).
thf(184,plain,
! [SV11: $i] :
( ( ~ ( ~ ! [SY140: $i,SY141: $i] :
( ~ ( shortest_path @ SV11 @ SY140 @ SY141 )
| ! [SY142: $i] :
( ~ ( path @ SV11 @ SY140 @ SY142 )
| ( less_or_equal @ ( length_of @ SY141 ) @ ( length_of @ SY142 ) ) ) )
| ~ ~ ( ~ ! [SY143: $i] :
( ! [SY144: $i] :
~ ( shortest_path @ SV11 @ SY143 @ SY144 )
| ( SV11 != SY143 ) )
| ~ ! [SY145: $i,SY146: $i] :
( ~ ( shortest_path @ SV11 @ SY145 @ SY146 )
| ( path @ SV11 @ SY145 @ SY146 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[161]) ).
thf(185,plain,
! [SV32: $i] :
( ( ! [SY205: $i] :
( ( SV32 = SY205 )
| ~ ( edge @ SV32 )
| ~ ( edge @ SY205 )
| ( ( head_of @ SV32 )
!= ( tail_of @ SY205 ) )
| ( sequential @ SV32 @ SY205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(186,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)],[163]) ).
thf(187,plain,
! [SV12: $i,SV33: $i,SV26: $i] :
( ( ( ~ ( path @ SV26 @ SV33 @ SV12 ) )
= $true )
| ( ( ~ ( ~ ! [SY149: $i,SY150: $i] :
( ~ ( on_path @ SY149 @ SV12 )
| ~ ( on_path @ SY150 @ SV12 )
| ! [SY151: $i] :
( ~ ( precedes @ SY151 @ SY150 @ SV12 )
| ~ ( sequential @ SY149 @ SY151 ) )
| ( precedes @ SY149 @ SY150 @ SV12 ) )
| ~ ! [SY152: $i,SY153: $i] :
( ~ ( on_path @ SY152 @ SV12 )
| ~ ( on_path @ SY153 @ SV12 )
| ~ ( sequential @ SY152 @ SY153 )
| ( precedes @ SY152 @ SY153 @ SV12 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(188,plain,
! [SV21: $i,SV13: $i,SV27: $i] :
( ( ~ ! [SY199: $i] :
( ! [SY200: $i] :
( ~ ( precedes @ SV27 @ SY199 @ SY200 )
| ~ ( shortest_path @ SV13 @ SV21 @ SY200 ) )
| ! [SY201: $i] :
( ( ( tail_of @ SY201 )
!= ( tail_of @ SV27 ) )
| ( ( head_of @ SY201 )
!= ( head_of @ SY199 ) ) ) )
| ~ ! [SY202: $i,SY203: $i] :
( ~ ( precedes @ SV27 @ SY202 @ SY203 )
| ~ ( shortest_path @ SV13 @ SV21 @ SY203 )
| ~ ( precedes @ SY202 @ SV27 @ SY203 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(189,plain,
! [SV14: $i,SV34: $i,SV28: $i] :
( ( ( ~ ( path @ SV28 @ SV34 @ SV14 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY163: $i] :
( ! [SY164: $i] :
~ ( precedes @ SY163 @ SY164 @ SV14 )
| ( on_path @ SY163 @ SV14 ) )
| ~ ! [SY165: $i,SY166: $i] :
( ~ ( precedes @ SY165 @ SY166 @ SV14 )
| ( on_path @ SY166 @ SV14 ) ) )
| ~ ~ ( ~ ! [SY167: $i,SY168: $i] :
( ~ ( precedes @ SY167 @ SY168 @ SV14 )
| ! [SY169: $i] :
( ~ ( precedes @ SY169 @ SY168 @ SV14 )
| ~ ( sequential @ SY167 @ SY169 ) )
| ~ ( sequential @ SY167 @ SY168 ) )
| ~ ! [SY170: $i,SY171: $i] :
( ~ ( precedes @ SY170 @ SY171 @ SV14 )
| ~ ( ~ ( precedes @ ( sK10_E3 @ SY171 @ SY170 @ SV14 ) @ SY171 @ SV14 )
| ~ ( sequential @ SY170 @ ( sK10_E3 @ SY171 @ SY170 @ SV14 ) ) )
| ( sequential @ SY170 @ SY171 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(190,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)],[168]) ).
thf(191,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)],[169]) ).
thf(192,plain,
! [SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK7_E1 @ SV5 ) @ SV5 )
| ~ ( on_path @ ( sK8_SY86 @ SV5 ) @ SV5 ) )
| ~ ( sequential @ ( sK7_E1 @ SV5 ) @ ( sK8_SY86 @ SV5 ) ) ) )
= $false )
| ( ( ! [SY98: $i,SY99: $i] :
~ ( path @ SY98 @ SY99 @ SV5 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV5 )
= ( number_of_in @ triangles @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[170]) ).
thf(193,plain,
! [SV5: $i] :
( ( ( ~ ! [SY97: $i] :
~ ( triangle @ ( sK7_E1 @ SV5 ) @ ( sK8_SY86 @ SV5 ) @ SY97 ) )
= $false )
| ( ( ! [SY98: $i,SY99: $i] :
~ ( path @ SY98 @ SY99 @ SV5 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV5 )
= ( number_of_in @ triangles @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[170]) ).
thf(194,plain,
! [SV35: $i,SV6: $i] :
( ( ! [SY206: $i] :
( ~ ( edge @ SV6 )
| ~ ( edge @ SV35 )
| ~ ( edge @ SY206 )
| ~ ( sequential @ SV6 @ SV35 )
| ~ ( sequential @ SV35 @ SY206 )
| ~ ( sequential @ SY206 @ SV6 )
| ( triangle @ SV6 @ SV35 @ SY206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(195,plain,
! [SV6: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY102: $i,SY103: $i] :
~ ( triangle @ SV6 @ SY102 @ SY103 )
| ( edge @ SV6 ) )
| ~ ! [SY104: $i] :
( ! [SY105: $i] :
~ ( triangle @ SV6 @ SY104 @ SY105 )
| ( edge @ SY104 ) ) )
| ~ ! [SY106: $i,SY107: $i] :
( ~ ( triangle @ SV6 @ SY106 @ SY107 )
| ( edge @ SY107 ) ) )
| ~ ! [SY108: $i] :
( ! [SY109: $i] :
~ ( triangle @ SV6 @ SY108 @ SY109 )
| ( sequential @ SV6 @ SY108 ) ) )
| ~ ! [SY110: $i,SY111: $i] :
( ~ ( triangle @ SV6 @ SY110 @ SY111 )
| ( sequential @ SY110 @ SY111 ) ) )
| ~ ! [SY112: $i,SY113: $i] :
( ~ ( triangle @ SV6 @ SY112 @ SY113 )
| ( sequential @ SY113 @ SV6 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(196,plain,
! [SV29: $i] :
( ( ( ~ ( edge @ SV29 ) )
= $true )
| ( ( vertex @ ( head_of @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(197,plain,
! [SV30: $i] :
( ( ( ~ ( edge @ SV30 ) )
= $true )
| ( ( vertex @ ( tail_of @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[174]) ).
thf(198,plain,
! [SV31: $i,SV24: $i] :
( ( ( ( SV24 = SV31 )
| ~ ( vertex @ SV24 )
| ~ ( vertex @ SV31 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV24
!= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
!= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
!= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
!= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV24
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
| ~ ( ( SV24
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) ) )
| ~ ~ ( ~ ( ( SV31
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
| ~ ( ( SV31
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) ) ) ) )
| ~ ( edge @ ( sK15_E @ SV31 @ SV24 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(199,plain,
! [SV7: $i] :
( ( ~ ( ! [SY114: $i,SY115: $i] :
~ ( path @ SV7 @ SY114 @ SY115 )
| ( vertex @ SV7 ) )
| ~ ! [SY116: $i] :
( ! [SY117: $i] :
~ ( path @ SV7 @ SY116 @ SY117 )
| ( vertex @ SY116 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(200,plain,
! [SV36: $i,SV7: $i] :
( ( ! [SY207: $i] :
( ~ ( path @ SV7 @ SV36 @ SY207 )
| ~ ( ~ ~ ( ( SV7
!= ( tail_of @ ( sK12_E @ SY207 @ SV36 @ SV7 ) ) )
| ~ ( edge @ ( sK12_E @ SY207 @ SV36 @ SV7 ) ) )
| ~ ~ ( ~ ( ( SV36
!= ( head_of @ ( sK12_E @ SY207 @ SV36 @ SV7 ) ) )
| ( SY207
!= ( path_cons @ ( sK12_E @ SY207 @ SV36 @ SV7 ) @ empty ) )
| ! [SY208: $i] :
( ( SY207
!= ( path_cons @ ( sK12_E @ SY207 @ SV36 @ SV7 ) @ SY208 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SY207 @ SV36 @ SV7 ) ) @ SV36 @ SY208 ) ) )
| ~ ~ ( ~ ( ( SV36
= ( head_of @ ( sK12_E @ SY207 @ SV36 @ SV7 ) ) )
| ~ ( ( SY207
!= ( path_cons @ ( sK12_E @ SY207 @ SV36 @ SV7 ) @ ( sK14_SY90 @ SY207 @ SV36 @ SV7 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SY207 @ SV36 @ SV7 ) ) @ SV36 @ ( sK14_SY90 @ SY207 @ SV36 @ SV7 ) ) ) )
| ~ ( ( SY207
= ( path_cons @ ( sK12_E @ SY207 @ SV36 @ SV7 ) @ empty ) )
| ~ ( ( SY207
!= ( path_cons @ ( sK12_E @ SY207 @ SV36 @ SV7 ) @ ( sK13_SY91 @ SY207 @ SV36 @ SV7 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SY207 @ SV36 @ SV7 ) ) @ SV36 @ ( sK13_SY91 @ SY207 @ SV36 @ SV7 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(201,plain,
! [SV25: $i,SV18: $i,SV8: $i] :
( ( ( ~ ( vertex @ SV8 )
| ~ ( vertex @ SV18 ) )
= $true )
| ( ( ~ ( ~ ! [SY195: $i] :
( ( SV8
!= ( tail_of @ SY195 ) )
| ~ ( edge @ SY195 )
| ( SV18
!= ( head_of @ SY195 ) )
| ( SV25
!= ( path_cons @ SY195 @ empty ) ) )
| ~ ! [SY196: $i] :
( ( SV8
!= ( tail_of @ SY196 ) )
| ~ ( edge @ SY196 )
| ! [SY197: $i] :
( ( SV25
!= ( path_cons @ SY196 @ SY197 ) )
| ~ ( path @ ( head_of @ SY196 ) @ SV18 @ SY197 ) ) ) ) )
= $true )
| ( ( path @ SV8 @ SV18 @ SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(202,plain,
! [SV19: $i,SV9: $i] :
( ( ~ ( ~ ! [SY178: $i,SY179: $i] :
( ~ ( on_path @ SY179 @ SY178 )
| ~ ( path @ SV9 @ SV19 @ SY178 )
| ( edge @ SY179 ) )
| ~ ! [SY180: $i,SY181: $i] :
( ~ ( on_path @ SY181 @ SY180 )
| ~ ( path @ SV9 @ SV19 @ SY180 )
| ( in_path @ ( head_of @ SY181 ) @ SY180 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[179]) ).
thf(203,plain,
! [SV19: $i,SV9: $i] :
( ( ! [SY182: $i,SY183: $i] :
( ~ ( on_path @ SY183 @ SY182 )
| ~ ( path @ SV9 @ SV19 @ SY182 )
| ( in_path @ ( tail_of @ SY183 ) @ SY182 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[180]) ).
thf(204,plain,
! [SV20: $i,SV10: $i] :
( ( ! [SY184: $i,SY185: $i] :
( ~ ( in_path @ SY185 @ SY184 )
| ~ ( path @ SV10 @ SV20 @ SY184 )
| ~ ( ~ ( on_path @ ( sK11_E @ SY185 @ SY184 @ SV20 @ SV10 ) @ SY184 )
| ~ ( ( SY185
= ( head_of @ ( sK11_E @ SY185 @ SY184 @ SV20 @ SV10 ) ) )
| ( SY185
= ( tail_of @ ( sK11_E @ SY185 @ SY184 @ SV20 @ SV10 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[181]) ).
thf(205,plain,
! [SV20: $i,SV10: $i] :
( ( ! [SY186: $i,SY187: $i] :
( ~ ( in_path @ SY187 @ SY186 )
| ~ ( path @ SV10 @ SV20 @ SY186 )
| ( vertex @ SY187 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[182]) ).
thf(206,plain,
! [SV37: $i,SV11: $i] :
( ( ! [SY209: $i] :
( ~ ( ~ ( path @ SV11 @ SV37 @ ( sK9_P @ SY209 @ SV37 @ SV11 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY209 ) @ ( length_of @ ( sK9_P @ SY209 @ SV37 @ SV11 ) ) ) )
| ( SV11 = SV37 )
| ~ ( path @ SV11 @ SV37 @ SY209 )
| ( shortest_path @ SV11 @ SV37 @ SY209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(207,plain,
! [SV11: $i] :
( ( ~ ! [SY140: $i,SY141: $i] :
( ~ ( shortest_path @ SV11 @ SY140 @ SY141 )
| ! [SY142: $i] :
( ~ ( path @ SV11 @ SY140 @ SY142 )
| ( less_or_equal @ ( length_of @ SY141 ) @ ( length_of @ SY142 ) ) ) )
| ~ ~ ( ~ ! [SY143: $i] :
( ! [SY144: $i] :
~ ( shortest_path @ SV11 @ SY143 @ SY144 )
| ( SV11 != SY143 ) )
| ~ ! [SY145: $i,SY146: $i] :
( ~ ( shortest_path @ SV11 @ SY145 @ SY146 )
| ( path @ SV11 @ SY145 @ SY146 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(208,plain,
! [SV38: $i,SV32: $i] :
( ( ( SV32 = SV38 )
| ~ ( edge @ SV32 )
| ~ ( edge @ SV38 )
| ( ( head_of @ SV32 )
!= ( tail_of @ SV38 ) )
| ( sequential @ SV32 @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(209,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)],[186]) ).
thf(210,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[186]) ).
thf(211,plain,
! [SV12: $i,SV33: $i,SV26: $i] :
( ( ( path @ SV26 @ SV33 @ SV12 )
= $false )
| ( ( ~ ( ~ ! [SY149: $i,SY150: $i] :
( ~ ( on_path @ SY149 @ SV12 )
| ~ ( on_path @ SY150 @ SV12 )
| ! [SY151: $i] :
( ~ ( precedes @ SY151 @ SY150 @ SV12 )
| ~ ( sequential @ SY149 @ SY151 ) )
| ( precedes @ SY149 @ SY150 @ SV12 ) )
| ~ ! [SY152: $i,SY153: $i] :
( ~ ( on_path @ SY152 @ SV12 )
| ~ ( on_path @ SY153 @ SV12 )
| ~ ( sequential @ SY152 @ SY153 )
| ( precedes @ SY152 @ SY153 @ SV12 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(212,plain,
! [SV21: $i,SV13: $i,SV27: $i] :
( ( ~ ! [SY199: $i] :
( ! [SY200: $i] :
( ~ ( precedes @ SV27 @ SY199 @ SY200 )
| ~ ( shortest_path @ SV13 @ SV21 @ SY200 ) )
| ! [SY201: $i] :
( ( ( tail_of @ SY201 )
!= ( tail_of @ SV27 ) )
| ( ( head_of @ SY201 )
!= ( head_of @ SY199 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[188]) ).
thf(213,plain,
! [SV21: $i,SV13: $i,SV27: $i] :
( ( ~ ! [SY202: $i,SY203: $i] :
( ~ ( precedes @ SV27 @ SY202 @ SY203 )
| ~ ( shortest_path @ SV13 @ SV21 @ SY203 )
| ~ ( precedes @ SY202 @ SV27 @ SY203 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[188]) ).
thf(214,plain,
! [SV14: $i,SV34: $i,SV28: $i] :
( ( ( path @ SV28 @ SV34 @ SV14 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY163: $i] :
( ! [SY164: $i] :
~ ( precedes @ SY163 @ SY164 @ SV14 )
| ( on_path @ SY163 @ SV14 ) )
| ~ ! [SY165: $i,SY166: $i] :
( ~ ( precedes @ SY165 @ SY166 @ SV14 )
| ( on_path @ SY166 @ SV14 ) ) )
| ~ ~ ( ~ ! [SY167: $i,SY168: $i] :
( ~ ( precedes @ SY167 @ SY168 @ SV14 )
| ! [SY169: $i] :
( ~ ( precedes @ SY169 @ SY168 @ SV14 )
| ~ ( sequential @ SY167 @ SY169 ) )
| ~ ( sequential @ SY167 @ SY168 ) )
| ~ ! [SY170: $i,SY171: $i] :
( ~ ( precedes @ SY170 @ SY171 @ SV14 )
| ~ ( ~ ( precedes @ ( sK10_E3 @ SY171 @ SY170 @ SV14 ) @ SY171 @ SV14 )
| ~ ( sequential @ SY170 @ ( sK10_E3 @ SY171 @ SY170 @ SV14 ) ) )
| ( sequential @ SY170 @ SY171 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(215,plain,
! [SV5: $i] :
( ( ( ~ ( ~ ~ ( ~ ( on_path @ ( sK7_E1 @ SV5 ) @ SV5 )
| ~ ( on_path @ ( sK8_SY86 @ SV5 ) @ SV5 ) )
| ~ ( sequential @ ( sK7_E1 @ SV5 ) @ ( sK8_SY86 @ SV5 ) ) ) )
= $true )
| ( ( ! [SY98: $i,SY99: $i] :
~ ( path @ SY98 @ SY99 @ SV5 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV5 )
= ( number_of_in @ triangles @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[192]) ).
thf(216,plain,
! [SV5: $i] :
( ( ( ! [SY97: $i] :
~ ( triangle @ ( sK7_E1 @ SV5 ) @ ( sK8_SY86 @ SV5 ) @ SY97 ) )
= $true )
| ( ( ! [SY98: $i,SY99: $i] :
~ ( path @ SY98 @ SY99 @ SV5 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV5 )
= ( number_of_in @ triangles @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[193]) ).
thf(217,plain,
! [SV39: $i,SV35: $i,SV6: $i] :
( ( ~ ( edge @ SV6 )
| ~ ( edge @ SV35 )
| ~ ( edge @ SV39 )
| ~ ( sequential @ SV6 @ SV35 )
| ~ ( sequential @ SV35 @ SV39 )
| ~ ( sequential @ SV39 @ SV6 )
| ( triangle @ SV6 @ SV35 @ SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(218,plain,
! [SV6: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY102: $i,SY103: $i] :
~ ( triangle @ SV6 @ SY102 @ SY103 )
| ( edge @ SV6 ) )
| ~ ! [SY104: $i] :
( ! [SY105: $i] :
~ ( triangle @ SV6 @ SY104 @ SY105 )
| ( edge @ SY104 ) ) )
| ~ ! [SY106: $i,SY107: $i] :
( ~ ( triangle @ SV6 @ SY106 @ SY107 )
| ( edge @ SY107 ) ) )
| ~ ! [SY108: $i] :
( ! [SY109: $i] :
~ ( triangle @ SV6 @ SY108 @ SY109 )
| ( sequential @ SV6 @ SY108 ) ) )
| ~ ! [SY110: $i,SY111: $i] :
( ~ ( triangle @ SV6 @ SY110 @ SY111 )
| ( sequential @ SY110 @ SY111 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[195]) ).
thf(219,plain,
! [SV6: $i] :
( ( ~ ! [SY112: $i,SY113: $i] :
( ~ ( triangle @ SV6 @ SY112 @ SY113 )
| ( sequential @ SY113 @ SV6 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[195]) ).
thf(220,plain,
! [SV29: $i] :
( ( ( edge @ SV29 )
= $false )
| ( ( vertex @ ( head_of @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(221,plain,
! [SV30: $i] :
( ( ( edge @ SV30 )
= $false )
| ( ( vertex @ ( tail_of @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(222,plain,
! [SV31: $i,SV24: $i] :
( ( ( SV24 = SV31 )
= $true )
| ( ( ~ ( vertex @ SV24 )
| ~ ( vertex @ SV31 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV24
!= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
!= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
!= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
!= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV24
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
| ~ ( ( SV24
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) ) )
| ~ ~ ( ~ ( ( SV31
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
| ~ ( ( SV31
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) ) ) ) )
| ~ ( edge @ ( sK15_E @ SV31 @ SV24 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(223,plain,
! [SV7: $i] :
( ( ~ ( ! [SY114: $i,SY115: $i] :
~ ( path @ SV7 @ SY114 @ SY115 )
| ( vertex @ SV7 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[199]) ).
thf(224,plain,
! [SV7: $i] :
( ( ~ ! [SY116: $i] :
( ! [SY117: $i] :
~ ( path @ SV7 @ SY116 @ SY117 )
| ( vertex @ SY116 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[199]) ).
thf(225,plain,
! [SV40: $i,SV36: $i,SV7: $i] :
( ( ~ ( path @ SV7 @ SV36 @ SV40 )
| ~ ( ~ ~ ( ( SV7
!= ( tail_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( edge @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
| ~ ~ ( ~ ( ( SV36
!= ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
| ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ empty ) )
| ! [SY210: $i] :
( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ SY210 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ SY210 ) ) )
| ~ ~ ( ~ ( ( SV36
= ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ ( sK14_SY90 @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ ( sK14_SY90 @ SV40 @ SV36 @ SV7 ) ) ) )
| ~ ( ( SV40
= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ empty ) )
| ~ ( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ ( sK13_SY91 @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ ( sK13_SY91 @ SV40 @ SV36 @ SV7 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(226,plain,
! [SV25: $i,SV18: $i,SV8: $i] :
( ( ( ~ ( vertex @ SV8 ) )
= $true )
| ( ( ~ ( vertex @ SV18 ) )
= $true )
| ( ( ~ ( ~ ! [SY195: $i] :
( ( SV8
!= ( tail_of @ SY195 ) )
| ~ ( edge @ SY195 )
| ( SV18
!= ( head_of @ SY195 ) )
| ( SV25
!= ( path_cons @ SY195 @ empty ) ) )
| ~ ! [SY196: $i] :
( ( SV8
!= ( tail_of @ SY196 ) )
| ~ ( edge @ SY196 )
| ! [SY197: $i] :
( ( SV25
!= ( path_cons @ SY196 @ SY197 ) )
| ~ ( path @ ( head_of @ SY196 ) @ SV18 @ SY197 ) ) ) ) )
= $true )
| ( ( path @ SV8 @ SV18 @ SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(227,plain,
! [SV19: $i,SV9: $i] :
( ( ~ ! [SY178: $i,SY179: $i] :
( ~ ( on_path @ SY179 @ SY178 )
| ~ ( path @ SV9 @ SV19 @ SY178 )
| ( edge @ SY179 ) )
| ~ ! [SY180: $i,SY181: $i] :
( ~ ( on_path @ SY181 @ SY180 )
| ~ ( path @ SV9 @ SV19 @ SY180 )
| ( in_path @ ( head_of @ SY181 ) @ SY180 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(228,plain,
! [SV19: $i,SV9: $i,SV41: $i] :
( ( ! [SY211: $i] :
( ~ ( on_path @ SY211 @ SV41 )
| ~ ( path @ SV9 @ SV19 @ SV41 )
| ( in_path @ ( tail_of @ SY211 ) @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(229,plain,
! [SV20: $i,SV10: $i,SV42: $i] :
( ( ! [SY212: $i] :
( ~ ( in_path @ SY212 @ SV42 )
| ~ ( path @ SV10 @ SV20 @ SV42 )
| ~ ( ~ ( on_path @ ( sK11_E @ SY212 @ SV42 @ SV20 @ SV10 ) @ SV42 )
| ~ ( ( SY212
= ( head_of @ ( sK11_E @ SY212 @ SV42 @ SV20 @ SV10 ) ) )
| ( SY212
= ( tail_of @ ( sK11_E @ SY212 @ SV42 @ SV20 @ SV10 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(230,plain,
! [SV20: $i,SV10: $i,SV43: $i] :
( ( ! [SY213: $i] :
( ~ ( in_path @ SY213 @ SV43 )
| ~ ( path @ SV10 @ SV20 @ SV43 )
| ( vertex @ SY213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(231,plain,
! [SV44: $i,SV37: $i,SV11: $i] :
( ( ~ ( ~ ( path @ SV11 @ SV37 @ ( sK9_P @ SV44 @ SV37 @ SV11 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SV44 ) @ ( length_of @ ( sK9_P @ SV44 @ SV37 @ SV11 ) ) ) )
| ( SV11 = SV37 )
| ~ ( path @ SV11 @ SV37 @ SV44 )
| ( shortest_path @ SV11 @ SV37 @ SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(232,plain,
! [SV11: $i] :
( ( ~ ! [SY140: $i,SY141: $i] :
( ~ ( shortest_path @ SV11 @ SY140 @ SY141 )
| ! [SY142: $i] :
( ~ ( path @ SV11 @ SY140 @ SY142 )
| ( less_or_equal @ ( length_of @ SY141 ) @ ( length_of @ SY142 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[207]) ).
thf(233,plain,
! [SV11: $i] :
( ( ~ ~ ( ~ ! [SY143: $i] :
( ! [SY144: $i] :
~ ( shortest_path @ SV11 @ SY143 @ SY144 )
| ( SV11 != SY143 ) )
| ~ ! [SY145: $i,SY146: $i] :
( ~ ( shortest_path @ SV11 @ SY145 @ SY146 )
| ( path @ SV11 @ SY145 @ SY146 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[207]) ).
thf(234,plain,
! [SV38: $i,SV32: $i] :
( ( ( ( SV32 = SV38 )
| ~ ( edge @ SV32 )
| ~ ( edge @ SV38 )
| ( ( head_of @ SV32 )
!= ( tail_of @ SV38 ) ) )
= $true )
| ( ( sequential @ SV32 @ SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[208]) ).
thf(235,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)],[209]) ).
thf(236,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[210]) ).
thf(237,plain,
! [SV33: $i,SV26: $i,SV12: $i] :
( ( ( ~ ! [SY149: $i,SY150: $i] :
( ~ ( on_path @ SY149 @ SV12 )
| ~ ( on_path @ SY150 @ SV12 )
| ! [SY151: $i] :
( ~ ( precedes @ SY151 @ SY150 @ SV12 )
| ~ ( sequential @ SY149 @ SY151 ) )
| ( precedes @ SY149 @ SY150 @ SV12 ) )
| ~ ! [SY152: $i,SY153: $i] :
( ~ ( on_path @ SY152 @ SV12 )
| ~ ( on_path @ SY153 @ SV12 )
| ~ ( sequential @ SY152 @ SY153 )
| ( precedes @ SY152 @ SY153 @ SV12 ) ) )
= $false )
| ( ( path @ SV26 @ SV33 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(238,plain,
! [SV21: $i,SV13: $i,SV27: $i] :
( ( ! [SY199: $i] :
( ! [SY200: $i] :
( ~ ( precedes @ SV27 @ SY199 @ SY200 )
| ~ ( shortest_path @ SV13 @ SV21 @ SY200 ) )
| ! [SY201: $i] :
( ( ( tail_of @ SY201 )
!= ( tail_of @ SV27 ) )
| ( ( head_of @ SY201 )
!= ( head_of @ SY199 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[212]) ).
thf(239,plain,
! [SV21: $i,SV13: $i,SV27: $i] :
( ( ! [SY202: $i,SY203: $i] :
( ~ ( precedes @ SV27 @ SY202 @ SY203 )
| ~ ( shortest_path @ SV13 @ SV21 @ SY203 )
| ~ ( precedes @ SY202 @ SV27 @ SY203 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[213]) ).
thf(240,plain,
! [SV34: $i,SV28: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ! [SY163: $i] :
( ! [SY164: $i] :
~ ( precedes @ SY163 @ SY164 @ SV14 )
| ( on_path @ SY163 @ SV14 ) )
| ~ ! [SY165: $i,SY166: $i] :
( ~ ( precedes @ SY165 @ SY166 @ SV14 )
| ( on_path @ SY166 @ SV14 ) ) )
| ~ ~ ( ~ ! [SY167: $i,SY168: $i] :
( ~ ( precedes @ SY167 @ SY168 @ SV14 )
| ! [SY169: $i] :
( ~ ( precedes @ SY169 @ SY168 @ SV14 )
| ~ ( sequential @ SY167 @ SY169 ) )
| ~ ( sequential @ SY167 @ SY168 ) )
| ~ ! [SY170: $i,SY171: $i] :
( ~ ( precedes @ SY170 @ SY171 @ SV14 )
| ~ ( ~ ( precedes @ ( sK10_E3 @ SY171 @ SY170 @ SV14 ) @ SY171 @ SV14 )
| ~ ( sequential @ SY170 @ ( sK10_E3 @ SY171 @ SY170 @ SV14 ) ) )
| ( sequential @ SY170 @ SY171 ) ) ) )
= $false )
| ( ( path @ SV28 @ SV34 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(241,plain,
! [SV5: $i] :
( ( ( ~ ~ ( ~ ( on_path @ ( sK7_E1 @ SV5 ) @ SV5 )
| ~ ( on_path @ ( sK8_SY86 @ SV5 ) @ SV5 ) )
| ~ ( sequential @ ( sK7_E1 @ SV5 ) @ ( sK8_SY86 @ SV5 ) ) )
= $false )
| ( ( ! [SY98: $i,SY99: $i] :
~ ( path @ SY98 @ SY99 @ SV5 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV5 )
= ( number_of_in @ triangles @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(242,plain,
! [SV45: $i,SV5: $i] :
( ( ( ~ ( triangle @ ( sK7_E1 @ SV5 ) @ ( sK8_SY86 @ SV5 ) @ SV45 ) )
= $true )
| ( ( ! [SY98: $i,SY99: $i] :
~ ( path @ SY98 @ SY99 @ SV5 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV5 )
= ( number_of_in @ triangles @ SV5 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(243,plain,
! [SV39: $i,SV35: $i,SV6: $i] :
( ( ( ~ ( edge @ SV6 )
| ~ ( edge @ SV35 )
| ~ ( edge @ SV39 )
| ~ ( sequential @ SV6 @ SV35 )
| ~ ( sequential @ SV35 @ SV39 )
| ~ ( sequential @ SV39 @ SV6 ) )
= $true )
| ( ( triangle @ SV6 @ SV35 @ SV39 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[217]) ).
thf(244,plain,
! [SV6: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY102: $i,SY103: $i] :
~ ( triangle @ SV6 @ SY102 @ SY103 )
| ( edge @ SV6 ) )
| ~ ! [SY104: $i] :
( ! [SY105: $i] :
~ ( triangle @ SV6 @ SY104 @ SY105 )
| ( edge @ SY104 ) ) )
| ~ ! [SY106: $i,SY107: $i] :
( ~ ( triangle @ SV6 @ SY106 @ SY107 )
| ( edge @ SY107 ) ) )
| ~ ! [SY108: $i] :
( ! [SY109: $i] :
~ ( triangle @ SV6 @ SY108 @ SY109 )
| ( sequential @ SV6 @ SY108 ) ) )
| ~ ! [SY110: $i,SY111: $i] :
( ~ ( triangle @ SV6 @ SY110 @ SY111 )
| ( sequential @ SY110 @ SY111 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[218]) ).
thf(245,plain,
! [SV6: $i] :
( ( ! [SY112: $i,SY113: $i] :
( ~ ( triangle @ SV6 @ SY112 @ SY113 )
| ( sequential @ SY113 @ SV6 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[219]) ).
thf(246,plain,
! [SV31: $i,SV24: $i] :
( ( ( ~ ( vertex @ SV24 ) )
= $true )
| ( ( ~ ( vertex @ SV31 ) )
= $true )
| ( ( SV24 = SV31 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV24
!= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
!= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
!= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
!= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV24
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
| ~ ( ( SV24
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) ) )
| ~ ~ ( ~ ( ( SV31
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
| ~ ( ( SV31
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) ) ) ) )
| ~ ( edge @ ( sK15_E @ SV31 @ SV24 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[222]) ).
thf(247,plain,
! [SV7: $i] :
( ( ! [SY114: $i,SY115: $i] :
~ ( path @ SV7 @ SY114 @ SY115 )
| ( vertex @ SV7 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[223]) ).
thf(248,plain,
! [SV7: $i] :
( ( ! [SY116: $i] :
( ! [SY117: $i] :
~ ( path @ SV7 @ SY116 @ SY117 )
| ( vertex @ SY116 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[224]) ).
thf(249,plain,
! [SV40: $i,SV36: $i,SV7: $i] :
( ( ( ~ ( path @ SV7 @ SV36 @ SV40 ) )
= $true )
| ( ( ~ ( ~ ~ ( ( SV7
!= ( tail_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( edge @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
| ~ ~ ( ~ ( ( SV36
!= ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
| ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ empty ) )
| ! [SY210: $i] :
( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ SY210 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ SY210 ) ) )
| ~ ~ ( ~ ( ( SV36
= ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ ( sK14_SY90 @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ ( sK14_SY90 @ SV40 @ SV36 @ SV7 ) ) ) )
| ~ ( ( SV40
= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ empty ) )
| ~ ( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ ( sK13_SY91 @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ ( sK13_SY91 @ SV40 @ SV36 @ SV7 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(250,plain,
! [SV25: $i,SV18: $i,SV8: $i] :
( ( ( vertex @ SV8 )
= $false )
| ( ( ~ ( vertex @ SV18 ) )
= $true )
| ( ( ~ ( ~ ! [SY195: $i] :
( ( SV8
!= ( tail_of @ SY195 ) )
| ~ ( edge @ SY195 )
| ( SV18
!= ( head_of @ SY195 ) )
| ( SV25
!= ( path_cons @ SY195 @ empty ) ) )
| ~ ! [SY196: $i] :
( ( SV8
!= ( tail_of @ SY196 ) )
| ~ ( edge @ SY196 )
| ! [SY197: $i] :
( ( SV25
!= ( path_cons @ SY196 @ SY197 ) )
| ~ ( path @ ( head_of @ SY196 ) @ SV18 @ SY197 ) ) ) ) )
= $true )
| ( ( path @ SV8 @ SV18 @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(251,plain,
! [SV19: $i,SV9: $i] :
( ( ~ ! [SY178: $i,SY179: $i] :
( ~ ( on_path @ SY179 @ SY178 )
| ~ ( path @ SV9 @ SV19 @ SY178 )
| ( edge @ SY179 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[227]) ).
thf(252,plain,
! [SV19: $i,SV9: $i] :
( ( ~ ! [SY180: $i,SY181: $i] :
( ~ ( on_path @ SY181 @ SY180 )
| ~ ( path @ SV9 @ SV19 @ SY180 )
| ( in_path @ ( head_of @ SY181 ) @ SY180 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[227]) ).
thf(253,plain,
! [SV19: $i,SV9: $i,SV41: $i,SV46: $i] :
( ( ~ ( on_path @ SV46 @ SV41 )
| ~ ( path @ SV9 @ SV19 @ SV41 )
| ( in_path @ ( tail_of @ SV46 ) @ SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(254,plain,
! [SV20: $i,SV10: $i,SV42: $i,SV47: $i] :
( ( ~ ( in_path @ SV47 @ SV42 )
| ~ ( path @ SV10 @ SV20 @ SV42 )
| ~ ( ~ ( on_path @ ( sK11_E @ SV47 @ SV42 @ SV20 @ SV10 ) @ SV42 )
| ~ ( ( SV47
= ( head_of @ ( sK11_E @ SV47 @ SV42 @ SV20 @ SV10 ) ) )
| ( SV47
= ( tail_of @ ( sK11_E @ SV47 @ SV42 @ SV20 @ SV10 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(255,plain,
! [SV20: $i,SV10: $i,SV43: $i,SV48: $i] :
( ( ~ ( in_path @ SV48 @ SV43 )
| ~ ( path @ SV10 @ SV20 @ SV43 )
| ( vertex @ SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(256,plain,
! [SV44: $i,SV37: $i,SV11: $i] :
( ( ( ~ ( ~ ( path @ SV11 @ SV37 @ ( sK9_P @ SV44 @ SV37 @ SV11 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SV44 ) @ ( length_of @ ( sK9_P @ SV44 @ SV37 @ SV11 ) ) ) )
| ( SV11 = SV37 )
| ~ ( path @ SV11 @ SV37 @ SV44 ) )
= $true )
| ( ( shortest_path @ SV11 @ SV37 @ SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[231]) ).
thf(257,plain,
! [SV11: $i] :
( ( ! [SY140: $i,SY141: $i] :
( ~ ( shortest_path @ SV11 @ SY140 @ SY141 )
| ! [SY142: $i] :
( ~ ( path @ SV11 @ SY140 @ SY142 )
| ( less_or_equal @ ( length_of @ SY141 ) @ ( length_of @ SY142 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[232]) ).
thf(258,plain,
! [SV11: $i] :
( ( ~ ( ~ ! [SY143: $i] :
( ! [SY144: $i] :
~ ( shortest_path @ SV11 @ SY143 @ SY144 )
| ( SV11 != SY143 ) )
| ~ ! [SY145: $i,SY146: $i] :
( ~ ( shortest_path @ SV11 @ SY145 @ SY146 )
| ( path @ SV11 @ SY145 @ SY146 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[233]) ).
thf(259,plain,
! [SV38: $i,SV32: $i] :
( ( ( ( SV32 = SV38 )
| ~ ( edge @ SV32 )
| ~ ( edge @ SV38 ) )
= $true )
| ( ( ( ( head_of @ SV32 )
!= ( tail_of @ SV38 ) ) )
= $true )
| ( ( sequential @ SV32 @ SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[234]) ).
thf(260,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)],[235]) ).
thf(261,plain,
! [SV49: $i] :
( ( ! [SY214: $i] :
( ~ ( sequential @ SV49 @ SY214 )
| ( ( head_of @ SV49 )
= ( tail_of @ SY214 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[236]) ).
thf(262,plain,
! [SV33: $i,SV26: $i,SV12: $i] :
( ( ( ~ ! [SY149: $i,SY150: $i] :
( ~ ( on_path @ SY149 @ SV12 )
| ~ ( on_path @ SY150 @ SV12 )
| ! [SY151: $i] :
( ~ ( precedes @ SY151 @ SY150 @ SV12 )
| ~ ( sequential @ SY149 @ SY151 ) )
| ( precedes @ SY149 @ SY150 @ SV12 ) ) )
= $false )
| ( ( path @ SV26 @ SV33 @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[237]) ).
thf(263,plain,
! [SV33: $i,SV26: $i,SV12: $i] :
( ( ( ~ ! [SY152: $i,SY153: $i] :
( ~ ( on_path @ SY152 @ SV12 )
| ~ ( on_path @ SY153 @ SV12 )
| ~ ( sequential @ SY152 @ SY153 )
| ( precedes @ SY152 @ SY153 @ SV12 ) ) )
= $false )
| ( ( path @ SV26 @ SV33 @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[237]) ).
thf(264,plain,
! [SV21: $i,SV13: $i,SV50: $i,SV27: $i] :
( ( ! [SY215: $i] :
( ~ ( precedes @ SV27 @ SV50 @ SY215 )
| ~ ( shortest_path @ SV13 @ SV21 @ SY215 ) )
| ! [SY216: $i] :
( ( ( tail_of @ SY216 )
!= ( tail_of @ SV27 ) )
| ( ( head_of @ SY216 )
!= ( head_of @ SV50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(265,plain,
! [SV21: $i,SV13: $i,SV51: $i,SV27: $i] :
( ( ! [SY217: $i] :
( ~ ( precedes @ SV27 @ SV51 @ SY217 )
| ~ ( shortest_path @ SV13 @ SV21 @ SY217 )
| ~ ( precedes @ SV51 @ SV27 @ SY217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(266,plain,
! [SV34: $i,SV28: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ! [SY163: $i] :
( ! [SY164: $i] :
~ ( precedes @ SY163 @ SY164 @ SV14 )
| ( on_path @ SY163 @ SV14 ) )
| ~ ! [SY165: $i,SY166: $i] :
( ~ ( precedes @ SY165 @ SY166 @ SV14 )
| ( on_path @ SY166 @ SV14 ) ) ) )
= $false )
| ( ( path @ SV28 @ SV34 @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[240]) ).
thf(267,plain,
! [SV34: $i,SV28: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ! [SY167: $i,SY168: $i] :
( ~ ( precedes @ SY167 @ SY168 @ SV14 )
| ! [SY169: $i] :
( ~ ( precedes @ SY169 @ SY168 @ SV14 )
| ~ ( sequential @ SY167 @ SY169 ) )
| ~ ( sequential @ SY167 @ SY168 ) )
| ~ ! [SY170: $i,SY171: $i] :
( ~ ( precedes @ SY170 @ SY171 @ SV14 )
| ~ ( ~ ( precedes @ ( sK10_E3 @ SY171 @ SY170 @ SV14 ) @ SY171 @ SV14 )
| ~ ( sequential @ SY170 @ ( sK10_E3 @ SY171 @ SY170 @ SV14 ) ) )
| ( sequential @ SY170 @ SY171 ) ) ) )
= $false )
| ( ( path @ SV28 @ SV34 @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[240]) ).
thf(268,plain,
! [SV5: $i] :
( ( ( ~ ~ ( ~ ( on_path @ ( sK7_E1 @ SV5 ) @ SV5 )
| ~ ( on_path @ ( sK8_SY86 @ SV5 ) @ SV5 ) ) )
= $false )
| ( ( ! [SY98: $i,SY99: $i] :
~ ( path @ SY98 @ SY99 @ SV5 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV5 )
= ( number_of_in @ triangles @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[241]) ).
thf(269,plain,
! [SV5: $i] :
( ( ( ~ ( sequential @ ( sK7_E1 @ SV5 ) @ ( sK8_SY86 @ SV5 ) ) )
= $false )
| ( ( ! [SY98: $i,SY99: $i] :
~ ( path @ SY98 @ SY99 @ SV5 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV5 )
= ( number_of_in @ triangles @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[241]) ).
thf(270,plain,
! [SV45: $i,SV5: $i] :
( ( ( triangle @ ( sK7_E1 @ SV5 ) @ ( sK8_SY86 @ SV5 ) @ SV45 )
= $false )
| ( ( ! [SY98: $i,SY99: $i] :
~ ( path @ SY98 @ SY99 @ SV5 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV5 )
= ( number_of_in @ triangles @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(271,plain,
! [SV39: $i,SV35: $i,SV6: $i] :
( ( ( ~ ( edge @ SV6 )
| ~ ( edge @ SV35 )
| ~ ( edge @ SV39 )
| ~ ( sequential @ SV6 @ SV35 )
| ~ ( sequential @ SV35 @ SV39 ) )
= $true )
| ( ( ~ ( sequential @ SV39 @ SV6 ) )
= $true )
| ( ( triangle @ SV6 @ SV35 @ SV39 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[243]) ).
thf(272,plain,
! [SV6: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY102: $i,SY103: $i] :
~ ( triangle @ SV6 @ SY102 @ SY103 )
| ( edge @ SV6 ) )
| ~ ! [SY104: $i] :
( ! [SY105: $i] :
~ ( triangle @ SV6 @ SY104 @ SY105 )
| ( edge @ SY104 ) ) )
| ~ ! [SY106: $i,SY107: $i] :
( ~ ( triangle @ SV6 @ SY106 @ SY107 )
| ( edge @ SY107 ) ) )
| ~ ! [SY108: $i] :
( ! [SY109: $i] :
~ ( triangle @ SV6 @ SY108 @ SY109 )
| ( sequential @ SV6 @ SY108 ) ) )
| ~ ! [SY110: $i,SY111: $i] :
( ~ ( triangle @ SV6 @ SY110 @ SY111 )
| ( sequential @ SY110 @ SY111 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(273,plain,
! [SV52: $i,SV6: $i] :
( ( ! [SY218: $i] :
( ~ ( triangle @ SV6 @ SV52 @ SY218 )
| ( sequential @ SY218 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[245]) ).
thf(274,plain,
! [SV31: $i,SV24: $i] :
( ( ( vertex @ SV24 )
= $false )
| ( ( ~ ( vertex @ SV31 ) )
= $true )
| ( ( SV24 = SV31 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV24
!= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
!= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
!= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
!= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV24
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
| ~ ( ( SV24
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) ) )
| ~ ~ ( ~ ( ( SV31
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
| ~ ( ( SV31
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) ) ) ) )
| ~ ( edge @ ( sK15_E @ SV31 @ SV24 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(275,plain,
! [SV7: $i] :
( ( ( ! [SY114: $i,SY115: $i] :
~ ( path @ SV7 @ SY114 @ SY115 ) )
= $true )
| ( ( vertex @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[247]) ).
thf(276,plain,
! [SV53: $i,SV7: $i] :
( ( ! [SY219: $i] :
~ ( path @ SV7 @ SV53 @ SY219 )
| ( vertex @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[248]) ).
thf(277,plain,
! [SV40: $i,SV36: $i,SV7: $i] :
( ( ( path @ SV7 @ SV36 @ SV40 )
= $false )
| ( ( ~ ( ~ ~ ( ( SV7
!= ( tail_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( edge @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
| ~ ~ ( ~ ( ( SV36
!= ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
| ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ empty ) )
| ! [SY210: $i] :
( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ SY210 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ SY210 ) ) )
| ~ ~ ( ~ ( ( SV36
= ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ ( sK14_SY90 @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ ( sK14_SY90 @ SV40 @ SV36 @ SV7 ) ) ) )
| ~ ( ( SV40
= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ empty ) )
| ~ ( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ ( sK13_SY91 @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ ( sK13_SY91 @ SV40 @ SV36 @ SV7 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(278,plain,
! [SV25: $i,SV8: $i,SV18: $i] :
( ( ( vertex @ SV18 )
= $false )
| ( ( vertex @ SV8 )
= $false )
| ( ( ~ ( ~ ! [SY195: $i] :
( ( SV8
!= ( tail_of @ SY195 ) )
| ~ ( edge @ SY195 )
| ( SV18
!= ( head_of @ SY195 ) )
| ( SV25
!= ( path_cons @ SY195 @ empty ) ) )
| ~ ! [SY196: $i] :
( ( SV8
!= ( tail_of @ SY196 ) )
| ~ ( edge @ SY196 )
| ! [SY197: $i] :
( ( SV25
!= ( path_cons @ SY196 @ SY197 ) )
| ~ ( path @ ( head_of @ SY196 ) @ SV18 @ SY197 ) ) ) ) )
= $true )
| ( ( path @ SV8 @ SV18 @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[250]) ).
thf(279,plain,
! [SV19: $i,SV9: $i] :
( ( ! [SY178: $i,SY179: $i] :
( ~ ( on_path @ SY179 @ SY178 )
| ~ ( path @ SV9 @ SV19 @ SY178 )
| ( edge @ SY179 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[251]) ).
thf(280,plain,
! [SV19: $i,SV9: $i] :
( ( ! [SY180: $i,SY181: $i] :
( ~ ( on_path @ SY181 @ SY180 )
| ~ ( path @ SV9 @ SV19 @ SY180 )
| ( in_path @ ( head_of @ SY181 ) @ SY180 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[252]) ).
thf(281,plain,
! [SV19: $i,SV9: $i,SV41: $i,SV46: $i] :
( ( ( ~ ( on_path @ SV46 @ SV41 )
| ~ ( path @ SV9 @ SV19 @ SV41 ) )
= $true )
| ( ( in_path @ ( tail_of @ SV46 ) @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[253]) ).
thf(282,plain,
! [SV20: $i,SV10: $i,SV42: $i,SV47: $i] :
( ( ( ~ ( in_path @ SV47 @ SV42 )
| ~ ( path @ SV10 @ SV20 @ SV42 ) )
= $true )
| ( ( ~ ( ~ ( on_path @ ( sK11_E @ SV47 @ SV42 @ SV20 @ SV10 ) @ SV42 )
| ~ ( ( SV47
= ( head_of @ ( sK11_E @ SV47 @ SV42 @ SV20 @ SV10 ) ) )
| ( SV47
= ( tail_of @ ( sK11_E @ SV47 @ SV42 @ SV20 @ SV10 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[254]) ).
thf(283,plain,
! [SV20: $i,SV10: $i,SV43: $i,SV48: $i] :
( ( ( ~ ( in_path @ SV48 @ SV43 )
| ~ ( path @ SV10 @ SV20 @ SV43 ) )
= $true )
| ( ( vertex @ SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[255]) ).
thf(284,plain,
! [SV44: $i,SV37: $i,SV11: $i] :
( ( ( ~ ( ~ ( path @ SV11 @ SV37 @ ( sK9_P @ SV44 @ SV37 @ SV11 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SV44 ) @ ( length_of @ ( sK9_P @ SV44 @ SV37 @ SV11 ) ) ) ) )
= $true )
| ( ( ( SV11 = SV37 )
| ~ ( path @ SV11 @ SV37 @ SV44 ) )
= $true )
| ( ( shortest_path @ SV11 @ SV37 @ SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[256]) ).
thf(285,plain,
! [SV54: $i,SV11: $i] :
( ( ! [SY220: $i] :
( ~ ( shortest_path @ SV11 @ SV54 @ SY220 )
| ! [SY221: $i] :
( ~ ( path @ SV11 @ SV54 @ SY221 )
| ( less_or_equal @ ( length_of @ SY220 ) @ ( length_of @ SY221 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(286,plain,
! [SV11: $i] :
( ( ~ ! [SY143: $i] :
( ! [SY144: $i] :
~ ( shortest_path @ SV11 @ SY143 @ SY144 )
| ( SV11 != SY143 ) )
| ~ ! [SY145: $i,SY146: $i] :
( ~ ( shortest_path @ SV11 @ SY145 @ SY146 )
| ( path @ SV11 @ SY145 @ SY146 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(287,plain,
! [SV38: $i,SV32: $i] :
( ( ( SV32 = SV38 )
= $true )
| ( ( ~ ( edge @ SV32 )
| ~ ( edge @ SV38 ) )
= $true )
| ( ( ( ( head_of @ SV32 )
!= ( tail_of @ SV38 ) ) )
= $true )
| ( ( sequential @ SV32 @ SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[259]) ).
thf(288,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[260]) ).
thf(289,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)],[260]) ).
thf(290,plain,
! [SV55: $i,SV49: $i] :
( ( ~ ( sequential @ SV49 @ SV55 )
| ( ( head_of @ SV49 )
= ( tail_of @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(291,plain,
! [SV33: $i,SV26: $i,SV12: $i] :
( ( ( ! [SY149: $i,SY150: $i] :
( ~ ( on_path @ SY149 @ SV12 )
| ~ ( on_path @ SY150 @ SV12 )
| ! [SY151: $i] :
( ~ ( precedes @ SY151 @ SY150 @ SV12 )
| ~ ( sequential @ SY149 @ SY151 ) )
| ( precedes @ SY149 @ SY150 @ SV12 ) ) )
= $true )
| ( ( path @ SV26 @ SV33 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[262]) ).
thf(292,plain,
! [SV33: $i,SV26: $i,SV12: $i] :
( ( ( ! [SY152: $i,SY153: $i] :
( ~ ( on_path @ SY152 @ SV12 )
| ~ ( on_path @ SY153 @ SV12 )
| ~ ( sequential @ SY152 @ SY153 )
| ( precedes @ SY152 @ SY153 @ SV12 ) ) )
= $true )
| ( ( path @ SV26 @ SV33 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[263]) ).
thf(293,plain,
! [SV21: $i,SV13: $i,SV50: $i,SV27: $i] :
( ( ( ! [SY215: $i] :
( ~ ( precedes @ SV27 @ SV50 @ SY215 )
| ~ ( shortest_path @ SV13 @ SV21 @ SY215 ) ) )
= $true )
| ( ( ! [SY216: $i] :
( ( ( tail_of @ SY216 )
!= ( tail_of @ SV27 ) )
| ( ( head_of @ SY216 )
!= ( head_of @ SV50 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[264]) ).
thf(294,plain,
! [SV21: $i,SV13: $i,SV56: $i,SV51: $i,SV27: $i] :
( ( ~ ( precedes @ SV27 @ SV51 @ SV56 )
| ~ ( shortest_path @ SV13 @ SV21 @ SV56 )
| ~ ( precedes @ SV51 @ SV27 @ SV56 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(295,plain,
! [SV34: $i,SV28: $i,SV14: $i] :
( ( ( ~ ( ~ ! [SY163: $i] :
( ! [SY164: $i] :
~ ( precedes @ SY163 @ SY164 @ SV14 )
| ( on_path @ SY163 @ SV14 ) )
| ~ ! [SY165: $i,SY166: $i] :
( ~ ( precedes @ SY165 @ SY166 @ SV14 )
| ( on_path @ SY166 @ SV14 ) ) ) )
= $true )
| ( ( path @ SV28 @ SV34 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[266]) ).
thf(296,plain,
! [SV34: $i,SV28: $i,SV14: $i] :
( ( ( ~ ( ~ ! [SY167: $i,SY168: $i] :
( ~ ( precedes @ SY167 @ SY168 @ SV14 )
| ! [SY169: $i] :
( ~ ( precedes @ SY169 @ SY168 @ SV14 )
| ~ ( sequential @ SY167 @ SY169 ) )
| ~ ( sequential @ SY167 @ SY168 ) )
| ~ ! [SY170: $i,SY171: $i] :
( ~ ( precedes @ SY170 @ SY171 @ SV14 )
| ~ ( ~ ( precedes @ ( sK10_E3 @ SY171 @ SY170 @ SV14 ) @ SY171 @ SV14 )
| ~ ( sequential @ SY170 @ ( sK10_E3 @ SY171 @ SY170 @ SV14 ) ) )
| ( sequential @ SY170 @ SY171 ) ) ) )
= $true )
| ( ( path @ SV28 @ SV34 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[267]) ).
thf(297,plain,
! [SV5: $i] :
( ( ( ~ ( ~ ( on_path @ ( sK7_E1 @ SV5 ) @ SV5 )
| ~ ( on_path @ ( sK8_SY86 @ SV5 ) @ SV5 ) ) )
= $true )
| ( ( ! [SY98: $i,SY99: $i] :
~ ( path @ SY98 @ SY99 @ SV5 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV5 )
= ( number_of_in @ triangles @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[268]) ).
thf(298,plain,
! [SV5: $i] :
( ( ( sequential @ ( sK7_E1 @ SV5 ) @ ( sK8_SY86 @ SV5 ) )
= $true )
| ( ( ! [SY98: $i,SY99: $i] :
~ ( path @ SY98 @ SY99 @ SV5 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV5 )
= ( number_of_in @ triangles @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[269]) ).
thf(299,plain,
! [SV45: $i,SV5: $i,SV57: $i] :
( ( ( ! [SY222: $i] :
~ ( path @ SV57 @ SY222 @ SV5 ) )
= $true )
| ( ( triangle @ ( sK7_E1 @ SV5 ) @ ( sK8_SY86 @ SV5 ) @ SV45 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV5 )
= ( number_of_in @ triangles @ SV5 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(300,plain,
! [SV39: $i,SV35: $i,SV6: $i] :
( ( ( ~ ( edge @ SV6 )
| ~ ( edge @ SV35 )
| ~ ( edge @ SV39 )
| ~ ( sequential @ SV6 @ SV35 ) )
= $true )
| ( ( ~ ( sequential @ SV35 @ SV39 ) )
= $true )
| ( ( ~ ( sequential @ SV39 @ SV6 ) )
= $true )
| ( ( triangle @ SV6 @ SV35 @ SV39 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[271]) ).
thf(301,plain,
! [SV6: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY102: $i,SY103: $i] :
~ ( triangle @ SV6 @ SY102 @ SY103 )
| ( edge @ SV6 ) )
| ~ ! [SY104: $i] :
( ! [SY105: $i] :
~ ( triangle @ SV6 @ SY104 @ SY105 )
| ( edge @ SY104 ) ) )
| ~ ! [SY106: $i,SY107: $i] :
( ~ ( triangle @ SV6 @ SY106 @ SY107 )
| ( edge @ SY107 ) ) )
| ~ ! [SY108: $i] :
( ! [SY109: $i] :
~ ( triangle @ SV6 @ SY108 @ SY109 )
| ( sequential @ SV6 @ SY108 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[272]) ).
thf(302,plain,
! [SV6: $i] :
( ( ~ ! [SY110: $i,SY111: $i] :
( ~ ( triangle @ SV6 @ SY110 @ SY111 )
| ( sequential @ SY110 @ SY111 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[272]) ).
thf(303,plain,
! [SV58: $i,SV52: $i,SV6: $i] :
( ( ~ ( triangle @ SV6 @ SV52 @ SV58 )
| ( sequential @ SV58 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(304,plain,
! [SV24: $i,SV31: $i] :
( ( ( vertex @ SV31 )
= $false )
| ( ( vertex @ SV24 )
= $false )
| ( ( SV24 = SV31 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV24
!= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
!= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
!= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
!= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV24
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
| ~ ( ( SV24
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) ) )
| ~ ~ ( ~ ( ( SV31
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
| ~ ( ( SV31
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) ) ) ) )
| ~ ( edge @ ( sK15_E @ SV31 @ SV24 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(305,plain,
! [SV59: $i,SV7: $i] :
( ( ( ! [SY223: $i] :
~ ( path @ SV7 @ SV59 @ SY223 ) )
= $true )
| ( ( vertex @ SV7 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(306,plain,
! [SV53: $i,SV7: $i] :
( ( ( ! [SY219: $i] :
~ ( path @ SV7 @ SV53 @ SY219 ) )
= $true )
| ( ( vertex @ SV53 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[276]) ).
thf(307,plain,
! [SV36: $i,SV40: $i,SV7: $i] :
( ( ( ~ ~ ( ( SV7
!= ( tail_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( edge @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
| ~ ~ ( ~ ( ( SV36
!= ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
| ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ empty ) )
| ! [SY210: $i] :
( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ SY210 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ SY210 ) ) )
| ~ ~ ( ~ ( ( SV36
= ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ ( sK14_SY90 @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ ( sK14_SY90 @ SV40 @ SV36 @ SV7 ) ) ) )
| ~ ( ( SV40
= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ empty ) )
| ~ ( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ ( sK13_SY91 @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ ( sK13_SY91 @ SV40 @ SV36 @ SV7 ) ) ) ) ) ) )
= $false )
| ( ( path @ SV7 @ SV36 @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(308,plain,
! [SV25: $i,SV18: $i,SV8: $i] :
( ( ( ~ ! [SY195: $i] :
( ( SV8
!= ( tail_of @ SY195 ) )
| ~ ( edge @ SY195 )
| ( SV18
!= ( head_of @ SY195 ) )
| ( SV25
!= ( path_cons @ SY195 @ empty ) ) )
| ~ ! [SY196: $i] :
( ( SV8
!= ( tail_of @ SY196 ) )
| ~ ( edge @ SY196 )
| ! [SY197: $i] :
( ( SV25
!= ( path_cons @ SY196 @ SY197 ) )
| ~ ( path @ ( head_of @ SY196 ) @ SV18 @ SY197 ) ) ) )
= $false )
| ( ( vertex @ SV8 )
= $false )
| ( ( vertex @ SV18 )
= $false )
| ( ( path @ SV8 @ SV18 @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(309,plain,
! [SV19: $i,SV9: $i,SV60: $i] :
( ( ! [SY224: $i] :
( ~ ( on_path @ SY224 @ SV60 )
| ~ ( path @ SV9 @ SV19 @ SV60 )
| ( edge @ SY224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(310,plain,
! [SV19: $i,SV9: $i,SV61: $i] :
( ( ! [SY225: $i] :
( ~ ( on_path @ SY225 @ SV61 )
| ~ ( path @ SV9 @ SV19 @ SV61 )
| ( in_path @ ( head_of @ SY225 ) @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(311,plain,
! [SV19: $i,SV9: $i,SV41: $i,SV46: $i] :
( ( ( ~ ( on_path @ SV46 @ SV41 ) )
= $true )
| ( ( ~ ( path @ SV9 @ SV19 @ SV41 ) )
= $true )
| ( ( in_path @ ( tail_of @ SV46 ) @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[281]) ).
thf(312,plain,
! [SV20: $i,SV10: $i,SV42: $i,SV47: $i] :
( ( ( ~ ( in_path @ SV47 @ SV42 ) )
= $true )
| ( ( ~ ( path @ SV10 @ SV20 @ SV42 ) )
= $true )
| ( ( ~ ( ~ ( on_path @ ( sK11_E @ SV47 @ SV42 @ SV20 @ SV10 ) @ SV42 )
| ~ ( ( SV47
= ( head_of @ ( sK11_E @ SV47 @ SV42 @ SV20 @ SV10 ) ) )
| ( SV47
= ( tail_of @ ( sK11_E @ SV47 @ SV42 @ SV20 @ SV10 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[282]) ).
thf(313,plain,
! [SV20: $i,SV10: $i,SV43: $i,SV48: $i] :
( ( ( ~ ( in_path @ SV48 @ SV43 ) )
= $true )
| ( ( ~ ( path @ SV10 @ SV20 @ SV43 ) )
= $true )
| ( ( vertex @ SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[283]) ).
thf(314,plain,
! [SV44: $i,SV37: $i,SV11: $i] :
( ( ( ~ ( path @ SV11 @ SV37 @ ( sK9_P @ SV44 @ SV37 @ SV11 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SV44 ) @ ( length_of @ ( sK9_P @ SV44 @ SV37 @ SV11 ) ) ) )
= $false )
| ( ( ( SV11 = SV37 )
| ~ ( path @ SV11 @ SV37 @ SV44 ) )
= $true )
| ( ( shortest_path @ SV11 @ SV37 @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(315,plain,
! [SV62: $i,SV54: $i,SV11: $i] :
( ( ~ ( shortest_path @ SV11 @ SV54 @ SV62 )
| ! [SY226: $i] :
( ~ ( path @ SV11 @ SV54 @ SY226 )
| ( less_or_equal @ ( length_of @ SV62 ) @ ( length_of @ SY226 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[285]) ).
thf(316,plain,
! [SV11: $i] :
( ( ~ ! [SY143: $i] :
( ! [SY144: $i] :
~ ( shortest_path @ SV11 @ SY143 @ SY144 )
| ( SV11 != SY143 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[286]) ).
thf(317,plain,
! [SV11: $i] :
( ( ~ ! [SY145: $i,SY146: $i] :
( ~ ( shortest_path @ SV11 @ SY145 @ SY146 )
| ( path @ SV11 @ SY145 @ SY146 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[286]) ).
thf(318,plain,
! [SV38: $i,SV32: $i] :
( ( ( ~ ( edge @ SV32 ) )
= $true )
| ( ( ~ ( edge @ SV38 ) )
= $true )
| ( ( SV32 = SV38 )
= $true )
| ( ( ( ( head_of @ SV32 )
!= ( tail_of @ SV38 ) ) )
= $true )
| ( ( sequential @ SV32 @ SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[287]) ).
thf(319,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[288]) ).
thf(320,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)],[289]) ).
thf(321,plain,
! [SV55: $i,SV49: $i] :
( ( ( ~ ( sequential @ SV49 @ SV55 ) )
= $true )
| ( ( ( head_of @ SV49 )
= ( tail_of @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[290]) ).
thf(322,plain,
! [SV33: $i,SV26: $i,SV12: $i,SV63: $i] :
( ( ( ! [SY227: $i] :
( ~ ( on_path @ SV63 @ SV12 )
| ~ ( on_path @ SY227 @ SV12 )
| ! [SY228: $i] :
( ~ ( precedes @ SY228 @ SY227 @ SV12 )
| ~ ( sequential @ SV63 @ SY228 ) )
| ( precedes @ SV63 @ SY227 @ SV12 ) ) )
= $true )
| ( ( path @ SV26 @ SV33 @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(323,plain,
! [SV33: $i,SV26: $i,SV12: $i,SV64: $i] :
( ( ( ! [SY229: $i] :
( ~ ( on_path @ SV64 @ SV12 )
| ~ ( on_path @ SY229 @ SV12 )
| ~ ( sequential @ SV64 @ SY229 )
| ( precedes @ SV64 @ SY229 @ SV12 ) ) )
= $true )
| ( ( path @ SV26 @ SV33 @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[292]) ).
thf(324,plain,
! [SV21: $i,SV13: $i,SV65: $i,SV50: $i,SV27: $i] :
( ( ( ~ ( precedes @ SV27 @ SV50 @ SV65 )
| ~ ( shortest_path @ SV13 @ SV21 @ SV65 ) )
= $true )
| ( ( ! [SY216: $i] :
( ( ( tail_of @ SY216 )
!= ( tail_of @ SV27 ) )
| ( ( head_of @ SY216 )
!= ( head_of @ SV50 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(325,plain,
! [SV21: $i,SV13: $i,SV56: $i,SV51: $i,SV27: $i] :
( ( ( ~ ( precedes @ SV27 @ SV51 @ SV56 )
| ~ ( shortest_path @ SV13 @ SV21 @ SV56 ) )
= $true )
| ( ( ~ ( precedes @ SV51 @ SV27 @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[294]) ).
thf(326,plain,
! [SV34: $i,SV28: $i,SV14: $i] :
( ( ( ~ ! [SY163: $i] :
( ! [SY164: $i] :
~ ( precedes @ SY163 @ SY164 @ SV14 )
| ( on_path @ SY163 @ SV14 ) )
| ~ ! [SY165: $i,SY166: $i] :
( ~ ( precedes @ SY165 @ SY166 @ SV14 )
| ( on_path @ SY166 @ SV14 ) ) )
= $false )
| ( ( path @ SV28 @ SV34 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(327,plain,
! [SV34: $i,SV28: $i,SV14: $i] :
( ( ( ~ ! [SY167: $i,SY168: $i] :
( ~ ( precedes @ SY167 @ SY168 @ SV14 )
| ! [SY169: $i] :
( ~ ( precedes @ SY169 @ SY168 @ SV14 )
| ~ ( sequential @ SY167 @ SY169 ) )
| ~ ( sequential @ SY167 @ SY168 ) )
| ~ ! [SY170: $i,SY171: $i] :
( ~ ( precedes @ SY170 @ SY171 @ SV14 )
| ~ ( ~ ( precedes @ ( sK10_E3 @ SY171 @ SY170 @ SV14 ) @ SY171 @ SV14 )
| ~ ( sequential @ SY170 @ ( sK10_E3 @ SY171 @ SY170 @ SV14 ) ) )
| ( sequential @ SY170 @ SY171 ) ) )
= $false )
| ( ( path @ SV28 @ SV34 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(328,plain,
! [SV5: $i] :
( ( ( ~ ( on_path @ ( sK7_E1 @ SV5 ) @ SV5 )
| ~ ( on_path @ ( sK8_SY86 @ SV5 ) @ SV5 ) )
= $false )
| ( ( ! [SY98: $i,SY99: $i] :
~ ( path @ SY98 @ SY99 @ SV5 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV5 )
= ( number_of_in @ triangles @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[297]) ).
thf(329,plain,
! [SV5: $i,SV66: $i] :
( ( ( ! [SY230: $i] :
~ ( path @ SV66 @ SY230 @ SV5 ) )
= $true )
| ( ( sequential @ ( sK7_E1 @ SV5 ) @ ( sK8_SY86 @ SV5 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV5 )
= ( number_of_in @ triangles @ SV5 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[298]) ).
thf(330,plain,
! [SV45: $i,SV5: $i,SV67: $i,SV57: $i] :
( ( ( ~ ( path @ SV57 @ SV67 @ SV5 ) )
= $true )
| ( ( triangle @ ( sK7_E1 @ SV5 ) @ ( sK8_SY86 @ SV5 ) @ SV45 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV5 )
= ( number_of_in @ triangles @ SV5 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(331,plain,
! [SV39: $i,SV35: $i,SV6: $i] :
( ( ( ~ ( edge @ SV6 )
| ~ ( edge @ SV35 )
| ~ ( edge @ SV39 ) )
= $true )
| ( ( ~ ( sequential @ SV6 @ SV35 ) )
= $true )
| ( ( ~ ( sequential @ SV35 @ SV39 ) )
= $true )
| ( ( ~ ( sequential @ SV39 @ SV6 ) )
= $true )
| ( ( triangle @ SV6 @ SV35 @ SV39 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[300]) ).
thf(332,plain,
! [SV6: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY102: $i,SY103: $i] :
~ ( triangle @ SV6 @ SY102 @ SY103 )
| ( edge @ SV6 ) )
| ~ ! [SY104: $i] :
( ! [SY105: $i] :
~ ( triangle @ SV6 @ SY104 @ SY105 )
| ( edge @ SY104 ) ) )
| ~ ! [SY106: $i,SY107: $i] :
( ~ ( triangle @ SV6 @ SY106 @ SY107 )
| ( edge @ SY107 ) ) )
| ~ ! [SY108: $i] :
( ! [SY109: $i] :
~ ( triangle @ SV6 @ SY108 @ SY109 )
| ( sequential @ SV6 @ SY108 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[301]) ).
thf(333,plain,
! [SV6: $i] :
( ( ! [SY110: $i,SY111: $i] :
( ~ ( triangle @ SV6 @ SY110 @ SY111 )
| ( sequential @ SY110 @ SY111 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[302]) ).
thf(334,plain,
! [SV58: $i,SV52: $i,SV6: $i] :
( ( ( ~ ( triangle @ SV6 @ SV52 @ SV58 ) )
= $true )
| ( ( sequential @ SV58 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[303]) ).
thf(335,plain,
! [SV31: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ( ( SV24
!= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
!= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
!= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
!= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV24
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
| ~ ( ( SV24
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) ) )
| ~ ~ ( ~ ( ( SV31
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
| ~ ( ( SV31
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) ) ) ) )
| ~ ( edge @ ( sK15_E @ SV31 @ SV24 ) ) )
= $false )
| ( ( SV24 = SV31 )
= $true )
| ( ( vertex @ SV24 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(336,plain,
! [SV68: $i,SV59: $i,SV7: $i] :
( ( ( ~ ( path @ SV7 @ SV59 @ SV68 ) )
= $true )
| ( ( vertex @ SV7 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(337,plain,
! [SV69: $i,SV53: $i,SV7: $i] :
( ( ( ~ ( path @ SV7 @ SV53 @ SV69 ) )
= $true )
| ( ( vertex @ SV53 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(338,plain,
! [SV36: $i,SV40: $i,SV7: $i] :
( ( ( ~ ~ ( ( SV7
!= ( tail_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( edge @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) ) )
= $false )
| ( ( path @ SV7 @ SV36 @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[307]) ).
thf(339,plain,
! [SV7: $i,SV40: $i,SV36: $i] :
( ( ( ~ ~ ( ~ ( ( SV36
!= ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
| ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ empty ) )
| ! [SY210: $i] :
( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ SY210 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ SY210 ) ) )
| ~ ~ ( ~ ( ( SV36
= ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ ( sK14_SY90 @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ ( sK14_SY90 @ SV40 @ SV36 @ SV7 ) ) ) )
| ~ ( ( SV40
= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ empty ) )
| ~ ( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ ( sK13_SY91 @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ ( sK13_SY91 @ SV40 @ SV36 @ SV7 ) ) ) ) ) ) )
= $false )
| ( ( path @ SV7 @ SV36 @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[307]) ).
thf(340,plain,
! [SV25: $i,SV18: $i,SV8: $i] :
( ( ( ~ ! [SY195: $i] :
( ( SV8
!= ( tail_of @ SY195 ) )
| ~ ( edge @ SY195 )
| ( SV18
!= ( head_of @ SY195 ) )
| ( SV25
!= ( path_cons @ SY195 @ empty ) ) ) )
= $false )
| ( ( vertex @ SV8 )
= $false )
| ( ( vertex @ SV18 )
= $false )
| ( ( path @ SV8 @ SV18 @ SV25 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[308]) ).
thf(341,plain,
! [SV18: $i,SV25: $i,SV8: $i] :
( ( ( ~ ! [SY196: $i] :
( ( SV8
!= ( tail_of @ SY196 ) )
| ~ ( edge @ SY196 )
| ! [SY197: $i] :
( ( SV25
!= ( path_cons @ SY196 @ SY197 ) )
| ~ ( path @ ( head_of @ SY196 ) @ SV18 @ SY197 ) ) ) )
= $false )
| ( ( vertex @ SV8 )
= $false )
| ( ( vertex @ SV18 )
= $false )
| ( ( path @ SV8 @ SV18 @ SV25 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[308]) ).
thf(342,plain,
! [SV19: $i,SV9: $i,SV60: $i,SV70: $i] :
( ( ~ ( on_path @ SV70 @ SV60 )
| ~ ( path @ SV9 @ SV19 @ SV60 )
| ( edge @ SV70 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(343,plain,
! [SV19: $i,SV9: $i,SV61: $i,SV71: $i] :
( ( ~ ( on_path @ SV71 @ SV61 )
| ~ ( path @ SV9 @ SV19 @ SV61 )
| ( in_path @ ( head_of @ SV71 ) @ SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(344,plain,
! [SV19: $i,SV9: $i,SV41: $i,SV46: $i] :
( ( ( on_path @ SV46 @ SV41 )
= $false )
| ( ( ~ ( path @ SV9 @ SV19 @ SV41 ) )
= $true )
| ( ( in_path @ ( tail_of @ SV46 ) @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[311]) ).
thf(345,plain,
! [SV20: $i,SV10: $i,SV42: $i,SV47: $i] :
( ( ( in_path @ SV47 @ SV42 )
= $false )
| ( ( ~ ( path @ SV10 @ SV20 @ SV42 ) )
= $true )
| ( ( ~ ( ~ ( on_path @ ( sK11_E @ SV47 @ SV42 @ SV20 @ SV10 ) @ SV42 )
| ~ ( ( SV47
= ( head_of @ ( sK11_E @ SV47 @ SV42 @ SV20 @ SV10 ) ) )
| ( SV47
= ( tail_of @ ( sK11_E @ SV47 @ SV42 @ SV20 @ SV10 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(346,plain,
! [SV20: $i,SV10: $i,SV43: $i,SV48: $i] :
( ( ( in_path @ SV48 @ SV43 )
= $false )
| ( ( ~ ( path @ SV10 @ SV20 @ SV43 ) )
= $true )
| ( ( vertex @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[313]) ).
thf(347,plain,
! [SV44: $i,SV37: $i,SV11: $i] :
( ( ( ~ ( path @ SV11 @ SV37 @ ( sK9_P @ SV44 @ SV37 @ SV11 ) ) )
= $false )
| ( ( ( SV11 = SV37 )
| ~ ( path @ SV11 @ SV37 @ SV44 ) )
= $true )
| ( ( shortest_path @ SV11 @ SV37 @ SV44 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[314]) ).
thf(348,plain,
! [SV11: $i,SV37: $i,SV44: $i] :
( ( ( ~ ~ ( less_or_equal @ ( length_of @ SV44 ) @ ( length_of @ ( sK9_P @ SV44 @ SV37 @ SV11 ) ) ) )
= $false )
| ( ( ( SV11 = SV37 )
| ~ ( path @ SV11 @ SV37 @ SV44 ) )
= $true )
| ( ( shortest_path @ SV11 @ SV37 @ SV44 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[314]) ).
thf(349,plain,
! [SV62: $i,SV54: $i,SV11: $i] :
( ( ( ~ ( shortest_path @ SV11 @ SV54 @ SV62 ) )
= $true )
| ( ( ! [SY226: $i] :
( ~ ( path @ SV11 @ SV54 @ SY226 )
| ( less_or_equal @ ( length_of @ SV62 ) @ ( length_of @ SY226 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[315]) ).
thf(350,plain,
! [SV11: $i] :
( ( ! [SY143: $i] :
( ! [SY144: $i] :
~ ( shortest_path @ SV11 @ SY143 @ SY144 )
| ( SV11 != SY143 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[316]) ).
thf(351,plain,
! [SV11: $i] :
( ( ! [SY145: $i,SY146: $i] :
( ~ ( shortest_path @ SV11 @ SY145 @ SY146 )
| ( path @ SV11 @ SY145 @ SY146 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[317]) ).
thf(352,plain,
! [SV38: $i,SV32: $i] :
( ( ( edge @ SV32 )
= $false )
| ( ( ~ ( edge @ SV38 ) )
= $true )
| ( ( SV32 = SV38 )
= $true )
| ( ( ( ( head_of @ SV32 )
!= ( tail_of @ SV38 ) ) )
= $true )
| ( ( sequential @ SV32 @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[318]) ).
thf(353,plain,
! [SV72: $i] :
( ( ! [SY231: $i] :
( ~ ( sequential @ SV72 @ SY231 )
| ( SV72 != SY231 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(354,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)],[320]) ).
thf(355,plain,
! [SV55: $i,SV49: $i] :
( ( ( sequential @ SV49 @ SV55 )
= $false )
| ( ( ( head_of @ SV49 )
= ( tail_of @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(356,plain,
! [SV33: $i,SV26: $i,SV73: $i,SV12: $i,SV63: $i] :
( ( ( ~ ( on_path @ SV63 @ SV12 )
| ~ ( on_path @ SV73 @ SV12 )
| ! [SY232: $i] :
( ~ ( precedes @ SY232 @ SV73 @ SV12 )
| ~ ( sequential @ SV63 @ SY232 ) )
| ( precedes @ SV63 @ SV73 @ SV12 ) )
= $true )
| ( ( path @ SV26 @ SV33 @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(357,plain,
! [SV33: $i,SV26: $i,SV74: $i,SV12: $i,SV64: $i] :
( ( ( ~ ( on_path @ SV64 @ SV12 )
| ~ ( on_path @ SV74 @ SV12 )
| ~ ( sequential @ SV64 @ SV74 )
| ( precedes @ SV64 @ SV74 @ SV12 ) )
= $true )
| ( ( path @ SV26 @ SV33 @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[323]) ).
thf(358,plain,
! [SV21: $i,SV13: $i,SV65: $i,SV50: $i,SV27: $i] :
( ( ( ~ ( precedes @ SV27 @ SV50 @ SV65 ) )
= $true )
| ( ( ~ ( shortest_path @ SV13 @ SV21 @ SV65 ) )
= $true )
| ( ( ! [SY216: $i] :
( ( ( tail_of @ SY216 )
!= ( tail_of @ SV27 ) )
| ( ( head_of @ SY216 )
!= ( head_of @ SV50 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[324]) ).
thf(359,plain,
! [SV21: $i,SV13: $i,SV56: $i,SV51: $i,SV27: $i] :
( ( ( ~ ( precedes @ SV27 @ SV51 @ SV56 ) )
= $true )
| ( ( ~ ( shortest_path @ SV13 @ SV21 @ SV56 ) )
= $true )
| ( ( ~ ( precedes @ SV51 @ SV27 @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[325]) ).
thf(360,plain,
! [SV34: $i,SV28: $i,SV14: $i] :
( ( ( ~ ! [SY163: $i] :
( ! [SY164: $i] :
~ ( precedes @ SY163 @ SY164 @ SV14 )
| ( on_path @ SY163 @ SV14 ) ) )
= $false )
| ( ( path @ SV28 @ SV34 @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[326]) ).
thf(361,plain,
! [SV34: $i,SV28: $i,SV14: $i] :
( ( ( ~ ! [SY165: $i,SY166: $i] :
( ~ ( precedes @ SY165 @ SY166 @ SV14 )
| ( on_path @ SY166 @ SV14 ) ) )
= $false )
| ( ( path @ SV28 @ SV34 @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[326]) ).
thf(362,plain,
! [SV34: $i,SV28: $i,SV14: $i] :
( ( ( ~ ! [SY167: $i,SY168: $i] :
( ~ ( precedes @ SY167 @ SY168 @ SV14 )
| ! [SY169: $i] :
( ~ ( precedes @ SY169 @ SY168 @ SV14 )
| ~ ( sequential @ SY167 @ SY169 ) )
| ~ ( sequential @ SY167 @ SY168 ) ) )
= $false )
| ( ( path @ SV28 @ SV34 @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[327]) ).
thf(363,plain,
! [SV34: $i,SV28: $i,SV14: $i] :
( ( ( ~ ! [SY170: $i,SY171: $i] :
( ~ ( precedes @ SY170 @ SY171 @ SV14 )
| ~ ( ~ ( precedes @ ( sK10_E3 @ SY171 @ SY170 @ SV14 ) @ SY171 @ SV14 )
| ~ ( sequential @ SY170 @ ( sK10_E3 @ SY171 @ SY170 @ SV14 ) ) )
| ( sequential @ SY170 @ SY171 ) ) )
= $false )
| ( ( path @ SV28 @ SV34 @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[327]) ).
thf(364,plain,
! [SV5: $i] :
( ( ( ~ ( on_path @ ( sK7_E1 @ SV5 ) @ SV5 ) )
= $false )
| ( ( ! [SY98: $i,SY99: $i] :
~ ( path @ SY98 @ SY99 @ SV5 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV5 )
= ( number_of_in @ triangles @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[328]) ).
thf(365,plain,
! [SV5: $i] :
( ( ( ~ ( on_path @ ( sK8_SY86 @ SV5 ) @ SV5 ) )
= $false )
| ( ( ! [SY98: $i,SY99: $i] :
~ ( path @ SY98 @ SY99 @ SV5 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV5 )
= ( number_of_in @ triangles @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[328]) ).
thf(366,plain,
! [SV5: $i,SV75: $i,SV66: $i] :
( ( ( ~ ( path @ SV66 @ SV75 @ SV5 ) )
= $true )
| ( ( sequential @ ( sK7_E1 @ SV5 ) @ ( sK8_SY86 @ SV5 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV5 )
= ( number_of_in @ triangles @ SV5 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[329]) ).
thf(367,plain,
! [SV45: $i,SV5: $i,SV67: $i,SV57: $i] :
( ( ( path @ SV57 @ SV67 @ SV5 )
= $false )
| ( ( triangle @ ( sK7_E1 @ SV5 ) @ ( sK8_SY86 @ SV5 ) @ SV45 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV5 )
= ( number_of_in @ triangles @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(368,plain,
! [SV39: $i,SV35: $i,SV6: $i] :
( ( ( ~ ( edge @ SV6 )
| ~ ( edge @ SV35 ) )
= $true )
| ( ( ~ ( edge @ SV39 ) )
= $true )
| ( ( ~ ( sequential @ SV6 @ SV35 ) )
= $true )
| ( ( ~ ( sequential @ SV35 @ SV39 ) )
= $true )
| ( ( ~ ( sequential @ SV39 @ SV6 ) )
= $true )
| ( ( triangle @ SV6 @ SV35 @ SV39 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[331]) ).
thf(369,plain,
! [SV6: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( ! [SY102: $i,SY103: $i] :
~ ( triangle @ SV6 @ SY102 @ SY103 )
| ( edge @ SV6 ) )
| ~ ! [SY104: $i] :
( ! [SY105: $i] :
~ ( triangle @ SV6 @ SY104 @ SY105 )
| ( edge @ SY104 ) ) )
| ~ ! [SY106: $i,SY107: $i] :
( ~ ( triangle @ SV6 @ SY106 @ SY107 )
| ( edge @ SY107 ) ) )
| ~ ! [SY108: $i] :
( ! [SY109: $i] :
~ ( triangle @ SV6 @ SY108 @ SY109 )
| ( sequential @ SV6 @ SY108 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(370,plain,
! [SV76: $i,SV6: $i] :
( ( ! [SY233: $i] :
( ~ ( triangle @ SV6 @ SV76 @ SY233 )
| ( sequential @ SV76 @ SY233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[333]) ).
thf(371,plain,
! [SV58: $i,SV52: $i,SV6: $i] :
( ( ( triangle @ SV6 @ SV52 @ SV58 )
= $false )
| ( ( sequential @ SV58 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(372,plain,
! [SV31: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ( ( SV24
!= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
!= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
!= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
!= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV24
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
| ~ ( ( SV24
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) ) )
| ~ ~ ( ~ ( ( SV31
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
| ~ ( ( SV31
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) ) ) ) ) )
= $false )
| ( ( SV24 = SV31 )
= $true )
| ( ( vertex @ SV24 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[335]) ).
thf(373,plain,
! [SV24: $i,SV31: $i] :
( ( ( ~ ( edge @ ( sK15_E @ SV31 @ SV24 ) ) )
= $false )
| ( ( SV24 = SV31 )
= $true )
| ( ( vertex @ SV24 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[335]) ).
thf(374,plain,
! [SV68: $i,SV59: $i,SV7: $i] :
( ( ( path @ SV7 @ SV59 @ SV68 )
= $false )
| ( ( vertex @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[336]) ).
thf(375,plain,
! [SV69: $i,SV53: $i,SV7: $i] :
( ( ( path @ SV7 @ SV53 @ SV69 )
= $false )
| ( ( vertex @ SV53 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[337]) ).
thf(376,plain,
! [SV36: $i,SV40: $i,SV7: $i] :
( ( ( ~ ( ( SV7
!= ( tail_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( edge @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) ) )
= $true )
| ( ( path @ SV7 @ SV36 @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[338]) ).
thf(377,plain,
! [SV7: $i,SV40: $i,SV36: $i] :
( ( ( ~ ( ~ ( ( SV36
!= ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
| ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ empty ) )
| ! [SY210: $i] :
( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ SY210 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ SY210 ) ) )
| ~ ~ ( ~ ( ( SV36
= ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ ( sK14_SY90 @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ ( sK14_SY90 @ SV40 @ SV36 @ SV7 ) ) ) )
| ~ ( ( SV40
= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ empty ) )
| ~ ( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ ( sK13_SY91 @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ ( sK13_SY91 @ SV40 @ SV36 @ SV7 ) ) ) ) ) ) )
= $true )
| ( ( path @ SV7 @ SV36 @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[339]) ).
thf(378,plain,
! [SV25: $i,SV18: $i,SV8: $i] :
( ( ( ! [SY195: $i] :
( ( SV8
!= ( tail_of @ SY195 ) )
| ~ ( edge @ SY195 )
| ( SV18
!= ( head_of @ SY195 ) )
| ( SV25
!= ( path_cons @ SY195 @ empty ) ) ) )
= $true )
| ( ( vertex @ SV8 )
= $false )
| ( ( vertex @ SV18 )
= $false )
| ( ( path @ SV8 @ SV18 @ SV25 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[340]) ).
thf(379,plain,
! [SV18: $i,SV25: $i,SV8: $i] :
( ( ( ! [SY196: $i] :
( ( SV8
!= ( tail_of @ SY196 ) )
| ~ ( edge @ SY196 )
| ! [SY197: $i] :
( ( SV25
!= ( path_cons @ SY196 @ SY197 ) )
| ~ ( path @ ( head_of @ SY196 ) @ SV18 @ SY197 ) ) ) )
= $true )
| ( ( vertex @ SV8 )
= $false )
| ( ( vertex @ SV18 )
= $false )
| ( ( path @ SV8 @ SV18 @ SV25 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[341]) ).
thf(380,plain,
! [SV19: $i,SV9: $i,SV60: $i,SV70: $i] :
( ( ( ~ ( on_path @ SV70 @ SV60 )
| ~ ( path @ SV9 @ SV19 @ SV60 ) )
= $true )
| ( ( edge @ SV70 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[342]) ).
thf(381,plain,
! [SV19: $i,SV9: $i,SV61: $i,SV71: $i] :
( ( ( ~ ( on_path @ SV71 @ SV61 )
| ~ ( path @ SV9 @ SV19 @ SV61 ) )
= $true )
| ( ( in_path @ ( head_of @ SV71 ) @ SV61 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[343]) ).
thf(382,plain,
! [SV46: $i,SV41: $i,SV19: $i,SV9: $i] :
( ( ( path @ SV9 @ SV19 @ SV41 )
= $false )
| ( ( on_path @ SV46 @ SV41 )
= $false )
| ( ( in_path @ ( tail_of @ SV46 ) @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(383,plain,
! [SV47: $i,SV42: $i,SV20: $i,SV10: $i] :
( ( ( path @ SV10 @ SV20 @ SV42 )
= $false )
| ( ( in_path @ SV47 @ SV42 )
= $false )
| ( ( ~ ( ~ ( on_path @ ( sK11_E @ SV47 @ SV42 @ SV20 @ SV10 ) @ SV42 )
| ~ ( ( SV47
= ( head_of @ ( sK11_E @ SV47 @ SV42 @ SV20 @ SV10 ) ) )
| ( SV47
= ( tail_of @ ( sK11_E @ SV47 @ SV42 @ SV20 @ SV10 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[345]) ).
thf(384,plain,
! [SV48: $i,SV43: $i,SV20: $i,SV10: $i] :
( ( ( path @ SV10 @ SV20 @ SV43 )
= $false )
| ( ( in_path @ SV48 @ SV43 )
= $false )
| ( ( vertex @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(385,plain,
! [SV44: $i,SV37: $i,SV11: $i] :
( ( ( path @ SV11 @ SV37 @ ( sK9_P @ SV44 @ SV37 @ SV11 ) )
= $true )
| ( ( ( SV11 = SV37 )
| ~ ( path @ SV11 @ SV37 @ SV44 ) )
= $true )
| ( ( shortest_path @ SV11 @ SV37 @ SV44 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[347]) ).
thf(386,plain,
! [SV11: $i,SV37: $i,SV44: $i] :
( ( ( ~ ( less_or_equal @ ( length_of @ SV44 ) @ ( length_of @ ( sK9_P @ SV44 @ SV37 @ SV11 ) ) ) )
= $true )
| ( ( ( SV11 = SV37 )
| ~ ( path @ SV11 @ SV37 @ SV44 ) )
= $true )
| ( ( shortest_path @ SV11 @ SV37 @ SV44 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[348]) ).
thf(387,plain,
! [SV62: $i,SV54: $i,SV11: $i] :
( ( ( shortest_path @ SV11 @ SV54 @ SV62 )
= $false )
| ( ( ! [SY226: $i] :
( ~ ( path @ SV11 @ SV54 @ SY226 )
| ( less_or_equal @ ( length_of @ SV62 ) @ ( length_of @ SY226 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[349]) ).
thf(388,plain,
! [SV77: $i,SV11: $i] :
( ( ! [SY234: $i] :
~ ( shortest_path @ SV11 @ SV77 @ SY234 )
| ( SV11 != SV77 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(389,plain,
! [SV78: $i,SV11: $i] :
( ( ! [SY235: $i] :
( ~ ( shortest_path @ SV11 @ SV78 @ SY235 )
| ( path @ SV11 @ SV78 @ SY235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[351]) ).
thf(390,plain,
! [SV32: $i,SV38: $i] :
( ( ( edge @ SV38 )
= $false )
| ( ( edge @ SV32 )
= $false )
| ( ( SV32 = SV38 )
= $true )
| ( ( ( ( head_of @ SV32 )
!= ( tail_of @ SV38 ) ) )
= $true )
| ( ( sequential @ SV32 @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[352]) ).
thf(391,plain,
! [SV79: $i,SV72: $i] :
( ( ~ ( sequential @ SV72 @ SV79 )
| ( SV72 != SV79 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(392,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[354]) ).
thf(393,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[354]) ).
thf(394,plain,
! [SV33: $i,SV26: $i,SV73: $i,SV12: $i,SV63: $i] :
( ( ( ~ ( on_path @ SV63 @ SV12 )
| ~ ( on_path @ SV73 @ SV12 )
| ! [SY232: $i] :
( ~ ( precedes @ SY232 @ SV73 @ SV12 )
| ~ ( sequential @ SV63 @ SY232 ) ) )
= $true )
| ( ( precedes @ SV63 @ SV73 @ SV12 )
= $true )
| ( ( path @ SV26 @ SV33 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[356]) ).
thf(395,plain,
! [SV33: $i,SV26: $i,SV74: $i,SV12: $i,SV64: $i] :
( ( ( ~ ( on_path @ SV64 @ SV12 )
| ~ ( on_path @ SV74 @ SV12 )
| ~ ( sequential @ SV64 @ SV74 ) )
= $true )
| ( ( precedes @ SV64 @ SV74 @ SV12 )
= $true )
| ( ( path @ SV26 @ SV33 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[357]) ).
thf(396,plain,
! [SV21: $i,SV13: $i,SV65: $i,SV50: $i,SV27: $i] :
( ( ( precedes @ SV27 @ SV50 @ SV65 )
= $false )
| ( ( ~ ( shortest_path @ SV13 @ SV21 @ SV65 ) )
= $true )
| ( ( ! [SY216: $i] :
( ( ( tail_of @ SY216 )
!= ( tail_of @ SV27 ) )
| ( ( head_of @ SY216 )
!= ( head_of @ SV50 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[358]) ).
thf(397,plain,
! [SV21: $i,SV13: $i,SV56: $i,SV51: $i,SV27: $i] :
( ( ( precedes @ SV27 @ SV51 @ SV56 )
= $false )
| ( ( ~ ( shortest_path @ SV13 @ SV21 @ SV56 ) )
= $true )
| ( ( ~ ( precedes @ SV51 @ SV27 @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[359]) ).
thf(398,plain,
! [SV34: $i,SV28: $i,SV14: $i] :
( ( ( ! [SY163: $i] :
( ! [SY164: $i] :
~ ( precedes @ SY163 @ SY164 @ SV14 )
| ( on_path @ SY163 @ SV14 ) ) )
= $true )
| ( ( path @ SV28 @ SV34 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[360]) ).
thf(399,plain,
! [SV34: $i,SV28: $i,SV14: $i] :
( ( ( ! [SY165: $i,SY166: $i] :
( ~ ( precedes @ SY165 @ SY166 @ SV14 )
| ( on_path @ SY166 @ SV14 ) ) )
= $true )
| ( ( path @ SV28 @ SV34 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[361]) ).
thf(400,plain,
! [SV34: $i,SV28: $i,SV14: $i] :
( ( ( ! [SY167: $i,SY168: $i] :
( ~ ( precedes @ SY167 @ SY168 @ SV14 )
| ! [SY169: $i] :
( ~ ( precedes @ SY169 @ SY168 @ SV14 )
| ~ ( sequential @ SY167 @ SY169 ) )
| ~ ( sequential @ SY167 @ SY168 ) ) )
= $true )
| ( ( path @ SV28 @ SV34 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[362]) ).
thf(401,plain,
! [SV34: $i,SV28: $i,SV14: $i] :
( ( ( ! [SY170: $i,SY171: $i] :
( ~ ( precedes @ SY170 @ SY171 @ SV14 )
| ~ ( ~ ( precedes @ ( sK10_E3 @ SY171 @ SY170 @ SV14 ) @ SY171 @ SV14 )
| ~ ( sequential @ SY170 @ ( sK10_E3 @ SY171 @ SY170 @ SV14 ) ) )
| ( sequential @ SY170 @ SY171 ) ) )
= $true )
| ( ( path @ SV28 @ SV34 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[363]) ).
thf(402,plain,
! [SV5: $i] :
( ( ( on_path @ ( sK7_E1 @ SV5 ) @ SV5 )
= $true )
| ( ( ! [SY98: $i,SY99: $i] :
~ ( path @ SY98 @ SY99 @ SV5 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV5 )
= ( number_of_in @ triangles @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[364]) ).
thf(403,plain,
! [SV5: $i] :
( ( ( on_path @ ( sK8_SY86 @ SV5 ) @ SV5 )
= $true )
| ( ( ! [SY98: $i,SY99: $i] :
~ ( path @ SY98 @ SY99 @ SV5 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV5 )
= ( number_of_in @ triangles @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[365]) ).
thf(404,plain,
! [SV5: $i,SV75: $i,SV66: $i] :
( ( ( path @ SV66 @ SV75 @ SV5 )
= $false )
| ( ( sequential @ ( sK7_E1 @ SV5 ) @ ( sK8_SY86 @ SV5 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV5 )
= ( number_of_in @ triangles @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[366]) ).
thf(405,plain,
! [SV39: $i,SV35: $i,SV6: $i] :
( ( ( ~ ( edge @ SV6 ) )
= $true )
| ( ( ~ ( edge @ SV35 ) )
= $true )
| ( ( ~ ( edge @ SV39 ) )
= $true )
| ( ( ~ ( sequential @ SV6 @ SV35 ) )
= $true )
| ( ( ~ ( sequential @ SV35 @ SV39 ) )
= $true )
| ( ( ~ ( sequential @ SV39 @ SV6 ) )
= $true )
| ( ( triangle @ SV6 @ SV35 @ SV39 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[368]) ).
thf(406,plain,
! [SV6: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( ! [SY102: $i,SY103: $i] :
~ ( triangle @ SV6 @ SY102 @ SY103 )
| ( edge @ SV6 ) )
| ~ ! [SY104: $i] :
( ! [SY105: $i] :
~ ( triangle @ SV6 @ SY104 @ SY105 )
| ( edge @ SY104 ) ) )
| ~ ! [SY106: $i,SY107: $i] :
( ~ ( triangle @ SV6 @ SY106 @ SY107 )
| ( edge @ SY107 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[369]) ).
thf(407,plain,
! [SV6: $i] :
( ( ~ ! [SY108: $i] :
( ! [SY109: $i] :
~ ( triangle @ SV6 @ SY108 @ SY109 )
| ( sequential @ SV6 @ SY108 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[369]) ).
thf(408,plain,
! [SV80: $i,SV76: $i,SV6: $i] :
( ( ~ ( triangle @ SV6 @ SV76 @ SV80 )
| ( sequential @ SV76 @ SV80 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[370]) ).
thf(409,plain,
! [SV31: $i,SV24: $i] :
( ( ( ~ ( ~ ( ( SV24
!= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
!= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
!= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
!= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV24
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
| ~ ( ( SV24
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) ) )
| ~ ~ ( ~ ( ( SV31
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
| ~ ( ( SV31
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) ) ) ) ) )
= $true )
| ( ( SV24 = SV31 )
= $true )
| ( ( vertex @ SV24 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[372]) ).
thf(410,plain,
! [SV24: $i,SV31: $i] :
( ( ( edge @ ( sK15_E @ SV31 @ SV24 ) )
= $true )
| ( ( SV24 = SV31 )
= $true )
| ( ( vertex @ SV24 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[373]) ).
thf(411,plain,
! [SV36: $i,SV40: $i,SV7: $i] :
( ( ( ( SV7
!= ( tail_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( edge @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
= $false )
| ( ( path @ SV7 @ SV36 @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(412,plain,
! [SV7: $i,SV40: $i,SV36: $i] :
( ( ( ~ ( ( SV36
!= ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
| ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ empty ) )
| ! [SY210: $i] :
( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ SY210 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ SY210 ) ) )
| ~ ~ ( ~ ( ( SV36
= ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ ( sK14_SY90 @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ ( sK14_SY90 @ SV40 @ SV36 @ SV7 ) ) ) )
| ~ ( ( SV40
= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ empty ) )
| ~ ( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ ( sK13_SY91 @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ ( sK13_SY91 @ SV40 @ SV36 @ SV7 ) ) ) ) ) )
= $false )
| ( ( path @ SV7 @ SV36 @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(413,plain,
! [SV25: $i,SV18: $i,SV81: $i,SV8: $i] :
( ( ( ( SV8
!= ( tail_of @ SV81 ) )
| ~ ( edge @ SV81 )
| ( SV18
!= ( head_of @ SV81 ) )
| ( SV25
!= ( path_cons @ SV81 @ empty ) ) )
= $true )
| ( ( vertex @ SV8 )
= $false )
| ( ( vertex @ SV18 )
= $false )
| ( ( path @ SV8 @ SV18 @ SV25 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[378]) ).
thf(414,plain,
! [SV18: $i,SV25: $i,SV82: $i,SV8: $i] :
( ( ( ( SV8
!= ( tail_of @ SV82 ) )
| ~ ( edge @ SV82 )
| ! [SY236: $i] :
( ( SV25
!= ( path_cons @ SV82 @ SY236 ) )
| ~ ( path @ ( head_of @ SV82 ) @ SV18 @ SY236 ) ) )
= $true )
| ( ( vertex @ SV8 )
= $false )
| ( ( vertex @ SV18 )
= $false )
| ( ( path @ SV8 @ SV18 @ SV25 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[379]) ).
thf(415,plain,
! [SV19: $i,SV9: $i,SV60: $i,SV70: $i] :
( ( ( ~ ( on_path @ SV70 @ SV60 ) )
= $true )
| ( ( ~ ( path @ SV9 @ SV19 @ SV60 ) )
= $true )
| ( ( edge @ SV70 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[380]) ).
thf(416,plain,
! [SV19: $i,SV9: $i,SV61: $i,SV71: $i] :
( ( ( ~ ( on_path @ SV71 @ SV61 ) )
= $true )
| ( ( ~ ( path @ SV9 @ SV19 @ SV61 ) )
= $true )
| ( ( in_path @ ( head_of @ SV71 ) @ SV61 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[381]) ).
thf(417,plain,
! [SV10: $i,SV20: $i,SV42: $i,SV47: $i] :
( ( ( ~ ( on_path @ ( sK11_E @ SV47 @ SV42 @ SV20 @ SV10 ) @ SV42 )
| ~ ( ( SV47
= ( head_of @ ( sK11_E @ SV47 @ SV42 @ SV20 @ SV10 ) ) )
| ( SV47
= ( tail_of @ ( sK11_E @ SV47 @ SV42 @ SV20 @ SV10 ) ) ) ) )
= $false )
| ( ( in_path @ SV47 @ SV42 )
= $false )
| ( ( path @ SV10 @ SV20 @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[383]) ).
thf(418,plain,
! [SV44: $i,SV37: $i,SV11: $i] :
( ( ( SV11 = SV37 )
= $true )
| ( ( ~ ( path @ SV11 @ SV37 @ SV44 ) )
= $true )
| ( ( path @ SV11 @ SV37 @ ( sK9_P @ SV44 @ SV37 @ SV11 ) )
= $true )
| ( ( shortest_path @ SV11 @ SV37 @ SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[385]) ).
thf(419,plain,
! [SV11: $i,SV37: $i,SV44: $i] :
( ( ( less_or_equal @ ( length_of @ SV44 ) @ ( length_of @ ( sK9_P @ SV44 @ SV37 @ SV11 ) ) )
= $false )
| ( ( ( SV11 = SV37 )
| ~ ( path @ SV11 @ SV37 @ SV44 ) )
= $true )
| ( ( shortest_path @ SV11 @ SV37 @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[386]) ).
thf(420,plain,
! [SV62: $i,SV83: $i,SV54: $i,SV11: $i] :
( ( ( ~ ( path @ SV11 @ SV54 @ SV83 )
| ( less_or_equal @ ( length_of @ SV62 ) @ ( length_of @ SV83 ) ) )
= $true )
| ( ( shortest_path @ SV11 @ SV54 @ SV62 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(421,plain,
! [SV77: $i,SV11: $i] :
( ( ( ! [SY234: $i] :
~ ( shortest_path @ SV11 @ SV77 @ SY234 ) )
= $true )
| ( ( ( SV11 != SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[388]) ).
thf(422,plain,
! [SV84: $i,SV78: $i,SV11: $i] :
( ( ~ ( shortest_path @ SV11 @ SV78 @ SV84 )
| ( path @ SV11 @ SV78 @ SV84 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(423,plain,
! [SV38: $i,SV32: $i] :
( ( ( ( head_of @ SV32 )
= ( tail_of @ SV38 ) )
= $false )
| ( ( SV32 = SV38 )
= $true )
| ( ( edge @ SV32 )
= $false )
| ( ( edge @ SV38 )
= $false )
| ( ( sequential @ SV32 @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[390]) ).
thf(424,plain,
! [SV79: $i,SV72: $i] :
( ( ( ~ ( sequential @ SV72 @ SV79 ) )
= $true )
| ( ( ( SV72 != SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[391]) ).
thf(425,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[392]) ).
thf(426,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[393]) ).
thf(427,plain,
! [SV33: $i,SV26: $i,SV73: $i,SV12: $i,SV63: $i] :
( ( ( ~ ( on_path @ SV63 @ SV12 )
| ~ ( on_path @ SV73 @ SV12 ) )
= $true )
| ( ( ! [SY232: $i] :
( ~ ( precedes @ SY232 @ SV73 @ SV12 )
| ~ ( sequential @ SV63 @ SY232 ) ) )
= $true )
| ( ( precedes @ SV63 @ SV73 @ SV12 )
= $true )
| ( ( path @ SV26 @ SV33 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[394]) ).
thf(428,plain,
! [SV33: $i,SV26: $i,SV74: $i,SV12: $i,SV64: $i] :
( ( ( ~ ( on_path @ SV64 @ SV12 )
| ~ ( on_path @ SV74 @ SV12 ) )
= $true )
| ( ( ~ ( sequential @ SV64 @ SV74 ) )
= $true )
| ( ( precedes @ SV64 @ SV74 @ SV12 )
= $true )
| ( ( path @ SV26 @ SV33 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[395]) ).
thf(429,plain,
! [SV50: $i,SV27: $i,SV65: $i,SV21: $i,SV13: $i] :
( ( ( shortest_path @ SV13 @ SV21 @ SV65 )
= $false )
| ( ( precedes @ SV27 @ SV50 @ SV65 )
= $false )
| ( ( ! [SY216: $i] :
( ( ( tail_of @ SY216 )
!= ( tail_of @ SV27 ) )
| ( ( head_of @ SY216 )
!= ( head_of @ SV50 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[396]) ).
thf(430,plain,
! [SV51: $i,SV27: $i,SV56: $i,SV21: $i,SV13: $i] :
( ( ( shortest_path @ SV13 @ SV21 @ SV56 )
= $false )
| ( ( precedes @ SV27 @ SV51 @ SV56 )
= $false )
| ( ( ~ ( precedes @ SV51 @ SV27 @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[397]) ).
thf(431,plain,
! [SV34: $i,SV28: $i,SV14: $i,SV85: $i] :
( ( ( ! [SY237: $i] :
~ ( precedes @ SV85 @ SY237 @ SV14 )
| ( on_path @ SV85 @ SV14 ) )
= $true )
| ( ( path @ SV28 @ SV34 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(432,plain,
! [SV34: $i,SV28: $i,SV14: $i,SV86: $i] :
( ( ( ! [SY238: $i] :
( ~ ( precedes @ SV86 @ SY238 @ SV14 )
| ( on_path @ SY238 @ SV14 ) ) )
= $true )
| ( ( path @ SV28 @ SV34 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(433,plain,
! [SV34: $i,SV28: $i,SV14: $i,SV87: $i] :
( ( ( ! [SY239: $i] :
( ~ ( precedes @ SV87 @ SY239 @ SV14 )
| ! [SY240: $i] :
( ~ ( precedes @ SY240 @ SY239 @ SV14 )
| ~ ( sequential @ SV87 @ SY240 ) )
| ~ ( sequential @ SV87 @ SY239 ) ) )
= $true )
| ( ( path @ SV28 @ SV34 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(434,plain,
! [SV34: $i,SV28: $i,SV14: $i,SV88: $i] :
( ( ( ! [SY241: $i] :
( ~ ( precedes @ SV88 @ SY241 @ SV14 )
| ~ ( ~ ( precedes @ ( sK10_E3 @ SY241 @ SV88 @ SV14 ) @ SY241 @ SV14 )
| ~ ( sequential @ SV88 @ ( sK10_E3 @ SY241 @ SV88 @ SV14 ) ) )
| ( sequential @ SV88 @ SY241 ) ) )
= $true )
| ( ( path @ SV28 @ SV34 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[401]) ).
thf(435,plain,
! [SV5: $i,SV89: $i] :
( ( ( ! [SY242: $i] :
~ ( path @ SV89 @ SY242 @ SV5 ) )
= $true )
| ( ( on_path @ ( sK7_E1 @ SV5 ) @ SV5 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV5 )
= ( number_of_in @ triangles @ SV5 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(436,plain,
! [SV5: $i,SV90: $i] :
( ( ( ! [SY243: $i] :
~ ( path @ SV90 @ SY243 @ SV5 ) )
= $true )
| ( ( on_path @ ( sK8_SY86 @ SV5 ) @ SV5 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV5 )
= ( number_of_in @ triangles @ SV5 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[403]) ).
thf(437,plain,
! [SV39: $i,SV35: $i,SV6: $i] :
( ( ( edge @ SV6 )
= $false )
| ( ( ~ ( edge @ SV35 ) )
= $true )
| ( ( ~ ( edge @ SV39 ) )
= $true )
| ( ( ~ ( sequential @ SV6 @ SV35 ) )
= $true )
| ( ( ~ ( sequential @ SV35 @ SV39 ) )
= $true )
| ( ( ~ ( sequential @ SV39 @ SV6 ) )
= $true )
| ( ( triangle @ SV6 @ SV35 @ SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[405]) ).
thf(438,plain,
! [SV6: $i] :
( ( ~ ( ~ ~ ( ~ ( ! [SY102: $i,SY103: $i] :
~ ( triangle @ SV6 @ SY102 @ SY103 )
| ( edge @ SV6 ) )
| ~ ! [SY104: $i] :
( ! [SY105: $i] :
~ ( triangle @ SV6 @ SY104 @ SY105 )
| ( edge @ SY104 ) ) )
| ~ ! [SY106: $i,SY107: $i] :
( ~ ( triangle @ SV6 @ SY106 @ SY107 )
| ( edge @ SY107 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[406]) ).
thf(439,plain,
! [SV6: $i] :
( ( ! [SY108: $i] :
( ! [SY109: $i] :
~ ( triangle @ SV6 @ SY108 @ SY109 )
| ( sequential @ SV6 @ SY108 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[407]) ).
thf(440,plain,
! [SV80: $i,SV76: $i,SV6: $i] :
( ( ( ~ ( triangle @ SV6 @ SV76 @ SV80 ) )
= $true )
| ( ( sequential @ SV76 @ SV80 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[408]) ).
thf(441,plain,
! [SV31: $i,SV24: $i] :
( ( ( ~ ( ( SV24
!= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
!= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
!= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
!= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV24
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
| ~ ( ( SV24
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) ) )
| ~ ~ ( ~ ( ( SV31
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
| ~ ( ( SV31
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) ) ) ) )
= $false )
| ( ( SV24 = SV31 )
= $true )
| ( ( vertex @ SV24 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[409]) ).
thf(442,plain,
! [SV36: $i,SV40: $i,SV7: $i] :
( ( ( ( SV7
!= ( tail_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) ) )
= $false )
| ( ( path @ SV7 @ SV36 @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[411]) ).
thf(443,plain,
! [SV7: $i,SV36: $i,SV40: $i] :
( ( ( ~ ( edge @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
= $false )
| ( ( path @ SV7 @ SV36 @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[411]) ).
thf(444,plain,
! [SV7: $i,SV40: $i,SV36: $i] :
( ( ( ~ ( ( SV36
!= ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
| ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ empty ) )
| ! [SY210: $i] :
( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ SY210 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ SY210 ) ) ) )
= $false )
| ( ( path @ SV7 @ SV36 @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[412]) ).
thf(445,plain,
! [SV7: $i,SV40: $i,SV36: $i] :
( ( ( ~ ~ ( ~ ( ( SV36
= ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ ( sK14_SY90 @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ ( sK14_SY90 @ SV40 @ SV36 @ SV7 ) ) ) )
| ~ ( ( SV40
= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ empty ) )
| ~ ( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ ( sK13_SY91 @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ ( sK13_SY91 @ SV40 @ SV36 @ SV7 ) ) ) ) ) )
= $false )
| ( ( path @ SV7 @ SV36 @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[412]) ).
thf(446,plain,
! [SV25: $i,SV18: $i,SV81: $i,SV8: $i] :
( ( ( ( SV8
!= ( tail_of @ SV81 ) )
| ~ ( edge @ SV81 ) )
= $true )
| ( ( ( SV18
!= ( head_of @ SV81 ) )
| ( SV25
!= ( path_cons @ SV81 @ empty ) ) )
= $true )
| ( ( vertex @ SV8 )
= $false )
| ( ( vertex @ SV18 )
= $false )
| ( ( path @ SV8 @ SV18 @ SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[413]) ).
thf(447,plain,
! [SV18: $i,SV25: $i,SV82: $i,SV8: $i] :
( ( ( ( SV8
!= ( tail_of @ SV82 ) )
| ~ ( edge @ SV82 ) )
= $true )
| ( ( ! [SY236: $i] :
( ( SV25
!= ( path_cons @ SV82 @ SY236 ) )
| ~ ( path @ ( head_of @ SV82 ) @ SV18 @ SY236 ) ) )
= $true )
| ( ( vertex @ SV8 )
= $false )
| ( ( vertex @ SV18 )
= $false )
| ( ( path @ SV8 @ SV18 @ SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(448,plain,
! [SV19: $i,SV9: $i,SV60: $i,SV70: $i] :
( ( ( on_path @ SV70 @ SV60 )
= $false )
| ( ( ~ ( path @ SV9 @ SV19 @ SV60 ) )
= $true )
| ( ( edge @ SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[415]) ).
thf(449,plain,
! [SV19: $i,SV9: $i,SV61: $i,SV71: $i] :
( ( ( on_path @ SV71 @ SV61 )
= $false )
| ( ( ~ ( path @ SV9 @ SV19 @ SV61 ) )
= $true )
| ( ( in_path @ ( head_of @ SV71 ) @ SV61 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[416]) ).
thf(450,plain,
! [SV10: $i,SV20: $i,SV42: $i,SV47: $i] :
( ( ( ~ ( on_path @ ( sK11_E @ SV47 @ SV42 @ SV20 @ SV10 ) @ SV42 ) )
= $false )
| ( ( in_path @ SV47 @ SV42 )
= $false )
| ( ( path @ SV10 @ SV20 @ SV42 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[417]) ).
thf(451,plain,
! [SV10: $i,SV20: $i,SV42: $i,SV47: $i] :
( ( ( ~ ( ( SV47
= ( head_of @ ( sK11_E @ SV47 @ SV42 @ SV20 @ SV10 ) ) )
| ( SV47
= ( tail_of @ ( sK11_E @ SV47 @ SV42 @ SV20 @ SV10 ) ) ) ) )
= $false )
| ( ( in_path @ SV47 @ SV42 )
= $false )
| ( ( path @ SV10 @ SV20 @ SV42 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[417]) ).
thf(452,plain,
! [SV44: $i,SV37: $i,SV11: $i] :
( ( ( path @ SV11 @ SV37 @ SV44 )
= $false )
| ( ( SV11 = SV37 )
= $true )
| ( ( path @ SV11 @ SV37 @ ( sK9_P @ SV44 @ SV37 @ SV11 ) )
= $true )
| ( ( shortest_path @ SV11 @ SV37 @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(453,plain,
! [SV44: $i,SV37: $i,SV11: $i] :
( ( ( SV11 = SV37 )
= $true )
| ( ( ~ ( path @ SV11 @ SV37 @ SV44 ) )
= $true )
| ( ( less_or_equal @ ( length_of @ SV44 ) @ ( length_of @ ( sK9_P @ SV44 @ SV37 @ SV11 ) ) )
= $false )
| ( ( shortest_path @ SV11 @ SV37 @ SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[419]) ).
thf(454,plain,
! [SV62: $i,SV83: $i,SV54: $i,SV11: $i] :
( ( ( ~ ( path @ SV11 @ SV54 @ SV83 ) )
= $true )
| ( ( less_or_equal @ ( length_of @ SV62 ) @ ( length_of @ SV83 ) )
= $true )
| ( ( shortest_path @ SV11 @ SV54 @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[420]) ).
thf(455,plain,
! [SV91: $i,SV77: $i,SV11: $i] :
( ( ( ~ ( shortest_path @ SV11 @ SV77 @ SV91 ) )
= $true )
| ( ( ( SV11 != SV77 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(456,plain,
! [SV84: $i,SV78: $i,SV11: $i] :
( ( ( ~ ( shortest_path @ SV11 @ SV78 @ SV84 ) )
= $true )
| ( ( path @ SV11 @ SV78 @ SV84 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[422]) ).
thf(457,plain,
! [SV79: $i,SV72: $i] :
( ( ( sequential @ SV72 @ SV79 )
= $false )
| ( ( ( SV72 != SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[424]) ).
thf(458,plain,
! [SV92: $i] :
( ( ! [SY244: $i] :
~ ( sequential @ SV92 @ SY244 )
| ( edge @ SV92 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(459,plain,
! [SV93: $i] :
( ( ! [SY245: $i] :
( ~ ( sequential @ SV93 @ SY245 )
| ( edge @ SY245 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(460,plain,
! [SV33: $i,SV26: $i,SV73: $i,SV12: $i,SV63: $i] :
( ( ( ~ ( on_path @ SV63 @ SV12 ) )
= $true )
| ( ( ~ ( on_path @ SV73 @ SV12 ) )
= $true )
| ( ( ! [SY232: $i] :
( ~ ( precedes @ SY232 @ SV73 @ SV12 )
| ~ ( sequential @ SV63 @ SY232 ) ) )
= $true )
| ( ( precedes @ SV63 @ SV73 @ SV12 )
= $true )
| ( ( path @ SV26 @ SV33 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[427]) ).
thf(461,plain,
! [SV33: $i,SV26: $i,SV74: $i,SV12: $i,SV64: $i] :
( ( ( ~ ( on_path @ SV64 @ SV12 ) )
= $true )
| ( ( ~ ( on_path @ SV74 @ SV12 ) )
= $true )
| ( ( ~ ( sequential @ SV64 @ SV74 ) )
= $true )
| ( ( precedes @ SV64 @ SV74 @ SV12 )
= $true )
| ( ( path @ SV26 @ SV33 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[428]) ).
thf(462,plain,
! [SV21: $i,SV13: $i,SV65: $i,SV50: $i,SV27: $i,SV94: $i] :
( ( ( ( ( tail_of @ SV94 )
!= ( tail_of @ SV27 ) )
| ( ( head_of @ SV94 )
!= ( head_of @ SV50 ) ) )
= $true )
| ( ( precedes @ SV27 @ SV50 @ SV65 )
= $false )
| ( ( shortest_path @ SV13 @ SV21 @ SV65 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(463,plain,
! [SV21: $i,SV13: $i,SV56: $i,SV27: $i,SV51: $i] :
( ( ( precedes @ SV51 @ SV27 @ SV56 )
= $false )
| ( ( precedes @ SV27 @ SV51 @ SV56 )
= $false )
| ( ( shortest_path @ SV13 @ SV21 @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[430]) ).
thf(464,plain,
! [SV34: $i,SV28: $i,SV14: $i,SV85: $i] :
( ( ( ! [SY237: $i] :
~ ( precedes @ SV85 @ SY237 @ SV14 ) )
= $true )
| ( ( on_path @ SV85 @ SV14 )
= $true )
| ( ( path @ SV28 @ SV34 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[431]) ).
thf(465,plain,
! [SV34: $i,SV28: $i,SV14: $i,SV95: $i,SV86: $i] :
( ( ( ~ ( precedes @ SV86 @ SV95 @ SV14 )
| ( on_path @ SV95 @ SV14 ) )
= $true )
| ( ( path @ SV28 @ SV34 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[432]) ).
thf(466,plain,
! [SV34: $i,SV28: $i,SV14: $i,SV96: $i,SV87: $i] :
( ( ( ~ ( precedes @ SV87 @ SV96 @ SV14 )
| ! [SY246: $i] :
( ~ ( precedes @ SY246 @ SV96 @ SV14 )
| ~ ( sequential @ SV87 @ SY246 ) )
| ~ ( sequential @ SV87 @ SV96 ) )
= $true )
| ( ( path @ SV28 @ SV34 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(467,plain,
! [SV34: $i,SV28: $i,SV14: $i,SV97: $i,SV88: $i] :
( ( ( ~ ( precedes @ SV88 @ SV97 @ SV14 )
| ~ ( ~ ( precedes @ ( sK10_E3 @ SV97 @ SV88 @ SV14 ) @ SV97 @ SV14 )
| ~ ( sequential @ SV88 @ ( sK10_E3 @ SV97 @ SV88 @ SV14 ) ) )
| ( sequential @ SV88 @ SV97 ) )
= $true )
| ( ( path @ SV28 @ SV34 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[434]) ).
thf(468,plain,
! [SV5: $i,SV98: $i,SV89: $i] :
( ( ( ~ ( path @ SV89 @ SV98 @ SV5 ) )
= $true )
| ( ( on_path @ ( sK7_E1 @ SV5 ) @ SV5 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV5 )
= ( number_of_in @ triangles @ SV5 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(469,plain,
! [SV5: $i,SV99: $i,SV90: $i] :
( ( ( ~ ( path @ SV90 @ SV99 @ SV5 ) )
= $true )
| ( ( on_path @ ( sK8_SY86 @ SV5 ) @ SV5 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV5 )
= ( number_of_in @ triangles @ SV5 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(470,plain,
! [SV39: $i,SV6: $i,SV35: $i] :
( ( ( edge @ SV35 )
= $false )
| ( ( edge @ SV6 )
= $false )
| ( ( ~ ( edge @ SV39 ) )
= $true )
| ( ( ~ ( sequential @ SV6 @ SV35 ) )
= $true )
| ( ( ~ ( sequential @ SV35 @ SV39 ) )
= $true )
| ( ( ~ ( sequential @ SV39 @ SV6 ) )
= $true )
| ( ( triangle @ SV6 @ SV35 @ SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[437]) ).
thf(471,plain,
! [SV6: $i] :
( ( ~ ~ ( ~ ( ! [SY102: $i,SY103: $i] :
~ ( triangle @ SV6 @ SY102 @ SY103 )
| ( edge @ SV6 ) )
| ~ ! [SY104: $i] :
( ! [SY105: $i] :
~ ( triangle @ SV6 @ SY104 @ SY105 )
| ( edge @ SY104 ) ) )
| ~ ! [SY106: $i,SY107: $i] :
( ~ ( triangle @ SV6 @ SY106 @ SY107 )
| ( edge @ SY107 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(472,plain,
! [SV100: $i,SV6: $i] :
( ( ! [SY247: $i] :
~ ( triangle @ SV6 @ SV100 @ SY247 )
| ( sequential @ SV6 @ SV100 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[439]) ).
thf(473,plain,
! [SV80: $i,SV76: $i,SV6: $i] :
( ( ( triangle @ SV6 @ SV76 @ SV80 )
= $false )
| ( ( sequential @ SV76 @ SV80 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[440]) ).
thf(474,plain,
! [SV31: $i,SV24: $i] :
( ( ( ~ ( ( SV24
!= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
!= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
!= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
!= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) ) )
= $false )
| ( ( SV24 = SV31 )
= $true )
| ( ( vertex @ SV24 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[441]) ).
thf(475,plain,
! [SV31: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( SV24
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
| ~ ( ( SV24
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) ) )
| ~ ~ ( ~ ( ( SV31
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
| ~ ( ( SV31
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) ) ) ) )
= $false )
| ( ( SV24 = SV31 )
= $true )
| ( ( vertex @ SV24 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[441]) ).
thf(476,plain,
! [SV36: $i,SV40: $i,SV7: $i] :
( ( ( SV7
= ( tail_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
= $true )
| ( ( path @ SV7 @ SV36 @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[442]) ).
thf(477,plain,
! [SV7: $i,SV36: $i,SV40: $i] :
( ( ( edge @ ( sK12_E @ SV40 @ SV36 @ SV7 ) )
= $true )
| ( ( path @ SV7 @ SV36 @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[443]) ).
thf(478,plain,
! [SV7: $i,SV40: $i,SV36: $i] :
( ( ( ( SV36
!= ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
| ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ empty ) )
| ! [SY210: $i] :
( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ SY210 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ SY210 ) ) )
= $true )
| ( ( path @ SV7 @ SV36 @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[444]) ).
thf(479,plain,
! [SV7: $i,SV40: $i,SV36: $i] :
( ( ( ~ ( ~ ( ( SV36
= ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ ( sK14_SY90 @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ ( sK14_SY90 @ SV40 @ SV36 @ SV7 ) ) ) )
| ~ ( ( SV40
= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ empty ) )
| ~ ( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ ( sK13_SY91 @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ ( sK13_SY91 @ SV40 @ SV36 @ SV7 ) ) ) ) ) )
= $true )
| ( ( path @ SV7 @ SV36 @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[445]) ).
thf(480,plain,
! [SV25: $i,SV18: $i,SV81: $i,SV8: $i] :
( ( ( ( SV8
!= ( tail_of @ SV81 ) ) )
= $true )
| ( ( ~ ( edge @ SV81 ) )
= $true )
| ( ( ( SV18
!= ( head_of @ SV81 ) )
| ( SV25
!= ( path_cons @ SV81 @ empty ) ) )
= $true )
| ( ( vertex @ SV8 )
= $false )
| ( ( vertex @ SV18 )
= $false )
| ( ( path @ SV8 @ SV18 @ SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[446]) ).
thf(481,plain,
! [SV18: $i,SV25: $i,SV82: $i,SV8: $i] :
( ( ( ( SV8
!= ( tail_of @ SV82 ) ) )
= $true )
| ( ( ~ ( edge @ SV82 ) )
= $true )
| ( ( ! [SY236: $i] :
( ( SV25
!= ( path_cons @ SV82 @ SY236 ) )
| ~ ( path @ ( head_of @ SV82 ) @ SV18 @ SY236 ) ) )
= $true )
| ( ( vertex @ SV8 )
= $false )
| ( ( vertex @ SV18 )
= $false )
| ( ( path @ SV8 @ SV18 @ SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[447]) ).
thf(482,plain,
! [SV70: $i,SV60: $i,SV19: $i,SV9: $i] :
( ( ( path @ SV9 @ SV19 @ SV60 )
= $false )
| ( ( on_path @ SV70 @ SV60 )
= $false )
| ( ( edge @ SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[448]) ).
thf(483,plain,
! [SV71: $i,SV61: $i,SV19: $i,SV9: $i] :
( ( ( path @ SV9 @ SV19 @ SV61 )
= $false )
| ( ( on_path @ SV71 @ SV61 )
= $false )
| ( ( in_path @ ( head_of @ SV71 ) @ SV61 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[449]) ).
thf(484,plain,
! [SV10: $i,SV20: $i,SV42: $i,SV47: $i] :
( ( ( on_path @ ( sK11_E @ SV47 @ SV42 @ SV20 @ SV10 ) @ SV42 )
= $true )
| ( ( in_path @ SV47 @ SV42 )
= $false )
| ( ( path @ SV10 @ SV20 @ SV42 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[450]) ).
thf(485,plain,
! [SV10: $i,SV20: $i,SV42: $i,SV47: $i] :
( ( ( ( SV47
= ( head_of @ ( sK11_E @ SV47 @ SV42 @ SV20 @ SV10 ) ) )
| ( SV47
= ( tail_of @ ( sK11_E @ SV47 @ SV42 @ SV20 @ SV10 ) ) ) )
= $true )
| ( ( in_path @ SV47 @ SV42 )
= $false )
| ( ( path @ SV10 @ SV20 @ SV42 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[451]) ).
thf(486,plain,
! [SV44: $i,SV37: $i,SV11: $i] :
( ( ( path @ SV11 @ SV37 @ SV44 )
= $false )
| ( ( SV11 = SV37 )
= $true )
| ( ( less_or_equal @ ( length_of @ SV44 ) @ ( length_of @ ( sK9_P @ SV44 @ SV37 @ SV11 ) ) )
= $false )
| ( ( shortest_path @ SV11 @ SV37 @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[453]) ).
thf(487,plain,
! [SV62: $i,SV83: $i,SV54: $i,SV11: $i] :
( ( ( path @ SV11 @ SV54 @ SV83 )
= $false )
| ( ( less_or_equal @ ( length_of @ SV62 ) @ ( length_of @ SV83 ) )
= $true )
| ( ( shortest_path @ SV11 @ SV54 @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[454]) ).
thf(488,plain,
! [SV91: $i,SV77: $i,SV11: $i] :
( ( ( shortest_path @ SV11 @ SV77 @ SV91 )
= $false )
| ( ( ( SV11 != SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[455]) ).
thf(489,plain,
! [SV84: $i,SV78: $i,SV11: $i] :
( ( ( shortest_path @ SV11 @ SV78 @ SV84 )
= $false )
| ( ( path @ SV11 @ SV78 @ SV84 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[456]) ).
thf(490,plain,
! [SV79: $i,SV72: $i] :
( ( ( SV72 = SV79 )
= $false )
| ( ( sequential @ SV72 @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[457]) ).
thf(491,plain,
! [SV92: $i] :
( ( ( ! [SY244: $i] :
~ ( sequential @ SV92 @ SY244 ) )
= $true )
| ( ( edge @ SV92 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[458]) ).
thf(492,plain,
! [SV101: $i,SV93: $i] :
( ( ~ ( sequential @ SV93 @ SV101 )
| ( edge @ SV101 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(493,plain,
! [SV33: $i,SV26: $i,SV73: $i,SV12: $i,SV63: $i] :
( ( ( on_path @ SV63 @ SV12 )
= $false )
| ( ( ~ ( on_path @ SV73 @ SV12 ) )
= $true )
| ( ( ! [SY232: $i] :
( ~ ( precedes @ SY232 @ SV73 @ SV12 )
| ~ ( sequential @ SV63 @ SY232 ) ) )
= $true )
| ( ( precedes @ SV63 @ SV73 @ SV12 )
= $true )
| ( ( path @ SV26 @ SV33 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[460]) ).
thf(494,plain,
! [SV33: $i,SV26: $i,SV74: $i,SV12: $i,SV64: $i] :
( ( ( on_path @ SV64 @ SV12 )
= $false )
| ( ( ~ ( on_path @ SV74 @ SV12 ) )
= $true )
| ( ( ~ ( sequential @ SV64 @ SV74 ) )
= $true )
| ( ( precedes @ SV64 @ SV74 @ SV12 )
= $true )
| ( ( path @ SV26 @ SV33 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[461]) ).
thf(495,plain,
! [SV21: $i,SV13: $i,SV65: $i,SV50: $i,SV27: $i,SV94: $i] :
( ( ( ( ( tail_of @ SV94 )
!= ( tail_of @ SV27 ) ) )
= $true )
| ( ( ( ( head_of @ SV94 )
!= ( head_of @ SV50 ) ) )
= $true )
| ( ( precedes @ SV27 @ SV50 @ SV65 )
= $false )
| ( ( shortest_path @ SV13 @ SV21 @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[462]) ).
thf(496,plain,
! [SV34: $i,SV28: $i,SV14: $i,SV102: $i,SV85: $i] :
( ( ( ~ ( precedes @ SV85 @ SV102 @ SV14 ) )
= $true )
| ( ( on_path @ SV85 @ SV14 )
= $true )
| ( ( path @ SV28 @ SV34 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[464]) ).
thf(497,plain,
! [SV34: $i,SV28: $i,SV14: $i,SV95: $i,SV86: $i] :
( ( ( ~ ( precedes @ SV86 @ SV95 @ SV14 ) )
= $true )
| ( ( on_path @ SV95 @ SV14 )
= $true )
| ( ( path @ SV28 @ SV34 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[465]) ).
thf(498,plain,
! [SV34: $i,SV28: $i,SV14: $i,SV96: $i,SV87: $i] :
( ( ( ~ ( precedes @ SV87 @ SV96 @ SV14 ) )
= $true )
| ( ( ! [SY246: $i] :
( ~ ( precedes @ SY246 @ SV96 @ SV14 )
| ~ ( sequential @ SV87 @ SY246 ) )
| ~ ( sequential @ SV87 @ SV96 ) )
= $true )
| ( ( path @ SV28 @ SV34 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[466]) ).
thf(499,plain,
! [SV34: $i,SV28: $i,SV14: $i,SV97: $i,SV88: $i] :
( ( ( ~ ( precedes @ SV88 @ SV97 @ SV14 ) )
= $true )
| ( ( ~ ( ~ ( precedes @ ( sK10_E3 @ SV97 @ SV88 @ SV14 ) @ SV97 @ SV14 )
| ~ ( sequential @ SV88 @ ( sK10_E3 @ SV97 @ SV88 @ SV14 ) ) )
| ( sequential @ SV88 @ SV97 ) )
= $true )
| ( ( path @ SV28 @ SV34 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[467]) ).
thf(500,plain,
! [SV5: $i,SV98: $i,SV89: $i] :
( ( ( path @ SV89 @ SV98 @ SV5 )
= $false )
| ( ( on_path @ ( sK7_E1 @ SV5 ) @ SV5 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV5 )
= ( number_of_in @ triangles @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[468]) ).
thf(501,plain,
! [SV5: $i,SV99: $i,SV90: $i] :
( ( ( path @ SV90 @ SV99 @ SV5 )
= $false )
| ( ( on_path @ ( sK8_SY86 @ SV5 ) @ SV5 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV5 )
= ( number_of_in @ triangles @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[469]) ).
thf(502,plain,
! [SV35: $i,SV6: $i,SV39: $i] :
( ( ( edge @ SV39 )
= $false )
| ( ( edge @ SV6 )
= $false )
| ( ( edge @ SV35 )
= $false )
| ( ( ~ ( sequential @ SV6 @ SV35 ) )
= $true )
| ( ( ~ ( sequential @ SV35 @ SV39 ) )
= $true )
| ( ( ~ ( sequential @ SV39 @ SV6 ) )
= $true )
| ( ( triangle @ SV6 @ SV35 @ SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[470]) ).
thf(503,plain,
! [SV6: $i] :
( ( ~ ~ ( ~ ( ! [SY102: $i,SY103: $i] :
~ ( triangle @ SV6 @ SY102 @ SY103 )
| ( edge @ SV6 ) )
| ~ ! [SY104: $i] :
( ! [SY105: $i] :
~ ( triangle @ SV6 @ SY104 @ SY105 )
| ( edge @ SY104 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[471]) ).
thf(504,plain,
! [SV6: $i] :
( ( ~ ! [SY106: $i,SY107: $i] :
( ~ ( triangle @ SV6 @ SY106 @ SY107 )
| ( edge @ SY107 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[471]) ).
thf(505,plain,
! [SV100: $i,SV6: $i] :
( ( ( ! [SY247: $i] :
~ ( triangle @ SV6 @ SV100 @ SY247 ) )
= $true )
| ( ( sequential @ SV6 @ SV100 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[472]) ).
thf(506,plain,
! [SV31: $i,SV24: $i] :
( ( ( ( SV24
!= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
!= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
!= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
!= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
= $true )
| ( ( SV24 = SV31 )
= $true )
| ( ( vertex @ SV24 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[474]) ).
thf(507,plain,
! [SV31: $i,SV24: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( SV24
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
| ~ ( ( SV24
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) ) )
| ~ ~ ( ~ ( ( SV31
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
| ~ ( ( SV31
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) ) ) ) )
= $true )
| ( ( SV24 = SV31 )
= $true )
| ( ( vertex @ SV24 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[475]) ).
thf(508,plain,
! [SV7: $i,SV40: $i,SV36: $i] :
( ( ( ( SV36
!= ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
| ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ empty ) ) )
= $true )
| ( ( ! [SY210: $i] :
( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ SY210 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ SY210 ) ) )
= $true )
| ( ( path @ SV7 @ SV36 @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[478]) ).
thf(509,plain,
! [SV7: $i,SV40: $i,SV36: $i] :
( ( ( ~ ( ( SV36
= ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ ( sK14_SY90 @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ ( sK14_SY90 @ SV40 @ SV36 @ SV7 ) ) ) )
| ~ ( ( SV40
= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ empty ) )
| ~ ( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ ( sK13_SY91 @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ ( sK13_SY91 @ SV40 @ SV36 @ SV7 ) ) ) ) )
= $false )
| ( ( path @ SV7 @ SV36 @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[479]) ).
thf(510,plain,
! [SV25: $i,SV18: $i,SV81: $i,SV8: $i] :
( ( ( SV8
= ( tail_of @ SV81 ) )
= $false )
| ( ( ~ ( edge @ SV81 ) )
= $true )
| ( ( ( SV18
!= ( head_of @ SV81 ) )
| ( SV25
!= ( path_cons @ SV81 @ empty ) ) )
= $true )
| ( ( vertex @ SV8 )
= $false )
| ( ( vertex @ SV18 )
= $false )
| ( ( path @ SV8 @ SV18 @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[480]) ).
thf(511,plain,
! [SV18: $i,SV25: $i,SV82: $i,SV8: $i] :
( ( ( SV8
= ( tail_of @ SV82 ) )
= $false )
| ( ( ~ ( edge @ SV82 ) )
= $true )
| ( ( ! [SY236: $i] :
( ( SV25
!= ( path_cons @ SV82 @ SY236 ) )
| ~ ( path @ ( head_of @ SV82 ) @ SV18 @ SY236 ) ) )
= $true )
| ( ( vertex @ SV8 )
= $false )
| ( ( vertex @ SV18 )
= $false )
| ( ( path @ SV8 @ SV18 @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[481]) ).
thf(512,plain,
! [SV10: $i,SV20: $i,SV42: $i,SV47: $i] :
( ( ( SV47
= ( head_of @ ( sK11_E @ SV47 @ SV42 @ SV20 @ SV10 ) ) )
= $true )
| ( ( SV47
= ( tail_of @ ( sK11_E @ SV47 @ SV42 @ SV20 @ SV10 ) ) )
= $true )
| ( ( in_path @ SV47 @ SV42 )
= $false )
| ( ( path @ SV10 @ SV20 @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[485]) ).
thf(513,plain,
! [SV91: $i,SV77: $i,SV11: $i] :
( ( ( SV11 = SV77 )
= $false )
| ( ( shortest_path @ SV11 @ SV77 @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[488]) ).
thf(514,plain,
! [SV103: $i,SV92: $i] :
( ( ( ~ ( sequential @ SV92 @ SV103 ) )
= $true )
| ( ( edge @ SV92 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(515,plain,
! [SV101: $i,SV93: $i] :
( ( ( ~ ( sequential @ SV93 @ SV101 ) )
= $true )
| ( ( edge @ SV101 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[492]) ).
thf(516,plain,
! [SV33: $i,SV26: $i,SV63: $i,SV12: $i,SV73: $i] :
( ( ( on_path @ SV73 @ SV12 )
= $false )
| ( ( on_path @ SV63 @ SV12 )
= $false )
| ( ( ! [SY232: $i] :
( ~ ( precedes @ SY232 @ SV73 @ SV12 )
| ~ ( sequential @ SV63 @ SY232 ) ) )
= $true )
| ( ( precedes @ SV63 @ SV73 @ SV12 )
= $true )
| ( ( path @ SV26 @ SV33 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[493]) ).
thf(517,plain,
! [SV33: $i,SV26: $i,SV64: $i,SV12: $i,SV74: $i] :
( ( ( on_path @ SV74 @ SV12 )
= $false )
| ( ( on_path @ SV64 @ SV12 )
= $false )
| ( ( ~ ( sequential @ SV64 @ SV74 ) )
= $true )
| ( ( precedes @ SV64 @ SV74 @ SV12 )
= $true )
| ( ( path @ SV26 @ SV33 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[494]) ).
thf(518,plain,
! [SV21: $i,SV13: $i,SV65: $i,SV50: $i,SV27: $i,SV94: $i] :
( ( ( ( tail_of @ SV94 )
= ( tail_of @ SV27 ) )
= $false )
| ( ( ( ( head_of @ SV94 )
!= ( head_of @ SV50 ) ) )
= $true )
| ( ( precedes @ SV27 @ SV50 @ SV65 )
= $false )
| ( ( shortest_path @ SV13 @ SV21 @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[495]) ).
thf(519,plain,
! [SV34: $i,SV28: $i,SV14: $i,SV102: $i,SV85: $i] :
( ( ( precedes @ SV85 @ SV102 @ SV14 )
= $false )
| ( ( on_path @ SV85 @ SV14 )
= $true )
| ( ( path @ SV28 @ SV34 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[496]) ).
thf(520,plain,
! [SV34: $i,SV28: $i,SV14: $i,SV95: $i,SV86: $i] :
( ( ( precedes @ SV86 @ SV95 @ SV14 )
= $false )
| ( ( on_path @ SV95 @ SV14 )
= $true )
| ( ( path @ SV28 @ SV34 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[497]) ).
thf(521,plain,
! [SV34: $i,SV28: $i,SV14: $i,SV96: $i,SV87: $i] :
( ( ( precedes @ SV87 @ SV96 @ SV14 )
= $false )
| ( ( ! [SY246: $i] :
( ~ ( precedes @ SY246 @ SV96 @ SV14 )
| ~ ( sequential @ SV87 @ SY246 ) )
| ~ ( sequential @ SV87 @ SV96 ) )
= $true )
| ( ( path @ SV28 @ SV34 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[498]) ).
thf(522,plain,
! [SV34: $i,SV28: $i,SV14: $i,SV97: $i,SV88: $i] :
( ( ( precedes @ SV88 @ SV97 @ SV14 )
= $false )
| ( ( ~ ( ~ ( precedes @ ( sK10_E3 @ SV97 @ SV88 @ SV14 ) @ SV97 @ SV14 )
| ~ ( sequential @ SV88 @ ( sK10_E3 @ SV97 @ SV88 @ SV14 ) ) )
| ( sequential @ SV88 @ SV97 ) )
= $true )
| ( ( path @ SV28 @ SV34 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[499]) ).
thf(523,plain,
! [SV39: $i,SV35: $i,SV6: $i] :
( ( ( sequential @ SV6 @ SV35 )
= $false )
| ( ( edge @ SV35 )
= $false )
| ( ( edge @ SV6 )
= $false )
| ( ( edge @ SV39 )
= $false )
| ( ( ~ ( sequential @ SV35 @ SV39 ) )
= $true )
| ( ( ~ ( sequential @ SV39 @ SV6 ) )
= $true )
| ( ( triangle @ SV6 @ SV35 @ SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[502]) ).
thf(524,plain,
! [SV6: $i] :
( ( ~ ( ~ ( ! [SY102: $i,SY103: $i] :
~ ( triangle @ SV6 @ SY102 @ SY103 )
| ( edge @ SV6 ) )
| ~ ! [SY104: $i] :
( ! [SY105: $i] :
~ ( triangle @ SV6 @ SY104 @ SY105 )
| ( edge @ SY104 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[503]) ).
thf(525,plain,
! [SV6: $i] :
( ( ! [SY106: $i,SY107: $i] :
( ~ ( triangle @ SV6 @ SY106 @ SY107 )
| ( edge @ SY107 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[504]) ).
thf(526,plain,
! [SV104: $i,SV100: $i,SV6: $i] :
( ( ( ~ ( triangle @ SV6 @ SV100 @ SV104 ) )
= $true )
| ( ( sequential @ SV6 @ SV100 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(527,plain,
! [SV31: $i,SV24: $i] :
( ( ( ( SV24
!= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
!= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
= $true )
| ( ( ( SV31
!= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
!= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
= $true )
| ( ( SV24 = SV31 )
= $true )
| ( ( vertex @ SV24 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[506]) ).
thf(528,plain,
! [SV31: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ( ( SV24
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
| ~ ( ( SV24
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) ) )
| ~ ~ ( ~ ( ( SV31
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
| ~ ( ( SV31
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) ) ) )
= $false )
| ( ( SV24 = SV31 )
= $true )
| ( ( vertex @ SV24 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[507]) ).
thf(529,plain,
! [SV7: $i,SV40: $i,SV36: $i] :
( ( ( ( SV36
!= ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) ) )
= $true )
| ( ( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ empty ) ) )
= $true )
| ( ( ! [SY210: $i] :
( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ SY210 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ SY210 ) ) )
= $true )
| ( ( path @ SV7 @ SV36 @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[508]) ).
thf(530,plain,
! [SV7: $i,SV40: $i,SV36: $i] :
( ( ( ~ ( ( SV36
= ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ ( sK14_SY90 @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ ( sK14_SY90 @ SV40 @ SV36 @ SV7 ) ) ) ) )
= $false )
| ( ( path @ SV7 @ SV36 @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[509]) ).
thf(531,plain,
! [SV7: $i,SV36: $i,SV40: $i] :
( ( ( ~ ( ( SV40
= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ empty ) )
| ~ ( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ ( sK13_SY91 @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ ( sK13_SY91 @ SV40 @ SV36 @ SV7 ) ) ) ) )
= $false )
| ( ( path @ SV7 @ SV36 @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[509]) ).
thf(532,plain,
! [SV25: $i,SV18: $i,SV8: $i,SV81: $i] :
( ( ( edge @ SV81 )
= $false )
| ( ( SV8
= ( tail_of @ SV81 ) )
= $false )
| ( ( ( SV18
!= ( head_of @ SV81 ) )
| ( SV25
!= ( path_cons @ SV81 @ empty ) ) )
= $true )
| ( ( vertex @ SV8 )
= $false )
| ( ( vertex @ SV18 )
= $false )
| ( ( path @ SV8 @ SV18 @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[510]) ).
thf(533,plain,
! [SV18: $i,SV25: $i,SV8: $i,SV82: $i] :
( ( ( edge @ SV82 )
= $false )
| ( ( SV8
= ( tail_of @ SV82 ) )
= $false )
| ( ( ! [SY236: $i] :
( ( SV25
!= ( path_cons @ SV82 @ SY236 ) )
| ~ ( path @ ( head_of @ SV82 ) @ SV18 @ SY236 ) ) )
= $true )
| ( ( vertex @ SV8 )
= $false )
| ( ( vertex @ SV18 )
= $false )
| ( ( path @ SV8 @ SV18 @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[511]) ).
thf(534,plain,
! [SV103: $i,SV92: $i] :
( ( ( sequential @ SV92 @ SV103 )
= $false )
| ( ( edge @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[514]) ).
thf(535,plain,
! [SV101: $i,SV93: $i] :
( ( ( sequential @ SV93 @ SV101 )
= $false )
| ( ( edge @ SV101 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[515]) ).
thf(536,plain,
! [SV33: $i,SV26: $i,SV63: $i,SV12: $i,SV73: $i,SV105: $i] :
( ( ( ~ ( precedes @ SV105 @ SV73 @ SV12 )
| ~ ( sequential @ SV63 @ SV105 ) )
= $true )
| ( ( on_path @ SV63 @ SV12 )
= $false )
| ( ( on_path @ SV73 @ SV12 )
= $false )
| ( ( precedes @ SV63 @ SV73 @ SV12 )
= $true )
| ( ( path @ SV26 @ SV33 @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[516]) ).
thf(537,plain,
! [SV33: $i,SV26: $i,SV12: $i,SV74: $i,SV64: $i] :
( ( ( sequential @ SV64 @ SV74 )
= $false )
| ( ( on_path @ SV64 @ SV12 )
= $false )
| ( ( on_path @ SV74 @ SV12 )
= $false )
| ( ( precedes @ SV64 @ SV74 @ SV12 )
= $true )
| ( ( path @ SV26 @ SV33 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[517]) ).
thf(538,plain,
! [SV21: $i,SV13: $i,SV65: $i,SV27: $i,SV50: $i,SV94: $i] :
( ( ( ( head_of @ SV94 )
= ( head_of @ SV50 ) )
= $false )
| ( ( ( tail_of @ SV94 )
= ( tail_of @ SV27 ) )
= $false )
| ( ( precedes @ SV27 @ SV50 @ SV65 )
= $false )
| ( ( shortest_path @ SV13 @ SV21 @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[518]) ).
thf(539,plain,
! [SV34: $i,SV28: $i,SV87: $i,SV14: $i,SV96: $i] :
( ( ( ! [SY246: $i] :
( ~ ( precedes @ SY246 @ SV96 @ SV14 )
| ~ ( sequential @ SV87 @ SY246 ) ) )
= $true )
| ( ( ~ ( sequential @ SV87 @ SV96 ) )
= $true )
| ( ( precedes @ SV87 @ SV96 @ SV14 )
= $false )
| ( ( path @ SV28 @ SV34 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[521]) ).
thf(540,plain,
! [SV34: $i,SV28: $i,SV14: $i,SV88: $i,SV97: $i] :
( ( ( ~ ( ~ ( precedes @ ( sK10_E3 @ SV97 @ SV88 @ SV14 ) @ SV97 @ SV14 )
| ~ ( sequential @ SV88 @ ( sK10_E3 @ SV97 @ SV88 @ SV14 ) ) ) )
= $true )
| ( ( sequential @ SV88 @ SV97 )
= $true )
| ( ( precedes @ SV88 @ SV97 @ SV14 )
= $false )
| ( ( path @ SV28 @ SV34 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[522]) ).
thf(541,plain,
! [SV6: $i,SV39: $i,SV35: $i] :
( ( ( sequential @ SV35 @ SV39 )
= $false )
| ( ( edge @ SV39 )
= $false )
| ( ( edge @ SV6 )
= $false )
| ( ( edge @ SV35 )
= $false )
| ( ( sequential @ SV6 @ SV35 )
= $false )
| ( ( ~ ( sequential @ SV39 @ SV6 ) )
= $true )
| ( ( triangle @ SV6 @ SV35 @ SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[523]) ).
thf(542,plain,
! [SV6: $i] :
( ( ~ ( ! [SY102: $i,SY103: $i] :
~ ( triangle @ SV6 @ SY102 @ SY103 )
| ( edge @ SV6 ) )
| ~ ! [SY104: $i] :
( ! [SY105: $i] :
~ ( triangle @ SV6 @ SY104 @ SY105 )
| ( edge @ SY104 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[524]) ).
thf(543,plain,
! [SV106: $i,SV6: $i] :
( ( ! [SY248: $i] :
( ~ ( triangle @ SV6 @ SV106 @ SY248 )
| ( edge @ SY248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[525]) ).
thf(544,plain,
! [SV104: $i,SV100: $i,SV6: $i] :
( ( ( triangle @ SV6 @ SV100 @ SV104 )
= $false )
| ( ( sequential @ SV6 @ SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[526]) ).
thf(545,plain,
! [SV31: $i,SV24: $i] :
( ( ( ( SV24
!= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
= $true )
| ( ( ( SV31
!= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
= $true )
| ( ( ( SV31
!= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
!= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
= $true )
| ( ( SV24 = SV31 )
= $true )
| ( ( vertex @ SV24 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[527]) ).
thf(546,plain,
! [SV31: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ( ( SV24
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
| ~ ( ( SV24
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) ) ) )
= $false )
| ( ( SV24 = SV31 )
= $true )
| ( ( vertex @ SV24 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[528]) ).
thf(547,plain,
! [SV24: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ( ( SV31
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
| ~ ( ( SV31
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) ) ) )
= $false )
| ( ( SV24 = SV31 )
= $true )
| ( ( vertex @ SV24 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[528]) ).
thf(548,plain,
! [SV7: $i,SV40: $i,SV36: $i] :
( ( ( SV36
= ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
= $false )
| ( ( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ empty ) ) )
= $true )
| ( ( ! [SY210: $i] :
( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ SY210 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ SY210 ) ) )
= $true )
| ( ( path @ SV7 @ SV36 @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[529]) ).
thf(549,plain,
! [SV7: $i,SV40: $i,SV36: $i] :
( ( ( ( SV36
= ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ ( sK14_SY90 @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ ( sK14_SY90 @ SV40 @ SV36 @ SV7 ) ) ) )
= $true )
| ( ( path @ SV7 @ SV36 @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[530]) ).
thf(550,plain,
! [SV7: $i,SV36: $i,SV40: $i] :
( ( ( ( SV40
= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ empty ) )
| ~ ( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ ( sK13_SY91 @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ ( sK13_SY91 @ SV40 @ SV36 @ SV7 ) ) ) )
= $true )
| ( ( path @ SV7 @ SV36 @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[531]) ).
thf(551,plain,
! [SV8: $i,SV25: $i,SV81: $i,SV18: $i] :
( ( ( ( SV18
!= ( head_of @ SV81 ) ) )
= $true )
| ( ( ( SV25
!= ( path_cons @ SV81 @ empty ) ) )
= $true )
| ( ( SV8
= ( tail_of @ SV81 ) )
= $false )
| ( ( edge @ SV81 )
= $false )
| ( ( vertex @ SV8 )
= $false )
| ( ( vertex @ SV18 )
= $false )
| ( ( path @ SV8 @ SV18 @ SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[532]) ).
thf(552,plain,
! [SV8: $i,SV18: $i,SV107: $i,SV82: $i,SV25: $i] :
( ( ( ( SV25
!= ( path_cons @ SV82 @ SV107 ) )
| ~ ( path @ ( head_of @ SV82 ) @ SV18 @ SV107 ) )
= $true )
| ( ( SV8
= ( tail_of @ SV82 ) )
= $false )
| ( ( edge @ SV82 )
= $false )
| ( ( vertex @ SV8 )
= $false )
| ( ( vertex @ SV18 )
= $false )
| ( ( path @ SV8 @ SV18 @ SV25 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(553,plain,
! [SV33: $i,SV26: $i,SV63: $i,SV12: $i,SV73: $i,SV105: $i] :
( ( ( ~ ( precedes @ SV105 @ SV73 @ SV12 ) )
= $true )
| ( ( ~ ( sequential @ SV63 @ SV105 ) )
= $true )
| ( ( on_path @ SV63 @ SV12 )
= $false )
| ( ( on_path @ SV73 @ SV12 )
= $false )
| ( ( precedes @ SV63 @ SV73 @ SV12 )
= $true )
| ( ( path @ SV26 @ SV33 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[536]) ).
thf(554,plain,
! [SV34: $i,SV28: $i,SV87: $i,SV14: $i,SV96: $i,SV108: $i] :
( ( ( ~ ( precedes @ SV108 @ SV96 @ SV14 )
| ~ ( sequential @ SV87 @ SV108 ) )
= $true )
| ( ( ~ ( sequential @ SV87 @ SV96 ) )
= $true )
| ( ( precedes @ SV87 @ SV96 @ SV14 )
= $false )
| ( ( path @ SV28 @ SV34 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(555,plain,
! [SV34: $i,SV28: $i,SV14: $i,SV88: $i,SV97: $i] :
( ( ( ~ ( precedes @ ( sK10_E3 @ SV97 @ SV88 @ SV14 ) @ SV97 @ SV14 )
| ~ ( sequential @ SV88 @ ( sK10_E3 @ SV97 @ SV88 @ SV14 ) ) )
= $false )
| ( ( sequential @ SV88 @ SV97 )
= $true )
| ( ( precedes @ SV88 @ SV97 @ SV14 )
= $false )
| ( ( path @ SV28 @ SV34 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[540]) ).
thf(556,plain,
! [SV35: $i,SV6: $i,SV39: $i] :
( ( ( sequential @ SV39 @ SV6 )
= $false )
| ( ( sequential @ SV6 @ SV35 )
= $false )
| ( ( edge @ SV35 )
= $false )
| ( ( edge @ SV6 )
= $false )
| ( ( edge @ SV39 )
= $false )
| ( ( sequential @ SV35 @ SV39 )
= $false )
| ( ( triangle @ SV6 @ SV35 @ SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[541]) ).
thf(557,plain,
! [SV6: $i] :
( ( ~ ( ! [SY102: $i,SY103: $i] :
~ ( triangle @ SV6 @ SY102 @ SY103 )
| ( edge @ SV6 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[542]) ).
thf(558,plain,
! [SV6: $i] :
( ( ~ ! [SY104: $i] :
( ! [SY105: $i] :
~ ( triangle @ SV6 @ SY104 @ SY105 )
| ( edge @ SY104 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[542]) ).
thf(559,plain,
! [SV109: $i,SV106: $i,SV6: $i] :
( ( ~ ( triangle @ SV6 @ SV106 @ SV109 )
| ( edge @ SV109 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(560,plain,
! [SV31: $i,SV24: $i] :
( ( ( SV24
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
= $false )
| ( ( ( SV31
!= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
= $true )
| ( ( ( SV31
!= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
!= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
= $true )
| ( ( SV24 = SV31 )
= $true )
| ( ( vertex @ SV24 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[545]) ).
thf(561,plain,
! [SV31: $i,SV24: $i] :
( ( ( ~ ( ~ ( ( SV24
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
| ~ ( ( SV24
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) ) ) )
= $true )
| ( ( SV24 = SV31 )
= $true )
| ( ( vertex @ SV24 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[546]) ).
thf(562,plain,
! [SV24: $i,SV31: $i] :
( ( ( ~ ( ~ ( ( SV31
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
| ~ ( ( SV31
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) ) ) )
= $true )
| ( ( SV24 = SV31 )
= $true )
| ( ( vertex @ SV24 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[547]) ).
thf(563,plain,
! [SV7: $i,SV36: $i,SV40: $i] :
( ( ( SV40
= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ empty ) )
= $false )
| ( ( SV36
= ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
= $false )
| ( ( ! [SY210: $i] :
( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ SY210 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ SY210 ) ) )
= $true )
| ( ( path @ SV7 @ SV36 @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[548]) ).
thf(564,plain,
! [SV7: $i,SV40: $i,SV36: $i] :
( ( ( SV36
= ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
= $true )
| ( ( ~ ( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ ( sK14_SY90 @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ ( sK14_SY90 @ SV40 @ SV36 @ SV7 ) ) ) )
= $true )
| ( ( path @ SV7 @ SV36 @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[549]) ).
thf(565,plain,
! [SV7: $i,SV36: $i,SV40: $i] :
( ( ( SV40
= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ empty ) )
= $true )
| ( ( ~ ( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ ( sK13_SY91 @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ ( sK13_SY91 @ SV40 @ SV36 @ SV7 ) ) ) )
= $true )
| ( ( path @ SV7 @ SV36 @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[550]) ).
thf(566,plain,
! [SV8: $i,SV25: $i,SV81: $i,SV18: $i] :
( ( ( SV18
= ( head_of @ SV81 ) )
= $false )
| ( ( ( SV25
!= ( path_cons @ SV81 @ empty ) ) )
= $true )
| ( ( SV8
= ( tail_of @ SV81 ) )
= $false )
| ( ( edge @ SV81 )
= $false )
| ( ( vertex @ SV8 )
= $false )
| ( ( vertex @ SV18 )
= $false )
| ( ( path @ SV8 @ SV18 @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[551]) ).
thf(567,plain,
! [SV8: $i,SV18: $i,SV107: $i,SV82: $i,SV25: $i] :
( ( ( ( SV25
!= ( path_cons @ SV82 @ SV107 ) ) )
= $true )
| ( ( ~ ( path @ ( head_of @ SV82 ) @ SV18 @ SV107 ) )
= $true )
| ( ( SV8
= ( tail_of @ SV82 ) )
= $false )
| ( ( edge @ SV82 )
= $false )
| ( ( vertex @ SV8 )
= $false )
| ( ( vertex @ SV18 )
= $false )
| ( ( path @ SV8 @ SV18 @ SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[552]) ).
thf(568,plain,
! [SV33: $i,SV26: $i,SV63: $i,SV12: $i,SV73: $i,SV105: $i] :
( ( ( precedes @ SV105 @ SV73 @ SV12 )
= $false )
| ( ( ~ ( sequential @ SV63 @ SV105 ) )
= $true )
| ( ( on_path @ SV63 @ SV12 )
= $false )
| ( ( on_path @ SV73 @ SV12 )
= $false )
| ( ( precedes @ SV63 @ SV73 @ SV12 )
= $true )
| ( ( path @ SV26 @ SV33 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[553]) ).
thf(569,plain,
! [SV34: $i,SV28: $i,SV87: $i,SV14: $i,SV96: $i,SV108: $i] :
( ( ( ~ ( precedes @ SV108 @ SV96 @ SV14 ) )
= $true )
| ( ( ~ ( sequential @ SV87 @ SV108 ) )
= $true )
| ( ( ~ ( sequential @ SV87 @ SV96 ) )
= $true )
| ( ( precedes @ SV87 @ SV96 @ SV14 )
= $false )
| ( ( path @ SV28 @ SV34 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[554]) ).
thf(570,plain,
! [SV34: $i,SV28: $i,SV14: $i,SV88: $i,SV97: $i] :
( ( ( ~ ( precedes @ ( sK10_E3 @ SV97 @ SV88 @ SV14 ) @ SV97 @ SV14 ) )
= $false )
| ( ( sequential @ SV88 @ SV97 )
= $true )
| ( ( precedes @ SV88 @ SV97 @ SV14 )
= $false )
| ( ( path @ SV28 @ SV34 @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[555]) ).
thf(571,plain,
! [SV34: $i,SV28: $i,SV14: $i,SV97: $i,SV88: $i] :
( ( ( ~ ( sequential @ SV88 @ ( sK10_E3 @ SV97 @ SV88 @ SV14 ) ) )
= $false )
| ( ( sequential @ SV88 @ SV97 )
= $true )
| ( ( precedes @ SV88 @ SV97 @ SV14 )
= $false )
| ( ( path @ SV28 @ SV34 @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[555]) ).
thf(572,plain,
! [SV6: $i] :
( ( ! [SY102: $i,SY103: $i] :
~ ( triangle @ SV6 @ SY102 @ SY103 )
| ( edge @ SV6 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[557]) ).
thf(573,plain,
! [SV6: $i] :
( ( ! [SY104: $i] :
( ! [SY105: $i] :
~ ( triangle @ SV6 @ SY104 @ SY105 )
| ( edge @ SY104 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[558]) ).
thf(574,plain,
! [SV109: $i,SV106: $i,SV6: $i] :
( ( ( ~ ( triangle @ SV6 @ SV106 @ SV109 ) )
= $true )
| ( ( edge @ SV109 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[559]) ).
thf(575,plain,
! [SV24: $i,SV31: $i] :
( ( ( SV31
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
= $false )
| ( ( SV24
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
= $false )
| ( ( ( SV31
!= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
!= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
= $true )
| ( ( SV24 = SV31 )
= $true )
| ( ( vertex @ SV24 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[560]) ).
thf(576,plain,
! [SV31: $i,SV24: $i] :
( ( ( ~ ( ( SV24
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
| ~ ( ( SV24
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) ) )
= $false )
| ( ( SV24 = SV31 )
= $true )
| ( ( vertex @ SV24 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[561]) ).
thf(577,plain,
! [SV24: $i,SV31: $i] :
( ( ( ~ ( ( SV31
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
| ~ ( ( SV31
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) ) )
= $false )
| ( ( SV24 = SV31 )
= $true )
| ( ( vertex @ SV24 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[562]) ).
thf(578,plain,
! [SV110: $i,SV7: $i,SV36: $i,SV40: $i] :
( ( ( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ SV110 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ SV110 ) )
= $true )
| ( ( SV36
= ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
= $false )
| ( ( SV40
= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ empty ) )
= $false )
| ( ( path @ SV7 @ SV36 @ SV40 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[563]) ).
thf(579,plain,
! [SV7: $i,SV36: $i,SV40: $i] :
( ( ( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ ( sK14_SY90 @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ ( sK14_SY90 @ SV40 @ SV36 @ SV7 ) ) )
= $false )
| ( ( SV36
= ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
= $true )
| ( ( path @ SV7 @ SV36 @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[564]) ).
thf(580,plain,
! [SV7: $i,SV36: $i,SV40: $i] :
( ( ( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ ( sK13_SY91 @ SV40 @ SV36 @ SV7 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ ( sK13_SY91 @ SV40 @ SV36 @ SV7 ) ) )
= $false )
| ( ( SV40
= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ empty ) )
= $true )
| ( ( path @ SV7 @ SV36 @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[565]) ).
thf(581,plain,
! [SV8: $i,SV18: $i,SV81: $i,SV25: $i] :
( ( ( SV25
= ( path_cons @ SV81 @ empty ) )
= $false )
| ( ( SV18
= ( head_of @ SV81 ) )
= $false )
| ( ( SV8
= ( tail_of @ SV81 ) )
= $false )
| ( ( edge @ SV81 )
= $false )
| ( ( vertex @ SV8 )
= $false )
| ( ( vertex @ SV18 )
= $false )
| ( ( path @ SV8 @ SV18 @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[566]) ).
thf(582,plain,
! [SV8: $i,SV18: $i,SV107: $i,SV82: $i,SV25: $i] :
( ( ( SV25
= ( path_cons @ SV82 @ SV107 ) )
= $false )
| ( ( ~ ( path @ ( head_of @ SV82 ) @ SV18 @ SV107 ) )
= $true )
| ( ( SV8
= ( tail_of @ SV82 ) )
= $false )
| ( ( edge @ SV82 )
= $false )
| ( ( vertex @ SV8 )
= $false )
| ( ( vertex @ SV18 )
= $false )
| ( ( path @ SV8 @ SV18 @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[567]) ).
thf(583,plain,
! [SV33: $i,SV26: $i,SV12: $i,SV73: $i,SV105: $i,SV63: $i] :
( ( ( sequential @ SV63 @ SV105 )
= $false )
| ( ( precedes @ SV105 @ SV73 @ SV12 )
= $false )
| ( ( on_path @ SV63 @ SV12 )
= $false )
| ( ( on_path @ SV73 @ SV12 )
= $false )
| ( ( precedes @ SV63 @ SV73 @ SV12 )
= $true )
| ( ( path @ SV26 @ SV33 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[568]) ).
thf(584,plain,
! [SV34: $i,SV28: $i,SV87: $i,SV14: $i,SV96: $i,SV108: $i] :
( ( ( precedes @ SV108 @ SV96 @ SV14 )
= $false )
| ( ( ~ ( sequential @ SV87 @ SV108 ) )
= $true )
| ( ( ~ ( sequential @ SV87 @ SV96 ) )
= $true )
| ( ( precedes @ SV87 @ SV96 @ SV14 )
= $false )
| ( ( path @ SV28 @ SV34 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[569]) ).
thf(585,plain,
! [SV34: $i,SV28: $i,SV14: $i,SV88: $i,SV97: $i] :
( ( ( precedes @ ( sK10_E3 @ SV97 @ SV88 @ SV14 ) @ SV97 @ SV14 )
= $true )
| ( ( sequential @ SV88 @ SV97 )
= $true )
| ( ( precedes @ SV88 @ SV97 @ SV14 )
= $false )
| ( ( path @ SV28 @ SV34 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[570]) ).
thf(586,plain,
! [SV34: $i,SV28: $i,SV14: $i,SV97: $i,SV88: $i] :
( ( ( sequential @ SV88 @ ( sK10_E3 @ SV97 @ SV88 @ SV14 ) )
= $true )
| ( ( sequential @ SV88 @ SV97 )
= $true )
| ( ( precedes @ SV88 @ SV97 @ SV14 )
= $false )
| ( ( path @ SV28 @ SV34 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[571]) ).
thf(587,plain,
! [SV6: $i] :
( ( ( ! [SY102: $i,SY103: $i] :
~ ( triangle @ SV6 @ SY102 @ SY103 ) )
= $true )
| ( ( edge @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[572]) ).
thf(588,plain,
! [SV111: $i,SV6: $i] :
( ( ! [SY249: $i] :
~ ( triangle @ SV6 @ SV111 @ SY249 )
| ( edge @ SV111 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(589,plain,
! [SV109: $i,SV106: $i,SV6: $i] :
( ( ( triangle @ SV6 @ SV106 @ SV109 )
= $false )
| ( ( edge @ SV109 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[574]) ).
thf(590,plain,
! [SV24: $i,SV31: $i] :
( ( ( ( SV31
!= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
= $true )
| ( ( ( SV24
!= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
= $true )
| ( ( SV24
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
= $false )
| ( ( SV31
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
= $false )
| ( ( SV24 = SV31 )
= $true )
| ( ( vertex @ SV24 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[575]) ).
thf(591,plain,
! [SV31: $i,SV24: $i] :
( ( ( ~ ( ( SV24
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) ) ) )
= $false )
| ( ( SV24 = SV31 )
= $true )
| ( ( vertex @ SV24 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[576]) ).
thf(592,plain,
! [SV31: $i,SV24: $i] :
( ( ( ~ ( ( SV24
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) ) )
= $false )
| ( ( SV24 = SV31 )
= $true )
| ( ( vertex @ SV24 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[576]) ).
thf(593,plain,
! [SV24: $i,SV31: $i] :
( ( ( ~ ( ( SV31
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) ) ) )
= $false )
| ( ( SV24 = SV31 )
= $true )
| ( ( vertex @ SV24 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[577]) ).
thf(594,plain,
! [SV24: $i,SV31: $i] :
( ( ( ~ ( ( SV31
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) ) )
= $false )
| ( ( SV24 = SV31 )
= $true )
| ( ( vertex @ SV24 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[577]) ).
thf(595,plain,
! [SV110: $i,SV7: $i,SV36: $i,SV40: $i] :
( ( ( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ SV110 ) ) )
= $true )
| ( ( ~ ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ SV110 ) )
= $true )
| ( ( SV36
= ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
= $false )
| ( ( SV40
= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ empty ) )
= $false )
| ( ( path @ SV7 @ SV36 @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[578]) ).
thf(596,plain,
! [SV7: $i,SV36: $i,SV40: $i] :
( ( ( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ ( sK14_SY90 @ SV40 @ SV36 @ SV7 ) ) ) )
= $false )
| ( ( SV36
= ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
= $true )
| ( ( path @ SV7 @ SV36 @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[579]) ).
thf(597,plain,
! [SV7: $i,SV36: $i,SV40: $i] :
( ( ( ~ ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ ( sK14_SY90 @ SV40 @ SV36 @ SV7 ) ) )
= $false )
| ( ( SV36
= ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
= $true )
| ( ( path @ SV7 @ SV36 @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[579]) ).
thf(598,plain,
! [SV7: $i,SV36: $i,SV40: $i] :
( ( ( ( SV40
!= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ ( sK13_SY91 @ SV40 @ SV36 @ SV7 ) ) ) )
= $false )
| ( ( SV40
= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ empty ) )
= $true )
| ( ( path @ SV7 @ SV36 @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[580]) ).
thf(599,plain,
! [SV7: $i,SV36: $i,SV40: $i] :
( ( ( ~ ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ ( sK13_SY91 @ SV40 @ SV36 @ SV7 ) ) )
= $false )
| ( ( SV40
= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ empty ) )
= $true )
| ( ( path @ SV7 @ SV36 @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[580]) ).
thf(600,plain,
! [SV8: $i,SV25: $i,SV107: $i,SV18: $i,SV82: $i] :
( ( ( path @ ( head_of @ SV82 ) @ SV18 @ SV107 )
= $false )
| ( ( SV25
= ( path_cons @ SV82 @ SV107 ) )
= $false )
| ( ( SV8
= ( tail_of @ SV82 ) )
= $false )
| ( ( edge @ SV82 )
= $false )
| ( ( vertex @ SV8 )
= $false )
| ( ( vertex @ SV18 )
= $false )
| ( ( path @ SV8 @ SV18 @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[582]) ).
thf(601,plain,
! [SV34: $i,SV28: $i,SV14: $i,SV96: $i,SV108: $i,SV87: $i] :
( ( ( sequential @ SV87 @ SV108 )
= $false )
| ( ( precedes @ SV108 @ SV96 @ SV14 )
= $false )
| ( ( ~ ( sequential @ SV87 @ SV96 ) )
= $true )
| ( ( precedes @ SV87 @ SV96 @ SV14 )
= $false )
| ( ( path @ SV28 @ SV34 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[584]) ).
thf(602,plain,
! [SV112: $i,SV6: $i] :
( ( ( ! [SY250: $i] :
~ ( triangle @ SV6 @ SV112 @ SY250 ) )
= $true )
| ( ( edge @ SV6 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[587]) ).
thf(603,plain,
! [SV111: $i,SV6: $i] :
( ( ( ! [SY249: $i] :
~ ( triangle @ SV6 @ SV111 @ SY249 ) )
= $true )
| ( ( edge @ SV111 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[588]) ).
thf(604,plain,
! [SV24: $i,SV31: $i] :
( ( ( SV31
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
= $false )
| ( ( ( SV24
!= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
= $true )
| ( ( SV24
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
= $false )
| ( ( SV31
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
= $false )
| ( ( SV24 = SV31 )
= $true )
| ( ( vertex @ SV24 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[590]) ).
thf(605,plain,
! [SV31: $i,SV24: $i] :
( ( ( ( SV24
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
= $true )
| ( ( SV24 = SV31 )
= $true )
| ( ( vertex @ SV24 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[591]) ).
thf(606,plain,
! [SV31: $i,SV24: $i] :
( ( ( ( SV24
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
= $true )
| ( ( SV24 = SV31 )
= $true )
| ( ( vertex @ SV24 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[592]) ).
thf(607,plain,
! [SV24: $i,SV31: $i] :
( ( ( ( SV31
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV31
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
= $true )
| ( ( SV24 = SV31 )
= $true )
| ( ( vertex @ SV24 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[593]) ).
thf(608,plain,
! [SV24: $i,SV31: $i] :
( ( ( ( SV31
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
| ( SV24
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) ) )
= $true )
| ( ( SV24 = SV31 )
= $true )
| ( ( vertex @ SV24 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[594]) ).
thf(609,plain,
! [SV110: $i,SV7: $i,SV36: $i,SV40: $i] :
( ( ( SV40
= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ SV110 ) )
= $false )
| ( ( ~ ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ SV110 ) )
= $true )
| ( ( SV36
= ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
= $false )
| ( ( SV40
= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ empty ) )
= $false )
| ( ( path @ SV7 @ SV36 @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[595]) ).
thf(610,plain,
! [SV7: $i,SV36: $i,SV40: $i] :
( ( ( SV40
= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ ( sK14_SY90 @ SV40 @ SV36 @ SV7 ) ) )
= $true )
| ( ( SV36
= ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
= $true )
| ( ( path @ SV7 @ SV36 @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[596]) ).
thf(611,plain,
! [SV7: $i,SV36: $i,SV40: $i] :
( ( ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ ( sK14_SY90 @ SV40 @ SV36 @ SV7 ) )
= $true )
| ( ( SV36
= ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
= $true )
| ( ( path @ SV7 @ SV36 @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[597]) ).
thf(612,plain,
! [SV7: $i,SV36: $i,SV40: $i] :
( ( ( SV40
= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ ( sK13_SY91 @ SV40 @ SV36 @ SV7 ) ) )
= $true )
| ( ( SV40
= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ empty ) )
= $true )
| ( ( path @ SV7 @ SV36 @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[598]) ).
thf(613,plain,
! [SV7: $i,SV36: $i,SV40: $i] :
( ( ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ ( sK13_SY91 @ SV40 @ SV36 @ SV7 ) )
= $true )
| ( ( SV40
= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ empty ) )
= $true )
| ( ( path @ SV7 @ SV36 @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[599]) ).
thf(614,plain,
! [SV34: $i,SV28: $i,SV14: $i,SV108: $i,SV96: $i,SV87: $i] :
( ( ( sequential @ SV87 @ SV96 )
= $false )
| ( ( precedes @ SV108 @ SV96 @ SV14 )
= $false )
| ( ( sequential @ SV87 @ SV108 )
= $false )
| ( ( precedes @ SV87 @ SV96 @ SV14 )
= $false )
| ( ( path @ SV28 @ SV34 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[601]) ).
thf(615,plain,
! [SV113: $i,SV112: $i,SV6: $i] :
( ( ( ~ ( triangle @ SV6 @ SV112 @ SV113 ) )
= $true )
| ( ( edge @ SV6 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(616,plain,
! [SV114: $i,SV111: $i,SV6: $i] :
( ( ( ~ ( triangle @ SV6 @ SV111 @ SV114 ) )
= $true )
| ( ( edge @ SV111 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[603]) ).
thf(617,plain,
! [SV31: $i,SV24: $i] :
( ( ( SV24
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
= $false )
| ( ( SV31
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
= $false )
| ( ( SV24
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
= $false )
| ( ( SV31
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
= $false )
| ( ( SV24 = SV31 )
= $true )
| ( ( vertex @ SV24 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[604]) ).
thf(618,plain,
! [SV31: $i,SV24: $i] :
( ( ( SV24
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
= $true )
| ( ( SV31
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
= $true )
| ( ( SV24 = SV31 )
= $true )
| ( ( vertex @ SV24 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[605]) ).
thf(619,plain,
! [SV31: $i,SV24: $i] :
( ( ( SV24
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
= $true )
| ( ( SV24
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
= $true )
| ( ( SV24 = SV31 )
= $true )
| ( ( vertex @ SV24 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[606]) ).
thf(620,plain,
! [SV24: $i,SV31: $i] :
( ( ( SV31
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
= $true )
| ( ( SV31
= ( head_of @ ( sK15_E @ SV31 @ SV24 ) ) )
= $true )
| ( ( SV24 = SV31 )
= $true )
| ( ( vertex @ SV24 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[607]) ).
thf(621,plain,
! [SV24: $i,SV31: $i] :
( ( ( SV31
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
= $true )
| ( ( SV24
= ( tail_of @ ( sK15_E @ SV31 @ SV24 ) ) )
= $true )
| ( ( SV24 = SV31 )
= $true )
| ( ( vertex @ SV24 )
= $false )
| ( ( vertex @ SV31 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[608]) ).
thf(622,plain,
! [SV110: $i,SV7: $i,SV36: $i,SV40: $i] :
( ( ( path @ ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) @ SV36 @ SV110 )
= $false )
| ( ( SV40
= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ SV110 ) )
= $false )
| ( ( SV36
= ( head_of @ ( sK12_E @ SV40 @ SV36 @ SV7 ) ) )
= $false )
| ( ( SV40
= ( path_cons @ ( sK12_E @ SV40 @ SV36 @ SV7 ) @ empty ) )
= $false )
| ( ( path @ SV7 @ SV36 @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[609]) ).
thf(623,plain,
! [SV113: $i,SV112: $i,SV6: $i] :
( ( ( triangle @ SV6 @ SV112 @ SV113 )
= $false )
| ( ( edge @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[615]) ).
thf(624,plain,
! [SV114: $i,SV111: $i,SV6: $i] :
( ( ( triangle @ SV6 @ SV111 @ SV114 )
= $false )
| ( ( edge @ SV111 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[616]) ).
thf(625,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[88,624,623,622,621,620,619,618,617,614,613,612,611,610,600,589,586,585,583,581,556,544,538,537,535,534,520,519,513,512,501,500,490,489,487,486,484,483,482,477,476,473,463,452,423,410,404,384,382,375,374,371,367,355,221,220,191,190,167,157,156,126,89]) ).
thf(626,plain,
( ( ! [E: $i] :
( ~ ( edge @ E )
| ( ( head_of @ E )
!= ( tail_of @ E ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(627,plain,
( ( ! [E: $i] :
( ~ ( edge @ E )
| ( vertex @ ( head_of @ E ) ) )
& ! [E: $i] :
( ~ ( edge @ E )
| ( vertex @ ( tail_of @ E ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(628,plain,
( ( ~ complete
| ! [V1: $i,V2: $i] :
( ( V1 = V2 )
| ~ ( vertex @ V1 )
| ~ ( vertex @ V2 )
| ( ( ( V1
!= ( head_of @ ( sK15_E @ V2 @ V1 ) ) )
| ( V2
!= ( tail_of @ ( sK15_E @ V2 @ V1 ) ) )
| ( V2
!= ( head_of @ ( sK15_E @ V2 @ V1 ) ) )
| ( V1
!= ( tail_of @ ( sK15_E @ V2 @ V1 ) ) ) )
& ( ( V1
= ( head_of @ ( sK15_E @ V2 @ V1 ) ) )
| ( V2
= ( head_of @ ( sK15_E @ V2 @ V1 ) ) ) )
& ( ( V1
= ( head_of @ ( sK15_E @ V2 @ V1 ) ) )
| ( V1
= ( tail_of @ ( sK15_E @ V2 @ V1 ) ) ) )
& ( ( V2
= ( tail_of @ ( sK15_E @ V2 @ V1 ) ) )
| ( V2
= ( head_of @ ( sK15_E @ V2 @ V1 ) ) ) )
& ( ( V2
= ( tail_of @ ( sK15_E @ V2 @ V1 ) ) )
| ( V1
= ( tail_of @ ( sK15_E @ V2 @ V1 ) ) ) )
& ( edge @ ( sK15_E @ V2 @ V1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(629,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)],[67]) ).
thf(630,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 @ ( sK12_E @ P @ V2 @ V1 ) ) )
& ( edge @ ( sK12_E @ P @ V2 @ V1 ) )
& ( ( V2
!= ( head_of @ ( sK12_E @ P @ V2 @ V1 ) ) )
| ( P
!= ( path_cons @ ( sK12_E @ P @ V2 @ V1 ) @ empty ) )
| ! [SY89: $i] :
( ( P
!= ( path_cons @ ( sK12_E @ P @ V2 @ V1 ) @ SY89 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ P @ V2 @ V1 ) ) @ V2 @ SY89 ) ) )
& ( ( V2
= ( head_of @ ( sK12_E @ P @ V2 @ V1 ) ) )
| ( ( P
= ( path_cons @ ( sK12_E @ P @ V2 @ V1 ) @ ( sK14_SY90 @ P @ V2 @ V1 ) ) )
& ( path @ ( head_of @ ( sK12_E @ P @ V2 @ V1 ) ) @ V2 @ ( sK14_SY90 @ P @ V2 @ V1 ) ) ) )
& ( ( P
= ( path_cons @ ( sK12_E @ P @ V2 @ V1 ) @ empty ) )
| ( ( P
= ( path_cons @ ( sK12_E @ P @ V2 @ V1 ) @ ( sK13_SY91 @ P @ V2 @ V1 ) ) )
& ( path @ ( head_of @ ( sK12_E @ P @ V2 @ V1 ) ) @ V2 @ ( sK13_SY91 @ P @ V2 @ V1 ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(631,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)],[65]) ).
thf(632,plain,
( ( ! [V1: $i,V2: $i] :
( ! [P: $i,V: $i] :
( ~ ( in_path @ V @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( ( on_path @ ( sK11_E @ V @ P @ V2 @ V1 ) @ P )
& ( ( V
= ( head_of @ ( sK11_E @ V @ P @ V2 @ V1 ) ) )
| ( V
= ( tail_of @ ( sK11_E @ V @ P @ V2 @ V1 ) ) ) ) ) )
& ! [P: $i,V: $i] :
( ~ ( in_path @ V @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( vertex @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(633,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)],[63]) ).
thf(634,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)],[62]) ).
thf(635,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 @ ( sK10_E3 @ E2 @ E1 @ P ) @ E2 @ P )
& ( sequential @ E1 @ ( sK10_E3 @ E2 @ E1 @ P ) ) )
| ( sequential @ E1 @ E2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(636,plain,
( ( ! [V1: $i] :
( ! [V2: $i,SP: $i] :
( ( ( path @ V1 @ V2 @ ( sK9_P @ SP @ V2 @ V1 ) )
& ~ ( less_or_equal @ ( length_of @ SP ) @ ( length_of @ ( sK9_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)],[60]) ).
thf(637,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)],[59]) ).
thf(638,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)],[58]) ).
thf(639,plain,
( ( ! [V1: $i,V2: $i,P: $i] :
( ~ ( path @ V1 @ V2 @ P )
| ( ( length_of @ P )
= ( number_of_in @ edges @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(640,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)],[56]) ).
thf(641,plain,
( ( ! [P: $i] :
( ( ( on_path @ ( sK7_E1 @ P ) @ P )
& ( on_path @ ( sK8_SY86 @ P ) @ P )
& ( sequential @ ( sK7_E1 @ P ) @ ( sK8_SY86 @ P ) )
& ! [SY88: $i] :
~ ( triangle @ ( sK7_E1 @ P ) @ ( sK8_SY86 @ P ) @ SY88 ) )
| ! [V1: $i,V2: $i] :
~ ( path @ V1 @ V2 @ P )
| ( ( number_of_in @ sequential_pairs @ P )
= ( number_of_in @ triangles @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(642,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(643,plain,
( ( precedes @ sK3_SY76 @ sK4_SY80 @ sK5_SY83 )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(644,plain,
( ( shortest_path @ sK1_V1 @ sK2_SY71 @ sK5_SY83 )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(645,plain,
( ( ( head_of @ sK4_SY80 )
= ( tail_of @ sK3_SY76 ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(646,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 @ ( sK12_E @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( edge @ ( sK12_E @ SX2 @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ( SX1
!= ( head_of @ ( sK12_E @ SX2 @ SX1 @ SX0 ) ) )
| ( SX2
!= ( path_cons @ ( sK12_E @ SX2 @ SX1 @ SX0 ) @ empty ) )
| ! [SX3: $i] :
( ( SX2
!= ( path_cons @ ( sK12_E @ SX2 @ SX1 @ SX0 ) @ SX3 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SX2 @ SX1 @ SX0 ) ) @ SX1 @ SX3 ) ) )
| ~ ~ ( ~ ( ( SX1
= ( head_of @ ( sK12_E @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( ( SX2
!= ( path_cons @ ( sK12_E @ SX2 @ SX1 @ SX0 ) @ ( sK14_SY90 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SX2 @ SX1 @ SX0 ) ) @ SX1 @ ( sK14_SY90 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX2
= ( path_cons @ ( sK12_E @ SX2 @ SX1 @ SX0 ) @ empty ) )
| ~ ( ( SX2
!= ( path_cons @ ( sK12_E @ SX2 @ SX1 @ SX0 ) @ ( sK13_SY91 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SX2 @ SX1 @ SX0 ) ) @ SX1 @ ( sK13_SY91 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[630]) ).
thf(647,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in_path @ SX3 @ SX2 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ~ ( ~ ( on_path @ ( sK11_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( ( SX3
= ( head_of @ ( sK11_E @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ( SX3
= ( tail_of @ ( sK11_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)],[632]) ).
thf(648,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)],[633]) ).
thf(649,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)],[631]) ).
thf(650,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( path @ SX0 @ SX1 @ ( sK9_P @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SX2 ) @ ( length_of @ ( sK9_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)],[636]) ).
thf(651,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)],[637]) ).
thf(652,plain,
( ( ~ complete
| ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( vertex @ SX0 )
| ~ ( vertex @ SX1 )
| ~ ( ~ ~ ( ~ ( ( SX0
!= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX0
!= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SX0
= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX0
= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) ) ) )
| ~ ~ ( ~ ( ( SX1
= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX1
= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) ) ) ) ) )
| ~ ( edge @ ( sK15_E @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[628]) ).
thf(653,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK7_E1 @ SX0 ) @ SX0 )
| ~ ( on_path @ ( sK8_SY86 @ SX0 ) @ SX0 ) )
| ~ ( sequential @ ( sK7_E1 @ SX0 ) @ ( sK8_SY86 @ SX0 ) ) )
| ~ ! [SX1: $i] :
~ ( triangle @ ( sK7_E1 @ SX0 ) @ ( sK8_SY86 @ 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)],[641]) ).
thf(654,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)],[629]) ).
thf(655,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)],[638]) ).
thf(656,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 @ ( sK10_E3 @ SX2 @ SX1 @ SX0 ) @ SX2 @ SX0 )
| ~ ( sequential @ SX1 @ ( sK10_E3 @ SX2 @ SX1 @ SX0 ) ) )
| ( sequential @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[635]) ).
thf(657,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( head_of @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( tail_of @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[627]) ).
thf(658,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)],[634]) ).
thf(659,plain,
! [SV115: $i] :
( ( ~ ( edge @ SV115 )
| ( ( head_of @ SV115 )
!= ( tail_of @ SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(660,plain,
! [SV116: $i] :
( ( ! [SY251: $i,SY252: $i] :
( ~ ( path @ SV116 @ SY251 @ SY252 )
| ( ( length_of @ SY252 )
= ( number_of_in @ edges @ SY252 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[639]) ).
thf(661,plain,
! [SV117: $i] :
( ( ! [SY253: $i,SY254: $i] :
( ~ ( path @ SV117 @ SY253 @ SY254 )
| ( ( number_of_in @ sequential_pairs @ SY254 )
= ( minus @ ( length_of @ SY254 ) @ n1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(662,plain,
! [SV118: $i] :
( ( ! [SY255: $i] : ( less_or_equal @ ( number_of_in @ SV118 @ SY255 ) @ ( number_of_in @ SV118 @ graph ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(663,plain,
! [SV119: $i] :
( ( ~ ( ~ ~ ( ~ ( ! [SY256: $i,SY257: $i] :
~ ( path @ SV119 @ SY256 @ SY257 )
| ( vertex @ SV119 ) )
| ~ ! [SY258: $i] :
( ! [SY259: $i] :
~ ( path @ SV119 @ SY258 @ SY259 )
| ( vertex @ SY258 ) ) )
| ~ ! [SY260: $i,SY261: $i] :
( ~ ( path @ SV119 @ SY260 @ SY261 )
| ~ ( ~ ~ ( ( SV119
!= ( tail_of @ ( sK12_E @ SY261 @ SY260 @ SV119 ) ) )
| ~ ( edge @ ( sK12_E @ SY261 @ SY260 @ SV119 ) ) )
| ~ ~ ( ~ ( ( SY260
!= ( head_of @ ( sK12_E @ SY261 @ SY260 @ SV119 ) ) )
| ( SY261
!= ( path_cons @ ( sK12_E @ SY261 @ SY260 @ SV119 ) @ empty ) )
| ! [SY262: $i] :
( ( SY261
!= ( path_cons @ ( sK12_E @ SY261 @ SY260 @ SV119 ) @ SY262 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SY261 @ SY260 @ SV119 ) ) @ SY260 @ SY262 ) ) )
| ~ ~ ( ~ ( ( SY260
= ( head_of @ ( sK12_E @ SY261 @ SY260 @ SV119 ) ) )
| ~ ( ( SY261
!= ( path_cons @ ( sK12_E @ SY261 @ SY260 @ SV119 ) @ ( sK14_SY90 @ SY261 @ SY260 @ SV119 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SY261 @ SY260 @ SV119 ) ) @ SY260 @ ( sK14_SY90 @ SY261 @ SY260 @ SV119 ) ) ) )
| ~ ( ( SY261
= ( path_cons @ ( sK12_E @ SY261 @ SY260 @ SV119 ) @ empty ) )
| ~ ( ( SY261
!= ( path_cons @ ( sK12_E @ SY261 @ SY260 @ SV119 ) @ ( sK13_SY91 @ SY261 @ SY260 @ SV119 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SY261 @ SY260 @ SV119 ) ) @ SY260 @ ( sK13_SY91 @ SY261 @ SY260 @ SV119 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(664,plain,
! [SV120: $i] :
( ( ! [SY263: $i] :
~ ( ~ ! [SY264: $i,SY265: $i] :
( ~ ( in_path @ SY265 @ SY264 )
| ~ ( path @ SV120 @ SY263 @ SY264 )
| ~ ( ~ ( on_path @ ( sK11_E @ SY265 @ SY264 @ SY263 @ SV120 ) @ SY264 )
| ~ ( ( SY265
= ( head_of @ ( sK11_E @ SY265 @ SY264 @ SY263 @ SV120 ) ) )
| ( SY265
= ( tail_of @ ( sK11_E @ SY265 @ SY264 @ SY263 @ SV120 ) ) ) ) ) )
| ~ ! [SY266: $i,SY267: $i] :
( ~ ( in_path @ SY267 @ SY266 )
| ~ ( path @ SV120 @ SY263 @ SY266 )
| ( vertex @ SY267 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(665,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)],[648]) ).
thf(666,plain,
! [SV121: $i] :
( ( ! [SY268: $i] :
~ ( ~ ~ ( ~ ! [SY269: $i,SY270: $i] :
( ~ ( on_path @ SY270 @ SY269 )
| ~ ( path @ SV121 @ SY268 @ SY269 )
| ( edge @ SY270 ) )
| ~ ! [SY271: $i,SY272: $i] :
( ~ ( on_path @ SY272 @ SY271 )
| ~ ( path @ SV121 @ SY268 @ SY271 )
| ( in_path @ ( head_of @ SY272 ) @ SY271 ) ) )
| ~ ! [SY273: $i,SY274: $i] :
( ~ ( on_path @ SY274 @ SY273 )
| ~ ( path @ SV121 @ SY268 @ SY273 )
| ( in_path @ ( tail_of @ SY274 ) @ SY273 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[649]) ).
thf(667,plain,
! [SV122: $i] :
( ( ~ ( ~ ! [SY275: $i,SY276: $i] :
( ~ ( ~ ( path @ SV122 @ SY275 @ ( sK9_P @ SY276 @ SY275 @ SV122 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY276 ) @ ( length_of @ ( sK9_P @ SY276 @ SY275 @ SV122 ) ) ) )
| ( SV122 = SY275 )
| ~ ( path @ SV122 @ SY275 @ SY276 )
| ( shortest_path @ SV122 @ SY275 @ SY276 ) )
| ~ ~ ( ~ ! [SY277: $i,SY278: $i] :
( ~ ( shortest_path @ SV122 @ SY277 @ SY278 )
| ! [SY279: $i] :
( ~ ( path @ SV122 @ SY277 @ SY279 )
| ( less_or_equal @ ( length_of @ SY278 ) @ ( length_of @ SY279 ) ) ) )
| ~ ~ ( ~ ! [SY280: $i] :
( ! [SY281: $i] :
~ ( shortest_path @ SV122 @ SY280 @ SY281 )
| ( SV122 != SY280 ) )
| ~ ! [SY282: $i,SY283: $i] :
( ~ ( shortest_path @ SV122 @ SY282 @ SY283 )
| ( path @ SV122 @ SY282 @ SY283 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(668,plain,
! [SV123: $i] :
( ( ! [SY284: $i,SY285: $i] :
~ ( ~ ! [SY286: $i] :
( ! [SY287: $i] :
( ~ ( precedes @ SY285 @ SY286 @ SY287 )
| ~ ( shortest_path @ SV123 @ SY284 @ SY287 ) )
| ! [SX4: $i] :
( ( ( tail_of @ SX4 )
!= ( tail_of @ SY285 ) )
| ( ( head_of @ SX4 )
!= ( head_of @ SY286 ) ) ) )
| ~ ! [SY289: $i,SY290: $i] :
( ~ ( precedes @ SY285 @ SY289 @ SY290 )
| ~ ( shortest_path @ SV123 @ SY284 @ SY290 )
| ~ ( precedes @ SY289 @ SY285 @ SY290 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(669,plain,
( ( ( ~ complete )
= $true )
| ( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( vertex @ SX0 )
| ~ ( vertex @ SX1 )
| ~ ( ~ ~ ( ~ ( ( SX0
!= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX0
!= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SX0
= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX0
= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) ) ) )
| ~ ~ ( ~ ( ( SX1
= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX1
= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) ) ) ) ) )
| ~ ( edge @ ( sK15_E @ SX1 @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[652]) ).
thf(670,plain,
! [SV124: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK7_E1 @ SV124 ) @ SV124 )
| ~ ( on_path @ ( sK8_SY86 @ SV124 ) @ SV124 ) )
| ~ ( sequential @ ( sK7_E1 @ SV124 ) @ ( sK8_SY86 @ SV124 ) ) )
| ~ ! [SY291: $i] :
~ ( triangle @ ( sK7_E1 @ SV124 ) @ ( sK8_SY86 @ SV124 ) @ SY291 ) )
| ! [SY292: $i,SY293: $i] :
~ ( path @ SY292 @ SY293 @ SV124 )
| ( ( number_of_in @ sequential_pairs @ SV124 )
= ( number_of_in @ triangles @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(671,plain,
! [SV125: $i] :
( ( ! [SY294: $i,SY295: $i] :
( ~ ( vertex @ SV125 )
| ~ ( vertex @ SY294 )
| ~ ( ~ ! [SY296: $i] :
( ( SV125
!= ( tail_of @ SY296 ) )
| ~ ( edge @ SY296 )
| ( SY294
!= ( head_of @ SY296 ) )
| ( SY295
!= ( path_cons @ SY296 @ empty ) ) )
| ~ ! [SY297: $i] :
( ( SV125
!= ( tail_of @ SY297 ) )
| ~ ( edge @ SY297 )
| ! [SX4: $i] :
( ( SY295
!= ( path_cons @ SY297 @ SX4 ) )
| ~ ( path @ ( head_of @ SY297 ) @ SY294 @ SX4 ) ) ) )
| ( path @ SV125 @ SY294 @ SY295 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(672,plain,
! [SV126: $i] :
( ( ~ ( ~ ! [SY299: $i,SY300: $i] :
( ~ ( edge @ SV126 )
| ~ ( edge @ SY299 )
| ~ ( edge @ SY300 )
| ~ ( sequential @ SV126 @ SY299 )
| ~ ( sequential @ SY299 @ SY300 )
| ~ ( sequential @ SY300 @ SV126 )
| ( triangle @ SV126 @ SY299 @ SY300 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY301: $i,SY302: $i] :
~ ( triangle @ SV126 @ SY301 @ SY302 )
| ( edge @ SV126 ) )
| ~ ! [SY303: $i] :
( ! [SY304: $i] :
~ ( triangle @ SV126 @ SY303 @ SY304 )
| ( edge @ SY303 ) ) )
| ~ ! [SY305: $i,SY306: $i] :
( ~ ( triangle @ SV126 @ SY305 @ SY306 )
| ( edge @ SY306 ) ) )
| ~ ! [SY307: $i] :
( ! [SY308: $i] :
~ ( triangle @ SV126 @ SY307 @ SY308 )
| ( sequential @ SV126 @ SY307 ) ) )
| ~ ! [SY309: $i,SY310: $i] :
( ~ ( triangle @ SV126 @ SY309 @ SY310 )
| ( sequential @ SY309 @ SY310 ) ) )
| ~ ! [SY311: $i,SY312: $i] :
( ~ ( triangle @ SV126 @ SY311 @ SY312 )
| ( sequential @ SY312 @ SV126 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(673,plain,
! [SV127: $i] :
( ( ! [SY313: $i,SY314: $i] :
~ ( path @ SY313 @ SY314 @ SV127 )
| ~ ( ~ ~ ( ~ ! [SY315: $i] :
( ! [SY316: $i] :
~ ( precedes @ SY315 @ SY316 @ SV127 )
| ( on_path @ SY315 @ SV127 ) )
| ~ ! [SY317: $i,SY318: $i] :
( ~ ( precedes @ SY317 @ SY318 @ SV127 )
| ( on_path @ SY318 @ SV127 ) ) )
| ~ ~ ( ~ ! [SY319: $i,SY320: $i] :
( ~ ( precedes @ SY319 @ SY320 @ SV127 )
| ! [SY321: $i] :
( ~ ( precedes @ SY321 @ SY320 @ SV127 )
| ~ ( sequential @ SY319 @ SY321 ) )
| ~ ( sequential @ SY319 @ SY320 ) )
| ~ ! [SY322: $i,SY323: $i] :
( ~ ( precedes @ SY322 @ SY323 @ SV127 )
| ~ ( ~ ( precedes @ ( sK10_E3 @ SY323 @ SY322 @ SV127 ) @ SY323 @ SV127 )
| ~ ( sequential @ SY322 @ ( sK10_E3 @ SY323 @ SY322 @ SV127 ) ) )
| ( sequential @ SY322 @ SY323 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[656]) ).
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)],[657]) ).
thf(675,plain,
! [SV128: $i] :
( ( ! [SY324: $i,SY325: $i] :
~ ( path @ SY324 @ SY325 @ SV128 )
| ~ ( ~ ! [SY326: $i,SY327: $i] :
( ~ ( on_path @ SY326 @ SV128 )
| ~ ( on_path @ SY327 @ SV128 )
| ! [SY328: $i] :
( ~ ( precedes @ SY328 @ SY327 @ SV128 )
| ~ ( sequential @ SY326 @ SY328 ) )
| ( precedes @ SY326 @ SY327 @ SV128 ) )
| ~ ! [SY329: $i,SY330: $i] :
( ~ ( on_path @ SY329 @ SV128 )
| ~ ( on_path @ SY330 @ SV128 )
| ~ ( sequential @ SY329 @ SY330 )
| ( precedes @ SY329 @ SY330 @ SV128 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(676,plain,
! [SV115: $i] :
( ( ( ~ ( edge @ SV115 ) )
= $true )
| ( ( ( ( head_of @ SV115 )
!= ( tail_of @ SV115 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[659]) ).
thf(677,plain,
! [SV129: $i,SV116: $i] :
( ( ! [SY331: $i] :
( ~ ( path @ SV116 @ SV129 @ SY331 )
| ( ( length_of @ SY331 )
= ( number_of_in @ edges @ SY331 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(678,plain,
! [SV130: $i,SV117: $i] :
( ( ! [SY332: $i] :
( ~ ( path @ SV117 @ SV130 @ SY332 )
| ( ( number_of_in @ sequential_pairs @ SY332 )
= ( minus @ ( length_of @ SY332 ) @ n1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(679,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)],[662]) ).
thf(680,plain,
! [SV119: $i] :
( ( ~ ~ ( ~ ( ! [SY256: $i,SY257: $i] :
~ ( path @ SV119 @ SY256 @ SY257 )
| ( vertex @ SV119 ) )
| ~ ! [SY258: $i] :
( ! [SY259: $i] :
~ ( path @ SV119 @ SY258 @ SY259 )
| ( vertex @ SY258 ) ) )
| ~ ! [SY260: $i,SY261: $i] :
( ~ ( path @ SV119 @ SY260 @ SY261 )
| ~ ( ~ ~ ( ( SV119
!= ( tail_of @ ( sK12_E @ SY261 @ SY260 @ SV119 ) ) )
| ~ ( edge @ ( sK12_E @ SY261 @ SY260 @ SV119 ) ) )
| ~ ~ ( ~ ( ( SY260
!= ( head_of @ ( sK12_E @ SY261 @ SY260 @ SV119 ) ) )
| ( SY261
!= ( path_cons @ ( sK12_E @ SY261 @ SY260 @ SV119 ) @ empty ) )
| ! [SY262: $i] :
( ( SY261
!= ( path_cons @ ( sK12_E @ SY261 @ SY260 @ SV119 ) @ SY262 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SY261 @ SY260 @ SV119 ) ) @ SY260 @ SY262 ) ) )
| ~ ~ ( ~ ( ( SY260
= ( head_of @ ( sK12_E @ SY261 @ SY260 @ SV119 ) ) )
| ~ ( ( SY261
!= ( path_cons @ ( sK12_E @ SY261 @ SY260 @ SV119 ) @ ( sK14_SY90 @ SY261 @ SY260 @ SV119 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SY261 @ SY260 @ SV119 ) ) @ SY260 @ ( sK14_SY90 @ SY261 @ SY260 @ SV119 ) ) ) )
| ~ ( ( SY261
= ( path_cons @ ( sK12_E @ SY261 @ SY260 @ SV119 ) @ empty ) )
| ~ ( ( SY261
!= ( path_cons @ ( sK12_E @ SY261 @ SY260 @ SV119 ) @ ( sK13_SY91 @ SY261 @ SY260 @ SV119 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SY261 @ SY260 @ SV119 ) ) @ SY260 @ ( sK13_SY91 @ SY261 @ SY260 @ SV119 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[663]) ).
thf(681,plain,
! [SV132: $i,SV120: $i] :
( ( ~ ( ~ ! [SY333: $i,SY334: $i] :
( ~ ( in_path @ SY334 @ SY333 )
| ~ ( path @ SV120 @ SV132 @ SY333 )
| ~ ( ~ ( on_path @ ( sK11_E @ SY334 @ SY333 @ SV132 @ SV120 ) @ SY333 )
| ~ ( ( SY334
= ( head_of @ ( sK11_E @ SY334 @ SY333 @ SV132 @ SV120 ) ) )
| ( SY334
= ( tail_of @ ( sK11_E @ SY334 @ SY333 @ SV132 @ SV120 ) ) ) ) ) )
| ~ ! [SY335: $i,SY336: $i] :
( ~ ( in_path @ SY336 @ SY335 )
| ~ ( path @ SV120 @ SV132 @ SY335 )
| ( vertex @ SY336 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(682,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)],[665]) ).
thf(683,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)],[665]) ).
thf(684,plain,
! [SV133: $i,SV121: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY337: $i,SY338: $i] :
( ~ ( on_path @ SY338 @ SY337 )
| ~ ( path @ SV121 @ SV133 @ SY337 )
| ( edge @ SY338 ) )
| ~ ! [SY339: $i,SY340: $i] :
( ~ ( on_path @ SY340 @ SY339 )
| ~ ( path @ SV121 @ SV133 @ SY339 )
| ( in_path @ ( head_of @ SY340 ) @ SY339 ) ) )
| ~ ! [SY341: $i,SY342: $i] :
( ~ ( on_path @ SY342 @ SY341 )
| ~ ( path @ SV121 @ SV133 @ SY341 )
| ( in_path @ ( tail_of @ SY342 ) @ SY341 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(685,plain,
! [SV122: $i] :
( ( ~ ! [SY275: $i,SY276: $i] :
( ~ ( ~ ( path @ SV122 @ SY275 @ ( sK9_P @ SY276 @ SY275 @ SV122 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY276 ) @ ( length_of @ ( sK9_P @ SY276 @ SY275 @ SV122 ) ) ) )
| ( SV122 = SY275 )
| ~ ( path @ SV122 @ SY275 @ SY276 )
| ( shortest_path @ SV122 @ SY275 @ SY276 ) )
| ~ ~ ( ~ ! [SY277: $i,SY278: $i] :
( ~ ( shortest_path @ SV122 @ SY277 @ SY278 )
| ! [SY279: $i] :
( ~ ( path @ SV122 @ SY277 @ SY279 )
| ( less_or_equal @ ( length_of @ SY278 ) @ ( length_of @ SY279 ) ) ) )
| ~ ~ ( ~ ! [SY280: $i] :
( ! [SY281: $i] :
~ ( shortest_path @ SV122 @ SY280 @ SY281 )
| ( SV122 != SY280 ) )
| ~ ! [SY282: $i,SY283: $i] :
( ~ ( shortest_path @ SV122 @ SY282 @ SY283 )
| ( path @ SV122 @ SY282 @ SY283 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[667]) ).
thf(686,plain,
! [SV134: $i,SV123: $i] :
( ( ! [SY343: $i] :
~ ( ~ ! [SY344: $i] :
( ! [SY345: $i] :
( ~ ( precedes @ SY343 @ SY344 @ SY345 )
| ~ ( shortest_path @ SV123 @ SV134 @ SY345 ) )
| ! [SX4: $i] :
( ( ( tail_of @ SX4 )
!= ( tail_of @ SY343 ) )
| ( ( head_of @ SX4 )
!= ( head_of @ SY344 ) ) ) )
| ~ ! [SY347: $i,SY348: $i] :
( ~ ( precedes @ SY343 @ SY347 @ SY348 )
| ~ ( shortest_path @ SV123 @ SV134 @ SY348 )
| ~ ( precedes @ SY347 @ SY343 @ SY348 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(687,plain,
( ( complete = $false )
| ( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( vertex @ SX0 )
| ~ ( vertex @ SX1 )
| ~ ( ~ ~ ( ~ ( ( SX0
!= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX0
!= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SX0
= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX0
= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) ) ) )
| ~ ~ ( ~ ( ( SX1
= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX1
= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) ) ) ) ) )
| ~ ( edge @ ( sK15_E @ SX1 @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[669]) ).
thf(688,plain,
! [SV124: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK7_E1 @ SV124 ) @ SV124 )
| ~ ( on_path @ ( sK8_SY86 @ SV124 ) @ SV124 ) )
| ~ ( sequential @ ( sK7_E1 @ SV124 ) @ ( sK8_SY86 @ SV124 ) ) )
| ~ ! [SY291: $i] :
~ ( triangle @ ( sK7_E1 @ SV124 ) @ ( sK8_SY86 @ SV124 ) @ SY291 ) )
| ! [SY292: $i,SY293: $i] :
~ ( path @ SY292 @ SY293 @ SV124 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV124 )
= ( number_of_in @ triangles @ SV124 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[670]) ).
thf(689,plain,
! [SV135: $i,SV125: $i] :
( ( ! [SY349: $i] :
( ~ ( vertex @ SV125 )
| ~ ( vertex @ SV135 )
| ~ ( ~ ! [SY350: $i] :
( ( SV125
!= ( tail_of @ SY350 ) )
| ~ ( edge @ SY350 )
| ( SV135
!= ( head_of @ SY350 ) )
| ( SY349
!= ( path_cons @ SY350 @ empty ) ) )
| ~ ! [SY351: $i] :
( ( SV125
!= ( tail_of @ SY351 ) )
| ~ ( edge @ SY351 )
| ! [SY352: $i] :
( ( SY349
!= ( path_cons @ SY351 @ SY352 ) )
| ~ ( path @ ( head_of @ SY351 ) @ SV135 @ SY352 ) ) ) )
| ( path @ SV125 @ SV135 @ SY349 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(690,plain,
! [SV126: $i] :
( ( ~ ! [SY299: $i,SY300: $i] :
( ~ ( edge @ SV126 )
| ~ ( edge @ SY299 )
| ~ ( edge @ SY300 )
| ~ ( sequential @ SV126 @ SY299 )
| ~ ( sequential @ SY299 @ SY300 )
| ~ ( sequential @ SY300 @ SV126 )
| ( triangle @ SV126 @ SY299 @ SY300 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY301: $i,SY302: $i] :
~ ( triangle @ SV126 @ SY301 @ SY302 )
| ( edge @ SV126 ) )
| ~ ! [SY303: $i] :
( ! [SY304: $i] :
~ ( triangle @ SV126 @ SY303 @ SY304 )
| ( edge @ SY303 ) ) )
| ~ ! [SY305: $i,SY306: $i] :
( ~ ( triangle @ SV126 @ SY305 @ SY306 )
| ( edge @ SY306 ) ) )
| ~ ! [SY307: $i] :
( ! [SY308: $i] :
~ ( triangle @ SV126 @ SY307 @ SY308 )
| ( sequential @ SV126 @ SY307 ) ) )
| ~ ! [SY309: $i,SY310: $i] :
( ~ ( triangle @ SV126 @ SY309 @ SY310 )
| ( sequential @ SY309 @ SY310 ) ) )
| ~ ! [SY311: $i,SY312: $i] :
( ~ ( triangle @ SV126 @ SY311 @ SY312 )
| ( sequential @ SY312 @ SV126 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[672]) ).
thf(691,plain,
! [SV127: $i] :
( ( ( ! [SY313: $i,SY314: $i] :
~ ( path @ SY313 @ SY314 @ SV127 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY315: $i] :
( ! [SY316: $i] :
~ ( precedes @ SY315 @ SY316 @ SV127 )
| ( on_path @ SY315 @ SV127 ) )
| ~ ! [SY317: $i,SY318: $i] :
( ~ ( precedes @ SY317 @ SY318 @ SV127 )
| ( on_path @ SY318 @ SV127 ) ) )
| ~ ~ ( ~ ! [SY319: $i,SY320: $i] :
( ~ ( precedes @ SY319 @ SY320 @ SV127 )
| ! [SY321: $i] :
( ~ ( precedes @ SY321 @ SY320 @ SV127 )
| ~ ( sequential @ SY319 @ SY321 ) )
| ~ ( sequential @ SY319 @ SY320 ) )
| ~ ! [SY322: $i,SY323: $i] :
( ~ ( precedes @ SY322 @ SY323 @ SV127 )
| ~ ( ~ ( precedes @ ( sK10_E3 @ SY323 @ SY322 @ SV127 ) @ SY323 @ SV127 )
| ~ ( sequential @ SY322 @ ( sK10_E3 @ SY323 @ SY322 @ SV127 ) ) )
| ( sequential @ SY322 @ SY323 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[673]) ).
thf(692,plain,
( ( ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( head_of @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[674]) ).
thf(693,plain,
( ( ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( tail_of @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[674]) ).
thf(694,plain,
! [SV128: $i] :
( ( ( ! [SY324: $i,SY325: $i] :
~ ( path @ SY324 @ SY325 @ SV128 ) )
= $true )
| ( ( ~ ( ~ ! [SY326: $i,SY327: $i] :
( ~ ( on_path @ SY326 @ SV128 )
| ~ ( on_path @ SY327 @ SV128 )
| ! [SY328: $i] :
( ~ ( precedes @ SY328 @ SY327 @ SV128 )
| ~ ( sequential @ SY326 @ SY328 ) )
| ( precedes @ SY326 @ SY327 @ SV128 ) )
| ~ ! [SY329: $i,SY330: $i] :
( ~ ( on_path @ SY329 @ SV128 )
| ~ ( on_path @ SY330 @ SV128 )
| ~ ( sequential @ SY329 @ SY330 )
| ( precedes @ SY329 @ SY330 @ SV128 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[675]) ).
thf(695,plain,
! [SV115: $i] :
( ( ( edge @ SV115 )
= $false )
| ( ( ( ( head_of @ SV115 )
!= ( tail_of @ SV115 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[676]) ).
thf(696,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)],[677]) ).
thf(697,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)],[678]) ).
thf(698,plain,
! [SV119: $i] :
( ( ~ ~ ( ~ ( ! [SY256: $i,SY257: $i] :
~ ( path @ SV119 @ SY256 @ SY257 )
| ( vertex @ SV119 ) )
| ~ ! [SY258: $i] :
( ! [SY259: $i] :
~ ( path @ SV119 @ SY258 @ SY259 )
| ( vertex @ SY258 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[680]) ).
thf(699,plain,
! [SV119: $i] :
( ( ~ ! [SY260: $i,SY261: $i] :
( ~ ( path @ SV119 @ SY260 @ SY261 )
| ~ ( ~ ~ ( ( SV119
!= ( tail_of @ ( sK12_E @ SY261 @ SY260 @ SV119 ) ) )
| ~ ( edge @ ( sK12_E @ SY261 @ SY260 @ SV119 ) ) )
| ~ ~ ( ~ ( ( SY260
!= ( head_of @ ( sK12_E @ SY261 @ SY260 @ SV119 ) ) )
| ( SY261
!= ( path_cons @ ( sK12_E @ SY261 @ SY260 @ SV119 ) @ empty ) )
| ! [SY262: $i] :
( ( SY261
!= ( path_cons @ ( sK12_E @ SY261 @ SY260 @ SV119 ) @ SY262 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SY261 @ SY260 @ SV119 ) ) @ SY260 @ SY262 ) ) )
| ~ ~ ( ~ ( ( SY260
= ( head_of @ ( sK12_E @ SY261 @ SY260 @ SV119 ) ) )
| ~ ( ( SY261
!= ( path_cons @ ( sK12_E @ SY261 @ SY260 @ SV119 ) @ ( sK14_SY90 @ SY261 @ SY260 @ SV119 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SY261 @ SY260 @ SV119 ) ) @ SY260 @ ( sK14_SY90 @ SY261 @ SY260 @ SV119 ) ) ) )
| ~ ( ( SY261
= ( path_cons @ ( sK12_E @ SY261 @ SY260 @ SV119 ) @ empty ) )
| ~ ( ( SY261
!= ( path_cons @ ( sK12_E @ SY261 @ SY260 @ SV119 ) @ ( sK13_SY91 @ SY261 @ SY260 @ SV119 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SY261 @ SY260 @ SV119 ) ) @ SY260 @ ( sK13_SY91 @ SY261 @ SY260 @ SV119 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[680]) ).
thf(700,plain,
! [SV132: $i,SV120: $i] :
( ( ~ ! [SY333: $i,SY334: $i] :
( ~ ( in_path @ SY334 @ SY333 )
| ~ ( path @ SV120 @ SV132 @ SY333 )
| ~ ( ~ ( on_path @ ( sK11_E @ SY334 @ SY333 @ SV132 @ SV120 ) @ SY333 )
| ~ ( ( SY334
= ( head_of @ ( sK11_E @ SY334 @ SY333 @ SV132 @ SV120 ) ) )
| ( SY334
= ( tail_of @ ( sK11_E @ SY334 @ SY333 @ SV132 @ SV120 ) ) ) ) ) )
| ~ ! [SY335: $i,SY336: $i] :
( ~ ( in_path @ SY336 @ SY335 )
| ~ ( path @ SV120 @ SV132 @ SY335 )
| ( vertex @ SY336 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[681]) ).
thf(701,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)],[682]) ).
thf(702,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)],[683]) ).
thf(703,plain,
! [SV133: $i,SV121: $i] :
( ( ~ ~ ( ~ ! [SY337: $i,SY338: $i] :
( ~ ( on_path @ SY338 @ SY337 )
| ~ ( path @ SV121 @ SV133 @ SY337 )
| ( edge @ SY338 ) )
| ~ ! [SY339: $i,SY340: $i] :
( ~ ( on_path @ SY340 @ SY339 )
| ~ ( path @ SV121 @ SV133 @ SY339 )
| ( in_path @ ( head_of @ SY340 ) @ SY339 ) ) )
| ~ ! [SY341: $i,SY342: $i] :
( ~ ( on_path @ SY342 @ SY341 )
| ~ ( path @ SV121 @ SV133 @ SY341 )
| ( in_path @ ( tail_of @ SY342 ) @ SY341 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[684]) ).
thf(704,plain,
! [SV122: $i] :
( ( ~ ! [SY275: $i,SY276: $i] :
( ~ ( ~ ( path @ SV122 @ SY275 @ ( sK9_P @ SY276 @ SY275 @ SV122 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY276 ) @ ( length_of @ ( sK9_P @ SY276 @ SY275 @ SV122 ) ) ) )
| ( SV122 = SY275 )
| ~ ( path @ SV122 @ SY275 @ SY276 )
| ( shortest_path @ SV122 @ SY275 @ SY276 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[685]) ).
thf(705,plain,
! [SV122: $i] :
( ( ~ ~ ( ~ ! [SY277: $i,SY278: $i] :
( ~ ( shortest_path @ SV122 @ SY277 @ SY278 )
| ! [SY279: $i] :
( ~ ( path @ SV122 @ SY277 @ SY279 )
| ( less_or_equal @ ( length_of @ SY278 ) @ ( length_of @ SY279 ) ) ) )
| ~ ~ ( ~ ! [SY280: $i] :
( ! [SY281: $i] :
~ ( shortest_path @ SV122 @ SY280 @ SY281 )
| ( SV122 != SY280 ) )
| ~ ! [SY282: $i,SY283: $i] :
( ~ ( shortest_path @ SV122 @ SY282 @ SY283 )
| ( path @ SV122 @ SY282 @ SY283 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[685]) ).
thf(706,plain,
! [SV134: $i,SV123: $i,SV138: $i] :
( ( ~ ( ~ ! [SY353: $i] :
( ! [SY354: $i] :
( ~ ( precedes @ SV138 @ SY353 @ SY354 )
| ~ ( shortest_path @ SV123 @ SV134 @ SY354 ) )
| ! [SY355: $i] :
( ( ( tail_of @ SY355 )
!= ( tail_of @ SV138 ) )
| ( ( head_of @ SY355 )
!= ( head_of @ SY353 ) ) ) )
| ~ ! [SY356: $i,SY357: $i] :
( ~ ( precedes @ SV138 @ SY356 @ SY357 )
| ~ ( shortest_path @ SV123 @ SV134 @ SY357 )
| ~ ( precedes @ SY356 @ SV138 @ SY357 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[686]) ).
thf(707,plain,
! [SV139: $i] :
( ( ( ! [SY358: $i] :
( ( SV139 = SY358 )
| ~ ( vertex @ SV139 )
| ~ ( vertex @ SY358 )
| ~ ( ~ ~ ( ~ ( ( SV139
!= ( head_of @ ( sK15_E @ SY358 @ SV139 ) ) )
| ( SY358
!= ( tail_of @ ( sK15_E @ SY358 @ SV139 ) ) )
| ( SY358
!= ( head_of @ ( sK15_E @ SY358 @ SV139 ) ) )
| ( SV139
!= ( tail_of @ ( sK15_E @ SY358 @ SV139 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV139
= ( head_of @ ( sK15_E @ SY358 @ SV139 ) ) )
| ( SY358
= ( head_of @ ( sK15_E @ SY358 @ SV139 ) ) ) )
| ~ ( ( SV139
= ( head_of @ ( sK15_E @ SY358 @ SV139 ) ) )
| ( SV139
= ( tail_of @ ( sK15_E @ SY358 @ SV139 ) ) ) ) )
| ~ ~ ( ~ ( ( SY358
= ( tail_of @ ( sK15_E @ SY358 @ SV139 ) ) )
| ( SY358
= ( head_of @ ( sK15_E @ SY358 @ SV139 ) ) ) )
| ~ ( ( SY358
= ( tail_of @ ( sK15_E @ SY358 @ SV139 ) ) )
| ( SV139
= ( tail_of @ ( sK15_E @ SY358 @ SV139 ) ) ) ) ) ) )
| ~ ( edge @ ( sK15_E @ SY358 @ SV139 ) ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(708,plain,
! [SV124: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK7_E1 @ SV124 ) @ SV124 )
| ~ ( on_path @ ( sK8_SY86 @ SV124 ) @ SV124 ) )
| ~ ( sequential @ ( sK7_E1 @ SV124 ) @ ( sK8_SY86 @ SV124 ) ) )
| ~ ! [SY291: $i] :
~ ( triangle @ ( sK7_E1 @ SV124 ) @ ( sK8_SY86 @ SV124 ) @ SY291 ) ) )
= $true )
| ( ( ! [SY292: $i,SY293: $i] :
~ ( path @ SY292 @ SY293 @ SV124 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV124 )
= ( number_of_in @ triangles @ SV124 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[688]) ).
thf(709,plain,
! [SV140: $i,SV135: $i,SV125: $i] :
( ( ~ ( vertex @ SV125 )
| ~ ( vertex @ SV135 )
| ~ ( ~ ! [SY359: $i] :
( ( SV125
!= ( tail_of @ SY359 ) )
| ~ ( edge @ SY359 )
| ( SV135
!= ( head_of @ SY359 ) )
| ( SV140
!= ( path_cons @ SY359 @ empty ) ) )
| ~ ! [SY360: $i] :
( ( SV125
!= ( tail_of @ SY360 ) )
| ~ ( edge @ SY360 )
| ! [SY361: $i] :
( ( SV140
!= ( path_cons @ SY360 @ SY361 ) )
| ~ ( path @ ( head_of @ SY360 ) @ SV135 @ SY361 ) ) ) )
| ( path @ SV125 @ SV135 @ SV140 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(710,plain,
! [SV126: $i] :
( ( ~ ! [SY299: $i,SY300: $i] :
( ~ ( edge @ SV126 )
| ~ ( edge @ SY299 )
| ~ ( edge @ SY300 )
| ~ ( sequential @ SV126 @ SY299 )
| ~ ( sequential @ SY299 @ SY300 )
| ~ ( sequential @ SY300 @ SV126 )
| ( triangle @ SV126 @ SY299 @ SY300 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[690]) ).
thf(711,plain,
! [SV126: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY301: $i,SY302: $i] :
~ ( triangle @ SV126 @ SY301 @ SY302 )
| ( edge @ SV126 ) )
| ~ ! [SY303: $i] :
( ! [SY304: $i] :
~ ( triangle @ SV126 @ SY303 @ SY304 )
| ( edge @ SY303 ) ) )
| ~ ! [SY305: $i,SY306: $i] :
( ~ ( triangle @ SV126 @ SY305 @ SY306 )
| ( edge @ SY306 ) ) )
| ~ ! [SY307: $i] :
( ! [SY308: $i] :
~ ( triangle @ SV126 @ SY307 @ SY308 )
| ( sequential @ SV126 @ SY307 ) ) )
| ~ ! [SY309: $i,SY310: $i] :
( ~ ( triangle @ SV126 @ SY309 @ SY310 )
| ( sequential @ SY309 @ SY310 ) ) )
| ~ ! [SY311: $i,SY312: $i] :
( ~ ( triangle @ SV126 @ SY311 @ SY312 )
| ( sequential @ SY312 @ SV126 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[690]) ).
thf(712,plain,
! [SV127: $i,SV141: $i] :
( ( ( ! [SY362: $i] :
~ ( path @ SV141 @ SY362 @ SV127 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY315: $i] :
( ! [SY316: $i] :
~ ( precedes @ SY315 @ SY316 @ SV127 )
| ( on_path @ SY315 @ SV127 ) )
| ~ ! [SY317: $i,SY318: $i] :
( ~ ( precedes @ SY317 @ SY318 @ SV127 )
| ( on_path @ SY318 @ SV127 ) ) )
| ~ ~ ( ~ ! [SY319: $i,SY320: $i] :
( ~ ( precedes @ SY319 @ SY320 @ SV127 )
| ! [SY321: $i] :
( ~ ( precedes @ SY321 @ SY320 @ SV127 )
| ~ ( sequential @ SY319 @ SY321 ) )
| ~ ( sequential @ SY319 @ SY320 ) )
| ~ ! [SY322: $i,SY323: $i] :
( ~ ( precedes @ SY322 @ SY323 @ SV127 )
| ~ ( ~ ( precedes @ ( sK10_E3 @ SY323 @ SY322 @ SV127 ) @ SY323 @ SV127 )
| ~ ( sequential @ SY322 @ ( sK10_E3 @ SY323 @ SY322 @ SV127 ) ) )
| ( sequential @ SY322 @ SY323 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[691]) ).
thf(713,plain,
( ( ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( head_of @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[692]) ).
thf(714,plain,
( ( ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( tail_of @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[693]) ).
thf(715,plain,
! [SV128: $i,SV142: $i] :
( ( ( ! [SY363: $i] :
~ ( path @ SV142 @ SY363 @ SV128 ) )
= $true )
| ( ( ~ ( ~ ! [SY326: $i,SY327: $i] :
( ~ ( on_path @ SY326 @ SV128 )
| ~ ( on_path @ SY327 @ SV128 )
| ! [SY328: $i] :
( ~ ( precedes @ SY328 @ SY327 @ SV128 )
| ~ ( sequential @ SY326 @ SY328 ) )
| ( precedes @ SY326 @ SY327 @ SV128 ) )
| ~ ! [SY329: $i,SY330: $i] :
( ~ ( on_path @ SY329 @ SV128 )
| ~ ( on_path @ SY330 @ SV128 )
| ~ ( sequential @ SY329 @ SY330 )
| ( precedes @ SY329 @ SY330 @ SV128 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(716,plain,
! [SV115: $i] :
( ( ( ( head_of @ SV115 )
= ( tail_of @ SV115 ) )
= $false )
| ( ( edge @ SV115 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[695]) ).
thf(717,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)],[696]) ).
thf(718,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)],[697]) ).
thf(719,plain,
! [SV119: $i] :
( ( ~ ( ~ ( ! [SY256: $i,SY257: $i] :
~ ( path @ SV119 @ SY256 @ SY257 )
| ( vertex @ SV119 ) )
| ~ ! [SY258: $i] :
( ! [SY259: $i] :
~ ( path @ SV119 @ SY258 @ SY259 )
| ( vertex @ SY258 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[698]) ).
thf(720,plain,
! [SV119: $i] :
( ( ! [SY260: $i,SY261: $i] :
( ~ ( path @ SV119 @ SY260 @ SY261 )
| ~ ( ~ ~ ( ( SV119
!= ( tail_of @ ( sK12_E @ SY261 @ SY260 @ SV119 ) ) )
| ~ ( edge @ ( sK12_E @ SY261 @ SY260 @ SV119 ) ) )
| ~ ~ ( ~ ( ( SY260
!= ( head_of @ ( sK12_E @ SY261 @ SY260 @ SV119 ) ) )
| ( SY261
!= ( path_cons @ ( sK12_E @ SY261 @ SY260 @ SV119 ) @ empty ) )
| ! [SY262: $i] :
( ( SY261
!= ( path_cons @ ( sK12_E @ SY261 @ SY260 @ SV119 ) @ SY262 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SY261 @ SY260 @ SV119 ) ) @ SY260 @ SY262 ) ) )
| ~ ~ ( ~ ( ( SY260
= ( head_of @ ( sK12_E @ SY261 @ SY260 @ SV119 ) ) )
| ~ ( ( SY261
!= ( path_cons @ ( sK12_E @ SY261 @ SY260 @ SV119 ) @ ( sK14_SY90 @ SY261 @ SY260 @ SV119 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SY261 @ SY260 @ SV119 ) ) @ SY260 @ ( sK14_SY90 @ SY261 @ SY260 @ SV119 ) ) ) )
| ~ ( ( SY261
= ( path_cons @ ( sK12_E @ SY261 @ SY260 @ SV119 ) @ empty ) )
| ~ ( ( SY261
!= ( path_cons @ ( sK12_E @ SY261 @ SY260 @ SV119 ) @ ( sK13_SY91 @ SY261 @ SY260 @ SV119 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SY261 @ SY260 @ SV119 ) ) @ SY260 @ ( sK13_SY91 @ SY261 @ SY260 @ SV119 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[699]) ).
thf(721,plain,
! [SV132: $i,SV120: $i] :
( ( ~ ! [SY333: $i,SY334: $i] :
( ~ ( in_path @ SY334 @ SY333 )
| ~ ( path @ SV120 @ SV132 @ SY333 )
| ~ ( ~ ( on_path @ ( sK11_E @ SY334 @ SY333 @ SV132 @ SV120 ) @ SY333 )
| ~ ( ( SY334
= ( head_of @ ( sK11_E @ SY334 @ SY333 @ SV132 @ SV120 ) ) )
| ( SY334
= ( tail_of @ ( sK11_E @ SY334 @ SY333 @ SV132 @ SV120 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[700]) ).
thf(722,plain,
! [SV132: $i,SV120: $i] :
( ( ~ ! [SY335: $i,SY336: $i] :
( ~ ( in_path @ SY336 @ SY335 )
| ~ ( path @ SV120 @ SV132 @ SY335 )
| ( vertex @ SY336 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[700]) ).
thf(723,plain,
! [SV143: $i] :
( ( ! [SY364: $i] :
( ( SV143 = SY364 )
| ~ ( edge @ SV143 )
| ~ ( edge @ SY364 )
| ( ( head_of @ SV143 )
!= ( tail_of @ SY364 ) )
| ( sequential @ SV143 @ SY364 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(724,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)],[702]) ).
thf(725,plain,
! [SV133: $i,SV121: $i] :
( ( ~ ~ ( ~ ! [SY337: $i,SY338: $i] :
( ~ ( on_path @ SY338 @ SY337 )
| ~ ( path @ SV121 @ SV133 @ SY337 )
| ( edge @ SY338 ) )
| ~ ! [SY339: $i,SY340: $i] :
( ~ ( on_path @ SY340 @ SY339 )
| ~ ( path @ SV121 @ SV133 @ SY339 )
| ( in_path @ ( head_of @ SY340 ) @ SY339 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[703]) ).
thf(726,plain,
! [SV133: $i,SV121: $i] :
( ( ~ ! [SY341: $i,SY342: $i] :
( ~ ( on_path @ SY342 @ SY341 )
| ~ ( path @ SV121 @ SV133 @ SY341 )
| ( in_path @ ( tail_of @ SY342 ) @ SY341 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[703]) ).
thf(727,plain,
! [SV122: $i] :
( ( ! [SY275: $i,SY276: $i] :
( ~ ( ~ ( path @ SV122 @ SY275 @ ( sK9_P @ SY276 @ SY275 @ SV122 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY276 ) @ ( length_of @ ( sK9_P @ SY276 @ SY275 @ SV122 ) ) ) )
| ( SV122 = SY275 )
| ~ ( path @ SV122 @ SY275 @ SY276 )
| ( shortest_path @ SV122 @ SY275 @ SY276 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[704]) ).
thf(728,plain,
! [SV122: $i] :
( ( ~ ( ~ ! [SY277: $i,SY278: $i] :
( ~ ( shortest_path @ SV122 @ SY277 @ SY278 )
| ! [SY279: $i] :
( ~ ( path @ SV122 @ SY277 @ SY279 )
| ( less_or_equal @ ( length_of @ SY278 ) @ ( length_of @ SY279 ) ) ) )
| ~ ~ ( ~ ! [SY280: $i] :
( ! [SY281: $i] :
~ ( shortest_path @ SV122 @ SY280 @ SY281 )
| ( SV122 != SY280 ) )
| ~ ! [SY282: $i,SY283: $i] :
( ~ ( shortest_path @ SV122 @ SY282 @ SY283 )
| ( path @ SV122 @ SY282 @ SY283 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[705]) ).
thf(729,plain,
! [SV134: $i,SV123: $i,SV138: $i] :
( ( ~ ! [SY353: $i] :
( ! [SY354: $i] :
( ~ ( precedes @ SV138 @ SY353 @ SY354 )
| ~ ( shortest_path @ SV123 @ SV134 @ SY354 ) )
| ! [SY355: $i] :
( ( ( tail_of @ SY355 )
!= ( tail_of @ SV138 ) )
| ( ( head_of @ SY355 )
!= ( head_of @ SY353 ) ) ) )
| ~ ! [SY356: $i,SY357: $i] :
( ~ ( precedes @ SV138 @ SY356 @ SY357 )
| ~ ( shortest_path @ SV123 @ SV134 @ SY357 )
| ~ ( precedes @ SY356 @ SV138 @ SY357 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[706]) ).
thf(730,plain,
! [SV144: $i,SV139: $i] :
( ( ( ( SV139 = SV144 )
| ~ ( vertex @ SV139 )
| ~ ( vertex @ SV144 )
| ~ ( ~ ~ ( ~ ( ( SV139
!= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
!= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
!= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
!= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV139
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
| ~ ( ( SV139
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) ) )
| ~ ~ ( ~ ( ( SV144
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
| ~ ( ( SV144
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) ) ) ) )
| ~ ( edge @ ( sK15_E @ SV144 @ SV139 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(731,plain,
! [SV124: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK7_E1 @ SV124 ) @ SV124 )
| ~ ( on_path @ ( sK8_SY86 @ SV124 ) @ SV124 ) )
| ~ ( sequential @ ( sK7_E1 @ SV124 ) @ ( sK8_SY86 @ SV124 ) ) )
| ~ ! [SY291: $i] :
~ ( triangle @ ( sK7_E1 @ SV124 ) @ ( sK8_SY86 @ SV124 ) @ SY291 ) )
= $false )
| ( ( ! [SY292: $i,SY293: $i] :
~ ( path @ SY292 @ SY293 @ SV124 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV124 )
= ( number_of_in @ triangles @ SV124 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[708]) ).
thf(732,plain,
! [SV140: $i,SV135: $i,SV125: $i] :
( ( ( ~ ( vertex @ SV125 )
| ~ ( vertex @ SV135 )
| ~ ( ~ ! [SY359: $i] :
( ( SV125
!= ( tail_of @ SY359 ) )
| ~ ( edge @ SY359 )
| ( SV135
!= ( head_of @ SY359 ) )
| ( SV140
!= ( path_cons @ SY359 @ empty ) ) )
| ~ ! [SY360: $i] :
( ( SV125
!= ( tail_of @ SY360 ) )
| ~ ( edge @ SY360 )
| ! [SY361: $i] :
( ( SV140
!= ( path_cons @ SY360 @ SY361 ) )
| ~ ( path @ ( head_of @ SY360 ) @ SV135 @ SY361 ) ) ) ) )
= $true )
| ( ( path @ SV125 @ SV135 @ SV140 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[709]) ).
thf(733,plain,
! [SV126: $i] :
( ( ! [SY299: $i,SY300: $i] :
( ~ ( edge @ SV126 )
| ~ ( edge @ SY299 )
| ~ ( edge @ SY300 )
| ~ ( sequential @ SV126 @ SY299 )
| ~ ( sequential @ SY299 @ SY300 )
| ~ ( sequential @ SY300 @ SV126 )
| ( triangle @ SV126 @ SY299 @ SY300 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[710]) ).
thf(734,plain,
! [SV126: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY301: $i,SY302: $i] :
~ ( triangle @ SV126 @ SY301 @ SY302 )
| ( edge @ SV126 ) )
| ~ ! [SY303: $i] :
( ! [SY304: $i] :
~ ( triangle @ SV126 @ SY303 @ SY304 )
| ( edge @ SY303 ) ) )
| ~ ! [SY305: $i,SY306: $i] :
( ~ ( triangle @ SV126 @ SY305 @ SY306 )
| ( edge @ SY306 ) ) )
| ~ ! [SY307: $i] :
( ! [SY308: $i] :
~ ( triangle @ SV126 @ SY307 @ SY308 )
| ( sequential @ SV126 @ SY307 ) ) )
| ~ ! [SY309: $i,SY310: $i] :
( ~ ( triangle @ SV126 @ SY309 @ SY310 )
| ( sequential @ SY309 @ SY310 ) ) )
| ~ ! [SY311: $i,SY312: $i] :
( ~ ( triangle @ SV126 @ SY311 @ SY312 )
| ( sequential @ SY312 @ SV126 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[711]) ).
thf(735,plain,
! [SV127: $i,SV145: $i,SV141: $i] :
( ( ( ~ ( path @ SV141 @ SV145 @ SV127 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY315: $i] :
( ! [SY316: $i] :
~ ( precedes @ SY315 @ SY316 @ SV127 )
| ( on_path @ SY315 @ SV127 ) )
| ~ ! [SY317: $i,SY318: $i] :
( ~ ( precedes @ SY317 @ SY318 @ SV127 )
| ( on_path @ SY318 @ SV127 ) ) )
| ~ ~ ( ~ ! [SY319: $i,SY320: $i] :
( ~ ( precedes @ SY319 @ SY320 @ SV127 )
| ! [SY321: $i] :
( ~ ( precedes @ SY321 @ SY320 @ SV127 )
| ~ ( sequential @ SY319 @ SY321 ) )
| ~ ( sequential @ SY319 @ SY320 ) )
| ~ ! [SY322: $i,SY323: $i] :
( ~ ( precedes @ SY322 @ SY323 @ SV127 )
| ~ ( ~ ( precedes @ ( sK10_E3 @ SY323 @ SY322 @ SV127 ) @ SY323 @ SV127 )
| ~ ( sequential @ SY322 @ ( sK10_E3 @ SY323 @ SY322 @ SV127 ) ) )
| ( sequential @ SY322 @ SY323 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[712]) ).
thf(736,plain,
! [SV146: $i] :
( ( ~ ( edge @ SV146 )
| ( vertex @ ( head_of @ SV146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[713]) ).
thf(737,plain,
! [SV147: $i] :
( ( ~ ( edge @ SV147 )
| ( vertex @ ( tail_of @ SV147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[714]) ).
thf(738,plain,
! [SV128: $i,SV148: $i,SV142: $i] :
( ( ( ~ ( path @ SV142 @ SV148 @ SV128 ) )
= $true )
| ( ( ~ ( ~ ! [SY326: $i,SY327: $i] :
( ~ ( on_path @ SY326 @ SV128 )
| ~ ( on_path @ SY327 @ SV128 )
| ! [SY328: $i] :
( ~ ( precedes @ SY328 @ SY327 @ SV128 )
| ~ ( sequential @ SY326 @ SY328 ) )
| ( precedes @ SY326 @ SY327 @ SV128 ) )
| ~ ! [SY329: $i,SY330: $i] :
( ~ ( on_path @ SY329 @ SV128 )
| ~ ( on_path @ SY330 @ SV128 )
| ~ ( sequential @ SY329 @ SY330 )
| ( precedes @ SY329 @ SY330 @ SV128 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[715]) ).
thf(739,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)],[717]) ).
thf(740,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)],[718]) ).
thf(741,plain,
! [SV119: $i] :
( ( ~ ( ! [SY256: $i,SY257: $i] :
~ ( path @ SV119 @ SY256 @ SY257 )
| ( vertex @ SV119 ) )
| ~ ! [SY258: $i] :
( ! [SY259: $i] :
~ ( path @ SV119 @ SY258 @ SY259 )
| ( vertex @ SY258 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[719]) ).
thf(742,plain,
! [SV149: $i,SV119: $i] :
( ( ! [SY365: $i] :
( ~ ( path @ SV119 @ SV149 @ SY365 )
| ~ ( ~ ~ ( ( SV119
!= ( tail_of @ ( sK12_E @ SY365 @ SV149 @ SV119 ) ) )
| ~ ( edge @ ( sK12_E @ SY365 @ SV149 @ SV119 ) ) )
| ~ ~ ( ~ ( ( SV149
!= ( head_of @ ( sK12_E @ SY365 @ SV149 @ SV119 ) ) )
| ( SY365
!= ( path_cons @ ( sK12_E @ SY365 @ SV149 @ SV119 ) @ empty ) )
| ! [SY366: $i] :
( ( SY365
!= ( path_cons @ ( sK12_E @ SY365 @ SV149 @ SV119 ) @ SY366 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SY365 @ SV149 @ SV119 ) ) @ SV149 @ SY366 ) ) )
| ~ ~ ( ~ ( ( SV149
= ( head_of @ ( sK12_E @ SY365 @ SV149 @ SV119 ) ) )
| ~ ( ( SY365
!= ( path_cons @ ( sK12_E @ SY365 @ SV149 @ SV119 ) @ ( sK14_SY90 @ SY365 @ SV149 @ SV119 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SY365 @ SV149 @ SV119 ) ) @ SV149 @ ( sK14_SY90 @ SY365 @ SV149 @ SV119 ) ) ) )
| ~ ( ( SY365
= ( path_cons @ ( sK12_E @ SY365 @ SV149 @ SV119 ) @ empty ) )
| ~ ( ( SY365
!= ( path_cons @ ( sK12_E @ SY365 @ SV149 @ SV119 ) @ ( sK13_SY91 @ SY365 @ SV149 @ SV119 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SY365 @ SV149 @ SV119 ) ) @ SV149 @ ( sK13_SY91 @ SY365 @ SV149 @ SV119 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[720]) ).
thf(743,plain,
! [SV132: $i,SV120: $i] :
( ( ! [SY333: $i,SY334: $i] :
( ~ ( in_path @ SY334 @ SY333 )
| ~ ( path @ SV120 @ SV132 @ SY333 )
| ~ ( ~ ( on_path @ ( sK11_E @ SY334 @ SY333 @ SV132 @ SV120 ) @ SY333 )
| ~ ( ( SY334
= ( head_of @ ( sK11_E @ SY334 @ SY333 @ SV132 @ SV120 ) ) )
| ( SY334
= ( tail_of @ ( sK11_E @ SY334 @ SY333 @ SV132 @ SV120 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[721]) ).
thf(744,plain,
! [SV132: $i,SV120: $i] :
( ( ! [SY335: $i,SY336: $i] :
( ~ ( in_path @ SY336 @ SY335 )
| ~ ( path @ SV120 @ SV132 @ SY335 )
| ( vertex @ SY336 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[722]) ).
thf(745,plain,
! [SV150: $i,SV143: $i] :
( ( ( SV143 = SV150 )
| ~ ( edge @ SV143 )
| ~ ( edge @ SV150 )
| ( ( head_of @ SV143 )
!= ( tail_of @ SV150 ) )
| ( sequential @ SV143 @ SV150 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(746,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)],[724]) ).
thf(747,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[724]) ).
thf(748,plain,
! [SV133: $i,SV121: $i] :
( ( ~ ( ~ ! [SY337: $i,SY338: $i] :
( ~ ( on_path @ SY338 @ SY337 )
| ~ ( path @ SV121 @ SV133 @ SY337 )
| ( edge @ SY338 ) )
| ~ ! [SY339: $i,SY340: $i] :
( ~ ( on_path @ SY340 @ SY339 )
| ~ ( path @ SV121 @ SV133 @ SY339 )
| ( in_path @ ( head_of @ SY340 ) @ SY339 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[725]) ).
thf(749,plain,
! [SV133: $i,SV121: $i] :
( ( ! [SY341: $i,SY342: $i] :
( ~ ( on_path @ SY342 @ SY341 )
| ~ ( path @ SV121 @ SV133 @ SY341 )
| ( in_path @ ( tail_of @ SY342 ) @ SY341 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[726]) ).
thf(750,plain,
! [SV151: $i,SV122: $i] :
( ( ! [SY367: $i] :
( ~ ( ~ ( path @ SV122 @ SV151 @ ( sK9_P @ SY367 @ SV151 @ SV122 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY367 ) @ ( length_of @ ( sK9_P @ SY367 @ SV151 @ SV122 ) ) ) )
| ( SV122 = SV151 )
| ~ ( path @ SV122 @ SV151 @ SY367 )
| ( shortest_path @ SV122 @ SV151 @ SY367 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(751,plain,
! [SV122: $i] :
( ( ~ ! [SY277: $i,SY278: $i] :
( ~ ( shortest_path @ SV122 @ SY277 @ SY278 )
| ! [SY279: $i] :
( ~ ( path @ SV122 @ SY277 @ SY279 )
| ( less_or_equal @ ( length_of @ SY278 ) @ ( length_of @ SY279 ) ) ) )
| ~ ~ ( ~ ! [SY280: $i] :
( ! [SY281: $i] :
~ ( shortest_path @ SV122 @ SY280 @ SY281 )
| ( SV122 != SY280 ) )
| ~ ! [SY282: $i,SY283: $i] :
( ~ ( shortest_path @ SV122 @ SY282 @ SY283 )
| ( path @ SV122 @ SY282 @ SY283 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[728]) ).
thf(752,plain,
! [SV134: $i,SV123: $i,SV138: $i] :
( ( ~ ! [SY353: $i] :
( ! [SY354: $i] :
( ~ ( precedes @ SV138 @ SY353 @ SY354 )
| ~ ( shortest_path @ SV123 @ SV134 @ SY354 ) )
| ! [SY355: $i] :
( ( ( tail_of @ SY355 )
!= ( tail_of @ SV138 ) )
| ( ( head_of @ SY355 )
!= ( head_of @ SY353 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[729]) ).
thf(753,plain,
! [SV134: $i,SV123: $i,SV138: $i] :
( ( ~ ! [SY356: $i,SY357: $i] :
( ~ ( precedes @ SV138 @ SY356 @ SY357 )
| ~ ( shortest_path @ SV123 @ SV134 @ SY357 )
| ~ ( precedes @ SY356 @ SV138 @ SY357 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[729]) ).
thf(754,plain,
! [SV144: $i,SV139: $i] :
( ( ( ( SV139 = SV144 )
| ~ ( vertex @ SV139 )
| ~ ( vertex @ SV144 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV139
!= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
!= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
!= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
!= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV139
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
| ~ ( ( SV139
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) ) )
| ~ ~ ( ~ ( ( SV144
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
| ~ ( ( SV144
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) ) ) ) )
| ~ ( edge @ ( sK15_E @ SV144 @ SV139 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[730]) ).
thf(755,plain,
! [SV124: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK7_E1 @ SV124 ) @ SV124 )
| ~ ( on_path @ ( sK8_SY86 @ SV124 ) @ SV124 ) )
| ~ ( sequential @ ( sK7_E1 @ SV124 ) @ ( sK8_SY86 @ SV124 ) ) ) )
= $false )
| ( ( ! [SY292: $i,SY293: $i] :
~ ( path @ SY292 @ SY293 @ SV124 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV124 )
= ( number_of_in @ triangles @ SV124 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[731]) ).
thf(756,plain,
! [SV124: $i] :
( ( ( ~ ! [SY291: $i] :
~ ( triangle @ ( sK7_E1 @ SV124 ) @ ( sK8_SY86 @ SV124 ) @ SY291 ) )
= $false )
| ( ( ! [SY292: $i,SY293: $i] :
~ ( path @ SY292 @ SY293 @ SV124 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV124 )
= ( number_of_in @ triangles @ SV124 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[731]) ).
thf(757,plain,
! [SV140: $i,SV135: $i,SV125: $i] :
( ( ( ~ ( vertex @ SV125 )
| ~ ( vertex @ SV135 ) )
= $true )
| ( ( ~ ( ~ ! [SY359: $i] :
( ( SV125
!= ( tail_of @ SY359 ) )
| ~ ( edge @ SY359 )
| ( SV135
!= ( head_of @ SY359 ) )
| ( SV140
!= ( path_cons @ SY359 @ empty ) ) )
| ~ ! [SY360: $i] :
( ( SV125
!= ( tail_of @ SY360 ) )
| ~ ( edge @ SY360 )
| ! [SY361: $i] :
( ( SV140
!= ( path_cons @ SY360 @ SY361 ) )
| ~ ( path @ ( head_of @ SY360 ) @ SV135 @ SY361 ) ) ) ) )
= $true )
| ( ( path @ SV125 @ SV135 @ SV140 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[732]) ).
thf(758,plain,
! [SV152: $i,SV126: $i] :
( ( ! [SY368: $i] :
( ~ ( edge @ SV126 )
| ~ ( edge @ SV152 )
| ~ ( edge @ SY368 )
| ~ ( sequential @ SV126 @ SV152 )
| ~ ( sequential @ SV152 @ SY368 )
| ~ ( sequential @ SY368 @ SV126 )
| ( triangle @ SV126 @ SV152 @ SY368 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[733]) ).
thf(759,plain,
! [SV126: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY301: $i,SY302: $i] :
~ ( triangle @ SV126 @ SY301 @ SY302 )
| ( edge @ SV126 ) )
| ~ ! [SY303: $i] :
( ! [SY304: $i] :
~ ( triangle @ SV126 @ SY303 @ SY304 )
| ( edge @ SY303 ) ) )
| ~ ! [SY305: $i,SY306: $i] :
( ~ ( triangle @ SV126 @ SY305 @ SY306 )
| ( edge @ SY306 ) ) )
| ~ ! [SY307: $i] :
( ! [SY308: $i] :
~ ( triangle @ SV126 @ SY307 @ SY308 )
| ( sequential @ SV126 @ SY307 ) ) )
| ~ ! [SY309: $i,SY310: $i] :
( ~ ( triangle @ SV126 @ SY309 @ SY310 )
| ( sequential @ SY309 @ SY310 ) ) )
| ~ ! [SY311: $i,SY312: $i] :
( ~ ( triangle @ SV126 @ SY311 @ SY312 )
| ( sequential @ SY312 @ SV126 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[734]) ).
thf(760,plain,
! [SV127: $i,SV145: $i,SV141: $i] :
( ( ( path @ SV141 @ SV145 @ SV127 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY315: $i] :
( ! [SY316: $i] :
~ ( precedes @ SY315 @ SY316 @ SV127 )
| ( on_path @ SY315 @ SV127 ) )
| ~ ! [SY317: $i,SY318: $i] :
( ~ ( precedes @ SY317 @ SY318 @ SV127 )
| ( on_path @ SY318 @ SV127 ) ) )
| ~ ~ ( ~ ! [SY319: $i,SY320: $i] :
( ~ ( precedes @ SY319 @ SY320 @ SV127 )
| ! [SY321: $i] :
( ~ ( precedes @ SY321 @ SY320 @ SV127 )
| ~ ( sequential @ SY319 @ SY321 ) )
| ~ ( sequential @ SY319 @ SY320 ) )
| ~ ! [SY322: $i,SY323: $i] :
( ~ ( precedes @ SY322 @ SY323 @ SV127 )
| ~ ( ~ ( precedes @ ( sK10_E3 @ SY323 @ SY322 @ SV127 ) @ SY323 @ SV127 )
| ~ ( sequential @ SY322 @ ( sK10_E3 @ SY323 @ SY322 @ SV127 ) ) )
| ( sequential @ SY322 @ SY323 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[735]) ).
thf(761,plain,
! [SV146: $i] :
( ( ( ~ ( edge @ SV146 ) )
= $true )
| ( ( vertex @ ( head_of @ SV146 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[736]) ).
thf(762,plain,
! [SV147: $i] :
( ( ( ~ ( edge @ SV147 ) )
= $true )
| ( ( vertex @ ( tail_of @ SV147 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[737]) ).
thf(763,plain,
! [SV128: $i,SV148: $i,SV142: $i] :
( ( ( path @ SV142 @ SV148 @ SV128 )
= $false )
| ( ( ~ ( ~ ! [SY326: $i,SY327: $i] :
( ~ ( on_path @ SY326 @ SV128 )
| ~ ( on_path @ SY327 @ SV128 )
| ! [SY328: $i] :
( ~ ( precedes @ SY328 @ SY327 @ SV128 )
| ~ ( sequential @ SY326 @ SY328 ) )
| ( precedes @ SY326 @ SY327 @ SV128 ) )
| ~ ! [SY329: $i,SY330: $i] :
( ~ ( on_path @ SY329 @ SV128 )
| ~ ( on_path @ SY330 @ SV128 )
| ~ ( sequential @ SY329 @ SY330 )
| ( precedes @ SY329 @ SY330 @ SV128 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[738]) ).
thf(764,plain,
! [SV119: $i] :
( ( ~ ( ! [SY256: $i,SY257: $i] :
~ ( path @ SV119 @ SY256 @ SY257 )
| ( vertex @ SV119 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[741]) ).
thf(765,plain,
! [SV119: $i] :
( ( ~ ! [SY258: $i] :
( ! [SY259: $i] :
~ ( path @ SV119 @ SY258 @ SY259 )
| ( vertex @ SY258 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[741]) ).
thf(766,plain,
! [SV153: $i,SV149: $i,SV119: $i] :
( ( ~ ( path @ SV119 @ SV149 @ SV153 )
| ~ ( ~ ~ ( ( SV119
!= ( tail_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( edge @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
| ~ ~ ( ~ ( ( SV149
!= ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
| ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ empty ) )
| ! [SY369: $i] :
( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ SY369 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ SY369 ) ) )
| ~ ~ ( ~ ( ( SV149
= ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ ( sK14_SY90 @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ ( sK14_SY90 @ SV153 @ SV149 @ SV119 ) ) ) )
| ~ ( ( SV153
= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ empty ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ ( sK13_SY91 @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ ( sK13_SY91 @ SV153 @ SV149 @ SV119 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[742]) ).
thf(767,plain,
! [SV132: $i,SV120: $i,SV154: $i] :
( ( ! [SY370: $i] :
( ~ ( in_path @ SY370 @ SV154 )
| ~ ( path @ SV120 @ SV132 @ SV154 )
| ~ ( ~ ( on_path @ ( sK11_E @ SY370 @ SV154 @ SV132 @ SV120 ) @ SV154 )
| ~ ( ( SY370
= ( head_of @ ( sK11_E @ SY370 @ SV154 @ SV132 @ SV120 ) ) )
| ( SY370
= ( tail_of @ ( sK11_E @ SY370 @ SV154 @ SV132 @ SV120 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[743]) ).
thf(768,plain,
! [SV132: $i,SV120: $i,SV155: $i] :
( ( ! [SY371: $i] :
( ~ ( in_path @ SY371 @ SV155 )
| ~ ( path @ SV120 @ SV132 @ SV155 )
| ( vertex @ SY371 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[744]) ).
thf(769,plain,
! [SV150: $i,SV143: $i] :
( ( ( ( SV143 = SV150 )
| ~ ( edge @ SV143 )
| ~ ( edge @ SV150 )
| ( ( head_of @ SV143 )
!= ( tail_of @ SV150 ) ) )
= $true )
| ( ( sequential @ SV143 @ SV150 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[745]) ).
thf(770,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)],[746]) ).
thf(771,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[747]) ).
thf(772,plain,
! [SV133: $i,SV121: $i] :
( ( ~ ! [SY337: $i,SY338: $i] :
( ~ ( on_path @ SY338 @ SY337 )
| ~ ( path @ SV121 @ SV133 @ SY337 )
| ( edge @ SY338 ) )
| ~ ! [SY339: $i,SY340: $i] :
( ~ ( on_path @ SY340 @ SY339 )
| ~ ( path @ SV121 @ SV133 @ SY339 )
| ( in_path @ ( head_of @ SY340 ) @ SY339 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[748]) ).
thf(773,plain,
! [SV133: $i,SV121: $i,SV156: $i] :
( ( ! [SY372: $i] :
( ~ ( on_path @ SY372 @ SV156 )
| ~ ( path @ SV121 @ SV133 @ SV156 )
| ( in_path @ ( tail_of @ SY372 ) @ SV156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[749]) ).
thf(774,plain,
! [SV157: $i,SV151: $i,SV122: $i] :
( ( ~ ( ~ ( path @ SV122 @ SV151 @ ( sK9_P @ SV157 @ SV151 @ SV122 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SV157 ) @ ( length_of @ ( sK9_P @ SV157 @ SV151 @ SV122 ) ) ) )
| ( SV122 = SV151 )
| ~ ( path @ SV122 @ SV151 @ SV157 )
| ( shortest_path @ SV122 @ SV151 @ SV157 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[750]) ).
thf(775,plain,
! [SV122: $i] :
( ( ~ ! [SY277: $i,SY278: $i] :
( ~ ( shortest_path @ SV122 @ SY277 @ SY278 )
| ! [SY279: $i] :
( ~ ( path @ SV122 @ SY277 @ SY279 )
| ( less_or_equal @ ( length_of @ SY278 ) @ ( length_of @ SY279 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[751]) ).
thf(776,plain,
! [SV122: $i] :
( ( ~ ~ ( ~ ! [SY280: $i] :
( ! [SY281: $i] :
~ ( shortest_path @ SV122 @ SY280 @ SY281 )
| ( SV122 != SY280 ) )
| ~ ! [SY282: $i,SY283: $i] :
( ~ ( shortest_path @ SV122 @ SY282 @ SY283 )
| ( path @ SV122 @ SY282 @ SY283 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[751]) ).
thf(777,plain,
! [SV134: $i,SV123: $i,SV138: $i] :
( ( ! [SY353: $i] :
( ! [SY354: $i] :
( ~ ( precedes @ SV138 @ SY353 @ SY354 )
| ~ ( shortest_path @ SV123 @ SV134 @ SY354 ) )
| ! [SY355: $i] :
( ( ( tail_of @ SY355 )
!= ( tail_of @ SV138 ) )
| ( ( head_of @ SY355 )
!= ( head_of @ SY353 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[752]) ).
thf(778,plain,
! [SV134: $i,SV123: $i,SV138: $i] :
( ( ! [SY356: $i,SY357: $i] :
( ~ ( precedes @ SV138 @ SY356 @ SY357 )
| ~ ( shortest_path @ SV123 @ SV134 @ SY357 )
| ~ ( precedes @ SY356 @ SV138 @ SY357 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[753]) ).
thf(779,plain,
! [SV144: $i,SV139: $i] :
( ( ( SV139 = SV144 )
= $true )
| ( ( ~ ( vertex @ SV139 )
| ~ ( vertex @ SV144 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV139
!= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
!= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
!= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
!= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV139
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
| ~ ( ( SV139
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) ) )
| ~ ~ ( ~ ( ( SV144
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
| ~ ( ( SV144
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) ) ) ) )
| ~ ( edge @ ( sK15_E @ SV144 @ SV139 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[754]) ).
thf(780,plain,
! [SV124: $i] :
( ( ( ~ ( ~ ~ ( ~ ( on_path @ ( sK7_E1 @ SV124 ) @ SV124 )
| ~ ( on_path @ ( sK8_SY86 @ SV124 ) @ SV124 ) )
| ~ ( sequential @ ( sK7_E1 @ SV124 ) @ ( sK8_SY86 @ SV124 ) ) ) )
= $true )
| ( ( ! [SY292: $i,SY293: $i] :
~ ( path @ SY292 @ SY293 @ SV124 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV124 )
= ( number_of_in @ triangles @ SV124 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[755]) ).
thf(781,plain,
! [SV124: $i] :
( ( ( ! [SY291: $i] :
~ ( triangle @ ( sK7_E1 @ SV124 ) @ ( sK8_SY86 @ SV124 ) @ SY291 ) )
= $true )
| ( ( ! [SY292: $i,SY293: $i] :
~ ( path @ SY292 @ SY293 @ SV124 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV124 )
= ( number_of_in @ triangles @ SV124 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[756]) ).
thf(782,plain,
! [SV140: $i,SV135: $i,SV125: $i] :
( ( ( ~ ( vertex @ SV125 ) )
= $true )
| ( ( ~ ( vertex @ SV135 ) )
= $true )
| ( ( ~ ( ~ ! [SY359: $i] :
( ( SV125
!= ( tail_of @ SY359 ) )
| ~ ( edge @ SY359 )
| ( SV135
!= ( head_of @ SY359 ) )
| ( SV140
!= ( path_cons @ SY359 @ empty ) ) )
| ~ ! [SY360: $i] :
( ( SV125
!= ( tail_of @ SY360 ) )
| ~ ( edge @ SY360 )
| ! [SY361: $i] :
( ( SV140
!= ( path_cons @ SY360 @ SY361 ) )
| ~ ( path @ ( head_of @ SY360 ) @ SV135 @ SY361 ) ) ) ) )
= $true )
| ( ( path @ SV125 @ SV135 @ SV140 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[757]) ).
thf(783,plain,
! [SV158: $i,SV152: $i,SV126: $i] :
( ( ~ ( edge @ SV126 )
| ~ ( edge @ SV152 )
| ~ ( edge @ SV158 )
| ~ ( sequential @ SV126 @ SV152 )
| ~ ( sequential @ SV152 @ SV158 )
| ~ ( sequential @ SV158 @ SV126 )
| ( triangle @ SV126 @ SV152 @ SV158 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[758]) ).
thf(784,plain,
! [SV126: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY301: $i,SY302: $i] :
~ ( triangle @ SV126 @ SY301 @ SY302 )
| ( edge @ SV126 ) )
| ~ ! [SY303: $i] :
( ! [SY304: $i] :
~ ( triangle @ SV126 @ SY303 @ SY304 )
| ( edge @ SY303 ) ) )
| ~ ! [SY305: $i,SY306: $i] :
( ~ ( triangle @ SV126 @ SY305 @ SY306 )
| ( edge @ SY306 ) ) )
| ~ ! [SY307: $i] :
( ! [SY308: $i] :
~ ( triangle @ SV126 @ SY307 @ SY308 )
| ( sequential @ SV126 @ SY307 ) ) )
| ~ ! [SY309: $i,SY310: $i] :
( ~ ( triangle @ SV126 @ SY309 @ SY310 )
| ( sequential @ SY309 @ SY310 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[759]) ).
thf(785,plain,
! [SV126: $i] :
( ( ~ ! [SY311: $i,SY312: $i] :
( ~ ( triangle @ SV126 @ SY311 @ SY312 )
| ( sequential @ SY312 @ SV126 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[759]) ).
thf(786,plain,
! [SV145: $i,SV141: $i,SV127: $i] :
( ( ( ~ ~ ( ~ ! [SY315: $i] :
( ! [SY316: $i] :
~ ( precedes @ SY315 @ SY316 @ SV127 )
| ( on_path @ SY315 @ SV127 ) )
| ~ ! [SY317: $i,SY318: $i] :
( ~ ( precedes @ SY317 @ SY318 @ SV127 )
| ( on_path @ SY318 @ SV127 ) ) )
| ~ ~ ( ~ ! [SY319: $i,SY320: $i] :
( ~ ( precedes @ SY319 @ SY320 @ SV127 )
| ! [SY321: $i] :
( ~ ( precedes @ SY321 @ SY320 @ SV127 )
| ~ ( sequential @ SY319 @ SY321 ) )
| ~ ( sequential @ SY319 @ SY320 ) )
| ~ ! [SY322: $i,SY323: $i] :
( ~ ( precedes @ SY322 @ SY323 @ SV127 )
| ~ ( ~ ( precedes @ ( sK10_E3 @ SY323 @ SY322 @ SV127 ) @ SY323 @ SV127 )
| ~ ( sequential @ SY322 @ ( sK10_E3 @ SY323 @ SY322 @ SV127 ) ) )
| ( sequential @ SY322 @ SY323 ) ) ) )
= $false )
| ( ( path @ SV141 @ SV145 @ SV127 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[760]) ).
thf(787,plain,
! [SV146: $i] :
( ( ( edge @ SV146 )
= $false )
| ( ( vertex @ ( head_of @ SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[761]) ).
thf(788,plain,
! [SV147: $i] :
( ( ( edge @ SV147 )
= $false )
| ( ( vertex @ ( tail_of @ SV147 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[762]) ).
thf(789,plain,
! [SV148: $i,SV142: $i,SV128: $i] :
( ( ( ~ ! [SY326: $i,SY327: $i] :
( ~ ( on_path @ SY326 @ SV128 )
| ~ ( on_path @ SY327 @ SV128 )
| ! [SY328: $i] :
( ~ ( precedes @ SY328 @ SY327 @ SV128 )
| ~ ( sequential @ SY326 @ SY328 ) )
| ( precedes @ SY326 @ SY327 @ SV128 ) )
| ~ ! [SY329: $i,SY330: $i] :
( ~ ( on_path @ SY329 @ SV128 )
| ~ ( on_path @ SY330 @ SV128 )
| ~ ( sequential @ SY329 @ SY330 )
| ( precedes @ SY329 @ SY330 @ SV128 ) ) )
= $false )
| ( ( path @ SV142 @ SV148 @ SV128 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[763]) ).
thf(790,plain,
! [SV119: $i] :
( ( ! [SY256: $i,SY257: $i] :
~ ( path @ SV119 @ SY256 @ SY257 )
| ( vertex @ SV119 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[764]) ).
thf(791,plain,
! [SV119: $i] :
( ( ! [SY258: $i] :
( ! [SY259: $i] :
~ ( path @ SV119 @ SY258 @ SY259 )
| ( vertex @ SY258 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[765]) ).
thf(792,plain,
! [SV153: $i,SV149: $i,SV119: $i] :
( ( ( ~ ( path @ SV119 @ SV149 @ SV153 ) )
= $true )
| ( ( ~ ( ~ ~ ( ( SV119
!= ( tail_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( edge @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
| ~ ~ ( ~ ( ( SV149
!= ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
| ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ empty ) )
| ! [SY369: $i] :
( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ SY369 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ SY369 ) ) )
| ~ ~ ( ~ ( ( SV149
= ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ ( sK14_SY90 @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ ( sK14_SY90 @ SV153 @ SV149 @ SV119 ) ) ) )
| ~ ( ( SV153
= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ empty ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ ( sK13_SY91 @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ ( sK13_SY91 @ SV153 @ SV149 @ SV119 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[766]) ).
thf(793,plain,
! [SV132: $i,SV120: $i,SV154: $i,SV159: $i] :
( ( ~ ( in_path @ SV159 @ SV154 )
| ~ ( path @ SV120 @ SV132 @ SV154 )
| ~ ( ~ ( on_path @ ( sK11_E @ SV159 @ SV154 @ SV132 @ SV120 ) @ SV154 )
| ~ ( ( SV159
= ( head_of @ ( sK11_E @ SV159 @ SV154 @ SV132 @ SV120 ) ) )
| ( SV159
= ( tail_of @ ( sK11_E @ SV159 @ SV154 @ SV132 @ SV120 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[767]) ).
thf(794,plain,
! [SV132: $i,SV120: $i,SV155: $i,SV160: $i] :
( ( ~ ( in_path @ SV160 @ SV155 )
| ~ ( path @ SV120 @ SV132 @ SV155 )
| ( vertex @ SV160 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[768]) ).
thf(795,plain,
! [SV150: $i,SV143: $i] :
( ( ( ( SV143 = SV150 )
| ~ ( edge @ SV143 )
| ~ ( edge @ SV150 ) )
= $true )
| ( ( ( ( head_of @ SV143 )
!= ( tail_of @ SV150 ) ) )
= $true )
| ( ( sequential @ SV143 @ SV150 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[769]) ).
thf(796,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)],[770]) ).
thf(797,plain,
! [SV161: $i] :
( ( ! [SY373: $i] :
( ~ ( sequential @ SV161 @ SY373 )
| ( ( head_of @ SV161 )
= ( tail_of @ SY373 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(798,plain,
! [SV133: $i,SV121: $i] :
( ( ~ ! [SY337: $i,SY338: $i] :
( ~ ( on_path @ SY338 @ SY337 )
| ~ ( path @ SV121 @ SV133 @ SY337 )
| ( edge @ SY338 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[772]) ).
thf(799,plain,
! [SV133: $i,SV121: $i] :
( ( ~ ! [SY339: $i,SY340: $i] :
( ~ ( on_path @ SY340 @ SY339 )
| ~ ( path @ SV121 @ SV133 @ SY339 )
| ( in_path @ ( head_of @ SY340 ) @ SY339 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[772]) ).
thf(800,plain,
! [SV133: $i,SV121: $i,SV156: $i,SV162: $i] :
( ( ~ ( on_path @ SV162 @ SV156 )
| ~ ( path @ SV121 @ SV133 @ SV156 )
| ( in_path @ ( tail_of @ SV162 ) @ SV156 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[773]) ).
thf(801,plain,
! [SV157: $i,SV151: $i,SV122: $i] :
( ( ( ~ ( ~ ( path @ SV122 @ SV151 @ ( sK9_P @ SV157 @ SV151 @ SV122 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SV157 ) @ ( length_of @ ( sK9_P @ SV157 @ SV151 @ SV122 ) ) ) )
| ( SV122 = SV151 )
| ~ ( path @ SV122 @ SV151 @ SV157 ) )
= $true )
| ( ( shortest_path @ SV122 @ SV151 @ SV157 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[774]) ).
thf(802,plain,
! [SV122: $i] :
( ( ! [SY277: $i,SY278: $i] :
( ~ ( shortest_path @ SV122 @ SY277 @ SY278 )
| ! [SY279: $i] :
( ~ ( path @ SV122 @ SY277 @ SY279 )
| ( less_or_equal @ ( length_of @ SY278 ) @ ( length_of @ SY279 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[775]) ).
thf(803,plain,
! [SV122: $i] :
( ( ~ ( ~ ! [SY280: $i] :
( ! [SY281: $i] :
~ ( shortest_path @ SV122 @ SY280 @ SY281 )
| ( SV122 != SY280 ) )
| ~ ! [SY282: $i,SY283: $i] :
( ~ ( shortest_path @ SV122 @ SY282 @ SY283 )
| ( path @ SV122 @ SY282 @ SY283 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[776]) ).
thf(804,plain,
! [SV134: $i,SV123: $i,SV163: $i,SV138: $i] :
( ( ! [SY374: $i] :
( ~ ( precedes @ SV138 @ SV163 @ SY374 )
| ~ ( shortest_path @ SV123 @ SV134 @ SY374 ) )
| ! [SY375: $i] :
( ( ( tail_of @ SY375 )
!= ( tail_of @ SV138 ) )
| ( ( head_of @ SY375 )
!= ( head_of @ SV163 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[777]) ).
thf(805,plain,
! [SV134: $i,SV123: $i,SV164: $i,SV138: $i] :
( ( ! [SY376: $i] :
( ~ ( precedes @ SV138 @ SV164 @ SY376 )
| ~ ( shortest_path @ SV123 @ SV134 @ SY376 )
| ~ ( precedes @ SV164 @ SV138 @ SY376 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[778]) ).
thf(806,plain,
! [SV144: $i,SV139: $i] :
( ( ( ~ ( vertex @ SV139 ) )
= $true )
| ( ( ~ ( vertex @ SV144 ) )
= $true )
| ( ( SV139 = SV144 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV139
!= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
!= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
!= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
!= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV139
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
| ~ ( ( SV139
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) ) )
| ~ ~ ( ~ ( ( SV144
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
| ~ ( ( SV144
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) ) ) ) )
| ~ ( edge @ ( sK15_E @ SV144 @ SV139 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[779]) ).
thf(807,plain,
! [SV124: $i] :
( ( ( ~ ~ ( ~ ( on_path @ ( sK7_E1 @ SV124 ) @ SV124 )
| ~ ( on_path @ ( sK8_SY86 @ SV124 ) @ SV124 ) )
| ~ ( sequential @ ( sK7_E1 @ SV124 ) @ ( sK8_SY86 @ SV124 ) ) )
= $false )
| ( ( ! [SY292: $i,SY293: $i] :
~ ( path @ SY292 @ SY293 @ SV124 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV124 )
= ( number_of_in @ triangles @ SV124 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[780]) ).
thf(808,plain,
! [SV165: $i,SV124: $i] :
( ( ( ~ ( triangle @ ( sK7_E1 @ SV124 ) @ ( sK8_SY86 @ SV124 ) @ SV165 ) )
= $true )
| ( ( ! [SY292: $i,SY293: $i] :
~ ( path @ SY292 @ SY293 @ SV124 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV124 )
= ( number_of_in @ triangles @ SV124 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[781]) ).
thf(809,plain,
! [SV140: $i,SV135: $i,SV125: $i] :
( ( ( vertex @ SV125 )
= $false )
| ( ( ~ ( vertex @ SV135 ) )
= $true )
| ( ( ~ ( ~ ! [SY359: $i] :
( ( SV125
!= ( tail_of @ SY359 ) )
| ~ ( edge @ SY359 )
| ( SV135
!= ( head_of @ SY359 ) )
| ( SV140
!= ( path_cons @ SY359 @ empty ) ) )
| ~ ! [SY360: $i] :
( ( SV125
!= ( tail_of @ SY360 ) )
| ~ ( edge @ SY360 )
| ! [SY361: $i] :
( ( SV140
!= ( path_cons @ SY360 @ SY361 ) )
| ~ ( path @ ( head_of @ SY360 ) @ SV135 @ SY361 ) ) ) ) )
= $true )
| ( ( path @ SV125 @ SV135 @ SV140 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[782]) ).
thf(810,plain,
! [SV158: $i,SV152: $i,SV126: $i] :
( ( ( ~ ( edge @ SV126 )
| ~ ( edge @ SV152 )
| ~ ( edge @ SV158 )
| ~ ( sequential @ SV126 @ SV152 )
| ~ ( sequential @ SV152 @ SV158 )
| ~ ( sequential @ SV158 @ SV126 ) )
= $true )
| ( ( triangle @ SV126 @ SV152 @ SV158 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[783]) ).
thf(811,plain,
! [SV126: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY301: $i,SY302: $i] :
~ ( triangle @ SV126 @ SY301 @ SY302 )
| ( edge @ SV126 ) )
| ~ ! [SY303: $i] :
( ! [SY304: $i] :
~ ( triangle @ SV126 @ SY303 @ SY304 )
| ( edge @ SY303 ) ) )
| ~ ! [SY305: $i,SY306: $i] :
( ~ ( triangle @ SV126 @ SY305 @ SY306 )
| ( edge @ SY306 ) ) )
| ~ ! [SY307: $i] :
( ! [SY308: $i] :
~ ( triangle @ SV126 @ SY307 @ SY308 )
| ( sequential @ SV126 @ SY307 ) ) )
| ~ ! [SY309: $i,SY310: $i] :
( ~ ( triangle @ SV126 @ SY309 @ SY310 )
| ( sequential @ SY309 @ SY310 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[784]) ).
thf(812,plain,
! [SV126: $i] :
( ( ! [SY311: $i,SY312: $i] :
( ~ ( triangle @ SV126 @ SY311 @ SY312 )
| ( sequential @ SY312 @ SV126 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[785]) ).
thf(813,plain,
! [SV145: $i,SV141: $i,SV127: $i] :
( ( ( ~ ~ ( ~ ! [SY315: $i] :
( ! [SY316: $i] :
~ ( precedes @ SY315 @ SY316 @ SV127 )
| ( on_path @ SY315 @ SV127 ) )
| ~ ! [SY317: $i,SY318: $i] :
( ~ ( precedes @ SY317 @ SY318 @ SV127 )
| ( on_path @ SY318 @ SV127 ) ) ) )
= $false )
| ( ( path @ SV141 @ SV145 @ SV127 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[786]) ).
thf(814,plain,
! [SV145: $i,SV141: $i,SV127: $i] :
( ( ( ~ ~ ( ~ ! [SY319: $i,SY320: $i] :
( ~ ( precedes @ SY319 @ SY320 @ SV127 )
| ! [SY321: $i] :
( ~ ( precedes @ SY321 @ SY320 @ SV127 )
| ~ ( sequential @ SY319 @ SY321 ) )
| ~ ( sequential @ SY319 @ SY320 ) )
| ~ ! [SY322: $i,SY323: $i] :
( ~ ( precedes @ SY322 @ SY323 @ SV127 )
| ~ ( ~ ( precedes @ ( sK10_E3 @ SY323 @ SY322 @ SV127 ) @ SY323 @ SV127 )
| ~ ( sequential @ SY322 @ ( sK10_E3 @ SY323 @ SY322 @ SV127 ) ) )
| ( sequential @ SY322 @ SY323 ) ) ) )
= $false )
| ( ( path @ SV141 @ SV145 @ SV127 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[786]) ).
thf(815,plain,
! [SV148: $i,SV142: $i,SV128: $i] :
( ( ( ~ ! [SY326: $i,SY327: $i] :
( ~ ( on_path @ SY326 @ SV128 )
| ~ ( on_path @ SY327 @ SV128 )
| ! [SY328: $i] :
( ~ ( precedes @ SY328 @ SY327 @ SV128 )
| ~ ( sequential @ SY326 @ SY328 ) )
| ( precedes @ SY326 @ SY327 @ SV128 ) ) )
= $false )
| ( ( path @ SV142 @ SV148 @ SV128 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[789]) ).
thf(816,plain,
! [SV148: $i,SV142: $i,SV128: $i] :
( ( ( ~ ! [SY329: $i,SY330: $i] :
( ~ ( on_path @ SY329 @ SV128 )
| ~ ( on_path @ SY330 @ SV128 )
| ~ ( sequential @ SY329 @ SY330 )
| ( precedes @ SY329 @ SY330 @ SV128 ) ) )
= $false )
| ( ( path @ SV142 @ SV148 @ SV128 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[789]) ).
thf(817,plain,
! [SV119: $i] :
( ( ( ! [SY256: $i,SY257: $i] :
~ ( path @ SV119 @ SY256 @ SY257 ) )
= $true )
| ( ( vertex @ SV119 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[790]) ).
thf(818,plain,
! [SV166: $i,SV119: $i] :
( ( ! [SY377: $i] :
~ ( path @ SV119 @ SV166 @ SY377 )
| ( vertex @ SV166 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[791]) ).
thf(819,plain,
! [SV153: $i,SV149: $i,SV119: $i] :
( ( ( path @ SV119 @ SV149 @ SV153 )
= $false )
| ( ( ~ ( ~ ~ ( ( SV119
!= ( tail_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( edge @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
| ~ ~ ( ~ ( ( SV149
!= ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
| ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ empty ) )
| ! [SY369: $i] :
( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ SY369 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ SY369 ) ) )
| ~ ~ ( ~ ( ( SV149
= ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ ( sK14_SY90 @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ ( sK14_SY90 @ SV153 @ SV149 @ SV119 ) ) ) )
| ~ ( ( SV153
= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ empty ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ ( sK13_SY91 @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ ( sK13_SY91 @ SV153 @ SV149 @ SV119 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[792]) ).
thf(820,plain,
! [SV132: $i,SV120: $i,SV154: $i,SV159: $i] :
( ( ( ~ ( in_path @ SV159 @ SV154 )
| ~ ( path @ SV120 @ SV132 @ SV154 ) )
= $true )
| ( ( ~ ( ~ ( on_path @ ( sK11_E @ SV159 @ SV154 @ SV132 @ SV120 ) @ SV154 )
| ~ ( ( SV159
= ( head_of @ ( sK11_E @ SV159 @ SV154 @ SV132 @ SV120 ) ) )
| ( SV159
= ( tail_of @ ( sK11_E @ SV159 @ SV154 @ SV132 @ SV120 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[793]) ).
thf(821,plain,
! [SV132: $i,SV120: $i,SV155: $i,SV160: $i] :
( ( ( ~ ( in_path @ SV160 @ SV155 )
| ~ ( path @ SV120 @ SV132 @ SV155 ) )
= $true )
| ( ( vertex @ SV160 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[794]) ).
thf(822,plain,
! [SV150: $i,SV143: $i] :
( ( ( SV143 = SV150 )
= $true )
| ( ( ~ ( edge @ SV143 )
| ~ ( edge @ SV150 ) )
= $true )
| ( ( ( ( head_of @ SV143 )
!= ( tail_of @ SV150 ) ) )
= $true )
| ( ( sequential @ SV143 @ SV150 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[795]) ).
thf(823,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[796]) ).
thf(824,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)],[796]) ).
thf(825,plain,
! [SV167: $i,SV161: $i] :
( ( ~ ( sequential @ SV161 @ SV167 )
| ( ( head_of @ SV161 )
= ( tail_of @ SV167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(826,plain,
! [SV133: $i,SV121: $i] :
( ( ! [SY337: $i,SY338: $i] :
( ~ ( on_path @ SY338 @ SY337 )
| ~ ( path @ SV121 @ SV133 @ SY337 )
| ( edge @ SY338 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[798]) ).
thf(827,plain,
! [SV133: $i,SV121: $i] :
( ( ! [SY339: $i,SY340: $i] :
( ~ ( on_path @ SY340 @ SY339 )
| ~ ( path @ SV121 @ SV133 @ SY339 )
| ( in_path @ ( head_of @ SY340 ) @ SY339 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[799]) ).
thf(828,plain,
! [SV133: $i,SV121: $i,SV156: $i,SV162: $i] :
( ( ( ~ ( on_path @ SV162 @ SV156 )
| ~ ( path @ SV121 @ SV133 @ SV156 ) )
= $true )
| ( ( in_path @ ( tail_of @ SV162 ) @ SV156 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[800]) ).
thf(829,plain,
! [SV157: $i,SV151: $i,SV122: $i] :
( ( ( ~ ( ~ ( path @ SV122 @ SV151 @ ( sK9_P @ SV157 @ SV151 @ SV122 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SV157 ) @ ( length_of @ ( sK9_P @ SV157 @ SV151 @ SV122 ) ) ) ) )
= $true )
| ( ( ( SV122 = SV151 )
| ~ ( path @ SV122 @ SV151 @ SV157 ) )
= $true )
| ( ( shortest_path @ SV122 @ SV151 @ SV157 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[801]) ).
thf(830,plain,
! [SV168: $i,SV122: $i] :
( ( ! [SY378: $i] :
( ~ ( shortest_path @ SV122 @ SV168 @ SY378 )
| ! [SY379: $i] :
( ~ ( path @ SV122 @ SV168 @ SY379 )
| ( less_or_equal @ ( length_of @ SY378 ) @ ( length_of @ SY379 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[802]) ).
thf(831,plain,
! [SV122: $i] :
( ( ~ ! [SY280: $i] :
( ! [SY281: $i] :
~ ( shortest_path @ SV122 @ SY280 @ SY281 )
| ( SV122 != SY280 ) )
| ~ ! [SY282: $i,SY283: $i] :
( ~ ( shortest_path @ SV122 @ SY282 @ SY283 )
| ( path @ SV122 @ SY282 @ SY283 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[803]) ).
thf(832,plain,
! [SV134: $i,SV123: $i,SV163: $i,SV138: $i] :
( ( ( ! [SY374: $i] :
( ~ ( precedes @ SV138 @ SV163 @ SY374 )
| ~ ( shortest_path @ SV123 @ SV134 @ SY374 ) ) )
= $true )
| ( ( ! [SY375: $i] :
( ( ( tail_of @ SY375 )
!= ( tail_of @ SV138 ) )
| ( ( head_of @ SY375 )
!= ( head_of @ SV163 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[804]) ).
thf(833,plain,
! [SV134: $i,SV123: $i,SV169: $i,SV164: $i,SV138: $i] :
( ( ~ ( precedes @ SV138 @ SV164 @ SV169 )
| ~ ( shortest_path @ SV123 @ SV134 @ SV169 )
| ~ ( precedes @ SV164 @ SV138 @ SV169 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(834,plain,
! [SV144: $i,SV139: $i] :
( ( ( vertex @ SV139 )
= $false )
| ( ( ~ ( vertex @ SV144 ) )
= $true )
| ( ( SV139 = SV144 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV139
!= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
!= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
!= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
!= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV139
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
| ~ ( ( SV139
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) ) )
| ~ ~ ( ~ ( ( SV144
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
| ~ ( ( SV144
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) ) ) ) )
| ~ ( edge @ ( sK15_E @ SV144 @ SV139 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[806]) ).
thf(835,plain,
! [SV124: $i] :
( ( ( ~ ~ ( ~ ( on_path @ ( sK7_E1 @ SV124 ) @ SV124 )
| ~ ( on_path @ ( sK8_SY86 @ SV124 ) @ SV124 ) ) )
= $false )
| ( ( ! [SY292: $i,SY293: $i] :
~ ( path @ SY292 @ SY293 @ SV124 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV124 )
= ( number_of_in @ triangles @ SV124 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[807]) ).
thf(836,plain,
! [SV124: $i] :
( ( ( ~ ( sequential @ ( sK7_E1 @ SV124 ) @ ( sK8_SY86 @ SV124 ) ) )
= $false )
| ( ( ! [SY292: $i,SY293: $i] :
~ ( path @ SY292 @ SY293 @ SV124 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV124 )
= ( number_of_in @ triangles @ SV124 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[807]) ).
thf(837,plain,
! [SV165: $i,SV124: $i] :
( ( ( triangle @ ( sK7_E1 @ SV124 ) @ ( sK8_SY86 @ SV124 ) @ SV165 )
= $false )
| ( ( ! [SY292: $i,SY293: $i] :
~ ( path @ SY292 @ SY293 @ SV124 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV124 )
= ( number_of_in @ triangles @ SV124 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[808]) ).
thf(838,plain,
! [SV140: $i,SV125: $i,SV135: $i] :
( ( ( vertex @ SV135 )
= $false )
| ( ( vertex @ SV125 )
= $false )
| ( ( ~ ( ~ ! [SY359: $i] :
( ( SV125
!= ( tail_of @ SY359 ) )
| ~ ( edge @ SY359 )
| ( SV135
!= ( head_of @ SY359 ) )
| ( SV140
!= ( path_cons @ SY359 @ empty ) ) )
| ~ ! [SY360: $i] :
( ( SV125
!= ( tail_of @ SY360 ) )
| ~ ( edge @ SY360 )
| ! [SY361: $i] :
( ( SV140
!= ( path_cons @ SY360 @ SY361 ) )
| ~ ( path @ ( head_of @ SY360 ) @ SV135 @ SY361 ) ) ) ) )
= $true )
| ( ( path @ SV125 @ SV135 @ SV140 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[809]) ).
thf(839,plain,
! [SV158: $i,SV152: $i,SV126: $i] :
( ( ( ~ ( edge @ SV126 )
| ~ ( edge @ SV152 )
| ~ ( edge @ SV158 )
| ~ ( sequential @ SV126 @ SV152 )
| ~ ( sequential @ SV152 @ SV158 ) )
= $true )
| ( ( ~ ( sequential @ SV158 @ SV126 ) )
= $true )
| ( ( triangle @ SV126 @ SV152 @ SV158 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[810]) ).
thf(840,plain,
! [SV126: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY301: $i,SY302: $i] :
~ ( triangle @ SV126 @ SY301 @ SY302 )
| ( edge @ SV126 ) )
| ~ ! [SY303: $i] :
( ! [SY304: $i] :
~ ( triangle @ SV126 @ SY303 @ SY304 )
| ( edge @ SY303 ) ) )
| ~ ! [SY305: $i,SY306: $i] :
( ~ ( triangle @ SV126 @ SY305 @ SY306 )
| ( edge @ SY306 ) ) )
| ~ ! [SY307: $i] :
( ! [SY308: $i] :
~ ( triangle @ SV126 @ SY307 @ SY308 )
| ( sequential @ SV126 @ SY307 ) ) )
| ~ ! [SY309: $i,SY310: $i] :
( ~ ( triangle @ SV126 @ SY309 @ SY310 )
| ( sequential @ SY309 @ SY310 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[811]) ).
thf(841,plain,
! [SV170: $i,SV126: $i] :
( ( ! [SY380: $i] :
( ~ ( triangle @ SV126 @ SV170 @ SY380 )
| ( sequential @ SY380 @ SV126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[812]) ).
thf(842,plain,
! [SV145: $i,SV141: $i,SV127: $i] :
( ( ( ~ ( ~ ! [SY315: $i] :
( ! [SY316: $i] :
~ ( precedes @ SY315 @ SY316 @ SV127 )
| ( on_path @ SY315 @ SV127 ) )
| ~ ! [SY317: $i,SY318: $i] :
( ~ ( precedes @ SY317 @ SY318 @ SV127 )
| ( on_path @ SY318 @ SV127 ) ) ) )
= $true )
| ( ( path @ SV141 @ SV145 @ SV127 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[813]) ).
thf(843,plain,
! [SV145: $i,SV141: $i,SV127: $i] :
( ( ( ~ ( ~ ! [SY319: $i,SY320: $i] :
( ~ ( precedes @ SY319 @ SY320 @ SV127 )
| ! [SY321: $i] :
( ~ ( precedes @ SY321 @ SY320 @ SV127 )
| ~ ( sequential @ SY319 @ SY321 ) )
| ~ ( sequential @ SY319 @ SY320 ) )
| ~ ! [SY322: $i,SY323: $i] :
( ~ ( precedes @ SY322 @ SY323 @ SV127 )
| ~ ( ~ ( precedes @ ( sK10_E3 @ SY323 @ SY322 @ SV127 ) @ SY323 @ SV127 )
| ~ ( sequential @ SY322 @ ( sK10_E3 @ SY323 @ SY322 @ SV127 ) ) )
| ( sequential @ SY322 @ SY323 ) ) ) )
= $true )
| ( ( path @ SV141 @ SV145 @ SV127 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[814]) ).
thf(844,plain,
! [SV148: $i,SV142: $i,SV128: $i] :
( ( ( ! [SY326: $i,SY327: $i] :
( ~ ( on_path @ SY326 @ SV128 )
| ~ ( on_path @ SY327 @ SV128 )
| ! [SY328: $i] :
( ~ ( precedes @ SY328 @ SY327 @ SV128 )
| ~ ( sequential @ SY326 @ SY328 ) )
| ( precedes @ SY326 @ SY327 @ SV128 ) ) )
= $true )
| ( ( path @ SV142 @ SV148 @ SV128 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[815]) ).
thf(845,plain,
! [SV148: $i,SV142: $i,SV128: $i] :
( ( ( ! [SY329: $i,SY330: $i] :
( ~ ( on_path @ SY329 @ SV128 )
| ~ ( on_path @ SY330 @ SV128 )
| ~ ( sequential @ SY329 @ SY330 )
| ( precedes @ SY329 @ SY330 @ SV128 ) ) )
= $true )
| ( ( path @ SV142 @ SV148 @ SV128 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[816]) ).
thf(846,plain,
! [SV171: $i,SV119: $i] :
( ( ( ! [SY381: $i] :
~ ( path @ SV119 @ SV171 @ SY381 ) )
= $true )
| ( ( vertex @ SV119 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[817]) ).
thf(847,plain,
! [SV166: $i,SV119: $i] :
( ( ( ! [SY377: $i] :
~ ( path @ SV119 @ SV166 @ SY377 ) )
= $true )
| ( ( vertex @ SV166 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[818]) ).
thf(848,plain,
! [SV149: $i,SV153: $i,SV119: $i] :
( ( ( ~ ~ ( ( SV119
!= ( tail_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( edge @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
| ~ ~ ( ~ ( ( SV149
!= ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
| ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ empty ) )
| ! [SY369: $i] :
( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ SY369 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ SY369 ) ) )
| ~ ~ ( ~ ( ( SV149
= ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ ( sK14_SY90 @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ ( sK14_SY90 @ SV153 @ SV149 @ SV119 ) ) ) )
| ~ ( ( SV153
= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ empty ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ ( sK13_SY91 @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ ( sK13_SY91 @ SV153 @ SV149 @ SV119 ) ) ) ) ) ) )
= $false )
| ( ( path @ SV119 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[819]) ).
thf(849,plain,
! [SV132: $i,SV120: $i,SV154: $i,SV159: $i] :
( ( ( ~ ( in_path @ SV159 @ SV154 ) )
= $true )
| ( ( ~ ( path @ SV120 @ SV132 @ SV154 ) )
= $true )
| ( ( ~ ( ~ ( on_path @ ( sK11_E @ SV159 @ SV154 @ SV132 @ SV120 ) @ SV154 )
| ~ ( ( SV159
= ( head_of @ ( sK11_E @ SV159 @ SV154 @ SV132 @ SV120 ) ) )
| ( SV159
= ( tail_of @ ( sK11_E @ SV159 @ SV154 @ SV132 @ SV120 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[820]) ).
thf(850,plain,
! [SV132: $i,SV120: $i,SV155: $i,SV160: $i] :
( ( ( ~ ( in_path @ SV160 @ SV155 ) )
= $true )
| ( ( ~ ( path @ SV120 @ SV132 @ SV155 ) )
= $true )
| ( ( vertex @ SV160 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[821]) ).
thf(851,plain,
! [SV150: $i,SV143: $i] :
( ( ( ~ ( edge @ SV143 ) )
= $true )
| ( ( ~ ( edge @ SV150 ) )
= $true )
| ( ( SV143 = SV150 )
= $true )
| ( ( ( ( head_of @ SV143 )
!= ( tail_of @ SV150 ) ) )
= $true )
| ( ( sequential @ SV143 @ SV150 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[822]) ).
thf(852,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[823]) ).
thf(853,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)],[824]) ).
thf(854,plain,
! [SV167: $i,SV161: $i] :
( ( ( ~ ( sequential @ SV161 @ SV167 ) )
= $true )
| ( ( ( head_of @ SV161 )
= ( tail_of @ SV167 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[825]) ).
thf(855,plain,
! [SV133: $i,SV121: $i,SV172: $i] :
( ( ! [SY382: $i] :
( ~ ( on_path @ SY382 @ SV172 )
| ~ ( path @ SV121 @ SV133 @ SV172 )
| ( edge @ SY382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[826]) ).
thf(856,plain,
! [SV133: $i,SV121: $i,SV173: $i] :
( ( ! [SY383: $i] :
( ~ ( on_path @ SY383 @ SV173 )
| ~ ( path @ SV121 @ SV133 @ SV173 )
| ( in_path @ ( head_of @ SY383 ) @ SV173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(857,plain,
! [SV133: $i,SV121: $i,SV156: $i,SV162: $i] :
( ( ( ~ ( on_path @ SV162 @ SV156 ) )
= $true )
| ( ( ~ ( path @ SV121 @ SV133 @ SV156 ) )
= $true )
| ( ( in_path @ ( tail_of @ SV162 ) @ SV156 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[828]) ).
thf(858,plain,
! [SV157: $i,SV151: $i,SV122: $i] :
( ( ( ~ ( path @ SV122 @ SV151 @ ( sK9_P @ SV157 @ SV151 @ SV122 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SV157 ) @ ( length_of @ ( sK9_P @ SV157 @ SV151 @ SV122 ) ) ) )
= $false )
| ( ( ( SV122 = SV151 )
| ~ ( path @ SV122 @ SV151 @ SV157 ) )
= $true )
| ( ( shortest_path @ SV122 @ SV151 @ SV157 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[829]) ).
thf(859,plain,
! [SV174: $i,SV168: $i,SV122: $i] :
( ( ~ ( shortest_path @ SV122 @ SV168 @ SV174 )
| ! [SY384: $i] :
( ~ ( path @ SV122 @ SV168 @ SY384 )
| ( less_or_equal @ ( length_of @ SV174 ) @ ( length_of @ SY384 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(860,plain,
! [SV122: $i] :
( ( ~ ! [SY280: $i] :
( ! [SY281: $i] :
~ ( shortest_path @ SV122 @ SY280 @ SY281 )
| ( SV122 != SY280 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[831]) ).
thf(861,plain,
! [SV122: $i] :
( ( ~ ! [SY282: $i,SY283: $i] :
( ~ ( shortest_path @ SV122 @ SY282 @ SY283 )
| ( path @ SV122 @ SY282 @ SY283 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[831]) ).
thf(862,plain,
! [SV134: $i,SV123: $i,SV175: $i,SV163: $i,SV138: $i] :
( ( ( ~ ( precedes @ SV138 @ SV163 @ SV175 )
| ~ ( shortest_path @ SV123 @ SV134 @ SV175 ) )
= $true )
| ( ( ! [SY375: $i] :
( ( ( tail_of @ SY375 )
!= ( tail_of @ SV138 ) )
| ( ( head_of @ SY375 )
!= ( head_of @ SV163 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(863,plain,
! [SV134: $i,SV123: $i,SV169: $i,SV164: $i,SV138: $i] :
( ( ( ~ ( precedes @ SV138 @ SV164 @ SV169 )
| ~ ( shortest_path @ SV123 @ SV134 @ SV169 ) )
= $true )
| ( ( ~ ( precedes @ SV164 @ SV138 @ SV169 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[833]) ).
thf(864,plain,
! [SV139: $i,SV144: $i] :
( ( ( vertex @ SV144 )
= $false )
| ( ( vertex @ SV139 )
= $false )
| ( ( SV139 = SV144 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV139
!= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
!= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
!= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
!= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV139
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
| ~ ( ( SV139
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) ) )
| ~ ~ ( ~ ( ( SV144
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
| ~ ( ( SV144
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) ) ) ) )
| ~ ( edge @ ( sK15_E @ SV144 @ SV139 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[834]) ).
thf(865,plain,
! [SV124: $i] :
( ( ( ~ ( ~ ( on_path @ ( sK7_E1 @ SV124 ) @ SV124 )
| ~ ( on_path @ ( sK8_SY86 @ SV124 ) @ SV124 ) ) )
= $true )
| ( ( ! [SY292: $i,SY293: $i] :
~ ( path @ SY292 @ SY293 @ SV124 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV124 )
= ( number_of_in @ triangles @ SV124 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[835]) ).
thf(866,plain,
! [SV124: $i] :
( ( ( sequential @ ( sK7_E1 @ SV124 ) @ ( sK8_SY86 @ SV124 ) )
= $true )
| ( ( ! [SY292: $i,SY293: $i] :
~ ( path @ SY292 @ SY293 @ SV124 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV124 )
= ( number_of_in @ triangles @ SV124 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[836]) ).
thf(867,plain,
! [SV165: $i,SV124: $i,SV176: $i] :
( ( ( ! [SY385: $i] :
~ ( path @ SV176 @ SY385 @ SV124 ) )
= $true )
| ( ( triangle @ ( sK7_E1 @ SV124 ) @ ( sK8_SY86 @ SV124 ) @ SV165 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV124 )
= ( number_of_in @ triangles @ SV124 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(868,plain,
! [SV140: $i,SV135: $i,SV125: $i] :
( ( ( ~ ! [SY359: $i] :
( ( SV125
!= ( tail_of @ SY359 ) )
| ~ ( edge @ SY359 )
| ( SV135
!= ( head_of @ SY359 ) )
| ( SV140
!= ( path_cons @ SY359 @ empty ) ) )
| ~ ! [SY360: $i] :
( ( SV125
!= ( tail_of @ SY360 ) )
| ~ ( edge @ SY360 )
| ! [SY361: $i] :
( ( SV140
!= ( path_cons @ SY360 @ SY361 ) )
| ~ ( path @ ( head_of @ SY360 ) @ SV135 @ SY361 ) ) ) )
= $false )
| ( ( vertex @ SV125 )
= $false )
| ( ( vertex @ SV135 )
= $false )
| ( ( path @ SV125 @ SV135 @ SV140 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[838]) ).
thf(869,plain,
! [SV158: $i,SV152: $i,SV126: $i] :
( ( ( ~ ( edge @ SV126 )
| ~ ( edge @ SV152 )
| ~ ( edge @ SV158 )
| ~ ( sequential @ SV126 @ SV152 ) )
= $true )
| ( ( ~ ( sequential @ SV152 @ SV158 ) )
= $true )
| ( ( ~ ( sequential @ SV158 @ SV126 ) )
= $true )
| ( ( triangle @ SV126 @ SV152 @ SV158 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[839]) ).
thf(870,plain,
! [SV126: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY301: $i,SY302: $i] :
~ ( triangle @ SV126 @ SY301 @ SY302 )
| ( edge @ SV126 ) )
| ~ ! [SY303: $i] :
( ! [SY304: $i] :
~ ( triangle @ SV126 @ SY303 @ SY304 )
| ( edge @ SY303 ) ) )
| ~ ! [SY305: $i,SY306: $i] :
( ~ ( triangle @ SV126 @ SY305 @ SY306 )
| ( edge @ SY306 ) ) )
| ~ ! [SY307: $i] :
( ! [SY308: $i] :
~ ( triangle @ SV126 @ SY307 @ SY308 )
| ( sequential @ SV126 @ SY307 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[840]) ).
thf(871,plain,
! [SV126: $i] :
( ( ~ ! [SY309: $i,SY310: $i] :
( ~ ( triangle @ SV126 @ SY309 @ SY310 )
| ( sequential @ SY309 @ SY310 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[840]) ).
thf(872,plain,
! [SV177: $i,SV170: $i,SV126: $i] :
( ( ~ ( triangle @ SV126 @ SV170 @ SV177 )
| ( sequential @ SV177 @ SV126 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[841]) ).
thf(873,plain,
! [SV145: $i,SV141: $i,SV127: $i] :
( ( ( ~ ! [SY315: $i] :
( ! [SY316: $i] :
~ ( precedes @ SY315 @ SY316 @ SV127 )
| ( on_path @ SY315 @ SV127 ) )
| ~ ! [SY317: $i,SY318: $i] :
( ~ ( precedes @ SY317 @ SY318 @ SV127 )
| ( on_path @ SY318 @ SV127 ) ) )
= $false )
| ( ( path @ SV141 @ SV145 @ SV127 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[842]) ).
thf(874,plain,
! [SV145: $i,SV141: $i,SV127: $i] :
( ( ( ~ ! [SY319: $i,SY320: $i] :
( ~ ( precedes @ SY319 @ SY320 @ SV127 )
| ! [SY321: $i] :
( ~ ( precedes @ SY321 @ SY320 @ SV127 )
| ~ ( sequential @ SY319 @ SY321 ) )
| ~ ( sequential @ SY319 @ SY320 ) )
| ~ ! [SY322: $i,SY323: $i] :
( ~ ( precedes @ SY322 @ SY323 @ SV127 )
| ~ ( ~ ( precedes @ ( sK10_E3 @ SY323 @ SY322 @ SV127 ) @ SY323 @ SV127 )
| ~ ( sequential @ SY322 @ ( sK10_E3 @ SY323 @ SY322 @ SV127 ) ) )
| ( sequential @ SY322 @ SY323 ) ) )
= $false )
| ( ( path @ SV141 @ SV145 @ SV127 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[843]) ).
thf(875,plain,
! [SV148: $i,SV142: $i,SV128: $i,SV178: $i] :
( ( ( ! [SY386: $i] :
( ~ ( on_path @ SV178 @ SV128 )
| ~ ( on_path @ SY386 @ SV128 )
| ! [SY387: $i] :
( ~ ( precedes @ SY387 @ SY386 @ SV128 )
| ~ ( sequential @ SV178 @ SY387 ) )
| ( precedes @ SV178 @ SY386 @ SV128 ) ) )
= $true )
| ( ( path @ SV142 @ SV148 @ SV128 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[844]) ).
thf(876,plain,
! [SV148: $i,SV142: $i,SV128: $i,SV179: $i] :
( ( ( ! [SY388: $i] :
( ~ ( on_path @ SV179 @ SV128 )
| ~ ( on_path @ SY388 @ SV128 )
| ~ ( sequential @ SV179 @ SY388 )
| ( precedes @ SV179 @ SY388 @ SV128 ) ) )
= $true )
| ( ( path @ SV142 @ SV148 @ SV128 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(877,plain,
! [SV180: $i,SV171: $i,SV119: $i] :
( ( ( ~ ( path @ SV119 @ SV171 @ SV180 ) )
= $true )
| ( ( vertex @ SV119 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[846]) ).
thf(878,plain,
! [SV181: $i,SV166: $i,SV119: $i] :
( ( ( ~ ( path @ SV119 @ SV166 @ SV181 ) )
= $true )
| ( ( vertex @ SV166 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(879,plain,
! [SV149: $i,SV153: $i,SV119: $i] :
( ( ( ~ ~ ( ( SV119
!= ( tail_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( edge @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) ) )
= $false )
| ( ( path @ SV119 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[848]) ).
thf(880,plain,
! [SV119: $i,SV153: $i,SV149: $i] :
( ( ( ~ ~ ( ~ ( ( SV149
!= ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
| ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ empty ) )
| ! [SY369: $i] :
( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ SY369 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ SY369 ) ) )
| ~ ~ ( ~ ( ( SV149
= ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ ( sK14_SY90 @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ ( sK14_SY90 @ SV153 @ SV149 @ SV119 ) ) ) )
| ~ ( ( SV153
= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ empty ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ ( sK13_SY91 @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ ( sK13_SY91 @ SV153 @ SV149 @ SV119 ) ) ) ) ) ) )
= $false )
| ( ( path @ SV119 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[848]) ).
thf(881,plain,
! [SV132: $i,SV120: $i,SV154: $i,SV159: $i] :
( ( ( in_path @ SV159 @ SV154 )
= $false )
| ( ( ~ ( path @ SV120 @ SV132 @ SV154 ) )
= $true )
| ( ( ~ ( ~ ( on_path @ ( sK11_E @ SV159 @ SV154 @ SV132 @ SV120 ) @ SV154 )
| ~ ( ( SV159
= ( head_of @ ( sK11_E @ SV159 @ SV154 @ SV132 @ SV120 ) ) )
| ( SV159
= ( tail_of @ ( sK11_E @ SV159 @ SV154 @ SV132 @ SV120 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[849]) ).
thf(882,plain,
! [SV132: $i,SV120: $i,SV155: $i,SV160: $i] :
( ( ( in_path @ SV160 @ SV155 )
= $false )
| ( ( ~ ( path @ SV120 @ SV132 @ SV155 ) )
= $true )
| ( ( vertex @ SV160 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[850]) ).
thf(883,plain,
! [SV150: $i,SV143: $i] :
( ( ( edge @ SV143 )
= $false )
| ( ( ~ ( edge @ SV150 ) )
= $true )
| ( ( SV143 = SV150 )
= $true )
| ( ( ( ( head_of @ SV143 )
!= ( tail_of @ SV150 ) ) )
= $true )
| ( ( sequential @ SV143 @ SV150 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[851]) ).
thf(884,plain,
! [SV182: $i] :
( ( ! [SY389: $i] :
( ~ ( sequential @ SV182 @ SY389 )
| ( SV182 != SY389 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[852]) ).
thf(885,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)],[853]) ).
thf(886,plain,
! [SV167: $i,SV161: $i] :
( ( ( sequential @ SV161 @ SV167 )
= $false )
| ( ( ( head_of @ SV161 )
= ( tail_of @ SV167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[854]) ).
thf(887,plain,
! [SV133: $i,SV121: $i,SV172: $i,SV183: $i] :
( ( ~ ( on_path @ SV183 @ SV172 )
| ~ ( path @ SV121 @ SV133 @ SV172 )
| ( edge @ SV183 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(888,plain,
! [SV133: $i,SV121: $i,SV173: $i,SV184: $i] :
( ( ~ ( on_path @ SV184 @ SV173 )
| ~ ( path @ SV121 @ SV133 @ SV173 )
| ( in_path @ ( head_of @ SV184 ) @ SV173 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[856]) ).
thf(889,plain,
! [SV133: $i,SV121: $i,SV156: $i,SV162: $i] :
( ( ( on_path @ SV162 @ SV156 )
= $false )
| ( ( ~ ( path @ SV121 @ SV133 @ SV156 ) )
= $true )
| ( ( in_path @ ( tail_of @ SV162 ) @ SV156 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[857]) ).
thf(890,plain,
! [SV157: $i,SV151: $i,SV122: $i] :
( ( ( ~ ( path @ SV122 @ SV151 @ ( sK9_P @ SV157 @ SV151 @ SV122 ) ) )
= $false )
| ( ( ( SV122 = SV151 )
| ~ ( path @ SV122 @ SV151 @ SV157 ) )
= $true )
| ( ( shortest_path @ SV122 @ SV151 @ SV157 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[858]) ).
thf(891,plain,
! [SV122: $i,SV151: $i,SV157: $i] :
( ( ( ~ ~ ( less_or_equal @ ( length_of @ SV157 ) @ ( length_of @ ( sK9_P @ SV157 @ SV151 @ SV122 ) ) ) )
= $false )
| ( ( ( SV122 = SV151 )
| ~ ( path @ SV122 @ SV151 @ SV157 ) )
= $true )
| ( ( shortest_path @ SV122 @ SV151 @ SV157 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[858]) ).
thf(892,plain,
! [SV174: $i,SV168: $i,SV122: $i] :
( ( ( ~ ( shortest_path @ SV122 @ SV168 @ SV174 ) )
= $true )
| ( ( ! [SY384: $i] :
( ~ ( path @ SV122 @ SV168 @ SY384 )
| ( less_or_equal @ ( length_of @ SV174 ) @ ( length_of @ SY384 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[859]) ).
thf(893,plain,
! [SV122: $i] :
( ( ! [SY280: $i] :
( ! [SY281: $i] :
~ ( shortest_path @ SV122 @ SY280 @ SY281 )
| ( SV122 != SY280 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[860]) ).
thf(894,plain,
! [SV122: $i] :
( ( ! [SY282: $i,SY283: $i] :
( ~ ( shortest_path @ SV122 @ SY282 @ SY283 )
| ( path @ SV122 @ SY282 @ SY283 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[861]) ).
thf(895,plain,
! [SV134: $i,SV123: $i,SV175: $i,SV163: $i,SV138: $i] :
( ( ( ~ ( precedes @ SV138 @ SV163 @ SV175 ) )
= $true )
| ( ( ~ ( shortest_path @ SV123 @ SV134 @ SV175 ) )
= $true )
| ( ( ! [SY375: $i] :
( ( ( tail_of @ SY375 )
!= ( tail_of @ SV138 ) )
| ( ( head_of @ SY375 )
!= ( head_of @ SV163 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[862]) ).
thf(896,plain,
! [SV134: $i,SV123: $i,SV169: $i,SV164: $i,SV138: $i] :
( ( ( ~ ( precedes @ SV138 @ SV164 @ SV169 ) )
= $true )
| ( ( ~ ( shortest_path @ SV123 @ SV134 @ SV169 ) )
= $true )
| ( ( ~ ( precedes @ SV164 @ SV138 @ SV169 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[863]) ).
thf(897,plain,
! [SV144: $i,SV139: $i] :
( ( ( ~ ~ ( ~ ( ( SV139
!= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
!= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
!= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
!= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV139
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
| ~ ( ( SV139
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) ) )
| ~ ~ ( ~ ( ( SV144
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
| ~ ( ( SV144
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) ) ) ) )
| ~ ( edge @ ( sK15_E @ SV144 @ SV139 ) ) )
= $false )
| ( ( SV139 = SV144 )
= $true )
| ( ( vertex @ SV139 )
= $false )
| ( ( vertex @ SV144 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[864]) ).
thf(898,plain,
! [SV124: $i] :
( ( ( ~ ( on_path @ ( sK7_E1 @ SV124 ) @ SV124 )
| ~ ( on_path @ ( sK8_SY86 @ SV124 ) @ SV124 ) )
= $false )
| ( ( ! [SY292: $i,SY293: $i] :
~ ( path @ SY292 @ SY293 @ SV124 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV124 )
= ( number_of_in @ triangles @ SV124 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[865]) ).
thf(899,plain,
! [SV124: $i,SV185: $i] :
( ( ( ! [SY390: $i] :
~ ( path @ SV185 @ SY390 @ SV124 ) )
= $true )
| ( ( sequential @ ( sK7_E1 @ SV124 ) @ ( sK8_SY86 @ SV124 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV124 )
= ( number_of_in @ triangles @ SV124 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[866]) ).
thf(900,plain,
! [SV165: $i,SV124: $i,SV186: $i,SV176: $i] :
( ( ( ~ ( path @ SV176 @ SV186 @ SV124 ) )
= $true )
| ( ( triangle @ ( sK7_E1 @ SV124 ) @ ( sK8_SY86 @ SV124 ) @ SV165 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV124 )
= ( number_of_in @ triangles @ SV124 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[867]) ).
thf(901,plain,
! [SV140: $i,SV135: $i,SV125: $i] :
( ( ( ~ ! [SY359: $i] :
( ( SV125
!= ( tail_of @ SY359 ) )
| ~ ( edge @ SY359 )
| ( SV135
!= ( head_of @ SY359 ) )
| ( SV140
!= ( path_cons @ SY359 @ empty ) ) ) )
= $false )
| ( ( vertex @ SV125 )
= $false )
| ( ( vertex @ SV135 )
= $false )
| ( ( path @ SV125 @ SV135 @ SV140 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[868]) ).
thf(902,plain,
! [SV135: $i,SV140: $i,SV125: $i] :
( ( ( ~ ! [SY360: $i] :
( ( SV125
!= ( tail_of @ SY360 ) )
| ~ ( edge @ SY360 )
| ! [SY361: $i] :
( ( SV140
!= ( path_cons @ SY360 @ SY361 ) )
| ~ ( path @ ( head_of @ SY360 ) @ SV135 @ SY361 ) ) ) )
= $false )
| ( ( vertex @ SV125 )
= $false )
| ( ( vertex @ SV135 )
= $false )
| ( ( path @ SV125 @ SV135 @ SV140 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[868]) ).
thf(903,plain,
! [SV158: $i,SV152: $i,SV126: $i] :
( ( ( ~ ( edge @ SV126 )
| ~ ( edge @ SV152 )
| ~ ( edge @ SV158 ) )
= $true )
| ( ( ~ ( sequential @ SV126 @ SV152 ) )
= $true )
| ( ( ~ ( sequential @ SV152 @ SV158 ) )
= $true )
| ( ( ~ ( sequential @ SV158 @ SV126 ) )
= $true )
| ( ( triangle @ SV126 @ SV152 @ SV158 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[869]) ).
thf(904,plain,
! [SV126: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY301: $i,SY302: $i] :
~ ( triangle @ SV126 @ SY301 @ SY302 )
| ( edge @ SV126 ) )
| ~ ! [SY303: $i] :
( ! [SY304: $i] :
~ ( triangle @ SV126 @ SY303 @ SY304 )
| ( edge @ SY303 ) ) )
| ~ ! [SY305: $i,SY306: $i] :
( ~ ( triangle @ SV126 @ SY305 @ SY306 )
| ( edge @ SY306 ) ) )
| ~ ! [SY307: $i] :
( ! [SY308: $i] :
~ ( triangle @ SV126 @ SY307 @ SY308 )
| ( sequential @ SV126 @ SY307 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[870]) ).
thf(905,plain,
! [SV126: $i] :
( ( ! [SY309: $i,SY310: $i] :
( ~ ( triangle @ SV126 @ SY309 @ SY310 )
| ( sequential @ SY309 @ SY310 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[871]) ).
thf(906,plain,
! [SV177: $i,SV170: $i,SV126: $i] :
( ( ( ~ ( triangle @ SV126 @ SV170 @ SV177 ) )
= $true )
| ( ( sequential @ SV177 @ SV126 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[872]) ).
thf(907,plain,
! [SV145: $i,SV141: $i,SV127: $i] :
( ( ( ~ ! [SY315: $i] :
( ! [SY316: $i] :
~ ( precedes @ SY315 @ SY316 @ SV127 )
| ( on_path @ SY315 @ SV127 ) ) )
= $false )
| ( ( path @ SV141 @ SV145 @ SV127 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[873]) ).
thf(908,plain,
! [SV145: $i,SV141: $i,SV127: $i] :
( ( ( ~ ! [SY317: $i,SY318: $i] :
( ~ ( precedes @ SY317 @ SY318 @ SV127 )
| ( on_path @ SY318 @ SV127 ) ) )
= $false )
| ( ( path @ SV141 @ SV145 @ SV127 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[873]) ).
thf(909,plain,
! [SV145: $i,SV141: $i,SV127: $i] :
( ( ( ~ ! [SY319: $i,SY320: $i] :
( ~ ( precedes @ SY319 @ SY320 @ SV127 )
| ! [SY321: $i] :
( ~ ( precedes @ SY321 @ SY320 @ SV127 )
| ~ ( sequential @ SY319 @ SY321 ) )
| ~ ( sequential @ SY319 @ SY320 ) ) )
= $false )
| ( ( path @ SV141 @ SV145 @ SV127 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[874]) ).
thf(910,plain,
! [SV145: $i,SV141: $i,SV127: $i] :
( ( ( ~ ! [SY322: $i,SY323: $i] :
( ~ ( precedes @ SY322 @ SY323 @ SV127 )
| ~ ( ~ ( precedes @ ( sK10_E3 @ SY323 @ SY322 @ SV127 ) @ SY323 @ SV127 )
| ~ ( sequential @ SY322 @ ( sK10_E3 @ SY323 @ SY322 @ SV127 ) ) )
| ( sequential @ SY322 @ SY323 ) ) )
= $false )
| ( ( path @ SV141 @ SV145 @ SV127 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[874]) ).
thf(911,plain,
! [SV148: $i,SV142: $i,SV187: $i,SV128: $i,SV178: $i] :
( ( ( ~ ( on_path @ SV178 @ SV128 )
| ~ ( on_path @ SV187 @ SV128 )
| ! [SY391: $i] :
( ~ ( precedes @ SY391 @ SV187 @ SV128 )
| ~ ( sequential @ SV178 @ SY391 ) )
| ( precedes @ SV178 @ SV187 @ SV128 ) )
= $true )
| ( ( path @ SV142 @ SV148 @ SV128 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[875]) ).
thf(912,plain,
! [SV148: $i,SV142: $i,SV188: $i,SV128: $i,SV179: $i] :
( ( ( ~ ( on_path @ SV179 @ SV128 )
| ~ ( on_path @ SV188 @ SV128 )
| ~ ( sequential @ SV179 @ SV188 )
| ( precedes @ SV179 @ SV188 @ SV128 ) )
= $true )
| ( ( path @ SV142 @ SV148 @ SV128 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[876]) ).
thf(913,plain,
! [SV180: $i,SV171: $i,SV119: $i] :
( ( ( path @ SV119 @ SV171 @ SV180 )
= $false )
| ( ( vertex @ SV119 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[877]) ).
thf(914,plain,
! [SV181: $i,SV166: $i,SV119: $i] :
( ( ( path @ SV119 @ SV166 @ SV181 )
= $false )
| ( ( vertex @ SV166 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[878]) ).
thf(915,plain,
! [SV149: $i,SV153: $i,SV119: $i] :
( ( ( ~ ( ( SV119
!= ( tail_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( edge @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) ) )
= $true )
| ( ( path @ SV119 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[879]) ).
thf(916,plain,
! [SV119: $i,SV153: $i,SV149: $i] :
( ( ( ~ ( ~ ( ( SV149
!= ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
| ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ empty ) )
| ! [SY369: $i] :
( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ SY369 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ SY369 ) ) )
| ~ ~ ( ~ ( ( SV149
= ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ ( sK14_SY90 @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ ( sK14_SY90 @ SV153 @ SV149 @ SV119 ) ) ) )
| ~ ( ( SV153
= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ empty ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ ( sK13_SY91 @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ ( sK13_SY91 @ SV153 @ SV149 @ SV119 ) ) ) ) ) ) )
= $true )
| ( ( path @ SV119 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[880]) ).
thf(917,plain,
! [SV159: $i,SV154: $i,SV132: $i,SV120: $i] :
( ( ( path @ SV120 @ SV132 @ SV154 )
= $false )
| ( ( in_path @ SV159 @ SV154 )
= $false )
| ( ( ~ ( ~ ( on_path @ ( sK11_E @ SV159 @ SV154 @ SV132 @ SV120 ) @ SV154 )
| ~ ( ( SV159
= ( head_of @ ( sK11_E @ SV159 @ SV154 @ SV132 @ SV120 ) ) )
| ( SV159
= ( tail_of @ ( sK11_E @ SV159 @ SV154 @ SV132 @ SV120 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[881]) ).
thf(918,plain,
! [SV160: $i,SV155: $i,SV132: $i,SV120: $i] :
( ( ( path @ SV120 @ SV132 @ SV155 )
= $false )
| ( ( in_path @ SV160 @ SV155 )
= $false )
| ( ( vertex @ SV160 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[882]) ).
thf(919,plain,
! [SV143: $i,SV150: $i] :
( ( ( edge @ SV150 )
= $false )
| ( ( edge @ SV143 )
= $false )
| ( ( SV143 = SV150 )
= $true )
| ( ( ( ( head_of @ SV143 )
!= ( tail_of @ SV150 ) ) )
= $true )
| ( ( sequential @ SV143 @ SV150 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[883]) ).
thf(920,plain,
! [SV189: $i,SV182: $i] :
( ( ~ ( sequential @ SV182 @ SV189 )
| ( SV182 != SV189 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[884]) ).
thf(921,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[885]) ).
thf(922,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[885]) ).
thf(923,plain,
! [SV133: $i,SV121: $i,SV172: $i,SV183: $i] :
( ( ( ~ ( on_path @ SV183 @ SV172 )
| ~ ( path @ SV121 @ SV133 @ SV172 ) )
= $true )
| ( ( edge @ SV183 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[887]) ).
thf(924,plain,
! [SV133: $i,SV121: $i,SV173: $i,SV184: $i] :
( ( ( ~ ( on_path @ SV184 @ SV173 )
| ~ ( path @ SV121 @ SV133 @ SV173 ) )
= $true )
| ( ( in_path @ ( head_of @ SV184 ) @ SV173 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[888]) ).
thf(925,plain,
! [SV162: $i,SV156: $i,SV133: $i,SV121: $i] :
( ( ( path @ SV121 @ SV133 @ SV156 )
= $false )
| ( ( on_path @ SV162 @ SV156 )
= $false )
| ( ( in_path @ ( tail_of @ SV162 ) @ SV156 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[889]) ).
thf(926,plain,
! [SV157: $i,SV151: $i,SV122: $i] :
( ( ( path @ SV122 @ SV151 @ ( sK9_P @ SV157 @ SV151 @ SV122 ) )
= $true )
| ( ( ( SV122 = SV151 )
| ~ ( path @ SV122 @ SV151 @ SV157 ) )
= $true )
| ( ( shortest_path @ SV122 @ SV151 @ SV157 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[890]) ).
thf(927,plain,
! [SV122: $i,SV151: $i,SV157: $i] :
( ( ( ~ ( less_or_equal @ ( length_of @ SV157 ) @ ( length_of @ ( sK9_P @ SV157 @ SV151 @ SV122 ) ) ) )
= $true )
| ( ( ( SV122 = SV151 )
| ~ ( path @ SV122 @ SV151 @ SV157 ) )
= $true )
| ( ( shortest_path @ SV122 @ SV151 @ SV157 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[891]) ).
thf(928,plain,
! [SV174: $i,SV168: $i,SV122: $i] :
( ( ( shortest_path @ SV122 @ SV168 @ SV174 )
= $false )
| ( ( ! [SY384: $i] :
( ~ ( path @ SV122 @ SV168 @ SY384 )
| ( less_or_equal @ ( length_of @ SV174 ) @ ( length_of @ SY384 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[892]) ).
thf(929,plain,
! [SV190: $i,SV122: $i] :
( ( ! [SY392: $i] :
~ ( shortest_path @ SV122 @ SV190 @ SY392 )
| ( SV122 != SV190 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[893]) ).
thf(930,plain,
! [SV191: $i,SV122: $i] :
( ( ! [SY393: $i] :
( ~ ( shortest_path @ SV122 @ SV191 @ SY393 )
| ( path @ SV122 @ SV191 @ SY393 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[894]) ).
thf(931,plain,
! [SV134: $i,SV123: $i,SV175: $i,SV163: $i,SV138: $i] :
( ( ( precedes @ SV138 @ SV163 @ SV175 )
= $false )
| ( ( ~ ( shortest_path @ SV123 @ SV134 @ SV175 ) )
= $true )
| ( ( ! [SY375: $i] :
( ( ( tail_of @ SY375 )
!= ( tail_of @ SV138 ) )
| ( ( head_of @ SY375 )
!= ( head_of @ SV163 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[895]) ).
thf(932,plain,
! [SV134: $i,SV123: $i,SV169: $i,SV164: $i,SV138: $i] :
( ( ( precedes @ SV138 @ SV164 @ SV169 )
= $false )
| ( ( ~ ( shortest_path @ SV123 @ SV134 @ SV169 ) )
= $true )
| ( ( ~ ( precedes @ SV164 @ SV138 @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[896]) ).
thf(933,plain,
! [SV144: $i,SV139: $i] :
( ( ( ~ ~ ( ~ ( ( SV139
!= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
!= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
!= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
!= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV139
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
| ~ ( ( SV139
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) ) )
| ~ ~ ( ~ ( ( SV144
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
| ~ ( ( SV144
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) ) ) ) ) )
= $false )
| ( ( SV139 = SV144 )
= $true )
| ( ( vertex @ SV139 )
= $false )
| ( ( vertex @ SV144 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[897]) ).
thf(934,plain,
! [SV139: $i,SV144: $i] :
( ( ( ~ ( edge @ ( sK15_E @ SV144 @ SV139 ) ) )
= $false )
| ( ( SV139 = SV144 )
= $true )
| ( ( vertex @ SV139 )
= $false )
| ( ( vertex @ SV144 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[897]) ).
thf(935,plain,
! [SV124: $i] :
( ( ( ~ ( on_path @ ( sK7_E1 @ SV124 ) @ SV124 ) )
= $false )
| ( ( ! [SY292: $i,SY293: $i] :
~ ( path @ SY292 @ SY293 @ SV124 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV124 )
= ( number_of_in @ triangles @ SV124 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[898]) ).
thf(936,plain,
! [SV124: $i] :
( ( ( ~ ( on_path @ ( sK8_SY86 @ SV124 ) @ SV124 ) )
= $false )
| ( ( ! [SY292: $i,SY293: $i] :
~ ( path @ SY292 @ SY293 @ SV124 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV124 )
= ( number_of_in @ triangles @ SV124 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[898]) ).
thf(937,plain,
! [SV124: $i,SV192: $i,SV185: $i] :
( ( ( ~ ( path @ SV185 @ SV192 @ SV124 ) )
= $true )
| ( ( sequential @ ( sK7_E1 @ SV124 ) @ ( sK8_SY86 @ SV124 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV124 )
= ( number_of_in @ triangles @ SV124 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[899]) ).
thf(938,plain,
! [SV165: $i,SV124: $i,SV186: $i,SV176: $i] :
( ( ( path @ SV176 @ SV186 @ SV124 )
= $false )
| ( ( triangle @ ( sK7_E1 @ SV124 ) @ ( sK8_SY86 @ SV124 ) @ SV165 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV124 )
= ( number_of_in @ triangles @ SV124 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[900]) ).
thf(939,plain,
! [SV140: $i,SV135: $i,SV125: $i] :
( ( ( ! [SY359: $i] :
( ( SV125
!= ( tail_of @ SY359 ) )
| ~ ( edge @ SY359 )
| ( SV135
!= ( head_of @ SY359 ) )
| ( SV140
!= ( path_cons @ SY359 @ empty ) ) ) )
= $true )
| ( ( vertex @ SV125 )
= $false )
| ( ( vertex @ SV135 )
= $false )
| ( ( path @ SV125 @ SV135 @ SV140 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[901]) ).
thf(940,plain,
! [SV135: $i,SV140: $i,SV125: $i] :
( ( ( ! [SY360: $i] :
( ( SV125
!= ( tail_of @ SY360 ) )
| ~ ( edge @ SY360 )
| ! [SY361: $i] :
( ( SV140
!= ( path_cons @ SY360 @ SY361 ) )
| ~ ( path @ ( head_of @ SY360 ) @ SV135 @ SY361 ) ) ) )
= $true )
| ( ( vertex @ SV125 )
= $false )
| ( ( vertex @ SV135 )
= $false )
| ( ( path @ SV125 @ SV135 @ SV140 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[902]) ).
thf(941,plain,
! [SV158: $i,SV152: $i,SV126: $i] :
( ( ( ~ ( edge @ SV126 )
| ~ ( edge @ SV152 ) )
= $true )
| ( ( ~ ( edge @ SV158 ) )
= $true )
| ( ( ~ ( sequential @ SV126 @ SV152 ) )
= $true )
| ( ( ~ ( sequential @ SV152 @ SV158 ) )
= $true )
| ( ( ~ ( sequential @ SV158 @ SV126 ) )
= $true )
| ( ( triangle @ SV126 @ SV152 @ SV158 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[903]) ).
thf(942,plain,
! [SV126: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( ! [SY301: $i,SY302: $i] :
~ ( triangle @ SV126 @ SY301 @ SY302 )
| ( edge @ SV126 ) )
| ~ ! [SY303: $i] :
( ! [SY304: $i] :
~ ( triangle @ SV126 @ SY303 @ SY304 )
| ( edge @ SY303 ) ) )
| ~ ! [SY305: $i,SY306: $i] :
( ~ ( triangle @ SV126 @ SY305 @ SY306 )
| ( edge @ SY306 ) ) )
| ~ ! [SY307: $i] :
( ! [SY308: $i] :
~ ( triangle @ SV126 @ SY307 @ SY308 )
| ( sequential @ SV126 @ SY307 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[904]) ).
thf(943,plain,
! [SV193: $i,SV126: $i] :
( ( ! [SY394: $i] :
( ~ ( triangle @ SV126 @ SV193 @ SY394 )
| ( sequential @ SV193 @ SY394 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[905]) ).
thf(944,plain,
! [SV177: $i,SV170: $i,SV126: $i] :
( ( ( triangle @ SV126 @ SV170 @ SV177 )
= $false )
| ( ( sequential @ SV177 @ SV126 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[906]) ).
thf(945,plain,
! [SV145: $i,SV141: $i,SV127: $i] :
( ( ( ! [SY315: $i] :
( ! [SY316: $i] :
~ ( precedes @ SY315 @ SY316 @ SV127 )
| ( on_path @ SY315 @ SV127 ) ) )
= $true )
| ( ( path @ SV141 @ SV145 @ SV127 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[907]) ).
thf(946,plain,
! [SV145: $i,SV141: $i,SV127: $i] :
( ( ( ! [SY317: $i,SY318: $i] :
( ~ ( precedes @ SY317 @ SY318 @ SV127 )
| ( on_path @ SY318 @ SV127 ) ) )
= $true )
| ( ( path @ SV141 @ SV145 @ SV127 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[908]) ).
thf(947,plain,
! [SV145: $i,SV141: $i,SV127: $i] :
( ( ( ! [SY319: $i,SY320: $i] :
( ~ ( precedes @ SY319 @ SY320 @ SV127 )
| ! [SY321: $i] :
( ~ ( precedes @ SY321 @ SY320 @ SV127 )
| ~ ( sequential @ SY319 @ SY321 ) )
| ~ ( sequential @ SY319 @ SY320 ) ) )
= $true )
| ( ( path @ SV141 @ SV145 @ SV127 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[909]) ).
thf(948,plain,
! [SV145: $i,SV141: $i,SV127: $i] :
( ( ( ! [SY322: $i,SY323: $i] :
( ~ ( precedes @ SY322 @ SY323 @ SV127 )
| ~ ( ~ ( precedes @ ( sK10_E3 @ SY323 @ SY322 @ SV127 ) @ SY323 @ SV127 )
| ~ ( sequential @ SY322 @ ( sK10_E3 @ SY323 @ SY322 @ SV127 ) ) )
| ( sequential @ SY322 @ SY323 ) ) )
= $true )
| ( ( path @ SV141 @ SV145 @ SV127 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[910]) ).
thf(949,plain,
! [SV148: $i,SV142: $i,SV187: $i,SV128: $i,SV178: $i] :
( ( ( ~ ( on_path @ SV178 @ SV128 )
| ~ ( on_path @ SV187 @ SV128 )
| ! [SY391: $i] :
( ~ ( precedes @ SY391 @ SV187 @ SV128 )
| ~ ( sequential @ SV178 @ SY391 ) ) )
= $true )
| ( ( precedes @ SV178 @ SV187 @ SV128 )
= $true )
| ( ( path @ SV142 @ SV148 @ SV128 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[911]) ).
thf(950,plain,
! [SV148: $i,SV142: $i,SV188: $i,SV128: $i,SV179: $i] :
( ( ( ~ ( on_path @ SV179 @ SV128 )
| ~ ( on_path @ SV188 @ SV128 )
| ~ ( sequential @ SV179 @ SV188 ) )
= $true )
| ( ( precedes @ SV179 @ SV188 @ SV128 )
= $true )
| ( ( path @ SV142 @ SV148 @ SV128 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[912]) ).
thf(951,plain,
! [SV149: $i,SV153: $i,SV119: $i] :
( ( ( ( SV119
!= ( tail_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( edge @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
= $false )
| ( ( path @ SV119 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[915]) ).
thf(952,plain,
! [SV119: $i,SV153: $i,SV149: $i] :
( ( ( ~ ( ( SV149
!= ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
| ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ empty ) )
| ! [SY369: $i] :
( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ SY369 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ SY369 ) ) )
| ~ ~ ( ~ ( ( SV149
= ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ ( sK14_SY90 @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ ( sK14_SY90 @ SV153 @ SV149 @ SV119 ) ) ) )
| ~ ( ( SV153
= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ empty ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ ( sK13_SY91 @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ ( sK13_SY91 @ SV153 @ SV149 @ SV119 ) ) ) ) ) )
= $false )
| ( ( path @ SV119 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[916]) ).
thf(953,plain,
! [SV120: $i,SV132: $i,SV154: $i,SV159: $i] :
( ( ( ~ ( on_path @ ( sK11_E @ SV159 @ SV154 @ SV132 @ SV120 ) @ SV154 )
| ~ ( ( SV159
= ( head_of @ ( sK11_E @ SV159 @ SV154 @ SV132 @ SV120 ) ) )
| ( SV159
= ( tail_of @ ( sK11_E @ SV159 @ SV154 @ SV132 @ SV120 ) ) ) ) )
= $false )
| ( ( in_path @ SV159 @ SV154 )
= $false )
| ( ( path @ SV120 @ SV132 @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[917]) ).
thf(954,plain,
! [SV150: $i,SV143: $i] :
( ( ( ( head_of @ SV143 )
= ( tail_of @ SV150 ) )
= $false )
| ( ( SV143 = SV150 )
= $true )
| ( ( edge @ SV143 )
= $false )
| ( ( edge @ SV150 )
= $false )
| ( ( sequential @ SV143 @ SV150 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[919]) ).
thf(955,plain,
! [SV189: $i,SV182: $i] :
( ( ( ~ ( sequential @ SV182 @ SV189 ) )
= $true )
| ( ( ( SV182 != SV189 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[920]) ).
thf(956,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[921]) ).
thf(957,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[922]) ).
thf(958,plain,
! [SV133: $i,SV121: $i,SV172: $i,SV183: $i] :
( ( ( ~ ( on_path @ SV183 @ SV172 ) )
= $true )
| ( ( ~ ( path @ SV121 @ SV133 @ SV172 ) )
= $true )
| ( ( edge @ SV183 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[923]) ).
thf(959,plain,
! [SV133: $i,SV121: $i,SV173: $i,SV184: $i] :
( ( ( ~ ( on_path @ SV184 @ SV173 ) )
= $true )
| ( ( ~ ( path @ SV121 @ SV133 @ SV173 ) )
= $true )
| ( ( in_path @ ( head_of @ SV184 ) @ SV173 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[924]) ).
thf(960,plain,
! [SV157: $i,SV151: $i,SV122: $i] :
( ( ( SV122 = SV151 )
= $true )
| ( ( ~ ( path @ SV122 @ SV151 @ SV157 ) )
= $true )
| ( ( path @ SV122 @ SV151 @ ( sK9_P @ SV157 @ SV151 @ SV122 ) )
= $true )
| ( ( shortest_path @ SV122 @ SV151 @ SV157 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[926]) ).
thf(961,plain,
! [SV122: $i,SV151: $i,SV157: $i] :
( ( ( less_or_equal @ ( length_of @ SV157 ) @ ( length_of @ ( sK9_P @ SV157 @ SV151 @ SV122 ) ) )
= $false )
| ( ( ( SV122 = SV151 )
| ~ ( path @ SV122 @ SV151 @ SV157 ) )
= $true )
| ( ( shortest_path @ SV122 @ SV151 @ SV157 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[927]) ).
thf(962,plain,
! [SV174: $i,SV194: $i,SV168: $i,SV122: $i] :
( ( ( ~ ( path @ SV122 @ SV168 @ SV194 )
| ( less_or_equal @ ( length_of @ SV174 ) @ ( length_of @ SV194 ) ) )
= $true )
| ( ( shortest_path @ SV122 @ SV168 @ SV174 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[928]) ).
thf(963,plain,
! [SV190: $i,SV122: $i] :
( ( ( ! [SY392: $i] :
~ ( shortest_path @ SV122 @ SV190 @ SY392 ) )
= $true )
| ( ( ( SV122 != SV190 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[929]) ).
thf(964,plain,
! [SV195: $i,SV191: $i,SV122: $i] :
( ( ~ ( shortest_path @ SV122 @ SV191 @ SV195 )
| ( path @ SV122 @ SV191 @ SV195 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[930]) ).
thf(965,plain,
! [SV163: $i,SV138: $i,SV175: $i,SV134: $i,SV123: $i] :
( ( ( shortest_path @ SV123 @ SV134 @ SV175 )
= $false )
| ( ( precedes @ SV138 @ SV163 @ SV175 )
= $false )
| ( ( ! [SY375: $i] :
( ( ( tail_of @ SY375 )
!= ( tail_of @ SV138 ) )
| ( ( head_of @ SY375 )
!= ( head_of @ SV163 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[931]) ).
thf(966,plain,
! [SV164: $i,SV138: $i,SV169: $i,SV134: $i,SV123: $i] :
( ( ( shortest_path @ SV123 @ SV134 @ SV169 )
= $false )
| ( ( precedes @ SV138 @ SV164 @ SV169 )
= $false )
| ( ( ~ ( precedes @ SV164 @ SV138 @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[932]) ).
thf(967,plain,
! [SV144: $i,SV139: $i] :
( ( ( ~ ( ~ ( ( SV139
!= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
!= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
!= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
!= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV139
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
| ~ ( ( SV139
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) ) )
| ~ ~ ( ~ ( ( SV144
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
| ~ ( ( SV144
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) ) ) ) ) )
= $true )
| ( ( SV139 = SV144 )
= $true )
| ( ( vertex @ SV139 )
= $false )
| ( ( vertex @ SV144 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[933]) ).
thf(968,plain,
! [SV139: $i,SV144: $i] :
( ( ( edge @ ( sK15_E @ SV144 @ SV139 ) )
= $true )
| ( ( SV139 = SV144 )
= $true )
| ( ( vertex @ SV139 )
= $false )
| ( ( vertex @ SV144 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[934]) ).
thf(969,plain,
! [SV124: $i] :
( ( ( on_path @ ( sK7_E1 @ SV124 ) @ SV124 )
= $true )
| ( ( ! [SY292: $i,SY293: $i] :
~ ( path @ SY292 @ SY293 @ SV124 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV124 )
= ( number_of_in @ triangles @ SV124 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[935]) ).
thf(970,plain,
! [SV124: $i] :
( ( ( on_path @ ( sK8_SY86 @ SV124 ) @ SV124 )
= $true )
| ( ( ! [SY292: $i,SY293: $i] :
~ ( path @ SY292 @ SY293 @ SV124 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV124 )
= ( number_of_in @ triangles @ SV124 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[936]) ).
thf(971,plain,
! [SV124: $i,SV192: $i,SV185: $i] :
( ( ( path @ SV185 @ SV192 @ SV124 )
= $false )
| ( ( sequential @ ( sK7_E1 @ SV124 ) @ ( sK8_SY86 @ SV124 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV124 )
= ( number_of_in @ triangles @ SV124 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[937]) ).
thf(972,plain,
! [SV140: $i,SV135: $i,SV196: $i,SV125: $i] :
( ( ( ( SV125
!= ( tail_of @ SV196 ) )
| ~ ( edge @ SV196 )
| ( SV135
!= ( head_of @ SV196 ) )
| ( SV140
!= ( path_cons @ SV196 @ empty ) ) )
= $true )
| ( ( vertex @ SV125 )
= $false )
| ( ( vertex @ SV135 )
= $false )
| ( ( path @ SV125 @ SV135 @ SV140 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[939]) ).
thf(973,plain,
! [SV135: $i,SV140: $i,SV197: $i,SV125: $i] :
( ( ( ( SV125
!= ( tail_of @ SV197 ) )
| ~ ( edge @ SV197 )
| ! [SY395: $i] :
( ( SV140
!= ( path_cons @ SV197 @ SY395 ) )
| ~ ( path @ ( head_of @ SV197 ) @ SV135 @ SY395 ) ) )
= $true )
| ( ( vertex @ SV125 )
= $false )
| ( ( vertex @ SV135 )
= $false )
| ( ( path @ SV125 @ SV135 @ SV140 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[940]) ).
thf(974,plain,
! [SV158: $i,SV152: $i,SV126: $i] :
( ( ( ~ ( edge @ SV126 ) )
= $true )
| ( ( ~ ( edge @ SV152 ) )
= $true )
| ( ( ~ ( edge @ SV158 ) )
= $true )
| ( ( ~ ( sequential @ SV126 @ SV152 ) )
= $true )
| ( ( ~ ( sequential @ SV152 @ SV158 ) )
= $true )
| ( ( ~ ( sequential @ SV158 @ SV126 ) )
= $true )
| ( ( triangle @ SV126 @ SV152 @ SV158 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[941]) ).
thf(975,plain,
! [SV126: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( ! [SY301: $i,SY302: $i] :
~ ( triangle @ SV126 @ SY301 @ SY302 )
| ( edge @ SV126 ) )
| ~ ! [SY303: $i] :
( ! [SY304: $i] :
~ ( triangle @ SV126 @ SY303 @ SY304 )
| ( edge @ SY303 ) ) )
| ~ ! [SY305: $i,SY306: $i] :
( ~ ( triangle @ SV126 @ SY305 @ SY306 )
| ( edge @ SY306 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[942]) ).
thf(976,plain,
! [SV126: $i] :
( ( ~ ! [SY307: $i] :
( ! [SY308: $i] :
~ ( triangle @ SV126 @ SY307 @ SY308 )
| ( sequential @ SV126 @ SY307 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[942]) ).
thf(977,plain,
! [SV198: $i,SV193: $i,SV126: $i] :
( ( ~ ( triangle @ SV126 @ SV193 @ SV198 )
| ( sequential @ SV193 @ SV198 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[943]) ).
thf(978,plain,
! [SV145: $i,SV141: $i,SV127: $i,SV199: $i] :
( ( ( ! [SY396: $i] :
~ ( precedes @ SV199 @ SY396 @ SV127 )
| ( on_path @ SV199 @ SV127 ) )
= $true )
| ( ( path @ SV141 @ SV145 @ SV127 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[945]) ).
thf(979,plain,
! [SV145: $i,SV141: $i,SV127: $i,SV200: $i] :
( ( ( ! [SY397: $i] :
( ~ ( precedes @ SV200 @ SY397 @ SV127 )
| ( on_path @ SY397 @ SV127 ) ) )
= $true )
| ( ( path @ SV141 @ SV145 @ SV127 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[946]) ).
thf(980,plain,
! [SV145: $i,SV141: $i,SV127: $i,SV201: $i] :
( ( ( ! [SY398: $i] :
( ~ ( precedes @ SV201 @ SY398 @ SV127 )
| ! [SY399: $i] :
( ~ ( precedes @ SY399 @ SY398 @ SV127 )
| ~ ( sequential @ SV201 @ SY399 ) )
| ~ ( sequential @ SV201 @ SY398 ) ) )
= $true )
| ( ( path @ SV141 @ SV145 @ SV127 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[947]) ).
thf(981,plain,
! [SV145: $i,SV141: $i,SV127: $i,SV202: $i] :
( ( ( ! [SY400: $i] :
( ~ ( precedes @ SV202 @ SY400 @ SV127 )
| ~ ( ~ ( precedes @ ( sK10_E3 @ SY400 @ SV202 @ SV127 ) @ SY400 @ SV127 )
| ~ ( sequential @ SV202 @ ( sK10_E3 @ SY400 @ SV202 @ SV127 ) ) )
| ( sequential @ SV202 @ SY400 ) ) )
= $true )
| ( ( path @ SV141 @ SV145 @ SV127 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[948]) ).
thf(982,plain,
! [SV148: $i,SV142: $i,SV187: $i,SV128: $i,SV178: $i] :
( ( ( ~ ( on_path @ SV178 @ SV128 )
| ~ ( on_path @ SV187 @ SV128 ) )
= $true )
| ( ( ! [SY391: $i] :
( ~ ( precedes @ SY391 @ SV187 @ SV128 )
| ~ ( sequential @ SV178 @ SY391 ) ) )
= $true )
| ( ( precedes @ SV178 @ SV187 @ SV128 )
= $true )
| ( ( path @ SV142 @ SV148 @ SV128 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[949]) ).
thf(983,plain,
! [SV148: $i,SV142: $i,SV188: $i,SV128: $i,SV179: $i] :
( ( ( ~ ( on_path @ SV179 @ SV128 )
| ~ ( on_path @ SV188 @ SV128 ) )
= $true )
| ( ( ~ ( sequential @ SV179 @ SV188 ) )
= $true )
| ( ( precedes @ SV179 @ SV188 @ SV128 )
= $true )
| ( ( path @ SV142 @ SV148 @ SV128 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[950]) ).
thf(984,plain,
! [SV149: $i,SV153: $i,SV119: $i] :
( ( ( ( SV119
!= ( tail_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) ) )
= $false )
| ( ( path @ SV119 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[951]) ).
thf(985,plain,
! [SV119: $i,SV149: $i,SV153: $i] :
( ( ( ~ ( edge @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
= $false )
| ( ( path @ SV119 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[951]) ).
thf(986,plain,
! [SV119: $i,SV153: $i,SV149: $i] :
( ( ( ~ ( ( SV149
!= ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
| ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ empty ) )
| ! [SY369: $i] :
( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ SY369 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ SY369 ) ) ) )
= $false )
| ( ( path @ SV119 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[952]) ).
thf(987,plain,
! [SV119: $i,SV153: $i,SV149: $i] :
( ( ( ~ ~ ( ~ ( ( SV149
= ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ ( sK14_SY90 @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ ( sK14_SY90 @ SV153 @ SV149 @ SV119 ) ) ) )
| ~ ( ( SV153
= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ empty ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ ( sK13_SY91 @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ ( sK13_SY91 @ SV153 @ SV149 @ SV119 ) ) ) ) ) )
= $false )
| ( ( path @ SV119 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[952]) ).
thf(988,plain,
! [SV120: $i,SV132: $i,SV154: $i,SV159: $i] :
( ( ( ~ ( on_path @ ( sK11_E @ SV159 @ SV154 @ SV132 @ SV120 ) @ SV154 ) )
= $false )
| ( ( in_path @ SV159 @ SV154 )
= $false )
| ( ( path @ SV120 @ SV132 @ SV154 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[953]) ).
thf(989,plain,
! [SV120: $i,SV132: $i,SV154: $i,SV159: $i] :
( ( ( ~ ( ( SV159
= ( head_of @ ( sK11_E @ SV159 @ SV154 @ SV132 @ SV120 ) ) )
| ( SV159
= ( tail_of @ ( sK11_E @ SV159 @ SV154 @ SV132 @ SV120 ) ) ) ) )
= $false )
| ( ( in_path @ SV159 @ SV154 )
= $false )
| ( ( path @ SV120 @ SV132 @ SV154 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[953]) ).
thf(990,plain,
! [SV189: $i,SV182: $i] :
( ( ( sequential @ SV182 @ SV189 )
= $false )
| ( ( ( SV182 != SV189 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[955]) ).
thf(991,plain,
! [SV203: $i] :
( ( ! [SY401: $i] :
~ ( sequential @ SV203 @ SY401 )
| ( edge @ SV203 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[956]) ).
thf(992,plain,
! [SV204: $i] :
( ( ! [SY402: $i] :
( ~ ( sequential @ SV204 @ SY402 )
| ( edge @ SY402 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[957]) ).
thf(993,plain,
! [SV133: $i,SV121: $i,SV172: $i,SV183: $i] :
( ( ( on_path @ SV183 @ SV172 )
= $false )
| ( ( ~ ( path @ SV121 @ SV133 @ SV172 ) )
= $true )
| ( ( edge @ SV183 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[958]) ).
thf(994,plain,
! [SV133: $i,SV121: $i,SV173: $i,SV184: $i] :
( ( ( on_path @ SV184 @ SV173 )
= $false )
| ( ( ~ ( path @ SV121 @ SV133 @ SV173 ) )
= $true )
| ( ( in_path @ ( head_of @ SV184 ) @ SV173 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[959]) ).
thf(995,plain,
! [SV157: $i,SV151: $i,SV122: $i] :
( ( ( path @ SV122 @ SV151 @ SV157 )
= $false )
| ( ( SV122 = SV151 )
= $true )
| ( ( path @ SV122 @ SV151 @ ( sK9_P @ SV157 @ SV151 @ SV122 ) )
= $true )
| ( ( shortest_path @ SV122 @ SV151 @ SV157 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[960]) ).
thf(996,plain,
! [SV157: $i,SV151: $i,SV122: $i] :
( ( ( SV122 = SV151 )
= $true )
| ( ( ~ ( path @ SV122 @ SV151 @ SV157 ) )
= $true )
| ( ( less_or_equal @ ( length_of @ SV157 ) @ ( length_of @ ( sK9_P @ SV157 @ SV151 @ SV122 ) ) )
= $false )
| ( ( shortest_path @ SV122 @ SV151 @ SV157 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[961]) ).
thf(997,plain,
! [SV174: $i,SV194: $i,SV168: $i,SV122: $i] :
( ( ( ~ ( path @ SV122 @ SV168 @ SV194 ) )
= $true )
| ( ( less_or_equal @ ( length_of @ SV174 ) @ ( length_of @ SV194 ) )
= $true )
| ( ( shortest_path @ SV122 @ SV168 @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[962]) ).
thf(998,plain,
! [SV205: $i,SV190: $i,SV122: $i] :
( ( ( ~ ( shortest_path @ SV122 @ SV190 @ SV205 ) )
= $true )
| ( ( ( SV122 != SV190 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[963]) ).
thf(999,plain,
! [SV195: $i,SV191: $i,SV122: $i] :
( ( ( ~ ( shortest_path @ SV122 @ SV191 @ SV195 ) )
= $true )
| ( ( path @ SV122 @ SV191 @ SV195 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[964]) ).
thf(1000,plain,
! [SV134: $i,SV123: $i,SV175: $i,SV163: $i,SV138: $i,SV206: $i] :
( ( ( ( ( tail_of @ SV206 )
!= ( tail_of @ SV138 ) )
| ( ( head_of @ SV206 )
!= ( head_of @ SV163 ) ) )
= $true )
| ( ( precedes @ SV138 @ SV163 @ SV175 )
= $false )
| ( ( shortest_path @ SV123 @ SV134 @ SV175 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[965]) ).
thf(1001,plain,
! [SV134: $i,SV123: $i,SV169: $i,SV138: $i,SV164: $i] :
( ( ( precedes @ SV164 @ SV138 @ SV169 )
= $false )
| ( ( precedes @ SV138 @ SV164 @ SV169 )
= $false )
| ( ( shortest_path @ SV123 @ SV134 @ SV169 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[966]) ).
thf(1002,plain,
! [SV144: $i,SV139: $i] :
( ( ( ~ ( ( SV139
!= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
!= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
!= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
!= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV139
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
| ~ ( ( SV139
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) ) )
| ~ ~ ( ~ ( ( SV144
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
| ~ ( ( SV144
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) ) ) ) )
= $false )
| ( ( SV139 = SV144 )
= $true )
| ( ( vertex @ SV139 )
= $false )
| ( ( vertex @ SV144 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[967]) ).
thf(1003,plain,
! [SV124: $i,SV207: $i] :
( ( ( ! [SY403: $i] :
~ ( path @ SV207 @ SY403 @ SV124 ) )
= $true )
| ( ( on_path @ ( sK7_E1 @ SV124 ) @ SV124 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV124 )
= ( number_of_in @ triangles @ SV124 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[969]) ).
thf(1004,plain,
! [SV124: $i,SV208: $i] :
( ( ( ! [SY404: $i] :
~ ( path @ SV208 @ SY404 @ SV124 ) )
= $true )
| ( ( on_path @ ( sK8_SY86 @ SV124 ) @ SV124 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV124 )
= ( number_of_in @ triangles @ SV124 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[970]) ).
thf(1005,plain,
! [SV140: $i,SV135: $i,SV196: $i,SV125: $i] :
( ( ( ( SV125
!= ( tail_of @ SV196 ) )
| ~ ( edge @ SV196 ) )
= $true )
| ( ( ( SV135
!= ( head_of @ SV196 ) )
| ( SV140
!= ( path_cons @ SV196 @ empty ) ) )
= $true )
| ( ( vertex @ SV125 )
= $false )
| ( ( vertex @ SV135 )
= $false )
| ( ( path @ SV125 @ SV135 @ SV140 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[972]) ).
thf(1006,plain,
! [SV135: $i,SV140: $i,SV197: $i,SV125: $i] :
( ( ( ( SV125
!= ( tail_of @ SV197 ) )
| ~ ( edge @ SV197 ) )
= $true )
| ( ( ! [SY395: $i] :
( ( SV140
!= ( path_cons @ SV197 @ SY395 ) )
| ~ ( path @ ( head_of @ SV197 ) @ SV135 @ SY395 ) ) )
= $true )
| ( ( vertex @ SV125 )
= $false )
| ( ( vertex @ SV135 )
= $false )
| ( ( path @ SV125 @ SV135 @ SV140 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[973]) ).
thf(1007,plain,
! [SV158: $i,SV152: $i,SV126: $i] :
( ( ( edge @ SV126 )
= $false )
| ( ( ~ ( edge @ SV152 ) )
= $true )
| ( ( ~ ( edge @ SV158 ) )
= $true )
| ( ( ~ ( sequential @ SV126 @ SV152 ) )
= $true )
| ( ( ~ ( sequential @ SV152 @ SV158 ) )
= $true )
| ( ( ~ ( sequential @ SV158 @ SV126 ) )
= $true )
| ( ( triangle @ SV126 @ SV152 @ SV158 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[974]) ).
thf(1008,plain,
! [SV126: $i] :
( ( ~ ( ~ ~ ( ~ ( ! [SY301: $i,SY302: $i] :
~ ( triangle @ SV126 @ SY301 @ SY302 )
| ( edge @ SV126 ) )
| ~ ! [SY303: $i] :
( ! [SY304: $i] :
~ ( triangle @ SV126 @ SY303 @ SY304 )
| ( edge @ SY303 ) ) )
| ~ ! [SY305: $i,SY306: $i] :
( ~ ( triangle @ SV126 @ SY305 @ SY306 )
| ( edge @ SY306 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[975]) ).
thf(1009,plain,
! [SV126: $i] :
( ( ! [SY307: $i] :
( ! [SY308: $i] :
~ ( triangle @ SV126 @ SY307 @ SY308 )
| ( sequential @ SV126 @ SY307 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[976]) ).
thf(1010,plain,
! [SV198: $i,SV193: $i,SV126: $i] :
( ( ( ~ ( triangle @ SV126 @ SV193 @ SV198 ) )
= $true )
| ( ( sequential @ SV193 @ SV198 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[977]) ).
thf(1011,plain,
! [SV145: $i,SV141: $i,SV127: $i,SV199: $i] :
( ( ( ! [SY396: $i] :
~ ( precedes @ SV199 @ SY396 @ SV127 ) )
= $true )
| ( ( on_path @ SV199 @ SV127 )
= $true )
| ( ( path @ SV141 @ SV145 @ SV127 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[978]) ).
thf(1012,plain,
! [SV145: $i,SV141: $i,SV127: $i,SV209: $i,SV200: $i] :
( ( ( ~ ( precedes @ SV200 @ SV209 @ SV127 )
| ( on_path @ SV209 @ SV127 ) )
= $true )
| ( ( path @ SV141 @ SV145 @ SV127 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[979]) ).
thf(1013,plain,
! [SV145: $i,SV141: $i,SV127: $i,SV210: $i,SV201: $i] :
( ( ( ~ ( precedes @ SV201 @ SV210 @ SV127 )
| ! [SY405: $i] :
( ~ ( precedes @ SY405 @ SV210 @ SV127 )
| ~ ( sequential @ SV201 @ SY405 ) )
| ~ ( sequential @ SV201 @ SV210 ) )
= $true )
| ( ( path @ SV141 @ SV145 @ SV127 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[980]) ).
thf(1014,plain,
! [SV145: $i,SV141: $i,SV127: $i,SV211: $i,SV202: $i] :
( ( ( ~ ( precedes @ SV202 @ SV211 @ SV127 )
| ~ ( ~ ( precedes @ ( sK10_E3 @ SV211 @ SV202 @ SV127 ) @ SV211 @ SV127 )
| ~ ( sequential @ SV202 @ ( sK10_E3 @ SV211 @ SV202 @ SV127 ) ) )
| ( sequential @ SV202 @ SV211 ) )
= $true )
| ( ( path @ SV141 @ SV145 @ SV127 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[981]) ).
thf(1015,plain,
! [SV148: $i,SV142: $i,SV187: $i,SV128: $i,SV178: $i] :
( ( ( ~ ( on_path @ SV178 @ SV128 ) )
= $true )
| ( ( ~ ( on_path @ SV187 @ SV128 ) )
= $true )
| ( ( ! [SY391: $i] :
( ~ ( precedes @ SY391 @ SV187 @ SV128 )
| ~ ( sequential @ SV178 @ SY391 ) ) )
= $true )
| ( ( precedes @ SV178 @ SV187 @ SV128 )
= $true )
| ( ( path @ SV142 @ SV148 @ SV128 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[982]) ).
thf(1016,plain,
! [SV148: $i,SV142: $i,SV188: $i,SV128: $i,SV179: $i] :
( ( ( ~ ( on_path @ SV179 @ SV128 ) )
= $true )
| ( ( ~ ( on_path @ SV188 @ SV128 ) )
= $true )
| ( ( ~ ( sequential @ SV179 @ SV188 ) )
= $true )
| ( ( precedes @ SV179 @ SV188 @ SV128 )
= $true )
| ( ( path @ SV142 @ SV148 @ SV128 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[983]) ).
thf(1017,plain,
! [SV149: $i,SV153: $i,SV119: $i] :
( ( ( SV119
= ( tail_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
= $true )
| ( ( path @ SV119 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[984]) ).
thf(1018,plain,
! [SV119: $i,SV149: $i,SV153: $i] :
( ( ( edge @ ( sK12_E @ SV153 @ SV149 @ SV119 ) )
= $true )
| ( ( path @ SV119 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[985]) ).
thf(1019,plain,
! [SV119: $i,SV153: $i,SV149: $i] :
( ( ( ( SV149
!= ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
| ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ empty ) )
| ! [SY369: $i] :
( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ SY369 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ SY369 ) ) )
= $true )
| ( ( path @ SV119 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[986]) ).
thf(1020,plain,
! [SV119: $i,SV153: $i,SV149: $i] :
( ( ( ~ ( ~ ( ( SV149
= ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ ( sK14_SY90 @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ ( sK14_SY90 @ SV153 @ SV149 @ SV119 ) ) ) )
| ~ ( ( SV153
= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ empty ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ ( sK13_SY91 @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ ( sK13_SY91 @ SV153 @ SV149 @ SV119 ) ) ) ) ) )
= $true )
| ( ( path @ SV119 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[987]) ).
thf(1021,plain,
! [SV120: $i,SV132: $i,SV154: $i,SV159: $i] :
( ( ( on_path @ ( sK11_E @ SV159 @ SV154 @ SV132 @ SV120 ) @ SV154 )
= $true )
| ( ( in_path @ SV159 @ SV154 )
= $false )
| ( ( path @ SV120 @ SV132 @ SV154 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[988]) ).
thf(1022,plain,
! [SV120: $i,SV132: $i,SV154: $i,SV159: $i] :
( ( ( ( SV159
= ( head_of @ ( sK11_E @ SV159 @ SV154 @ SV132 @ SV120 ) ) )
| ( SV159
= ( tail_of @ ( sK11_E @ SV159 @ SV154 @ SV132 @ SV120 ) ) ) )
= $true )
| ( ( in_path @ SV159 @ SV154 )
= $false )
| ( ( path @ SV120 @ SV132 @ SV154 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[989]) ).
thf(1023,plain,
! [SV189: $i,SV182: $i] :
( ( ( SV182 = SV189 )
= $false )
| ( ( sequential @ SV182 @ SV189 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[990]) ).
thf(1024,plain,
! [SV203: $i] :
( ( ( ! [SY401: $i] :
~ ( sequential @ SV203 @ SY401 ) )
= $true )
| ( ( edge @ SV203 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[991]) ).
thf(1025,plain,
! [SV212: $i,SV204: $i] :
( ( ~ ( sequential @ SV204 @ SV212 )
| ( edge @ SV212 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[992]) ).
thf(1026,plain,
! [SV183: $i,SV172: $i,SV133: $i,SV121: $i] :
( ( ( path @ SV121 @ SV133 @ SV172 )
= $false )
| ( ( on_path @ SV183 @ SV172 )
= $false )
| ( ( edge @ SV183 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[993]) ).
thf(1027,plain,
! [SV184: $i,SV173: $i,SV133: $i,SV121: $i] :
( ( ( path @ SV121 @ SV133 @ SV173 )
= $false )
| ( ( on_path @ SV184 @ SV173 )
= $false )
| ( ( in_path @ ( head_of @ SV184 ) @ SV173 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[994]) ).
thf(1028,plain,
! [SV157: $i,SV151: $i,SV122: $i] :
( ( ( path @ SV122 @ SV151 @ SV157 )
= $false )
| ( ( SV122 = SV151 )
= $true )
| ( ( less_or_equal @ ( length_of @ SV157 ) @ ( length_of @ ( sK9_P @ SV157 @ SV151 @ SV122 ) ) )
= $false )
| ( ( shortest_path @ SV122 @ SV151 @ SV157 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[996]) ).
thf(1029,plain,
! [SV174: $i,SV194: $i,SV168: $i,SV122: $i] :
( ( ( path @ SV122 @ SV168 @ SV194 )
= $false )
| ( ( less_or_equal @ ( length_of @ SV174 ) @ ( length_of @ SV194 ) )
= $true )
| ( ( shortest_path @ SV122 @ SV168 @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[997]) ).
thf(1030,plain,
! [SV205: $i,SV190: $i,SV122: $i] :
( ( ( shortest_path @ SV122 @ SV190 @ SV205 )
= $false )
| ( ( ( SV122 != SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[998]) ).
thf(1031,plain,
! [SV195: $i,SV191: $i,SV122: $i] :
( ( ( shortest_path @ SV122 @ SV191 @ SV195 )
= $false )
| ( ( path @ SV122 @ SV191 @ SV195 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[999]) ).
thf(1032,plain,
! [SV134: $i,SV123: $i,SV175: $i,SV163: $i,SV138: $i,SV206: $i] :
( ( ( ( ( tail_of @ SV206 )
!= ( tail_of @ SV138 ) ) )
= $true )
| ( ( ( ( head_of @ SV206 )
!= ( head_of @ SV163 ) ) )
= $true )
| ( ( precedes @ SV138 @ SV163 @ SV175 )
= $false )
| ( ( shortest_path @ SV123 @ SV134 @ SV175 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1000]) ).
thf(1033,plain,
! [SV144: $i,SV139: $i] :
( ( ( ~ ( ( SV139
!= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
!= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
!= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
!= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) ) )
= $false )
| ( ( SV139 = SV144 )
= $true )
| ( ( vertex @ SV139 )
= $false )
| ( ( vertex @ SV144 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[1002]) ).
thf(1034,plain,
! [SV144: $i,SV139: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( SV139
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
| ~ ( ( SV139
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) ) )
| ~ ~ ( ~ ( ( SV144
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
| ~ ( ( SV144
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) ) ) ) )
= $false )
| ( ( SV139 = SV144 )
= $true )
| ( ( vertex @ SV139 )
= $false )
| ( ( vertex @ SV144 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[1002]) ).
thf(1035,plain,
! [SV124: $i,SV213: $i,SV207: $i] :
( ( ( ~ ( path @ SV207 @ SV213 @ SV124 ) )
= $true )
| ( ( on_path @ ( sK7_E1 @ SV124 ) @ SV124 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV124 )
= ( number_of_in @ triangles @ SV124 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1003]) ).
thf(1036,plain,
! [SV124: $i,SV214: $i,SV208: $i] :
( ( ( ~ ( path @ SV208 @ SV214 @ SV124 ) )
= $true )
| ( ( on_path @ ( sK8_SY86 @ SV124 ) @ SV124 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV124 )
= ( number_of_in @ triangles @ SV124 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1004]) ).
thf(1037,plain,
! [SV140: $i,SV135: $i,SV196: $i,SV125: $i] :
( ( ( ( SV125
!= ( tail_of @ SV196 ) ) )
= $true )
| ( ( ~ ( edge @ SV196 ) )
= $true )
| ( ( ( SV135
!= ( head_of @ SV196 ) )
| ( SV140
!= ( path_cons @ SV196 @ empty ) ) )
= $true )
| ( ( vertex @ SV125 )
= $false )
| ( ( vertex @ SV135 )
= $false )
| ( ( path @ SV125 @ SV135 @ SV140 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1005]) ).
thf(1038,plain,
! [SV135: $i,SV140: $i,SV197: $i,SV125: $i] :
( ( ( ( SV125
!= ( tail_of @ SV197 ) ) )
= $true )
| ( ( ~ ( edge @ SV197 ) )
= $true )
| ( ( ! [SY395: $i] :
( ( SV140
!= ( path_cons @ SV197 @ SY395 ) )
| ~ ( path @ ( head_of @ SV197 ) @ SV135 @ SY395 ) ) )
= $true )
| ( ( vertex @ SV125 )
= $false )
| ( ( vertex @ SV135 )
= $false )
| ( ( path @ SV125 @ SV135 @ SV140 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1006]) ).
thf(1039,plain,
! [SV158: $i,SV126: $i,SV152: $i] :
( ( ( edge @ SV152 )
= $false )
| ( ( edge @ SV126 )
= $false )
| ( ( ~ ( edge @ SV158 ) )
= $true )
| ( ( ~ ( sequential @ SV126 @ SV152 ) )
= $true )
| ( ( ~ ( sequential @ SV152 @ SV158 ) )
= $true )
| ( ( ~ ( sequential @ SV158 @ SV126 ) )
= $true )
| ( ( triangle @ SV126 @ SV152 @ SV158 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1007]) ).
thf(1040,plain,
! [SV126: $i] :
( ( ~ ~ ( ~ ( ! [SY301: $i,SY302: $i] :
~ ( triangle @ SV126 @ SY301 @ SY302 )
| ( edge @ SV126 ) )
| ~ ! [SY303: $i] :
( ! [SY304: $i] :
~ ( triangle @ SV126 @ SY303 @ SY304 )
| ( edge @ SY303 ) ) )
| ~ ! [SY305: $i,SY306: $i] :
( ~ ( triangle @ SV126 @ SY305 @ SY306 )
| ( edge @ SY306 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1008]) ).
thf(1041,plain,
! [SV215: $i,SV126: $i] :
( ( ! [SY406: $i] :
~ ( triangle @ SV126 @ SV215 @ SY406 )
| ( sequential @ SV126 @ SV215 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1009]) ).
thf(1042,plain,
! [SV198: $i,SV193: $i,SV126: $i] :
( ( ( triangle @ SV126 @ SV193 @ SV198 )
= $false )
| ( ( sequential @ SV193 @ SV198 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1010]) ).
thf(1043,plain,
! [SV145: $i,SV141: $i,SV127: $i,SV216: $i,SV199: $i] :
( ( ( ~ ( precedes @ SV199 @ SV216 @ SV127 ) )
= $true )
| ( ( on_path @ SV199 @ SV127 )
= $true )
| ( ( path @ SV141 @ SV145 @ SV127 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1011]) ).
thf(1044,plain,
! [SV145: $i,SV141: $i,SV127: $i,SV209: $i,SV200: $i] :
( ( ( ~ ( precedes @ SV200 @ SV209 @ SV127 ) )
= $true )
| ( ( on_path @ SV209 @ SV127 )
= $true )
| ( ( path @ SV141 @ SV145 @ SV127 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1012]) ).
thf(1045,plain,
! [SV145: $i,SV141: $i,SV127: $i,SV210: $i,SV201: $i] :
( ( ( ~ ( precedes @ SV201 @ SV210 @ SV127 ) )
= $true )
| ( ( ! [SY405: $i] :
( ~ ( precedes @ SY405 @ SV210 @ SV127 )
| ~ ( sequential @ SV201 @ SY405 ) )
| ~ ( sequential @ SV201 @ SV210 ) )
= $true )
| ( ( path @ SV141 @ SV145 @ SV127 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1013]) ).
thf(1046,plain,
! [SV145: $i,SV141: $i,SV127: $i,SV211: $i,SV202: $i] :
( ( ( ~ ( precedes @ SV202 @ SV211 @ SV127 ) )
= $true )
| ( ( ~ ( ~ ( precedes @ ( sK10_E3 @ SV211 @ SV202 @ SV127 ) @ SV211 @ SV127 )
| ~ ( sequential @ SV202 @ ( sK10_E3 @ SV211 @ SV202 @ SV127 ) ) )
| ( sequential @ SV202 @ SV211 ) )
= $true )
| ( ( path @ SV141 @ SV145 @ SV127 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1014]) ).
thf(1047,plain,
! [SV148: $i,SV142: $i,SV187: $i,SV128: $i,SV178: $i] :
( ( ( on_path @ SV178 @ SV128 )
= $false )
| ( ( ~ ( on_path @ SV187 @ SV128 ) )
= $true )
| ( ( ! [SY391: $i] :
( ~ ( precedes @ SY391 @ SV187 @ SV128 )
| ~ ( sequential @ SV178 @ SY391 ) ) )
= $true )
| ( ( precedes @ SV178 @ SV187 @ SV128 )
= $true )
| ( ( path @ SV142 @ SV148 @ SV128 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1015]) ).
thf(1048,plain,
! [SV148: $i,SV142: $i,SV188: $i,SV128: $i,SV179: $i] :
( ( ( on_path @ SV179 @ SV128 )
= $false )
| ( ( ~ ( on_path @ SV188 @ SV128 ) )
= $true )
| ( ( ~ ( sequential @ SV179 @ SV188 ) )
= $true )
| ( ( precedes @ SV179 @ SV188 @ SV128 )
= $true )
| ( ( path @ SV142 @ SV148 @ SV128 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1016]) ).
thf(1049,plain,
! [SV119: $i,SV153: $i,SV149: $i] :
( ( ( ( SV149
!= ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
| ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ empty ) ) )
= $true )
| ( ( ! [SY369: $i] :
( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ SY369 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ SY369 ) ) )
= $true )
| ( ( path @ SV119 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1019]) ).
thf(1050,plain,
! [SV119: $i,SV153: $i,SV149: $i] :
( ( ( ~ ( ( SV149
= ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ ( sK14_SY90 @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ ( sK14_SY90 @ SV153 @ SV149 @ SV119 ) ) ) )
| ~ ( ( SV153
= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ empty ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ ( sK13_SY91 @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ ( sK13_SY91 @ SV153 @ SV149 @ SV119 ) ) ) ) )
= $false )
| ( ( path @ SV119 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1020]) ).
thf(1051,plain,
! [SV120: $i,SV132: $i,SV154: $i,SV159: $i] :
( ( ( SV159
= ( head_of @ ( sK11_E @ SV159 @ SV154 @ SV132 @ SV120 ) ) )
= $true )
| ( ( SV159
= ( tail_of @ ( sK11_E @ SV159 @ SV154 @ SV132 @ SV120 ) ) )
= $true )
| ( ( in_path @ SV159 @ SV154 )
= $false )
| ( ( path @ SV120 @ SV132 @ SV154 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1022]) ).
thf(1052,plain,
! [SV217: $i,SV203: $i] :
( ( ( ~ ( sequential @ SV203 @ SV217 ) )
= $true )
| ( ( edge @ SV203 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1024]) ).
thf(1053,plain,
! [SV212: $i,SV204: $i] :
( ( ( ~ ( sequential @ SV204 @ SV212 ) )
= $true )
| ( ( edge @ SV212 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1025]) ).
thf(1054,plain,
! [SV205: $i,SV190: $i,SV122: $i] :
( ( ( SV122 = SV190 )
= $false )
| ( ( shortest_path @ SV122 @ SV190 @ SV205 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1030]) ).
thf(1055,plain,
! [SV134: $i,SV123: $i,SV175: $i,SV163: $i,SV138: $i,SV206: $i] :
( ( ( ( tail_of @ SV206 )
= ( tail_of @ SV138 ) )
= $false )
| ( ( ( ( head_of @ SV206 )
!= ( head_of @ SV163 ) ) )
= $true )
| ( ( precedes @ SV138 @ SV163 @ SV175 )
= $false )
| ( ( shortest_path @ SV123 @ SV134 @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1032]) ).
thf(1056,plain,
! [SV144: $i,SV139: $i] :
( ( ( ( SV139
!= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
!= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
!= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
!= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
= $true )
| ( ( SV139 = SV144 )
= $true )
| ( ( vertex @ SV139 )
= $false )
| ( ( vertex @ SV144 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1033]) ).
thf(1057,plain,
! [SV144: $i,SV139: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( SV139
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
| ~ ( ( SV139
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) ) )
| ~ ~ ( ~ ( ( SV144
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
| ~ ( ( SV144
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) ) ) ) )
= $true )
| ( ( SV139 = SV144 )
= $true )
| ( ( vertex @ SV139 )
= $false )
| ( ( vertex @ SV144 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1034]) ).
thf(1058,plain,
! [SV124: $i,SV213: $i,SV207: $i] :
( ( ( path @ SV207 @ SV213 @ SV124 )
= $false )
| ( ( on_path @ ( sK7_E1 @ SV124 ) @ SV124 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV124 )
= ( number_of_in @ triangles @ SV124 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1035]) ).
thf(1059,plain,
! [SV124: $i,SV214: $i,SV208: $i] :
( ( ( path @ SV208 @ SV214 @ SV124 )
= $false )
| ( ( on_path @ ( sK8_SY86 @ SV124 ) @ SV124 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV124 )
= ( number_of_in @ triangles @ SV124 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1036]) ).
thf(1060,plain,
! [SV140: $i,SV135: $i,SV196: $i,SV125: $i] :
( ( ( SV125
= ( tail_of @ SV196 ) )
= $false )
| ( ( ~ ( edge @ SV196 ) )
= $true )
| ( ( ( SV135
!= ( head_of @ SV196 ) )
| ( SV140
!= ( path_cons @ SV196 @ empty ) ) )
= $true )
| ( ( vertex @ SV125 )
= $false )
| ( ( vertex @ SV135 )
= $false )
| ( ( path @ SV125 @ SV135 @ SV140 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1037]) ).
thf(1061,plain,
! [SV135: $i,SV140: $i,SV197: $i,SV125: $i] :
( ( ( SV125
= ( tail_of @ SV197 ) )
= $false )
| ( ( ~ ( edge @ SV197 ) )
= $true )
| ( ( ! [SY395: $i] :
( ( SV140
!= ( path_cons @ SV197 @ SY395 ) )
| ~ ( path @ ( head_of @ SV197 ) @ SV135 @ SY395 ) ) )
= $true )
| ( ( vertex @ SV125 )
= $false )
| ( ( vertex @ SV135 )
= $false )
| ( ( path @ SV125 @ SV135 @ SV140 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1038]) ).
thf(1062,plain,
! [SV152: $i,SV126: $i,SV158: $i] :
( ( ( edge @ SV158 )
= $false )
| ( ( edge @ SV126 )
= $false )
| ( ( edge @ SV152 )
= $false )
| ( ( ~ ( sequential @ SV126 @ SV152 ) )
= $true )
| ( ( ~ ( sequential @ SV152 @ SV158 ) )
= $true )
| ( ( ~ ( sequential @ SV158 @ SV126 ) )
= $true )
| ( ( triangle @ SV126 @ SV152 @ SV158 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1039]) ).
thf(1063,plain,
! [SV126: $i] :
( ( ~ ~ ( ~ ( ! [SY301: $i,SY302: $i] :
~ ( triangle @ SV126 @ SY301 @ SY302 )
| ( edge @ SV126 ) )
| ~ ! [SY303: $i] :
( ! [SY304: $i] :
~ ( triangle @ SV126 @ SY303 @ SY304 )
| ( edge @ SY303 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1040]) ).
thf(1064,plain,
! [SV126: $i] :
( ( ~ ! [SY305: $i,SY306: $i] :
( ~ ( triangle @ SV126 @ SY305 @ SY306 )
| ( edge @ SY306 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1040]) ).
thf(1065,plain,
! [SV215: $i,SV126: $i] :
( ( ( ! [SY406: $i] :
~ ( triangle @ SV126 @ SV215 @ SY406 ) )
= $true )
| ( ( sequential @ SV126 @ SV215 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1041]) ).
thf(1066,plain,
! [SV145: $i,SV141: $i,SV127: $i,SV216: $i,SV199: $i] :
( ( ( precedes @ SV199 @ SV216 @ SV127 )
= $false )
| ( ( on_path @ SV199 @ SV127 )
= $true )
| ( ( path @ SV141 @ SV145 @ SV127 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1043]) ).
thf(1067,plain,
! [SV145: $i,SV141: $i,SV127: $i,SV209: $i,SV200: $i] :
( ( ( precedes @ SV200 @ SV209 @ SV127 )
= $false )
| ( ( on_path @ SV209 @ SV127 )
= $true )
| ( ( path @ SV141 @ SV145 @ SV127 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1044]) ).
thf(1068,plain,
! [SV145: $i,SV141: $i,SV127: $i,SV210: $i,SV201: $i] :
( ( ( precedes @ SV201 @ SV210 @ SV127 )
= $false )
| ( ( ! [SY405: $i] :
( ~ ( precedes @ SY405 @ SV210 @ SV127 )
| ~ ( sequential @ SV201 @ SY405 ) )
| ~ ( sequential @ SV201 @ SV210 ) )
= $true )
| ( ( path @ SV141 @ SV145 @ SV127 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1045]) ).
thf(1069,plain,
! [SV145: $i,SV141: $i,SV127: $i,SV211: $i,SV202: $i] :
( ( ( precedes @ SV202 @ SV211 @ SV127 )
= $false )
| ( ( ~ ( ~ ( precedes @ ( sK10_E3 @ SV211 @ SV202 @ SV127 ) @ SV211 @ SV127 )
| ~ ( sequential @ SV202 @ ( sK10_E3 @ SV211 @ SV202 @ SV127 ) ) )
| ( sequential @ SV202 @ SV211 ) )
= $true )
| ( ( path @ SV141 @ SV145 @ SV127 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1046]) ).
thf(1070,plain,
! [SV148: $i,SV142: $i,SV178: $i,SV128: $i,SV187: $i] :
( ( ( on_path @ SV187 @ SV128 )
= $false )
| ( ( on_path @ SV178 @ SV128 )
= $false )
| ( ( ! [SY391: $i] :
( ~ ( precedes @ SY391 @ SV187 @ SV128 )
| ~ ( sequential @ SV178 @ SY391 ) ) )
= $true )
| ( ( precedes @ SV178 @ SV187 @ SV128 )
= $true )
| ( ( path @ SV142 @ SV148 @ SV128 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1047]) ).
thf(1071,plain,
! [SV148: $i,SV142: $i,SV179: $i,SV128: $i,SV188: $i] :
( ( ( on_path @ SV188 @ SV128 )
= $false )
| ( ( on_path @ SV179 @ SV128 )
= $false )
| ( ( ~ ( sequential @ SV179 @ SV188 ) )
= $true )
| ( ( precedes @ SV179 @ SV188 @ SV128 )
= $true )
| ( ( path @ SV142 @ SV148 @ SV128 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1048]) ).
thf(1072,plain,
! [SV119: $i,SV153: $i,SV149: $i] :
( ( ( ( SV149
!= ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) ) )
= $true )
| ( ( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ empty ) ) )
= $true )
| ( ( ! [SY369: $i] :
( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ SY369 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ SY369 ) ) )
= $true )
| ( ( path @ SV119 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1049]) ).
thf(1073,plain,
! [SV119: $i,SV153: $i,SV149: $i] :
( ( ( ~ ( ( SV149
= ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ ( sK14_SY90 @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ ( sK14_SY90 @ SV153 @ SV149 @ SV119 ) ) ) ) )
= $false )
| ( ( path @ SV119 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1050]) ).
thf(1074,plain,
! [SV119: $i,SV149: $i,SV153: $i] :
( ( ( ~ ( ( SV153
= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ empty ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ ( sK13_SY91 @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ ( sK13_SY91 @ SV153 @ SV149 @ SV119 ) ) ) ) )
= $false )
| ( ( path @ SV119 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1050]) ).
thf(1075,plain,
! [SV217: $i,SV203: $i] :
( ( ( sequential @ SV203 @ SV217 )
= $false )
| ( ( edge @ SV203 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1052]) ).
thf(1076,plain,
! [SV212: $i,SV204: $i] :
( ( ( sequential @ SV204 @ SV212 )
= $false )
| ( ( edge @ SV212 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1053]) ).
thf(1077,plain,
! [SV134: $i,SV123: $i,SV175: $i,SV138: $i,SV163: $i,SV206: $i] :
( ( ( ( head_of @ SV206 )
= ( head_of @ SV163 ) )
= $false )
| ( ( ( tail_of @ SV206 )
= ( tail_of @ SV138 ) )
= $false )
| ( ( precedes @ SV138 @ SV163 @ SV175 )
= $false )
| ( ( shortest_path @ SV123 @ SV134 @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1055]) ).
thf(1078,plain,
! [SV144: $i,SV139: $i] :
( ( ( ( SV139
!= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
!= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
= $true )
| ( ( ( SV144
!= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
!= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
= $true )
| ( ( SV139 = SV144 )
= $true )
| ( ( vertex @ SV139 )
= $false )
| ( ( vertex @ SV144 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[1056]) ).
thf(1079,plain,
! [SV144: $i,SV139: $i] :
( ( ( ~ ~ ( ~ ( ( SV139
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
| ~ ( ( SV139
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) ) )
| ~ ~ ( ~ ( ( SV144
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
| ~ ( ( SV144
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) ) ) )
= $false )
| ( ( SV139 = SV144 )
= $true )
| ( ( vertex @ SV139 )
= $false )
| ( ( vertex @ SV144 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1057]) ).
thf(1080,plain,
! [SV140: $i,SV135: $i,SV125: $i,SV196: $i] :
( ( ( edge @ SV196 )
= $false )
| ( ( SV125
= ( tail_of @ SV196 ) )
= $false )
| ( ( ( SV135
!= ( head_of @ SV196 ) )
| ( SV140
!= ( path_cons @ SV196 @ empty ) ) )
= $true )
| ( ( vertex @ SV125 )
= $false )
| ( ( vertex @ SV135 )
= $false )
| ( ( path @ SV125 @ SV135 @ SV140 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1060]) ).
thf(1081,plain,
! [SV135: $i,SV140: $i,SV125: $i,SV197: $i] :
( ( ( edge @ SV197 )
= $false )
| ( ( SV125
= ( tail_of @ SV197 ) )
= $false )
| ( ( ! [SY395: $i] :
( ( SV140
!= ( path_cons @ SV197 @ SY395 ) )
| ~ ( path @ ( head_of @ SV197 ) @ SV135 @ SY395 ) ) )
= $true )
| ( ( vertex @ SV125 )
= $false )
| ( ( vertex @ SV135 )
= $false )
| ( ( path @ SV125 @ SV135 @ SV140 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1061]) ).
thf(1082,plain,
! [SV158: $i,SV152: $i,SV126: $i] :
( ( ( sequential @ SV126 @ SV152 )
= $false )
| ( ( edge @ SV152 )
= $false )
| ( ( edge @ SV126 )
= $false )
| ( ( edge @ SV158 )
= $false )
| ( ( ~ ( sequential @ SV152 @ SV158 ) )
= $true )
| ( ( ~ ( sequential @ SV158 @ SV126 ) )
= $true )
| ( ( triangle @ SV126 @ SV152 @ SV158 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1062]) ).
thf(1083,plain,
! [SV126: $i] :
( ( ~ ( ~ ( ! [SY301: $i,SY302: $i] :
~ ( triangle @ SV126 @ SY301 @ SY302 )
| ( edge @ SV126 ) )
| ~ ! [SY303: $i] :
( ! [SY304: $i] :
~ ( triangle @ SV126 @ SY303 @ SY304 )
| ( edge @ SY303 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1063]) ).
thf(1084,plain,
! [SV126: $i] :
( ( ! [SY305: $i,SY306: $i] :
( ~ ( triangle @ SV126 @ SY305 @ SY306 )
| ( edge @ SY306 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1064]) ).
thf(1085,plain,
! [SV218: $i,SV215: $i,SV126: $i] :
( ( ( ~ ( triangle @ SV126 @ SV215 @ SV218 ) )
= $true )
| ( ( sequential @ SV126 @ SV215 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1065]) ).
thf(1086,plain,
! [SV145: $i,SV141: $i,SV201: $i,SV127: $i,SV210: $i] :
( ( ( ! [SY405: $i] :
( ~ ( precedes @ SY405 @ SV210 @ SV127 )
| ~ ( sequential @ SV201 @ SY405 ) ) )
= $true )
| ( ( ~ ( sequential @ SV201 @ SV210 ) )
= $true )
| ( ( precedes @ SV201 @ SV210 @ SV127 )
= $false )
| ( ( path @ SV141 @ SV145 @ SV127 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1068]) ).
thf(1087,plain,
! [SV145: $i,SV141: $i,SV127: $i,SV202: $i,SV211: $i] :
( ( ( ~ ( ~ ( precedes @ ( sK10_E3 @ SV211 @ SV202 @ SV127 ) @ SV211 @ SV127 )
| ~ ( sequential @ SV202 @ ( sK10_E3 @ SV211 @ SV202 @ SV127 ) ) ) )
= $true )
| ( ( sequential @ SV202 @ SV211 )
= $true )
| ( ( precedes @ SV202 @ SV211 @ SV127 )
= $false )
| ( ( path @ SV141 @ SV145 @ SV127 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1069]) ).
thf(1088,plain,
! [SV148: $i,SV142: $i,SV178: $i,SV128: $i,SV187: $i,SV219: $i] :
( ( ( ~ ( precedes @ SV219 @ SV187 @ SV128 )
| ~ ( sequential @ SV178 @ SV219 ) )
= $true )
| ( ( on_path @ SV178 @ SV128 )
= $false )
| ( ( on_path @ SV187 @ SV128 )
= $false )
| ( ( precedes @ SV178 @ SV187 @ SV128 )
= $true )
| ( ( path @ SV142 @ SV148 @ SV128 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1070]) ).
thf(1089,plain,
! [SV148: $i,SV142: $i,SV128: $i,SV188: $i,SV179: $i] :
( ( ( sequential @ SV179 @ SV188 )
= $false )
| ( ( on_path @ SV179 @ SV128 )
= $false )
| ( ( on_path @ SV188 @ SV128 )
= $false )
| ( ( precedes @ SV179 @ SV188 @ SV128 )
= $true )
| ( ( path @ SV142 @ SV148 @ SV128 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1071]) ).
thf(1090,plain,
! [SV119: $i,SV153: $i,SV149: $i] :
( ( ( SV149
= ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
= $false )
| ( ( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ empty ) ) )
= $true )
| ( ( ! [SY369: $i] :
( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ SY369 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ SY369 ) ) )
= $true )
| ( ( path @ SV119 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1072]) ).
thf(1091,plain,
! [SV119: $i,SV153: $i,SV149: $i] :
( ( ( ( SV149
= ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ ( sK14_SY90 @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ ( sK14_SY90 @ SV153 @ SV149 @ SV119 ) ) ) )
= $true )
| ( ( path @ SV119 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1073]) ).
thf(1092,plain,
! [SV119: $i,SV149: $i,SV153: $i] :
( ( ( ( SV153
= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ empty ) )
| ~ ( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ ( sK13_SY91 @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ ( sK13_SY91 @ SV153 @ SV149 @ SV119 ) ) ) )
= $true )
| ( ( path @ SV119 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1074]) ).
thf(1093,plain,
! [SV144: $i,SV139: $i] :
( ( ( ( SV139
!= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
= $true )
| ( ( ( SV144
!= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
= $true )
| ( ( ( SV144
!= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
!= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
= $true )
| ( ( SV139 = SV144 )
= $true )
| ( ( vertex @ SV139 )
= $false )
| ( ( vertex @ SV144 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[1078]) ).
thf(1094,plain,
! [SV144: $i,SV139: $i] :
( ( ( ~ ~ ( ~ ( ( SV139
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
| ~ ( ( SV139
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) ) ) )
= $false )
| ( ( SV139 = SV144 )
= $true )
| ( ( vertex @ SV139 )
= $false )
| ( ( vertex @ SV144 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[1079]) ).
thf(1095,plain,
! [SV139: $i,SV144: $i] :
( ( ( ~ ~ ( ~ ( ( SV144
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
| ~ ( ( SV144
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) ) ) )
= $false )
| ( ( SV139 = SV144 )
= $true )
| ( ( vertex @ SV139 )
= $false )
| ( ( vertex @ SV144 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[1079]) ).
thf(1096,plain,
! [SV125: $i,SV140: $i,SV196: $i,SV135: $i] :
( ( ( ( SV135
!= ( head_of @ SV196 ) ) )
= $true )
| ( ( ( SV140
!= ( path_cons @ SV196 @ empty ) ) )
= $true )
| ( ( SV125
= ( tail_of @ SV196 ) )
= $false )
| ( ( edge @ SV196 )
= $false )
| ( ( vertex @ SV125 )
= $false )
| ( ( vertex @ SV135 )
= $false )
| ( ( path @ SV125 @ SV135 @ SV140 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1080]) ).
thf(1097,plain,
! [SV125: $i,SV135: $i,SV220: $i,SV197: $i,SV140: $i] :
( ( ( ( SV140
!= ( path_cons @ SV197 @ SV220 ) )
| ~ ( path @ ( head_of @ SV197 ) @ SV135 @ SV220 ) )
= $true )
| ( ( SV125
= ( tail_of @ SV197 ) )
= $false )
| ( ( edge @ SV197 )
= $false )
| ( ( vertex @ SV125 )
= $false )
| ( ( vertex @ SV135 )
= $false )
| ( ( path @ SV125 @ SV135 @ SV140 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1081]) ).
thf(1098,plain,
! [SV126: $i,SV158: $i,SV152: $i] :
( ( ( sequential @ SV152 @ SV158 )
= $false )
| ( ( edge @ SV158 )
= $false )
| ( ( edge @ SV126 )
= $false )
| ( ( edge @ SV152 )
= $false )
| ( ( sequential @ SV126 @ SV152 )
= $false )
| ( ( ~ ( sequential @ SV158 @ SV126 ) )
= $true )
| ( ( triangle @ SV126 @ SV152 @ SV158 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1082]) ).
thf(1099,plain,
! [SV126: $i] :
( ( ~ ( ! [SY301: $i,SY302: $i] :
~ ( triangle @ SV126 @ SY301 @ SY302 )
| ( edge @ SV126 ) )
| ~ ! [SY303: $i] :
( ! [SY304: $i] :
~ ( triangle @ SV126 @ SY303 @ SY304 )
| ( edge @ SY303 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1083]) ).
thf(1100,plain,
! [SV221: $i,SV126: $i] :
( ( ! [SY407: $i] :
( ~ ( triangle @ SV126 @ SV221 @ SY407 )
| ( edge @ SY407 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1084]) ).
thf(1101,plain,
! [SV218: $i,SV215: $i,SV126: $i] :
( ( ( triangle @ SV126 @ SV215 @ SV218 )
= $false )
| ( ( sequential @ SV126 @ SV215 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1085]) ).
thf(1102,plain,
! [SV145: $i,SV141: $i,SV201: $i,SV127: $i,SV210: $i,SV222: $i] :
( ( ( ~ ( precedes @ SV222 @ SV210 @ SV127 )
| ~ ( sequential @ SV201 @ SV222 ) )
= $true )
| ( ( ~ ( sequential @ SV201 @ SV210 ) )
= $true )
| ( ( precedes @ SV201 @ SV210 @ SV127 )
= $false )
| ( ( path @ SV141 @ SV145 @ SV127 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1086]) ).
thf(1103,plain,
! [SV145: $i,SV141: $i,SV127: $i,SV202: $i,SV211: $i] :
( ( ( ~ ( precedes @ ( sK10_E3 @ SV211 @ SV202 @ SV127 ) @ SV211 @ SV127 )
| ~ ( sequential @ SV202 @ ( sK10_E3 @ SV211 @ SV202 @ SV127 ) ) )
= $false )
| ( ( sequential @ SV202 @ SV211 )
= $true )
| ( ( precedes @ SV202 @ SV211 @ SV127 )
= $false )
| ( ( path @ SV141 @ SV145 @ SV127 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1087]) ).
thf(1104,plain,
! [SV148: $i,SV142: $i,SV178: $i,SV128: $i,SV187: $i,SV219: $i] :
( ( ( ~ ( precedes @ SV219 @ SV187 @ SV128 ) )
= $true )
| ( ( ~ ( sequential @ SV178 @ SV219 ) )
= $true )
| ( ( on_path @ SV178 @ SV128 )
= $false )
| ( ( on_path @ SV187 @ SV128 )
= $false )
| ( ( precedes @ SV178 @ SV187 @ SV128 )
= $true )
| ( ( path @ SV142 @ SV148 @ SV128 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1088]) ).
thf(1105,plain,
! [SV119: $i,SV149: $i,SV153: $i] :
( ( ( SV153
= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ empty ) )
= $false )
| ( ( SV149
= ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
= $false )
| ( ( ! [SY369: $i] :
( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ SY369 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ SY369 ) ) )
= $true )
| ( ( path @ SV119 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1090]) ).
thf(1106,plain,
! [SV119: $i,SV153: $i,SV149: $i] :
( ( ( SV149
= ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
= $true )
| ( ( ~ ( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ ( sK14_SY90 @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ ( sK14_SY90 @ SV153 @ SV149 @ SV119 ) ) ) )
= $true )
| ( ( path @ SV119 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1091]) ).
thf(1107,plain,
! [SV119: $i,SV149: $i,SV153: $i] :
( ( ( SV153
= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ empty ) )
= $true )
| ( ( ~ ( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ ( sK13_SY91 @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ ( sK13_SY91 @ SV153 @ SV149 @ SV119 ) ) ) )
= $true )
| ( ( path @ SV119 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1092]) ).
thf(1108,plain,
! [SV144: $i,SV139: $i] :
( ( ( SV139
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
= $false )
| ( ( ( SV144
!= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
= $true )
| ( ( ( SV144
!= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
!= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
= $true )
| ( ( SV139 = SV144 )
= $true )
| ( ( vertex @ SV139 )
= $false )
| ( ( vertex @ SV144 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1093]) ).
thf(1109,plain,
! [SV144: $i,SV139: $i] :
( ( ( ~ ( ~ ( ( SV139
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
| ~ ( ( SV139
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) ) ) )
= $true )
| ( ( SV139 = SV144 )
= $true )
| ( ( vertex @ SV139 )
= $false )
| ( ( vertex @ SV144 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1094]) ).
thf(1110,plain,
! [SV139: $i,SV144: $i] :
( ( ( ~ ( ~ ( ( SV144
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
| ~ ( ( SV144
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) ) ) )
= $true )
| ( ( SV139 = SV144 )
= $true )
| ( ( vertex @ SV139 )
= $false )
| ( ( vertex @ SV144 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1095]) ).
thf(1111,plain,
! [SV125: $i,SV140: $i,SV196: $i,SV135: $i] :
( ( ( SV135
= ( head_of @ SV196 ) )
= $false )
| ( ( ( SV140
!= ( path_cons @ SV196 @ empty ) ) )
= $true )
| ( ( SV125
= ( tail_of @ SV196 ) )
= $false )
| ( ( edge @ SV196 )
= $false )
| ( ( vertex @ SV125 )
= $false )
| ( ( vertex @ SV135 )
= $false )
| ( ( path @ SV125 @ SV135 @ SV140 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1096]) ).
thf(1112,plain,
! [SV125: $i,SV135: $i,SV220: $i,SV197: $i,SV140: $i] :
( ( ( ( SV140
!= ( path_cons @ SV197 @ SV220 ) ) )
= $true )
| ( ( ~ ( path @ ( head_of @ SV197 ) @ SV135 @ SV220 ) )
= $true )
| ( ( SV125
= ( tail_of @ SV197 ) )
= $false )
| ( ( edge @ SV197 )
= $false )
| ( ( vertex @ SV125 )
= $false )
| ( ( vertex @ SV135 )
= $false )
| ( ( path @ SV125 @ SV135 @ SV140 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1097]) ).
thf(1113,plain,
! [SV152: $i,SV126: $i,SV158: $i] :
( ( ( sequential @ SV158 @ SV126 )
= $false )
| ( ( sequential @ SV126 @ SV152 )
= $false )
| ( ( edge @ SV152 )
= $false )
| ( ( edge @ SV126 )
= $false )
| ( ( edge @ SV158 )
= $false )
| ( ( sequential @ SV152 @ SV158 )
= $false )
| ( ( triangle @ SV126 @ SV152 @ SV158 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1098]) ).
thf(1114,plain,
! [SV126: $i] :
( ( ~ ( ! [SY301: $i,SY302: $i] :
~ ( triangle @ SV126 @ SY301 @ SY302 )
| ( edge @ SV126 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1099]) ).
thf(1115,plain,
! [SV126: $i] :
( ( ~ ! [SY303: $i] :
( ! [SY304: $i] :
~ ( triangle @ SV126 @ SY303 @ SY304 )
| ( edge @ SY303 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1099]) ).
thf(1116,plain,
! [SV223: $i,SV221: $i,SV126: $i] :
( ( ~ ( triangle @ SV126 @ SV221 @ SV223 )
| ( edge @ SV223 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1100]) ).
thf(1117,plain,
! [SV145: $i,SV141: $i,SV201: $i,SV127: $i,SV210: $i,SV222: $i] :
( ( ( ~ ( precedes @ SV222 @ SV210 @ SV127 ) )
= $true )
| ( ( ~ ( sequential @ SV201 @ SV222 ) )
= $true )
| ( ( ~ ( sequential @ SV201 @ SV210 ) )
= $true )
| ( ( precedes @ SV201 @ SV210 @ SV127 )
= $false )
| ( ( path @ SV141 @ SV145 @ SV127 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1102]) ).
thf(1118,plain,
! [SV145: $i,SV141: $i,SV127: $i,SV202: $i,SV211: $i] :
( ( ( ~ ( precedes @ ( sK10_E3 @ SV211 @ SV202 @ SV127 ) @ SV211 @ SV127 ) )
= $false )
| ( ( sequential @ SV202 @ SV211 )
= $true )
| ( ( precedes @ SV202 @ SV211 @ SV127 )
= $false )
| ( ( path @ SV141 @ SV145 @ SV127 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1103]) ).
thf(1119,plain,
! [SV145: $i,SV141: $i,SV127: $i,SV211: $i,SV202: $i] :
( ( ( ~ ( sequential @ SV202 @ ( sK10_E3 @ SV211 @ SV202 @ SV127 ) ) )
= $false )
| ( ( sequential @ SV202 @ SV211 )
= $true )
| ( ( precedes @ SV202 @ SV211 @ SV127 )
= $false )
| ( ( path @ SV141 @ SV145 @ SV127 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1103]) ).
thf(1120,plain,
! [SV148: $i,SV142: $i,SV178: $i,SV128: $i,SV187: $i,SV219: $i] :
( ( ( precedes @ SV219 @ SV187 @ SV128 )
= $false )
| ( ( ~ ( sequential @ SV178 @ SV219 ) )
= $true )
| ( ( on_path @ SV178 @ SV128 )
= $false )
| ( ( on_path @ SV187 @ SV128 )
= $false )
| ( ( precedes @ SV178 @ SV187 @ SV128 )
= $true )
| ( ( path @ SV142 @ SV148 @ SV128 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1104]) ).
thf(1121,plain,
! [SV224: $i,SV119: $i,SV149: $i,SV153: $i] :
( ( ( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ SV224 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ SV224 ) )
= $true )
| ( ( SV149
= ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
= $false )
| ( ( SV153
= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ empty ) )
= $false )
| ( ( path @ SV119 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1105]) ).
thf(1122,plain,
! [SV119: $i,SV149: $i,SV153: $i] :
( ( ( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ ( sK14_SY90 @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ ( sK14_SY90 @ SV153 @ SV149 @ SV119 ) ) )
= $false )
| ( ( SV149
= ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
= $true )
| ( ( path @ SV119 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1106]) ).
thf(1123,plain,
! [SV119: $i,SV149: $i,SV153: $i] :
( ( ( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ ( sK13_SY91 @ SV153 @ SV149 @ SV119 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ ( sK13_SY91 @ SV153 @ SV149 @ SV119 ) ) )
= $false )
| ( ( SV153
= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ empty ) )
= $true )
| ( ( path @ SV119 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1107]) ).
thf(1124,plain,
! [SV139: $i,SV144: $i] :
( ( ( SV144
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
= $false )
| ( ( SV139
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
= $false )
| ( ( ( SV144
!= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
!= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
= $true )
| ( ( SV139 = SV144 )
= $true )
| ( ( vertex @ SV139 )
= $false )
| ( ( vertex @ SV144 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1108]) ).
thf(1125,plain,
! [SV144: $i,SV139: $i] :
( ( ( ~ ( ( SV139
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
| ~ ( ( SV139
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) ) )
= $false )
| ( ( SV139 = SV144 )
= $true )
| ( ( vertex @ SV139 )
= $false )
| ( ( vertex @ SV144 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1109]) ).
thf(1126,plain,
! [SV139: $i,SV144: $i] :
( ( ( ~ ( ( SV144
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
| ~ ( ( SV144
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) ) )
= $false )
| ( ( SV139 = SV144 )
= $true )
| ( ( vertex @ SV139 )
= $false )
| ( ( vertex @ SV144 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1110]) ).
thf(1127,plain,
! [SV125: $i,SV135: $i,SV196: $i,SV140: $i] :
( ( ( SV140
= ( path_cons @ SV196 @ empty ) )
= $false )
| ( ( SV135
= ( head_of @ SV196 ) )
= $false )
| ( ( SV125
= ( tail_of @ SV196 ) )
= $false )
| ( ( edge @ SV196 )
= $false )
| ( ( vertex @ SV125 )
= $false )
| ( ( vertex @ SV135 )
= $false )
| ( ( path @ SV125 @ SV135 @ SV140 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1111]) ).
thf(1128,plain,
! [SV125: $i,SV135: $i,SV220: $i,SV197: $i,SV140: $i] :
( ( ( SV140
= ( path_cons @ SV197 @ SV220 ) )
= $false )
| ( ( ~ ( path @ ( head_of @ SV197 ) @ SV135 @ SV220 ) )
= $true )
| ( ( SV125
= ( tail_of @ SV197 ) )
= $false )
| ( ( edge @ SV197 )
= $false )
| ( ( vertex @ SV125 )
= $false )
| ( ( vertex @ SV135 )
= $false )
| ( ( path @ SV125 @ SV135 @ SV140 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1112]) ).
thf(1129,plain,
! [SV126: $i] :
( ( ! [SY301: $i,SY302: $i] :
~ ( triangle @ SV126 @ SY301 @ SY302 )
| ( edge @ SV126 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1114]) ).
thf(1130,plain,
! [SV126: $i] :
( ( ! [SY303: $i] :
( ! [SY304: $i] :
~ ( triangle @ SV126 @ SY303 @ SY304 )
| ( edge @ SY303 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1115]) ).
thf(1131,plain,
! [SV223: $i,SV221: $i,SV126: $i] :
( ( ( ~ ( triangle @ SV126 @ SV221 @ SV223 ) )
= $true )
| ( ( edge @ SV223 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1116]) ).
thf(1132,plain,
! [SV145: $i,SV141: $i,SV201: $i,SV127: $i,SV210: $i,SV222: $i] :
( ( ( precedes @ SV222 @ SV210 @ SV127 )
= $false )
| ( ( ~ ( sequential @ SV201 @ SV222 ) )
= $true )
| ( ( ~ ( sequential @ SV201 @ SV210 ) )
= $true )
| ( ( precedes @ SV201 @ SV210 @ SV127 )
= $false )
| ( ( path @ SV141 @ SV145 @ SV127 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1117]) ).
thf(1133,plain,
! [SV145: $i,SV141: $i,SV127: $i,SV202: $i,SV211: $i] :
( ( ( precedes @ ( sK10_E3 @ SV211 @ SV202 @ SV127 ) @ SV211 @ SV127 )
= $true )
| ( ( sequential @ SV202 @ SV211 )
= $true )
| ( ( precedes @ SV202 @ SV211 @ SV127 )
= $false )
| ( ( path @ SV141 @ SV145 @ SV127 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1118]) ).
thf(1134,plain,
! [SV145: $i,SV141: $i,SV127: $i,SV211: $i,SV202: $i] :
( ( ( sequential @ SV202 @ ( sK10_E3 @ SV211 @ SV202 @ SV127 ) )
= $true )
| ( ( sequential @ SV202 @ SV211 )
= $true )
| ( ( precedes @ SV202 @ SV211 @ SV127 )
= $false )
| ( ( path @ SV141 @ SV145 @ SV127 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1119]) ).
thf(1135,plain,
! [SV148: $i,SV142: $i,SV128: $i,SV187: $i,SV219: $i,SV178: $i] :
( ( ( sequential @ SV178 @ SV219 )
= $false )
| ( ( precedes @ SV219 @ SV187 @ SV128 )
= $false )
| ( ( on_path @ SV178 @ SV128 )
= $false )
| ( ( on_path @ SV187 @ SV128 )
= $false )
| ( ( precedes @ SV178 @ SV187 @ SV128 )
= $true )
| ( ( path @ SV142 @ SV148 @ SV128 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1120]) ).
thf(1136,plain,
! [SV224: $i,SV119: $i,SV149: $i,SV153: $i] :
( ( ( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ SV224 ) ) )
= $true )
| ( ( ~ ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ SV224 ) )
= $true )
| ( ( SV149
= ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
= $false )
| ( ( SV153
= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ empty ) )
= $false )
| ( ( path @ SV119 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1121]) ).
thf(1137,plain,
! [SV119: $i,SV149: $i,SV153: $i] :
( ( ( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ ( sK14_SY90 @ SV153 @ SV149 @ SV119 ) ) ) )
= $false )
| ( ( SV149
= ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
= $true )
| ( ( path @ SV119 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1122]) ).
thf(1138,plain,
! [SV119: $i,SV149: $i,SV153: $i] :
( ( ( ~ ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ ( sK14_SY90 @ SV153 @ SV149 @ SV119 ) ) )
= $false )
| ( ( SV149
= ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
= $true )
| ( ( path @ SV119 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1122]) ).
thf(1139,plain,
! [SV119: $i,SV149: $i,SV153: $i] :
( ( ( ( SV153
!= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ ( sK13_SY91 @ SV153 @ SV149 @ SV119 ) ) ) )
= $false )
| ( ( SV153
= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ empty ) )
= $true )
| ( ( path @ SV119 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1123]) ).
thf(1140,plain,
! [SV119: $i,SV149: $i,SV153: $i] :
( ( ( ~ ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ ( sK13_SY91 @ SV153 @ SV149 @ SV119 ) ) )
= $false )
| ( ( SV153
= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ empty ) )
= $true )
| ( ( path @ SV119 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1123]) ).
thf(1141,plain,
! [SV139: $i,SV144: $i] :
( ( ( ( SV144
!= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
= $true )
| ( ( ( SV139
!= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
= $true )
| ( ( SV139
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
= $false )
| ( ( SV144
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
= $false )
| ( ( SV139 = SV144 )
= $true )
| ( ( vertex @ SV139 )
= $false )
| ( ( vertex @ SV144 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[1124]) ).
thf(1142,plain,
! [SV144: $i,SV139: $i] :
( ( ( ~ ( ( SV139
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) ) ) )
= $false )
| ( ( SV139 = SV144 )
= $true )
| ( ( vertex @ SV139 )
= $false )
| ( ( vertex @ SV144 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[1125]) ).
thf(1143,plain,
! [SV144: $i,SV139: $i] :
( ( ( ~ ( ( SV139
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) ) )
= $false )
| ( ( SV139 = SV144 )
= $true )
| ( ( vertex @ SV139 )
= $false )
| ( ( vertex @ SV144 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[1125]) ).
thf(1144,plain,
! [SV139: $i,SV144: $i] :
( ( ( ~ ( ( SV144
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) ) ) )
= $false )
| ( ( SV139 = SV144 )
= $true )
| ( ( vertex @ SV139 )
= $false )
| ( ( vertex @ SV144 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[1126]) ).
thf(1145,plain,
! [SV139: $i,SV144: $i] :
( ( ( ~ ( ( SV144
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) ) )
= $false )
| ( ( SV139 = SV144 )
= $true )
| ( ( vertex @ SV139 )
= $false )
| ( ( vertex @ SV144 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[1126]) ).
thf(1146,plain,
! [SV125: $i,SV140: $i,SV220: $i,SV135: $i,SV197: $i] :
( ( ( path @ ( head_of @ SV197 ) @ SV135 @ SV220 )
= $false )
| ( ( SV140
= ( path_cons @ SV197 @ SV220 ) )
= $false )
| ( ( SV125
= ( tail_of @ SV197 ) )
= $false )
| ( ( edge @ SV197 )
= $false )
| ( ( vertex @ SV125 )
= $false )
| ( ( vertex @ SV135 )
= $false )
| ( ( path @ SV125 @ SV135 @ SV140 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1128]) ).
thf(1147,plain,
! [SV126: $i] :
( ( ( ! [SY301: $i,SY302: $i] :
~ ( triangle @ SV126 @ SY301 @ SY302 ) )
= $true )
| ( ( edge @ SV126 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1129]) ).
thf(1148,plain,
! [SV225: $i,SV126: $i] :
( ( ! [SY408: $i] :
~ ( triangle @ SV126 @ SV225 @ SY408 )
| ( edge @ SV225 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1130]) ).
thf(1149,plain,
! [SV223: $i,SV221: $i,SV126: $i] :
( ( ( triangle @ SV126 @ SV221 @ SV223 )
= $false )
| ( ( edge @ SV223 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1131]) ).
thf(1150,plain,
! [SV145: $i,SV141: $i,SV127: $i,SV210: $i,SV222: $i,SV201: $i] :
( ( ( sequential @ SV201 @ SV222 )
= $false )
| ( ( precedes @ SV222 @ SV210 @ SV127 )
= $false )
| ( ( ~ ( sequential @ SV201 @ SV210 ) )
= $true )
| ( ( precedes @ SV201 @ SV210 @ SV127 )
= $false )
| ( ( path @ SV141 @ SV145 @ SV127 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1132]) ).
thf(1151,plain,
! [SV224: $i,SV119: $i,SV149: $i,SV153: $i] :
( ( ( SV153
= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ SV224 ) )
= $false )
| ( ( ~ ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ SV224 ) )
= $true )
| ( ( SV149
= ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
= $false )
| ( ( SV153
= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ empty ) )
= $false )
| ( ( path @ SV119 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1136]) ).
thf(1152,plain,
! [SV119: $i,SV149: $i,SV153: $i] :
( ( ( SV153
= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ ( sK14_SY90 @ SV153 @ SV149 @ SV119 ) ) )
= $true )
| ( ( SV149
= ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
= $true )
| ( ( path @ SV119 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1137]) ).
thf(1153,plain,
! [SV119: $i,SV149: $i,SV153: $i] :
( ( ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ ( sK14_SY90 @ SV153 @ SV149 @ SV119 ) )
= $true )
| ( ( SV149
= ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
= $true )
| ( ( path @ SV119 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1138]) ).
thf(1154,plain,
! [SV119: $i,SV149: $i,SV153: $i] :
( ( ( SV153
= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ ( sK13_SY91 @ SV153 @ SV149 @ SV119 ) ) )
= $true )
| ( ( SV153
= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ empty ) )
= $true )
| ( ( path @ SV119 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1139]) ).
thf(1155,plain,
! [SV119: $i,SV149: $i,SV153: $i] :
( ( ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ ( sK13_SY91 @ SV153 @ SV149 @ SV119 ) )
= $true )
| ( ( SV153
= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ empty ) )
= $true )
| ( ( path @ SV119 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1140]) ).
thf(1156,plain,
! [SV139: $i,SV144: $i] :
( ( ( SV144
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
= $false )
| ( ( ( SV139
!= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
= $true )
| ( ( SV139
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
= $false )
| ( ( SV144
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
= $false )
| ( ( SV139 = SV144 )
= $true )
| ( ( vertex @ SV139 )
= $false )
| ( ( vertex @ SV144 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1141]) ).
thf(1157,plain,
! [SV144: $i,SV139: $i] :
( ( ( ( SV139
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
= $true )
| ( ( SV139 = SV144 )
= $true )
| ( ( vertex @ SV139 )
= $false )
| ( ( vertex @ SV144 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1142]) ).
thf(1158,plain,
! [SV144: $i,SV139: $i] :
( ( ( ( SV139
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
= $true )
| ( ( SV139 = SV144 )
= $true )
| ( ( vertex @ SV139 )
= $false )
| ( ( vertex @ SV144 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1143]) ).
thf(1159,plain,
! [SV139: $i,SV144: $i] :
( ( ( ( SV144
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV144
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
= $true )
| ( ( SV139 = SV144 )
= $true )
| ( ( vertex @ SV139 )
= $false )
| ( ( vertex @ SV144 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1144]) ).
thf(1160,plain,
! [SV139: $i,SV144: $i] :
( ( ( ( SV144
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
| ( SV139
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) ) )
= $true )
| ( ( SV139 = SV144 )
= $true )
| ( ( vertex @ SV139 )
= $false )
| ( ( vertex @ SV144 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1145]) ).
thf(1161,plain,
! [SV226: $i,SV126: $i] :
( ( ( ! [SY409: $i] :
~ ( triangle @ SV126 @ SV226 @ SY409 ) )
= $true )
| ( ( edge @ SV126 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1147]) ).
thf(1162,plain,
! [SV225: $i,SV126: $i] :
( ( ( ! [SY408: $i] :
~ ( triangle @ SV126 @ SV225 @ SY408 ) )
= $true )
| ( ( edge @ SV225 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1148]) ).
thf(1163,plain,
! [SV145: $i,SV141: $i,SV127: $i,SV222: $i,SV210: $i,SV201: $i] :
( ( ( sequential @ SV201 @ SV210 )
= $false )
| ( ( precedes @ SV222 @ SV210 @ SV127 )
= $false )
| ( ( sequential @ SV201 @ SV222 )
= $false )
| ( ( precedes @ SV201 @ SV210 @ SV127 )
= $false )
| ( ( path @ SV141 @ SV145 @ SV127 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1150]) ).
thf(1164,plain,
! [SV224: $i,SV119: $i,SV149: $i,SV153: $i] :
( ( ( path @ ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) @ SV149 @ SV224 )
= $false )
| ( ( SV153
= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ SV224 ) )
= $false )
| ( ( SV149
= ( head_of @ ( sK12_E @ SV153 @ SV149 @ SV119 ) ) )
= $false )
| ( ( SV153
= ( path_cons @ ( sK12_E @ SV153 @ SV149 @ SV119 ) @ empty ) )
= $false )
| ( ( path @ SV119 @ SV149 @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1151]) ).
thf(1165,plain,
! [SV144: $i,SV139: $i] :
( ( ( SV139
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
= $false )
| ( ( SV144
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
= $false )
| ( ( SV139
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
= $false )
| ( ( SV144
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
= $false )
| ( ( SV139 = SV144 )
= $true )
| ( ( vertex @ SV139 )
= $false )
| ( ( vertex @ SV144 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1156]) ).
thf(1166,plain,
! [SV144: $i,SV139: $i] :
( ( ( SV139
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
= $true )
| ( ( SV144
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
= $true )
| ( ( SV139 = SV144 )
= $true )
| ( ( vertex @ SV139 )
= $false )
| ( ( vertex @ SV144 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[1157]) ).
thf(1167,plain,
! [SV144: $i,SV139: $i] :
( ( ( SV139
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
= $true )
| ( ( SV139
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
= $true )
| ( ( SV139 = SV144 )
= $true )
| ( ( vertex @ SV139 )
= $false )
| ( ( vertex @ SV144 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[1158]) ).
thf(1168,plain,
! [SV139: $i,SV144: $i] :
( ( ( SV144
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
= $true )
| ( ( SV144
= ( head_of @ ( sK15_E @ SV144 @ SV139 ) ) )
= $true )
| ( ( SV139 = SV144 )
= $true )
| ( ( vertex @ SV139 )
= $false )
| ( ( vertex @ SV144 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[1159]) ).
thf(1169,plain,
! [SV139: $i,SV144: $i] :
( ( ( SV144
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
= $true )
| ( ( SV139
= ( tail_of @ ( sK15_E @ SV144 @ SV139 ) ) )
= $true )
| ( ( SV139 = SV144 )
= $true )
| ( ( vertex @ SV139 )
= $false )
| ( ( vertex @ SV144 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[1160]) ).
thf(1170,plain,
! [SV227: $i,SV226: $i,SV126: $i] :
( ( ( ~ ( triangle @ SV126 @ SV226 @ SV227 ) )
= $true )
| ( ( edge @ SV126 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1161]) ).
thf(1171,plain,
! [SV228: $i,SV225: $i,SV126: $i] :
( ( ( ~ ( triangle @ SV126 @ SV225 @ SV228 ) )
= $true )
| ( ( edge @ SV225 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1162]) ).
thf(1172,plain,
! [SV227: $i,SV226: $i,SV126: $i] :
( ( ( triangle @ SV126 @ SV226 @ SV227 )
= $false )
| ( ( edge @ SV126 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1170]) ).
thf(1173,plain,
! [SV228: $i,SV225: $i,SV126: $i] :
( ( ( triangle @ SV126 @ SV225 @ SV228 )
= $false )
| ( ( edge @ SV225 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1171]) ).
thf(1174,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[643,1173,1172,1169,1168,1167,1166,1165,1164,1163,1155,1154,1153,1152,1149,1146,1135,1134,1133,1127,1113,1101,1089,1077,1076,1075,1067,1066,1059,1058,1054,1051,1042,1031,1029,1028,1027,1026,1023,1021,1018,1017,1001,995,971,968,954,944,938,925,918,914,913,886,788,787,740,739,716,679,645,644]) ).
thf(1175,plain,
( ( ! [E: $i] :
( ~ ( edge @ E )
| ( ( head_of @ E )
!= ( tail_of @ E ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(1176,plain,
( ( ! [E: $i] :
( ~ ( edge @ E )
| ( vertex @ ( head_of @ E ) ) )
& ! [E: $i] :
( ~ ( edge @ E )
| ( vertex @ ( tail_of @ E ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(1177,plain,
( ( ~ complete
| ! [V1: $i,V2: $i] :
( ( V1 = V2 )
| ~ ( vertex @ V1 )
| ~ ( vertex @ V2 )
| ( ( ( V1
!= ( head_of @ ( sK15_E @ V2 @ V1 ) ) )
| ( V2
!= ( tail_of @ ( sK15_E @ V2 @ V1 ) ) )
| ( V2
!= ( head_of @ ( sK15_E @ V2 @ V1 ) ) )
| ( V1
!= ( tail_of @ ( sK15_E @ V2 @ V1 ) ) ) )
& ( ( V1
= ( head_of @ ( sK15_E @ V2 @ V1 ) ) )
| ( V2
= ( head_of @ ( sK15_E @ V2 @ V1 ) ) ) )
& ( ( V1
= ( head_of @ ( sK15_E @ V2 @ V1 ) ) )
| ( V1
= ( tail_of @ ( sK15_E @ V2 @ V1 ) ) ) )
& ( ( V2
= ( tail_of @ ( sK15_E @ V2 @ V1 ) ) )
| ( V2
= ( head_of @ ( sK15_E @ V2 @ V1 ) ) ) )
& ( ( V2
= ( tail_of @ ( sK15_E @ V2 @ V1 ) ) )
| ( V1
= ( tail_of @ ( sK15_E @ V2 @ V1 ) ) ) )
& ( edge @ ( sK15_E @ V2 @ V1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(1178,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)],[67]) ).
thf(1179,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 @ ( sK12_E @ P @ V2 @ V1 ) ) )
& ( edge @ ( sK12_E @ P @ V2 @ V1 ) )
& ( ( V2
!= ( head_of @ ( sK12_E @ P @ V2 @ V1 ) ) )
| ( P
!= ( path_cons @ ( sK12_E @ P @ V2 @ V1 ) @ empty ) )
| ! [SY89: $i] :
( ( P
!= ( path_cons @ ( sK12_E @ P @ V2 @ V1 ) @ SY89 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ P @ V2 @ V1 ) ) @ V2 @ SY89 ) ) )
& ( ( V2
= ( head_of @ ( sK12_E @ P @ V2 @ V1 ) ) )
| ( ( P
= ( path_cons @ ( sK12_E @ P @ V2 @ V1 ) @ ( sK14_SY90 @ P @ V2 @ V1 ) ) )
& ( path @ ( head_of @ ( sK12_E @ P @ V2 @ V1 ) ) @ V2 @ ( sK14_SY90 @ P @ V2 @ V1 ) ) ) )
& ( ( P
= ( path_cons @ ( sK12_E @ P @ V2 @ V1 ) @ empty ) )
| ( ( P
= ( path_cons @ ( sK12_E @ P @ V2 @ V1 ) @ ( sK13_SY91 @ P @ V2 @ V1 ) ) )
& ( path @ ( head_of @ ( sK12_E @ P @ V2 @ V1 ) ) @ V2 @ ( sK13_SY91 @ P @ V2 @ V1 ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(1180,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)],[65]) ).
thf(1181,plain,
( ( ! [V1: $i,V2: $i] :
( ! [P: $i,V: $i] :
( ~ ( in_path @ V @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( ( on_path @ ( sK11_E @ V @ P @ V2 @ V1 ) @ P )
& ( ( V
= ( head_of @ ( sK11_E @ V @ P @ V2 @ V1 ) ) )
| ( V
= ( tail_of @ ( sK11_E @ V @ P @ V2 @ V1 ) ) ) ) ) )
& ! [P: $i,V: $i] :
( ~ ( in_path @ V @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( vertex @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(1182,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)],[63]) ).
thf(1183,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)],[62]) ).
thf(1184,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 @ ( sK10_E3 @ E2 @ E1 @ P ) @ E2 @ P )
& ( sequential @ E1 @ ( sK10_E3 @ E2 @ E1 @ P ) ) )
| ( sequential @ E1 @ E2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(1185,plain,
( ( ! [V1: $i] :
( ! [V2: $i,SP: $i] :
( ( ( path @ V1 @ V2 @ ( sK9_P @ SP @ V2 @ V1 ) )
& ~ ( less_or_equal @ ( length_of @ SP ) @ ( length_of @ ( sK9_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)],[60]) ).
thf(1186,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)],[59]) ).
thf(1187,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)],[58]) ).
thf(1188,plain,
( ( ! [V1: $i,V2: $i,P: $i] :
( ~ ( path @ V1 @ V2 @ P )
| ( ( length_of @ P )
= ( number_of_in @ edges @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(1189,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)],[56]) ).
thf(1190,plain,
( ( ! [P: $i] :
( ( ( on_path @ ( sK7_E1 @ P ) @ P )
& ( on_path @ ( sK8_SY86 @ P ) @ P )
& ( sequential @ ( sK7_E1 @ P ) @ ( sK8_SY86 @ P ) )
& ! [SY88: $i] :
~ ( triangle @ ( sK7_E1 @ P ) @ ( sK8_SY86 @ P ) @ SY88 ) )
| ! [V1: $i,V2: $i] :
~ ( path @ V1 @ V2 @ P )
| ( ( number_of_in @ sequential_pairs @ P )
= ( number_of_in @ triangles @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(1191,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(1192,plain,
( ( precedes @ sK3_SY76 @ sK4_SY80 @ sK5_SY83 )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(1193,plain,
( ( shortest_path @ sK1_V1 @ sK2_SY71 @ sK5_SY83 )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(1194,plain,
( ( ( head_of @ sK4_SY80 )
= ( head_of @ sK3_SY76 ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(1195,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 @ ( sK12_E @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( edge @ ( sK12_E @ SX2 @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ( SX1
!= ( head_of @ ( sK12_E @ SX2 @ SX1 @ SX0 ) ) )
| ( SX2
!= ( path_cons @ ( sK12_E @ SX2 @ SX1 @ SX0 ) @ empty ) )
| ! [SX3: $i] :
( ( SX2
!= ( path_cons @ ( sK12_E @ SX2 @ SX1 @ SX0 ) @ SX3 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SX2 @ SX1 @ SX0 ) ) @ SX1 @ SX3 ) ) )
| ~ ~ ( ~ ( ( SX1
= ( head_of @ ( sK12_E @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( ( SX2
!= ( path_cons @ ( sK12_E @ SX2 @ SX1 @ SX0 ) @ ( sK14_SY90 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SX2 @ SX1 @ SX0 ) ) @ SX1 @ ( sK14_SY90 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX2
= ( path_cons @ ( sK12_E @ SX2 @ SX1 @ SX0 ) @ empty ) )
| ~ ( ( SX2
!= ( path_cons @ ( sK12_E @ SX2 @ SX1 @ SX0 ) @ ( sK13_SY91 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SX2 @ SX1 @ SX0 ) ) @ SX1 @ ( sK13_SY91 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1179]) ).
thf(1196,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)],[1180]) ).
thf(1197,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)],[1183]) ).
thf(1198,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)],[1186]) ).
thf(1199,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 @ ( sK10_E3 @ SX2 @ SX1 @ SX0 ) @ SX2 @ SX0 )
| ~ ( sequential @ SX1 @ ( sK10_E3 @ SX2 @ SX1 @ SX0 ) ) )
| ( sequential @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1184]) ).
thf(1200,plain,
( ( ~ complete
| ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( vertex @ SX0 )
| ~ ( vertex @ SX1 )
| ~ ( ~ ~ ( ~ ( ( SX0
!= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX0
!= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SX0
= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX0
= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) ) ) )
| ~ ~ ( ~ ( ( SX1
= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX1
= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) ) ) ) ) )
| ~ ( edge @ ( sK15_E @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1177]) ).
thf(1201,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK7_E1 @ SX0 ) @ SX0 )
| ~ ( on_path @ ( sK8_SY86 @ SX0 ) @ SX0 ) )
| ~ ( sequential @ ( sK7_E1 @ SX0 ) @ ( sK8_SY86 @ SX0 ) ) )
| ~ ! [SX1: $i] :
~ ( triangle @ ( sK7_E1 @ SX0 ) @ ( sK8_SY86 @ 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)],[1190]) ).
thf(1202,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( head_of @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( tail_of @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1176]) ).
thf(1203,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)],[1182]) ).
thf(1204,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in_path @ SX3 @ SX2 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ~ ( ~ ( on_path @ ( sK11_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( ( SX3
= ( head_of @ ( sK11_E @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ( SX3
= ( tail_of @ ( sK11_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)],[1181]) ).
thf(1205,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)],[1178]) ).
thf(1206,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( path @ SX0 @ SX1 @ ( sK9_P @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SX2 ) @ ( length_of @ ( sK9_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)],[1185]) ).
thf(1207,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)],[1187]) ).
thf(1208,plain,
! [SV229: $i] :
( ( ~ ( edge @ SV229 )
| ( ( head_of @ SV229 )
!= ( tail_of @ SV229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1175]) ).
thf(1209,plain,
! [SV230: $i] :
( ( ! [SY410: $i,SY411: $i] :
( ~ ( path @ SV230 @ SY410 @ SY411 )
| ( ( length_of @ SY411 )
= ( number_of_in @ edges @ SY411 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1188]) ).
thf(1210,plain,
! [SV231: $i] :
( ( ! [SY412: $i,SY413: $i] :
( ~ ( path @ SV231 @ SY412 @ SY413 )
| ( ( number_of_in @ sequential_pairs @ SY413 )
= ( minus @ ( length_of @ SY413 ) @ n1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1189]) ).
thf(1211,plain,
! [SV232: $i] :
( ( ! [SY414: $i] : ( less_or_equal @ ( number_of_in @ SV232 @ SY414 ) @ ( number_of_in @ SV232 @ graph ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1191]) ).
thf(1212,plain,
! [SV233: $i] :
( ( ~ ( ~ ~ ( ~ ( ! [SY415: $i,SY416: $i] :
~ ( path @ SV233 @ SY415 @ SY416 )
| ( vertex @ SV233 ) )
| ~ ! [SY417: $i] :
( ! [SY418: $i] :
~ ( path @ SV233 @ SY417 @ SY418 )
| ( vertex @ SY417 ) ) )
| ~ ! [SY419: $i,SY420: $i] :
( ~ ( path @ SV233 @ SY419 @ SY420 )
| ~ ( ~ ~ ( ( SV233
!= ( tail_of @ ( sK12_E @ SY420 @ SY419 @ SV233 ) ) )
| ~ ( edge @ ( sK12_E @ SY420 @ SY419 @ SV233 ) ) )
| ~ ~ ( ~ ( ( SY419
!= ( head_of @ ( sK12_E @ SY420 @ SY419 @ SV233 ) ) )
| ( SY420
!= ( path_cons @ ( sK12_E @ SY420 @ SY419 @ SV233 ) @ empty ) )
| ! [SY421: $i] :
( ( SY420
!= ( path_cons @ ( sK12_E @ SY420 @ SY419 @ SV233 ) @ SY421 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SY420 @ SY419 @ SV233 ) ) @ SY419 @ SY421 ) ) )
| ~ ~ ( ~ ( ( SY419
= ( head_of @ ( sK12_E @ SY420 @ SY419 @ SV233 ) ) )
| ~ ( ( SY420
!= ( path_cons @ ( sK12_E @ SY420 @ SY419 @ SV233 ) @ ( sK14_SY90 @ SY420 @ SY419 @ SV233 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SY420 @ SY419 @ SV233 ) ) @ SY419 @ ( sK14_SY90 @ SY420 @ SY419 @ SV233 ) ) ) )
| ~ ( ( SY420
= ( path_cons @ ( sK12_E @ SY420 @ SY419 @ SV233 ) @ empty ) )
| ~ ( ( SY420
!= ( path_cons @ ( sK12_E @ SY420 @ SY419 @ SV233 ) @ ( sK13_SY91 @ SY420 @ SY419 @ SV233 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SY420 @ SY419 @ SV233 ) ) @ SY419 @ ( sK13_SY91 @ SY420 @ SY419 @ SV233 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1195]) ).
thf(1213,plain,
! [SV234: $i] :
( ( ! [SY422: $i] :
~ ( ~ ~ ( ~ ! [SY423: $i,SY424: $i] :
( ~ ( on_path @ SY424 @ SY423 )
| ~ ( path @ SV234 @ SY422 @ SY423 )
| ( edge @ SY424 ) )
| ~ ! [SY425: $i,SY426: $i] :
( ~ ( on_path @ SY426 @ SY425 )
| ~ ( path @ SV234 @ SY422 @ SY425 )
| ( in_path @ ( head_of @ SY426 ) @ SY425 ) ) )
| ~ ! [SY427: $i,SY428: $i] :
( ~ ( on_path @ SY428 @ SY427 )
| ~ ( path @ SV234 @ SY422 @ SY427 )
| ( in_path @ ( tail_of @ SY428 ) @ SY427 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1196]) ).
thf(1214,plain,
! [SV235: $i] :
( ( ! [SY429: $i,SY430: $i] :
~ ( path @ SY429 @ SY430 @ SV235 )
| ~ ( ~ ! [SY431: $i,SY432: $i] :
( ~ ( on_path @ SY431 @ SV235 )
| ~ ( on_path @ SY432 @ SV235 )
| ! [SY433: $i] :
( ~ ( precedes @ SY433 @ SY432 @ SV235 )
| ~ ( sequential @ SY431 @ SY433 ) )
| ( precedes @ SY431 @ SY432 @ SV235 ) )
| ~ ! [SY434: $i,SY435: $i] :
( ~ ( on_path @ SY434 @ SV235 )
| ~ ( on_path @ SY435 @ SV235 )
| ~ ( sequential @ SY434 @ SY435 )
| ( precedes @ SY434 @ SY435 @ SV235 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1197]) ).
thf(1215,plain,
! [SV236: $i] :
( ( ! [SY436: $i,SY437: $i] :
~ ( ~ ! [SY438: $i] :
( ! [SY439: $i] :
( ~ ( precedes @ SY437 @ SY438 @ SY439 )
| ~ ( shortest_path @ SV236 @ SY436 @ SY439 ) )
| ! [SX4: $i] :
( ( ( tail_of @ SX4 )
!= ( tail_of @ SY437 ) )
| ( ( head_of @ SX4 )
!= ( head_of @ SY438 ) ) ) )
| ~ ! [SY441: $i,SY442: $i] :
( ~ ( precedes @ SY437 @ SY441 @ SY442 )
| ~ ( shortest_path @ SV236 @ SY436 @ SY442 )
| ~ ( precedes @ SY441 @ SY437 @ SY442 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1198]) ).
thf(1216,plain,
! [SV237: $i] :
( ( ! [SY443: $i,SY444: $i] :
~ ( path @ SY443 @ SY444 @ SV237 )
| ~ ( ~ ~ ( ~ ! [SY445: $i] :
( ! [SY446: $i] :
~ ( precedes @ SY445 @ SY446 @ SV237 )
| ( on_path @ SY445 @ SV237 ) )
| ~ ! [SY447: $i,SY448: $i] :
( ~ ( precedes @ SY447 @ SY448 @ SV237 )
| ( on_path @ SY448 @ SV237 ) ) )
| ~ ~ ( ~ ! [SY449: $i,SY450: $i] :
( ~ ( precedes @ SY449 @ SY450 @ SV237 )
| ! [SY451: $i] :
( ~ ( precedes @ SY451 @ SY450 @ SV237 )
| ~ ( sequential @ SY449 @ SY451 ) )
| ~ ( sequential @ SY449 @ SY450 ) )
| ~ ! [SY452: $i,SY453: $i] :
( ~ ( precedes @ SY452 @ SY453 @ SV237 )
| ~ ( ~ ( precedes @ ( sK10_E3 @ SY453 @ SY452 @ SV237 ) @ SY453 @ SV237 )
| ~ ( sequential @ SY452 @ ( sK10_E3 @ SY453 @ SY452 @ SV237 ) ) )
| ( sequential @ SY452 @ SY453 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1199]) ).
thf(1217,plain,
( ( ( ~ complete )
= $true )
| ( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( vertex @ SX0 )
| ~ ( vertex @ SX1 )
| ~ ( ~ ~ ( ~ ( ( SX0
!= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX0
!= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SX0
= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX0
= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) ) ) )
| ~ ~ ( ~ ( ( SX1
= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX1
= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) ) ) ) ) )
| ~ ( edge @ ( sK15_E @ SX1 @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1200]) ).
thf(1218,plain,
! [SV238: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK7_E1 @ SV238 ) @ SV238 )
| ~ ( on_path @ ( sK8_SY86 @ SV238 ) @ SV238 ) )
| ~ ( sequential @ ( sK7_E1 @ SV238 ) @ ( sK8_SY86 @ SV238 ) ) )
| ~ ! [SY454: $i] :
~ ( triangle @ ( sK7_E1 @ SV238 ) @ ( sK8_SY86 @ SV238 ) @ SY454 ) )
| ! [SY455: $i,SY456: $i] :
~ ( path @ SY455 @ SY456 @ SV238 )
| ( ( number_of_in @ sequential_pairs @ SV238 )
= ( number_of_in @ triangles @ SV238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1201]) ).
thf(1219,plain,
( ( ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( head_of @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( tail_of @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1202]) ).
thf(1220,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)],[1203]) ).
thf(1221,plain,
! [SV239: $i] :
( ( ! [SY457: $i] :
~ ( ~ ! [SY458: $i,SY459: $i] :
( ~ ( in_path @ SY459 @ SY458 )
| ~ ( path @ SV239 @ SY457 @ SY458 )
| ~ ( ~ ( on_path @ ( sK11_E @ SY459 @ SY458 @ SY457 @ SV239 ) @ SY458 )
| ~ ( ( SY459
= ( head_of @ ( sK11_E @ SY459 @ SY458 @ SY457 @ SV239 ) ) )
| ( SY459
= ( tail_of @ ( sK11_E @ SY459 @ SY458 @ SY457 @ SV239 ) ) ) ) ) )
| ~ ! [SY460: $i,SY461: $i] :
( ~ ( in_path @ SY461 @ SY460 )
| ~ ( path @ SV239 @ SY457 @ SY460 )
| ( vertex @ SY461 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1204]) ).
thf(1222,plain,
! [SV240: $i] :
( ( ! [SY462: $i,SY463: $i] :
( ~ ( vertex @ SV240 )
| ~ ( vertex @ SY462 )
| ~ ( ~ ! [SY464: $i] :
( ( SV240
!= ( tail_of @ SY464 ) )
| ~ ( edge @ SY464 )
| ( SY462
!= ( head_of @ SY464 ) )
| ( SY463
!= ( path_cons @ SY464 @ empty ) ) )
| ~ ! [SY465: $i] :
( ( SV240
!= ( tail_of @ SY465 ) )
| ~ ( edge @ SY465 )
| ! [SX4: $i] :
( ( SY463
!= ( path_cons @ SY465 @ SX4 ) )
| ~ ( path @ ( head_of @ SY465 ) @ SY462 @ SX4 ) ) ) )
| ( path @ SV240 @ SY462 @ SY463 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1205]) ).
thf(1223,plain,
! [SV241: $i] :
( ( ~ ( ~ ! [SY467: $i,SY468: $i] :
( ~ ( ~ ( path @ SV241 @ SY467 @ ( sK9_P @ SY468 @ SY467 @ SV241 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY468 ) @ ( length_of @ ( sK9_P @ SY468 @ SY467 @ SV241 ) ) ) )
| ( SV241 = SY467 )
| ~ ( path @ SV241 @ SY467 @ SY468 )
| ( shortest_path @ SV241 @ SY467 @ SY468 ) )
| ~ ~ ( ~ ! [SY469: $i,SY470: $i] :
( ~ ( shortest_path @ SV241 @ SY469 @ SY470 )
| ! [SY471: $i] :
( ~ ( path @ SV241 @ SY469 @ SY471 )
| ( less_or_equal @ ( length_of @ SY470 ) @ ( length_of @ SY471 ) ) ) )
| ~ ~ ( ~ ! [SY472: $i] :
( ! [SY473: $i] :
~ ( shortest_path @ SV241 @ SY472 @ SY473 )
| ( SV241 != SY472 ) )
| ~ ! [SY474: $i,SY475: $i] :
( ~ ( shortest_path @ SV241 @ SY474 @ SY475 )
| ( path @ SV241 @ SY474 @ SY475 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1206]) ).
thf(1224,plain,
! [SV242: $i] :
( ( ~ ( ~ ! [SY476: $i,SY477: $i] :
( ~ ( edge @ SV242 )
| ~ ( edge @ SY476 )
| ~ ( edge @ SY477 )
| ~ ( sequential @ SV242 @ SY476 )
| ~ ( sequential @ SY476 @ SY477 )
| ~ ( sequential @ SY477 @ SV242 )
| ( triangle @ SV242 @ SY476 @ SY477 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY478: $i,SY479: $i] :
~ ( triangle @ SV242 @ SY478 @ SY479 )
| ( edge @ SV242 ) )
| ~ ! [SY480: $i] :
( ! [SY481: $i] :
~ ( triangle @ SV242 @ SY480 @ SY481 )
| ( edge @ SY480 ) ) )
| ~ ! [SY482: $i,SY483: $i] :
( ~ ( triangle @ SV242 @ SY482 @ SY483 )
| ( edge @ SY483 ) ) )
| ~ ! [SY484: $i] :
( ! [SY485: $i] :
~ ( triangle @ SV242 @ SY484 @ SY485 )
| ( sequential @ SV242 @ SY484 ) ) )
| ~ ! [SY486: $i,SY487: $i] :
( ~ ( triangle @ SV242 @ SY486 @ SY487 )
| ( sequential @ SY486 @ SY487 ) ) )
| ~ ! [SY488: $i,SY489: $i] :
( ~ ( triangle @ SV242 @ SY488 @ SY489 )
| ( sequential @ SY489 @ SV242 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1207]) ).
thf(1225,plain,
! [SV229: $i] :
( ( ( ~ ( edge @ SV229 ) )
= $true )
| ( ( ( ( head_of @ SV229 )
!= ( tail_of @ SV229 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1208]) ).
thf(1226,plain,
! [SV243: $i,SV230: $i] :
( ( ! [SY490: $i] :
( ~ ( path @ SV230 @ SV243 @ SY490 )
| ( ( length_of @ SY490 )
= ( number_of_in @ edges @ SY490 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1209]) ).
thf(1227,plain,
! [SV244: $i,SV231: $i] :
( ( ! [SY491: $i] :
( ~ ( path @ SV231 @ SV244 @ SY491 )
| ( ( number_of_in @ sequential_pairs @ SY491 )
= ( minus @ ( length_of @ SY491 ) @ n1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1210]) ).
thf(1228,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)],[1211]) ).
thf(1229,plain,
! [SV233: $i] :
( ( ~ ~ ( ~ ( ! [SY415: $i,SY416: $i] :
~ ( path @ SV233 @ SY415 @ SY416 )
| ( vertex @ SV233 ) )
| ~ ! [SY417: $i] :
( ! [SY418: $i] :
~ ( path @ SV233 @ SY417 @ SY418 )
| ( vertex @ SY417 ) ) )
| ~ ! [SY419: $i,SY420: $i] :
( ~ ( path @ SV233 @ SY419 @ SY420 )
| ~ ( ~ ~ ( ( SV233
!= ( tail_of @ ( sK12_E @ SY420 @ SY419 @ SV233 ) ) )
| ~ ( edge @ ( sK12_E @ SY420 @ SY419 @ SV233 ) ) )
| ~ ~ ( ~ ( ( SY419
!= ( head_of @ ( sK12_E @ SY420 @ SY419 @ SV233 ) ) )
| ( SY420
!= ( path_cons @ ( sK12_E @ SY420 @ SY419 @ SV233 ) @ empty ) )
| ! [SY421: $i] :
( ( SY420
!= ( path_cons @ ( sK12_E @ SY420 @ SY419 @ SV233 ) @ SY421 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SY420 @ SY419 @ SV233 ) ) @ SY419 @ SY421 ) ) )
| ~ ~ ( ~ ( ( SY419
= ( head_of @ ( sK12_E @ SY420 @ SY419 @ SV233 ) ) )
| ~ ( ( SY420
!= ( path_cons @ ( sK12_E @ SY420 @ SY419 @ SV233 ) @ ( sK14_SY90 @ SY420 @ SY419 @ SV233 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SY420 @ SY419 @ SV233 ) ) @ SY419 @ ( sK14_SY90 @ SY420 @ SY419 @ SV233 ) ) ) )
| ~ ( ( SY420
= ( path_cons @ ( sK12_E @ SY420 @ SY419 @ SV233 ) @ empty ) )
| ~ ( ( SY420
!= ( path_cons @ ( sK12_E @ SY420 @ SY419 @ SV233 ) @ ( sK13_SY91 @ SY420 @ SY419 @ SV233 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SY420 @ SY419 @ SV233 ) ) @ SY419 @ ( sK13_SY91 @ SY420 @ SY419 @ SV233 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1212]) ).
thf(1230,plain,
! [SV246: $i,SV234: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY492: $i,SY493: $i] :
( ~ ( on_path @ SY493 @ SY492 )
| ~ ( path @ SV234 @ SV246 @ SY492 )
| ( edge @ SY493 ) )
| ~ ! [SY494: $i,SY495: $i] :
( ~ ( on_path @ SY495 @ SY494 )
| ~ ( path @ SV234 @ SV246 @ SY494 )
| ( in_path @ ( head_of @ SY495 ) @ SY494 ) ) )
| ~ ! [SY496: $i,SY497: $i] :
( ~ ( on_path @ SY497 @ SY496 )
| ~ ( path @ SV234 @ SV246 @ SY496 )
| ( in_path @ ( tail_of @ SY497 ) @ SY496 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1213]) ).
thf(1231,plain,
! [SV235: $i] :
( ( ( ! [SY429: $i,SY430: $i] :
~ ( path @ SY429 @ SY430 @ SV235 ) )
= $true )
| ( ( ~ ( ~ ! [SY431: $i,SY432: $i] :
( ~ ( on_path @ SY431 @ SV235 )
| ~ ( on_path @ SY432 @ SV235 )
| ! [SY433: $i] :
( ~ ( precedes @ SY433 @ SY432 @ SV235 )
| ~ ( sequential @ SY431 @ SY433 ) )
| ( precedes @ SY431 @ SY432 @ SV235 ) )
| ~ ! [SY434: $i,SY435: $i] :
( ~ ( on_path @ SY434 @ SV235 )
| ~ ( on_path @ SY435 @ SV235 )
| ~ ( sequential @ SY434 @ SY435 )
| ( precedes @ SY434 @ SY435 @ SV235 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1214]) ).
thf(1232,plain,
! [SV247: $i,SV236: $i] :
( ( ! [SY498: $i] :
~ ( ~ ! [SY499: $i] :
( ! [SY500: $i] :
( ~ ( precedes @ SY498 @ SY499 @ SY500 )
| ~ ( shortest_path @ SV236 @ SV247 @ SY500 ) )
| ! [SX4: $i] :
( ( ( tail_of @ SX4 )
!= ( tail_of @ SY498 ) )
| ( ( head_of @ SX4 )
!= ( head_of @ SY499 ) ) ) )
| ~ ! [SY502: $i,SY503: $i] :
( ~ ( precedes @ SY498 @ SY502 @ SY503 )
| ~ ( shortest_path @ SV236 @ SV247 @ SY503 )
| ~ ( precedes @ SY502 @ SY498 @ SY503 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1215]) ).
thf(1233,plain,
! [SV237: $i] :
( ( ( ! [SY443: $i,SY444: $i] :
~ ( path @ SY443 @ SY444 @ SV237 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY445: $i] :
( ! [SY446: $i] :
~ ( precedes @ SY445 @ SY446 @ SV237 )
| ( on_path @ SY445 @ SV237 ) )
| ~ ! [SY447: $i,SY448: $i] :
( ~ ( precedes @ SY447 @ SY448 @ SV237 )
| ( on_path @ SY448 @ SV237 ) ) )
| ~ ~ ( ~ ! [SY449: $i,SY450: $i] :
( ~ ( precedes @ SY449 @ SY450 @ SV237 )
| ! [SY451: $i] :
( ~ ( precedes @ SY451 @ SY450 @ SV237 )
| ~ ( sequential @ SY449 @ SY451 ) )
| ~ ( sequential @ SY449 @ SY450 ) )
| ~ ! [SY452: $i,SY453: $i] :
( ~ ( precedes @ SY452 @ SY453 @ SV237 )
| ~ ( ~ ( precedes @ ( sK10_E3 @ SY453 @ SY452 @ SV237 ) @ SY453 @ SV237 )
| ~ ( sequential @ SY452 @ ( sK10_E3 @ SY453 @ SY452 @ SV237 ) ) )
| ( sequential @ SY452 @ SY453 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1216]) ).
thf(1234,plain,
( ( complete = $false )
| ( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( vertex @ SX0 )
| ~ ( vertex @ SX1 )
| ~ ( ~ ~ ( ~ ( ( SX0
!= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX0
!= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SX0
= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX0
= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) ) ) )
| ~ ~ ( ~ ( ( SX1
= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK15_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX1
= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK15_E @ SX1 @ SX0 ) ) ) ) ) ) )
| ~ ( edge @ ( sK15_E @ SX1 @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1217]) ).
thf(1235,plain,
! [SV238: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK7_E1 @ SV238 ) @ SV238 )
| ~ ( on_path @ ( sK8_SY86 @ SV238 ) @ SV238 ) )
| ~ ( sequential @ ( sK7_E1 @ SV238 ) @ ( sK8_SY86 @ SV238 ) ) )
| ~ ! [SY454: $i] :
~ ( triangle @ ( sK7_E1 @ SV238 ) @ ( sK8_SY86 @ SV238 ) @ SY454 ) )
| ! [SY455: $i,SY456: $i] :
~ ( path @ SY455 @ SY456 @ SV238 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV238 )
= ( number_of_in @ triangles @ SV238 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1218]) ).
thf(1236,plain,
( ( ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( head_of @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1219]) ).
thf(1237,plain,
( ( ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( tail_of @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1219]) ).
thf(1238,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)],[1220]) ).
thf(1239,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)],[1220]) ).
thf(1240,plain,
! [SV248: $i,SV239: $i] :
( ( ~ ( ~ ! [SY504: $i,SY505: $i] :
( ~ ( in_path @ SY505 @ SY504 )
| ~ ( path @ SV239 @ SV248 @ SY504 )
| ~ ( ~ ( on_path @ ( sK11_E @ SY505 @ SY504 @ SV248 @ SV239 ) @ SY504 )
| ~ ( ( SY505
= ( head_of @ ( sK11_E @ SY505 @ SY504 @ SV248 @ SV239 ) ) )
| ( SY505
= ( tail_of @ ( sK11_E @ SY505 @ SY504 @ SV248 @ SV239 ) ) ) ) ) )
| ~ ! [SY506: $i,SY507: $i] :
( ~ ( in_path @ SY507 @ SY506 )
| ~ ( path @ SV239 @ SV248 @ SY506 )
| ( vertex @ SY507 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1221]) ).
thf(1241,plain,
! [SV249: $i,SV240: $i] :
( ( ! [SY508: $i] :
( ~ ( vertex @ SV240 )
| ~ ( vertex @ SV249 )
| ~ ( ~ ! [SY509: $i] :
( ( SV240
!= ( tail_of @ SY509 ) )
| ~ ( edge @ SY509 )
| ( SV249
!= ( head_of @ SY509 ) )
| ( SY508
!= ( path_cons @ SY509 @ empty ) ) )
| ~ ! [SY510: $i] :
( ( SV240
!= ( tail_of @ SY510 ) )
| ~ ( edge @ SY510 )
| ! [SY511: $i] :
( ( SY508
!= ( path_cons @ SY510 @ SY511 ) )
| ~ ( path @ ( head_of @ SY510 ) @ SV249 @ SY511 ) ) ) )
| ( path @ SV240 @ SV249 @ SY508 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1222]) ).
thf(1242,plain,
! [SV241: $i] :
( ( ~ ! [SY467: $i,SY468: $i] :
( ~ ( ~ ( path @ SV241 @ SY467 @ ( sK9_P @ SY468 @ SY467 @ SV241 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY468 ) @ ( length_of @ ( sK9_P @ SY468 @ SY467 @ SV241 ) ) ) )
| ( SV241 = SY467 )
| ~ ( path @ SV241 @ SY467 @ SY468 )
| ( shortest_path @ SV241 @ SY467 @ SY468 ) )
| ~ ~ ( ~ ! [SY469: $i,SY470: $i] :
( ~ ( shortest_path @ SV241 @ SY469 @ SY470 )
| ! [SY471: $i] :
( ~ ( path @ SV241 @ SY469 @ SY471 )
| ( less_or_equal @ ( length_of @ SY470 ) @ ( length_of @ SY471 ) ) ) )
| ~ ~ ( ~ ! [SY472: $i] :
( ! [SY473: $i] :
~ ( shortest_path @ SV241 @ SY472 @ SY473 )
| ( SV241 != SY472 ) )
| ~ ! [SY474: $i,SY475: $i] :
( ~ ( shortest_path @ SV241 @ SY474 @ SY475 )
| ( path @ SV241 @ SY474 @ SY475 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1223]) ).
thf(1243,plain,
! [SV242: $i] :
( ( ~ ! [SY476: $i,SY477: $i] :
( ~ ( edge @ SV242 )
| ~ ( edge @ SY476 )
| ~ ( edge @ SY477 )
| ~ ( sequential @ SV242 @ SY476 )
| ~ ( sequential @ SY476 @ SY477 )
| ~ ( sequential @ SY477 @ SV242 )
| ( triangle @ SV242 @ SY476 @ SY477 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY478: $i,SY479: $i] :
~ ( triangle @ SV242 @ SY478 @ SY479 )
| ( edge @ SV242 ) )
| ~ ! [SY480: $i] :
( ! [SY481: $i] :
~ ( triangle @ SV242 @ SY480 @ SY481 )
| ( edge @ SY480 ) ) )
| ~ ! [SY482: $i,SY483: $i] :
( ~ ( triangle @ SV242 @ SY482 @ SY483 )
| ( edge @ SY483 ) ) )
| ~ ! [SY484: $i] :
( ! [SY485: $i] :
~ ( triangle @ SV242 @ SY484 @ SY485 )
| ( sequential @ SV242 @ SY484 ) ) )
| ~ ! [SY486: $i,SY487: $i] :
( ~ ( triangle @ SV242 @ SY486 @ SY487 )
| ( sequential @ SY486 @ SY487 ) ) )
| ~ ! [SY488: $i,SY489: $i] :
( ~ ( triangle @ SV242 @ SY488 @ SY489 )
| ( sequential @ SY489 @ SV242 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1224]) ).
thf(1244,plain,
! [SV229: $i] :
( ( ( edge @ SV229 )
= $false )
| ( ( ( ( head_of @ SV229 )
!= ( tail_of @ SV229 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1225]) ).
thf(1245,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)],[1226]) ).
thf(1246,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)],[1227]) ).
thf(1247,plain,
! [SV233: $i] :
( ( ~ ~ ( ~ ( ! [SY415: $i,SY416: $i] :
~ ( path @ SV233 @ SY415 @ SY416 )
| ( vertex @ SV233 ) )
| ~ ! [SY417: $i] :
( ! [SY418: $i] :
~ ( path @ SV233 @ SY417 @ SY418 )
| ( vertex @ SY417 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1229]) ).
thf(1248,plain,
! [SV233: $i] :
( ( ~ ! [SY419: $i,SY420: $i] :
( ~ ( path @ SV233 @ SY419 @ SY420 )
| ~ ( ~ ~ ( ( SV233
!= ( tail_of @ ( sK12_E @ SY420 @ SY419 @ SV233 ) ) )
| ~ ( edge @ ( sK12_E @ SY420 @ SY419 @ SV233 ) ) )
| ~ ~ ( ~ ( ( SY419
!= ( head_of @ ( sK12_E @ SY420 @ SY419 @ SV233 ) ) )
| ( SY420
!= ( path_cons @ ( sK12_E @ SY420 @ SY419 @ SV233 ) @ empty ) )
| ! [SY421: $i] :
( ( SY420
!= ( path_cons @ ( sK12_E @ SY420 @ SY419 @ SV233 ) @ SY421 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SY420 @ SY419 @ SV233 ) ) @ SY419 @ SY421 ) ) )
| ~ ~ ( ~ ( ( SY419
= ( head_of @ ( sK12_E @ SY420 @ SY419 @ SV233 ) ) )
| ~ ( ( SY420
!= ( path_cons @ ( sK12_E @ SY420 @ SY419 @ SV233 ) @ ( sK14_SY90 @ SY420 @ SY419 @ SV233 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SY420 @ SY419 @ SV233 ) ) @ SY419 @ ( sK14_SY90 @ SY420 @ SY419 @ SV233 ) ) ) )
| ~ ( ( SY420
= ( path_cons @ ( sK12_E @ SY420 @ SY419 @ SV233 ) @ empty ) )
| ~ ( ( SY420
!= ( path_cons @ ( sK12_E @ SY420 @ SY419 @ SV233 ) @ ( sK13_SY91 @ SY420 @ SY419 @ SV233 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SY420 @ SY419 @ SV233 ) ) @ SY419 @ ( sK13_SY91 @ SY420 @ SY419 @ SV233 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1229]) ).
thf(1249,plain,
! [SV246: $i,SV234: $i] :
( ( ~ ~ ( ~ ! [SY492: $i,SY493: $i] :
( ~ ( on_path @ SY493 @ SY492 )
| ~ ( path @ SV234 @ SV246 @ SY492 )
| ( edge @ SY493 ) )
| ~ ! [SY494: $i,SY495: $i] :
( ~ ( on_path @ SY495 @ SY494 )
| ~ ( path @ SV234 @ SV246 @ SY494 )
| ( in_path @ ( head_of @ SY495 ) @ SY494 ) ) )
| ~ ! [SY496: $i,SY497: $i] :
( ~ ( on_path @ SY497 @ SY496 )
| ~ ( path @ SV234 @ SV246 @ SY496 )
| ( in_path @ ( tail_of @ SY497 ) @ SY496 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1230]) ).
thf(1250,plain,
! [SV235: $i,SV252: $i] :
( ( ( ! [SY512: $i] :
~ ( path @ SV252 @ SY512 @ SV235 ) )
= $true )
| ( ( ~ ( ~ ! [SY431: $i,SY432: $i] :
( ~ ( on_path @ SY431 @ SV235 )
| ~ ( on_path @ SY432 @ SV235 )
| ! [SY433: $i] :
( ~ ( precedes @ SY433 @ SY432 @ SV235 )
| ~ ( sequential @ SY431 @ SY433 ) )
| ( precedes @ SY431 @ SY432 @ SV235 ) )
| ~ ! [SY434: $i,SY435: $i] :
( ~ ( on_path @ SY434 @ SV235 )
| ~ ( on_path @ SY435 @ SV235 )
| ~ ( sequential @ SY434 @ SY435 )
| ( precedes @ SY434 @ SY435 @ SV235 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1231]) ).
thf(1251,plain,
! [SV247: $i,SV236: $i,SV253: $i] :
( ( ~ ( ~ ! [SY513: $i] :
( ! [SY514: $i] :
( ~ ( precedes @ SV253 @ SY513 @ SY514 )
| ~ ( shortest_path @ SV236 @ SV247 @ SY514 ) )
| ! [SY515: $i] :
( ( ( tail_of @ SY515 )
!= ( tail_of @ SV253 ) )
| ( ( head_of @ SY515 )
!= ( head_of @ SY513 ) ) ) )
| ~ ! [SY516: $i,SY517: $i] :
( ~ ( precedes @ SV253 @ SY516 @ SY517 )
| ~ ( shortest_path @ SV236 @ SV247 @ SY517 )
| ~ ( precedes @ SY516 @ SV253 @ SY517 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1232]) ).
thf(1252,plain,
! [SV237: $i,SV254: $i] :
( ( ( ! [SY518: $i] :
~ ( path @ SV254 @ SY518 @ SV237 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY445: $i] :
( ! [SY446: $i] :
~ ( precedes @ SY445 @ SY446 @ SV237 )
| ( on_path @ SY445 @ SV237 ) )
| ~ ! [SY447: $i,SY448: $i] :
( ~ ( precedes @ SY447 @ SY448 @ SV237 )
| ( on_path @ SY448 @ SV237 ) ) )
| ~ ~ ( ~ ! [SY449: $i,SY450: $i] :
( ~ ( precedes @ SY449 @ SY450 @ SV237 )
| ! [SY451: $i] :
( ~ ( precedes @ SY451 @ SY450 @ SV237 )
| ~ ( sequential @ SY449 @ SY451 ) )
| ~ ( sequential @ SY449 @ SY450 ) )
| ~ ! [SY452: $i,SY453: $i] :
( ~ ( precedes @ SY452 @ SY453 @ SV237 )
| ~ ( ~ ( precedes @ ( sK10_E3 @ SY453 @ SY452 @ SV237 ) @ SY453 @ SV237 )
| ~ ( sequential @ SY452 @ ( sK10_E3 @ SY453 @ SY452 @ SV237 ) ) )
| ( sequential @ SY452 @ SY453 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1233]) ).
thf(1253,plain,
! [SV255: $i] :
( ( ( ! [SY519: $i] :
( ( SV255 = SY519 )
| ~ ( vertex @ SV255 )
| ~ ( vertex @ SY519 )
| ~ ( ~ ~ ( ~ ( ( SV255
!= ( head_of @ ( sK15_E @ SY519 @ SV255 ) ) )
| ( SY519
!= ( tail_of @ ( sK15_E @ SY519 @ SV255 ) ) )
| ( SY519
!= ( head_of @ ( sK15_E @ SY519 @ SV255 ) ) )
| ( SV255
!= ( tail_of @ ( sK15_E @ SY519 @ SV255 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV255
= ( head_of @ ( sK15_E @ SY519 @ SV255 ) ) )
| ( SY519
= ( head_of @ ( sK15_E @ SY519 @ SV255 ) ) ) )
| ~ ( ( SV255
= ( head_of @ ( sK15_E @ SY519 @ SV255 ) ) )
| ( SV255
= ( tail_of @ ( sK15_E @ SY519 @ SV255 ) ) ) ) )
| ~ ~ ( ~ ( ( SY519
= ( tail_of @ ( sK15_E @ SY519 @ SV255 ) ) )
| ( SY519
= ( head_of @ ( sK15_E @ SY519 @ SV255 ) ) ) )
| ~ ( ( SY519
= ( tail_of @ ( sK15_E @ SY519 @ SV255 ) ) )
| ( SV255
= ( tail_of @ ( sK15_E @ SY519 @ SV255 ) ) ) ) ) ) )
| ~ ( edge @ ( sK15_E @ SY519 @ SV255 ) ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1234]) ).
thf(1254,plain,
! [SV238: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK7_E1 @ SV238 ) @ SV238 )
| ~ ( on_path @ ( sK8_SY86 @ SV238 ) @ SV238 ) )
| ~ ( sequential @ ( sK7_E1 @ SV238 ) @ ( sK8_SY86 @ SV238 ) ) )
| ~ ! [SY454: $i] :
~ ( triangle @ ( sK7_E1 @ SV238 ) @ ( sK8_SY86 @ SV238 ) @ SY454 ) ) )
= $true )
| ( ( ! [SY455: $i,SY456: $i] :
~ ( path @ SY455 @ SY456 @ SV238 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV238 )
= ( number_of_in @ triangles @ SV238 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1235]) ).
thf(1255,plain,
( ( ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( head_of @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1236]) ).
thf(1256,plain,
( ( ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( tail_of @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1237]) ).
thf(1257,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)],[1238]) ).
thf(1258,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)],[1239]) ).
thf(1259,plain,
! [SV248: $i,SV239: $i] :
( ( ~ ! [SY504: $i,SY505: $i] :
( ~ ( in_path @ SY505 @ SY504 )
| ~ ( path @ SV239 @ SV248 @ SY504 )
| ~ ( ~ ( on_path @ ( sK11_E @ SY505 @ SY504 @ SV248 @ SV239 ) @ SY504 )
| ~ ( ( SY505
= ( head_of @ ( sK11_E @ SY505 @ SY504 @ SV248 @ SV239 ) ) )
| ( SY505
= ( tail_of @ ( sK11_E @ SY505 @ SY504 @ SV248 @ SV239 ) ) ) ) ) )
| ~ ! [SY506: $i,SY507: $i] :
( ~ ( in_path @ SY507 @ SY506 )
| ~ ( path @ SV239 @ SV248 @ SY506 )
| ( vertex @ SY507 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1240]) ).
thf(1260,plain,
! [SV256: $i,SV249: $i,SV240: $i] :
( ( ~ ( vertex @ SV240 )
| ~ ( vertex @ SV249 )
| ~ ( ~ ! [SY520: $i] :
( ( SV240
!= ( tail_of @ SY520 ) )
| ~ ( edge @ SY520 )
| ( SV249
!= ( head_of @ SY520 ) )
| ( SV256
!= ( path_cons @ SY520 @ empty ) ) )
| ~ ! [SY521: $i] :
( ( SV240
!= ( tail_of @ SY521 ) )
| ~ ( edge @ SY521 )
| ! [SY522: $i] :
( ( SV256
!= ( path_cons @ SY521 @ SY522 ) )
| ~ ( path @ ( head_of @ SY521 ) @ SV249 @ SY522 ) ) ) )
| ( path @ SV240 @ SV249 @ SV256 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1241]) ).
thf(1261,plain,
! [SV241: $i] :
( ( ~ ! [SY467: $i,SY468: $i] :
( ~ ( ~ ( path @ SV241 @ SY467 @ ( sK9_P @ SY468 @ SY467 @ SV241 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY468 ) @ ( length_of @ ( sK9_P @ SY468 @ SY467 @ SV241 ) ) ) )
| ( SV241 = SY467 )
| ~ ( path @ SV241 @ SY467 @ SY468 )
| ( shortest_path @ SV241 @ SY467 @ SY468 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1242]) ).
thf(1262,plain,
! [SV241: $i] :
( ( ~ ~ ( ~ ! [SY469: $i,SY470: $i] :
( ~ ( shortest_path @ SV241 @ SY469 @ SY470 )
| ! [SY471: $i] :
( ~ ( path @ SV241 @ SY469 @ SY471 )
| ( less_or_equal @ ( length_of @ SY470 ) @ ( length_of @ SY471 ) ) ) )
| ~ ~ ( ~ ! [SY472: $i] :
( ! [SY473: $i] :
~ ( shortest_path @ SV241 @ SY472 @ SY473 )
| ( SV241 != SY472 ) )
| ~ ! [SY474: $i,SY475: $i] :
( ~ ( shortest_path @ SV241 @ SY474 @ SY475 )
| ( path @ SV241 @ SY474 @ SY475 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1242]) ).
thf(1263,plain,
! [SV242: $i] :
( ( ~ ! [SY476: $i,SY477: $i] :
( ~ ( edge @ SV242 )
| ~ ( edge @ SY476 )
| ~ ( edge @ SY477 )
| ~ ( sequential @ SV242 @ SY476 )
| ~ ( sequential @ SY476 @ SY477 )
| ~ ( sequential @ SY477 @ SV242 )
| ( triangle @ SV242 @ SY476 @ SY477 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1243]) ).
thf(1264,plain,
! [SV242: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY478: $i,SY479: $i] :
~ ( triangle @ SV242 @ SY478 @ SY479 )
| ( edge @ SV242 ) )
| ~ ! [SY480: $i] :
( ! [SY481: $i] :
~ ( triangle @ SV242 @ SY480 @ SY481 )
| ( edge @ SY480 ) ) )
| ~ ! [SY482: $i,SY483: $i] :
( ~ ( triangle @ SV242 @ SY482 @ SY483 )
| ( edge @ SY483 ) ) )
| ~ ! [SY484: $i] :
( ! [SY485: $i] :
~ ( triangle @ SV242 @ SY484 @ SY485 )
| ( sequential @ SV242 @ SY484 ) ) )
| ~ ! [SY486: $i,SY487: $i] :
( ~ ( triangle @ SV242 @ SY486 @ SY487 )
| ( sequential @ SY486 @ SY487 ) ) )
| ~ ! [SY488: $i,SY489: $i] :
( ~ ( triangle @ SV242 @ SY488 @ SY489 )
| ( sequential @ SY489 @ SV242 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1243]) ).
thf(1265,plain,
! [SV229: $i] :
( ( ( ( head_of @ SV229 )
= ( tail_of @ SV229 ) )
= $false )
| ( ( edge @ SV229 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1244]) ).
thf(1266,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)],[1245]) ).
thf(1267,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)],[1246]) ).
thf(1268,plain,
! [SV233: $i] :
( ( ~ ( ~ ( ! [SY415: $i,SY416: $i] :
~ ( path @ SV233 @ SY415 @ SY416 )
| ( vertex @ SV233 ) )
| ~ ! [SY417: $i] :
( ! [SY418: $i] :
~ ( path @ SV233 @ SY417 @ SY418 )
| ( vertex @ SY417 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1247]) ).
thf(1269,plain,
! [SV233: $i] :
( ( ! [SY419: $i,SY420: $i] :
( ~ ( path @ SV233 @ SY419 @ SY420 )
| ~ ( ~ ~ ( ( SV233
!= ( tail_of @ ( sK12_E @ SY420 @ SY419 @ SV233 ) ) )
| ~ ( edge @ ( sK12_E @ SY420 @ SY419 @ SV233 ) ) )
| ~ ~ ( ~ ( ( SY419
!= ( head_of @ ( sK12_E @ SY420 @ SY419 @ SV233 ) ) )
| ( SY420
!= ( path_cons @ ( sK12_E @ SY420 @ SY419 @ SV233 ) @ empty ) )
| ! [SY421: $i] :
( ( SY420
!= ( path_cons @ ( sK12_E @ SY420 @ SY419 @ SV233 ) @ SY421 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SY420 @ SY419 @ SV233 ) ) @ SY419 @ SY421 ) ) )
| ~ ~ ( ~ ( ( SY419
= ( head_of @ ( sK12_E @ SY420 @ SY419 @ SV233 ) ) )
| ~ ( ( SY420
!= ( path_cons @ ( sK12_E @ SY420 @ SY419 @ SV233 ) @ ( sK14_SY90 @ SY420 @ SY419 @ SV233 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SY420 @ SY419 @ SV233 ) ) @ SY419 @ ( sK14_SY90 @ SY420 @ SY419 @ SV233 ) ) ) )
| ~ ( ( SY420
= ( path_cons @ ( sK12_E @ SY420 @ SY419 @ SV233 ) @ empty ) )
| ~ ( ( SY420
!= ( path_cons @ ( sK12_E @ SY420 @ SY419 @ SV233 ) @ ( sK13_SY91 @ SY420 @ SY419 @ SV233 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SY420 @ SY419 @ SV233 ) ) @ SY419 @ ( sK13_SY91 @ SY420 @ SY419 @ SV233 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1248]) ).
thf(1270,plain,
! [SV246: $i,SV234: $i] :
( ( ~ ~ ( ~ ! [SY492: $i,SY493: $i] :
( ~ ( on_path @ SY493 @ SY492 )
| ~ ( path @ SV234 @ SV246 @ SY492 )
| ( edge @ SY493 ) )
| ~ ! [SY494: $i,SY495: $i] :
( ~ ( on_path @ SY495 @ SY494 )
| ~ ( path @ SV234 @ SV246 @ SY494 )
| ( in_path @ ( head_of @ SY495 ) @ SY494 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1249]) ).
thf(1271,plain,
! [SV246: $i,SV234: $i] :
( ( ~ ! [SY496: $i,SY497: $i] :
( ~ ( on_path @ SY497 @ SY496 )
| ~ ( path @ SV234 @ SV246 @ SY496 )
| ( in_path @ ( tail_of @ SY497 ) @ SY496 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1249]) ).
thf(1272,plain,
! [SV235: $i,SV257: $i,SV252: $i] :
( ( ( ~ ( path @ SV252 @ SV257 @ SV235 ) )
= $true )
| ( ( ~ ( ~ ! [SY431: $i,SY432: $i] :
( ~ ( on_path @ SY431 @ SV235 )
| ~ ( on_path @ SY432 @ SV235 )
| ! [SY433: $i] :
( ~ ( precedes @ SY433 @ SY432 @ SV235 )
| ~ ( sequential @ SY431 @ SY433 ) )
| ( precedes @ SY431 @ SY432 @ SV235 ) )
| ~ ! [SY434: $i,SY435: $i] :
( ~ ( on_path @ SY434 @ SV235 )
| ~ ( on_path @ SY435 @ SV235 )
| ~ ( sequential @ SY434 @ SY435 )
| ( precedes @ SY434 @ SY435 @ SV235 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1250]) ).
thf(1273,plain,
! [SV247: $i,SV236: $i,SV253: $i] :
( ( ~ ! [SY513: $i] :
( ! [SY514: $i] :
( ~ ( precedes @ SV253 @ SY513 @ SY514 )
| ~ ( shortest_path @ SV236 @ SV247 @ SY514 ) )
| ! [SY515: $i] :
( ( ( tail_of @ SY515 )
!= ( tail_of @ SV253 ) )
| ( ( head_of @ SY515 )
!= ( head_of @ SY513 ) ) ) )
| ~ ! [SY516: $i,SY517: $i] :
( ~ ( precedes @ SV253 @ SY516 @ SY517 )
| ~ ( shortest_path @ SV236 @ SV247 @ SY517 )
| ~ ( precedes @ SY516 @ SV253 @ SY517 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1251]) ).
thf(1274,plain,
! [SV237: $i,SV258: $i,SV254: $i] :
( ( ( ~ ( path @ SV254 @ SV258 @ SV237 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY445: $i] :
( ! [SY446: $i] :
~ ( precedes @ SY445 @ SY446 @ SV237 )
| ( on_path @ SY445 @ SV237 ) )
| ~ ! [SY447: $i,SY448: $i] :
( ~ ( precedes @ SY447 @ SY448 @ SV237 )
| ( on_path @ SY448 @ SV237 ) ) )
| ~ ~ ( ~ ! [SY449: $i,SY450: $i] :
( ~ ( precedes @ SY449 @ SY450 @ SV237 )
| ! [SY451: $i] :
( ~ ( precedes @ SY451 @ SY450 @ SV237 )
| ~ ( sequential @ SY449 @ SY451 ) )
| ~ ( sequential @ SY449 @ SY450 ) )
| ~ ! [SY452: $i,SY453: $i] :
( ~ ( precedes @ SY452 @ SY453 @ SV237 )
| ~ ( ~ ( precedes @ ( sK10_E3 @ SY453 @ SY452 @ SV237 ) @ SY453 @ SV237 )
| ~ ( sequential @ SY452 @ ( sK10_E3 @ SY453 @ SY452 @ SV237 ) ) )
| ( sequential @ SY452 @ SY453 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1252]) ).
thf(1275,plain,
! [SV259: $i,SV255: $i] :
( ( ( ( SV255 = SV259 )
| ~ ( vertex @ SV255 )
| ~ ( vertex @ SV259 )
| ~ ( ~ ~ ( ~ ( ( SV255
!= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
!= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
!= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
!= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV255
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
| ~ ( ( SV255
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) ) )
| ~ ~ ( ~ ( ( SV259
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
| ~ ( ( SV259
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) ) ) ) )
| ~ ( edge @ ( sK15_E @ SV259 @ SV255 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1253]) ).
thf(1276,plain,
! [SV238: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK7_E1 @ SV238 ) @ SV238 )
| ~ ( on_path @ ( sK8_SY86 @ SV238 ) @ SV238 ) )
| ~ ( sequential @ ( sK7_E1 @ SV238 ) @ ( sK8_SY86 @ SV238 ) ) )
| ~ ! [SY454: $i] :
~ ( triangle @ ( sK7_E1 @ SV238 ) @ ( sK8_SY86 @ SV238 ) @ SY454 ) )
= $false )
| ( ( ! [SY455: $i,SY456: $i] :
~ ( path @ SY455 @ SY456 @ SV238 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV238 )
= ( number_of_in @ triangles @ SV238 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1254]) ).
thf(1277,plain,
! [SV260: $i] :
( ( ~ ( edge @ SV260 )
| ( vertex @ ( head_of @ SV260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1255]) ).
thf(1278,plain,
! [SV261: $i] :
( ( ~ ( edge @ SV261 )
| ( vertex @ ( tail_of @ SV261 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1256]) ).
thf(1279,plain,
! [SV262: $i] :
( ( ! [SY523: $i] :
( ( SV262 = SY523 )
| ~ ( edge @ SV262 )
| ~ ( edge @ SY523 )
| ( ( head_of @ SV262 )
!= ( tail_of @ SY523 ) )
| ( sequential @ SV262 @ SY523 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1257]) ).
thf(1280,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)],[1258]) ).
thf(1281,plain,
! [SV248: $i,SV239: $i] :
( ( ~ ! [SY504: $i,SY505: $i] :
( ~ ( in_path @ SY505 @ SY504 )
| ~ ( path @ SV239 @ SV248 @ SY504 )
| ~ ( ~ ( on_path @ ( sK11_E @ SY505 @ SY504 @ SV248 @ SV239 ) @ SY504 )
| ~ ( ( SY505
= ( head_of @ ( sK11_E @ SY505 @ SY504 @ SV248 @ SV239 ) ) )
| ( SY505
= ( tail_of @ ( sK11_E @ SY505 @ SY504 @ SV248 @ SV239 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1259]) ).
thf(1282,plain,
! [SV248: $i,SV239: $i] :
( ( ~ ! [SY506: $i,SY507: $i] :
( ~ ( in_path @ SY507 @ SY506 )
| ~ ( path @ SV239 @ SV248 @ SY506 )
| ( vertex @ SY507 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1259]) ).
thf(1283,plain,
! [SV256: $i,SV249: $i,SV240: $i] :
( ( ( ~ ( vertex @ SV240 )
| ~ ( vertex @ SV249 )
| ~ ( ~ ! [SY520: $i] :
( ( SV240
!= ( tail_of @ SY520 ) )
| ~ ( edge @ SY520 )
| ( SV249
!= ( head_of @ SY520 ) )
| ( SV256
!= ( path_cons @ SY520 @ empty ) ) )
| ~ ! [SY521: $i] :
( ( SV240
!= ( tail_of @ SY521 ) )
| ~ ( edge @ SY521 )
| ! [SY522: $i] :
( ( SV256
!= ( path_cons @ SY521 @ SY522 ) )
| ~ ( path @ ( head_of @ SY521 ) @ SV249 @ SY522 ) ) ) ) )
= $true )
| ( ( path @ SV240 @ SV249 @ SV256 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1260]) ).
thf(1284,plain,
! [SV241: $i] :
( ( ! [SY467: $i,SY468: $i] :
( ~ ( ~ ( path @ SV241 @ SY467 @ ( sK9_P @ SY468 @ SY467 @ SV241 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY468 ) @ ( length_of @ ( sK9_P @ SY468 @ SY467 @ SV241 ) ) ) )
| ( SV241 = SY467 )
| ~ ( path @ SV241 @ SY467 @ SY468 )
| ( shortest_path @ SV241 @ SY467 @ SY468 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1261]) ).
thf(1285,plain,
! [SV241: $i] :
( ( ~ ( ~ ! [SY469: $i,SY470: $i] :
( ~ ( shortest_path @ SV241 @ SY469 @ SY470 )
| ! [SY471: $i] :
( ~ ( path @ SV241 @ SY469 @ SY471 )
| ( less_or_equal @ ( length_of @ SY470 ) @ ( length_of @ SY471 ) ) ) )
| ~ ~ ( ~ ! [SY472: $i] :
( ! [SY473: $i] :
~ ( shortest_path @ SV241 @ SY472 @ SY473 )
| ( SV241 != SY472 ) )
| ~ ! [SY474: $i,SY475: $i] :
( ~ ( shortest_path @ SV241 @ SY474 @ SY475 )
| ( path @ SV241 @ SY474 @ SY475 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1262]) ).
thf(1286,plain,
! [SV242: $i] :
( ( ! [SY476: $i,SY477: $i] :
( ~ ( edge @ SV242 )
| ~ ( edge @ SY476 )
| ~ ( edge @ SY477 )
| ~ ( sequential @ SV242 @ SY476 )
| ~ ( sequential @ SY476 @ SY477 )
| ~ ( sequential @ SY477 @ SV242 )
| ( triangle @ SV242 @ SY476 @ SY477 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1263]) ).
thf(1287,plain,
! [SV242: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY478: $i,SY479: $i] :
~ ( triangle @ SV242 @ SY478 @ SY479 )
| ( edge @ SV242 ) )
| ~ ! [SY480: $i] :
( ! [SY481: $i] :
~ ( triangle @ SV242 @ SY480 @ SY481 )
| ( edge @ SY480 ) ) )
| ~ ! [SY482: $i,SY483: $i] :
( ~ ( triangle @ SV242 @ SY482 @ SY483 )
| ( edge @ SY483 ) ) )
| ~ ! [SY484: $i] :
( ! [SY485: $i] :
~ ( triangle @ SV242 @ SY484 @ SY485 )
| ( sequential @ SV242 @ SY484 ) ) )
| ~ ! [SY486: $i,SY487: $i] :
( ~ ( triangle @ SV242 @ SY486 @ SY487 )
| ( sequential @ SY486 @ SY487 ) ) )
| ~ ! [SY488: $i,SY489: $i] :
( ~ ( triangle @ SV242 @ SY488 @ SY489 )
| ( sequential @ SY489 @ SV242 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1264]) ).
thf(1288,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)],[1266]) ).
thf(1289,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)],[1267]) ).
thf(1290,plain,
! [SV233: $i] :
( ( ~ ( ! [SY415: $i,SY416: $i] :
~ ( path @ SV233 @ SY415 @ SY416 )
| ( vertex @ SV233 ) )
| ~ ! [SY417: $i] :
( ! [SY418: $i] :
~ ( path @ SV233 @ SY417 @ SY418 )
| ( vertex @ SY417 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1268]) ).
thf(1291,plain,
! [SV263: $i,SV233: $i] :
( ( ! [SY524: $i] :
( ~ ( path @ SV233 @ SV263 @ SY524 )
| ~ ( ~ ~ ( ( SV233
!= ( tail_of @ ( sK12_E @ SY524 @ SV263 @ SV233 ) ) )
| ~ ( edge @ ( sK12_E @ SY524 @ SV263 @ SV233 ) ) )
| ~ ~ ( ~ ( ( SV263
!= ( head_of @ ( sK12_E @ SY524 @ SV263 @ SV233 ) ) )
| ( SY524
!= ( path_cons @ ( sK12_E @ SY524 @ SV263 @ SV233 ) @ empty ) )
| ! [SY525: $i] :
( ( SY524
!= ( path_cons @ ( sK12_E @ SY524 @ SV263 @ SV233 ) @ SY525 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SY524 @ SV263 @ SV233 ) ) @ SV263 @ SY525 ) ) )
| ~ ~ ( ~ ( ( SV263
= ( head_of @ ( sK12_E @ SY524 @ SV263 @ SV233 ) ) )
| ~ ( ( SY524
!= ( path_cons @ ( sK12_E @ SY524 @ SV263 @ SV233 ) @ ( sK14_SY90 @ SY524 @ SV263 @ SV233 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SY524 @ SV263 @ SV233 ) ) @ SV263 @ ( sK14_SY90 @ SY524 @ SV263 @ SV233 ) ) ) )
| ~ ( ( SY524
= ( path_cons @ ( sK12_E @ SY524 @ SV263 @ SV233 ) @ empty ) )
| ~ ( ( SY524
!= ( path_cons @ ( sK12_E @ SY524 @ SV263 @ SV233 ) @ ( sK13_SY91 @ SY524 @ SV263 @ SV233 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SY524 @ SV263 @ SV233 ) ) @ SV263 @ ( sK13_SY91 @ SY524 @ SV263 @ SV233 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1269]) ).
thf(1292,plain,
! [SV246: $i,SV234: $i] :
( ( ~ ( ~ ! [SY492: $i,SY493: $i] :
( ~ ( on_path @ SY493 @ SY492 )
| ~ ( path @ SV234 @ SV246 @ SY492 )
| ( edge @ SY493 ) )
| ~ ! [SY494: $i,SY495: $i] :
( ~ ( on_path @ SY495 @ SY494 )
| ~ ( path @ SV234 @ SV246 @ SY494 )
| ( in_path @ ( head_of @ SY495 ) @ SY494 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1270]) ).
thf(1293,plain,
! [SV246: $i,SV234: $i] :
( ( ! [SY496: $i,SY497: $i] :
( ~ ( on_path @ SY497 @ SY496 )
| ~ ( path @ SV234 @ SV246 @ SY496 )
| ( in_path @ ( tail_of @ SY497 ) @ SY496 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1271]) ).
thf(1294,plain,
! [SV235: $i,SV257: $i,SV252: $i] :
( ( ( path @ SV252 @ SV257 @ SV235 )
= $false )
| ( ( ~ ( ~ ! [SY431: $i,SY432: $i] :
( ~ ( on_path @ SY431 @ SV235 )
| ~ ( on_path @ SY432 @ SV235 )
| ! [SY433: $i] :
( ~ ( precedes @ SY433 @ SY432 @ SV235 )
| ~ ( sequential @ SY431 @ SY433 ) )
| ( precedes @ SY431 @ SY432 @ SV235 ) )
| ~ ! [SY434: $i,SY435: $i] :
( ~ ( on_path @ SY434 @ SV235 )
| ~ ( on_path @ SY435 @ SV235 )
| ~ ( sequential @ SY434 @ SY435 )
| ( precedes @ SY434 @ SY435 @ SV235 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1272]) ).
thf(1295,plain,
! [SV247: $i,SV236: $i,SV253: $i] :
( ( ~ ! [SY513: $i] :
( ! [SY514: $i] :
( ~ ( precedes @ SV253 @ SY513 @ SY514 )
| ~ ( shortest_path @ SV236 @ SV247 @ SY514 ) )
| ! [SY515: $i] :
( ( ( tail_of @ SY515 )
!= ( tail_of @ SV253 ) )
| ( ( head_of @ SY515 )
!= ( head_of @ SY513 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1273]) ).
thf(1296,plain,
! [SV247: $i,SV236: $i,SV253: $i] :
( ( ~ ! [SY516: $i,SY517: $i] :
( ~ ( precedes @ SV253 @ SY516 @ SY517 )
| ~ ( shortest_path @ SV236 @ SV247 @ SY517 )
| ~ ( precedes @ SY516 @ SV253 @ SY517 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1273]) ).
thf(1297,plain,
! [SV237: $i,SV258: $i,SV254: $i] :
( ( ( path @ SV254 @ SV258 @ SV237 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY445: $i] :
( ! [SY446: $i] :
~ ( precedes @ SY445 @ SY446 @ SV237 )
| ( on_path @ SY445 @ SV237 ) )
| ~ ! [SY447: $i,SY448: $i] :
( ~ ( precedes @ SY447 @ SY448 @ SV237 )
| ( on_path @ SY448 @ SV237 ) ) )
| ~ ~ ( ~ ! [SY449: $i,SY450: $i] :
( ~ ( precedes @ SY449 @ SY450 @ SV237 )
| ! [SY451: $i] :
( ~ ( precedes @ SY451 @ SY450 @ SV237 )
| ~ ( sequential @ SY449 @ SY451 ) )
| ~ ( sequential @ SY449 @ SY450 ) )
| ~ ! [SY452: $i,SY453: $i] :
( ~ ( precedes @ SY452 @ SY453 @ SV237 )
| ~ ( ~ ( precedes @ ( sK10_E3 @ SY453 @ SY452 @ SV237 ) @ SY453 @ SV237 )
| ~ ( sequential @ SY452 @ ( sK10_E3 @ SY453 @ SY452 @ SV237 ) ) )
| ( sequential @ SY452 @ SY453 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1274]) ).
thf(1298,plain,
! [SV259: $i,SV255: $i] :
( ( ( ( SV255 = SV259 )
| ~ ( vertex @ SV255 )
| ~ ( vertex @ SV259 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV255
!= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
!= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
!= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
!= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV255
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
| ~ ( ( SV255
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) ) )
| ~ ~ ( ~ ( ( SV259
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
| ~ ( ( SV259
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) ) ) ) )
| ~ ( edge @ ( sK15_E @ SV259 @ SV255 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[1275]) ).
thf(1299,plain,
! [SV238: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK7_E1 @ SV238 ) @ SV238 )
| ~ ( on_path @ ( sK8_SY86 @ SV238 ) @ SV238 ) )
| ~ ( sequential @ ( sK7_E1 @ SV238 ) @ ( sK8_SY86 @ SV238 ) ) ) )
= $false )
| ( ( ! [SY455: $i,SY456: $i] :
~ ( path @ SY455 @ SY456 @ SV238 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV238 )
= ( number_of_in @ triangles @ SV238 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1276]) ).
thf(1300,plain,
! [SV238: $i] :
( ( ( ~ ! [SY454: $i] :
~ ( triangle @ ( sK7_E1 @ SV238 ) @ ( sK8_SY86 @ SV238 ) @ SY454 ) )
= $false )
| ( ( ! [SY455: $i,SY456: $i] :
~ ( path @ SY455 @ SY456 @ SV238 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV238 )
= ( number_of_in @ triangles @ SV238 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1276]) ).
thf(1301,plain,
! [SV260: $i] :
( ( ( ~ ( edge @ SV260 ) )
= $true )
| ( ( vertex @ ( head_of @ SV260 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1277]) ).
thf(1302,plain,
! [SV261: $i] :
( ( ( ~ ( edge @ SV261 ) )
= $true )
| ( ( vertex @ ( tail_of @ SV261 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1278]) ).
thf(1303,plain,
! [SV264: $i,SV262: $i] :
( ( ( SV262 = SV264 )
| ~ ( edge @ SV262 )
| ~ ( edge @ SV264 )
| ( ( head_of @ SV262 )
!= ( tail_of @ SV264 ) )
| ( sequential @ SV262 @ SV264 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1279]) ).
thf(1304,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)],[1280]) ).
thf(1305,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1280]) ).
thf(1306,plain,
! [SV248: $i,SV239: $i] :
( ( ! [SY504: $i,SY505: $i] :
( ~ ( in_path @ SY505 @ SY504 )
| ~ ( path @ SV239 @ SV248 @ SY504 )
| ~ ( ~ ( on_path @ ( sK11_E @ SY505 @ SY504 @ SV248 @ SV239 ) @ SY504 )
| ~ ( ( SY505
= ( head_of @ ( sK11_E @ SY505 @ SY504 @ SV248 @ SV239 ) ) )
| ( SY505
= ( tail_of @ ( sK11_E @ SY505 @ SY504 @ SV248 @ SV239 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1281]) ).
thf(1307,plain,
! [SV248: $i,SV239: $i] :
( ( ! [SY506: $i,SY507: $i] :
( ~ ( in_path @ SY507 @ SY506 )
| ~ ( path @ SV239 @ SV248 @ SY506 )
| ( vertex @ SY507 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1282]) ).
thf(1308,plain,
! [SV256: $i,SV249: $i,SV240: $i] :
( ( ( ~ ( vertex @ SV240 )
| ~ ( vertex @ SV249 ) )
= $true )
| ( ( ~ ( ~ ! [SY520: $i] :
( ( SV240
!= ( tail_of @ SY520 ) )
| ~ ( edge @ SY520 )
| ( SV249
!= ( head_of @ SY520 ) )
| ( SV256
!= ( path_cons @ SY520 @ empty ) ) )
| ~ ! [SY521: $i] :
( ( SV240
!= ( tail_of @ SY521 ) )
| ~ ( edge @ SY521 )
| ! [SY522: $i] :
( ( SV256
!= ( path_cons @ SY521 @ SY522 ) )
| ~ ( path @ ( head_of @ SY521 ) @ SV249 @ SY522 ) ) ) ) )
= $true )
| ( ( path @ SV240 @ SV249 @ SV256 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1283]) ).
thf(1309,plain,
! [SV265: $i,SV241: $i] :
( ( ! [SY526: $i] :
( ~ ( ~ ( path @ SV241 @ SV265 @ ( sK9_P @ SY526 @ SV265 @ SV241 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY526 ) @ ( length_of @ ( sK9_P @ SY526 @ SV265 @ SV241 ) ) ) )
| ( SV241 = SV265 )
| ~ ( path @ SV241 @ SV265 @ SY526 )
| ( shortest_path @ SV241 @ SV265 @ SY526 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1284]) ).
thf(1310,plain,
! [SV241: $i] :
( ( ~ ! [SY469: $i,SY470: $i] :
( ~ ( shortest_path @ SV241 @ SY469 @ SY470 )
| ! [SY471: $i] :
( ~ ( path @ SV241 @ SY469 @ SY471 )
| ( less_or_equal @ ( length_of @ SY470 ) @ ( length_of @ SY471 ) ) ) )
| ~ ~ ( ~ ! [SY472: $i] :
( ! [SY473: $i] :
~ ( shortest_path @ SV241 @ SY472 @ SY473 )
| ( SV241 != SY472 ) )
| ~ ! [SY474: $i,SY475: $i] :
( ~ ( shortest_path @ SV241 @ SY474 @ SY475 )
| ( path @ SV241 @ SY474 @ SY475 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1285]) ).
thf(1311,plain,
! [SV266: $i,SV242: $i] :
( ( ! [SY527: $i] :
( ~ ( edge @ SV242 )
| ~ ( edge @ SV266 )
| ~ ( edge @ SY527 )
| ~ ( sequential @ SV242 @ SV266 )
| ~ ( sequential @ SV266 @ SY527 )
| ~ ( sequential @ SY527 @ SV242 )
| ( triangle @ SV242 @ SV266 @ SY527 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1286]) ).
thf(1312,plain,
! [SV242: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY478: $i,SY479: $i] :
~ ( triangle @ SV242 @ SY478 @ SY479 )
| ( edge @ SV242 ) )
| ~ ! [SY480: $i] :
( ! [SY481: $i] :
~ ( triangle @ SV242 @ SY480 @ SY481 )
| ( edge @ SY480 ) ) )
| ~ ! [SY482: $i,SY483: $i] :
( ~ ( triangle @ SV242 @ SY482 @ SY483 )
| ( edge @ SY483 ) ) )
| ~ ! [SY484: $i] :
( ! [SY485: $i] :
~ ( triangle @ SV242 @ SY484 @ SY485 )
| ( sequential @ SV242 @ SY484 ) ) )
| ~ ! [SY486: $i,SY487: $i] :
( ~ ( triangle @ SV242 @ SY486 @ SY487 )
| ( sequential @ SY486 @ SY487 ) ) )
| ~ ! [SY488: $i,SY489: $i] :
( ~ ( triangle @ SV242 @ SY488 @ SY489 )
| ( sequential @ SY489 @ SV242 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1287]) ).
thf(1313,plain,
! [SV233: $i] :
( ( ~ ( ! [SY415: $i,SY416: $i] :
~ ( path @ SV233 @ SY415 @ SY416 )
| ( vertex @ SV233 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1290]) ).
thf(1314,plain,
! [SV233: $i] :
( ( ~ ! [SY417: $i] :
( ! [SY418: $i] :
~ ( path @ SV233 @ SY417 @ SY418 )
| ( vertex @ SY417 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1290]) ).
thf(1315,plain,
! [SV267: $i,SV263: $i,SV233: $i] :
( ( ~ ( path @ SV233 @ SV263 @ SV267 )
| ~ ( ~ ~ ( ( SV233
!= ( tail_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( edge @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
| ~ ~ ( ~ ( ( SV263
!= ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
| ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ empty ) )
| ! [SY528: $i] :
( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ SY528 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ SY528 ) ) )
| ~ ~ ( ~ ( ( SV263
= ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ ( sK14_SY90 @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ ( sK14_SY90 @ SV267 @ SV263 @ SV233 ) ) ) )
| ~ ( ( SV267
= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ empty ) )
| ~ ( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ ( sK13_SY91 @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ ( sK13_SY91 @ SV267 @ SV263 @ SV233 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1291]) ).
thf(1316,plain,
! [SV246: $i,SV234: $i] :
( ( ~ ! [SY492: $i,SY493: $i] :
( ~ ( on_path @ SY493 @ SY492 )
| ~ ( path @ SV234 @ SV246 @ SY492 )
| ( edge @ SY493 ) )
| ~ ! [SY494: $i,SY495: $i] :
( ~ ( on_path @ SY495 @ SY494 )
| ~ ( path @ SV234 @ SV246 @ SY494 )
| ( in_path @ ( head_of @ SY495 ) @ SY494 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1292]) ).
thf(1317,plain,
! [SV246: $i,SV234: $i,SV268: $i] :
( ( ! [SY529: $i] :
( ~ ( on_path @ SY529 @ SV268 )
| ~ ( path @ SV234 @ SV246 @ SV268 )
| ( in_path @ ( tail_of @ SY529 ) @ SV268 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1293]) ).
thf(1318,plain,
! [SV257: $i,SV252: $i,SV235: $i] :
( ( ( ~ ! [SY431: $i,SY432: $i] :
( ~ ( on_path @ SY431 @ SV235 )
| ~ ( on_path @ SY432 @ SV235 )
| ! [SY433: $i] :
( ~ ( precedes @ SY433 @ SY432 @ SV235 )
| ~ ( sequential @ SY431 @ SY433 ) )
| ( precedes @ SY431 @ SY432 @ SV235 ) )
| ~ ! [SY434: $i,SY435: $i] :
( ~ ( on_path @ SY434 @ SV235 )
| ~ ( on_path @ SY435 @ SV235 )
| ~ ( sequential @ SY434 @ SY435 )
| ( precedes @ SY434 @ SY435 @ SV235 ) ) )
= $false )
| ( ( path @ SV252 @ SV257 @ SV235 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1294]) ).
thf(1319,plain,
! [SV247: $i,SV236: $i,SV253: $i] :
( ( ! [SY513: $i] :
( ! [SY514: $i] :
( ~ ( precedes @ SV253 @ SY513 @ SY514 )
| ~ ( shortest_path @ SV236 @ SV247 @ SY514 ) )
| ! [SY515: $i] :
( ( ( tail_of @ SY515 )
!= ( tail_of @ SV253 ) )
| ( ( head_of @ SY515 )
!= ( head_of @ SY513 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1295]) ).
thf(1320,plain,
! [SV247: $i,SV236: $i,SV253: $i] :
( ( ! [SY516: $i,SY517: $i] :
( ~ ( precedes @ SV253 @ SY516 @ SY517 )
| ~ ( shortest_path @ SV236 @ SV247 @ SY517 )
| ~ ( precedes @ SY516 @ SV253 @ SY517 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1296]) ).
thf(1321,plain,
! [SV258: $i,SV254: $i,SV237: $i] :
( ( ( ~ ~ ( ~ ! [SY445: $i] :
( ! [SY446: $i] :
~ ( precedes @ SY445 @ SY446 @ SV237 )
| ( on_path @ SY445 @ SV237 ) )
| ~ ! [SY447: $i,SY448: $i] :
( ~ ( precedes @ SY447 @ SY448 @ SV237 )
| ( on_path @ SY448 @ SV237 ) ) )
| ~ ~ ( ~ ! [SY449: $i,SY450: $i] :
( ~ ( precedes @ SY449 @ SY450 @ SV237 )
| ! [SY451: $i] :
( ~ ( precedes @ SY451 @ SY450 @ SV237 )
| ~ ( sequential @ SY449 @ SY451 ) )
| ~ ( sequential @ SY449 @ SY450 ) )
| ~ ! [SY452: $i,SY453: $i] :
( ~ ( precedes @ SY452 @ SY453 @ SV237 )
| ~ ( ~ ( precedes @ ( sK10_E3 @ SY453 @ SY452 @ SV237 ) @ SY453 @ SV237 )
| ~ ( sequential @ SY452 @ ( sK10_E3 @ SY453 @ SY452 @ SV237 ) ) )
| ( sequential @ SY452 @ SY453 ) ) ) )
= $false )
| ( ( path @ SV254 @ SV258 @ SV237 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1297]) ).
thf(1322,plain,
! [SV259: $i,SV255: $i] :
( ( ( SV255 = SV259 )
= $true )
| ( ( ~ ( vertex @ SV255 )
| ~ ( vertex @ SV259 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV255
!= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
!= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
!= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
!= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV255
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
| ~ ( ( SV255
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) ) )
| ~ ~ ( ~ ( ( SV259
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
| ~ ( ( SV259
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) ) ) ) )
| ~ ( edge @ ( sK15_E @ SV259 @ SV255 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[1298]) ).
thf(1323,plain,
! [SV238: $i] :
( ( ( ~ ( ~ ~ ( ~ ( on_path @ ( sK7_E1 @ SV238 ) @ SV238 )
| ~ ( on_path @ ( sK8_SY86 @ SV238 ) @ SV238 ) )
| ~ ( sequential @ ( sK7_E1 @ SV238 ) @ ( sK8_SY86 @ SV238 ) ) ) )
= $true )
| ( ( ! [SY455: $i,SY456: $i] :
~ ( path @ SY455 @ SY456 @ SV238 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV238 )
= ( number_of_in @ triangles @ SV238 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1299]) ).
thf(1324,plain,
! [SV238: $i] :
( ( ( ! [SY454: $i] :
~ ( triangle @ ( sK7_E1 @ SV238 ) @ ( sK8_SY86 @ SV238 ) @ SY454 ) )
= $true )
| ( ( ! [SY455: $i,SY456: $i] :
~ ( path @ SY455 @ SY456 @ SV238 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV238 )
= ( number_of_in @ triangles @ SV238 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1300]) ).
thf(1325,plain,
! [SV260: $i] :
( ( ( edge @ SV260 )
= $false )
| ( ( vertex @ ( head_of @ SV260 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1301]) ).
thf(1326,plain,
! [SV261: $i] :
( ( ( edge @ SV261 )
= $false )
| ( ( vertex @ ( tail_of @ SV261 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1302]) ).
thf(1327,plain,
! [SV264: $i,SV262: $i] :
( ( ( ( SV262 = SV264 )
| ~ ( edge @ SV262 )
| ~ ( edge @ SV264 )
| ( ( head_of @ SV262 )
!= ( tail_of @ SV264 ) ) )
= $true )
| ( ( sequential @ SV262 @ SV264 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1303]) ).
thf(1328,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)],[1304]) ).
thf(1329,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1305]) ).
thf(1330,plain,
! [SV248: $i,SV239: $i,SV269: $i] :
( ( ! [SY530: $i] :
( ~ ( in_path @ SY530 @ SV269 )
| ~ ( path @ SV239 @ SV248 @ SV269 )
| ~ ( ~ ( on_path @ ( sK11_E @ SY530 @ SV269 @ SV248 @ SV239 ) @ SV269 )
| ~ ( ( SY530
= ( head_of @ ( sK11_E @ SY530 @ SV269 @ SV248 @ SV239 ) ) )
| ( SY530
= ( tail_of @ ( sK11_E @ SY530 @ SV269 @ SV248 @ SV239 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1306]) ).
thf(1331,plain,
! [SV248: $i,SV239: $i,SV270: $i] :
( ( ! [SY531: $i] :
( ~ ( in_path @ SY531 @ SV270 )
| ~ ( path @ SV239 @ SV248 @ SV270 )
| ( vertex @ SY531 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1307]) ).
thf(1332,plain,
! [SV256: $i,SV249: $i,SV240: $i] :
( ( ( ~ ( vertex @ SV240 ) )
= $true )
| ( ( ~ ( vertex @ SV249 ) )
= $true )
| ( ( ~ ( ~ ! [SY520: $i] :
( ( SV240
!= ( tail_of @ SY520 ) )
| ~ ( edge @ SY520 )
| ( SV249
!= ( head_of @ SY520 ) )
| ( SV256
!= ( path_cons @ SY520 @ empty ) ) )
| ~ ! [SY521: $i] :
( ( SV240
!= ( tail_of @ SY521 ) )
| ~ ( edge @ SY521 )
| ! [SY522: $i] :
( ( SV256
!= ( path_cons @ SY521 @ SY522 ) )
| ~ ( path @ ( head_of @ SY521 ) @ SV249 @ SY522 ) ) ) ) )
= $true )
| ( ( path @ SV240 @ SV249 @ SV256 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1308]) ).
thf(1333,plain,
! [SV271: $i,SV265: $i,SV241: $i] :
( ( ~ ( ~ ( path @ SV241 @ SV265 @ ( sK9_P @ SV271 @ SV265 @ SV241 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SV271 ) @ ( length_of @ ( sK9_P @ SV271 @ SV265 @ SV241 ) ) ) )
| ( SV241 = SV265 )
| ~ ( path @ SV241 @ SV265 @ SV271 )
| ( shortest_path @ SV241 @ SV265 @ SV271 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1309]) ).
thf(1334,plain,
! [SV241: $i] :
( ( ~ ! [SY469: $i,SY470: $i] :
( ~ ( shortest_path @ SV241 @ SY469 @ SY470 )
| ! [SY471: $i] :
( ~ ( path @ SV241 @ SY469 @ SY471 )
| ( less_or_equal @ ( length_of @ SY470 ) @ ( length_of @ SY471 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1310]) ).
thf(1335,plain,
! [SV241: $i] :
( ( ~ ~ ( ~ ! [SY472: $i] :
( ! [SY473: $i] :
~ ( shortest_path @ SV241 @ SY472 @ SY473 )
| ( SV241 != SY472 ) )
| ~ ! [SY474: $i,SY475: $i] :
( ~ ( shortest_path @ SV241 @ SY474 @ SY475 )
| ( path @ SV241 @ SY474 @ SY475 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1310]) ).
thf(1336,plain,
! [SV272: $i,SV266: $i,SV242: $i] :
( ( ~ ( edge @ SV242 )
| ~ ( edge @ SV266 )
| ~ ( edge @ SV272 )
| ~ ( sequential @ SV242 @ SV266 )
| ~ ( sequential @ SV266 @ SV272 )
| ~ ( sequential @ SV272 @ SV242 )
| ( triangle @ SV242 @ SV266 @ SV272 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1311]) ).
thf(1337,plain,
! [SV242: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY478: $i,SY479: $i] :
~ ( triangle @ SV242 @ SY478 @ SY479 )
| ( edge @ SV242 ) )
| ~ ! [SY480: $i] :
( ! [SY481: $i] :
~ ( triangle @ SV242 @ SY480 @ SY481 )
| ( edge @ SY480 ) ) )
| ~ ! [SY482: $i,SY483: $i] :
( ~ ( triangle @ SV242 @ SY482 @ SY483 )
| ( edge @ SY483 ) ) )
| ~ ! [SY484: $i] :
( ! [SY485: $i] :
~ ( triangle @ SV242 @ SY484 @ SY485 )
| ( sequential @ SV242 @ SY484 ) ) )
| ~ ! [SY486: $i,SY487: $i] :
( ~ ( triangle @ SV242 @ SY486 @ SY487 )
| ( sequential @ SY486 @ SY487 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1312]) ).
thf(1338,plain,
! [SV242: $i] :
( ( ~ ! [SY488: $i,SY489: $i] :
( ~ ( triangle @ SV242 @ SY488 @ SY489 )
| ( sequential @ SY489 @ SV242 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1312]) ).
thf(1339,plain,
! [SV233: $i] :
( ( ! [SY415: $i,SY416: $i] :
~ ( path @ SV233 @ SY415 @ SY416 )
| ( vertex @ SV233 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1313]) ).
thf(1340,plain,
! [SV233: $i] :
( ( ! [SY417: $i] :
( ! [SY418: $i] :
~ ( path @ SV233 @ SY417 @ SY418 )
| ( vertex @ SY417 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1314]) ).
thf(1341,plain,
! [SV267: $i,SV263: $i,SV233: $i] :
( ( ( ~ ( path @ SV233 @ SV263 @ SV267 ) )
= $true )
| ( ( ~ ( ~ ~ ( ( SV233
!= ( tail_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( edge @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
| ~ ~ ( ~ ( ( SV263
!= ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
| ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ empty ) )
| ! [SY528: $i] :
( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ SY528 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ SY528 ) ) )
| ~ ~ ( ~ ( ( SV263
= ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ ( sK14_SY90 @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ ( sK14_SY90 @ SV267 @ SV263 @ SV233 ) ) ) )
| ~ ( ( SV267
= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ empty ) )
| ~ ( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ ( sK13_SY91 @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ ( sK13_SY91 @ SV267 @ SV263 @ SV233 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1315]) ).
thf(1342,plain,
! [SV246: $i,SV234: $i] :
( ( ~ ! [SY492: $i,SY493: $i] :
( ~ ( on_path @ SY493 @ SY492 )
| ~ ( path @ SV234 @ SV246 @ SY492 )
| ( edge @ SY493 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1316]) ).
thf(1343,plain,
! [SV246: $i,SV234: $i] :
( ( ~ ! [SY494: $i,SY495: $i] :
( ~ ( on_path @ SY495 @ SY494 )
| ~ ( path @ SV234 @ SV246 @ SY494 )
| ( in_path @ ( head_of @ SY495 ) @ SY494 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1316]) ).
thf(1344,plain,
! [SV246: $i,SV234: $i,SV268: $i,SV273: $i] :
( ( ~ ( on_path @ SV273 @ SV268 )
| ~ ( path @ SV234 @ SV246 @ SV268 )
| ( in_path @ ( tail_of @ SV273 ) @ SV268 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1317]) ).
thf(1345,plain,
! [SV257: $i,SV252: $i,SV235: $i] :
( ( ( ~ ! [SY431: $i,SY432: $i] :
( ~ ( on_path @ SY431 @ SV235 )
| ~ ( on_path @ SY432 @ SV235 )
| ! [SY433: $i] :
( ~ ( precedes @ SY433 @ SY432 @ SV235 )
| ~ ( sequential @ SY431 @ SY433 ) )
| ( precedes @ SY431 @ SY432 @ SV235 ) ) )
= $false )
| ( ( path @ SV252 @ SV257 @ SV235 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1318]) ).
thf(1346,plain,
! [SV257: $i,SV252: $i,SV235: $i] :
( ( ( ~ ! [SY434: $i,SY435: $i] :
( ~ ( on_path @ SY434 @ SV235 )
| ~ ( on_path @ SY435 @ SV235 )
| ~ ( sequential @ SY434 @ SY435 )
| ( precedes @ SY434 @ SY435 @ SV235 ) ) )
= $false )
| ( ( path @ SV252 @ SV257 @ SV235 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1318]) ).
thf(1347,plain,
! [SV247: $i,SV236: $i,SV274: $i,SV253: $i] :
( ( ! [SY532: $i] :
( ~ ( precedes @ SV253 @ SV274 @ SY532 )
| ~ ( shortest_path @ SV236 @ SV247 @ SY532 ) )
| ! [SY533: $i] :
( ( ( tail_of @ SY533 )
!= ( tail_of @ SV253 ) )
| ( ( head_of @ SY533 )
!= ( head_of @ SV274 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1319]) ).
thf(1348,plain,
! [SV247: $i,SV236: $i,SV275: $i,SV253: $i] :
( ( ! [SY534: $i] :
( ~ ( precedes @ SV253 @ SV275 @ SY534 )
| ~ ( shortest_path @ SV236 @ SV247 @ SY534 )
| ~ ( precedes @ SV275 @ SV253 @ SY534 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1320]) ).
thf(1349,plain,
! [SV258: $i,SV254: $i,SV237: $i] :
( ( ( ~ ~ ( ~ ! [SY445: $i] :
( ! [SY446: $i] :
~ ( precedes @ SY445 @ SY446 @ SV237 )
| ( on_path @ SY445 @ SV237 ) )
| ~ ! [SY447: $i,SY448: $i] :
( ~ ( precedes @ SY447 @ SY448 @ SV237 )
| ( on_path @ SY448 @ SV237 ) ) ) )
= $false )
| ( ( path @ SV254 @ SV258 @ SV237 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1321]) ).
thf(1350,plain,
! [SV258: $i,SV254: $i,SV237: $i] :
( ( ( ~ ~ ( ~ ! [SY449: $i,SY450: $i] :
( ~ ( precedes @ SY449 @ SY450 @ SV237 )
| ! [SY451: $i] :
( ~ ( precedes @ SY451 @ SY450 @ SV237 )
| ~ ( sequential @ SY449 @ SY451 ) )
| ~ ( sequential @ SY449 @ SY450 ) )
| ~ ! [SY452: $i,SY453: $i] :
( ~ ( precedes @ SY452 @ SY453 @ SV237 )
| ~ ( ~ ( precedes @ ( sK10_E3 @ SY453 @ SY452 @ SV237 ) @ SY453 @ SV237 )
| ~ ( sequential @ SY452 @ ( sK10_E3 @ SY453 @ SY452 @ SV237 ) ) )
| ( sequential @ SY452 @ SY453 ) ) ) )
= $false )
| ( ( path @ SV254 @ SV258 @ SV237 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1321]) ).
thf(1351,plain,
! [SV259: $i,SV255: $i] :
( ( ( ~ ( vertex @ SV255 ) )
= $true )
| ( ( ~ ( vertex @ SV259 ) )
= $true )
| ( ( SV255 = SV259 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV255
!= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
!= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
!= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
!= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV255
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
| ~ ( ( SV255
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) ) )
| ~ ~ ( ~ ( ( SV259
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
| ~ ( ( SV259
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) ) ) ) )
| ~ ( edge @ ( sK15_E @ SV259 @ SV255 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[1322]) ).
thf(1352,plain,
! [SV238: $i] :
( ( ( ~ ~ ( ~ ( on_path @ ( sK7_E1 @ SV238 ) @ SV238 )
| ~ ( on_path @ ( sK8_SY86 @ SV238 ) @ SV238 ) )
| ~ ( sequential @ ( sK7_E1 @ SV238 ) @ ( sK8_SY86 @ SV238 ) ) )
= $false )
| ( ( ! [SY455: $i,SY456: $i] :
~ ( path @ SY455 @ SY456 @ SV238 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV238 )
= ( number_of_in @ triangles @ SV238 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1323]) ).
thf(1353,plain,
! [SV276: $i,SV238: $i] :
( ( ( ~ ( triangle @ ( sK7_E1 @ SV238 ) @ ( sK8_SY86 @ SV238 ) @ SV276 ) )
= $true )
| ( ( ! [SY455: $i,SY456: $i] :
~ ( path @ SY455 @ SY456 @ SV238 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV238 )
= ( number_of_in @ triangles @ SV238 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1324]) ).
thf(1354,plain,
! [SV264: $i,SV262: $i] :
( ( ( ( SV262 = SV264 )
| ~ ( edge @ SV262 )
| ~ ( edge @ SV264 ) )
= $true )
| ( ( ( ( head_of @ SV262 )
!= ( tail_of @ SV264 ) ) )
= $true )
| ( ( sequential @ SV262 @ SV264 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1327]) ).
thf(1355,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)],[1328]) ).
thf(1356,plain,
! [SV277: $i] :
( ( ! [SY535: $i] :
( ~ ( sequential @ SV277 @ SY535 )
| ( ( head_of @ SV277 )
= ( tail_of @ SY535 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1329]) ).
thf(1357,plain,
! [SV248: $i,SV239: $i,SV269: $i,SV278: $i] :
( ( ~ ( in_path @ SV278 @ SV269 )
| ~ ( path @ SV239 @ SV248 @ SV269 )
| ~ ( ~ ( on_path @ ( sK11_E @ SV278 @ SV269 @ SV248 @ SV239 ) @ SV269 )
| ~ ( ( SV278
= ( head_of @ ( sK11_E @ SV278 @ SV269 @ SV248 @ SV239 ) ) )
| ( SV278
= ( tail_of @ ( sK11_E @ SV278 @ SV269 @ SV248 @ SV239 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1330]) ).
thf(1358,plain,
! [SV248: $i,SV239: $i,SV270: $i,SV279: $i] :
( ( ~ ( in_path @ SV279 @ SV270 )
| ~ ( path @ SV239 @ SV248 @ SV270 )
| ( vertex @ SV279 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1331]) ).
thf(1359,plain,
! [SV256: $i,SV249: $i,SV240: $i] :
( ( ( vertex @ SV240 )
= $false )
| ( ( ~ ( vertex @ SV249 ) )
= $true )
| ( ( ~ ( ~ ! [SY520: $i] :
( ( SV240
!= ( tail_of @ SY520 ) )
| ~ ( edge @ SY520 )
| ( SV249
!= ( head_of @ SY520 ) )
| ( SV256
!= ( path_cons @ SY520 @ empty ) ) )
| ~ ! [SY521: $i] :
( ( SV240
!= ( tail_of @ SY521 ) )
| ~ ( edge @ SY521 )
| ! [SY522: $i] :
( ( SV256
!= ( path_cons @ SY521 @ SY522 ) )
| ~ ( path @ ( head_of @ SY521 ) @ SV249 @ SY522 ) ) ) ) )
= $true )
| ( ( path @ SV240 @ SV249 @ SV256 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1332]) ).
thf(1360,plain,
! [SV271: $i,SV265: $i,SV241: $i] :
( ( ( ~ ( ~ ( path @ SV241 @ SV265 @ ( sK9_P @ SV271 @ SV265 @ SV241 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SV271 ) @ ( length_of @ ( sK9_P @ SV271 @ SV265 @ SV241 ) ) ) )
| ( SV241 = SV265 )
| ~ ( path @ SV241 @ SV265 @ SV271 ) )
= $true )
| ( ( shortest_path @ SV241 @ SV265 @ SV271 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1333]) ).
thf(1361,plain,
! [SV241: $i] :
( ( ! [SY469: $i,SY470: $i] :
( ~ ( shortest_path @ SV241 @ SY469 @ SY470 )
| ! [SY471: $i] :
( ~ ( path @ SV241 @ SY469 @ SY471 )
| ( less_or_equal @ ( length_of @ SY470 ) @ ( length_of @ SY471 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1334]) ).
thf(1362,plain,
! [SV241: $i] :
( ( ~ ( ~ ! [SY472: $i] :
( ! [SY473: $i] :
~ ( shortest_path @ SV241 @ SY472 @ SY473 )
| ( SV241 != SY472 ) )
| ~ ! [SY474: $i,SY475: $i] :
( ~ ( shortest_path @ SV241 @ SY474 @ SY475 )
| ( path @ SV241 @ SY474 @ SY475 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1335]) ).
thf(1363,plain,
! [SV272: $i,SV266: $i,SV242: $i] :
( ( ( ~ ( edge @ SV242 )
| ~ ( edge @ SV266 )
| ~ ( edge @ SV272 )
| ~ ( sequential @ SV242 @ SV266 )
| ~ ( sequential @ SV266 @ SV272 )
| ~ ( sequential @ SV272 @ SV242 ) )
= $true )
| ( ( triangle @ SV242 @ SV266 @ SV272 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1336]) ).
thf(1364,plain,
! [SV242: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY478: $i,SY479: $i] :
~ ( triangle @ SV242 @ SY478 @ SY479 )
| ( edge @ SV242 ) )
| ~ ! [SY480: $i] :
( ! [SY481: $i] :
~ ( triangle @ SV242 @ SY480 @ SY481 )
| ( edge @ SY480 ) ) )
| ~ ! [SY482: $i,SY483: $i] :
( ~ ( triangle @ SV242 @ SY482 @ SY483 )
| ( edge @ SY483 ) ) )
| ~ ! [SY484: $i] :
( ! [SY485: $i] :
~ ( triangle @ SV242 @ SY484 @ SY485 )
| ( sequential @ SV242 @ SY484 ) ) )
| ~ ! [SY486: $i,SY487: $i] :
( ~ ( triangle @ SV242 @ SY486 @ SY487 )
| ( sequential @ SY486 @ SY487 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1337]) ).
thf(1365,plain,
! [SV242: $i] :
( ( ! [SY488: $i,SY489: $i] :
( ~ ( triangle @ SV242 @ SY488 @ SY489 )
| ( sequential @ SY489 @ SV242 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1338]) ).
thf(1366,plain,
! [SV233: $i] :
( ( ( ! [SY415: $i,SY416: $i] :
~ ( path @ SV233 @ SY415 @ SY416 ) )
= $true )
| ( ( vertex @ SV233 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1339]) ).
thf(1367,plain,
! [SV280: $i,SV233: $i] :
( ( ! [SY536: $i] :
~ ( path @ SV233 @ SV280 @ SY536 )
| ( vertex @ SV280 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1340]) ).
thf(1368,plain,
! [SV267: $i,SV263: $i,SV233: $i] :
( ( ( path @ SV233 @ SV263 @ SV267 )
= $false )
| ( ( ~ ( ~ ~ ( ( SV233
!= ( tail_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( edge @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
| ~ ~ ( ~ ( ( SV263
!= ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
| ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ empty ) )
| ! [SY528: $i] :
( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ SY528 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ SY528 ) ) )
| ~ ~ ( ~ ( ( SV263
= ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ ( sK14_SY90 @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ ( sK14_SY90 @ SV267 @ SV263 @ SV233 ) ) ) )
| ~ ( ( SV267
= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ empty ) )
| ~ ( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ ( sK13_SY91 @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ ( sK13_SY91 @ SV267 @ SV263 @ SV233 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1341]) ).
thf(1369,plain,
! [SV246: $i,SV234: $i] :
( ( ! [SY492: $i,SY493: $i] :
( ~ ( on_path @ SY493 @ SY492 )
| ~ ( path @ SV234 @ SV246 @ SY492 )
| ( edge @ SY493 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1342]) ).
thf(1370,plain,
! [SV246: $i,SV234: $i] :
( ( ! [SY494: $i,SY495: $i] :
( ~ ( on_path @ SY495 @ SY494 )
| ~ ( path @ SV234 @ SV246 @ SY494 )
| ( in_path @ ( head_of @ SY495 ) @ SY494 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1343]) ).
thf(1371,plain,
! [SV246: $i,SV234: $i,SV268: $i,SV273: $i] :
( ( ( ~ ( on_path @ SV273 @ SV268 )
| ~ ( path @ SV234 @ SV246 @ SV268 ) )
= $true )
| ( ( in_path @ ( tail_of @ SV273 ) @ SV268 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1344]) ).
thf(1372,plain,
! [SV257: $i,SV252: $i,SV235: $i] :
( ( ( ! [SY431: $i,SY432: $i] :
( ~ ( on_path @ SY431 @ SV235 )
| ~ ( on_path @ SY432 @ SV235 )
| ! [SY433: $i] :
( ~ ( precedes @ SY433 @ SY432 @ SV235 )
| ~ ( sequential @ SY431 @ SY433 ) )
| ( precedes @ SY431 @ SY432 @ SV235 ) ) )
= $true )
| ( ( path @ SV252 @ SV257 @ SV235 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1345]) ).
thf(1373,plain,
! [SV257: $i,SV252: $i,SV235: $i] :
( ( ( ! [SY434: $i,SY435: $i] :
( ~ ( on_path @ SY434 @ SV235 )
| ~ ( on_path @ SY435 @ SV235 )
| ~ ( sequential @ SY434 @ SY435 )
| ( precedes @ SY434 @ SY435 @ SV235 ) ) )
= $true )
| ( ( path @ SV252 @ SV257 @ SV235 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1346]) ).
thf(1374,plain,
! [SV247: $i,SV236: $i,SV274: $i,SV253: $i] :
( ( ( ! [SY532: $i] :
( ~ ( precedes @ SV253 @ SV274 @ SY532 )
| ~ ( shortest_path @ SV236 @ SV247 @ SY532 ) ) )
= $true )
| ( ( ! [SY533: $i] :
( ( ( tail_of @ SY533 )
!= ( tail_of @ SV253 ) )
| ( ( head_of @ SY533 )
!= ( head_of @ SV274 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1347]) ).
thf(1375,plain,
! [SV247: $i,SV236: $i,SV281: $i,SV275: $i,SV253: $i] :
( ( ~ ( precedes @ SV253 @ SV275 @ SV281 )
| ~ ( shortest_path @ SV236 @ SV247 @ SV281 )
| ~ ( precedes @ SV275 @ SV253 @ SV281 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1348]) ).
thf(1376,plain,
! [SV258: $i,SV254: $i,SV237: $i] :
( ( ( ~ ( ~ ! [SY445: $i] :
( ! [SY446: $i] :
~ ( precedes @ SY445 @ SY446 @ SV237 )
| ( on_path @ SY445 @ SV237 ) )
| ~ ! [SY447: $i,SY448: $i] :
( ~ ( precedes @ SY447 @ SY448 @ SV237 )
| ( on_path @ SY448 @ SV237 ) ) ) )
= $true )
| ( ( path @ SV254 @ SV258 @ SV237 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1349]) ).
thf(1377,plain,
! [SV258: $i,SV254: $i,SV237: $i] :
( ( ( ~ ( ~ ! [SY449: $i,SY450: $i] :
( ~ ( precedes @ SY449 @ SY450 @ SV237 )
| ! [SY451: $i] :
( ~ ( precedes @ SY451 @ SY450 @ SV237 )
| ~ ( sequential @ SY449 @ SY451 ) )
| ~ ( sequential @ SY449 @ SY450 ) )
| ~ ! [SY452: $i,SY453: $i] :
( ~ ( precedes @ SY452 @ SY453 @ SV237 )
| ~ ( ~ ( precedes @ ( sK10_E3 @ SY453 @ SY452 @ SV237 ) @ SY453 @ SV237 )
| ~ ( sequential @ SY452 @ ( sK10_E3 @ SY453 @ SY452 @ SV237 ) ) )
| ( sequential @ SY452 @ SY453 ) ) ) )
= $true )
| ( ( path @ SV254 @ SV258 @ SV237 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1350]) ).
thf(1378,plain,
! [SV259: $i,SV255: $i] :
( ( ( vertex @ SV255 )
= $false )
| ( ( ~ ( vertex @ SV259 ) )
= $true )
| ( ( SV255 = SV259 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV255
!= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
!= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
!= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
!= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV255
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
| ~ ( ( SV255
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) ) )
| ~ ~ ( ~ ( ( SV259
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
| ~ ( ( SV259
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) ) ) ) )
| ~ ( edge @ ( sK15_E @ SV259 @ SV255 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1351]) ).
thf(1379,plain,
! [SV238: $i] :
( ( ( ~ ~ ( ~ ( on_path @ ( sK7_E1 @ SV238 ) @ SV238 )
| ~ ( on_path @ ( sK8_SY86 @ SV238 ) @ SV238 ) ) )
= $false )
| ( ( ! [SY455: $i,SY456: $i] :
~ ( path @ SY455 @ SY456 @ SV238 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV238 )
= ( number_of_in @ triangles @ SV238 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1352]) ).
thf(1380,plain,
! [SV238: $i] :
( ( ( ~ ( sequential @ ( sK7_E1 @ SV238 ) @ ( sK8_SY86 @ SV238 ) ) )
= $false )
| ( ( ! [SY455: $i,SY456: $i] :
~ ( path @ SY455 @ SY456 @ SV238 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV238 )
= ( number_of_in @ triangles @ SV238 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1352]) ).
thf(1381,plain,
! [SV276: $i,SV238: $i] :
( ( ( triangle @ ( sK7_E1 @ SV238 ) @ ( sK8_SY86 @ SV238 ) @ SV276 )
= $false )
| ( ( ! [SY455: $i,SY456: $i] :
~ ( path @ SY455 @ SY456 @ SV238 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV238 )
= ( number_of_in @ triangles @ SV238 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1353]) ).
thf(1382,plain,
! [SV264: $i,SV262: $i] :
( ( ( SV262 = SV264 )
= $true )
| ( ( ~ ( edge @ SV262 )
| ~ ( edge @ SV264 ) )
= $true )
| ( ( ( ( head_of @ SV262 )
!= ( tail_of @ SV264 ) ) )
= $true )
| ( ( sequential @ SV262 @ SV264 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1354]) ).
thf(1383,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1355]) ).
thf(1384,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)],[1355]) ).
thf(1385,plain,
! [SV282: $i,SV277: $i] :
( ( ~ ( sequential @ SV277 @ SV282 )
| ( ( head_of @ SV277 )
= ( tail_of @ SV282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1356]) ).
thf(1386,plain,
! [SV248: $i,SV239: $i,SV269: $i,SV278: $i] :
( ( ( ~ ( in_path @ SV278 @ SV269 )
| ~ ( path @ SV239 @ SV248 @ SV269 ) )
= $true )
| ( ( ~ ( ~ ( on_path @ ( sK11_E @ SV278 @ SV269 @ SV248 @ SV239 ) @ SV269 )
| ~ ( ( SV278
= ( head_of @ ( sK11_E @ SV278 @ SV269 @ SV248 @ SV239 ) ) )
| ( SV278
= ( tail_of @ ( sK11_E @ SV278 @ SV269 @ SV248 @ SV239 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1357]) ).
thf(1387,plain,
! [SV248: $i,SV239: $i,SV270: $i,SV279: $i] :
( ( ( ~ ( in_path @ SV279 @ SV270 )
| ~ ( path @ SV239 @ SV248 @ SV270 ) )
= $true )
| ( ( vertex @ SV279 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1358]) ).
thf(1388,plain,
! [SV256: $i,SV240: $i,SV249: $i] :
( ( ( vertex @ SV249 )
= $false )
| ( ( vertex @ SV240 )
= $false )
| ( ( ~ ( ~ ! [SY520: $i] :
( ( SV240
!= ( tail_of @ SY520 ) )
| ~ ( edge @ SY520 )
| ( SV249
!= ( head_of @ SY520 ) )
| ( SV256
!= ( path_cons @ SY520 @ empty ) ) )
| ~ ! [SY521: $i] :
( ( SV240
!= ( tail_of @ SY521 ) )
| ~ ( edge @ SY521 )
| ! [SY522: $i] :
( ( SV256
!= ( path_cons @ SY521 @ SY522 ) )
| ~ ( path @ ( head_of @ SY521 ) @ SV249 @ SY522 ) ) ) ) )
= $true )
| ( ( path @ SV240 @ SV249 @ SV256 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1359]) ).
thf(1389,plain,
! [SV271: $i,SV265: $i,SV241: $i] :
( ( ( ~ ( ~ ( path @ SV241 @ SV265 @ ( sK9_P @ SV271 @ SV265 @ SV241 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SV271 ) @ ( length_of @ ( sK9_P @ SV271 @ SV265 @ SV241 ) ) ) ) )
= $true )
| ( ( ( SV241 = SV265 )
| ~ ( path @ SV241 @ SV265 @ SV271 ) )
= $true )
| ( ( shortest_path @ SV241 @ SV265 @ SV271 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1360]) ).
thf(1390,plain,
! [SV283: $i,SV241: $i] :
( ( ! [SY537: $i] :
( ~ ( shortest_path @ SV241 @ SV283 @ SY537 )
| ! [SY538: $i] :
( ~ ( path @ SV241 @ SV283 @ SY538 )
| ( less_or_equal @ ( length_of @ SY537 ) @ ( length_of @ SY538 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1361]) ).
thf(1391,plain,
! [SV241: $i] :
( ( ~ ! [SY472: $i] :
( ! [SY473: $i] :
~ ( shortest_path @ SV241 @ SY472 @ SY473 )
| ( SV241 != SY472 ) )
| ~ ! [SY474: $i,SY475: $i] :
( ~ ( shortest_path @ SV241 @ SY474 @ SY475 )
| ( path @ SV241 @ SY474 @ SY475 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1362]) ).
thf(1392,plain,
! [SV272: $i,SV266: $i,SV242: $i] :
( ( ( ~ ( edge @ SV242 )
| ~ ( edge @ SV266 )
| ~ ( edge @ SV272 )
| ~ ( sequential @ SV242 @ SV266 )
| ~ ( sequential @ SV266 @ SV272 ) )
= $true )
| ( ( ~ ( sequential @ SV272 @ SV242 ) )
= $true )
| ( ( triangle @ SV242 @ SV266 @ SV272 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1363]) ).
thf(1393,plain,
! [SV242: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY478: $i,SY479: $i] :
~ ( triangle @ SV242 @ SY478 @ SY479 )
| ( edge @ SV242 ) )
| ~ ! [SY480: $i] :
( ! [SY481: $i] :
~ ( triangle @ SV242 @ SY480 @ SY481 )
| ( edge @ SY480 ) ) )
| ~ ! [SY482: $i,SY483: $i] :
( ~ ( triangle @ SV242 @ SY482 @ SY483 )
| ( edge @ SY483 ) ) )
| ~ ! [SY484: $i] :
( ! [SY485: $i] :
~ ( triangle @ SV242 @ SY484 @ SY485 )
| ( sequential @ SV242 @ SY484 ) ) )
| ~ ! [SY486: $i,SY487: $i] :
( ~ ( triangle @ SV242 @ SY486 @ SY487 )
| ( sequential @ SY486 @ SY487 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1364]) ).
thf(1394,plain,
! [SV284: $i,SV242: $i] :
( ( ! [SY539: $i] :
( ~ ( triangle @ SV242 @ SV284 @ SY539 )
| ( sequential @ SY539 @ SV242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1365]) ).
thf(1395,plain,
! [SV285: $i,SV233: $i] :
( ( ( ! [SY540: $i] :
~ ( path @ SV233 @ SV285 @ SY540 ) )
= $true )
| ( ( vertex @ SV233 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1366]) ).
thf(1396,plain,
! [SV280: $i,SV233: $i] :
( ( ( ! [SY536: $i] :
~ ( path @ SV233 @ SV280 @ SY536 ) )
= $true )
| ( ( vertex @ SV280 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1367]) ).
thf(1397,plain,
! [SV263: $i,SV267: $i,SV233: $i] :
( ( ( ~ ~ ( ( SV233
!= ( tail_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( edge @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
| ~ ~ ( ~ ( ( SV263
!= ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
| ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ empty ) )
| ! [SY528: $i] :
( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ SY528 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ SY528 ) ) )
| ~ ~ ( ~ ( ( SV263
= ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ ( sK14_SY90 @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ ( sK14_SY90 @ SV267 @ SV263 @ SV233 ) ) ) )
| ~ ( ( SV267
= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ empty ) )
| ~ ( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ ( sK13_SY91 @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ ( sK13_SY91 @ SV267 @ SV263 @ SV233 ) ) ) ) ) ) )
= $false )
| ( ( path @ SV233 @ SV263 @ SV267 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1368]) ).
thf(1398,plain,
! [SV246: $i,SV234: $i,SV286: $i] :
( ( ! [SY541: $i] :
( ~ ( on_path @ SY541 @ SV286 )
| ~ ( path @ SV234 @ SV246 @ SV286 )
| ( edge @ SY541 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1369]) ).
thf(1399,plain,
! [SV246: $i,SV234: $i,SV287: $i] :
( ( ! [SY542: $i] :
( ~ ( on_path @ SY542 @ SV287 )
| ~ ( path @ SV234 @ SV246 @ SV287 )
| ( in_path @ ( head_of @ SY542 ) @ SV287 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1370]) ).
thf(1400,plain,
! [SV246: $i,SV234: $i,SV268: $i,SV273: $i] :
( ( ( ~ ( on_path @ SV273 @ SV268 ) )
= $true )
| ( ( ~ ( path @ SV234 @ SV246 @ SV268 ) )
= $true )
| ( ( in_path @ ( tail_of @ SV273 ) @ SV268 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1371]) ).
thf(1401,plain,
! [SV257: $i,SV252: $i,SV235: $i,SV288: $i] :
( ( ( ! [SY543: $i] :
( ~ ( on_path @ SV288 @ SV235 )
| ~ ( on_path @ SY543 @ SV235 )
| ! [SY544: $i] :
( ~ ( precedes @ SY544 @ SY543 @ SV235 )
| ~ ( sequential @ SV288 @ SY544 ) )
| ( precedes @ SV288 @ SY543 @ SV235 ) ) )
= $true )
| ( ( path @ SV252 @ SV257 @ SV235 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1372]) ).
thf(1402,plain,
! [SV257: $i,SV252: $i,SV235: $i,SV289: $i] :
( ( ( ! [SY545: $i] :
( ~ ( on_path @ SV289 @ SV235 )
| ~ ( on_path @ SY545 @ SV235 )
| ~ ( sequential @ SV289 @ SY545 )
| ( precedes @ SV289 @ SY545 @ SV235 ) ) )
= $true )
| ( ( path @ SV252 @ SV257 @ SV235 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1373]) ).
thf(1403,plain,
! [SV247: $i,SV236: $i,SV290: $i,SV274: $i,SV253: $i] :
( ( ( ~ ( precedes @ SV253 @ SV274 @ SV290 )
| ~ ( shortest_path @ SV236 @ SV247 @ SV290 ) )
= $true )
| ( ( ! [SY533: $i] :
( ( ( tail_of @ SY533 )
!= ( tail_of @ SV253 ) )
| ( ( head_of @ SY533 )
!= ( head_of @ SV274 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1374]) ).
thf(1404,plain,
! [SV247: $i,SV236: $i,SV281: $i,SV275: $i,SV253: $i] :
( ( ( ~ ( precedes @ SV253 @ SV275 @ SV281 )
| ~ ( shortest_path @ SV236 @ SV247 @ SV281 ) )
= $true )
| ( ( ~ ( precedes @ SV275 @ SV253 @ SV281 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1375]) ).
thf(1405,plain,
! [SV258: $i,SV254: $i,SV237: $i] :
( ( ( ~ ! [SY445: $i] :
( ! [SY446: $i] :
~ ( precedes @ SY445 @ SY446 @ SV237 )
| ( on_path @ SY445 @ SV237 ) )
| ~ ! [SY447: $i,SY448: $i] :
( ~ ( precedes @ SY447 @ SY448 @ SV237 )
| ( on_path @ SY448 @ SV237 ) ) )
= $false )
| ( ( path @ SV254 @ SV258 @ SV237 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1376]) ).
thf(1406,plain,
! [SV258: $i,SV254: $i,SV237: $i] :
( ( ( ~ ! [SY449: $i,SY450: $i] :
( ~ ( precedes @ SY449 @ SY450 @ SV237 )
| ! [SY451: $i] :
( ~ ( precedes @ SY451 @ SY450 @ SV237 )
| ~ ( sequential @ SY449 @ SY451 ) )
| ~ ( sequential @ SY449 @ SY450 ) )
| ~ ! [SY452: $i,SY453: $i] :
( ~ ( precedes @ SY452 @ SY453 @ SV237 )
| ~ ( ~ ( precedes @ ( sK10_E3 @ SY453 @ SY452 @ SV237 ) @ SY453 @ SV237 )
| ~ ( sequential @ SY452 @ ( sK10_E3 @ SY453 @ SY452 @ SV237 ) ) )
| ( sequential @ SY452 @ SY453 ) ) )
= $false )
| ( ( path @ SV254 @ SV258 @ SV237 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1377]) ).
thf(1407,plain,
! [SV255: $i,SV259: $i] :
( ( ( vertex @ SV259 )
= $false )
| ( ( vertex @ SV255 )
= $false )
| ( ( SV255 = SV259 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV255
!= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
!= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
!= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
!= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV255
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
| ~ ( ( SV255
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) ) )
| ~ ~ ( ~ ( ( SV259
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
| ~ ( ( SV259
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) ) ) ) )
| ~ ( edge @ ( sK15_E @ SV259 @ SV255 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1378]) ).
thf(1408,plain,
! [SV238: $i] :
( ( ( ~ ( ~ ( on_path @ ( sK7_E1 @ SV238 ) @ SV238 )
| ~ ( on_path @ ( sK8_SY86 @ SV238 ) @ SV238 ) ) )
= $true )
| ( ( ! [SY455: $i,SY456: $i] :
~ ( path @ SY455 @ SY456 @ SV238 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV238 )
= ( number_of_in @ triangles @ SV238 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1379]) ).
thf(1409,plain,
! [SV238: $i] :
( ( ( sequential @ ( sK7_E1 @ SV238 ) @ ( sK8_SY86 @ SV238 ) )
= $true )
| ( ( ! [SY455: $i,SY456: $i] :
~ ( path @ SY455 @ SY456 @ SV238 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV238 )
= ( number_of_in @ triangles @ SV238 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1380]) ).
thf(1410,plain,
! [SV276: $i,SV238: $i,SV291: $i] :
( ( ( ! [SY546: $i] :
~ ( path @ SV291 @ SY546 @ SV238 ) )
= $true )
| ( ( triangle @ ( sK7_E1 @ SV238 ) @ ( sK8_SY86 @ SV238 ) @ SV276 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV238 )
= ( number_of_in @ triangles @ SV238 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1381]) ).
thf(1411,plain,
! [SV264: $i,SV262: $i] :
( ( ( ~ ( edge @ SV262 ) )
= $true )
| ( ( ~ ( edge @ SV264 ) )
= $true )
| ( ( SV262 = SV264 )
= $true )
| ( ( ( ( head_of @ SV262 )
!= ( tail_of @ SV264 ) ) )
= $true )
| ( ( sequential @ SV262 @ SV264 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1382]) ).
thf(1412,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1383]) ).
thf(1413,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)],[1384]) ).
thf(1414,plain,
! [SV282: $i,SV277: $i] :
( ( ( ~ ( sequential @ SV277 @ SV282 ) )
= $true )
| ( ( ( head_of @ SV277 )
= ( tail_of @ SV282 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1385]) ).
thf(1415,plain,
! [SV248: $i,SV239: $i,SV269: $i,SV278: $i] :
( ( ( ~ ( in_path @ SV278 @ SV269 ) )
= $true )
| ( ( ~ ( path @ SV239 @ SV248 @ SV269 ) )
= $true )
| ( ( ~ ( ~ ( on_path @ ( sK11_E @ SV278 @ SV269 @ SV248 @ SV239 ) @ SV269 )
| ~ ( ( SV278
= ( head_of @ ( sK11_E @ SV278 @ SV269 @ SV248 @ SV239 ) ) )
| ( SV278
= ( tail_of @ ( sK11_E @ SV278 @ SV269 @ SV248 @ SV239 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1386]) ).
thf(1416,plain,
! [SV248: $i,SV239: $i,SV270: $i,SV279: $i] :
( ( ( ~ ( in_path @ SV279 @ SV270 ) )
= $true )
| ( ( ~ ( path @ SV239 @ SV248 @ SV270 ) )
= $true )
| ( ( vertex @ SV279 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1387]) ).
thf(1417,plain,
! [SV256: $i,SV249: $i,SV240: $i] :
( ( ( ~ ! [SY520: $i] :
( ( SV240
!= ( tail_of @ SY520 ) )
| ~ ( edge @ SY520 )
| ( SV249
!= ( head_of @ SY520 ) )
| ( SV256
!= ( path_cons @ SY520 @ empty ) ) )
| ~ ! [SY521: $i] :
( ( SV240
!= ( tail_of @ SY521 ) )
| ~ ( edge @ SY521 )
| ! [SY522: $i] :
( ( SV256
!= ( path_cons @ SY521 @ SY522 ) )
| ~ ( path @ ( head_of @ SY521 ) @ SV249 @ SY522 ) ) ) )
= $false )
| ( ( vertex @ SV240 )
= $false )
| ( ( vertex @ SV249 )
= $false )
| ( ( path @ SV240 @ SV249 @ SV256 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1388]) ).
thf(1418,plain,
! [SV271: $i,SV265: $i,SV241: $i] :
( ( ( ~ ( path @ SV241 @ SV265 @ ( sK9_P @ SV271 @ SV265 @ SV241 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SV271 ) @ ( length_of @ ( sK9_P @ SV271 @ SV265 @ SV241 ) ) ) )
= $false )
| ( ( ( SV241 = SV265 )
| ~ ( path @ SV241 @ SV265 @ SV271 ) )
= $true )
| ( ( shortest_path @ SV241 @ SV265 @ SV271 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1389]) ).
thf(1419,plain,
! [SV292: $i,SV283: $i,SV241: $i] :
( ( ~ ( shortest_path @ SV241 @ SV283 @ SV292 )
| ! [SY547: $i] :
( ~ ( path @ SV241 @ SV283 @ SY547 )
| ( less_or_equal @ ( length_of @ SV292 ) @ ( length_of @ SY547 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1390]) ).
thf(1420,plain,
! [SV241: $i] :
( ( ~ ! [SY472: $i] :
( ! [SY473: $i] :
~ ( shortest_path @ SV241 @ SY472 @ SY473 )
| ( SV241 != SY472 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1391]) ).
thf(1421,plain,
! [SV241: $i] :
( ( ~ ! [SY474: $i,SY475: $i] :
( ~ ( shortest_path @ SV241 @ SY474 @ SY475 )
| ( path @ SV241 @ SY474 @ SY475 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1391]) ).
thf(1422,plain,
! [SV272: $i,SV266: $i,SV242: $i] :
( ( ( ~ ( edge @ SV242 )
| ~ ( edge @ SV266 )
| ~ ( edge @ SV272 )
| ~ ( sequential @ SV242 @ SV266 ) )
= $true )
| ( ( ~ ( sequential @ SV266 @ SV272 ) )
= $true )
| ( ( ~ ( sequential @ SV272 @ SV242 ) )
= $true )
| ( ( triangle @ SV242 @ SV266 @ SV272 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1392]) ).
thf(1423,plain,
! [SV242: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY478: $i,SY479: $i] :
~ ( triangle @ SV242 @ SY478 @ SY479 )
| ( edge @ SV242 ) )
| ~ ! [SY480: $i] :
( ! [SY481: $i] :
~ ( triangle @ SV242 @ SY480 @ SY481 )
| ( edge @ SY480 ) ) )
| ~ ! [SY482: $i,SY483: $i] :
( ~ ( triangle @ SV242 @ SY482 @ SY483 )
| ( edge @ SY483 ) ) )
| ~ ! [SY484: $i] :
( ! [SY485: $i] :
~ ( triangle @ SV242 @ SY484 @ SY485 )
| ( sequential @ SV242 @ SY484 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1393]) ).
thf(1424,plain,
! [SV242: $i] :
( ( ~ ! [SY486: $i,SY487: $i] :
( ~ ( triangle @ SV242 @ SY486 @ SY487 )
| ( sequential @ SY486 @ SY487 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1393]) ).
thf(1425,plain,
! [SV293: $i,SV284: $i,SV242: $i] :
( ( ~ ( triangle @ SV242 @ SV284 @ SV293 )
| ( sequential @ SV293 @ SV242 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1394]) ).
thf(1426,plain,
! [SV294: $i,SV285: $i,SV233: $i] :
( ( ( ~ ( path @ SV233 @ SV285 @ SV294 ) )
= $true )
| ( ( vertex @ SV233 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1395]) ).
thf(1427,plain,
! [SV295: $i,SV280: $i,SV233: $i] :
( ( ( ~ ( path @ SV233 @ SV280 @ SV295 ) )
= $true )
| ( ( vertex @ SV280 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1396]) ).
thf(1428,plain,
! [SV263: $i,SV267: $i,SV233: $i] :
( ( ( ~ ~ ( ( SV233
!= ( tail_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( edge @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) ) )
= $false )
| ( ( path @ SV233 @ SV263 @ SV267 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1397]) ).
thf(1429,plain,
! [SV233: $i,SV267: $i,SV263: $i] :
( ( ( ~ ~ ( ~ ( ( SV263
!= ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
| ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ empty ) )
| ! [SY528: $i] :
( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ SY528 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ SY528 ) ) )
| ~ ~ ( ~ ( ( SV263
= ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ ( sK14_SY90 @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ ( sK14_SY90 @ SV267 @ SV263 @ SV233 ) ) ) )
| ~ ( ( SV267
= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ empty ) )
| ~ ( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ ( sK13_SY91 @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ ( sK13_SY91 @ SV267 @ SV263 @ SV233 ) ) ) ) ) ) )
= $false )
| ( ( path @ SV233 @ SV263 @ SV267 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1397]) ).
thf(1430,plain,
! [SV246: $i,SV234: $i,SV286: $i,SV296: $i] :
( ( ~ ( on_path @ SV296 @ SV286 )
| ~ ( path @ SV234 @ SV246 @ SV286 )
| ( edge @ SV296 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1398]) ).
thf(1431,plain,
! [SV246: $i,SV234: $i,SV287: $i,SV297: $i] :
( ( ~ ( on_path @ SV297 @ SV287 )
| ~ ( path @ SV234 @ SV246 @ SV287 )
| ( in_path @ ( head_of @ SV297 ) @ SV287 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1399]) ).
thf(1432,plain,
! [SV246: $i,SV234: $i,SV268: $i,SV273: $i] :
( ( ( on_path @ SV273 @ SV268 )
= $false )
| ( ( ~ ( path @ SV234 @ SV246 @ SV268 ) )
= $true )
| ( ( in_path @ ( tail_of @ SV273 ) @ SV268 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1400]) ).
thf(1433,plain,
! [SV257: $i,SV252: $i,SV298: $i,SV235: $i,SV288: $i] :
( ( ( ~ ( on_path @ SV288 @ SV235 )
| ~ ( on_path @ SV298 @ SV235 )
| ! [SY548: $i] :
( ~ ( precedes @ SY548 @ SV298 @ SV235 )
| ~ ( sequential @ SV288 @ SY548 ) )
| ( precedes @ SV288 @ SV298 @ SV235 ) )
= $true )
| ( ( path @ SV252 @ SV257 @ SV235 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1401]) ).
thf(1434,plain,
! [SV257: $i,SV252: $i,SV299: $i,SV235: $i,SV289: $i] :
( ( ( ~ ( on_path @ SV289 @ SV235 )
| ~ ( on_path @ SV299 @ SV235 )
| ~ ( sequential @ SV289 @ SV299 )
| ( precedes @ SV289 @ SV299 @ SV235 ) )
= $true )
| ( ( path @ SV252 @ SV257 @ SV235 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1402]) ).
thf(1435,plain,
! [SV247: $i,SV236: $i,SV290: $i,SV274: $i,SV253: $i] :
( ( ( ~ ( precedes @ SV253 @ SV274 @ SV290 ) )
= $true )
| ( ( ~ ( shortest_path @ SV236 @ SV247 @ SV290 ) )
= $true )
| ( ( ! [SY533: $i] :
( ( ( tail_of @ SY533 )
!= ( tail_of @ SV253 ) )
| ( ( head_of @ SY533 )
!= ( head_of @ SV274 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1403]) ).
thf(1436,plain,
! [SV247: $i,SV236: $i,SV281: $i,SV275: $i,SV253: $i] :
( ( ( ~ ( precedes @ SV253 @ SV275 @ SV281 ) )
= $true )
| ( ( ~ ( shortest_path @ SV236 @ SV247 @ SV281 ) )
= $true )
| ( ( ~ ( precedes @ SV275 @ SV253 @ SV281 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1404]) ).
thf(1437,plain,
! [SV258: $i,SV254: $i,SV237: $i] :
( ( ( ~ ! [SY445: $i] :
( ! [SY446: $i] :
~ ( precedes @ SY445 @ SY446 @ SV237 )
| ( on_path @ SY445 @ SV237 ) ) )
= $false )
| ( ( path @ SV254 @ SV258 @ SV237 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1405]) ).
thf(1438,plain,
! [SV258: $i,SV254: $i,SV237: $i] :
( ( ( ~ ! [SY447: $i,SY448: $i] :
( ~ ( precedes @ SY447 @ SY448 @ SV237 )
| ( on_path @ SY448 @ SV237 ) ) )
= $false )
| ( ( path @ SV254 @ SV258 @ SV237 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1405]) ).
thf(1439,plain,
! [SV258: $i,SV254: $i,SV237: $i] :
( ( ( ~ ! [SY449: $i,SY450: $i] :
( ~ ( precedes @ SY449 @ SY450 @ SV237 )
| ! [SY451: $i] :
( ~ ( precedes @ SY451 @ SY450 @ SV237 )
| ~ ( sequential @ SY449 @ SY451 ) )
| ~ ( sequential @ SY449 @ SY450 ) ) )
= $false )
| ( ( path @ SV254 @ SV258 @ SV237 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1406]) ).
thf(1440,plain,
! [SV258: $i,SV254: $i,SV237: $i] :
( ( ( ~ ! [SY452: $i,SY453: $i] :
( ~ ( precedes @ SY452 @ SY453 @ SV237 )
| ~ ( ~ ( precedes @ ( sK10_E3 @ SY453 @ SY452 @ SV237 ) @ SY453 @ SV237 )
| ~ ( sequential @ SY452 @ ( sK10_E3 @ SY453 @ SY452 @ SV237 ) ) )
| ( sequential @ SY452 @ SY453 ) ) )
= $false )
| ( ( path @ SV254 @ SV258 @ SV237 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1406]) ).
thf(1441,plain,
! [SV259: $i,SV255: $i] :
( ( ( ~ ~ ( ~ ( ( SV255
!= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
!= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
!= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
!= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV255
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
| ~ ( ( SV255
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) ) )
| ~ ~ ( ~ ( ( SV259
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
| ~ ( ( SV259
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) ) ) ) )
| ~ ( edge @ ( sK15_E @ SV259 @ SV255 ) ) )
= $false )
| ( ( SV255 = SV259 )
= $true )
| ( ( vertex @ SV255 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1407]) ).
thf(1442,plain,
! [SV238: $i] :
( ( ( ~ ( on_path @ ( sK7_E1 @ SV238 ) @ SV238 )
| ~ ( on_path @ ( sK8_SY86 @ SV238 ) @ SV238 ) )
= $false )
| ( ( ! [SY455: $i,SY456: $i] :
~ ( path @ SY455 @ SY456 @ SV238 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV238 )
= ( number_of_in @ triangles @ SV238 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1408]) ).
thf(1443,plain,
! [SV238: $i,SV300: $i] :
( ( ( ! [SY549: $i] :
~ ( path @ SV300 @ SY549 @ SV238 ) )
= $true )
| ( ( sequential @ ( sK7_E1 @ SV238 ) @ ( sK8_SY86 @ SV238 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV238 )
= ( number_of_in @ triangles @ SV238 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1409]) ).
thf(1444,plain,
! [SV276: $i,SV238: $i,SV301: $i,SV291: $i] :
( ( ( ~ ( path @ SV291 @ SV301 @ SV238 ) )
= $true )
| ( ( triangle @ ( sK7_E1 @ SV238 ) @ ( sK8_SY86 @ SV238 ) @ SV276 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV238 )
= ( number_of_in @ triangles @ SV238 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1410]) ).
thf(1445,plain,
! [SV264: $i,SV262: $i] :
( ( ( edge @ SV262 )
= $false )
| ( ( ~ ( edge @ SV264 ) )
= $true )
| ( ( SV262 = SV264 )
= $true )
| ( ( ( ( head_of @ SV262 )
!= ( tail_of @ SV264 ) ) )
= $true )
| ( ( sequential @ SV262 @ SV264 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1411]) ).
thf(1446,plain,
! [SV302: $i] :
( ( ! [SY550: $i] :
( ~ ( sequential @ SV302 @ SY550 )
| ( SV302 != SY550 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1412]) ).
thf(1447,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)],[1413]) ).
thf(1448,plain,
! [SV282: $i,SV277: $i] :
( ( ( sequential @ SV277 @ SV282 )
= $false )
| ( ( ( head_of @ SV277 )
= ( tail_of @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1414]) ).
thf(1449,plain,
! [SV248: $i,SV239: $i,SV269: $i,SV278: $i] :
( ( ( in_path @ SV278 @ SV269 )
= $false )
| ( ( ~ ( path @ SV239 @ SV248 @ SV269 ) )
= $true )
| ( ( ~ ( ~ ( on_path @ ( sK11_E @ SV278 @ SV269 @ SV248 @ SV239 ) @ SV269 )
| ~ ( ( SV278
= ( head_of @ ( sK11_E @ SV278 @ SV269 @ SV248 @ SV239 ) ) )
| ( SV278
= ( tail_of @ ( sK11_E @ SV278 @ SV269 @ SV248 @ SV239 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1415]) ).
thf(1450,plain,
! [SV248: $i,SV239: $i,SV270: $i,SV279: $i] :
( ( ( in_path @ SV279 @ SV270 )
= $false )
| ( ( ~ ( path @ SV239 @ SV248 @ SV270 ) )
= $true )
| ( ( vertex @ SV279 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1416]) ).
thf(1451,plain,
! [SV256: $i,SV249: $i,SV240: $i] :
( ( ( ~ ! [SY520: $i] :
( ( SV240
!= ( tail_of @ SY520 ) )
| ~ ( edge @ SY520 )
| ( SV249
!= ( head_of @ SY520 ) )
| ( SV256
!= ( path_cons @ SY520 @ empty ) ) ) )
= $false )
| ( ( vertex @ SV240 )
= $false )
| ( ( vertex @ SV249 )
= $false )
| ( ( path @ SV240 @ SV249 @ SV256 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1417]) ).
thf(1452,plain,
! [SV249: $i,SV256: $i,SV240: $i] :
( ( ( ~ ! [SY521: $i] :
( ( SV240
!= ( tail_of @ SY521 ) )
| ~ ( edge @ SY521 )
| ! [SY522: $i] :
( ( SV256
!= ( path_cons @ SY521 @ SY522 ) )
| ~ ( path @ ( head_of @ SY521 ) @ SV249 @ SY522 ) ) ) )
= $false )
| ( ( vertex @ SV240 )
= $false )
| ( ( vertex @ SV249 )
= $false )
| ( ( path @ SV240 @ SV249 @ SV256 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1417]) ).
thf(1453,plain,
! [SV271: $i,SV265: $i,SV241: $i] :
( ( ( ~ ( path @ SV241 @ SV265 @ ( sK9_P @ SV271 @ SV265 @ SV241 ) ) )
= $false )
| ( ( ( SV241 = SV265 )
| ~ ( path @ SV241 @ SV265 @ SV271 ) )
= $true )
| ( ( shortest_path @ SV241 @ SV265 @ SV271 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1418]) ).
thf(1454,plain,
! [SV241: $i,SV265: $i,SV271: $i] :
( ( ( ~ ~ ( less_or_equal @ ( length_of @ SV271 ) @ ( length_of @ ( sK9_P @ SV271 @ SV265 @ SV241 ) ) ) )
= $false )
| ( ( ( SV241 = SV265 )
| ~ ( path @ SV241 @ SV265 @ SV271 ) )
= $true )
| ( ( shortest_path @ SV241 @ SV265 @ SV271 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1418]) ).
thf(1455,plain,
! [SV292: $i,SV283: $i,SV241: $i] :
( ( ( ~ ( shortest_path @ SV241 @ SV283 @ SV292 ) )
= $true )
| ( ( ! [SY547: $i] :
( ~ ( path @ SV241 @ SV283 @ SY547 )
| ( less_or_equal @ ( length_of @ SV292 ) @ ( length_of @ SY547 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1419]) ).
thf(1456,plain,
! [SV241: $i] :
( ( ! [SY472: $i] :
( ! [SY473: $i] :
~ ( shortest_path @ SV241 @ SY472 @ SY473 )
| ( SV241 != SY472 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1420]) ).
thf(1457,plain,
! [SV241: $i] :
( ( ! [SY474: $i,SY475: $i] :
( ~ ( shortest_path @ SV241 @ SY474 @ SY475 )
| ( path @ SV241 @ SY474 @ SY475 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1421]) ).
thf(1458,plain,
! [SV272: $i,SV266: $i,SV242: $i] :
( ( ( ~ ( edge @ SV242 )
| ~ ( edge @ SV266 )
| ~ ( edge @ SV272 ) )
= $true )
| ( ( ~ ( sequential @ SV242 @ SV266 ) )
= $true )
| ( ( ~ ( sequential @ SV266 @ SV272 ) )
= $true )
| ( ( ~ ( sequential @ SV272 @ SV242 ) )
= $true )
| ( ( triangle @ SV242 @ SV266 @ SV272 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1422]) ).
thf(1459,plain,
! [SV242: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY478: $i,SY479: $i] :
~ ( triangle @ SV242 @ SY478 @ SY479 )
| ( edge @ SV242 ) )
| ~ ! [SY480: $i] :
( ! [SY481: $i] :
~ ( triangle @ SV242 @ SY480 @ SY481 )
| ( edge @ SY480 ) ) )
| ~ ! [SY482: $i,SY483: $i] :
( ~ ( triangle @ SV242 @ SY482 @ SY483 )
| ( edge @ SY483 ) ) )
| ~ ! [SY484: $i] :
( ! [SY485: $i] :
~ ( triangle @ SV242 @ SY484 @ SY485 )
| ( sequential @ SV242 @ SY484 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1423]) ).
thf(1460,plain,
! [SV242: $i] :
( ( ! [SY486: $i,SY487: $i] :
( ~ ( triangle @ SV242 @ SY486 @ SY487 )
| ( sequential @ SY486 @ SY487 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1424]) ).
thf(1461,plain,
! [SV293: $i,SV284: $i,SV242: $i] :
( ( ( ~ ( triangle @ SV242 @ SV284 @ SV293 ) )
= $true )
| ( ( sequential @ SV293 @ SV242 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1425]) ).
thf(1462,plain,
! [SV294: $i,SV285: $i,SV233: $i] :
( ( ( path @ SV233 @ SV285 @ SV294 )
= $false )
| ( ( vertex @ SV233 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1426]) ).
thf(1463,plain,
! [SV295: $i,SV280: $i,SV233: $i] :
( ( ( path @ SV233 @ SV280 @ SV295 )
= $false )
| ( ( vertex @ SV280 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1427]) ).
thf(1464,plain,
! [SV263: $i,SV267: $i,SV233: $i] :
( ( ( ~ ( ( SV233
!= ( tail_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( edge @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) ) )
= $true )
| ( ( path @ SV233 @ SV263 @ SV267 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1428]) ).
thf(1465,plain,
! [SV233: $i,SV267: $i,SV263: $i] :
( ( ( ~ ( ~ ( ( SV263
!= ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
| ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ empty ) )
| ! [SY528: $i] :
( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ SY528 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ SY528 ) ) )
| ~ ~ ( ~ ( ( SV263
= ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ ( sK14_SY90 @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ ( sK14_SY90 @ SV267 @ SV263 @ SV233 ) ) ) )
| ~ ( ( SV267
= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ empty ) )
| ~ ( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ ( sK13_SY91 @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ ( sK13_SY91 @ SV267 @ SV263 @ SV233 ) ) ) ) ) ) )
= $true )
| ( ( path @ SV233 @ SV263 @ SV267 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1429]) ).
thf(1466,plain,
! [SV246: $i,SV234: $i,SV286: $i,SV296: $i] :
( ( ( ~ ( on_path @ SV296 @ SV286 )
| ~ ( path @ SV234 @ SV246 @ SV286 ) )
= $true )
| ( ( edge @ SV296 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1430]) ).
thf(1467,plain,
! [SV246: $i,SV234: $i,SV287: $i,SV297: $i] :
( ( ( ~ ( on_path @ SV297 @ SV287 )
| ~ ( path @ SV234 @ SV246 @ SV287 ) )
= $true )
| ( ( in_path @ ( head_of @ SV297 ) @ SV287 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1431]) ).
thf(1468,plain,
! [SV273: $i,SV268: $i,SV246: $i,SV234: $i] :
( ( ( path @ SV234 @ SV246 @ SV268 )
= $false )
| ( ( on_path @ SV273 @ SV268 )
= $false )
| ( ( in_path @ ( tail_of @ SV273 ) @ SV268 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1432]) ).
thf(1469,plain,
! [SV257: $i,SV252: $i,SV298: $i,SV235: $i,SV288: $i] :
( ( ( ~ ( on_path @ SV288 @ SV235 )
| ~ ( on_path @ SV298 @ SV235 )
| ! [SY548: $i] :
( ~ ( precedes @ SY548 @ SV298 @ SV235 )
| ~ ( sequential @ SV288 @ SY548 ) ) )
= $true )
| ( ( precedes @ SV288 @ SV298 @ SV235 )
= $true )
| ( ( path @ SV252 @ SV257 @ SV235 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1433]) ).
thf(1470,plain,
! [SV257: $i,SV252: $i,SV299: $i,SV235: $i,SV289: $i] :
( ( ( ~ ( on_path @ SV289 @ SV235 )
| ~ ( on_path @ SV299 @ SV235 )
| ~ ( sequential @ SV289 @ SV299 ) )
= $true )
| ( ( precedes @ SV289 @ SV299 @ SV235 )
= $true )
| ( ( path @ SV252 @ SV257 @ SV235 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1434]) ).
thf(1471,plain,
! [SV247: $i,SV236: $i,SV290: $i,SV274: $i,SV253: $i] :
( ( ( precedes @ SV253 @ SV274 @ SV290 )
= $false )
| ( ( ~ ( shortest_path @ SV236 @ SV247 @ SV290 ) )
= $true )
| ( ( ! [SY533: $i] :
( ( ( tail_of @ SY533 )
!= ( tail_of @ SV253 ) )
| ( ( head_of @ SY533 )
!= ( head_of @ SV274 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1435]) ).
thf(1472,plain,
! [SV247: $i,SV236: $i,SV281: $i,SV275: $i,SV253: $i] :
( ( ( precedes @ SV253 @ SV275 @ SV281 )
= $false )
| ( ( ~ ( shortest_path @ SV236 @ SV247 @ SV281 ) )
= $true )
| ( ( ~ ( precedes @ SV275 @ SV253 @ SV281 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1436]) ).
thf(1473,plain,
! [SV258: $i,SV254: $i,SV237: $i] :
( ( ( ! [SY445: $i] :
( ! [SY446: $i] :
~ ( precedes @ SY445 @ SY446 @ SV237 )
| ( on_path @ SY445 @ SV237 ) ) )
= $true )
| ( ( path @ SV254 @ SV258 @ SV237 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1437]) ).
thf(1474,plain,
! [SV258: $i,SV254: $i,SV237: $i] :
( ( ( ! [SY447: $i,SY448: $i] :
( ~ ( precedes @ SY447 @ SY448 @ SV237 )
| ( on_path @ SY448 @ SV237 ) ) )
= $true )
| ( ( path @ SV254 @ SV258 @ SV237 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1438]) ).
thf(1475,plain,
! [SV258: $i,SV254: $i,SV237: $i] :
( ( ( ! [SY449: $i,SY450: $i] :
( ~ ( precedes @ SY449 @ SY450 @ SV237 )
| ! [SY451: $i] :
( ~ ( precedes @ SY451 @ SY450 @ SV237 )
| ~ ( sequential @ SY449 @ SY451 ) )
| ~ ( sequential @ SY449 @ SY450 ) ) )
= $true )
| ( ( path @ SV254 @ SV258 @ SV237 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1439]) ).
thf(1476,plain,
! [SV258: $i,SV254: $i,SV237: $i] :
( ( ( ! [SY452: $i,SY453: $i] :
( ~ ( precedes @ SY452 @ SY453 @ SV237 )
| ~ ( ~ ( precedes @ ( sK10_E3 @ SY453 @ SY452 @ SV237 ) @ SY453 @ SV237 )
| ~ ( sequential @ SY452 @ ( sK10_E3 @ SY453 @ SY452 @ SV237 ) ) )
| ( sequential @ SY452 @ SY453 ) ) )
= $true )
| ( ( path @ SV254 @ SV258 @ SV237 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1440]) ).
thf(1477,plain,
! [SV259: $i,SV255: $i] :
( ( ( ~ ~ ( ~ ( ( SV255
!= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
!= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
!= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
!= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV255
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
| ~ ( ( SV255
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) ) )
| ~ ~ ( ~ ( ( SV259
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
| ~ ( ( SV259
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) ) ) ) ) )
= $false )
| ( ( SV255 = SV259 )
= $true )
| ( ( vertex @ SV255 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[1441]) ).
thf(1478,plain,
! [SV255: $i,SV259: $i] :
( ( ( ~ ( edge @ ( sK15_E @ SV259 @ SV255 ) ) )
= $false )
| ( ( SV255 = SV259 )
= $true )
| ( ( vertex @ SV255 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[1441]) ).
thf(1479,plain,
! [SV238: $i] :
( ( ( ~ ( on_path @ ( sK7_E1 @ SV238 ) @ SV238 ) )
= $false )
| ( ( ! [SY455: $i,SY456: $i] :
~ ( path @ SY455 @ SY456 @ SV238 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV238 )
= ( number_of_in @ triangles @ SV238 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1442]) ).
thf(1480,plain,
! [SV238: $i] :
( ( ( ~ ( on_path @ ( sK8_SY86 @ SV238 ) @ SV238 ) )
= $false )
| ( ( ! [SY455: $i,SY456: $i] :
~ ( path @ SY455 @ SY456 @ SV238 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV238 )
= ( number_of_in @ triangles @ SV238 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1442]) ).
thf(1481,plain,
! [SV238: $i,SV303: $i,SV300: $i] :
( ( ( ~ ( path @ SV300 @ SV303 @ SV238 ) )
= $true )
| ( ( sequential @ ( sK7_E1 @ SV238 ) @ ( sK8_SY86 @ SV238 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV238 )
= ( number_of_in @ triangles @ SV238 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1443]) ).
thf(1482,plain,
! [SV276: $i,SV238: $i,SV301: $i,SV291: $i] :
( ( ( path @ SV291 @ SV301 @ SV238 )
= $false )
| ( ( triangle @ ( sK7_E1 @ SV238 ) @ ( sK8_SY86 @ SV238 ) @ SV276 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV238 )
= ( number_of_in @ triangles @ SV238 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1444]) ).
thf(1483,plain,
! [SV262: $i,SV264: $i] :
( ( ( edge @ SV264 )
= $false )
| ( ( edge @ SV262 )
= $false )
| ( ( SV262 = SV264 )
= $true )
| ( ( ( ( head_of @ SV262 )
!= ( tail_of @ SV264 ) ) )
= $true )
| ( ( sequential @ SV262 @ SV264 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1445]) ).
thf(1484,plain,
! [SV304: $i,SV302: $i] :
( ( ~ ( sequential @ SV302 @ SV304 )
| ( SV302 != SV304 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1446]) ).
thf(1485,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1447]) ).
thf(1486,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1447]) ).
thf(1487,plain,
! [SV278: $i,SV269: $i,SV248: $i,SV239: $i] :
( ( ( path @ SV239 @ SV248 @ SV269 )
= $false )
| ( ( in_path @ SV278 @ SV269 )
= $false )
| ( ( ~ ( ~ ( on_path @ ( sK11_E @ SV278 @ SV269 @ SV248 @ SV239 ) @ SV269 )
| ~ ( ( SV278
= ( head_of @ ( sK11_E @ SV278 @ SV269 @ SV248 @ SV239 ) ) )
| ( SV278
= ( tail_of @ ( sK11_E @ SV278 @ SV269 @ SV248 @ SV239 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1449]) ).
thf(1488,plain,
! [SV279: $i,SV270: $i,SV248: $i,SV239: $i] :
( ( ( path @ SV239 @ SV248 @ SV270 )
= $false )
| ( ( in_path @ SV279 @ SV270 )
= $false )
| ( ( vertex @ SV279 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1450]) ).
thf(1489,plain,
! [SV256: $i,SV249: $i,SV240: $i] :
( ( ( ! [SY520: $i] :
( ( SV240
!= ( tail_of @ SY520 ) )
| ~ ( edge @ SY520 )
| ( SV249
!= ( head_of @ SY520 ) )
| ( SV256
!= ( path_cons @ SY520 @ empty ) ) ) )
= $true )
| ( ( vertex @ SV240 )
= $false )
| ( ( vertex @ SV249 )
= $false )
| ( ( path @ SV240 @ SV249 @ SV256 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1451]) ).
thf(1490,plain,
! [SV249: $i,SV256: $i,SV240: $i] :
( ( ( ! [SY521: $i] :
( ( SV240
!= ( tail_of @ SY521 ) )
| ~ ( edge @ SY521 )
| ! [SY522: $i] :
( ( SV256
!= ( path_cons @ SY521 @ SY522 ) )
| ~ ( path @ ( head_of @ SY521 ) @ SV249 @ SY522 ) ) ) )
= $true )
| ( ( vertex @ SV240 )
= $false )
| ( ( vertex @ SV249 )
= $false )
| ( ( path @ SV240 @ SV249 @ SV256 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1452]) ).
thf(1491,plain,
! [SV271: $i,SV265: $i,SV241: $i] :
( ( ( path @ SV241 @ SV265 @ ( sK9_P @ SV271 @ SV265 @ SV241 ) )
= $true )
| ( ( ( SV241 = SV265 )
| ~ ( path @ SV241 @ SV265 @ SV271 ) )
= $true )
| ( ( shortest_path @ SV241 @ SV265 @ SV271 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1453]) ).
thf(1492,plain,
! [SV241: $i,SV265: $i,SV271: $i] :
( ( ( ~ ( less_or_equal @ ( length_of @ SV271 ) @ ( length_of @ ( sK9_P @ SV271 @ SV265 @ SV241 ) ) ) )
= $true )
| ( ( ( SV241 = SV265 )
| ~ ( path @ SV241 @ SV265 @ SV271 ) )
= $true )
| ( ( shortest_path @ SV241 @ SV265 @ SV271 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1454]) ).
thf(1493,plain,
! [SV292: $i,SV283: $i,SV241: $i] :
( ( ( shortest_path @ SV241 @ SV283 @ SV292 )
= $false )
| ( ( ! [SY547: $i] :
( ~ ( path @ SV241 @ SV283 @ SY547 )
| ( less_or_equal @ ( length_of @ SV292 ) @ ( length_of @ SY547 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1455]) ).
thf(1494,plain,
! [SV305: $i,SV241: $i] :
( ( ! [SY551: $i] :
~ ( shortest_path @ SV241 @ SV305 @ SY551 )
| ( SV241 != SV305 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1456]) ).
thf(1495,plain,
! [SV306: $i,SV241: $i] :
( ( ! [SY552: $i] :
( ~ ( shortest_path @ SV241 @ SV306 @ SY552 )
| ( path @ SV241 @ SV306 @ SY552 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1457]) ).
thf(1496,plain,
! [SV272: $i,SV266: $i,SV242: $i] :
( ( ( ~ ( edge @ SV242 )
| ~ ( edge @ SV266 ) )
= $true )
| ( ( ~ ( edge @ SV272 ) )
= $true )
| ( ( ~ ( sequential @ SV242 @ SV266 ) )
= $true )
| ( ( ~ ( sequential @ SV266 @ SV272 ) )
= $true )
| ( ( ~ ( sequential @ SV272 @ SV242 ) )
= $true )
| ( ( triangle @ SV242 @ SV266 @ SV272 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1458]) ).
thf(1497,plain,
! [SV242: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( ! [SY478: $i,SY479: $i] :
~ ( triangle @ SV242 @ SY478 @ SY479 )
| ( edge @ SV242 ) )
| ~ ! [SY480: $i] :
( ! [SY481: $i] :
~ ( triangle @ SV242 @ SY480 @ SY481 )
| ( edge @ SY480 ) ) )
| ~ ! [SY482: $i,SY483: $i] :
( ~ ( triangle @ SV242 @ SY482 @ SY483 )
| ( edge @ SY483 ) ) )
| ~ ! [SY484: $i] :
( ! [SY485: $i] :
~ ( triangle @ SV242 @ SY484 @ SY485 )
| ( sequential @ SV242 @ SY484 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1459]) ).
thf(1498,plain,
! [SV307: $i,SV242: $i] :
( ( ! [SY553: $i] :
( ~ ( triangle @ SV242 @ SV307 @ SY553 )
| ( sequential @ SV307 @ SY553 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1460]) ).
thf(1499,plain,
! [SV293: $i,SV284: $i,SV242: $i] :
( ( ( triangle @ SV242 @ SV284 @ SV293 )
= $false )
| ( ( sequential @ SV293 @ SV242 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1461]) ).
thf(1500,plain,
! [SV263: $i,SV267: $i,SV233: $i] :
( ( ( ( SV233
!= ( tail_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( edge @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
= $false )
| ( ( path @ SV233 @ SV263 @ SV267 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1464]) ).
thf(1501,plain,
! [SV233: $i,SV267: $i,SV263: $i] :
( ( ( ~ ( ( SV263
!= ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
| ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ empty ) )
| ! [SY528: $i] :
( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ SY528 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ SY528 ) ) )
| ~ ~ ( ~ ( ( SV263
= ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ ( sK14_SY90 @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ ( sK14_SY90 @ SV267 @ SV263 @ SV233 ) ) ) )
| ~ ( ( SV267
= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ empty ) )
| ~ ( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ ( sK13_SY91 @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ ( sK13_SY91 @ SV267 @ SV263 @ SV233 ) ) ) ) ) )
= $false )
| ( ( path @ SV233 @ SV263 @ SV267 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1465]) ).
thf(1502,plain,
! [SV246: $i,SV234: $i,SV286: $i,SV296: $i] :
( ( ( ~ ( on_path @ SV296 @ SV286 ) )
= $true )
| ( ( ~ ( path @ SV234 @ SV246 @ SV286 ) )
= $true )
| ( ( edge @ SV296 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1466]) ).
thf(1503,plain,
! [SV246: $i,SV234: $i,SV287: $i,SV297: $i] :
( ( ( ~ ( on_path @ SV297 @ SV287 ) )
= $true )
| ( ( ~ ( path @ SV234 @ SV246 @ SV287 ) )
= $true )
| ( ( in_path @ ( head_of @ SV297 ) @ SV287 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1467]) ).
thf(1504,plain,
! [SV257: $i,SV252: $i,SV298: $i,SV235: $i,SV288: $i] :
( ( ( ~ ( on_path @ SV288 @ SV235 )
| ~ ( on_path @ SV298 @ SV235 ) )
= $true )
| ( ( ! [SY548: $i] :
( ~ ( precedes @ SY548 @ SV298 @ SV235 )
| ~ ( sequential @ SV288 @ SY548 ) ) )
= $true )
| ( ( precedes @ SV288 @ SV298 @ SV235 )
= $true )
| ( ( path @ SV252 @ SV257 @ SV235 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1469]) ).
thf(1505,plain,
! [SV257: $i,SV252: $i,SV299: $i,SV235: $i,SV289: $i] :
( ( ( ~ ( on_path @ SV289 @ SV235 )
| ~ ( on_path @ SV299 @ SV235 ) )
= $true )
| ( ( ~ ( sequential @ SV289 @ SV299 ) )
= $true )
| ( ( precedes @ SV289 @ SV299 @ SV235 )
= $true )
| ( ( path @ SV252 @ SV257 @ SV235 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1470]) ).
thf(1506,plain,
! [SV274: $i,SV253: $i,SV290: $i,SV247: $i,SV236: $i] :
( ( ( shortest_path @ SV236 @ SV247 @ SV290 )
= $false )
| ( ( precedes @ SV253 @ SV274 @ SV290 )
= $false )
| ( ( ! [SY533: $i] :
( ( ( tail_of @ SY533 )
!= ( tail_of @ SV253 ) )
| ( ( head_of @ SY533 )
!= ( head_of @ SV274 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1471]) ).
thf(1507,plain,
! [SV275: $i,SV253: $i,SV281: $i,SV247: $i,SV236: $i] :
( ( ( shortest_path @ SV236 @ SV247 @ SV281 )
= $false )
| ( ( precedes @ SV253 @ SV275 @ SV281 )
= $false )
| ( ( ~ ( precedes @ SV275 @ SV253 @ SV281 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1472]) ).
thf(1508,plain,
! [SV258: $i,SV254: $i,SV237: $i,SV308: $i] :
( ( ( ! [SY554: $i] :
~ ( precedes @ SV308 @ SY554 @ SV237 )
| ( on_path @ SV308 @ SV237 ) )
= $true )
| ( ( path @ SV254 @ SV258 @ SV237 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1473]) ).
thf(1509,plain,
! [SV258: $i,SV254: $i,SV237: $i,SV309: $i] :
( ( ( ! [SY555: $i] :
( ~ ( precedes @ SV309 @ SY555 @ SV237 )
| ( on_path @ SY555 @ SV237 ) ) )
= $true )
| ( ( path @ SV254 @ SV258 @ SV237 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1474]) ).
thf(1510,plain,
! [SV258: $i,SV254: $i,SV237: $i,SV310: $i] :
( ( ( ! [SY556: $i] :
( ~ ( precedes @ SV310 @ SY556 @ SV237 )
| ! [SY557: $i] :
( ~ ( precedes @ SY557 @ SY556 @ SV237 )
| ~ ( sequential @ SV310 @ SY557 ) )
| ~ ( sequential @ SV310 @ SY556 ) ) )
= $true )
| ( ( path @ SV254 @ SV258 @ SV237 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1475]) ).
thf(1511,plain,
! [SV258: $i,SV254: $i,SV237: $i,SV311: $i] :
( ( ( ! [SY558: $i] :
( ~ ( precedes @ SV311 @ SY558 @ SV237 )
| ~ ( ~ ( precedes @ ( sK10_E3 @ SY558 @ SV311 @ SV237 ) @ SY558 @ SV237 )
| ~ ( sequential @ SV311 @ ( sK10_E3 @ SY558 @ SV311 @ SV237 ) ) )
| ( sequential @ SV311 @ SY558 ) ) )
= $true )
| ( ( path @ SV254 @ SV258 @ SV237 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1476]) ).
thf(1512,plain,
! [SV259: $i,SV255: $i] :
( ( ( ~ ( ~ ( ( SV255
!= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
!= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
!= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
!= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV255
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
| ~ ( ( SV255
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) ) )
| ~ ~ ( ~ ( ( SV259
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
| ~ ( ( SV259
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) ) ) ) ) )
= $true )
| ( ( SV255 = SV259 )
= $true )
| ( ( vertex @ SV255 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1477]) ).
thf(1513,plain,
! [SV255: $i,SV259: $i] :
( ( ( edge @ ( sK15_E @ SV259 @ SV255 ) )
= $true )
| ( ( SV255 = SV259 )
= $true )
| ( ( vertex @ SV255 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1478]) ).
thf(1514,plain,
! [SV238: $i] :
( ( ( on_path @ ( sK7_E1 @ SV238 ) @ SV238 )
= $true )
| ( ( ! [SY455: $i,SY456: $i] :
~ ( path @ SY455 @ SY456 @ SV238 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV238 )
= ( number_of_in @ triangles @ SV238 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1479]) ).
thf(1515,plain,
! [SV238: $i] :
( ( ( on_path @ ( sK8_SY86 @ SV238 ) @ SV238 )
= $true )
| ( ( ! [SY455: $i,SY456: $i] :
~ ( path @ SY455 @ SY456 @ SV238 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV238 )
= ( number_of_in @ triangles @ SV238 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1480]) ).
thf(1516,plain,
! [SV238: $i,SV303: $i,SV300: $i] :
( ( ( path @ SV300 @ SV303 @ SV238 )
= $false )
| ( ( sequential @ ( sK7_E1 @ SV238 ) @ ( sK8_SY86 @ SV238 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV238 )
= ( number_of_in @ triangles @ SV238 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1481]) ).
thf(1517,plain,
! [SV264: $i,SV262: $i] :
( ( ( ( head_of @ SV262 )
= ( tail_of @ SV264 ) )
= $false )
| ( ( SV262 = SV264 )
= $true )
| ( ( edge @ SV262 )
= $false )
| ( ( edge @ SV264 )
= $false )
| ( ( sequential @ SV262 @ SV264 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1483]) ).
thf(1518,plain,
! [SV304: $i,SV302: $i] :
( ( ( ~ ( sequential @ SV302 @ SV304 ) )
= $true )
| ( ( ( SV302 != SV304 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1484]) ).
thf(1519,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1485]) ).
thf(1520,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1486]) ).
thf(1521,plain,
! [SV239: $i,SV248: $i,SV269: $i,SV278: $i] :
( ( ( ~ ( on_path @ ( sK11_E @ SV278 @ SV269 @ SV248 @ SV239 ) @ SV269 )
| ~ ( ( SV278
= ( head_of @ ( sK11_E @ SV278 @ SV269 @ SV248 @ SV239 ) ) )
| ( SV278
= ( tail_of @ ( sK11_E @ SV278 @ SV269 @ SV248 @ SV239 ) ) ) ) )
= $false )
| ( ( in_path @ SV278 @ SV269 )
= $false )
| ( ( path @ SV239 @ SV248 @ SV269 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1487]) ).
thf(1522,plain,
! [SV256: $i,SV249: $i,SV312: $i,SV240: $i] :
( ( ( ( SV240
!= ( tail_of @ SV312 ) )
| ~ ( edge @ SV312 )
| ( SV249
!= ( head_of @ SV312 ) )
| ( SV256
!= ( path_cons @ SV312 @ empty ) ) )
= $true )
| ( ( vertex @ SV240 )
= $false )
| ( ( vertex @ SV249 )
= $false )
| ( ( path @ SV240 @ SV249 @ SV256 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1489]) ).
thf(1523,plain,
! [SV249: $i,SV256: $i,SV313: $i,SV240: $i] :
( ( ( ( SV240
!= ( tail_of @ SV313 ) )
| ~ ( edge @ SV313 )
| ! [SY559: $i] :
( ( SV256
!= ( path_cons @ SV313 @ SY559 ) )
| ~ ( path @ ( head_of @ SV313 ) @ SV249 @ SY559 ) ) )
= $true )
| ( ( vertex @ SV240 )
= $false )
| ( ( vertex @ SV249 )
= $false )
| ( ( path @ SV240 @ SV249 @ SV256 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1490]) ).
thf(1524,plain,
! [SV271: $i,SV265: $i,SV241: $i] :
( ( ( SV241 = SV265 )
= $true )
| ( ( ~ ( path @ SV241 @ SV265 @ SV271 ) )
= $true )
| ( ( path @ SV241 @ SV265 @ ( sK9_P @ SV271 @ SV265 @ SV241 ) )
= $true )
| ( ( shortest_path @ SV241 @ SV265 @ SV271 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1491]) ).
thf(1525,plain,
! [SV241: $i,SV265: $i,SV271: $i] :
( ( ( less_or_equal @ ( length_of @ SV271 ) @ ( length_of @ ( sK9_P @ SV271 @ SV265 @ SV241 ) ) )
= $false )
| ( ( ( SV241 = SV265 )
| ~ ( path @ SV241 @ SV265 @ SV271 ) )
= $true )
| ( ( shortest_path @ SV241 @ SV265 @ SV271 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1492]) ).
thf(1526,plain,
! [SV292: $i,SV314: $i,SV283: $i,SV241: $i] :
( ( ( ~ ( path @ SV241 @ SV283 @ SV314 )
| ( less_or_equal @ ( length_of @ SV292 ) @ ( length_of @ SV314 ) ) )
= $true )
| ( ( shortest_path @ SV241 @ SV283 @ SV292 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1493]) ).
thf(1527,plain,
! [SV305: $i,SV241: $i] :
( ( ( ! [SY551: $i] :
~ ( shortest_path @ SV241 @ SV305 @ SY551 ) )
= $true )
| ( ( ( SV241 != SV305 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1494]) ).
thf(1528,plain,
! [SV315: $i,SV306: $i,SV241: $i] :
( ( ~ ( shortest_path @ SV241 @ SV306 @ SV315 )
| ( path @ SV241 @ SV306 @ SV315 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1495]) ).
thf(1529,plain,
! [SV272: $i,SV266: $i,SV242: $i] :
( ( ( ~ ( edge @ SV242 ) )
= $true )
| ( ( ~ ( edge @ SV266 ) )
= $true )
| ( ( ~ ( edge @ SV272 ) )
= $true )
| ( ( ~ ( sequential @ SV242 @ SV266 ) )
= $true )
| ( ( ~ ( sequential @ SV266 @ SV272 ) )
= $true )
| ( ( ~ ( sequential @ SV272 @ SV242 ) )
= $true )
| ( ( triangle @ SV242 @ SV266 @ SV272 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1496]) ).
thf(1530,plain,
! [SV242: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( ! [SY478: $i,SY479: $i] :
~ ( triangle @ SV242 @ SY478 @ SY479 )
| ( edge @ SV242 ) )
| ~ ! [SY480: $i] :
( ! [SY481: $i] :
~ ( triangle @ SV242 @ SY480 @ SY481 )
| ( edge @ SY480 ) ) )
| ~ ! [SY482: $i,SY483: $i] :
( ~ ( triangle @ SV242 @ SY482 @ SY483 )
| ( edge @ SY483 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1497]) ).
thf(1531,plain,
! [SV242: $i] :
( ( ~ ! [SY484: $i] :
( ! [SY485: $i] :
~ ( triangle @ SV242 @ SY484 @ SY485 )
| ( sequential @ SV242 @ SY484 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1497]) ).
thf(1532,plain,
! [SV316: $i,SV307: $i,SV242: $i] :
( ( ~ ( triangle @ SV242 @ SV307 @ SV316 )
| ( sequential @ SV307 @ SV316 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1498]) ).
thf(1533,plain,
! [SV263: $i,SV267: $i,SV233: $i] :
( ( ( ( SV233
!= ( tail_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) ) )
= $false )
| ( ( path @ SV233 @ SV263 @ SV267 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1500]) ).
thf(1534,plain,
! [SV233: $i,SV263: $i,SV267: $i] :
( ( ( ~ ( edge @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
= $false )
| ( ( path @ SV233 @ SV263 @ SV267 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1500]) ).
thf(1535,plain,
! [SV233: $i,SV267: $i,SV263: $i] :
( ( ( ~ ( ( SV263
!= ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
| ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ empty ) )
| ! [SY528: $i] :
( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ SY528 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ SY528 ) ) ) )
= $false )
| ( ( path @ SV233 @ SV263 @ SV267 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1501]) ).
thf(1536,plain,
! [SV233: $i,SV267: $i,SV263: $i] :
( ( ( ~ ~ ( ~ ( ( SV263
= ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ ( sK14_SY90 @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ ( sK14_SY90 @ SV267 @ SV263 @ SV233 ) ) ) )
| ~ ( ( SV267
= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ empty ) )
| ~ ( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ ( sK13_SY91 @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ ( sK13_SY91 @ SV267 @ SV263 @ SV233 ) ) ) ) ) )
= $false )
| ( ( path @ SV233 @ SV263 @ SV267 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1501]) ).
thf(1537,plain,
! [SV246: $i,SV234: $i,SV286: $i,SV296: $i] :
( ( ( on_path @ SV296 @ SV286 )
= $false )
| ( ( ~ ( path @ SV234 @ SV246 @ SV286 ) )
= $true )
| ( ( edge @ SV296 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1502]) ).
thf(1538,plain,
! [SV246: $i,SV234: $i,SV287: $i,SV297: $i] :
( ( ( on_path @ SV297 @ SV287 )
= $false )
| ( ( ~ ( path @ SV234 @ SV246 @ SV287 ) )
= $true )
| ( ( in_path @ ( head_of @ SV297 ) @ SV287 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1503]) ).
thf(1539,plain,
! [SV257: $i,SV252: $i,SV298: $i,SV235: $i,SV288: $i] :
( ( ( ~ ( on_path @ SV288 @ SV235 ) )
= $true )
| ( ( ~ ( on_path @ SV298 @ SV235 ) )
= $true )
| ( ( ! [SY548: $i] :
( ~ ( precedes @ SY548 @ SV298 @ SV235 )
| ~ ( sequential @ SV288 @ SY548 ) ) )
= $true )
| ( ( precedes @ SV288 @ SV298 @ SV235 )
= $true )
| ( ( path @ SV252 @ SV257 @ SV235 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1504]) ).
thf(1540,plain,
! [SV257: $i,SV252: $i,SV299: $i,SV235: $i,SV289: $i] :
( ( ( ~ ( on_path @ SV289 @ SV235 ) )
= $true )
| ( ( ~ ( on_path @ SV299 @ SV235 ) )
= $true )
| ( ( ~ ( sequential @ SV289 @ SV299 ) )
= $true )
| ( ( precedes @ SV289 @ SV299 @ SV235 )
= $true )
| ( ( path @ SV252 @ SV257 @ SV235 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1505]) ).
thf(1541,plain,
! [SV247: $i,SV236: $i,SV290: $i,SV274: $i,SV253: $i,SV317: $i] :
( ( ( ( ( tail_of @ SV317 )
!= ( tail_of @ SV253 ) )
| ( ( head_of @ SV317 )
!= ( head_of @ SV274 ) ) )
= $true )
| ( ( precedes @ SV253 @ SV274 @ SV290 )
= $false )
| ( ( shortest_path @ SV236 @ SV247 @ SV290 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1506]) ).
thf(1542,plain,
! [SV247: $i,SV236: $i,SV281: $i,SV253: $i,SV275: $i] :
( ( ( precedes @ SV275 @ SV253 @ SV281 )
= $false )
| ( ( precedes @ SV253 @ SV275 @ SV281 )
= $false )
| ( ( shortest_path @ SV236 @ SV247 @ SV281 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1507]) ).
thf(1543,plain,
! [SV258: $i,SV254: $i,SV237: $i,SV308: $i] :
( ( ( ! [SY554: $i] :
~ ( precedes @ SV308 @ SY554 @ SV237 ) )
= $true )
| ( ( on_path @ SV308 @ SV237 )
= $true )
| ( ( path @ SV254 @ SV258 @ SV237 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1508]) ).
thf(1544,plain,
! [SV258: $i,SV254: $i,SV237: $i,SV318: $i,SV309: $i] :
( ( ( ~ ( precedes @ SV309 @ SV318 @ SV237 )
| ( on_path @ SV318 @ SV237 ) )
= $true )
| ( ( path @ SV254 @ SV258 @ SV237 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1509]) ).
thf(1545,plain,
! [SV258: $i,SV254: $i,SV237: $i,SV319: $i,SV310: $i] :
( ( ( ~ ( precedes @ SV310 @ SV319 @ SV237 )
| ! [SY560: $i] :
( ~ ( precedes @ SY560 @ SV319 @ SV237 )
| ~ ( sequential @ SV310 @ SY560 ) )
| ~ ( sequential @ SV310 @ SV319 ) )
= $true )
| ( ( path @ SV254 @ SV258 @ SV237 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1510]) ).
thf(1546,plain,
! [SV258: $i,SV254: $i,SV237: $i,SV320: $i,SV311: $i] :
( ( ( ~ ( precedes @ SV311 @ SV320 @ SV237 )
| ~ ( ~ ( precedes @ ( sK10_E3 @ SV320 @ SV311 @ SV237 ) @ SV320 @ SV237 )
| ~ ( sequential @ SV311 @ ( sK10_E3 @ SV320 @ SV311 @ SV237 ) ) )
| ( sequential @ SV311 @ SV320 ) )
= $true )
| ( ( path @ SV254 @ SV258 @ SV237 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1511]) ).
thf(1547,plain,
! [SV259: $i,SV255: $i] :
( ( ( ~ ( ( SV255
!= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
!= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
!= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
!= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV255
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
| ~ ( ( SV255
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) ) )
| ~ ~ ( ~ ( ( SV259
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
| ~ ( ( SV259
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) ) ) ) )
= $false )
| ( ( SV255 = SV259 )
= $true )
| ( ( vertex @ SV255 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1512]) ).
thf(1548,plain,
! [SV238: $i,SV321: $i] :
( ( ( ! [SY561: $i] :
~ ( path @ SV321 @ SY561 @ SV238 ) )
= $true )
| ( ( on_path @ ( sK7_E1 @ SV238 ) @ SV238 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV238 )
= ( number_of_in @ triangles @ SV238 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1514]) ).
thf(1549,plain,
! [SV238: $i,SV322: $i] :
( ( ( ! [SY562: $i] :
~ ( path @ SV322 @ SY562 @ SV238 ) )
= $true )
| ( ( on_path @ ( sK8_SY86 @ SV238 ) @ SV238 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV238 )
= ( number_of_in @ triangles @ SV238 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1515]) ).
thf(1550,plain,
! [SV304: $i,SV302: $i] :
( ( ( sequential @ SV302 @ SV304 )
= $false )
| ( ( ( SV302 != SV304 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1518]) ).
thf(1551,plain,
! [SV323: $i] :
( ( ! [SY563: $i] :
~ ( sequential @ SV323 @ SY563 )
| ( edge @ SV323 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1519]) ).
thf(1552,plain,
! [SV324: $i] :
( ( ! [SY564: $i] :
( ~ ( sequential @ SV324 @ SY564 )
| ( edge @ SY564 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1520]) ).
thf(1553,plain,
! [SV239: $i,SV248: $i,SV269: $i,SV278: $i] :
( ( ( ~ ( on_path @ ( sK11_E @ SV278 @ SV269 @ SV248 @ SV239 ) @ SV269 ) )
= $false )
| ( ( in_path @ SV278 @ SV269 )
= $false )
| ( ( path @ SV239 @ SV248 @ SV269 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1521]) ).
thf(1554,plain,
! [SV239: $i,SV248: $i,SV269: $i,SV278: $i] :
( ( ( ~ ( ( SV278
= ( head_of @ ( sK11_E @ SV278 @ SV269 @ SV248 @ SV239 ) ) )
| ( SV278
= ( tail_of @ ( sK11_E @ SV278 @ SV269 @ SV248 @ SV239 ) ) ) ) )
= $false )
| ( ( in_path @ SV278 @ SV269 )
= $false )
| ( ( path @ SV239 @ SV248 @ SV269 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1521]) ).
thf(1555,plain,
! [SV256: $i,SV249: $i,SV312: $i,SV240: $i] :
( ( ( ( SV240
!= ( tail_of @ SV312 ) )
| ~ ( edge @ SV312 ) )
= $true )
| ( ( ( SV249
!= ( head_of @ SV312 ) )
| ( SV256
!= ( path_cons @ SV312 @ empty ) ) )
= $true )
| ( ( vertex @ SV240 )
= $false )
| ( ( vertex @ SV249 )
= $false )
| ( ( path @ SV240 @ SV249 @ SV256 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1522]) ).
thf(1556,plain,
! [SV249: $i,SV256: $i,SV313: $i,SV240: $i] :
( ( ( ( SV240
!= ( tail_of @ SV313 ) )
| ~ ( edge @ SV313 ) )
= $true )
| ( ( ! [SY559: $i] :
( ( SV256
!= ( path_cons @ SV313 @ SY559 ) )
| ~ ( path @ ( head_of @ SV313 ) @ SV249 @ SY559 ) ) )
= $true )
| ( ( vertex @ SV240 )
= $false )
| ( ( vertex @ SV249 )
= $false )
| ( ( path @ SV240 @ SV249 @ SV256 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1523]) ).
thf(1557,plain,
! [SV271: $i,SV265: $i,SV241: $i] :
( ( ( path @ SV241 @ SV265 @ SV271 )
= $false )
| ( ( SV241 = SV265 )
= $true )
| ( ( path @ SV241 @ SV265 @ ( sK9_P @ SV271 @ SV265 @ SV241 ) )
= $true )
| ( ( shortest_path @ SV241 @ SV265 @ SV271 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1524]) ).
thf(1558,plain,
! [SV271: $i,SV265: $i,SV241: $i] :
( ( ( SV241 = SV265 )
= $true )
| ( ( ~ ( path @ SV241 @ SV265 @ SV271 ) )
= $true )
| ( ( less_or_equal @ ( length_of @ SV271 ) @ ( length_of @ ( sK9_P @ SV271 @ SV265 @ SV241 ) ) )
= $false )
| ( ( shortest_path @ SV241 @ SV265 @ SV271 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1525]) ).
thf(1559,plain,
! [SV292: $i,SV314: $i,SV283: $i,SV241: $i] :
( ( ( ~ ( path @ SV241 @ SV283 @ SV314 ) )
= $true )
| ( ( less_or_equal @ ( length_of @ SV292 ) @ ( length_of @ SV314 ) )
= $true )
| ( ( shortest_path @ SV241 @ SV283 @ SV292 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1526]) ).
thf(1560,plain,
! [SV325: $i,SV305: $i,SV241: $i] :
( ( ( ~ ( shortest_path @ SV241 @ SV305 @ SV325 ) )
= $true )
| ( ( ( SV241 != SV305 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1527]) ).
thf(1561,plain,
! [SV315: $i,SV306: $i,SV241: $i] :
( ( ( ~ ( shortest_path @ SV241 @ SV306 @ SV315 ) )
= $true )
| ( ( path @ SV241 @ SV306 @ SV315 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1528]) ).
thf(1562,plain,
! [SV272: $i,SV266: $i,SV242: $i] :
( ( ( edge @ SV242 )
= $false )
| ( ( ~ ( edge @ SV266 ) )
= $true )
| ( ( ~ ( edge @ SV272 ) )
= $true )
| ( ( ~ ( sequential @ SV242 @ SV266 ) )
= $true )
| ( ( ~ ( sequential @ SV266 @ SV272 ) )
= $true )
| ( ( ~ ( sequential @ SV272 @ SV242 ) )
= $true )
| ( ( triangle @ SV242 @ SV266 @ SV272 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1529]) ).
thf(1563,plain,
! [SV242: $i] :
( ( ~ ( ~ ~ ( ~ ( ! [SY478: $i,SY479: $i] :
~ ( triangle @ SV242 @ SY478 @ SY479 )
| ( edge @ SV242 ) )
| ~ ! [SY480: $i] :
( ! [SY481: $i] :
~ ( triangle @ SV242 @ SY480 @ SY481 )
| ( edge @ SY480 ) ) )
| ~ ! [SY482: $i,SY483: $i] :
( ~ ( triangle @ SV242 @ SY482 @ SY483 )
| ( edge @ SY483 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1530]) ).
thf(1564,plain,
! [SV242: $i] :
( ( ! [SY484: $i] :
( ! [SY485: $i] :
~ ( triangle @ SV242 @ SY484 @ SY485 )
| ( sequential @ SV242 @ SY484 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1531]) ).
thf(1565,plain,
! [SV316: $i,SV307: $i,SV242: $i] :
( ( ( ~ ( triangle @ SV242 @ SV307 @ SV316 ) )
= $true )
| ( ( sequential @ SV307 @ SV316 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1532]) ).
thf(1566,plain,
! [SV263: $i,SV267: $i,SV233: $i] :
( ( ( SV233
= ( tail_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
= $true )
| ( ( path @ SV233 @ SV263 @ SV267 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1533]) ).
thf(1567,plain,
! [SV233: $i,SV263: $i,SV267: $i] :
( ( ( edge @ ( sK12_E @ SV267 @ SV263 @ SV233 ) )
= $true )
| ( ( path @ SV233 @ SV263 @ SV267 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1534]) ).
thf(1568,plain,
! [SV233: $i,SV267: $i,SV263: $i] :
( ( ( ( SV263
!= ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
| ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ empty ) )
| ! [SY528: $i] :
( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ SY528 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ SY528 ) ) )
= $true )
| ( ( path @ SV233 @ SV263 @ SV267 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1535]) ).
thf(1569,plain,
! [SV233: $i,SV267: $i,SV263: $i] :
( ( ( ~ ( ~ ( ( SV263
= ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ ( sK14_SY90 @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ ( sK14_SY90 @ SV267 @ SV263 @ SV233 ) ) ) )
| ~ ( ( SV267
= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ empty ) )
| ~ ( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ ( sK13_SY91 @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ ( sK13_SY91 @ SV267 @ SV263 @ SV233 ) ) ) ) ) )
= $true )
| ( ( path @ SV233 @ SV263 @ SV267 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1536]) ).
thf(1570,plain,
! [SV296: $i,SV286: $i,SV246: $i,SV234: $i] :
( ( ( path @ SV234 @ SV246 @ SV286 )
= $false )
| ( ( on_path @ SV296 @ SV286 )
= $false )
| ( ( edge @ SV296 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1537]) ).
thf(1571,plain,
! [SV297: $i,SV287: $i,SV246: $i,SV234: $i] :
( ( ( path @ SV234 @ SV246 @ SV287 )
= $false )
| ( ( on_path @ SV297 @ SV287 )
= $false )
| ( ( in_path @ ( head_of @ SV297 ) @ SV287 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1538]) ).
thf(1572,plain,
! [SV257: $i,SV252: $i,SV298: $i,SV235: $i,SV288: $i] :
( ( ( on_path @ SV288 @ SV235 )
= $false )
| ( ( ~ ( on_path @ SV298 @ SV235 ) )
= $true )
| ( ( ! [SY548: $i] :
( ~ ( precedes @ SY548 @ SV298 @ SV235 )
| ~ ( sequential @ SV288 @ SY548 ) ) )
= $true )
| ( ( precedes @ SV288 @ SV298 @ SV235 )
= $true )
| ( ( path @ SV252 @ SV257 @ SV235 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1539]) ).
thf(1573,plain,
! [SV257: $i,SV252: $i,SV299: $i,SV235: $i,SV289: $i] :
( ( ( on_path @ SV289 @ SV235 )
= $false )
| ( ( ~ ( on_path @ SV299 @ SV235 ) )
= $true )
| ( ( ~ ( sequential @ SV289 @ SV299 ) )
= $true )
| ( ( precedes @ SV289 @ SV299 @ SV235 )
= $true )
| ( ( path @ SV252 @ SV257 @ SV235 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1540]) ).
thf(1574,plain,
! [SV247: $i,SV236: $i,SV290: $i,SV274: $i,SV253: $i,SV317: $i] :
( ( ( ( ( tail_of @ SV317 )
!= ( tail_of @ SV253 ) ) )
= $true )
| ( ( ( ( head_of @ SV317 )
!= ( head_of @ SV274 ) ) )
= $true )
| ( ( precedes @ SV253 @ SV274 @ SV290 )
= $false )
| ( ( shortest_path @ SV236 @ SV247 @ SV290 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1541]) ).
thf(1575,plain,
! [SV258: $i,SV254: $i,SV237: $i,SV326: $i,SV308: $i] :
( ( ( ~ ( precedes @ SV308 @ SV326 @ SV237 ) )
= $true )
| ( ( on_path @ SV308 @ SV237 )
= $true )
| ( ( path @ SV254 @ SV258 @ SV237 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1543]) ).
thf(1576,plain,
! [SV258: $i,SV254: $i,SV237: $i,SV318: $i,SV309: $i] :
( ( ( ~ ( precedes @ SV309 @ SV318 @ SV237 ) )
= $true )
| ( ( on_path @ SV318 @ SV237 )
= $true )
| ( ( path @ SV254 @ SV258 @ SV237 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1544]) ).
thf(1577,plain,
! [SV258: $i,SV254: $i,SV237: $i,SV319: $i,SV310: $i] :
( ( ( ~ ( precedes @ SV310 @ SV319 @ SV237 ) )
= $true )
| ( ( ! [SY560: $i] :
( ~ ( precedes @ SY560 @ SV319 @ SV237 )
| ~ ( sequential @ SV310 @ SY560 ) )
| ~ ( sequential @ SV310 @ SV319 ) )
= $true )
| ( ( path @ SV254 @ SV258 @ SV237 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1545]) ).
thf(1578,plain,
! [SV258: $i,SV254: $i,SV237: $i,SV320: $i,SV311: $i] :
( ( ( ~ ( precedes @ SV311 @ SV320 @ SV237 ) )
= $true )
| ( ( ~ ( ~ ( precedes @ ( sK10_E3 @ SV320 @ SV311 @ SV237 ) @ SV320 @ SV237 )
| ~ ( sequential @ SV311 @ ( sK10_E3 @ SV320 @ SV311 @ SV237 ) ) )
| ( sequential @ SV311 @ SV320 ) )
= $true )
| ( ( path @ SV254 @ SV258 @ SV237 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1546]) ).
thf(1579,plain,
! [SV259: $i,SV255: $i] :
( ( ( ~ ( ( SV255
!= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
!= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
!= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
!= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) ) )
= $false )
| ( ( SV255 = SV259 )
= $true )
| ( ( vertex @ SV255 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[1547]) ).
thf(1580,plain,
! [SV259: $i,SV255: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( SV255
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
| ~ ( ( SV255
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) ) )
| ~ ~ ( ~ ( ( SV259
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
| ~ ( ( SV259
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) ) ) ) )
= $false )
| ( ( SV255 = SV259 )
= $true )
| ( ( vertex @ SV255 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[1547]) ).
thf(1581,plain,
! [SV238: $i,SV327: $i,SV321: $i] :
( ( ( ~ ( path @ SV321 @ SV327 @ SV238 ) )
= $true )
| ( ( on_path @ ( sK7_E1 @ SV238 ) @ SV238 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV238 )
= ( number_of_in @ triangles @ SV238 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1548]) ).
thf(1582,plain,
! [SV238: $i,SV328: $i,SV322: $i] :
( ( ( ~ ( path @ SV322 @ SV328 @ SV238 ) )
= $true )
| ( ( on_path @ ( sK8_SY86 @ SV238 ) @ SV238 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV238 )
= ( number_of_in @ triangles @ SV238 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1549]) ).
thf(1583,plain,
! [SV304: $i,SV302: $i] :
( ( ( SV302 = SV304 )
= $false )
| ( ( sequential @ SV302 @ SV304 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1550]) ).
thf(1584,plain,
! [SV323: $i] :
( ( ( ! [SY563: $i] :
~ ( sequential @ SV323 @ SY563 ) )
= $true )
| ( ( edge @ SV323 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1551]) ).
thf(1585,plain,
! [SV329: $i,SV324: $i] :
( ( ~ ( sequential @ SV324 @ SV329 )
| ( edge @ SV329 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1552]) ).
thf(1586,plain,
! [SV239: $i,SV248: $i,SV269: $i,SV278: $i] :
( ( ( on_path @ ( sK11_E @ SV278 @ SV269 @ SV248 @ SV239 ) @ SV269 )
= $true )
| ( ( in_path @ SV278 @ SV269 )
= $false )
| ( ( path @ SV239 @ SV248 @ SV269 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1553]) ).
thf(1587,plain,
! [SV239: $i,SV248: $i,SV269: $i,SV278: $i] :
( ( ( ( SV278
= ( head_of @ ( sK11_E @ SV278 @ SV269 @ SV248 @ SV239 ) ) )
| ( SV278
= ( tail_of @ ( sK11_E @ SV278 @ SV269 @ SV248 @ SV239 ) ) ) )
= $true )
| ( ( in_path @ SV278 @ SV269 )
= $false )
| ( ( path @ SV239 @ SV248 @ SV269 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1554]) ).
thf(1588,plain,
! [SV256: $i,SV249: $i,SV312: $i,SV240: $i] :
( ( ( ( SV240
!= ( tail_of @ SV312 ) ) )
= $true )
| ( ( ~ ( edge @ SV312 ) )
= $true )
| ( ( ( SV249
!= ( head_of @ SV312 ) )
| ( SV256
!= ( path_cons @ SV312 @ empty ) ) )
= $true )
| ( ( vertex @ SV240 )
= $false )
| ( ( vertex @ SV249 )
= $false )
| ( ( path @ SV240 @ SV249 @ SV256 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1555]) ).
thf(1589,plain,
! [SV249: $i,SV256: $i,SV313: $i,SV240: $i] :
( ( ( ( SV240
!= ( tail_of @ SV313 ) ) )
= $true )
| ( ( ~ ( edge @ SV313 ) )
= $true )
| ( ( ! [SY559: $i] :
( ( SV256
!= ( path_cons @ SV313 @ SY559 ) )
| ~ ( path @ ( head_of @ SV313 ) @ SV249 @ SY559 ) ) )
= $true )
| ( ( vertex @ SV240 )
= $false )
| ( ( vertex @ SV249 )
= $false )
| ( ( path @ SV240 @ SV249 @ SV256 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1556]) ).
thf(1590,plain,
! [SV271: $i,SV265: $i,SV241: $i] :
( ( ( path @ SV241 @ SV265 @ SV271 )
= $false )
| ( ( SV241 = SV265 )
= $true )
| ( ( less_or_equal @ ( length_of @ SV271 ) @ ( length_of @ ( sK9_P @ SV271 @ SV265 @ SV241 ) ) )
= $false )
| ( ( shortest_path @ SV241 @ SV265 @ SV271 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1558]) ).
thf(1591,plain,
! [SV292: $i,SV314: $i,SV283: $i,SV241: $i] :
( ( ( path @ SV241 @ SV283 @ SV314 )
= $false )
| ( ( less_or_equal @ ( length_of @ SV292 ) @ ( length_of @ SV314 ) )
= $true )
| ( ( shortest_path @ SV241 @ SV283 @ SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1559]) ).
thf(1592,plain,
! [SV325: $i,SV305: $i,SV241: $i] :
( ( ( shortest_path @ SV241 @ SV305 @ SV325 )
= $false )
| ( ( ( SV241 != SV305 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1560]) ).
thf(1593,plain,
! [SV315: $i,SV306: $i,SV241: $i] :
( ( ( shortest_path @ SV241 @ SV306 @ SV315 )
= $false )
| ( ( path @ SV241 @ SV306 @ SV315 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1561]) ).
thf(1594,plain,
! [SV272: $i,SV242: $i,SV266: $i] :
( ( ( edge @ SV266 )
= $false )
| ( ( edge @ SV242 )
= $false )
| ( ( ~ ( edge @ SV272 ) )
= $true )
| ( ( ~ ( sequential @ SV242 @ SV266 ) )
= $true )
| ( ( ~ ( sequential @ SV266 @ SV272 ) )
= $true )
| ( ( ~ ( sequential @ SV272 @ SV242 ) )
= $true )
| ( ( triangle @ SV242 @ SV266 @ SV272 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1562]) ).
thf(1595,plain,
! [SV242: $i] :
( ( ~ ~ ( ~ ( ! [SY478: $i,SY479: $i] :
~ ( triangle @ SV242 @ SY478 @ SY479 )
| ( edge @ SV242 ) )
| ~ ! [SY480: $i] :
( ! [SY481: $i] :
~ ( triangle @ SV242 @ SY480 @ SY481 )
| ( edge @ SY480 ) ) )
| ~ ! [SY482: $i,SY483: $i] :
( ~ ( triangle @ SV242 @ SY482 @ SY483 )
| ( edge @ SY483 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1563]) ).
thf(1596,plain,
! [SV330: $i,SV242: $i] :
( ( ! [SY565: $i] :
~ ( triangle @ SV242 @ SV330 @ SY565 )
| ( sequential @ SV242 @ SV330 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1564]) ).
thf(1597,plain,
! [SV316: $i,SV307: $i,SV242: $i] :
( ( ( triangle @ SV242 @ SV307 @ SV316 )
= $false )
| ( ( sequential @ SV307 @ SV316 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1565]) ).
thf(1598,plain,
! [SV233: $i,SV267: $i,SV263: $i] :
( ( ( ( SV263
!= ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
| ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ empty ) ) )
= $true )
| ( ( ! [SY528: $i] :
( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ SY528 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ SY528 ) ) )
= $true )
| ( ( path @ SV233 @ SV263 @ SV267 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1568]) ).
thf(1599,plain,
! [SV233: $i,SV267: $i,SV263: $i] :
( ( ( ~ ( ( SV263
= ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ ( sK14_SY90 @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ ( sK14_SY90 @ SV267 @ SV263 @ SV233 ) ) ) )
| ~ ( ( SV267
= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ empty ) )
| ~ ( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ ( sK13_SY91 @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ ( sK13_SY91 @ SV267 @ SV263 @ SV233 ) ) ) ) )
= $false )
| ( ( path @ SV233 @ SV263 @ SV267 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1569]) ).
thf(1600,plain,
! [SV257: $i,SV252: $i,SV288: $i,SV235: $i,SV298: $i] :
( ( ( on_path @ SV298 @ SV235 )
= $false )
| ( ( on_path @ SV288 @ SV235 )
= $false )
| ( ( ! [SY548: $i] :
( ~ ( precedes @ SY548 @ SV298 @ SV235 )
| ~ ( sequential @ SV288 @ SY548 ) ) )
= $true )
| ( ( precedes @ SV288 @ SV298 @ SV235 )
= $true )
| ( ( path @ SV252 @ SV257 @ SV235 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1572]) ).
thf(1601,plain,
! [SV257: $i,SV252: $i,SV289: $i,SV235: $i,SV299: $i] :
( ( ( on_path @ SV299 @ SV235 )
= $false )
| ( ( on_path @ SV289 @ SV235 )
= $false )
| ( ( ~ ( sequential @ SV289 @ SV299 ) )
= $true )
| ( ( precedes @ SV289 @ SV299 @ SV235 )
= $true )
| ( ( path @ SV252 @ SV257 @ SV235 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1573]) ).
thf(1602,plain,
! [SV247: $i,SV236: $i,SV290: $i,SV274: $i,SV253: $i,SV317: $i] :
( ( ( ( tail_of @ SV317 )
= ( tail_of @ SV253 ) )
= $false )
| ( ( ( ( head_of @ SV317 )
!= ( head_of @ SV274 ) ) )
= $true )
| ( ( precedes @ SV253 @ SV274 @ SV290 )
= $false )
| ( ( shortest_path @ SV236 @ SV247 @ SV290 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1574]) ).
thf(1603,plain,
! [SV258: $i,SV254: $i,SV237: $i,SV326: $i,SV308: $i] :
( ( ( precedes @ SV308 @ SV326 @ SV237 )
= $false )
| ( ( on_path @ SV308 @ SV237 )
= $true )
| ( ( path @ SV254 @ SV258 @ SV237 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1575]) ).
thf(1604,plain,
! [SV258: $i,SV254: $i,SV237: $i,SV318: $i,SV309: $i] :
( ( ( precedes @ SV309 @ SV318 @ SV237 )
= $false )
| ( ( on_path @ SV318 @ SV237 )
= $true )
| ( ( path @ SV254 @ SV258 @ SV237 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1576]) ).
thf(1605,plain,
! [SV258: $i,SV254: $i,SV237: $i,SV319: $i,SV310: $i] :
( ( ( precedes @ SV310 @ SV319 @ SV237 )
= $false )
| ( ( ! [SY560: $i] :
( ~ ( precedes @ SY560 @ SV319 @ SV237 )
| ~ ( sequential @ SV310 @ SY560 ) )
| ~ ( sequential @ SV310 @ SV319 ) )
= $true )
| ( ( path @ SV254 @ SV258 @ SV237 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1577]) ).
thf(1606,plain,
! [SV258: $i,SV254: $i,SV237: $i,SV320: $i,SV311: $i] :
( ( ( precedes @ SV311 @ SV320 @ SV237 )
= $false )
| ( ( ~ ( ~ ( precedes @ ( sK10_E3 @ SV320 @ SV311 @ SV237 ) @ SV320 @ SV237 )
| ~ ( sequential @ SV311 @ ( sK10_E3 @ SV320 @ SV311 @ SV237 ) ) )
| ( sequential @ SV311 @ SV320 ) )
= $true )
| ( ( path @ SV254 @ SV258 @ SV237 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1578]) ).
thf(1607,plain,
! [SV259: $i,SV255: $i] :
( ( ( ( SV255
!= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
!= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
!= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
!= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
= $true )
| ( ( SV255 = SV259 )
= $true )
| ( ( vertex @ SV255 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1579]) ).
thf(1608,plain,
! [SV259: $i,SV255: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( SV255
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
| ~ ( ( SV255
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) ) )
| ~ ~ ( ~ ( ( SV259
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
| ~ ( ( SV259
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) ) ) ) )
= $true )
| ( ( SV255 = SV259 )
= $true )
| ( ( vertex @ SV255 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1580]) ).
thf(1609,plain,
! [SV238: $i,SV327: $i,SV321: $i] :
( ( ( path @ SV321 @ SV327 @ SV238 )
= $false )
| ( ( on_path @ ( sK7_E1 @ SV238 ) @ SV238 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV238 )
= ( number_of_in @ triangles @ SV238 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1581]) ).
thf(1610,plain,
! [SV238: $i,SV328: $i,SV322: $i] :
( ( ( path @ SV322 @ SV328 @ SV238 )
= $false )
| ( ( on_path @ ( sK8_SY86 @ SV238 ) @ SV238 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV238 )
= ( number_of_in @ triangles @ SV238 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1582]) ).
thf(1611,plain,
! [SV331: $i,SV323: $i] :
( ( ( ~ ( sequential @ SV323 @ SV331 ) )
= $true )
| ( ( edge @ SV323 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1584]) ).
thf(1612,plain,
! [SV329: $i,SV324: $i] :
( ( ( ~ ( sequential @ SV324 @ SV329 ) )
= $true )
| ( ( edge @ SV329 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1585]) ).
thf(1613,plain,
! [SV239: $i,SV248: $i,SV269: $i,SV278: $i] :
( ( ( SV278
= ( head_of @ ( sK11_E @ SV278 @ SV269 @ SV248 @ SV239 ) ) )
= $true )
| ( ( SV278
= ( tail_of @ ( sK11_E @ SV278 @ SV269 @ SV248 @ SV239 ) ) )
= $true )
| ( ( in_path @ SV278 @ SV269 )
= $false )
| ( ( path @ SV239 @ SV248 @ SV269 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1587]) ).
thf(1614,plain,
! [SV256: $i,SV249: $i,SV312: $i,SV240: $i] :
( ( ( SV240
= ( tail_of @ SV312 ) )
= $false )
| ( ( ~ ( edge @ SV312 ) )
= $true )
| ( ( ( SV249
!= ( head_of @ SV312 ) )
| ( SV256
!= ( path_cons @ SV312 @ empty ) ) )
= $true )
| ( ( vertex @ SV240 )
= $false )
| ( ( vertex @ SV249 )
= $false )
| ( ( path @ SV240 @ SV249 @ SV256 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1588]) ).
thf(1615,plain,
! [SV249: $i,SV256: $i,SV313: $i,SV240: $i] :
( ( ( SV240
= ( tail_of @ SV313 ) )
= $false )
| ( ( ~ ( edge @ SV313 ) )
= $true )
| ( ( ! [SY559: $i] :
( ( SV256
!= ( path_cons @ SV313 @ SY559 ) )
| ~ ( path @ ( head_of @ SV313 ) @ SV249 @ SY559 ) ) )
= $true )
| ( ( vertex @ SV240 )
= $false )
| ( ( vertex @ SV249 )
= $false )
| ( ( path @ SV240 @ SV249 @ SV256 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1589]) ).
thf(1616,plain,
! [SV325: $i,SV305: $i,SV241: $i] :
( ( ( SV241 = SV305 )
= $false )
| ( ( shortest_path @ SV241 @ SV305 @ SV325 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1592]) ).
thf(1617,plain,
! [SV266: $i,SV242: $i,SV272: $i] :
( ( ( edge @ SV272 )
= $false )
| ( ( edge @ SV242 )
= $false )
| ( ( edge @ SV266 )
= $false )
| ( ( ~ ( sequential @ SV242 @ SV266 ) )
= $true )
| ( ( ~ ( sequential @ SV266 @ SV272 ) )
= $true )
| ( ( ~ ( sequential @ SV272 @ SV242 ) )
= $true )
| ( ( triangle @ SV242 @ SV266 @ SV272 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1594]) ).
thf(1618,plain,
! [SV242: $i] :
( ( ~ ~ ( ~ ( ! [SY478: $i,SY479: $i] :
~ ( triangle @ SV242 @ SY478 @ SY479 )
| ( edge @ SV242 ) )
| ~ ! [SY480: $i] :
( ! [SY481: $i] :
~ ( triangle @ SV242 @ SY480 @ SY481 )
| ( edge @ SY480 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1595]) ).
thf(1619,plain,
! [SV242: $i] :
( ( ~ ! [SY482: $i,SY483: $i] :
( ~ ( triangle @ SV242 @ SY482 @ SY483 )
| ( edge @ SY483 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1595]) ).
thf(1620,plain,
! [SV330: $i,SV242: $i] :
( ( ( ! [SY565: $i] :
~ ( triangle @ SV242 @ SV330 @ SY565 ) )
= $true )
| ( ( sequential @ SV242 @ SV330 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1596]) ).
thf(1621,plain,
! [SV233: $i,SV267: $i,SV263: $i] :
( ( ( ( SV263
!= ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) ) )
= $true )
| ( ( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ empty ) ) )
= $true )
| ( ( ! [SY528: $i] :
( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ SY528 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ SY528 ) ) )
= $true )
| ( ( path @ SV233 @ SV263 @ SV267 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1598]) ).
thf(1622,plain,
! [SV233: $i,SV267: $i,SV263: $i] :
( ( ( ~ ( ( SV263
= ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ ( sK14_SY90 @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ ( sK14_SY90 @ SV267 @ SV263 @ SV233 ) ) ) ) )
= $false )
| ( ( path @ SV233 @ SV263 @ SV267 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1599]) ).
thf(1623,plain,
! [SV233: $i,SV263: $i,SV267: $i] :
( ( ( ~ ( ( SV267
= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ empty ) )
| ~ ( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ ( sK13_SY91 @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ ( sK13_SY91 @ SV267 @ SV263 @ SV233 ) ) ) ) )
= $false )
| ( ( path @ SV233 @ SV263 @ SV267 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1599]) ).
thf(1624,plain,
! [SV257: $i,SV252: $i,SV288: $i,SV235: $i,SV298: $i,SV332: $i] :
( ( ( ~ ( precedes @ SV332 @ SV298 @ SV235 )
| ~ ( sequential @ SV288 @ SV332 ) )
= $true )
| ( ( on_path @ SV288 @ SV235 )
= $false )
| ( ( on_path @ SV298 @ SV235 )
= $false )
| ( ( precedes @ SV288 @ SV298 @ SV235 )
= $true )
| ( ( path @ SV252 @ SV257 @ SV235 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1600]) ).
thf(1625,plain,
! [SV257: $i,SV252: $i,SV235: $i,SV299: $i,SV289: $i] :
( ( ( sequential @ SV289 @ SV299 )
= $false )
| ( ( on_path @ SV289 @ SV235 )
= $false )
| ( ( on_path @ SV299 @ SV235 )
= $false )
| ( ( precedes @ SV289 @ SV299 @ SV235 )
= $true )
| ( ( path @ SV252 @ SV257 @ SV235 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1601]) ).
thf(1626,plain,
! [SV247: $i,SV236: $i,SV290: $i,SV253: $i,SV274: $i,SV317: $i] :
( ( ( ( head_of @ SV317 )
= ( head_of @ SV274 ) )
= $false )
| ( ( ( tail_of @ SV317 )
= ( tail_of @ SV253 ) )
= $false )
| ( ( precedes @ SV253 @ SV274 @ SV290 )
= $false )
| ( ( shortest_path @ SV236 @ SV247 @ SV290 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1602]) ).
thf(1627,plain,
! [SV258: $i,SV254: $i,SV310: $i,SV237: $i,SV319: $i] :
( ( ( ! [SY560: $i] :
( ~ ( precedes @ SY560 @ SV319 @ SV237 )
| ~ ( sequential @ SV310 @ SY560 ) ) )
= $true )
| ( ( ~ ( sequential @ SV310 @ SV319 ) )
= $true )
| ( ( precedes @ SV310 @ SV319 @ SV237 )
= $false )
| ( ( path @ SV254 @ SV258 @ SV237 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1605]) ).
thf(1628,plain,
! [SV258: $i,SV254: $i,SV237: $i,SV311: $i,SV320: $i] :
( ( ( ~ ( ~ ( precedes @ ( sK10_E3 @ SV320 @ SV311 @ SV237 ) @ SV320 @ SV237 )
| ~ ( sequential @ SV311 @ ( sK10_E3 @ SV320 @ SV311 @ SV237 ) ) ) )
= $true )
| ( ( sequential @ SV311 @ SV320 )
= $true )
| ( ( precedes @ SV311 @ SV320 @ SV237 )
= $false )
| ( ( path @ SV254 @ SV258 @ SV237 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1606]) ).
thf(1629,plain,
! [SV259: $i,SV255: $i] :
( ( ( ( SV255
!= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
!= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
= $true )
| ( ( ( SV259
!= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
!= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
= $true )
| ( ( SV255 = SV259 )
= $true )
| ( ( vertex @ SV255 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[1607]) ).
thf(1630,plain,
! [SV259: $i,SV255: $i] :
( ( ( ~ ~ ( ~ ( ( SV255
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
| ~ ( ( SV255
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) ) )
| ~ ~ ( ~ ( ( SV259
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
| ~ ( ( SV259
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) ) ) )
= $false )
| ( ( SV255 = SV259 )
= $true )
| ( ( vertex @ SV255 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1608]) ).
thf(1631,plain,
! [SV331: $i,SV323: $i] :
( ( ( sequential @ SV323 @ SV331 )
= $false )
| ( ( edge @ SV323 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1611]) ).
thf(1632,plain,
! [SV329: $i,SV324: $i] :
( ( ( sequential @ SV324 @ SV329 )
= $false )
| ( ( edge @ SV329 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1612]) ).
thf(1633,plain,
! [SV256: $i,SV249: $i,SV240: $i,SV312: $i] :
( ( ( edge @ SV312 )
= $false )
| ( ( SV240
= ( tail_of @ SV312 ) )
= $false )
| ( ( ( SV249
!= ( head_of @ SV312 ) )
| ( SV256
!= ( path_cons @ SV312 @ empty ) ) )
= $true )
| ( ( vertex @ SV240 )
= $false )
| ( ( vertex @ SV249 )
= $false )
| ( ( path @ SV240 @ SV249 @ SV256 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1614]) ).
thf(1634,plain,
! [SV249: $i,SV256: $i,SV240: $i,SV313: $i] :
( ( ( edge @ SV313 )
= $false )
| ( ( SV240
= ( tail_of @ SV313 ) )
= $false )
| ( ( ! [SY559: $i] :
( ( SV256
!= ( path_cons @ SV313 @ SY559 ) )
| ~ ( path @ ( head_of @ SV313 ) @ SV249 @ SY559 ) ) )
= $true )
| ( ( vertex @ SV240 )
= $false )
| ( ( vertex @ SV249 )
= $false )
| ( ( path @ SV240 @ SV249 @ SV256 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1615]) ).
thf(1635,plain,
! [SV272: $i,SV266: $i,SV242: $i] :
( ( ( sequential @ SV242 @ SV266 )
= $false )
| ( ( edge @ SV266 )
= $false )
| ( ( edge @ SV242 )
= $false )
| ( ( edge @ SV272 )
= $false )
| ( ( ~ ( sequential @ SV266 @ SV272 ) )
= $true )
| ( ( ~ ( sequential @ SV272 @ SV242 ) )
= $true )
| ( ( triangle @ SV242 @ SV266 @ SV272 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1617]) ).
thf(1636,plain,
! [SV242: $i] :
( ( ~ ( ~ ( ! [SY478: $i,SY479: $i] :
~ ( triangle @ SV242 @ SY478 @ SY479 )
| ( edge @ SV242 ) )
| ~ ! [SY480: $i] :
( ! [SY481: $i] :
~ ( triangle @ SV242 @ SY480 @ SY481 )
| ( edge @ SY480 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1618]) ).
thf(1637,plain,
! [SV242: $i] :
( ( ! [SY482: $i,SY483: $i] :
( ~ ( triangle @ SV242 @ SY482 @ SY483 )
| ( edge @ SY483 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1619]) ).
thf(1638,plain,
! [SV333: $i,SV330: $i,SV242: $i] :
( ( ( ~ ( triangle @ SV242 @ SV330 @ SV333 ) )
= $true )
| ( ( sequential @ SV242 @ SV330 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1620]) ).
thf(1639,plain,
! [SV233: $i,SV267: $i,SV263: $i] :
( ( ( SV263
= ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
= $false )
| ( ( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ empty ) ) )
= $true )
| ( ( ! [SY528: $i] :
( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ SY528 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ SY528 ) ) )
= $true )
| ( ( path @ SV233 @ SV263 @ SV267 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1621]) ).
thf(1640,plain,
! [SV233: $i,SV267: $i,SV263: $i] :
( ( ( ( SV263
= ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ ( sK14_SY90 @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ ( sK14_SY90 @ SV267 @ SV263 @ SV233 ) ) ) )
= $true )
| ( ( path @ SV233 @ SV263 @ SV267 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1622]) ).
thf(1641,plain,
! [SV233: $i,SV263: $i,SV267: $i] :
( ( ( ( SV267
= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ empty ) )
| ~ ( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ ( sK13_SY91 @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ ( sK13_SY91 @ SV267 @ SV263 @ SV233 ) ) ) )
= $true )
| ( ( path @ SV233 @ SV263 @ SV267 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1623]) ).
thf(1642,plain,
! [SV257: $i,SV252: $i,SV288: $i,SV235: $i,SV298: $i,SV332: $i] :
( ( ( ~ ( precedes @ SV332 @ SV298 @ SV235 ) )
= $true )
| ( ( ~ ( sequential @ SV288 @ SV332 ) )
= $true )
| ( ( on_path @ SV288 @ SV235 )
= $false )
| ( ( on_path @ SV298 @ SV235 )
= $false )
| ( ( precedes @ SV288 @ SV298 @ SV235 )
= $true )
| ( ( path @ SV252 @ SV257 @ SV235 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1624]) ).
thf(1643,plain,
! [SV258: $i,SV254: $i,SV310: $i,SV237: $i,SV319: $i,SV334: $i] :
( ( ( ~ ( precedes @ SV334 @ SV319 @ SV237 )
| ~ ( sequential @ SV310 @ SV334 ) )
= $true )
| ( ( ~ ( sequential @ SV310 @ SV319 ) )
= $true )
| ( ( precedes @ SV310 @ SV319 @ SV237 )
= $false )
| ( ( path @ SV254 @ SV258 @ SV237 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1627]) ).
thf(1644,plain,
! [SV258: $i,SV254: $i,SV237: $i,SV311: $i,SV320: $i] :
( ( ( ~ ( precedes @ ( sK10_E3 @ SV320 @ SV311 @ SV237 ) @ SV320 @ SV237 )
| ~ ( sequential @ SV311 @ ( sK10_E3 @ SV320 @ SV311 @ SV237 ) ) )
= $false )
| ( ( sequential @ SV311 @ SV320 )
= $true )
| ( ( precedes @ SV311 @ SV320 @ SV237 )
= $false )
| ( ( path @ SV254 @ SV258 @ SV237 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1628]) ).
thf(1645,plain,
! [SV259: $i,SV255: $i] :
( ( ( ( SV255
!= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
= $true )
| ( ( ( SV259
!= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
= $true )
| ( ( ( SV259
!= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
!= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
= $true )
| ( ( SV255 = SV259 )
= $true )
| ( ( vertex @ SV255 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[1629]) ).
thf(1646,plain,
! [SV259: $i,SV255: $i] :
( ( ( ~ ~ ( ~ ( ( SV255
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
| ~ ( ( SV255
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) ) ) )
= $false )
| ( ( SV255 = SV259 )
= $true )
| ( ( vertex @ SV255 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[1630]) ).
thf(1647,plain,
! [SV255: $i,SV259: $i] :
( ( ( ~ ~ ( ~ ( ( SV259
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
| ~ ( ( SV259
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) ) ) )
= $false )
| ( ( SV255 = SV259 )
= $true )
| ( ( vertex @ SV255 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[1630]) ).
thf(1648,plain,
! [SV240: $i,SV256: $i,SV312: $i,SV249: $i] :
( ( ( ( SV249
!= ( head_of @ SV312 ) ) )
= $true )
| ( ( ( SV256
!= ( path_cons @ SV312 @ empty ) ) )
= $true )
| ( ( SV240
= ( tail_of @ SV312 ) )
= $false )
| ( ( edge @ SV312 )
= $false )
| ( ( vertex @ SV240 )
= $false )
| ( ( vertex @ SV249 )
= $false )
| ( ( path @ SV240 @ SV249 @ SV256 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1633]) ).
thf(1649,plain,
! [SV240: $i,SV249: $i,SV335: $i,SV313: $i,SV256: $i] :
( ( ( ( SV256
!= ( path_cons @ SV313 @ SV335 ) )
| ~ ( path @ ( head_of @ SV313 ) @ SV249 @ SV335 ) )
= $true )
| ( ( SV240
= ( tail_of @ SV313 ) )
= $false )
| ( ( edge @ SV313 )
= $false )
| ( ( vertex @ SV240 )
= $false )
| ( ( vertex @ SV249 )
= $false )
| ( ( path @ SV240 @ SV249 @ SV256 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1634]) ).
thf(1650,plain,
! [SV242: $i,SV272: $i,SV266: $i] :
( ( ( sequential @ SV266 @ SV272 )
= $false )
| ( ( edge @ SV272 )
= $false )
| ( ( edge @ SV242 )
= $false )
| ( ( edge @ SV266 )
= $false )
| ( ( sequential @ SV242 @ SV266 )
= $false )
| ( ( ~ ( sequential @ SV272 @ SV242 ) )
= $true )
| ( ( triangle @ SV242 @ SV266 @ SV272 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1635]) ).
thf(1651,plain,
! [SV242: $i] :
( ( ~ ( ! [SY478: $i,SY479: $i] :
~ ( triangle @ SV242 @ SY478 @ SY479 )
| ( edge @ SV242 ) )
| ~ ! [SY480: $i] :
( ! [SY481: $i] :
~ ( triangle @ SV242 @ SY480 @ SY481 )
| ( edge @ SY480 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1636]) ).
thf(1652,plain,
! [SV336: $i,SV242: $i] :
( ( ! [SY566: $i] :
( ~ ( triangle @ SV242 @ SV336 @ SY566 )
| ( edge @ SY566 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1637]) ).
thf(1653,plain,
! [SV333: $i,SV330: $i,SV242: $i] :
( ( ( triangle @ SV242 @ SV330 @ SV333 )
= $false )
| ( ( sequential @ SV242 @ SV330 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1638]) ).
thf(1654,plain,
! [SV233: $i,SV263: $i,SV267: $i] :
( ( ( SV267
= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ empty ) )
= $false )
| ( ( SV263
= ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
= $false )
| ( ( ! [SY528: $i] :
( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ SY528 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ SY528 ) ) )
= $true )
| ( ( path @ SV233 @ SV263 @ SV267 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1639]) ).
thf(1655,plain,
! [SV233: $i,SV267: $i,SV263: $i] :
( ( ( SV263
= ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
= $true )
| ( ( ~ ( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ ( sK14_SY90 @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ ( sK14_SY90 @ SV267 @ SV263 @ SV233 ) ) ) )
= $true )
| ( ( path @ SV233 @ SV263 @ SV267 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1640]) ).
thf(1656,plain,
! [SV233: $i,SV263: $i,SV267: $i] :
( ( ( SV267
= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ empty ) )
= $true )
| ( ( ~ ( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ ( sK13_SY91 @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ ( sK13_SY91 @ SV267 @ SV263 @ SV233 ) ) ) )
= $true )
| ( ( path @ SV233 @ SV263 @ SV267 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1641]) ).
thf(1657,plain,
! [SV257: $i,SV252: $i,SV288: $i,SV235: $i,SV298: $i,SV332: $i] :
( ( ( precedes @ SV332 @ SV298 @ SV235 )
= $false )
| ( ( ~ ( sequential @ SV288 @ SV332 ) )
= $true )
| ( ( on_path @ SV288 @ SV235 )
= $false )
| ( ( on_path @ SV298 @ SV235 )
= $false )
| ( ( precedes @ SV288 @ SV298 @ SV235 )
= $true )
| ( ( path @ SV252 @ SV257 @ SV235 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1642]) ).
thf(1658,plain,
! [SV258: $i,SV254: $i,SV310: $i,SV237: $i,SV319: $i,SV334: $i] :
( ( ( ~ ( precedes @ SV334 @ SV319 @ SV237 ) )
= $true )
| ( ( ~ ( sequential @ SV310 @ SV334 ) )
= $true )
| ( ( ~ ( sequential @ SV310 @ SV319 ) )
= $true )
| ( ( precedes @ SV310 @ SV319 @ SV237 )
= $false )
| ( ( path @ SV254 @ SV258 @ SV237 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1643]) ).
thf(1659,plain,
! [SV258: $i,SV254: $i,SV237: $i,SV311: $i,SV320: $i] :
( ( ( ~ ( precedes @ ( sK10_E3 @ SV320 @ SV311 @ SV237 ) @ SV320 @ SV237 ) )
= $false )
| ( ( sequential @ SV311 @ SV320 )
= $true )
| ( ( precedes @ SV311 @ SV320 @ SV237 )
= $false )
| ( ( path @ SV254 @ SV258 @ SV237 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1644]) ).
thf(1660,plain,
! [SV258: $i,SV254: $i,SV237: $i,SV320: $i,SV311: $i] :
( ( ( ~ ( sequential @ SV311 @ ( sK10_E3 @ SV320 @ SV311 @ SV237 ) ) )
= $false )
| ( ( sequential @ SV311 @ SV320 )
= $true )
| ( ( precedes @ SV311 @ SV320 @ SV237 )
= $false )
| ( ( path @ SV254 @ SV258 @ SV237 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1644]) ).
thf(1661,plain,
! [SV259: $i,SV255: $i] :
( ( ( SV255
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
= $false )
| ( ( ( SV259
!= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
= $true )
| ( ( ( SV259
!= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
!= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
= $true )
| ( ( SV255 = SV259 )
= $true )
| ( ( vertex @ SV255 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1645]) ).
thf(1662,plain,
! [SV259: $i,SV255: $i] :
( ( ( ~ ( ~ ( ( SV255
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
| ~ ( ( SV255
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) ) ) )
= $true )
| ( ( SV255 = SV259 )
= $true )
| ( ( vertex @ SV255 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1646]) ).
thf(1663,plain,
! [SV255: $i,SV259: $i] :
( ( ( ~ ( ~ ( ( SV259
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
| ~ ( ( SV259
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) ) ) )
= $true )
| ( ( SV255 = SV259 )
= $true )
| ( ( vertex @ SV255 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1647]) ).
thf(1664,plain,
! [SV240: $i,SV256: $i,SV312: $i,SV249: $i] :
( ( ( SV249
= ( head_of @ SV312 ) )
= $false )
| ( ( ( SV256
!= ( path_cons @ SV312 @ empty ) ) )
= $true )
| ( ( SV240
= ( tail_of @ SV312 ) )
= $false )
| ( ( edge @ SV312 )
= $false )
| ( ( vertex @ SV240 )
= $false )
| ( ( vertex @ SV249 )
= $false )
| ( ( path @ SV240 @ SV249 @ SV256 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1648]) ).
thf(1665,plain,
! [SV240: $i,SV249: $i,SV335: $i,SV313: $i,SV256: $i] :
( ( ( ( SV256
!= ( path_cons @ SV313 @ SV335 ) ) )
= $true )
| ( ( ~ ( path @ ( head_of @ SV313 ) @ SV249 @ SV335 ) )
= $true )
| ( ( SV240
= ( tail_of @ SV313 ) )
= $false )
| ( ( edge @ SV313 )
= $false )
| ( ( vertex @ SV240 )
= $false )
| ( ( vertex @ SV249 )
= $false )
| ( ( path @ SV240 @ SV249 @ SV256 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1649]) ).
thf(1666,plain,
! [SV266: $i,SV242: $i,SV272: $i] :
( ( ( sequential @ SV272 @ SV242 )
= $false )
| ( ( sequential @ SV242 @ SV266 )
= $false )
| ( ( edge @ SV266 )
= $false )
| ( ( edge @ SV242 )
= $false )
| ( ( edge @ SV272 )
= $false )
| ( ( sequential @ SV266 @ SV272 )
= $false )
| ( ( triangle @ SV242 @ SV266 @ SV272 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1650]) ).
thf(1667,plain,
! [SV242: $i] :
( ( ~ ( ! [SY478: $i,SY479: $i] :
~ ( triangle @ SV242 @ SY478 @ SY479 )
| ( edge @ SV242 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1651]) ).
thf(1668,plain,
! [SV242: $i] :
( ( ~ ! [SY480: $i] :
( ! [SY481: $i] :
~ ( triangle @ SV242 @ SY480 @ SY481 )
| ( edge @ SY480 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1651]) ).
thf(1669,plain,
! [SV337: $i,SV336: $i,SV242: $i] :
( ( ~ ( triangle @ SV242 @ SV336 @ SV337 )
| ( edge @ SV337 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1652]) ).
thf(1670,plain,
! [SV338: $i,SV233: $i,SV263: $i,SV267: $i] :
( ( ( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ SV338 ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ SV338 ) )
= $true )
| ( ( SV263
= ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
= $false )
| ( ( SV267
= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ empty ) )
= $false )
| ( ( path @ SV233 @ SV263 @ SV267 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1654]) ).
thf(1671,plain,
! [SV233: $i,SV263: $i,SV267: $i] :
( ( ( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ ( sK14_SY90 @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ ( sK14_SY90 @ SV267 @ SV263 @ SV233 ) ) )
= $false )
| ( ( SV263
= ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
= $true )
| ( ( path @ SV233 @ SV263 @ SV267 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1655]) ).
thf(1672,plain,
! [SV233: $i,SV263: $i,SV267: $i] :
( ( ( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ ( sK13_SY91 @ SV267 @ SV263 @ SV233 ) ) )
| ~ ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ ( sK13_SY91 @ SV267 @ SV263 @ SV233 ) ) )
= $false )
| ( ( SV267
= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ empty ) )
= $true )
| ( ( path @ SV233 @ SV263 @ SV267 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1656]) ).
thf(1673,plain,
! [SV257: $i,SV252: $i,SV235: $i,SV298: $i,SV332: $i,SV288: $i] :
( ( ( sequential @ SV288 @ SV332 )
= $false )
| ( ( precedes @ SV332 @ SV298 @ SV235 )
= $false )
| ( ( on_path @ SV288 @ SV235 )
= $false )
| ( ( on_path @ SV298 @ SV235 )
= $false )
| ( ( precedes @ SV288 @ SV298 @ SV235 )
= $true )
| ( ( path @ SV252 @ SV257 @ SV235 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1657]) ).
thf(1674,plain,
! [SV258: $i,SV254: $i,SV310: $i,SV237: $i,SV319: $i,SV334: $i] :
( ( ( precedes @ SV334 @ SV319 @ SV237 )
= $false )
| ( ( ~ ( sequential @ SV310 @ SV334 ) )
= $true )
| ( ( ~ ( sequential @ SV310 @ SV319 ) )
= $true )
| ( ( precedes @ SV310 @ SV319 @ SV237 )
= $false )
| ( ( path @ SV254 @ SV258 @ SV237 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1658]) ).
thf(1675,plain,
! [SV258: $i,SV254: $i,SV237: $i,SV311: $i,SV320: $i] :
( ( ( precedes @ ( sK10_E3 @ SV320 @ SV311 @ SV237 ) @ SV320 @ SV237 )
= $true )
| ( ( sequential @ SV311 @ SV320 )
= $true )
| ( ( precedes @ SV311 @ SV320 @ SV237 )
= $false )
| ( ( path @ SV254 @ SV258 @ SV237 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1659]) ).
thf(1676,plain,
! [SV258: $i,SV254: $i,SV237: $i,SV320: $i,SV311: $i] :
( ( ( sequential @ SV311 @ ( sK10_E3 @ SV320 @ SV311 @ SV237 ) )
= $true )
| ( ( sequential @ SV311 @ SV320 )
= $true )
| ( ( precedes @ SV311 @ SV320 @ SV237 )
= $false )
| ( ( path @ SV254 @ SV258 @ SV237 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1660]) ).
thf(1677,plain,
! [SV255: $i,SV259: $i] :
( ( ( SV259
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
= $false )
| ( ( SV255
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
= $false )
| ( ( ( SV259
!= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
!= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
= $true )
| ( ( SV255 = SV259 )
= $true )
| ( ( vertex @ SV255 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1661]) ).
thf(1678,plain,
! [SV259: $i,SV255: $i] :
( ( ( ~ ( ( SV255
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
| ~ ( ( SV255
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) ) )
= $false )
| ( ( SV255 = SV259 )
= $true )
| ( ( vertex @ SV255 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1662]) ).
thf(1679,plain,
! [SV255: $i,SV259: $i] :
( ( ( ~ ( ( SV259
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
| ~ ( ( SV259
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) ) )
= $false )
| ( ( SV255 = SV259 )
= $true )
| ( ( vertex @ SV255 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1663]) ).
thf(1680,plain,
! [SV240: $i,SV249: $i,SV312: $i,SV256: $i] :
( ( ( SV256
= ( path_cons @ SV312 @ empty ) )
= $false )
| ( ( SV249
= ( head_of @ SV312 ) )
= $false )
| ( ( SV240
= ( tail_of @ SV312 ) )
= $false )
| ( ( edge @ SV312 )
= $false )
| ( ( vertex @ SV240 )
= $false )
| ( ( vertex @ SV249 )
= $false )
| ( ( path @ SV240 @ SV249 @ SV256 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1664]) ).
thf(1681,plain,
! [SV240: $i,SV249: $i,SV335: $i,SV313: $i,SV256: $i] :
( ( ( SV256
= ( path_cons @ SV313 @ SV335 ) )
= $false )
| ( ( ~ ( path @ ( head_of @ SV313 ) @ SV249 @ SV335 ) )
= $true )
| ( ( SV240
= ( tail_of @ SV313 ) )
= $false )
| ( ( edge @ SV313 )
= $false )
| ( ( vertex @ SV240 )
= $false )
| ( ( vertex @ SV249 )
= $false )
| ( ( path @ SV240 @ SV249 @ SV256 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1665]) ).
thf(1682,plain,
! [SV242: $i] :
( ( ! [SY478: $i,SY479: $i] :
~ ( triangle @ SV242 @ SY478 @ SY479 )
| ( edge @ SV242 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1667]) ).
thf(1683,plain,
! [SV242: $i] :
( ( ! [SY480: $i] :
( ! [SY481: $i] :
~ ( triangle @ SV242 @ SY480 @ SY481 )
| ( edge @ SY480 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1668]) ).
thf(1684,plain,
! [SV337: $i,SV336: $i,SV242: $i] :
( ( ( ~ ( triangle @ SV242 @ SV336 @ SV337 ) )
= $true )
| ( ( edge @ SV337 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1669]) ).
thf(1685,plain,
! [SV338: $i,SV233: $i,SV263: $i,SV267: $i] :
( ( ( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ SV338 ) ) )
= $true )
| ( ( ~ ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ SV338 ) )
= $true )
| ( ( SV263
= ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
= $false )
| ( ( SV267
= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ empty ) )
= $false )
| ( ( path @ SV233 @ SV263 @ SV267 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1670]) ).
thf(1686,plain,
! [SV233: $i,SV263: $i,SV267: $i] :
( ( ( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ ( sK14_SY90 @ SV267 @ SV263 @ SV233 ) ) ) )
= $false )
| ( ( SV263
= ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
= $true )
| ( ( path @ SV233 @ SV263 @ SV267 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1671]) ).
thf(1687,plain,
! [SV233: $i,SV263: $i,SV267: $i] :
( ( ( ~ ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ ( sK14_SY90 @ SV267 @ SV263 @ SV233 ) ) )
= $false )
| ( ( SV263
= ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
= $true )
| ( ( path @ SV233 @ SV263 @ SV267 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1671]) ).
thf(1688,plain,
! [SV233: $i,SV263: $i,SV267: $i] :
( ( ( ( SV267
!= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ ( sK13_SY91 @ SV267 @ SV263 @ SV233 ) ) ) )
= $false )
| ( ( SV267
= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ empty ) )
= $true )
| ( ( path @ SV233 @ SV263 @ SV267 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1672]) ).
thf(1689,plain,
! [SV233: $i,SV263: $i,SV267: $i] :
( ( ( ~ ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ ( sK13_SY91 @ SV267 @ SV263 @ SV233 ) ) )
= $false )
| ( ( SV267
= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ empty ) )
= $true )
| ( ( path @ SV233 @ SV263 @ SV267 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1672]) ).
thf(1690,plain,
! [SV258: $i,SV254: $i,SV237: $i,SV319: $i,SV334: $i,SV310: $i] :
( ( ( sequential @ SV310 @ SV334 )
= $false )
| ( ( precedes @ SV334 @ SV319 @ SV237 )
= $false )
| ( ( ~ ( sequential @ SV310 @ SV319 ) )
= $true )
| ( ( precedes @ SV310 @ SV319 @ SV237 )
= $false )
| ( ( path @ SV254 @ SV258 @ SV237 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1674]) ).
thf(1691,plain,
! [SV255: $i,SV259: $i] :
( ( ( ( SV259
!= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
= $true )
| ( ( ( SV255
!= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
= $true )
| ( ( SV255
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
= $false )
| ( ( SV259
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
= $false )
| ( ( SV255 = SV259 )
= $true )
| ( ( vertex @ SV255 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[1677]) ).
thf(1692,plain,
! [SV259: $i,SV255: $i] :
( ( ( ~ ( ( SV255
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) ) ) )
= $false )
| ( ( SV255 = SV259 )
= $true )
| ( ( vertex @ SV255 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[1678]) ).
thf(1693,plain,
! [SV259: $i,SV255: $i] :
( ( ( ~ ( ( SV255
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) ) )
= $false )
| ( ( SV255 = SV259 )
= $true )
| ( ( vertex @ SV255 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[1678]) ).
thf(1694,plain,
! [SV255: $i,SV259: $i] :
( ( ( ~ ( ( SV259
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) ) ) )
= $false )
| ( ( SV255 = SV259 )
= $true )
| ( ( vertex @ SV255 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[1679]) ).
thf(1695,plain,
! [SV255: $i,SV259: $i] :
( ( ( ~ ( ( SV259
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) ) )
= $false )
| ( ( SV255 = SV259 )
= $true )
| ( ( vertex @ SV255 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[1679]) ).
thf(1696,plain,
! [SV240: $i,SV256: $i,SV335: $i,SV249: $i,SV313: $i] :
( ( ( path @ ( head_of @ SV313 ) @ SV249 @ SV335 )
= $false )
| ( ( SV256
= ( path_cons @ SV313 @ SV335 ) )
= $false )
| ( ( SV240
= ( tail_of @ SV313 ) )
= $false )
| ( ( edge @ SV313 )
= $false )
| ( ( vertex @ SV240 )
= $false )
| ( ( vertex @ SV249 )
= $false )
| ( ( path @ SV240 @ SV249 @ SV256 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1681]) ).
thf(1697,plain,
! [SV242: $i] :
( ( ( ! [SY478: $i,SY479: $i] :
~ ( triangle @ SV242 @ SY478 @ SY479 ) )
= $true )
| ( ( edge @ SV242 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1682]) ).
thf(1698,plain,
! [SV339: $i,SV242: $i] :
( ( ! [SY567: $i] :
~ ( triangle @ SV242 @ SV339 @ SY567 )
| ( edge @ SV339 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1683]) ).
thf(1699,plain,
! [SV337: $i,SV336: $i,SV242: $i] :
( ( ( triangle @ SV242 @ SV336 @ SV337 )
= $false )
| ( ( edge @ SV337 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1684]) ).
thf(1700,plain,
! [SV338: $i,SV233: $i,SV263: $i,SV267: $i] :
( ( ( SV267
= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ SV338 ) )
= $false )
| ( ( ~ ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ SV338 ) )
= $true )
| ( ( SV263
= ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
= $false )
| ( ( SV267
= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ empty ) )
= $false )
| ( ( path @ SV233 @ SV263 @ SV267 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1685]) ).
thf(1701,plain,
! [SV233: $i,SV263: $i,SV267: $i] :
( ( ( SV267
= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ ( sK14_SY90 @ SV267 @ SV263 @ SV233 ) ) )
= $true )
| ( ( SV263
= ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
= $true )
| ( ( path @ SV233 @ SV263 @ SV267 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1686]) ).
thf(1702,plain,
! [SV233: $i,SV263: $i,SV267: $i] :
( ( ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ ( sK14_SY90 @ SV267 @ SV263 @ SV233 ) )
= $true )
| ( ( SV263
= ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
= $true )
| ( ( path @ SV233 @ SV263 @ SV267 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1687]) ).
thf(1703,plain,
! [SV233: $i,SV263: $i,SV267: $i] :
( ( ( SV267
= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ ( sK13_SY91 @ SV267 @ SV263 @ SV233 ) ) )
= $true )
| ( ( SV267
= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ empty ) )
= $true )
| ( ( path @ SV233 @ SV263 @ SV267 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1688]) ).
thf(1704,plain,
! [SV233: $i,SV263: $i,SV267: $i] :
( ( ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ ( sK13_SY91 @ SV267 @ SV263 @ SV233 ) )
= $true )
| ( ( SV267
= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ empty ) )
= $true )
| ( ( path @ SV233 @ SV263 @ SV267 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1689]) ).
thf(1705,plain,
! [SV258: $i,SV254: $i,SV237: $i,SV334: $i,SV319: $i,SV310: $i] :
( ( ( sequential @ SV310 @ SV319 )
= $false )
| ( ( precedes @ SV334 @ SV319 @ SV237 )
= $false )
| ( ( sequential @ SV310 @ SV334 )
= $false )
| ( ( precedes @ SV310 @ SV319 @ SV237 )
= $false )
| ( ( path @ SV254 @ SV258 @ SV237 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1690]) ).
thf(1706,plain,
! [SV255: $i,SV259: $i] :
( ( ( SV259
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
= $false )
| ( ( ( SV255
!= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
= $true )
| ( ( SV255
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
= $false )
| ( ( SV259
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
= $false )
| ( ( SV255 = SV259 )
= $true )
| ( ( vertex @ SV255 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1691]) ).
thf(1707,plain,
! [SV259: $i,SV255: $i] :
( ( ( ( SV255
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
= $true )
| ( ( SV255 = SV259 )
= $true )
| ( ( vertex @ SV255 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1692]) ).
thf(1708,plain,
! [SV259: $i,SV255: $i] :
( ( ( ( SV255
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
= $true )
| ( ( SV255 = SV259 )
= $true )
| ( ( vertex @ SV255 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1693]) ).
thf(1709,plain,
! [SV255: $i,SV259: $i] :
( ( ( ( SV259
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV259
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
= $true )
| ( ( SV255 = SV259 )
= $true )
| ( ( vertex @ SV255 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1694]) ).
thf(1710,plain,
! [SV255: $i,SV259: $i] :
( ( ( ( SV259
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
| ( SV255
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) ) )
= $true )
| ( ( SV255 = SV259 )
= $true )
| ( ( vertex @ SV255 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1695]) ).
thf(1711,plain,
! [SV340: $i,SV242: $i] :
( ( ( ! [SY568: $i] :
~ ( triangle @ SV242 @ SV340 @ SY568 ) )
= $true )
| ( ( edge @ SV242 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1697]) ).
thf(1712,plain,
! [SV339: $i,SV242: $i] :
( ( ( ! [SY567: $i] :
~ ( triangle @ SV242 @ SV339 @ SY567 ) )
= $true )
| ( ( edge @ SV339 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1698]) ).
thf(1713,plain,
! [SV338: $i,SV233: $i,SV263: $i,SV267: $i] :
( ( ( path @ ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) @ SV263 @ SV338 )
= $false )
| ( ( SV267
= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ SV338 ) )
= $false )
| ( ( SV263
= ( head_of @ ( sK12_E @ SV267 @ SV263 @ SV233 ) ) )
= $false )
| ( ( SV267
= ( path_cons @ ( sK12_E @ SV267 @ SV263 @ SV233 ) @ empty ) )
= $false )
| ( ( path @ SV233 @ SV263 @ SV267 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1700]) ).
thf(1714,plain,
! [SV259: $i,SV255: $i] :
( ( ( SV255
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
= $false )
| ( ( SV259
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
= $false )
| ( ( SV255
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
= $false )
| ( ( SV259
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
= $false )
| ( ( SV255 = SV259 )
= $true )
| ( ( vertex @ SV255 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1706]) ).
thf(1715,plain,
! [SV259: $i,SV255: $i] :
( ( ( SV255
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
= $true )
| ( ( SV259
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
= $true )
| ( ( SV255 = SV259 )
= $true )
| ( ( vertex @ SV255 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[1707]) ).
thf(1716,plain,
! [SV259: $i,SV255: $i] :
( ( ( SV255
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
= $true )
| ( ( SV255
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
= $true )
| ( ( SV255 = SV259 )
= $true )
| ( ( vertex @ SV255 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[1708]) ).
thf(1717,plain,
! [SV255: $i,SV259: $i] :
( ( ( SV259
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
= $true )
| ( ( SV259
= ( head_of @ ( sK15_E @ SV259 @ SV255 ) ) )
= $true )
| ( ( SV255 = SV259 )
= $true )
| ( ( vertex @ SV255 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[1709]) ).
thf(1718,plain,
! [SV255: $i,SV259: $i] :
( ( ( SV259
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
= $true )
| ( ( SV255
= ( tail_of @ ( sK15_E @ SV259 @ SV255 ) ) )
= $true )
| ( ( SV255 = SV259 )
= $true )
| ( ( vertex @ SV255 )
= $false )
| ( ( vertex @ SV259 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[1710]) ).
thf(1719,plain,
! [SV341: $i,SV340: $i,SV242: $i] :
( ( ( ~ ( triangle @ SV242 @ SV340 @ SV341 ) )
= $true )
| ( ( edge @ SV242 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1711]) ).
thf(1720,plain,
! [SV342: $i,SV339: $i,SV242: $i] :
( ( ( ~ ( triangle @ SV242 @ SV339 @ SV342 ) )
= $true )
| ( ( edge @ SV339 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1712]) ).
thf(1721,plain,
! [SV341: $i,SV340: $i,SV242: $i] :
( ( ( triangle @ SV242 @ SV340 @ SV341 )
= $false )
| ( ( edge @ SV242 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1719]) ).
thf(1722,plain,
! [SV342: $i,SV339: $i,SV242: $i] :
( ( ( triangle @ SV242 @ SV339 @ SV342 )
= $false )
| ( ( edge @ SV339 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1720]) ).
thf(1723,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[1192,1722,1721,1718,1717,1716,1715,1714,1713,1705,1704,1703,1702,1701,1699,1696,1680,1676,1675,1673,1666,1653,1632,1631,1626,1625,1616,1613,1610,1609,1604,1603,1597,1593,1591,1590,1586,1583,1571,1570,1567,1566,1557,1542,1517,1516,1513,1499,1488,1482,1468,1463,1462,1448,1326,1325,1289,1288,1265,1228,1194,1193]) ).
thf(1724,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1723,625,1174]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRA004+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.06/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n017.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue May 31 03:02:25 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.38
% 0.19/0.38 No.of.Axioms: 17
% 0.19/0.38
% 0.19/0.38 Length.of.Defs: 0
% 0.19/0.38
% 0.19/0.38 Contains.Choice.Funs: false
% 0.19/0.42 .
% 0.19/0.42 (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).................................................................................................................................
% 1.24/1.48
% 1.24/1.48 ********************************
% 1.24/1.48 * All subproblems solved! *
% 1.24/1.48 ********************************
% 1.24/1.48 % 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:1723,loop_count:0,foatp_calls:1,translation:fof_full)
% 2.27/2.45
% 2.27/2.45 %**** Beginning of derivation protocol ****
% 2.27/2.45 % SZS output start CNFRefutation
% See solution above
% 2.27/2.46
% 2.27/2.46 %**** End of derivation protocol ****
% 2.27/2.46 %**** no. of clauses in derivation: 1724 ****
% 2.27/2.46 %**** clause counter: 1723 ****
% 2.27/2.46
% 2.27/2.46 % 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:1723,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------