TSTP Solution File: GRA007+2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GRA007+2 : 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 : n023.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 07:19:18 EDT 2022
% Result : Theorem 18.88s 19.07s
% Output : CNFRefutation 19.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 56
% Syntax : Number of formulae : 679 ( 262 unt; 37 typ; 0 def)
% Number of atoms : 6475 (2483 equ; 0 cnn)
% Maximal formula atoms : 9 ( 10 avg)
% Number of connectives : 15077 (2891 ~;2608 |; 201 &;9319 @)
% ( 6 <=>; 42 =>; 4 <=; 6 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 54 ( 54 >; 0 *; 0 +; 0 <<)
% Number of symbols : 40 ( 37 usr; 14 con; 0-4 aty)
% Number of variables : 2737 ( 0 ^2710 !; 27 ?;2737 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_complete,type,
complete: $o ).
thf(tp_edge,type,
edge: $i > $o ).
thf(tp_edges,type,
edges: $i ).
thf(tp_empty,type,
empty: $i ).
thf(tp_graph,type,
graph: $i ).
thf(tp_head_of,type,
head_of: $i > $i ).
thf(tp_in_path,type,
in_path: $i > $i > $o ).
thf(tp_length_of,type,
length_of: $i > $i ).
thf(tp_less_or_equal,type,
less_or_equal: $i > $i > $o ).
thf(tp_minus,type,
minus: $i > $i > $i ).
thf(tp_n1,type,
n1: $i ).
thf(tp_number_of_in,type,
number_of_in: $i > $i > $i ).
thf(tp_on_path,type,
on_path: $i > $i > $o ).
thf(tp_path,type,
path: $i > $i > $i > $o ).
thf(tp_path_cons,type,
path_cons: $i > $i > $i ).
thf(tp_precedes,type,
precedes: $i > $i > $i > $o ).
thf(tp_sK10_E,type,
sK10_E: $i > $i > $i > $i > $i ).
thf(tp_sK11_E,type,
sK11_E: $i > $i > $i > $i ).
thf(tp_sK12_SY96,type,
sK12_SY96: $i > $i > $i > $i ).
thf(tp_sK13_SY95,type,
sK13_SY95: $i > $i > $i > $i ).
thf(tp_sK14_E,type,
sK14_E: $i > $i > $i ).
thf(tp_sK1_V1,type,
sK1_V1: $i ).
thf(tp_sK2_SY77,type,
sK2_SY77: $i ).
thf(tp_sK3_SY82,type,
sK3_SY82: $i ).
thf(tp_sK4_SY86,type,
sK4_SY86: $i ).
thf(tp_sK5_SY89,type,
sK5_SY89: $i ).
thf(tp_sK6_E1,type,
sK6_E1: $i > $i ).
thf(tp_sK7_SY91,type,
sK7_SY91: $i > $i ).
thf(tp_sK8_P,type,
sK8_P: $i > $i > $i > $i ).
thf(tp_sK9_E3,type,
sK9_E3: $i > $i > $i > $i ).
thf(tp_sequential,type,
sequential: $i > $i > $o ).
thf(tp_sequential_pairs,type,
sequential_pairs: $i ).
thf(tp_shortest_path,type,
shortest_path: $i > $i > $i > $o ).
thf(tp_tail_of,type,
tail_of: $i > $i ).
thf(tp_triangle,type,
triangle: $i > $i > $i > $o ).
thf(tp_triangles,type,
triangles: $i ).
thf(tp_vertex,type,
vertex: $i > $o ).
thf(1,axiom,
! [Things: $i,InThese: $i] : ( less_or_equal @ ( number_of_in @ Things @ InThese ) @ ( number_of_in @ Things @ graph ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',graph_has_them_all) ).
thf(2,axiom,
! [P: $i,V1: $i,V2: $i] :
( ( ( path @ V1 @ V2 @ P )
& ! [E1: $i,E2: $i] :
( ( ( on_path @ E1 @ P )
& ( on_path @ E2 @ P )
& ( sequential @ E1 @ E2 ) )
=> ? [E3: $i] : ( triangle @ E1 @ E2 @ E3 ) ) )
=> ( ( number_of_in @ sequential_pairs @ P )
= ( number_of_in @ triangles @ P ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sequential_pairs_and_triangles) ).
thf(3,axiom,
! [V1: $i,V2: $i,P: $i] :
( ( path @ V1 @ V2 @ P )
=> ( ( number_of_in @ sequential_pairs @ P )
= ( minus @ ( length_of @ P ) @ n1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',path_length_sequential_pairs) ).
thf(4,axiom,
! [V1: $i,V2: $i,P: $i] :
( ( path @ V1 @ V2 @ P )
=> ( ( length_of @ P )
= ( number_of_in @ edges @ P ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',length_defn) ).
thf(5,axiom,
! [E1: $i,E2: $i,E3: $i] :
( ( triangle @ E1 @ E2 @ E3 )
<=> ( ( edge @ E1 )
& ( edge @ E2 )
& ( edge @ E3 )
& ( sequential @ E1 @ E2 )
& ( sequential @ E2 @ E3 )
& ( sequential @ E3 @ E1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',triangle_defn) ).
thf(6,axiom,
! [V1: $i,V2: $i,E1: $i,E2: $i,P: $i] :
( ( ( shortest_path @ V1 @ V2 @ P )
& ( precedes @ E1 @ E2 @ P ) )
=> ( ~ ? [E3: $i] :
( ( ( tail_of @ E3 )
= ( tail_of @ E1 ) )
& ( ( head_of @ E3 )
= ( head_of @ E2 ) ) )
& ~ ( precedes @ E2 @ E1 @ P ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',shortest_path_properties) ).
thf(7,axiom,
! [V1: $i,V2: $i,SP: $i] :
( ( shortest_path @ V1 @ V2 @ SP )
<=> ( ( path @ V1 @ V2 @ SP )
& ( V1 != V2 )
& ! [P: $i] :
( ( path @ V1 @ V2 @ P )
=> ( less_or_equal @ ( length_of @ SP ) @ ( length_of @ P ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',shortest_path_defn) ).
thf(8,axiom,
! [P: $i,V1: $i,V2: $i] :
( ( path @ V1 @ V2 @ P )
=> ! [E1: $i,E2: $i] :
( ( precedes @ E1 @ E2 @ P )
=> ( ( on_path @ E1 @ P )
& ( on_path @ E2 @ P )
& ( ( sequential @ E1 @ E2 )
<~> ? [E3: $i] :
( ( sequential @ E1 @ E3 )
& ( precedes @ E3 @ E2 @ P ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',precedes_properties) ).
thf(9,axiom,
! [P: $i,V1: $i,V2: $i] :
( ( path @ V1 @ V2 @ P )
=> ! [E1: $i,E2: $i] :
( ( precedes @ E1 @ E2 @ P )
<= ( ( on_path @ E1 @ P )
& ( on_path @ E2 @ P )
& ( ( sequential @ E1 @ E2 )
| ? [E3: $i] :
( ( sequential @ E1 @ E3 )
& ( precedes @ E3 @ E2 @ P ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',precedes_defn) ).
thf(10,axiom,
! [E1: $i,E2: $i] :
( ( sequential @ E1 @ E2 )
<=> ( ( edge @ E1 )
& ( edge @ E2 )
& ( E1 != E2 )
& ( ( head_of @ E1 )
= ( tail_of @ E2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sequential_defn) ).
thf(11,axiom,
! [V1: $i,V2: $i,P: $i,V: $i] :
( ( ( path @ V1 @ V2 @ P )
& ( in_path @ V @ P ) )
=> ( ( vertex @ V )
& ? [E: $i] :
( ( on_path @ E @ P )
& ( ( V
= ( head_of @ E ) )
| ( V
= ( tail_of @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in_path_properties) ).
thf(12,axiom,
! [V1: $i,V2: $i,P: $i,E: $i] :
( ( ( path @ V1 @ V2 @ P )
& ( on_path @ E @ P ) )
=> ( ( edge @ E )
& ( in_path @ ( head_of @ E ) @ P )
& ( in_path @ ( tail_of @ E ) @ P ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',on_path_properties) ).
thf(13,axiom,
! [V1: $i,V2: $i,P: $i] :
( ( path @ V1 @ V2 @ P )
=> ( ( vertex @ V1 )
& ( vertex @ V2 )
& ? [E: $i] :
( ( edge @ E )
& ( V1
= ( tail_of @ E ) )
& ( ( ( V2
= ( head_of @ E ) )
& ( P
= ( path_cons @ E @ empty ) ) )
<~> ? [TP: $i] :
( ( path @ ( head_of @ E ) @ V2 @ TP )
& ( P
= ( path_cons @ E @ TP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',path_properties) ).
thf(14,axiom,
! [V1: $i,V2: $i,P: $i] :
( ( path @ V1 @ V2 @ P )
<= ( ( vertex @ V1 )
& ( vertex @ V2 )
& ? [E: $i] :
( ( edge @ E )
& ( V1
= ( tail_of @ E ) )
& ( ( ( V2
= ( head_of @ E ) )
& ( P
= ( path_cons @ E @ empty ) ) )
| ? [TP: $i] :
( ( path @ ( head_of @ E ) @ V2 @ TP )
& ( P
= ( path_cons @ E @ TP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',path_defn) ).
thf(15,axiom,
( complete
=> ! [V1: $i,V2: $i] :
( ( ( vertex @ V1 )
& ( vertex @ V2 )
& ( V1 != V2 ) )
=> ? [E: $i] :
( ( edge @ E )
& ( ( ( V1
= ( head_of @ E ) )
& ( V2
= ( tail_of @ E ) ) )
<~> ( ( V2
= ( head_of @ E ) )
& ( V1
= ( tail_of @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complete_properties) ).
thf(16,axiom,
! [E: $i] :
( ( edge @ E )
=> ( ( vertex @ ( head_of @ E ) )
& ( vertex @ ( tail_of @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',edge_ends_are_vertices) ).
thf(17,axiom,
! [E: $i] :
( ( edge @ E )
=> ( ( head_of @ E )
!= ( tail_of @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_loops) ).
thf(18,axiom,
! [V1: $i,V2: $i,E1: $i,E2: $i,P: $i] :
( ( ( shortest_path @ V1 @ V2 @ P )
& ( precedes @ E1 @ E2 @ P ) )
=> ~ ? [E3: $i] :
( ( edge @ E3 )
& ( ( tail_of @ E3 )
= ( tail_of @ E1 ) )
& ( ( head_of @ E3 )
= ( head_of @ E2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_short_cut_edge) ).
thf(19,conjecture,
( complete
=> ! [V1: $i,V2: $i,E1: $i,E2: $i,P: $i] :
( ( ( shortest_path @ V1 @ V2 @ P )
& ( precedes @ E1 @ E2 @ P ) )
=> ? [E3: $i] :
( ( edge @ E3 )
& ( ( tail_of @ E3 )
= ( head_of @ E2 ) )
& ( ( head_of @ E3 )
= ( tail_of @ E1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',back_edge) ).
thf(20,negated_conjecture,
( ( complete
=> ! [V1: $i,V2: $i,E1: $i,E2: $i,P: $i] :
( ( ( shortest_path @ V1 @ V2 @ P )
& ( precedes @ E1 @ E2 @ P ) )
=> ? [E3: $i] :
( ( edge @ E3 )
& ( ( tail_of @ E3 )
= ( head_of @ E2 ) )
& ( ( head_of @ E3 )
= ( tail_of @ E1 ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[19]) ).
thf(21,plain,
( ( complete
=> ! [V1: $i,V2: $i,E1: $i,E2: $i,P: $i] :
( ( ( shortest_path @ V1 @ V2 @ P )
& ( precedes @ E1 @ E2 @ P ) )
=> ? [E3: $i] :
( ( edge @ E3 )
& ( ( tail_of @ E3 )
= ( head_of @ E2 ) )
& ( ( head_of @ E3 )
= ( tail_of @ E1 ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[20]) ).
thf(22,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(23,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(24,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(25,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(26,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(27,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(28,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(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)],[8]) ).
thf(30,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(31,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(32,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(33,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(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)],[13]) ).
thf(35,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(36,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(37,plain,
( ( ! [E: $i] :
( ( edge @ E )
=> ( ( vertex @ ( head_of @ E ) )
& ( vertex @ ( tail_of @ E ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(38,plain,
( ( ! [E: $i] :
( ( edge @ E )
=> ( ( head_of @ E )
!= ( tail_of @ E ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(39,plain,
( ( ! [V1: $i,V2: $i,E1: $i,E2: $i,P: $i] :
( ( ( shortest_path @ V1 @ V2 @ P )
& ( precedes @ E1 @ E2 @ P ) )
=> ~ ? [E3: $i] :
( ( edge @ E3 )
& ( ( tail_of @ E3 )
= ( tail_of @ E1 ) )
& ( ( head_of @ E3 )
= ( head_of @ E2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(40,plain,
complete = $true,
inference(standard_cnf,[status(thm)],[21]) ).
thf(41,plain,
( ( ! [V1: $i,V2: $i,E1: $i,E2: $i,P: $i] :
( ( ( shortest_path @ V1 @ V2 @ P )
& ( precedes @ E1 @ E2 @ P ) )
=> ? [E3: $i] :
( ( edge @ E3 )
& ( ( tail_of @ E3 )
= ( head_of @ E2 ) )
& ( ( head_of @ E3 )
= ( tail_of @ E1 ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[21]) ).
thf(42,plain,
( ( ~ ! [V1: $i,V2: $i,E1: $i,E2: $i,P: $i] :
( ( ( shortest_path @ V1 @ V2 @ P )
& ( precedes @ E1 @ E2 @ P ) )
=> ? [E3: $i] :
( ( edge @ E3 )
& ( ( tail_of @ E3 )
= ( head_of @ E2 ) )
& ( ( head_of @ E3 )
= ( tail_of @ E1 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[41]) ).
thf(43,plain,
( ( ( precedes @ sK3_SY82 @ sK4_SY86 @ sK5_SY89 )
& ( shortest_path @ sK1_V1 @ sK2_SY77 @ sK5_SY89 )
& ! [SY90: $i] :
( ( ( tail_of @ SY90 )
!= ( head_of @ sK4_SY86 ) )
| ~ ( edge @ SY90 )
| ( ( head_of @ SY90 )
!= ( tail_of @ sK3_SY82 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[42]) ).
thf(44,plain,
( ( ! [P: $i] :
( ( ( on_path @ ( sK6_E1 @ P ) @ P )
& ( on_path @ ( sK7_SY91 @ P ) @ P )
& ( sequential @ ( sK6_E1 @ P ) @ ( sK7_SY91 @ P ) )
& ! [SY93: $i] :
~ ( triangle @ ( sK6_E1 @ P ) @ ( sK7_SY91 @ P ) @ SY93 ) )
| ! [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)],[23]) ).
thf(45,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)],[24]) ).
thf(46,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)],[25]) ).
thf(47,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)],[26]) ).
thf(48,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)],[27]) ).
thf(49,plain,
( ( ! [V1: $i] :
( ! [V2: $i,SP: $i] :
( ( ( path @ V1 @ V2 @ ( sK8_P @ SP @ V2 @ V1 ) )
& ~ ( less_or_equal @ ( length_of @ SP ) @ ( length_of @ ( sK8_P @ SP @ V2 @ V1 ) ) ) )
| ( V1 = V2 )
| ~ ( path @ V1 @ V2 @ SP )
| ( shortest_path @ V1 @ V2 @ SP ) )
& ! [V2: $i,SP: $i] :
( ~ ( shortest_path @ V1 @ V2 @ SP )
| ! [P: $i] :
( ~ ( path @ V1 @ V2 @ P )
| ( less_or_equal @ ( length_of @ SP ) @ ( length_of @ P ) ) ) )
& ! [V2: $i] :
( ! [SP: $i] :
~ ( shortest_path @ V1 @ V2 @ SP )
| ( V1 != V2 ) )
& ! [V2: $i,SP: $i] :
( ~ ( shortest_path @ V1 @ V2 @ SP )
| ( path @ V1 @ V2 @ SP ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[28]) ).
thf(50,plain,
( ( ! [P: $i] :
( ! [V1: $i,V2: $i] :
~ ( path @ V1 @ V2 @ P )
| ( ! [E1: $i] :
( ! [E2: $i] :
~ ( precedes @ E1 @ E2 @ P )
| ( on_path @ E1 @ P ) )
& ! [E1: $i,E2: $i] :
( ~ ( precedes @ E1 @ E2 @ P )
| ( on_path @ E2 @ P ) )
& ! [E1: $i,E2: $i] :
( ~ ( precedes @ E1 @ E2 @ P )
| ! [E3: $i] :
( ~ ( precedes @ E3 @ E2 @ P )
| ~ ( sequential @ E1 @ E3 ) )
| ~ ( sequential @ E1 @ E2 ) )
& ! [E1: $i,E2: $i] :
( ~ ( precedes @ E1 @ E2 @ P )
| ( ( precedes @ ( sK9_E3 @ E2 @ E1 @ P ) @ E2 @ P )
& ( sequential @ E1 @ ( sK9_E3 @ E2 @ E1 @ P ) ) )
| ( sequential @ E1 @ E2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[29]) ).
thf(51,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)],[30]) ).
thf(52,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)],[31]) ).
thf(53,plain,
( ( ! [V1: $i,V2: $i] :
( ! [P: $i,V: $i] :
( ~ ( in_path @ V @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( ( on_path @ ( sK10_E @ V @ P @ V2 @ V1 ) @ P )
& ( ( V
= ( head_of @ ( sK10_E @ V @ P @ V2 @ V1 ) ) )
| ( V
= ( tail_of @ ( sK10_E @ V @ P @ V2 @ V1 ) ) ) ) ) )
& ! [P: $i,V: $i] :
( ~ ( in_path @ V @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( vertex @ V ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[32]) ).
thf(54,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)],[33]) ).
thf(55,plain,
( ( ! [V1: $i] :
( ( ! [V2: $i,P: $i] :
~ ( path @ V1 @ V2 @ P )
| ( vertex @ V1 ) )
& ! [V2: $i] :
( ! [P: $i] :
~ ( path @ V1 @ V2 @ P )
| ( vertex @ V2 ) )
& ! [V2: $i,P: $i] :
( ~ ( path @ V1 @ V2 @ P )
| ( ( V1
= ( tail_of @ ( sK11_E @ P @ V2 @ V1 ) ) )
& ( edge @ ( sK11_E @ P @ V2 @ V1 ) )
& ( ( V2
!= ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) )
| ( P
!= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ empty ) )
| ! [SY94: $i] :
( ( P
!= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ SY94 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) @ V2 @ SY94 ) ) )
& ( ( V2
= ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) )
| ( ( P
= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ ( sK13_SY95 @ P @ V2 @ V1 ) ) )
& ( path @ ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) @ V2 @ ( sK13_SY95 @ P @ V2 @ V1 ) ) ) )
& ( ( P
= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ empty ) )
| ( ( P
= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ ( sK12_SY96 @ P @ V2 @ V1 ) ) )
& ( path @ ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) @ V2 @ ( sK12_SY96 @ P @ V2 @ V1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[34]) ).
thf(56,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)],[35]) ).
thf(57,plain,
( ( ~ complete
| ! [V1: $i,V2: $i] :
( ( V1 = V2 )
| ~ ( vertex @ V1 )
| ~ ( vertex @ V2 )
| ( ( ( V1
!= ( head_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V2
!= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V2
!= ( head_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V1
!= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( ( V1
= ( head_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V2
= ( head_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( ( V1
= ( head_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V1
= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( ( V2
= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V2
= ( head_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( ( V2
= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V1
= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( edge @ ( sK14_E @ V2 @ V1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[36]) ).
thf(58,plain,
( ( ! [E: $i] :
( ~ ( edge @ E )
| ( vertex @ ( head_of @ E ) ) )
& ! [E: $i] :
( ~ ( edge @ E )
| ( vertex @ ( tail_of @ E ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[37]) ).
thf(59,plain,
( ( ! [E: $i] :
( ~ ( edge @ E )
| ( ( head_of @ E )
!= ( tail_of @ E ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[38]) ).
thf(60,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 ) )
| ~ ( edge @ E3 )
| ( ( head_of @ E3 )
!= ( head_of @ E2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[39]) ).
thf(61,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 ) )
| ~ ( edge @ E3 )
| ( ( head_of @ E3 )
!= ( head_of @ E2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(62,plain,
( ( ! [E: $i] :
( ~ ( edge @ E )
| ( ( head_of @ E )
!= ( tail_of @ E ) ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(63,plain,
( ( ! [E: $i] :
( ~ ( edge @ E )
| ( vertex @ ( head_of @ E ) ) )
& ! [E: $i] :
( ~ ( edge @ E )
| ( vertex @ ( tail_of @ E ) ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(64,plain,
( ( ~ complete
| ! [V1: $i,V2: $i] :
( ( V1 = V2 )
| ~ ( vertex @ V1 )
| ~ ( vertex @ V2 )
| ( ( ( V1
!= ( head_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V2
!= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V2
!= ( head_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V1
!= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( ( V1
= ( head_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V2
= ( head_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( ( V1
= ( head_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V1
= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( ( V2
= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V2
= ( head_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( ( V2
= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) )
| ( V1
= ( tail_of @ ( sK14_E @ V2 @ V1 ) ) ) )
& ( edge @ ( sK14_E @ V2 @ V1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(65,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)],[56]) ).
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 @ ( sK11_E @ P @ V2 @ V1 ) ) )
& ( edge @ ( sK11_E @ P @ V2 @ V1 ) )
& ( ( V2
!= ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) )
| ( P
!= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ empty ) )
| ! [SY94: $i] :
( ( P
!= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ SY94 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) @ V2 @ SY94 ) ) )
& ( ( V2
= ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) )
| ( ( P
= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ ( sK13_SY95 @ P @ V2 @ V1 ) ) )
& ( path @ ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) @ V2 @ ( sK13_SY95 @ P @ V2 @ V1 ) ) ) )
& ( ( P
= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ empty ) )
| ( ( P
= ( path_cons @ ( sK11_E @ P @ V2 @ V1 ) @ ( sK12_SY96 @ P @ V2 @ V1 ) ) )
& ( path @ ( head_of @ ( sK11_E @ P @ V2 @ V1 ) ) @ V2 @ ( sK12_SY96 @ P @ V2 @ V1 ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(67,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)],[54]) ).
thf(68,plain,
( ( ! [V1: $i,V2: $i] :
( ! [P: $i,V: $i] :
( ~ ( in_path @ V @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( ( on_path @ ( sK10_E @ V @ P @ V2 @ V1 ) @ P )
& ( ( V
= ( head_of @ ( sK10_E @ V @ P @ V2 @ V1 ) ) )
| ( V
= ( tail_of @ ( sK10_E @ V @ P @ V2 @ V1 ) ) ) ) ) )
& ! [P: $i,V: $i] :
( ~ ( in_path @ V @ P )
| ~ ( path @ V1 @ V2 @ P )
| ( vertex @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(69,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)],[52]) ).
thf(70,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)],[51]) ).
thf(71,plain,
( ( ! [P: $i] :
( ! [V1: $i,V2: $i] :
~ ( path @ V1 @ V2 @ P )
| ( ! [E1: $i] :
( ! [E2: $i] :
~ ( precedes @ E1 @ E2 @ P )
| ( on_path @ E1 @ P ) )
& ! [E1: $i,E2: $i] :
( ~ ( precedes @ E1 @ E2 @ P )
| ( on_path @ E2 @ P ) )
& ! [E1: $i,E2: $i] :
( ~ ( precedes @ E1 @ E2 @ P )
| ! [E3: $i] :
( ~ ( precedes @ E3 @ E2 @ P )
| ~ ( sequential @ E1 @ E3 ) )
| ~ ( sequential @ E1 @ E2 ) )
& ! [E1: $i,E2: $i] :
( ~ ( precedes @ E1 @ E2 @ P )
| ( ( precedes @ ( sK9_E3 @ E2 @ E1 @ P ) @ E2 @ P )
& ( sequential @ E1 @ ( sK9_E3 @ E2 @ E1 @ P ) ) )
| ( sequential @ E1 @ E2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(72,plain,
( ( ! [V1: $i] :
( ! [V2: $i,SP: $i] :
( ( ( path @ V1 @ V2 @ ( sK8_P @ SP @ V2 @ V1 ) )
& ~ ( less_or_equal @ ( length_of @ SP ) @ ( length_of @ ( sK8_P @ SP @ V2 @ V1 ) ) ) )
| ( V1 = V2 )
| ~ ( path @ V1 @ V2 @ SP )
| ( shortest_path @ V1 @ V2 @ SP ) )
& ! [V2: $i,SP: $i] :
( ~ ( shortest_path @ V1 @ V2 @ SP )
| ! [P: $i] :
( ~ ( path @ V1 @ V2 @ P )
| ( less_or_equal @ ( length_of @ SP ) @ ( length_of @ P ) ) ) )
& ! [V2: $i] :
( ! [SP: $i] :
~ ( shortest_path @ V1 @ V2 @ SP )
| ( V1 != V2 ) )
& ! [V2: $i,SP: $i] :
( ~ ( shortest_path @ V1 @ V2 @ SP )
| ( path @ V1 @ V2 @ SP ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(73,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)],[48]) ).
thf(74,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)],[47]) ).
thf(75,plain,
( ( ! [V1: $i,V2: $i,P: $i] :
( ~ ( path @ V1 @ V2 @ P )
| ( ( length_of @ P )
= ( number_of_in @ edges @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(76,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)],[45]) ).
thf(77,plain,
( ( ! [P: $i] :
( ( ( on_path @ ( sK6_E1 @ P ) @ P )
& ( on_path @ ( sK7_SY91 @ P ) @ P )
& ( sequential @ ( sK6_E1 @ P ) @ ( sK7_SY91 @ P ) )
& ! [SY93: $i] :
~ ( triangle @ ( sK6_E1 @ P ) @ ( sK7_SY91 @ P ) @ SY93 ) )
| ! [V1: $i,V2: $i] :
~ ( path @ V1 @ V2 @ P )
| ( ( number_of_in @ sequential_pairs @ P )
= ( number_of_in @ triangles @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(78,plain,
( ( ! [Things: $i,InThese: $i] : ( less_or_equal @ ( number_of_in @ Things @ InThese ) @ ( number_of_in @ Things @ graph ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(79,plain,
complete = $true,
inference(copy,[status(thm)],[40]) ).
thf(80,plain,
( ( ( precedes @ sK3_SY82 @ sK4_SY86 @ sK5_SY89 )
& ( shortest_path @ sK1_V1 @ sK2_SY77 @ sK5_SY89 )
& ! [SY90: $i] :
( ( ( tail_of @ SY90 )
!= ( head_of @ sK4_SY86 ) )
| ~ ( edge @ SY90 )
| ( ( head_of @ SY90 )
!= ( tail_of @ sK3_SY82 ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(81,plain,
( ( ! [SX0: $i] :
~ ( ~ ~ ( ~ ( ! [SX1: $i,SX2: $i] :
~ ( path @ SX0 @ SX1 @ SX2 )
| ( vertex @ SX0 ) )
| ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( path @ SX0 @ SX1 @ SX2 )
| ( vertex @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( path @ SX0 @ SX1 @ SX2 )
| ~ ( ~ ~ ( ( SX0
!= ( tail_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( edge @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ( SX1
!= ( head_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) )
| ( SX2
!= ( path_cons @ ( sK11_E @ SX2 @ SX1 @ SX0 ) @ empty ) )
| ! [SX3: $i] :
( ( SX2
!= ( path_cons @ ( sK11_E @ SX2 @ SX1 @ SX0 ) @ SX3 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) @ SX1 @ SX3 ) ) )
| ~ ~ ( ~ ( ( SX1
= ( head_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( ( SX2
!= ( path_cons @ ( sK11_E @ SX2 @ SX1 @ SX0 ) @ ( sK13_SY95 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) @ SX1 @ ( sK13_SY95 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX2
= ( path_cons @ ( sK11_E @ SX2 @ SX1 @ SX0 ) @ empty ) )
| ~ ( ( SX2
!= ( path_cons @ ( sK11_E @ SX2 @ SX1 @ SX0 ) @ ( sK12_SY96 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SX2 @ SX1 @ SX0 ) ) @ SX1 @ ( sK12_SY96 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(82,plain,
( ( ~ complete
| ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( vertex @ SX0 )
| ~ ( vertex @ SX1 )
| ~ ( ~ ~ ( ~ ( ( SX0
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
| ~ ~ ( ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(83,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( path @ SX0 @ SX1 @ ( sK8_P @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SX2 ) @ ( length_of @ ( sK8_P @ SX2 @ SX1 @ SX0 ) ) ) )
| ( SX0 = SX1 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ( shortest_path @ SX0 @ SX1 @ SX2 ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( shortest_path @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( path @ SX0 @ SX1 @ SX3 )
| ( less_or_equal @ ( length_of @ SX2 ) @ ( length_of @ SX3 ) ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( shortest_path @ SX0 @ SX1 @ SX2 )
| ( SX0 != SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( shortest_path @ SX0 @ SX1 @ SX2 )
| ( path @ SX0 @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(84,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)],[73]) ).
thf(85,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)],[65]) ).
thf(86,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i,SX2: $i] :
~ ( path @ SX1 @ SX2 @ SX0 )
| ~ ( ~ ~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( precedes @ SX1 @ SX2 @ SX0 )
| ( on_path @ SX1 @ SX0 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( precedes @ SX1 @ SX2 @ SX0 )
| ( on_path @ SX2 @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( precedes @ SX1 @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( precedes @ SX3 @ SX2 @ SX0 )
| ~ ( sequential @ SX1 @ SX3 ) )
| ~ ( sequential @ SX1 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( precedes @ SX1 @ SX2 @ SX0 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SX2 @ SX1 @ SX0 ) @ SX2 @ SX0 )
| ~ ( sequential @ SX1 @ ( sK9_E3 @ SX2 @ SX1 @ SX0 ) ) )
| ( sequential @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(87,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)],[74]) ).
thf(88,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)],[67]) ).
thf(89,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( head_of @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( tail_of @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(90,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in_path @ SX3 @ SX2 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ~ ( ~ ( on_path @ ( sK10_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( ( SX3
= ( head_of @ ( sK10_E @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ( SX3
= ( tail_of @ ( sK10_E @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( in_path @ SX3 @ SX2 )
| ~ ( path @ SX0 @ SX1 @ SX2 )
| ( vertex @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(91,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)],[70]) ).
thf(92,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SX0 ) @ SX0 )
| ~ ( on_path @ ( sK7_SY91 @ SX0 ) @ SX0 ) )
| ~ ( sequential @ ( sK6_E1 @ SX0 ) @ ( sK7_SY91 @ SX0 ) ) )
| ~ ! [SX1: $i] :
~ ( triangle @ ( sK6_E1 @ SX0 ) @ ( sK7_SY91 @ 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)],[77]) ).
thf(93,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)],[69]) ).
thf(94,plain,
( ( ~ ( ~ ~ ( ~ ( precedes @ sK3_SY82 @ sK4_SY86 @ sK5_SY89 )
| ~ ( shortest_path @ sK1_V1 @ sK2_SY77 @ sK5_SY89 ) )
| ~ ! [SX0: $i] :
( ( ( tail_of @ SX0 )
!= ( head_of @ sK4_SY86 ) )
| ~ ( edge @ SX0 )
| ( ( head_of @ SX0 )
!= ( tail_of @ sK3_SY82 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(95,plain,
! [SV1: $i] :
( ( ! [SY97: $i,SY98: $i,SY99: $i] :
( ! [SY100: $i] :
( ~ ( precedes @ SY98 @ SY99 @ SY100 )
| ~ ( shortest_path @ SV1 @ SY97 @ SY100 ) )
| ! [E3: $i] :
( ( ( tail_of @ E3 )
!= ( tail_of @ SY98 ) )
| ~ ( edge @ E3 )
| ( ( head_of @ E3 )
!= ( head_of @ SY99 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(96,plain,
! [SV2: $i] :
( ( ~ ( edge @ SV2 )
| ( ( head_of @ SV2 )
!= ( tail_of @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(97,plain,
! [SV3: $i] :
( ( ! [SY102: $i,SY103: $i] :
( ~ ( path @ SV3 @ SY102 @ SY103 )
| ( ( length_of @ SY103 )
= ( number_of_in @ edges @ SY103 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(98,plain,
! [SV4: $i] :
( ( ! [SY104: $i,SY105: $i] :
( ~ ( path @ SV4 @ SY104 @ SY105 )
| ( ( number_of_in @ sequential_pairs @ SY105 )
= ( minus @ ( length_of @ SY105 ) @ n1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(99,plain,
! [SV5: $i] :
( ( ! [SY106: $i] : ( less_or_equal @ ( number_of_in @ SV5 @ SY106 ) @ ( number_of_in @ SV5 @ graph ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(100,plain,
! [SV6: $i] :
( ( ~ ( ~ ~ ( ~ ( ! [SY107: $i,SY108: $i] :
~ ( path @ SV6 @ SY107 @ SY108 )
| ( vertex @ SV6 ) )
| ~ ! [SY109: $i] :
( ! [SY110: $i] :
~ ( path @ SV6 @ SY109 @ SY110 )
| ( vertex @ SY109 ) ) )
| ~ ! [SY111: $i,SY112: $i] :
( ~ ( path @ SV6 @ SY111 @ SY112 )
| ~ ( ~ ~ ( ( SV6
!= ( tail_of @ ( sK11_E @ SY112 @ SY111 @ SV6 ) ) )
| ~ ( edge @ ( sK11_E @ SY112 @ SY111 @ SV6 ) ) )
| ~ ~ ( ~ ( ( SY111
!= ( head_of @ ( sK11_E @ SY112 @ SY111 @ SV6 ) ) )
| ( SY112
!= ( path_cons @ ( sK11_E @ SY112 @ SY111 @ SV6 ) @ empty ) )
| ! [SY113: $i] :
( ( SY112
!= ( path_cons @ ( sK11_E @ SY112 @ SY111 @ SV6 ) @ SY113 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY112 @ SY111 @ SV6 ) ) @ SY111 @ SY113 ) ) )
| ~ ~ ( ~ ( ( SY111
= ( head_of @ ( sK11_E @ SY112 @ SY111 @ SV6 ) ) )
| ~ ( ( SY112
!= ( path_cons @ ( sK11_E @ SY112 @ SY111 @ SV6 ) @ ( sK13_SY95 @ SY112 @ SY111 @ SV6 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY112 @ SY111 @ SV6 ) ) @ SY111 @ ( sK13_SY95 @ SY112 @ SY111 @ SV6 ) ) ) )
| ~ ( ( SY112
= ( path_cons @ ( sK11_E @ SY112 @ SY111 @ SV6 ) @ empty ) )
| ~ ( ( SY112
!= ( path_cons @ ( sK11_E @ SY112 @ SY111 @ SV6 ) @ ( sK12_SY96 @ SY112 @ SY111 @ SV6 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY112 @ SY111 @ SV6 ) ) @ SY111 @ ( sK12_SY96 @ SY112 @ SY111 @ SV6 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(101,plain,
( ( ( ~ complete )
= $true )
| ( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( vertex @ SX0 )
| ~ ( vertex @ SX1 )
| ~ ( ~ ~ ( ~ ( ( SX0
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
| ~ ~ ( ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(102,plain,
! [SV7: $i] :
( ( ~ ( ~ ! [SY114: $i,SY115: $i] :
( ~ ( ~ ( path @ SV7 @ SY114 @ ( sK8_P @ SY115 @ SY114 @ SV7 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY115 ) @ ( length_of @ ( sK8_P @ SY115 @ SY114 @ SV7 ) ) ) )
| ( SV7 = SY114 )
| ~ ( path @ SV7 @ SY114 @ SY115 )
| ( shortest_path @ SV7 @ SY114 @ SY115 ) )
| ~ ~ ( ~ ! [SY116: $i,SY117: $i] :
( ~ ( shortest_path @ SV7 @ SY116 @ SY117 )
| ! [SY118: $i] :
( ~ ( path @ SV7 @ SY116 @ SY118 )
| ( less_or_equal @ ( length_of @ SY117 ) @ ( length_of @ SY118 ) ) ) )
| ~ ~ ( ~ ! [SY119: $i] :
( ! [SY120: $i] :
~ ( shortest_path @ SV7 @ SY119 @ SY120 )
| ( SV7 != SY119 ) )
| ~ ! [SY121: $i,SY122: $i] :
( ~ ( shortest_path @ SV7 @ SY121 @ SY122 )
| ( path @ SV7 @ SY121 @ SY122 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(103,plain,
! [SV8: $i] :
( ( ! [SY123: $i,SY124: $i] :
~ ( ~ ! [SY125: $i] :
( ! [SY126: $i] :
( ~ ( precedes @ SY124 @ SY125 @ SY126 )
| ~ ( shortest_path @ SV8 @ SY123 @ SY126 ) )
| ! [SX4: $i] :
( ( ( tail_of @ SX4 )
!= ( tail_of @ SY124 ) )
| ( ( head_of @ SX4 )
!= ( head_of @ SY125 ) ) ) )
| ~ ! [SY128: $i,SY129: $i] :
( ~ ( precedes @ SY124 @ SY128 @ SY129 )
| ~ ( shortest_path @ SV8 @ SY123 @ SY129 )
| ~ ( precedes @ SY128 @ SY124 @ SY129 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(104,plain,
! [SV9: $i] :
( ( ! [SY130: $i,SY131: $i] :
( ~ ( vertex @ SV9 )
| ~ ( vertex @ SY130 )
| ~ ( ~ ! [SY132: $i] :
( ( SV9
!= ( tail_of @ SY132 ) )
| ~ ( edge @ SY132 )
| ( SY130
!= ( head_of @ SY132 ) )
| ( SY131
!= ( path_cons @ SY132 @ empty ) ) )
| ~ ! [SY133: $i] :
( ( SV9
!= ( tail_of @ SY133 ) )
| ~ ( edge @ SY133 )
| ! [SX4: $i] :
( ( SY131
!= ( path_cons @ SY133 @ SX4 ) )
| ~ ( path @ ( head_of @ SY133 ) @ SY130 @ SX4 ) ) ) )
| ( path @ SV9 @ SY130 @ SY131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(105,plain,
! [SV10: $i] :
( ( ! [SY135: $i,SY136: $i] :
~ ( path @ SY135 @ SY136 @ SV10 )
| ~ ( ~ ~ ( ~ ! [SY137: $i] :
( ! [SY138: $i] :
~ ( precedes @ SY137 @ SY138 @ SV10 )
| ( on_path @ SY137 @ SV10 ) )
| ~ ! [SY139: $i,SY140: $i] :
( ~ ( precedes @ SY139 @ SY140 @ SV10 )
| ( on_path @ SY140 @ SV10 ) ) )
| ~ ~ ( ~ ! [SY141: $i,SY142: $i] :
( ~ ( precedes @ SY141 @ SY142 @ SV10 )
| ! [SY143: $i] :
( ~ ( precedes @ SY143 @ SY142 @ SV10 )
| ~ ( sequential @ SY141 @ SY143 ) )
| ~ ( sequential @ SY141 @ SY142 ) )
| ~ ! [SY144: $i,SY145: $i] :
( ~ ( precedes @ SY144 @ SY145 @ SV10 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY145 @ SY144 @ SV10 ) @ SY145 @ SV10 )
| ~ ( sequential @ SY144 @ ( sK9_E3 @ SY145 @ SY144 @ SV10 ) ) )
| ( sequential @ SY144 @ SY145 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(106,plain,
! [SV11: $i] :
( ( ~ ( ~ ! [SY146: $i,SY147: $i] :
( ~ ( edge @ SV11 )
| ~ ( edge @ SY146 )
| ~ ( edge @ SY147 )
| ~ ( sequential @ SV11 @ SY146 )
| ~ ( sequential @ SY146 @ SY147 )
| ~ ( sequential @ SY147 @ SV11 )
| ( triangle @ SV11 @ SY146 @ SY147 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY148: $i,SY149: $i] :
~ ( triangle @ SV11 @ SY148 @ SY149 )
| ( edge @ SV11 ) )
| ~ ! [SY150: $i] :
( ! [SY151: $i] :
~ ( triangle @ SV11 @ SY150 @ SY151 )
| ( edge @ SY150 ) ) )
| ~ ! [SY152: $i,SY153: $i] :
( ~ ( triangle @ SV11 @ SY152 @ SY153 )
| ( edge @ SY153 ) ) )
| ~ ! [SY154: $i] :
( ! [SY155: $i] :
~ ( triangle @ SV11 @ SY154 @ SY155 )
| ( sequential @ SV11 @ SY154 ) ) )
| ~ ! [SY156: $i,SY157: $i] :
( ~ ( triangle @ SV11 @ SY156 @ SY157 )
| ( sequential @ SY156 @ SY157 ) ) )
| ~ ! [SY158: $i,SY159: $i] :
( ~ ( triangle @ SV11 @ SY158 @ SY159 )
| ( sequential @ SY159 @ SV11 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(107,plain,
! [SV12: $i] :
( ( ! [SY160: $i] :
~ ( ~ ~ ( ~ ! [SY161: $i,SY162: $i] :
( ~ ( on_path @ SY162 @ SY161 )
| ~ ( path @ SV12 @ SY160 @ SY161 )
| ( edge @ SY162 ) )
| ~ ! [SY163: $i,SY164: $i] :
( ~ ( on_path @ SY164 @ SY163 )
| ~ ( path @ SV12 @ SY160 @ SY163 )
| ( in_path @ ( head_of @ SY164 ) @ SY163 ) ) )
| ~ ! [SY165: $i,SY166: $i] :
( ~ ( on_path @ SY166 @ SY165 )
| ~ ( path @ SV12 @ SY160 @ SY165 )
| ( in_path @ ( tail_of @ SY166 ) @ SY165 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(108,plain,
( ( ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( head_of @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( tail_of @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(109,plain,
! [SV13: $i] :
( ( ! [SY167: $i] :
~ ( ~ ! [SY168: $i,SY169: $i] :
( ~ ( in_path @ SY169 @ SY168 )
| ~ ( path @ SV13 @ SY167 @ SY168 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY169 @ SY168 @ SY167 @ SV13 ) @ SY168 )
| ~ ( ( SY169
= ( head_of @ ( sK10_E @ SY169 @ SY168 @ SY167 @ SV13 ) ) )
| ( SY169
= ( tail_of @ ( sK10_E @ SY169 @ SY168 @ SY167 @ SV13 ) ) ) ) ) )
| ~ ! [SY170: $i,SY171: $i] :
( ~ ( in_path @ SY171 @ SY170 )
| ~ ( path @ SV13 @ SY167 @ SY170 )
| ( vertex @ SY171 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(110,plain,
! [SV14: $i] :
( ( ! [SY172: $i,SY173: $i] :
~ ( path @ SY172 @ SY173 @ SV14 )
| ~ ( ~ ! [SY174: $i,SY175: $i] :
( ~ ( on_path @ SY174 @ SV14 )
| ~ ( on_path @ SY175 @ SV14 )
| ! [SY176: $i] :
( ~ ( precedes @ SY176 @ SY175 @ SV14 )
| ~ ( sequential @ SY174 @ SY176 ) )
| ( precedes @ SY174 @ SY175 @ SV14 ) )
| ~ ! [SY177: $i,SY178: $i] :
( ~ ( on_path @ SY177 @ SV14 )
| ~ ( on_path @ SY178 @ SV14 )
| ~ ( sequential @ SY177 @ SY178 )
| ( precedes @ SY177 @ SY178 @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(111,plain,
! [SV15: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV15 ) @ SV15 )
| ~ ( on_path @ ( sK7_SY91 @ SV15 ) @ SV15 ) )
| ~ ( sequential @ ( sK6_E1 @ SV15 ) @ ( sK7_SY91 @ SV15 ) ) )
| ~ ! [SY179: $i] :
~ ( triangle @ ( sK6_E1 @ SV15 ) @ ( sK7_SY91 @ SV15 ) @ SY179 ) )
| ! [SY180: $i,SY181: $i] :
~ ( path @ SY180 @ SY181 @ SV15 )
| ( ( number_of_in @ sequential_pairs @ SV15 )
= ( number_of_in @ triangles @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(112,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)],[93]) ).
thf(113,plain,
( ( ~ ~ ( ~ ( precedes @ sK3_SY82 @ sK4_SY86 @ sK5_SY89 )
| ~ ( shortest_path @ sK1_V1 @ sK2_SY77 @ sK5_SY89 ) )
| ~ ! [SX0: $i] :
( ( ( tail_of @ SX0 )
!= ( head_of @ sK4_SY86 ) )
| ~ ( edge @ SX0 )
| ( ( head_of @ SX0 )
!= ( tail_of @ sK3_SY82 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(114,plain,
! [SV16: $i,SV1: $i] :
( ( ! [SY182: $i,SY183: $i] :
( ! [SY184: $i] :
( ~ ( precedes @ SY182 @ SY183 @ SY184 )
| ~ ( shortest_path @ SV1 @ SV16 @ SY184 ) )
| ! [E3: $i] :
( ( ( tail_of @ E3 )
!= ( tail_of @ SY182 ) )
| ~ ( edge @ E3 )
| ( ( head_of @ E3 )
!= ( head_of @ SY183 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(115,plain,
! [SV2: $i] :
( ( ( ~ ( edge @ SV2 ) )
= $true )
| ( ( ( ( head_of @ SV2 )
!= ( tail_of @ SV2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(116,plain,
! [SV17: $i,SV3: $i] :
( ( ! [SY186: $i] :
( ~ ( path @ SV3 @ SV17 @ SY186 )
| ( ( length_of @ SY186 )
= ( number_of_in @ edges @ SY186 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(117,plain,
! [SV18: $i,SV4: $i] :
( ( ! [SY187: $i] :
( ~ ( path @ SV4 @ SV18 @ SY187 )
| ( ( number_of_in @ sequential_pairs @ SY187 )
= ( minus @ ( length_of @ SY187 ) @ n1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(118,plain,
! [SV19: $i,SV5: $i] :
( ( less_or_equal @ ( number_of_in @ SV5 @ SV19 ) @ ( number_of_in @ SV5 @ graph ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(119,plain,
! [SV6: $i] :
( ( ~ ~ ( ~ ( ! [SY107: $i,SY108: $i] :
~ ( path @ SV6 @ SY107 @ SY108 )
| ( vertex @ SV6 ) )
| ~ ! [SY109: $i] :
( ! [SY110: $i] :
~ ( path @ SV6 @ SY109 @ SY110 )
| ( vertex @ SY109 ) ) )
| ~ ! [SY111: $i,SY112: $i] :
( ~ ( path @ SV6 @ SY111 @ SY112 )
| ~ ( ~ ~ ( ( SV6
!= ( tail_of @ ( sK11_E @ SY112 @ SY111 @ SV6 ) ) )
| ~ ( edge @ ( sK11_E @ SY112 @ SY111 @ SV6 ) ) )
| ~ ~ ( ~ ( ( SY111
!= ( head_of @ ( sK11_E @ SY112 @ SY111 @ SV6 ) ) )
| ( SY112
!= ( path_cons @ ( sK11_E @ SY112 @ SY111 @ SV6 ) @ empty ) )
| ! [SY113: $i] :
( ( SY112
!= ( path_cons @ ( sK11_E @ SY112 @ SY111 @ SV6 ) @ SY113 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY112 @ SY111 @ SV6 ) ) @ SY111 @ SY113 ) ) )
| ~ ~ ( ~ ( ( SY111
= ( head_of @ ( sK11_E @ SY112 @ SY111 @ SV6 ) ) )
| ~ ( ( SY112
!= ( path_cons @ ( sK11_E @ SY112 @ SY111 @ SV6 ) @ ( sK13_SY95 @ SY112 @ SY111 @ SV6 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY112 @ SY111 @ SV6 ) ) @ SY111 @ ( sK13_SY95 @ SY112 @ SY111 @ SV6 ) ) ) )
| ~ ( ( SY112
= ( path_cons @ ( sK11_E @ SY112 @ SY111 @ SV6 ) @ empty ) )
| ~ ( ( SY112
!= ( path_cons @ ( sK11_E @ SY112 @ SY111 @ SV6 ) @ ( sK12_SY96 @ SY112 @ SY111 @ SV6 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY112 @ SY111 @ SV6 ) ) @ SY111 @ ( sK12_SY96 @ SY112 @ SY111 @ SV6 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(120,plain,
( ( complete = $false )
| ( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( vertex @ SX0 )
| ~ ( vertex @ SX1 )
| ~ ( ~ ~ ( ~ ( ( SX0
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
!= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
!= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX0
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
| ~ ~ ( ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX1
= ( head_of @ ( sK14_E @ SX1 @ SX0 ) ) ) )
| ~ ( ( SX1
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) )
| ( SX0
= ( tail_of @ ( sK14_E @ SX1 @ SX0 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SX1 @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(121,plain,
! [SV7: $i] :
( ( ~ ! [SY114: $i,SY115: $i] :
( ~ ( ~ ( path @ SV7 @ SY114 @ ( sK8_P @ SY115 @ SY114 @ SV7 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY115 ) @ ( length_of @ ( sK8_P @ SY115 @ SY114 @ SV7 ) ) ) )
| ( SV7 = SY114 )
| ~ ( path @ SV7 @ SY114 @ SY115 )
| ( shortest_path @ SV7 @ SY114 @ SY115 ) )
| ~ ~ ( ~ ! [SY116: $i,SY117: $i] :
( ~ ( shortest_path @ SV7 @ SY116 @ SY117 )
| ! [SY118: $i] :
( ~ ( path @ SV7 @ SY116 @ SY118 )
| ( less_or_equal @ ( length_of @ SY117 ) @ ( length_of @ SY118 ) ) ) )
| ~ ~ ( ~ ! [SY119: $i] :
( ! [SY120: $i] :
~ ( shortest_path @ SV7 @ SY119 @ SY120 )
| ( SV7 != SY119 ) )
| ~ ! [SY121: $i,SY122: $i] :
( ~ ( shortest_path @ SV7 @ SY121 @ SY122 )
| ( path @ SV7 @ SY121 @ SY122 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(122,plain,
! [SV20: $i,SV8: $i] :
( ( ! [SY188: $i] :
~ ( ~ ! [SY189: $i] :
( ! [SY190: $i] :
( ~ ( precedes @ SY188 @ SY189 @ SY190 )
| ~ ( shortest_path @ SV8 @ SV20 @ 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 @ SV8 @ SV20 @ SY193 )
| ~ ( precedes @ SY192 @ SY188 @ SY193 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(123,plain,
! [SV21: $i,SV9: $i] :
( ( ! [SY194: $i] :
( ~ ( vertex @ SV9 )
| ~ ( vertex @ SV21 )
| ~ ( ~ ! [SY195: $i] :
( ( SV9
!= ( tail_of @ SY195 ) )
| ~ ( edge @ SY195 )
| ( SV21
!= ( head_of @ SY195 ) )
| ( SY194
!= ( path_cons @ SY195 @ empty ) ) )
| ~ ! [SY196: $i] :
( ( SV9
!= ( tail_of @ SY196 ) )
| ~ ( edge @ SY196 )
| ! [SY197: $i] :
( ( SY194
!= ( path_cons @ SY196 @ SY197 ) )
| ~ ( path @ ( head_of @ SY196 ) @ SV21 @ SY197 ) ) ) )
| ( path @ SV9 @ SV21 @ SY194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(124,plain,
! [SV10: $i] :
( ( ( ! [SY135: $i,SY136: $i] :
~ ( path @ SY135 @ SY136 @ SV10 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY137: $i] :
( ! [SY138: $i] :
~ ( precedes @ SY137 @ SY138 @ SV10 )
| ( on_path @ SY137 @ SV10 ) )
| ~ ! [SY139: $i,SY140: $i] :
( ~ ( precedes @ SY139 @ SY140 @ SV10 )
| ( on_path @ SY140 @ SV10 ) ) )
| ~ ~ ( ~ ! [SY141: $i,SY142: $i] :
( ~ ( precedes @ SY141 @ SY142 @ SV10 )
| ! [SY143: $i] :
( ~ ( precedes @ SY143 @ SY142 @ SV10 )
| ~ ( sequential @ SY141 @ SY143 ) )
| ~ ( sequential @ SY141 @ SY142 ) )
| ~ ! [SY144: $i,SY145: $i] :
( ~ ( precedes @ SY144 @ SY145 @ SV10 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY145 @ SY144 @ SV10 ) @ SY145 @ SV10 )
| ~ ( sequential @ SY144 @ ( sK9_E3 @ SY145 @ SY144 @ SV10 ) ) )
| ( sequential @ SY144 @ SY145 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(125,plain,
! [SV11: $i] :
( ( ~ ! [SY146: $i,SY147: $i] :
( ~ ( edge @ SV11 )
| ~ ( edge @ SY146 )
| ~ ( edge @ SY147 )
| ~ ( sequential @ SV11 @ SY146 )
| ~ ( sequential @ SY146 @ SY147 )
| ~ ( sequential @ SY147 @ SV11 )
| ( triangle @ SV11 @ SY146 @ SY147 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY148: $i,SY149: $i] :
~ ( triangle @ SV11 @ SY148 @ SY149 )
| ( edge @ SV11 ) )
| ~ ! [SY150: $i] :
( ! [SY151: $i] :
~ ( triangle @ SV11 @ SY150 @ SY151 )
| ( edge @ SY150 ) ) )
| ~ ! [SY152: $i,SY153: $i] :
( ~ ( triangle @ SV11 @ SY152 @ SY153 )
| ( edge @ SY153 ) ) )
| ~ ! [SY154: $i] :
( ! [SY155: $i] :
~ ( triangle @ SV11 @ SY154 @ SY155 )
| ( sequential @ SV11 @ SY154 ) ) )
| ~ ! [SY156: $i,SY157: $i] :
( ~ ( triangle @ SV11 @ SY156 @ SY157 )
| ( sequential @ SY156 @ SY157 ) ) )
| ~ ! [SY158: $i,SY159: $i] :
( ~ ( triangle @ SV11 @ SY158 @ SY159 )
| ( sequential @ SY159 @ SV11 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(126,plain,
! [SV22: $i,SV12: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY198: $i,SY199: $i] :
( ~ ( on_path @ SY199 @ SY198 )
| ~ ( path @ SV12 @ SV22 @ SY198 )
| ( edge @ SY199 ) )
| ~ ! [SY200: $i,SY201: $i] :
( ~ ( on_path @ SY201 @ SY200 )
| ~ ( path @ SV12 @ SV22 @ SY200 )
| ( in_path @ ( head_of @ SY201 ) @ SY200 ) ) )
| ~ ! [SY202: $i,SY203: $i] :
( ~ ( on_path @ SY203 @ SY202 )
| ~ ( path @ SV12 @ SV22 @ SY202 )
| ( in_path @ ( tail_of @ SY203 ) @ SY202 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(127,plain,
( ( ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( head_of @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[108]) ).
thf(128,plain,
( ( ~ ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( tail_of @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[108]) ).
thf(129,plain,
! [SV23: $i,SV13: $i] :
( ( ~ ( ~ ! [SY204: $i,SY205: $i] :
( ~ ( in_path @ SY205 @ SY204 )
| ~ ( path @ SV13 @ SV23 @ SY204 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY205 @ SY204 @ SV23 @ SV13 ) @ SY204 )
| ~ ( ( SY205
= ( head_of @ ( sK10_E @ SY205 @ SY204 @ SV23 @ SV13 ) ) )
| ( SY205
= ( tail_of @ ( sK10_E @ SY205 @ SY204 @ SV23 @ SV13 ) ) ) ) ) )
| ~ ! [SY206: $i,SY207: $i] :
( ~ ( in_path @ SY207 @ SY206 )
| ~ ( path @ SV13 @ SV23 @ SY206 )
| ( vertex @ SY207 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(130,plain,
! [SV14: $i] :
( ( ( ! [SY172: $i,SY173: $i] :
~ ( path @ SY172 @ SY173 @ SV14 ) )
= $true )
| ( ( ~ ( ~ ! [SY174: $i,SY175: $i] :
( ~ ( on_path @ SY174 @ SV14 )
| ~ ( on_path @ SY175 @ SV14 )
| ! [SY176: $i] :
( ~ ( precedes @ SY176 @ SY175 @ SV14 )
| ~ ( sequential @ SY174 @ SY176 ) )
| ( precedes @ SY174 @ SY175 @ SV14 ) )
| ~ ! [SY177: $i,SY178: $i] :
( ~ ( on_path @ SY177 @ SV14 )
| ~ ( on_path @ SY178 @ SV14 )
| ~ ( sequential @ SY177 @ SY178 )
| ( precedes @ SY177 @ SY178 @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(131,plain,
! [SV15: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV15 ) @ SV15 )
| ~ ( on_path @ ( sK7_SY91 @ SV15 ) @ SV15 ) )
| ~ ( sequential @ ( sK6_E1 @ SV15 ) @ ( sK7_SY91 @ SV15 ) ) )
| ~ ! [SY179: $i] :
~ ( triangle @ ( sK6_E1 @ SV15 ) @ ( sK7_SY91 @ SV15 ) @ SY179 ) )
| ! [SY180: $i,SY181: $i] :
~ ( path @ SY180 @ SY181 @ SV15 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV15 )
= ( number_of_in @ triangles @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(132,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)],[112]) ).
thf(133,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)],[112]) ).
thf(134,plain,
( ( ~ ~ ( ~ ( precedes @ sK3_SY82 @ sK4_SY86 @ sK5_SY89 )
| ~ ( shortest_path @ sK1_V1 @ sK2_SY77 @ sK5_SY89 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[113]) ).
thf(135,plain,
( ( ~ ! [SX0: $i] :
( ( ( tail_of @ SX0 )
!= ( head_of @ sK4_SY86 ) )
| ~ ( edge @ SX0 )
| ( ( head_of @ SX0 )
!= ( tail_of @ sK3_SY82 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[113]) ).
thf(136,plain,
! [SV16: $i,SV1: $i,SV24: $i] :
( ( ! [SY208: $i] :
( ! [SY209: $i] :
( ~ ( precedes @ SV24 @ SY208 @ SY209 )
| ~ ( shortest_path @ SV1 @ SV16 @ SY209 ) )
| ! [SY210: $i] :
( ( ( tail_of @ SY210 )
!= ( tail_of @ SV24 ) )
| ~ ( edge @ SY210 )
| ( ( head_of @ SY210 )
!= ( head_of @ SY208 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(137,plain,
! [SV2: $i] :
( ( ( edge @ SV2 )
= $false )
| ( ( ( ( head_of @ SV2 )
!= ( tail_of @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(138,plain,
! [SV25: $i,SV17: $i,SV3: $i] :
( ( ~ ( path @ SV3 @ SV17 @ SV25 )
| ( ( length_of @ SV25 )
= ( number_of_in @ edges @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(139,plain,
! [SV26: $i,SV18: $i,SV4: $i] :
( ( ~ ( path @ SV4 @ SV18 @ SV26 )
| ( ( number_of_in @ sequential_pairs @ SV26 )
= ( minus @ ( length_of @ SV26 ) @ n1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(140,plain,
! [SV6: $i] :
( ( ~ ~ ( ~ ( ! [SY107: $i,SY108: $i] :
~ ( path @ SV6 @ SY107 @ SY108 )
| ( vertex @ SV6 ) )
| ~ ! [SY109: $i] :
( ! [SY110: $i] :
~ ( path @ SV6 @ SY109 @ SY110 )
| ( vertex @ SY109 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[119]) ).
thf(141,plain,
! [SV6: $i] :
( ( ~ ! [SY111: $i,SY112: $i] :
( ~ ( path @ SV6 @ SY111 @ SY112 )
| ~ ( ~ ~ ( ( SV6
!= ( tail_of @ ( sK11_E @ SY112 @ SY111 @ SV6 ) ) )
| ~ ( edge @ ( sK11_E @ SY112 @ SY111 @ SV6 ) ) )
| ~ ~ ( ~ ( ( SY111
!= ( head_of @ ( sK11_E @ SY112 @ SY111 @ SV6 ) ) )
| ( SY112
!= ( path_cons @ ( sK11_E @ SY112 @ SY111 @ SV6 ) @ empty ) )
| ! [SY113: $i] :
( ( SY112
!= ( path_cons @ ( sK11_E @ SY112 @ SY111 @ SV6 ) @ SY113 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY112 @ SY111 @ SV6 ) ) @ SY111 @ SY113 ) ) )
| ~ ~ ( ~ ( ( SY111
= ( head_of @ ( sK11_E @ SY112 @ SY111 @ SV6 ) ) )
| ~ ( ( SY112
!= ( path_cons @ ( sK11_E @ SY112 @ SY111 @ SV6 ) @ ( sK13_SY95 @ SY112 @ SY111 @ SV6 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY112 @ SY111 @ SV6 ) ) @ SY111 @ ( sK13_SY95 @ SY112 @ SY111 @ SV6 ) ) ) )
| ~ ( ( SY112
= ( path_cons @ ( sK11_E @ SY112 @ SY111 @ SV6 ) @ empty ) )
| ~ ( ( SY112
!= ( path_cons @ ( sK11_E @ SY112 @ SY111 @ SV6 ) @ ( sK12_SY96 @ SY112 @ SY111 @ SV6 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY112 @ SY111 @ SV6 ) ) @ SY111 @ ( sK12_SY96 @ SY112 @ SY111 @ SV6 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[119]) ).
thf(142,plain,
! [SV27: $i] :
( ( ( ! [SY211: $i] :
( ( SV27 = SY211 )
| ~ ( vertex @ SV27 )
| ~ ( vertex @ SY211 )
| ~ ( ~ ~ ( ~ ( ( SV27
!= ( head_of @ ( sK14_E @ SY211 @ SV27 ) ) )
| ( SY211
!= ( tail_of @ ( sK14_E @ SY211 @ SV27 ) ) )
| ( SY211
!= ( head_of @ ( sK14_E @ SY211 @ SV27 ) ) )
| ( SV27
!= ( tail_of @ ( sK14_E @ SY211 @ SV27 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV27
= ( head_of @ ( sK14_E @ SY211 @ SV27 ) ) )
| ( SY211
= ( head_of @ ( sK14_E @ SY211 @ SV27 ) ) ) )
| ~ ( ( SV27
= ( head_of @ ( sK14_E @ SY211 @ SV27 ) ) )
| ( SV27
= ( tail_of @ ( sK14_E @ SY211 @ SV27 ) ) ) ) )
| ~ ~ ( ~ ( ( SY211
= ( tail_of @ ( sK14_E @ SY211 @ SV27 ) ) )
| ( SY211
= ( head_of @ ( sK14_E @ SY211 @ SV27 ) ) ) )
| ~ ( ( SY211
= ( tail_of @ ( sK14_E @ SY211 @ SV27 ) ) )
| ( SV27
= ( tail_of @ ( sK14_E @ SY211 @ SV27 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SY211 @ SV27 ) ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(143,plain,
! [SV7: $i] :
( ( ~ ! [SY114: $i,SY115: $i] :
( ~ ( ~ ( path @ SV7 @ SY114 @ ( sK8_P @ SY115 @ SY114 @ SV7 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY115 ) @ ( length_of @ ( sK8_P @ SY115 @ SY114 @ SV7 ) ) ) )
| ( SV7 = SY114 )
| ~ ( path @ SV7 @ SY114 @ SY115 )
| ( shortest_path @ SV7 @ SY114 @ SY115 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[121]) ).
thf(144,plain,
! [SV7: $i] :
( ( ~ ~ ( ~ ! [SY116: $i,SY117: $i] :
( ~ ( shortest_path @ SV7 @ SY116 @ SY117 )
| ! [SY118: $i] :
( ~ ( path @ SV7 @ SY116 @ SY118 )
| ( less_or_equal @ ( length_of @ SY117 ) @ ( length_of @ SY118 ) ) ) )
| ~ ~ ( ~ ! [SY119: $i] :
( ! [SY120: $i] :
~ ( shortest_path @ SV7 @ SY119 @ SY120 )
| ( SV7 != SY119 ) )
| ~ ! [SY121: $i,SY122: $i] :
( ~ ( shortest_path @ SV7 @ SY121 @ SY122 )
| ( path @ SV7 @ SY121 @ SY122 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[121]) ).
thf(145,plain,
! [SV20: $i,SV8: $i,SV28: $i] :
( ( ~ ( ~ ! [SY212: $i] :
( ! [SY213: $i] :
( ~ ( precedes @ SV28 @ SY212 @ SY213 )
| ~ ( shortest_path @ SV8 @ SV20 @ SY213 ) )
| ! [SY214: $i] :
( ( ( tail_of @ SY214 )
!= ( tail_of @ SV28 ) )
| ( ( head_of @ SY214 )
!= ( head_of @ SY212 ) ) ) )
| ~ ! [SY215: $i,SY216: $i] :
( ~ ( precedes @ SV28 @ SY215 @ SY216 )
| ~ ( shortest_path @ SV8 @ SV20 @ SY216 )
| ~ ( precedes @ SY215 @ SV28 @ SY216 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(146,plain,
! [SV29: $i,SV21: $i,SV9: $i] :
( ( ~ ( vertex @ SV9 )
| ~ ( vertex @ SV21 )
| ~ ( ~ ! [SY217: $i] :
( ( SV9
!= ( tail_of @ SY217 ) )
| ~ ( edge @ SY217 )
| ( SV21
!= ( head_of @ SY217 ) )
| ( SV29
!= ( path_cons @ SY217 @ empty ) ) )
| ~ ! [SY218: $i] :
( ( SV9
!= ( tail_of @ SY218 ) )
| ~ ( edge @ SY218 )
| ! [SY219: $i] :
( ( SV29
!= ( path_cons @ SY218 @ SY219 ) )
| ~ ( path @ ( head_of @ SY218 ) @ SV21 @ SY219 ) ) ) )
| ( path @ SV9 @ SV21 @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(147,plain,
! [SV10: $i,SV30: $i] :
( ( ( ! [SY220: $i] :
~ ( path @ SV30 @ SY220 @ SV10 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY137: $i] :
( ! [SY138: $i] :
~ ( precedes @ SY137 @ SY138 @ SV10 )
| ( on_path @ SY137 @ SV10 ) )
| ~ ! [SY139: $i,SY140: $i] :
( ~ ( precedes @ SY139 @ SY140 @ SV10 )
| ( on_path @ SY140 @ SV10 ) ) )
| ~ ~ ( ~ ! [SY141: $i,SY142: $i] :
( ~ ( precedes @ SY141 @ SY142 @ SV10 )
| ! [SY143: $i] :
( ~ ( precedes @ SY143 @ SY142 @ SV10 )
| ~ ( sequential @ SY141 @ SY143 ) )
| ~ ( sequential @ SY141 @ SY142 ) )
| ~ ! [SY144: $i,SY145: $i] :
( ~ ( precedes @ SY144 @ SY145 @ SV10 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY145 @ SY144 @ SV10 ) @ SY145 @ SV10 )
| ~ ( sequential @ SY144 @ ( sK9_E3 @ SY145 @ SY144 @ SV10 ) ) )
| ( sequential @ SY144 @ SY145 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(148,plain,
! [SV11: $i] :
( ( ~ ! [SY146: $i,SY147: $i] :
( ~ ( edge @ SV11 )
| ~ ( edge @ SY146 )
| ~ ( edge @ SY147 )
| ~ ( sequential @ SV11 @ SY146 )
| ~ ( sequential @ SY146 @ SY147 )
| ~ ( sequential @ SY147 @ SV11 )
| ( triangle @ SV11 @ SY146 @ SY147 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[125]) ).
thf(149,plain,
! [SV11: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY148: $i,SY149: $i] :
~ ( triangle @ SV11 @ SY148 @ SY149 )
| ( edge @ SV11 ) )
| ~ ! [SY150: $i] :
( ! [SY151: $i] :
~ ( triangle @ SV11 @ SY150 @ SY151 )
| ( edge @ SY150 ) ) )
| ~ ! [SY152: $i,SY153: $i] :
( ~ ( triangle @ SV11 @ SY152 @ SY153 )
| ( edge @ SY153 ) ) )
| ~ ! [SY154: $i] :
( ! [SY155: $i] :
~ ( triangle @ SV11 @ SY154 @ SY155 )
| ( sequential @ SV11 @ SY154 ) ) )
| ~ ! [SY156: $i,SY157: $i] :
( ~ ( triangle @ SV11 @ SY156 @ SY157 )
| ( sequential @ SY156 @ SY157 ) ) )
| ~ ! [SY158: $i,SY159: $i] :
( ~ ( triangle @ SV11 @ SY158 @ SY159 )
| ( sequential @ SY159 @ SV11 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[125]) ).
thf(150,plain,
! [SV22: $i,SV12: $i] :
( ( ~ ~ ( ~ ! [SY198: $i,SY199: $i] :
( ~ ( on_path @ SY199 @ SY198 )
| ~ ( path @ SV12 @ SV22 @ SY198 )
| ( edge @ SY199 ) )
| ~ ! [SY200: $i,SY201: $i] :
( ~ ( on_path @ SY201 @ SY200 )
| ~ ( path @ SV12 @ SV22 @ SY200 )
| ( in_path @ ( head_of @ SY201 ) @ SY200 ) ) )
| ~ ! [SY202: $i,SY203: $i] :
( ~ ( on_path @ SY203 @ SY202 )
| ~ ( path @ SV12 @ SV22 @ SY202 )
| ( in_path @ ( tail_of @ SY203 ) @ SY202 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(151,plain,
( ( ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( head_of @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(152,plain,
( ( ! [SX0: $i] :
( ~ ( edge @ SX0 )
| ( vertex @ ( tail_of @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[128]) ).
thf(153,plain,
! [SV23: $i,SV13: $i] :
( ( ~ ! [SY204: $i,SY205: $i] :
( ~ ( in_path @ SY205 @ SY204 )
| ~ ( path @ SV13 @ SV23 @ SY204 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY205 @ SY204 @ SV23 @ SV13 ) @ SY204 )
| ~ ( ( SY205
= ( head_of @ ( sK10_E @ SY205 @ SY204 @ SV23 @ SV13 ) ) )
| ( SY205
= ( tail_of @ ( sK10_E @ SY205 @ SY204 @ SV23 @ SV13 ) ) ) ) ) )
| ~ ! [SY206: $i,SY207: $i] :
( ~ ( in_path @ SY207 @ SY206 )
| ~ ( path @ SV13 @ SV23 @ SY206 )
| ( vertex @ SY207 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(154,plain,
! [SV14: $i,SV31: $i] :
( ( ( ! [SY221: $i] :
~ ( path @ SV31 @ SY221 @ SV14 ) )
= $true )
| ( ( ~ ( ~ ! [SY174: $i,SY175: $i] :
( ~ ( on_path @ SY174 @ SV14 )
| ~ ( on_path @ SY175 @ SV14 )
| ! [SY176: $i] :
( ~ ( precedes @ SY176 @ SY175 @ SV14 )
| ~ ( sequential @ SY174 @ SY176 ) )
| ( precedes @ SY174 @ SY175 @ SV14 ) )
| ~ ! [SY177: $i,SY178: $i] :
( ~ ( on_path @ SY177 @ SV14 )
| ~ ( on_path @ SY178 @ SV14 )
| ~ ( sequential @ SY177 @ SY178 )
| ( precedes @ SY177 @ SY178 @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(155,plain,
! [SV15: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV15 ) @ SV15 )
| ~ ( on_path @ ( sK7_SY91 @ SV15 ) @ SV15 ) )
| ~ ( sequential @ ( sK6_E1 @ SV15 ) @ ( sK7_SY91 @ SV15 ) ) )
| ~ ! [SY179: $i] :
~ ( triangle @ ( sK6_E1 @ SV15 ) @ ( sK7_SY91 @ SV15 ) @ SY179 ) ) )
= $true )
| ( ( ! [SY180: $i,SY181: $i] :
~ ( path @ SY180 @ SY181 @ SV15 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV15 )
= ( number_of_in @ triangles @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(156,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)],[132]) ).
thf(157,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)],[133]) ).
thf(158,plain,
( ( ~ ( ~ ( precedes @ sK3_SY82 @ sK4_SY86 @ sK5_SY89 )
| ~ ( shortest_path @ sK1_V1 @ sK2_SY77 @ sK5_SY89 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[134]) ).
thf(159,plain,
( ( ! [SX0: $i] :
( ( ( tail_of @ SX0 )
!= ( head_of @ sK4_SY86 ) )
| ~ ( edge @ SX0 )
| ( ( head_of @ SX0 )
!= ( tail_of @ sK3_SY82 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(160,plain,
! [SV16: $i,SV1: $i,SV32: $i,SV24: $i] :
( ( ! [SY222: $i] :
( ~ ( precedes @ SV24 @ SV32 @ SY222 )
| ~ ( shortest_path @ SV1 @ SV16 @ SY222 ) )
| ! [SY223: $i] :
( ( ( tail_of @ SY223 )
!= ( tail_of @ SV24 ) )
| ~ ( edge @ SY223 )
| ( ( head_of @ SY223 )
!= ( head_of @ SV32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(161,plain,
! [SV2: $i] :
( ( ( ( head_of @ SV2 )
= ( tail_of @ SV2 ) )
= $false )
| ( ( edge @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(162,plain,
! [SV25: $i,SV17: $i,SV3: $i] :
( ( ( ~ ( path @ SV3 @ SV17 @ SV25 ) )
= $true )
| ( ( ( length_of @ SV25 )
= ( number_of_in @ edges @ SV25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(163,plain,
! [SV26: $i,SV18: $i,SV4: $i] :
( ( ( ~ ( path @ SV4 @ SV18 @ SV26 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV26 )
= ( minus @ ( length_of @ SV26 ) @ n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(164,plain,
! [SV6: $i] :
( ( ~ ( ~ ( ! [SY107: $i,SY108: $i] :
~ ( path @ SV6 @ SY107 @ SY108 )
| ( vertex @ SV6 ) )
| ~ ! [SY109: $i] :
( ! [SY110: $i] :
~ ( path @ SV6 @ SY109 @ SY110 )
| ( vertex @ SY109 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[140]) ).
thf(165,plain,
! [SV6: $i] :
( ( ! [SY111: $i,SY112: $i] :
( ~ ( path @ SV6 @ SY111 @ SY112 )
| ~ ( ~ ~ ( ( SV6
!= ( tail_of @ ( sK11_E @ SY112 @ SY111 @ SV6 ) ) )
| ~ ( edge @ ( sK11_E @ SY112 @ SY111 @ SV6 ) ) )
| ~ ~ ( ~ ( ( SY111
!= ( head_of @ ( sK11_E @ SY112 @ SY111 @ SV6 ) ) )
| ( SY112
!= ( path_cons @ ( sK11_E @ SY112 @ SY111 @ SV6 ) @ empty ) )
| ! [SY113: $i] :
( ( SY112
!= ( path_cons @ ( sK11_E @ SY112 @ SY111 @ SV6 ) @ SY113 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY112 @ SY111 @ SV6 ) ) @ SY111 @ SY113 ) ) )
| ~ ~ ( ~ ( ( SY111
= ( head_of @ ( sK11_E @ SY112 @ SY111 @ SV6 ) ) )
| ~ ( ( SY112
!= ( path_cons @ ( sK11_E @ SY112 @ SY111 @ SV6 ) @ ( sK13_SY95 @ SY112 @ SY111 @ SV6 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY112 @ SY111 @ SV6 ) ) @ SY111 @ ( sK13_SY95 @ SY112 @ SY111 @ SV6 ) ) ) )
| ~ ( ( SY112
= ( path_cons @ ( sK11_E @ SY112 @ SY111 @ SV6 ) @ empty ) )
| ~ ( ( SY112
!= ( path_cons @ ( sK11_E @ SY112 @ SY111 @ SV6 ) @ ( sK12_SY96 @ SY112 @ SY111 @ SV6 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY112 @ SY111 @ SV6 ) ) @ SY111 @ ( sK12_SY96 @ SY112 @ SY111 @ SV6 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(166,plain,
! [SV33: $i,SV27: $i] :
( ( ( ( SV27 = SV33 )
| ~ ( vertex @ SV27 )
| ~ ( vertex @ SV33 )
| ~ ( ~ ~ ( ~ ( ( SV27
!= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
!= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
!= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
!= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV27
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
| ~ ( ( SV27
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) ) )
| ~ ~ ( ~ ( ( SV33
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
| ~ ( ( SV33
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV33 @ SV27 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(167,plain,
! [SV7: $i] :
( ( ! [SY114: $i,SY115: $i] :
( ~ ( ~ ( path @ SV7 @ SY114 @ ( sK8_P @ SY115 @ SY114 @ SV7 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY115 ) @ ( length_of @ ( sK8_P @ SY115 @ SY114 @ SV7 ) ) ) )
| ( SV7 = SY114 )
| ~ ( path @ SV7 @ SY114 @ SY115 )
| ( shortest_path @ SV7 @ SY114 @ SY115 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[143]) ).
thf(168,plain,
! [SV7: $i] :
( ( ~ ( ~ ! [SY116: $i,SY117: $i] :
( ~ ( shortest_path @ SV7 @ SY116 @ SY117 )
| ! [SY118: $i] :
( ~ ( path @ SV7 @ SY116 @ SY118 )
| ( less_or_equal @ ( length_of @ SY117 ) @ ( length_of @ SY118 ) ) ) )
| ~ ~ ( ~ ! [SY119: $i] :
( ! [SY120: $i] :
~ ( shortest_path @ SV7 @ SY119 @ SY120 )
| ( SV7 != SY119 ) )
| ~ ! [SY121: $i,SY122: $i] :
( ~ ( shortest_path @ SV7 @ SY121 @ SY122 )
| ( path @ SV7 @ SY121 @ SY122 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[144]) ).
thf(169,plain,
! [SV20: $i,SV8: $i,SV28: $i] :
( ( ~ ! [SY212: $i] :
( ! [SY213: $i] :
( ~ ( precedes @ SV28 @ SY212 @ SY213 )
| ~ ( shortest_path @ SV8 @ SV20 @ SY213 ) )
| ! [SY214: $i] :
( ( ( tail_of @ SY214 )
!= ( tail_of @ SV28 ) )
| ( ( head_of @ SY214 )
!= ( head_of @ SY212 ) ) ) )
| ~ ! [SY215: $i,SY216: $i] :
( ~ ( precedes @ SV28 @ SY215 @ SY216 )
| ~ ( shortest_path @ SV8 @ SV20 @ SY216 )
| ~ ( precedes @ SY215 @ SV28 @ SY216 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(170,plain,
! [SV29: $i,SV21: $i,SV9: $i] :
( ( ( ~ ( vertex @ SV9 )
| ~ ( vertex @ SV21 )
| ~ ( ~ ! [SY217: $i] :
( ( SV9
!= ( tail_of @ SY217 ) )
| ~ ( edge @ SY217 )
| ( SV21
!= ( head_of @ SY217 ) )
| ( SV29
!= ( path_cons @ SY217 @ empty ) ) )
| ~ ! [SY218: $i] :
( ( SV9
!= ( tail_of @ SY218 ) )
| ~ ( edge @ SY218 )
| ! [SY219: $i] :
( ( SV29
!= ( path_cons @ SY218 @ SY219 ) )
| ~ ( path @ ( head_of @ SY218 ) @ SV21 @ SY219 ) ) ) ) )
= $true )
| ( ( path @ SV9 @ SV21 @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(171,plain,
! [SV10: $i,SV34: $i,SV30: $i] :
( ( ( ~ ( path @ SV30 @ SV34 @ SV10 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY137: $i] :
( ! [SY138: $i] :
~ ( precedes @ SY137 @ SY138 @ SV10 )
| ( on_path @ SY137 @ SV10 ) )
| ~ ! [SY139: $i,SY140: $i] :
( ~ ( precedes @ SY139 @ SY140 @ SV10 )
| ( on_path @ SY140 @ SV10 ) ) )
| ~ ~ ( ~ ! [SY141: $i,SY142: $i] :
( ~ ( precedes @ SY141 @ SY142 @ SV10 )
| ! [SY143: $i] :
( ~ ( precedes @ SY143 @ SY142 @ SV10 )
| ~ ( sequential @ SY141 @ SY143 ) )
| ~ ( sequential @ SY141 @ SY142 ) )
| ~ ! [SY144: $i,SY145: $i] :
( ~ ( precedes @ SY144 @ SY145 @ SV10 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY145 @ SY144 @ SV10 ) @ SY145 @ SV10 )
| ~ ( sequential @ SY144 @ ( sK9_E3 @ SY145 @ SY144 @ SV10 ) ) )
| ( sequential @ SY144 @ SY145 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(172,plain,
! [SV11: $i] :
( ( ! [SY146: $i,SY147: $i] :
( ~ ( edge @ SV11 )
| ~ ( edge @ SY146 )
| ~ ( edge @ SY147 )
| ~ ( sequential @ SV11 @ SY146 )
| ~ ( sequential @ SY146 @ SY147 )
| ~ ( sequential @ SY147 @ SV11 )
| ( triangle @ SV11 @ SY146 @ SY147 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[148]) ).
thf(173,plain,
! [SV11: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY148: $i,SY149: $i] :
~ ( triangle @ SV11 @ SY148 @ SY149 )
| ( edge @ SV11 ) )
| ~ ! [SY150: $i] :
( ! [SY151: $i] :
~ ( triangle @ SV11 @ SY150 @ SY151 )
| ( edge @ SY150 ) ) )
| ~ ! [SY152: $i,SY153: $i] :
( ~ ( triangle @ SV11 @ SY152 @ SY153 )
| ( edge @ SY153 ) ) )
| ~ ! [SY154: $i] :
( ! [SY155: $i] :
~ ( triangle @ SV11 @ SY154 @ SY155 )
| ( sequential @ SV11 @ SY154 ) ) )
| ~ ! [SY156: $i,SY157: $i] :
( ~ ( triangle @ SV11 @ SY156 @ SY157 )
| ( sequential @ SY156 @ SY157 ) ) )
| ~ ! [SY158: $i,SY159: $i] :
( ~ ( triangle @ SV11 @ SY158 @ SY159 )
| ( sequential @ SY159 @ SV11 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(174,plain,
! [SV22: $i,SV12: $i] :
( ( ~ ~ ( ~ ! [SY198: $i,SY199: $i] :
( ~ ( on_path @ SY199 @ SY198 )
| ~ ( path @ SV12 @ SV22 @ SY198 )
| ( edge @ SY199 ) )
| ~ ! [SY200: $i,SY201: $i] :
( ~ ( on_path @ SY201 @ SY200 )
| ~ ( path @ SV12 @ SV22 @ SY200 )
| ( in_path @ ( head_of @ SY201 ) @ SY200 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[150]) ).
thf(175,plain,
! [SV22: $i,SV12: $i] :
( ( ~ ! [SY202: $i,SY203: $i] :
( ~ ( on_path @ SY203 @ SY202 )
| ~ ( path @ SV12 @ SV22 @ SY202 )
| ( in_path @ ( tail_of @ SY203 ) @ SY202 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[150]) ).
thf(176,plain,
! [SV35: $i] :
( ( ~ ( edge @ SV35 )
| ( vertex @ ( head_of @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(177,plain,
! [SV36: $i] :
( ( ~ ( edge @ SV36 )
| ( vertex @ ( tail_of @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(178,plain,
! [SV23: $i,SV13: $i] :
( ( ~ ! [SY204: $i,SY205: $i] :
( ~ ( in_path @ SY205 @ SY204 )
| ~ ( path @ SV13 @ SV23 @ SY204 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY205 @ SY204 @ SV23 @ SV13 ) @ SY204 )
| ~ ( ( SY205
= ( head_of @ ( sK10_E @ SY205 @ SY204 @ SV23 @ SV13 ) ) )
| ( SY205
= ( tail_of @ ( sK10_E @ SY205 @ SY204 @ SV23 @ SV13 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[153]) ).
thf(179,plain,
! [SV23: $i,SV13: $i] :
( ( ~ ! [SY206: $i,SY207: $i] :
( ~ ( in_path @ SY207 @ SY206 )
| ~ ( path @ SV13 @ SV23 @ SY206 )
| ( vertex @ SY207 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[153]) ).
thf(180,plain,
! [SV14: $i,SV37: $i,SV31: $i] :
( ( ( ~ ( path @ SV31 @ SV37 @ SV14 ) )
= $true )
| ( ( ~ ( ~ ! [SY174: $i,SY175: $i] :
( ~ ( on_path @ SY174 @ SV14 )
| ~ ( on_path @ SY175 @ SV14 )
| ! [SY176: $i] :
( ~ ( precedes @ SY176 @ SY175 @ SV14 )
| ~ ( sequential @ SY174 @ SY176 ) )
| ( precedes @ SY174 @ SY175 @ SV14 ) )
| ~ ! [SY177: $i,SY178: $i] :
( ~ ( on_path @ SY177 @ SV14 )
| ~ ( on_path @ SY178 @ SV14 )
| ~ ( sequential @ SY177 @ SY178 )
| ( precedes @ SY177 @ SY178 @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(181,plain,
! [SV15: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV15 ) @ SV15 )
| ~ ( on_path @ ( sK7_SY91 @ SV15 ) @ SV15 ) )
| ~ ( sequential @ ( sK6_E1 @ SV15 ) @ ( sK7_SY91 @ SV15 ) ) )
| ~ ! [SY179: $i] :
~ ( triangle @ ( sK6_E1 @ SV15 ) @ ( sK7_SY91 @ SV15 ) @ SY179 ) )
= $false )
| ( ( ! [SY180: $i,SY181: $i] :
~ ( path @ SY180 @ SY181 @ SV15 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV15 )
= ( number_of_in @ triangles @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(182,plain,
! [SV38: $i] :
( ( ! [SY224: $i] :
( ( SV38 = SY224 )
| ~ ( edge @ SV38 )
| ~ ( edge @ SY224 )
| ( ( head_of @ SV38 )
!= ( tail_of @ SY224 ) )
| ( sequential @ SV38 @ SY224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(183,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)],[157]) ).
thf(184,plain,
( ( ~ ( precedes @ sK3_SY82 @ sK4_SY86 @ sK5_SY89 )
| ~ ( shortest_path @ sK1_V1 @ sK2_SY77 @ sK5_SY89 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(185,plain,
! [SV39: $i] :
( ( ( ( tail_of @ SV39 )
!= ( head_of @ sK4_SY86 ) )
| ~ ( edge @ SV39 )
| ( ( head_of @ SV39 )
!= ( tail_of @ sK3_SY82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(186,plain,
! [SV16: $i,SV1: $i,SV32: $i,SV24: $i] :
( ( ( ! [SY222: $i] :
( ~ ( precedes @ SV24 @ SV32 @ SY222 )
| ~ ( shortest_path @ SV1 @ SV16 @ SY222 ) ) )
= $true )
| ( ( ! [SY223: $i] :
( ( ( tail_of @ SY223 )
!= ( tail_of @ SV24 ) )
| ~ ( edge @ SY223 )
| ( ( head_of @ SY223 )
!= ( head_of @ SV32 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[160]) ).
thf(187,plain,
! [SV25: $i,SV17: $i,SV3: $i] :
( ( ( path @ SV3 @ SV17 @ SV25 )
= $false )
| ( ( ( length_of @ SV25 )
= ( number_of_in @ edges @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(188,plain,
! [SV26: $i,SV18: $i,SV4: $i] :
( ( ( path @ SV4 @ SV18 @ SV26 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV26 )
= ( minus @ ( length_of @ SV26 ) @ n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(189,plain,
! [SV6: $i] :
( ( ~ ( ! [SY107: $i,SY108: $i] :
~ ( path @ SV6 @ SY107 @ SY108 )
| ( vertex @ SV6 ) )
| ~ ! [SY109: $i] :
( ! [SY110: $i] :
~ ( path @ SV6 @ SY109 @ SY110 )
| ( vertex @ SY109 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(190,plain,
! [SV40: $i,SV6: $i] :
( ( ! [SY225: $i] :
( ~ ( path @ SV6 @ SV40 @ SY225 )
| ~ ( ~ ~ ( ( SV6
!= ( tail_of @ ( sK11_E @ SY225 @ SV40 @ SV6 ) ) )
| ~ ( edge @ ( sK11_E @ SY225 @ SV40 @ SV6 ) ) )
| ~ ~ ( ~ ( ( SV40
!= ( head_of @ ( sK11_E @ SY225 @ SV40 @ SV6 ) ) )
| ( SY225
!= ( path_cons @ ( sK11_E @ SY225 @ SV40 @ SV6 ) @ empty ) )
| ! [SY226: $i] :
( ( SY225
!= ( path_cons @ ( sK11_E @ SY225 @ SV40 @ SV6 ) @ SY226 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY225 @ SV40 @ SV6 ) ) @ SV40 @ SY226 ) ) )
| ~ ~ ( ~ ( ( SV40
= ( head_of @ ( sK11_E @ SY225 @ SV40 @ SV6 ) ) )
| ~ ( ( SY225
!= ( path_cons @ ( sK11_E @ SY225 @ SV40 @ SV6 ) @ ( sK13_SY95 @ SY225 @ SV40 @ SV6 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY225 @ SV40 @ SV6 ) ) @ SV40 @ ( sK13_SY95 @ SY225 @ SV40 @ SV6 ) ) ) )
| ~ ( ( SY225
= ( path_cons @ ( sK11_E @ SY225 @ SV40 @ SV6 ) @ empty ) )
| ~ ( ( SY225
!= ( path_cons @ ( sK11_E @ SY225 @ SV40 @ SV6 ) @ ( sK12_SY96 @ SY225 @ SV40 @ SV6 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SY225 @ SV40 @ SV6 ) ) @ SV40 @ ( sK12_SY96 @ SY225 @ SV40 @ SV6 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(191,plain,
! [SV33: $i,SV27: $i] :
( ( ( ( SV27 = SV33 )
| ~ ( vertex @ SV27 )
| ~ ( vertex @ SV33 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV27
!= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
!= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
!= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
!= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV27
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
| ~ ( ( SV27
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) ) )
| ~ ~ ( ~ ( ( SV33
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
| ~ ( ( SV33
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV33 @ SV27 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(192,plain,
! [SV41: $i,SV7: $i] :
( ( ! [SY227: $i] :
( ~ ( ~ ( path @ SV7 @ SV41 @ ( sK8_P @ SY227 @ SV41 @ SV7 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SY227 ) @ ( length_of @ ( sK8_P @ SY227 @ SV41 @ SV7 ) ) ) )
| ( SV7 = SV41 )
| ~ ( path @ SV7 @ SV41 @ SY227 )
| ( shortest_path @ SV7 @ SV41 @ SY227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(193,plain,
! [SV7: $i] :
( ( ~ ! [SY116: $i,SY117: $i] :
( ~ ( shortest_path @ SV7 @ SY116 @ SY117 )
| ! [SY118: $i] :
( ~ ( path @ SV7 @ SY116 @ SY118 )
| ( less_or_equal @ ( length_of @ SY117 ) @ ( length_of @ SY118 ) ) ) )
| ~ ~ ( ~ ! [SY119: $i] :
( ! [SY120: $i] :
~ ( shortest_path @ SV7 @ SY119 @ SY120 )
| ( SV7 != SY119 ) )
| ~ ! [SY121: $i,SY122: $i] :
( ~ ( shortest_path @ SV7 @ SY121 @ SY122 )
| ( path @ SV7 @ SY121 @ SY122 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(194,plain,
! [SV20: $i,SV8: $i,SV28: $i] :
( ( ~ ! [SY212: $i] :
( ! [SY213: $i] :
( ~ ( precedes @ SV28 @ SY212 @ SY213 )
| ~ ( shortest_path @ SV8 @ SV20 @ SY213 ) )
| ! [SY214: $i] :
( ( ( tail_of @ SY214 )
!= ( tail_of @ SV28 ) )
| ( ( head_of @ SY214 )
!= ( head_of @ SY212 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[169]) ).
thf(195,plain,
! [SV20: $i,SV8: $i,SV28: $i] :
( ( ~ ! [SY215: $i,SY216: $i] :
( ~ ( precedes @ SV28 @ SY215 @ SY216 )
| ~ ( shortest_path @ SV8 @ SV20 @ SY216 )
| ~ ( precedes @ SY215 @ SV28 @ SY216 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[169]) ).
thf(196,plain,
! [SV29: $i,SV21: $i,SV9: $i] :
( ( ( ~ ( vertex @ SV9 )
| ~ ( vertex @ SV21 ) )
= $true )
| ( ( ~ ( ~ ! [SY217: $i] :
( ( SV9
!= ( tail_of @ SY217 ) )
| ~ ( edge @ SY217 )
| ( SV21
!= ( head_of @ SY217 ) )
| ( SV29
!= ( path_cons @ SY217 @ empty ) ) )
| ~ ! [SY218: $i] :
( ( SV9
!= ( tail_of @ SY218 ) )
| ~ ( edge @ SY218 )
| ! [SY219: $i] :
( ( SV29
!= ( path_cons @ SY218 @ SY219 ) )
| ~ ( path @ ( head_of @ SY218 ) @ SV21 @ SY219 ) ) ) ) )
= $true )
| ( ( path @ SV9 @ SV21 @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(197,plain,
! [SV10: $i,SV34: $i,SV30: $i] :
( ( ( path @ SV30 @ SV34 @ SV10 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY137: $i] :
( ! [SY138: $i] :
~ ( precedes @ SY137 @ SY138 @ SV10 )
| ( on_path @ SY137 @ SV10 ) )
| ~ ! [SY139: $i,SY140: $i] :
( ~ ( precedes @ SY139 @ SY140 @ SV10 )
| ( on_path @ SY140 @ SV10 ) ) )
| ~ ~ ( ~ ! [SY141: $i,SY142: $i] :
( ~ ( precedes @ SY141 @ SY142 @ SV10 )
| ! [SY143: $i] :
( ~ ( precedes @ SY143 @ SY142 @ SV10 )
| ~ ( sequential @ SY141 @ SY143 ) )
| ~ ( sequential @ SY141 @ SY142 ) )
| ~ ! [SY144: $i,SY145: $i] :
( ~ ( precedes @ SY144 @ SY145 @ SV10 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY145 @ SY144 @ SV10 ) @ SY145 @ SV10 )
| ~ ( sequential @ SY144 @ ( sK9_E3 @ SY145 @ SY144 @ SV10 ) ) )
| ( sequential @ SY144 @ SY145 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(198,plain,
! [SV42: $i,SV11: $i] :
( ( ! [SY228: $i] :
( ~ ( edge @ SV11 )
| ~ ( edge @ SV42 )
| ~ ( edge @ SY228 )
| ~ ( sequential @ SV11 @ SV42 )
| ~ ( sequential @ SV42 @ SY228 )
| ~ ( sequential @ SY228 @ SV11 )
| ( triangle @ SV11 @ SV42 @ SY228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(199,plain,
! [SV11: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY148: $i,SY149: $i] :
~ ( triangle @ SV11 @ SY148 @ SY149 )
| ( edge @ SV11 ) )
| ~ ! [SY150: $i] :
( ! [SY151: $i] :
~ ( triangle @ SV11 @ SY150 @ SY151 )
| ( edge @ SY150 ) ) )
| ~ ! [SY152: $i,SY153: $i] :
( ~ ( triangle @ SV11 @ SY152 @ SY153 )
| ( edge @ SY153 ) ) )
| ~ ! [SY154: $i] :
( ! [SY155: $i] :
~ ( triangle @ SV11 @ SY154 @ SY155 )
| ( sequential @ SV11 @ SY154 ) ) )
| ~ ! [SY156: $i,SY157: $i] :
( ~ ( triangle @ SV11 @ SY156 @ SY157 )
| ( sequential @ SY156 @ SY157 ) ) )
| ~ ! [SY158: $i,SY159: $i] :
( ~ ( triangle @ SV11 @ SY158 @ SY159 )
| ( sequential @ SY159 @ SV11 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(200,plain,
! [SV22: $i,SV12: $i] :
( ( ~ ( ~ ! [SY198: $i,SY199: $i] :
( ~ ( on_path @ SY199 @ SY198 )
| ~ ( path @ SV12 @ SV22 @ SY198 )
| ( edge @ SY199 ) )
| ~ ! [SY200: $i,SY201: $i] :
( ~ ( on_path @ SY201 @ SY200 )
| ~ ( path @ SV12 @ SV22 @ SY200 )
| ( in_path @ ( head_of @ SY201 ) @ SY200 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[174]) ).
thf(201,plain,
! [SV22: $i,SV12: $i] :
( ( ! [SY202: $i,SY203: $i] :
( ~ ( on_path @ SY203 @ SY202 )
| ~ ( path @ SV12 @ SV22 @ SY202 )
| ( in_path @ ( tail_of @ SY203 ) @ SY202 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[175]) ).
thf(202,plain,
! [SV35: $i] :
( ( ( ~ ( edge @ SV35 ) )
= $true )
| ( ( vertex @ ( head_of @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(203,plain,
! [SV36: $i] :
( ( ( ~ ( edge @ SV36 ) )
= $true )
| ( ( vertex @ ( tail_of @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(204,plain,
! [SV23: $i,SV13: $i] :
( ( ! [SY204: $i,SY205: $i] :
( ~ ( in_path @ SY205 @ SY204 )
| ~ ( path @ SV13 @ SV23 @ SY204 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY205 @ SY204 @ SV23 @ SV13 ) @ SY204 )
| ~ ( ( SY205
= ( head_of @ ( sK10_E @ SY205 @ SY204 @ SV23 @ SV13 ) ) )
| ( SY205
= ( tail_of @ ( sK10_E @ SY205 @ SY204 @ SV23 @ SV13 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[178]) ).
thf(205,plain,
! [SV23: $i,SV13: $i] :
( ( ! [SY206: $i,SY207: $i] :
( ~ ( in_path @ SY207 @ SY206 )
| ~ ( path @ SV13 @ SV23 @ SY206 )
| ( vertex @ SY207 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[179]) ).
thf(206,plain,
! [SV14: $i,SV37: $i,SV31: $i] :
( ( ( path @ SV31 @ SV37 @ SV14 )
= $false )
| ( ( ~ ( ~ ! [SY174: $i,SY175: $i] :
( ~ ( on_path @ SY174 @ SV14 )
| ~ ( on_path @ SY175 @ SV14 )
| ! [SY176: $i] :
( ~ ( precedes @ SY176 @ SY175 @ SV14 )
| ~ ( sequential @ SY174 @ SY176 ) )
| ( precedes @ SY174 @ SY175 @ SV14 ) )
| ~ ! [SY177: $i,SY178: $i] :
( ~ ( on_path @ SY177 @ SV14 )
| ~ ( on_path @ SY178 @ SV14 )
| ~ ( sequential @ SY177 @ SY178 )
| ( precedes @ SY177 @ SY178 @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(207,plain,
! [SV15: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV15 ) @ SV15 )
| ~ ( on_path @ ( sK7_SY91 @ SV15 ) @ SV15 ) )
| ~ ( sequential @ ( sK6_E1 @ SV15 ) @ ( sK7_SY91 @ SV15 ) ) ) )
= $false )
| ( ( ! [SY180: $i,SY181: $i] :
~ ( path @ SY180 @ SY181 @ SV15 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV15 )
= ( number_of_in @ triangles @ SV15 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[181]) ).
thf(208,plain,
! [SV15: $i] :
( ( ( ~ ! [SY179: $i] :
~ ( triangle @ ( sK6_E1 @ SV15 ) @ ( sK7_SY91 @ SV15 ) @ SY179 ) )
= $false )
| ( ( ! [SY180: $i,SY181: $i] :
~ ( path @ SY180 @ SY181 @ SV15 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV15 )
= ( number_of_in @ triangles @ SV15 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[181]) ).
thf(209,plain,
! [SV43: $i,SV38: $i] :
( ( ( SV38 = SV43 )
| ~ ( edge @ SV38 )
| ~ ( edge @ SV43 )
| ( ( head_of @ SV38 )
!= ( tail_of @ SV43 ) )
| ( sequential @ SV38 @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(210,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)],[183]) ).
thf(211,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(212,plain,
( ( ~ ( precedes @ sK3_SY82 @ sK4_SY86 @ sK5_SY89 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[184]) ).
thf(213,plain,
( ( ~ ( shortest_path @ sK1_V1 @ sK2_SY77 @ sK5_SY89 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[184]) ).
thf(214,plain,
! [SV39: $i] :
( ( ( ( ( tail_of @ SV39 )
!= ( head_of @ sK4_SY86 ) )
| ~ ( edge @ SV39 ) )
= $true )
| ( ( ( ( head_of @ SV39 )
!= ( tail_of @ sK3_SY82 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(215,plain,
! [SV16: $i,SV1: $i,SV44: $i,SV32: $i,SV24: $i] :
( ( ( ~ ( precedes @ SV24 @ SV32 @ SV44 )
| ~ ( shortest_path @ SV1 @ SV16 @ SV44 ) )
= $true )
| ( ( ! [SY223: $i] :
( ( ( tail_of @ SY223 )
!= ( tail_of @ SV24 ) )
| ~ ( edge @ SY223 )
| ( ( head_of @ SY223 )
!= ( head_of @ SV32 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(216,plain,
! [SV6: $i] :
( ( ~ ( ! [SY107: $i,SY108: $i] :
~ ( path @ SV6 @ SY107 @ SY108 )
| ( vertex @ SV6 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[189]) ).
thf(217,plain,
! [SV6: $i] :
( ( ~ ! [SY109: $i] :
( ! [SY110: $i] :
~ ( path @ SV6 @ SY109 @ SY110 )
| ( vertex @ SY109 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[189]) ).
thf(218,plain,
! [SV45: $i,SV40: $i,SV6: $i] :
( ( ~ ( path @ SV6 @ SV40 @ SV45 )
| ~ ( ~ ~ ( ( SV6
!= ( tail_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( edge @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
| ~ ~ ( ~ ( ( SV40
!= ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
| ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ empty ) )
| ! [SY229: $i] :
( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ SY229 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ SY229 ) ) )
| ~ ~ ( ~ ( ( SV40
= ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ ( sK13_SY95 @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ ( sK13_SY95 @ SV45 @ SV40 @ SV6 ) ) ) )
| ~ ( ( SV45
= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ empty ) )
| ~ ( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ ( sK12_SY96 @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ ( sK12_SY96 @ SV45 @ SV40 @ SV6 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(219,plain,
! [SV33: $i,SV27: $i] :
( ( ( SV27 = SV33 )
= $true )
| ( ( ~ ( vertex @ SV27 )
| ~ ( vertex @ SV33 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV27
!= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
!= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
!= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
!= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV27
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
| ~ ( ( SV27
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) ) )
| ~ ~ ( ~ ( ( SV33
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
| ~ ( ( SV33
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV33 @ SV27 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(220,plain,
! [SV46: $i,SV41: $i,SV7: $i] :
( ( ~ ( ~ ( path @ SV7 @ SV41 @ ( sK8_P @ SV46 @ SV41 @ SV7 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SV46 ) @ ( length_of @ ( sK8_P @ SV46 @ SV41 @ SV7 ) ) ) )
| ( SV7 = SV41 )
| ~ ( path @ SV7 @ SV41 @ SV46 )
| ( shortest_path @ SV7 @ SV41 @ SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(221,plain,
! [SV7: $i] :
( ( ~ ! [SY116: $i,SY117: $i] :
( ~ ( shortest_path @ SV7 @ SY116 @ SY117 )
| ! [SY118: $i] :
( ~ ( path @ SV7 @ SY116 @ SY118 )
| ( less_or_equal @ ( length_of @ SY117 ) @ ( length_of @ SY118 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[193]) ).
thf(222,plain,
! [SV7: $i] :
( ( ~ ~ ( ~ ! [SY119: $i] :
( ! [SY120: $i] :
~ ( shortest_path @ SV7 @ SY119 @ SY120 )
| ( SV7 != SY119 ) )
| ~ ! [SY121: $i,SY122: $i] :
( ~ ( shortest_path @ SV7 @ SY121 @ SY122 )
| ( path @ SV7 @ SY121 @ SY122 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[193]) ).
thf(223,plain,
! [SV20: $i,SV8: $i,SV28: $i] :
( ( ! [SY212: $i] :
( ! [SY213: $i] :
( ~ ( precedes @ SV28 @ SY212 @ SY213 )
| ~ ( shortest_path @ SV8 @ SV20 @ SY213 ) )
| ! [SY214: $i] :
( ( ( tail_of @ SY214 )
!= ( tail_of @ SV28 ) )
| ( ( head_of @ SY214 )
!= ( head_of @ SY212 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[194]) ).
thf(224,plain,
! [SV20: $i,SV8: $i,SV28: $i] :
( ( ! [SY215: $i,SY216: $i] :
( ~ ( precedes @ SV28 @ SY215 @ SY216 )
| ~ ( shortest_path @ SV8 @ SV20 @ SY216 )
| ~ ( precedes @ SY215 @ SV28 @ SY216 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[195]) ).
thf(225,plain,
! [SV29: $i,SV21: $i,SV9: $i] :
( ( ( ~ ( vertex @ SV9 ) )
= $true )
| ( ( ~ ( vertex @ SV21 ) )
= $true )
| ( ( ~ ( ~ ! [SY217: $i] :
( ( SV9
!= ( tail_of @ SY217 ) )
| ~ ( edge @ SY217 )
| ( SV21
!= ( head_of @ SY217 ) )
| ( SV29
!= ( path_cons @ SY217 @ empty ) ) )
| ~ ! [SY218: $i] :
( ( SV9
!= ( tail_of @ SY218 ) )
| ~ ( edge @ SY218 )
| ! [SY219: $i] :
( ( SV29
!= ( path_cons @ SY218 @ SY219 ) )
| ~ ( path @ ( head_of @ SY218 ) @ SV21 @ SY219 ) ) ) ) )
= $true )
| ( ( path @ SV9 @ SV21 @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(226,plain,
! [SV34: $i,SV30: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ! [SY137: $i] :
( ! [SY138: $i] :
~ ( precedes @ SY137 @ SY138 @ SV10 )
| ( on_path @ SY137 @ SV10 ) )
| ~ ! [SY139: $i,SY140: $i] :
( ~ ( precedes @ SY139 @ SY140 @ SV10 )
| ( on_path @ SY140 @ SV10 ) ) )
| ~ ~ ( ~ ! [SY141: $i,SY142: $i] :
( ~ ( precedes @ SY141 @ SY142 @ SV10 )
| ! [SY143: $i] :
( ~ ( precedes @ SY143 @ SY142 @ SV10 )
| ~ ( sequential @ SY141 @ SY143 ) )
| ~ ( sequential @ SY141 @ SY142 ) )
| ~ ! [SY144: $i,SY145: $i] :
( ~ ( precedes @ SY144 @ SY145 @ SV10 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY145 @ SY144 @ SV10 ) @ SY145 @ SV10 )
| ~ ( sequential @ SY144 @ ( sK9_E3 @ SY145 @ SY144 @ SV10 ) ) )
| ( sequential @ SY144 @ SY145 ) ) ) )
= $false )
| ( ( path @ SV30 @ SV34 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(227,plain,
! [SV47: $i,SV42: $i,SV11: $i] :
( ( ~ ( edge @ SV11 )
| ~ ( edge @ SV42 )
| ~ ( edge @ SV47 )
| ~ ( sequential @ SV11 @ SV42 )
| ~ ( sequential @ SV42 @ SV47 )
| ~ ( sequential @ SV47 @ SV11 )
| ( triangle @ SV11 @ SV42 @ SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(228,plain,
! [SV11: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY148: $i,SY149: $i] :
~ ( triangle @ SV11 @ SY148 @ SY149 )
| ( edge @ SV11 ) )
| ~ ! [SY150: $i] :
( ! [SY151: $i] :
~ ( triangle @ SV11 @ SY150 @ SY151 )
| ( edge @ SY150 ) ) )
| ~ ! [SY152: $i,SY153: $i] :
( ~ ( triangle @ SV11 @ SY152 @ SY153 )
| ( edge @ SY153 ) ) )
| ~ ! [SY154: $i] :
( ! [SY155: $i] :
~ ( triangle @ SV11 @ SY154 @ SY155 )
| ( sequential @ SV11 @ SY154 ) ) )
| ~ ! [SY156: $i,SY157: $i] :
( ~ ( triangle @ SV11 @ SY156 @ SY157 )
| ( sequential @ SY156 @ SY157 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[199]) ).
thf(229,plain,
! [SV11: $i] :
( ( ~ ! [SY158: $i,SY159: $i] :
( ~ ( triangle @ SV11 @ SY158 @ SY159 )
| ( sequential @ SY159 @ SV11 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[199]) ).
thf(230,plain,
! [SV22: $i,SV12: $i] :
( ( ~ ! [SY198: $i,SY199: $i] :
( ~ ( on_path @ SY199 @ SY198 )
| ~ ( path @ SV12 @ SV22 @ SY198 )
| ( edge @ SY199 ) )
| ~ ! [SY200: $i,SY201: $i] :
( ~ ( on_path @ SY201 @ SY200 )
| ~ ( path @ SV12 @ SV22 @ SY200 )
| ( in_path @ ( head_of @ SY201 ) @ SY200 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(231,plain,
! [SV22: $i,SV12: $i,SV48: $i] :
( ( ! [SY230: $i] :
( ~ ( on_path @ SY230 @ SV48 )
| ~ ( path @ SV12 @ SV22 @ SV48 )
| ( in_path @ ( tail_of @ SY230 ) @ SV48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(232,plain,
! [SV35: $i] :
( ( ( edge @ SV35 )
= $false )
| ( ( vertex @ ( head_of @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(233,plain,
! [SV36: $i] :
( ( ( edge @ SV36 )
= $false )
| ( ( vertex @ ( tail_of @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(234,plain,
! [SV23: $i,SV13: $i,SV49: $i] :
( ( ! [SY231: $i] :
( ~ ( in_path @ SY231 @ SV49 )
| ~ ( path @ SV13 @ SV23 @ SV49 )
| ~ ( ~ ( on_path @ ( sK10_E @ SY231 @ SV49 @ SV23 @ SV13 ) @ SV49 )
| ~ ( ( SY231
= ( head_of @ ( sK10_E @ SY231 @ SV49 @ SV23 @ SV13 ) ) )
| ( SY231
= ( tail_of @ ( sK10_E @ SY231 @ SV49 @ SV23 @ SV13 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(235,plain,
! [SV23: $i,SV13: $i,SV50: $i] :
( ( ! [SY232: $i] :
( ~ ( in_path @ SY232 @ SV50 )
| ~ ( path @ SV13 @ SV23 @ SV50 )
| ( vertex @ SY232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(236,plain,
! [SV37: $i,SV31: $i,SV14: $i] :
( ( ( ~ ! [SY174: $i,SY175: $i] :
( ~ ( on_path @ SY174 @ SV14 )
| ~ ( on_path @ SY175 @ SV14 )
| ! [SY176: $i] :
( ~ ( precedes @ SY176 @ SY175 @ SV14 )
| ~ ( sequential @ SY174 @ SY176 ) )
| ( precedes @ SY174 @ SY175 @ SV14 ) )
| ~ ! [SY177: $i,SY178: $i] :
( ~ ( on_path @ SY177 @ SV14 )
| ~ ( on_path @ SY178 @ SV14 )
| ~ ( sequential @ SY177 @ SY178 )
| ( precedes @ SY177 @ SY178 @ SV14 ) ) )
= $false )
| ( ( path @ SV31 @ SV37 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(237,plain,
! [SV15: $i] :
( ( ( ~ ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV15 ) @ SV15 )
| ~ ( on_path @ ( sK7_SY91 @ SV15 ) @ SV15 ) )
| ~ ( sequential @ ( sK6_E1 @ SV15 ) @ ( sK7_SY91 @ SV15 ) ) ) )
= $true )
| ( ( ! [SY180: $i,SY181: $i] :
~ ( path @ SY180 @ SY181 @ SV15 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV15 )
= ( number_of_in @ triangles @ SV15 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[207]) ).
thf(238,plain,
! [SV15: $i] :
( ( ( ! [SY179: $i] :
~ ( triangle @ ( sK6_E1 @ SV15 ) @ ( sK7_SY91 @ SV15 ) @ SY179 ) )
= $true )
| ( ( ! [SY180: $i,SY181: $i] :
~ ( path @ SY180 @ SY181 @ SV15 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV15 )
= ( number_of_in @ triangles @ SV15 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[208]) ).
thf(239,plain,
! [SV43: $i,SV38: $i] :
( ( ( ( SV38 = SV43 )
| ~ ( edge @ SV38 )
| ~ ( edge @ SV43 )
| ( ( head_of @ SV38 )
!= ( tail_of @ SV43 ) ) )
= $true )
| ( ( sequential @ SV38 @ SV43 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(240,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)],[210]) ).
thf(241,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( ( head_of @ SX0 )
= ( tail_of @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[211]) ).
thf(242,plain,
( ( precedes @ sK3_SY82 @ sK4_SY86 @ sK5_SY89 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[212]) ).
thf(243,plain,
( ( shortest_path @ sK1_V1 @ sK2_SY77 @ sK5_SY89 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[213]) ).
thf(244,plain,
! [SV39: $i] :
( ( ( ( ( tail_of @ SV39 )
!= ( head_of @ sK4_SY86 ) ) )
= $true )
| ( ( ~ ( edge @ SV39 ) )
= $true )
| ( ( ( ( head_of @ SV39 )
!= ( tail_of @ sK3_SY82 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[214]) ).
thf(245,plain,
! [SV16: $i,SV1: $i,SV44: $i,SV32: $i,SV24: $i] :
( ( ( ~ ( precedes @ SV24 @ SV32 @ SV44 ) )
= $true )
| ( ( ~ ( shortest_path @ SV1 @ SV16 @ SV44 ) )
= $true )
| ( ( ! [SY223: $i] :
( ( ( tail_of @ SY223 )
!= ( tail_of @ SV24 ) )
| ~ ( edge @ SY223 )
| ( ( head_of @ SY223 )
!= ( head_of @ SV32 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[215]) ).
thf(246,plain,
! [SV6: $i] :
( ( ! [SY107: $i,SY108: $i] :
~ ( path @ SV6 @ SY107 @ SY108 )
| ( vertex @ SV6 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[216]) ).
thf(247,plain,
! [SV6: $i] :
( ( ! [SY109: $i] :
( ! [SY110: $i] :
~ ( path @ SV6 @ SY109 @ SY110 )
| ( vertex @ SY109 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[217]) ).
thf(248,plain,
! [SV45: $i,SV40: $i,SV6: $i] :
( ( ( ~ ( path @ SV6 @ SV40 @ SV45 ) )
= $true )
| ( ( ~ ( ~ ~ ( ( SV6
!= ( tail_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( edge @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
| ~ ~ ( ~ ( ( SV40
!= ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
| ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ empty ) )
| ! [SY229: $i] :
( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ SY229 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ SY229 ) ) )
| ~ ~ ( ~ ( ( SV40
= ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ ( sK13_SY95 @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ ( sK13_SY95 @ SV45 @ SV40 @ SV6 ) ) ) )
| ~ ( ( SV45
= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ empty ) )
| ~ ( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ ( sK12_SY96 @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ ( sK12_SY96 @ SV45 @ SV40 @ SV6 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[218]) ).
thf(249,plain,
! [SV33: $i,SV27: $i] :
( ( ( ~ ( vertex @ SV27 ) )
= $true )
| ( ( ~ ( vertex @ SV33 ) )
= $true )
| ( ( SV27 = SV33 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV27
!= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
!= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
!= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
!= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV27
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
| ~ ( ( SV27
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) ) )
| ~ ~ ( ~ ( ( SV33
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
| ~ ( ( SV33
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV33 @ SV27 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(250,plain,
! [SV46: $i,SV41: $i,SV7: $i] :
( ( ( ~ ( ~ ( path @ SV7 @ SV41 @ ( sK8_P @ SV46 @ SV41 @ SV7 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SV46 ) @ ( length_of @ ( sK8_P @ SV46 @ SV41 @ SV7 ) ) ) )
| ( SV7 = SV41 )
| ~ ( path @ SV7 @ SV41 @ SV46 ) )
= $true )
| ( ( shortest_path @ SV7 @ SV41 @ SV46 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(251,plain,
! [SV7: $i] :
( ( ! [SY116: $i,SY117: $i] :
( ~ ( shortest_path @ SV7 @ SY116 @ SY117 )
| ! [SY118: $i] :
( ~ ( path @ SV7 @ SY116 @ SY118 )
| ( less_or_equal @ ( length_of @ SY117 ) @ ( length_of @ SY118 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[221]) ).
thf(252,plain,
! [SV7: $i] :
( ( ~ ( ~ ! [SY119: $i] :
( ! [SY120: $i] :
~ ( shortest_path @ SV7 @ SY119 @ SY120 )
| ( SV7 != SY119 ) )
| ~ ! [SY121: $i,SY122: $i] :
( ~ ( shortest_path @ SV7 @ SY121 @ SY122 )
| ( path @ SV7 @ SY121 @ SY122 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[222]) ).
thf(253,plain,
! [SV20: $i,SV8: $i,SV51: $i,SV28: $i] :
( ( ! [SY233: $i] :
( ~ ( precedes @ SV28 @ SV51 @ SY233 )
| ~ ( shortest_path @ SV8 @ SV20 @ SY233 ) )
| ! [SY234: $i] :
( ( ( tail_of @ SY234 )
!= ( tail_of @ SV28 ) )
| ( ( head_of @ SY234 )
!= ( head_of @ SV51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(254,plain,
! [SV20: $i,SV8: $i,SV52: $i,SV28: $i] :
( ( ! [SY235: $i] :
( ~ ( precedes @ SV28 @ SV52 @ SY235 )
| ~ ( shortest_path @ SV8 @ SV20 @ SY235 )
| ~ ( precedes @ SV52 @ SV28 @ SY235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(255,plain,
! [SV29: $i,SV21: $i,SV9: $i] :
( ( ( vertex @ SV9 )
= $false )
| ( ( ~ ( vertex @ SV21 ) )
= $true )
| ( ( ~ ( ~ ! [SY217: $i] :
( ( SV9
!= ( tail_of @ SY217 ) )
| ~ ( edge @ SY217 )
| ( SV21
!= ( head_of @ SY217 ) )
| ( SV29
!= ( path_cons @ SY217 @ empty ) ) )
| ~ ! [SY218: $i] :
( ( SV9
!= ( tail_of @ SY218 ) )
| ~ ( edge @ SY218 )
| ! [SY219: $i] :
( ( SV29
!= ( path_cons @ SY218 @ SY219 ) )
| ~ ( path @ ( head_of @ SY218 ) @ SV21 @ SY219 ) ) ) ) )
= $true )
| ( ( path @ SV9 @ SV21 @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(256,plain,
! [SV34: $i,SV30: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ! [SY137: $i] :
( ! [SY138: $i] :
~ ( precedes @ SY137 @ SY138 @ SV10 )
| ( on_path @ SY137 @ SV10 ) )
| ~ ! [SY139: $i,SY140: $i] :
( ~ ( precedes @ SY139 @ SY140 @ SV10 )
| ( on_path @ SY140 @ SV10 ) ) ) )
= $false )
| ( ( path @ SV30 @ SV34 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[226]) ).
thf(257,plain,
! [SV34: $i,SV30: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ! [SY141: $i,SY142: $i] :
( ~ ( precedes @ SY141 @ SY142 @ SV10 )
| ! [SY143: $i] :
( ~ ( precedes @ SY143 @ SY142 @ SV10 )
| ~ ( sequential @ SY141 @ SY143 ) )
| ~ ( sequential @ SY141 @ SY142 ) )
| ~ ! [SY144: $i,SY145: $i] :
( ~ ( precedes @ SY144 @ SY145 @ SV10 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY145 @ SY144 @ SV10 ) @ SY145 @ SV10 )
| ~ ( sequential @ SY144 @ ( sK9_E3 @ SY145 @ SY144 @ SV10 ) ) )
| ( sequential @ SY144 @ SY145 ) ) ) )
= $false )
| ( ( path @ SV30 @ SV34 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[226]) ).
thf(258,plain,
! [SV47: $i,SV42: $i,SV11: $i] :
( ( ( ~ ( edge @ SV11 )
| ~ ( edge @ SV42 )
| ~ ( edge @ SV47 )
| ~ ( sequential @ SV11 @ SV42 )
| ~ ( sequential @ SV42 @ SV47 )
| ~ ( sequential @ SV47 @ SV11 ) )
= $true )
| ( ( triangle @ SV11 @ SV42 @ SV47 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(259,plain,
! [SV11: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY148: $i,SY149: $i] :
~ ( triangle @ SV11 @ SY148 @ SY149 )
| ( edge @ SV11 ) )
| ~ ! [SY150: $i] :
( ! [SY151: $i] :
~ ( triangle @ SV11 @ SY150 @ SY151 )
| ( edge @ SY150 ) ) )
| ~ ! [SY152: $i,SY153: $i] :
( ~ ( triangle @ SV11 @ SY152 @ SY153 )
| ( edge @ SY153 ) ) )
| ~ ! [SY154: $i] :
( ! [SY155: $i] :
~ ( triangle @ SV11 @ SY154 @ SY155 )
| ( sequential @ SV11 @ SY154 ) ) )
| ~ ! [SY156: $i,SY157: $i] :
( ~ ( triangle @ SV11 @ SY156 @ SY157 )
| ( sequential @ SY156 @ SY157 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[228]) ).
thf(260,plain,
! [SV11: $i] :
( ( ! [SY158: $i,SY159: $i] :
( ~ ( triangle @ SV11 @ SY158 @ SY159 )
| ( sequential @ SY159 @ SV11 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[229]) ).
thf(261,plain,
! [SV22: $i,SV12: $i] :
( ( ~ ! [SY198: $i,SY199: $i] :
( ~ ( on_path @ SY199 @ SY198 )
| ~ ( path @ SV12 @ SV22 @ SY198 )
| ( edge @ SY199 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[230]) ).
thf(262,plain,
! [SV22: $i,SV12: $i] :
( ( ~ ! [SY200: $i,SY201: $i] :
( ~ ( on_path @ SY201 @ SY200 )
| ~ ( path @ SV12 @ SV22 @ SY200 )
| ( in_path @ ( head_of @ SY201 ) @ SY200 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[230]) ).
thf(263,plain,
! [SV22: $i,SV12: $i,SV48: $i,SV53: $i] :
( ( ~ ( on_path @ SV53 @ SV48 )
| ~ ( path @ SV12 @ SV22 @ SV48 )
| ( in_path @ ( tail_of @ SV53 ) @ SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(264,plain,
! [SV23: $i,SV13: $i,SV49: $i,SV54: $i] :
( ( ~ ( in_path @ SV54 @ SV49 )
| ~ ( path @ SV13 @ SV23 @ SV49 )
| ~ ( ~ ( on_path @ ( sK10_E @ SV54 @ SV49 @ SV23 @ SV13 ) @ SV49 )
| ~ ( ( SV54
= ( head_of @ ( sK10_E @ SV54 @ SV49 @ SV23 @ SV13 ) ) )
| ( SV54
= ( tail_of @ ( sK10_E @ SV54 @ SV49 @ SV23 @ SV13 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(265,plain,
! [SV23: $i,SV13: $i,SV50: $i,SV55: $i] :
( ( ~ ( in_path @ SV55 @ SV50 )
| ~ ( path @ SV13 @ SV23 @ SV50 )
| ( vertex @ SV55 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[235]) ).
thf(266,plain,
! [SV37: $i,SV31: $i,SV14: $i] :
( ( ( ~ ! [SY174: $i,SY175: $i] :
( ~ ( on_path @ SY174 @ SV14 )
| ~ ( on_path @ SY175 @ SV14 )
| ! [SY176: $i] :
( ~ ( precedes @ SY176 @ SY175 @ SV14 )
| ~ ( sequential @ SY174 @ SY176 ) )
| ( precedes @ SY174 @ SY175 @ SV14 ) ) )
= $false )
| ( ( path @ SV31 @ SV37 @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[236]) ).
thf(267,plain,
! [SV37: $i,SV31: $i,SV14: $i] :
( ( ( ~ ! [SY177: $i,SY178: $i] :
( ~ ( on_path @ SY177 @ SV14 )
| ~ ( on_path @ SY178 @ SV14 )
| ~ ( sequential @ SY177 @ SY178 )
| ( precedes @ SY177 @ SY178 @ SV14 ) ) )
= $false )
| ( ( path @ SV31 @ SV37 @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[236]) ).
thf(268,plain,
! [SV15: $i] :
( ( ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV15 ) @ SV15 )
| ~ ( on_path @ ( sK7_SY91 @ SV15 ) @ SV15 ) )
| ~ ( sequential @ ( sK6_E1 @ SV15 ) @ ( sK7_SY91 @ SV15 ) ) )
= $false )
| ( ( ! [SY180: $i,SY181: $i] :
~ ( path @ SY180 @ SY181 @ SV15 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV15 )
= ( number_of_in @ triangles @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(269,plain,
! [SV56: $i,SV15: $i] :
( ( ( ~ ( triangle @ ( sK6_E1 @ SV15 ) @ ( sK7_SY91 @ SV15 ) @ SV56 ) )
= $true )
| ( ( ! [SY180: $i,SY181: $i] :
~ ( path @ SY180 @ SY181 @ SV15 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV15 )
= ( number_of_in @ triangles @ SV15 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(270,plain,
! [SV43: $i,SV38: $i] :
( ( ( ( SV38 = SV43 )
| ~ ( edge @ SV38 )
| ~ ( edge @ SV43 ) )
= $true )
| ( ( ( ( head_of @ SV38 )
!= ( tail_of @ SV43 ) ) )
= $true )
| ( ( sequential @ SV38 @ SV43 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[239]) ).
thf(271,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)],[240]) ).
thf(272,plain,
! [SV57: $i] :
( ( ! [SY236: $i] :
( ~ ( sequential @ SV57 @ SY236 )
| ( ( head_of @ SV57 )
= ( tail_of @ SY236 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(273,plain,
! [SV39: $i] :
( ( ( ( tail_of @ SV39 )
= ( head_of @ sK4_SY86 ) )
= $false )
| ( ( ~ ( edge @ SV39 ) )
= $true )
| ( ( ( ( head_of @ SV39 )
!= ( tail_of @ sK3_SY82 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(274,plain,
! [SV16: $i,SV1: $i,SV44: $i,SV32: $i,SV24: $i] :
( ( ( precedes @ SV24 @ SV32 @ SV44 )
= $false )
| ( ( ~ ( shortest_path @ SV1 @ SV16 @ SV44 ) )
= $true )
| ( ( ! [SY223: $i] :
( ( ( tail_of @ SY223 )
!= ( tail_of @ SV24 ) )
| ~ ( edge @ SY223 )
| ( ( head_of @ SY223 )
!= ( head_of @ SV32 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(275,plain,
! [SV6: $i] :
( ( ( ! [SY107: $i,SY108: $i] :
~ ( path @ SV6 @ SY107 @ SY108 ) )
= $true )
| ( ( vertex @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(276,plain,
! [SV58: $i,SV6: $i] :
( ( ! [SY237: $i] :
~ ( path @ SV6 @ SV58 @ SY237 )
| ( vertex @ SV58 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(277,plain,
! [SV45: $i,SV40: $i,SV6: $i] :
( ( ( path @ SV6 @ SV40 @ SV45 )
= $false )
| ( ( ~ ( ~ ~ ( ( SV6
!= ( tail_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( edge @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
| ~ ~ ( ~ ( ( SV40
!= ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
| ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ empty ) )
| ! [SY229: $i] :
( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ SY229 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ SY229 ) ) )
| ~ ~ ( ~ ( ( SV40
= ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ ( sK13_SY95 @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ ( sK13_SY95 @ SV45 @ SV40 @ SV6 ) ) ) )
| ~ ( ( SV45
= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ empty ) )
| ~ ( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ ( sK12_SY96 @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ ( sK12_SY96 @ SV45 @ SV40 @ SV6 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(278,plain,
! [SV33: $i,SV27: $i] :
( ( ( vertex @ SV27 )
= $false )
| ( ( ~ ( vertex @ SV33 ) )
= $true )
| ( ( SV27 = SV33 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV27
!= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
!= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
!= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
!= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV27
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
| ~ ( ( SV27
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) ) )
| ~ ~ ( ~ ( ( SV33
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
| ~ ( ( SV33
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV33 @ SV27 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(279,plain,
! [SV46: $i,SV41: $i,SV7: $i] :
( ( ( ~ ( ~ ( path @ SV7 @ SV41 @ ( sK8_P @ SV46 @ SV41 @ SV7 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SV46 ) @ ( length_of @ ( sK8_P @ SV46 @ SV41 @ SV7 ) ) ) ) )
= $true )
| ( ( ( SV7 = SV41 )
| ~ ( path @ SV7 @ SV41 @ SV46 ) )
= $true )
| ( ( shortest_path @ SV7 @ SV41 @ SV46 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[250]) ).
thf(280,plain,
! [SV59: $i,SV7: $i] :
( ( ! [SY238: $i] :
( ~ ( shortest_path @ SV7 @ SV59 @ SY238 )
| ! [SY239: $i] :
( ~ ( path @ SV7 @ SV59 @ SY239 )
| ( less_or_equal @ ( length_of @ SY238 ) @ ( length_of @ SY239 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(281,plain,
! [SV7: $i] :
( ( ~ ! [SY119: $i] :
( ! [SY120: $i] :
~ ( shortest_path @ SV7 @ SY119 @ SY120 )
| ( SV7 != SY119 ) )
| ~ ! [SY121: $i,SY122: $i] :
( ~ ( shortest_path @ SV7 @ SY121 @ SY122 )
| ( path @ SV7 @ SY121 @ SY122 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(282,plain,
! [SV20: $i,SV8: $i,SV51: $i,SV28: $i] :
( ( ( ! [SY233: $i] :
( ~ ( precedes @ SV28 @ SV51 @ SY233 )
| ~ ( shortest_path @ SV8 @ SV20 @ SY233 ) ) )
= $true )
| ( ( ! [SY234: $i] :
( ( ( tail_of @ SY234 )
!= ( tail_of @ SV28 ) )
| ( ( head_of @ SY234 )
!= ( head_of @ SV51 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[253]) ).
thf(283,plain,
! [SV20: $i,SV8: $i,SV60: $i,SV52: $i,SV28: $i] :
( ( ~ ( precedes @ SV28 @ SV52 @ SV60 )
| ~ ( shortest_path @ SV8 @ SV20 @ SV60 )
| ~ ( precedes @ SV52 @ SV28 @ SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[254]) ).
thf(284,plain,
! [SV29: $i,SV9: $i,SV21: $i] :
( ( ( vertex @ SV21 )
= $false )
| ( ( vertex @ SV9 )
= $false )
| ( ( ~ ( ~ ! [SY217: $i] :
( ( SV9
!= ( tail_of @ SY217 ) )
| ~ ( edge @ SY217 )
| ( SV21
!= ( head_of @ SY217 ) )
| ( SV29
!= ( path_cons @ SY217 @ empty ) ) )
| ~ ! [SY218: $i] :
( ( SV9
!= ( tail_of @ SY218 ) )
| ~ ( edge @ SY218 )
| ! [SY219: $i] :
( ( SV29
!= ( path_cons @ SY218 @ SY219 ) )
| ~ ( path @ ( head_of @ SY218 ) @ SV21 @ SY219 ) ) ) ) )
= $true )
| ( ( path @ SV9 @ SV21 @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(285,plain,
! [SV34: $i,SV30: $i,SV10: $i] :
( ( ( ~ ( ~ ! [SY137: $i] :
( ! [SY138: $i] :
~ ( precedes @ SY137 @ SY138 @ SV10 )
| ( on_path @ SY137 @ SV10 ) )
| ~ ! [SY139: $i,SY140: $i] :
( ~ ( precedes @ SY139 @ SY140 @ SV10 )
| ( on_path @ SY140 @ SV10 ) ) ) )
= $true )
| ( ( path @ SV30 @ SV34 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[256]) ).
thf(286,plain,
! [SV34: $i,SV30: $i,SV10: $i] :
( ( ( ~ ( ~ ! [SY141: $i,SY142: $i] :
( ~ ( precedes @ SY141 @ SY142 @ SV10 )
| ! [SY143: $i] :
( ~ ( precedes @ SY143 @ SY142 @ SV10 )
| ~ ( sequential @ SY141 @ SY143 ) )
| ~ ( sequential @ SY141 @ SY142 ) )
| ~ ! [SY144: $i,SY145: $i] :
( ~ ( precedes @ SY144 @ SY145 @ SV10 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY145 @ SY144 @ SV10 ) @ SY145 @ SV10 )
| ~ ( sequential @ SY144 @ ( sK9_E3 @ SY145 @ SY144 @ SV10 ) ) )
| ( sequential @ SY144 @ SY145 ) ) ) )
= $true )
| ( ( path @ SV30 @ SV34 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[257]) ).
thf(287,plain,
! [SV47: $i,SV42: $i,SV11: $i] :
( ( ( ~ ( edge @ SV11 )
| ~ ( edge @ SV42 )
| ~ ( edge @ SV47 )
| ~ ( sequential @ SV11 @ SV42 )
| ~ ( sequential @ SV42 @ SV47 ) )
= $true )
| ( ( ~ ( sequential @ SV47 @ SV11 ) )
= $true )
| ( ( triangle @ SV11 @ SV42 @ SV47 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[258]) ).
thf(288,plain,
! [SV11: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY148: $i,SY149: $i] :
~ ( triangle @ SV11 @ SY148 @ SY149 )
| ( edge @ SV11 ) )
| ~ ! [SY150: $i] :
( ! [SY151: $i] :
~ ( triangle @ SV11 @ SY150 @ SY151 )
| ( edge @ SY150 ) ) )
| ~ ! [SY152: $i,SY153: $i] :
( ~ ( triangle @ SV11 @ SY152 @ SY153 )
| ( edge @ SY153 ) ) )
| ~ ! [SY154: $i] :
( ! [SY155: $i] :
~ ( triangle @ SV11 @ SY154 @ SY155 )
| ( sequential @ SV11 @ SY154 ) ) )
| ~ ! [SY156: $i,SY157: $i] :
( ~ ( triangle @ SV11 @ SY156 @ SY157 )
| ( sequential @ SY156 @ SY157 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(289,plain,
! [SV61: $i,SV11: $i] :
( ( ! [SY240: $i] :
( ~ ( triangle @ SV11 @ SV61 @ SY240 )
| ( sequential @ SY240 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[260]) ).
thf(290,plain,
! [SV22: $i,SV12: $i] :
( ( ! [SY198: $i,SY199: $i] :
( ~ ( on_path @ SY199 @ SY198 )
| ~ ( path @ SV12 @ SV22 @ SY198 )
| ( edge @ SY199 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[261]) ).
thf(291,plain,
! [SV22: $i,SV12: $i] :
( ( ! [SY200: $i,SY201: $i] :
( ~ ( on_path @ SY201 @ SY200 )
| ~ ( path @ SV12 @ SV22 @ SY200 )
| ( in_path @ ( head_of @ SY201 ) @ SY200 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[262]) ).
thf(292,plain,
! [SV22: $i,SV12: $i,SV48: $i,SV53: $i] :
( ( ( ~ ( on_path @ SV53 @ SV48 )
| ~ ( path @ SV12 @ SV22 @ SV48 ) )
= $true )
| ( ( in_path @ ( tail_of @ SV53 ) @ SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[263]) ).
thf(293,plain,
! [SV23: $i,SV13: $i,SV49: $i,SV54: $i] :
( ( ( ~ ( in_path @ SV54 @ SV49 )
| ~ ( path @ SV13 @ SV23 @ SV49 ) )
= $true )
| ( ( ~ ( ~ ( on_path @ ( sK10_E @ SV54 @ SV49 @ SV23 @ SV13 ) @ SV49 )
| ~ ( ( SV54
= ( head_of @ ( sK10_E @ SV54 @ SV49 @ SV23 @ SV13 ) ) )
| ( SV54
= ( tail_of @ ( sK10_E @ SV54 @ SV49 @ SV23 @ SV13 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[264]) ).
thf(294,plain,
! [SV23: $i,SV13: $i,SV50: $i,SV55: $i] :
( ( ( ~ ( in_path @ SV55 @ SV50 )
| ~ ( path @ SV13 @ SV23 @ SV50 ) )
= $true )
| ( ( vertex @ SV55 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(295,plain,
! [SV37: $i,SV31: $i,SV14: $i] :
( ( ( ! [SY174: $i,SY175: $i] :
( ~ ( on_path @ SY174 @ SV14 )
| ~ ( on_path @ SY175 @ SV14 )
| ! [SY176: $i] :
( ~ ( precedes @ SY176 @ SY175 @ SV14 )
| ~ ( sequential @ SY174 @ SY176 ) )
| ( precedes @ SY174 @ SY175 @ SV14 ) ) )
= $true )
| ( ( path @ SV31 @ SV37 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[266]) ).
thf(296,plain,
! [SV37: $i,SV31: $i,SV14: $i] :
( ( ( ! [SY177: $i,SY178: $i] :
( ~ ( on_path @ SY177 @ SV14 )
| ~ ( on_path @ SY178 @ SV14 )
| ~ ( sequential @ SY177 @ SY178 )
| ( precedes @ SY177 @ SY178 @ SV14 ) ) )
= $true )
| ( ( path @ SV31 @ SV37 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[267]) ).
thf(297,plain,
! [SV15: $i] :
( ( ( ~ ~ ( ~ ( on_path @ ( sK6_E1 @ SV15 ) @ SV15 )
| ~ ( on_path @ ( sK7_SY91 @ SV15 ) @ SV15 ) ) )
= $false )
| ( ( ! [SY180: $i,SY181: $i] :
~ ( path @ SY180 @ SY181 @ SV15 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV15 )
= ( number_of_in @ triangles @ SV15 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[268]) ).
thf(298,plain,
! [SV15: $i] :
( ( ( ~ ( sequential @ ( sK6_E1 @ SV15 ) @ ( sK7_SY91 @ SV15 ) ) )
= $false )
| ( ( ! [SY180: $i,SY181: $i] :
~ ( path @ SY180 @ SY181 @ SV15 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV15 )
= ( number_of_in @ triangles @ SV15 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[268]) ).
thf(299,plain,
! [SV56: $i,SV15: $i] :
( ( ( triangle @ ( sK6_E1 @ SV15 ) @ ( sK7_SY91 @ SV15 ) @ SV56 )
= $false )
| ( ( ! [SY180: $i,SY181: $i] :
~ ( path @ SY180 @ SY181 @ SV15 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV15 )
= ( number_of_in @ triangles @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(300,plain,
! [SV43: $i,SV38: $i] :
( ( ( SV38 = SV43 )
= $true )
| ( ( ~ ( edge @ SV38 )
| ~ ( edge @ SV43 ) )
= $true )
| ( ( ( ( head_of @ SV38 )
!= ( tail_of @ SV43 ) ) )
= $true )
| ( ( sequential @ SV38 @ SV43 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[270]) ).
thf(301,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[271]) ).
thf(302,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)],[271]) ).
thf(303,plain,
! [SV62: $i,SV57: $i] :
( ( ~ ( sequential @ SV57 @ SV62 )
| ( ( head_of @ SV57 )
= ( tail_of @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(304,plain,
! [SV39: $i] :
( ( ( edge @ SV39 )
= $false )
| ( ( ( tail_of @ SV39 )
= ( head_of @ sK4_SY86 ) )
= $false )
| ( ( ( ( head_of @ SV39 )
!= ( tail_of @ sK3_SY82 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[273]) ).
thf(305,plain,
! [SV32: $i,SV24: $i,SV44: $i,SV16: $i,SV1: $i] :
( ( ( shortest_path @ SV1 @ SV16 @ SV44 )
= $false )
| ( ( precedes @ SV24 @ SV32 @ SV44 )
= $false )
| ( ( ! [SY223: $i] :
( ( ( tail_of @ SY223 )
!= ( tail_of @ SV24 ) )
| ~ ( edge @ SY223 )
| ( ( head_of @ SY223 )
!= ( head_of @ SV32 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(306,plain,
! [SV63: $i,SV6: $i] :
( ( ( ! [SY241: $i] :
~ ( path @ SV6 @ SV63 @ SY241 ) )
= $true )
| ( ( vertex @ SV6 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(307,plain,
! [SV58: $i,SV6: $i] :
( ( ( ! [SY237: $i] :
~ ( path @ SV6 @ SV58 @ SY237 ) )
= $true )
| ( ( vertex @ SV58 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[276]) ).
thf(308,plain,
! [SV40: $i,SV45: $i,SV6: $i] :
( ( ( ~ ~ ( ( SV6
!= ( tail_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( edge @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
| ~ ~ ( ~ ( ( SV40
!= ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
| ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ empty ) )
| ! [SY229: $i] :
( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ SY229 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ SY229 ) ) )
| ~ ~ ( ~ ( ( SV40
= ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ ( sK13_SY95 @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ ( sK13_SY95 @ SV45 @ SV40 @ SV6 ) ) ) )
| ~ ( ( SV45
= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ empty ) )
| ~ ( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ ( sK12_SY96 @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ ( sK12_SY96 @ SV45 @ SV40 @ SV6 ) ) ) ) ) ) )
= $false )
| ( ( path @ SV6 @ SV40 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(309,plain,
! [SV27: $i,SV33: $i] :
( ( ( vertex @ SV33 )
= $false )
| ( ( vertex @ SV27 )
= $false )
| ( ( SV27 = SV33 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV27
!= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
!= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
!= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
!= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV27
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
| ~ ( ( SV27
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) ) )
| ~ ~ ( ~ ( ( SV33
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
| ~ ( ( SV33
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV33 @ SV27 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(310,plain,
! [SV46: $i,SV41: $i,SV7: $i] :
( ( ( ~ ( path @ SV7 @ SV41 @ ( sK8_P @ SV46 @ SV41 @ SV7 ) )
| ~ ~ ( less_or_equal @ ( length_of @ SV46 ) @ ( length_of @ ( sK8_P @ SV46 @ SV41 @ SV7 ) ) ) )
= $false )
| ( ( ( SV7 = SV41 )
| ~ ( path @ SV7 @ SV41 @ SV46 ) )
= $true )
| ( ( shortest_path @ SV7 @ SV41 @ SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(311,plain,
! [SV64: $i,SV59: $i,SV7: $i] :
( ( ~ ( shortest_path @ SV7 @ SV59 @ SV64 )
| ! [SY242: $i] :
( ~ ( path @ SV7 @ SV59 @ SY242 )
| ( less_or_equal @ ( length_of @ SV64 ) @ ( length_of @ SY242 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(312,plain,
! [SV7: $i] :
( ( ~ ! [SY119: $i] :
( ! [SY120: $i] :
~ ( shortest_path @ SV7 @ SY119 @ SY120 )
| ( SV7 != SY119 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[281]) ).
thf(313,plain,
! [SV7: $i] :
( ( ~ ! [SY121: $i,SY122: $i] :
( ~ ( shortest_path @ SV7 @ SY121 @ SY122 )
| ( path @ SV7 @ SY121 @ SY122 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[281]) ).
thf(314,plain,
! [SV20: $i,SV8: $i,SV65: $i,SV51: $i,SV28: $i] :
( ( ( ~ ( precedes @ SV28 @ SV51 @ SV65 )
| ~ ( shortest_path @ SV8 @ SV20 @ SV65 ) )
= $true )
| ( ( ! [SY234: $i] :
( ( ( tail_of @ SY234 )
!= ( tail_of @ SV28 ) )
| ( ( head_of @ SY234 )
!= ( head_of @ SV51 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[282]) ).
thf(315,plain,
! [SV20: $i,SV8: $i,SV60: $i,SV52: $i,SV28: $i] :
( ( ( ~ ( precedes @ SV28 @ SV52 @ SV60 )
| ~ ( shortest_path @ SV8 @ SV20 @ SV60 ) )
= $true )
| ( ( ~ ( precedes @ SV52 @ SV28 @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[283]) ).
thf(316,plain,
! [SV29: $i,SV21: $i,SV9: $i] :
( ( ( ~ ! [SY217: $i] :
( ( SV9
!= ( tail_of @ SY217 ) )
| ~ ( edge @ SY217 )
| ( SV21
!= ( head_of @ SY217 ) )
| ( SV29
!= ( path_cons @ SY217 @ empty ) ) )
| ~ ! [SY218: $i] :
( ( SV9
!= ( tail_of @ SY218 ) )
| ~ ( edge @ SY218 )
| ! [SY219: $i] :
( ( SV29
!= ( path_cons @ SY218 @ SY219 ) )
| ~ ( path @ ( head_of @ SY218 ) @ SV21 @ SY219 ) ) ) )
= $false )
| ( ( vertex @ SV9 )
= $false )
| ( ( vertex @ SV21 )
= $false )
| ( ( path @ SV9 @ SV21 @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(317,plain,
! [SV34: $i,SV30: $i,SV10: $i] :
( ( ( ~ ! [SY137: $i] :
( ! [SY138: $i] :
~ ( precedes @ SY137 @ SY138 @ SV10 )
| ( on_path @ SY137 @ SV10 ) )
| ~ ! [SY139: $i,SY140: $i] :
( ~ ( precedes @ SY139 @ SY140 @ SV10 )
| ( on_path @ SY140 @ SV10 ) ) )
= $false )
| ( ( path @ SV30 @ SV34 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(318,plain,
! [SV34: $i,SV30: $i,SV10: $i] :
( ( ( ~ ! [SY141: $i,SY142: $i] :
( ~ ( precedes @ SY141 @ SY142 @ SV10 )
| ! [SY143: $i] :
( ~ ( precedes @ SY143 @ SY142 @ SV10 )
| ~ ( sequential @ SY141 @ SY143 ) )
| ~ ( sequential @ SY141 @ SY142 ) )
| ~ ! [SY144: $i,SY145: $i] :
( ~ ( precedes @ SY144 @ SY145 @ SV10 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY145 @ SY144 @ SV10 ) @ SY145 @ SV10 )
| ~ ( sequential @ SY144 @ ( sK9_E3 @ SY145 @ SY144 @ SV10 ) ) )
| ( sequential @ SY144 @ SY145 ) ) )
= $false )
| ( ( path @ SV30 @ SV34 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[286]) ).
thf(319,plain,
! [SV47: $i,SV42: $i,SV11: $i] :
( ( ( ~ ( edge @ SV11 )
| ~ ( edge @ SV42 )
| ~ ( edge @ SV47 )
| ~ ( sequential @ SV11 @ SV42 ) )
= $true )
| ( ( ~ ( sequential @ SV42 @ SV47 ) )
= $true )
| ( ( ~ ( sequential @ SV47 @ SV11 ) )
= $true )
| ( ( triangle @ SV11 @ SV42 @ SV47 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[287]) ).
thf(320,plain,
! [SV11: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY148: $i,SY149: $i] :
~ ( triangle @ SV11 @ SY148 @ SY149 )
| ( edge @ SV11 ) )
| ~ ! [SY150: $i] :
( ! [SY151: $i] :
~ ( triangle @ SV11 @ SY150 @ SY151 )
| ( edge @ SY150 ) ) )
| ~ ! [SY152: $i,SY153: $i] :
( ~ ( triangle @ SV11 @ SY152 @ SY153 )
| ( edge @ SY153 ) ) )
| ~ ! [SY154: $i] :
( ! [SY155: $i] :
~ ( triangle @ SV11 @ SY154 @ SY155 )
| ( sequential @ SV11 @ SY154 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[288]) ).
thf(321,plain,
! [SV11: $i] :
( ( ~ ! [SY156: $i,SY157: $i] :
( ~ ( triangle @ SV11 @ SY156 @ SY157 )
| ( sequential @ SY156 @ SY157 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[288]) ).
thf(322,plain,
! [SV66: $i,SV61: $i,SV11: $i] :
( ( ~ ( triangle @ SV11 @ SV61 @ SV66 )
| ( sequential @ SV66 @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[289]) ).
thf(323,plain,
! [SV22: $i,SV12: $i,SV67: $i] :
( ( ! [SY243: $i] :
( ~ ( on_path @ SY243 @ SV67 )
| ~ ( path @ SV12 @ SV22 @ SV67 )
| ( edge @ SY243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[290]) ).
thf(324,plain,
! [SV22: $i,SV12: $i,SV68: $i] :
( ( ! [SY244: $i] :
( ~ ( on_path @ SY244 @ SV68 )
| ~ ( path @ SV12 @ SV22 @ SV68 )
| ( in_path @ ( head_of @ SY244 ) @ SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(325,plain,
! [SV22: $i,SV12: $i,SV48: $i,SV53: $i] :
( ( ( ~ ( on_path @ SV53 @ SV48 ) )
= $true )
| ( ( ~ ( path @ SV12 @ SV22 @ SV48 ) )
= $true )
| ( ( in_path @ ( tail_of @ SV53 ) @ SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[292]) ).
thf(326,plain,
! [SV23: $i,SV13: $i,SV49: $i,SV54: $i] :
( ( ( ~ ( in_path @ SV54 @ SV49 ) )
= $true )
| ( ( ~ ( path @ SV13 @ SV23 @ SV49 ) )
= $true )
| ( ( ~ ( ~ ( on_path @ ( sK10_E @ SV54 @ SV49 @ SV23 @ SV13 ) @ SV49 )
| ~ ( ( SV54
= ( head_of @ ( sK10_E @ SV54 @ SV49 @ SV23 @ SV13 ) ) )
| ( SV54
= ( tail_of @ ( sK10_E @ SV54 @ SV49 @ SV23 @ SV13 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[293]) ).
thf(327,plain,
! [SV23: $i,SV13: $i,SV50: $i,SV55: $i] :
( ( ( ~ ( in_path @ SV55 @ SV50 ) )
= $true )
| ( ( ~ ( path @ SV13 @ SV23 @ SV50 ) )
= $true )
| ( ( vertex @ SV55 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[294]) ).
thf(328,plain,
! [SV37: $i,SV31: $i,SV14: $i,SV69: $i] :
( ( ( ! [SY245: $i] :
( ~ ( on_path @ SV69 @ SV14 )
| ~ ( on_path @ SY245 @ SV14 )
| ! [SY246: $i] :
( ~ ( precedes @ SY246 @ SY245 @ SV14 )
| ~ ( sequential @ SV69 @ SY246 ) )
| ( precedes @ SV69 @ SY245 @ SV14 ) ) )
= $true )
| ( ( path @ SV31 @ SV37 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(329,plain,
! [SV37: $i,SV31: $i,SV14: $i,SV70: $i] :
( ( ( ! [SY247: $i] :
( ~ ( on_path @ SV70 @ SV14 )
| ~ ( on_path @ SY247 @ SV14 )
| ~ ( sequential @ SV70 @ SY247 )
| ( precedes @ SV70 @ SY247 @ SV14 ) ) )
= $true )
| ( ( path @ SV31 @ SV37 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[296]) ).
thf(330,plain,
! [SV15: $i] :
( ( ( ~ ( ~ ( on_path @ ( sK6_E1 @ SV15 ) @ SV15 )
| ~ ( on_path @ ( sK7_SY91 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( ! [SY180: $i,SY181: $i] :
~ ( path @ SY180 @ SY181 @ SV15 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV15 )
= ( number_of_in @ triangles @ SV15 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[297]) ).
thf(331,plain,
! [SV15: $i] :
( ( ( sequential @ ( sK6_E1 @ SV15 ) @ ( sK7_SY91 @ SV15 ) )
= $true )
| ( ( ! [SY180: $i,SY181: $i] :
~ ( path @ SY180 @ SY181 @ SV15 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV15 )
= ( number_of_in @ triangles @ SV15 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[298]) ).
thf(332,plain,
! [SV56: $i,SV15: $i,SV71: $i] :
( ( ( ! [SY248: $i] :
~ ( path @ SV71 @ SY248 @ SV15 ) )
= $true )
| ( ( triangle @ ( sK6_E1 @ SV15 ) @ ( sK7_SY91 @ SV15 ) @ SV56 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV15 )
= ( number_of_in @ triangles @ SV15 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(333,plain,
! [SV43: $i,SV38: $i] :
( ( ( ~ ( edge @ SV38 ) )
= $true )
| ( ( ~ ( edge @ SV43 ) )
= $true )
| ( ( SV38 = SV43 )
= $true )
| ( ( ( ( head_of @ SV38 )
!= ( tail_of @ SV43 ) ) )
= $true )
| ( ( sequential @ SV38 @ SV43 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[300]) ).
thf(334,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[301]) ).
thf(335,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)],[302]) ).
thf(336,plain,
! [SV62: $i,SV57: $i] :
( ( ( ~ ( sequential @ SV57 @ SV62 ) )
= $true )
| ( ( ( head_of @ SV57 )
= ( tail_of @ SV62 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[303]) ).
thf(337,plain,
! [SV39: $i] :
( ( ( ( head_of @ SV39 )
= ( tail_of @ sK3_SY82 ) )
= $false )
| ( ( ( tail_of @ SV39 )
= ( head_of @ sK4_SY86 ) )
= $false )
| ( ( edge @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(338,plain,
! [SV16: $i,SV1: $i,SV44: $i,SV32: $i,SV24: $i,SV72: $i] :
( ( ( ( ( tail_of @ SV72 )
!= ( tail_of @ SV24 ) )
| ~ ( edge @ SV72 )
| ( ( head_of @ SV72 )
!= ( head_of @ SV32 ) ) )
= $true )
| ( ( precedes @ SV24 @ SV32 @ SV44 )
= $false )
| ( ( shortest_path @ SV1 @ SV16 @ SV44 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(339,plain,
! [SV73: $i,SV63: $i,SV6: $i] :
( ( ( ~ ( path @ SV6 @ SV63 @ SV73 ) )
= $true )
| ( ( vertex @ SV6 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(340,plain,
! [SV74: $i,SV58: $i,SV6: $i] :
( ( ( ~ ( path @ SV6 @ SV58 @ SV74 ) )
= $true )
| ( ( vertex @ SV58 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[307]) ).
thf(341,plain,
! [SV40: $i,SV45: $i,SV6: $i] :
( ( ( ~ ~ ( ( SV6
!= ( tail_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( edge @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) ) )
= $false )
| ( ( path @ SV6 @ SV40 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[308]) ).
thf(342,plain,
! [SV6: $i,SV45: $i,SV40: $i] :
( ( ( ~ ~ ( ~ ( ( SV40
!= ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
| ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ empty ) )
| ! [SY229: $i] :
( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ SY229 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ SY229 ) ) )
| ~ ~ ( ~ ( ( SV40
= ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ ( sK13_SY95 @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ ( sK13_SY95 @ SV45 @ SV40 @ SV6 ) ) ) )
| ~ ( ( SV45
= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ empty ) )
| ~ ( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ ( sK12_SY96 @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ ( sK12_SY96 @ SV45 @ SV40 @ SV6 ) ) ) ) ) ) )
= $false )
| ( ( path @ SV6 @ SV40 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[308]) ).
thf(343,plain,
! [SV33: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ( ( SV27
!= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
!= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
!= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
!= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV27
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
| ~ ( ( SV27
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) ) )
| ~ ~ ( ~ ( ( SV33
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
| ~ ( ( SV33
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) ) ) ) )
| ~ ( edge @ ( sK14_E @ SV33 @ SV27 ) ) )
= $false )
| ( ( SV27 = SV33 )
= $true )
| ( ( vertex @ SV27 )
= $false )
| ( ( vertex @ SV33 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[309]) ).
thf(344,plain,
! [SV46: $i,SV41: $i,SV7: $i] :
( ( ( ~ ( path @ SV7 @ SV41 @ ( sK8_P @ SV46 @ SV41 @ SV7 ) ) )
= $false )
| ( ( ( SV7 = SV41 )
| ~ ( path @ SV7 @ SV41 @ SV46 ) )
= $true )
| ( ( shortest_path @ SV7 @ SV41 @ SV46 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[310]) ).
thf(345,plain,
! [SV7: $i,SV41: $i,SV46: $i] :
( ( ( ~ ~ ( less_or_equal @ ( length_of @ SV46 ) @ ( length_of @ ( sK8_P @ SV46 @ SV41 @ SV7 ) ) ) )
= $false )
| ( ( ( SV7 = SV41 )
| ~ ( path @ SV7 @ SV41 @ SV46 ) )
= $true )
| ( ( shortest_path @ SV7 @ SV41 @ SV46 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[310]) ).
thf(346,plain,
! [SV64: $i,SV59: $i,SV7: $i] :
( ( ( ~ ( shortest_path @ SV7 @ SV59 @ SV64 ) )
= $true )
| ( ( ! [SY242: $i] :
( ~ ( path @ SV7 @ SV59 @ SY242 )
| ( less_or_equal @ ( length_of @ SV64 ) @ ( length_of @ SY242 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[311]) ).
thf(347,plain,
! [SV7: $i] :
( ( ! [SY119: $i] :
( ! [SY120: $i] :
~ ( shortest_path @ SV7 @ SY119 @ SY120 )
| ( SV7 != SY119 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[312]) ).
thf(348,plain,
! [SV7: $i] :
( ( ! [SY121: $i,SY122: $i] :
( ~ ( shortest_path @ SV7 @ SY121 @ SY122 )
| ( path @ SV7 @ SY121 @ SY122 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[313]) ).
thf(349,plain,
! [SV20: $i,SV8: $i,SV65: $i,SV51: $i,SV28: $i] :
( ( ( ~ ( precedes @ SV28 @ SV51 @ SV65 ) )
= $true )
| ( ( ~ ( shortest_path @ SV8 @ SV20 @ SV65 ) )
= $true )
| ( ( ! [SY234: $i] :
( ( ( tail_of @ SY234 )
!= ( tail_of @ SV28 ) )
| ( ( head_of @ SY234 )
!= ( head_of @ SV51 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[314]) ).
thf(350,plain,
! [SV20: $i,SV8: $i,SV60: $i,SV52: $i,SV28: $i] :
( ( ( ~ ( precedes @ SV28 @ SV52 @ SV60 ) )
= $true )
| ( ( ~ ( shortest_path @ SV8 @ SV20 @ SV60 ) )
= $true )
| ( ( ~ ( precedes @ SV52 @ SV28 @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[315]) ).
thf(351,plain,
! [SV29: $i,SV21: $i,SV9: $i] :
( ( ( ~ ! [SY217: $i] :
( ( SV9
!= ( tail_of @ SY217 ) )
| ~ ( edge @ SY217 )
| ( SV21
!= ( head_of @ SY217 ) )
| ( SV29
!= ( path_cons @ SY217 @ empty ) ) ) )
= $false )
| ( ( vertex @ SV9 )
= $false )
| ( ( vertex @ SV21 )
= $false )
| ( ( path @ SV9 @ SV21 @ SV29 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[316]) ).
thf(352,plain,
! [SV21: $i,SV29: $i,SV9: $i] :
( ( ( ~ ! [SY218: $i] :
( ( SV9
!= ( tail_of @ SY218 ) )
| ~ ( edge @ SY218 )
| ! [SY219: $i] :
( ( SV29
!= ( path_cons @ SY218 @ SY219 ) )
| ~ ( path @ ( head_of @ SY218 ) @ SV21 @ SY219 ) ) ) )
= $false )
| ( ( vertex @ SV9 )
= $false )
| ( ( vertex @ SV21 )
= $false )
| ( ( path @ SV9 @ SV21 @ SV29 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[316]) ).
thf(353,plain,
! [SV34: $i,SV30: $i,SV10: $i] :
( ( ( ~ ! [SY137: $i] :
( ! [SY138: $i] :
~ ( precedes @ SY137 @ SY138 @ SV10 )
| ( on_path @ SY137 @ SV10 ) ) )
= $false )
| ( ( path @ SV30 @ SV34 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[317]) ).
thf(354,plain,
! [SV34: $i,SV30: $i,SV10: $i] :
( ( ( ~ ! [SY139: $i,SY140: $i] :
( ~ ( precedes @ SY139 @ SY140 @ SV10 )
| ( on_path @ SY140 @ SV10 ) ) )
= $false )
| ( ( path @ SV30 @ SV34 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[317]) ).
thf(355,plain,
! [SV34: $i,SV30: $i,SV10: $i] :
( ( ( ~ ! [SY141: $i,SY142: $i] :
( ~ ( precedes @ SY141 @ SY142 @ SV10 )
| ! [SY143: $i] :
( ~ ( precedes @ SY143 @ SY142 @ SV10 )
| ~ ( sequential @ SY141 @ SY143 ) )
| ~ ( sequential @ SY141 @ SY142 ) ) )
= $false )
| ( ( path @ SV30 @ SV34 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[318]) ).
thf(356,plain,
! [SV34: $i,SV30: $i,SV10: $i] :
( ( ( ~ ! [SY144: $i,SY145: $i] :
( ~ ( precedes @ SY144 @ SY145 @ SV10 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY145 @ SY144 @ SV10 ) @ SY145 @ SV10 )
| ~ ( sequential @ SY144 @ ( sK9_E3 @ SY145 @ SY144 @ SV10 ) ) )
| ( sequential @ SY144 @ SY145 ) ) )
= $false )
| ( ( path @ SV30 @ SV34 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[318]) ).
thf(357,plain,
! [SV47: $i,SV42: $i,SV11: $i] :
( ( ( ~ ( edge @ SV11 )
| ~ ( edge @ SV42 )
| ~ ( edge @ SV47 ) )
= $true )
| ( ( ~ ( sequential @ SV11 @ SV42 ) )
= $true )
| ( ( ~ ( sequential @ SV42 @ SV47 ) )
= $true )
| ( ( ~ ( sequential @ SV47 @ SV11 ) )
= $true )
| ( ( triangle @ SV11 @ SV42 @ SV47 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[319]) ).
thf(358,plain,
! [SV11: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ! [SY148: $i,SY149: $i] :
~ ( triangle @ SV11 @ SY148 @ SY149 )
| ( edge @ SV11 ) )
| ~ ! [SY150: $i] :
( ! [SY151: $i] :
~ ( triangle @ SV11 @ SY150 @ SY151 )
| ( edge @ SY150 ) ) )
| ~ ! [SY152: $i,SY153: $i] :
( ~ ( triangle @ SV11 @ SY152 @ SY153 )
| ( edge @ SY153 ) ) )
| ~ ! [SY154: $i] :
( ! [SY155: $i] :
~ ( triangle @ SV11 @ SY154 @ SY155 )
| ( sequential @ SV11 @ SY154 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[320]) ).
thf(359,plain,
! [SV11: $i] :
( ( ! [SY156: $i,SY157: $i] :
( ~ ( triangle @ SV11 @ SY156 @ SY157 )
| ( sequential @ SY156 @ SY157 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[321]) ).
thf(360,plain,
! [SV66: $i,SV61: $i,SV11: $i] :
( ( ( ~ ( triangle @ SV11 @ SV61 @ SV66 ) )
= $true )
| ( ( sequential @ SV66 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[322]) ).
thf(361,plain,
! [SV22: $i,SV12: $i,SV67: $i,SV75: $i] :
( ( ~ ( on_path @ SV75 @ SV67 )
| ~ ( path @ SV12 @ SV22 @ SV67 )
| ( edge @ SV75 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[323]) ).
thf(362,plain,
! [SV22: $i,SV12: $i,SV68: $i,SV76: $i] :
( ( ~ ( on_path @ SV76 @ SV68 )
| ~ ( path @ SV12 @ SV22 @ SV68 )
| ( in_path @ ( head_of @ SV76 ) @ SV68 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(363,plain,
! [SV22: $i,SV12: $i,SV48: $i,SV53: $i] :
( ( ( on_path @ SV53 @ SV48 )
= $false )
| ( ( ~ ( path @ SV12 @ SV22 @ SV48 ) )
= $true )
| ( ( in_path @ ( tail_of @ SV53 ) @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(364,plain,
! [SV23: $i,SV13: $i,SV49: $i,SV54: $i] :
( ( ( in_path @ SV54 @ SV49 )
= $false )
| ( ( ~ ( path @ SV13 @ SV23 @ SV49 ) )
= $true )
| ( ( ~ ( ~ ( on_path @ ( sK10_E @ SV54 @ SV49 @ SV23 @ SV13 ) @ SV49 )
| ~ ( ( SV54
= ( head_of @ ( sK10_E @ SV54 @ SV49 @ SV23 @ SV13 ) ) )
| ( SV54
= ( tail_of @ ( sK10_E @ SV54 @ SV49 @ SV23 @ SV13 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(365,plain,
! [SV23: $i,SV13: $i,SV50: $i,SV55: $i] :
( ( ( in_path @ SV55 @ SV50 )
= $false )
| ( ( ~ ( path @ SV13 @ SV23 @ SV50 ) )
= $true )
| ( ( vertex @ SV55 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[327]) ).
thf(366,plain,
! [SV37: $i,SV31: $i,SV77: $i,SV14: $i,SV69: $i] :
( ( ( ~ ( on_path @ SV69 @ SV14 )
| ~ ( on_path @ SV77 @ SV14 )
| ! [SY249: $i] :
( ~ ( precedes @ SY249 @ SV77 @ SV14 )
| ~ ( sequential @ SV69 @ SY249 ) )
| ( precedes @ SV69 @ SV77 @ SV14 ) )
= $true )
| ( ( path @ SV31 @ SV37 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[328]) ).
thf(367,plain,
! [SV37: $i,SV31: $i,SV78: $i,SV14: $i,SV70: $i] :
( ( ( ~ ( on_path @ SV70 @ SV14 )
| ~ ( on_path @ SV78 @ SV14 )
| ~ ( sequential @ SV70 @ SV78 )
| ( precedes @ SV70 @ SV78 @ SV14 ) )
= $true )
| ( ( path @ SV31 @ SV37 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[329]) ).
thf(368,plain,
! [SV15: $i] :
( ( ( ~ ( on_path @ ( sK6_E1 @ SV15 ) @ SV15 )
| ~ ( on_path @ ( sK7_SY91 @ SV15 ) @ SV15 ) )
= $false )
| ( ( ! [SY180: $i,SY181: $i] :
~ ( path @ SY180 @ SY181 @ SV15 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV15 )
= ( number_of_in @ triangles @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(369,plain,
! [SV15: $i,SV79: $i] :
( ( ( ! [SY250: $i] :
~ ( path @ SV79 @ SY250 @ SV15 ) )
= $true )
| ( ( sequential @ ( sK6_E1 @ SV15 ) @ ( sK7_SY91 @ SV15 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV15 )
= ( number_of_in @ triangles @ SV15 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[331]) ).
thf(370,plain,
! [SV56: $i,SV15: $i,SV80: $i,SV71: $i] :
( ( ( ~ ( path @ SV71 @ SV80 @ SV15 ) )
= $true )
| ( ( triangle @ ( sK6_E1 @ SV15 ) @ ( sK7_SY91 @ SV15 ) @ SV56 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV15 )
= ( number_of_in @ triangles @ SV15 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[332]) ).
thf(371,plain,
! [SV43: $i,SV38: $i] :
( ( ( edge @ SV38 )
= $false )
| ( ( ~ ( edge @ SV43 ) )
= $true )
| ( ( SV38 = SV43 )
= $true )
| ( ( ( ( head_of @ SV38 )
!= ( tail_of @ SV43 ) ) )
= $true )
| ( ( sequential @ SV38 @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[333]) ).
thf(372,plain,
! [SV81: $i] :
( ( ! [SY251: $i] :
( ~ ( sequential @ SV81 @ SY251 )
| ( SV81 != SY251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[334]) ).
thf(373,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)],[335]) ).
thf(374,plain,
! [SV62: $i,SV57: $i] :
( ( ( sequential @ SV57 @ SV62 )
= $false )
| ( ( ( head_of @ SV57 )
= ( tail_of @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[336]) ).
thf(375,plain,
! [SV16: $i,SV1: $i,SV44: $i,SV32: $i,SV24: $i,SV72: $i] :
( ( ( ( ( tail_of @ SV72 )
!= ( tail_of @ SV24 ) )
| ~ ( edge @ SV72 ) )
= $true )
| ( ( ( ( head_of @ SV72 )
!= ( head_of @ SV32 ) ) )
= $true )
| ( ( precedes @ SV24 @ SV32 @ SV44 )
= $false )
| ( ( shortest_path @ SV1 @ SV16 @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[338]) ).
thf(376,plain,
! [SV73: $i,SV63: $i,SV6: $i] :
( ( ( path @ SV6 @ SV63 @ SV73 )
= $false )
| ( ( vertex @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(377,plain,
! [SV74: $i,SV58: $i,SV6: $i] :
( ( ( path @ SV6 @ SV58 @ SV74 )
= $false )
| ( ( vertex @ SV58 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[340]) ).
thf(378,plain,
! [SV40: $i,SV45: $i,SV6: $i] :
( ( ( ~ ( ( SV6
!= ( tail_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( edge @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) ) )
= $true )
| ( ( path @ SV6 @ SV40 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[341]) ).
thf(379,plain,
! [SV6: $i,SV45: $i,SV40: $i] :
( ( ( ~ ( ~ ( ( SV40
!= ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
| ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ empty ) )
| ! [SY229: $i] :
( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ SY229 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ SY229 ) ) )
| ~ ~ ( ~ ( ( SV40
= ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ ( sK13_SY95 @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ ( sK13_SY95 @ SV45 @ SV40 @ SV6 ) ) ) )
| ~ ( ( SV45
= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ empty ) )
| ~ ( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ ( sK12_SY96 @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ ( sK12_SY96 @ SV45 @ SV40 @ SV6 ) ) ) ) ) ) )
= $true )
| ( ( path @ SV6 @ SV40 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[342]) ).
thf(380,plain,
! [SV33: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ( ( SV27
!= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
!= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
!= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
!= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV27
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
| ~ ( ( SV27
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) ) )
| ~ ~ ( ~ ( ( SV33
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
| ~ ( ( SV33
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) ) ) ) ) )
= $false )
| ( ( SV27 = SV33 )
= $true )
| ( ( vertex @ SV27 )
= $false )
| ( ( vertex @ SV33 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[343]) ).
thf(381,plain,
! [SV27: $i,SV33: $i] :
( ( ( ~ ( edge @ ( sK14_E @ SV33 @ SV27 ) ) )
= $false )
| ( ( SV27 = SV33 )
= $true )
| ( ( vertex @ SV27 )
= $false )
| ( ( vertex @ SV33 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[343]) ).
thf(382,plain,
! [SV46: $i,SV41: $i,SV7: $i] :
( ( ( path @ SV7 @ SV41 @ ( sK8_P @ SV46 @ SV41 @ SV7 ) )
= $true )
| ( ( ( SV7 = SV41 )
| ~ ( path @ SV7 @ SV41 @ SV46 ) )
= $true )
| ( ( shortest_path @ SV7 @ SV41 @ SV46 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[344]) ).
thf(383,plain,
! [SV7: $i,SV41: $i,SV46: $i] :
( ( ( ~ ( less_or_equal @ ( length_of @ SV46 ) @ ( length_of @ ( sK8_P @ SV46 @ SV41 @ SV7 ) ) ) )
= $true )
| ( ( ( SV7 = SV41 )
| ~ ( path @ SV7 @ SV41 @ SV46 ) )
= $true )
| ( ( shortest_path @ SV7 @ SV41 @ SV46 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[345]) ).
thf(384,plain,
! [SV64: $i,SV59: $i,SV7: $i] :
( ( ( shortest_path @ SV7 @ SV59 @ SV64 )
= $false )
| ( ( ! [SY242: $i] :
( ~ ( path @ SV7 @ SV59 @ SY242 )
| ( less_or_equal @ ( length_of @ SV64 ) @ ( length_of @ SY242 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(385,plain,
! [SV82: $i,SV7: $i] :
( ( ! [SY252: $i] :
~ ( shortest_path @ SV7 @ SV82 @ SY252 )
| ( SV7 != SV82 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(386,plain,
! [SV83: $i,SV7: $i] :
( ( ! [SY253: $i] :
( ~ ( shortest_path @ SV7 @ SV83 @ SY253 )
| ( path @ SV7 @ SV83 @ SY253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(387,plain,
! [SV20: $i,SV8: $i,SV65: $i,SV51: $i,SV28: $i] :
( ( ( precedes @ SV28 @ SV51 @ SV65 )
= $false )
| ( ( ~ ( shortest_path @ SV8 @ SV20 @ SV65 ) )
= $true )
| ( ( ! [SY234: $i] :
( ( ( tail_of @ SY234 )
!= ( tail_of @ SV28 ) )
| ( ( head_of @ SY234 )
!= ( head_of @ SV51 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[349]) ).
thf(388,plain,
! [SV20: $i,SV8: $i,SV60: $i,SV52: $i,SV28: $i] :
( ( ( precedes @ SV28 @ SV52 @ SV60 )
= $false )
| ( ( ~ ( shortest_path @ SV8 @ SV20 @ SV60 ) )
= $true )
| ( ( ~ ( precedes @ SV52 @ SV28 @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[350]) ).
thf(389,plain,
! [SV29: $i,SV21: $i,SV9: $i] :
( ( ( ! [SY217: $i] :
( ( SV9
!= ( tail_of @ SY217 ) )
| ~ ( edge @ SY217 )
| ( SV21
!= ( head_of @ SY217 ) )
| ( SV29
!= ( path_cons @ SY217 @ empty ) ) ) )
= $true )
| ( ( vertex @ SV9 )
= $false )
| ( ( vertex @ SV21 )
= $false )
| ( ( path @ SV9 @ SV21 @ SV29 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[351]) ).
thf(390,plain,
! [SV21: $i,SV29: $i,SV9: $i] :
( ( ( ! [SY218: $i] :
( ( SV9
!= ( tail_of @ SY218 ) )
| ~ ( edge @ SY218 )
| ! [SY219: $i] :
( ( SV29
!= ( path_cons @ SY218 @ SY219 ) )
| ~ ( path @ ( head_of @ SY218 ) @ SV21 @ SY219 ) ) ) )
= $true )
| ( ( vertex @ SV9 )
= $false )
| ( ( vertex @ SV21 )
= $false )
| ( ( path @ SV9 @ SV21 @ SV29 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[352]) ).
thf(391,plain,
! [SV34: $i,SV30: $i,SV10: $i] :
( ( ( ! [SY137: $i] :
( ! [SY138: $i] :
~ ( precedes @ SY137 @ SY138 @ SV10 )
| ( on_path @ SY137 @ SV10 ) ) )
= $true )
| ( ( path @ SV30 @ SV34 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[353]) ).
thf(392,plain,
! [SV34: $i,SV30: $i,SV10: $i] :
( ( ( ! [SY139: $i,SY140: $i] :
( ~ ( precedes @ SY139 @ SY140 @ SV10 )
| ( on_path @ SY140 @ SV10 ) ) )
= $true )
| ( ( path @ SV30 @ SV34 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[354]) ).
thf(393,plain,
! [SV34: $i,SV30: $i,SV10: $i] :
( ( ( ! [SY141: $i,SY142: $i] :
( ~ ( precedes @ SY141 @ SY142 @ SV10 )
| ! [SY143: $i] :
( ~ ( precedes @ SY143 @ SY142 @ SV10 )
| ~ ( sequential @ SY141 @ SY143 ) )
| ~ ( sequential @ SY141 @ SY142 ) ) )
= $true )
| ( ( path @ SV30 @ SV34 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[355]) ).
thf(394,plain,
! [SV34: $i,SV30: $i,SV10: $i] :
( ( ( ! [SY144: $i,SY145: $i] :
( ~ ( precedes @ SY144 @ SY145 @ SV10 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY145 @ SY144 @ SV10 ) @ SY145 @ SV10 )
| ~ ( sequential @ SY144 @ ( sK9_E3 @ SY145 @ SY144 @ SV10 ) ) )
| ( sequential @ SY144 @ SY145 ) ) )
= $true )
| ( ( path @ SV30 @ SV34 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[356]) ).
thf(395,plain,
! [SV47: $i,SV42: $i,SV11: $i] :
( ( ( ~ ( edge @ SV11 )
| ~ ( edge @ SV42 ) )
= $true )
| ( ( ~ ( edge @ SV47 ) )
= $true )
| ( ( ~ ( sequential @ SV11 @ SV42 ) )
= $true )
| ( ( ~ ( sequential @ SV42 @ SV47 ) )
= $true )
| ( ( ~ ( sequential @ SV47 @ SV11 ) )
= $true )
| ( ( triangle @ SV11 @ SV42 @ SV47 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[357]) ).
thf(396,plain,
! [SV11: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( ! [SY148: $i,SY149: $i] :
~ ( triangle @ SV11 @ SY148 @ SY149 )
| ( edge @ SV11 ) )
| ~ ! [SY150: $i] :
( ! [SY151: $i] :
~ ( triangle @ SV11 @ SY150 @ SY151 )
| ( edge @ SY150 ) ) )
| ~ ! [SY152: $i,SY153: $i] :
( ~ ( triangle @ SV11 @ SY152 @ SY153 )
| ( edge @ SY153 ) ) )
| ~ ! [SY154: $i] :
( ! [SY155: $i] :
~ ( triangle @ SV11 @ SY154 @ SY155 )
| ( sequential @ SV11 @ SY154 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[358]) ).
thf(397,plain,
! [SV84: $i,SV11: $i] :
( ( ! [SY254: $i] :
( ~ ( triangle @ SV11 @ SV84 @ SY254 )
| ( sequential @ SV84 @ SY254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[359]) ).
thf(398,plain,
! [SV66: $i,SV61: $i,SV11: $i] :
( ( ( triangle @ SV11 @ SV61 @ SV66 )
= $false )
| ( ( sequential @ SV66 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[360]) ).
thf(399,plain,
! [SV22: $i,SV12: $i,SV67: $i,SV75: $i] :
( ( ( ~ ( on_path @ SV75 @ SV67 )
| ~ ( path @ SV12 @ SV22 @ SV67 ) )
= $true )
| ( ( edge @ SV75 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[361]) ).
thf(400,plain,
! [SV22: $i,SV12: $i,SV68: $i,SV76: $i] :
( ( ( ~ ( on_path @ SV76 @ SV68 )
| ~ ( path @ SV12 @ SV22 @ SV68 ) )
= $true )
| ( ( in_path @ ( head_of @ SV76 ) @ SV68 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[362]) ).
thf(401,plain,
! [SV53: $i,SV48: $i,SV22: $i,SV12: $i] :
( ( ( path @ SV12 @ SV22 @ SV48 )
= $false )
| ( ( on_path @ SV53 @ SV48 )
= $false )
| ( ( in_path @ ( tail_of @ SV53 ) @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(402,plain,
! [SV54: $i,SV49: $i,SV23: $i,SV13: $i] :
( ( ( path @ SV13 @ SV23 @ SV49 )
= $false )
| ( ( in_path @ SV54 @ SV49 )
= $false )
| ( ( ~ ( ~ ( on_path @ ( sK10_E @ SV54 @ SV49 @ SV23 @ SV13 ) @ SV49 )
| ~ ( ( SV54
= ( head_of @ ( sK10_E @ SV54 @ SV49 @ SV23 @ SV13 ) ) )
| ( SV54
= ( tail_of @ ( sK10_E @ SV54 @ SV49 @ SV23 @ SV13 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[364]) ).
thf(403,plain,
! [SV55: $i,SV50: $i,SV23: $i,SV13: $i] :
( ( ( path @ SV13 @ SV23 @ SV50 )
= $false )
| ( ( in_path @ SV55 @ SV50 )
= $false )
| ( ( vertex @ SV55 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[365]) ).
thf(404,plain,
! [SV37: $i,SV31: $i,SV77: $i,SV14: $i,SV69: $i] :
( ( ( ~ ( on_path @ SV69 @ SV14 )
| ~ ( on_path @ SV77 @ SV14 )
| ! [SY249: $i] :
( ~ ( precedes @ SY249 @ SV77 @ SV14 )
| ~ ( sequential @ SV69 @ SY249 ) ) )
= $true )
| ( ( precedes @ SV69 @ SV77 @ SV14 )
= $true )
| ( ( path @ SV31 @ SV37 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[366]) ).
thf(405,plain,
! [SV37: $i,SV31: $i,SV78: $i,SV14: $i,SV70: $i] :
( ( ( ~ ( on_path @ SV70 @ SV14 )
| ~ ( on_path @ SV78 @ SV14 )
| ~ ( sequential @ SV70 @ SV78 ) )
= $true )
| ( ( precedes @ SV70 @ SV78 @ SV14 )
= $true )
| ( ( path @ SV31 @ SV37 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[367]) ).
thf(406,plain,
! [SV15: $i] :
( ( ( ~ ( on_path @ ( sK6_E1 @ SV15 ) @ SV15 ) )
= $false )
| ( ( ! [SY180: $i,SY181: $i] :
~ ( path @ SY180 @ SY181 @ SV15 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV15 )
= ( number_of_in @ triangles @ SV15 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[368]) ).
thf(407,plain,
! [SV15: $i] :
( ( ( ~ ( on_path @ ( sK7_SY91 @ SV15 ) @ SV15 ) )
= $false )
| ( ( ! [SY180: $i,SY181: $i] :
~ ( path @ SY180 @ SY181 @ SV15 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV15 )
= ( number_of_in @ triangles @ SV15 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[368]) ).
thf(408,plain,
! [SV15: $i,SV85: $i,SV79: $i] :
( ( ( ~ ( path @ SV79 @ SV85 @ SV15 ) )
= $true )
| ( ( sequential @ ( sK6_E1 @ SV15 ) @ ( sK7_SY91 @ SV15 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV15 )
= ( number_of_in @ triangles @ SV15 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[369]) ).
thf(409,plain,
! [SV56: $i,SV15: $i,SV80: $i,SV71: $i] :
( ( ( path @ SV71 @ SV80 @ SV15 )
= $false )
| ( ( triangle @ ( sK6_E1 @ SV15 ) @ ( sK7_SY91 @ SV15 ) @ SV56 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV15 )
= ( number_of_in @ triangles @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[370]) ).
thf(410,plain,
! [SV38: $i,SV43: $i] :
( ( ( edge @ SV43 )
= $false )
| ( ( edge @ SV38 )
= $false )
| ( ( SV38 = SV43 )
= $true )
| ( ( ( ( head_of @ SV38 )
!= ( tail_of @ SV43 ) ) )
= $true )
| ( ( sequential @ SV38 @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[371]) ).
thf(411,plain,
! [SV86: $i,SV81: $i] :
( ( ~ ( sequential @ SV81 @ SV86 )
| ( SV81 != SV86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[372]) ).
thf(412,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[373]) ).
thf(413,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[373]) ).
thf(414,plain,
! [SV16: $i,SV1: $i,SV44: $i,SV32: $i,SV24: $i,SV72: $i] :
( ( ( ( ( tail_of @ SV72 )
!= ( tail_of @ SV24 ) ) )
= $true )
| ( ( ~ ( edge @ SV72 ) )
= $true )
| ( ( ( ( head_of @ SV72 )
!= ( head_of @ SV32 ) ) )
= $true )
| ( ( precedes @ SV24 @ SV32 @ SV44 )
= $false )
| ( ( shortest_path @ SV1 @ SV16 @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[375]) ).
thf(415,plain,
! [SV40: $i,SV45: $i,SV6: $i] :
( ( ( ( SV6
!= ( tail_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( edge @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
= $false )
| ( ( path @ SV6 @ SV40 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(416,plain,
! [SV6: $i,SV45: $i,SV40: $i] :
( ( ( ~ ( ( SV40
!= ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
| ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ empty ) )
| ! [SY229: $i] :
( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ SY229 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ SY229 ) ) )
| ~ ~ ( ~ ( ( SV40
= ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ ( sK13_SY95 @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ ( sK13_SY95 @ SV45 @ SV40 @ SV6 ) ) ) )
| ~ ( ( SV45
= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ empty ) )
| ~ ( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ ( sK12_SY96 @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ ( sK12_SY96 @ SV45 @ SV40 @ SV6 ) ) ) ) ) )
= $false )
| ( ( path @ SV6 @ SV40 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(417,plain,
! [SV33: $i,SV27: $i] :
( ( ( ~ ( ~ ( ( SV27
!= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
!= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
!= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
!= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV27
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
| ~ ( ( SV27
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) ) )
| ~ ~ ( ~ ( ( SV33
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
| ~ ( ( SV33
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) ) ) ) ) )
= $true )
| ( ( SV27 = SV33 )
= $true )
| ( ( vertex @ SV27 )
= $false )
| ( ( vertex @ SV33 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[380]) ).
thf(418,plain,
! [SV27: $i,SV33: $i] :
( ( ( edge @ ( sK14_E @ SV33 @ SV27 ) )
= $true )
| ( ( SV27 = SV33 )
= $true )
| ( ( vertex @ SV27 )
= $false )
| ( ( vertex @ SV33 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[381]) ).
thf(419,plain,
! [SV46: $i,SV41: $i,SV7: $i] :
( ( ( SV7 = SV41 )
= $true )
| ( ( ~ ( path @ SV7 @ SV41 @ SV46 ) )
= $true )
| ( ( path @ SV7 @ SV41 @ ( sK8_P @ SV46 @ SV41 @ SV7 ) )
= $true )
| ( ( shortest_path @ SV7 @ SV41 @ SV46 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[382]) ).
thf(420,plain,
! [SV7: $i,SV41: $i,SV46: $i] :
( ( ( less_or_equal @ ( length_of @ SV46 ) @ ( length_of @ ( sK8_P @ SV46 @ SV41 @ SV7 ) ) )
= $false )
| ( ( ( SV7 = SV41 )
| ~ ( path @ SV7 @ SV41 @ SV46 ) )
= $true )
| ( ( shortest_path @ SV7 @ SV41 @ SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[383]) ).
thf(421,plain,
! [SV64: $i,SV87: $i,SV59: $i,SV7: $i] :
( ( ( ~ ( path @ SV7 @ SV59 @ SV87 )
| ( less_or_equal @ ( length_of @ SV64 ) @ ( length_of @ SV87 ) ) )
= $true )
| ( ( shortest_path @ SV7 @ SV59 @ SV64 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[384]) ).
thf(422,plain,
! [SV82: $i,SV7: $i] :
( ( ( ! [SY252: $i] :
~ ( shortest_path @ SV7 @ SV82 @ SY252 ) )
= $true )
| ( ( ( SV7 != SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[385]) ).
thf(423,plain,
! [SV88: $i,SV83: $i,SV7: $i] :
( ( ~ ( shortest_path @ SV7 @ SV83 @ SV88 )
| ( path @ SV7 @ SV83 @ SV88 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[386]) ).
thf(424,plain,
! [SV51: $i,SV28: $i,SV65: $i,SV20: $i,SV8: $i] :
( ( ( shortest_path @ SV8 @ SV20 @ SV65 )
= $false )
| ( ( precedes @ SV28 @ SV51 @ SV65 )
= $false )
| ( ( ! [SY234: $i] :
( ( ( tail_of @ SY234 )
!= ( tail_of @ SV28 ) )
| ( ( head_of @ SY234 )
!= ( head_of @ SV51 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[387]) ).
thf(425,plain,
! [SV52: $i,SV28: $i,SV60: $i,SV20: $i,SV8: $i] :
( ( ( shortest_path @ SV8 @ SV20 @ SV60 )
= $false )
| ( ( precedes @ SV28 @ SV52 @ SV60 )
= $false )
| ( ( ~ ( precedes @ SV52 @ SV28 @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[388]) ).
thf(426,plain,
! [SV29: $i,SV21: $i,SV89: $i,SV9: $i] :
( ( ( ( SV9
!= ( tail_of @ SV89 ) )
| ~ ( edge @ SV89 )
| ( SV21
!= ( head_of @ SV89 ) )
| ( SV29
!= ( path_cons @ SV89 @ empty ) ) )
= $true )
| ( ( vertex @ SV9 )
= $false )
| ( ( vertex @ SV21 )
= $false )
| ( ( path @ SV9 @ SV21 @ SV29 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(427,plain,
! [SV21: $i,SV29: $i,SV90: $i,SV9: $i] :
( ( ( ( SV9
!= ( tail_of @ SV90 ) )
| ~ ( edge @ SV90 )
| ! [SY255: $i] :
( ( SV29
!= ( path_cons @ SV90 @ SY255 ) )
| ~ ( path @ ( head_of @ SV90 ) @ SV21 @ SY255 ) ) )
= $true )
| ( ( vertex @ SV9 )
= $false )
| ( ( vertex @ SV21 )
= $false )
| ( ( path @ SV9 @ SV21 @ SV29 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(428,plain,
! [SV34: $i,SV30: $i,SV10: $i,SV91: $i] :
( ( ( ! [SY256: $i] :
~ ( precedes @ SV91 @ SY256 @ SV10 )
| ( on_path @ SV91 @ SV10 ) )
= $true )
| ( ( path @ SV30 @ SV34 @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(429,plain,
! [SV34: $i,SV30: $i,SV10: $i,SV92: $i] :
( ( ( ! [SY257: $i] :
( ~ ( precedes @ SV92 @ SY257 @ SV10 )
| ( on_path @ SY257 @ SV10 ) ) )
= $true )
| ( ( path @ SV30 @ SV34 @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(430,plain,
! [SV34: $i,SV30: $i,SV10: $i,SV93: $i] :
( ( ( ! [SY258: $i] :
( ~ ( precedes @ SV93 @ SY258 @ SV10 )
| ! [SY259: $i] :
( ~ ( precedes @ SY259 @ SY258 @ SV10 )
| ~ ( sequential @ SV93 @ SY259 ) )
| ~ ( sequential @ SV93 @ SY258 ) ) )
= $true )
| ( ( path @ SV30 @ SV34 @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[393]) ).
thf(431,plain,
! [SV34: $i,SV30: $i,SV10: $i,SV94: $i] :
( ( ( ! [SY260: $i] :
( ~ ( precedes @ SV94 @ SY260 @ SV10 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SY260 @ SV94 @ SV10 ) @ SY260 @ SV10 )
| ~ ( sequential @ SV94 @ ( sK9_E3 @ SY260 @ SV94 @ SV10 ) ) )
| ( sequential @ SV94 @ SY260 ) ) )
= $true )
| ( ( path @ SV30 @ SV34 @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[394]) ).
thf(432,plain,
! [SV47: $i,SV42: $i,SV11: $i] :
( ( ( ~ ( edge @ SV11 ) )
= $true )
| ( ( ~ ( edge @ SV42 ) )
= $true )
| ( ( ~ ( edge @ SV47 ) )
= $true )
| ( ( ~ ( sequential @ SV11 @ SV42 ) )
= $true )
| ( ( ~ ( sequential @ SV42 @ SV47 ) )
= $true )
| ( ( ~ ( sequential @ SV47 @ SV11 ) )
= $true )
| ( ( triangle @ SV11 @ SV42 @ SV47 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[395]) ).
thf(433,plain,
! [SV11: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( ! [SY148: $i,SY149: $i] :
~ ( triangle @ SV11 @ SY148 @ SY149 )
| ( edge @ SV11 ) )
| ~ ! [SY150: $i] :
( ! [SY151: $i] :
~ ( triangle @ SV11 @ SY150 @ SY151 )
| ( edge @ SY150 ) ) )
| ~ ! [SY152: $i,SY153: $i] :
( ~ ( triangle @ SV11 @ SY152 @ SY153 )
| ( edge @ SY153 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[396]) ).
thf(434,plain,
! [SV11: $i] :
( ( ~ ! [SY154: $i] :
( ! [SY155: $i] :
~ ( triangle @ SV11 @ SY154 @ SY155 )
| ( sequential @ SV11 @ SY154 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[396]) ).
thf(435,plain,
! [SV95: $i,SV84: $i,SV11: $i] :
( ( ~ ( triangle @ SV11 @ SV84 @ SV95 )
| ( sequential @ SV84 @ SV95 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(436,plain,
! [SV22: $i,SV12: $i,SV67: $i,SV75: $i] :
( ( ( ~ ( on_path @ SV75 @ SV67 ) )
= $true )
| ( ( ~ ( path @ SV12 @ SV22 @ SV67 ) )
= $true )
| ( ( edge @ SV75 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[399]) ).
thf(437,plain,
! [SV22: $i,SV12: $i,SV68: $i,SV76: $i] :
( ( ( ~ ( on_path @ SV76 @ SV68 ) )
= $true )
| ( ( ~ ( path @ SV12 @ SV22 @ SV68 ) )
= $true )
| ( ( in_path @ ( head_of @ SV76 ) @ SV68 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[400]) ).
thf(438,plain,
! [SV13: $i,SV23: $i,SV49: $i,SV54: $i] :
( ( ( ~ ( on_path @ ( sK10_E @ SV54 @ SV49 @ SV23 @ SV13 ) @ SV49 )
| ~ ( ( SV54
= ( head_of @ ( sK10_E @ SV54 @ SV49 @ SV23 @ SV13 ) ) )
| ( SV54
= ( tail_of @ ( sK10_E @ SV54 @ SV49 @ SV23 @ SV13 ) ) ) ) )
= $false )
| ( ( in_path @ SV54 @ SV49 )
= $false )
| ( ( path @ SV13 @ SV23 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[402]) ).
thf(439,plain,
! [SV37: $i,SV31: $i,SV77: $i,SV14: $i,SV69: $i] :
( ( ( ~ ( on_path @ SV69 @ SV14 )
| ~ ( on_path @ SV77 @ SV14 ) )
= $true )
| ( ( ! [SY249: $i] :
( ~ ( precedes @ SY249 @ SV77 @ SV14 )
| ~ ( sequential @ SV69 @ SY249 ) ) )
= $true )
| ( ( precedes @ SV69 @ SV77 @ SV14 )
= $true )
| ( ( path @ SV31 @ SV37 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[404]) ).
thf(440,plain,
! [SV37: $i,SV31: $i,SV78: $i,SV14: $i,SV70: $i] :
( ( ( ~ ( on_path @ SV70 @ SV14 )
| ~ ( on_path @ SV78 @ SV14 ) )
= $true )
| ( ( ~ ( sequential @ SV70 @ SV78 ) )
= $true )
| ( ( precedes @ SV70 @ SV78 @ SV14 )
= $true )
| ( ( path @ SV31 @ SV37 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[405]) ).
thf(441,plain,
! [SV15: $i] :
( ( ( on_path @ ( sK6_E1 @ SV15 ) @ SV15 )
= $true )
| ( ( ! [SY180: $i,SY181: $i] :
~ ( path @ SY180 @ SY181 @ SV15 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV15 )
= ( number_of_in @ triangles @ SV15 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[406]) ).
thf(442,plain,
! [SV15: $i] :
( ( ( on_path @ ( sK7_SY91 @ SV15 ) @ SV15 )
= $true )
| ( ( ! [SY180: $i,SY181: $i] :
~ ( path @ SY180 @ SY181 @ SV15 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV15 )
= ( number_of_in @ triangles @ SV15 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[407]) ).
thf(443,plain,
! [SV15: $i,SV85: $i,SV79: $i] :
( ( ( path @ SV79 @ SV85 @ SV15 )
= $false )
| ( ( sequential @ ( sK6_E1 @ SV15 ) @ ( sK7_SY91 @ SV15 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV15 )
= ( number_of_in @ triangles @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(444,plain,
! [SV43: $i,SV38: $i] :
( ( ( ( head_of @ SV38 )
= ( tail_of @ SV43 ) )
= $false )
| ( ( SV38 = SV43 )
= $true )
| ( ( edge @ SV38 )
= $false )
| ( ( edge @ SV43 )
= $false )
| ( ( sequential @ SV38 @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[410]) ).
thf(445,plain,
! [SV86: $i,SV81: $i] :
( ( ( ~ ( sequential @ SV81 @ SV86 ) )
= $true )
| ( ( ( SV81 != SV86 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[411]) ).
thf(446,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[412]) ).
thf(447,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( sequential @ SX0 @ SX1 )
| ( edge @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[413]) ).
thf(448,plain,
! [SV16: $i,SV1: $i,SV44: $i,SV32: $i,SV24: $i,SV72: $i] :
( ( ( ( tail_of @ SV72 )
= ( tail_of @ SV24 ) )
= $false )
| ( ( ~ ( edge @ SV72 ) )
= $true )
| ( ( ( ( head_of @ SV72 )
!= ( head_of @ SV32 ) ) )
= $true )
| ( ( precedes @ SV24 @ SV32 @ SV44 )
= $false )
| ( ( shortest_path @ SV1 @ SV16 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[414]) ).
thf(449,plain,
! [SV40: $i,SV45: $i,SV6: $i] :
( ( ( ( SV6
!= ( tail_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) ) )
= $false )
| ( ( path @ SV6 @ SV40 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[415]) ).
thf(450,plain,
! [SV6: $i,SV40: $i,SV45: $i] :
( ( ( ~ ( edge @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
= $false )
| ( ( path @ SV6 @ SV40 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[415]) ).
thf(451,plain,
! [SV6: $i,SV45: $i,SV40: $i] :
( ( ( ~ ( ( SV40
!= ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
| ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ empty ) )
| ! [SY229: $i] :
( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ SY229 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ SY229 ) ) ) )
= $false )
| ( ( path @ SV6 @ SV40 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[416]) ).
thf(452,plain,
! [SV6: $i,SV45: $i,SV40: $i] :
( ( ( ~ ~ ( ~ ( ( SV40
= ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ ( sK13_SY95 @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ ( sK13_SY95 @ SV45 @ SV40 @ SV6 ) ) ) )
| ~ ( ( SV45
= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ empty ) )
| ~ ( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ ( sK12_SY96 @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ ( sK12_SY96 @ SV45 @ SV40 @ SV6 ) ) ) ) ) )
= $false )
| ( ( path @ SV6 @ SV40 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[416]) ).
thf(453,plain,
! [SV33: $i,SV27: $i] :
( ( ( ~ ( ( SV27
!= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
!= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
!= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
!= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( SV27
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
| ~ ( ( SV27
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) ) )
| ~ ~ ( ~ ( ( SV33
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
| ~ ( ( SV33
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) ) ) ) )
= $false )
| ( ( SV27 = SV33 )
= $true )
| ( ( vertex @ SV27 )
= $false )
| ( ( vertex @ SV33 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(454,plain,
! [SV46: $i,SV41: $i,SV7: $i] :
( ( ( path @ SV7 @ SV41 @ SV46 )
= $false )
| ( ( SV7 = SV41 )
= $true )
| ( ( path @ SV7 @ SV41 @ ( sK8_P @ SV46 @ SV41 @ SV7 ) )
= $true )
| ( ( shortest_path @ SV7 @ SV41 @ SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[419]) ).
thf(455,plain,
! [SV46: $i,SV41: $i,SV7: $i] :
( ( ( SV7 = SV41 )
= $true )
| ( ( ~ ( path @ SV7 @ SV41 @ SV46 ) )
= $true )
| ( ( less_or_equal @ ( length_of @ SV46 ) @ ( length_of @ ( sK8_P @ SV46 @ SV41 @ SV7 ) ) )
= $false )
| ( ( shortest_path @ SV7 @ SV41 @ SV46 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[420]) ).
thf(456,plain,
! [SV64: $i,SV87: $i,SV59: $i,SV7: $i] :
( ( ( ~ ( path @ SV7 @ SV59 @ SV87 ) )
= $true )
| ( ( less_or_equal @ ( length_of @ SV64 ) @ ( length_of @ SV87 ) )
= $true )
| ( ( shortest_path @ SV7 @ SV59 @ SV64 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[421]) ).
thf(457,plain,
! [SV96: $i,SV82: $i,SV7: $i] :
( ( ( ~ ( shortest_path @ SV7 @ SV82 @ SV96 ) )
= $true )
| ( ( ( SV7 != SV82 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[422]) ).
thf(458,plain,
! [SV88: $i,SV83: $i,SV7: $i] :
( ( ( ~ ( shortest_path @ SV7 @ SV83 @ SV88 ) )
= $true )
| ( ( path @ SV7 @ SV83 @ SV88 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[423]) ).
thf(459,plain,
! [SV20: $i,SV8: $i,SV65: $i,SV51: $i,SV28: $i,SV97: $i] :
( ( ( ( ( tail_of @ SV97 )
!= ( tail_of @ SV28 ) )
| ( ( head_of @ SV97 )
!= ( head_of @ SV51 ) ) )
= $true )
| ( ( precedes @ SV28 @ SV51 @ SV65 )
= $false )
| ( ( shortest_path @ SV8 @ SV20 @ SV65 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[424]) ).
thf(460,plain,
! [SV20: $i,SV8: $i,SV60: $i,SV28: $i,SV52: $i] :
( ( ( precedes @ SV52 @ SV28 @ SV60 )
= $false )
| ( ( precedes @ SV28 @ SV52 @ SV60 )
= $false )
| ( ( shortest_path @ SV8 @ SV20 @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(461,plain,
! [SV29: $i,SV21: $i,SV89: $i,SV9: $i] :
( ( ( ( SV9
!= ( tail_of @ SV89 ) )
| ~ ( edge @ SV89 ) )
= $true )
| ( ( ( SV21
!= ( head_of @ SV89 ) )
| ( SV29
!= ( path_cons @ SV89 @ empty ) ) )
= $true )
| ( ( vertex @ SV9 )
= $false )
| ( ( vertex @ SV21 )
= $false )
| ( ( path @ SV9 @ SV21 @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[426]) ).
thf(462,plain,
! [SV21: $i,SV29: $i,SV90: $i,SV9: $i] :
( ( ( ( SV9
!= ( tail_of @ SV90 ) )
| ~ ( edge @ SV90 ) )
= $true )
| ( ( ! [SY255: $i] :
( ( SV29
!= ( path_cons @ SV90 @ SY255 ) )
| ~ ( path @ ( head_of @ SV90 ) @ SV21 @ SY255 ) ) )
= $true )
| ( ( vertex @ SV9 )
= $false )
| ( ( vertex @ SV21 )
= $false )
| ( ( path @ SV9 @ SV21 @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[427]) ).
thf(463,plain,
! [SV34: $i,SV30: $i,SV10: $i,SV91: $i] :
( ( ( ! [SY256: $i] :
~ ( precedes @ SV91 @ SY256 @ SV10 ) )
= $true )
| ( ( on_path @ SV91 @ SV10 )
= $true )
| ( ( path @ SV30 @ SV34 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[428]) ).
thf(464,plain,
! [SV34: $i,SV30: $i,SV10: $i,SV98: $i,SV92: $i] :
( ( ( ~ ( precedes @ SV92 @ SV98 @ SV10 )
| ( on_path @ SV98 @ SV10 ) )
= $true )
| ( ( path @ SV30 @ SV34 @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(465,plain,
! [SV34: $i,SV30: $i,SV10: $i,SV99: $i,SV93: $i] :
( ( ( ~ ( precedes @ SV93 @ SV99 @ SV10 )
| ! [SY261: $i] :
( ~ ( precedes @ SY261 @ SV99 @ SV10 )
| ~ ( sequential @ SV93 @ SY261 ) )
| ~ ( sequential @ SV93 @ SV99 ) )
= $true )
| ( ( path @ SV30 @ SV34 @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[430]) ).
thf(466,plain,
! [SV34: $i,SV30: $i,SV10: $i,SV100: $i,SV94: $i] :
( ( ( ~ ( precedes @ SV94 @ SV100 @ SV10 )
| ~ ( ~ ( precedes @ ( sK9_E3 @ SV100 @ SV94 @ SV10 ) @ SV100 @ SV10 )
| ~ ( sequential @ SV94 @ ( sK9_E3 @ SV100 @ SV94 @ SV10 ) ) )
| ( sequential @ SV94 @ SV100 ) )
= $true )
| ( ( path @ SV30 @ SV34 @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(467,plain,
! [SV47: $i,SV42: $i,SV11: $i] :
( ( ( edge @ SV11 )
= $false )
| ( ( ~ ( edge @ SV42 ) )
= $true )
| ( ( ~ ( edge @ SV47 ) )
= $true )
| ( ( ~ ( sequential @ SV11 @ SV42 ) )
= $true )
| ( ( ~ ( sequential @ SV42 @ SV47 ) )
= $true )
| ( ( ~ ( sequential @ SV47 @ SV11 ) )
= $true )
| ( ( triangle @ SV11 @ SV42 @ SV47 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[432]) ).
thf(468,plain,
! [SV11: $i] :
( ( ~ ( ~ ~ ( ~ ( ! [SY148: $i,SY149: $i] :
~ ( triangle @ SV11 @ SY148 @ SY149 )
| ( edge @ SV11 ) )
| ~ ! [SY150: $i] :
( ! [SY151: $i] :
~ ( triangle @ SV11 @ SY150 @ SY151 )
| ( edge @ SY150 ) ) )
| ~ ! [SY152: $i,SY153: $i] :
( ~ ( triangle @ SV11 @ SY152 @ SY153 )
| ( edge @ SY153 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[433]) ).
thf(469,plain,
! [SV11: $i] :
( ( ! [SY154: $i] :
( ! [SY155: $i] :
~ ( triangle @ SV11 @ SY154 @ SY155 )
| ( sequential @ SV11 @ SY154 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[434]) ).
thf(470,plain,
! [SV95: $i,SV84: $i,SV11: $i] :
( ( ( ~ ( triangle @ SV11 @ SV84 @ SV95 ) )
= $true )
| ( ( sequential @ SV84 @ SV95 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[435]) ).
thf(471,plain,
! [SV22: $i,SV12: $i,SV67: $i,SV75: $i] :
( ( ( on_path @ SV75 @ SV67 )
= $false )
| ( ( ~ ( path @ SV12 @ SV22 @ SV67 ) )
= $true )
| ( ( edge @ SV75 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[436]) ).
thf(472,plain,
! [SV22: $i,SV12: $i,SV68: $i,SV76: $i] :
( ( ( on_path @ SV76 @ SV68 )
= $false )
| ( ( ~ ( path @ SV12 @ SV22 @ SV68 ) )
= $true )
| ( ( in_path @ ( head_of @ SV76 ) @ SV68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[437]) ).
thf(473,plain,
! [SV13: $i,SV23: $i,SV49: $i,SV54: $i] :
( ( ( ~ ( on_path @ ( sK10_E @ SV54 @ SV49 @ SV23 @ SV13 ) @ SV49 ) )
= $false )
| ( ( in_path @ SV54 @ SV49 )
= $false )
| ( ( path @ SV13 @ SV23 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[438]) ).
thf(474,plain,
! [SV13: $i,SV23: $i,SV49: $i,SV54: $i] :
( ( ( ~ ( ( SV54
= ( head_of @ ( sK10_E @ SV54 @ SV49 @ SV23 @ SV13 ) ) )
| ( SV54
= ( tail_of @ ( sK10_E @ SV54 @ SV49 @ SV23 @ SV13 ) ) ) ) )
= $false )
| ( ( in_path @ SV54 @ SV49 )
= $false )
| ( ( path @ SV13 @ SV23 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[438]) ).
thf(475,plain,
! [SV37: $i,SV31: $i,SV77: $i,SV14: $i,SV69: $i] :
( ( ( ~ ( on_path @ SV69 @ SV14 ) )
= $true )
| ( ( ~ ( on_path @ SV77 @ SV14 ) )
= $true )
| ( ( ! [SY249: $i] :
( ~ ( precedes @ SY249 @ SV77 @ SV14 )
| ~ ( sequential @ SV69 @ SY249 ) ) )
= $true )
| ( ( precedes @ SV69 @ SV77 @ SV14 )
= $true )
| ( ( path @ SV31 @ SV37 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[439]) ).
thf(476,plain,
! [SV37: $i,SV31: $i,SV78: $i,SV14: $i,SV70: $i] :
( ( ( ~ ( on_path @ SV70 @ SV14 ) )
= $true )
| ( ( ~ ( on_path @ SV78 @ SV14 ) )
= $true )
| ( ( ~ ( sequential @ SV70 @ SV78 ) )
= $true )
| ( ( precedes @ SV70 @ SV78 @ SV14 )
= $true )
| ( ( path @ SV31 @ SV37 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[440]) ).
thf(477,plain,
! [SV15: $i,SV101: $i] :
( ( ( ! [SY262: $i] :
~ ( path @ SV101 @ SY262 @ SV15 ) )
= $true )
| ( ( on_path @ ( sK6_E1 @ SV15 ) @ SV15 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV15 )
= ( number_of_in @ triangles @ SV15 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(478,plain,
! [SV15: $i,SV102: $i] :
( ( ( ! [SY263: $i] :
~ ( path @ SV102 @ SY263 @ SV15 ) )
= $true )
| ( ( on_path @ ( sK7_SY91 @ SV15 ) @ SV15 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV15 )
= ( number_of_in @ triangles @ SV15 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(479,plain,
! [SV86: $i,SV81: $i] :
( ( ( sequential @ SV81 @ SV86 )
= $false )
| ( ( ( SV81 != SV86 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[445]) ).
thf(480,plain,
! [SV103: $i] :
( ( ! [SY264: $i] :
~ ( sequential @ SV103 @ SY264 )
| ( edge @ SV103 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(481,plain,
! [SV104: $i] :
( ( ! [SY265: $i] :
( ~ ( sequential @ SV104 @ SY265 )
| ( edge @ SY265 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(482,plain,
! [SV16: $i,SV1: $i,SV44: $i,SV32: $i,SV24: $i,SV72: $i] :
( ( ( edge @ SV72 )
= $false )
| ( ( ( tail_of @ SV72 )
= ( tail_of @ SV24 ) )
= $false )
| ( ( ( ( head_of @ SV72 )
!= ( head_of @ SV32 ) ) )
= $true )
| ( ( precedes @ SV24 @ SV32 @ SV44 )
= $false )
| ( ( shortest_path @ SV1 @ SV16 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[448]) ).
thf(483,plain,
! [SV40: $i,SV45: $i,SV6: $i] :
( ( ( SV6
= ( tail_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
= $true )
| ( ( path @ SV6 @ SV40 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[449]) ).
thf(484,plain,
! [SV6: $i,SV40: $i,SV45: $i] :
( ( ( edge @ ( sK11_E @ SV45 @ SV40 @ SV6 ) )
= $true )
| ( ( path @ SV6 @ SV40 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[450]) ).
thf(485,plain,
! [SV6: $i,SV45: $i,SV40: $i] :
( ( ( ( SV40
!= ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
| ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ empty ) )
| ! [SY229: $i] :
( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ SY229 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ SY229 ) ) )
= $true )
| ( ( path @ SV6 @ SV40 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[451]) ).
thf(486,plain,
! [SV6: $i,SV45: $i,SV40: $i] :
( ( ( ~ ( ~ ( ( SV40
= ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ ( sK13_SY95 @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ ( sK13_SY95 @ SV45 @ SV40 @ SV6 ) ) ) )
| ~ ( ( SV45
= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ empty ) )
| ~ ( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ ( sK12_SY96 @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ ( sK12_SY96 @ SV45 @ SV40 @ SV6 ) ) ) ) ) )
= $true )
| ( ( path @ SV6 @ SV40 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[452]) ).
thf(487,plain,
! [SV33: $i,SV27: $i] :
( ( ( ~ ( ( SV27
!= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
!= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
!= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
!= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) ) )
= $false )
| ( ( SV27 = SV33 )
= $true )
| ( ( vertex @ SV27 )
= $false )
| ( ( vertex @ SV33 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[453]) ).
thf(488,plain,
! [SV33: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( SV27
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
| ~ ( ( SV27
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) ) )
| ~ ~ ( ~ ( ( SV33
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
| ~ ( ( SV33
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) ) ) ) )
= $false )
| ( ( SV27 = SV33 )
= $true )
| ( ( vertex @ SV27 )
= $false )
| ( ( vertex @ SV33 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[453]) ).
thf(489,plain,
! [SV46: $i,SV41: $i,SV7: $i] :
( ( ( path @ SV7 @ SV41 @ SV46 )
= $false )
| ( ( SV7 = SV41 )
= $true )
| ( ( less_or_equal @ ( length_of @ SV46 ) @ ( length_of @ ( sK8_P @ SV46 @ SV41 @ SV7 ) ) )
= $false )
| ( ( shortest_path @ SV7 @ SV41 @ SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[455]) ).
thf(490,plain,
! [SV64: $i,SV87: $i,SV59: $i,SV7: $i] :
( ( ( path @ SV7 @ SV59 @ SV87 )
= $false )
| ( ( less_or_equal @ ( length_of @ SV64 ) @ ( length_of @ SV87 ) )
= $true )
| ( ( shortest_path @ SV7 @ SV59 @ SV64 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[456]) ).
thf(491,plain,
! [SV96: $i,SV82: $i,SV7: $i] :
( ( ( shortest_path @ SV7 @ SV82 @ SV96 )
= $false )
| ( ( ( SV7 != SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[457]) ).
thf(492,plain,
! [SV88: $i,SV83: $i,SV7: $i] :
( ( ( shortest_path @ SV7 @ SV83 @ SV88 )
= $false )
| ( ( path @ SV7 @ SV83 @ SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[458]) ).
thf(493,plain,
! [SV20: $i,SV8: $i,SV65: $i,SV51: $i,SV28: $i,SV97: $i] :
( ( ( ( ( tail_of @ SV97 )
!= ( tail_of @ SV28 ) ) )
= $true )
| ( ( ( ( head_of @ SV97 )
!= ( head_of @ SV51 ) ) )
= $true )
| ( ( precedes @ SV28 @ SV51 @ SV65 )
= $false )
| ( ( shortest_path @ SV8 @ SV20 @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[459]) ).
thf(494,plain,
! [SV29: $i,SV21: $i,SV89: $i,SV9: $i] :
( ( ( ( SV9
!= ( tail_of @ SV89 ) ) )
= $true )
| ( ( ~ ( edge @ SV89 ) )
= $true )
| ( ( ( SV21
!= ( head_of @ SV89 ) )
| ( SV29
!= ( path_cons @ SV89 @ empty ) ) )
= $true )
| ( ( vertex @ SV9 )
= $false )
| ( ( vertex @ SV21 )
= $false )
| ( ( path @ SV9 @ SV21 @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[461]) ).
thf(495,plain,
! [SV21: $i,SV29: $i,SV90: $i,SV9: $i] :
( ( ( ( SV9
!= ( tail_of @ SV90 ) ) )
= $true )
| ( ( ~ ( edge @ SV90 ) )
= $true )
| ( ( ! [SY255: $i] :
( ( SV29
!= ( path_cons @ SV90 @ SY255 ) )
| ~ ( path @ ( head_of @ SV90 ) @ SV21 @ SY255 ) ) )
= $true )
| ( ( vertex @ SV9 )
= $false )
| ( ( vertex @ SV21 )
= $false )
| ( ( path @ SV9 @ SV21 @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[462]) ).
thf(496,plain,
! [SV34: $i,SV30: $i,SV10: $i,SV105: $i,SV91: $i] :
( ( ( ~ ( precedes @ SV91 @ SV105 @ SV10 ) )
= $true )
| ( ( on_path @ SV91 @ SV10 )
= $true )
| ( ( path @ SV30 @ SV34 @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[463]) ).
thf(497,plain,
! [SV34: $i,SV30: $i,SV10: $i,SV98: $i,SV92: $i] :
( ( ( ~ ( precedes @ SV92 @ SV98 @ SV10 ) )
= $true )
| ( ( on_path @ SV98 @ SV10 )
= $true )
| ( ( path @ SV30 @ SV34 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[464]) ).
thf(498,plain,
! [SV34: $i,SV30: $i,SV10: $i,SV99: $i,SV93: $i] :
( ( ( ~ ( precedes @ SV93 @ SV99 @ SV10 ) )
= $true )
| ( ( ! [SY261: $i] :
( ~ ( precedes @ SY261 @ SV99 @ SV10 )
| ~ ( sequential @ SV93 @ SY261 ) )
| ~ ( sequential @ SV93 @ SV99 ) )
= $true )
| ( ( path @ SV30 @ SV34 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[465]) ).
thf(499,plain,
! [SV34: $i,SV30: $i,SV10: $i,SV100: $i,SV94: $i] :
( ( ( ~ ( precedes @ SV94 @ SV100 @ SV10 ) )
= $true )
| ( ( ~ ( ~ ( precedes @ ( sK9_E3 @ SV100 @ SV94 @ SV10 ) @ SV100 @ SV10 )
| ~ ( sequential @ SV94 @ ( sK9_E3 @ SV100 @ SV94 @ SV10 ) ) )
| ( sequential @ SV94 @ SV100 ) )
= $true )
| ( ( path @ SV30 @ SV34 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[466]) ).
thf(500,plain,
! [SV47: $i,SV11: $i,SV42: $i] :
( ( ( edge @ SV42 )
= $false )
| ( ( edge @ SV11 )
= $false )
| ( ( ~ ( edge @ SV47 ) )
= $true )
| ( ( ~ ( sequential @ SV11 @ SV42 ) )
= $true )
| ( ( ~ ( sequential @ SV42 @ SV47 ) )
= $true )
| ( ( ~ ( sequential @ SV47 @ SV11 ) )
= $true )
| ( ( triangle @ SV11 @ SV42 @ SV47 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[467]) ).
thf(501,plain,
! [SV11: $i] :
( ( ~ ~ ( ~ ( ! [SY148: $i,SY149: $i] :
~ ( triangle @ SV11 @ SY148 @ SY149 )
| ( edge @ SV11 ) )
| ~ ! [SY150: $i] :
( ! [SY151: $i] :
~ ( triangle @ SV11 @ SY150 @ SY151 )
| ( edge @ SY150 ) ) )
| ~ ! [SY152: $i,SY153: $i] :
( ~ ( triangle @ SV11 @ SY152 @ SY153 )
| ( edge @ SY153 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[468]) ).
thf(502,plain,
! [SV106: $i,SV11: $i] :
( ( ! [SY266: $i] :
~ ( triangle @ SV11 @ SV106 @ SY266 )
| ( sequential @ SV11 @ SV106 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(503,plain,
! [SV95: $i,SV84: $i,SV11: $i] :
( ( ( triangle @ SV11 @ SV84 @ SV95 )
= $false )
| ( ( sequential @ SV84 @ SV95 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[470]) ).
thf(504,plain,
! [SV75: $i,SV67: $i,SV22: $i,SV12: $i] :
( ( ( path @ SV12 @ SV22 @ SV67 )
= $false )
| ( ( on_path @ SV75 @ SV67 )
= $false )
| ( ( edge @ SV75 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[471]) ).
thf(505,plain,
! [SV76: $i,SV68: $i,SV22: $i,SV12: $i] :
( ( ( path @ SV12 @ SV22 @ SV68 )
= $false )
| ( ( on_path @ SV76 @ SV68 )
= $false )
| ( ( in_path @ ( head_of @ SV76 ) @ SV68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[472]) ).
thf(506,plain,
! [SV13: $i,SV23: $i,SV49: $i,SV54: $i] :
( ( ( on_path @ ( sK10_E @ SV54 @ SV49 @ SV23 @ SV13 ) @ SV49 )
= $true )
| ( ( in_path @ SV54 @ SV49 )
= $false )
| ( ( path @ SV13 @ SV23 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[473]) ).
thf(507,plain,
! [SV13: $i,SV23: $i,SV49: $i,SV54: $i] :
( ( ( ( SV54
= ( head_of @ ( sK10_E @ SV54 @ SV49 @ SV23 @ SV13 ) ) )
| ( SV54
= ( tail_of @ ( sK10_E @ SV54 @ SV49 @ SV23 @ SV13 ) ) ) )
= $true )
| ( ( in_path @ SV54 @ SV49 )
= $false )
| ( ( path @ SV13 @ SV23 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[474]) ).
thf(508,plain,
! [SV37: $i,SV31: $i,SV77: $i,SV14: $i,SV69: $i] :
( ( ( on_path @ SV69 @ SV14 )
= $false )
| ( ( ~ ( on_path @ SV77 @ SV14 ) )
= $true )
| ( ( ! [SY249: $i] :
( ~ ( precedes @ SY249 @ SV77 @ SV14 )
| ~ ( sequential @ SV69 @ SY249 ) ) )
= $true )
| ( ( precedes @ SV69 @ SV77 @ SV14 )
= $true )
| ( ( path @ SV31 @ SV37 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[475]) ).
thf(509,plain,
! [SV37: $i,SV31: $i,SV78: $i,SV14: $i,SV70: $i] :
( ( ( on_path @ SV70 @ SV14 )
= $false )
| ( ( ~ ( on_path @ SV78 @ SV14 ) )
= $true )
| ( ( ~ ( sequential @ SV70 @ SV78 ) )
= $true )
| ( ( precedes @ SV70 @ SV78 @ SV14 )
= $true )
| ( ( path @ SV31 @ SV37 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[476]) ).
thf(510,plain,
! [SV15: $i,SV107: $i,SV101: $i] :
( ( ( ~ ( path @ SV101 @ SV107 @ SV15 ) )
= $true )
| ( ( on_path @ ( sK6_E1 @ SV15 ) @ SV15 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV15 )
= ( number_of_in @ triangles @ SV15 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(511,plain,
! [SV15: $i,SV108: $i,SV102: $i] :
( ( ( ~ ( path @ SV102 @ SV108 @ SV15 ) )
= $true )
| ( ( on_path @ ( sK7_SY91 @ SV15 ) @ SV15 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV15 )
= ( number_of_in @ triangles @ SV15 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(512,plain,
! [SV86: $i,SV81: $i] :
( ( ( SV81 = SV86 )
= $false )
| ( ( sequential @ SV81 @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[479]) ).
thf(513,plain,
! [SV103: $i] :
( ( ( ! [SY264: $i] :
~ ( sequential @ SV103 @ SY264 ) )
= $true )
| ( ( edge @ SV103 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[480]) ).
thf(514,plain,
! [SV109: $i,SV104: $i] :
( ( ~ ( sequential @ SV104 @ SV109 )
| ( edge @ SV109 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(515,plain,
! [SV16: $i,SV1: $i,SV44: $i,SV24: $i,SV32: $i,SV72: $i] :
( ( ( ( head_of @ SV72 )
= ( head_of @ SV32 ) )
= $false )
| ( ( ( tail_of @ SV72 )
= ( tail_of @ SV24 ) )
= $false )
| ( ( edge @ SV72 )
= $false )
| ( ( precedes @ SV24 @ SV32 @ SV44 )
= $false )
| ( ( shortest_path @ SV1 @ SV16 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[482]) ).
thf(516,plain,
! [SV6: $i,SV45: $i,SV40: $i] :
( ( ( ( SV40
!= ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
| ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ empty ) ) )
= $true )
| ( ( ! [SY229: $i] :
( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ SY229 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ SY229 ) ) )
= $true )
| ( ( path @ SV6 @ SV40 @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[485]) ).
thf(517,plain,
! [SV6: $i,SV45: $i,SV40: $i] :
( ( ( ~ ( ( SV40
= ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ ( sK13_SY95 @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ ( sK13_SY95 @ SV45 @ SV40 @ SV6 ) ) ) )
| ~ ( ( SV45
= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ empty ) )
| ~ ( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ ( sK12_SY96 @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ ( sK12_SY96 @ SV45 @ SV40 @ SV6 ) ) ) ) )
= $false )
| ( ( path @ SV6 @ SV40 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[486]) ).
thf(518,plain,
! [SV33: $i,SV27: $i] :
( ( ( ( SV27
!= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
!= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
!= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
!= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
= $true )
| ( ( SV27 = SV33 )
= $true )
| ( ( vertex @ SV27 )
= $false )
| ( ( vertex @ SV33 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[487]) ).
thf(519,plain,
! [SV33: $i,SV27: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( SV27
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
| ~ ( ( SV27
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) ) )
| ~ ~ ( ~ ( ( SV33
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
| ~ ( ( SV33
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) ) ) ) )
= $true )
| ( ( SV27 = SV33 )
= $true )
| ( ( vertex @ SV27 )
= $false )
| ( ( vertex @ SV33 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[488]) ).
thf(520,plain,
! [SV96: $i,SV82: $i,SV7: $i] :
( ( ( SV7 = SV82 )
= $false )
| ( ( shortest_path @ SV7 @ SV82 @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[491]) ).
thf(521,plain,
! [SV20: $i,SV8: $i,SV65: $i,SV51: $i,SV28: $i,SV97: $i] :
( ( ( ( tail_of @ SV97 )
= ( tail_of @ SV28 ) )
= $false )
| ( ( ( ( head_of @ SV97 )
!= ( head_of @ SV51 ) ) )
= $true )
| ( ( precedes @ SV28 @ SV51 @ SV65 )
= $false )
| ( ( shortest_path @ SV8 @ SV20 @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[493]) ).
thf(522,plain,
! [SV29: $i,SV21: $i,SV89: $i,SV9: $i] :
( ( ( SV9
= ( tail_of @ SV89 ) )
= $false )
| ( ( ~ ( edge @ SV89 ) )
= $true )
| ( ( ( SV21
!= ( head_of @ SV89 ) )
| ( SV29
!= ( path_cons @ SV89 @ empty ) ) )
= $true )
| ( ( vertex @ SV9 )
= $false )
| ( ( vertex @ SV21 )
= $false )
| ( ( path @ SV9 @ SV21 @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[494]) ).
thf(523,plain,
! [SV21: $i,SV29: $i,SV90: $i,SV9: $i] :
( ( ( SV9
= ( tail_of @ SV90 ) )
= $false )
| ( ( ~ ( edge @ SV90 ) )
= $true )
| ( ( ! [SY255: $i] :
( ( SV29
!= ( path_cons @ SV90 @ SY255 ) )
| ~ ( path @ ( head_of @ SV90 ) @ SV21 @ SY255 ) ) )
= $true )
| ( ( vertex @ SV9 )
= $false )
| ( ( vertex @ SV21 )
= $false )
| ( ( path @ SV9 @ SV21 @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[495]) ).
thf(524,plain,
! [SV34: $i,SV30: $i,SV10: $i,SV105: $i,SV91: $i] :
( ( ( precedes @ SV91 @ SV105 @ SV10 )
= $false )
| ( ( on_path @ SV91 @ SV10 )
= $true )
| ( ( path @ SV30 @ SV34 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[496]) ).
thf(525,plain,
! [SV34: $i,SV30: $i,SV10: $i,SV98: $i,SV92: $i] :
( ( ( precedes @ SV92 @ SV98 @ SV10 )
= $false )
| ( ( on_path @ SV98 @ SV10 )
= $true )
| ( ( path @ SV30 @ SV34 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[497]) ).
thf(526,plain,
! [SV34: $i,SV30: $i,SV10: $i,SV99: $i,SV93: $i] :
( ( ( precedes @ SV93 @ SV99 @ SV10 )
= $false )
| ( ( ! [SY261: $i] :
( ~ ( precedes @ SY261 @ SV99 @ SV10 )
| ~ ( sequential @ SV93 @ SY261 ) )
| ~ ( sequential @ SV93 @ SV99 ) )
= $true )
| ( ( path @ SV30 @ SV34 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[498]) ).
thf(527,plain,
! [SV34: $i,SV30: $i,SV10: $i,SV100: $i,SV94: $i] :
( ( ( precedes @ SV94 @ SV100 @ SV10 )
= $false )
| ( ( ~ ( ~ ( precedes @ ( sK9_E3 @ SV100 @ SV94 @ SV10 ) @ SV100 @ SV10 )
| ~ ( sequential @ SV94 @ ( sK9_E3 @ SV100 @ SV94 @ SV10 ) ) )
| ( sequential @ SV94 @ SV100 ) )
= $true )
| ( ( path @ SV30 @ SV34 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[499]) ).
thf(528,plain,
! [SV42: $i,SV11: $i,SV47: $i] :
( ( ( edge @ SV47 )
= $false )
| ( ( edge @ SV11 )
= $false )
| ( ( edge @ SV42 )
= $false )
| ( ( ~ ( sequential @ SV11 @ SV42 ) )
= $true )
| ( ( ~ ( sequential @ SV42 @ SV47 ) )
= $true )
| ( ( ~ ( sequential @ SV47 @ SV11 ) )
= $true )
| ( ( triangle @ SV11 @ SV42 @ SV47 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[500]) ).
thf(529,plain,
! [SV11: $i] :
( ( ~ ~ ( ~ ( ! [SY148: $i,SY149: $i] :
~ ( triangle @ SV11 @ SY148 @ SY149 )
| ( edge @ SV11 ) )
| ~ ! [SY150: $i] :
( ! [SY151: $i] :
~ ( triangle @ SV11 @ SY150 @ SY151 )
| ( edge @ SY150 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[501]) ).
thf(530,plain,
! [SV11: $i] :
( ( ~ ! [SY152: $i,SY153: $i] :
( ~ ( triangle @ SV11 @ SY152 @ SY153 )
| ( edge @ SY153 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[501]) ).
thf(531,plain,
! [SV106: $i,SV11: $i] :
( ( ( ! [SY266: $i] :
~ ( triangle @ SV11 @ SV106 @ SY266 ) )
= $true )
| ( ( sequential @ SV11 @ SV106 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[502]) ).
thf(532,plain,
! [SV13: $i,SV23: $i,SV49: $i,SV54: $i] :
( ( ( SV54
= ( head_of @ ( sK10_E @ SV54 @ SV49 @ SV23 @ SV13 ) ) )
= $true )
| ( ( SV54
= ( tail_of @ ( sK10_E @ SV54 @ SV49 @ SV23 @ SV13 ) ) )
= $true )
| ( ( in_path @ SV54 @ SV49 )
= $false )
| ( ( path @ SV13 @ SV23 @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[507]) ).
thf(533,plain,
! [SV37: $i,SV31: $i,SV69: $i,SV14: $i,SV77: $i] :
( ( ( on_path @ SV77 @ SV14 )
= $false )
| ( ( on_path @ SV69 @ SV14 )
= $false )
| ( ( ! [SY249: $i] :
( ~ ( precedes @ SY249 @ SV77 @ SV14 )
| ~ ( sequential @ SV69 @ SY249 ) ) )
= $true )
| ( ( precedes @ SV69 @ SV77 @ SV14 )
= $true )
| ( ( path @ SV31 @ SV37 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[508]) ).
thf(534,plain,
! [SV37: $i,SV31: $i,SV70: $i,SV14: $i,SV78: $i] :
( ( ( on_path @ SV78 @ SV14 )
= $false )
| ( ( on_path @ SV70 @ SV14 )
= $false )
| ( ( ~ ( sequential @ SV70 @ SV78 ) )
= $true )
| ( ( precedes @ SV70 @ SV78 @ SV14 )
= $true )
| ( ( path @ SV31 @ SV37 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[509]) ).
thf(535,plain,
! [SV15: $i,SV107: $i,SV101: $i] :
( ( ( path @ SV101 @ SV107 @ SV15 )
= $false )
| ( ( on_path @ ( sK6_E1 @ SV15 ) @ SV15 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV15 )
= ( number_of_in @ triangles @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[510]) ).
thf(536,plain,
! [SV15: $i,SV108: $i,SV102: $i] :
( ( ( path @ SV102 @ SV108 @ SV15 )
= $false )
| ( ( on_path @ ( sK7_SY91 @ SV15 ) @ SV15 )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV15 )
= ( number_of_in @ triangles @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[511]) ).
thf(537,plain,
! [SV110: $i,SV103: $i] :
( ( ( ~ ( sequential @ SV103 @ SV110 ) )
= $true )
| ( ( edge @ SV103 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[513]) ).
thf(538,plain,
! [SV109: $i,SV104: $i] :
( ( ( ~ ( sequential @ SV104 @ SV109 ) )
= $true )
| ( ( edge @ SV109 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[514]) ).
thf(539,plain,
! [SV6: $i,SV45: $i,SV40: $i] :
( ( ( ( SV40
!= ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) ) )
= $true )
| ( ( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ empty ) ) )
= $true )
| ( ( ! [SY229: $i] :
( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ SY229 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ SY229 ) ) )
= $true )
| ( ( path @ SV6 @ SV40 @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[516]) ).
thf(540,plain,
! [SV6: $i,SV45: $i,SV40: $i] :
( ( ( ~ ( ( SV40
= ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ ( sK13_SY95 @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ ( sK13_SY95 @ SV45 @ SV40 @ SV6 ) ) ) ) )
= $false )
| ( ( path @ SV6 @ SV40 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[517]) ).
thf(541,plain,
! [SV6: $i,SV40: $i,SV45: $i] :
( ( ( ~ ( ( SV45
= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ empty ) )
| ~ ( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ ( sK12_SY96 @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ ( sK12_SY96 @ SV45 @ SV40 @ SV6 ) ) ) ) )
= $false )
| ( ( path @ SV6 @ SV40 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[517]) ).
thf(542,plain,
! [SV33: $i,SV27: $i] :
( ( ( ( SV27
!= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
!= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
= $true )
| ( ( ( SV33
!= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
!= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
= $true )
| ( ( SV27 = SV33 )
= $true )
| ( ( vertex @ SV27 )
= $false )
| ( ( vertex @ SV33 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[518]) ).
thf(543,plain,
! [SV33: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ( ( SV27
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
| ~ ( ( SV27
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) ) )
| ~ ~ ( ~ ( ( SV33
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
| ~ ( ( SV33
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) ) ) )
= $false )
| ( ( SV27 = SV33 )
= $true )
| ( ( vertex @ SV27 )
= $false )
| ( ( vertex @ SV33 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[519]) ).
thf(544,plain,
! [SV20: $i,SV8: $i,SV65: $i,SV28: $i,SV51: $i,SV97: $i] :
( ( ( ( head_of @ SV97 )
= ( head_of @ SV51 ) )
= $false )
| ( ( ( tail_of @ SV97 )
= ( tail_of @ SV28 ) )
= $false )
| ( ( precedes @ SV28 @ SV51 @ SV65 )
= $false )
| ( ( shortest_path @ SV8 @ SV20 @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[521]) ).
thf(545,plain,
! [SV29: $i,SV21: $i,SV9: $i,SV89: $i] :
( ( ( edge @ SV89 )
= $false )
| ( ( SV9
= ( tail_of @ SV89 ) )
= $false )
| ( ( ( SV21
!= ( head_of @ SV89 ) )
| ( SV29
!= ( path_cons @ SV89 @ empty ) ) )
= $true )
| ( ( vertex @ SV9 )
= $false )
| ( ( vertex @ SV21 )
= $false )
| ( ( path @ SV9 @ SV21 @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[522]) ).
thf(546,plain,
! [SV21: $i,SV29: $i,SV9: $i,SV90: $i] :
( ( ( edge @ SV90 )
= $false )
| ( ( SV9
= ( tail_of @ SV90 ) )
= $false )
| ( ( ! [SY255: $i] :
( ( SV29
!= ( path_cons @ SV90 @ SY255 ) )
| ~ ( path @ ( head_of @ SV90 ) @ SV21 @ SY255 ) ) )
= $true )
| ( ( vertex @ SV9 )
= $false )
| ( ( vertex @ SV21 )
= $false )
| ( ( path @ SV9 @ SV21 @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[523]) ).
thf(547,plain,
! [SV34: $i,SV30: $i,SV93: $i,SV10: $i,SV99: $i] :
( ( ( ! [SY261: $i] :
( ~ ( precedes @ SY261 @ SV99 @ SV10 )
| ~ ( sequential @ SV93 @ SY261 ) ) )
= $true )
| ( ( ~ ( sequential @ SV93 @ SV99 ) )
= $true )
| ( ( precedes @ SV93 @ SV99 @ SV10 )
= $false )
| ( ( path @ SV30 @ SV34 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[526]) ).
thf(548,plain,
! [SV34: $i,SV30: $i,SV10: $i,SV94: $i,SV100: $i] :
( ( ( ~ ( ~ ( precedes @ ( sK9_E3 @ SV100 @ SV94 @ SV10 ) @ SV100 @ SV10 )
| ~ ( sequential @ SV94 @ ( sK9_E3 @ SV100 @ SV94 @ SV10 ) ) ) )
= $true )
| ( ( sequential @ SV94 @ SV100 )
= $true )
| ( ( precedes @ SV94 @ SV100 @ SV10 )
= $false )
| ( ( path @ SV30 @ SV34 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[527]) ).
thf(549,plain,
! [SV47: $i,SV42: $i,SV11: $i] :
( ( ( sequential @ SV11 @ SV42 )
= $false )
| ( ( edge @ SV42 )
= $false )
| ( ( edge @ SV11 )
= $false )
| ( ( edge @ SV47 )
= $false )
| ( ( ~ ( sequential @ SV42 @ SV47 ) )
= $true )
| ( ( ~ ( sequential @ SV47 @ SV11 ) )
= $true )
| ( ( triangle @ SV11 @ SV42 @ SV47 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[528]) ).
thf(550,plain,
! [SV11: $i] :
( ( ~ ( ~ ( ! [SY148: $i,SY149: $i] :
~ ( triangle @ SV11 @ SY148 @ SY149 )
| ( edge @ SV11 ) )
| ~ ! [SY150: $i] :
( ! [SY151: $i] :
~ ( triangle @ SV11 @ SY150 @ SY151 )
| ( edge @ SY150 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[529]) ).
thf(551,plain,
! [SV11: $i] :
( ( ! [SY152: $i,SY153: $i] :
( ~ ( triangle @ SV11 @ SY152 @ SY153 )
| ( edge @ SY153 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[530]) ).
thf(552,plain,
! [SV111: $i,SV106: $i,SV11: $i] :
( ( ( ~ ( triangle @ SV11 @ SV106 @ SV111 ) )
= $true )
| ( ( sequential @ SV11 @ SV106 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(553,plain,
! [SV37: $i,SV31: $i,SV69: $i,SV14: $i,SV77: $i,SV112: $i] :
( ( ( ~ ( precedes @ SV112 @ SV77 @ SV14 )
| ~ ( sequential @ SV69 @ SV112 ) )
= $true )
| ( ( on_path @ SV69 @ SV14 )
= $false )
| ( ( on_path @ SV77 @ SV14 )
= $false )
| ( ( precedes @ SV69 @ SV77 @ SV14 )
= $true )
| ( ( path @ SV31 @ SV37 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(554,plain,
! [SV37: $i,SV31: $i,SV14: $i,SV78: $i,SV70: $i] :
( ( ( sequential @ SV70 @ SV78 )
= $false )
| ( ( on_path @ SV70 @ SV14 )
= $false )
| ( ( on_path @ SV78 @ SV14 )
= $false )
| ( ( precedes @ SV70 @ SV78 @ SV14 )
= $true )
| ( ( path @ SV31 @ SV37 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[534]) ).
thf(555,plain,
! [SV110: $i,SV103: $i] :
( ( ( sequential @ SV103 @ SV110 )
= $false )
| ( ( edge @ SV103 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[537]) ).
thf(556,plain,
! [SV109: $i,SV104: $i] :
( ( ( sequential @ SV104 @ SV109 )
= $false )
| ( ( edge @ SV109 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[538]) ).
thf(557,plain,
! [SV6: $i,SV45: $i,SV40: $i] :
( ( ( SV40
= ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
= $false )
| ( ( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ empty ) ) )
= $true )
| ( ( ! [SY229: $i] :
( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ SY229 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ SY229 ) ) )
= $true )
| ( ( path @ SV6 @ SV40 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[539]) ).
thf(558,plain,
! [SV6: $i,SV45: $i,SV40: $i] :
( ( ( ( SV40
= ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ ( sK13_SY95 @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ ( sK13_SY95 @ SV45 @ SV40 @ SV6 ) ) ) )
= $true )
| ( ( path @ SV6 @ SV40 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[540]) ).
thf(559,plain,
! [SV6: $i,SV40: $i,SV45: $i] :
( ( ( ( SV45
= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ empty ) )
| ~ ( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ ( sK12_SY96 @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ ( sK12_SY96 @ SV45 @ SV40 @ SV6 ) ) ) )
= $true )
| ( ( path @ SV6 @ SV40 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[541]) ).
thf(560,plain,
! [SV33: $i,SV27: $i] :
( ( ( ( SV27
!= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
= $true )
| ( ( ( SV33
!= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
= $true )
| ( ( ( SV33
!= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
!= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
= $true )
| ( ( SV27 = SV33 )
= $true )
| ( ( vertex @ SV27 )
= $false )
| ( ( vertex @ SV33 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[542]) ).
thf(561,plain,
! [SV33: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ( ( SV27
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
| ~ ( ( SV27
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) ) ) )
= $false )
| ( ( SV27 = SV33 )
= $true )
| ( ( vertex @ SV27 )
= $false )
| ( ( vertex @ SV33 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[543]) ).
thf(562,plain,
! [SV27: $i,SV33: $i] :
( ( ( ~ ~ ( ~ ( ( SV33
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
| ~ ( ( SV33
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) ) ) )
= $false )
| ( ( SV27 = SV33 )
= $true )
| ( ( vertex @ SV27 )
= $false )
| ( ( vertex @ SV33 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[543]) ).
thf(563,plain,
! [SV9: $i,SV29: $i,SV89: $i,SV21: $i] :
( ( ( ( SV21
!= ( head_of @ SV89 ) ) )
= $true )
| ( ( ( SV29
!= ( path_cons @ SV89 @ empty ) ) )
= $true )
| ( ( SV9
= ( tail_of @ SV89 ) )
= $false )
| ( ( edge @ SV89 )
= $false )
| ( ( vertex @ SV9 )
= $false )
| ( ( vertex @ SV21 )
= $false )
| ( ( path @ SV9 @ SV21 @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[545]) ).
thf(564,plain,
! [SV9: $i,SV21: $i,SV113: $i,SV90: $i,SV29: $i] :
( ( ( ( SV29
!= ( path_cons @ SV90 @ SV113 ) )
| ~ ( path @ ( head_of @ SV90 ) @ SV21 @ SV113 ) )
= $true )
| ( ( SV9
= ( tail_of @ SV90 ) )
= $false )
| ( ( edge @ SV90 )
= $false )
| ( ( vertex @ SV9 )
= $false )
| ( ( vertex @ SV21 )
= $false )
| ( ( path @ SV9 @ SV21 @ SV29 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(565,plain,
! [SV34: $i,SV30: $i,SV93: $i,SV10: $i,SV99: $i,SV114: $i] :
( ( ( ~ ( precedes @ SV114 @ SV99 @ SV10 )
| ~ ( sequential @ SV93 @ SV114 ) )
= $true )
| ( ( ~ ( sequential @ SV93 @ SV99 ) )
= $true )
| ( ( precedes @ SV93 @ SV99 @ SV10 )
= $false )
| ( ( path @ SV30 @ SV34 @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(566,plain,
! [SV34: $i,SV30: $i,SV10: $i,SV94: $i,SV100: $i] :
( ( ( ~ ( precedes @ ( sK9_E3 @ SV100 @ SV94 @ SV10 ) @ SV100 @ SV10 )
| ~ ( sequential @ SV94 @ ( sK9_E3 @ SV100 @ SV94 @ SV10 ) ) )
= $false )
| ( ( sequential @ SV94 @ SV100 )
= $true )
| ( ( precedes @ SV94 @ SV100 @ SV10 )
= $false )
| ( ( path @ SV30 @ SV34 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[548]) ).
thf(567,plain,
! [SV11: $i,SV47: $i,SV42: $i] :
( ( ( sequential @ SV42 @ SV47 )
= $false )
| ( ( edge @ SV47 )
= $false )
| ( ( edge @ SV11 )
= $false )
| ( ( edge @ SV42 )
= $false )
| ( ( sequential @ SV11 @ SV42 )
= $false )
| ( ( ~ ( sequential @ SV47 @ SV11 ) )
= $true )
| ( ( triangle @ SV11 @ SV42 @ SV47 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[549]) ).
thf(568,plain,
! [SV11: $i] :
( ( ~ ( ! [SY148: $i,SY149: $i] :
~ ( triangle @ SV11 @ SY148 @ SY149 )
| ( edge @ SV11 ) )
| ~ ! [SY150: $i] :
( ! [SY151: $i] :
~ ( triangle @ SV11 @ SY150 @ SY151 )
| ( edge @ SY150 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[550]) ).
thf(569,plain,
! [SV115: $i,SV11: $i] :
( ( ! [SY267: $i] :
( ~ ( triangle @ SV11 @ SV115 @ SY267 )
| ( edge @ SY267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[551]) ).
thf(570,plain,
! [SV111: $i,SV106: $i,SV11: $i] :
( ( ( triangle @ SV11 @ SV106 @ SV111 )
= $false )
| ( ( sequential @ SV11 @ SV106 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[552]) ).
thf(571,plain,
! [SV37: $i,SV31: $i,SV69: $i,SV14: $i,SV77: $i,SV112: $i] :
( ( ( ~ ( precedes @ SV112 @ SV77 @ SV14 ) )
= $true )
| ( ( ~ ( sequential @ SV69 @ SV112 ) )
= $true )
| ( ( on_path @ SV69 @ SV14 )
= $false )
| ( ( on_path @ SV77 @ SV14 )
= $false )
| ( ( precedes @ SV69 @ SV77 @ SV14 )
= $true )
| ( ( path @ SV31 @ SV37 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[553]) ).
thf(572,plain,
! [SV6: $i,SV40: $i,SV45: $i] :
( ( ( SV45
= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ empty ) )
= $false )
| ( ( SV40
= ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
= $false )
| ( ( ! [SY229: $i] :
( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ SY229 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ SY229 ) ) )
= $true )
| ( ( path @ SV6 @ SV40 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[557]) ).
thf(573,plain,
! [SV6: $i,SV45: $i,SV40: $i] :
( ( ( SV40
= ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
= $true )
| ( ( ~ ( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ ( sK13_SY95 @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ ( sK13_SY95 @ SV45 @ SV40 @ SV6 ) ) ) )
= $true )
| ( ( path @ SV6 @ SV40 @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[558]) ).
thf(574,plain,
! [SV6: $i,SV40: $i,SV45: $i] :
( ( ( SV45
= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ empty ) )
= $true )
| ( ( ~ ( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ ( sK12_SY96 @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ ( sK12_SY96 @ SV45 @ SV40 @ SV6 ) ) ) )
= $true )
| ( ( path @ SV6 @ SV40 @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[559]) ).
thf(575,plain,
! [SV33: $i,SV27: $i] :
( ( ( SV27
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
= $false )
| ( ( ( SV33
!= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
= $true )
| ( ( ( SV33
!= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
!= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
= $true )
| ( ( SV27 = SV33 )
= $true )
| ( ( vertex @ SV27 )
= $false )
| ( ( vertex @ SV33 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[560]) ).
thf(576,plain,
! [SV33: $i,SV27: $i] :
( ( ( ~ ( ~ ( ( SV27
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
| ~ ( ( SV27
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) ) ) )
= $true )
| ( ( SV27 = SV33 )
= $true )
| ( ( vertex @ SV27 )
= $false )
| ( ( vertex @ SV33 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[561]) ).
thf(577,plain,
! [SV27: $i,SV33: $i] :
( ( ( ~ ( ~ ( ( SV33
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
| ~ ( ( SV33
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) ) ) )
= $true )
| ( ( SV27 = SV33 )
= $true )
| ( ( vertex @ SV27 )
= $false )
| ( ( vertex @ SV33 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[562]) ).
thf(578,plain,
! [SV9: $i,SV29: $i,SV89: $i,SV21: $i] :
( ( ( SV21
= ( head_of @ SV89 ) )
= $false )
| ( ( ( SV29
!= ( path_cons @ SV89 @ empty ) ) )
= $true )
| ( ( SV9
= ( tail_of @ SV89 ) )
= $false )
| ( ( edge @ SV89 )
= $false )
| ( ( vertex @ SV9 )
= $false )
| ( ( vertex @ SV21 )
= $false )
| ( ( path @ SV9 @ SV21 @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[563]) ).
thf(579,plain,
! [SV9: $i,SV21: $i,SV113: $i,SV90: $i,SV29: $i] :
( ( ( ( SV29
!= ( path_cons @ SV90 @ SV113 ) ) )
= $true )
| ( ( ~ ( path @ ( head_of @ SV90 ) @ SV21 @ SV113 ) )
= $true )
| ( ( SV9
= ( tail_of @ SV90 ) )
= $false )
| ( ( edge @ SV90 )
= $false )
| ( ( vertex @ SV9 )
= $false )
| ( ( vertex @ SV21 )
= $false )
| ( ( path @ SV9 @ SV21 @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[564]) ).
thf(580,plain,
! [SV34: $i,SV30: $i,SV93: $i,SV10: $i,SV99: $i,SV114: $i] :
( ( ( ~ ( precedes @ SV114 @ SV99 @ SV10 ) )
= $true )
| ( ( ~ ( sequential @ SV93 @ SV114 ) )
= $true )
| ( ( ~ ( sequential @ SV93 @ SV99 ) )
= $true )
| ( ( precedes @ SV93 @ SV99 @ SV10 )
= $false )
| ( ( path @ SV30 @ SV34 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[565]) ).
thf(581,plain,
! [SV34: $i,SV30: $i,SV10: $i,SV94: $i,SV100: $i] :
( ( ( ~ ( precedes @ ( sK9_E3 @ SV100 @ SV94 @ SV10 ) @ SV100 @ SV10 ) )
= $false )
| ( ( sequential @ SV94 @ SV100 )
= $true )
| ( ( precedes @ SV94 @ SV100 @ SV10 )
= $false )
| ( ( path @ SV30 @ SV34 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[566]) ).
thf(582,plain,
! [SV34: $i,SV30: $i,SV10: $i,SV100: $i,SV94: $i] :
( ( ( ~ ( sequential @ SV94 @ ( sK9_E3 @ SV100 @ SV94 @ SV10 ) ) )
= $false )
| ( ( sequential @ SV94 @ SV100 )
= $true )
| ( ( precedes @ SV94 @ SV100 @ SV10 )
= $false )
| ( ( path @ SV30 @ SV34 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[566]) ).
thf(583,plain,
! [SV42: $i,SV11: $i,SV47: $i] :
( ( ( sequential @ SV47 @ SV11 )
= $false )
| ( ( sequential @ SV11 @ SV42 )
= $false )
| ( ( edge @ SV42 )
= $false )
| ( ( edge @ SV11 )
= $false )
| ( ( edge @ SV47 )
= $false )
| ( ( sequential @ SV42 @ SV47 )
= $false )
| ( ( triangle @ SV11 @ SV42 @ SV47 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[567]) ).
thf(584,plain,
! [SV11: $i] :
( ( ~ ( ! [SY148: $i,SY149: $i] :
~ ( triangle @ SV11 @ SY148 @ SY149 )
| ( edge @ SV11 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[568]) ).
thf(585,plain,
! [SV11: $i] :
( ( ~ ! [SY150: $i] :
( ! [SY151: $i] :
~ ( triangle @ SV11 @ SY150 @ SY151 )
| ( edge @ SY150 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[568]) ).
thf(586,plain,
! [SV116: $i,SV115: $i,SV11: $i] :
( ( ~ ( triangle @ SV11 @ SV115 @ SV116 )
| ( edge @ SV116 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(587,plain,
! [SV37: $i,SV31: $i,SV69: $i,SV14: $i,SV77: $i,SV112: $i] :
( ( ( precedes @ SV112 @ SV77 @ SV14 )
= $false )
| ( ( ~ ( sequential @ SV69 @ SV112 ) )
= $true )
| ( ( on_path @ SV69 @ SV14 )
= $false )
| ( ( on_path @ SV77 @ SV14 )
= $false )
| ( ( precedes @ SV69 @ SV77 @ SV14 )
= $true )
| ( ( path @ SV31 @ SV37 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[571]) ).
thf(588,plain,
! [SV117: $i,SV6: $i,SV40: $i,SV45: $i] :
( ( ( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ SV117 ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ SV117 ) )
= $true )
| ( ( SV40
= ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
= $false )
| ( ( SV45
= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ empty ) )
= $false )
| ( ( path @ SV6 @ SV40 @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[572]) ).
thf(589,plain,
! [SV6: $i,SV40: $i,SV45: $i] :
( ( ( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ ( sK13_SY95 @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ ( sK13_SY95 @ SV45 @ SV40 @ SV6 ) ) )
= $false )
| ( ( SV40
= ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
= $true )
| ( ( path @ SV6 @ SV40 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[573]) ).
thf(590,plain,
! [SV6: $i,SV40: $i,SV45: $i] :
( ( ( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ ( sK12_SY96 @ SV45 @ SV40 @ SV6 ) ) )
| ~ ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ ( sK12_SY96 @ SV45 @ SV40 @ SV6 ) ) )
= $false )
| ( ( SV45
= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ empty ) )
= $true )
| ( ( path @ SV6 @ SV40 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[574]) ).
thf(591,plain,
! [SV27: $i,SV33: $i] :
( ( ( SV33
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
= $false )
| ( ( SV27
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
= $false )
| ( ( ( SV33
!= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
!= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
= $true )
| ( ( SV27 = SV33 )
= $true )
| ( ( vertex @ SV27 )
= $false )
| ( ( vertex @ SV33 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[575]) ).
thf(592,plain,
! [SV33: $i,SV27: $i] :
( ( ( ~ ( ( SV27
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
| ~ ( ( SV27
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) ) )
= $false )
| ( ( SV27 = SV33 )
= $true )
| ( ( vertex @ SV27 )
= $false )
| ( ( vertex @ SV33 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[576]) ).
thf(593,plain,
! [SV27: $i,SV33: $i] :
( ( ( ~ ( ( SV33
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
| ~ ( ( SV33
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) ) )
= $false )
| ( ( SV27 = SV33 )
= $true )
| ( ( vertex @ SV27 )
= $false )
| ( ( vertex @ SV33 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[577]) ).
thf(594,plain,
! [SV9: $i,SV21: $i,SV89: $i,SV29: $i] :
( ( ( SV29
= ( path_cons @ SV89 @ empty ) )
= $false )
| ( ( SV21
= ( head_of @ SV89 ) )
= $false )
| ( ( SV9
= ( tail_of @ SV89 ) )
= $false )
| ( ( edge @ SV89 )
= $false )
| ( ( vertex @ SV9 )
= $false )
| ( ( vertex @ SV21 )
= $false )
| ( ( path @ SV9 @ SV21 @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[578]) ).
thf(595,plain,
! [SV9: $i,SV21: $i,SV113: $i,SV90: $i,SV29: $i] :
( ( ( SV29
= ( path_cons @ SV90 @ SV113 ) )
= $false )
| ( ( ~ ( path @ ( head_of @ SV90 ) @ SV21 @ SV113 ) )
= $true )
| ( ( SV9
= ( tail_of @ SV90 ) )
= $false )
| ( ( edge @ SV90 )
= $false )
| ( ( vertex @ SV9 )
= $false )
| ( ( vertex @ SV21 )
= $false )
| ( ( path @ SV9 @ SV21 @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[579]) ).
thf(596,plain,
! [SV34: $i,SV30: $i,SV93: $i,SV10: $i,SV99: $i,SV114: $i] :
( ( ( precedes @ SV114 @ SV99 @ SV10 )
= $false )
| ( ( ~ ( sequential @ SV93 @ SV114 ) )
= $true )
| ( ( ~ ( sequential @ SV93 @ SV99 ) )
= $true )
| ( ( precedes @ SV93 @ SV99 @ SV10 )
= $false )
| ( ( path @ SV30 @ SV34 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[580]) ).
thf(597,plain,
! [SV34: $i,SV30: $i,SV10: $i,SV94: $i,SV100: $i] :
( ( ( precedes @ ( sK9_E3 @ SV100 @ SV94 @ SV10 ) @ SV100 @ SV10 )
= $true )
| ( ( sequential @ SV94 @ SV100 )
= $true )
| ( ( precedes @ SV94 @ SV100 @ SV10 )
= $false )
| ( ( path @ SV30 @ SV34 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[581]) ).
thf(598,plain,
! [SV34: $i,SV30: $i,SV10: $i,SV100: $i,SV94: $i] :
( ( ( sequential @ SV94 @ ( sK9_E3 @ SV100 @ SV94 @ SV10 ) )
= $true )
| ( ( sequential @ SV94 @ SV100 )
= $true )
| ( ( precedes @ SV94 @ SV100 @ SV10 )
= $false )
| ( ( path @ SV30 @ SV34 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[582]) ).
thf(599,plain,
! [SV11: $i] :
( ( ! [SY148: $i,SY149: $i] :
~ ( triangle @ SV11 @ SY148 @ SY149 )
| ( edge @ SV11 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[584]) ).
thf(600,plain,
! [SV11: $i] :
( ( ! [SY150: $i] :
( ! [SY151: $i] :
~ ( triangle @ SV11 @ SY150 @ SY151 )
| ( edge @ SY150 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[585]) ).
thf(601,plain,
! [SV116: $i,SV115: $i,SV11: $i] :
( ( ( ~ ( triangle @ SV11 @ SV115 @ SV116 ) )
= $true )
| ( ( edge @ SV116 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[586]) ).
thf(602,plain,
! [SV37: $i,SV31: $i,SV14: $i,SV77: $i,SV112: $i,SV69: $i] :
( ( ( sequential @ SV69 @ SV112 )
= $false )
| ( ( precedes @ SV112 @ SV77 @ SV14 )
= $false )
| ( ( on_path @ SV69 @ SV14 )
= $false )
| ( ( on_path @ SV77 @ SV14 )
= $false )
| ( ( precedes @ SV69 @ SV77 @ SV14 )
= $true )
| ( ( path @ SV31 @ SV37 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[587]) ).
thf(603,plain,
! [SV117: $i,SV6: $i,SV40: $i,SV45: $i] :
( ( ( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ SV117 ) ) )
= $true )
| ( ( ~ ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ SV117 ) )
= $true )
| ( ( SV40
= ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
= $false )
| ( ( SV45
= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ empty ) )
= $false )
| ( ( path @ SV6 @ SV40 @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[588]) ).
thf(604,plain,
! [SV6: $i,SV40: $i,SV45: $i] :
( ( ( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ ( sK13_SY95 @ SV45 @ SV40 @ SV6 ) ) ) )
= $false )
| ( ( SV40
= ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
= $true )
| ( ( path @ SV6 @ SV40 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[589]) ).
thf(605,plain,
! [SV6: $i,SV40: $i,SV45: $i] :
( ( ( ~ ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ ( sK13_SY95 @ SV45 @ SV40 @ SV6 ) ) )
= $false )
| ( ( SV40
= ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
= $true )
| ( ( path @ SV6 @ SV40 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[589]) ).
thf(606,plain,
! [SV6: $i,SV40: $i,SV45: $i] :
( ( ( ( SV45
!= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ ( sK12_SY96 @ SV45 @ SV40 @ SV6 ) ) ) )
= $false )
| ( ( SV45
= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ empty ) )
= $true )
| ( ( path @ SV6 @ SV40 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[590]) ).
thf(607,plain,
! [SV6: $i,SV40: $i,SV45: $i] :
( ( ( ~ ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ ( sK12_SY96 @ SV45 @ SV40 @ SV6 ) ) )
= $false )
| ( ( SV45
= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ empty ) )
= $true )
| ( ( path @ SV6 @ SV40 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[590]) ).
thf(608,plain,
! [SV27: $i,SV33: $i] :
( ( ( ( SV33
!= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
= $true )
| ( ( ( SV27
!= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
= $true )
| ( ( SV27
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
= $false )
| ( ( SV33
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
= $false )
| ( ( SV27 = SV33 )
= $true )
| ( ( vertex @ SV27 )
= $false )
| ( ( vertex @ SV33 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[591]) ).
thf(609,plain,
! [SV33: $i,SV27: $i] :
( ( ( ~ ( ( SV27
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) ) ) )
= $false )
| ( ( SV27 = SV33 )
= $true )
| ( ( vertex @ SV27 )
= $false )
| ( ( vertex @ SV33 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[592]) ).
thf(610,plain,
! [SV33: $i,SV27: $i] :
( ( ( ~ ( ( SV27
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) ) )
= $false )
| ( ( SV27 = SV33 )
= $true )
| ( ( vertex @ SV27 )
= $false )
| ( ( vertex @ SV33 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[592]) ).
thf(611,plain,
! [SV27: $i,SV33: $i] :
( ( ( ~ ( ( SV33
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) ) ) )
= $false )
| ( ( SV27 = SV33 )
= $true )
| ( ( vertex @ SV27 )
= $false )
| ( ( vertex @ SV33 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[593]) ).
thf(612,plain,
! [SV27: $i,SV33: $i] :
( ( ( ~ ( ( SV33
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) ) )
= $false )
| ( ( SV27 = SV33 )
= $true )
| ( ( vertex @ SV27 )
= $false )
| ( ( vertex @ SV33 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[593]) ).
thf(613,plain,
! [SV9: $i,SV29: $i,SV113: $i,SV21: $i,SV90: $i] :
( ( ( path @ ( head_of @ SV90 ) @ SV21 @ SV113 )
= $false )
| ( ( SV29
= ( path_cons @ SV90 @ SV113 ) )
= $false )
| ( ( SV9
= ( tail_of @ SV90 ) )
= $false )
| ( ( edge @ SV90 )
= $false )
| ( ( vertex @ SV9 )
= $false )
| ( ( vertex @ SV21 )
= $false )
| ( ( path @ SV9 @ SV21 @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[595]) ).
thf(614,plain,
! [SV34: $i,SV30: $i,SV10: $i,SV99: $i,SV114: $i,SV93: $i] :
( ( ( sequential @ SV93 @ SV114 )
= $false )
| ( ( precedes @ SV114 @ SV99 @ SV10 )
= $false )
| ( ( ~ ( sequential @ SV93 @ SV99 ) )
= $true )
| ( ( precedes @ SV93 @ SV99 @ SV10 )
= $false )
| ( ( path @ SV30 @ SV34 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[596]) ).
thf(615,plain,
! [SV11: $i] :
( ( ( ! [SY148: $i,SY149: $i] :
~ ( triangle @ SV11 @ SY148 @ SY149 ) )
= $true )
| ( ( edge @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[599]) ).
thf(616,plain,
! [SV118: $i,SV11: $i] :
( ( ! [SY268: $i] :
~ ( triangle @ SV11 @ SV118 @ SY268 )
| ( edge @ SV118 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[600]) ).
thf(617,plain,
! [SV116: $i,SV115: $i,SV11: $i] :
( ( ( triangle @ SV11 @ SV115 @ SV116 )
= $false )
| ( ( edge @ SV116 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[601]) ).
thf(618,plain,
! [SV117: $i,SV6: $i,SV40: $i,SV45: $i] :
( ( ( SV45
= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ SV117 ) )
= $false )
| ( ( ~ ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ SV117 ) )
= $true )
| ( ( SV40
= ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
= $false )
| ( ( SV45
= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ empty ) )
= $false )
| ( ( path @ SV6 @ SV40 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[603]) ).
thf(619,plain,
! [SV6: $i,SV40: $i,SV45: $i] :
( ( ( SV45
= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ ( sK13_SY95 @ SV45 @ SV40 @ SV6 ) ) )
= $true )
| ( ( SV40
= ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
= $true )
| ( ( path @ SV6 @ SV40 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[604]) ).
thf(620,plain,
! [SV6: $i,SV40: $i,SV45: $i] :
( ( ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ ( sK13_SY95 @ SV45 @ SV40 @ SV6 ) )
= $true )
| ( ( SV40
= ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
= $true )
| ( ( path @ SV6 @ SV40 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[605]) ).
thf(621,plain,
! [SV6: $i,SV40: $i,SV45: $i] :
( ( ( SV45
= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ ( sK12_SY96 @ SV45 @ SV40 @ SV6 ) ) )
= $true )
| ( ( SV45
= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ empty ) )
= $true )
| ( ( path @ SV6 @ SV40 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[606]) ).
thf(622,plain,
! [SV6: $i,SV40: $i,SV45: $i] :
( ( ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ ( sK12_SY96 @ SV45 @ SV40 @ SV6 ) )
= $true )
| ( ( SV45
= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ empty ) )
= $true )
| ( ( path @ SV6 @ SV40 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[607]) ).
thf(623,plain,
! [SV27: $i,SV33: $i] :
( ( ( SV33
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
= $false )
| ( ( ( SV27
!= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
= $true )
| ( ( SV27
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
= $false )
| ( ( SV33
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
= $false )
| ( ( SV27 = SV33 )
= $true )
| ( ( vertex @ SV27 )
= $false )
| ( ( vertex @ SV33 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[608]) ).
thf(624,plain,
! [SV33: $i,SV27: $i] :
( ( ( ( SV27
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
= $true )
| ( ( SV27 = SV33 )
= $true )
| ( ( vertex @ SV27 )
= $false )
| ( ( vertex @ SV33 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[609]) ).
thf(625,plain,
! [SV33: $i,SV27: $i] :
( ( ( ( SV27
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
= $true )
| ( ( SV27 = SV33 )
= $true )
| ( ( vertex @ SV27 )
= $false )
| ( ( vertex @ SV33 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[610]) ).
thf(626,plain,
! [SV27: $i,SV33: $i] :
( ( ( ( SV33
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV33
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
= $true )
| ( ( SV27 = SV33 )
= $true )
| ( ( vertex @ SV27 )
= $false )
| ( ( vertex @ SV33 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[611]) ).
thf(627,plain,
! [SV27: $i,SV33: $i] :
( ( ( ( SV33
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
| ( SV27
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) ) )
= $true )
| ( ( SV27 = SV33 )
= $true )
| ( ( vertex @ SV27 )
= $false )
| ( ( vertex @ SV33 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[612]) ).
thf(628,plain,
! [SV34: $i,SV30: $i,SV10: $i,SV114: $i,SV99: $i,SV93: $i] :
( ( ( sequential @ SV93 @ SV99 )
= $false )
| ( ( precedes @ SV114 @ SV99 @ SV10 )
= $false )
| ( ( sequential @ SV93 @ SV114 )
= $false )
| ( ( precedes @ SV93 @ SV99 @ SV10 )
= $false )
| ( ( path @ SV30 @ SV34 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[614]) ).
thf(629,plain,
! [SV119: $i,SV11: $i] :
( ( ( ! [SY269: $i] :
~ ( triangle @ SV11 @ SV119 @ SY269 ) )
= $true )
| ( ( edge @ SV11 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[615]) ).
thf(630,plain,
! [SV118: $i,SV11: $i] :
( ( ( ! [SY268: $i] :
~ ( triangle @ SV11 @ SV118 @ SY268 ) )
= $true )
| ( ( edge @ SV118 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[616]) ).
thf(631,plain,
! [SV117: $i,SV6: $i,SV40: $i,SV45: $i] :
( ( ( path @ ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) @ SV40 @ SV117 )
= $false )
| ( ( SV45
= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ SV117 ) )
= $false )
| ( ( SV40
= ( head_of @ ( sK11_E @ SV45 @ SV40 @ SV6 ) ) )
= $false )
| ( ( SV45
= ( path_cons @ ( sK11_E @ SV45 @ SV40 @ SV6 ) @ empty ) )
= $false )
| ( ( path @ SV6 @ SV40 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[618]) ).
thf(632,plain,
! [SV33: $i,SV27: $i] :
( ( ( SV27
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
= $false )
| ( ( SV33
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
= $false )
| ( ( SV27
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
= $false )
| ( ( SV33
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
= $false )
| ( ( SV27 = SV33 )
= $true )
| ( ( vertex @ SV27 )
= $false )
| ( ( vertex @ SV33 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[623]) ).
thf(633,plain,
! [SV33: $i,SV27: $i] :
( ( ( SV27
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
= $true )
| ( ( SV33
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
= $true )
| ( ( SV27 = SV33 )
= $true )
| ( ( vertex @ SV27 )
= $false )
| ( ( vertex @ SV33 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[624]) ).
thf(634,plain,
! [SV33: $i,SV27: $i] :
( ( ( SV27
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
= $true )
| ( ( SV27
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
= $true )
| ( ( SV27 = SV33 )
= $true )
| ( ( vertex @ SV27 )
= $false )
| ( ( vertex @ SV33 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[625]) ).
thf(635,plain,
! [SV27: $i,SV33: $i] :
( ( ( SV33
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
= $true )
| ( ( SV33
= ( head_of @ ( sK14_E @ SV33 @ SV27 ) ) )
= $true )
| ( ( SV27 = SV33 )
= $true )
| ( ( vertex @ SV27 )
= $false )
| ( ( vertex @ SV33 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[626]) ).
thf(636,plain,
! [SV27: $i,SV33: $i] :
( ( ( SV33
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
= $true )
| ( ( SV27
= ( tail_of @ ( sK14_E @ SV33 @ SV27 ) ) )
= $true )
| ( ( SV27 = SV33 )
= $true )
| ( ( vertex @ SV27 )
= $false )
| ( ( vertex @ SV33 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[627]) ).
thf(637,plain,
! [SV120: $i,SV119: $i,SV11: $i] :
( ( ( ~ ( triangle @ SV11 @ SV119 @ SV120 ) )
= $true )
| ( ( edge @ SV11 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(638,plain,
! [SV121: $i,SV118: $i,SV11: $i] :
( ( ( ~ ( triangle @ SV11 @ SV118 @ SV121 ) )
= $true )
| ( ( edge @ SV118 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(639,plain,
! [SV120: $i,SV119: $i,SV11: $i] :
( ( ( triangle @ SV11 @ SV119 @ SV120 )
= $false )
| ( ( edge @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[637]) ).
thf(640,plain,
! [SV121: $i,SV118: $i,SV11: $i] :
( ( ( triangle @ SV11 @ SV118 @ SV121 )
= $false )
| ( ( edge @ SV118 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[638]) ).
thf(641,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[79,640,639,636,635,634,633,632,631,628,622,621,620,619,617,613,602,598,597,594,583,570,556,555,554,544,536,535,532,525,524,520,515,512,506,505,504,503,492,490,489,484,483,460,454,444,443,418,409,403,401,398,377,376,374,337,243,242,233,232,188,187,161,118]) ).
thf(642,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[641]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GRA007+2 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.10/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue May 31 03:35:11 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.38
% 0.12/0.38 No.of.Axioms: 18
% 0.12/0.38
% 0.12/0.38 Length.of.Defs: 0
% 0.12/0.38
% 0.12/0.38 Contains.Choice.Funs: false
% 0.18/0.42 .
% 0.18/0.42 (rf:0,axioms:18,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:20,loop_count:0,foatp_calls:0,translation:fof_full)........................................................
% 18.88/19.07
% 18.88/19.07 ********************************
% 18.88/19.07 * All subproblems solved! *
% 18.88/19.07 ********************************
% 18.88/19.07 % 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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:641,loop_count:0,foatp_calls:1,translation:fof_full)
% 19.06/19.29
% 19.06/19.29 %**** Beginning of derivation protocol ****
% 19.06/19.29 % SZS output start CNFRefutation
% See solution above
% 19.06/19.29
% 19.06/19.29 %**** End of derivation protocol ****
% 19.06/19.29 %**** no. of clauses in derivation: 642 ****
% 19.06/19.29 %**** clause counter: 641 ****
% 19.06/19.29
% 19.06/19.29 % 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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:641,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------