# command: python3 bergeron_certificate.py
# started: 2026-10-27 02:02:26 UTC
# Python 3.13.17, python-flint 0.9.0, numpy 2.5.3, sympy 1.14.0
# machine: 2 cores, 7 GB RAM, Linux x86_64
# sha256 of the scripts in the directory:
#   62ba14c054023c20a139428938aa4561365d93366172e919afde228d09b40d4e  band_check.py
#   e3b29b32dee33a3771e46eee7fd3c7feb9d5281a0f880fb0ea2a9dc9bde9ea99  bergeron_certificate.py
#   a86969c6ce89c5a3aba23d4d30aa55d8fb9924613d794ab271728fe3f2035110  circle_check.py
#   0ad5f6f485561df541b4e83a0e780275e5077b2e3a6baa864ca0419d01ef15af  corner_check.py
#   85f217ba1cc63c5421bb2df726223642e8289baab3f46dc55e026417f27cbb21  cww_certificate.py
#   1b487046af3818f1b6e61f9903bb4dd3cbdb45e7d451c23cdce74faad8cf4eb0  pn_certificate.py
#   ea6a0e64e29ea4599808a3cb8023f9a18bfb4469f6b282d051f24034a5903108  pn_families.py
#   33684b0c7134b1b7da3e1e5fd944fe28c067fcc4255b832d327d3aea4043f665  row_check.py
#   0dd9195b2ba9a6ca36055c39fd90cd069ab530072d01786042400059e129e650  row_sweep.py
#   b077df5d9e0b9b7bf8be56cf2ab6763e5d8167a7408763c6ba54667837f077b3  rq_certificate.py
#
a= 3: step proved on {c >= C_a(b)} for 4 <= b < 8 and on {b >= 8, c >= b} (81 cells); C_a(4)=21; FT on |F_a|=30 pairs (max area 80) verified exactly: OK; FStep on F_a: OK  [0.0s]
a= 4: step proved on {c >= C_a(b)} for 5 <= b < 11 and on {b >= 11, c >= b} (125 cells); C_a(5)=37; FT on |F_a|=77 pairs (max area 180) verified exactly: OK; FStep on F_a: OK  [0.1s]
a= 5: step proved on {c >= C_a(b)} for 6 <= b < 15 and on {b >= 15, c >= b} (294 cells); C_a(6)=59; FT on |F_a|=157 pairs (max area 348) verified exactly: OK; FStep on F_a: OK  [0.2s]
a= 6: step proved on {c >= C_a(b)} for 7 <= b < 19 and on {b >= 19, c >= b} (954 cells); C_a(7)=85; FT on |F_a|=282 pairs (max area 588) verified exactly: OK; FStep on F_a: OK  [0.7s]
a= 7: step proved on {c >= C_a(b)} for 8 <= b < 23 and on {b >= 23, c >= b} (817 cells); C_a(8)=116; FT on |F_a|=462 pairs (max area 920) verified exactly: OK; FStep on F_a: OK  [0.8s]
a= 8: step proved on {c >= C_a(b)} for 9 <= b < 27 and on {b >= 27, c >= b} (3418 cells); C_a(9)=152; FT on |F_a|=706 pairs (max area 1359) verified exactly: OK; FStep on F_a: OK  [4.0s]
a= 9: step proved on {c >= C_a(b)} for 10 <= b < 31 and on {b >= 31, c >= b} (2555 cells); C_a(10)=192; FT on |F_a|=1023 pairs (max area 1910) verified exactly: OK; FStep on F_a: OK  [3.9s]
a=10: step proved on {c >= C_a(b)} for 11 <= b < 36 and on {b >= 36, c >= b} (3844 cells); C_a(11)=236; FT on |F_a|=1429 pairs (max area 2585) verified exactly: OK; FStep on F_a: OK  [6.7s]
a=11: step proved on {c >= C_a(b)} for 12 <= b < 41 and on {b >= 41, c >= b} (3748 cells); C_a(12)=286; FT on |F_a|=1933 pairs (max area 3420) verified exactly: OK; FStep on F_a: OK  [8.3s]
a=12: step proved on {c >= C_a(b)} for 13 <= b < 46 and on {b >= 46, c >= b} (4791 cells); C_a(13)=339; FT on |F_a|=2543 pairs (max area 4394) verified exactly: OK; FStep on F_a: OK  [13.1s]
a=13: step proved on {c >= C_a(b)} for 14 <= b < 51 and on {b >= 51, c >= b} (7664 cells); C_a(14)=398; FT on |F_a|=3270 pairs (max area 5558) verified exactly: OK; FStep on F_a: OK  [23.8s]
a=14: step proved on {c >= C_a(b)} for 15 <= b < 56 and on {b >= 56, c >= b} (10056 cells); C_a(15)=461; FT on |F_a|=4137 pairs (max area 6900) verified exactly: OK; FStep on F_a: OK  [35.8s]
a=15: step proved on {c >= C_a(b)} for 16 <= b < 61 and on {b >= 61, c >= b} (13504 cells); C_a(16)=528; FT on |F_a|=5139 pairs (max area 8432) verified exactly: OK; FStep on F_a: OK  [81.5s]
a=16: step proved on {c >= C_a(b)} for 17 <= b < 67 and on {b >= 67, c >= b} (14411 cells); C_a(17)=600; FT on |F_a|=6299 pairs (max area 10183) verified exactly: OK; FStep on F_a: OK  [80.1s]
a=17: step proved on {c >= C_a(b)} for 18 <= b < 73 and on {b >= 73, c >= b} (21292 cells); C_a(18)=676; FT on |F_a|=7624 pairs (max area 12150) verified exactly: OK; FStep on F_a: OK  [127.1s]
a=18: step proved on {c >= C_a(b)} for 19 <= b < 79 and on {b >= 79, c >= b} (25172 cells); C_a(19)=757; FT on |F_a|=9129 pairs (max area 14364) verified exactly: OK; FStep on F_a: OK  [173.7s]
a=19: step proved on {c >= C_a(b)} for 20 <= b < 85 and on {b >= 85, c >= b} (31307 cells); C_a(20)=843; FT on |F_a|=10822 pairs (max area 16840) verified exactly: OK; FStep on F_a: OK  [240.6s]
a=20: step proved on {c >= C_a(b)} for 21 <= b < 91 and on {b >= 91, c >= b} (31355 cells); C_a(21)=933; FT on |F_a|=12722 pairs (max area 19572) verified exactly: OK; FStep on F_a: OK  [343.3s]
ALL CHECKS PASSED

real	19m11.157s
user	17m30.050s
sys	0m1.666s
# finished: 2026-10-27 02:21:37 UTC