;---------------------- A KenKen Puzzle from a book ----------------------
; 3 2 4 5 1
; 2 5 1 4 3
; 1 3 5 2 4
; 5 4 3 1 2
; 4 1 2 3 5
; 
; --
; 
; operators
; 
; b11 : 6+
; b12 : 8*
; b14 : 4-
; 
; b22: 15+
; b23: 14-
; b24: 1-
; 
; b34: 4x
; b35: 4
; 
; b41: 1-
; b52: 2/
; b54: 2-
; 
; --
; 
; Plots
; 
; b11,b21,b31
; b12,b13
; b14,b15
; b22,b32,b42,b43
; b23,b33
; b24,b25
; b34,b44,b45
; b34
; b41,b51
; b52,b53
; b54,b55
; 
; 
; --
; 
; b11+b21+b31 = 6
; b121*b13 = 4
; b14-b15=4 OR b15-b14=4
; b22+b32+b42+b43=15
; b32-b33=4 OR b33-b32=4
; b24-b25=1 OR b25-b24=1
; b34+b44*b45=4
; b35=4
; b41-b51=1 OR b51-b41=1
; b53/b52=2 OR b52/b53=2
; b54-b55=2 OR b55-b54=2

;---------------------- The above is encoded below ----------------------
  
(declare-const b11 Int)
(declare-const b12 Int)
(declare-const b13 Int)
(declare-const b14 Int)
(declare-const b15 Int)
(declare-const b21 Int)
(declare-const b22 Int)
(declare-const b23 Int)
(declare-const b24 Int)
(declare-const b25 Int)
(declare-const b31 Int)
(declare-const b32 Int)
(declare-const b33 Int)
(declare-const b34 Int)
(declare-const b35 Int)
(declare-const b41 Int)
(declare-const b42 Int)
(declare-const b43 Int)
(declare-const b44 Int)
(declare-const b45 Int)
(declare-const b51 Int)
(declare-const b52 Int)
(declare-const b53 Int)
(declare-const b54 Int)
(declare-const b55 Int)


(assert (> b11 0))
(assert (> b12 0))
(assert (> b13 0))
(assert (> b14 0))
(assert (> b15 0))
(assert (> b21 0))
(assert (> b22 0))
(assert (> b23 0))
(assert (> b24 0))
(assert (> b25 0))
(assert (> b31 0))
(assert (> b32 0))
(assert (> b33 0))
(assert (> b34 0))
(assert (> b35 0))
(assert (> b41 0))
(assert (> b42 0))
(assert (> b43 0))
(assert (> b44 0))
(assert (> b45 0))
(assert (> b51 0))
(assert (> b52 0))
(assert (> b53 0))
(assert (> b54 0))
(assert (> b55 0))


(assert (<= b11 5))
(assert (<= b12 5))
(assert (<= b13 5))
(assert (<= b14 5))
(assert (<= b15 5))
(assert (<= b21 5))
(assert (<= b22 5))
(assert (<= b23 5))
(assert (<= b24 5))
(assert (<= b25 5))
(assert (<= b31 5))
(assert (<= b32 5))
(assert (<= b33 5))
(assert (<= b34 5))
(assert (<= b35 5))
(assert (<= b41 5))
(assert (<= b42 5))
(assert (<= b43 5))
(assert (<= b44 5))
(assert (<= b45 5))
(assert (<= b51 5))
(assert (<= b52 5))
(assert (<= b53 5))
(assert (<= b54 5))
(assert (<= b55 5))

(assert (not (= b11 b12)))
(assert (not (= b11 b13)))
(assert (not (= b11 b14)))
(assert (not (= b11 b15 )))
(assert (not (= b12 b13)))
(assert (not (= b12 b14)))
(assert (not (= b12 b15)))
(assert (not (= b13 b14)))
(assert (not (= b13 b15)))
(assert (not (= b14 b15)))

(assert (not (= b21 b22)))
(assert (not (= b21 b23)))
(assert (not (= b21 b24)))
(assert (not (= b21 b25 )))
(assert (not (= b22 b23)))
(assert (not (= b22 b24)))
(assert (not (= b22 b25)))
(assert (not (= b23 b24)))
(assert (not (= b23 b25)))
(assert (not (= b24 b25)))

(assert (not (= b31 b32)))
(assert (not (= b31 b33)))
(assert (not (= b31 b34)))
(assert (not (= b31 b35 )))
(assert (not (= b32 b33)))
(assert (not (= b32 b34)))
(assert (not (= b32 b35)))
(assert (not (= b33 b34)))
(assert (not (= b33 b35)))
(assert (not (= b34 b35)))

(assert (not (= b41 b42)))
(assert (not (= b41 b43)))
(assert (not (= b41 b44)))
(assert (not (= b41 b45 )))
(assert (not (= b42 b43)))
(assert (not (= b42 b44)))
(assert (not (= b42 b45)))
(assert (not (= b43 b44)))
(assert (not (= b43 b45)))
(assert (not (= b44 b45)))

(assert (not (= b51 b52)))
(assert (not (= b51 b53)))
(assert (not (= b51 b54)))
(assert (not (= b51 b55 )))
(assert (not (= b52 b53)))
(assert (not (= b52 b54)))
(assert (not (= b52 b55)))
(assert (not (= b53 b54)))
(assert (not (= b53 b55)))
(assert (not (= b54 b55)))

(assert (not (= b11 b21)))
(assert (not (= b11 b31)))
(assert (not (= b11 b41)))
(assert (not (= b11 b51)))
(assert (not (= b21 b31)))
(assert (not (= b21 b41)))
(assert (not (= b21 b51)))
(assert (not (= b31 b41)))
(assert (not (= b31 b51)))
(assert (not (= b41 b51)))

(assert (not (= b12 b22)))
(assert (not (= b12 b32)))
(assert (not (= b12 b42)))
(assert (not (= b12 b52)))
(assert (not (= b22 b32)))
(assert (not (= b22 b42)))
(assert (not (= b22 b52)))
(assert (not (= b32 b42)))
(assert (not (= b32 b52)))
(assert (not (= b42 b52)))

(assert (not (= b13 b23)))
(assert (not (= b13 b33)))
(assert (not (= b13 b43)))
(assert (not (= b13 b53)))
(assert (not (= b23 b33)))
(assert (not (= b23 b43)))
(assert (not (= b23 b53)))
(assert (not (= b33 b43)))
(assert (not (= b33 b53)))
(assert (not (= b43 b53)))

(assert (not (= b14 b24)))
(assert (not (= b14 b34)))
(assert (not (= b14 b44)))
(assert (not (= b14 b54)))
(assert (not (= b24 b34)))
(assert (not (= b24 b44)))
(assert (not (= b24 b54)))
(assert (not (= b34 b44)))
(assert (not (= b34 b54)))
(assert (not (= b44 b54)))

(assert (not (= b15 b25)))
(assert (not (= b15 b35)))
(assert (not (= b15 b45)))
(assert (not (= b15 b55)))
(assert (not (= b25 b35)))
(assert (not (= b25 b45)))
(assert (not (= b25 b55)))
(assert (not (= b35 b45)))
(assert (not (= b35 b55)))
(assert (not (= b45 b55)))

(check-sat)
(get-model)

(assert (= (+ b11 b21 b31) 6))
(assert (= (* b12 b13) 8))
(assert (= (+ b22 b32 b42 b43) 15))

(assert (= (* b34 b44 b45) 4))

(assert (= b35 4))

(check-sat)
(get-model)

(assert (or (= (- b14 b15) 4) (= (- b15 b14) 4)))
(check-sat)
(get-model)

(assert (or (= (- b23 b33) 4) (= (- b33 b23) 4)))
(check-sat)
(get-model)

(assert (or (= (- b24 b25) 1) (= (- b25 b24) 1)))
(check-sat)
(get-model)

(assert (or (= (- b41 b51) 1) (= (- b51 b41) 1)))
(check-sat)
(get-model)

(assert (or (= (div b52 b53) 2) (= (div b53 b52) 2)))
(check-sat)
(get-model)

(assert (or (= (- b54 b55) 2) (= (- b55 b54) 2)))
(check-sat)
(get-model)

(check-sat)
(get-model)