(benchmark Isabelle
:extrasorts ( T2 T1 T4 T3)
:extrafuns (
(uf_3 Int T1)
(uf_7 T2 T4 T4)
(uf_1 T2 T1 T1)
(uf_6 T3 T4 Int)
(uf_4 T1 Int)
(uf_5 T2)
(uf_2 T2)
(uf_10 Int)
(uf_8 T3)
(uf_9 T4)
)
:assumption (forall (?x1 T1) (= (uf_1 uf_2 ?x1) (uf_3 (div (uf_4 ?x1) 2))))
:assumption (forall (?x2 T1) (= (uf_1 uf_5 ?x2) (uf_3 (mod (uf_4 ?x2) 2))))
:assumption (forall (?x3 T1) (= (uf_3 (uf_4 ?x3)) ?x3))
:assumption (forall (?x4 Int) (implies (<= 0 ?x4) (= (uf_4 (uf_3 ?x4)) ?x4)))
:assumption (forall (?x5 Int) (implies (< ?x5 0) (= (uf_4 (uf_3 ?x5)) 0)))
:assumption (forall (?x6 T3) (?x7 T4) (= (mod (uf_6 ?x6 ?x7) 2) (mod (uf_6 ?x6 (uf_7 uf_5 ?x7)) 2)))
:assumption (forall (?x8 T3) (?x9 T4) (= (+ (* (uf_6 ?x8 (uf_7 uf_2 ?x9)) 2) (uf_6 ?x8 (uf_7 uf_5 ?x9))) (uf_6 ?x8 ?x9)))
:assumption (iff (= (uf_6 uf_8 uf_9) uf_10) (implies (= (mod (uf_6 uf_8 (uf_7 uf_5 uf_9)) 2) (mod uf_10 2)) (not (= (uf_6 uf_8 (uf_7 uf_2 uf_9)) (div (- uf_10 (uf_6 uf_8 (uf_7 uf_5 uf_9))) 2)))))
:formula true
)