Prelims
a) R1C34 = {49/58/67}, no 1,2,3
b) R1C67 = {29/38/47/56}, no 1
c) R34C1 = {16/25/34}, no 7,8,9
d) R34C9 = {19/28/37/46}, no 5
e) R4C6 + R6C4 = {29/38/47/56}, no 1
f) R67C1 = {79}
g) R67C9 = {16/25/34}, no 7,8,9
h) R9C34 = {12}
i) R9C67 = {18/27/36/45}, no 5
j) 8(3) cage at R2C7 = {125/134}
k) 10(3) cage at R3C3 = {127/136/145/235}, no 8,9
l) 19(3) cage at R3C7 = {289/379/469/478/568}, no 1
m) 22(3) cage at R6C3 = {589/679}
Steps resulting directly and indirectly from Prelims
1a. Naked pair {79} in R67C1, locked for C1
1b. Naked pair {12} in R9C34, locked for R9, clean-up: no 7,8 in R9C67
1c. 8(3) cage at R2C7 = {125/134}, 1 locked for N3, clean-up: no 9 in R4C9
2. 45 rule on N5 1 innie R5C5 = 5, clean-up: no 6 in R4C6 + R6C4
3. Caged X-Wing for 9 in R67C1 and 22(3) cage at R6C3, no other 9 in R67, clean-up: no 2 in R4C6
3a. 18(3) cage at R6C7 = {378/468/567}, no 1,2
3b. 10(3) cage at R3C3 = {127/136/145/235}
3c. 7 of {127} must be in R34C3 (R34C3 cannot be {12} which clashes with R9C3), no 7 in R3C4
4. 45 rule on N3 3 innies R1C7 + R3C79 = 20 = {389/479/569/578}, no 2, clean-up: no 9 in R1C6, no 8 in R4C9
5. 45 rule on N7 3 innies R7C13 + R9C3 = 16 = {169/178/259} (cannot be {268} because R7C1 only contains 7,9)
5a. R7C1 = 7,9 -> no 7,9 in R7C3
5b. 22(3) cage at R6C3 = {589/679}
5c. 6 of {679} must be in R7C3 -> no 6 in R6C3 + R7C4
6. 45 rule on R1 2 outies R2C19 = 1 innie R1C5 + 10
6a. Min R2C19 = 11, no 1 in R2C1, no 2 in R2C9
6b. Max R2C19 = 17 -> max R1C5 = 7
7. 45 rule on R9 1 innie R9C5 = 2 outies R8C19 + 2
7a. Max R8C19 = 7, no 7,8,9 in R8C19
7b. Min R8C19 = 3 -> no 3,4 in R9C5
8. 45 rule on C89 3 outies R258C7 = 1 innie R5C9 + 2
8a. Max R258C7 = 11, no 9 in R58C7
8b. Min R258C7 = 6 -> min R5C9 = 4
9. 45 rule on N7 4(2+2) outies R6C13 + R79C4 = 25, max R6C13 = 17 -> min R79C4 = 8, no 5 in R7C4
9a. R67C1 and 22(3) cage both contain 9 -> R6C13 + R79C4 = [7972/7981/9592] (R6C13 cannot be [97/98] which together with R7C4 = 9 make R6C13 + R79C4 more than 25) -> no 7,8 in R6C3
10. 45 rule on N4 5 innies R456C1 + R46C3 = 22, R6C13 = [79/95/97] = 14,16 -> R4C13 + R5C1 = 6,8 = {123/125/134}, no 6,7,8, 1 locked for N4, clean-up: no 1 in R3C1
11. 45 rule on N8 5 innies R7C46 + R9C456 = 23 = {13469/13478/13568/14567/23468/23567} (cannot be {12389/12479/12569/12578} because 1,2 only in R9C4, cannot be {23459} because R7C4 + R9C5 are both at least 6)
11a. R7C46 + R9C456 only contain two of 6,7,8,9 -> no 6,7,8 in R7C4 + R9C6, clean-up: no 3 in R9C7
11b. 18(3) cage at R6C7 (step 3) = {378/468/567}
11c. R7C6 = {345} -> no 3,4,5 in R67C7
12. 45 rule on N9 3 innies R7C79 + R9C7 = 14
12a. 14(3) cage must contain at least one of 1,2,3 -> R7C9 = {123}, clean-up: no 1,2,3 in R6C9
13. R7C46 + R9C456 (step 11) = {13469/13478/13568/14567/23468/23567}
13a. R6C13 + R79C4 (step 9a) = [7972/7981] (cannot be [9592] because R7C46 + R9C456 cannot contain both of 2,9) -> R6C13 = [79], R7C1 = 9, clean-up: no 4 in R1C4, no 4 in R4C6
13b. 22(3) cage at R6C3 = {589/679}, 5,6 only in R7C3 -> R7C3 = {56}
13c. R456C1 + R46C3 = 22 (step 10), R6C13 = [79] = 16 -> R4C13 + R5C1 = 6 = {123}, locked for N4, clean-up: no 2,3 in R3C1
13d. 23(4) cage at R4C2 = {4568}, 5 locked for C2
13e. R79C4 = [72/81] -> R7C46 + R9C456 = {13478/13568/23567}, no 9, 3 locked for C6 and N8, clean-up: no 8 in R1C7, no 8 in R6C4
14. 9 in R9 only in R9C89, locked for N9
14a. 16(3) cage at R8C9 contains 9 = {169/259/349}, no 7,8
15. Hidden killer pair 7,8 in 15(3) cage at R8C1 and R9C5 for R9, 15(3) cage cannot contain both of 7,8 -> 15(3) cage must contain one of 7,8 and R9C5 = {78}
15a. Naked pair {78} in R7C4 + R9C5, locked for N8
15b. R7C46 + R9C456 (step 13e) = {13478} (only remaining combination) -> R9C4 = 1, R79C6 = {34}, locked for C6 and N8, clean-up: no 7 in R1C7, no 4 in R9C7
15c. R7C13 + R9C3 = 16 (step 5), R7C1 = 9, R9C3 = 2 -> R7C3 = 5, R7C4 = 8 (cage sum for 22(3) cage), R9C5 = 7
16. 18(3) cage at R6C7 (step 3) = {378/468} -> R6C7 = 8
16a. R8C8 = 8 (hidden single in N9)
16b. 15(3) cage at R7C8 = {168/258/348}, no 7
16c. R7C7 = 7 (hidden single in N9) -> R7C6 = 3, R9C6 = 4 -> R9C7 = 5
16d. R7C79 + R9C7 = 14 (step 12), R79C7 = [75] -> R7C9 = 2, R6C9 = 5, R7C5 = 6, clean-up: no 6 in R1C6, no 8 in R3C9
16e. 23(4) cage at R4C2 = {4568} -> R4C2 = 5, 8 locked for R5
17. R1C7 + R3C79 (step 4) = {479} (only remaining combination) R3C9 = 7, R13C7 = {49}, locked for C7 and N3 -> 8(3) cage at R2C7 = {125}, locked for N3, R4C9 = 3, R4C13 = [21], R5C1 = 3, R3C1 = 5, R4C7 = 6, clean-up: no 5,8 in R1C6
17a. Naked pair {68} in R12C9, locked for C9 and N3 -> R1C8 = 3, R9C89 = [69] , R5C9 = 4, R8C9 = 1
17b. R9C12 = [83], R8C1 = 4 (cage sum), R12C1 = [16], R1C2 = 7 (cage sum)
18. R6C2 = 4 (hidden single in N4)
18a. 1 in N5 only in 14(3) cage at R5C6 = {167} (only possible combination) -> R5C6 = 7, R6C56 = [16], R6C8 = 2, R6C4 = 3 -> R4C6 = 8
and the rest is naked singles.