#    Appendix to `Excluded minors in cubic graphs'
#    Neil Robertson, Paul Seymour and Robin Thomas
#
# This file contains details of the case-checking needed for
# the paper 
# [1] N.Robertson, P.D.Seymour and R.Thomas, Excluded minors
# in cubic graphs, manuscript.
#
# Lines that start with the character '#' are comments; all
# other lines are of the form
# G=Antibox
# or a pair of lines of the form
# G+(1,2,7,10) contains Petersen
#    via 2 15 5 13 6 8 12 10 16 14 removing 1-4 3-7 9-11
#
# The meaning of the latter pair is that Antibox+(v1v2,v7v10)
# (see [1] for definition) contains Petersen, where a containment
# can be obtained by deleting the edges v1v4, v3v7 and v9v11,
# and mapping the vertices of Petersen onto the vertices of
# Antibox+(v1v2,v7v10) by the rule 1->2, 2->15, 3->5, ..., 10->14.
# The file `graphs' contains all the graphs referred to herein
# with the appropriate vertex numberings. 
#
# To make checking easier, (except for a few exeptions) this file 
# contains all cases, even when some are obviously isomorphic to 
# earlier ones. The best way to proceed is perhaps to write 
# a simple computer program to check all the containment relations
# claimed herein, and verify by inspection that all cases are covered.
#
##############################################################
# Proof of (11.2)
G=Antibox
# A-expansions:
G+(1,2,7,10) contains Petersen
   via 2 15 5 13 6 8 12 10 16 14 removing 1-4 3-7 9-11
G+(1,2,7,14) contains Petersen
   via 2 15 5 13 6 8 12 10 16 14 removing 1-4 3-7 9-11
G+(1,2,8,11) contains Petersen
   via 2 3 5 13 6 16 12 10 7 14 removing 1-15 4-8 9-11
G+(1,2,8,12) contains Petersen
   via 2 3 5 13 6 16 12 10 7 14 removing 1-15 4-8 9-11
G+(1,2,9,11) contains Petersen
   via 2 3 5 12 6 16 9 13 14 11 removing 1-15 4-8 7-10
G+(1,2,9,13) contains Box
   via 1 5 9 4 8 11 16 13 14 15 2 3 12 6 removing 7-10
G+(1,2,10,12) contains Triplex
   via 1 15 2 6 10 7 14 8 4 13 16 3 removing 5-12 9-11
G+(1,2,11,14) contains Petersen
   via 2 3 7 10 6 16 14 13 9 11 removing 1-15 4-8 5-12
G+(1,2,13,14) contains Petersen
   via 2 15 5 10 6 11 9 13 16 14 removing 1-4 3-7 8-12
G+(2,3,5,9) contains Petersen
   via 3 4 6 10 7 16 13 14 8 12 removing 1-5 2-15 9-11
G+(2,3,5,12) contains Petersen
   via 3 4 6 10 7 16 13 14 8 12 removing 1-5 2-15 9-11
G+(2,3,8,11) contains Petersen
   via 3 5 13 6 15 7 14 16 12 10 removing 1-2 4-8 9-11
G+(2,3,8,12) contains Petersen
   via 3 5 13 6 15 7 14 16 12 10 removing 1-2 4-8 9-11
G+(2,3,9,11) contains Petersen
   via 3 5 12 6 15 14 11 16 9 13 removing 1-2 4-8 7-10
G+(2,3,9,13) contains Petersen
   via 3 4 6 10 7 16 13 14 11 9 removing 1-5 2-15 8-12
G+(2,3,10,12) contains Box
   via 1 5 13 4 8 14 6 10 7 2 15 3 12 16 removing 9-11
G+(2,3,11,14) contains Petersen
   via 3 15 6 10 7 9 13 14 16 11 removing 1-2 4-8 5-12
G+(2,3,13,14) contains Triplex
   via 3 8 12 5 9 13 16 14 7 15 11 10 removing 1-4 2-6
G+(3,4,5,9) contains Petersen
   via 4 6 10 7 15 8 12 16 13 14 removing 1-5 2-3 9-11
G+(3,4,5,12) contains Petersen
   via 4 6 10 7 15 8 12 16 13 14 removing 1-5 2-3 9-11
G+(3,4,6,10) contains Petersen
   via 3 5 12 10 7 15 8 14 13 16 removing 1-4 2-6 9-11
G+(3,4,6,13) contains Petersen
   via 3 5 12 10 7 15 8 14 13 16 removing 1-4 2-6 9-11
G+(3,4,9,11) contains Petersen
   via 4 15 7 12 8 13 14 11 16 9 removing 1-5 2-3 6-10
G+(3,4,9,13) contains Petersen
   via 3 5 12 8 15 14 13 16 9 11 removing 1-4 2-6 7-10
G+(3,4,10,12) contains Triplex
   via 2 3 15 4 8 12 5 13 6 1 14 16 removing 7-10 9-11
G+(3,4,11,14) contains Box
   via 1 4 15 9 11 16 3 7 14 2 6 13 8 10 removing 5-12
G+(3,4,13,14) contains Petersen
   via 3 7 10 8 15 9 13 16 14 11 removing 1-4 2-6 5-12
G+(4,1,6,10) contains Petersen
   via 3 4 8 12 5 7 14 13 16 10 removing 1-15 2-6 9-11
G+(4,1,6,13) contains Petersen
   via 3 4 8 12 5 7 14 13 16 10 removing 1-15 2-6 9-11
G+(4,1,7,10) contains Petersen
   via 4 15 5 13 6 8 12 10 16 14 removing 1-2 3-7 9-11
G+(4,1,7,14) contains Petersen
   via 4 15 5 13 6 8 12 10 16 14 removing 1-2 3-7 9-11
G+(4,1,9,11) contains Triplex
   via 2 5 9 16 11 14 7 10 6 3 12 13 removing 1-15 4-8
G+(4,1,9,13) contains Petersen
   via 3 4 8 12 5 14 11 9 16 13 removing 1-15 2-6 7-10
G+(4,1,10,12) contains Box
   via 1 15 4 5 12 8 3 7 14 2 6 13 16 10 removing 9-11
G+(4,1,11,14) contains Petersen
   via 4 15 5 12 8 13 9 11 16 14 removing 1-2 3-7 6-10
G+(4,1,13,14) contains Petersen
   via 4 15 5 10 6 11 9 13 16 14 removing 1-2 3-7 8-12
# B-expansions via (1,2,5,9)
G+(1,2,5,9)+(5,16,2,3) contains Petersen
   via 3 4 8 14 7 17 12 10 15 16 removing 1-5 2-18 6-13 9-11
G+(1,2,5,9)+(5,16,2,6) contains Triplex
   via 4 16 17 18 6 10 7 14 8 3 13 12 removing 1-5 2-15 9-11
G+(1,2,5,9)+(5,16,3,4) contains Petersen
   via 4 18 7 14 8 15 10 12 17 16 removing 1-5 2-3 6-13 9-11
G+(1,2,5,9)+(5,16,3,7) contains Petersen
   via 3 6 10 7 18 8 12 17 13 14 removing 1-15 2-16 4-5 9-11
G+(1,2,5,9)+(5,16,4,8) contains Triplex
   via 2 6 10 7 14 8 18 16 15 3 13 12 removing 1-4 5-17 9-11
G+(1,2,5,9)+(5,16,6,10) contains Triplex
   via 2 16 17 5 12 10 7 14 6 3 11 18 removing 1-15 4-8 9-13
G+(1,2,5,9)+(5,16,6,13) contains Petersen
   via 2 3 5 12 6 16 17 18 14 11 removing 1-15 4-8 7-10 9-13
G+(1,2,5,9)+(5,16,7,10) contains Petersen
   via 3 5 12 10 6 7 14 13 17 18 removing 1-15 2-16 4-8 9-11
G+(1,2,5,9)+(5,16,7,14) contains Petersen
   via 3 7 10 12 8 16 13 14 18 17 removing 1-15 2-6 4-5 9-11
G+(1,2,5,9)+(5,16,8,11) contains Box
   via 1 5 17 4 8 18 16 13 14 15 2 3 12 6 removing 7-10 9-11
G+(1,2,5,9)+(5,16,11,14) contains Petersen
   via 3 8 11 9 16 14 18 17 12 13 removing 1-15 2-6 4-5 7-10
G+(1,2,5,9)+(5,16,13,14) contains Petersen
   via 7 16 9 13 10 14 11 12 17 18 removing 1-15 2-6 3-4 5-8
# C-expansions via (1,2,5,9)
G+(1,2,5,9)+(5,1,8,11) contains Triplex
   via 3 7 10 6 13 16 15 18 8 2 14 12 removing 1-4 5-17 9-11
G+(1,2,5,9)+(15,16,6,10) contains Triplex
   via 3 7 14 6 18 17 15 12 8 2 10 11 removing 1-4 5-16 9-13
G+(1,2,5,9)+(15,16,6,13) contains Box
   via 1 5 16 4 8 11 17 18 14 15 2 3 12 6 removing 7-10 9-13
# D-expansion via (1,2,5,9)
G+(1,2,5,9)+(1,15,3,7) contains Petersen
   via 3 6 10 7 18 8 12 16 13 14 removing 1-17 2-15 4-5 9-11
# E-expansions via (1,2,5,9)
G+(1,2,5,9)+(15,1,4,3)+(4,18,7,10) contains Triplex
   via 3 6 13 16 12 8 19 20 7 18 10 14 removing 1-17 2-15 4-5 9-11
G+(1,2,5,9)+(15,1,4,3)+(4,18,7,14) contains Box
   via 2 6 14 3 7 20 11 8 19 15 17 18 10 12 removing 1-4 5-16 9-13
G+(1,2,5,12) contains Triplex
   via 2 16 5 4 8 14 7 10 6 3 12 13 removing 1-15 9-11
# B-expansions via (2,3,6,10)
G+(2,3,6,10)+(6,16,1,4) contains Petersen
   via 3 4 8 10 7 15 11 14 17 16 removing 1-18 2-6 5-12 9-13
G+(2,3,6,10)+(6,16,1,5) contains Triplex
   via 3 15 16 18 5 12 8 14 7 4 13 10 removing 1-2 6-17 9-11
G+(2,3,6,10)+(6,16,3,4) contains Petersen
   via 3 7 10 8 18 15 16 17 14 11 removing 1-4 2-6 5-12 9-13
G+(2,3,6,10)+(6,16,3,7) contains Triplex
   via 15 5 12 8 14 7 18 17 16 3 13 10 removing 1-4 2-6 9-11
G+(2,3,6,10)+(6,16,4,8) contains Petersen
   via 4 5 12 10 7 18 8 14 13 17 removing 1-2 3-15 6-16 9-11
G+(2,3,6,10)+(6,16,5,9) contains Petersen
   via 2 5 12 8 15 14 10 16 18 11 removing 1-4 3-7 6-17 9-13
G+(2,3,6,10)+(6,16,5,12) contains Triplex
   via 3 8 11 5 18 17 16 10 7 15 12 14 removing 1-4 2-6 9-13
G+(2,3,6,10)+(6,16,7,14) contains Box
   via 1 5 13 4 8 14 6 17 18 2 15 3 12 16 removing 7-10 9-11
G+(2,3,6,10)+(6,16,8,11) contains Petersen
   via 3 7 10 12 8 15 16 18 14 13 removing 1-2 4-5 6-17 9-11
G+(2,3,6,10)+(6,16,8,12) contains Petersen
   via 4 5 12 18 8 16 10 14 13 17 removing 1-2 3-7 6-15 9-11
G+(2,3,6,10)+(6,16,9,11) contains Petersen
   via 8 12 9 18 11 15 13 14 10 16 removing 1-2 3-7 4-5 6-17
G+(2,3,6,10)+(6,16,11,14) contains Petersen
   via 3 7 10 9 11 15 16 18 14 13 removing 1-2 4-5 6-17 8-12
# C-expansions via (2,3,6,10)
G+(2,3,6,10)+(6,2,5,9) contains Box
   via 1 5 18 4 8 11 17 6 14 2 15 3 12 16 removing 7-10 9-13
G+(2,3,6,10)+(6,2,5,12) contains Triplex
   via 4 5 18 15 16 10 7 14 8 3 13 12 removing 1-2 6-17 9-11
G+(2,3,6,10)+(15,16,7,14) contains Triplex
   via 3 8 12 5 13 16 17 18 7 15 14 10 removing 1-4 2-6 9-11
# D-expansion via (2,3,6,10)
G+(2,3,6,10)+(2,15,4,8) contains Petersen
   via 4 5 12 10 7 18 8 14 13 16 removing 1-2 3-15 6-17 9-11
# E-expansions via (2,3,6,10)
G+(2,3,6,10)+(15,2,1,4)+(1,18,8,11) contains Triplex
   via 4 8 20 19 5 13 16 10 7 18 12 14 removing 1-2 3-15 6-17 9-11
G+(2,3,6,10)+(15,2,1,4)+(1,18,8,12) contains Box
   via 2 5 11 17 20 8 14 7 3 6 16 15 12 10 removing 1-19 4-18 9-13
G+(2,3,6,13) contains Triplex
   via 1 6 16 3 7 14 8 12 5 4 10 13 removing 2-15 9-11
G+(3,4,7,10) contains Triplex
   via 2 7 16 4 8 12 5 13 6 1 14 10 removing 3-15 9-11
# B-expansions via (3,4,7,14)
G+(3,4,7,14)+(7,16,1,2) contains Petersen
   via 2 6 10 8 15 18 17 16 14 11 removing 1-4 3-7 5-12 9-13
G+(3,4,7,14)+(7,16,1,4) contains Petersen
   via 4 15 6 10 8 18 13 14 16 17 removing 1-2 3-7 5-12 9-11
G+(3,4,7,14)+(7,16,1,5) contains Petersen
   via 4 15 6 10 8 18 13 14 16 17 removing 1-2 3-7 5-12 9-11
G+(3,4,7,14)+(7,16,2,6) contains Triplex
   via 3 7 17 18 6 14 11 8 15 2 10 16 removing 1-4 5-12 9-13
G+(3,4,7,14)+(7,16,4,8) contains Triplex
   via 5 13 6 15 16 17 18 8 12 4 14 10 removing 1-2 3-7 9-11
G+(3,4,7,14)+(7,16,5,9) contains Petersen
   via 5 15 6 10 12 18 13 14 16 17 removing 1-2 3-7 4-8 9-11
G+(3,4,7,14)+(7,16,5,12) contains Petersen
   via 4 5 13 14 8 15 10 12 18 16 removing 1-2 3-6 7-17 9-11
G+(3,4,7,14)+(7,16,6,13) contains Box
   via 1 4 15 13 14 16 3 7 17 2 6 18 8 10 removing 5-12 9-11
G+(3,4,7,14)+(7,16,8,11) contains Petersen
   via 3 7 10 8 15 11 14 16 17 18 removing 1-4 2-6 5-12 9-13
G+(3,4,7,14)+(7,16,8,12) contains Triplex
   via 5 12 10 7 17 16 15 8 11 3 18 14 removing 1-4 2-6 9-13
G+(3,4,7,14)+(7,16,9,11) contains Petersen
   via 5 9 13 10 12 16 14 11 18 17 removing 1-2 3-6 4-8 7-15
G+(3,4,7,14)+(7,16,9,13) contains Petersen
   via 6 15 9 11 10 13 18 17 16 14 removing 1-2 3-7 4-8 5-12
# C-expansions via (3,4,7,14)
G+(3,4,7,14)+(7,3,6,13) contains Triplex
   via 2 6 18 17 7 16 15 8 11 3 10 14 removing 1-4 5-12 9-13
G+(3,4,7,14)+(15,16,8,11) contains Box
   via 1 4 15 11 18 17 3 7 16 2 6 14 8 10 removing 5-12 9-13
G+(3,4,7,14)+(15,16,8,12) contains Triplex
   via 4 5 13 6 10 16 17 18 8 15 12 14 removing 1-2 3-7 9-11
# D-expansion via (3,4,7,14)
G+(3,4,7,14)+(3,15,1,5) contains Petersen
   via 4 15 5 13 6 8 12 10 16 14 removing 1-18 2-3 7-17 9-11
# E-expansions via (3,4,7,14)
G+(3,4,7,14)+(15,3,2,1)+(2,18,5,9) contains Box
   via 2 6 14 3 7 16 11 8 15 19 18 17 10 12 removing 1-4 5-20 9-13
G+(3,4,7,14)+(15,3,2,1)+(2,18,5,12) contains Triplex
   via 4 5 20 17 6 10 16 14 8 15 13 12 removing 1-18 2-19 3-7 9-11
G+(4,1,8,11) contains Triplex
   via 1 16 8 3 7 10 6 13 5 2 14 12 removing 4-15 9-11
# B-expansions via (4,1,8,12)
G+(4,1,8,12)+(8,16,1,2) contains Petersen
   via 2 3 7 10 6 17 14 13 15 16 removing 1-18 4-8 5-12 9-11
G+(4,1,8,12)+(8,16,1,5) contains Triplex
   via 3 16 17 18 5 13 6 10 7 2 12 14 removing 1-15 4-8 9-11
G+(4,1,8,12)+(8,16,2,3) contains Petersen
   via 3 18 6 10 7 15 13 14 17 16 removing 1-2 4-8 5-12 9-11
G+(4,1,8,12)+(8,16,2,6) contains Petersen
   via 3 18 6 10 7 15 13 14 17 16 removing 1-2 4-8 5-12 9-11
G+(4,1,8,12)+(8,16,3,7) contains Triplex
   via 4 15 13 6 10 7 18 17 8 3 16 14 removing 1-2 5-12 9-11
G+(4,1,8,12)+(8,16,5,9) contains Box
   via 1 15 4 18 17 8 3 7 14 2 6 13 16 10 removing 5-12 9-11
G+(4,1,8,12)+(8,16,6,10) contains Petersen
   via 3 6 18 10 7 16 17 14 13 12 removing 1-2 4-8 5-15 9-11
G+(4,1,8,12)+(8,16,6,13) contains Petersen
   via 4 6 10 14 8 15 16 17 18 13 removing 1-2 3-7 5-12 9-11
G+(4,1,8,12)+(8,16,7,10) contains Triplex
   via 2 5 12 16 17 18 7 14 6 3 11 10 removing 1-15 4-8 9-13
G+(4,1,8,12)+(8,16,7,14) contains Petersen
   via 4 7 12 11 8 15 16 17 18 14 removing 1-5 2-3 6-10 9-13
G+(4,1,8,12)+(8,16,9,13) contains Petersen
   via 4 8 11 9 15 13 14 16 17 18 removing 1-2 3-7 5-12 6-10
G+(4,1,8,12)+(8,16,13,14) contains Petersen
   via 6 8 11 9 13 10 14 18 17 12 removing 1-2 3-7 4-15 5-16
# C-expansions via (4,1,8,12)
G+(4,1,8,12)+(8,4,7,10) contains Triplex
   via 3 6 13 15 16 8 17 18 7 4 10 14 removing 1-2 5-12 9-11
G+(4,1,8,12)+(8,4,7,14) contains Box
   via 1 15 4 11 8 17 3 7 18 2 6 14 16 10 removing 5-12 9-13
G+(4,1,8,12)+(15,16,5,9) contains Triplex
   via 2 5 18 17 16 14 7 10 6 3 12 13 removing 1-15 4-8 9-11
# D-expansion via (4,1,8,12)
G+(4,1,8,12)+(4,15,2,6) contains Petersen
   via 3 5 13 6 17 7 14 16 12 10 removing 1-15 2-18 4-8 9-11
# E-expansions via (4,1,8,12)
G+(4,1,8,12)+(15,4,3,2)+(3,18,6,10) contains Box
   via 2 5 11 18 16 8 14 7 3 6 20 19 12 10 removing 1-15 4-17 9-13
G+(4,1,8,12)+(15,4,3,2)+(3,18,6,13) contains Triplex
   via 3 7 14 8 16 15 17 18 19 4 10 13 removing 1-2 5-12 6-20 9-11


##############################################################
# Proof of (11.3)
G=Drape
# A-expansions:
G+(5,12,2,3) contains Petersen
   via 3 4 6 10 7 13 9 11 8 14 removing 1-5 2-16 12-15
G+(5,12,2,6) contains Triplex
   via 3 16 15 5 13 14 8 11 7 4 9 12 removing 1-2 6-10
G+(5,12,3,4) contains Petersen
   via 4 6 10 7 16 8 14 13 9 11 removing 1-5 2-3 12-15
G+(5,12,3,7) contains Petersen
   via 4 5 13 9 6 8 14 12 15 11 removing 1-2 3-16 7-10
G+(5,12,4,8) contains Box
   via 2 6 9 3 7 11 13 14 8 5 15 16 10 12 removing 1-4
G+(5,12,6,9) contains Triplex
   via 5 15 16 6 10 11 8 14 13 4 12 9 removing 1-2 3-7
G+(5,12,7,11) contains Petersen
   via 4 5 13 14 8 10 9 11 15 12 removing 1-2 3-6 7-16
G+(5,12,8,11) contains Petersen
   via 4 5 13 14 8 10 9 16 15 12 removing 1-2 3-6 7-11
G+(5,12,9,11) contains Petersen
   via 5 7 10 9 13 15 12 14 11 16 removing 1-2 3-6 4-8
G+(12,14,1,2) contains Petersen
   via 2 4 5 13 9 15 12 11 8 14 removing 1-16 3-7 6-10
G+(12,14,1,4) contains Box
   via 1 16 4 13 14 8 3 7 11 2 6 9 15 10 removing 5-12
G+(12,14,2,3) contains Petersen
   via 4 5 13 14 8 16 9 11 12 15 removing 1-2 3-7 6-10
G+(12,14,2,6) contains Petersen
   via 4 5 13 14 8 16 9 11 12 15 removing 1-2 3-7 6-10
G+(12,14,3,4) contains Petersen
   via 4 5 13 14 8 16 9 11 12 15 removing 1-2 3-7 6-10
G+(12,14,3,7) contains Petersen
   via 3 4 11 9 6 16 7 10 12 15 removing 1-2 5-13 8-14
G+(12,14,6,9) contains Petersen
   via 4 5 13 14 8 16 9 11 12 15 removing 1-2 3-7 6-10
G+(12,14,7,11) contains Triplex
   via 5 12 10 7 16 11 8 14 13 4 15 9 removing 1-2 3-6
G+(12,14,9,11) contains Triplex
   via 4 5 13 14 15 16 11 10 6 8 12 9 removing 1-2 3-7
G+(14,13,1,2) contains Petersen
   via 3 4 5 12 10 15 13 9 8 14 removing 1-16 2-6 7-11
G+(14,13,1,4) contains Triplex
   via 2 5 13 15 14 11 7 10 6 3 12 9 removing 1-16 4-8
G+(14,13,2,3) contains Petersen
   via 4 5 12 14 8 16 10 11 13 15 removing 1-2 3-7 6-9
G+(14,13,2,6) contains Petersen
   via 4 5 12 14 8 16 10 11 13 15 removing 1-2 3-7 6-9
G+(14,13,3,4) contains Petersen
   via 4 5 13 9 8 16 15 14 12 10 removing 1-2 3-6 7-11
G+(14,13,3,7) contains Petersen
   via 4 5 13 9 8 16 15 14 12 10 removing 1-2 3-6 7-11
G+(14,13,6,10) contains Petersen
   via 4 5 12 14 8 16 10 11 13 15 removing 1-2 3-7 6-9
G+(14,13,7,10) contains Petersen
   via 5 7 11 9 13 12 14 15 16 10 removing 1-2 3-6 4-8
G+(14,13,7,11) contains Petersen
   via 4 7 10 14 8 13 9 11 16 15 removing 1-2 3-6 5-12
G+(13,5,2,3) contains Petersen
   via 3 4 6 10 7 13 9 11 8 14 removing 1-5 2-16 12-15
G+(13,5,2,6) contains Box
   via 3 7 11 16 6 9 8 14 13 4 5 15 10 12 removing 1-2
G+(13,5,3,4) contains Petersen
   via 4 6 10 7 16 8 14 13 9 11 removing 1-5 2-3 12-15
G+(13,5,3,7) contains Petersen
   via 4 6 10 7 15 8 14 13 9 11 removing 1-2 3-16 5-12
G+(13,5,4,8) contains Triplex
   via 2 3 7 11 8 14 13 15 5 9 16 12 removing 1-4 6-10
G+(13,5,6,10) contains Triplex
   via 5 15 16 6 9 11 8 14 12 4 13 10 removing 1-2 3-7
G+(13,5,7,10) contains Petersen
   via 4 6 9 11 8 15 13 14 10 16 removing 1-2 3-7 5-12
G+(13,5,7,11) contains Petersen
   via 4 6 9 11 8 15 13 14 10 16 removing 1-2 3-7 5-12
G+(13,5,8,11) contains Petersen
   via 4 5 12 14 8 9 11 16 15 13 removing 1-2 3-7 6-10
# Jumps creating quadrangles:
G+(5,12,1,2) contains Triplex
   via 2 3 7 11 8 14 13 5 15 9 4 12 removing 1-16 6-10
G+(5,12,1,4) contains Box
   via 2 6 9 3 7 11 13 14 8 5 15 4 10 12 removing 1-16
G+(12,14,10,6) contains Petersen
   via 4 5 13 9 6 8 14 15 12 11 removing 1-2 3-7 10-16
G+(12,14,10,7) contains Triplex
   via 3 6 12 5 13 14 8 11 7 4 9 15 removing 1-2 10-16
G+(14,13,8,4) contains Triplex
   via 2 5 13 15 14 11 7 10 6 3 12 9 removing 1-4 8-16
G+(14,13,8,11) contains Antibox
   via 1 2 3 4 5 6 7 14 13 10 15 12 9 11 removing 8-16
G+(13,5,9,6) contains Antibox
   via 1 2 3 4 5 6 7 14 15 10 13 12 16 9 removing 8-11
G+(13,5,9,11) contains Petersen
   via 4 5 12 10 6 8 14 13 15 11 removing 1-2 3-7 9-16


##############################################################
# Checking (E2) for the proof of (11.4)
G=Window
G+(1,2,3,7) contains Petersen
   via 3 14 5 9 6 8 12 10 7 11 removing 1-4 2-13
G+(1,2,4,8) contains Petersen
   via 4 5 9 6 14 7 11 8 12 10 removing 1-13 2-3
G+(1,2,5,12) contains Triplex
   via 2 14 5 4 8 11 7 10 6 3 12 9 removing 1-13
G+(1,2,6,10) contains Triplex
   via 1 14 6 3 7 11 8 12 5 4 10 9 removing 2-13
G+(1,2,7,10) contains Petersen
   via 2 13 5 9 6 8 12 10 14 11 removing 1-4 3-7
G+(1,2,7,11) contains Petersen
   via 2 13 5 9 6 8 12 10 14 11 removing 1-4 3-7
G+(1,2,8,11) contains Petersen
   via 2 3 5 9 6 14 12 10 7 11 removing 1-13 4-8
G+(1,2,8,12) contains Petersen
   via 2 3 5 9 6 14 12 10 7 11 removing 1-13 4-8
G+(1,2,9,11) contains Box
   via 1 13 2 5 9 6 3 7 10 4 8 12 14 11
G+(1,2,10,12) contains Triplex
   via 1 13 2 6 10 7 11 8 4 9 14 3 removing 5-12
G+(1,4,2,6) contains Petersen
   via 3 4 6 9 5 7 10 12 8 11 removing 1-13 2-14
G+(1,4,3,7) contains Petersen
   via 4 13 5 9 6 8 12 10 7 11 removing 1-2 3-14
G+(1,4,5,9) contains Triplex
   via 2 5 14 4 8 11 7 10 6 3 12 9 removing 1-13
G+(1,4,6,9) contains Petersen
   via 3 4 8 12 5 7 11 9 14 10 removing 1-13 2-6
G+(1,4,6,10) contains Petersen
   via 3 4 8 12 5 7 11 9 14 10 removing 1-13 2-6
G+(1,4,7,10) contains Petersen
   via 4 13 5 9 6 8 12 10 14 11 removing 1-2 3-7
G+(1,4,7,11) contains Petersen
   via 4 13 5 9 6 8 12 10 14 11 removing 1-2 3-7
G+(1,4,8,11) contains Triplex
   via 1 14 8 3 7 10 6 9 5 2 11 12 removing 4-13
G+(1,4,9,11) contains Triplex
   via 1 2 6 10 7 11 8 4 13 12 3 14 removing 5-9
G+(1,4,10,12) contains Box
   via 1 13 4 5 12 8 3 7 11 2 6 9 14 10
G+(1,5,2,3) contains Petersen
   via 3 4 6 9 5 7 10 12 8 11 removing 1-13 2-14
G+(1,5,3,4) contains Petersen
   via 4 14 5 9 6 8 12 10 7 11 removing 1-13 2-3
G+(1,5,3,7) contains Petersen
   via 4 13 5 9 6 8 12 10 7 11 removing 1-2 3-14
G+(1,5,6,10) contains Triplex
   via 3 6 14 13 5 12 8 11 7 4 9 10 removing 1-2
G+(1,5,7,10) contains Petersen
   via 4 13 5 9 6 8 12 10 14 11 removing 1-2 3-7
G+(1,5,7,11) contains Petersen
   via 4 13 5 9 6 8 12 10 14 11 removing 1-2 3-7
G+(1,5,8,11) contains Triplex
   via 3 8 14 13 5 9 6 10 7 2 12 11 removing 1-4
G+(1,5,9,11) contains Drape
   via 1 4 3 2 13 8 7 6 12 11 10 14 5 9
G+(1,5,10,12) contains Drape
   via 1 2 3 4 13 6 7 8 9 10 11 14 5 12
G+(2,3,4,8) contains Petersen
   via 4 5 9 6 14 7 11 8 12 10 removing 1-2 3-13
G+(2,3,5,9) contains Petersen
   via 3 4 6 10 7 14 9 11 8 12 removing 1-5 2-13
G+(2,3,5,12) contains Petersen
   via 3 4 6 10 7 14 9 11 8 12 removing 1-5 2-13
G+(2,3,6,9) contains Triplex
   via 1 6 14 3 7 11 8 12 5 4 10 9 removing 2-13
G+(2,3,7,11) contains Triplex
   via 2 14 7 4 8 12 5 9 6 1 11 10 removing 3-13
G+(2,3,8,11) contains Petersen
   via 3 5 9 6 13 7 11 14 12 10 removing 1-2 4-8
G+(2,3,8,12) contains Petersen
   via 3 5 9 6 13 7 11 14 12 10 removing 1-2 4-8
G+(2,3,9,11) contains Triplex
   via 1 2 13 3 7 11 8 12 5 4 10 14 removing 6-9
G+(2,3,10,12) contains Box
   via 1 5 9 4 8 11 6 10 7 2 13 3 12 14
G+(2,6,3,4) contains Petersen
   via 3 5 9 6 14 7 11 8 12 10 removing 1-4 2-13
G+(2,6,4,8) contains Petersen
   via 4 5 9 6 14 7 11 8 12 10 removing 1-2 3-13
G+(2,6,5,12) contains Triplex
   via 4 5 14 13 6 10 7 11 8 3 9 12 removing 1-2
G+(2,6,7,11) contains Triplex
   via 3 8 12 5 9 6 13 14 7 2 11 10 removing 1-4
G+(2,6,8,11) contains Petersen
   via 3 5 9 6 13 7 11 14 12 10 removing 1-2 4-8
G+(2,6,8,12) contains Petersen
   via 3 5 9 6 13 7 11 14 12 10 removing 1-2 4-8
G+(2,6,9,11) contains Drape
   via 2 3 4 1 13 7 8 5 10 11 12 14 6 9
G+(2,6,10,12) contains Drape
   via 2 1 4 3 13 5 8 7 9 12 11 14 6 10
G+(3,4,5,9) contains Petersen
   via 4 6 10 7 13 8 12 14 9 11 removing 1-5 2-3
G+(3,4,5,12) contains Petersen
   via 4 6 10 7 13 8 12 14 9 11 removing 1-5 2-3
G+(3,4,6,9) contains Petersen
   via 3 5 12 10 7 13 8 11 9 14 removing 1-4 2-6
G+(3,4,6,10) contains Petersen
   via 3 5 12 10 7 13 8 11 9 14 removing 1-4 2-6
G+(3,4,7,10) contains Triplex
   via 2 7 14 4 8 12 5 9 6 1 11 10 removing 3-13
G+(3,4,8,12) contains Triplex
   via 1 8 14 3 7 10 6 9 5 2 11 12 removing 4-13
G+(3,4,9,11) contains Box
   via 1 5 12 2 6 10 8 11 7 4 13 3 9 14
G+(3,4,10,12) contains Triplex
   via 2 3 13 4 8 12 5 9 6 1 11 14 removing 7-10
G+(3,7,5,9) contains Petersen
   via 3 6 10 7 13 8 12 14 9 11 removing 1-2 4-5
G+(3,7,5,12) contains Petersen
   via 3 6 10 7 13 8 12 14 9 11 removing 1-2 4-5
G+(3,7,6,9) contains Triplex
   via 2 5 12 8 11 7 13 14 6 3 9 10 removing 1-4
G+(3,7,8,12) contains Triplex
   via 4 5 9 6 10 7 13 14 8 3 12 11 removing 1-2
G+(3,7,9,11) contains Drape
   via 3 2 1 4 13 6 5 8 10 9 12 14 7 11
G+(3,7,10,12) contains Drape
   via 3 4 1 2 13 8 5 6 11 12 9 14 7 10
G+(4,8,5,9) contains Triplex
   via 2 5 14 13 8 11 7 10 6 3 12 9 removing 1-4
G+(4,8,6,9) contains Petersen
   via 4 5 12 10 7 13 8 11 9 14 removing 1-2 3-6
G+(4,8,6,10) contains Petersen
   via 4 5 12 10 7 13 8 11 9 14 removing 1-2 3-6
G+(4,8,7,10) contains Triplex
   via 3 6 9 5 12 8 13 14 7 4 10 11 removing 1-2
G+(4,8,9,11) contains Drape
   via 4 1 2 3 13 5 6 7 12 9 10 14 8 11
G+(4,8,10,12) contains Drape
   via 4 3 2 1 13 7 6 5 11 10 9 14 8 12
G+(5,9,6,10) contains Drape
   via 2 3 4 1 6 7 8 5 10 11 12 9 14 13
G+(5,9,7,10) contains Petersen
   via 3 5 13 9 6 7 14 10 12 11 removing 1-2 4-8
G+(5,9,7,11) contains Petersen
   via 2 3 7 14 5 6 10 12 8 11 removing 1-4 9-13
G+(5,9,8,11) contains Antibox
   via 1 2 3 4 5 6 7 8 13 10 14 12 9 11
G+(5,9,8,12) contains Drape
   via 1 2 3 4 5 6 7 8 9 10 11 12 13 14
G+(5,12,6,9) contains Drape
   via 1 4 3 2 5 8 7 6 12 11 10 9 13 14
G+(5,12,6,10) contains Antibox
   via 1 4 3 2 5 8 7 6 13 11 14 9 12 10
G+(5,12,7,10) contains Petersen
   via 3 4 5 9 6 7 13 12 8 11 removing 1-2 10-14
G+(5,12,7,11) contains Petersen
   via 4 5 9 10 7 8 11 14 13 12 removing 1-2 3-6
G+(5,12,8,11) contains Drape
   via 4 3 2 1 8 7 6 5 11 10 9 12 14 13
G+(6,9,7,10) contains Drape
   via 2 1 4 3 6 5 8 7 9 12 11 10 13 14
G+(6,9,7,11) contains Antibox
   via 1 2 3 4 5 6 7 8 9 10 11 12 13 14
G+(6,9,8,11) contains Petersen
   via 2 3 7 11 5 6 10 12 8 14 removing 1-4 9-13
G+(6,9,8,12) contains Petersen
   via 4 5 9 13 6 8 11 10 12 14 removing 1-2 3-7
G+(6,10,7,11) contains Drape
   via 3 4 1 2 7 8 5 6 11 12 9 10 14 13
G+(6,10,8,11) contains Petersen
   via 3 6 9 11 7 8 12 10 13 14 removing 1-2 4-5
G+(6,10,8,12) contains Petersen
   via 3 4 5 9 6 7 12 14 8 11 removing 1-2 10-13
G+(7,10,8,11) contains Drape
   via 3 2 1 4 7 6 5 8 10 9 12 11 13 14
G+(7,10,8,12) contains Antibox
   via 1 4 3 2 5 8 7 6 12 11 10 9 14 13
G+(7,11,8,12) contains Drape
   via 4 1 2 3 8 5 6 7 12 9 10 11 14 13


##############################################################
# Proof of (13.2)
G=Box
G+(1,2,3,6) contains Triplex
   via 1 16 3 7 8 14 11 12 4 10 9 13 removing 2-15 5-6
G+(1,2,4,12) contains Petersen
   via 2 13 5 10 7 12 9 8 14 11 removing 1-15 3-6 4-16
G+(1,2,5,6) contains Triplex
   via 3 6 16 5 12 11 14 8 7 13 9 10 removing 1-4 2-15
G+(1,2,6,9) contains Petersen
   via 5 7 8 9 12 13 14 11 10 15 removing 1-4 2-3 6-16
G+(1,2,7,8) contains Petersen
   via 4 5 6 7 16 12 9 8 14 11 removing 1-10 2-15 3-13
G+(1,2,8,9) contains Petersen
   via 6 7 8 16 9 13 14 11 10 15 removing 1-4 2-3 5-12
G+(1,2,8,14) contains Petersen
   via 3 6 9 8 7 15 12 11 14 16 removing 1-10 2-13 4-5
G+(1,2,9,12) contains Petersen
   via 2 13 5 10 7 16 9 8 14 11 removing 1-15 3-6 4-12
G+(1,2,10,11) contains Petersen
   via 4 5 6 16 10 12 9 8 14 11 removing 1-15 2-13 3-7
G+(1,2,11,12) contains Petersen
   via 3 5 4 10 7 16 12 8 14 11 removing 1-15 2-13 6-9
G+(1,2,11,14) contains Petersen
   via 3 6 5 10 7 16 14 8 9 11 removing 1-15 2-13 4-12
G+(1,4,2,3) contains Triplex
   via 2 16 3 6 9 8 14 11 10 13 12 7 removing 1-15 4-5
G+(1,4,3,6) contains Triplex
   via 3 16 15 4 12 11 14 8 7 13 9 10 removing 1-2 5-6
G+(1,4,3,7) contains Petersen
   via 4 5 6 10 7 12 9 8 14 11 removing 1-15 2-13 3-16
G+(1,4,5,6) contains Triplex
   via 3 6 16 5 12 11 14 8 7 13 9 10 removing 1-2 4-15
G+(1,4,6,9) contains Petersen
   via 2 3 11 4 15 13 14 16 6 5 removing 1-10 7-8 9-12
G+(1,4,7,8) contains Petersen
   via 4 5 6 10 15 12 9 8 14 11 removing 1-2 3-13 7-16
G+(1,4,7,10) contains Petersen
   via 4 5 6 10 16 12 9 8 14 11 removing 1-15 2-13 3-7
G+(1,4,8,9) contains Petersen
   via 5 6 7 8 14 15 10 11 9 16 removing 1-2 3-13 4-12
G+(1,4,8,14) contains Petersen
   via 4 5 7 8 12 15 10 11 14 16 removing 1-2 3-13 6-9
G+(1,4,9,12) contains Petersen
   via 2 3 6 5 13 16 9 14 11 12 removing 1-10 4-15 7-8
G+(1,4,11,14) contains Triplex
   via 15 4 5 6 9 8 7 11 16 3 12 14 removing 1-10 2-13
G+(1,10,2,13) contains Triplex
   via 2 3 6 9 8 14 11 10 16 12 7 13 removing 1-15 4-5
G+(1,10,3,6) contains Petersen
   via 4 5 6 10 7 12 9 8 14 11 removing 1-15 2-13 3-16
G+(1,10,4,5) contains Petersen
   via 2 13 5 10 7 12 9 8 14 11 removing 1-15 3-6 4-16
G+(1,10,5,6) contains Petersen
   via 4 5 14 8 7 12 11 10 16 9 removing 1-15 2-13 3-6
G+(1,10,5,13) contains Petersen
   via 2 7 8 9 12 13 14 11 10 16 removing 1-15 3-6 4-5
G+(1,10,6,9) contains Petersen
   via 5 7 8 9 12 13 14 11 10 15 removing 1-4 2-3 6-16
G+(1,10,7,8) contains Petersen
   via 4 5 6 10 15 12 9 8 14 11 removing 1-2 3-13 7-16
G+(1,10,8,9) contains Petersen
   via 5 6 7 8 14 15 10 11 9 16 removing 1-2 3-13 4-12
G+(1,10,8,14) contains Petersen
   via 4 5 7 8 12 15 10 11 14 16 removing 1-2 3-13 6-9
G+(1,10,9,12) contains Petersen
   via 5 7 8 16 12 13 14 11 10 15 removing 1-4 2-3 6-9
G+(1,10,11,14) contains Triplex
   via 1 4 5 6 9 8 7 11 16 3 12 14 removing 2-13 10-15
G+(1,10,13,14) contains Triplex
   via 1 3 6 9 8 14 11 10 15 12 7 16 removing 2-13 4-5
G+(2,3,4,5) contains Triplex
   via 2 15 3 6 9 8 14 11 10 13 12 7 removing 1-4 5-16
G+(2,3,4,12) contains Petersen
   via 5 10 7 8 9 13 15 12 11 14 removing 1-2 3-6 4-16
G+(2,3,6,9) contains Petersen
   via 2 13 5 7 10 9 12 11 14 8 removing 1-4 3-15 6-16
G+(2,3,7,8) contains Petersen
   via 4 5 6 7 16 12 9 8 14 11 removing 1-10 2-13 3-15
G+(2,3,8,9) contains Petersen
   via 2 13 6 7 10 16 9 11 14 8 removing 1-4 3-15 5-12
G+(2,3,8,14) contains Petersen
   via 3 6 9 8 7 15 12 11 14 16 removing 1-10 2-13 4-5
G+(2,3,9,12) contains Petersen
   via 5 10 7 8 9 13 15 16 11 14 removing 1-2 3-6 4-12
G+(2,3,10,11) contains Petersen
   via 4 10 8 9 12 13 14 11 16 15 removing 1-2 3-7 5-6
G+(2,3,11,12) contains Petersen
   via 5 10 7 8 9 13 15 16 11 14 removing 1-2 3-6 4-12
G+(2,3,11,14) contains Petersen
   via 3 6 5 10 7 16 14 8 9 11 removing 1-2 4-12 13-15
G+(2,13,3,7) contains Triplex
   via 1 3 16 7 8 14 11 12 4 10 9 13 removing 2-15 5-6
G+(2,13,4,12) contains Petersen
   via 5 10 7 8 9 13 15 12 11 14 removing 1-2 3-6 4-16
G+(2,13,6,9) contains Petersen
   via 5 7 8 9 12 13 14 11 10 15 removing 1-4 2-3 6-16
G+(2,13,7,8) contains Petersen
   via 6 7 16 8 9 13 15 12 11 14 removing 1-10 2-3 4-5
G+(2,13,7,10) contains Triplex
   via 2 3 6 9 8 14 11 16 15 12 7 13 removing 1-10 4-5
G+(2,13,8,9) contains Petersen
   via 6 7 8 16 9 13 14 11 10 15 removing 1-4 2-3 5-12
G+(2,13,8,14) contains Petersen
   via 2 3 6 14 16 12 9 8 7 11 removing 1-10 4-5 13-15
G+(2,13,9,12) contains Petersen
   via 5 10 7 8 9 13 15 16 11 14 removing 1-2 3-6 4-12
G+(2,13,10,11) contains Petersen
   via 4 10 8 9 12 13 14 11 16 15 removing 1-2 3-7 5-6
G+(2,13,11,12) contains Petersen
   via 5 10 7 8 9 13 15 16 11 14 removing 1-2 3-6 4-12
G+(2,13,11,14) contains Petersen
   via 3 6 5 10 7 16 14 8 9 11 removing 1-2 4-12 13-15
G+(3,6,4,5) contains Triplex
   via 1 4 15 6 9 8 14 11 10 13 12 7 removing 2-3 5-16
G+(3,6,4,12) contains Petersen
   via 3 13 5 10 7 12 9 8 14 11 removing 1-2 4-16 6-15
G+(3,6,7,10) contains Petersen
   via 4 5 6 16 7 12 9 8 14 11 removing 1-10 2-13 3-15
G+(3,6,8,14) contains Triplex
   via 3 13 5 10 11 9 8 16 15 7 14 6 removing 1-2 4-12
G+(3,6,9,12) contains Petersen
   via 3 13 5 10 7 16 9 8 14 11 removing 1-2 4-12 6-15
G+(3,6,10,11) contains Petersen
   via 4 5 6 16 10 12 9 8 14 11 removing 1-2 3-13 7-15
G+(3,6,11,12) contains Petersen
   via 4 5 15 7 10 12 16 11 14 8 removing 1-2 3-13 6-9
G+(3,6,11,14) contains Petersen
   via 5 6 15 7 10 14 16 11 9 8 removing 1-2 3-13 4-12
G+(3,7,4,5) contains Petersen
   via 5 6 10 7 16 14 11 12 9 8 removing 1-4 2-13 3-15
G+(3,7,4,12) contains Petersen
   via 5 10 7 8 9 13 15 12 11 14 removing 1-2 3-6 4-16
G+(3,7,5,6) contains Petersen
   via 2 13 5 7 10 9 12 11 14 8 removing 1-4 3-15 6-16
G+(3,7,5,13) contains Petersen
   via 2 10 7 8 9 13 16 12 11 14 removing 1-4 3-15 5-6
G+(3,7,8,14) contains Triplex
   via 3 6 5 4 12 11 10 8 16 1 9 14 removing 2-13 7-15
G+(3,7,9,12) contains Petersen
   via 5 10 7 8 9 13 15 16 11 14 removing 1-2 3-6 4-12
G+(3,7,10,11) contains Petersen
   via 4 5 6 16 10 12 9 8 14 11 removing 1-2 3-13 7-15
G+(3,7,11,12) contains Petersen
   via 4 5 15 7 10 12 16 11 14 8 removing 1-2 3-13 6-9
G+(3,7,11,14) contains Petersen
   via 5 6 15 7 10 14 16 11 9 8 removing 1-2 3-13 4-12
G+(3,7,13,14) contains Triplex
   via 2 3 15 7 8 14 11 12 13 10 9 16 removing 1-4 5-6
G+(4,5,7,8) contains Petersen
   via 5 6 7 11 14 15 16 8 9 12 removing 1-2 3-13 4-10
G+(4,5,7,10) contains Petersen
   via 5 6 9 8 14 15 12 11 10 16 removing 1-4 2-13 3-7
G+(4,5,8,9) contains Petersen
   via 5 6 7 8 14 15 10 11 9 16 removing 1-2 3-13 4-12
G+(4,5,8,14) contains Petersen
   via 5 13 7 8 9 15 10 11 14 16 removing 1-2 3-6 4-12
G+(4,5,10,11) contains Petersen
   via 2 13 5 16 7 12 9 8 14 11 removing 1-10 3-6 4-15
G+(4,5,11,12) contains Petersen
   via 2 3 6 5 13 12 9 14 11 16 removing 1-10 4-15 7-8
G+(4,5,11,14) contains Petersen
   via 2 3 6 16 14 12 9 8 7 11 removing 1-10 4-15 5-13
G+(4,12,5,13) contains Triplex
   via 3 6 5 16 12 11 14 8 7 13 9 10 removing 1-2 4-15
G+(4,12,7,8) contains Petersen
   via 5 6 7 11 14 15 16 8 9 12 removing 1-2 3-13 4-10
G+(4,12,7,10) contains Petersen
   via 5 6 9 8 14 15 12 11 10 16 removing 1-4 2-13 3-7
G+(4,12,8,9) contains Petersen
   via 4 5 6 7 10 15 12 11 14 8 removing 1-2 3-13 9-16
G+(4,12,8,14) contains Petersen
   via 4 5 9 8 10 15 12 11 14 16 removing 1-2 3-13 6-7
G+(4,12,11,14) contains Triplex
   via 1 2 3 7 8 9 12 15 4 10 14 6 removing 5-13 11-16
G+(4,12,13,14) contains Triplex
   via 4 5 13 7 8 14 11 12 15 10 9 16 removing 1-2 3-6
G+(5,6,7,8) contains Petersen
   via 3 13 5 16 7 9 12 11 14 8 removing 1-2 4-10 6-15
G+(5,6,7,10) contains Petersen
   via 2 13 5 12 9 10 16 8 14 11 removing 1-4 3-7 6-15
G+(5,6,8,9) contains Petersen
   via 3 13 5 10 7 9 16 8 14 11 removing 1-2 4-12 6-15
G+(5,6,8,14) contains Petersen
   via 3 6 9 8 7 14 11 10 15 16 removing 1-2 4-12 5-13
G+(5,6,10,11) contains Petersen
   via 4 5 14 8 10 12 11 16 15 9 removing 1-2 3-13 6-7
G+(5,6,11,12) contains Petersen
   via 4 5 15 7 10 12 16 11 14 8 removing 1-2 3-13 6-9
G+(5,6,11,14) contains Petersen
   via 3 6 9 8 7 13 12 11 16 14 removing 1-2 4-10 5-15
G+(5,13,6,9) contains Triplex
   via 1 4 6 16 9 8 14 11 10 13 12 7 removing 2-3 5-15
G+(5,13,7,8) contains Petersen
   via 3 7 16 8 9 13 15 12 11 14 removing 1-2 4-10 5-6
G+(5,13,7,10) contains Petersen
   via 2 9 8 16 10 13 14 11 12 15 removing 1-4 3-7 5-6
G+(5,13,8,9) contains Petersen
   via 3 7 8 16 9 13 14 11 10 15 removing 1-2 4-12 5-6
G+(5,13,8,14) contains Petersen
   via 3 6 5 10 7 14 16 8 9 11 removing 1-2 4-12 13-15
G+(5,13,9,12) contains Triplex
   via 3 6 5 15 16 11 14 8 7 13 9 10 removing 1-2 4-12
G+(5,13,10,11) contains Petersen
   via 2 7 8 9 12 13 14 11 16 15 removing 1-10 3-6 4-5
G+(5,13,11,12) contains Petersen
   via 2 3 6 9 12 13 15 16 11 14 removing 1-10 4-5 7-8
G+(5,13,11,14) contains Petersen
   via 2 3 6 16 14 12 9 8 7 11 removing 1-10 4-5 13-15
G+(6,9,7,10) contains Petersen
   via 4 5 14 8 7 12 11 16 15 9 removing 1-10 2-13 3-6
G+(6,9,8,14) contains Triplex
   via 1 2 3 6 15 9 12 11 10 4 14 7 removing 5-13 8-16
G+(6,9,10,11) contains Petersen
   via 4 5 14 8 10 12 11 16 15 9 removing 1-2 3-13 6-7
G+(6,9,11,12) contains Petersen
   via 4 5 6 7 10 12 16 11 14 8 removing 1-2 3-13 9-15
G+(6,9,11,14) contains Petersen
   via 5 6 7 8 14 12 11 16 15 9 removing 1-2 3-13 4-10
G+(6,9,13,14) contains Triplex
   via 5 6 15 9 8 14 11 10 13 12 7 16 removing 1-4 2-3
G+(7,8,9,12) contains Triplex
   via 1 2 3 6 9 16 12 11 10 4 14 7 removing 5-13 8-15
G+(7,8,11,12) contains Triplex
   via 4 5 6 9 8 15 16 11 10 12 14 7 removing 1-2 3-13
G+(7,10,8,9) contains Triplex
   via 3 6 5 4 12 11 10 16 8 1 9 14 removing 2-13 7-15
G+(7,10,9,12) contains Triplex
   via 3 6 5 4 12 11 10 15 7 1 16 14 removing 2-13 8-9
G+(7,10,11,12) contains Triplex
   via 1 4 5 6 9 8 7 16 11 3 12 14 removing 2-13 10-15
G+(8,9,10,11) contains Triplex
   via 4 5 6 7 8 15 16 11 12 10 14 9 removing 1-2 3-13
G+(9,12,10,11) contains Triplex
   via 1 2 3 7 8 9 15 12 4 10 14 6 removing 5-13 11-16

##############################################################
# Proof of (13.3)
G=Box
# Checking (E4):
G+(1,2,13,14)+(3,6,13,16) contains Triplex
   via 2 15 10 7 8 9 17 18 13 3 16 12 removing 1-4 5-6 11-14
G+(1,2,13,14)+(3,6,14,16) contains Triplex
   via 3 17 9 8 14 11 10 16 13 7 18 12 removing 1-4 2-15 5-6
G+(1,2,13,14)+(5,6,13,16) contains Triplex
   via 2 13 18 6 9 8 7 10 15 3 12 16 removing 1-4 5-17 11-14
G+(1,4,13,14)+(3,6,13,16) contains Triplex
   via 4 13 18 9 8 14 11 10 15 12 7 16 removing 1-2 3-17 5-6

##############################################################
# Proof of (13.5)
G=Superbox
# Checking (E5):
G+(1,11,15,16)+(6,11,15,18)+(11,17,10,14) contains Triplex
   via 5 14 16 9 10 20 15 21 17 8 22 18 removing 1-2 3-12 4-13 6-7 11-19
G+(1,11,15,16)+(6,11,15,18)+(11,19,5,14) contains Triplex
   via 5 22 14 10 19 20 15 11 17 9 21 18 removing 1-2 3-12 4-8 6-7 13-16
# Checking (E6):
G+(11,1,14,10)+(1,5,10,6) contains Petersen
   via 5 8 9 10 20 14 16 15 12 18 removing 1-19 2-3 4-13 6-7 11-17
G+(11,1,14,10)+(5,14,6,11) contains Petersen
   via 5 13 10 18 17 19 20 11 16 14 removing 1-2 3-12 4-8 6-7 9-15
G+(1,5,10,6)+(5,14,6,11) contains Petersen
   via 5 13 9 10 17 19 20 11 16 14 removing 1-2 3-12 4-8 6-18 7-15
G+(11,1,14,10)+(17,1,18,10) contains Petersen
   via 6 7 12 20 10 11 15 16 14 18 removing 1-5 2-3 4-13 8-9 17-19
G+(1,5,10,6)+(17,5,18,6) contains Petersen
   via 2 4 5 14 12 18 20 7 9 10 removing 1-11 3-8 6-15 13-16 17-19
G+(5,14,6,11)+(17,14,18,11) contains Petersen
   via 6 10 9 11 15 18 13 16 14 20 removing 1-5 2-12 3-4 7-8 17-19


##############################################################
# Proof of (14.1)
G=Triplex
G+(1,2,4,5) contains Petersen
   via 3 4 14 5 11 12 9 8 7 6 removing 1-10 2-13
G+(1,2,5,6) contains Petersen
   via 2 3 4 5 11 13 10 8 12 14 removing 1-9 6-7
G+(1,2,6,7) contains Petersen
   via 2 3 4 5 11 14 10 9 12 6 removing 1-13 7-8
G+(1,2,6,12) contains Petersen
   via 4 5 6 7 10 12 14 13 11 8 removing 1-9 2-3
G+(1,2,7,8) contains Petersen
   via 3 4 5 6 12 14 8 9 10 7 removing 1-13 2-11
G+(1,9,3,4) contains Petersen
   via 2 10 4 5 11 12 9 8 7 6 removing 1-13 3-14
G+(1,9,4,5) contains Petersen
   via 3 11 5 6 12 10 13 9 8 7 removing 1-2 4-14
G+(1,9,5,6) contains Petersen
   via 4 5 14 6 12 10 13 9 8 7 removing 1-2 3-11
G+(1,9,5,11) contains Petersen
   via 3 12 6 7 10 11 14 13 9 8 removing 1-2 4-5
G+(1,9,6,7) contains Petersen
   via 2 3 12 6 11 13 9 8 7 14 removing 1-10 4-5
G+(1,10,3,12) contains Drum
   via 2 11 1 3 8 5 13 14 7 6 9 4 12 10
G+(1,10,5,6) contains Petersen
   via 4 5 14 6 12 10 13 9 8 7 removing 1-2 3-11
G+(1,10,5,11) contains Petersen
   via 3 12 6 7 10 11 14 13 9 8 removing 1-2 4-5
G+(1,10,6,12) contains Petersen
   via 4 5 6 7 10 12 14 13 11 8 removing 1-9 2-3
G+(1,10,8,11) contains Drum
   via 9 12 1 8 3 6 13 14 4 5 2 7 11 10
G+(2,3,5,6) contains Petersen
   via 2 13 3 4 10 11 8 7 14 5 removing 1-9 6-12
G+(2,3,6,7) contains Petersen
   via 3 4 5 6 12 13 11 9 10 14 removing 1-2 7-8
G+(2,3,7,8) contains Petersen
   via 3 4 5 6 12 13 11 9 10 7 removing 1-2 8-14
G+(2,3,7,10) contains Petersen
   via 5 6 7 8 11 10 14 13 12 9 removing 1-2 3-4
G+(2,3,8,9) contains Petersen
   via 1 10 4 5 11 9 14 8 7 6 removing 2-13 3-12
G+(2,11,4,10) contains Drum
   via 3 12 2 4 9 6 13 14 8 7 1 5 10 11
G+(2,11,6,7) contains Petersen
   via 3 4 5 6 12 13 11 9 10 14 removing 1-2 7-8
G+(2,11,6,12) contains Petersen
   via 4 5 6 7 10 12 14 13 11 8 removing 1-9 2-3
G+(2,11,7,10) contains Petersen
   via 5 6 7 8 11 10 14 13 12 9 removing 1-2 3-4
G+(2,11,9,12) contains Drum
   via 1 10 2 9 4 7 13 14 5 6 3 8 12 11
G+(3,4,6,7) contains Petersen
   via 3 13 4 5 11 12 9 8 14 6 removing 1-2 7-10
G+(3,4,7,8) contains Petersen
   via 4 5 6 7 10 13 12 9 8 14 removing 1-2 3-11
G+(3,4,8,9) contains Petersen
   via 2 10 4 5 11 12 14 8 7 6 removing 1-9 3-13
G+(3,4,8,11) contains Petersen
   via 2 3 13 4 10 11 14 8 12 5 removing 1-9 6-7
G+(3,12,5,11) contains Drum
   via 10 4 1 7 3 5 9 8 13 14 2 6 11 12
G+(3,12,7,8) contains Petersen
   via 4 5 6 7 10 13 12 9 8 14 removing 1-2 3-11
G+(3,12,7,10) contains Petersen
   via 5 6 7 8 11 10 14 13 12 9 removing 1-2 3-4
G+(3,12,8,11) contains Petersen
   via 2 3 7 6 11 9 8 14 13 12 removing 1-10 4-5
G+(4,5,7,8) contains Petersen
   via 4 13 5 6 12 10 11 8 14 7 removing 1-9 2-3
G+(4,5,8,9) contains Petersen
   via 3 4 13 6 12 8 14 9 10 7 removing 1-2 5-11
G+(4,5,9,12) contains Petersen
   via 3 4 13 5 11 12 14 9 10 6 removing 1-2 7-8
G+(4,10,6,12) contains Drum
   via 11 5 2 8 4 6 1 9 13 14 3 7 12 10
G+(4,10,8,9) contains Petersen
   via 2 11 5 6 12 10 13 14 8 7 removing 1-9 3-4
G+(4,10,8,11) contains Petersen
   via 2 3 4 5 11 10 13 14 8 7 removing 1-9 6-12
G+(4,10,9,12) contains Petersen
   via 2 11 5 6 12 10 13 14 8 7 removing 1-9 3-4
G+(5,6,8,9) contains Petersen
   via 5 13 6 7 10 11 12 9 14 8 removing 1-2 3-4
G+(5,11,7,10) contains Drum
   via 12 6 9 3 7 5 1 2 14 13 8 4 11 10
G+(5,11,9,12) contains Petersen
   via 3 4 5 6 12 11 13 14 9 8 removing 1-2 7-10
G+(6,12,8,11) contains Drum
   via 10 7 1 4 8 6 2 3 14 13 9 5 12 11
G+(7,10,9,12) contains Drum
   via 11 8 2 5 9 7 3 4 14 13 1 6 10 12


##############################################################
# Proof of (14.2)
G=Drum
G+(1,2,7,8) contains Petersen
   via 2 5 9 10 6 16 14 12 11 13 removing 1-15 3-7 4-8
G+(1,2,7,14) contains Petersen
   via 2 5 9 10 6 16 14 12 11 13 removing 1-15 3-7 4-8
G+(1,2,8,13) contains Petersen
   via 2 5 9 10 6 16 14 12 11 13 removing 1-15 3-7 4-8
G+(1,2,9,10) contains Petersen
   via 2 5 13 10 6 15 8 14 9 16 removing 1-3 4-12 7-11
G+(1,2,9,14) contains Petersen
   via 2 5 9 10 6 15 16 14 11 13 removing 1-3 4-12 7-8
G+(1,2,10,13) contains Petersen
   via 2 5 9 10 6 15 14 12 13 16 removing 1-4 3-11 7-8
G+(1,2,11,13) contains Firstapex
   via 4 1 15 2 6 12 7 3 11 5 9 14 8 16 10 13
G+(1,2,12,14) contains Firstapex
   via 3 1 15 2 5 11 8 4 12 6 10 13 7 16 9 14
G+(1,3,5,9) contains Petersen
   via 4 16 5 6 12 13 11 14 9 10 removing 1-2 3-15 7-8
G+(1,3,6,10) contains Petersen
   via 3 11 5 6 16 14 9 10 13 12 removing 1-2 4-15 7-8
G+(1,3,6,12) contains Petersen
   via 3 5 4 8 7 16 12 14 9 10 removing 1-15 2-6 11-13
G+(1,3,8,13) contains Fourthapex
   via 1 2 6 12 4 3 5 9 14 7 15 8 16 11 10 13
G+(1,3,9,10) contains Petersen
   via 5 6 10 16 9 11 13 14 12 15 removing 1-2 3-7 4-8
G+(1,3,9,14) contains Petersen
   via 3 15 4 8 7 11 12 14 16 13 removing 1-2 5-9 6-10
G+(1,3,10,13) contains Petersen
   via 3 15 4 8 7 11 12 14 16 13 removing 1-2 5-9 6-10
G+(1,3,12,14) contains Petersen
   via 4 5 9 14 8 12 10 13 11 16 removing 1-15 2-6 3-7
G+(1,4,5,9) contains Petersen
   via 4 16 5 6 12 13 11 14 9 10 removing 1-2 3-15 7-8
G+(1,4,5,11) contains Petersen
   via 3 16 4 12 6 7 8 10 9 14 removing 1-15 2-5 11-13
G+(1,4,6,10) contains Petersen
   via 3 11 5 6 16 14 9 10 13 12 removing 1-2 4-15 7-8
G+(1,4,7,14) contains Fourthapex
   via 1 2 5 11 3 4 6 10 13 8 15 7 16 12 9 14
G+(1,4,9,10) contains Petersen
   via 5 6 10 16 9 11 13 14 12 15 removing 1-2 3-7 4-8
G+(1,4,9,14) contains Petersen
   via 3 15 4 8 7 11 12 14 16 13 removing 1-2 5-9 6-10
G+(1,4,10,13) contains Petersen
   via 3 15 4 8 7 11 12 14 16 13 removing 1-2 5-9 6-10
G+(1,4,11,13) contains Petersen
   via 3 6 10 13 7 11 9 14 12 16 removing 1-15 2-5 4-8
G+(2,5,3,7) contains Petersen
   via 5 15 6 10 9 11 12 14 7 13 removing 1-2 3-16 4-8
G+(2,5,4,8) contains Petersen
   via 5 15 6 10 9 11 12 14 8 13 removing 1-2 3-7 4-16
G+(2,5,4,12) contains Petersen
   via 3 5 16 12 6 7 8 10 9 14 removing 1-4 2-15 11-13
G+(2,5,7,8) contains Petersen
   via 5 15 6 10 9 11 12 14 16 13 removing 1-2 3-7 4-8
G+(2,5,7,14) contains Petersen
   via 5 15 6 10 9 11 12 14 16 13 removing 1-2 3-7 4-8
G+(2,5,8,13) contains Petersen
   via 5 15 6 10 9 11 12 14 16 13 removing 1-2 3-7 4-8
G+(2,5,10,13) contains Fourthapex
   via 2 1 4 12 6 5 3 7 14 9 15 10 16 11 8 13
G+(2,5,12,14) contains Petersen
   via 3 6 12 8 7 11 16 14 10 13 removing 1-4 2-15 5-9
G+(2,6,3,7) contains Petersen
   via 5 15 6 10 9 11 12 14 7 13 removing 1-2 3-16 4-8
G+(2,6,3,11) contains Petersen
   via 4 5 16 6 12 8 7 14 9 10 removing 1-3 2-15 11-13
G+(2,6,4,8) contains Petersen
   via 5 15 6 10 9 11 12 14 8 13 removing 1-2 3-7 4-16
G+(2,6,7,8) contains Petersen
   via 5 15 6 10 9 11 12 14 16 13 removing 1-2 3-7 4-8
G+(2,6,7,14) contains Petersen
   via 5 15 6 10 9 11 12 14 16 13 removing 1-2 3-7 4-8
G+(2,6,8,13) contains Petersen
   via 5 15 6 10 9 11 12 14 16 13 removing 1-2 3-7 4-8
G+(2,6,9,14) contains Fourthapex
   via 2 1 3 11 5 6 4 8 13 10 15 9 16 12 7 14
G+(2,6,11,13) contains Petersen
   via 4 5 11 7 8 12 16 13 9 14 removing 1-3 2-15 6-10
G+(3,7,4,12) contains Petersen
   via 4 5 14 7 8 16 12 13 11 15 removing 1-3 2-6 9-10
G+(3,7,5,9) contains Secondapex
   via 1 4 12 6 2 15 7 14 9 16 3 5 11 8 10 13
G+(3,7,6,10) contains Petersen
   via 5 6 16 10 9 11 15 14 12 13 removing 1-2 3-4 7-8
G+(3,7,6,12) contains Petersen
   via 3 4 8 7 15 11 13 16 12 14 removing 1-2 5-6 9-10
G+(3,7,9,10) contains Petersen
   via 3 15 7 13 11 12 14 9 16 10 removing 1-2 4-8 5-6
G+(3,7,10,13) contains Petersen
   via 3 4 8 7 15 11 13 16 12 14 removing 1-2 5-6 9-10
G+(3,11,4,8) contains Petersen
   via 3 6 13 8 7 15 11 14 12 16 removing 1-4 2-5 9-10
G+(3,11,4,12) contains Petersen
   via 4 5 14 7 8 16 12 13 11 15 removing 1-3 2-6 9-10
G+(3,11,6,10) contains Petersen
   via 5 6 16 10 9 11 15 14 12 13 removing 1-2 3-4 7-8
G+(3,11,6,12) contains Petersen
   via 4 5 15 7 8 12 16 10 9 14 removing 1-3 2-6 11-13
G+(3,11,9,10) contains Petersen
   via 5 6 10 16 9 11 13 14 12 15 removing 1-2 3-7 4-8
G+(3,11,9,14) contains Thirdapex
   via 1 2 5 15 3 12 6 9 16 14 4 7 8 10 11 13
G+(3,11,12,14) contains Petersen
   via 4 5 9 14 8 12 10 13 11 16 removing 1-3 2-6 7-15
G+(4,8,5,9) contains Petersen
   via 5 6 10 9 16 11 13 15 12 14 removing 1-2 3-4 7-8
G+(4,8,5,11) contains Petersen
   via 3 4 15 8 7 11 16 14 12 13 removing 1-2 5-6 9-10
G+(4,8,6,10) contains Secondapex
   via 1 3 11 5 2 15 8 13 10 16 4 6 12 7 9 14
G+(4,8,9,10) contains Petersen
   via 4 15 8 13 11 12 14 9 16 10 removing 1-2 3-7 5-6
G+(4,8,9,14) contains Petersen
   via 3 4 15 8 7 11 16 14 12 13 removing 1-2 5-6 9-10
G+(4,12,5,9) contains Petersen
   via 5 6 10 9 16 11 13 15 12 14 removing 1-2 3-4 7-8
G+(4,12,5,11) contains Petersen
   via 2 5 9 10 6 8 14 12 16 13 removing 1-3 4-15 7-11
G+(4,12,9,10) contains Petersen
   via 5 6 10 16 9 11 13 14 12 15 removing 1-2 3-7 4-8
G+(4,12,10,13) contains Thirdapex
   via 1 2 6 15 4 11 5 10 16 13 3 8 7 9 12 14
G+(4,12,11,13) contains Petersen
   via 4 5 11 7 8 15 16 13 10 12 removing 1-3 2-6 9-14
G+(5,9,6,12) contains Petersen
   via 3 6 10 9 14 11 13 12 16 15 removing 1-4 2-5 7-8
G+(5,9,7,8) contains Petersen
   via 5 11 7 14 12 15 16 8 13 9 removing 1-2 3-4 6-10
G+(5,9,8,13) contains Petersen
   via 5 6 10 9 15 11 13 16 12 14 removing 1-2 3-4 7-8
G+(5,11,6,10) contains Petersen
   via 4 5 9 10 13 12 14 11 15 16 removing 1-3 2-6 7-8
G+(5,11,6,12) contains Petersen
   via 4 5 9 10 13 12 14 11 15 16 removing 1-3 2-6 7-8
G+(5,11,7,8) contains Petersen
   via 3 4 8 16 7 11 13 14 12 15 removing 1-2 5-9 6-10
G+(5,11,7,14) contains Thirdapex
   via 2 1 3 15 5 12 4 7 16 14 6 9 10 8 11 13
G+(5,11,12,14) contains Petersen
   via 4 5 9 14 8 12 10 13 15 16 removing 1-3 2-6 7-11
G+(6,10,7,8) contains Petersen
   via 6 11 7 14 12 15 16 8 13 10 removing 1-2 3-4 5-9
G+(6,10,7,14) contains Petersen
   via 5 6 15 10 9 11 16 14 12 13 removing 1-2 3-4 7-8
G+(6,12,7,8) contains Petersen
   via 3 4 8 16 7 11 13 14 12 15 removing 1-2 5-9 6-10
G+(6,12,8,13) contains Thirdapex
   via 2 1 4 15 6 11 3 8 16 13 5 10 9 7 12 14
G+(6,12,11,13) contains Petersen
   via 4 5 11 7 8 12 16 13 9 14 removing 1-3 2-6 10-15
G+(7,8,9,10) contains Petersen
   via 4 5 11 7 15 12 10 16 9 14 removing 1-3 2-6 8-13
G+(7,14,10,13) contains Petersen
   via 3 6 10 9 11 15 16 13 12 14 removing 1-4 2-5 7-8
G+(7,14,11,13) contains Sailboat
   via 5 2 1 3 11 9 6 4 7 16 10 12 8 15 14 13
G+(8,13,9,14) contains Petersen
   via 4 5 9 10 12 15 16 14 11 13 removing 1-3 2-6 7-8
G+(8,13,12,14) contains Sailboat
   via 6 2 1 4 12 10 5 3 8 16 9 11 7 15 13 14
G+(9,14,11,13) contains Sailboat
   via 3 1 2 5 11 7 4 6 9 16 8 12 10 15 14 13
G+(10,13,12,14) contains Sailboat
   via 4 1 2 6 12 8 3 5 10 16 7 11 9 15 13 14
G+(11,13,12,14) contains Petersen
   via 6 11 7 8 12 10 14 16 15 13 removing 1-2 3-4 5-9


##############################################################
# Proof of (14.5)
G=Sailboat
G+(1,2,3,8) contains Petersen
   via 3 18 6 11 7 14 15 12 8 16 removing 1-5 2-17 4-10 9-13
G+(1,2,4,9) contains Petersen
   via 4 8 13 9 18 10 16 11 15 14 removing 1-17 2-3 5-6 7-12
G+(1,2,5,10) contains Petersen
   via 5 18 8 13 9 11 12 14 10 16 removing 1-17 2-7 3-4 6-15
G+(1,2,6,15) contains Thirdapex
   via 4 3 2 6 5 13 8 7 11 16 9 10 14 12 18 15 removing 1-17
G+(1,2,7,12) contains Petersen
   via 7 9 14 10 18 11 15 12 13 16 removing 1-6 2-17 3-8 4-5
G+(1,2,8,12) contains Petersen
   via 2 17 6 11 7 14 15 12 18 16 removing 1-5 3-8 4-10 9-13
G+(1,2,8,13) contains Petersen
   via 2 17 6 11 7 14 15 12 18 16 removing 1-5 3-8 4-10 9-13
G+(1,2,9,13) contains Petersen
   via 4 11 7 12 8 9 18 13 16 14 removing 1-17 2-3 5-10 6-15
G+(1,2,9,14) contains Petersen
   via 6 11 7 18 9 15 12 13 16 14 removing 1-17 2-3 4-8 5-10
G+(1,2,10,14) contains Petersen
   via 3 4 9 13 8 18 14 12 11 16 removing 1-17 2-7 5-10 6-15
G+(1,2,10,16) contains Petersen
   via 3 4 9 13 8 18 14 12 11 16 removing 1-17 2-7 5-10 6-15
G+(1,2,11,16) contains Thirdapex
   via 6 15 14 5 1 7 12 9 4 2 11 17 18 13 10 16 removing 3-8
G+(1,2,12,15) contains Petersen
   via 4 5 10 14 9 11 16 13 18 15 removing 1-6 2-17 3-8 7-12
G+(1,2,13,16) contains Petersen
   via 3 8 12 16 10 17 15 14 13 18 removing 1-5 2-7 4-9 6-11
G+(1,2,14,15) contains Petersen
   via 2 4 6 11 7 18 15 12 13 16 removing 1-17 3-8 5-10 9-14
G+(1,5,2,7) contains Petersen
   via 4 5 10 16 6 9 14 15 12 13 removing 1-17 2-18 3-8 7-11
G+(1,5,3,8) contains Petersen
   via 5 17 6 11 7 14 15 12 8 13 removing 1-2 3-18 4-9 10-16
G+(1,5,4,9) contains Petersen
   via 5 8 13 9 17 10 16 11 12 14 removing 1-2 3-7 4-18 6-15
G+(1,5,6,11) contains Thirdapex
   via 4 3 2 18 5 13 8 7 11 16 9 10 14 12 6 15 removing 1-17
G+(1,5,7,11) contains Petersen
   via 4 5 10 15 6 13 16 11 18 12 removing 1-17 2-7 3-8 9-14
G+(1,5,7,12) contains Petersen
   via 7 9 14 10 18 11 15 12 13 16 removing 1-2 3-8 4-5 6-17
G+(1,5,8,12) contains Petersen
   via 5 17 6 11 7 14 15 12 18 13 removing 1-2 3-8 4-9 10-16
G+(1,5,8,13) contains Petersen
   via 4 5 10 14 9 12 16 13 17 15 removing 1-2 3-7 6-11 8-18
G+(1,5,9,13) contains Petersen
   via 5 8 12 14 10 17 11 16 13 18 removing 1-2 3-7 4-9 6-15
G+(1,5,9,14) contains Petersen
   via 5 8 12 14 10 17 11 16 13 18 removing 1-2 3-7 4-9 6-15
G+(1,5,10,14) contains Thirdapex
   via 2 3 4 18 1 12 8 9 14 15 7 6 11 13 10 16 removing 5-17
G+(1,5,11,16) contains Thirdapex
   via 16 18 7 8 13 5 17 2 3 4 10 9 14 1 12 15 removing 6-11
G+(1,5,12,15) contains Petersen
   via 4 5 10 14 9 11 16 13 18 15 removing 1-2 3-8 6-17 7-12
G+(1,5,13,16) contains Petersen
   via 5 8 12 16 10 17 15 14 13 18 removing 1-2 3-7 4-9 6-11
G+(1,5,14,15) contains Thirdapex
   via 2 3 4 17 1 12 8 9 18 15 7 6 11 13 5 16 removing 10-14
G+(1,6,2,3) contains Petersen
   via 4 5 10 16 6 9 14 15 12 13 removing 1-17 2-18 3-8 7-11
G+(1,6,3,4) contains Petersen
   via 4 5 8 13 9 11 12 14 10 16 removing 1-17 2-7 3-18 6-15
G+(1,6,3,8) contains Petersen
   via 5 17 6 11 7 14 15 12 8 13 removing 1-2 3-18 4-9 10-16
G+(1,6,4,5) contains Petersen
   via 5 8 13 9 18 10 16 11 12 14 removing 1-17 2-7 3-4 6-15
G+(1,6,4,9) contains Petersen
   via 5 8 13 9 17 10 16 11 12 14 removing 1-2 3-7 4-18 6-15
G+(1,6,7,12) contains Petersen
   via 7 9 14 10 18 11 15 12 13 16 removing 1-2 3-8 4-5 6-17
G+(1,6,8,12) contains Petersen
   via 5 17 6 11 7 14 15 12 18 13 removing 1-2 3-8 4-9 10-16
G+(1,6,8,13) contains Petersen
   via 4 5 10 14 9 12 16 13 17 15 removing 1-2 3-7 6-11 8-18
G+(1,6,9,13) contains Petersen
   via 5 8 12 14 10 17 11 16 13 18 removing 1-2 3-7 4-9 6-15
G+(1,6,9,14) contains Petersen
   via 5 8 12 14 10 17 11 16 13 18 removing 1-2 3-7 4-9 6-15
G+(1,6,10,14) contains Secondapex
   via 3 2 1 5 4 15 6 17 18 14 8 9 13 11 10 16 removing 7-12
G+(1,6,11,16) contains Boat3
   via 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
G+(1,6,12,15) contains Petersen
   via 4 5 10 14 9 11 16 13 18 15 removing 1-2 3-8 6-17 7-12
G+(1,6,13,16) contains Petersen
   via 5 8 12 16 10 17 15 14 13 18 removing 1-2 3-7 4-9 6-11
G+(1,6,14,15) contains Boat5
   via 1 2 3 4 5 17 7 8 9 10 11 12 13 14 18 16 6 15
G+(2,7,3,4) contains Petersen
   via 3 6 11 7 18 8 16 14 15 12 removing 1-5 2-17 4-10 9-13
G+(2,7,4,5) contains Petersen
   via 4 6 16 13 9 18 10 14 15 12 removing 1-5 2-17 3-8 7-11
G+(2,7,4,9) contains Petersen
   via 4 8 13 9 18 10 16 11 15 14 removing 1-2 3-17 5-6 7-12
G+(2,7,5,10) contains Petersen
   via 5 6 16 13 9 18 10 14 15 12 removing 1-2 3-17 4-8 7-11
G+(2,7,6,15) contains Thirdapex
   via 4 3 17 6 5 13 8 7 11 16 9 10 14 12 18 15 removing 1-2
G+(2,7,8,13) contains Petersen
   via 2 3 16 7 17 15 13 18 8 12 removing 1-5 4-9 6-11 10-14
G+(2,7,9,13) contains Petersen
   via 4 11 7 12 8 9 18 13 16 14 removing 1-2 3-17 5-10 6-15
G+(2,7,9,14) contains Petersen
   via 6 11 7 18 9 15 12 13 16 14 removing 1-2 3-17 4-8 5-10
G+(2,7,10,14) contains Petersen
   via 5 6 11 7 18 8 13 14 15 12 removing 1-2 3-17 4-9 10-16
G+(2,7,10,16) contains Petersen
   via 5 6 15 12 8 10 14 13 16 18 removing 1-2 3-17 4-9 7-11
G+(2,7,11,16) contains Boat4
   via 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
G+(2,7,12,15) contains Boat1
   via 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
G+(2,7,13,16) contains Petersen
   via 2 3 8 12 15 18 13 14 10 16 removing 1-5 4-9 6-11 7-17
G+(2,7,14,15) contains Petersen
   via 4 6 11 7 17 13 16 18 15 12 removing 1-2 3-8 5-10 9-14
G+(2,3,4,9) contains Petersen
   via 4 8 13 9 18 10 16 11 15 14 removing 1-2 3-17 5-6 7-12
G+(2,3,5,10) contains Petersen
   via 5 6 16 13 9 18 10 14 15 12 removing 1-2 3-17 4-8 7-11
G+(2,3,6,11) contains Petersen
   via 4 5 10 14 9 18 16 13 12 15 removing 1-6 2-17 3-8 7-11
G+(2,3,6,15) contains Petersen
   via 4 5 10 14 9 18 16 13 12 15 removing 1-6 2-17 3-8 7-11
G+(2,3,7,11) contains Petersen
   via 7 18 9 14 10 12 13 16 11 15 removing 1-6 2-17 3-8 4-5
G+(2,3,8,13) contains Petersen
   via 1 5 4 9 13 15 12 16 10 14 removing 2-7 3-17 6-11 8-18
G+(2,3,9,13) contains Petersen
   via 4 11 7 12 8 9 18 13 16 14 removing 1-2 3-17 5-10 6-15
G+(2,3,9,14) contains Petersen
   via 6 11 7 18 9 15 12 13 16 14 removing 1-2 3-17 4-8 5-10
G+(2,3,10,14) contains Petersen
   via 5 6 11 7 18 8 13 14 15 12 removing 1-2 3-17 4-9 10-16
G+(2,3,10,16) contains Petersen
   via 5 6 15 12 8 10 14 13 16 18 removing 1-2 3-17 4-9 7-11
G+(2,3,11,16) contains Petersen
   via 4 5 10 14 9 18 16 13 12 15 removing 1-6 2-17 3-8 7-11
G+(2,3,12,15) contains Firstapex
   via 1 2 17 3 4 5 11 7 12 8 13 16 6 18 9 15 removing 10-14
G+(2,3,13,16) contains Petersen
   via 3 8 12 16 10 17 15 14 13 18 removing 1-5 2-7 4-9 6-11
G+(2,3,14,15) contains Petersen
   via 4 6 11 7 17 13 16 18 15 12 removing 1-2 3-8 5-10 9-14
G+(3,4,5,10) contains Petersen
   via 5 18 8 13 9 11 12 14 10 16 removing 1-2 3-7 4-17 6-15
G+(3,4,6,11) contains Petersen
   via 4 5 8 13 9 18 15 14 10 16 removing 1-6 2-7 3-17 11-12
G+(3,4,6,15) contains Petersen
   via 4 5 8 13 9 18 15 14 10 16 removing 1-6 2-7 3-17 11-12
G+(3,4,7,11) contains Petersen
   via 3 6 11 16 8 17 18 12 15 14 removing 1-5 2-7 4-10 9-13
G+(3,4,7,12) contains Petersen
   via 3 6 11 16 8 17 18 12 15 14 removing 1-5 2-7 4-10 9-13
G+(3,4,8,12) contains Petersen
   via 1 5 4 9 13 15 12 16 10 14 removing 2-7 3-17 6-11 8-18
G+(3,4,9,14) contains Petersen
   via 6 11 7 18 9 15 12 13 16 14 removing 1-2 3-8 4-17 5-10
G+(3,4,10,14) contains Petersen
   via 4 17 8 13 9 11 12 14 18 16 removing 1-2 3-7 5-10 6-15
G+(3,4,10,16) contains Petersen
   via 4 17 8 13 9 11 12 14 18 16 removing 1-2 3-7 5-10 6-15
G+(3,4,11,16) contains Petersen
   via 4 5 8 13 9 18 12 14 10 16 removing 1-6 2-7 3-17 11-15
G+(3,4,12,15) contains Petersen
   via 3 6 11 12 8 17 16 13 15 18 removing 1-5 2-7 4-9 10-14
G+(3,4,13,16) contains Firstapex
   via 2 1 5 4 17 3 12 15 14 9 13 8 7 10 18 16 removing 6-11
G+(3,4,14,15) contains Petersen
   via 4 6 11 7 17 13 16 18 15 12 removing 1-2 3-8 5-10 9-14
G+(3,8,4,5) contains Petersen
   via 4 18 8 13 9 11 15 14 10 16 removing 1-2 3-17 5-6 7-12
G+(3,8,5,10) contains Petersen
   via 5 18 8 13 9 11 12 14 10 16 removing 1-2 3-7 4-17 6-15
G+(3,8,6,11) contains Petersen
   via 4 6 18 11 7 13 8 12 15 16 removing 1-2 3-17 5-10 9-14
G+(3,8,6,15) contains Petersen
   via 4 5 10 16 7 9 14 15 18 13 removing 1-2 3-17 6-11 8-12
G+(3,8,7,11) contains Petersen
   via 7 18 9 14 10 12 13 16 11 15 removing 1-6 2-3 4-5 8-17
G+(3,8,9,14) contains Petersen
   via 6 15 8 13 9 11 17 18 14 16 removing 1-2 3-4 5-10 7-12
G+(3,8,10,14) contains Petersen
   via 4 17 8 13 9 11 12 14 18 16 removing 1-2 3-7 5-10 6-15
G+(3,8,10,16) contains Petersen
   via 4 17 8 13 9 11 12 14 18 16 removing 1-2 3-7 5-10 6-15
G+(3,8,11,16) contains Petersen
   via 4 5 10 14 9 18 16 13 12 15 removing 1-6 2-3 7-11 8-17
G+(3,8,12,15) contains Secondapex
   via 5 1 2 3 4 16 11 7 12 13 10 9 14 6 18 15 removing 8-17
G+(3,8,13,16) contains Secondapex
   via 1 5 4 3 2 15 14 9 13 12 6 7 11 10 18 16 removing 8-17
G+(3,8,14,15) contains Petersen
   via 3 4 13 16 7 17 8 12 15 18 removing 1-2 5-10 6-11 9-14
G+(4,5,6,11) contains Petersen
   via 5 8 13 9 17 10 16 18 15 14 removing 1-6 2-7 3-4 11-12
G+(4,5,6,15) contains Petersen
   via 5 8 13 9 17 10 16 18 15 14 removing 1-6 2-7 3-4 11-12
G+(4,5,7,11) contains Petersen
   via 4 6 15 10 17 13 12 18 11 16 removing 1-5 2-7 3-8 9-14
G+(4,5,7,12) contains Petersen
   via 7 9 14 10 18 11 15 12 13 16 removing 1-2 3-8 4-17 5-6
G+(4,5,8,12) contains Petersen
   via 4 9 14 10 17 11 15 18 13 16 removing 1-2 3-8 5-6 7-12
G+(4,5,8,13) contains Petersen
   via 4 9 14 10 17 11 15 18 13 16 removing 1-2 3-8 5-6 7-12
G+(4,5,9,13) contains Petersen
   via 6 11 7 9 18 15 12 13 16 14 removing 1-2 3-8 4-17 5-10
G+(4,5,10,16) contains Thirdapex
   via 2 3 4 10 1 12 8 9 14 15 7 6 11 13 18 16 removing 5-17
G+(4,5,11,16) contains Petersen
   via 5 8 13 9 17 10 16 18 12 14 removing 1-6 2-7 3-4 11-15
G+(4,5,12,15) contains Petersen
   via 4 9 14 10 17 11 15 18 13 16 removing 1-2 3-8 5-6 7-12
G+(4,5,13,16) contains Petersen
   via 4 7 12 13 9 17 15 14 16 18 removing 1-2 3-8 5-10 6-11
G+(4,5,14,15) contains Thirdapex
   via 10 16 11 1 5 9 13 7 2 4 14 17 18 12 6 15 removing 3-8
G+(4,9,6,11) contains Petersen
   via 5 8 13 9 18 10 16 11 12 14 removing 1-2 3-7 4-17 6-15
G+(4,9,6,15) contains Petersen
   via 5 6 11 12 8 10 16 13 18 15 removing 1-2 3-7 4-17 9-14
G+(4,9,7,11) contains Petersen
   via 4 8 13 9 17 10 16 18 12 14 removing 1-2 3-7 5-6 11-15
G+(4,9,7,12) contains Petersen
   via 4 8 13 9 17 10 16 18 12 14 removing 1-2 3-7 5-6 11-15
G+(4,9,8,12) contains Petersen
   via 3 4 17 9 13 15 12 16 10 14 removing 1-5 2-7 6-11 8-18
G+(4,9,10,16) contains Thirdapex
   via 2 3 17 10 1 12 8 9 14 15 7 6 11 13 18 16 removing 4-5
G+(4,9,11,16) contains Petersen
   via 4 8 13 9 17 10 16 18 12 14 removing 1-2 3-7 5-6 11-15
G+(4,9,12,15) contains Petersen
   via 3 4 17 9 13 15 18 16 10 14 removing 1-5 2-7 6-11 8-12
G+(4,9,13,16) contains Boat1
   via 5 4 3 2 1 10 9 8 7 6 14 13 12 11 16 15 17 18
G+(4,9,14,15) contains Boat4
   via 5 4 3 2 1 10 9 8 7 6 14 13 12 11 16 15 17 18
G+(5,10,6,11) contains Secondapex
   via 2 1 5 4 3 11 18 17 10 16 7 8 12 6 14 15 removing 9-13
G+(5,10,7,11) contains Petersen
   via 5 6 15 10 17 13 12 18 11 16 removing 1-2 3-7 4-8 9-14
G+(5,10,7,12) contains Petersen
   via 5 6 15 10 17 13 12 18 11 16 removing 1-2 3-7 4-8 9-14
G+(5,10,8,12) contains Petersen
   via 5 9 14 10 17 11 12 18 13 16 removing 1-2 3-7 4-8 6-15
G+(5,10,8,13) contains Petersen
   via 5 9 14 10 17 11 12 18 13 16 removing 1-2 3-7 4-8 6-15
G+(5,10,9,13) contains Petersen
   via 6 11 9 18 17 15 14 10 16 13 removing 1-2 3-8 4-5 7-12
G+(5,10,11,16) contains Boat5
   via 5 4 3 2 1 17 9 8 7 6 14 13 12 11 18 15 10 16
G+(5,10,12,15) contains Petersen
   via 5 6 16 13 9 17 10 14 15 18 removing 1-2 3-7 4-8 11-12
G+(5,10,13,16) contains Petersen
   via 4 5 15 12 7 9 14 16 18 13 removing 1-2 3-8 6-11 10-17
G+(5,10,14,15) contains Boat3
   via 5 4 3 2 1 10 9 8 7 6 14 13 12 11 16 15 17 18
G+(6,11,7,12) contains Boat4
   via 1 2 3 4 5 6 18 8 9 10 17 12 13 14 15 16 7 11
G+(6,11,8,12) contains Petersen
   via 4 6 17 11 7 13 18 12 15 16 removing 1-2 3-8 5-10 9-14
G+(6,11,8,13) contains Petersen
   via 5 6 17 18 8 16 11 12 15 13 removing 1-2 3-7 4-9 10-14
G+(6,11,9,13) contains Petersen
   via 5 8 12 14 10 17 11 16 13 18 removing 1-2 3-7 4-9 6-15
G+(6,11,9,14) contains Petersen
   via 5 6 15 13 9 10 14 18 17 16 removing 1-2 3-7 4-8 11-12
G+(6,11,10,14) contains Petersen
   via 4 5 16 11 7 9 13 12 15 14 removing 1-2 3-8 6-17 10-18
G+(6,11,10,16) contains Boat6
   via 2 3 4 5 1 7 8 9 10 6 12 13 14 17 11 15 18 16
G+(6,11,12,15) contains Boat5
   via 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
G+(6,11,13,16) contains Petersen
   via 5 6 15 12 8 10 14 13 18 16 removing 1-2 3-7 4-9 11-17
G+(6,11,14,15) contains Petersen
   via 4 5 10 14 9 11 16 13 15 18 removing 1-2 3-8 6-17 7-12
G+(6,15,7,11) contains Boat3
   via 1 2 3 4 5 17 7 8 9 10 18 12 13 14 15 16 6 11
G+(6,15,7,12) contains Boat2
   via 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 17
G+(6,15,8,12) contains Petersen
   via 4 5 10 16 7 9 14 15 17 13 removing 1-2 3-8 6-11 12-18
G+(6,15,8,13) contains Petersen
   via 5 6 11 12 8 14 13 18 17 15 removing 1-2 3-7 4-9 10-16
G+(6,15,9,13) contains Petersen
   via 5 6 11 12 8 10 16 13 17 15 removing 1-2 3-7 4-9 14-18
G+(6,15,9,14) contains Petersen
   via 5 6 11 12 8 10 16 13 17 15 removing 1-2 3-7 4-9 14-18
G+(6,15,10,14) contains Boat6
   via 1 2 3 4 5 6 7 8 9 10 11 12 13 18 17 16 14 15
G+(6,15,12,15) contains Boat7
   via 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
G+(6,15,13,16) contains Petersen
   via 6 9 13 12 11 17 18 16 14 15 removing 1-2 3-7 4-8 5-10
G+(6,15,14,15) contains Boat7
   via 1 2 3 4 5 6 7 8 9 10 11 12 13 14 18 16 17 15
G+(7,11,8,12) contains Boat1
   via 1 2 3 4 5 6 17 8 9 10 11 18 13 14 15 16 7 12
G+(7,11,8,13) contains Secondapex
   via 5 1 2 3 4 16 11 17 18 13 10 9 14 6 8 15 removing 7-12
G+(7,11,9,13) contains Petersen
   via 4 8 12 14 9 11 17 18 13 16 removing 1-2 3-7 5-10 6-15
G+(7,11,9,14) contains Petersen
   via 6 9 13 16 11 15 12 17 18 14 removing 1-2 3-7 4-8 5-10
G+(7,11,10,14) contains Petersen
   via 5 6 11 13 8 18 17 12 15 14 removing 1-2 3-7 4-9 10-16
G+(7,11,10,16) contains Petersen
   via 5 6 15 12 8 10 14 13 16 18 removing 1-2 3-7 4-9 11-17
G+(7,11,13,16) contains Boat6
   via 2 3 4 5 1 7 8 9 10 6 12 13 14 11 17 15 16 18
G+(7,11,14,15) contains Petersen
   via 5 6 11 17 7 14 13 12 15 18 removing 1-2 3-8 4-9 10-16
G+(7,12,8,13) contains Secondapex
   via 5 1 2 3 4 16 11 7 17 13 10 9 14 6 12 15 removing 8-18
G+(7,12,9,13) contains Petersen
   via 4 8 12 14 9 11 17 18 13 16 removing 1-2 3-7 5-10 6-15
G+(7,12,9,14) contains Petersen
   via 6 9 13 16 11 15 12 17 18 14 removing 1-2 3-7 4-8 5-10
G+(7,12,10,14) contains Petersen
   via 5 6 11 13 8 18 17 12 15 14 removing 1-2 3-7 4-9 10-16
G+(7,12,10,16) contains Petersen
   via 5 6 15 12 8 10 14 13 16 18 removing 1-2 3-7 4-9 11-17
G+(7,12,13,16) contains Secondapex
   via 5 1 2 3 4 16 11 7 17 18 10 9 14 6 12 15 removing 8-13
G+(7,12,14,15) contains Petersen
   via 4 5 10 16 7 9 14 18 15 13 removing 1-2 3-8 6-11 12-17
G+(8,12,9,13) contains Secondapex
   via 1 5 4 3 2 15 14 9 18 12 6 7 11 10 13 16 removing 8-17
G+(8,12,9,14) contains Secondapex
   via 3 2 1 5 4 17 12 15 14 18 8 9 13 7 10 16 removing 6-11
G+(8,12,10,14) contains Petersen
   via 5 8 17 18 10 15 12 16 13 14 removing 1-2 3-7 4-9 6-11
G+(8,12,10,16) contains Petersen
   via 5 8 17 18 10 11 12 14 13 16 removing 1-2 3-7 4-9 6-15
G+(8,12,11,16) contains Thirdapex
   via 16 18 11 1 5 8 17 7 2 3 13 4 9 12 6 15 removing 10-14
G+(8,12,14,15) contains Boat2
   via 1 2 3 4 5 6 7 8 9 10 11 17 13 14 18 16 12 15
G+(8,13,9,14) contains Boat1
   via 5 4 3 2 1 10 18 8 7 6 14 17 12 11 16 15 9 13
G+(8,13,10,14) contains Petersen
   via 4 8 12 14 9 10 16 13 17 18 removing 1-2 3-7 5-6 11-15
G+(8,13,10,16) contains Petersen
   via 4 5 10 18 8 9 14 12 11 16 removing 1-2 3-7 6-15 13-17
G+(8,13,11,16) contains Boat2
   via 5 4 3 2 1 10 9 8 7 6 14 17 12 11 18 15 13 16
G+(8,13,14,15) contains Thirdapex
   via 15 18 14 5 1 8 17 9 4 3 12 2 7 13 10 16 removing 6-11
G+(9,13,10,14) contains Boat4
   via 5 4 3 2 1 10 17 8 7 6 18 13 12 11 16 15 9 14
G+(9,13,10,16) contains Boat2
   via 5 4 3 2 1 10 9 8 7 6 14 13 12 11 16 15 17 18
G+(9,13,11,16) contains Petersen
   via 4 5 10 16 8 9 14 12 11 18 removing 1-2 3-7 6-15 13-17
G+(9,13,12,15) contains Secondapex
   via 1 5 4 3 2 15 14 9 17 18 6 7 11 10 13 16 removing 8-12
G+(9,14,10,16) contains Boat3
   via 5 4 3 2 1 18 9 8 7 6 17 13 12 11 16 15 10 14
G+(9,14,11,16) contains Petersen
   via 5 9 13 16 10 11 12 14 17 18 removing 1-2 3-7 4-8 6-15
G+(9,14,12,15) contains Boat6
   via 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
G+(10,14,11,16) contains Petersen
   via 4 5 15 12 7 9 14 18 16 13 removing 1-2 3-8 6-11 10-17
G+(10,14,12,15) contains Petersen
   via 5 6 11 12 8 10 16 13 15 18 removing 1-2 3-7 4-9 14-17
G+(10,14,13,16) contains Boat5
   via 5 4 3 2 1 10 9 8 7 6 14 13 12 11 16 15 17 18
G+(10,16,11,16) contains Boat7
   via 5 4 3 2 1 10 9 8 7 6 14 13 12 11 18 15 17 16
G+(10,16,12,15) contains Petersen
   via 5 6 11 12 8 17 16 13 15 18 removing 1-2 3-7 4-9 10-14
G+(10,16,13,16) contains Boat7
   via 5 4 3 2 1 10 9 8 7 6 14 13 12 11 16 15 17 18
G+(11,16,13,16) contains Boat7
   via 5 4 3 2 1 10 9 8 7 6 14 13 12 11 17 15 16 18
G+(11,16,14,15) contains Petersen
   via 6 11 9 14 10 15 13 16 17 18 removing 1-2 3-8 4-5 7-12
G+(12,15,14,15) contains Boat7
   via 1 2 3 4 5 6 7 8 9 10 11 12 13 14 18 16 15 17


##############################################################
# Proof of (14.6), claim (1)
G=Boat1
# A-expansions:
G+(7,12,1,2) contains Petersen
   via 2 17 7 16 8 20 19 12 18 15 removing 1-5 3-4 6-11 9-10 13-14
G+(7,12,1,5) contains Petersen
   via 7 17 9 13 11 19 14 15 18 12 removing 1-2 3-8 4-5 6-20 10-16
G+(7,12,1,6) contains Petersen
   via 7 17 9 13 11 19 14 15 18 12 removing 1-2 3-8 4-5 6-20 10-16
G+(7,12,2,3) contains Petersen
   via 7 17 10 16 11 19 14 15 18 12 removing 1-6 2-20 3-8 4-5 9-13
G+(7,12,3,4) contains Petersen
   via 3 17 7 16 8 20 19 12 18 14 removing 1-2 4-5 6-10 9-13 11-15
G+(7,12,4,5) contains Petersen
   via 7 17 9 13 11 19 14 15 18 12 removing 1-2 3-8 4-20 5-6 10-16
G+(7,12,4,9) contains Petersen
   via 4 8 13 9 20 10 16 19 12 14 removing 1-2 3-17 5-6 7-18 11-15
G+(7,12,5,10) contains Petersen
   via 5 9 14 10 20 11 18 12 13 16 removing 1-2 3-17 4-8 6-15 7-19
G+(7,12,6,15) contains Petersen
   via 4 17 7 16 13 20 19 12 18 15 removing 1-2 3-8 5-10 6-11 9-14
G+(7,12,9,13) contains Petersen
   via 4 8 12 14 9 11 19 20 13 16 removing 1-2 3-17 5-10 6-15 7-18
G+(7,12,9,14) contains Petersen
   via 6 9 13 16 11 15 12 19 20 14 removing 1-2 3-17 4-8 5-10 7-18
G+(7,12,10,14) contains Petersen
   via 5 8 12 20 10 15 18 16 13 14 removing 1-2 3-17 4-9 6-11 7-19
G+(7,12,10,16) contains Petersen
   via 5 8 12 20 10 11 18 14 13 16 removing 1-2 3-17 4-9 6-15 7-19
G+(7,12,13,16) contains Secondapex
   via 2 1 5 4 3 7 11 16 20 19 17 12 18 6 9 15 removing 8-13 10-14
G+(7,12,14,15) contains Petersen
   via 7 11 16 12 19 17 14 20 15 18 removing 1-2 3-8 4-5 6-10 9-13
G+(12,18,1,2) contains Petersen
   via 2 17 7 12 8 20 11 16 18 19 removing 1-5 3-4 6-15 9-10 13-14
G+(12,18,1,5) contains Petersen
   via 5 20 6 11 17 14 15 18 19 13 removing 1-2 3-8 4-9 7-12 10-16
G+(12,18,1,6) contains Petersen
   via 5 20 6 11 17 14 15 18 19 13 removing 1-2 3-8 4-9 7-12 10-16
G+(12,18,2,3) contains Firstapex
   via 1 2 20 3 4 5 11 7 12 8 13 16 6 19 9 15 removing 10-14 17-18
G+(12,18,3,4) contains Petersen
   via 3 17 7 12 8 20 16 13 18 19 removing 1-2 4-9 5-6 10-14 11-15
G+(12,18,4,5) contains Petersen
   via 4 9 14 10 20 17 18 19 13 16 removing 1-2 3-8 5-6 7-12 11-15
G+(12,18,4,9) contains Petersen
   via 3 4 20 9 13 18 19 16 10 14 removing 1-2 5-6 7-17 8-12 11-15
G+(12,18,5,10) contains Petersen
   via 5 9 14 10 20 11 18 19 13 16 removing 1-2 3-17 4-8 6-15 7-12
G+(12,18,6,11) contains Petersen
   via 4 17 7 11 20 13 12 19 18 16 removing 1-2 3-8 5-10 6-15 9-14
G+(12,18,9,13) contains Petersen
   via 3 4 9 20 13 18 14 16 11 19 removing 1-2 5-10 6-15 7-17 8-12
G+(12,18,9,14) contains Petersen
   via 6 9 13 16 11 15 18 19 20 14 removing 1-2 3-4 5-10 7-17 8-12
G+(12,18,10,14) contains Petersen
   via 5 8 13 16 10 15 14 20 19 18 removing 1-2 3-17 4-9 6-11 7-12
G+(12,18,10,16) contains Petersen
   via 5 8 13 14 10 11 16 20 19 18 removing 1-2 3-17 4-9 6-15 7-12
G+(12,18,11,16) contains Petersen
   via 7 11 15 13 12 17 18 19 20 16 removing 1-2 3-8 4-9 5-6 10-14
G+(12,18,13,16) contains Petersen
   via 7 17 10 16 11 13 14 15 18 20 removing 1-2 3-8 4-9 5-6 12-19
G+(18,17,1,5) contains Petersen
   via 9 14 10 19 17 13 16 11 15 18 removing 1-2 3-8 4-5 6-20 7-12
G+(18,17,1,6) contains Petersen
   via 9 14 10 19 17 13 16 11 15 18 removing 1-2 3-8 4-5 6-20 7-12
G+(18,17,3,4) contains Petersen
   via 3 6 11 16 8 20 19 18 15 14 removing 1-5 2-17 4-10 7-12 9-13
G+(18,17,3,8) contains Firstapex
   via 1 5 4 20 19 17 11 16 13 8 12 7 6 9 18 15 removing 2-3 10-14
G+(18,17,4,5) contains Petersen
   via 9 14 10 19 17 13 16 11 15 18 removing 1-2 3-8 4-20 5-6 7-12
G+(18,17,4,9) contains Petersen
   via 4 8 13 9 20 10 16 19 18 14 removing 1-2 3-17 5-6 7-12 11-15
G+(18,17,5,10) contains Petersen
   via 5 6 16 13 9 20 10 14 15 18 removing 1-2 3-17 4-8 7-19 11-12
G+(18,17,6,11) contains Thirdapex
   via 18 15 14 13 12 20 6 10 16 11 19 7 17 5 9 4 removing 1-2 3-8
G+(18,17,8,13) contains Petersen
   via 3 17 7 12 8 14 16 20 19 18 removing 1-2 4-5 6-10 9-13 11-15
G+(18,17,9,13) contains Petersen
   via 4 8 13 20 9 11 16 14 18 19 removing 1-2 3-17 5-10 6-15 7-12
G+(18,17,9,14) contains Petersen
   via 6 9 13 16 11 15 18 19 20 14 removing 1-2 3-17 4-8 5-10 7-12
G+(18,17,10,14) contains Petersen
   via 5 6 11 12 8 10 16 13 15 18 removing 1-2 3-17 4-9 7-19 14-20
G+(18,17,10,16) contains Petersen
   via 5 6 11 12 8 20 16 13 15 18 removing 1-2 3-17 4-9 7-19 10-14
G+(18,17,11,16) contains Petersen
   via 7 11 15 18 12 17 14 16 20 19 removing 1-2 3-8 4-5 6-10 9-13
G+(18,17,13,16) contains Petersen
   via 7 17 9 13 12 16 14 18 19 20 removing 1-2 3-8 4-5 6-10 11-15
G+(17,7,1,5) contains Petersen
   via 4 5 10 16 6 9 14 15 18 13 removing 1-20 2-17 3-8 7-19 11-12
G+(17,7,1,6) contains Firstapex
   via 4 3 17 19 20 5 13 8 12 7 11 16 9 18 6 15 removing 1-2 10-14
G+(17,7,3,4) contains Petersen
   via 3 6 11 16 8 20 19 18 15 14 removing 1-5 2-17 4-10 7-12 9-13
G+(17,7,3,8) contains Petersen
   via 9 14 10 17 19 13 16 11 15 18 removing 1-6 2-3 4-5 7-12 8-20
G+(17,7,4,5) contains Petersen
   via 4 6 16 13 9 20 10 14 15 18 removing 1-5 2-17 3-8 7-19 11-12
G+(17,7,4,9) contains Petersen
   via 4 8 13 9 20 10 16 19 18 14 removing 1-2 3-17 5-6 7-12 11-15
G+(17,7,5,10) contains Petersen
   via 5 6 16 13 9 20 10 14 15 18 removing 1-2 3-17 4-8 7-19 11-12
G+(17,7,6,15) contains Thirdapex
   via 4 3 19 6 5 13 8 7 11 16 9 10 14 12 20 15 removing 1-2 17-18
G+(17,7,8,13) contains Petersen
   via 3 16 7 12 8 17 19 20 13 18 removing 1-2 4-9 5-6 10-14 11-15
G+(17,7,9,13) contains Petersen
   via 4 8 13 20 9 11 16 14 18 19 removing 1-2 3-17 5-10 6-15 7-12
G+(17,7,9,14) contains Petersen
   via 6 9 13 16 11 15 18 19 20 14 removing 1-2 3-17 4-8 5-10 7-12
G+(17,7,10,14) contains Petersen
   via 5 6 11 12 8 10 16 13 15 18 removing 1-2 3-17 4-9 7-19 14-20
G+(17,7,10,16) contains Petersen
   via 5 6 11 12 8 20 16 13 15 18 removing 1-2 3-17 4-9 7-19 10-14
G+(17,7,13,16) contains Petersen
   via 4 9 13 12 11 17 20 16 14 18 removing 1-2 3-8 5-10 6-15 7-19
G+(17,7,14,15) contains Petersen
   via 7 11 16 13 12 19 17 18 15 20 removing 1-2 3-8 4-9 5-6 10-14
# Jumps creating quadrangles:
G+(7,12,11,6) contains Petersen
   via 4 6 20 11 17 13 12 18 15 16 removing 1-2 3-8 5-10 7-19 9-14
G+(7,12,11,16) contains Thirdapex
   via 16 20 11 1 5 8 12 17 2 3 13 4 9 18 6 15 removing 7-19 10-14
G+(12,18,8,3) contains Secondapex
   via 2 1 5 4 3 7 11 16 13 12 17 19 18 6 9 15 removing 8-20 10-14
G+(12,18,8,13) contains Petersen
   via 7 17 10 16 11 12 14 15 18 19 removing 1-6 2-3 4-5 8-20 9-13
G+(18,17,15,6) contains Thirdapex
   via 4 3 17 6 5 13 8 7 11 16 9 10 14 12 19 18 removing 1-2 15-20
G+(18,17,15,14) contains Petersen
   via 4 6 11 7 17 13 16 19 18 12 removing 1-2 3-8 5-10 9-14 15-20
G+(17,7,2,1) contains Firstapex
   via 1 5 4 3 17 19 11 16 13 8 12 7 6 9 18 15 removing 2-20 10-14
G+(17,7,2,3) contains Petersen
   via 9 14 10 17 19 13 16 11 15 18 removing 1-6 2-20 3-8 4-5 7-12

##############################################################
# Proof of (14.6), claim (2)
G=Boat2
# A-expansions:
G+(12,15,1,2) contains Petersen
   via 2 4 13 16 7 19 12 17 18 15 removing 1-20 3-8 5-10 6-11 9-14
G+(12,15,1,5) contains Petersen
   via 5 20 6 18 17 14 13 12 19 15 removing 1-2 3-8 4-9 7-11 10-16
G+(12,15,1,6) contains Petersen
   via 5 20 6 18 17 14 13 12 19 15 removing 1-2 3-8 4-9 7-11 10-16
G+(12,15,2,7) contains Petersen
   via 4 20 7 16 13 18 17 12 19 15 removing 1-2 3-8 5-10 6-11 9-14
G+(12,15,2,3) contains Petersen
   via 4 20 7 16 13 18 17 12 19 15 removing 1-2 3-8 5-10 6-11 9-14
G+(12,15,3,4) contains Petersen
   via 4 20 7 16 13 18 17 12 19 15 removing 1-2 3-8 5-10 6-11 9-14
G+(12,15,4,5) contains Petersen
   via 4 9 13 12 17 20 16 18 15 19 removing 1-2 3-8 5-6 7-11 10-14
G+(12,15,4,9) contains Petersen
   via 3 4 20 9 13 18 17 16 10 14 removing 1-5 2-7 6-11 8-12 15-19
G+(12,15,5,10) contains Petersen
   via 5 9 14 10 20 18 15 19 13 16 removing 1-2 3-7 4-8 6-11 12-17
G+(12,15,6,11) contains Petersen
   via 6 20 11 16 13 18 17 12 19 15 removing 1-2 3-7 4-8 5-10 9-14
G+(12,15,7,11) contains Petersen
   via 7 20 11 18 17 14 16 12 19 15 removing 1-2 3-8 4-5 6-10 9-13
G+(12,15,9,13) contains Secondapex
   via 3 2 1 5 4 12 17 18 15 19 8 20 13 7 10 16 removing 6-11 9-14
G+(12,15,10,16) contains Petersen
   via 5 8 12 17 18 20 19 15 13 16 removing 1-2 3-7 4-9 6-11 10-14
G+(12,15,11,16) contains Petersen
   via 7 9 13 12 17 20 16 18 15 19 removing 1-2 3-8 4-5 6-11 10-14
G+(12,15,13,16) contains Secondapex
   via 4 3 8 13 9 18 17 12 19 15 5 14 10 7 20 16 removing 1-2 6-11
G+(15,18,1,2) contains Petersen
   via 2 7 17 12 8 19 18 13 16 15 removing 1-20 3-4 5-10 6-11 9-14
G+(15,18,1,5) contains Thirdapex
   via 2 4 9 12 17 20 5 14 15 19 1 18 6 10 13 16 removing 3-8 7-11
G+(15,18,2,7) contains Petersen
   via 7 20 8 12 17 16 13 18 19 15 removing 1-2 3-4 5-10 6-11 9-14
G+(15,18,2,3) contains Petersen
   via 7 20 8 12 17 16 13 18 19 15 removing 1-2 3-4 5-10 6-11 9-14
G+(15,18,3,4) contains Petersen
   via 4 6 11 7 20 13 16 19 18 17 removing 1-2 3-8 5-10 9-14 12-15
G+(15,18,3,8) contains Petersen
   via 7 20 8 12 17 16 13 18 19 15 removing 1-2 3-4 5-10 6-11 9-14
G+(15,18,4,5) contains Petersen
   via 5 8 13 9 20 10 16 19 15 14 removing 1-6 2-7 3-4 11-18 12-17
G+(15,18,4,9) contains Petersen
   via 5 8 12 15 10 18 17 16 13 19 removing 1-2 3-7 4-20 6-11 9-14
G+(15,18,5,10) contains Secondapex
   via 3 2 1 5 4 12 17 18 19 15 8 9 13 7 20 16 removing 6-11 10-14
G+(15,18,7,11) contains Petersen
   via 7 14 10 18 17 20 16 12 15 19 removing 1-2 3-8 4-5 6-11 9-13
G+(15,18,8,13) contains Petersen
   via 5 8 12 15 14 18 17 13 20 19 removing 1-2 3-7 4-9 6-11 10-16
G+(15,18,9,13) contains Petersen
   via 5 8 12 15 10 18 17 16 13 19 removing 1-2 3-7 4-9 6-11 14-20
G+(15,18,10,16) contains Secondapex
   via 4 9 14 10 5 17 12 15 19 18 7 6 11 13 20 16 removing 1-2 3-8
G+(15,18,11,16) contains Petersen
   via 7 14 10 18 17 20 16 12 15 19 removing 1-2 3-8 4-5 6-11 9-13
G+(15,18,13,16) contains Petersen
   via 9 13 12 15 14 18 17 16 20 19 removing 1-2 3-7 4-8 5-10 6-11
G+(18,17,1,2) contains Petersen
   via 7 14 10 16 11 17 19 18 15 12 removing 1-6 2-20 3-8 4-5 9-13
G+(18,17,1,5) contains Petersen
   via 7 14 10 16 11 17 19 18 15 12 removing 1-2 3-8 4-5 6-20 9-13
G+(18,17,2,3) contains Petersen
   via 9 14 10 16 13 19 17 12 15 18 removing 1-6 2-20 3-8 4-5 7-11
G+(18,17,3,4) contains Petersen
   via 6 8 12 17 11 18 15 16 13 19 removing 1-5 2-7 3-20 4-10 9-14
G+(18,17,3,8) contains Petersen
   via 4 5 10 16 7 9 14 17 19 13 removing 1-2 3-20 6-11 8-12 15-18
G+(18,17,4,5) contains Petersen
   via 7 14 10 16 11 17 19 18 15 12 removing 1-2 3-8 4-20 5-6 9-13
G+(18,17,4,9) contains Petersen
   via 6 8 12 17 11 18 15 16 13 19 removing 1-2 3-7 4-20 5-10 9-14
G+(18,17,5,10) contains Petersen
   via 5 6 11 10 20 12 17 19 18 15 removing 1-2 3-7 4-8 9-14 13-16
G+(18,17,8,13) contains Petersen
   via 6 8 12 17 11 18 15 16 20 19 removing 1-2 3-7 4-9 5-10 13-14
G+(18,17,9,13) contains Petersen
   via 6 8 12 17 11 18 15 14 20 19 removing 1-2 3-7 4-9 5-10 13-16
G+(18,17,9,14) contains Petersen
   via 6 9 12 17 11 18 15 14 20 19 removing 1-2 3-7 4-8 5-10 13-16
G+(18,17,10,14) contains Petersen
   via 5 6 11 17 12 20 14 15 18 19 removing 1-2 3-7 4-9 8-13 10-16
G+(18,17,10,16) contains Petersen
   via 5 6 11 17 12 20 16 15 18 19 removing 1-2 3-7 4-9 8-13 10-14
G+(18,17,11,16) contains Thirdapex
   via 7 4 9 12 17 6 5 14 15 18 11 19 20 10 13 16 removing 1-2 3-8
G+(18,17,13,16) contains Petersen
   via 6 11 17 12 13 18 19 20 16 15 removing 1-2 3-7 4-8 5-10 9-14
G+(17,12,1,2) contains Petersen
   via 2 20 6 11 7 14 18 17 19 16 removing 1-5 3-8 4-10 9-13 12-15
G+(17,12,1,5) contains Petersen
   via 9 14 10 16 13 17 19 12 15 18 removing 1-2 3-8 4-5 6-20 7-11
G+(17,12,1,6) contains Petersen
   via 9 14 10 16 13 17 19 12 15 18 removing 1-2 3-8 4-5 6-20 7-11
G+(17,12,2,3) contains Thirdapex
   via 18 15 14 5 1 19 12 9 4 20 17 2 7 13 10 16 removing 3-8 6-11
G+(17,12,3,4) contains Petersen
   via 3 8 12 19 20 18 15 14 16 17 removing 1-5 2-7 4-10 6-11 9-13
G+(17,12,4,5) contains Petersen
   via 9 14 10 16 13 17 19 12 15 18 removing 1-2 3-8 4-20 5-6 7-11
G+(17,12,4,9) contains Petersen
   via 4 8 13 9 20 10 16 17 15 14 removing 1-2 3-7 5-6 11-18 12-19
G+(17,12,5,10) contains Petersen
   via 5 20 10 16 13 18 15 12 19 17 removing 1-2 3-7 4-8 6-11 9-14
G+(17,12,6,11) contains Petersen
   via 6 8 7 11 20 18 17 19 12 15 removing 1-2 3-4 5-10 9-14 13-16
G+(17,12,9,13) contains Petersen
   via 4 8 12 19 9 18 15 14 16 17 removing 1-2 3-7 5-10 6-11 13-20
G+(17,12,9,14) contains Petersen
   via 9 13 12 19 20 18 15 14 16 17 removing 1-2 3-7 4-8 5-10 6-11
G+(17,12,10,14) contains Petersen
   via 5 8 12 19 20 18 15 14 13 17 removing 1-2 3-7 4-9 6-11 10-16
G+(17,12,10,16) contains Petersen
   via 5 8 12 19 10 18 15 14 13 17 removing 1-2 3-7 4-9 6-11 16-20
G+(17,12,11,16) contains Thirdapex
   via 4 3 17 6 5 13 8 19 20 16 9 10 14 12 18 15 removing 1-2 7-11
G+(17,12,13,16) contains Petersen
   via 7 8 12 15 16 17 19 20 13 18 removing 1-2 3-4 5-10 6-11 9-14
G+(12,15,8,3) contains Petersen
   via 3 4 13 16 7 19 12 17 18 15 removing 1-2 5-10 6-11 8-20 9-14
G+(12,15,8,13) contains Thirdapex
   via 18 15 14 5 1 12 19 9 4 3 17 2 7 13 10 16 removing 6-11 8-20
G+(15,18,14,9) contains Petersen
   via 5 8 12 15 10 18 17 16 13 19 removing 1-2 3-7 4-9 6-11 14-20
G+(15,18,14,10) contains Secondapex
   via 3 2 1 5 4 12 17 18 19 15 8 9 13 7 10 16 removing 6-11 14-20
G+(18,17,6,1) contains Petersen
   via 7 14 10 16 11 17 19 18 15 12 removing 1-2 3-8 4-5 6-20 9-13
# B-expansions via (18,17,6,11)
G+(18,17,6,11)+(6,20,2,7) contains Thirdapex
   via 22 4 9 12 17 6 5 14 15 18 21 19 20 10 13 16 removing 1-2 3-8 7-11
G+(18,17,6,11)+(6,20,2,3) contains Petersen
   via 6 7 11 20 21 18 15 12 17 19 removing 1-5 2-22 3-4 8-13 9-10
G+(18,17,6,11)+(6,20,3,4) contains Petersen
   via 6 7 11 20 21 18 15 12 17 19 removing 1-5 2-3 4-22 8-13 9-10
G+(18,17,6,11)+(6,20,3,8) contains Petersen
   via 6 7 11 20 21 18 15 12 17 19 removing 1-2 3-22 4-9 5-10 8-13
G+(18,17,6,11)+(6,20,4,5) contains Petersen
   via 6 7 11 20 21 18 16 13 17 19 removing 1-5 2-3 4-8 9-14 10-22 12-15
G+(18,17,6,11)+(6,20,4,9) contains Petersen
   via 5 8 9 14 10 18 19 17 12 15 removing 1-2 3-7 4-22 6-21 11-20 13-16
G+(18,17,6,11)+(6,20,5,10) contains Petersen
   via 6 7 11 20 21 18 16 13 17 19 removing 1-5 2-3 4-8 9-14 10-22 12-15
G+(18,17,6,11)+(6,20,7,17) contains Petersen
   via 7 14 10 16 11 22 21 20 19 17 removing 1-2 3-8 4-5 6-18 9-13 12-15
G+(18,17,6,11)+(6,20,8,12) contains Petersen
   via 7 8 22 20 11 17 12 15 18 19 removing 1-2 3-4 5-10 6-21 9-14 13-16
G+(18,17,6,11)+(6,20,8,13) contains Petersen
   via 5 8 12 17 16 18 15 13 22 19 removing 1-2 3-7 4-9 6-21 10-14 11-20
G+(18,17,6,11)+(6,20,9,13) contains Petersen
   via 5 8 12 17 10 18 15 14 22 19 removing 1-2 3-7 4-9 6-21 11-20 13-16
G+(18,17,6,11)+(6,20,9,14) contains Petersen
   via 5 9 13 16 10 18 15 14 22 19 removing 1-2 3-7 4-8 6-21 11-20 12-17
G+(18,17,6,11)+(6,20,10,14) contains Petersen
   via 4 5 16 12 17 14 20 19 18 15 removing 1-2 3-8 6-21 7-11 9-13 10-22
G+(18,17,6,11)+(6,20,10,16) contains Petersen
   via 6 7 11 16 18 21 20 19 17 22 removing 1-5 2-3 4-9 8-13 10-14 12-15
G+(18,17,6,11)+(6,20,12,17) contains Petersen
   via 6 13 16 15 18 21 20 19 17 22 removing 1-2 3-4 5-10 7-11 8-12 9-14
G+(18,17,6,11)+(6,20,12,15) contains Petersen
   via 6 13 12 19 18 21 22 15 16 20 removing 1-2 3-7 4-8 5-10 9-14 11-17
G+(18,17,6,11)+(6,20,13,16) contains Petersen
   via 5 8 12 17 10 18 15 14 13 19 removing 1-2 3-7 4-9 6-21 11-20 16-22
G+(18,17,6,11)+(6,20,14,15) contains Petersen
   via 10 16 12 17 14 18 15 22 20 19 removing 1-2 3-8 4-5 6-21 7-11 9-13
# C-expansions via (18,17,6,11)
G+(18,17,6,11)+(6,18,14,9) contains Petersen
   via 5 8 13 16 10 21 22 14 15 18 removing 1-2 3-7 4-9 6-20 11-19 12-17
G+(18,17,6,11)+(6,18,14,10) contains Secondapex
   via 3 2 1 5 4 15 18 21 22 14 8 9 13 19 10 16 removing 6-20 7-11 12-17
G+(18,17,6,11)+(19,20,7,2) contains Thirdapex
   via 19 18 14 13 17 20 6 10 16 11 21 7 22 5 9 4 removing 1-2 3-8 12-15
# D-expansion via (18,17,6,11)
G+(18,17,6,11)+(18,19,12,8) contains Petersen
   via 4 17 12 22 13 18 15 16 19 21 removing 1-2 3-8 5-10 6-20 7-11 9-14
# E-expansions via (18,17,6,11)
G+(18,17,6,11)+(19,18,15,12)+(15,22,8,3) contains Petersen
   via 3 4 13 22 23 19 16 15 18 21 removing 1-2 5-10 6-20 7-11 8-24 9-14 12-17
G+(18,17,6,11)+(19,18,15,12)+(15,22,8,13) contains Secondapex
   via 2 17 12 8 3 18 21 22 23 15 1 14 10 19 24 16 removing 4-5 6-20 7-11 9-13
# B-expansions via (17,12,7,2)
G+(17,12,7,2)+(7,20,1,5) contains Petersen
   via 4 5 10 16 13 18 15 12 19 17 removing 1-22 2-20 3-8 6-11 7-21 9-14
G+(17,12,7,2)+(7,20,1,6) contains Thirdapex
   via 20 4 9 12 19 22 5 14 15 18 21 17 7 10 13 16 removing 1-2 3-8 6-11
G+(17,12,7,2)+(7,20,3,4) contains Petersen
   via 3 8 12 19 22 18 15 14 16 17 removing 1-5 2-20 4-10 6-11 7-21 9-13
G+(17,12,7,2)+(7,20,3,8) contains Petersen
   via 6 11 7 17 18 20 21 14 16 19 removing 1-5 2-3 4-10 8-22 9-13 12-15
G+(17,12,7,2)+(7,20,4,5) contains Petersen
   via 4 22 10 16 13 18 15 12 19 17 removing 1-5 2-20 3-8 6-11 7-21 9-14
G+(17,12,7,2)+(7,20,4,9) contains Petersen
   via 4 8 13 9 22 10 16 17 15 14 removing 1-2 3-20 5-6 7-21 11-18 12-19
G+(17,12,7,2)+(7,20,5,10) contains Petersen
   via 5 22 10 16 13 18 15 12 19 17 removing 1-2 3-20 4-8 6-11 7-21 9-14
G+(17,12,7,2)+(7,20,6,18) contains Thirdapex
   via 20 4 9 12 19 22 5 14 15 18 21 17 7 10 13 16 removing 1-2 3-8 6-11
G+(17,12,7,2)+(7,20,8,12) contains Thirdapex
   via 12 15 14 13 22 17 18 10 16 7 19 21 20 5 9 4 removing 1-2 3-8 6-11
G+(17,12,7,2)+(7,20,8,13) contains Petersen
   via 6 11 7 17 18 20 21 13 16 19 removing 1-5 2-3 4-9 8-22 10-14 12-15
G+(17,12,7,2)+(7,20,9,13) contains Petersen
   via 4 8 12 19 9 18 15 14 16 17 removing 1-2 3-20 5-10 6-11 7-21 13-22
G+(17,12,7,2)+(7,20,9,14) contains Petersen
   via 9 13 12 19 22 18 15 14 16 17 removing 1-2 3-20 4-8 5-10 6-11 7-21
G+(17,12,7,2)+(7,20,10,14) contains Petersen
   via 5 8 12 19 22 18 15 14 13 17 removing 1-2 3-20 4-9 6-11 7-21 10-16
G+(17,12,7,2)+(7,20,10,16) contains Petersen
   via 5 8 12 19 10 18 15 14 13 17 removing 1-2 3-20 4-9 6-11 7-21 16-22
G+(17,12,7,2)+(7,20,12,15) contains Petersen
   via 11 16 12 19 18 21 22 15 14 20 removing 1-2 3-8 4-5 6-10 7-17 9-13
G+(17,12,7,2)+(7,20,13,16) contains Petersen
   via 6 11 7 17 18 20 21 22 16 19 removing 1-5 2-3 4-9 8-13 10-14 12-15
G+(17,12,7,2)+(7,20,14,15) contains Petersen
   via 9 14 10 16 13 20 18 15 22 21 removing 1-2 3-8 4-5 6-11 7-17 12-19
G+(17,12,7,2)+(7,20,15,18) contains Petersen
   via 7 16 13 18 17 21 20 19 15 22 removing 1-2 3-4 5-10 6-11 8-12 9-14
# C-expansions via (17,12,7,2)
G+(17,12,7,2)+(7,17,6,1) contains Petersen
   via 10 16 11 20 14 17 18 15 12 19 removing 1-2 3-8 4-5 6-22 7-21 9-13
G+(17,12,7,2)+(19,20,8,3) contains Secondapex
   via 2 20 21 22 3 18 17 19 12 15 1 14 10 7 8 16 removing 4-5 6-11 9-13
G+(17,12,7,2)+(19,20,8,13) contains Petersen
   via 3 4 13 22 8 20 16 15 18 21 removing 1-2 5-10 6-11 7-17 9-14 12-19
# D-expansion via (17,12,7,2)
G+(17,12,7,2)+(17,19,15,14) contains Petersen
   via 5 19 12 13 14 18 15 22 21 17 removing 1-2 3-8 4-9 6-11 7-20 10-16
# E-expansions via (17,12,7,2)
G+(17,12,7,2)+(19,17,18,15)+(18,22,14,9) contains Petersen
   via 5 8 13 16 10 23 24 14 15 22 removing 1-2 3-20 4-9 6-11 7-19 12-21 17-18
G+(17,12,7,2)+(19,17,18,15)+(18,22,14,10) contains Secondapex
   via 1 5 4 3 2 23 24 14 15 22 18 21 17 10 8 16 removing 6-11 7-20 9-13 12-19
G+(17,12,7,11) contains Thirdapex
   via 4 3 17 6 5 13 8 19 11 16 9 10 14 12 18 15 removing 1-2 7-20


##############################################################
# Proof of (14.6), claim (3)
G=Boat3
# A-expansions:
G+(6,11,1,2) contains Thirdapex
   via 4 3 19 17 5 13 8 11 18 16 9 10 14 12 6 15 removing 1-20 2-7
G+(6,11,1,5) contains Petersen
   via 6 17 8 13 19 15 12 11 18 16 removing 1-20 2-7 3-4 5-10 9-14
G+(6,11,2,3) contains Petersen
   via 2 17 6 15 7 20 19 11 18 16 removing 1-5 3-4 8-12 9-10 13-14
G+(6,11,3,4) contains Petersen
   via 6 17 8 13 19 15 12 11 18 16 removing 1-5 2-7 3-20 4-10 9-14
G+(6,11,3,8) contains Petersen
   via 4 17 6 15 7 13 19 11 18 16 removing 1-2 3-20 5-10 8-12 9-14
G+(6,11,4,5) contains Petersen
   via 6 17 8 13 19 15 12 11 18 16 removing 1-5 2-7 3-4 9-14 10-20
G+(6,11,4,9) contains Petersen
   via 6 17 8 13 19 15 12 11 18 16 removing 1-2 3-7 4-20 5-10 9-14
G+(6,11,5,10) contains Petersen
   via 5 20 10 16 13 17 15 12 11 18 removing 1-2 3-7 4-8 6-19 9-14
G+(6,11,8,12) contains Petersen
   via 4 17 6 15 7 13 19 11 18 16 removing 1-2 3-8 5-10 9-14 12-20
G+(6,11,8,13) contains Petersen
   via 6 17 8 20 19 15 12 11 18 16 removing 1-2 3-7 4-9 5-10 13-14
G+(6,11,9,13) contains Petersen
   via 6 17 8 20 19 15 12 11 18 14 removing 1-2 3-7 4-9 5-10 13-16
G+(6,11,9,14) contains Petersen
   via 9 20 11 12 13 17 18 16 14 15 removing 1-2 3-7 4-8 5-10 6-19
G+(6,11,10,14) contains Petersen
   via 5 8 12 11 20 17 15 14 13 18 removing 1-2 3-7 4-9 6-19 10-16
G+(6,11,10,16) contains Petersen
   via 5 8 12 20 10 17 15 14 13 16 removing 1-2 3-7 4-9 6-19 11-18
G+(6,11,13,16) contains Petersen
   via 6 19 11 12 15 17 18 16 20 13 removing 1-2 3-7 4-8 5-10 9-14
G+(11,18,1,2) contains Thirdapex
   via 6 15 14 5 1 7 12 9 4 2 11 20 19 13 10 16 removing 3-8 17-18
G+(11,18,1,5) contains Petersen
   via 4 5 10 16 13 17 15 12 19 18 removing 1-20 2-7 3-8 6-11 9-14
G+(11,18,2,3) contains Petersen
   via 2 17 6 11 7 20 14 16 18 19 removing 1-5 3-8 4-10 9-13 12-15
G+(11,18,3,4) contains Petersen
   via 3 8 12 19 20 17 15 14 16 18 removing 1-5 2-7 4-10 6-11 9-13
G+(11,18,3,8) contains Petersen
   via 2 3 20 8 12 18 19 15 14 16 removing 1-5 4-10 6-17 7-11 9-13
G+(11,18,4,5) contains Petersen
   via 4 20 10 16 13 17 15 12 19 18 removing 1-5 2-7 3-8 6-11 9-14
G+(11,18,4,9) contains Petersen
   via 4 8 13 9 20 10 16 19 12 14 removing 1-2 3-7 5-17 6-18 11-15
G+(11,18,5,10) contains Petersen
   via 5 20 10 16 13 17 15 12 19 18 removing 1-2 3-7 4-8 6-11 9-14
G+(11,18,8,12) contains Thirdapex
   via 4 3 11 17 5 13 8 19 18 16 9 10 14 20 6 15 removing 1-2 7-12
G+(11,18,8,13) contains Secondapex
   via 5 1 2 3 4 16 18 19 20 13 10 9 14 17 8 15 removing 6-11 7-12
G+(11,18,9,13) contains Petersen
   via 4 8 12 14 9 18 19 20 13 16 removing 1-2 3-7 5-10 6-17 11-15
G+(11,18,9,14) contains Petersen
   via 9 13 12 19 20 17 15 14 16 18 removing 1-2 3-7 4-8 5-10 6-11
G+(11,18,10,14) contains Petersen
   via 5 8 12 19 20 17 15 14 13 18 removing 1-2 3-7 4-9 6-11 10-16
G+(11,18,12,15) contains Thirdapex
   via 4 7 11 17 5 13 12 19 18 16 9 10 14 20 6 15 removing 1-2 3-8
G+(11,18,14,15) contains Petersen
   via 6 11 9 13 15 17 14 20 19 18 removing 1-2 3-8 4-5 7-12 10-16
G+(18,17,2,7) contains Thirdapex
   via 20 4 9 12 7 17 5 14 15 6 19 11 18 10 13 16 removing 1-2 3-8
G+(18,17,2,3) contains Petersen
   via 4 5 10 14 9 18 16 13 12 15 removing 1-17 2-20 3-8 6-19 7-11
G+(18,17,3,4) contains Petersen
   via 4 5 8 13 9 18 12 14 10 16 removing 1-17 2-7 3-20 6-19 11-15
G+(18,17,3,8) contains Petersen
   via 5 17 6 11 7 16 15 12 19 18 removing 1-2 3-20 4-9 8-13 10-14
G+(18,17,4,5) contains Petersen
   via 5 8 13 9 20 10 16 18 12 14 removing 1-17 2-7 3-4 6-19 11-15
G+(18,17,4,9) contains Petersen
   via 5 8 13 9 19 10 16 18 12 14 removing 1-2 3-7 4-20 6-17 11-15
G+(18,17,5,10) contains Secondapex
   via 2 1 5 4 3 18 19 20 10 16 7 8 12 17 14 15 removing 6-11 9-13
G+(18,17,7,12) contains Petersen
   via 6 11 8 12 15 17 13 16 18 19 removing 1-2 3-4 5-10 7-20 9-14
G+(18,17,8,12) contains Petersen
   via 6 11 8 13 17 15 20 19 18 16 removing 1-2 3-4 5-10 7-12 9-14
G+(18,17,8,13) contains Petersen
   via 5 8 12 18 16 17 15 13 20 19 removing 1-2 3-7 4-9 6-11 10-14
G+(18,17,9,13) contains Petersen
   via 5 8 12 14 10 19 18 16 13 20 removing 1-2 3-7 4-9 6-17 11-15
G+(18,17,9,14) contains Petersen
   via 5 9 13 16 10 17 15 14 20 19 removing 1-2 3-7 4-8 6-11 12-18
G+(18,17,10,14) contains Petersen
   via 4 5 10 20 14 18 16 15 17 19 removing 1-2 3-8 6-11 7-12 9-13
G+(18,17,12,15) contains Petersen
   via 6 11 12 13 17 15 20 19 18 16 removing 1-2 3-7 4-8 5-10 9-14
G+(18,17,14,15) contains Petersen
   via 6 17 10 14 11 15 16 18 19 20 removing 1-2 3-8 4-5 7-12 9-13
G+(17,6,2,7) contains Thirdapex
   via 4 3 20 17 5 13 8 7 18 16 9 10 14 12 19 15 removing 1-2 6-11
G+(17,6,2,3) contains Petersen
   via 4 5 10 14 9 18 16 13 12 15 removing 1-17 2-20 3-8 6-19 7-11
G+(17,6,3,4) contains Petersen
   via 4 5 8 13 9 18 12 14 10 16 removing 1-17 2-7 3-20 6-19 11-15
G+(17,6,3,8) contains Petersen
   via 5 14 6 11 7 17 19 8 13 18 removing 1-2 3-20 4-9 10-16 12-15
G+(17,6,4,5) contains Petersen
   via 5 8 13 9 20 10 16 18 12 14 removing 1-17 2-7 3-4 6-19 11-15
G+(17,6,4,9) contains Petersen
   via 5 8 13 9 17 10 16 18 12 14 removing 1-2 3-7 4-20 6-19 11-15
G+(17,6,5,10) contains Secondapex
   via 5 1 2 3 4 6 11 7 12 15 20 14 10 18 8 16 removing 9-13 17-19
G+(17,6,7,12) contains Petersen
   via 7 9 13 18 11 20 12 15 14 17 removing 1-2 3-8 4-5 6-19 10-16
G+(17,6,8,12) contains Petersen
   via 5 14 6 11 7 17 19 20 13 18 removing 1-2 3-8 4-9 10-16 12-15
G+(17,6,8,13) contains Petersen
   via 5 8 12 15 14 17 18 13 20 19 removing 1-2 3-7 4-9 6-11 10-16
G+(17,6,9,13) contains Petersen
   via 5 8 12 14 10 17 18 16 13 20 removing 1-2 3-7 4-9 6-19 11-15
G+(17,6,9,14) contains Petersen
   via 5 8 12 14 10 17 18 16 13 20 removing 1-2 3-7 4-9 6-19 11-15
G+(17,6,10,14) contains Secondapex
   via 1 5 4 3 2 19 20 14 15 6 17 11 18 10 8 16 removing 7-12 9-13
G+(17,6,10,16) contains Thirdapex
   via 4 5 17 11 7 14 10 19 6 15 9 12 13 20 18 16 removing 1-2 3-8
G+(17,6,13,16) contains Petersen
   via 9 13 12 15 14 17 18 16 20 19 removing 1-2 3-7 4-8 5-10 6-11
# Jumps creating quadrangles:
G+(6,11,15,12) contains Boat2
   via 1 2 3 4 5 17 11 8 9 10 18 20 13 14 15 16 19 6 removing 7-12
G+(6,11,15,14) contains Petersen
   via 5 7 11 20 14 17 18 13 12 15 removing 1-2 3-8 4-9 6-19 10-16
G+(11,18,7,2) contains Boat2
   via 1 2 3 4 5 17 19 8 9 10 18 12 13 14 15 16 11 6 removing 7-20
G+(11,18,7,12) contains Thirdapex
   via 4 3 11 17 5 13 8 19 18 16 9 10 14 12 6 15 removing 1-2 7-20
G+(18,17,16,10) contains Boat2
   via 2 1 5 4 3 11 17 10 9 8 6 20 14 13 16 15 19 18 removing 7-12
G+(18,17,16,13) contains Petersen
   via 5 8 12 18 10 17 15 14 13 19 removing 1-2 3-7 4-9 6-11 16-20
G+(17,6,1,2) contains Thirdapex
   via 4 3 2 17 5 13 8 7 18 16 9 10 14 12 19 15 removing 1-20 6-11
G+(17,6,1,5) contains Thirdapex
   via 2 4 9 12 7 19 5 14 15 6 17 11 18 10 13 16 removing 1-20 3-8


##############################################################
# Proof of (14.6), claim (3)
G=Boat4
# A-expansions:
G+(7,11,1,2) contains Petersen
   via 7 19 10 16 12 17 14 15 11 18 removing 1-6 2-20 3-8 4-5 9-13
G+(7,11,1,5) contains Petersen
   via 7 19 10 16 12 17 14 15 11 18 removing 1-2 3-8 4-5 6-20 9-13
G+(7,11,2,3) contains Petersen
   via 2 6 15 7 17 20 16 18 11 19 removing 1-5 3-4 8-12 9-10 13-14
G+(7,11,3,4) contains Petersen
   via 3 6 11 16 8 20 19 12 15 14 removing 1-5 2-17 4-10 7-18 9-13
G+(7,11,3,8) contains Petersen
   via 4 6 11 8 13 17 18 16 15 12 removing 1-2 3-20 5-10 7-19 9-14
G+(7,11,4,5) contains Petersen
   via 7 19 10 16 12 17 14 15 11 18 removing 1-2 3-8 4-20 5-6 9-13
G+(7,11,4,9) contains Petersen
   via 5 8 13 9 11 10 16 18 12 14 removing 1-2 3-17 4-20 6-15 7-19
G+(7,11,5,10) contains Petersen
   via 5 6 15 10 20 13 12 19 11 16 removing 1-2 3-17 4-8 7-18 9-14
G+(7,11,8,13) contains Petersen
   via 5 6 11 20 8 16 18 12 15 13 removing 1-2 3-17 4-9 7-19 10-14
G+(7,11,9,13) contains Petersen
   via 5 8 12 14 10 11 18 16 13 20 removing 1-2 3-17 4-9 6-15 7-19
G+(7,11,9,14) contains Petersen
   via 6 9 13 16 11 15 12 19 20 14 removing 1-2 3-17 4-8 5-10 7-18
G+(7,11,10,14) contains Petersen
   via 5 6 11 13 8 20 19 12 15 14 removing 1-2 3-17 4-9 7-18 10-16
G+(7,11,10,16) contains Petersen
   via 5 6 15 12 8 10 14 13 16 20 removing 1-2 3-17 4-9 7-18 11-19
G+(7,11,13,16) contains Petersen
   via 5 6 15 12 8 10 14 13 20 16 removing 1-2 3-17 4-9 7-19 11-18
G+(7,11,14,15) contains Petersen
   via 5 6 12 7 17 14 13 18 11 19 removing 1-2 3-8 4-9 10-16 15-20
G+(11,18,1,2) contains Thirdapex
   via 6 15 14 5 1 7 12 9 4 2 11 20 19 13 10 16 removing 3-8 17-18
G+(11,18,1,5) contains Petersen
   via 2 6 11 7 17 8 19 18 15 12 removing 1-20 3-4 5-10 9-14 13-16
G+(11,18,2,3) contains Petersen
   via 2 6 11 7 17 20 19 18 15 12 removing 1-5 3-4 8-13 9-10
G+(11,18,3,4) contains Petersen
   via 2 6 11 7 17 8 19 18 15 12 removing 1-5 3-20 4-10 9-14 13-16
G+(11,18,3,8) contains Petersen
   via 4 6 19 8 13 17 18 16 15 12 removing 1-2 3-20 5-10 7-11 9-14
G+(11,18,4,5) contains Petersen
   via 2 6 11 7 17 8 19 18 15 12 removing 1-5 3-4 9-14 10-20 13-16
G+(11,18,4,9) contains Petersen
   via 5 8 13 9 19 10 16 18 12 14 removing 1-2 3-17 4-20 6-15 7-11
G+(11,18,5,10) contains Petersen
   via 2 6 11 7 17 8 19 18 15 12 removing 1-5 3-4 9-14 10-20 13-16
G+(11,18,8,12) contains Petersen
   via 7 17 8 13 11 12 20 19 18 16 removing 1-2 3-4 5-10 6-15 9-14
G+(11,18,8,13) contains Petersen
   via 5 6 15 12 8 16 13 20 19 18 removing 1-2 3-17 4-9 7-11 10-14
G+(11,18,9,13) contains Petersen
   via 5 8 12 14 10 19 18 16 13 20 removing 1-2 3-17 4-9 6-15 7-11
G+(11,18,9,14) contains Petersen
   via 5 9 13 16 10 11 12 14 20 19 removing 1-2 3-17 4-8 6-15 7-18
G+(11,18,10,14) contains Petersen
   via 4 5 10 20 9 18 16 13 12 19 removing 1-2 3-8 6-11 7-17 14-15
G+(11,18,12,15) contains Petersen
   via 7 11 10 16 12 17 14 20 19 18 removing 1-2 3-8 4-5 6-15 9-13
G+(11,18,14,15) contains Petersen
   via 7 11 10 16 12 17 14 20 19 18 removing 1-2 3-8 4-5 6-15 9-13
G+(18,17,1,5) contains Petersen
   via 4 5 10 15 6 13 16 18 19 12 removing 1-20 2-17 3-8 7-11 9-14
G+(18,17,1,6) contains Thirdapex
   via 17 4 9 12 7 20 5 14 15 6 19 11 18 10 13 16 removing 1-2 3-8
G+(18,17,3,4) contains Petersen
   via 3 6 15 12 8 20 14 16 18 19 removing 1-5 2-17 4-10 7-11 9-13
G+(18,17,3,8) contains Petersen
   via 9 14 10 16 13 19 17 12 15 18 removing 1-6 2-3 4-5 7-11 8-20
G+(18,17,4,5) contains Petersen
   via 4 6 15 10 20 13 12 19 18 16 removing 1-5 2-17 3-8 7-11 9-14
G+(18,17,4,9) contains Petersen
   via 4 8 13 9 20 10 16 18 12 14 removing 1-2 3-17 5-6 7-19 11-15
G+(18,17,5,10) contains Petersen
   via 5 6 15 10 20 13 12 19 18 16 removing 1-2 3-17 4-8 7-11 9-14
G+(18,17,6,15) contains Petersen
   via 6 13 8 12 11 20 19 18 16 15 removing 1-2 3-4 5-10 7-17 9-14
G+(18,17,8,12) contains Thirdapex
   via 12 15 14 13 20 11 6 10 16 18 7 19 17 5 9 4 removing 1-2 3-8
G+(18,17,8,13) contains Petersen
   via 2 3 8 12 15 19 20 13 16 18 removing 1-5 4-9 6-11 7-17 10-14
G+(18,17,9,13) contains Petersen
   via 4 8 12 14 9 18 19 20 13 16 removing 1-2 3-17 5-10 6-15 7-11
G+(18,17,9,14) contains Petersen
   via 6 9 13 12 15 18 16 14 20 19 removing 1-2 3-17 4-8 5-10 7-11
G+(18,17,10,14) contains Petersen
   via 5 6 15 12 8 20 14 13 18 19 removing 1-2 3-17 4-9 7-11 10-16
G+(18,17,12,15) contains Petersen
   via 7 11 15 20 12 17 14 16 18 19 removing 1-2 3-8 4-5 6-10 9-13
G+(18,17,14,15) contains Petersen
   via 7 17 9 14 11 12 13 18 19 20 removing 1-2 3-8 4-5 6-15 10-16
G+(17,7,1,5) contains Petersen
   via 9 14 10 16 13 17 19 12 15 18 removing 1-2 3-8 4-5 6-20 7-11
G+(17,7,1,6) contains Petersen
   via 9 14 10 16 13 17 19 12 15 18 removing 1-2 3-8 4-5 6-20 7-11
G+(17,7,3,4) contains Petersen
   via 3 6 15 12 8 20 14 16 18 19 removing 1-5 2-17 4-10 7-11 9-13
G+(17,7,3,8) contains Secondapex
   via 2 17 19 20 3 6 11 7 12 15 1 14 10 18 8 16 removing 4-5 9-13
G+(17,7,4,5) contains Petersen
   via 9 14 10 16 13 17 19 12 15 18 removing 1-2 3-8 4-20 5-6 7-11
G+(17,7,4,9) contains Petersen
   via 4 8 13 9 20 10 16 18 12 14 removing 1-2 3-17 5-6 7-19 11-15
G+(17,7,5,10) contains Petersen
   via 5 6 15 10 20 13 12 19 18 16 removing 1-2 3-17 4-8 7-11 9-14
G+(17,7,6,15) contains Petersen
   via 6 13 8 12 11 20 17 18 16 15 removing 1-2 3-4 5-10 7-19 9-14
G+(17,7,8,13) contains Petersen
   via 3 4 11 7 12 17 18 16 13 19 removing 1-2 5-10 6-15 8-20 9-14
G+(17,7,9,13) contains Petersen
   via 4 8 12 14 9 18 19 20 13 16 removing 1-2 3-17 5-10 6-15 7-11
G+(17,7,9,14) contains Petersen
   via 6 9 13 12 15 18 16 14 20 19 removing 1-2 3-17 4-8 5-10 7-11
G+(17,7,10,14) contains Petersen
   via 5 6 15 12 8 20 14 13 18 19 removing 1-2 3-17 4-9 7-11 10-16
G+(17,7,10,16) contains Petersen
   via 5 6 15 12 8 10 14 13 18 19 removing 1-2 3-17 4-9 7-11 16-20
G+(17,7,13,16) contains Petersen
   via 7 12 8 13 11 19 17 18 16 20 removing 1-2 3-4 5-10 6-15 9-14
G+(17,7,14,15) contains Petersen
   via 4 6 11 7 13 17 18 16 20 19 removing 1-2 3-8 5-10 9-14 12-15
# Jumps creating quadrangles:
G+(7,11,12,8) contains Petersen
   via 4 6 11 18 17 13 20 12 15 16 removing 1-2 3-8 5-10 7-19 9-14
G+(7,11,12,15) contains Boat2
   via 1 2 3 4 5 11 17 8 9 10 18 12 13 14 20 16 7 19 removing 6-15
G+(11,18,6,1) contains Boat2
   via 1 2 3 4 5 19 17 8 9 10 18 12 13 14 15 16 7 11 removing 6-20
G+(11,18,6,15) contains Petersen
   via 7 11 10 16 12 17 14 15 19 18 removing 1-2 3-8 4-5 6-20 9-13
G+(18,17,16,10) contains Petersen
   via 5 6 15 12 8 10 14 13 18 19 removing 1-2 3-17 4-9 7-11 16-20
G+(18,17,16,13) contains Petersen
   via 2 3 8 12 15 19 13 14 10 18 removing 1-5 4-9 6-11 7-17 16-20
G+(17,7,2,1) contains Petersen
   via 9 14 10 16 13 17 19 12 15 18 removing 1-6 2-20 3-8 4-5 7-11
G+(17,7,2,3) contains Thirdapex
   via 6 15 14 5 1 7 12 9 4 19 11 17 18 13 10 16 removing 2-20 3-8


##############################################################
# Proof of (14.6), claim (4)
G=Boat5
# A-expansions:
G+(6,15,2,7) contains Petersen
   via 6 19 7 11 17 13 12 18 15 16 removing 1-2 3-20 4-8 5-10 9-14
G+(6,15,2,3) contains Petersen
   via 6 19 7 11 17 13 12 18 15 16 removing 1-2 3-20 4-8 5-10 9-14
G+(6,15,3,4) contains Petersen
   via 6 19 7 11 17 13 12 18 15 16 removing 1-2 3-8 4-20 5-10 9-14
G+(6,15,3,8) contains Petersen
   via 6 13 8 18 17 19 20 11 16 15 removing 1-2 3-4 5-10 7-12 9-14
G+(6,15,4,5) contains Petersen
   via 5 8 13 9 20 10 16 17 18 14 removing 1-6 2-7 3-4 11-12 15-19
G+(6,15,4,9) contains Petersen
   via 5 6 19 13 8 10 15 18 17 16 removing 1-2 3-7 4-20 9-14 11-12
G+(6,15,5,10) contains Secondapex
   via 3 2 1 5 4 18 17 6 19 15 8 9 13 11 20 16 removing 7-12 10-14
G+(6,15,7,11) contains Petersen
   via 6 17 11 16 13 19 20 12 18 15 removing 1-2 3-7 4-8 5-10 9-14
G+(6,15,7,12) contains Petersen
   via 6 17 11 16 13 19 20 12 18 15 removing 1-2 3-7 4-8 5-10 9-14
G+(6,15,8,12) contains Petersen
   via 5 6 17 18 12 14 13 20 19 15 removing 1-2 3-8 4-9 7-11 10-16
G+(6,15,8,13) contains Petersen
   via 5 6 17 18 8 14 13 20 19 15 removing 1-2 3-7 4-9 10-16 11-12
G+(6,15,9,13) contains Petersen
   via 5 6 19 13 8 10 15 18 17 16 removing 1-2 3-7 4-9 11-12 14-20
G+(6,15,10,16) contains Secondapex
   via 3 2 1 5 4 18 17 6 19 15 8 9 13 11 20 16 removing 7-12 10-14
G+(6,15,11,16) contains Petersen
   via 9 14 10 17 11 13 16 20 15 18 removing 1-2 3-8 4-5 6-19 7-12
G+(6,15,13,16) contains Petersen
   via 6 9 13 20 19 17 18 15 14 16 removing 1-2 3-7 4-8 5-10 11-12
G+(15,18,1,2) contains Petersen
   via 2 4 17 11 7 19 18 12 13 16 removing 1-20 3-8 5-10 6-15 9-14
G+(15,18,1,5) contains Petersen
   via 4 5 10 14 9 11 16 13 18 17 removing 1-2 3-8 6-20 7-12 15-19
G+(15,18,2,7) contains Petersen
   via 4 20 7 11 17 13 12 18 19 16 removing 1-2 3-8 5-10 6-15 9-14
G+(15,18,2,3) contains Petersen
   via 4 20 7 11 17 13 12 18 19 16 removing 1-2 3-8 5-10 6-15 9-14
G+(15,18,3,4) contains Petersen
   via 4 20 7 11 17 13 12 18 19 16 removing 1-2 3-8 5-10 6-15 9-14
G+(15,18,3,8) contains Petersen
   via 3 4 17 11 7 19 18 12 13 16 removing 1-2 5-10 6-15 8-20 9-14
G+(15,18,4,5) contains Petersen
   via 4 9 14 10 20 11 17 18 13 16 removing 1-2 3-8 5-6 7-12 15-19
G+(15,18,4,9) contains Petersen
   via 3 4 20 9 13 15 19 16 10 14 removing 1-5 2-7 6-17 8-12
G+(15,18,5,10) contains Petersen
   via 5 6 17 18 9 20 10 14 15 19 removing 1-2 3-7 4-8 11-12 13-16
G+(15,18,7,11) contains Petersen
   via 6 7 20 11 17 15 19 18 12 16 removing 1-2 3-8 4-9 5-10 13-14
G+(15,18,8,13) contains Secondapex
   via 2 7 12 8 3 6 17 18 19 15 1 14 10 11 20 16 removing 4-5 9-13
G+(15,18,9,13) contains Firstapex
   via 7 1 5 4 8 12 17 6 14 9 20 18 11 10 13 16 removing 2-3 15-19
G+(15,18,10,16) contains Petersen
   via 5 6 15 13 8 20 19 18 17 16 removing 1-2 3-7 4-9 10-14 11-12
G+(15,18,11,16) contains Petersen
   via 9 14 10 17 11 13 16 20 19 18 removing 1-2 3-8 4-5 6-15 7-12
G+(15,18,13,16) contains Secondapex
   via 4 7 12 13 9 6 17 18 19 15 5 14 10 11 20 16 removing 1-2 3-8
G+(18,17,1,2) contains Petersen
   via 4 5 10 14 9 11 16 13 19 17 removing 1-6 2-20 3-8 7-12 15-18
G+(18,17,1,5) contains Petersen
   via 4 5 10 14 9 11 16 13 19 17 removing 1-2 3-8 6-20 7-12 15-18
G+(18,17,2,7) contains Thirdapex
   via 18 15 14 13 12 17 6 10 16 11 19 7 20 5 9 4 removing 1-2 3-8
G+(18,17,2,3) contains Petersen
   via 2 7 12 8 20 15 18 19 11 16 removing 1-5 3-4 6-17 9-10 13-14
G+(18,17,3,4) contains Petersen
   via 6 8 12 11 17 15 18 19 13 16 removing 1-5 2-7 3-20 4-10 9-14
G+(18,17,3,8) contains Petersen
   via 4 6 17 11 7 13 19 18 15 16 removing 1-2 3-20 5-10 8-12 9-14
G+(18,17,4,5) contains Petersen
   via 4 9 14 10 20 11 17 19 13 16 removing 1-2 3-8 5-6 7-12 15-18
G+(18,17,4,9) contains Petersen
   via 6 8 12 11 17 15 18 19 13 16 removing 1-2 3-7 4-20 5-10 9-14
G+(18,17,5,10) contains Petersen
   via 5 6 15 10 20 13 18 19 17 16 removing 1-2 3-7 4-8 9-14 11-12
G+(18,17,8,13) contains Petersen
   via 6 8 12 11 17 15 18 19 20 16 removing 1-2 3-7 4-9 5-10 13-14
G+(18,17,9,13) contains Petersen
   via 6 8 12 11 17 15 18 19 20 14 removing 1-2 3-7 4-9 5-10 13-16
G+(18,17,9,14) contains Petersen
   via 6 9 13 18 15 17 16 14 20 19 removing 1-2 3-7 4-8 5-10 11-12
G+(18,17,10,14) contains Petersen
   via 5 6 17 11 12 20 19 18 15 14 removing 1-2 3-7 4-9 8-13 10-16
G+(18,17,10,16) contains Petersen
   via 5 6 17 11 12 20 19 18 15 16 removing 1-2 3-7 4-9 8-13 10-14
G+(18,17,13,16) contains Petersen
   via 9 17 11 12 13 14 16 20 19 18 removing 1-2 3-7 4-8 5-10 6-15
G+(17,6,2,7) contains Thirdapex
   via 20 3 4 6 19 12 8 9 15 18 7 17 11 13 5 16 removing 1-2 10-14
G+(17,6,2,3) contains Petersen
   via 6 7 12 8 19 15 18 17 11 16 removing 1-5 2-20 3-4 9-10 13-14
G+(17,6,3,4) contains Petersen
   via 6 7 12 8 19 15 18 17 11 16 removing 1-5 2-3 4-20 9-10 13-14
G+(17,6,3,8) contains Petersen
   via 6 7 12 8 19 15 18 17 11 16 removing 1-2 3-20 4-9 5-10 13-14
G+(17,6,4,5) contains Petersen
   via 6 7 11 17 19 15 16 13 12 18 removing 1-5 2-3 4-8 9-14 10-20
G+(17,6,4,9) contains Petersen
   via 5 8 13 9 19 10 16 17 18 14 removing 1-2 3-7 4-20 6-15 11-12
G+(17,6,5,10) contains Petersen
   via 6 7 11 17 19 15 16 13 12 18 removing 1-5 2-3 4-8 9-14 10-20
G+(17,6,7,12) contains Petersen
   via 7 14 10 16 11 20 19 17 18 12 removing 1-2 3-8 4-5 6-15 9-13
G+(17,6,8,12) contains Petersen
   via 6 7 11 16 15 19 17 18 12 20 removing 1-2 3-8 4-9 5-10 13-14
G+(17,6,8,13) contains Petersen
   via 5 6 15 18 8 16 13 20 19 17 removing 1-2 3-7 4-9 10-14 11-12
G+(17,6,9,13) contains Petersen
   via 5 8 13 16 10 19 20 14 18 17 removing 1-2 3-7 4-9 6-15 11-12
G+(17,6,9,14) contains Petersen
   via 5 6 15 18 9 10 14 20 19 17 removing 1-2 3-7 4-8 11-12 13-16
G+(17,6,10,14) contains Petersen
   via 4 5 10 13 9 17 20 14 15 18 removing 1-2 3-8 6-19 7-12 11-16
G+(17,6,10,16) contains Petersen
   via 6 7 11 16 15 19 17 18 12 20 removing 1-5 2-3 4-9 8-13 10-14
G+(17,6,13,16) contains Petersen
   via 5 8 12 16 10 19 18 14 13 20 removing 1-2 3-7 4-9 6-15 11-17
# Jumps creating quadrangles:
G+(6,15,1,2) contains Petersen
   via 6 19 7 11 17 13 12 18 15 16 removing 1-20 2-3 4-8 5-10 9-14
G+(6,15,1,5) contains Thirdapex
   via 2 3 4 19 6 12 8 9 15 18 7 17 11 13 5 16 removing 1-20 10-14
G+(15,18,14,9) contains Secondapex
   via 3 2 1 5 4 18 17 6 15 19 8 9 13 11 10 16 removing 7-12 14-20
G+(15,18,14,10) contains Petersen
   via 5 6 15 13 8 10 19 18 17 16 removing 1-2 3-7 4-9 11-12 14-20
G+(18,17,12,7) contains Boat4
   via 1 2 3 4 5 6 19 8 9 10 17 18 13 14 15 16 7 11 removing 12-20
G+(18,17,12,8) contains Petersen
   via 4 6 17 11 7 13 19 18 15 16 removing 1-2 3-8 5-10 9-14 12-20
G+(17,6,11,7) contains Boat4
   via 12 7 2 3 8 18 19 1 4 13 17 6 5 9 15 16 20 11 removing 10-14
G+(17,6,11,16) contains Boat3
   via 1 2 3 4 5 17 7 8 9 10 11 12 13 14 18 16 19 20 removing 6-15


##############################################################
# Proof of (14.6), claim (4)
G=Boat6
# A-expansions:
G+(14,15,1,2) contains Petersen
   via 6 9 8 12 11 15 19 14 17 18 removing 1-20 2-7 3-4 5-10 13-16
G+(14,15,1,5) contains Secondapex
   via 3 2 20 5 4 18 15 19 14 17 8 9 13 11 10 16 removing 1-6 7-12
G+(14,15,2,7) contains Petersen
   via 5 6 11 7 12 14 17 18 15 19 removing 1-2 3-20 4-9 8-13 10-16
G+(14,15,2,3) contains Petersen
   via 5 6 11 7 12 14 17 18 15 19 removing 1-2 3-20 4-9 8-13 10-16
G+(14,15,3,4) contains Petersen
   via 6 9 8 12 11 15 19 14 17 18 removing 1-2 3-7 4-20 5-10 13-16
G+(14,15,3,8) contains Petersen
   via 6 9 8 12 11 15 19 14 17 18 removing 1-2 3-7 4-20 5-10 13-16
G+(14,15,4,5) contains Petersen
   via 5 20 9 16 10 18 17 14 19 15 removing 1-6 2-7 3-4 8-13 11-12
G+(14,15,4,9) contains Petersen
   via 5 6 11 12 8 10 16 13 15 18 removing 1-2 3-7 4-20 9-17 14-19
G+(14,15,7,11) contains Petersen
   via 5 6 11 20 12 14 17 18 15 19 removing 1-2 3-7 4-9 8-13 10-16
G+(14,15,7,12) contains Petersen
   via 5 6 11 20 12 14 17 18 15 19 removing 1-2 3-7 4-9 8-13 10-16
G+(14,15,8,12) contains Petersen
   via 6 9 20 12 11 15 19 14 17 18 removing 1-2 3-7 4-8 5-10 13-16
G+(14,15,8,13) contains Petersen
   via 6 9 20 12 11 15 19 14 17 18 removing 1-2 3-7 4-8 5-10 13-16
G+(14,15,9,13) contains Petersen
   via 6 9 20 13 16 15 19 14 17 18 removing 1-2 3-7 4-8 5-10 11-12
G+(14,15,11,16) contains Petersen
   via 6 10 14 17 11 15 19 20 16 18 removing 1-2 3-8 4-5 7-12 9-13
G+(14,15,13,16) contains Petersen
   via 6 9 13 12 11 15 20 16 17 18 removing 1-2 3-7 4-8 5-10 14-19
G+(15,18,1,2) contains Petersen
   via 6 9 13 16 11 15 19 18 17 14 removing 1-20 2-7 3-4 5-10 8-12
G+(15,18,1,5) contains Petersen
   via 4 5 10 16 11 17 14 15 19 18 removing 1-2 3-8 6-20 7-12 9-13
G+(15,18,2,7) contains Petersen
   via 6 9 13 16 11 15 19 18 17 14 removing 1-2 3-4 5-10 7-20 8-12
G+(15,18,2,3) contains Petersen
   via 6 9 13 16 11 15 19 18 17 14 removing 1-2 3-4 5-10 7-20 8-12
G+(15,18,3,4) contains Petersen
   via 6 9 13 16 11 15 19 18 17 14 removing 1-2 3-7 4-20 5-10 8-12
G+(15,18,3,8) contains Petersen
   via 6 9 13 16 11 15 19 18 17 14 removing 1-2 3-7 4-20 5-10 8-12
G+(15,18,4,5) contains Petersen
   via 4 20 10 16 11 17 14 15 19 18 removing 1-2 3-8 5-6 7-12 9-13
G+(15,18,4,9) contains Petersen
   via 5 6 11 12 8 10 16 13 19 18 removing 1-2 3-7 4-20 9-17 14-15
G+(15,18,5,10) contains Petersen
   via 5 6 16 10 20 17 18 19 15 14 removing 1-2 3-7 4-8 9-13 11-12
G+(15,18,7,11) contains Secondapex
   via 3 2 1 5 4 18 19 15 14 17 8 9 13 20 10 16 removing 6-11 7-12
G+(15,18,8,13) contains Petersen
   via 6 9 13 16 11 15 19 18 17 14 removing 1-2 3-7 4-8 5-10 12-20
G+(15,18,9,13) contains Petersen
   via 6 9 20 13 12 15 19 18 17 14 removing 1-2 3-7 4-8 5-10 11-16
G+(15,18,10,16) contains Petersen
   via 10 12 11 15 14 20 16 17 18 19 removing 1-2 3-7 4-9 5-6 8-13
G+(15,18,11,16) contains Secondapex
   via 4 5 6 11 7 17 14 15 19 18 9 12 13 10 20 16 removing 1-2 3-8
G+(15,18,13,16) contains Petersen
   via 6 9 17 18 11 15 14 16 20 19 removing 1-2 3-7 4-8 5-10 12-13
G+(18,17,1,2) contains Petersen
   via 6 9 13 16 11 15 18 19 17 14 removing 1-20 2-3 4-8 5-10 7-12
G+(18,17,1,5) contains Petersen
   via 5 8 12 18 10 20 11 16 13 19 removing 1-2 3-7 4-9 6-15 14-17
G+(18,17,1,6) contains Petersen
   via 5 8 12 18 10 20 11 16 13 19 removing 1-2 3-7 4-9 6-15 14-17
G+(18,17,2,7) contains Petersen
   via 6 9 13 16 11 15 18 19 17 14 removing 1-2 3-20 4-8 5-10 7-12
G+(18,17,2,3) contains Petersen
   via 6 9 13 16 11 15 18 19 17 14 removing 1-2 3-20 4-8 5-10 7-12
G+(18,17,3,4) contains Petersen
   via 6 9 13 16 11 15 18 19 17 14 removing 1-2 3-8 4-20 5-10 7-12
G+(18,17,3,8) contains Petersen
   via 6 9 13 16 11 15 18 19 17 14 removing 1-2 3-4 5-10 7-12 8-20
G+(18,17,4,5) contains Petersen
   via 5 6 11 16 10 19 17 14 15 18 removing 1-2 3-8 4-20 7-12 9-13
G+(18,17,5,10) contains Petersen
   via 5 9 13 10 20 15 18 19 17 14 removing 1-2 3-7 4-8 6-11 12-16
G+(18,17,6,11) contains Petersen
   via 6 9 13 18 15 20 16 14 17 19 removing 1-2 3-7 4-8 5-10 11-12
G+(18,17,7,11) contains Petersen
   via 6 9 13 16 11 15 18 19 17 14 removing 1-2 3-7 4-8 5-10 12-20
G+(18,17,8,13) contains Secondapex
   via 3 2 1 5 4 19 18 15 14 17 20 9 13 7 10 16 removing 6-11 8-12
G+(18,17,10,16) contains Petersen
   via 8 10 14 17 13 18 15 16 20 19 removing 1-2 3-7 4-9 5-6 11-12
G+(18,17,11,16) contains Petersen
   via 6 9 13 18 15 20 16 14 17 19 removing 1-2 3-7 4-8 5-10 11-12
G+(18,17,13,16) contains Secondapex
   via 3 4 9 13 8 15 14 17 19 18 6 12 11 10 20 16 removing 1-5 2-7
G+(17,14,1,2) contains Petersen
   via 3 4 9 16 12 19 17 18 15 14 removing 1-20 2-7 5-10 6-11 8-13
G+(17,14,1,5) contains Petersen
   via 5 8 12 18 10 20 11 16 13 17 removing 1-2 3-7 4-9 6-15 14-19
G+(17,14,1,6) contains Petersen
   via 5 8 12 18 10 20 11 16 13 17 removing 1-2 3-7 4-9 6-15 14-19
G+(17,14,2,7) contains Petersen
   via 6 7 12 13 9 15 18 17 19 14 removing 1-2 3-20 4-8 5-10 11-16
G+(17,14,2,3) contains Petersen
   via 6 7 12 13 9 15 18 17 19 14 removing 1-2 3-20 4-8 5-10 11-16
G+(17,14,3,4) contains Petersen
   via 4 9 16 12 20 15 14 19 17 18 removing 1-2 3-7 5-10 6-11 8-13
G+(17,14,3,8) contains Petersen
   via 4 9 16 12 20 15 14 19 17 18 removing 1-2 3-7 5-10 6-11 8-13
G+(17,14,4,5) contains Secondapex
   via 1 5 20 4 3 15 14 19 17 18 6 12 11 10 9 16 removing 2-7 8-13
G+(17,14,6,11) contains Petersen
   via 6 9 13 12 20 15 14 19 17 18 removing 1-2 3-7 4-8 5-10 11-16
G+(17,14,7,11) contains Petersen
   via 6 9 13 12 20 15 14 19 17 18 removing 1-2 3-7 4-8 5-10 11-16
G+(17,14,7,12) contains Petersen
   via 6 9 13 12 20 15 14 19 17 18 removing 1-2 3-7 4-8 5-10 11-16
G+(17,14,8,12) contains Petersen
   via 8 20 12 16 13 15 18 17 19 14 removing 1-2 3-7 4-9 5-10 6-11
G+(17,14,8,13) contains Petersen
   via 4 8 20 13 9 14 19 17 18 15 removing 1-2 3-7 5-6 10-16 11-12
G+(17,14,11,16) contains Petersen
   via 6 9 13 12 11 15 16 20 17 18 removing 1-2 3-7 4-8 5-10 14-19
G+(17,14,13,16) contains Petersen
   via 9 10 14 15 13 17 19 20 16 18 removing 1-5 2-7 3-4 6-11 8-12
# Jumps creating quadrangles:
G+(14,15,10,5) contains Boat3
   via 5 4 3 2 1 10 9 8 7 6 14 13 12 11 16 15 20 19 removing 17-18
G+(14,15,10,16) contains Boat3
   via 5 1 2 3 4 20 6 7 8 9 19 11 12 13 16 17 10 14 removing 15-18
G+(15,18,6,1) contains Petersen
   via 4 5 10 16 11 17 14 15 19 18 removing 1-2 3-8 6-20 7-12 9-13
G+(15,18,6,11) contains Secondapex
   via 3 2 1 5 4 18 19 15 14 17 8 9 13 11 10 16 removing 6-20 7-12
G+(18,17,12,7) contains Petersen
   via 6 9 13 16 11 15 18 19 17 14 removing 1-2 3-7 4-8 5-10 12-20
G+(18,17,12,8) contains Secondapex
   via 3 2 1 5 4 19 18 15 14 17 8 9 13 7 10 16 removing 6-11 12-20
G+(17,14,9,4) contains Secondapex
   via 1 5 4 3 2 15 14 19 17 18 6 7 11 10 13 16 removing 8-12 9-20
G+(17,14,9,13) contains Petersen
   via 3 4 10 16 13 15 14 19 17 18 removing 1-5 2-7 6-11 8-12 9-20


##############################################################
# Proof of (14.6), claim (5)
G=Boat7
# Testing augmenting paths from X={15 17 18}
G+(15,17,1,2) contains Petersen
   via 2 4 6 11 7 19 17 12 13 16 removing 1-20 3-8 5-10 9-14 15-18
G+(15,17,1,5) contains Thirdapex
   via 2 3 4 20 1 12 8 9 19 17 7 6 11 13 5 16 removing 10-14 15-18
G+(15,17,1,6) contains Boat5
   via 1 2 3 4 5 19 7 8 9 10 11 12 13 14 15 16 17 18 removing 6-20
G+(15,17,2,7) contains Petersen
   via 4 6 11 7 20 13 16 19 17 12 removing 1-2 3-8 5-10 9-14 15-18
G+(15,17,2,3) contains Petersen
   via 4 6 11 7 20 13 16 19 17 12 removing 1-2 3-8 5-10 9-14 15-18
G+(15,17,3,4) contains Petersen
   via 4 6 11 7 20 13 16 19 17 12 removing 1-2 3-8 5-10 9-14 15-18
G+(15,17,3,8) contains Petersen
   via 4 5 10 16 7 9 14 18 17 13 removing 1-2 3-20 6-11 8-12 15-19
G+(15,17,4,5) contains Petersen
   via 5 8 13 9 20 10 16 17 18 14 removing 1-6 2-7 3-4 11-12 15-19
G+(15,17,4,9) contains Petersen
   via 5 6 11 12 8 10 16 13 17 18 removing 1-2 3-7 4-20 9-14 15-19
G+(15,17,5,10) contains Boat2
   via 4 5 1 2 3 14 20 6 7 8 10 17 11 12 18 16 19 15 removing 9-13
G+(15,17,6,11) contains Petersen
   via 4 5 10 14 9 11 16 13 17 19 removing 1-2 3-8 6-20 7-12 15-18
G+(15,17,7,11) contains Petersen
   via 5 6 11 20 7 14 13 12 17 19 removing 1-2 3-8 4-9 10-16 15-18
G+(15,17,7,12) contains Petersen
   via 4 5 10 16 7 9 14 19 17 13 removing 1-2 3-8 6-11 12-20 15-18
G+(15,17,8,12) contains Petersen
   via 4 5 10 16 7 9 14 18 17 13 removing 1-2 3-8 6-11 12-20 15-19
G+(15,17,8,13) contains Petersen
   via 5 6 11 12 8 14 13 20 17 18 removing 1-2 3-7 4-9 10-16 15-19
G+(15,17,9,13) contains Petersen
   via 5 6 11 12 8 10 16 13 17 18 removing 1-2 3-7 4-9 14-20 15-19
G+(15,17,9,14) contains Petersen
   via 5 6 11 12 8 10 16 13 17 18 removing 1-2 3-7 4-9 14-20 15-19
G+(15,17,10,14) contains Boat6
   via 1 2 3 4 5 6 7 8 9 10 11 12 13 19 17 16 15 18 removing 14-20
G+(15,17,10,16) contains Boat5
   via 1 5 4 3 2 17 10 9 8 7 20 14 13 12 18 16 19 15 removing 6-11
G+(15,17,11,16) contains Petersen
   via 6 11 9 14 10 17 13 16 20 19 removing 1-2 3-8 4-5 7-12 15-18
G+(15,17,13,16) contains Petersen
   via 6 9 13 12 11 17 20 16 14 18 removing 1-2 3-7 4-8 5-10 15-19
G+(15,18,1,2) contains Petersen
   via 2 4 6 11 7 19 18 12 13 16 removing 1-20 3-8 5-10 9-14 15-17
G+(15,18,1,5) contains Petersen
   via 4 5 10 14 9 11 16 13 18 17 removing 1-2 3-8 6-20 7-12 15-19
G+(15,18,1,6) contains Petersen
   via 4 5 10 14 9 11 16 13 18 17 removing 1-2 3-8 6-20 7-12 15-19
G+(15,18,2,7) contains Petersen
   via 4 6 11 7 20 13 16 19 18 12 removing 1-2 3-8 5-10 9-14 15-17
G+(15,18,2,3) contains Petersen
   via 4 6 11 7 20 13 16 19 18 12 removing 1-2 3-8 5-10 9-14 15-17
G+(15,18,3,4) contains Petersen
   via 4 6 11 7 20 13 16 19 18 12 removing 1-2 3-8 5-10 9-14 15-17
G+(15,18,3,8) contains Petersen
   via 3 4 13 16 7 20 8 12 18 19 removing 1-2 5-10 6-11 9-14 15-17
G+(15,18,4,5) contains Petersen
   via 4 9 14 10 20 11 17 18 13 16 removing 1-2 3-8 5-6 7-12 15-19
G+(15,18,4,9) contains Petersen
   via 3 4 20 9 13 17 18 16 10 14 removing 1-5 2-7 6-11 8-12 15-19
G+(15,18,5,10) contains Petersen
   via 5 6 16 13 9 20 10 14 17 18 removing 1-2 3-7 4-8 11-12 15-19
G+(15,18,6,11) contains Petersen
   via 4 5 10 14 9 11 16 13 18 19 removing 1-2 3-8 6-20 7-12 15-17
G+(15,18,7,11) contains Petersen
   via 5 6 11 20 7 14 13 12 18 19 removing 1-2 3-8 4-9 10-16 15-17
G+(15,18,7,12) contains Petersen
   via 4 5 10 16 7 9 14 19 18 13 removing 1-2 3-8 6-11 12-20 15-17
G+(15,18,8,12) contains Boat2
   via 1 2 3 4 5 6 7 8 9 10 11 19 13 14 15 16 18 17 removing 12-20
G+(15,18,8,13) contains Thirdapex
   via 18 19 14 5 1 8 20 9 4 3 12 2 7 13 10 16 removing 6-11 15-17
G+(15,18,9,13) contains Secondapex
   via 1 5 4 3 2 17 14 9 20 18 6 7 11 10 13 16 removing 8-12 15-19
G+(15,18,9,14) contains Boat6
   via 1 2 3 4 5 6 7 8 9 10 11 12 13 15 17 16 19 18 removing 14-20
G+(15,18,10,14) contains Petersen
   via 5 6 11 12 8 10 16 13 17 18 removing 1-2 3-7 4-9 14-20 15-19
G+(15,18,10,16) contains Petersen
   via 5 6 11 12 8 20 16 13 17 18 removing 1-2 3-7 4-9 10-14 15-19
G+(15,18,11,16) contains Petersen
   via 6 11 9 14 10 18 13 16 20 19 removing 1-2 3-8 4-5 7-12 15-17
G+(15,18,13,16) contains Boat5
   via 12 8 3 2 7 18 13 4 1 11 20 9 5 6 17 16 19 15 removing 10-14
G+(17,18,1,2) contains Petersen
   via 4 5 10 14 9 11 16 13 19 17 removing 1-6 2-20 3-8 7-12 15-18
G+(17,18,1,5) contains Petersen
   via 4 5 10 14 9 11 16 13 19 17 removing 1-2 3-8 6-20 7-12 15-18
G+(17,18,1,6) contains Petersen
   via 4 5 10 14 9 11 16 13 19 17 removing 1-2 3-8 6-20 7-12 15-18
G+(17,18,2,7) contains Thirdapex
   via 4 3 20 6 5 13 8 7 11 16 9 10 14 12 19 18 removing 1-2 15-17
G+(17,18,2,3) contains Petersen
   via 4 5 10 14 9 19 16 13 12 18 removing 1-6 2-20 3-8 7-11 15-17
G+(17,18,3,4) contains Petersen
   via 3 6 11 12 8 20 16 13 17 19 removing 1-5 2-7 4-9 10-14 15-18
G+(17,18,3,8) contains Petersen
   via 4 5 10 16 7 9 14 18 19 13 removing 1-2 3-20 6-11 8-12 15-17
G+(17,18,4,5) contains Petersen
   via 4 9 14 10 20 11 17 19 13 16 removing 1-2 3-8 5-6 7-12 15-18
G+(17,18,4,9) contains Petersen
   via 5 6 11 12 8 10 16 13 19 18 removing 1-2 3-7 4-20 9-14 15-17
G+(17,18,5,10) contains Petersen
   via 5 6 16 13 9 20 10 14 17 19 removing 1-2 3-7 4-8 11-12 15-18
G+(17,18,6,11) contains Boat5
   via 1 2 3 4 5 17 7 8 9 10 11 12 13 14 15 16 19 18 removing 6-20
G+(17,18,7,11) contains Boat2
   via 1 2 3 4 5 6 20 8 9 10 11 18 13 14 15 16 19 17 removing 7-12
G+(17,18,7,12) contains Boat2
   via 1 2 3 4 5 6 7 8 9 10 11 18 13 14 15 16 19 17 removing 12-20
G+(17,18,8,12) contains Petersen
   via 4 5 10 16 7 9 14 18 19 13 removing 1-2 3-8 6-11 12-20 15-17
G+(17,18,8,13) contains Petersen
   via 5 6 11 12 8 14 13 20 19 18 removing 1-2 3-7 4-9 10-16 15-17
G+(17,18,9,13) contains Petersen
   via 5 6 11 12 8 10 16 13 19 18 removing 1-2 3-7 4-9 14-20 15-17
G+(17,18,9,14) contains Petersen
   via 5 6 11 12 8 10 16 13 19 18 removing 1-2 3-7 4-9 14-20 15-17
G+(17,18,10,14) contains Petersen
   via 5 6 11 12 8 10 16 13 17 19 removing 1-2 3-7 4-9 14-20 15-18
G+(17,18,10,16) contains Petersen
   via 5 6 11 12 8 20 16 13 17 19 removing 1-2 3-7 4-9 10-14 15-18
G+(17,18,11,16) contains Boat5
   via 1 2 3 4 5 17 7 8 9 10 20 12 13 14 15 16 19 18 removing 6-11
G+(17,18,13,16) contains Petersen
   via 6 9 13 12 11 19 20 16 14 18 removing 1-2 3-7 4-8 5-10 15-17


##############################################################
# Proof of (14.4)
G=Sailboat
# Checking (E6) for path 15  6  1  5 10 16 
G+(6,15,10,16)+(1,6,16,18) contains Thirdapex
   via 3 2 19 18 10 12 7 6 17 15 8 14 13 11 20 16 removing 1-5 4-9
G+(15,6,5,10)+(6,1,10,16) contains Petersen
   via 6 19 8 12 11 17 13 16 20 15 removing 1-5 2-7 3-4 9-14 10-18
G+(15,6,5,10)+(17,6,18,10) contains Boat3
   via 5 1 2 3 4 20 6 7 8 9 19 11 12 13 16 15 18 17 removing 10-14
G+(15,6,10,16)+(17,6,18,16) contains Boat3
   via 1 5 4 3 2 17 10 9 8 7 18 14 13 12 15 16 19 20 removing 6-11
# Checking (E6) for path 16 11  7 12 15 
G+(16,11,12,15)+(17,11,18,15) contains Boat3
   via 12 7 2 3 8 20 11 1 4 13 19 6 5 9 15 16 18 17 removing 10-14
# Checking (E6) for path 15 12  8 13 16 
G+(15,12,13,16)+(17,12,18,16) contains Boat3
   via 13 8 3 4 9 20 12 2 5 14 19 7 1 10 16 15 18 17 removing 6-11


##############################################################
# Proof of (15.2), claim (1)
G=Square1
# A-expansions:
G+(13,16,1,2) contains Petersen
   via 5 11 6 7 8 12 10 9 16 19 removing 1-20 2-3 4-15 13-18 14-17
G+(13,16,1,5) contains Petersen
   via 5 12 10 11 20 17 16 19 13 18 removing 1-2 3-14 4-15 6-7 8-9
G+(13,16,1,11) contains Petersen
   via 5 12 10 11 20 17 16 19 13 18 removing 1-2 3-14 4-15 6-7 8-9
G+(13,16,2,3) contains Petersen
   via 5 11 6 7 8 12 10 9 16 19 removing 1-2 3-20 4-15 13-18 14-17
G+(13,16,2,14) contains Petersen
   via 5 11 6 7 8 12 10 9 16 19 removing 1-2 3-20 4-15 13-18 14-17
G+(13,16,3,4) contains Petersen
   via 4 20 8 9 15 18 17 16 19 13 removing 1-2 3-14 5-12 6-7 10-11
G+(13,16,3,8) contains Petersen
   via 4 20 8 9 15 18 17 16 19 13 removing 1-2 3-14 5-12 6-7 10-11
G+(13,16,4,5) contains Petersen
   via 6 7 14 12 10 18 17 16 19 13 removing 1-11 2-3 4-15 5-20 8-9
G+(13,16,6,7) contains Petersen
   via 7 9 15 11 20 17 16 19 13 18 removing 1-2 3-14 4-8 5-12 6-10
G+(13,16,6,10) contains Petersen
   via 6 7 9 15 11 19 13 18 17 16 removing 1-2 3-14 4-8 5-12 10-20
G+(13,16,6,11) contains Petersen
   via 7 9 15 11 20 17 16 19 13 18 removing 1-2 3-14 4-8 5-12 6-10
G+(13,16,7,14) contains Petersen
   via 5 11 6 7 8 12 10 9 17 20 removing 1-2 3-14 4-15 13-18 16-19
G+(13,16,7,8) contains Petersen
   via 7 20 8 9 10 17 18 13 19 16 removing 1-2 3-14 4-15 5-12 6-11
G+(13,16,8,9) contains Petersen
   via 4 8 20 9 15 13 19 16 17 18 removing 1-2 3-14 5-11 6-7 10-12
G+(13,16,9,10) contains Petersen
   via 9 20 10 12 15 18 17 16 19 13 removing 1-5 2-14 3-4 6-11 7-8
G+(16,17,1,2) contains Petersen
   via 3 8 9 11 20 13 16 19 17 18 removing 1-5 2-14 4-15 6-7 10-12
G+(16,17,1,5) contains Petersen
   via 5 8 9 11 20 13 16 19 17 18 removing 1-2 3-14 4-15 6-7 10-12
G+(16,17,1,11) contains Petersen
   via 5 8 9 11 20 13 16 19 17 18 removing 1-2 3-14 4-15 6-7 10-12
G+(16,17,2,3) contains Petersen
   via 3 8 9 11 20 13 16 19 17 18 removing 1-5 2-14 4-15 6-7 10-12
G+(16,17,3,4) contains Petersen
   via 3 9 10 12 20 18 17 19 16 13 removing 1-5 2-14 4-15 6-11 7-8
G+(16,17,3,8) contains Starfish
   via 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
G+(16,17,4,5) contains Petersen
   via 4 15 9 12 20 18 17 19 16 13 removing 1-5 2-14 3-8 6-7 10-11
G+(16,17,5,12) contains Petersen
   via 5 15 9 12 20 18 17 19 16 13 removing 1-2 3-14 4-8 6-7 10-11
G+(16,17,6,7) contains Petersen
   via 6 10 9 15 11 19 17 18 13 16 removing 1-2 3-14 4-8 5-12 7-20
G+(16,17,6,10) contains Petersen
   via 9 10 20 11 15 17 19 16 13 18 removing 1-2 3-14 4-8 5-12 6-7
G+(16,17,6,11) contains Petersen
   via 9 10 20 11 15 17 19 16 13 18 removing 1-2 3-14 4-8 5-12 6-7
G+(16,17,7,8) contains Petersen
   via 6 10 9 15 11 19 17 18 13 16 removing 1-2 3-4 5-12 7-14 8-20
G+(16,17,8,9) contains Petersen
   via 6 7 14 12 10 18 17 19 16 13 removing 1-11 2-3 4-5 8-20 9-15
G+(16,17,9,10) contains Petersen
   via 6 7 14 12 10 18 17 19 16 13 removing 1-2 3-8 4-15 5-11 9-20
G+(16,17,10,12) contains Petersen
   via 8 9 10 20 12 17 18 13 16 19 removing 1-2 3-14 4-15 5-11 6-7
G+(17,18,1,2) contains Petersen
   via 6 10 9 15 11 17 19 18 13 16 removing 1-20 2-14 3-4 5-12 7-8
G+(17,18,1,5) contains Petersen
   via 5 15 9 10 12 19 18 13 16 17 removing 1-20 2-14 3-4 6-11 7-8
G+(17,18,2,3) contains Petersen
   via 6 10 9 15 11 17 19 18 13 16 removing 1-2 3-4 5-12 7-8 14-20
G+(17,18,3,4) contains Petersen
   via 6 10 9 15 11 17 19 18 13 16 removing 1-2 3-14 4-20 5-12 7-8
G+(17,18,3,8) contains Petersen
   via 6 10 9 15 11 17 19 18 13 16 removing 1-2 3-14 4-20 5-12 7-8
G+(17,18,4,5) contains Petersen
   via 9 10 12 13 18 15 20 19 17 16 removing 1-5 2-14 3-4 6-11 7-8
G+(17,18,4,15) contains Petersen
   via 5 11 6 7 8 12 10 9 19 17 removing 1-2 3-14 4-20 13-18 15-16
G+(17,18,5,12) contains Petersen
   via 5 11 10 12 20 16 17 19 18 13 removing 1-2 3-14 4-8 6-7 9-15
G+(17,18,6,7) contains Petersen
   via 6 20 7 14 11 16 13 18 19 17 removing 1-5 2-3 4-15 8-9 10-12
G+(17,18,6,10) contains Petersen
   via 7 9 10 12 14 18 19 17 16 13 removing 1-2 3-8 4-15 5-11 6-20
G+(17,18,7,8) contains Petersen
   via 6 10 9 15 11 17 19 18 13 16 removing 1-2 3-14 4-8 5-12 7-20
G+(17,18,8,9) contains Petersen
   via 6 10 9 15 11 17 19 18 13 16 removing 1-2 3-14 4-8 5-12 7-20
G+(17,18,9,15) contains Petersen
   via 7 9 13 18 11 17 16 15 20 19 removing 1-2 3-14 4-8 5-12 6-10
G+(17,18,9,10) contains Petersen
   via 6 10 13 18 11 17 16 15 20 19 removing 1-2 3-14 4-8 5-12 7-9
G+(17,18,10,12) contains Petersen
   via 6 7 12 20 10 18 13 16 17 19 removing 1-2 3-14 4-15 5-11 8-9
G+(18,13,1,2) contains Petersen
   via 5 11 6 7 8 12 10 9 18 19 removing 1-20 2-3 4-15 13-16 14-17
G+(18,13,1,5) contains Jaws
   via 17 18 11 1 2 14 7 6 19 20 3 8 16 13 12 5 4 15 9 10
G+(18,13,2,3) contains Petersen
   via 5 11 6 7 8 12 10 9 18 19 removing 1-2 3-20 4-15 13-16 14-17
G+(18,13,2,14) contains Petersen
   via 5 11 6 7 8 12 10 9 18 19 removing 1-2 3-20 4-15 13-16 14-17
G+(18,13,3,4) contains Petersen
   via 6 7 8 15 11 13 19 18 17 16 removing 1-2 3-14 4-20 5-12 9-10
G+(18,13,3,8) contains Petersen
   via 6 7 8 15 11 13 19 18 17 16 removing 1-2 3-14 4-20 5-12 9-10
G+(18,13,4,5) contains Petersen
   via 5 12 10 15 20 17 18 19 13 16 removing 1-11 2-3 4-8 6-7 9-14
G+(18,13,4,15) contains Petersen
   via 5 11 6 7 8 12 10 9 18 17 removing 1-2 3-14 4-20 13-19 15-16
G+(18,13,6,7) contains Petersen
   via 5 11 6 20 8 12 10 9 18 19 removing 1-2 3-14 4-15 7-17 13-16
G+(18,13,6,10) contains Jaws
   via 1 2 14 7 6 11 18 17 3 8 20 19 5 4 15 9 10 12 13 16
G+(18,13,7,14) contains Petersen
   via 5 11 6 7 8 12 10 9 18 19 removing 1-2 3-14 4-15 13-16 17-20
G+(18,13,7,8) contains Petersen
   via 6 7 20 15 11 13 19 18 17 16 removing 1-2 3-14 4-8 5-12 9-10
G+(18,13,8,9) contains Petersen
   via 6 7 20 15 11 13 19 18 17 16 removing 1-2 3-14 4-8 5-12 9-10
G+(18,13,9,15) contains Petersen
   via 9 10 11 15 20 17 18 19 13 16 removing 1-2 3-14 4-8 5-12 6-7
G+(18,13,9,10) contains Petersen
   via 6 7 9 15 11 13 19 18 17 16 removing 1-2 3-14 4-8 5-12 10-20
# B-expansions via (13,16,12,5)
G+(13,16,12,5)+(12,20,1,2) contains Petersen
   via 10 11 18 13 12 16 17 21 20 19 removing 1-22 2-3 4-8 5-15 6-7 9-14
G+(13,16,12,5)+(12,20,1,11) contains Petersen
   via 8 9 12 13 18 20 21 17 16 19 removing 1-5 2-3 4-15 6-10 7-14 11-22
G+(13,16,12,5)+(12,20,2,3) contains Petersen
   via 10 11 18 13 12 16 17 21 20 19 removing 1-2 3-22 4-8 5-15 6-7 9-14
G+(13,16,12,5)+(12,20,2,14) contains Petersen
   via 10 11 18 13 12 16 17 21 20 19 removing 1-2 3-22 4-8 5-15 6-7 9-14
G+(13,16,12,5)+(12,20,3,4) contains Petersen
   via 10 11 18 13 12 16 17 21 20 19 removing 1-2 3-14 4-22 5-15 6-7 8-9
G+(13,16,12,5)+(12,20,3,8) contains Petersen
   via 10 11 18 13 12 16 17 21 20 19 removing 1-2 3-14 4-22 5-15 6-7 8-9
G+(13,16,12,5)+(12,20,4,15) contains Petersen
   via 10 11 18 13 12 16 17 21 20 19 removing 1-2 3-14 4-5 6-7 8-9 15-22
G+(13,16,12,5)+(12,20,6,7) contains Petersen
   via 10 11 18 13 12 16 17 21 20 19 removing 1-2 3-14 4-8 5-15 6-22 7-9
G+(13,16,12,5)+(12,20,6,11) contains Petersen
   via 7 9 15 11 22 17 16 19 13 18 removing 1-2 3-14 4-8 5-20 6-10 12-21
G+(13,16,12,5)+(12,20,7,14) contains Petersen
   via 10 11 18 13 12 16 17 21 20 19 removing 1-2 3-14 4-8 5-15 6-7 9-22
G+(13,16,12,5)+(12,20,7,8) contains Petersen
   via 10 11 18 13 12 16 17 21 20 19 removing 1-2 3-14 4-8 5-15 6-7 9-22
G+(13,16,12,5)+(12,20,8,9) contains Petersen
   via 10 11 18 13 12 16 17 21 20 19 removing 1-2 3-14 4-8 5-15 6-7 9-22
G+(13,16,12,5)+(12,20,9,15) contains Jaws
   via 1 2 14 7 6 11 18 17 3 8 12 13 5 4 15 22 21 20 19 16 removing 9-10
G+(13,16,12,5)+(12,20,11,18) contains Diamond
   via 8 9 7 6 10 14 3 2 11 17 16 22 18 21 12 13 20 19 removing 1-5 4-15
G+(13,16,12,5)+(12,20,14,17) contains Petersen
   via 10 11 18 13 12 16 17 21 20 19 removing 1-2 3-14 4-8 5-15 6-7 9-22
G+(13,16,12,5)+(12,20,15,16) contains Concertina
   via 17 18 11 6 7 8 3 10 9 13 12 16 19 20 21 22 15 4 removing 1-5 2-14
G+(13,16,12,5)+(12,20,16,17) contains Petersen
   via 10 11 18 13 12 16 22 21 20 19 removing 1-2 3-14 4-8 5-15 6-7 9-17
G+(13,16,12,5)+(12,20,17,18) contains Petersen
   via 10 11 18 13 12 17 22 21 20 19 removing 1-2 3-14 4-8 5-15 6-7 9-16
# C-expansions via (13,16,12,5)
G+(13,16,12,5)+(12,13,11,1) contains Petersen
   via 6 7 19 16 10 18 13 21 14 17 removing 1-5 2-3 4-15 8-9 11-22 12-20
G+(13,16,12,5)+(12,13,11,6) contains Jaws
   via 1 2 14 7 22 11 18 17 3 8 21 13 5 4 15 9 12 20 19 16 removing 6-10
G+(13,16,12,5)+(19,20,15,4) contains Petersen
   via 12 13 19 16 15 20 21 22 18 17 removing 1-11 2-3 4-5 6-10 7-14 8-9
G+(13,16,12,5)+(19,20,15,9) contains Petersen
   via 3 4 20 10 9 18 21 22 15 17 removing 1-5 2-14 6-11 7-8 12-13 16-19
# D-expansion via (13,16,12,5)
G+(13,16,12,5)+(13,19,17,14) contains Petersen
   via 7 9 13 18 11 22 21 19 16 17 removing 1-2 3-14 4-8 5-15 6-10 12-20
# E-expansions via (13,16,12,5)
G+(13,16,12,5)+(19,13,18,17)+(18,22,14,2) contains Petersen
   via 6 10 9 23 11 17 16 19 21 22 removing 1-2 3-4 5-15 7-8 12-20 13-18 14-24
G+(13,16,12,5)+(19,13,18,17)+(18,22,14,7) contains Petersen
   via 2 3 8 9 18 14 24 23 22 17 removing 1-5 4-15 6-7 10-11 12-20 13-21 16-19
# B-expansions via (13,16,12,10)
G+(13,16,12,10)+(12,20,1,2) contains Petersen
   via 10 15 12 13 18 20 21 17 16 19 removing 1-22 2-3 4-8 5-11 6-7 9-14
G+(13,16,12,10)+(12,20,1,11) contains Petersen
   via 10 15 12 13 18 20 21 17 16 19 removing 1-5 2-3 4-8 6-7 9-14 11-22
G+(13,16,12,10)+(12,20,2,3) contains Petersen
   via 10 15 12 13 18 20 21 17 16 19 removing 1-2 3-22 4-8 5-11 6-7 9-14
G+(13,16,12,10)+(12,20,2,14) contains Petersen
   via 10 15 12 13 18 20 21 17 16 19 removing 1-2 3-22 4-8 5-11 6-7 9-14
G+(13,16,12,10)+(12,20,3,4) contains Petersen
   via 10 15 12 13 18 20 21 17 16 19 removing 1-2 3-14 4-22 5-11 6-7 8-9
G+(13,16,12,10)+(12,20,3,8) contains Petersen
   via 10 15 12 13 18 20 21 17 16 19 removing 1-2 3-14 4-22 5-11 6-7 8-9
G+(13,16,12,10)+(12,20,4,15) contains Jaws
   via 17 18 11 1 2 14 7 6 13 12 3 8 16 19 20 21 22 15 9 10 removing 4-5
G+(13,16,12,10)+(12,20,6,7) contains Petersen
   via 10 15 12 13 18 20 21 17 16 19 removing 1-2 3-14 4-8 5-11 6-22 7-9
G+(13,16,12,10)+(12,20,6,11) contains Petersen
   via 9 15 12 13 18 20 21 17 16 19 removing 1-5 2-14 3-4 6-10 7-8 11-22
G+(13,16,12,10)+(12,20,7,14) contains Petersen
   via 10 15 12 13 18 20 21 17 16 19 removing 1-2 3-14 4-8 5-11 6-7 9-22
G+(13,16,12,10)+(12,20,7,8) contains Petersen
   via 10 15 12 13 18 20 21 17 16 19 removing 1-2 3-14 4-8 5-11 6-7 9-22
G+(13,16,12,10)+(12,20,8,9) contains Petersen
   via 10 15 12 13 18 20 21 17 16 19 removing 1-2 3-14 4-8 5-11 6-7 9-22
G+(13,16,12,10)+(12,20,9,15) contains Petersen
   via 9 10 11 15 22 17 18 21 20 16 removing 1-2 3-14 4-8 5-12 6-7 13-19
G+(13,16,12,10)+(12,20,11,18) contains Diamond
   via 9 15 8 3 4 7 10 6 11 17 16 22 18 21 12 13 20 19 removing 1-5 2-14
G+(13,16,12,10)+(12,20,14,17) contains Petersen
   via 10 15 12 13 18 20 21 17 16 19 removing 1-2 3-14 4-8 5-11 6-7 9-22
G+(13,16,12,10)+(12,20,15,16) contains Concertina
   via 17 18 11 2 14 7 6 3 8 13 12 16 19 20 21 22 9 10 removing 1-5 4-15
G+(13,16,12,10)+(12,20,16,17) contains Petersen
   via 10 15 12 13 18 20 21 22 16 19 removing 1-2 3-14 4-8 5-11 6-7 9-17
G+(13,16,12,10)+(12,20,17,18) contains Petersen
   via 10 15 12 13 18 20 21 22 16 19 removing 1-2 3-14 4-8 5-11 6-7 9-17
# C-expansions via (13,16,12,10)
G+(13,16,12,10)+(12,13,11,1) contains Jaws
   via 6 7 14 2 22 11 18 17 8 3 21 13 10 9 15 4 12 20 19 16 removing 1-5
G+(13,16,12,10)+(12,13,11,6) contains Petersen
   via 6 10 9 15 21 17 18 13 19 16 removing 1-5 2-14 3-4 7-8 11-22 12-20
G+(13,16,12,10)+(19,20,15,4) contains Petersen
   via 6 7 14 20 10 18 17 15 22 21 removing 1-11 2-3 4-5 8-9 12-13 16-19
G+(13,16,12,10)+(19,20,15,9) contains Petersen
   via 12 13 19 16 15 20 21 22 18 17 removing 1-5 2-14 3-4 6-11 7-8 9-10
# D-expansion via (13,16,12,10)
G+(13,16,12,10)+(13,19,17,14) contains Petersen
   via 9 10 18 13 15 22 17 16 19 21 removing 1-2 3-14 4-8 5-11 6-7 12-20
# E-expansions via (13,16,12,10)
G+(13,16,12,10)+(19,13,18,17)+(18,22,14,2) contains Petersen
   via 6 10 9 24 14 18 15 17 22 23 removing 1-2 3-4 5-11 7-8 12-20 13-21 16-19
G+(13,16,12,10)+(19,13,18,17)+(18,22,14,7) contains Petersen
   via 9 10 11 14 24 15 18 23 22 17 removing 1-5 2-3 4-8 6-7 12-20 13-21 16-19
G+(16,17,15,4) contains Petersen
   via 3 4 12 10 9 18 13 16 19 17 removing 1-5 2-14 6-11 7-8 15-20
G+(16,17,15,9) contains Petersen
   via 6 7 14 12 10 18 17 19 16 13 removing 1-11 2-3 4-5 8-9 15-20
G+(17,18,14,2) contains Petersen
   via 6 10 9 15 11 17 19 18 13 16 removing 1-2 3-4 5-12 7-8 14-20
G+(17,18,14,7) contains Petersen
   via 2 3 8 9 11 17 19 18 13 16 removing 1-5 4-15 6-7 10-12 14-20
# B-expansions via (18,13,11,1)
G+(18,13,11,1)+(11,20,2,3) contains Petersen
   via 6 11 21 16 13 14 20 19 18 17 remo