0.11/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.13 % Command : do_CVC4 %s 0.13/0.34 % Computer : n025.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 180 0.13/0.34 % DateTime : Thu Aug 29 15:16:00 EDT 2019 0.13/0.34 % CPUTime : 0.92/1.14 %----Proving TF0_NAR, FOF, or CNF 0.92/1.15 ------- cvc4-fof casc 27 : /export/starexec/sandbox2/benchmark/theBenchmark.p at 180... 0.92/1.15 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-quant-cf --full-saturate-quant at 20... 15.16/15.39 % SZS status Theorem for theBenchmark 15.16/15.39 % SZS output start Proof for theBenchmark 15.16/15.39 (skolem (forall ((K_2 $$unsorted)) (not (forall ((X $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (norm_norm real) (hAPP complex real im X))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real (norm_norm complex) X)) K_2))) )) ) 15.16/15.39 ( skv_1 ) 15.16/15.39 ) 15.16/15.39 (skolem (forall ((K_2 $$unsorted)) (or (not (forall ((X $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (norm_norm real) (hAPP complex real re X))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real (norm_norm complex) X)) K_2))) )) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) K_2)))) ) 15.16/15.39 ( skv_2 ) 15.16/15.39 ) 15.16/15.39 (skolem (forall ((K_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) K_2))) (not (forall ((X $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (norm_norm real) (hAPP complex real im X))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real (norm_norm complex) X)) K_2))) ))) ) 15.16/15.39 ( skv_3 ) 15.16/15.39 ) 15.16/15.39 (skolem (forall ((X $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (hAPP int int (hAPP int _let_1 (plus_plus int) (hAPP int int (hAPP int _let_1 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (zero_zero int)) X))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) X) _let_2))) (not (forall ((Y $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) Y) _let_2))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) Y) _let_2))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (zero_zero int)) Y))) (= (ti int Y) (ti int X))) )) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) X) _let_2))))))) ) 15.16/15.39 ( skv_4 ) 15.16/15.39 ) 15.16/15.39 (skolem (forall ((X $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (zero_zero real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (not (forall ((Y $$unsorted)) (or (not (= _let_2 (hAPP real real cos Y))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Y) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 _let_2) Y))) (= X Y)) )) (not (= _let_2 (hAPP real real cos X))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 _let_2) X))))))) ) 15.16/15.39 ( skv_5 ) 15.16/15.39 ) 15.16/15.39 (skolem (forall ((K_2 $$unsorted)) (not (forall ((X $$unsorted)) (let ((_let_0 (norm_norm complex))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP complex real _let_0 (hAPP complex complex cnj X))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real _let_0 X)) K_2)))) )) ) 15.16/15.39 ( skv_6 ) 15.16/15.39 ) 15.16/15.39 (skolem (forall ((K_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) K_2))) (not (forall ((X $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (norm_norm real) (hAPP complex real re X))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real (norm_norm complex) X)) K_2))) ))) ) 15.16/15.39 ( skv_7 ) 15.16/15.39 ) 15.16/15.39 (skolem (forall ((K_2 $$unsorted)) (or (not (forall ((X $$unsorted)) (let ((_let_0 (norm_norm complex))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP complex real _let_0 (hAPP complex complex cnj X))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real _let_0 X)) K_2)))) )) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) K_2)))) ) 15.16/15.39 ( skv_8 ) 15.16/15.39 ) 15.16/15.39 (skolem (forall ((K_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) K_2))) (not (forall ((X $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (norm_norm real) (hAPP complex real im X))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real (norm_norm complex) X)) K_2))) ))) ) 15.16/15.39 ( skv_9 ) 15.16/15.39 ) 15.16/15.39 (skolem (forall ((S_1 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (hAPP int int (hAPP int _let_1 (plus_plus int) (hAPP int int (hAPP int _let_1 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (zero_zero int)) S_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) S_1) _let_2))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) S_1) _let_2))))))) ) 15.16/15.39 ( skv_10 ) 15.16/15.39 ) 15.16/15.39 (skolem (forall ((K_2 $$unsorted)) (not (forall ((X $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (norm_norm real) (hAPP complex real re X))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real (norm_norm complex) X)) K_2))) )) ) 15.16/15.39 ( skv_11 ) 15.16/15.39 ) 15.16/15.39 (skolem (forall ((K_2 $$unsorted)) (or (not (forall ((X $$unsorted)) (let ((_let_0 (norm_norm complex))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP complex real _let_0 (hAPP complex complex cnj X))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real _let_0 X)) K_2)))) )) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) K_2)))) ) 15.16/15.39 ( skv_12 ) 15.16/15.39 ) 15.16/15.39 (skolem (forall ((T_4 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (one_one int))) (let ((_let_3 (plus_plus int))) (let ((_let_4 (hAPP int int bit0 (hAPP int int bit1 pls)))) (not (= (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) _let_4))) _let_2) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_4))) m)) _let_2)) T_4)))))))) ) 15.16/15.39 ( skv_13 ) 15.16/15.39 ) 15.16/15.39 (skolem (forall ((S1 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (number_number_of int))) (let ((_let_3 (hAPP int int bit0 (hAPP int int bit1 pls)))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) S1) (hAPP int nat (number_number_of nat) _let_3))) (hAPP int int _let_2 min_1)) (hAPP int int (hAPP int _let_1 (plus_plus int) (hAPP int int (hAPP int _let_1 (times_times int) (hAPP int int _let_2 (hAPP int int bit0 _let_3))) m)) (one_one int))))))))) ) 15.16/15.39 ( skv_14 ) 15.16/15.39 ) 15.16/15.39 (skolem (forall ((P_1 $$unsorted)) (hBOOL P_1) ) 15.16/15.39 ( skv_15 ) 15.16/15.39 ) 15.16/15.39 (instantiation (forall ((K $$unsorted)) (let ((_let_0 (fun int bool))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (hAPP int int bit1 K)) pls)) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) K) pls)))) ) 15.16/15.39 ( (one_one int) ) 15.16/15.39 ( pls ) 15.16/15.39 ( (hAPP int int bit1 pls) ) 15.16/15.39 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.16/15.39 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.16/15.39 ( min_1 ) 15.16/15.39 ( s ) 15.16/15.39 ( t ) 15.16/15.39 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.16/15.39 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.16/15.39 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 15.16/15.39 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 15.16/15.39 ( skv_4 ) 15.16/15.39 ( skv_10 ) 15.16/15.39 ) 15.16/15.39 (instantiation (forall ((X_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real cos X_1)) (one_one real))) ) 15.16/15.39 ( (zero_zero real) ) 15.16/15.39 ( pi ) 15.16/15.39 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.39 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.39 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.16/15.39 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.16/15.39 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.16/15.39 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.16/15.39 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.16/15.39 ( skv_5 ) 15.16/15.39 ) 15.16/15.39 (instantiation (forall ((N $$unsorted) (Ma $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP int real (number_number_of real) N)) (hAPP int real (real_1 int) Ma))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP int int (number_number_of int) N)) Ma))) ) 15.16/15.39 ( pls, (one_one int) ) 15.16/15.39 ( pls, min_1 ) 15.16/15.39 ( pls, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.39 ( pls, s ) 15.16/15.39 ( pls, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.16/15.39 ( pls, (hAPP int int (number_number_of int) pls) ) 15.16/15.39 ( pls, skv_4 ) 15.16/15.39 ( pls, skv_10 ) 15.16/15.39 ( (hAPP int int bit1 pls), t ) 15.16/15.39 ) 15.16/15.39 (instantiation (forall ((Ma $$unsorted) (N $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP int real (real_1 int) Ma)) (hAPP int real (number_number_of real) N))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) Ma) (hAPP int int (number_number_of int) N)))) ) 15.16/15.39 ( (zero_zero int), pls ) 15.16/15.39 ( (zero_zero int), (hAPP int int bit1 pls) ) 15.16/15.39 ( (zero_zero int), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.16/15.39 ( (zero_zero int), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.16/15.39 ( min_1, pls ) 15.16/15.39 ) 15.16/15.39 (instantiation (forall ((N_1 $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) (hAPP nat nat fact N_1))) ) 15.16/15.39 ( (zero_zero nat) ) 15.16/15.39 ) 15.16/15.39 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_0 (fun int bool))) (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong A_1) B) (one_one int)))) ) 15.16/15.39 ( s1, s ) 15.16/15.39 ( s1, skv_4 ) 15.16/15.39 ( s1, skv_10 ) 15.16/15.39 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.16/15.39 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.39 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.16/15.39 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.16/15.39 ) 15.16/15.39 (instantiation (forall ((Ma $$unsorted) (X $$unsorted) (Xa $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int _let_1 zcong X) Xa) Ma)) (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int _let_1 zcongm Ma) X) Xa))))) ) 15.16/15.39 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s1, s ) 15.16/15.39 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s1, skv_4 ) 15.16/15.39 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s1, skv_10 ) 15.16/15.39 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.16/15.39 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.39 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.16/15.39 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.16/15.39 ) 15.16/15.39 (instantiation (forall ((X_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (abs_abs real) (hAPP complex real im X_1))) (hAPP complex real (norm_norm complex) X_1))) ) 15.16/15.39 ( (one_one complex) ) 15.16/15.39 ( ii ) 15.16/15.39 ( (zero_zero complex) ) 15.16/15.39 ) 15.16/15.39 (instantiation (forall ((K $$unsorted)) (= (hBOOL (hAPP int bool (iszero int) (hAPP int int (number_number_of int) K))) (hBOOL (hAPP rat bool (iszero rat) (hAPP int rat (number_number_of rat) K)))) ) 15.16/15.39 ( pls ) 15.16/15.39 ( (hAPP int int bit1 pls) ) 15.16/15.39 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.16/15.39 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.16/15.39 ( min_1 ) 15.16/15.39 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.39 ) 15.16/15.39 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real (fun real real)))) (let ((_let_2 (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP real real cos X_2)) (hAPP real real sin X_2)))) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP (fun real real) (fun real _let_0) (deriv real) (hAPP (fun real real) (fun real real) (hAPP _let_1 (fun (fun real real) (fun real real)) (combs real real real) (hAPP (fun real real) _let_1 (hAPP _let_1 (fun (fun real real) _let_1) (combb real (fun real real) real) (times_times real)) sin)) sin)) X_2) (hAPP real real (hAPP real (fun real real) (plus_plus real) _let_2) _let_2)))))) ) 15.16/15.39 ( (zero_zero real) ) 15.16/15.39 ( pi ) 15.16/15.39 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.39 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.39 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.16/15.39 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.16/15.39 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.16/15.39 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.16/15.39 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.16/15.39 ( skv_5 ) 15.16/15.39 ) 15.16/15.39 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted)) (let ((_let_0 (combc X_a X_b X_c))) (= _let_0 (ti (fun (fun X_a (fun X_b X_c)) (fun X_b (fun X_a X_c))) _let_0))) ) 15.16/15.39 ( bool, bool, bool ) 15.16/15.39 ( bool, nat, bool ) 15.16/15.39 ( bool, int, bool ) 15.16/15.39 ( bool, real, bool ) 15.16/15.39 ( bool, (product_prod int int), bool ) 15.16/15.39 ( nat, nat, bool ) 15.16/15.39 ( nat, nat, nat ) 15.16/15.39 ( nat, nat, (fun nat bool) ) 15.16/15.39 ( nat, nat, (product_prod nat nat) ) 15.16/15.39 ( nat, nat, (fun (product_prod nat nat) bool) ) 15.16/15.39 ( nat, nat, (product_prod int int) ) 15.16/15.39 ( nat, int, bool ) 15.16/15.39 ( nat, int, nat ) 15.16/15.39 ( nat, int, int ) 15.16/15.39 ( nat, int, real ) 15.16/15.39 ( nat, int, (fun bool bool) ) 15.16/15.39 ( nat, (fun nat bool), bool ) 15.16/15.39 ( nat, (fun nat bool), (fun bool bool) ) 15.16/15.39 ( nat, (fun nat nat), (fun nat bool) ) 15.16/15.39 ( nat, (fun nat nat), (fun nat nat) ) 15.16/15.39 ( nat, (fun nat nat), real ) 15.16/15.39 ( nat, real, real ) 15.16/15.39 ( nat, real, (product_prod real real) ) 15.16/15.39 ( nat, (fun nat real), bool ) 15.16/15.39 ( nat, (fun nat real), real ) 15.16/15.39 ( nat, (fun nat real), (fun real real) ) 15.16/15.39 ( nat, code_code_numeral, nat ) 15.16/15.39 ( int, nat, int ) 15.16/15.39 ( int, int, bool ) 15.16/15.39 ( int, int, int ) 15.16/15.39 ( int, int, (fun int bool) ) 15.16/15.39 ( int, int, (fun int (fun int bool)) ) 15.16/15.39 ( int, int, real ) 15.16/15.39 ( int, int, rat ) 15.16/15.39 ( int, int, (product_prod int int) ) 15.16/15.39 ( int, int, (fun (fun int bool) bool) ) 15.16/15.39 ( int, int, (fun bool bool) ) 15.16/15.39 ( int, int, (fun (product_prod int int) bool) ) 15.16/15.39 ( int, int, (product_prod int (product_prod int int)) ) 15.16/15.39 ( int, int, (fun int (product_prod int (product_prod int int))) ) 15.16/15.39 ( int, int, (fun int (fun int (product_prod int (product_prod int int)))) ) 15.16/15.39 ( int, int, (fun int (fun int (fun int (product_prod int (product_prod int int))))) ) 15.16/15.39 ( int, int, (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))) ) 15.16/15.39 ( int, int, (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))) ) 15.16/15.39 ( int, int, (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))) ) 15.16/15.39 ( int, (fun int bool), bool ) 15.16/15.39 ( int, (fun int bool), (fun int bool) ) 15.16/15.39 ( int, (fun int bool), (fun int int) ) 15.16/15.39 ( int, (fun int bool), (fun bool bool) ) 15.16/15.39 ( int, (fun int (fun int bool)), bool ) 15.16/15.39 ( int, (fun int (fun int bool)), (fun int bool) ) 15.16/15.39 ( int, (fun int (fun int bool)), (fun int (fun bool bool)) ) 15.16/15.39 ( int, (fun int (fun int bool)), (fun (fun int int) (fun int bool)) ) 15.16/15.39 ( int, (fun int int), bool ) 15.16/15.39 ( int, (fun int int), int ) 15.16/15.39 ( int, (fun int int), (fun int bool) ) 15.16/15.39 ( int, (fun int int), (fun int int) ) 15.16/15.39 ( int, (fun nat bool), (fun nat bool) ) 15.16/15.39 ( int, real, bool ) 15.16/15.39 ( int, real, (fun int bool) ) 15.16/15.39 ( int, real, (fun nat bool) ) 15.16/15.39 ( int, real, (fun int (fun bool bool)) ) 15.16/15.39 ( int, real, (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 15.16/15.39 ( int, real, (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 15.16/15.39 ( int, real, (fun nat (fun bool bool)) ) 15.16/15.39 ( int, (fun nat real), (fun nat real) ) 15.16/15.39 ( int, (fun int (fun int int)), (fun int (fun int bool)) ) 15.16/15.39 ( int, (fun int (fun int int)), (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 15.16/15.39 ( int, (product_prod int int), bool ) 15.16/15.39 ( int, (product_prod int int), int ) 15.16/15.39 ( int, (fun int (fun int (fun int bool))), (fun int (fun int bool)) ) 15.16/15.39 ( int, (fun int real), bool ) 15.16/15.39 ( int, (fun int real), real ) 15.16/15.39 ( int, (fun int real), (fun real real) ) 15.16/15.39 ( int, (fun int real), (fun int real) ) 15.16/15.39 ( int, (fun int (fun int (fun bool bool))), (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 15.16/15.39 ( int, (fun int (fun int real)), (fun int bool) ) 15.16/15.39 ( int, (fun int (fun real real)), (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 15.16/15.39 ( int, (fun int (fun real real)), (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 15.16/15.39 ( int, (fun int (fun nat bool)), bool ) 15.16/15.39 ( int, (fun int (fun nat bool)), (fun nat (fun bool bool)) ) 15.16/15.39 ( int, (fun int (fun nat (fun bool bool))), (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 15.16/15.39 ( int, (fun int (fun nat real)), (fun nat bool) ) 15.16/15.39 ( (fun int bool), int, bool ) 15.16/15.39 ( (fun int bool), int, (fun int bool) ) 15.16/15.39 ( (fun int bool), real, (fun int (fun int bool)) ) 15.16/15.39 ( (fun int bool), (fun int (fun bool bool)), (fun int bool) ) 15.16/15.39 ( (fun int bool), (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))), (fun int (fun int bool)) ) 15.16/15.39 ( (fun int int), int, (fun int bool) ) 15.16/15.39 ( (fun int int), int, (fun int int) ) 15.16/15.39 ( (fun int int), (fun int bool), (fun int bool) ) 15.16/15.39 ( (fun int int), (fun int int), (fun int int) ) 15.16/15.39 ( (fun nat bool), int, (fun nat bool) ) 15.16/15.39 ( (fun nat bool), real, (fun int (fun nat bool)) ) 15.16/15.39 ( (fun nat bool), (fun nat (fun bool bool)), (fun nat bool) ) 15.16/15.39 ( (fun nat bool), (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))), (fun int (fun nat bool)) ) 15.16/15.39 ( (product_prod nat nat), nat, bool ) 15.16/15.39 ( (product_prod nat nat), (product_prod nat nat), bool ) 15.16/15.39 ( real, nat, real ) 15.16/15.39 ( real, int, real ) 15.16/15.39 ( real, (fun int bool), (fun int (fun int bool)) ) 15.16/15.39 ( real, (fun nat bool), (fun int (fun nat bool)) ) 15.16/15.39 ( real, real, bool ) 15.16/15.39 ( real, real, real ) 15.16/15.39 ( real, real, complex ) 15.16/15.39 ( real, real, (fun nat (product_prod real real)) ) 15.16/15.39 ( real, (fun real bool), bool ) 15.16/15.39 ( real, (fun real bool), (fun bool bool) ) 15.16/15.39 ( real, (fun real real), real ) 15.16/15.39 ( real, (fun real real), (fun real bool) ) 15.16/15.39 ( real, (fun real real), (fun real real) ) 15.16/15.39 ( real, (fun real (fun real bool)), (fun (fun int real) (fun int bool)) ) 15.16/15.39 ( real, (fun real (fun real bool)), (fun (fun nat real) (fun nat bool)) ) 15.16/15.39 ( real, (fun (product_prod real real) bool), (fun real (fun nat (product_prod real real))) ) 15.16/15.39 ( real, (fun real (fun int bool)), bool ) 15.16/15.39 ( real, (fun real (fun int (fun int bool))), (fun int bool) ) 15.16/15.39 ( real, (fun real (fun int (fun int bool))), (fun int (fun int (fun bool bool))) ) 15.16/15.39 ( real, (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun int bool))) (fun _let_0 (fun int _let_0))) ) 15.16/15.39 ( real, (fun real (fun int (fun int (fun bool bool)))), (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 15.16/15.39 ( real, (fun int (fun int real)), (fun int (fun int bool)) ) 15.16/15.39 ( real, (fun real (fun (fun int real) (fun int bool))), (fun (fun int (fun int real)) (fun int (fun int bool))) ) 15.16/15.39 ( real, (fun real (fun int (fun nat bool))), (fun int bool) ) 15.16/15.39 ( real, (fun real (fun int (fun nat bool))), (fun int (fun nat (fun bool bool))) ) 15.16/15.39 ( real, (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun nat bool))) (fun _let_0 (fun int _let_0))) ) 15.16/15.39 ( real, (fun real (fun int (fun nat (fun bool bool)))), (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 15.16/15.39 ( real, (fun int (fun nat real)), (fun int (fun nat bool)) ) 15.16/15.39 ( real, (fun real (fun (fun nat real) (fun nat bool))), (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 15.16/15.39 ( (fun nat real), int, (fun nat real) ) 15.16/15.39 ( (fun nat real), real, (fun nat bool) ) 15.16/15.39 ( (fun nat real), (fun real bool), (fun nat bool) ) 15.16/15.39 ( (fun nat real), (fun real real), (fun nat real) ) 15.16/15.39 ( (filter nat), real, bool ) 15.16/15.39 ( (product_prod int int), int, bool ) 15.16/15.39 ( (product_prod int int), int, int ) 15.16/15.39 ( (product_prod int int), int, (product_prod int int) ) 15.16/15.39 ( (product_prod int int), (product_prod int int), bool ) 15.16/15.39 ( (product_prod int int), (product_prod int int), int ) 15.16/15.39 ( (product_prod int int), (product_prod int int), (fun int bool) ) 15.16/15.39 ( (product_prod int int), (fun (product_prod int int) bool), bool ) 15.16/15.39 ( (product_prod int int), (fun (product_prod int int) bool), (fun bool bool) ) 15.16/15.39 ( (product_prod int int), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (fun (product_prod int int) bool) ) 15.16/15.39 ( (product_prod int int), (fun (product_prod int int) (fun bool bool)), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 15.16/15.39 ( (product_prod int int), (fun (product_prod int int) int), bool ) 15.16/15.39 ( (product_prod int int), (fun (product_prod int int) int), int ) 15.16/15.39 ( (product_prod int int), (fun (product_prod int int) int), (fun int bool) ) 15.16/15.39 ( (product_prod int int), (fun (product_prod int int) int), (fun int int) ) 15.16/15.39 ( (product_prod int int), (fun (product_prod int int) int), (fun (product_prod int int) int) ) 15.16/15.39 ( (product_prod int int), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (fun (product_prod int int) bool) ) 15.16/15.39 ( (product_prod int int), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (fun (product_prod int int) (fun int bool)) ) 15.16/15.39 ( (product_prod int int), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 (fun int bool)))), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 15.16/15.39 ( (product_prod int int), (fun (product_prod int int) (fun int int)), (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 15.16/15.39 ( quickcheck_code_int, quickcheck_code_int, (product_prod quickcheck_code_int quickcheck_code_int) ) 15.16/15.39 ( code_code_numeral, code_code_numeral, (product_prod code_code_numeral code_code_numeral) ) 15.16/15.39 ( (fun (product_prod int int) bool), (product_prod int int), (fun (product_prod int int) bool) ) 15.16/15.39 ( (fun (product_prod int int) bool), (fun bool bool), (fun (product_prod int int) bool) ) 15.16/15.39 ( (filter real), real, bool ) 15.16/15.39 ( (fun (product_prod int int) int), (fun int int), (fun (product_prod int int) int) ) 15.16/15.39 ( (fun (product_prod int int) int), (product_prod int int), (fun (product_prod int int) bool) ) 15.16/15.39 ( (fun (product_prod int int) int), (product_prod int int), (fun (product_prod int int) int) ) 15.16/15.39 ( (fun (product_prod int int) int), (fun (product_prod int int) (fun int bool)), (fun (product_prod int int) bool) ) 15.16/15.39 ( (fun int real), int, (fun int real) ) 15.16/15.39 ( (fun int real), real, (fun int bool) ) 15.16/15.39 ( (fun int real), (fun real bool), (fun int bool) ) 15.16/15.39 ( (fun int real), (fun real real), (fun int real) ) 15.16/15.39 ( (fun int (fun int real)), real, (fun int (fun int bool)) ) 15.16/15.39 ( (fun int (fun int real)), (fun (fun int real) (fun int bool)), (fun int (fun int bool)) ) 15.16/15.39 ( (fun int (fun nat real)), real, (fun int (fun nat bool)) ) 15.16/15.39 ( (fun int (fun nat real)), (fun (fun nat real) (fun nat bool)), (fun int (fun nat bool)) ) 15.16/15.39 ) 15.16/15.39 (instantiation (forall ((W $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) W) W)) ) 15.16/15.39 ( (zero_zero real) ) 15.16/15.39 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.39 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.39 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.39 ( skv_5 ) 15.16/15.39 ) 15.16/15.39 (instantiation (forall ((N_1 $$unsorted) (M $$unsorted)) (let ((_let_0 (semiring_1_of_nat int))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP int int (uminus_uminus int) (hAPP nat int _let_0 (hAPP nat nat suc N_1)))) (hAPP nat int _let_0 M)))) ) 15.16/15.39 ( (zero_zero nat), (zero_zero nat) ) 15.16/15.39 ) 15.16/15.39 (instantiation (forall ((N_1 $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) (hAPP nat nat (fact_fact nat) N_1))) ) 15.16/15.39 ( (zero_zero nat) ) 15.16/15.39 ( (hAPP nat nat suc (zero_zero nat)) ) 15.16/15.39 ) 15.16/15.39 (instantiation (forall ((N $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun real real))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun nat real))) (let ((_let_4 (power_power real))) (= _let_2 (hAPP real real (hAPP real _let_1 (times_times real) (hAPP real real (hAPP real _let_1 (hAPP bool (fun real _let_1) (if real) (hAPP nat bool (even_odd_even nat) N)) _let_2) (hAPP real real (hAPP real _let_1 (inverse_divide real) (hAPP nat real (hAPP real _let_3 _let_4 (hAPP int real (number_number_of real) min_1)) (hAPP nat nat (hAPP nat _let_0 (div_div nat) (hAPP nat nat (hAPP nat _let_0 (minus_minus nat) N) (hAPP nat nat suc (zero_zero nat)))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP nat real (real_1 nat) (hAPP nat nat (fact_fact nat) N))))) (hAPP nat real (hAPP real _let_3 _let_4 _let_2) N)))))))) ) 15.16/15.39 ( (zero_zero nat) ) 15.16/15.39 ( (hAPP nat nat suc (zero_zero nat)) ) 15.16/15.39 ( (one_one nat) ) 15.16/15.39 ) 15.16/15.39 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (hBOOL (hAPP _let_1 bool (summable real) (hAPP _let_1 _let_1 (hAPP _let_2 (fun _let_1 _let_1) (combs nat real real) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 nat) (times_times real)) sin_coeff)) (hAPP real _let_1 (power_power real) X_2))))))) ) 15.16/15.39 ( (hAPP int real (number_number_of real) min_1) ) 15.16/15.39 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.39 ) 15.16/15.39 (instantiation (forall ((M $$unsorted)) (not (= (zero_zero nat) (hAPP nat nat suc M))) ) 15.16/15.39 ( (zero_zero nat) ) 15.16/15.39 ( (hAPP nat nat suc (zero_zero nat)) ) 15.16/15.39 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 15.16/15.39 ) 15.16/15.39 (instantiation (forall ((X_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP complex real re X_1)) (hAPP complex real (norm_norm complex) X_1))) ) 15.16/15.39 ( (one_one complex) ) 15.16/15.39 ( ii ) 15.16/15.39 ( (zero_zero complex) ) 15.16/15.39 ) 15.16/15.39 (instantiation (forall ((X_2 $$unsorted)) (= (hBOOL (hAPP nat bool (even_odd_even nat) X_2)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (dvd_dvd nat) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) X_2))) ) 15.16/15.39 ( (zero_zero nat) ) 15.16/15.39 ( (one_one nat) ) 15.16/15.39 ) 15.16/15.39 (instantiation (forall ((N_1 $$unsorted)) (not (hBOOL (hAPP int bool nat_neg (hAPP nat int (semiring_1_of_nat int) N_1)))) ) 15.16/15.39 ( (zero_zero nat) ) 15.16/15.39 ( (hAPP nat nat suc (zero_zero nat)) ) 15.16/15.39 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.16/15.39 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.39 ) 15.16/15.39 (instantiation (forall ((Ma $$unsorted) (N $$unsorted)) (let ((_let_0 (even_odd_even nat))) (= (hBOOL (hAPP nat bool _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) Ma) N))) (= (hBOOL (hAPP nat bool _let_0 N)) (hBOOL (hAPP nat bool _let_0 Ma))))) ) 15.16/15.39 ( (one_one nat), (one_one nat) ) 15.16/15.39 ) 15.16/15.39 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun real _let_1))) (let ((_let_3 (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP real real cos X_2)) (hAPP real real sin X_2)))) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP (fun real real) (fun real _let_0) (deriv real) (hAPP nat (fun real real) (hAPP _let_2 (fun nat (fun real real)) (combc real nat real) (hAPP (fun real real) _let_2 (hAPP _let_2 (fun (fun real real) _let_2) (combb real _let_1 real) (power_power real)) sin)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) X_2) (hAPP real real (hAPP real (fun real real) (plus_plus real) _let_3) _let_3))))))) ) 15.16/15.39 ( (zero_zero real) ) 15.16/15.39 ( pi ) 15.16/15.39 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.39 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.39 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.16/15.39 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.16/15.39 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.16/15.39 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.16/15.39 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.16/15.39 ( skv_5 ) 15.16/15.39 ) 15.16/15.39 (instantiation (forall ((N_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) (hAPP real real (inverse_inverse real) (hAPP nat real (real_1 nat) (hAPP nat nat (fact_fact nat) N_1))))) ) 15.16/15.39 ( (zero_zero nat) ) 15.16/15.39 ( (hAPP nat nat suc (zero_zero nat)) ) 15.16/15.39 ) 15.16/15.39 (instantiation (forall ((N $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) N)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) (hAPP int real (real_1 int) N)))) ) 15.16/15.39 ( (one_one int) ) 15.16/15.39 ( (zero_zero int) ) 15.16/15.39 ( pls ) 15.16/15.39 ( min_1 ) 15.16/15.39 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.39 ) 15.16/15.39 (instantiation (forall ((N $$unsorted)) (let ((_let_0 (zero_zero nat))) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) N) (hAPP nat nat suc _let_0))) (= _let_0 N))) ) 15.16/15.39 ( (zero_zero nat) ) 15.16/15.39 ) 15.16/15.39 (instantiation (forall ((N $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) (hAPP nat real (real_1 nat) N))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N))) ) 15.16/15.39 ( (zero_zero nat) ) 15.16/15.39 ( (hAPP nat nat suc (zero_zero nat)) ) 15.16/15.39 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.39 ) 15.16/15.39 (instantiation (forall ((T $$unsorted) (A $$unsorted)) (let ((_let_0 (ti T A))) (= _let_0 (ti T _let_0))) ) 15.16/15.39 ( bool, fFalse ) 15.16/15.39 ( bool, fTrue ) 15.16/15.39 ( int, pls ) 15.16/15.39 ( int, min_1 ) 15.16/15.39 ( int, s ) 15.16/15.39 ( int, m ) 15.16/15.39 ( int, s1 ) 15.16/15.39 ( int, t ) 15.16/15.39 ( (fun int bool), nat_neg ) 15.16/15.39 ( (fun int bool), zprime ) 15.16/15.39 ( (fun int bool), zEven ) 15.16/15.39 ( (fun int bool), zOdd ) 15.16/15.39 ( (fun int bool), (even_odd_even int) ) 15.16/15.39 ( (fun int bool), twoSqu1091635170sum2sq ) 15.16/15.39 ( (fun int bool), nat_is_nat ) 15.16/15.39 ( (fun int (fun int bool)), norRRset ) 15.16/15.39 ( (fun int (fun int bool)), quadRes ) 15.16/15.39 ( (fun int (fun int bool)), sRStar ) 15.16/15.39 ( (fun int (fun int bool)), d22set ) 15.16/15.39 ( (fun int (fun int bool)), sr ) 15.16/15.39 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 15.16/15.39 ( (fun int int), zfact ) 15.16/15.39 ( (fun int int), bit0 ) 15.16/15.39 ( (fun int int), bit1 ) 15.16/15.39 ( (fun int int), (fact_fact int) ) 15.16/15.39 ( (fun int int), pred ) 15.16/15.39 ( (fun int int), succ ) 15.16/15.39 ( (fun nat bool), (even_odd_even nat) ) 15.16/15.39 ( (fun nat bool), prime ) 15.16/15.39 ( (fun nat nat), suc ) 15.16/15.39 ( (fun nat nat), (fact_fact nat) ) 15.16/15.39 ( (fun nat nat), fact ) 15.16/15.39 ( (fun nat nat), nat_size ) 15.16/15.39 ( (fun nat nat), (size_size nat) ) 15.16/15.39 ( (fun (product_prod nat nat) bool), pred_nat ) 15.16/15.39 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 15.16/15.39 ( real, pi ) 15.16/15.39 ( (fun real real), ln ) 15.16/15.39 ( (fun real real), cos ) 15.16/15.39 ( (fun real real), sqrt ) 15.16/15.39 ( (fun real real), sin ) 15.16/15.39 ( (fun real real), arccos ) 15.16/15.39 ( (fun real real), arcsin ) 15.16/15.39 ( (fun real real), tan ) 15.16/15.39 ( (fun real real), arctan ) 15.16/15.39 ( (fun nat (fun nat bool)), coprime ) 15.16/15.39 ( complex, ii ) 15.16/15.39 ( (fun nat real), (real_1 nat) ) 15.16/15.39 ( (fun nat real), sin_coeff ) 15.16/15.39 ( (fun nat real), cos_coeff ) 15.16/15.39 ( (filter nat), sequentially ) 15.16/15.39 ( (fun int (fun int int)), (gcd_gcd int) ) 15.16/15.39 ( (fun int (fun int int)), legendre ) 15.16/15.39 ( (fun int (fun int int)), legacy_zgcd ) 15.16/15.39 ( (fun int (fun int int)), standardRes ) 15.16/15.39 ( (fun int (fun int int)), nat_tsub ) 15.16/15.39 ( (fun int (fun int int)), multInv ) 15.16/15.39 ( (fun int (fun int int)), z3mod ) 15.16/15.39 ( (fun int (fun int int)), z3div ) 15.16/15.39 ( (fun int (fun int int)), int_gcd ) 15.16/15.39 ( (fun int (fun int int)), int_lcm ) 15.16/15.39 ( (fun int (fun int int)), inv ) 15.16/15.39 ( (fun complex complex), expi ) 15.16/15.39 ( (fun complex complex), cnj ) 15.16/15.39 ( (fun real complex), cis ) 15.16/15.39 ( (fun int nat), nat_1 ) 15.16/15.39 ( (fun int nat), phi ) 15.16/15.39 ( (fun (fun int bool) bool), nat_nat_set ) 15.16/15.39 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 15.16/15.39 ( (fun nat (fun nat nat)), nat_gcd ) 15.16/15.39 ( (fun nat (fun nat nat)), nat_lcm ) 15.16/15.39 ( (fun (fun int bool) int), (the int) ) 15.16/15.39 ( (fun complex real), re ) 15.16/15.39 ( (fun complex real), im ) 15.16/15.39 ( (fun complex real), arg ) 15.16/15.39 ( (fun bool bool), fNot ) 15.16/15.39 ( (fun nat (fun real real)), root ) 15.16/15.39 ( (fun real (fun real real)), log ) 15.16/15.39 ( (fun real (fun real real)), powr ) 15.16/15.39 ( (fun bool (fun bool bool)), fimplies ) 15.16/15.39 ( (fun bool (fun bool bool)), fconj ) 15.16/15.39 ( (fun bool (fun bool bool)), fdisj ) 15.16/15.39 ( (fun int (fun int (product_prod int int))), negDivAlg ) 15.16/15.39 ( (fun int (fun int (product_prod int int))), posDivAlg ) 15.16/15.39 ( (fun int (fun int (product_prod int int))), divmod_int ) 15.16/15.39 ( (fun int (fun int (product_prod int int))), pdivmod ) 15.16/15.39 ( (fun int (fun int (product_prod int int))), norm_frac ) 15.16/15.39 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 15.16/15.39 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 15.16/15.39 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 15.16/15.39 ( (fun int (fun int (fun int bool))), zcong ) 15.16/15.39 ( (fun int (fun int (fun int bool))), zcongm ) 15.16/15.39 ( (fun int (fun int (fun int bool))), noXRRset ) 15.16/15.39 ( (fun int (fun int (fun int bool))), bnorRset ) 15.16/15.39 ( (fun int (fun int (fun int bool))), wset ) 15.16/15.39 ( (fun (product_prod int int) bool), frac_1 ) 15.16/15.39 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 15.16/15.40 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 15.16/15.40 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 15.16/15.40 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 15.16/15.40 ( (fun (fun nat rat) bool), vanishes ) 15.16/15.40 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 15.16/15.40 ( (fun code_code_numeral nat), code_c271388182l_size ) 15.16/15.40 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 15.16/15.40 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 15.16/15.40 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 15.16/15.40 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 15.16/15.40 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 15.16/15.40 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 15.16/15.40 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 15.16/15.40 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 15.16/15.40 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 15.16/15.40 ( (fun complex nat), complex_size ) 15.16/15.40 ( (fun complex nat), (size_size complex) ) 15.16/15.40 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 15.16/15.40 ( (fun nat (fun nat (product_prod int int))), bezw ) 15.16/15.40 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 15.16/15.40 ( (fun int (fun nat nat)), nat_aux ) 15.16/15.40 ( (fun int (fun (fun int bool) bool)), rsetR ) 15.16/15.40 ( (fun int (fun (fun int bool) bool)), resSet ) 15.16/15.40 ( (fun int (list int)), quickc666637781d_zero ) 15.16/15.40 ( (fun (product_prod int int) rat), frct ) 15.16/15.40 ( (fun int (fun int rat)), fract ) 15.16/15.40 ( (fun real (fun real complex)), complex_1 ) 15.16/15.40 ( (fun real (fun real complex)), rcis ) 15.16/15.40 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 15.16/15.40 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 15.16/15.40 ( (fun int real), (real_1 int) ) 15.16/15.40 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 15.16/15.40 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 15.16/15.40 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 15.16/15.40 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 15.16/15.40 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 15.16/15.40 ( (fun real nat), natfloor ) 15.16/15.40 ( (fun real nat), natceiling ) 15.16/15.40 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 15.16/15.40 ( (fun quickcheck_code_int int), quickcheck_int_of ) 15.16/15.40 ( (fun rat (product_prod int int)), quotient_of ) 15.16/15.40 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 15.16/15.40 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 15.16/15.40 ( (fun rat real), ratreal ) 15.16/15.40 ( (fun code_code_numeral int), code_int_of ) 15.16/15.40 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 15.16/15.40 ( (fun int quickcheck_code_int), quickcheck_of_int ) 15.16/15.40 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 15.16/15.40 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((K $$unsorted) (L $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (let ((_let_2 (number_number_of int))) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int _let_2 K)) (hAPP int int _let_2 L))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) L)))))) ) 15.16/15.40 ( pls, pls ) 15.16/15.40 ( pls, (hAPP int int bit1 pls) ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((W_1 $$unsorted)) (let ((_let_0 (number_number_of int))) (= (hBOOL (hAPP int bool nat_neg (hAPP int int _let_0 W_1))) (hBOOL (hAPP int bool nat_neg (hAPP int int _let_0 (hAPP int int bit1 W_1)))))) ) 15.16/15.40 ( pls ) 15.16/15.40 ( (hAPP int int bit1 pls) ) 15.16/15.40 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.16/15.40 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.16/15.40 ( min_1 ) 15.16/15.40 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.16/15.40 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.16/15.40 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 15.16/15.40 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((W_1 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (let ((_let_2 (ord_less int))) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 (hAPP int int bit1 W_1)) _let_1)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 W_1) _let_1)))))) ) 15.16/15.40 ( pls ) 15.16/15.40 ( (hAPP int int bit1 pls) ) 15.16/15.40 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.16/15.40 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.16/15.40 ( min_1 ) 15.16/15.40 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.16/15.40 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.16/15.40 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 15.16/15.40 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((N_1 $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) N_1) (hAPP nat nat suc N_1))) ) 15.16/15.40 ( (zero_zero nat) ) 15.16/15.40 ( (hAPP nat nat suc (zero_zero nat)) ) 15.16/15.40 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_0 (real_1 int))) (= (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP int real _let_0 X_2)) (hAPP int real _let_0 Y_2))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) X_2) Y_2)))) ) 15.16/15.40 ( (one_one int), t ) 15.16/15.40 ( pls, (one_one int) ) 15.16/15.40 ( pls, pls ) 15.16/15.40 ( pls, min_1 ) 15.16/15.40 ( pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.40 ( min_1, pls ) 15.16/15.40 ( min_1, min_1 ) 15.16/15.40 ( s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.40 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.40 ( skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.40 ( skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((X_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) X_1) (hAPP nat real (real_1 nat) (hAPP real nat natceiling X_1)))) ) 15.16/15.40 ( (one_one real) ) 15.16/15.40 ( (zero_zero real) ) 15.16/15.40 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.40 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.40 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.40 ( skv_5 ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((T_1 $$unsorted)) (order (filter T_1)) ) 15.16/15.40 ( nat ) 15.16/15.40 ( real ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((A_2 $$unsorted) (X_2 $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP int real (real_1 int) A_2)) X_2)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) A_2) (hAPP real int (archimedean_ceiling real) X_2)))) ) 15.16/15.40 ( (one_one int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.40 ( (zero_zero int), pi ) 15.16/15.40 ( (zero_zero int), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.40 ( (zero_zero int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.40 ( (zero_zero int), skv_2 ) 15.16/15.40 ( (zero_zero int), skv_8 ) 15.16/15.40 ( (zero_zero int), skv_9 ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((K_4 $$unsorted)) (= K_4 (hAPP int quickcheck_code_int quickcheck_of_int (hAPP quickcheck_code_int int quickcheck_int_of K_4))) ) 15.16/15.40 ( (zero_zero quickcheck_code_int) ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= X_1 (hAPP complex real re (hAPP real complex (hAPP real (fun real complex) complex_1 X_1) Y_1))) ) 15.16/15.40 ( (one_one real), (zero_zero real) ) 15.16/15.40 ( (zero_zero real), (one_one real) ) 15.16/15.40 ( (zero_zero real), (zero_zero real) ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((D $$unsorted)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (dvd_dvd int) D) (hAPP int int (abs_abs int) D))) ) 15.16/15.40 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((I $$unsorted)) (= (= (zero_zero nat) (hAPP int nat nat_1 I)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) I) (zero_zero int)))) ) 15.16/15.40 ( (one_one int) ) 15.16/15.40 ( (zero_zero int) ) 15.16/15.40 ( min_1 ) 15.16/15.40 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.40 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_0 (product_Pair X_a X_b))) (= _let_0 (ti (fun X_a (fun X_b (product_prod X_a X_b))) _let_0))) ) 15.16/15.40 ( nat, nat ) 15.16/15.40 ( int, int ) 15.16/15.40 ( int, (product_prod int int) ) 15.16/15.40 ( (product_prod nat nat), (product_prod nat nat) ) 15.16/15.40 ( real, real ) 15.16/15.40 ( (product_prod int int), (product_prod int int) ) 15.16/15.40 ( quickcheck_code_int, quickcheck_code_int ) 15.16/15.40 ( code_code_numeral, code_code_numeral ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((I_1 $$unsorted) (J_2 $$unsorted)) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) I_1) J_2)) I_1))) ) 15.16/15.40 ( (one_one nat), (one_one nat) ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (hAPP real _let_0 _let_1 _let_2))) (= (and (or (hBOOL (hAPP real bool _let_3 X_2)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Y_2) _let_2))) (or (hBOOL (hAPP real bool _let_3 Y_2)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_2) _let_2)))) (hBOOL (hAPP real bool _let_3 (hAPP real real (hAPP real (fun real real) (inverse_divide real) X_2) Y_2)))))))) ) 15.16/15.40 ( (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.40 ( (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.16/15.40 ( (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.40 ( (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 15.16/15.40 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.40 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.40 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.16/15.40 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.16/15.40 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.40 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.40 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((X_2 $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) X_2)) (hBOOL (hAPP int bool (even_odd_even int) X_2))) ) 15.16/15.40 ( (one_one int) ) 15.16/15.40 ( (zero_zero int) ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP (fun real real) (fun real _let_0) (deriv real) sin) X_2) (hAPP real real cos X_2)))) ) 15.16/15.40 ( (zero_zero real) ) 15.16/15.40 ( pi ) 15.16/15.40 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.40 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.40 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.16/15.40 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.16/15.40 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.16/15.40 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.16/15.40 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.16/15.40 ( skv_5 ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((Y_2 $$unsorted)) (let ((_let_0 (hAPP real (fun real bool) (ord_less_eq real) (one_one real)))) (= (hBOOL (hAPP real bool _let_0 Y_2)) (hBOOL (hAPP real bool _let_0 (hAPP real real sqrt Y_2))))) ) 15.16/15.40 ( (one_one real) ) 15.16/15.40 ( (zero_zero real) ) 15.16/15.40 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.40 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((K $$unsorted)) (let ((_let_0 (fun int bool))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) pls) (hAPP int int bit1 K))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) pls) K)))) ) 15.16/15.40 ( (one_one int) ) 15.16/15.40 ( pls ) 15.16/15.40 ( (hAPP int int bit1 pls) ) 15.16/15.40 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.16/15.40 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.16/15.40 ( min_1 ) 15.16/15.40 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.40 ( s ) 15.16/15.40 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.16/15.40 ( (hAPP int int (number_number_of int) pls) ) 15.16/15.40 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.16/15.40 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.16/15.40 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 15.16/15.40 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 15.16/15.40 ( skv_4 ) 15.16/15.40 ( skv_10 ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((X_2 $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) X_2) (one_one real))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP real nat natceiling X_2)) (one_one nat)))) ) 15.16/15.40 ( (one_one real) ) 15.16/15.40 ( (zero_zero real) ) 15.16/15.40 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.40 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.40 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.40 ( skv_5 ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((Z $$unsorted)) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (hAPP nat nat suc (zero_zero nat))) (hAPP int nat nat_1 Z))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (one_one int)) Z))) ) 15.16/15.40 ( (one_one int) ) 15.16/15.40 ( (zero_zero int) ) 15.16/15.40 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.40 ( t ) 15.16/15.40 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((X_2 $$unsorted)) (= (hBOOL (hAPP int bool (even_odd_even int) (hAPP nat int (semiring_1_of_nat int) X_2))) (hBOOL (hAPP nat bool (even_odd_even nat) X_2))) ) 15.16/15.40 ( (zero_zero nat) ) 15.16/15.40 ( (hAPP nat nat suc (zero_zero nat)) ) 15.16/15.40 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.16/15.40 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.40 ( (one_one nat) ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((N_1 $$unsorted) (M $$unsorted)) (let ((_let_0 (semiring_1_of_nat int))) (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP nat int _let_0 N_1)) (hAPP int int (uminus_uminus int) (hAPP nat int _let_0 M)))))) ) 15.16/15.40 ( (zero_zero nat), (zero_zero nat) ) 15.16/15.40 ( (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((K $$unsorted) (L $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) L)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int bit1 K)) (hAPP int int bit1 L)))))) ) 15.16/15.40 ( min_1, min_1 ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((K_4 $$unsorted)) (= (zero_zero rat) (hAPP int rat (hAPP int (fun int rat) fract K_4) (zero_zero int))) ) 15.16/15.40 ( (one_one int) ) 15.16/15.40 ( (zero_zero int) ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((N $$unsorted)) (let ((_let_0 (fun real bool))) (hBOOL (hAPP _let_0 bool (hAPP real (fun _let_0 bool) (member real) (hAPP nat real (real_1 nat) N)) (field_char_0_Rats real)))) ) 15.16/15.40 ( (zero_zero nat) ) 15.16/15.40 ( (hAPP nat nat suc (zero_zero nat)) ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) X_2)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (one_one real)) (hAPP real real (exp real) X_2)))))) ) 15.16/15.40 ( pi ) 15.16/15.40 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.40 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.40 ( skv_3 ) 15.16/15.40 ( skv_5 ) 15.16/15.40 ( skv_7 ) 15.16/15.40 ( skv_12 ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat real))) (let ((_let_3 (fun nat _let_1))) (let ((_let_4 (fun _let_2 _let_2))) (hBOOL (hAPP _let_2 bool (summable real) (hAPP _let_2 _let_2 (hAPP _let_3 _let_4 (combs nat real real) (hAPP _let_2 _let_3 (hAPP (fun real _let_1) (fun _let_2 _let_3) (combb real _let_1 nat) (times_times real)) (hAPP _let_2 _let_2 (hAPP _let_1 _let_4 (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_2 (hAPP _let_2 (fun _let_0 _let_2) (combb nat real nat) (real_1 nat)) (fact_fact nat))))) (hAPP real _let_2 (power_power real) X_2))))))))) ) 15.16/15.40 ( (hAPP int real (number_number_of real) min_1) ) 15.16/15.40 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((V $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) pls) V)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) (hAPP int nat (number_number_of nat) V)))) ) 15.16/15.40 ( (one_one int) ) 15.16/15.40 ( pls ) 15.16/15.40 ( (hAPP int int bit1 pls) ) 15.16/15.40 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.16/15.40 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.16/15.40 ( min_1 ) 15.16/15.40 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat real))) (let ((_let_3 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_4 (times_times real))) (let ((_let_5 (fun real _let_2))) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP _let_1 (fun real _let_0) (deriv real) (hAPP nat _let_1 (hAPP _let_5 (fun nat _let_1) (combc real nat real) (hAPP _let_1 _let_5 (hAPP _let_5 (fun _let_1 _let_5) (combb real _let_2 real) (power_power real)) cos)) (hAPP int nat (number_number_of nat) _let_3))) X_2) (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real _let_1 _let_4 (hAPP real real (hAPP real _let_1 _let_4 (hAPP int real (number_number_of real) _let_3)) (hAPP real real cos X_2))) (hAPP real real sin X_2))))))))))) ) 15.16/15.40 ( (zero_zero real) ) 15.16/15.40 ( pi ) 15.16/15.40 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.40 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.40 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.16/15.40 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.16/15.40 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.16/15.40 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.16/15.40 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.16/15.40 ( skv_5 ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((Ma $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat bool))) (= (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) (hAPP nat nat suc Ma)) N)) (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) Ma) N)))) ) 15.16/15.40 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_0 (in_rel X_a X_b))) (= _let_0 (ti (fun (fun (product_prod X_a X_b) bool) (fun X_a (fun X_b bool))) _let_0))) ) 15.16/15.40 ( bool, bool ) 15.16/15.40 ( nat, bool ) 15.16/15.40 ( nat, nat ) 15.16/15.40 ( nat, (product_prod nat nat) ) 15.16/15.40 ( int, bool ) 15.16/15.40 ( int, nat ) 15.16/15.40 ( int, int ) 15.16/15.40 ( int, (fun int bool) ) 15.16/15.40 ( int, (product_prod int int) ) 15.16/15.40 ( (fun int bool), int ) 15.16/15.40 ( (fun int (fun int bool)), int ) 15.16/15.40 ( (fun int int), int ) 15.16/15.40 ( (fun nat bool), nat ) 15.16/15.40 ( (product_prod nat nat), (product_prod nat nat) ) 15.16/15.40 ( real, bool ) 15.16/15.40 ( real, int ) 15.16/15.40 ( real, real ) 15.16/15.40 ( real, (filter nat) ) 15.16/15.40 ( real, (filter real) ) 15.16/15.40 ( (fun real bool), real ) 15.16/15.40 ( (fun nat real), nat ) 15.16/15.40 ( (product_prod int int), bool ) 15.16/15.40 ( (product_prod int int), int ) 15.16/15.40 ( (product_prod int int), (product_prod int int) ) 15.16/15.40 ( quickcheck_code_int, quickcheck_code_int ) 15.16/15.40 ( code_code_numeral, code_code_numeral ) 15.16/15.40 ( (fun (product_prod int int) bool), (product_prod int int) ) 15.16/15.40 ( (fun (product_prod int int) int), (product_prod int int) ) 15.16/15.40 ( (fun int real), int ) 15.16/15.40 ( (fun real (fun int bool)), real ) 15.16/15.40 ( (fun int (fun nat bool)), int ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((X_2 $$unsorted) (P_4 $$unsorted)) (let ((_let_0 (fun int bool))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (dvd_dvd int) P_4) X_2)) (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong X_2) (zero_zero int)) P_4)))) ) 15.16/15.40 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (fEx X_a))) (= _let_0 (ti (fun (fun X_a bool) bool) _let_0))) ) 15.16/15.40 ( nat ) 15.16/15.40 ( int ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (power_power real))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (= (one_one real) (hAPP real real (hAPP real (fun real real) (plus_plus real) (hAPP nat real (hAPP real _let_0 _let_1 (hAPP real real sin X_1)) _let_2)) (hAPP nat real (hAPP real _let_0 _let_1 (hAPP real real cos X_1)) _let_2)))))) ) 15.16/15.40 ( (zero_zero real) ) 15.16/15.40 ( pi ) 15.16/15.40 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.40 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.40 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.16/15.40 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.16/15.40 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.16/15.40 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.16/15.40 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.16/15.40 ( skv_5 ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (hAPP real real (hAPP real (fun real real) (inverse_divide real) X_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (= X_1 (hAPP real real (hAPP real (fun real real) (plus_plus real) _let_0) _let_0))) ) 15.16/15.40 ( (one_one real) ) 15.16/15.40 ( pi ) 15.16/15.40 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.16/15.40 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.16/15.40 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((W_1 $$unsorted) (Z $$unsorted)) (let ((_let_0 (fun int bool))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) W_1) Z)) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) W_1) (hAPP int int (hAPP int (fun int int) (minus_minus int) Z) (one_one int)))))) ) 15.16/15.40 ( (one_one int), t ) 15.16/15.40 ( pls, (one_one int) ) 15.16/15.40 ( pls, pls ) 15.16/15.40 ( pls, min_1 ) 15.16/15.40 ( pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.40 ( min_1, pls ) 15.16/15.40 ( min_1, min_1 ) 15.16/15.40 ( s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.40 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.40 ( skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.40 ( skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((K1 $$unsorted) (K2 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K1) K2)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int bit0 K1)) (hAPP int int bit1 K2)))))) ) 15.16/15.40 ( pls, min_1 ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((X_2 $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (one_one real)) X_2)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (one_one nat)) (hAPP real nat natfloor X_2)))) ) 15.16/15.40 ( (one_one real) ) 15.16/15.40 ( (zero_zero real) ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((R_4 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) R_4) (hAPP int real (real_1 int) (hAPP real int (archimedean_ceiling real) R_4)))) ) 15.16/15.40 ( (zero_zero real) ) 15.16/15.40 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.40 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.40 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.40 ( skv_5 ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((N_1 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (one_one int))) (= _let_1 (hAPP int int (hAPP int _let_0 (gcd_gcd int) (hAPP int int (hAPP int _let_0 (plus_plus int) N_1) _let_1)) N_1)))) ) 15.16/15.40 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.16/15.40 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (one_one real))) (let ((_let_2 (ord_less_eq real))) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 X_2) _let_1)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 (hAPP real real sqrt X_2)) _let_1)))))) ) 15.16/15.40 ( (one_one real) ) 15.16/15.40 ( (zero_zero real) ) 15.16/15.40 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.40 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((Z_1 $$unsorted)) (hBOOL (hAPP int bool nat_is_nat (hAPP nat int (semiring_1_of_nat int) Z_1))) ) 15.16/15.40 ( (zero_zero nat) ) 15.16/15.40 ( (hAPP nat nat suc (zero_zero nat)) ) 15.16/15.40 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.16/15.40 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((K $$unsorted) (L $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int bit0 K)) (hAPP int int bit0 L))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) L))))) ) 15.16/15.40 ( pls, pls ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat real))) (let ((_let_3 (times_times real))) (let ((_let_4 (fun real _let_2))) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP _let_1 (fun real _let_0) (deriv real) (hAPP nat _let_1 (hAPP _let_4 (fun nat _let_1) (combc real nat real) (hAPP _let_1 _let_4 (hAPP _let_4 (fun _let_1 _let_4) (combb real _let_2 real) (power_power real)) cos)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) X_2) (hAPP real real (hAPP real _let_1 _let_3 (hAPP real real (hAPP real _let_1 _let_3 (hAPP int real (number_number_of real) (hAPP int int bit0 min_1))) (hAPP real real cos X_2))) (hAPP real real sin X_2))))))))) ) 15.16/15.40 ( (zero_zero real) ) 15.16/15.40 ( pi ) 15.16/15.40 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.40 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.40 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.16/15.40 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.16/15.40 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.16/15.40 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.16/15.40 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.16/15.40 ( skv_5 ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((X_1 $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (zero_zero nat)) (hAPP real nat natceiling X_1))) ) 15.16/15.40 ( (one_one real) ) 15.16/15.40 ( (zero_zero real) ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted)) (let ((_let_0 (combs X_a X_b X_c))) (= _let_0 (ti (fun (fun X_a (fun X_b X_c)) (fun (fun X_a X_b) (fun X_a X_c))) _let_0))) ) 15.16/15.40 ( nat, bool, bool ) 15.16/15.40 ( nat, bool, (fun bool bool) ) 15.16/15.40 ( nat, nat, (fun nat bool) ) 15.16/15.40 ( nat, nat, (fun nat nat) ) 15.16/15.40 ( nat, nat, real ) 15.16/15.40 ( nat, real, bool ) 15.16/15.40 ( nat, real, real ) 15.16/15.40 ( nat, real, (fun real real) ) 15.16/15.40 ( int, bool, bool ) 15.16/15.40 ( int, bool, (fun int bool) ) 15.16/15.40 ( int, bool, (fun int int) ) 15.16/15.40 ( int, bool, (fun bool bool) ) 15.16/15.40 ( int, int, bool ) 15.16/15.40 ( int, int, int ) 15.16/15.40 ( int, int, (fun int bool) ) 15.16/15.40 ( int, int, (fun int int) ) 15.16/15.40 ( int, (fun int bool), bool ) 15.16/15.40 ( int, (fun int bool), (fun int bool) ) 15.16/15.40 ( int, (fun int bool), (fun int (fun bool bool)) ) 15.16/15.40 ( int, (fun int bool), (fun (fun int int) (fun int bool)) ) 15.16/15.40 ( int, (fun int (fun int bool)), (fun int (fun int bool)) ) 15.16/15.40 ( int, (fun int int), (fun int (fun int bool)) ) 15.16/15.40 ( int, (fun int int), (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 15.16/15.40 ( int, (fun nat bool), bool ) 15.16/15.40 ( int, (fun nat bool), (fun nat (fun bool bool)) ) 15.16/15.40 ( int, real, bool ) 15.16/15.40 ( int, real, real ) 15.16/15.40 ( int, real, (fun real real) ) 15.16/15.40 ( int, real, (fun int real) ) 15.16/15.40 ( int, (fun real real), (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 15.16/15.40 ( int, (fun real real), (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 15.16/15.40 ( int, (fun nat real), (fun nat bool) ) 15.16/15.40 ( int, (fun int (fun bool bool)), (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 15.16/15.40 ( int, (fun int real), (fun int bool) ) 15.16/15.40 ( int, (fun nat (fun bool bool)), (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 15.16/15.40 ( real, bool, bool ) 15.16/15.40 ( real, bool, (fun bool bool) ) 15.16/15.40 ( real, (fun int bool), bool ) 15.16/15.40 ( real, (fun int (fun int bool)), (fun int bool) ) 15.16/15.40 ( real, (fun int (fun int bool)), (fun int (fun int (fun bool bool))) ) 15.16/15.40 ( real, real, real ) 15.16/15.40 ( real, real, (fun real bool) ) 15.16/15.40 ( real, real, (fun real real) ) 15.16/15.40 ( real, (fun real bool), (fun (fun int real) (fun int bool)) ) 15.16/15.40 ( real, (fun real bool), (fun (fun nat real) (fun nat bool)) ) 15.16/15.40 ( real, (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun int bool))) (fun _let_0 (fun int _let_0))) ) 15.16/15.40 ( real, (fun int (fun int (fun bool bool))), (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 15.16/15.40 ( real, (fun (fun int real) (fun int bool)), (fun (fun int (fun int real)) (fun int (fun int bool))) ) 15.16/15.40 ( real, (fun int (fun nat bool)), (fun int bool) ) 15.16/15.40 ( real, (fun int (fun nat bool)), (fun int (fun nat (fun bool bool))) ) 15.16/15.40 ( real, (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun nat bool))) (fun _let_0 (fun int _let_0))) ) 15.16/15.40 ( real, (fun int (fun nat (fun bool bool))), (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 15.16/15.40 ( real, (fun (fun nat real) (fun nat bool)), (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 15.16/15.40 ( (product_prod int int), bool, bool ) 15.16/15.40 ( (product_prod int int), bool, (fun bool bool) ) 15.16/15.40 ( (product_prod int int), int, bool ) 15.16/15.40 ( (product_prod int int), int, int ) 15.16/15.40 ( (product_prod int int), int, (fun int bool) ) 15.16/15.40 ( (product_prod int int), int, (fun int int) ) 15.16/15.40 ( (product_prod int int), int, (fun (product_prod int int) int) ) 15.16/15.40 ( (product_prod int int), (fun int int), (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 15.16/15.40 ( (product_prod int int), (fun bool bool), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 15.16/15.40 ( (product_prod int int), (fun (product_prod int int) bool), (fun (product_prod int int) bool) ) 15.16/15.40 ( (product_prod int int), (fun (product_prod int int) (fun int bool)), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 15.16/15.40 ( (product_prod int int), (fun (product_prod int int) int), (fun (product_prod int int) bool) ) 15.16/15.40 ( (product_prod int int), (fun (product_prod int int) int), (fun (product_prod int int) (fun int bool)) ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP _let_1 (fun real _let_0) (deriv real) arctan) X_2) (hAPP real real (inverse_inverse real) (hAPP real real (hAPP real _let_1 (plus_plus real) (one_one real)) (hAPP nat real (hAPP real (fun nat real) (power_power real) X_2) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))))) ) 15.16/15.40 ( (hAPP int real (number_number_of real) min_1) ) 15.16/15.40 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (even_odd_even nat))) (= (not (hBOOL (hAPP nat bool _let_0 X_2))) (hBOOL (hAPP nat bool _let_0 (hAPP nat nat suc X_2))))) ) 15.16/15.40 ( (zero_zero nat) ) 15.16/15.40 ( (hAPP nat nat suc (zero_zero nat)) ) 15.16/15.40 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((N_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) (hAPP real real (inverse_inverse real) (hAPP nat real (real_1 nat) (hAPP nat nat (fact_fact nat) N_1))))) ) 15.16/15.40 ( (zero_zero nat) ) 15.16/15.40 ( (hAPP nat nat suc (zero_zero nat)) ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((K $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int bit1 K)) pls)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) pls))))) ) 15.16/15.40 ( pls ) 15.16/15.40 ( (hAPP int int bit1 pls) ) 15.16/15.40 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.16/15.40 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.16/15.40 ( min_1 ) 15.16/15.40 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.16/15.40 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.16/15.40 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 15.16/15.40 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (one_one real)) (hAPP real real (exp real) X_2))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) X_2))))) ) 15.16/15.40 ( pi ) 15.16/15.40 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.40 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.40 ( skv_2 ) 15.16/15.40 ( skv_8 ) 15.16/15.40 ( skv_9 ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (member X_a))) (= _let_0 (ti (fun X_a (fun (fun X_a bool) bool)) _let_0))) ) 15.16/15.40 ( nat ) 15.16/15.40 ( int ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((X_2 $$unsorted)) (= (hBOOL (hAPP int bool nat_is_nat X_2)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) X_2))) ) 15.16/15.40 ( (one_one int) ) 15.16/15.40 ( (zero_zero int) ) 15.16/15.40 ( min_1 ) 15.16/15.40 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.40 ( s ) 15.16/15.40 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.16/15.40 ( (hAPP int int (number_number_of int) pls) ) 15.16/15.40 ( skv_4 ) 15.16/15.40 ( skv_10 ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((N_1 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (times_times real))) (= (one_one real) (hAPP real real cos (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real (hAPP real _let_0 _let_1 (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP nat real (real_1 nat) N_1))) pi))))) ) 15.16/15.40 ( (zero_zero nat) ) 15.16/15.40 ( (hAPP nat nat suc (zero_zero nat)) ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((X_1 $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (zero_zero nat)) (hAPP real nat natfloor X_1))) ) 15.16/15.40 ( (one_one real) ) 15.16/15.40 ( (zero_zero real) ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((N $$unsorted) (Ma $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP quickcheck_code_int int quickcheck_int_of N)) (hAPP quickcheck_code_int int quickcheck_int_of Ma))) (hBOOL (hAPP quickcheck_code_int bool (hAPP quickcheck_code_int (fun quickcheck_code_int bool) (ord_less_eq quickcheck_code_int) N) Ma))) ) 15.16/15.40 ( (zero_zero quickcheck_code_int), (zero_zero quickcheck_code_int) ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((N $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP int real (real_1 int) N)) (zero_zero real))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) N) (zero_zero int)))) ) 15.16/15.40 ( (one_one int) ) 15.16/15.40 ( (zero_zero int) ) 15.16/15.40 ( pls ) 15.16/15.40 ( min_1 ) 15.16/15.40 ( s ) 15.16/15.40 ( t ) 15.16/15.40 ( skv_4 ) 15.16/15.40 ( skv_10 ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (zero_zero real))) (= (= _let_0 (hAPP real real sqrt X_2)) (= _let_0 X_2))) ) 15.16/15.40 ( (one_one real) ) 15.16/15.40 ( (zero_zero real) ) 15.16/15.40 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.40 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((X_2 $$unsorted)) (= (not (hBOOL (hAPP int bool nat_neg X_2))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) X_2))) ) 15.16/15.40 ( (one_one int) ) 15.16/15.40 ( min_1 ) 15.16/15.40 ( (hAPP int int (number_number_of int) min_1) ) 15.16/15.40 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.40 ( s ) 15.16/15.40 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.16/15.40 ( (hAPP int int (number_number_of int) pls) ) 15.16/15.40 ( skv_4 ) 15.16/15.40 ( skv_10 ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (list X_a))) (let ((_let_1 (size_size _let_0))) (= _let_1 (ti (fun _let_0 nat) _let_1)))) ) 15.16/15.40 ( int ) 15.16/15.40 ) 15.16/15.40 (instantiation (forall ((X_a $$unsorted) (X_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_a bool))) (= (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) X_2) A_3)) (hBOOL (hAPP X_a bool A_3 X_2)))) ) 15.16/15.40 ( nat, (zero_zero nat), (even_odd_even nat) ) 15.16/15.40 ( nat, (zero_zero nat), prime ) 15.16/15.40 ( nat, (hAPP nat nat suc (zero_zero nat)), prime ) 15.16/15.40 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) ) 15.16/15.40 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), prime ) 15.16/15.40 ( nat, (one_one nat), (even_odd_even nat) ) 15.16/15.40 ( int, (one_one int), nat_neg ) 15.16/15.40 ( int, (one_one int), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 15.16/15.40 ( int, (one_one int), (hAPP int (fun int bool) (ord_less int) (zero_zero int)) ) 15.16/15.40 ( int, (one_one int), zEven ) 15.16/15.40 ( int, (one_one int), (even_odd_even int) ) 15.16/15.40 ( int, (one_one int), nat_is_nat ) 15.16/15.40 ( int, (zero_zero int), (even_odd_even int) ) 15.16/15.40 ( int, (zero_zero int), nat_is_nat ) 15.16/15.40 ( int, pls, (hAPP int (fun int bool) (ord_less int) pls) ) 15.16/15.40 ( int, pls, (hAPP int (fun int bool) (ord_less int) min_1) ) 15.16/15.40 ( int, pls, (hAPP int (fun int bool) (ord_less_eq int) min_1) ) 15.16/15.40 ( int, min_1, (hAPP int (fun int bool) (ord_less int) pls) ) 15.16/15.40 ( int, min_1, (hAPP int (fun int bool) (ord_less_eq int) pls) ) 15.16/15.40 ( int, min_1, (hAPP int (fun int bool) (ord_less int) min_1) ) 15.16/15.40 ( int, min_1, (hAPP int (fun int bool) (ord_less_eq int) min_1) ) 15.16/15.40 ( int, (hAPP int int (number_number_of int) min_1), nat_neg ) 15.16/15.40 ( int, (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int (fun int bool) quadRes (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))) ) 15.16/15.40 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 15.16/15.40 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), zprime ) 15.16/15.40 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), nat_is_nat ) 15.16/15.40 ( int, s, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 15.16/15.40 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int (fun int bool) (ord_less int) (zero_zero int)) ) 15.16/15.40 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), zprime ) 15.16/15.40 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int (fun int bool) (ord_less int) s) ) 15.16/15.40 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) s)) ) 15.16/15.40 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (let ((_let_3 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int _let_1 _let_2 s) _let_3)) (hAPP nat int (hAPP int _let_1 _let_2 s1) _let_3)))))) ) 15.16/15.40 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))) ) 15.16/15.40 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int (fun int bool) (ord_less int) t) ) 15.16/15.40 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))) ) 15.16/15.40 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_4)) ) 15.16/15.40 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int (fun int bool) (ord_less int) skv_4) ) 15.16/15.40 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int (fun int bool) (ord_less int) skv_10) ) 15.16/15.40 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_10)) ) 15.16/15.40 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))) ) 15.16/15.40 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))) ) 15.16/15.40 ( int, t, (hAPP int (fun int bool) (ord_less_eq int) (one_one int)) ) 15.16/15.40 ( int, t, (hAPP int (fun int bool) (ord_less int) (one_one int)) ) 15.16/15.40 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) t))), twoSqu1091635170sum2sq ) 15.16/15.40 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 15.16/15.40 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), nat_is_nat ) 15.16/15.40 ( int, (hAPP int int (number_number_of int) pls), nat_neg ) 15.16/15.40 ( int, (hAPP int int (number_number_of int) pls), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 15.16/15.40 ( int, skv_4, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 15.16/15.40 ( int, skv_10, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 15.16/15.40 ( (fun int bool), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP (fun int nat) (fun (fun int bool) bool) (nat_tr1645093318rphism int nat) nat_1) ) 15.16/15.40 ( (fun int bool), zEven, (hAPP int (fun (fun int bool) bool) (member int) (one_one int)) ) 15.16/15.40 ( (fun nat bool), (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)), (finite_finite_1 nat) ) 15.16/15.40 ( (fun nat bool), (hAPP bool (fun nat bool) (combk bool nat) fTrue), (hAPP (fun nat int) (fun (fun nat bool) bool) (nat_tr1645093318rphism nat int) (semiring_1_of_nat int)) ) 15.16/15.40 ( real, (one_one real), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 (fun real bool) (sums real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (hAPP real _let_1 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc)))) ) 15.16/15.40 ( real, (zero_zero real), (hAPP real (fun real bool) (ord_less real) (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.16/15.40 ( real, (zero_zero real), (hAPP real (fun real bool) (ord_less real) pi) ) 15.16/15.40 ( real, (zero_zero real), (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.16/15.40 ( real, (zero_zero real), (hAPP real (fun real bool) (ord_less real) (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.16/15.40 ( real, pi, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) ) 15.16/15.40 ( real, pi, (hAPP real (fun real bool) (ord_less real) (zero_zero real)) ) 15.16/15.41 ( real, pi, (hAPP real (fun real bool) (ord_less real) (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi))) ) 15.16/15.41 ( real, pi, (hAPP real (fun real bool) (ord_less_eq real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.41 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.16/15.41 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real (fun real bool) (ord_less real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.16/15.41 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real (fun real bool) (ord_less_eq real) skv_5) ) 15.16/15.41 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) ) 15.16/15.41 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real (fun real bool) (ord_less real) (zero_zero real)) ) 15.16/15.41 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real (fun real bool) (ord_less real) pi) ) 15.16/15.41 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) ) 15.16/15.41 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real (fun real bool) (ord_less real) (zero_zero real)) ) 15.16/15.41 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real (fun real bool) (ord_less real) (one_one real)) ) 15.16/15.41 ( real, skv_2, (hAPP real (fun real bool) (ord_less real) (zero_zero real)) ) 15.16/15.41 ( real, skv_3, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) ) 15.16/15.41 ( real, skv_5, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) ) 15.16/15.41 ( real, skv_7, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) ) 15.16/15.41 ( real, skv_8, (hAPP real (fun real bool) (ord_less real) (zero_zero real)) ) 15.16/15.41 ( real, skv_9, (hAPP real (fun real bool) (ord_less real) (zero_zero real)) ) 15.16/15.41 ( real, skv_12, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) ) 15.16/15.41 ( (filter nat), sequentially, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun (filter nat) bool))) (hAPP real _let_2 (hAPP _let_1 (fun real _let_2) (tendsto nat real) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))) (zero_zero real))))) ) 15.16/15.41 ( (filter nat), sequentially, (trivial_limit nat) ) 15.16/15.41 ( (filter real), (hAPP real (filter real) (at real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (filter real) bool))) (hAPP real _let_2 (hAPP _let_0 (fun real _let_2) (tendsto real real) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin)) (zero_zero real))))) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((K $$unsorted)) (let ((_let_0 (fun int bool))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) min_1) K)) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) min_1) (hAPP int int bit0 K))))) ) 15.16/15.41 ( pls ) 15.16/15.41 ( (hAPP int int bit1 pls) ) 15.16/15.41 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.16/15.41 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.16/15.41 ( min_1 ) 15.16/15.41 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (if X_a))) (= _let_0 (ti (fun bool (fun X_a (fun X_a X_a))) _let_0))) ) 15.16/15.41 ( bool ) 15.16/15.41 ( nat ) 15.16/15.41 ( int ) 15.16/15.41 ( (fun int bool) ) 15.16/15.41 ( (fun int (fun int bool)) ) 15.16/15.41 ( (fun int int) ) 15.16/15.41 ( (fun nat bool) ) 15.16/15.41 ( real ) 15.16/15.41 ( (fun real bool) ) 15.16/15.41 ( (fun real real) ) 15.16/15.41 ( complex ) 15.16/15.41 ( (fun nat real) ) 15.16/15.41 ( (product_prod int int) ) 15.16/15.41 ( code_code_numeral ) 15.16/15.41 ( (fun int (fun int (fun int bool))) ) 15.16/15.41 ( (fun (product_prod int int) bool) ) 15.16/15.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 15.16/15.41 ( (fun (product_prod int int) int) ) 15.16/15.41 ( (fun int real) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((P_5 $$unsorted)) (let ((_let_0 (zero_zero int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (product_Pair int int))) (= (hAPP int _let_1 (hAPP int _let_2 _let_3 _let_0) (one_one int)) (hAPP _let_1 _let_1 normalize (hAPP int _let_1 (hAPP int _let_2 _let_3 P_5) _let_0))))))) ) 15.16/15.41 ( (one_one int) ) 15.16/15.41 ( (zero_zero int) ) 15.16/15.41 ( s ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((Y_2 $$unsorted)) (let ((_let_0 (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)))) (= (hBOOL (hAPP real bool _let_0 (hAPP real real sqrt Y_2))) (hBOOL (hAPP real bool _let_0 Y_2)))) ) 15.16/15.41 ( (one_one real) ) 15.16/15.41 ( (zero_zero real) ) 15.16/15.41 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.41 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (times_times real))) (let ((_let_3 (fun real _let_1))) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP _let_1 (fun real _let_0) (deriv real) (hAPP _let_1 _let_1 (hAPP _let_3 (fun _let_1 _let_1) (combs real real real) (hAPP _let_1 _let_3 (hAPP _let_3 (fun _let_1 _let_3) (combb real _let_1 real) _let_2) cos)) cos)) X_2) (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real _let_1 _let_2 (hAPP real real (hAPP real _let_1 _let_2 (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real cos X_2))) (hAPP real real sin X_2))))))))) ) 15.16/15.41 ( (zero_zero real) ) 15.16/15.41 ( pi ) 15.16/15.41 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.41 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.41 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.16/15.41 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.16/15.41 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.16/15.41 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.16/15.41 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.16/15.41 ( skv_5 ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((Z_1 $$unsorted) (W $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (or (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 W) Z_1)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 Z_1) W))))) ) 15.16/15.41 ( (one_one int), (zero_zero int) ) 15.16/15.41 ( (one_one int), t ) 15.16/15.41 ( (zero_zero int), (one_one int) ) 15.16/15.41 ( (zero_zero int), min_1 ) 15.16/15.41 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.41 ( (zero_zero int), s ) 15.16/15.41 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.16/15.41 ( (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.16/15.41 ( (zero_zero int), skv_4 ) 15.16/15.41 ( (zero_zero int), skv_10 ) 15.16/15.41 ( pls, min_1 ) 15.16/15.41 ( min_1, (zero_zero int) ) 15.16/15.41 ( min_1, pls ) 15.16/15.41 ( min_1, min_1 ) 15.16/15.41 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 15.16/15.41 ( s, (zero_zero int) ) 15.16/15.41 ( t, (one_one int) ) 15.16/15.41 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 15.16/15.41 ( (hAPP int int (number_number_of int) pls), (zero_zero int) ) 15.16/15.41 ( skv_4, (zero_zero int) ) 15.16/15.41 ( skv_10, (zero_zero int) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((N_1 $$unsorted)) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) N_1) (zero_zero nat)))) ) 15.16/15.41 ( (zero_zero nat) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (collect X_a))) (= _let_1 (ti (fun _let_0 _let_0) _let_1)))) ) 15.16/15.41 ( bool ) 15.16/15.41 ( nat ) 15.16/15.41 ( int ) 15.16/15.41 ( (fun int bool) ) 15.16/15.41 ( (fun nat bool) ) 15.16/15.41 ( (product_prod nat nat) ) 15.16/15.41 ( real ) 15.16/15.41 ( (filter nat) ) 15.16/15.41 ( (product_prod int int) ) 15.16/15.41 ( (product_prod real real) ) 15.16/15.41 ( (fun nat rat) ) 15.16/15.41 ( (filter real) ) 15.16/15.41 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 15.16/15.41 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_0 (even_odd_even nat))) (let ((_let_1 (hBOOL (hAPP nat bool _let_0 Y_2)))) (let ((_let_2 (hBOOL (hAPP nat bool _let_0 X_2)))) (= (or (and _let_1 _let_2) (and (not _let_2) (not _let_1))) (hBOOL (hAPP nat bool _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) X_2) Y_2))))))) ) 15.16/15.41 ( (one_one nat), (one_one nat) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((N_1 $$unsorted)) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP nat nat suc N_1)) N_1))) ) 15.16/15.41 ( (zero_zero nat) ) 15.16/15.41 ( (hAPP nat nat suc (zero_zero nat)) ) 15.16/15.41 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((N_1 $$unsorted)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) (hAPP nat int (semiring_1_of_nat int) N_1))) ) 15.16/15.41 ( (zero_zero nat) ) 15.16/15.41 ( (hAPP nat nat suc (zero_zero nat)) ) 15.16/15.41 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.16/15.41 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (zero_zero real))) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_2) _let_2)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real sqrt X_2)) _let_2)))))) ) 15.16/15.41 ( (one_one real) ) 15.16/15.41 ( (zero_zero real) ) 15.16/15.41 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.41 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_0 (even_odd_even int))) (let ((_let_1 (hBOOL (hAPP int bool _let_0 Y_2)))) (let ((_let_2 (hBOOL (hAPP int bool _let_0 X_2)))) (= (hBOOL (hAPP int bool _let_0 (hAPP int int (hAPP int (fun int int) (minus_minus int) X_2) Y_2))) (or (and _let_1 _let_2) (and (not _let_1) (not _let_2))))))) ) 15.16/15.41 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((N_1 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (times_times real))) (= (zero_zero real) (hAPP real real sin (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real (hAPP real _let_0 _let_1 (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP nat real (real_1 nat) N_1))) pi))))) ) 15.16/15.41 ( (zero_zero nat) ) 15.16/15.41 ( (hAPP nat nat suc (zero_zero nat)) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((N_1 $$unsorted)) (= (zero_zero real) (hAPP real real tan (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP nat real (real_1 nat) N_1)) pi))) ) 15.16/15.41 ( (zero_zero nat) ) 15.16/15.41 ( (hAPP nat nat suc (zero_zero nat)) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((N_1 $$unsorted)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP int int (uminus_uminus int) (hAPP nat int (semiring_1_of_nat int) N_1))) (zero_zero int))) ) 15.16/15.41 ( (zero_zero nat) ) 15.16/15.41 ( (hAPP nat nat suc (zero_zero nat)) ) 15.16/15.41 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.16/15.41 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((X_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP real real (hAPP real (fun real real) (minus_minus real) X_1) (one_one real))) (hAPP nat real (real_1 nat) (hAPP real nat natfloor X_1)))) ) 15.16/15.41 ( (one_one real) ) 15.16/15.41 ( (zero_zero real) ) 15.16/15.41 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((N $$unsorted) (Ma $$unsorted)) (let ((_let_0 (real_1 nat))) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) N) Ma)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (hAPP real (fun real real) (plus_plus real) (hAPP nat real _let_0 N)) (one_one real))) (hAPP nat real _let_0 Ma))))) ) 15.16/15.41 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((I_1 $$unsorted) (M $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) I_1) (hAPP nat nat suc (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) I_1) M)))) ) 15.16/15.41 ( (one_one nat), (one_one nat) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (complex_case X_a))) (= _let_0 (ti (fun (fun real (fun real X_a)) (fun complex X_a)) _let_0))) ) 15.16/15.41 ( bool ) 15.16/15.41 ( nat ) 15.16/15.41 ( real ) 15.16/15.41 ( complex ) 15.16/15.41 ( (fun nat (product_prod real real)) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((N_1 $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP nat nat suc (zero_zero nat))) (hAPP nat nat (fact_fact nat) N_1))) ) 15.16/15.41 ( (zero_zero nat) ) 15.16/15.41 ( (hAPP nat nat suc (zero_zero nat)) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((N_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) (hAPP nat real (real_1 nat) (hAPP nat nat suc N_1)))) ) 15.16/15.41 ( (zero_zero nat) ) 15.16/15.41 ( (hAPP nat nat suc (zero_zero nat)) ) 15.16/15.41 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((A_2 $$unsorted)) (let ((_let_0 (filter complex))) (let ((_let_1 (fun _let_0 bool))) (hBOOL (hAPP _let_0 bool (hAPP complex _let_1 (hAPP (fun complex complex) (fun complex _let_1) (tendsto complex complex) cnj) (hAPP complex complex cnj A_2)) (hAPP complex _let_0 (at complex) A_2))))) ) 15.16/15.41 ( (one_one complex) ) 15.16/15.41 ( ii ) 15.16/15.41 ( (zero_zero complex) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((K $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int bit1 K)) min_1)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) min_1))))) ) 15.16/15.41 ( pls ) 15.16/15.41 ( (hAPP int int bit1 pls) ) 15.16/15.41 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.16/15.41 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.16/15.41 ( min_1 ) 15.16/15.41 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.16/15.41 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.16/15.41 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 15.16/15.41 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (fun (product_prod X_a X_a) bool))) (let ((_let_1 (mlex_prod X_a))) (= _let_1 (ti (fun (fun X_a nat) (fun _let_0 _let_0)) _let_1)))) ) 15.16/15.41 ( nat ) 15.16/15.41 ( int ) 15.16/15.41 ( (product_prod nat nat) ) 15.16/15.41 ( real ) 15.16/15.41 ( complex ) 15.16/15.41 ( (product_prod int int) ) 15.16/15.41 ( quickcheck_code_int ) 15.16/15.41 ( code_code_numeral ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_2) Y_2)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real sqrt X_2)) (hAPP real real sqrt Y_2)))))) ) 15.16/15.41 ( (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.41 ( (zero_zero real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((N_1 $$unsorted) (M $$unsorted)) (let ((_let_0 (semiring_1_of_nat int))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP int int (uminus_uminus int) (hAPP nat int _let_0 N_1))) (hAPP nat int _let_0 M)))) ) 15.16/15.41 ( (zero_zero nat), (zero_zero nat) ) 15.16/15.41 ( (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 15.16/15.41 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.16/15.41 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.41 ( (hAPP nat nat suc (zero_zero nat)), (zero_zero nat) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((R_1 $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat real))) (let ((_let_3 (fun _let_2 _let_2))) (let ((_let_4 (fun (filter nat) bool))) (let ((_let_5 (combb real real nat))) (hBOOL (hAPP (filter nat) bool (hAPP real _let_4 (hAPP _let_2 (fun real _let_4) (tendsto nat real) (hAPP _let_2 _let_2 (hAPP _let_1 _let_3 _let_5 (hAPP real _let_1 (times_times real) R_1)) (hAPP _let_2 _let_2 (hAPP _let_1 _let_3 _let_5 (hAPP real _let_1 (plus_plus real) (one_one real))) (hAPP _let_2 _let_2 (hAPP _let_1 _let_3 _let_5 (uminus_uminus real)) (hAPP _let_2 _let_2 (hAPP _let_1 _let_3 _let_5 (inverse_inverse real)) (hAPP _let_0 _let_2 (hAPP _let_2 (fun _let_0 _let_2) (combb nat real nat) (real_1 nat)) suc)))))) R_1) sequentially)))))))) ) 15.16/15.41 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.41 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.41 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_0 (semiring_1_of_nat int))) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) X_2) Y_2)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP nat int _let_0 X_2)) (hAPP nat int _let_0 Y_2))))) ) 15.16/15.41 ( (zero_zero nat), (zero_zero nat) ) 15.16/15.41 ( (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 15.16/15.41 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.16/15.41 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((X_2 $$unsorted) (A_2 $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) X_2) (hAPP int real (real_1 int) A_2))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP real int (archimedean_ceiling real) X_2)) A_2))) ) 15.16/15.41 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero int) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((Z_1 $$unsorted)) (= Z_1 (hAPP complex real re (hAPP real complex (of_real complex) Z_1))) ) 15.16/15.41 ( pi ) 15.16/15.41 ( (hAPP int real (number_number_of real) min_1) ) 15.16/15.41 ( (hAPP real real (uminus_uminus real) (one_one real)) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((I_1 $$unsorted) (M $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) I_1) (hAPP nat nat suc (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) M) I_1)))) ) 15.16/15.41 ( (one_one nat), (one_one nat) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((Z_5 $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) Z_5) (zero_zero int))) (hBOOL (hAPP int bool nat_neg Z_5))) ) 15.16/15.41 ( (one_one int) ) 15.16/15.41 ( pls ) 15.16/15.41 ( min_1 ) 15.16/15.41 ( (hAPP int int (number_number_of int) min_1) ) 15.16/15.41 ( s ) 15.16/15.41 ( t ) 15.16/15.41 ( (hAPP int int (number_number_of int) pls) ) 15.16/15.41 ( skv_4 ) 15.16/15.41 ( skv_10 ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((K1 $$unsorted) (K2 $$unsorted)) (let ((_let_0 (fun int bool))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (hAPP int int bit0 K1)) (hAPP int int bit1 K2))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) K1) K2)))) ) 15.16/15.41 ( (one_one int), t ) 15.16/15.41 ( (zero_zero int), (one_one int) ) 15.16/15.41 ( (zero_zero int), min_1 ) 15.16/15.41 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.41 ( (zero_zero int), s ) 15.16/15.41 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.16/15.41 ( (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.16/15.41 ( (zero_zero int), skv_4 ) 15.16/15.41 ( (zero_zero int), skv_10 ) 15.16/15.41 ( pls, min_1 ) 15.16/15.41 ( min_1, pls ) 15.16/15.41 ( min_1, min_1 ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (accp X_a))) (= _let_1 (ti (fun (fun X_a _let_0) _let_0) _let_1)))) ) 15.16/15.41 ( bool ) 15.16/15.41 ( nat ) 15.16/15.41 ( int ) 15.16/15.41 ( (fun int bool) ) 15.16/15.41 ( (fun nat bool) ) 15.16/15.41 ( (product_prod nat nat) ) 15.16/15.41 ( real ) 15.16/15.41 ( (filter nat) ) 15.16/15.41 ( (product_prod int int) ) 15.16/15.41 ( (product_prod real real) ) 15.16/15.41 ( (fun nat rat) ) 15.16/15.41 ( (filter real) ) 15.16/15.41 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 15.16/15.41 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((K $$unsorted)) (let ((_let_0 (hAPP int (fun int bool) (ord_less int) pls))) (= (hBOOL (hAPP int bool _let_0 (hAPP int int bit0 K))) (hBOOL (hAPP int bool _let_0 K)))) ) 15.16/15.41 ( pls ) 15.16/15.41 ( (hAPP int int bit1 pls) ) 15.16/15.41 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.16/15.41 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.16/15.41 ( min_1 ) 15.16/15.41 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((Real1_1 $$unsorted) (Real2_1 $$unsorted)) (= (zero_zero nat) (hAPP complex nat (size_size complex) (hAPP real complex (hAPP real (fun real complex) complex_1 Real1_1) Real2_1))) ) 15.16/15.41 ( (one_one real), (zero_zero real) ) 15.16/15.41 ( (zero_zero real), (one_one real) ) 15.16/15.41 ( (zero_zero real), (zero_zero real) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((K $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int bit0 K)) pls)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) pls))))) ) 15.16/15.41 ( pls ) 15.16/15.41 ( (hAPP int int bit1 pls) ) 15.16/15.41 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.16/15.41 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.16/15.41 ( min_1 ) 15.16/15.41 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((N_1 $$unsorted)) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP nat real (real_1 nat) N_1)) (zero_zero real)))) ) 15.16/15.41 ( (zero_zero nat) ) 15.16/15.41 ( (hAPP nat nat suc (zero_zero nat)) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((N $$unsorted) (Ma $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP quickcheck_code_int int quickcheck_int_of N)) (hAPP quickcheck_code_int int quickcheck_int_of Ma))) (hBOOL (hAPP quickcheck_code_int bool (hAPP quickcheck_code_int (fun quickcheck_code_int bool) (ord_less quickcheck_code_int) N) Ma))) ) 15.16/15.41 ( (zero_zero quickcheck_code_int), (zero_zero quickcheck_code_int) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((Z_1 $$unsorted)) (= (zero_zero int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP int int (uminus_uminus int) Z_1)) Z_1)) ) 15.16/15.41 ( (one_one int) ) 15.16/15.41 ( pls ) 15.16/15.41 ( min_1 ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((X_2 $$unsorted)) (= (= (zero_zero int) (ti int X_2)) (= (zero_zero real) (hAPP int real (real_1 int) X_2))) ) 15.16/15.41 ( (one_one int) ) 15.16/15.41 ( (zero_zero int) ) 15.16/15.41 ( pls ) 15.16/15.41 ( min_1 ) 15.16/15.41 ( s ) 15.16/15.41 ( m ) 15.16/15.41 ( s1 ) 15.16/15.41 ( t ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((R_4 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) R_4) (hAPP real real (hAPP real (fun real real) (plus_plus real) (hAPP int real (real_1 int) (hAPP real int (archim2085082626_floor real) R_4))) (one_one real)))) ) 15.16/15.41 ( (zero_zero real) ) 15.16/15.41 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.41 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.41 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.41 ( skv_5 ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (hBOOL (hAPP real bool (hAPP _let_1 (fun real bool) (sums real) (hAPP _let_1 _let_1 (hAPP _let_2 (fun _let_1 _let_1) (combs nat real real) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 nat) (times_times real)) sin_coeff)) (hAPP real _let_1 (power_power real) X_2))) (hAPP real real sin X_2)))))) ) 15.16/15.41 ( (zero_zero real) ) 15.16/15.41 ( pi ) 15.16/15.41 ( (hAPP int real (number_number_of real) min_1) ) 15.16/15.41 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.41 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.41 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.16/15.41 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.16/15.41 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.16/15.41 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.16/15.41 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (powp X_a))) (= _let_1 (ti (fun _let_0 (fun _let_0 bool)) _let_1)))) ) 15.16/15.41 ( nat ) 15.16/15.41 ( int ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_0 (even_odd_even nat))) (let ((_let_1 (hBOOL (hAPP nat bool _let_0 X_2)))) (let ((_let_2 (hBOOL (hAPP nat bool _let_0 Y_2)))) (= (hBOOL (hAPP nat bool _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) X_2) Y_2))) (or (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) X_2) Y_2)) (and (not _let_1) (not _let_2)) (and _let_1 _let_2)))))) ) 15.16/15.41 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((K $$unsorted)) (let ((_let_0 (fun int bool))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (hAPP int int bit0 K)) min_1)) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) K) min_1)))) ) 15.16/15.41 ( (one_one int) ) 15.16/15.41 ( (zero_zero int) ) 15.16/15.41 ( pls ) 15.16/15.41 ( (hAPP int int bit1 pls) ) 15.16/15.41 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.16/15.41 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.16/15.41 ( min_1 ) 15.16/15.41 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP (fun real real) (fun real _let_0) (deriv real) cos) X_2) (hAPP real real (uminus_uminus real) (hAPP real real sin X_2))))) ) 15.16/15.41 ( (zero_zero real) ) 15.16/15.41 ( pi ) 15.16/15.41 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.41 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.16/15.41 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.16/15.41 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.16/15.41 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.16/15.41 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member int))) (= (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP int int (hAPP int (fun int int) (minus_minus int) X_2) Y_2)) zEven)) (= (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 Y_2) zEven)) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 X_2) zEven))))))) ) 15.16/15.41 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_0 (real_1 int))) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) X_2) Y_2)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP int real _let_0 X_2)) (hAPP int real _let_0 Y_2))))) ) 15.16/15.41 ( (one_one int), t ) 15.16/15.41 ( (zero_zero int), (one_one int) ) 15.16/15.41 ( (zero_zero int), min_1 ) 15.16/15.41 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.41 ( (zero_zero int), s ) 15.16/15.41 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.16/15.41 ( (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.16/15.41 ( (zero_zero int), skv_4 ) 15.16/15.41 ( (zero_zero int), skv_10 ) 15.16/15.41 ( min_1, pls ) 15.16/15.41 ( min_1, min_1 ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((Ma $$unsorted) (N $$unsorted)) (let ((_let_0 (hAPP nat (fun nat bool) (ord_less nat) Ma))) (= (hBOOL (hAPP nat bool _let_0 (hAPP nat nat suc N))) (or (= Ma N) (hBOOL (hAPP nat bool _let_0 N))))) ) 15.16/15.41 ( (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((K $$unsorted) (N $$unsorted)) (let ((_let_0 (hAPP nat (fun nat bool) (dvd_dvd nat) K))) (= (hBOOL (hAPP nat bool _let_0 N)) (hBOOL (hAPP nat bool _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) N) K))))) ) 15.16/15.41 ( (one_one nat), (one_one nat) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (times_times real))) (let ((_let_3 (fun real _let_1))) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP _let_1 (fun real _let_0) (deriv real) (hAPP _let_1 _let_1 (hAPP _let_3 (fun _let_1 _let_1) (combs real real real) (hAPP _let_1 _let_3 (hAPP _let_3 (fun _let_1 _let_3) (combb real _let_1 real) _let_2) cos)) cos)) X_2) (hAPP real real (hAPP real _let_1 _let_2 (hAPP real real (hAPP real _let_1 _let_2 (hAPP int real (number_number_of real) (hAPP int int bit0 min_1))) (hAPP real real cos X_2))) (hAPP real real sin X_2)))))))) ) 15.16/15.41 ( (zero_zero real) ) 15.16/15.41 ( pi ) 15.16/15.41 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.41 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.41 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.16/15.41 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.16/15.41 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.16/15.41 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.16/15.41 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.16/15.41 ( skv_5 ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((M $$unsorted)) (let ((_let_0 (fun int bool))) (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong M) (zero_zero int)) M))) ) 15.16/15.41 ( s1 ) 15.16/15.41 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.41 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.41 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((N_1 $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (one_one nat)) (hAPP nat nat fact N_1))) ) 15.16/15.41 ( (zero_zero nat) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((N_1 $$unsorted)) (= N_1 (hAPP int nat nat_1 (hAPP nat int (semiring_1_of_nat int) N_1))) ) 15.16/15.41 ( (zero_zero nat) ) 15.16/15.41 ( (hAPP nat nat suc (zero_zero nat)) ) 15.16/15.41 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.16/15.41 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (measure X_a))) (= _let_0 (ti (fun (fun X_a nat) (fun (product_prod X_a X_a) bool)) _let_0))) ) 15.16/15.41 ( nat ) 15.16/15.41 ( int ) 15.16/15.41 ( (product_prod nat nat) ) 15.16/15.41 ( real ) 15.16/15.41 ( complex ) 15.16/15.41 ( (product_prod int int) ) 15.16/15.41 ( quickcheck_code_int ) 15.16/15.41 ( code_code_numeral ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((Ma $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat bool))) (= (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) Ma) N)) (or (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) Ma) N)) (= Ma N)))) ) 15.16/15.41 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun real _let_1))) (let ((_let_3 (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP real real (uminus_uminus real) (hAPP real real sin X_2))) (hAPP real real cos X_2)))) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP (fun real real) (fun real _let_0) (deriv real) (hAPP nat (fun real real) (hAPP _let_2 (fun nat (fun real real)) (combc real nat real) (hAPP (fun real real) _let_2 (hAPP _let_2 (fun (fun real real) _let_2) (combb real _let_1 real) (power_power real)) cos)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) X_2) (hAPP real real (hAPP real (fun real real) (plus_plus real) _let_3) _let_3))))))) ) 15.16/15.41 ( (zero_zero real) ) 15.16/15.41 ( pi ) 15.16/15.41 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.41 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.41 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.16/15.41 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.16/15.41 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.16/15.41 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.16/15.41 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.16/15.41 ( skv_5 ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_0 (fun real bool))) (= (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) X_2) Y_2)) (or (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) X_2) Y_2)) (= X_2 Y_2)))) ) 15.16/15.41 ( (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.41 ( (zero_zero real), pi ) 15.16/15.41 ( (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.41 ( (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.41 ( (zero_zero real), skv_2 ) 15.16/15.41 ( (zero_zero real), skv_3 ) 15.16/15.41 ( (zero_zero real), skv_5 ) 15.16/15.41 ( (zero_zero real), skv_7 ) 15.16/15.41 ( (zero_zero real), skv_8 ) 15.16/15.41 ( (zero_zero real), skv_9 ) 15.16/15.41 ( (zero_zero real), skv_12 ) 15.16/15.41 ( pi, (zero_zero real) ) 15.16/15.41 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.41 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.16/15.41 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.41 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 15.16/15.41 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.16/15.41 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 15.16/15.41 ( skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (finite_card X_a))) (= _let_0 (ti (fun (fun X_a bool) nat) _let_0))) ) 15.16/15.41 ( bool ) 15.16/15.41 ( nat ) 15.16/15.41 ( int ) 15.16/15.41 ( (fun int bool) ) 15.16/15.41 ( (fun nat bool) ) 15.16/15.41 ( (product_prod nat nat) ) 15.16/15.41 ( real ) 15.16/15.41 ( (filter nat) ) 15.16/15.41 ( (product_prod int int) ) 15.16/15.41 ( (product_prod real real) ) 15.16/15.41 ( (fun nat rat) ) 15.16/15.41 ( (filter real) ) 15.16/15.41 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 15.16/15.41 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((X_2 $$unsorted) (A_2 $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) X_2) (hAPP int real (real_1 int) A_2))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP real int (archim2085082626_floor real) X_2)) A_2))) ) 15.16/15.41 ( pi, (zero_zero int) ) 15.16/15.41 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero int) ) 15.16/15.41 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero int) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((N $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) (hAPP int real (real_1 int) N))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) N))) ) 15.16/15.41 ( (one_one int) ) 15.16/15.41 ( (zero_zero int) ) 15.16/15.41 ( min_1 ) 15.16/15.41 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.41 ( s ) 15.16/15.41 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.16/15.41 ( (hAPP int int (number_number_of int) pls) ) 15.16/15.41 ( skv_4 ) 15.16/15.41 ( skv_10 ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat real))) (let ((_let_3 (power_power real))) (let ((_let_4 (fun nat _let_0))) (let ((_let_5 (fun nat _let_1))) (let ((_let_6 (fun _let_2 _let_2))) (let ((_let_7 (combs nat real real))) (let ((_let_8 (fun real _let_1))) (let ((_let_9 (fun _let_2 _let_5))) (let ((_let_10 (combb real _let_1 nat))) (let ((_let_11 (fun _let_0 _let_2))) (let ((_let_12 (combb nat real nat))) (let ((_let_13 (hAPP nat _let_0 (hAPP _let_4 _let_4 (combc nat nat nat) (hAPP _let_0 _let_4 (hAPP _let_4 (fun _let_0 _let_4) (combb nat _let_0 nat) (plus_plus nat)) (hAPP nat _let_0 (times_times nat) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))) (hBOOL (hAPP real bool (hAPP _let_2 (fun real bool) (sums real) (hAPP _let_2 _let_2 (hAPP _let_5 _let_6 _let_7 (hAPP _let_2 _let_5 (hAPP _let_8 _let_9 _let_10 (times_times real)) (hAPP _let_2 _let_2 (hAPP _let_5 _let_6 _let_7 (hAPP _let_2 _let_5 (hAPP _let_8 _let_9 _let_10 (inverse_divide real)) (hAPP real _let_2 _let_3 (hAPP int real (number_number_of real) min_1)))) (hAPP _let_0 _let_2 (hAPP _let_2 _let_11 _let_12 (real_1 nat)) (hAPP _let_0 _let_0 (hAPP _let_0 (fun _let_0 _let_0) (combb nat nat nat) (fact_fact nat)) _let_13))))) (hAPP _let_0 _let_2 (hAPP _let_2 _let_11 _let_12 (hAPP real _let_2 _let_3 X_2)) _let_13))) (hAPP real real sin X_2))))))))))))))))) ) 15.16/15.41 ( (zero_zero real) ) 15.16/15.41 ( pi ) 15.16/15.41 ( (hAPP int real (number_number_of real) min_1) ) 15.16/15.41 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.41 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.41 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.16/15.41 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.16/15.41 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.16/15.41 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.16/15.41 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((N $$unsorted)) (= (= (zero_zero nat) N) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP nat real (real_1 nat) N)) (zero_zero real)))) ) 15.16/15.41 ( (zero_zero nat) ) 15.16/15.41 ( (hAPP nat nat suc (zero_zero nat)) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat real))) (let ((_let_3 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_4 (times_times real))) (let ((_let_5 (fun nat _let_1))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun real _let_2))) (let ((_let_8 (combc real nat real))) (let ((_let_9 (hAPP _let_7 (fun _let_1 _let_7) (combb real _let_2 real) (power_power real)))) (let ((_let_10 (hAPP real real (hAPP real _let_1 _let_4 (hAPP real real (hAPP real _let_1 _let_4 (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real cos X))) (hAPP real real sin X)))) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP _let_1 (fun real _let_0) (deriv real) (hAPP _let_1 _let_1 (hAPP _let_6 (fun _let_1 _let_1) (combs real real real) (hAPP _let_1 _let_6 (hAPP _let_6 (fun _let_1 _let_6) (combb real _let_1 real) (plus_plus real)) (hAPP nat _let_1 (hAPP _let_7 _let_5 _let_8 (hAPP _let_1 _let_7 _let_9 sin)) _let_3))) (hAPP nat _let_1 (hAPP _let_7 _let_5 _let_8 (hAPP _let_1 _let_7 _let_9 cos)) _let_3))) X) (hAPP real real (hAPP real _let_1 (minus_minus real) _let_10) _let_10)))))))))))))) ) 15.16/15.41 ( (zero_zero real) ) 15.16/15.41 ( pi ) 15.16/15.41 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.41 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.41 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.16/15.41 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.16/15.41 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.16/15.41 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.16/15.41 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.16/15.41 ( skv_5 ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((M $$unsorted)) (let ((_let_0 (hAPP nat int (semiring_1_of_nat int) M))) (= _let_0 (hAPP int int (abs_abs int) _let_0))) ) 15.16/15.41 ( (zero_zero nat) ) 15.16/15.41 ( (hAPP nat nat suc (zero_zero nat)) ) 15.16/15.41 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.16/15.41 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((X_2 $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) X_2)) (= X_2 (hAPP real real (hAPP real (fun real real) powr X_2) (one_one real)))) ) 15.16/15.41 ( pi ) 15.16/15.41 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.41 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.41 ( skv_2 ) 15.16/15.41 ( skv_8 ) 15.16/15.41 ( skv_9 ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((Ma $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat bool))) (= (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) Ma) (hAPP nat nat suc N))) (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) Ma) N)))) ) 15.16/15.41 ( (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (times_times real))) (let ((_let_3 (fun real _let_1))) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP _let_1 (fun real _let_0) (deriv real) (hAPP _let_1 _let_1 (hAPP _let_3 (fun _let_1 _let_1) (combs real real real) (hAPP _let_1 _let_3 (hAPP _let_3 (fun _let_1 _let_3) (combb real _let_1 real) _let_2) sin)) sin)) X_2) (hAPP real real (hAPP real _let_1 _let_2 (hAPP real real (hAPP real _let_1 _let_2 (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real cos X_2))) (hAPP real real sin X_2)))))))) ) 15.16/15.41 ( (zero_zero real) ) 15.16/15.41 ( pi ) 15.16/15.41 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.41 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.41 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.16/15.41 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.16/15.41 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.16/15.41 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.16/15.41 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.16/15.41 ( skv_5 ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((K_4 $$unsorted)) (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP nat int (semiring_1_of_nat int) K_4)) (zero_zero int)))) ) 15.16/15.41 ( (zero_zero nat) ) 15.16/15.41 ( (hAPP nat nat suc (zero_zero nat)) ) 15.16/15.41 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.16/15.41 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((J_2 $$unsorted) (I_1 $$unsorted)) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) J_2) I_1)) I_1))) ) 15.16/15.41 ( (one_one nat), (one_one nat) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_0 (even_odd_even int))) (let ((_let_1 (hBOOL (hAPP int bool _let_0 Y_2)))) (let ((_let_2 (hBOOL (hAPP int bool _let_0 X_2)))) (= (hBOOL (hAPP int bool _let_0 (hAPP int int (hAPP int (fun int int) (plus_plus int) X_2) Y_2))) (or (and _let_1 _let_2) (and (not _let_2) (not _let_1))))))) ) 15.16/15.41 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 15.16/15.41 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((Ma $$unsorted) (N $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) Ma) (hAPP int int (number_number_of int) N))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP int real (real_1 int) Ma)) (hAPP int real (number_number_of real) N)))) ) 15.16/15.41 ( pls, pls ) 15.16/15.41 ( pls, (hAPP int int bit1 pls) ) 15.16/15.41 ( min_1, pls ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((Ma $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less nat))) (= (not (= Ma N)) (or (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 Ma) N)) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 N) Ma)))))) ) 15.16/15.41 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.41 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 15.16/15.41 ) 15.16/15.41 (instantiation (forall ((A_2 $$unsorted) (B_1 $$unsorted) (Ma $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int _let_1 zcong B_1) A_2) Ma)) (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int _let_1 zcong A_2) B_1) Ma))))) ) 15.16/15.41 ( (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.41 ( (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.41 ( (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.41 ( s, s1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.41 ( s1, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.41 ( s1, skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.41 ( s1, skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.41 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.41 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.41 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.42 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.42 ( skv_4, s1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.42 ( skv_10, s1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.42 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((K $$unsorted) (L $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (let ((_let_2 (number_number_of int))) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int _let_2 K)) (hAPP int int _let_2 L))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) L)))))) ) 15.16/15.42 ( pls, pls ) 15.16/15.42 ( pls, (hAPP int int bit1 pls) ) 15.16/15.42 ( pls, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.16/15.42 ( pls, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((K $$unsorted) (L $$unsorted)) (let ((_let_0 (fun int bool))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (hAPP int int pred K)) L)) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) K) L)))) ) 15.16/15.42 ( (one_one int), t ) 15.16/15.42 ( (zero_zero int), (one_one int) ) 15.16/15.42 ( (zero_zero int), min_1 ) 15.16/15.42 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.42 ( (zero_zero int), s ) 15.16/15.42 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.16/15.42 ( (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.16/15.42 ( (zero_zero int), skv_4 ) 15.16/15.42 ( (zero_zero int), skv_10 ) 15.16/15.42 ( pls, pls ) 15.16/15.42 ( pls, min_1 ) 15.16/15.42 ( min_1, pls ) 15.16/15.42 ( min_1, min_1 ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (exp real) X_2)) (one_one real))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_2) (zero_zero real)))))) ) 15.16/15.42 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (hilbert_Eps X_a))) (= _let_0 (ti (fun (fun X_a bool) X_a) _let_0))) ) 15.16/15.42 ( bool ) 15.16/15.42 ( nat ) 15.16/15.42 ( int ) 15.16/15.42 ( (fun int bool) ) 15.16/15.42 ( (fun nat bool) ) 15.16/15.42 ( (product_prod nat nat) ) 15.16/15.42 ( real ) 15.16/15.42 ( (filter nat) ) 15.16/15.42 ( (product_prod int int) ) 15.16/15.42 ( (product_prod real real) ) 15.16/15.42 ( (fun nat rat) ) 15.16/15.42 ( (filter real) ) 15.16/15.42 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 15.16/15.42 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_0 (product_prod_size X_a X_b))) (= _let_0 (ti (fun (fun X_a nat) (fun (fun X_b nat) (fun (product_prod X_a X_b) nat))) _let_0))) ) 15.16/15.42 ( nat, nat ) 15.16/15.42 ( int, int ) 15.16/15.42 ( int, (product_prod int int) ) 15.16/15.42 ( (product_prod nat nat), (product_prod nat nat) ) 15.16/15.42 ( real, real ) 15.16/15.42 ( (product_prod int int), (product_prod int int) ) 15.16/15.42 ( quickcheck_code_int, quickcheck_code_int ) 15.16/15.42 ( code_code_numeral, code_code_numeral ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat real))) (let ((_let_3 (power_power real))) (let ((_let_4 (fun nat _let_1))) (let ((_let_5 (fun _let_2 _let_2))) (let ((_let_6 (combs nat real real))) (let ((_let_7 (fun real _let_1))) (let ((_let_8 (fun _let_2 _let_4))) (let ((_let_9 (combb real _let_1 nat))) (let ((_let_10 (fun _let_0 _let_2))) (let ((_let_11 (combb nat real nat))) (let ((_let_12 (hAPP nat _let_0 (times_times nat) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hBOOL (hAPP real bool (hAPP _let_2 (fun real bool) (sums real) (hAPP _let_2 _let_2 (hAPP _let_4 _let_5 _let_6 (hAPP _let_2 _let_4 (hAPP _let_7 _let_8 _let_9 (times_times real)) (hAPP _let_2 _let_2 (hAPP _let_4 _let_5 _let_6 (hAPP _let_2 _let_4 (hAPP _let_7 _let_8 _let_9 (inverse_divide real)) (hAPP real _let_2 _let_3 (hAPP int real (number_number_of real) min_1)))) (hAPP _let_0 _let_2 (hAPP _let_2 _let_10 _let_11 (real_1 nat)) (hAPP _let_0 _let_0 (hAPP _let_0 (fun _let_0 _let_0) (combb nat nat nat) (fact_fact nat)) _let_12))))) (hAPP _let_0 _let_2 (hAPP _let_2 _let_10 _let_11 (hAPP real _let_2 _let_3 X_2)) _let_12))) (hAPP real real cos X_2)))))))))))))))) ) 15.16/15.42 ( (zero_zero real) ) 15.16/15.42 ( pi ) 15.16/15.42 ( (hAPP int real (number_number_of real) min_1) ) 15.16/15.42 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.42 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.42 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.42 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.16/15.42 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.16/15.42 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.16/15.42 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.16/15.42 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.16/15.42 ( skv_5 ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((K $$unsorted)) (let ((_let_0 (hAPP int (fun int bool) (ord_less int) min_1))) (= (hBOOL (hAPP int bool _let_0 (hAPP int int bit0 K))) (hBOOL (hAPP int bool _let_0 K)))) ) 15.16/15.42 ( pls ) 15.16/15.42 ( (hAPP int int bit1 pls) ) 15.16/15.42 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.16/15.42 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.16/15.42 ( min_1 ) 15.16/15.42 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((K $$unsorted)) (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) min_1))) (= (hBOOL (hAPP int bool _let_0 K)) (hBOOL (hAPP int bool _let_0 (hAPP int int bit1 K))))) ) 15.16/15.42 ( pls ) 15.16/15.42 ( (hAPP int int bit1 pls) ) 15.16/15.42 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.16/15.42 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.16/15.42 ( min_1 ) 15.16/15.42 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.16/15.42 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.16/15.42 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 15.16/15.42 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((Ma $$unsorted) (Z $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP nat int (semiring_1_of_nat int) Ma)) Z)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) Ma) (hAPP int nat nat_1 Z)))) ) 15.16/15.42 ( (zero_zero nat), (one_one int) ) 15.16/15.42 ( (zero_zero nat), pls ) 15.16/15.42 ( (zero_zero nat), min_1 ) 15.16/15.42 ( (zero_zero nat), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.42 ( (zero_zero nat), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.42 ( (hAPP nat nat suc (zero_zero nat)), t ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((N $$unsorted) (Ma $$unsorted)) (let ((_let_0 (real_1 int))) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) N) Ma)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP int real _let_0 N)) (hAPP real real (hAPP real (fun real real) (plus_plus real) (hAPP int real _let_0 Ma)) (one_one real)))))) ) 15.16/15.42 ( (one_one int), t ) 15.16/15.42 ( (zero_zero int), (one_one int) ) 15.16/15.42 ( (zero_zero int), min_1 ) 15.16/15.42 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.42 ( (zero_zero int), s ) 15.16/15.42 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.16/15.42 ( (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.16/15.42 ( (zero_zero int), skv_4 ) 15.16/15.42 ( (zero_zero int), skv_10 ) 15.16/15.42 ( min_1, pls ) 15.16/15.42 ( min_1, min_1 ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((Z_1 $$unsorted) (W $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (or (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 W) Z_1)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Z_1) W))))) ) 15.16/15.42 ( (zero_zero real), pi ) 15.16/15.42 ( (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.42 ( (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.42 ( (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.42 ( (zero_zero real), skv_3 ) 15.16/15.42 ( (zero_zero real), skv_5 ) 15.16/15.42 ( (zero_zero real), skv_7 ) 15.16/15.42 ( (zero_zero real), skv_12 ) 15.16/15.42 ( pi, (zero_zero real) ) 15.16/15.42 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.42 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.16/15.42 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.42 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_5 ) 15.16/15.42 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.16/15.42 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.42 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.16/15.42 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.16/15.42 ( skv_3, (zero_zero real) ) 15.16/15.42 ( skv_5, (zero_zero real) ) 15.16/15.42 ( skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.42 ( skv_7, (zero_zero real) ) 15.16/15.42 ( skv_12, (zero_zero real) ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (one_one real))) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_2) _let_2)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real sqrt X_2)) _let_2)))))) ) 15.16/15.42 ( (one_one real) ) 15.16/15.42 ( (zero_zero real) ) 15.16/15.42 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.42 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((K_4 $$unsorted)) (let ((_let_0 (product_prod int int))) (= (zero_zero rat) (hAPP _let_0 rat frct (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) K_4) (zero_zero int))))) ) 15.16/15.42 ( (one_one int) ) 15.16/15.42 ( (zero_zero int) ) 15.16/15.42 ( s ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_a bool))) (hBOOL (hAPP _let_0 bool (hAPP (fun X_a X_b) (fun _let_0 bool) (nat_tr1645093318rphism X_a X_b) F) A_3))) ) 15.16/15.42 ( nat, int, (semiring_1_of_nat int), (hAPP bool (fun nat bool) (combk bool nat) fTrue) ) 15.16/15.42 ( int, nat, nat_1, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((Z $$unsorted)) (let ((_let_0 (fun int bool))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (zero_zero int)) Z)) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (one_one int)) Z)))) ) 15.16/15.42 ( (one_one int) ) 15.16/15.42 ( pls ) 15.16/15.42 ( min_1 ) 15.16/15.42 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.42 ( t ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (power_power real))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (= (one_one real) (hAPP real real (hAPP real (fun real real) (plus_plus real) (hAPP nat real (hAPP real _let_0 _let_1 (hAPP real real cos X_1)) _let_2)) (hAPP nat real (hAPP real _let_0 _let_1 (hAPP real real sin X_1)) _let_2)))))) ) 15.16/15.42 ( (zero_zero real) ) 15.16/15.42 ( pi ) 15.16/15.42 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.42 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.42 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.16/15.42 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.16/15.42 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.16/15.42 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.16/15.42 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.16/15.42 ( skv_5 ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((N_1 $$unsorted)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP int int (uminus_uminus int) (hAPP nat int (semiring_1_of_nat int) (hAPP nat nat suc N_1)))) (zero_zero int))) ) 15.16/15.42 ( (zero_zero nat) ) 15.16/15.42 ( (hAPP nat nat suc (zero_zero nat)) ) 15.16/15.42 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((R_4 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (hAPP real (fun real real) (minus_minus real) R_4) (one_one real))) (hAPP int real (real_1 int) (hAPP real int (archim2085082626_floor real) R_4)))) ) 15.16/15.42 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))) ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((Y_2 $$unsorted)) (let ((_let_0 (hAPP real (fun real bool) (ord_less real) (zero_zero real)))) (= (hBOOL (hAPP real bool _let_0 Y_2)) (hBOOL (hAPP real bool _let_0 (hAPP real real sqrt Y_2))))) ) 15.16/15.42 ( (one_one real) ) 15.16/15.42 ( (zero_zero real) ) 15.16/15.42 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.42 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((K1 $$unsorted) (K2 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int bit1 K1)) (hAPP int int bit0 K2))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K1) K2))))) ) 15.16/15.42 ( min_1, pls ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((X_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP int real (number_number_of real) min_1)) (hAPP real real cos X_1))) ) 15.16/15.42 ( (zero_zero real) ) 15.16/15.42 ( pi ) 15.16/15.42 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.42 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.42 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.16/15.42 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.16/15.42 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.16/15.42 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.16/15.42 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.16/15.42 ( skv_5 ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((N_1 $$unsorted)) (= (zero_zero real) (hAPP real real sin (hAPP real real (hAPP real (fun real real) (times_times real) pi) (hAPP nat real (real_1 nat) N_1)))) ) 15.16/15.42 ( (zero_zero nat) ) 15.16/15.42 ( (hAPP nat nat suc (zero_zero nat)) ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat real))) (let ((_let_3 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_4 (times_times real))) (let ((_let_5 (fun real _let_2))) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP _let_1 (fun real _let_0) (deriv real) (hAPP nat _let_1 (hAPP _let_5 (fun nat _let_1) (combc real nat real) (hAPP _let_1 _let_5 (hAPP _let_5 (fun _let_1 _let_5) (combb real _let_2 real) (power_power real)) sin)) (hAPP int nat (number_number_of nat) _let_3))) X_2) (hAPP real real (hAPP real _let_1 _let_4 (hAPP real real (hAPP real _let_1 _let_4 (hAPP int real (number_number_of real) _let_3)) (hAPP real real cos X_2))) (hAPP real real sin X_2)))))))))) ) 15.16/15.42 ( (zero_zero real) ) 15.16/15.42 ( pi ) 15.16/15.42 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.42 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.42 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.16/15.42 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.16/15.42 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.16/15.42 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.16/15.42 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.16/15.42 ( skv_5 ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((K $$unsorted)) (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) pls))) (= (hBOOL (hAPP int bool _let_0 K)) (hBOOL (hAPP int bool _let_0 (hAPP int int bit0 K))))) ) 15.16/15.42 ( pls ) 15.16/15.42 ( (hAPP int int bit1 pls) ) 15.16/15.42 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.16/15.42 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.16/15.42 ( min_1 ) 15.16/15.42 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((N_1 $$unsorted)) (let ((_let_0 (zero_zero real))) (= _let_0 (hAPP real real (hAPP nat (fun real real) root N_1) _let_0))) ) 15.16/15.42 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((X_a $$unsorted) (P $$unsorted) (X_1 $$unsorted)) (or (hBOOL (hAPP (fun X_a bool) bool (fEx X_a) P)) (not (hBOOL (hAPP X_a bool P X_1)))) ) 15.16/15.42 ( nat, (even_odd_even nat), (zero_zero nat) ) 15.16/15.42 ( nat, (even_odd_even nat), (one_one nat) ) 15.16/15.42 ( nat, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.42 ( nat, prime, (zero_zero nat) ) 15.16/15.42 ( nat, prime, (hAPP nat nat suc (zero_zero nat)) ) 15.16/15.42 ( nat, prime, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.42 ( int, (hAPP int (fun int bool) (ord_less int) pls), pls ) 15.16/15.42 ( int, (hAPP int (fun int bool) (ord_less int) pls), min_1 ) 15.16/15.42 ( int, (hAPP int (fun int bool) (ord_less_eq int) pls), min_1 ) 15.16/15.42 ( int, (hAPP int (fun int bool) (ord_less_eq int) (one_one int)), t ) 15.16/15.42 ( int, nat_neg, (one_one int) ) 15.16/15.42 ( int, nat_neg, (hAPP int int (number_number_of int) min_1) ) 15.16/15.42 ( int, nat_neg, (hAPP int int (number_number_of int) pls) ) 15.16/15.42 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (one_one int) ) 15.16/15.42 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.42 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), s ) 15.16/15.42 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.16/15.42 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) pls) ) 15.16/15.42 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_4 ) 15.16/15.42 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_10 ) 15.16/15.42 ( int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (one_one int) ) 15.16/15.42 ( int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.42 ( int, zprime, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.42 ( int, zprime, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.42 ( int, (hAPP int (fun int bool) (ord_less int) s), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.42 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) s)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.42 ( int, (let ((_let_0 (fun int int))) (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 15.16/15.42 ( int, (hAPP int (fun int bool) (ord_less int) (one_one int)), t ) 15.16/15.42 ( int, (even_odd_even int), (one_one int) ) 15.16/15.42 ( int, (even_odd_even int), (zero_zero int) ) 15.16/15.42 ( int, twoSqu1091635170sum2sq, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) t))) ) 15.16/15.42 ( int, nat_is_nat, (one_one int) ) 15.16/15.42 ( int, nat_is_nat, (zero_zero int) ) 15.16/15.42 ( int, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.42 ( int, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.16/15.42 ( int, (hAPP int (fun int bool) (ord_less int) min_1), pls ) 15.16/15.42 ( int, (hAPP int (fun int bool) (ord_less int) min_1), min_1 ) 15.16/15.42 ( int, (hAPP int (fun int bool) (ord_less_eq int) min_1), pls ) 15.16/15.42 ( int, (hAPP int (fun int bool) (ord_less_eq int) min_1), min_1 ) 15.16/15.42 ( int, (let ((_let_0 (fun int int))) (hAPP int (fun int bool) quadRes (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int int (number_number_of int) min_1) ) 15.16/15.42 ( int, (let ((_let_0 (fun int bool))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (let ((_let_3 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int _let_1 _let_2 s) _let_3)) (hAPP nat int (hAPP int _let_1 _let_2 s1) _let_3)))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.42 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.42 ( int, (hAPP int (fun int bool) (ord_less int) t), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.42 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.42 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_4)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.42 ( int, (hAPP int (fun int bool) (ord_less int) skv_4), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.42 ( int, (hAPP int (fun int bool) (ord_less int) skv_10), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.42 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_10)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.42 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.42 ( (fun int bool), (hAPP (fun int nat) (fun (fun int bool) bool) (nat_tr1645093318rphism int nat) nat_1), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 15.16/15.42 ( (fun int bool), (hAPP int (fun (fun int bool) bool) (member int) (one_one int)), zEven ) 15.16/15.42 ( (fun nat bool), (finite_finite_1 nat), (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 15.16/15.42 ( (fun nat bool), (hAPP (fun nat int) (fun (fun nat bool) bool) (nat_tr1645093318rphism nat int) (semiring_1_of_nat int)), (hAPP bool (fun nat bool) (combk bool nat) fTrue) ) 15.16/15.42 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), pi ) 15.16/15.42 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.42 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.42 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_3 ) 15.16/15.42 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_5 ) 15.16/15.42 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_7 ) 15.16/15.42 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_12 ) 15.16/15.42 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), pi ) 15.16/15.42 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.42 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.42 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_2 ) 15.16/15.42 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_8 ) 15.16/15.42 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_9 ) 15.16/15.42 ( real, (hAPP real (fun real bool) (ord_less real) (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))), (zero_zero real) ) 15.16/15.42 ( real, (hAPP real (fun real bool) (ord_less real) (one_one real)), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.42 ( real, (hAPP real (fun real bool) (ord_less real) pi), (zero_zero real) ) 15.16/15.42 ( real, (hAPP real (fun real bool) (ord_less real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.42 ( real, (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.42 ( real, (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 15.16/15.42 ( real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 (fun real bool) (sums real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (hAPP real _let_1 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc)))), (one_one real) ) 15.16/15.42 ( real, (hAPP real (fun real bool) (ord_less real) (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi))), pi ) 15.16/15.42 ( real, (hAPP real (fun real bool) (ord_less real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.42 ( real, (hAPP real (fun real bool) (ord_less real) (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 15.16/15.42 ( real, (hAPP real (fun real bool) (ord_less_eq real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 15.16/15.42 ( real, (hAPP real (fun real bool) (ord_less_eq real) skv_5), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.42 ( (filter nat), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun (filter nat) bool))) (hAPP real _let_2 (hAPP _let_1 (fun real _let_2) (tendsto nat real) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))) (zero_zero real))))), sequentially ) 15.16/15.42 ( (filter nat), (trivial_limit nat), sequentially ) 15.16/15.42 ( (filter real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (filter real) bool))) (hAPP real _let_2 (hAPP _let_0 (fun real _let_2) (tendsto real real) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin)) (zero_zero real))))), (hAPP real (filter real) (at real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((R_4 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) R_4) (hAPP real real (hAPP real (fun real real) (plus_plus real) (hAPP int real (real_1 int) (hAPP real int (archim2085082626_floor real) R_4))) (one_one real)))) ) 15.16/15.42 ( (one_one real) ) 15.16/15.42 ( (zero_zero real) ) 15.16/15.42 ( pi ) 15.16/15.42 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.42 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.16/15.42 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.42 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((T_1 $$unsorted)) (comple44059174attice (filter T_1)) ) 15.16/15.42 ( nat ) 15.16/15.42 ( real ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((X_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real sin X_1)) (one_one real))) ) 15.16/15.42 ( (zero_zero real) ) 15.16/15.42 ( pi ) 15.16/15.42 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.42 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.16/15.42 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.16/15.42 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.16/15.42 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.16/15.42 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((X_1 $$unsorted)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) X_1) (hAPP nat int (hAPP int (fun nat int) (power_power int) X_1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.16/15.42 ( (one_one int) ) 15.16/15.42 ( (zero_zero int) ) 15.16/15.42 ( min_1 ) 15.16/15.42 ( s ) 15.16/15.42 ( s1 ) 15.16/15.42 ( skv_14 ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((K $$unsorted) (L $$unsorted)) (let ((_let_0 (fun int bool))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (hAPP int int bit1 K)) (hAPP int int bit0 L))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) K) L)))) ) 15.16/15.42 ( (one_one int), t ) 15.16/15.42 ( pls, (one_one int) ) 15.16/15.42 ( pls, pls ) 15.16/15.42 ( pls, min_1 ) 15.16/15.42 ( pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.42 ( min_1, pls ) 15.16/15.42 ( min_1, min_1 ) 15.16/15.42 ( s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.42 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.42 ( skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.42 ( skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((N_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP nat real (real_1 nat) N_1)) (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) N_1))) ) 15.16/15.42 ( (zero_zero nat) ) 15.16/15.42 ( (hAPP nat nat suc (zero_zero nat)) ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((K $$unsorted)) (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) pls))) (= (hBOOL (hAPP int bool _let_0 (hAPP int int bit1 K))) (hBOOL (hAPP int bool _let_0 K)))) ) 15.16/15.42 ( pls ) 15.16/15.42 ( (hAPP int int bit1 pls) ) 15.16/15.42 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.16/15.42 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.16/15.42 ( min_1 ) 15.16/15.42 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.16/15.42 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.16/15.42 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 15.16/15.42 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((Z_1 $$unsorted)) (= Z_1 (hAPP complex complex cnj (hAPP complex complex cnj Z_1))) ) 15.16/15.42 ( (one_one complex) ) 15.16/15.42 ( (zero_zero complex) ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((Y_2 $$unsorted)) (let ((_let_0 (hAPP real (fun real bool) (ord_less real) (one_one real)))) (= (hBOOL (hAPP real bool _let_0 Y_2)) (hBOOL (hAPP real bool _let_0 (hAPP real real sqrt Y_2))))) ) 15.16/15.42 ( (one_one real) ) 15.16/15.42 ( (zero_zero real) ) 15.16/15.42 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.42 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((Ma $$unsorted) (N $$unsorted)) (let ((_let_0 (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)))) (= (or (hBOOL (hAPP nat bool _let_0 Ma)) (hBOOL (hAPP nat bool _let_0 N))) (hBOOL (hAPP nat bool _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) Ma) N))))) ) 15.16/15.42 ( (one_one nat), (one_one nat) ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((M $$unsorted)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) (hAPP int int (fact_fact int) M))) ) 15.16/15.42 ( (one_one int) ) 15.16/15.42 ( (zero_zero int) ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (even_odd_even int))) (= (hBOOL (hAPP int bool _let_0 (hAPP int int (uminus_uminus int) X_2))) (hBOOL (hAPP int bool _let_0 X_2)))) ) 15.16/15.42 ( (one_one int) ) 15.16/15.42 ( pls ) 15.16/15.42 ( min_1 ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((X_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (abs_abs real) (hAPP complex real re X_1))) (hAPP complex real (norm_norm complex) X_1))) ) 15.16/15.42 ( (one_one complex) ) 15.16/15.42 ( ii ) 15.16/15.42 ( (zero_zero complex) ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((N $$unsorted) (Ma $$unsorted)) (let ((_let_0 (real_1 int))) (= (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (hAPP real (fun real real) (plus_plus real) (hAPP int real _let_0 N)) (one_one real))) (hAPP int real _let_0 Ma))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) N) Ma)))) ) 15.16/15.42 ( (one_one int), t ) 15.16/15.42 ( pls, (one_one int) ) 15.16/15.42 ( pls, pls ) 15.16/15.42 ( pls, min_1 ) 15.16/15.42 ( pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.42 ( min_1, pls ) 15.16/15.42 ( min_1, min_1 ) 15.16/15.42 ( s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.42 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.42 ( skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.42 ( skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((A_2 $$unsorted) (B_1 $$unsorted) (Ma $$unsorted)) (let ((_let_0 (fun int bool))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (dvd_dvd int) Ma) (hAPP int int (hAPP int (fun int int) (minus_minus int) A_2) B_1))) (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong A_2) B_1) Ma)))) ) 15.16/15.42 ( s1, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.42 ( s1, skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.42 ( s1, skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.42 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.42 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.42 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.42 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((X_2 $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) X_2)) (= X_2 (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP real real sqrt X_2)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.16/15.42 ( (one_one real) ) 15.16/15.42 ( (zero_zero real) ) 15.16/15.42 ( pi ) 15.16/15.42 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.42 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.42 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.16/15.42 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.42 ( skv_3 ) 15.16/15.42 ( skv_5 ) 15.16/15.42 ( skv_7 ) 15.16/15.42 ( skv_12 ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((X_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (abs_abs real) (hAPP real real sin X_1))) (one_one real))) ) 15.16/15.42 ( (zero_zero real) ) 15.16/15.42 ( pi ) 15.16/15.42 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.42 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.16/15.42 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.16/15.42 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.16/15.42 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.16/15.42 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((W_1 $$unsorted)) (let ((_let_0 (number_number_of int))) (= (hBOOL (hAPP int bool nat_neg (hAPP int int _let_0 (hAPP int int bit0 W_1)))) (hBOOL (hAPP int bool nat_neg (hAPP int int _let_0 W_1))))) ) 15.16/15.42 ( pls ) 15.16/15.42 ( (hAPP int int bit1 pls) ) 15.16/15.42 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.16/15.42 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.16/15.42 ( min_1 ) 15.16/15.42 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((N $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP int real (real_1 int) N)) (zero_zero real))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) N) (zero_zero int)))) ) 15.16/15.42 ( (one_one int) ) 15.16/15.42 ( (zero_zero int) ) 15.16/15.42 ( min_1 ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((K1 $$unsorted) (K2 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int bit0 K1)) (hAPP int int bit0 K2))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K1) K2))))) ) 15.16/15.42 ( pls, pls ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((N $$unsorted)) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) (hAPP nat int (semiring_1_of_nat int) N)))) ) 15.16/15.42 ( (zero_zero nat) ) 15.16/15.42 ( (hAPP nat nat suc (zero_zero nat)) ) 15.16/15.42 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.16/15.42 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (finite_finite_1 X_a))) (= _let_0 (ti (fun (fun X_a bool) bool) _let_0))) ) 15.16/15.42 ( nat ) 15.16/15.42 ( int ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((K $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int bit0 K)) min_1)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) min_1))))) ) 15.16/15.42 ( pls ) 15.16/15.42 ( (hAPP int int bit1 pls) ) 15.16/15.42 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.16/15.42 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.16/15.42 ( min_1 ) 15.16/15.42 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((A_2 $$unsorted)) (let ((_let_0 (filter complex))) (let ((_let_1 (fun _let_0 bool))) (hBOOL (hAPP _let_0 bool (hAPP real _let_1 (hAPP (fun complex real) (fun real _let_1) (tendsto complex real) re) (hAPP complex real re A_2)) (hAPP complex _let_0 (at complex) A_2))))) ) 15.16/15.42 ( (one_one complex) ) 15.16/15.42 ( ii ) 15.16/15.42 ( (zero_zero complex) ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_0 (even_odd_even int))) (= (hBOOL (hAPP int bool _let_0 (hAPP int int (hAPP int (fun int int) (times_times int) X_2) Y_2))) (or (hBOOL (hAPP int bool _let_0 Y_2)) (hBOOL (hAPP int bool _let_0 X_2))))) ) 15.16/15.42 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 15.16/15.42 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.16/15.42 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13 ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real sqrt X_2)) (hAPP real real sqrt Y_2))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_2) Y_2))))) ) 15.16/15.42 ( (zero_zero real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((N_1 $$unsorted) (M $$unsorted)) (let ((_let_0 (fun nat nat))) (= M (hAPP nat nat (hAPP nat _let_0 (minus_minus nat) (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) N_1) M)) N_1))) ) 15.16/15.42 ( (one_one nat), (one_one nat) ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((N $$unsorted) (Ma $$unsorted)) (let ((_let_0 (real_1 nat))) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) N) Ma)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP nat real _let_0 N)) (hAPP nat real _let_0 Ma))))) ) 15.16/15.42 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (hBOOL (hAPP _let_0 bool (hAPP real (fun _let_0 bool) (member real) (hAPP int real (real_1 int) X_2)) (ring_1_Ints real)))) ) 15.16/15.42 ( (one_one int) ) 15.16/15.42 ( (zero_zero int) ) 15.16/15.42 ) 15.16/15.42 (instantiation (forall ((Z $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) Z)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) (hAPP int nat nat_1 Z)))) ) 15.16/15.42 ( (one_one int) ) 15.16/15.42 ( (zero_zero int) ) 15.16/15.42 ( pls ) 15.16/15.42 ( min_1 ) 15.16/15.42 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.42 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.42 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.16/15.42 ) 15.16/15.43 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real (fun real real)))) (let ((_let_2 (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP real real (uminus_uminus real) (hAPP real real sin X_2))) (hAPP real real cos X_2)))) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP (fun real real) (fun real _let_0) (deriv real) (hAPP (fun real real) (fun real real) (hAPP _let_1 (fun (fun real real) (fun real real)) (combs real real real) (hAPP (fun real real) _let_1 (hAPP _let_1 (fun (fun real real) _let_1) (combb real (fun real real) real) (times_times real)) cos)) cos)) X_2) (hAPP real real (hAPP real (fun real real) (plus_plus real) _let_2) _let_2)))))) ) 15.16/15.43 ( (zero_zero real) ) 15.16/15.43 ( pi ) 15.16/15.43 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.43 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.43 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.16/15.43 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.16/15.43 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.16/15.43 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.16/15.43 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.16/15.43 ( skv_5 ) 15.16/15.43 ) 15.16/15.43 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) (hAPP real real (hAPP real (fun real real) (plus_plus real) X_2) Y_2))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (uminus_uminus real) X_2)) Y_2))))) ) 15.16/15.43 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.16/15.43 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi), pi ) 15.16/15.43 ) 15.16/15.43 (instantiation (forall ((V_1 $$unsorted)) (= (zero_zero real) (hAPP complex real im (hAPP int complex (number_number_of complex) V_1))) ) 15.16/15.43 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.16/15.43 ( min_1 ) 15.16/15.43 ) 15.16/15.43 (instantiation (forall ((N_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) (hAPP nat real (real_1 nat) (hAPP nat nat (fact_fact nat) N_1)))) ) 15.16/15.43 ( (zero_zero nat) ) 15.16/15.43 ( (hAPP nat nat suc (zero_zero nat)) ) 15.16/15.43 ) 15.16/15.43 (instantiation (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (zero_zero real))) (= (and (= _let_0 B_1) (= _let_0 A_2)) (= (zero_zero complex) (hAPP real complex (hAPP real (fun real complex) complex_1 A_2) B_1)))) ) 15.16/15.43 ( (one_one real), (zero_zero real) ) 15.16/15.43 ( (zero_zero real), (one_one real) ) 15.16/15.43 ( (zero_zero real), (zero_zero real) ) 15.16/15.43 ) 15.16/15.43 (instantiation (forall ((N $$unsorted)) (let ((_let_0 (fun real bool))) (hBOOL (hAPP _let_0 bool (hAPP real (fun _let_0 bool) (member real) (hAPP nat real (real_1 nat) N)) (ring_1_Ints real)))) ) 15.16/15.43 ( (zero_zero nat) ) 15.16/15.43 ( (hAPP nat nat suc (zero_zero nat)) ) 15.16/15.43 ) 15.16/15.43 (instantiation (forall ((W $$unsorted)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) W) W)) ) 15.16/15.43 ( (one_one int) ) 15.16/15.43 ( (zero_zero int) ) 15.16/15.43 ( min_1 ) 15.16/15.43 ) 15.16/15.43 (instantiation (forall ((R_4 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP real real (hAPP real (fun real real) (minus_minus real) R_4) (one_one real))) (hAPP int real (real_1 int) (hAPP real int (archim2085082626_floor real) R_4)))) ) 15.16/15.43 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))) ) 15.16/15.43 ) 15.16/15.43 (instantiation (forall ((Ma $$unsorted) (N $$unsorted)) (let ((_let_0 (semiring_1_of_nat int))) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP nat int _let_0 Ma)) (hAPP nat int _let_0 N))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) Ma) N)))) ) 15.16/15.43 ( (zero_zero nat), (zero_zero nat) ) 15.16/15.43 ( (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 15.16/15.43 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.43 ) 15.16/15.43 (instantiation (forall ((A_2 $$unsorted)) (let ((_let_0 (filter complex))) (let ((_let_1 (fun _let_0 bool))) (hBOOL (hAPP _let_0 bool (hAPP real _let_1 (hAPP (fun complex real) (fun real _let_1) (tendsto complex real) im) (hAPP complex real im A_2)) (hAPP complex _let_0 (at complex) A_2))))) ) 15.16/15.43 ( (one_one complex) ) 15.16/15.43 ( ii ) 15.16/15.43 ( (zero_zero complex) ) 15.16/15.43 ) 15.16/15.43 (instantiation (forall ((X_2 $$unsorted)) (= (hBOOL (hAPP int bool (even_odd_even int) X_2)) (= (zero_zero int) (hAPP int int (hAPP int (fun int int) (div_mod int) X_2) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.16/15.43 ( (one_one int) ) 15.16/15.43 ( (zero_zero int) ) 15.16/15.43 ) 15.16/15.43 (instantiation (forall ((K $$unsorted)) (let ((_let_0 (hAPP int (fun int bool) (ord_less int) min_1))) (= (hBOOL (hAPP int bool _let_0 (hAPP int int bit1 K))) (hBOOL (hAPP int bool _let_0 K)))) ) 15.16/15.43 ( pls ) 15.16/15.43 ( (hAPP int int bit1 pls) ) 15.16/15.43 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.16/15.43 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.16/15.43 ( min_1 ) 15.16/15.43 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.16/15.43 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.16/15.43 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 15.16/15.43 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 15.16/15.43 ) 15.16/15.43 (instantiation (forall ((N_1 $$unsorted) (M $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) N_1) (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) M) N_1))) ) 15.16/15.43 ( (one_one nat), (one_one nat) ) 15.16/15.43 ) 15.16/15.43 (instantiation (forall ((A_2 $$unsorted) (X_2 $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) A_2) (hAPP real int (archim2085082626_floor real) X_2))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP int real (real_1 int) A_2)) X_2))) ) 15.16/15.43 ( (zero_zero int), pi ) 15.16/15.43 ( (zero_zero int), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.43 ( (zero_zero int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.43 ( (zero_zero int), skv_3 ) 15.16/15.43 ( (zero_zero int), skv_5 ) 15.16/15.43 ( (zero_zero int), skv_7 ) 15.16/15.43 ( (zero_zero int), skv_12 ) 15.16/15.43 ) 15.16/15.43 (instantiation (forall ((N_1 $$unsorted) (M $$unsorted)) (let ((_let_0 (fun nat nat))) (= (zero_zero nat) (hAPP nat nat (hAPP nat _let_0 (minus_minus nat) N_1) (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) N_1) M)))) ) 15.16/15.43 ( (one_one nat), (one_one nat) ) 15.16/15.43 ) 15.16/15.43 (instantiation (forall ((Ma $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less nat))) (= (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 N) (hAPP nat nat suc Ma))) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 Ma) N)))))) ) 15.16/15.43 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.16/15.43 ( (hAPP nat nat suc (zero_zero nat)), (zero_zero nat) ) 15.16/15.43 ) 15.16/15.43 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (nat_rec X_a))) (= _let_0 (ti (fun X_a (fun (fun nat (fun X_a X_a)) (fun nat X_a))) _let_0))) ) 15.16/15.43 ( bool ) 15.16/15.43 ( nat ) 15.16/15.43 ( int ) 15.16/15.43 ( (fun int bool) ) 15.16/15.43 ( (fun int (fun int bool)) ) 15.16/15.43 ( (fun int int) ) 15.16/15.43 ( (fun nat bool) ) 15.16/15.43 ( real ) 15.16/15.43 ( (fun real bool) ) 15.16/15.43 ( (fun real real) ) 15.16/15.43 ( complex ) 15.16/15.43 ( (fun nat real) ) 15.16/15.43 ( (product_prod int int) ) 15.16/15.43 ( code_code_numeral ) 15.16/15.43 ( (fun int (fun int (fun int bool))) ) 15.16/15.43 ( (fun (product_prod int int) bool) ) 15.16/15.43 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 15.16/15.43 ( (fun (product_prod int int) int) ) 15.16/15.43 ( (fun int real) ) 15.16/15.43 ) 15.16/15.43 (instantiation (forall ((B_1_1 $$unsorted)) (= (hBOOL B_1_1) (hBOOL (ti bool B_1_1))) ) 15.16/15.43 ( fFalse ) 15.16/15.43 ( fTrue ) 15.16/15.43 ) 15.16/15.43 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (hBOOL (hAPP _let_1 bool (summable real) (hAPP _let_1 _let_1 (hAPP _let_2 (fun _let_1 _let_1) (combs nat real real) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 nat) (times_times real)) cos_coeff)) (hAPP real _let_1 (power_power real) X_2))))))) ) 15.16/15.43 ( (hAPP int real (number_number_of real) min_1) ) 15.16/15.43 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.43 ) 15.16/15.43 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (exp real) X_2)) (one_one real))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_2) (zero_zero real)))))) ) 15.16/15.43 ( pi ) 15.16/15.43 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.16/15.43 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.43 ) 15.16/15.43 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (inverse_divide real))) (let ((_let_2 (fun nat real))) (let ((_let_3 (power_power real))) (let ((_let_4 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_5 (hAPP int real (number_number_of real) _let_4))) (let ((_let_6 (hAPP nat real (hAPP real _let_2 _let_3 X_2) (hAPP int nat (number_number_of nat) _let_4)))) (hBOOL (hAPP real bool (hAPP _let_2 (fun real bool) (sums real) (hAPP _let_2 _let_2 (hAPP _let_0 (fun _let_2 _let_2) (combb real real nat) (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 _let_1 _let_6) _let_5))) (hAPP real _let_2 _let_3 (hAPP real real (hAPP real _let_0 _let_1 (one_one real)) _let_5)))) _let_6))))))))) ) 15.16/15.43 ( (hAPP int real (number_number_of real) min_1) ) 15.16/15.43 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.16/15.43 ) 15.16/15.43 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_0 (combk X_a X_b))) (= _let_0 (ti (fun X_a (fun X_b X_a)) _let_0))) ) 15.16/15.43 ( bool, bool ) 15.16/15.43 ( bool, nat ) 15.16/15.43 ( bool, int ) 15.16/15.43 ( bool, (fun int bool) ) 15.16/15.43 ( bool, (fun nat bool) ) 15.16/15.43 ( bool, (product_prod nat nat) ) 15.16/15.43 ( bool, real ) 15.16/15.43 ( bool, (filter nat) ) 15.16/15.43 ( bool, (product_prod int int) ) 15.16/15.43 ( bool, (product_prod real real) ) 15.16/15.43 ( bool, (fun nat rat) ) 15.16/15.43 ( bool, (filter real) ) 15.16/15.43 ( bool, (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 15.16/15.43 ( bool, (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 15.16/15.43 ( nat, nat ) 15.16/15.43 ( nat, int ) 15.16/15.43 ( nat, real ) 15.16/15.43 ( nat, complex ) 15.16/15.43 ( nat, quickcheck_code_int ) 15.16/15.43 ( nat, code_code_numeral ) 15.16/15.43 ( int, nat ) 15.16/15.43 ( int, int ) 15.16/15.43 ( int, (fun int bool) ) 15.16/15.43 ( int, (product_prod int int) ) 15.16/15.43 ( int, quickcheck_code_int ) 15.16/15.43 ( int, code_code_numeral ) 15.16/15.43 ( (fun int bool), int ) 15.16/15.43 ( (fun int bool), (fun int bool) ) 15.16/15.43 ( (fun int bool), (fun int (fun int bool)) ) 15.16/15.43 ( (fun int bool), (fun int int) ) 15.16/15.43 ( (fun int bool), real ) 15.16/15.43 ( (fun int bool), (product_prod int int) ) 15.16/15.43 ( (fun int bool), (fun int real) ) 15.16/15.43 ( (fun int bool), (fun int (fun nat bool)) ) 15.16/15.43 ( (fun int (fun int bool)), int ) 15.16/15.43 ( (fun int (fun int bool)), (fun int bool) ) 15.16/15.43 ( (fun int (fun int bool)), (fun int (fun int bool)) ) 15.16/15.43 ( (fun int (fun int bool)), (fun int int) ) 15.16/15.43 ( (fun int (fun int bool)), real ) 15.16/15.43 ( (fun int (fun int bool)), (fun int (fun int real)) ) 15.16/15.43 ( (fun int int), nat ) 15.16/15.43 ( (fun int int), int ) 15.16/15.43 ( (fun int int), (fun int int) ) 15.16/15.43 ( (fun int int), (product_prod int int) ) 15.16/15.43 ( (fun nat bool), nat ) 15.16/15.43 ( (fun nat bool), int ) 15.16/15.43 ( (fun nat bool), (fun nat bool) ) 15.16/15.43 ( (fun nat bool), (fun nat real) ) 15.16/15.43 ( (fun nat nat), nat ) 15.16/15.43 ( (fun nat nat), int ) 15.16/15.43 ( (fun nat nat), code_code_numeral ) 15.16/15.43 ( (product_prod nat nat), nat ) 15.16/15.43 ( (fun (product_prod nat nat) bool), nat ) 15.16/15.43 ( (fun (product_prod nat nat) bool), (product_prod nat nat) ) 15.16/15.43 ( (fun nat (fun (product_prod nat nat) bool)), nat ) 15.16/15.43 ( real, nat ) 15.16/15.43 ( real, int ) 15.16/15.43 ( real, real ) 15.16/15.43 ( real, (fun real bool) ) 15.16/15.43 ( real, rat ) 15.16/15.43 ( real, complex ) 15.16/15.43 ( (fun real bool), real ) 15.16/15.43 ( (fun real bool), (fun real bool) ) 15.16/15.43 ( (fun real bool), (fun real (fun int bool)) ) 15.16/15.43 ( (fun real real), nat ) 15.16/15.43 ( (fun real real), int ) 15.16/15.43 ( (fun real real), real ) 15.16/15.43 ( (fun real real), (fun real real) ) 15.16/15.43 ( rat, nat ) 15.16/15.43 ( rat, int ) 15.16/15.43 ( rat, (product_prod int int) ) 15.16/15.43 ( (fun int rat), int ) 15.16/15.43 ( (fun nat (fun nat bool)), nat ) 15.16/15.43 ( (fun nat (fun nat bool)), (fun nat nat) ) 15.16/15.43 ( (fun nat int), int ) 15.16/15.43 ( complex, nat ) 15.16/15.43 ( complex, real ) 15.16/15.43 ( complex, complex ) 15.16/15.43 ( (fun nat real), int ) 15.16/15.43 ( (fun nat real), (fun nat nat) ) 15.16/15.43 ( (fun nat real), real ) 15.16/15.43 ( (fun nat real), (fun nat real) ) 15.16/15.43 ( (fun int (fun int int)), (fun int bool) ) 15.16/15.43 ( (fun int (fun int int)), (fun int int) ) 15.16/15.43 ( (fun real complex), real ) 15.16/15.43 ( (product_prod int int), nat ) 15.16/15.43 ( (product_prod int int), int ) 15.16/15.43 ( (product_prod int int), rat ) 15.16/15.43 ( (product_prod int int), (product_prod int int) ) 15.16/15.43 ( (fun int (product_prod int int)), int ) 15.16/15.43 ( (fun (fun int bool) bool), int ) 15.16/15.43 ( quickcheck_code_int, int ) 15.16/15.43 ( (fun nat (fun nat nat)), (fun nat nat) ) 15.16/15.43 ( (fun bool bool), bool ) 15.16/15.43 ( (fun bool bool), nat ) 15.16/15.43 ( (fun bool bool), int ) 15.16/15.43 ( (fun bool bool), real ) 15.16/15.43 ( (fun bool bool), (product_prod int int) ) 15.16/15.43 ( (fun nat (fun real real)), (fun nat real) ) 15.16/15.43 ( (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)), int ) 15.16/15.43 ( (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)), (fun real real) ) 15.16/15.43 ( (fun real (fun real real)), (fun real real) ) 15.16/15.43 ( (fun (filter nat) bool), real ) 15.16/15.43 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), int ) 15.16/15.43 ( code_code_numeral, code_code_numeral ) 15.16/15.43 ( (fun int (fun int (fun int bool))), int ) 15.16/15.43 ( (fun int (fun int (fun int bool))), (fun int (fun int int)) ) 15.16/15.43 ( (fun int (fun int (fun int bool))), (fun int (fun int (fun int bool))) ) 15.16/15.43 ( (fun real (fun real bool)), (fun real real) ) 15.16/15.43 ( (product_prod real real), nat ) 15.16/15.43 ( (fun nat (product_prod real real)), real ) 15.16/15.43 ( (fun real (fun nat (product_prod real real))), real ) 15.16/15.43 ( (fun real (fun real (fun nat (product_prod real real)))), (fun (product_prod real real) bool) ) 15.16/15.43 ( (fun (product_prod int int) bool), int ) 15.16/15.43 ( (fun (product_prod int int) bool), (product_prod int int) ) 15.16/15.43 ( (fun (product_prod int int) bool), (fun (product_prod int int) bool) ) 15.16/15.43 ( (fun (product_prod int int) bool), (fun (product_prod int int) int) ) 15.16/15.43 ( (fun int (fun (product_prod int int) bool)), int ) 15.16/15.43 ( (fun int (fun bool bool)), int ) 15.16/15.43 ( (fun int (fun bool bool)), (fun int bool) ) 15.16/15.43 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), int ) 15.16/15.43 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), (fun int (fun bool bool)) ) 15.16/15.43 ( (fun (fun int int) (fun int bool)), int ) 15.16/15.43 ( (fun (fun int int) (fun int bool)), (fun int bool) ) 15.16/15.43 ( (fun int (fun (fun int int) (fun int bool))), (fun int (fun int bool)) ) 15.16/15.43 ( (fun nat (product_prod nat nat)), nat ) 15.16/15.43 ( (fun (filter real) bool), real ) 15.16/15.43 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 15.16/15.43 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))) ) 15.16/15.43 ( (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)), (product_prod int int) ) 15.16/15.43 ( (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)), (fun bool bool) ) 15.16/15.43 ( (let ((_let_0 (fun (product_prod int int) bool))) (fun (product_prod int int) (fun _let_0 _let_0))), (fun (product_prod int int) (fun bool bool)) ) 15.16/15.43 ( (fun (product_prod int int) (fun bool bool)), (fun (product_prod int int) bool) ) 15.16/15.43 ( (fun (product_prod int int) (fun int bool)), (product_prod int int) ) 15.16/15.43 ( (fun (product_prod int int) (fun int bool)), (fun (product_prod int int) int) ) 15.16/15.43 ( (fun (product_prod int int) int), int ) 15.16/15.43 ( (fun (product_prod int int) int), (product_prod int int) ) 15.16/15.43 ( (fun (product_prod int int) int), (fun (product_prod int int) int) ) 15.16/15.43 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (fun (product_prod int int) int) ) 15.16/15.43 ( (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))), (product_prod int int) ) 15.16/15.43 ( (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))), (fun (product_prod int int) (fun int bool)) ) 15.16/15.43 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun (fun _let_0 int) (fun _let_0 bool)))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 (fun int bool)))) ) 15.16/15.43 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 (fun int bool)))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))) ) 15.16/15.43 ( (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)), (fun int int) ) 15.16/15.43 ( (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)), (product_prod int int) ) 15.16/15.43 ( (let ((_let_0 (fun (product_prod int int) int))) (fun (product_prod int int) (fun _let_0 _let_0))), (fun (product_prod int int) (fun int int)) ) 15.16/15.43 ( (fun (product_prod int int) (fun int int)), (fun (product_prod int int) int) ) 15.16/15.43 ( (product_prod int (product_prod int int)), int ) 15.16/15.43 ( (fun int (product_prod int (product_prod int int))), int ) 15.16/15.43 ( (fun nat (product_prod int int)), nat ) 15.16/15.43 ( (fun int (fun int (product_prod int (product_prod int int)))), int ) 15.16/15.43 ( (fun int (fun int (fun int (product_prod int (product_prod int int))))), int ) 15.16/15.43 ( (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))), int ) 15.16/15.43 ( (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))), int ) 15.16/15.43 ( (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))), int ) 15.16/15.43 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))))), int ) 15.16/15.43 ( (fun int (fun (fun int bool) bool)), int ) 15.16/15.43 ( (list int), int ) 15.16/15.43 ( (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)), int ) 15.16/15.43 ( (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)), (fun nat (fun bool bool)) ) 15.16/15.43 ( (fun real (fun bool bool)), (fun real bool) ) 15.16/15.43 ( (fun int real), int ) 15.16/15.43 ( (fun int real), (fun int real) ) 15.16/15.43 ( (product_prod quickcheck_code_int quickcheck_code_int), quickcheck_code_int ) 15.16/15.43 ( (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int)), quickcheck_code_int ) 15.16/15.43 ( (fun nat (fun bool bool)), int ) 15.16/15.43 ( (fun nat (fun bool bool)), (fun nat bool) ) 15.16/15.43 ( (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))), real ) 15.16/15.43 ( (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))), (fun int (fun int (fun bool bool))) ) 15.16/15.43 ( (let ((_let_0 (fun int bool))) (fun _let_0 (fun int _let_0))), real ) 15.16/15.43 ( (let ((_let_0 (fun int bool))) (fun _let_0 (fun int _let_0))), (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 15.16/15.43 ( (fun int (fun int (fun bool bool))), (fun int (fun int bool)) ) 15.16/15.43 ( (fun int (fun int (fun bool bool))), real ) 15.16/15.43 ( (fun real (fun int bool)), (fun real (fun int (fun int bool))) ) 15.16/15.43 ( (fun real (fun int bool)), (fun real (fun int (fun nat bool))) ) 15.16/15.43 ( (fun real (fun int (fun int bool))), (fun int bool) ) 15.16/15.43 ( (fun real (fun int (fun int bool))), (fun int (fun int real)) ) 15.16/15.43 ( (let ((_let_0 (fun int bool))) (fun real (fun _let_0 (fun int _let_0)))), (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))) ) 15.16/15.43 ( (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))), (fun real (fun int (fun int (fun bool bool)))) ) 15.16/15.43 ( (fun real (fun int (fun int (fun bool bool)))), (fun real (fun int (fun int bool))) ) 15.16/15.43 ( (fun int (fun int real)), (fun int real) ) 15.16/15.43 ( (fun (fun int (fun int real)) (fun int (fun int bool))), real ) 15.16/15.43 ( (fun (fun int (fun int real)) (fun int (fun int bool))), (fun (fun int real) (fun int bool)) ) 15.16/15.43 ( (fun real (fun (fun int (fun int real)) (fun int (fun int bool)))), (fun real (fun (fun int real) (fun int bool))) ) 15.16/15.43 ( (fun (fun int real) (fun int bool)), real ) 15.16/15.43 ( (fun (fun int real) (fun int bool)), (fun real bool) ) 15.16/15.43 ( (fun real (fun (fun int real) (fun int bool))), (fun real (fun real bool)) ) 15.16/15.43 ( (let ((_let_0 (fun int real))) (fun _let_0 _let_0)), int ) 15.16/15.43 ( (let ((_let_0 (fun int real))) (fun _let_0 _let_0)), (fun real real) ) 15.16/15.43 ( (let ((_let_0 (fun int real))) (fun int (fun _let_0 _let_0))), (fun int (fun real real)) ) 15.16/15.43 ( (fun int (fun real real)), (fun int real) ) 15.16/15.43 ( (product_prod code_code_numeral code_code_numeral), code_code_numeral ) 15.16/15.43 ( (fun code_code_numeral (product_prod code_code_numeral code_code_numeral)), code_code_numeral ) 15.16/15.43 ( (fun int (fun nat bool)), (fun nat bool) ) 15.16/15.43 ( (fun int (fun nat bool)), real ) 15.16/15.43 ( (fun int (fun nat bool)), (fun int (fun nat real)) ) 15.16/15.43 ( (fun real (fun int (fun nat bool))), (fun nat bool) ) 15.16/15.43 ( (fun real (fun int (fun nat bool))), (fun int (fun nat real)) ) 15.16/15.43 ( (let ((_let_0 (fun nat bool))) (fun _let_0 (fun int _let_0))), real ) 15.16/15.43 ( (let ((_let_0 (fun nat bool))) (fun _let_0 (fun int _let_0))), (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 15.16/15.43 ( (let ((_let_0 (fun nat bool))) (fun real (fun _let_0 (fun int _let_0)))), (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))) ) 15.16/15.43 ( (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))), real ) 15.16/15.43 ( (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))), (fun int (fun nat (fun bool bool))) ) 15.16/15.43 ( (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))), (fun real (fun int (fun nat (fun bool bool)))) ) 15.16/15.43 ( (fun int (fun nat (fun bool bool))), real ) 15.16/15.43 ( (fun int (fun nat (fun bool bool))), (fun int (fun nat bool)) ) 15.16/15.43 ( (fun real (fun int (fun nat (fun bool bool)))), (fun real (fun int (fun nat bool))) ) 15.16/15.43 ( (fun int (fun nat real)), (fun nat real) ) 15.16/15.43 ( (fun (fun int (fun nat real)) (fun int (fun nat bool))), real ) 15.16/15.43 ( (fun (fun int (fun nat real)) (fun int (fun nat bool))), (fun (fun nat real) (fun nat bool)) ) 15.16/15.43 ( (fun real (fun (fun int (fun nat real)) (fun int (fun nat bool)))), (fun real (fun (fun nat real) (fun nat bool))) ) 15.16/15.43 ( (fun (fun nat real) (fun nat bool)), real ) 15.16/15.43 ( (fun (fun nat real) (fun nat bool)), (fun real bool) ) 15.16/15.43 ( (fun real (fun (fun nat real) (fun nat bool))), (fun real (fun real bool)) ) 15.16/15.43 ( (let ((_let_0 (fun nat real))) (fun int (fun _let_0 _let_0))), (fun int (fun real real)) ) 15.16/15.43 ( (let ((_let_0 (fun int int))) (fun _let_0 _let_0)), int ) 15.16/15.43 ( (let ((_let_0 (fun int int))) (fun _let_0 _let_0)), (fun int int) ) 15.16/15.43 ( (let ((_let_0 (fun int int))) (fun int (fun _let_0 _let_0))), (fun int (fun int int)) ) 15.16/15.43 ) 15.16/15.43 (instantiation (forall ((W_1 $$unsorted) (Z $$unsorted)) (let ((_let_0 (fun int bool))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) W_1) Z)) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (hAPP int int (hAPP int (fun int int) (plus_plus int) W_1) (one_one int))) Z)))) ) 15.16/15.43 ( (one_one int), t ) 15.16/15.43 ( pls, (one_one int) ) 15.16/15.43 ( pls, pls ) 15.16/15.43 ( pls, min_1 ) 15.16/15.43 ( pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.43 ( min_1, pls ) 15.16/15.43 ( min_1, min_1 ) 15.16/15.43 ( s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.16/15.43 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.27/15.43 ( skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.27/15.43 ( skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.27/15.43 ) 15.27/15.43 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (let ((_let_3 (fun _let_1 _let_1))) (let ((_let_4 (fun (fun nat nat) _let_1))) (let ((_let_5 (combb nat real nat))) (let ((_let_6 (hAPP nat (fun nat nat) (hAPP (fun nat (fun nat nat)) (fun nat (fun nat nat)) (combc nat nat nat) (plus_plus nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hBOOL (hAPP _let_1 bool (summable real) (hAPP _let_1 _let_1 (hAPP _let_2 _let_3 (combs nat real real) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 nat) (times_times real)) (hAPP _let_1 _let_1 (hAPP _let_0 _let_3 (combb real real nat) (inverse_inverse real)) (hAPP (fun nat nat) _let_1 (hAPP _let_1 _let_4 _let_5 (real_1 nat)) (hAPP (fun nat nat) (fun nat nat) (hAPP (fun nat nat) (fun (fun nat nat) (fun nat nat)) (combb nat nat nat) (fact_fact nat)) _let_6))))) (hAPP (fun nat nat) _let_1 (hAPP _let_1 _let_4 _let_5 (hAPP real _let_1 (power_power real) X_2)) _let_6))))))))))) ) 15.27/15.43 ( (hAPP int real (number_number_of real) min_1) ) 15.27/15.43 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.43 ) 15.27/15.43 (instantiation (forall ((N_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) (hAPP nat real (real_1 nat) N_1))) ) 15.27/15.43 ( (zero_zero nat) ) 15.27/15.43 ( (hAPP nat nat suc (zero_zero nat)) ) 15.27/15.43 ) 15.27/15.43 (instantiation (forall ((K $$unsorted) (L $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) L)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int (hAPP int (fun int int) (minus_minus int) K) L)) (zero_zero int)))))) ) 15.27/15.43 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.27/15.43 ) 15.27/15.43 (instantiation (forall ((N_1 $$unsorted)) (hBOOL (hAPP int bool nat_neg (hAPP int int (uminus_uminus int) (hAPP nat int (semiring_1_of_nat int) (hAPP nat nat suc N_1))))) ) 15.27/15.43 ( (zero_zero nat) ) 15.27/15.43 ( (hAPP nat nat suc (zero_zero nat)) ) 15.27/15.43 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 15.27/15.43 ) 15.27/15.43 (instantiation (forall ((K1 $$unsorted) (K2 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int bit1 K1)) (hAPP int int bit1 K2))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K1) K2))))) ) 15.27/15.43 ( min_1, min_1 ) 15.27/15.43 ) 15.27/15.43 (instantiation (forall ((N_1 $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) coprime (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) N_1) (one_one nat))) N_1)) ) 15.27/15.43 ( (one_one nat) ) 15.27/15.43 ) 15.27/15.43 (instantiation (forall ((V $$unsorted)) (= (hBOOL (hAPP int bool nat_neg (hAPP int int (number_number_of int) (hAPP int int pred V)))) (= (zero_zero nat) (hAPP int nat (number_number_of nat) V))) ) 15.27/15.43 ( pls ) 15.27/15.43 ( (hAPP int int bit1 pls) ) 15.27/15.43 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.27/15.43 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.27/15.43 ( min_1 ) 15.27/15.43 ) 15.27/15.43 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (hAPP int (fun _let_0 bool) (member int) X_2))) (= (not (hBOOL (hAPP _let_0 bool _let_1 zEven))) (hBOOL (hAPP _let_0 bool _let_1 zOdd))))) ) 15.27/15.43 ( (one_one int) ) 15.27/15.43 ) 15.27/15.43 (instantiation (forall ((N $$unsorted)) (= (= (zero_zero nat) N) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP nat int (semiring_1_of_nat int) N)) (zero_zero int)))) ) 15.27/15.43 ( (zero_zero nat) ) 15.27/15.43 ( (hAPP nat nat suc (zero_zero nat)) ) 15.27/15.43 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.27/15.43 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.43 ) 15.27/15.43 (instantiation (forall ((N_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) (hAPP nat real (real_1 nat) (hAPP nat nat (fact_fact nat) N_1)))) ) 15.27/15.43 ( (zero_zero nat) ) 15.27/15.43 ( (hAPP nat nat suc (zero_zero nat)) ) 15.27/15.43 ) 15.27/15.43 (instantiation (forall ((N_1 $$unsorted)) (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) (hAPP int int (uminus_uminus int) (hAPP nat int (semiring_1_of_nat int) (hAPP nat nat suc N_1)))))) ) 15.27/15.43 ( (zero_zero nat) ) 15.27/15.43 ( (hAPP nat nat suc (zero_zero nat)) ) 15.27/15.43 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 15.27/15.43 ) 15.27/15.43 (instantiation (forall ((T_1 $$unsorted)) (ord (filter T_1)) ) 15.27/15.43 ( nat ) 15.27/15.43 ( real ) 15.27/15.43 ) 15.27/15.43 (instantiation (forall ((N_1 $$unsorted)) (= (zero_zero real) (hAPP real real sin (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP nat real (real_1 nat) N_1)) pi))) ) 15.27/15.43 ( (zero_zero nat) ) 15.27/15.43 ( (hAPP nat nat suc (zero_zero nat)) ) 15.27/15.43 ) 15.27/15.43 (instantiation (forall ((X_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP int real (number_number_of real) min_1)) (hAPP real real sin X_1))) ) 15.27/15.43 ( (zero_zero real) ) 15.27/15.43 ( pi ) 15.27/15.43 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.43 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.27/15.43 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.27/15.43 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.27/15.43 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.27/15.43 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.27/15.43 ) 15.27/15.43 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_0 (product_prod X_a X_b))) (let ((_let_1 (the _let_0))) (= _let_1 (ti (fun (fun _let_0 bool) _let_0) _let_1)))) ) 15.27/15.43 ( nat, nat ) 15.27/15.43 ( int, int ) 15.27/15.43 ( int, (product_prod int int) ) 15.27/15.43 ( (product_prod nat nat), (product_prod nat nat) ) 15.27/15.43 ( real, real ) 15.27/15.43 ( (product_prod int int), (product_prod int int) ) 15.27/15.43 ( quickcheck_code_int, quickcheck_code_int ) 15.27/15.43 ( code_code_numeral, code_code_numeral ) 15.27/15.43 ) 15.27/15.43 (instantiation (forall ((N $$unsorted) (Ma $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP int real (number_number_of real) N)) (hAPP int real (real_1 int) Ma))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP int int (number_number_of int) N)) Ma))) ) 15.27/15.43 ( pls, (one_one int) ) 15.27/15.43 ( pls, pls ) 15.27/15.43 ( pls, min_1 ) 15.27/15.43 ( pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.27/15.43 ( (hAPP int int bit1 pls), t ) 15.27/15.43 ) 15.27/15.43 (instantiation (forall ((N_1 $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (one_one nat)) (hAPP nat nat (fact_fact nat) N_1))) ) 15.27/15.43 ( (zero_zero nat) ) 15.27/15.43 ( (hAPP nat nat suc (zero_zero nat)) ) 15.27/15.43 ) 15.27/15.43 (instantiation (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted)) (let ((_let_0 (combb X_b X_c X_a))) (= _let_0 (ti (fun (fun X_b X_c) (fun (fun X_a X_b) (fun X_a X_c))) _let_0))) ) 15.27/15.43 ( bool, bool, nat ) 15.27/15.43 ( bool, bool, int ) 15.27/15.43 ( bool, bool, real ) 15.27/15.43 ( bool, bool, (product_prod int int) ) 15.27/15.43 ( bool, (fun int bool), int ) 15.27/15.43 ( bool, (fun int int), int ) 15.27/15.43 ( bool, (fun bool bool), nat ) 15.27/15.43 ( bool, (fun bool bool), int ) 15.27/15.43 ( bool, (fun bool bool), real ) 15.27/15.43 ( bool, (fun bool bool), (product_prod int int) ) 15.27/15.43 ( nat, (fun nat bool), nat ) 15.27/15.43 ( nat, (fun nat nat), nat ) 15.27/15.43 ( nat, real, nat ) 15.27/15.43 ( int, bool, int ) 15.27/15.43 ( int, bool, (product_prod int int) ) 15.27/15.43 ( int, int, int ) 15.27/15.43 ( int, int, (product_prod int int) ) 15.27/15.43 ( int, (fun int bool), int ) 15.27/15.43 ( int, (fun int bool), (product_prod int int) ) 15.27/15.43 ( int, (fun int int), int ) 15.27/15.43 ( int, (fun int int), (product_prod int int) ) 15.27/15.43 ( int, (fun (product_prod int int) int), (product_prod int int) ) 15.27/15.43 ( (fun int bool), bool, int ) 15.27/15.43 ( (fun int bool), bool, real ) 15.27/15.43 ( (fun int bool), (fun int bool), int ) 15.27/15.43 ( (fun int bool), (fun int (fun bool bool)), int ) 15.27/15.43 ( (fun int bool), (fun (fun int int) (fun int bool)), int ) 15.27/15.43 ( (fun int (fun int bool)), (fun int bool), real ) 15.27/15.43 ( (fun int (fun int bool)), (fun int (fun int bool)), int ) 15.27/15.43 ( (fun int (fun int bool)), (fun int (fun int (fun bool bool))), real ) 15.27/15.43 ( (fun int int), (fun int (fun int bool)), int ) 15.27/15.43 ( (fun int int), (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)), (product_prod int int) ) 15.27/15.43 ( (fun int int), (let ((_let_0 (fun int int))) (fun _let_0 _let_0)), int ) 15.27/15.43 ( (fun nat bool), bool, int ) 15.27/15.43 ( (fun nat bool), (fun nat (fun bool bool)), int ) 15.27/15.43 ( real, bool, nat ) 15.27/15.43 ( real, bool, int ) 15.27/15.43 ( real, real, nat ) 15.27/15.43 ( real, real, int ) 15.27/15.43 ( real, real, real ) 15.27/15.43 ( real, (fun real bool), real ) 15.27/15.43 ( real, (fun real real), nat ) 15.27/15.43 ( real, (fun real real), int ) 15.27/15.43 ( real, (fun real real), real ) 15.27/15.43 ( real, (fun int real), int ) 15.27/15.43 ( (fun real bool), (fun (fun int real) (fun int bool)), real ) 15.27/15.43 ( (fun real bool), (fun (fun nat real) (fun nat bool)), real ) 15.27/15.43 ( (fun real real), (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)), int ) 15.27/15.43 ( (fun real real), (let ((_let_0 (fun int real))) (fun _let_0 _let_0)), int ) 15.27/15.43 ( (fun nat real), (fun nat bool), int ) 15.27/15.43 ( (fun bool bool), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)), (product_prod int int) ) 15.27/15.43 ( (fun (product_prod int int) bool), (fun (product_prod int int) bool), (product_prod int int) ) 15.27/15.43 ( (fun int (fun bool bool)), (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), int ) 15.27/15.43 ( (fun (product_prod int int) (fun int bool)), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))), (product_prod int int) ) 15.27/15.43 ( (fun (product_prod int int) int), (fun (product_prod int int) bool), (product_prod int int) ) 15.27/15.43 ( (fun (product_prod int int) int), (fun (product_prod int int) (fun int bool)), (product_prod int int) ) 15.27/15.43 ( (fun int real), (fun int bool), int ) 15.27/15.43 ( (fun nat (fun bool bool)), (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)), int ) 15.27/15.43 ( (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun int bool))) (fun _let_0 (fun int _let_0))), real ) 15.27/15.43 ( (fun int (fun int (fun bool bool))), (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))), real ) 15.27/15.43 ( (fun (fun int real) (fun int bool)), (fun (fun int (fun int real)) (fun int (fun int bool))), real ) 15.27/15.43 ( (fun int (fun nat bool)), (fun int bool), real ) 15.27/15.43 ( (fun int (fun nat bool)), (fun int (fun nat (fun bool bool))), real ) 15.27/15.43 ( (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun nat bool))) (fun _let_0 (fun int _let_0))), real ) 15.27/15.43 ( (fun int (fun nat (fun bool bool))), (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))), real ) 15.27/15.43 ( (fun (fun nat real) (fun nat bool)), (fun (fun int (fun nat real)) (fun int (fun nat bool))), real ) 15.27/15.43 ) 15.27/15.43 (instantiation (forall ((K $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) min_1)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int bit1 K)) min_1))))) ) 15.27/15.43 ( pls ) 15.27/15.43 ( (hAPP int int bit1 pls) ) 15.27/15.43 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.27/15.43 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.27/15.43 ( min_1 ) 15.27/15.43 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.27/15.43 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.27/15.43 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 15.27/15.43 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 15.27/15.43 ) 15.27/15.43 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (hBOOL (hAPP real bool (hAPP _let_1 (fun real bool) (sums real) (hAPP _let_1 _let_1 (hAPP _let_2 (fun _let_1 _let_1) (combs nat real real) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 nat) (times_times real)) cos_coeff)) (hAPP real _let_1 (power_power real) X_2))) (hAPP real real cos X_2)))))) ) 15.27/15.43 ( (zero_zero real) ) 15.27/15.43 ( pi ) 15.27/15.43 ( (hAPP int real (number_number_of real) min_1) ) 15.27/15.43 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.43 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.43 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.43 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.27/15.43 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.27/15.43 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.27/15.43 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.27/15.43 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.27/15.43 ( skv_5 ) 15.27/15.43 ) 15.27/15.43 (instantiation (forall ((W_1 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (let ((_let_2 (ord_less int))) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 (hAPP int int bit0 W_1)) _let_1)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 W_1) _let_1)))))) ) 15.27/15.43 ( pls ) 15.27/15.43 ( (hAPP int int bit1 pls) ) 15.27/15.43 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.27/15.43 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.27/15.43 ( min_1 ) 15.27/15.43 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.27/15.43 ) 15.27/15.43 (instantiation (forall ((W_1 $$unsorted) (Z $$unsorted)) (let ((_let_0 (fun int bool))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) W_1) Z)) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) W_1) (hAPP int int (hAPP int (fun int int) (plus_plus int) Z) (one_one int)))))) ) 15.27/15.43 ( (one_one int), t ) 15.27/15.43 ( (zero_zero int), (one_one int) ) 15.27/15.43 ( (zero_zero int), min_1 ) 15.27/15.43 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.43 ( (zero_zero int), s ) 15.27/15.43 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.27/15.43 ( (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.27/15.43 ( (zero_zero int), skv_4 ) 15.27/15.43 ( (zero_zero int), skv_10 ) 15.27/15.43 ( pls, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.27/15.43 ( min_1, pls ) 15.27/15.43 ( min_1, min_1 ) 15.27/15.43 ( s, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.27/15.43 ( t, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.27/15.43 ( skv_4, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.27/15.43 ( skv_10, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.27/15.43 ) 15.27/15.43 (instantiation (forall ((K_4 $$unsorted)) (let ((_let_0 (product_prod int int))) (= (zero_zero rat) (hAPP _let_0 rat frct (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) (zero_zero int)) K_4)))) ) 15.27/15.43 ( (one_one int) ) 15.27/15.43 ) 15.27/15.43 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (times_times real))) (let ((_let_2 (hAPP real real cos X_1))) (let ((_let_3 (hAPP real real sin X_1))) (= (one_one real) (hAPP real real (hAPP real _let_0 (plus_plus real) (hAPP real real (hAPP real _let_0 _let_1 _let_2) _let_2)) (hAPP real real (hAPP real _let_0 _let_1 _let_3) _let_3))))))) ) 15.27/15.43 ( (zero_zero real) ) 15.27/15.43 ( pi ) 15.27/15.43 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.43 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.43 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.27/15.43 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.27/15.43 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.27/15.43 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.27/15.43 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.27/15.43 ( skv_5 ) 15.27/15.43 ) 15.27/15.43 (instantiation (forall ((T_1 $$unsorted)) (preorder (filter T_1)) ) 15.27/15.43 ( nat ) 15.27/15.43 ( real ) 15.27/15.43 ) 15.27/15.43 (instantiation (forall ((K $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) pls)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int bit0 K)) pls))))) ) 15.27/15.43 ( pls ) 15.27/15.43 ( (hAPP int int bit1 pls) ) 15.27/15.43 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.27/15.43 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.27/15.43 ( min_1 ) 15.27/15.43 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.27/15.43 ) 15.27/15.43 (instantiation (forall ((N_1 $$unsorted) (M $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) N_1) (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) N_1) M))) ) 15.27/15.43 ( (one_one nat), (one_one nat) ) 15.27/15.43 ) 15.27/15.43 (instantiation (forall ((X_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (abs_abs real) (hAPP real real cos X_1))) (one_one real))) ) 15.27/15.43 ( (zero_zero real) ) 15.27/15.43 ( pi ) 15.27/15.43 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.43 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.43 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.27/15.43 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.27/15.43 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.27/15.43 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.27/15.43 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.27/15.43 ( skv_5 ) 15.27/15.43 ) 15.27/15.43 (instantiation (forall ((A_3 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun nat bool))) (= (hBOOL (hAPP _let_1 bool (finite_finite_1 nat) A_3)) (hBOOL (hAPP _let_0 bool (finite_finite_1 int) (hAPP _let_1 _let_0 (hAPP (fun nat int) (fun _let_1 _let_0) (image nat int) (semiring_1_of_nat int)) A_3)))))) ) 15.27/15.43 ( (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 15.27/15.43 ) 15.27/15.43 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (hAPP real (fun real real) (minus_minus real) X_2) Y_2)) (zero_zero real))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_2) Y_2))))) ) 15.27/15.43 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 15.27/15.43 ) 15.27/15.43 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (hAPP real complex (of_real complex) X_1))) (= _let_0 (hAPP complex complex cnj _let_0))) ) 15.27/15.43 ( pi ) 15.27/15.43 ( (hAPP int real (number_number_of real) min_1) ) 15.27/15.43 ( (hAPP real real (uminus_uminus real) (one_one real)) ) 15.27/15.43 ) 15.27/15.43 (instantiation (forall ((W_1 $$unsorted) (Z $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (= (and (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 W_1) Z)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (zero_zero int)) Z))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (hAPP int nat nat_1 W_1)) (hAPP int nat nat_1 Z)))))) ) 15.27/15.43 ( (one_one int), t ) 15.27/15.43 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.43 ( pls, (one_one int) ) 15.27/15.43 ( pls, pls ) 15.27/15.43 ( pls, min_1 ) 15.27/15.43 ( pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.27/15.43 ( min_1, pls ) 15.27/15.43 ( min_1, min_1 ) 15.27/15.43 ( s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.27/15.43 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.27/15.43 ( skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.27/15.43 ( skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.27/15.43 ) 15.27/15.43 (instantiation (forall ((N_1 $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) (hAPP nat nat suc N_1))) ) 15.27/15.43 ( (zero_zero nat) ) 15.27/15.43 ( (hAPP nat nat suc (zero_zero nat)) ) 15.27/15.43 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 15.27/15.43 ) 15.27/15.43 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (zero_zero real))) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_2) _let_2)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real sqrt X_2)) _let_2)))))) ) 15.27/15.43 ( (one_one real) ) 15.27/15.43 ( (zero_zero real) ) 15.27/15.43 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.43 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.27/15.43 ) 15.27/15.43 (instantiation (forall ((X_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) X_1) (hAPP real real (hAPP real (fun real real) (plus_plus real) (hAPP nat real (real_1 nat) (hAPP real nat natfloor X_1))) (one_one real)))) ) 15.27/15.43 ( (one_one real) ) 15.27/15.43 ( (zero_zero real) ) 15.27/15.43 ( pi ) 15.27/15.43 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.43 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.27/15.43 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.43 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 15.27/15.43 ) 15.27/15.43 (instantiation (forall ((X_a $$unsorted) (X_2 $$unsorted) (Y_2 $$unsorted) (F $$unsorted)) (let ((_let_0 (product_prod X_a X_a))) (let ((_let_1 (fun _let_0 bool))) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (hAPP X_a nat F X_2)) (hAPP X_a nat F Y_2))) (hBOOL (hAPP _let_1 bool (hAPP _let_0 (fun _let_1 bool) (member _let_0) (hAPP X_a _let_0 (hAPP X_a (fun X_a _let_0) (product_Pair X_a X_a) X_2) Y_2)) (hAPP (fun X_a nat) _let_1 (measure X_a) F)))))) ) 15.27/15.43 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), nat_1 ) 15.27/15.43 ) 15.27/15.43 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (zero_zero nat))) (let ((_let_1 (hAPP nat nat suc _let_0))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) X_1) (hAPP nat nat suc _let_1)))) (= _let_0 X_1) (= X_1 _let_1)))) ) 15.27/15.43 ( (zero_zero nat) ) 15.27/15.43 ) 15.27/15.43 (instantiation (forall ((N_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) N_1) (zero_zero int)))) (= (one_one int) (hAPP int int zfact N_1))) ) 15.27/15.43 ( (one_one int) ) 15.27/15.43 ( (zero_zero int) ) 15.27/15.43 ( min_1 ) 15.27/15.43 ) 15.27/15.43 (instantiation (forall ((N_1 $$unsorted)) (let ((_let_0 (fun int int))) (or (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) N_1) (zero_zero int))) (= (hAPP int int zfact N_1) (hAPP int int (hAPP int _let_0 (times_times int) N_1) (hAPP int int zfact (hAPP int int (hAPP int _let_0 (minus_minus int) N_1) (one_one int))))))) ) 15.27/15.43 ( (one_one int) ) 15.27/15.43 ( (zero_zero int) ) 15.27/15.43 ( min_1 ) 15.27/15.43 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.43 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.43 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.27/15.43 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.43 ) 15.27/15.43 (instantiation (forall ((K_4 $$unsorted) (L_4 $$unsorted)) (not (= (hAPP int int bit1 L_4) (hAPP int int bit0 K_4))) ) 15.27/15.43 ( pls, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.27/15.43 ( (hAPP int int bit1 pls), pls ) 15.27/15.43 ( (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.27/15.43 ( (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit1 pls) ) 15.27/15.43 ( min_1, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 15.27/15.43 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.27/15.43 ) 15.27/15.43 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_101870 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hAPP int int (number_number_of int) BOUND_VARIABLE_101870) (hAPP X_a int (archim2085082626_floor X_a) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_101870)))) ) 15.27/15.43 ( nat, pls ) 15.27/15.43 ( nat, (hAPP int int bit1 pls) ) 15.27/15.43 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.27/15.43 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.27/15.43 ( int, pls ) 15.27/15.43 ( int, (hAPP int int bit1 pls) ) 15.27/15.43 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.27/15.43 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.27/15.43 ( int, min_1 ) 15.27/15.43 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.43 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.27/15.43 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.27/15.43 ( real, min_1 ) 15.27/15.43 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.43 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.27/15.43 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.43 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 15.27/15.43 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.27/15.43 ( complex, min_1 ) 15.27/15.43 ( quickcheck_code_int, (one_one int) ) 15.27/15.43 ( quickcheck_code_int, (zero_zero int) ) 15.27/15.43 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 15.27/15.43 ( code_code_numeral, pls ) 15.27/15.43 ( code_code_numeral, (hAPP int int bit1 pls) ) 15.27/15.43 ) 15.27/15.44 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (one_one real))) (let ((_let_2 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 (zero_zero real)) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) X_1) _let_1))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 (hAPP real real ln (hAPP real real (hAPP real (fun real real) (minus_minus real) _let_1) X_1))) (hAPP real real (uminus_uminus real) X_1))))))) ) 15.27/15.44 ( (one_one real) ) 15.27/15.44 ( (zero_zero real) ) 15.27/15.44 ( pi ) 15.27/15.44 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.44 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.27/15.44 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.27/15.44 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.44 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.44 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 15.27/15.44 ( skv_3 ) 15.27/15.44 ( skv_5 ) 15.27/15.44 ( skv_7 ) 15.27/15.44 ( skv_12 ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((P_1 $$unsorted) (BOUND_VARIABLE_101937 $$unsorted)) (or (hBOOL (hAPP nat bool P_1 (zero_zero nat))) (not (hBOOL (hAPP nat bool P_1 BOUND_VARIABLE_101937))) (not (forall ((N_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool P_1 (hAPP nat nat suc N_2)))) (hBOOL (hAPP nat bool P_1 N_2))) ))) ) 15.27/15.44 ( (even_odd_even nat), (zero_zero nat) ) 15.27/15.44 ( (even_odd_even nat), (one_one nat) ) 15.27/15.44 ( (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.44 ( prime, (zero_zero nat) ) 15.27/15.44 ( prime, (hAPP nat nat suc (zero_zero nat)) ) 15.27/15.44 ( prime, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int rat (hAPP int (fun int rat) fract K_4) (one_one int)) (hAPP int rat (ring_1_of_int rat) K_4)) ) 15.27/15.44 ( (one_one int) ) 15.27/15.44 ( (zero_zero int) ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_101996 $$unsorted) (BOUND_VARIABLE_101997 $$unsorted)) (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) pls))) (let ((_let_1 (number_number_of X_a))) (or (not (number_semiring X_a)) (not (hBOOL (hAPP int bool _let_0 BOUND_VARIABLE_101997))) (not (hBOOL (hAPP int bool _let_0 BOUND_VARIABLE_101996))) (= (hAPP int X_a _let_1 (hAPP int int (hAPP int (fun int int) (plus_plus int) BOUND_VARIABLE_101997) BOUND_VARIABLE_101996)) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (hAPP int X_a _let_1 BOUND_VARIABLE_101997)) (hAPP int X_a _let_1 BOUND_VARIABLE_101996)))))) ) 15.27/15.44 ( nat, (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (uminus_uminus real) pi)) Y_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Y_1) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) (zero_zero real)))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real cos Y_1)) (hAPP real real cos X_1)))))) ) 15.27/15.44 ( skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((A_1 $$unsorted)) (= (hAPP real complex cis (hAPP real real (uminus_uminus real) A_1)) (hAPP complex complex (inverse_inverse complex) (hAPP real complex cis A_1))) ) 15.27/15.44 ( (one_one real) ) 15.27/15.44 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.44 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((Z_1 $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (power_power real))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (= (hAPP complex real (norm_norm complex) Z_1) (hAPP real real sqrt (hAPP real real (hAPP real (fun real real) (plus_plus real) (hAPP nat real (hAPP real _let_0 _let_1 (hAPP complex real re Z_1)) _let_2)) (hAPP nat real (hAPP real _let_0 _let_1 (hAPP complex real im Z_1)) _let_2))))))) ) 15.27/15.44 ( (one_one complex) ) 15.27/15.44 ( ii ) 15.27/15.44 ( (zero_zero complex) ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((E_1 $$unsorted) (B $$unsorted) (D $$unsorted) (A_1 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (one_one int))) (let ((_let_3 (gcd_gcd int))) (let ((_let_4 (dvd_dvd int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_4 D) A_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_4 E_1) B))) (not (= _let_2 (hAPP int int (hAPP int _let_1 _let_3 A_1) B))) (= _let_2 (hAPP int int (hAPP int _let_1 _let_3 D) E_1)))))))) ) 15.27/15.44 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((N_1 $$unsorted) (M $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (one_one int)) M))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 M) N_1))) (hBOOL (hAPP int bool (hAPP int _let_0 (dvd_dvd int) M) (hAPP int int (fact_fact int) N_1)))))) ) 15.27/15.44 ( (one_one int), (zero_zero int) ) 15.27/15.44 ( pls, min_1 ) 15.27/15.44 ( min_1, (zero_zero int) ) 15.27/15.44 ( min_1, min_1 ) 15.27/15.44 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 15.27/15.44 ( s, (zero_zero int) ) 15.27/15.44 ( t, (one_one int) ) 15.27/15.44 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 15.27/15.44 ( (hAPP int int (number_number_of int) pls), (zero_zero int) ) 15.27/15.44 ( skv_4, (zero_zero int) ) 15.27/15.44 ( skv_10, (zero_zero int) ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (hAPP nat real (real_1 nat) X_1))) (= _let_0 (hAPP real real (abs_abs real) _let_0))) ) 15.27/15.44 ( (zero_zero nat) ) 15.27/15.44 ( (hAPP nat nat suc (zero_zero nat)) ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_0 (hAPP nat (fun nat bool) (ord_less nat) M))) (or (not (hBOOL (hAPP nat bool _let_0 N_1))) (hBOOL (hAPP nat bool _let_0 (hAPP nat nat suc N_1))))) ) 15.27/15.44 ( (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((Z_1 $$unsorted)) (or (not (hBOOL (hAPP int bool nat_neg Z_1))) (= (zero_zero nat) (hAPP int nat nat_1 Z_1))) ) 15.27/15.44 ( (one_one int) ) 15.27/15.44 ( (hAPP int int (number_number_of int) min_1) ) 15.27/15.44 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.44 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.27/15.44 ( (hAPP int int (number_number_of int) pls) ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_102103 $$unsorted) (BOUND_VARIABLE_102104 $$unsorted) (BOUND_VARIABLE_102105 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (let ((_let_3 (ord_less_eq X_a))) (let ((_let_4 (fun X_a X_a))) (let ((_let_5 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_102105)))) (let ((_let_6 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_102105) _let_2)))) (let ((_let_7 (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_102103))) (let ((_let_8 (hAPP X_a X_a (hAPP X_a _let_4 (times_times X_a) _let_7) BOUND_VARIABLE_102105))) (let ((_let_9 (hAPP X_a _let_0 _let_3 _let_7))) (or (not (linord1117847801e_zero X_a)) (not (number X_a)) (= (and (or _let_5 (and (or (not _let_6) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_3 BOUND_VARIABLE_102104) _let_8))) (or _let_6 (hBOOL (hAPP X_a bool _let_9 _let_2))))) (or (not _let_5) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_3 _let_8) BOUND_VARIABLE_102104)))) (hBOOL (hAPP X_a bool _let_9 (hAPP X_a X_a (hAPP X_a _let_4 (inverse_divide X_a) BOUND_VARIABLE_102104) BOUND_VARIABLE_102105))))))))))))))) ) 15.27/15.44 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)), (zero_zero real), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.27/15.44 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((Y_1 $$unsorted)) (let ((_let_0 (zero_zero real))) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) _let_0) Y_1))) (= _let_0 (hAPP real real cos (hAPP complex real arg (hAPP real complex (hAPP real (fun real complex) complex_1 _let_0) Y_1)))))) ) 15.27/15.44 ( (one_one real) ) 15.27/15.44 ( (zero_zero real) ) 15.27/15.44 ( pi ) 15.27/15.44 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.44 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.44 ( skv_2 ) 15.27/15.44 ( skv_8 ) 15.27/15.44 ( skv_9 ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (uminus_uminus real))) (= (hAPP complex complex (uminus_uminus complex) X_1) (hAPP real complex (hAPP real (fun real complex) complex_1 (hAPP real real _let_0 (hAPP complex real re X_1))) (hAPP real real _let_0 (hAPP complex real im X_1))))) ) 15.27/15.44 ( (one_one complex) ) 15.27/15.44 ( ii ) 15.27/15.44 ( (zero_zero complex) ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_102225 $$unsorted) (BOUND_VARIABLE_102226 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_102225) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_102226))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP X_a int (archimedean_ceiling X_a) BOUND_VARIABLE_102225)) (hAPP int int (number_number_of int) BOUND_VARIABLE_102226))))) ) 15.27/15.44 ( int, (zero_zero int), pls ) 15.27/15.44 ( int, (zero_zero int), (hAPP int int bit1 pls) ) 15.27/15.44 ( int, (zero_zero int), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.27/15.44 ( int, (zero_zero int), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.27/15.44 ( int, min_1, pls ) 15.27/15.44 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.27/15.44 ( real, skv_5, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((A_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong A_1) _let_1) P_5))) (= _let_1 (hAPP int int (hAPP int (fun int int) legendre A_1) P_5))))) ) 15.27/15.44 ( (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((A_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_0 (hAPP int int (hAPP int (fun int int) legendre A_1) P_5))) (let ((_let_1 (hBOOL (hAPP int bool (hAPP int (fun int bool) quadRes P_5) A_1)))) (or (hBOOL (hAPP int bool (hAPP int (fun int bool) (hAPP int (fun int (fun int bool)) zcong A_1) (zero_zero int)) P_5)) (and (or (not _let_1) (= (one_one int) _let_0)) (or _let_1 (= _let_0 (hAPP int int (number_number_of int) min_1))))))) ) 15.27/15.44 ( (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_102286 $$unsorted)) (or (not (ordere142940540dd_abs X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) BOUND_VARIABLE_102286))) (= (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_102286) (ti X_a BOUND_VARIABLE_102286))) ) 15.27/15.44 ( bool, fFalse ) 15.27/15.44 ( bool, fTrue ) 15.27/15.44 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.44 ( int, (one_one int) ) 15.27/15.44 ( int, pls ) 15.27/15.44 ( int, min_1 ) 15.27/15.44 ( int, s ) 15.27/15.44 ( int, m ) 15.27/15.44 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.27/15.44 ( int, s1 ) 15.27/15.44 ( int, t ) 15.27/15.44 ( (fun int bool), nat_neg ) 15.27/15.44 ( (fun int bool), zprime ) 15.27/15.44 ( (fun int bool), zEven ) 15.27/15.44 ( (fun int bool), zOdd ) 15.27/15.44 ( (fun int bool), (even_odd_even int) ) 15.27/15.44 ( (fun int bool), twoSqu1091635170sum2sq ) 15.27/15.44 ( (fun int bool), nat_is_nat ) 15.27/15.44 ( (fun int (fun int bool)), norRRset ) 15.27/15.44 ( (fun int (fun int bool)), quadRes ) 15.27/15.44 ( (fun int (fun int bool)), sRStar ) 15.27/15.44 ( (fun int (fun int bool)), d22set ) 15.27/15.44 ( (fun int (fun int bool)), sr ) 15.27/15.44 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 15.27/15.44 ( (fun int int), zfact ) 15.27/15.44 ( (fun int int), bit0 ) 15.27/15.44 ( (fun int int), bit1 ) 15.27/15.44 ( (fun int int), (fact_fact int) ) 15.27/15.44 ( (fun int int), pred ) 15.27/15.44 ( (fun int int), succ ) 15.27/15.44 ( (fun nat bool), (even_odd_even nat) ) 15.27/15.44 ( (fun nat bool), prime ) 15.27/15.44 ( (fun nat nat), suc ) 15.27/15.44 ( (fun nat nat), (fact_fact nat) ) 15.27/15.44 ( (fun nat nat), fact ) 15.27/15.44 ( (fun nat nat), nat_size ) 15.27/15.44 ( (fun nat nat), (size_size nat) ) 15.27/15.44 ( (fun (product_prod nat nat) bool), pred_nat ) 15.27/15.44 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 15.27/15.44 ( real, pi ) 15.27/15.44 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.44 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.44 ( real, skv_2 ) 15.27/15.44 ( real, skv_8 ) 15.27/15.44 ( real, skv_9 ) 15.27/15.44 ( (fun real real), ln ) 15.27/15.44 ( (fun real real), cos ) 15.27/15.44 ( (fun real real), sqrt ) 15.27/15.44 ( (fun real real), sin ) 15.27/15.44 ( (fun real real), arccos ) 15.27/15.44 ( (fun real real), arcsin ) 15.27/15.44 ( (fun real real), tan ) 15.27/15.44 ( (fun real real), arctan ) 15.27/15.44 ( (fun nat (fun nat bool)), coprime ) 15.27/15.44 ( complex, ii ) 15.27/15.44 ( (fun nat real), (real_1 nat) ) 15.27/15.44 ( (fun nat real), sin_coeff ) 15.27/15.44 ( (fun nat real), cos_coeff ) 15.27/15.44 ( (filter nat), sequentially ) 15.27/15.44 ( (fun int (fun int int)), (gcd_gcd int) ) 15.27/15.44 ( (fun int (fun int int)), legendre ) 15.27/15.44 ( (fun int (fun int int)), legacy_zgcd ) 15.27/15.44 ( (fun int (fun int int)), standardRes ) 15.27/15.44 ( (fun int (fun int int)), nat_tsub ) 15.27/15.44 ( (fun int (fun int int)), multInv ) 15.27/15.44 ( (fun int (fun int int)), z3mod ) 15.27/15.44 ( (fun int (fun int int)), z3div ) 15.27/15.44 ( (fun int (fun int int)), int_gcd ) 15.27/15.44 ( (fun int (fun int int)), int_lcm ) 15.27/15.44 ( (fun int (fun int int)), inv ) 15.27/15.44 ( (fun complex complex), expi ) 15.27/15.44 ( (fun complex complex), cnj ) 15.27/15.44 ( (fun real complex), cis ) 15.27/15.44 ( (fun int nat), nat_1 ) 15.27/15.44 ( (fun int nat), phi ) 15.27/15.44 ( (fun (fun int bool) bool), nat_nat_set ) 15.27/15.44 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 15.27/15.44 ( (fun nat (fun nat nat)), nat_gcd ) 15.27/15.44 ( (fun nat (fun nat nat)), nat_lcm ) 15.27/15.44 ( (fun (fun int bool) int), (the int) ) 15.27/15.44 ( (fun complex real), re ) 15.27/15.44 ( (fun complex real), im ) 15.27/15.44 ( (fun complex real), arg ) 15.27/15.44 ( (fun bool bool), fNot ) 15.27/15.44 ( (fun nat (fun real real)), root ) 15.27/15.44 ( (fun real (fun real real)), log ) 15.27/15.44 ( (fun real (fun real real)), powr ) 15.27/15.44 ( (fun bool (fun bool bool)), fimplies ) 15.27/15.44 ( (fun bool (fun bool bool)), fconj ) 15.27/15.44 ( (fun bool (fun bool bool)), fdisj ) 15.27/15.44 ( (fun int (fun int (product_prod int int))), negDivAlg ) 15.27/15.44 ( (fun int (fun int (product_prod int int))), posDivAlg ) 15.27/15.44 ( (fun int (fun int (product_prod int int))), divmod_int ) 15.27/15.44 ( (fun int (fun int (product_prod int int))), pdivmod ) 15.27/15.44 ( (fun int (fun int (product_prod int int))), norm_frac ) 15.27/15.44 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 15.27/15.44 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 15.27/15.44 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 15.27/15.44 ( (fun int (fun int (fun int bool))), zcong ) 15.27/15.44 ( (fun int (fun int (fun int bool))), zcongm ) 15.27/15.44 ( (fun int (fun int (fun int bool))), noXRRset ) 15.27/15.44 ( (fun int (fun int (fun int bool))), bnorRset ) 15.27/15.44 ( (fun int (fun int (fun int bool))), wset ) 15.27/15.44 ( (fun (product_prod int int) bool), frac_1 ) 15.27/15.44 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 15.27/15.44 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 15.27/15.44 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 15.27/15.44 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 15.27/15.44 ( (fun (fun nat rat) bool), vanishes ) 15.27/15.44 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 15.27/15.44 ( (fun code_code_numeral nat), code_c271388182l_size ) 15.27/15.44 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 15.27/15.44 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 15.27/15.44 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 15.27/15.44 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 15.27/15.44 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 15.27/15.44 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 15.27/15.44 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 15.27/15.44 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 15.27/15.44 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 15.27/15.44 ( (fun complex nat), complex_size ) 15.27/15.44 ( (fun complex nat), (size_size complex) ) 15.27/15.44 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 15.27/15.44 ( (fun nat (fun nat (product_prod int int))), bezw ) 15.27/15.44 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 15.27/15.44 ( (fun int (fun nat nat)), nat_aux ) 15.27/15.44 ( (fun int (fun (fun int bool) bool)), rsetR ) 15.27/15.44 ( (fun int (fun (fun int bool) bool)), resSet ) 15.27/15.44 ( (fun int (list int)), quickc666637781d_zero ) 15.27/15.44 ( (fun (product_prod int int) rat), frct ) 15.27/15.44 ( (fun int (fun int rat)), fract ) 15.27/15.44 ( (fun real (fun real complex)), complex_1 ) 15.27/15.44 ( (fun real (fun real complex)), rcis ) 15.27/15.44 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 15.27/15.44 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 15.27/15.44 ( (fun int real), (real_1 int) ) 15.27/15.44 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 15.27/15.44 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 15.27/15.44 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 15.27/15.44 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 15.27/15.44 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 15.27/15.44 ( (fun real nat), natfloor ) 15.27/15.44 ( (fun real nat), natceiling ) 15.27/15.44 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 15.27/15.44 ( (fun quickcheck_code_int int), quickcheck_int_of ) 15.27/15.44 ( (fun rat (product_prod int int)), quotient_of ) 15.27/15.44 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 15.27/15.44 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 15.27/15.44 ( (fun rat real), ratreal ) 15.27/15.44 ( (fun code_code_numeral int), code_int_of ) 15.27/15.44 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 15.27/15.44 ( (fun int quickcheck_code_int), quickcheck_of_int ) 15.27/15.44 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 15.27/15.44 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((B $$unsorted)) (let ((_let_0 (hAPP int int (number_number_of int) min_1))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun int _let_1))) (= (hAPP int _let_1 (hAPP int _let_2 negDivAlg _let_0) B) (hAPP int _let_1 (hAPP int _let_2 (product_Pair int int) _let_0) (hAPP int int (hAPP int (fun int int) (minus_minus int) B) (one_one int))))))) ) 15.27/15.44 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_102349 $$unsorted)) (or (not (linordered_semidom X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) (hAPP nat X_a (semiring_1_of_nat X_a) (hAPP nat nat (fact_fact nat) BOUND_VARIABLE_102349))))) ) 15.27/15.44 ( int, (hAPP nat nat suc (zero_zero nat)) ) 15.27/15.44 ( real, (hAPP nat nat suc (zero_zero nat)) ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (hAPP real _let_0 _let_1 (zero_zero real)))) (or (not (hBOOL (hAPP real bool _let_2 X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))) (hBOOL (hAPP real bool _let_2 (hAPP real real sin X_1))))))) ) 15.27/15.44 ( (one_one real) ) 15.27/15.44 ( (zero_zero real) ) 15.27/15.44 ( pi ) 15.27/15.44 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.44 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.27/15.44 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.27/15.44 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.27/15.44 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.27/15.44 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.44 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 15.27/15.44 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.27/15.44 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((Z_1 $$unsorted) (W $$unsorted)) (let ((_let_0 (fun int int))) (= (hAPP int int (hAPP int _let_0 (minus_minus int) Z_1) W) (hAPP int int (hAPP int _let_0 (plus_plus int) Z_1) (hAPP int int (uminus_uminus int) W)))) ) 15.27/15.44 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_102412 $$unsorted) (BOUND_VARIABLE_102413 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (inverse_divide X_a))) (let ((_let_2 (uminus_uminus X_a))) (or (not (division_ring X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_102413)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_102412)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_102413)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_102412) BOUND_VARIABLE_102413)))))) ) 15.27/15.44 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.44 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.27/15.44 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.44 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 15.27/15.44 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.44 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.44 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.27/15.44 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.27/15.44 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.44 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.44 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((V_1 $$unsorted)) (let ((_let_0 (number_number_of nat))) (or (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) V_1) pls)) (= (hAPP int nat _let_0 (hAPP int int pred V_1)) (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) (hAPP int nat _let_0 V_1)) (one_one nat))))) ) 15.27/15.44 ( (one_one int) ) 15.27/15.44 ( (zero_zero int) ) 15.27/15.44 ( pls ) 15.27/15.44 ( min_1 ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((V_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) V_1) pls))) (= (zero_zero nat) (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) (hAPP int nat (number_number_of nat) V_1)) (one_one nat)))) ) 15.27/15.44 ( (one_one int) ) 15.27/15.44 ( (zero_zero int) ) 15.27/15.44 ( pls ) 15.27/15.44 ( (hAPP int int bit1 pls) ) 15.27/15.44 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.27/15.44 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.27/15.44 ( min_1 ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_102452 $$unsorted)) (let ((_let_0 (one_one X_a))) (or (not (field_inverse_zero X_a)) (= (= _let_0 (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_102452)) (= _let_0 (ti X_a BOUND_VARIABLE_102452))))) ) 15.27/15.44 ( bool, fFalse ) 15.27/15.44 ( bool, fTrue ) 15.27/15.44 ( int, pls ) 15.27/15.44 ( int, min_1 ) 15.27/15.44 ( int, s ) 15.27/15.44 ( int, m ) 15.27/15.44 ( int, s1 ) 15.27/15.44 ( int, t ) 15.27/15.44 ( (fun int bool), nat_neg ) 15.27/15.44 ( (fun int bool), zprime ) 15.27/15.44 ( (fun int bool), zEven ) 15.27/15.44 ( (fun int bool), zOdd ) 15.27/15.44 ( (fun int bool), (even_odd_even int) ) 15.27/15.44 ( (fun int bool), twoSqu1091635170sum2sq ) 15.27/15.44 ( (fun int bool), nat_is_nat ) 15.27/15.44 ( (fun int (fun int bool)), norRRset ) 15.27/15.44 ( (fun int (fun int bool)), quadRes ) 15.27/15.44 ( (fun int (fun int bool)), sRStar ) 15.27/15.44 ( (fun int (fun int bool)), d22set ) 15.27/15.44 ( (fun int (fun int bool)), sr ) 15.27/15.44 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 15.27/15.44 ( (fun int int), zfact ) 15.27/15.44 ( (fun int int), bit0 ) 15.27/15.44 ( (fun int int), bit1 ) 15.27/15.44 ( (fun int int), (fact_fact int) ) 15.27/15.44 ( (fun int int), pred ) 15.27/15.44 ( (fun int int), succ ) 15.27/15.44 ( (fun nat bool), (even_odd_even nat) ) 15.27/15.44 ( (fun nat bool), prime ) 15.27/15.44 ( (fun nat nat), suc ) 15.27/15.44 ( (fun nat nat), (fact_fact nat) ) 15.27/15.44 ( (fun nat nat), fact ) 15.27/15.44 ( (fun nat nat), nat_size ) 15.27/15.44 ( (fun nat nat), (size_size nat) ) 15.27/15.44 ( (fun (product_prod nat nat) bool), pred_nat ) 15.27/15.44 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 15.27/15.44 ( real, (zero_zero real) ) 15.27/15.44 ( real, pi ) 15.27/15.44 ( (fun real real), ln ) 15.27/15.44 ( (fun real real), cos ) 15.27/15.44 ( (fun real real), sqrt ) 15.27/15.44 ( (fun real real), sin ) 15.27/15.44 ( (fun real real), arccos ) 15.27/15.44 ( (fun real real), arcsin ) 15.27/15.44 ( (fun real real), tan ) 15.27/15.44 ( (fun real real), arctan ) 15.27/15.44 ( (fun nat (fun nat bool)), coprime ) 15.27/15.44 ( complex, ii ) 15.27/15.44 ( (fun nat real), (real_1 nat) ) 15.27/15.44 ( (fun nat real), sin_coeff ) 15.27/15.44 ( (fun nat real), cos_coeff ) 15.27/15.44 ( (filter nat), sequentially ) 15.27/15.44 ( (fun int (fun int int)), (gcd_gcd int) ) 15.27/15.44 ( (fun int (fun int int)), legendre ) 15.27/15.44 ( (fun int (fun int int)), legacy_zgcd ) 15.27/15.44 ( (fun int (fun int int)), standardRes ) 15.27/15.44 ( (fun int (fun int int)), nat_tsub ) 15.27/15.44 ( (fun int (fun int int)), multInv ) 15.27/15.44 ( (fun int (fun int int)), z3mod ) 15.27/15.44 ( (fun int (fun int int)), z3div ) 15.27/15.44 ( (fun int (fun int int)), int_gcd ) 15.27/15.44 ( (fun int (fun int int)), int_lcm ) 15.27/15.44 ( (fun int (fun int int)), inv ) 15.27/15.44 ( (fun complex complex), expi ) 15.27/15.44 ( (fun complex complex), cnj ) 15.27/15.44 ( (fun real complex), cis ) 15.27/15.44 ( (fun int nat), nat_1 ) 15.27/15.44 ( (fun int nat), phi ) 15.27/15.44 ( (fun (fun int bool) bool), nat_nat_set ) 15.27/15.44 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 15.27/15.44 ( (fun nat (fun nat nat)), nat_gcd ) 15.27/15.44 ( (fun nat (fun nat nat)), nat_lcm ) 15.27/15.44 ( (fun (fun int bool) int), (the int) ) 15.27/15.44 ( (fun complex real), re ) 15.27/15.44 ( (fun complex real), im ) 15.27/15.44 ( (fun complex real), arg ) 15.27/15.44 ( (fun bool bool), fNot ) 15.27/15.44 ( (fun nat (fun real real)), root ) 15.27/15.44 ( (fun real (fun real real)), log ) 15.27/15.44 ( (fun real (fun real real)), powr ) 15.27/15.44 ( (fun bool (fun bool bool)), fimplies ) 15.27/15.44 ( (fun bool (fun bool bool)), fconj ) 15.27/15.44 ( (fun bool (fun bool bool)), fdisj ) 15.27/15.44 ( (fun int (fun int (product_prod int int))), negDivAlg ) 15.27/15.44 ( (fun int (fun int (product_prod int int))), posDivAlg ) 15.27/15.44 ( (fun int (fun int (product_prod int int))), divmod_int ) 15.27/15.44 ( (fun int (fun int (product_prod int int))), pdivmod ) 15.27/15.44 ( (fun int (fun int (product_prod int int))), norm_frac ) 15.27/15.44 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 15.27/15.44 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 15.27/15.44 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 15.27/15.44 ( (fun int (fun int (fun int bool))), zcong ) 15.27/15.44 ( (fun int (fun int (fun int bool))), zcongm ) 15.27/15.44 ( (fun int (fun int (fun int bool))), noXRRset ) 15.27/15.44 ( (fun int (fun int (fun int bool))), bnorRset ) 15.27/15.44 ( (fun int (fun int (fun int bool))), wset ) 15.27/15.44 ( (fun (product_prod int int) bool), frac_1 ) 15.27/15.44 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 15.27/15.44 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 15.27/15.44 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 15.27/15.44 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 15.27/15.44 ( (fun (fun nat rat) bool), vanishes ) 15.27/15.44 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 15.27/15.44 ( (fun code_code_numeral nat), code_c271388182l_size ) 15.27/15.44 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 15.27/15.44 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 15.27/15.44 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 15.27/15.44 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 15.27/15.44 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 15.27/15.44 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 15.27/15.44 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 15.27/15.44 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 15.27/15.44 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 15.27/15.44 ( (fun complex nat), complex_size ) 15.27/15.44 ( (fun complex nat), (size_size complex) ) 15.27/15.44 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 15.27/15.44 ( (fun nat (fun nat (product_prod int int))), bezw ) 15.27/15.44 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 15.27/15.44 ( (fun int (fun nat nat)), nat_aux ) 15.27/15.44 ( (fun int (fun (fun int bool) bool)), rsetR ) 15.27/15.44 ( (fun int (fun (fun int bool) bool)), resSet ) 15.27/15.44 ( (fun int (list int)), quickc666637781d_zero ) 15.27/15.44 ( (fun (product_prod int int) rat), frct ) 15.27/15.44 ( (fun int (fun int rat)), fract ) 15.27/15.44 ( (fun real (fun real complex)), complex_1 ) 15.27/15.44 ( (fun real (fun real complex)), rcis ) 15.27/15.44 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 15.27/15.44 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 15.27/15.44 ( (fun int real), (real_1 int) ) 15.27/15.44 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 15.27/15.44 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 15.27/15.44 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 15.27/15.44 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 15.27/15.44 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 15.27/15.44 ( (fun real nat), natfloor ) 15.27/15.44 ( (fun real nat), natceiling ) 15.27/15.44 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 15.27/15.44 ( (fun quickcheck_code_int int), quickcheck_int_of ) 15.27/15.44 ( (fun rat (product_prod int int)), quotient_of ) 15.27/15.44 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 15.27/15.44 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 15.27/15.44 ( (fun rat real), ratreal ) 15.27/15.44 ( (fun code_code_numeral int), code_int_of ) 15.27/15.44 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 15.27/15.44 ( (fun int quickcheck_code_int), quickcheck_of_int ) 15.27/15.44 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 15.27/15.44 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_102469 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP X_a int (archim2085082626_floor X_a) BOUND_VARIABLE_102469)) (zero_zero int))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_102469) (zero_zero X_a))))) ) 15.27/15.44 ( nat, (zero_zero nat) ) 15.27/15.44 ( int, (one_one int) ) 15.27/15.44 ( int, pls ) 15.27/15.44 ( int, min_1 ) 15.27/15.44 ( int, s ) 15.27/15.44 ( int, t ) 15.27/15.44 ( int, skv_4 ) 15.27/15.44 ( int, skv_10 ) 15.27/15.44 ( real, (one_one real) ) 15.27/15.44 ( real, (zero_zero real) ) 15.27/15.44 ( real, pi ) 15.27/15.44 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.44 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.27/15.44 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.44 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_102541 $$unsorted) (BOUND_VARIABLE_102542 $$unsorted)) (let ((_let_0 (inverse_inverse X_a))) (or (not (divisi14063676e_zero X_a)) (not (= (hAPP X_a X_a _let_0 BOUND_VARIABLE_102541) (hAPP X_a X_a _let_0 BOUND_VARIABLE_102542))) (= (ti X_a BOUND_VARIABLE_102542) (ti X_a BOUND_VARIABLE_102541)))) ) 15.27/15.44 ( real, (zero_zero real), (zero_zero real) ) 15.27/15.44 ( complex, ii, ii ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((A_1 $$unsorted) (X_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) X_1))) (= (hAPP real nat natfloor (hAPP real real (hAPP real (fun real real) (plus_plus real) X_1) (hAPP nat real (real_1 nat) A_1))) (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP real nat natfloor X_1)) A_1))) ) 15.27/15.44 ( (one_one nat), (one_one real) ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_0 (fun nat bool))) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) M) N_1))) (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) M) N_1)))) ) 15.27/15.44 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_102575 $$unsorted) (BOUND_VARIABLE_102576 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (or (not (ordere216010020id_add X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_102576) _let_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_102575) _let_2))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_102576) BOUND_VARIABLE_102575)) _let_2)))))) ) 15.27/15.44 ( nat, (one_one nat), (one_one nat) ) 15.27/15.44 ( int, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.27/15.44 ( int, (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((Y_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP int real (number_number_of real) min_1)) Y_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Y_1) (one_one real)))) (= Y_1 (hAPP real real cos (hAPP real real arccos Y_1)))))) ) 15.27/15.44 ( (zero_zero real) ) 15.27/15.44 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.44 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.44 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.44 ( skv_5 ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_102659 $$unsorted) (BOUND_VARIABLE_102660 $$unsorted) (BOUND_VARIABLE_102661 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (fun X_a X_a))) (let ((_let_3 (zero_zero X_a))) (let ((_let_4 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) _let_3) BOUND_VARIABLE_102660)))) (let ((_let_5 (hAPP X_a X_a (hAPP X_a _let_2 (times_times X_a) BOUND_VARIABLE_102661) BOUND_VARIABLE_102660))) (let ((_let_6 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_102660) _let_3)))) (or (not (linord1117847801e_zero X_a)) (= (and (or (not _let_4) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_102659) _let_5))) (or _let_4 (and (or _let_6 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_3) BOUND_VARIABLE_102661))) (or (not _let_6) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_5) BOUND_VARIABLE_102659)))))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_2 (inverse_divide X_a) BOUND_VARIABLE_102659) BOUND_VARIABLE_102660)) BOUND_VARIABLE_102661))))))))))) ) 15.27/15.44 ( real, (zero_zero real), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.44 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.44 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((X_a $$unsorted)) (or (not (ring_1 X_a)) (= (hAPP int X_a (ring_1_of_int X_a) (zero_zero int)) (zero_zero X_a))) ) 15.27/15.44 ( nat ) 15.27/15.44 ( int ) 15.27/15.44 ( real ) 15.27/15.44 ( rat ) 15.27/15.44 ( complex ) 15.27/15.44 ( quickcheck_code_int ) 15.27/15.44 ( code_code_numeral ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_102737 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (times_times X_a))) (let ((_let_2 (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_102737))) (or (not (linordered_idom X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_102737) BOUND_VARIABLE_102737) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 _let_2) _let_2)))))) ) 15.27/15.44 ( complex, ii ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_0 (big_co1399186613setsum X_a X_b))) (or (not (comm_monoid_add X_b)) (= _let_0 (ti (fun (fun X_a X_b) (fun (fun X_a bool) X_b)) _let_0)))) ) 15.27/15.44 ( bool, (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 15.27/15.44 ( nat, bool ) 15.27/15.44 ( nat, (fun nat bool) ) 15.27/15.44 ( nat, (fun nat (fun bool bool)) ) 15.27/15.44 ( nat, (fun int (fun nat bool)) ) 15.27/15.44 ( nat, (fun real (fun int (fun nat bool))) ) 15.27/15.44 ( int, bool ) 15.27/15.44 ( int, int ) 15.27/15.44 ( int, (fun int bool) ) 15.27/15.44 ( int, (fun int (fun int bool)) ) 15.27/15.44 ( int, (fun int (fun int int)) ) 15.27/15.44 ( int, (fun int (fun bool bool)) ) 15.27/15.44 ( int, (fun (fun int int) (fun int bool)) ) 15.27/15.44 ( int, (fun real (fun int (fun int bool))) ) 15.27/15.44 ( real, real ) 15.27/15.44 ( real, (fun real bool) ) 15.27/15.44 ( real, (fun real (fun bool bool)) ) 15.27/15.44 ( real, (fun (fun int real) (fun int bool)) ) 15.27/15.44 ( real, (fun (fun nat real) (fun nat bool)) ) 15.27/15.44 ( (product_prod int int), (fun (product_prod int int) bool) ) 15.27/15.44 ( (product_prod int int), (fun (product_prod int int) (fun bool bool)) ) 15.27/15.44 ( (product_prod real real), (fun real (fun real (fun nat (product_prod real real)))) ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_102760 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (real_normed_algebra X_a)) (= _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_102760) _let_0)))) ) 15.27/15.44 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.44 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.44 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.27/15.44 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.44 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.44 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 15.27/15.44 ( complex, ii ) 15.27/15.44 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.44 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (field_inverse_zero X_a)) (= _let_0 (hAPP X_a X_a (inverse_inverse X_a) _let_0)))) ) 15.27/15.44 ( nat ) 15.27/15.44 ( int ) 15.27/15.44 ( real ) 15.27/15.44 ( rat ) 15.27/15.44 ( complex ) 15.27/15.44 ( quickcheck_code_int ) 15.27/15.44 ( code_code_numeral ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_102776 $$unsorted) (BOUND_VARIABLE_102777 $$unsorted)) (let ((_let_0 (filter X_a))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun X_a X_a))) (let ((_let_3 (fun X_a _let_2))) (let ((_let_4 (inverse_divide X_a))) (or (not (real_normed_field X_a)) (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 (hAPP _let_2 (fun X_a _let_1) (tendsto X_a X_a) (hAPP X_a _let_2 (hAPP _let_3 _let_3 (combc X_a X_a X_a) _let_4) BOUND_VARIABLE_102776)) (hAPP X_a X_a (hAPP X_a _let_2 _let_4 BOUND_VARIABLE_102777) BOUND_VARIABLE_102776)) (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_102777))))))))) ) 15.27/15.44 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 15.27/15.44 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.27/15.44 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.27/15.44 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.27/15.44 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.44 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 15.27/15.44 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), pi ) 15.27/15.44 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (one_one real) ) 15.27/15.44 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))), pi ) 15.27/15.44 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 15.27/15.44 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))), (one_one real) ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (minus_minus real))) (let ((_let_2 (times_times real))) (= (hAPP real real sin (hAPP real real (hAPP real _let_0 _let_1 X_1) Y_1)) (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real (hAPP real _let_0 _let_2 (hAPP real real sin X_1)) (hAPP real real cos Y_1))) (hAPP real real (hAPP real _let_0 _let_2 (hAPP real real cos X_1)) (hAPP real real sin Y_1))))))) ) 15.27/15.44 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_102799 $$unsorted) (BOUND_VARIABLE_102800 $$unsorted)) (let ((_let_0 (number_number_of X_a))) (or (not (number_ring X_a)) (not (linordered_idom X_a)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) BOUND_VARIABLE_102799) BOUND_VARIABLE_102800)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP int X_a _let_0 BOUND_VARIABLE_102799)) (hAPP int X_a _let_0 BOUND_VARIABLE_102800)))))) ) 15.27/15.44 ( nat, pls, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.27/15.44 ( int, pls, pls ) 15.27/15.44 ( int, pls, (hAPP int int bit1 pls) ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (div_div X_a))) (or (not (semiring_div X_a)) (= _let_0 (ti (fun X_a (fun X_a X_a)) _let_0)))) ) 15.27/15.44 ( bool ) 15.27/15.44 ( nat ) 15.27/15.44 ( int ) 15.27/15.44 ( (fun int bool) ) 15.27/15.44 ( (fun int (fun int bool)) ) 15.27/15.44 ( (fun int int) ) 15.27/15.44 ( (fun nat bool) ) 15.27/15.44 ( real ) 15.27/15.44 ( (fun real bool) ) 15.27/15.44 ( (fun real real) ) 15.27/15.44 ( complex ) 15.27/15.44 ( (fun nat real) ) 15.27/15.44 ( (product_prod int int) ) 15.27/15.44 ( quickcheck_code_int ) 15.27/15.44 ( code_code_numeral ) 15.27/15.44 ( (fun int (fun int (fun int bool))) ) 15.27/15.44 ( (fun (product_prod int int) bool) ) 15.27/15.44 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 15.27/15.44 ( (fun (product_prod int int) int) ) 15.27/15.44 ( (fun int real) ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (ord_max X_a))) (or (not (ord X_a)) (= _let_0 (ti (fun X_a (fun X_a X_a)) _let_0)))) ) 15.27/15.44 ( bool ) 15.27/15.44 ( nat ) 15.27/15.44 ( int ) 15.27/15.44 ( (fun int bool) ) 15.27/15.44 ( (fun int (fun int bool)) ) 15.27/15.44 ( (fun int int) ) 15.27/15.44 ( (fun nat bool) ) 15.27/15.44 ( real ) 15.27/15.44 ( (fun real bool) ) 15.27/15.44 ( (fun real real) ) 15.27/15.44 ( rat ) 15.27/15.44 ( complex ) 15.27/15.44 ( (fun nat real) ) 15.27/15.44 ( (product_prod int int) ) 15.27/15.44 ( quickcheck_code_int ) 15.27/15.44 ( code_code_numeral ) 15.27/15.44 ( (fun int (fun int (fun int bool))) ) 15.27/15.44 ( (fun (product_prod int int) bool) ) 15.27/15.44 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 15.27/15.44 ( (fun (product_prod int int) int) ) 15.27/15.44 ( (fun int real) ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_102898 $$unsorted) (BOUND_VARIABLE_102899 $$unsorted) (BOUND_VARIABLE_102900 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (hAPP X_a _let_0 _let_1 (zero_zero X_a)))) (let ((_let_3 (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_102899))) (let ((_let_4 (hBOOL (hAPP X_a bool _let_2 _let_3)))) (let ((_let_5 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_3) (zero_zero X_a))))) (let ((_let_6 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_102900) _let_3))) (or (not (number X_a)) (not (linord1117847801e_zero X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_102898) _let_3)) BOUND_VARIABLE_102900)) (and (or _let_4 (and (or (not _let_5) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_6) BOUND_VARIABLE_102898))) (or _let_5 (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_102900))))) (or (not _let_4) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_102898) _let_6))))))))))))) ) 15.27/15.44 ( real, pi, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_102957 $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat _let_0))) (let ((_let_2 (fun (filter nat) bool))) (let ((_let_3 (fun nat X_a))) (let ((_let_4 (fun _let_0 X_a))) (or (not (comm_monoid_add X_a)) (not (t2_space X_a)) (not (hBOOL (hAPP _let_3 bool (summable X_a) BOUND_VARIABLE_102957))) (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_2 (hAPP _let_3 (fun X_a _let_2) (tendsto nat X_a) (hAPP _let_1 _let_3 (hAPP _let_4 (fun _let_1 _let_3) (combb _let_0 X_a nat) (hAPP _let_3 _let_4 (big_co1399186613setsum nat X_a) BOUND_VARIABLE_102957)) (hAPP nat _let_1 (ord_atLeastLessThan nat) (zero_zero nat)))) (hAPP _let_3 X_a (suminf X_a) BOUND_VARIABLE_102957)) sequentially)))))))) ) 15.27/15.44 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat (fun nat nat)))) (let ((_let_3 (fun nat _let_0))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun _let_1 _let_3))) (let ((_let_6 (combb real _let_0 nat))) (let ((_let_7 (combc nat nat nat))) (hAPP _let_1 _let_1 (hAPP _let_3 (fun _let_1 _let_1) (combs nat real real) (hAPP _let_1 _let_3 (hAPP _let_4 _let_5 _let_6 (inverse_divide real)) (hAPP real _let_1 (hAPP _let_3 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_3 (hAPP _let_4 _let_5 _let_6 (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) (one_one real)))) (hAPP (fun nat nat) _let_1 (hAPP _let_1 (fun (fun nat nat) _let_1) (combb nat real nat) (real_1 nat)) (hAPP nat (fun nat nat) (hAPP _let_2 _let_2 _let_7 (hAPP (fun nat nat) _let_2 (hAPP _let_2 (fun (fun nat nat) _let_2) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_2 _let_2 _let_7 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))))))))))) ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (min X_a))) (or (not (ord X_a)) (= _let_0 (ti (fun (fun X_a (fun X_a bool)) (fun X_a (fun X_a X_a))) _let_0)))) ) 15.27/15.44 ( bool ) 15.27/15.44 ( nat ) 15.27/15.44 ( int ) 15.27/15.44 ( (fun int bool) ) 15.27/15.44 ( (fun int (fun int bool)) ) 15.27/15.44 ( (fun int int) ) 15.27/15.44 ( (fun nat bool) ) 15.27/15.44 ( (product_prod nat nat) ) 15.27/15.44 ( real ) 15.27/15.44 ( (fun real bool) ) 15.27/15.44 ( (fun real real) ) 15.27/15.44 ( rat ) 15.27/15.44 ( complex ) 15.27/15.44 ( (fun nat real) ) 15.27/15.44 ( (filter nat) ) 15.27/15.44 ( (product_prod int int) ) 15.27/15.44 ( quickcheck_code_int ) 15.27/15.44 ( code_code_numeral ) 15.27/15.44 ( (fun int (fun int (fun int bool))) ) 15.27/15.44 ( (product_prod real real) ) 15.27/15.44 ( (fun (product_prod int int) bool) ) 15.27/15.44 ( (fun nat rat) ) 15.27/15.44 ( (filter real) ) 15.27/15.44 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 15.27/15.44 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 15.27/15.44 ( (fun (product_prod int int) int) ) 15.27/15.44 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 15.27/15.44 ( (fun int real) ) 15.27/15.44 ) 15.27/15.44 (instantiation (forall ((P_4 $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) P_4))) (= (hAPP nat int (semiring_1_of_nat int) (hAPP _let_0 nat (finite_card int) (hAPP int _let_0 sRStar P_4))) (hAPP int int (hAPP int (fun int int) (minus_minus int) P_4) (one_one int))))) ) 15.27/15.44 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.44 ) 15.27/15.45 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_0 (fun bool bool))) (let ((_let_1 (product_prod X_a X_b))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun X_b bool))) (let ((_let_4 (fun X_a _let_3))) (let ((_let_5 (fun _let_3 _let_3))) (let ((_let_6 (fun X_a _let_5))) (let ((_let_7 (fun X_a _let_0))) (let ((_let_8 (fun X_a bool))) (= (hAPP _let_2 _let_1 (hilbert_Eps _let_1) (hAPP _let_4 _let_2 (product_prod_case X_a X_b bool) (hAPP _let_3 _let_4 (hAPP _let_6 (fun _let_3 _let_4) (combc X_a _let_3 _let_3) (hAPP _let_7 _let_6 (hAPP (fun _let_0 _let_5) (fun _let_7 _let_6) (combb _let_0 _let_5 X_a) (combb bool bool X_b)) (hAPP _let_8 _let_7 (hAPP (fun bool _let_0) (fun _let_8 _let_7) (combb bool _let_0 X_a) fconj) (hAPP X_a _let_8 (fequal X_a) X_2)))) (hAPP X_b _let_3 (fequal X_b) Y_2)))) (hAPP X_b _let_1 (hAPP X_a (fun X_b _let_1) (product_Pair X_a X_b) X_2) Y_2))))))))))) ) 15.27/15.45 ( int, int, (one_one int), (one_one int) ) 15.27/15.45 ( int, int, (zero_zero int), (one_one int) ) 15.27/15.45 ( int, int, s, (one_one int) ) 15.27/15.45 ) 15.27/15.45 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (zero_zero nat))) (= (= _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (div_mod nat) X_2) (hAPP nat nat suc (hAPP nat nat suc _let_0)))) (hBOOL (hAPP nat bool (even_odd_even nat) X_2)))) ) 15.27/15.45 ( (zero_zero nat) ) 15.27/15.45 ( (one_one nat) ) 15.27/15.45 ) 15.27/15.45 (instantiation (forall ((P_5 $$unsorted)) (let ((_let_0 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) _let_0) P_5))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) (hAPP int nat nat_1 (hAPP int int (hAPP int (fun int int) (minus_minus int) P_5) _let_0)))))) ) 15.27/15.45 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.45 ) 15.27/15.45 (instantiation (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) X_1))) (= (hAPP real nat natceiling (hAPP real real (hAPP real (fun real real) (plus_plus real) X_1) (one_one real))) (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP real nat natceiling X_1)) (one_one nat)))) ) 15.27/15.45 ( (one_one real) ) 15.27/15.45 ( pi ) 15.27/15.45 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.45 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.45 ( skv_3 ) 15.27/15.45 ( skv_5 ) 15.27/15.45 ( skv_7 ) 15.27/15.45 ( skv_12 ) 15.27/15.45 ) 15.27/15.45 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_103187 $$unsorted)) (or (not (number_ring X_a)) (= (ti X_a BOUND_VARIABLE_103187) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) (hAPP int X_a (number_number_of X_a) (hAPP int int bit1 pls))) BOUND_VARIABLE_103187))) ) 15.27/15.45 ( bool, fFalse ) 15.27/15.45 ( bool, fTrue ) 15.27/15.45 ( int, pls ) 15.27/15.45 ( int, min_1 ) 15.27/15.45 ( int, s ) 15.27/15.45 ( int, m ) 15.27/15.45 ( int, s1 ) 15.27/15.45 ( int, t ) 15.27/15.45 ( (fun int bool), nat_neg ) 15.27/15.45 ( (fun int bool), zprime ) 15.27/15.45 ( (fun int bool), zEven ) 15.27/15.45 ( (fun int bool), zOdd ) 15.27/15.45 ( (fun int bool), (even_odd_even int) ) 15.27/15.45 ( (fun int bool), twoSqu1091635170sum2sq ) 15.27/15.45 ( (fun int bool), nat_is_nat ) 15.27/15.45 ( (fun int (fun int bool)), norRRset ) 15.27/15.45 ( (fun int (fun int bool)), quadRes ) 15.27/15.45 ( (fun int (fun int bool)), sRStar ) 15.27/15.45 ( (fun int (fun int bool)), d22set ) 15.27/15.45 ( (fun int (fun int bool)), sr ) 15.27/15.45 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 15.27/15.45 ( (fun int int), zfact ) 15.27/15.45 ( (fun int int), bit0 ) 15.27/15.45 ( (fun int int), bit1 ) 15.27/15.45 ( (fun int int), (fact_fact int) ) 15.27/15.45 ( (fun int int), pred ) 15.27/15.45 ( (fun int int), succ ) 15.27/15.45 ( (fun nat bool), (even_odd_even nat) ) 15.27/15.45 ( (fun nat bool), prime ) 15.27/15.45 ( (fun nat nat), suc ) 15.27/15.45 ( (fun nat nat), (fact_fact nat) ) 15.27/15.45 ( (fun nat nat), fact ) 15.27/15.45 ( (fun nat nat), nat_size ) 15.27/15.45 ( (fun nat nat), (size_size nat) ) 15.27/15.45 ( (fun (product_prod nat nat) bool), pred_nat ) 15.27/15.45 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 15.27/15.45 ( real, pi ) 15.27/15.45 ( (fun real real), ln ) 15.27/15.45 ( (fun real real), cos ) 15.27/15.45 ( (fun real real), sqrt ) 15.27/15.45 ( (fun real real), sin ) 15.27/15.45 ( (fun real real), arccos ) 15.27/15.45 ( (fun real real), arcsin ) 15.27/15.45 ( (fun real real), tan ) 15.27/15.45 ( (fun real real), arctan ) 15.27/15.45 ( (fun nat (fun nat bool)), coprime ) 15.27/15.45 ( complex, ii ) 15.27/15.45 ( (fun nat real), (real_1 nat) ) 15.27/15.45 ( (fun nat real), sin_coeff ) 15.27/15.45 ( (fun nat real), cos_coeff ) 15.27/15.45 ( (filter nat), sequentially ) 15.27/15.45 ( (fun int (fun int int)), (gcd_gcd int) ) 15.27/15.45 ( (fun int (fun int int)), legendre ) 15.27/15.45 ( (fun int (fun int int)), legacy_zgcd ) 15.27/15.45 ( (fun int (fun int int)), standardRes ) 15.27/15.45 ( (fun int (fun int int)), nat_tsub ) 15.27/15.45 ( (fun int (fun int int)), multInv ) 15.27/15.45 ( (fun int (fun int int)), z3mod ) 15.27/15.45 ( (fun int (fun int int)), z3div ) 15.27/15.45 ( (fun int (fun int int)), int_gcd ) 15.27/15.45 ( (fun int (fun int int)), int_lcm ) 15.27/15.45 ( (fun int (fun int int)), inv ) 15.27/15.45 ( (fun complex complex), expi ) 15.27/15.45 ( (fun complex complex), cnj ) 15.27/15.45 ( (fun real complex), cis ) 15.27/15.45 ( (fun int nat), nat_1 ) 15.27/15.45 ( (fun int nat), phi ) 15.27/15.45 ( (fun (fun int bool) bool), nat_nat_set ) 15.27/15.45 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 15.27/15.45 ( (fun nat (fun nat nat)), nat_gcd ) 15.27/15.45 ( (fun nat (fun nat nat)), nat_lcm ) 15.27/15.45 ( (fun (fun int bool) int), (the int) ) 15.27/15.45 ( (fun complex real), re ) 15.27/15.45 ( (fun complex real), im ) 15.27/15.45 ( (fun complex real), arg ) 15.27/15.45 ( (fun bool bool), fNot ) 15.27/15.45 ( (fun nat (fun real real)), root ) 15.27/15.45 ( (fun real (fun real real)), log ) 15.27/15.45 ( (fun real (fun real real)), powr ) 15.27/15.45 ( (fun bool (fun bool bool)), fimplies ) 15.27/15.45 ( (fun bool (fun bool bool)), fconj ) 15.27/15.45 ( (fun bool (fun bool bool)), fdisj ) 15.27/15.45 ( (fun int (fun int (product_prod int int))), negDivAlg ) 15.27/15.45 ( (fun int (fun int (product_prod int int))), posDivAlg ) 15.27/15.45 ( (fun int (fun int (product_prod int int))), divmod_int ) 15.27/15.45 ( (fun int (fun int (product_prod int int))), pdivmod ) 15.27/15.45 ( (fun int (fun int (product_prod int int))), norm_frac ) 15.27/15.45 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 15.27/15.45 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 15.27/15.45 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 15.27/15.45 ( (fun int (fun int (fun int bool))), zcong ) 15.27/15.45 ( (fun int (fun int (fun int bool))), zcongm ) 15.27/15.45 ( (fun int (fun int (fun int bool))), noXRRset ) 15.27/15.45 ( (fun int (fun int (fun int bool))), bnorRset ) 15.27/15.45 ( (fun int (fun int (fun int bool))), wset ) 15.27/15.45 ( (fun (product_prod int int) bool), frac_1 ) 15.27/15.45 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 15.27/15.45 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 15.27/15.45 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 15.27/15.45 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 15.27/15.45 ( (fun (fun nat rat) bool), vanishes ) 15.27/15.45 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 15.27/15.45 ( (fun code_code_numeral nat), code_c271388182l_size ) 15.27/15.45 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 15.27/15.45 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 15.27/15.45 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 15.27/15.45 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 15.27/15.45 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 15.27/15.45 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 15.27/15.45 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 15.27/15.45 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 15.27/15.45 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 15.27/15.45 ( (fun complex nat), complex_size ) 15.27/15.45 ( (fun complex nat), (size_size complex) ) 15.27/15.45 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 15.27/15.45 ( (fun nat (fun nat (product_prod int int))), bezw ) 15.27/15.45 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 15.27/15.45 ( (fun int (fun nat nat)), nat_aux ) 15.27/15.45 ( (fun int (fun (fun int bool) bool)), rsetR ) 15.27/15.45 ( (fun int (fun (fun int bool) bool)), resSet ) 15.27/15.45 ( (fun int (list int)), quickc666637781d_zero ) 15.27/15.45 ( (fun (product_prod int int) rat), frct ) 15.27/15.45 ( (fun int (fun int rat)), fract ) 15.27/15.45 ( (fun real (fun real complex)), complex_1 ) 15.27/15.45 ( (fun real (fun real complex)), rcis ) 15.27/15.45 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 15.27/15.45 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 15.27/15.45 ( (fun int real), (real_1 int) ) 15.27/15.45 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 15.27/15.45 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 15.27/15.45 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 15.27/15.45 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 15.27/15.45 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 15.27/15.45 ( (fun real nat), natfloor ) 15.27/15.45 ( (fun real nat), natceiling ) 15.27/15.45 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 15.27/15.45 ( (fun quickcheck_code_int int), quickcheck_int_of ) 15.27/15.45 ( (fun rat (product_prod int int)), quotient_of ) 15.27/15.45 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 15.27/15.45 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 15.27/15.45 ( (fun rat real), ratreal ) 15.27/15.45 ( (fun code_code_numeral int), code_int_of ) 15.27/15.45 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 15.27/15.45 ( (fun int quickcheck_code_int), quickcheck_of_int ) 15.27/15.45 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 15.27/15.45 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 15.27/15.45 ) 15.27/15.45 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_103237 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hAPP X_a int (archim2085082626_floor X_a) (hAPP nat X_a (semiring_1_of_nat X_a) BOUND_VARIABLE_103237)) (hAPP nat int (semiring_1_of_nat int) BOUND_VARIABLE_103237))) ) 15.27/15.45 ( int, (zero_zero nat) ) 15.27/15.45 ( int, (hAPP nat nat suc (zero_zero nat)) ) 15.27/15.45 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.27/15.45 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.45 ( real, (zero_zero nat) ) 15.27/15.45 ( real, (hAPP nat nat suc (zero_zero nat)) ) 15.27/15.45 ) 15.27/15.45 (instantiation (forall ((N_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (or (not (hBOOL (hAPP int bool zprime P_5))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (zero_zero int)) N_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 N_1) P_5))) (= (one_one int) (hAPP int int (hAPP int (fun int int) legacy_zgcd N_1) P_5))))) ) 15.27/15.45 ( (one_one int), t ) 15.27/15.45 ( pls, (one_one int) ) 15.27/15.45 ( pls, pls ) 15.27/15.45 ( pls, min_1 ) 15.27/15.45 ( pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.27/15.45 ( min_1, pls ) 15.27/15.45 ( min_1, min_1 ) 15.27/15.45 ( s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.27/15.45 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.27/15.45 ( skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.27/15.45 ( skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.27/15.45 ) 15.27/15.45 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (bseq X_a))) (or (not (real_normed_vector X_a)) (= _let_0 (ti (fun (fun nat X_a) bool) _let_0)))) ) 15.27/15.45 ( bool ) 15.27/15.45 ( nat ) 15.27/15.45 ( int ) 15.27/15.45 ( (fun int int) ) 15.27/15.45 ( (fun nat bool) ) 15.27/15.45 ( (fun nat nat) ) 15.27/15.45 ( (product_prod nat nat) ) 15.27/15.45 ( (fun (product_prod nat nat) bool) ) 15.27/15.45 ( (fun nat (fun (product_prod nat nat) bool)) ) 15.27/15.45 ( real ) 15.27/15.45 ( (fun real real) ) 15.27/15.45 ( rat ) 15.27/15.45 ( (fun nat (fun nat bool)) ) 15.27/15.45 ( complex ) 15.27/15.45 ( (product_prod int int) ) 15.27/15.45 ( (fun bool bool) ) 15.27/15.45 ( (product_prod real real) ) 15.27/15.45 ( (fun nat (product_prod nat nat)) ) 15.27/15.45 ( (fun nat (product_prod int int)) ) 15.27/15.45 ) 15.27/15.45 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_103585 $$unsorted) (BOUND_VARIABLE_103586 $$unsorted) (BOUND_VARIABLE_103587 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (fun X_a X_a))) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_103587) (zero_zero X_a)))) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_2 (inverse_divide X_a) BOUND_VARIABLE_103585) BOUND_VARIABLE_103587)) BOUND_VARIABLE_103586)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_2 (times_times X_a) BOUND_VARIABLE_103586) BOUND_VARIABLE_103587)) BOUND_VARIABLE_103585))))))) ) 15.27/15.45 ( real, (zero_zero real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.27/15.45 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.45 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.27/15.45 ) 15.27/15.45 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_103616 $$unsorted) (BOUND_VARIABLE_103617 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (times_times X_a))) (let ((_let_2 (sgn_sgn X_a))) (or (not (linordered_idom X_a)) (= (hAPP X_a X_a _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_103616) BOUND_VARIABLE_103617)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_103616)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_103617))))))) ) 15.27/15.45 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 15.27/15.45 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.27/15.45 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13 ) 15.27/15.45 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.27/15.45 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.27/15.45 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.27/15.45 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 15.27/15.45 ( complex, ii, ii ) 15.27/15.45 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 15.27/15.45 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 15.27/15.45 ) 15.27/15.45 (instantiation (forall ((Z_1 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) _let_1) Z_1))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) _let_1) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) Z_1)))))) ) 15.27/15.45 ( (one_one int) ) 15.27/15.45 ( min_1 ) 15.27/15.45 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.45 ( s ) 15.27/15.45 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.27/15.45 ( (hAPP int int (number_number_of int) pls) ) 15.27/15.45 ( skv_4 ) 15.27/15.45 ( skv_10 ) 15.27/15.45 ) 15.27/15.45 (instantiation (forall ((B_5 $$unsorted) (Q_5 $$unsorted) (R_5 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (zero_zero int))) (let ((_let_3 (ord_less int))) (let ((_let_4 (hAPP int _let_0 (ord_less_eq int) _let_2))) (or (not (hBOOL (hAPP int bool _let_4 (hAPP int int (hAPP int _let_1 (plus_plus int) (hAPP int int (hAPP int _let_1 (times_times int) B_5) Q_5)) R_5)))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_3 R_5) B_5))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_3 _let_2) B_5))) (hBOOL (hAPP int bool _let_4 Q_5)))))))) ) 15.27/15.45 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m, (one_one int) ) 15.27/15.45 ) 15.27/15.45 (instantiation (forall ((X_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (one_one int))) (let ((_let_4 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) _let_4) P_5))) (not (hBOOL (hAPP int bool zprime P_5))) (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int _let_1 zcong X_1) (zero_zero int)) P_5)) (not (hBOOL (hAPP int bool (hAPP int _let_0 quadRes P_5) X_1))) (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int _let_1 zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) X_1) (hAPP int nat nat_1 (hAPP int int (hAPP int _let_2 (div_div int) (hAPP int int (hAPP int _let_2 (minus_minus int) P_5) _let_3)) _let_4)))) _let_3) P_5)))))))) ) 15.27/15.45 ( (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.27/15.45 ) 15.27/15.45 (instantiation (forall ((P_5 $$unsorted)) (or (not (hBOOL (hAPP nat bool prime P_5))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (hAPP nat nat suc (zero_zero nat))) P_5))) ) 15.27/15.45 ( (zero_zero nat) ) 15.27/15.45 ( (hAPP nat nat suc (zero_zero nat)) ) 15.27/15.45 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.45 ) 15.27/15.45 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_103712 $$unsorted) (BOUND_VARIABLE_103713 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (or (not (semiring_div X_a)) (= (zero_zero X_a) (hAPP X_a X_a (hAPP X_a _let_0 (div_mod X_a) (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_103712) BOUND_VARIABLE_103713)) BOUND_VARIABLE_103713)))) ) 15.27/15.45 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 15.27/15.45 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.27/15.45 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13 ) 15.27/15.45 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.27/15.45 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.27/15.45 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.27/15.45 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 15.27/15.45 ( complex, ii, ii ) 15.27/15.45 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 15.27/15.45 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 15.27/15.45 ) 15.27/15.45 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_103729 $$unsorted) (BOUND_VARIABLE_103730 $$unsorted)) (let ((_let_0 (number_number_of nat))) (let ((_let_1 (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_103729))) (let ((_let_2 (hAPP nat X_a _let_1 (hAPP int nat _let_0 BOUND_VARIABLE_103730)))) (or (not (monoid_mult X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) _let_2) _let_2) (hAPP nat X_a _let_1 (hAPP int nat _let_0 (hAPP int int bit0 BOUND_VARIABLE_103730)))))))) ) 15.27/15.45 ( int, s, (hAPP int int bit1 pls) ) 15.27/15.45 ( int, s1, (hAPP int int bit1 pls) ) 15.27/15.45 ( int, skv_14, (hAPP int int bit1 pls) ) 15.27/15.45 ( complex, ii, (hAPP int int bit1 pls) ) 15.27/15.45 ) 15.27/15.45 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_103754 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)))) (or (not (linord1117847801e_zero X_a)) (not (number_ring X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_103754))) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_103754) (hAPP int X_a (number_number_of X_a) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 15.27/15.45 ( real, (one_one real) ) 15.27/15.45 ( real, pi ) 15.27/15.45 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.27/15.45 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.27/15.45 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.45 ) 15.27/15.45 (instantiation (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (let ((_let_0 (fun X_b X_c))) (let ((_let_1 (fun X_a X_c))) (= (hAPP X_a X_c (hAPP X_b _let_1 (hAPP (fun X_a _let_0) (fun X_b _let_1) (combc X_a X_b X_c) P) Q) R) (hAPP X_b X_c (hAPP X_a _let_0 P R) Q)))) ) 15.27/15.45 ( nat, bool, nat, (ord_less nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 15.27/15.45 ( nat, nat, nat, (plus_plus nat), (one_one nat), (one_one nat) ) 15.27/15.45 ( nat, real, real, root, (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.45 ( nat, real, real, root, (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.45 ( nat, real, real, root, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.45 ( nat, real, real, root, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.45 ( int, bool, int, (ord_less_eq int), (one_one int), (zero_zero int) ) 15.27/15.45 ( int, bool, int, (ord_less_eq int), pls, min_1 ) 15.27/15.45 ( int, bool, int, (ord_less_eq int), min_1, (zero_zero int) ) 15.27/15.45 ( int, bool, int, (ord_less_eq int), min_1, min_1 ) 15.27/15.45 ( int, bool, int, (ord_less_eq int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 15.27/15.45 ( int, bool, int, (ord_less_eq int), s, (zero_zero int) ) 15.27/15.45 ( int, bool, int, (ord_less_eq int), t, (one_one int) ) 15.27/15.45 ( int, bool, int, (ord_less_eq int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 15.27/15.45 ( int, bool, int, (ord_less_eq int), (hAPP int int (number_number_of int) pls), (zero_zero int) ) 15.27/15.45 ( int, bool, int, (ord_less_eq int), skv_4, (zero_zero int) ) 15.27/15.45 ( int, bool, int, (ord_less_eq int), skv_10, (zero_zero int) ) 15.27/15.45 ( int, bool, int, (ord_less int), (one_one int), pls ) 15.27/15.45 ( int, bool, int, (ord_less int), pls, pls ) 15.27/15.45 ( int, bool, int, (ord_less int), pls, min_1 ) 15.27/15.45 ( int, bool, int, (ord_less int), min_1, pls ) 15.27/15.45 ( int, bool, int, (ord_less int), min_1, min_1 ) 15.27/15.45 ( int, bool, int, (ord_less int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), pls ) 15.27/15.45 ( int, bool, int, (ord_less int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s ) 15.27/15.45 ( int, bool, int, (ord_less int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.27/15.45 ( int, bool, int, (ord_less int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_4 ) 15.27/15.45 ( int, bool, int, (ord_less int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_10 ) 15.27/15.45 ( int, bool, int, (ord_less int), t, (one_one int) ) 15.27/15.45 ( int, bool, int, (dvd_dvd int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.27/15.45 ( int, bool, int, quadRes, (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.27/15.45 ( int, bool, int, (hAPP int (fun int (fun int bool)) zcong s1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s ) 15.27/15.45 ( int, bool, int, (hAPP int (fun int (fun int bool)) zcong s1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_4 ) 15.27/15.45 ( int, bool, int, (hAPP int (fun int (fun int bool)) zcong s1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_10 ) 15.27/15.45 ( int, bool, int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (number_number_of int) min_1) ) 15.27/15.45 ( int, bool, int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.45 ( int, bool, int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (number_number_of int) min_1) ) 15.27/15.45 ( int, bool, int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (number_number_of int) min_1) ) 15.27/15.45 ( int, bool, (fun int bool), (member int), zEven, (one_one int) ) 15.27/15.45 ( int, int, nat, (power_power int), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 15.27/15.45 ( int, int, nat, (power_power int), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 15.27/15.45 ( int, int, nat, (power_power int), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_14 ) 15.27/15.45 ( int, int, int, (times_times int), m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.45 ( int, int, int, (times_times int), t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.27/15.45 ( int, int, int, (times_times int), skv_13, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.27/15.45 ( int, int, int, (minus_minus int), (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.45 ( int, int, int, (plus_plus int), (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.27/15.45 ( int, int, int, (plus_plus int), (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.45 ( int, int, int, legendre, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (number_number_of int) min_1) ) 15.27/15.45 ( int, (fun int bool), int, zcong, (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.45 ( int, (fun int bool), int, zcong, (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.45 ( int, (fun int bool), int, zcong, (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.45 ( int, (fun int bool), int, zcong, s, s1 ) 15.27/15.45 ( int, (fun int bool), int, zcong, (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.45 ( int, (fun int bool), int, zcong, skv_4, s1 ) 15.27/15.45 ( int, (fun int bool), int, zcong, skv_10, s1 ) 15.27/15.45 ( int, rat, int, fract, (one_one int), (one_one int) ) 15.27/15.45 ( int, rat, int, fract, (one_one int), (zero_zero int) ) 15.27/15.45 ( int, (product_prod int int), int, (product_Pair int int), (one_one int), (one_one int) ) 15.27/15.45 ( int, (product_prod int int), int, (product_Pair int int), (one_one int), (zero_zero int) ) 15.27/15.45 ( int, (product_prod int int), int, (product_Pair int int), (one_one int), s ) 15.27/15.45 ( (fun int (fun int bool)), (fun int bool), int, (combc int int bool), (zero_zero int), (fequal int) ) 15.27/15.45 ( (fun int (fun int bool)), (fun (product_prod int int) (fun int bool)), (fun (product_prod int int) int), (combb int (fun int bool) (product_prod int int)), (product_snd int int), (fequal int) ) 15.27/15.45 ( real, bool, real, (ord_less real), (zero_zero real), pi ) 15.27/15.45 ( real, bool, real, (ord_less real), (zero_zero real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.27/15.45 ( real, bool, real, (ord_less real), (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.45 ( real, bool, real, (ord_less real), pi, (zero_zero real) ) 15.27/15.45 ( real, bool, real, (ord_less real), pi, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 15.27/15.45 ( real, bool, real, (ord_less real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.45 ( real, bool, real, (ord_less real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.27/15.45 ( real, bool, real, (ord_less real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 15.27/15.45 ( real, bool, real, (ord_less real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 15.27/15.45 ( real, bool, real, (ord_less real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.27/15.45 ( real, bool, real, (ord_less real), skv_2, (zero_zero real) ) 15.27/15.45 ( real, bool, real, (ord_less real), skv_8, (zero_zero real) ) 15.27/15.45 ( real, bool, real, (ord_less real), skv_9, (zero_zero real) ) 15.27/15.45 ( real, bool, real, (ord_less_eq real), (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.45 ( real, bool, real, (ord_less_eq real), pi, (zero_zero real) ) 15.27/15.45 ( real, bool, real, (ord_less_eq real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.45 ( real, bool, real, (ord_less_eq real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.45 ( real, bool, real, (ord_less_eq real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_5 ) 15.27/15.45 ( real, bool, real, (ord_less_eq real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.27/15.45 ( real, bool, real, (ord_less_eq real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.27/15.45 ( real, bool, real, (ord_less_eq real), skv_3, (zero_zero real) ) 15.27/15.45 ( real, bool, real, (ord_less_eq real), skv_5, (zero_zero real) ) 15.27/15.45 ( real, bool, real, (ord_less_eq real), skv_7, (zero_zero real) ) 15.27/15.45 ( real, bool, real, (ord_less_eq real), skv_12, (zero_zero real) ) 15.27/15.45 ( real, bool, (filter nat), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 (fun real (fun (filter nat) bool)) (tendsto nat real) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))))), sequentially, (zero_zero real) ) 15.27/15.45 ( real, bool, (filter real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 (fun real (fun (filter real) bool)) (tendsto real real) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin)))), (hAPP real (filter real) (at real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 15.27/15.45 ( real, real, real, (minus_minus real), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))), (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))) ) 15.27/15.45 ( real, real, real, (inverse_divide real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 15.27/15.45 ( real, real, real, (inverse_divide real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.27/15.45 ( real, real, real, (inverse_divide real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.27/15.45 ( real, real, real, (inverse_divide real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.27/15.45 ( real, real, real, (inverse_divide real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.45 ( real, real, real, (inverse_divide real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 15.27/15.45 ( real, real, real, (inverse_divide real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), pi ) 15.27/15.45 ( real, real, real, (inverse_divide real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (one_one real) ) 15.27/15.45 ( real, real, real, (inverse_divide real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))), pi ) 15.27/15.45 ( real, real, real, (inverse_divide real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 15.27/15.45 ( real, real, real, (inverse_divide real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))), (one_one real) ) 15.27/15.45 ( real, real, real, (times_times real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.45 ( real, real, real, (times_times real), pi, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 15.27/15.45 ( real, real, real, (times_times real), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.45 ( real, real, real, (times_times real), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.45 ( real, complex, real, complex_1, (one_one real), (zero_zero real) ) 15.27/15.45 ( real, complex, real, complex_1, (zero_zero real), (one_one real) ) 15.27/15.45 ( real, complex, real, complex_1, (zero_zero real), (zero_zero real) ) 15.27/15.45 ( (fun real real), (fun nat real), (fun nat real), (combb real real nat), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))), (inverse_inverse real) ) 15.27/15.45 ( (fun real real), (fun (filter real) bool), real, (tendsto real real), (zero_zero real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))) ) 15.27/15.45 ( (fun nat (fun nat bool)), (fun nat bool), nat, (combc nat nat bool), (zero_zero nat), (fequal nat) ) 15.27/15.45 ( (fun nat (fun nat bool)), (fun nat (fun nat bool)), (fun nat nat), (combb nat (fun nat bool) nat), suc, (let ((_let_0 (fun nat (fun nat bool)))) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat))) ) 15.27/15.45 ( (fun nat int), bool, (fun nat bool), (nat_tr1645093318rphism nat int), (hAPP bool (fun nat bool) (combk bool nat) fTrue), (semiring_1_of_nat int) ) 15.27/15.45 ( complex, complex, nat, (power_power complex), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), ii ) 15.27/15.45 ( complex, complex, complex, (times_times complex), ii, ii ) 15.27/15.45 ( complex, complex, complex, (times_times complex), ii, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 15.27/15.45 ( complex, complex, complex, (times_times complex), (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.45 ( (fun nat real), bool, real, (sums real), (one_one real), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (hAPP real _let_1 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc))) ) 15.27/15.45 ( (fun nat real), (fun nat real), (fun nat nat), (combb nat real nat), suc, (real_1 nat) ) 15.27/15.45 ( (fun nat real), (fun nat real), (fun nat nat), (combb nat real nat), suc, (hAPP real (fun nat real) (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.27/15.45 ( (fun nat real), (fun nat real), (fun nat nat), (combb nat real nat), (let ((_let_0 (fun nat (fun nat nat)))) (let ((_let_1 (combc nat nat nat))) (hAPP nat (fun nat nat) (hAPP _let_0 _let_0 _let_1 (hAPP (fun nat nat) _let_0 (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_0 _let_0 _let_1 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))), (real_1 nat) ) 15.27/15.45 ( (fun nat real), (fun (filter nat) bool), real, (tendsto nat real), (zero_zero real), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))) ) 15.27/15.45 ( (fun int (fun int int)), int, (product_prod int int), (product_prod_case int int int), (let ((_let_0 (product_prod int int))) (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) s) (one_one int))), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun _let_0 _let_1))) (let ((_let_3 (fun _let_0 _let_0))) (let ((_let_4 (fun int _let_3))) (let ((_let_5 (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP _let_0 _let_1 (hAPP _let_4 _let_2 (combc int _let_0 _let_0) (hAPP _let_1 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_1 _let_4) (combb _let_0 _let_3 int) (combb int int int)) (hAPP _let_0 _let_1 (hAPP _let_1 _let_2 (combb int _let_0 int) (plus_plus int)) _let_5))) _let_5))))))) ) 15.27/15.45 ( (fun int (fun int int)), (fun int int), int, (combc int int int), (one_one int), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)) (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 15.27/15.45 ( (fun int (fun int int)), (fun int (fun int int)), (fun int int), (combb int (fun int int) int), (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))), (plus_plus int) ) 15.27/15.45 ( (fun int (fun int int)), (fun int (fun int int)), (fun int int), (combb int (fun int int) int), (let ((_let_0 (fun int int))) (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (plus_plus int) ) 15.27/15.45 ( (fun int (fun int int)), (fun (product_prod int int) (fun int int)), (fun (product_prod int int) int), (combb int (fun int int) (product_prod int int)), (product_fst int int), (times_times int) ) 15.27/15.45 ( (fun int nat), bool, (fun int bool), (nat_tr1645093318rphism int nat), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), nat_1 ) 15.27/15.45 ( (fun (fun int bool) bool), (fun int bool), (fun int (fun int bool)), (combb (fun int bool) bool int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun _let_2 _let_0))) (let ((_let_4 (fun int _let_3))) (hAPP _let_2 _let_1 (hAPP _let_4 (fun _let_2 _let_1) (combc int _let_2 _let_0) (hAPP _let_1 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_1 _let_4) (combb _let_0 _let_3 int) (combb int bool int)) (fequal int))) (hAPP int _let_2 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))))))), (fEx int) ) 15.27/15.45 ( (fun (fun int bool) bool), (fun int bool), (fun int (fun int bool)), (combb (fun int bool) bool int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun _let_2 _let_0))) (let ((_let_5 (fun int _let_4))) (hAPP _let_2 _let_1 (hAPP _let_5 (fun _let_2 _let_1) (combc int _let_2 _let_0) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_1 _let_5) (combb _let_0 _let_4 int) (combb int bool int)) (fequal int))) (hAPP int _let_2 (hAPP _let_3 _let_3 (combc int int int) (hAPP _let_2 _let_3 (hAPP _let_3 (fun _let_2 _let_3) (combb int _let_2 int) (plus_plus int)) (hAPP int _let_2 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one int))))))))), (fEx int) ) 15.27/15.45 ( (fun (fun int bool) bool), (fun real bool), (fun real (fun int bool)), (combb (fun int bool) bool real), (let ((_let_0 (fun int (fun int bool)))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real real))) (let ((_let_3 (real_1 int))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun int _let_4))) (let ((_let_7 (fun (fun int bool) (fun int bool)))) (let ((_let_8 (fun (fun int bool) _let_6))) (let ((_let_9 (fun _let_0 (fun int bool)))) (let ((_let_10 (fun int real))) (let ((_let_11 (fun int _let_7))) (let ((_let_12 (fun (fun int bool) _let_0))) (let ((_let_13 (fun int _let_6))) (let ((_let_14 (fun _let_13 _let_11))) (let ((_let_15 (fun _let_0 _let_13))) (let ((_let_16 (fun real (fun int bool)))) (let ((_let_17 (fun real _let_0))) (let ((_let_18 (fun real _let_12))) (let ((_let_19 (fun real _let_11))) (let ((_let_20 (fun real _let_13))) (let ((_let_21 (fun int _let_10))) (let ((_let_22 (fun _let_21 _let_0))) (let ((_let_23 (fun real _let_22))) (let ((_let_24 (fun _let_10 (fun int bool)))) (let ((_let_25 (fun real _let_24))) (let ((_let_26 (fun _let_10 _let_10))) (let ((_let_27 (fun int _let_26))) (let ((_let_28 (fun int _let_2))) (hAPP _let_17 _let_16 (hAPP _let_9 (fun _let_17 _let_16) (combb _let_0 (fun int bool) real) (hAPP (fun (fun int bool) bool) _let_9 (combb (fun int bool) bool int) (fEx int))) (hAPP (fun int bool) _let_17 (hAPP _let_18 (fun (fun int bool) _let_17) (combc real (fun int bool) _let_0) (hAPP _let_19 _let_18 (hAPP (fun _let_11 _let_12) (fun _let_19 _let_18) (combb _let_11 _let_12 real) (combc int (fun int bool) (fun int bool))) (hAPP _let_20 _let_19 (hAPP _let_14 (fun _let_20 _let_19) (combb _let_13 _let_11 real) (hAPP (fun _let_6 _let_7) _let_14 (combb _let_6 _let_7 int) (combs int bool bool))) (hAPP _let_17 _let_20 (hAPP _let_15 (fun _let_17 _let_20) (combb _let_0 _let_13 real) (hAPP _let_8 _let_15 (combb (fun int bool) _let_6 int) (hAPP (fun bool _let_4) _let_8 (combb bool _let_4 int) fconj))) (hAPP _let_21 _let_17 (hAPP _let_23 (fun _let_21 _let_17) (combc real _let_21 _let_0) (hAPP _let_25 _let_23 (hAPP (fun _let_24 _let_22) (fun _let_25 _let_23) (combb _let_24 _let_22 real) (combb _let_10 (fun int bool) int)) (hAPP _let_5 _let_25 (hAPP (fun _let_1 _let_24) (fun _let_5 _let_25) (combb _let_1 _let_24 real) (combb real bool int)) (fequal real)))) (hAPP _let_10 _let_21 (hAPP _let_27 (fun _let_10 _let_21) (combc int _let_10 _let_10) (hAPP _let_28 _let_27 (hAPP (fun _let_2 _let_26) (fun _let_28 _let_27) (combb _let_2 _let_26 int) (combb real real int)) (hAPP _let_10 _let_28 (hAPP (fun real _let_2) (fun _let_10 _let_28) (combb real _let_2 int) (inverse_divide real)) _let_3))) _let_3)))))) (hAPP (fun int bool) (fun int bool) (hAPP _let_4 _let_7 (combb bool bool int) fNot) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (fequal int)) (zero_zero int)))))))))))))))))))))))))))))))))), (fEx int) ) 15.27/15.46 ( (fun (fun int bool) bool), (fun real bool), (fun real (fun int bool)), (combb (fun int bool) bool real), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real real))) (let ((_let_3 (fun nat (fun nat bool)))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun (fun nat real) (fun nat real)))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun (fun nat bool) (fun nat bool)))) (let ((_let_8 (fun int real))) (let ((_let_9 (fun nat _let_4))) (let ((_let_10 (fun (fun nat bool) _let_9))) (let ((_let_11 (fun real _let_0))) (let ((_let_12 (fun int _let_2))) (let ((_let_13 (fun real (fun int (fun nat bool))))) (let ((_let_14 (fun (fun int (fun nat bool)) _let_0))) (let ((_let_15 (fun (fun nat bool) (fun int (fun nat bool))))) (let ((_let_16 (fun real _let_15))) (let ((_let_17 (fun int _let_7))) (let ((_let_18 (fun real _let_17))) (let ((_let_19 (fun int _let_9))) (let ((_let_20 (fun real _let_19))) (let ((_let_21 (fun _let_19 _let_17))) (let ((_let_22 (fun (fun int (fun nat bool)) _let_19))) (let ((_let_23 (fun int (fun nat real)))) (let ((_let_24 (fun _let_23 (fun int (fun nat bool))))) (let ((_let_25 (fun real _let_24))) (let ((_let_26 (fun (fun nat real) (fun nat bool)))) (let ((_let_27 (fun real _let_26))) (let ((_let_28 (fun int _let_5))) (hAPP _let_13 _let_11 (hAPP _let_14 (fun _let_13 _let_11) (combb (fun int (fun nat bool)) _let_0 real) (hAPP (fun (fun nat bool) bool) _let_14 (combb (fun nat bool) bool int) (fEx nat))) (hAPP (fun nat bool) _let_13 (hAPP _let_16 (fun (fun nat bool) _let_13) (combc real (fun nat bool) (fun int (fun nat bool))) (hAPP _let_18 _let_16 (hAPP (fun _let_17 _let_15) (fun _let_18 _let_16) (combb _let_17 _let_15 real) (combc int (fun nat bool) (fun nat bool))) (hAPP _let_20 _let_18 (hAPP _let_21 (fun _let_20 _let_18) (combb _let_19 _let_17 real) (hAPP (fun _let_9 _let_7) _let_21 (combb _let_9 _let_7 int) (combs nat bool bool))) (hAPP _let_13 _let_20 (hAPP _let_22 (fun _let_13 _let_20) (combb (fun int (fun nat bool)) _let_19 real) (hAPP _let_10 _let_22 (combb (fun nat bool) _let_9 int) (hAPP (fun bool _let_4) _let_10 (combb bool _let_4 nat) fconj))) (hAPP _let_23 _let_13 (hAPP _let_25 (fun _let_23 _let_13) (combc real _let_23 (fun int (fun nat bool))) (hAPP _let_27 _let_25 (hAPP (fun _let_26 _let_24) (fun _let_27 _let_25) (combb _let_26 _let_24 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_6 _let_27 (hAPP (fun _let_1 _let_26) (fun _let_6 _let_27) (combb _let_1 _let_26 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_23 (hAPP _let_28 (fun (fun nat real) _let_23) (combc int (fun nat real) (fun nat real)) (hAPP _let_12 _let_28 (hAPP (fun _let_2 _let_5) (fun _let_12 _let_28) (combb _let_2 _let_5 int) (combb real real nat)) (hAPP _let_8 _let_12 (hAPP (fun real _let_2) (fun _let_8 _let_12) (combb real _let_2 int) (inverse_divide real)) (real_1 int)))) (real_1 nat))))))) (hAPP (fun nat bool) (fun nat bool) (hAPP _let_4 _let_7 (combb bool bool nat) fNot) (hAPP nat (fun nat bool) (hAPP _let_3 _let_3 (combc nat nat bool) (fequal nat)) (zero_zero nat)))))))))))))))))))))))))))))))))), (fEx int) ) 15.27/15.46 ( (fun nat (fun nat nat)), (fun nat nat), nat, (combc nat nat nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (times_times nat) ) 15.27/15.46 ( (fun nat (fun nat nat)), (fun nat nat), nat, (combc nat nat nat), (one_one nat), (let ((_let_0 (fun nat (fun nat nat)))) (hAPP (fun nat nat) _let_0 (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_0 _let_0 (combc nat nat nat) (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.27/15.46 ( (fun nat (fun nat nat)), (fun nat (fun nat nat)), (fun nat nat), (combb nat (fun nat nat) nat), (let ((_let_0 (fun nat (fun nat nat)))) (hAPP nat (fun nat nat) (hAPP _let_0 _let_0 (combc nat nat nat) (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (plus_plus nat) ) 15.27/15.46 ( (fun bool bool), (fun int bool), (fun int bool), (combb bool bool int), (let ((_let_0 (fun int (fun int bool)))) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (fequal int)) (zero_zero int))), fNot ) 15.27/15.46 ( (fun bool bool), (fun nat bool), (fun nat bool), (combb bool bool nat), (let ((_let_0 (fun nat (fun nat bool)))) (hAPP nat (fun nat bool) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat)) (zero_zero nat))), fNot ) 15.27/15.46 ( (fun bool bool), (fun (product_prod int int) bool), (fun (product_prod int int) bool), (combb bool bool (product_prod int int)), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun _let_1 _let_0))) (let ((_let_4 (fun _let_1 int))) (hAPP int _let_2 (hAPP _let_3 (fun int _let_2) (combc _let_1 int bool) (hAPP _let_4 _let_3 (hAPP (fun int _let_0) (fun _let_4 _let_3) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))), fNot ) 15.27/15.46 ( (fun nat (fun real real)), (fun nat real), real, (combc nat real real), (one_one real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 nat) (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))))) ) 15.27/15.46 ( (fun nat (fun real real)), (fun nat real), (fun nat real), (combs nat real real), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat (fun nat nat)))) (let ((_let_2 (combc nat nat nat))) (hAPP (fun nat nat) _let_0 (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat real nat) (real_1 nat)) (hAPP nat (fun nat nat) (hAPP _let_1 _let_1 _let_2 (hAPP (fun nat nat) _let_1 (hAPP _let_1 (fun (fun nat nat) _let_1) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_1 _let_1 _let_2 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (let ((_let_3 (fun real _let_0))) (let ((_let_4 (fun _let_1 _let_2))) (let ((_let_5 (combb real _let_0 nat))) (hAPP _let_1 _let_2 (hAPP _let_3 _let_4 _let_5 (inverse_divide real)) (hAPP real _let_1 (hAPP _let_2 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_2 (hAPP _let_3 _let_4 _let_5 (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) (one_one real))))))))) ) 15.27/15.46 ( (fun real (fun real real)), (fun real real), (fun real real), (combs real real real), sin, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos))) ) 15.27/15.46 ( (fun real (fun real real)), (fun nat (fun real real)), (fun nat real), (combb real (fun real real) nat), (hAPP real (fun nat real) (power_power real) (hAPP int real (number_number_of real) min_1)), (times_times real) ) 15.27/15.46 ( (fun real (fun real real)), (fun nat (fun real real)), (fun nat real), (combb real (fun real real) nat), (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (hAPP real _let_1 (hAPP _let_2 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 nat) (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) (one_one real))))), (inverse_divide real) ) 15.27/15.46 ( (fun real (fun real real)), (fun real (fun real real)), (fun real real), (combb real (fun real real) real), cos, (inverse_divide real) ) 15.27/15.46 ( (fun real (fun real real)), (fun int (fun real real)), (fun int real), (combb real (fun real real) int), (real_1 int), (inverse_divide real) ) 15.27/15.46 ( (fun bool (fun bool bool)), (fun int (fun bool bool)), (fun int bool), (combb bool (fun bool bool) int), (hAPP int (fun int bool) (ord_less int) (zero_zero int)), fconj ) 15.27/15.46 ( (fun bool (fun bool bool)), (fun (product_prod int int) (fun bool bool)), (fun (product_prod int int) bool), (combb bool (fun bool bool) (product_prod int int)), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun _let_1 _let_0))) (let ((_let_4 (fun _let_1 int))) (hAPP _let_2 _let_2 (hAPP (fun bool bool) (fun _let_2 _let_2) (combb bool bool _let_1) fNot) (hAPP int _let_2 (hAPP _let_3 (fun int _let_2) (combc _let_1 int bool) (hAPP _let_4 _let_3 (hAPP (fun int _let_0) (fun _let_4 _let_3) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int)))))))), fconj ) 15.27/15.46 ( (fun bool (fun bool bool)), (fun real (fun bool bool)), (fun real bool), (combb bool (fun bool bool) real), (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), fconj ) 15.27/15.46 ( (fun bool (fun bool bool)), (fun real (fun bool bool)), (fun real bool), (combb bool (fun bool bool) real), (let ((_let_0 (fun real (fun real bool)))) (hAPP real (fun real bool) (hAPP _let_0 _let_0 (combc real real bool) (ord_less_eq real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), fconj ) 15.27/15.46 ( code_code_numeral, code_code_numeral, code_code_numeral, (minus_minus code_code_numeral), (one_one code_code_numeral), (zero_zero code_code_numeral) ) 15.27/15.46 ( (fun int (fun int (fun int bool))), (fun int (fun int bool)), int, (combc int int (fun int bool)), (one_one int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int _let_1))) (let ((_let_5 (fun _let_2 _let_1))) (hAPP _let_4 _let_4 (hAPP (fun _let_1 _let_1) (fun _let_4 _let_4) (combb _let_1 _let_1 int) (combc int int bool)) (hAPP _let_3 _let_4 (hAPP _let_5 (fun _let_3 _let_4) (combb _let_2 _let_1 int) (hAPP _let_1 _let_5 (combb int _let_0 int) (fequal int))) int_gcd)))))))) ) 15.27/15.46 ( (fun real (fun real bool)), (fun real bool), real, (combc real real bool), (zero_zero real), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun real _let_0))) (hAPP _let_1 _let_2 (hAPP _let_2 (fun _let_1 _let_2) (combb real _let_0 real) (fequal real)) cos)))) ) 15.27/15.46 ( (fun real (fun real bool)), (fun real bool), real, (combc real real bool), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (ord_less_eq real) ) 15.27/15.46 ( (fun real (fun real bool)), (fun real (fun real bool)), (fun real real), (combb real (fun real bool) real), cos, (fequal real) ) 15.27/15.46 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), (fun int (fun int bool)), (fun int (fun int bool)), (let ((_let_0 (fun int bool))) (combb _let_0 _let_0 int)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int _let_1))) (let ((_let_5 (fun _let_2 _let_1))) (hAPP int _let_1 (hAPP _let_4 _let_4 (combc int int _let_0) (hAPP _let_4 _let_4 (hAPP (fun _let_1 _let_1) (fun _let_4 _let_4) (combb _let_1 _let_1 int) (combc int int bool)) (hAPP _let_3 _let_4 (hAPP _let_5 (fun _let_3 _let_4) (combb _let_2 _let_1 int) (hAPP _let_1 _let_5 (combb int _let_0 int) (fequal int))) int_gcd))) (one_one int)))))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun int _let_1))) (hAPP _let_2 (fun _let_0 _let_0) (combs int bool bool) (hAPP _let_0 _let_2 (hAPP (fun bool _let_1) (fun _let_0 _let_2) (combb bool _let_1 int) fconj) (hAPP int _let_0 (ord_less int) (zero_zero int))))))) ) 15.27/15.46 ( (let ((_let_0 (fun int bool))) (fun (fun int _let_0) _let_0)), (fun real (fun int bool)), (fun real (fun int (fun int bool))), (let ((_let_0 (fun int bool))) (combb (fun int _let_0) _let_0 real)), (let ((_let_0 (fun int (fun int bool)))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real real))) (let ((_let_3 (real_1 int))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun int _let_4))) (let ((_let_7 (fun (fun int bool) (fun int bool)))) (let ((_let_8 (fun (fun int bool) _let_6))) (let ((_let_9 (fun int real))) (let ((_let_10 (fun int _let_7))) (let ((_let_11 (fun (fun int bool) _let_0))) (let ((_let_12 (fun int _let_6))) (let ((_let_13 (fun _let_12 _let_10))) (let ((_let_14 (fun _let_0 _let_12))) (let ((_let_15 (fun real _let_0))) (let ((_let_16 (fun real _let_11))) (let ((_let_17 (fun real _let_10))) (let ((_let_18 (fun real _let_12))) (let ((_let_19 (fun int _let_9))) (let ((_let_20 (fun _let_19 _let_0))) (let ((_let_21 (fun real _let_20))) (let ((_let_22 (fun _let_9 (fun int bool)))) (let ((_let_23 (fun real _let_22))) (let ((_let_24 (fun _let_9 _let_9))) (let ((_let_25 (fun int _let_24))) (let ((_let_26 (fun int _let_2))) (hAPP (fun int bool) _let_15 (hAPP _let_16 (fun (fun int bool) _let_15) (combc real (fun int bool) _let_0) (hAPP _let_17 _let_16 (hAPP (fun _let_10 _let_11) (fun _let_17 _let_16) (combb _let_10 _let_11 real) (combc int (fun int bool) (fun int bool))) (hAPP _let_18 _let_17 (hAPP _let_13 (fun _let_18 _let_17) (combb _let_12 _let_10 real) (hAPP (fun _let_6 _let_7) _let_13 (combb _let_6 _let_7 int) (combs int bool bool))) (hAPP _let_15 _let_18 (hAPP _let_14 (fun _let_15 _let_18) (combb _let_0 _let_12 real) (hAPP _let_8 _let_14 (combb (fun int bool) _let_6 int) (hAPP (fun bool _let_4) _let_8 (combb bool _let_4 int) fconj))) (hAPP _let_19 _let_15 (hAPP _let_21 (fun _let_19 _let_15) (combc real _let_19 _let_0) (hAPP _let_23 _let_21 (hAPP (fun _let_22 _let_20) (fun _let_23 _let_21) (combb _let_22 _let_20 real) (combb _let_9 (fun int bool) int)) (hAPP _let_5 _let_23 (hAPP (fun _let_1 _let_22) (fun _let_5 _let_23) (combb _let_1 _let_22 real) (combb real bool int)) (fequal real)))) (hAPP _let_9 _let_19 (hAPP _let_25 (fun _let_9 _let_19) (combc int _let_9 _let_9) (hAPP _let_26 _let_25 (hAPP (fun _let_2 _let_24) (fun _let_26 _let_25) (combb _let_2 _let_24 int) (combb real real int)) (hAPP _let_9 _let_26 (hAPP (fun real _let_2) (fun _let_9 _let_26) (combb real _let_2 int) (inverse_divide real)) _let_3))) _let_3)))))) (hAPP (fun int bool) (fun int bool) (hAPP _let_4 _let_7 (combb bool bool int) fNot) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (fequal int)) (zero_zero int))))))))))))))))))))))))))))))), (let ((_let_0 (fun int bool))) (hAPP (fun _let_0 bool) (fun (fun int _let_0) _let_0) (combb _let_0 bool int) (fEx int))) ) 15.27/15.46 ( (fun int (fun (fun int int) (fun int bool))), (fun int (fun int bool)), (fun int int), (combc int (fun int int) (fun int bool)), (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun (fun int int) _let_0))) (let ((_let_3 (fun int _let_2))) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 int) (combb int bool int)) (fequal int)))))) ) 15.27/15.46 ( (fun int (fun (fun int int) (fun int bool))), (fun int (fun int bool)), (fun int int), (combc int (fun int int) (fun int bool)), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (hAPP int _let_0 (hAPP _let_1 _let_1 (combc int int int) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)) (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one int)))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun (fun int int) _let_0))) (let ((_let_3 (fun int _let_2))) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 int) (combb int bool int)) (fequal int)))))) ) 15.27/15.46 ( (fun (fun int int) (fun int (fun int bool))), (fun int (fun int (fun int bool))), (fun int (fun int int)), (combb (fun int int) (fun int (fun int bool)) int), int_gcd, (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (hAPP _let_1 (fun (fun int int) _let_1) (combb int _let_0 int) (fequal int)))) ) 15.27/15.46 ( (let ((_let_0 (fun int bool))) (fun _let_0 (fun (fun int int) _let_0))), (fun int (fun (fun int int) (fun int bool))), (fun int (fun int bool)), (let ((_let_0 (fun int bool))) (combb _let_0 (fun (fun int int) _let_0) int)), (fequal int), (combb int bool int) ) 15.27/15.46 ( (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 bool))) (combb _let_1 _let_1 _let_0))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun _let_2 (fun _let_2 bool)))) (let ((_let_4 (fun _let_2 _let_0))) (let ((_let_5 (fun _let_2 int))) (let ((_let_6 (fun _let_5 _let_4))) (let ((_let_7 (product_snd int int))) (let ((_let_8 (fun _let_2 _let_5))) (let ((_let_9 (fun _let_5 (fun _let_2 bool)))) (let ((_let_10 (fun _let_2 _let_9))) (let ((_let_11 (fun _let_2 _let_4))) (let ((_let_12 (fun _let_5 _let_5))) (let ((_let_13 (fun _let_2 _let_12))) (let ((_let_14 (fun _let_5 _let_8))) (let ((_let_15 (fun _let_2 _let_1))) (let ((_let_16 (hAPP _let_5 _let_15 (hAPP (fun int _let_1) (fun _let_5 _let_15) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (let ((_let_17 (fun int _let_5))) (hAPP _let_8 _let_3 (hAPP _let_10 (fun _let_8 _let_3) (combs _let_2 _let_5 (fun _let_2 bool)) (hAPP _let_11 _let_10 (hAPP (fun _let_4 _let_9) (fun _let_11 _let_10) (combb _let_4 _let_9 _let_2) (combs _let_2 int bool)) (hAPP _let_8 _let_11 (hAPP _let_6 (fun _let_8 _let_11) (combb _let_5 _let_4 _let_2) (hAPP (fun int _let_0) _let_6 (combb int _let_0 _let_2) (fequal int))) (hAPP _let_5 _let_8 (hAPP _let_13 _let_14 (combc _let_2 _let_5 _let_5) (hAPP _let_15 _let_13 (hAPP (fun _let_1 _let_12) (fun _let_15 _let_13) (combb _let_1 _let_12 _let_2) (combb int int _let_2)) _let_16)) _let_7)))) (hAPP _let_5 _let_8 (hAPP _let_17 _let_14 (combb int _let_5 _let_2) (hAPP _let_15 _let_17 (combc _let_2 int int) _let_16)) _let_7)))))))))))))))))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_3 _let_3))) (let ((_let_5 (fun _let_1 _let_2))) (let ((_let_6 (fun _let_1 _let_0))) (let ((_let_7 (fun _let_1 int))) (hAPP _let_5 _let_4 (combs _let_1 bool bool) (hAPP _let_3 _let_5 (hAPP (fun bool _let_2) (fun _let_3 _let_5) (combb bool _let_2 _let_1) fconj) (hAPP _let_3 _let_3 (hAPP _let_2 _let_4 (combb bool bool _let_1) fNot) (hAPP int _let_3 (hAPP _let_6 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_7 _let_6 (hAPP (fun int _let_0) (fun _let_7 _let_6) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))))))))) ) 15.27/15.46 ( (let ((_let_0 (fun (product_prod int int) bool))) (fun (product_prod int int) (fun _let_0 _let_0))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (fun (product_prod int int) bool))) (combs (product_prod int int) _let_0 _let_0)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun _let_2 (fun _let_2 bool)))) (let ((_let_5 (fun (fun _let_2 bool) (fun _let_2 bool)))) (let ((_let_6 (fun _let_2 _let_3))) (let ((_let_7 (fun _let_2 _let_0))) (let ((_let_8 (fun _let_2 int))) (let ((_let_9 (fun _let_8 _let_7))) (let ((_let_10 (hAPP (fun int _let_0) _let_9 (combb int _let_0 _let_2) (fequal int)))) (let ((_let_11 (product_snd int int))) (let ((_let_12 (fun _let_2 _let_8))) (let ((_let_13 (fun _let_8 (fun _let_2 bool)))) (let ((_let_14 (fun _let_2 _let_13))) (let ((_let_15 (fun _let_2 _let_7))) (let ((_let_16 (fun _let_8 _let_8))) (let ((_let_17 (fun _let_2 _let_16))) (let ((_let_18 (fun _let_8 _let_12))) (let ((_let_19 (fun _let_2 _let_1))) (let ((_let_20 (hAPP _let_8 _let_19 (hAPP (fun int _let_1) (fun _let_8 _let_19) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (let ((_let_21 (fun int _let_8))) (hAPP _let_4 _let_4 (hAPP _let_5 (fun _let_4 _let_4) (combb (fun _let_2 bool) (fun _let_2 bool) _let_2) (hAPP _let_6 _let_5 (combs _let_2 bool bool) (hAPP (fun _let_2 bool) _let_6 (hAPP (fun bool _let_3) (fun (fun _let_2 bool) _let_6) (combb bool _let_3 _let_2) fconj) (hAPP (fun _let_2 bool) (fun _let_2 bool) (hAPP _let_3 _let_5 (combb bool bool _let_2) fNot) (hAPP int (fun _let_2 bool) (hAPP _let_7 (fun int (fun _let_2 bool)) (combc _let_2 int bool) (hAPP _let_8 _let_7 _let_10 _let_11)) (zero_zero int)))))) (hAPP _let_12 _let_4 (hAPP _let_14 (fun _let_12 _let_4) (combs _let_2 _let_8 (fun _let_2 bool)) (hAPP _let_15 _let_14 (hAPP (fun _let_7 _let_13) (fun _let_15 _let_14) (combb _let_7 _let_13 _let_2) (combs _let_2 int bool)) (hAPP _let_12 _let_15 (hAPP _let_9 (fun _let_12 _let_15) (combb _let_8 _let_7 _let_2) _let_10) (hAPP _let_8 _let_12 (hAPP _let_17 _let_18 (combc _let_2 _let_8 _let_8) (hAPP _let_19 _let_17 (hAPP (fun _let_1 _let_16) (fun _let_19 _let_17) (combb _let_1 _let_16 _let_2) (combb int int _let_2)) _let_20)) _let_11)))) (hAPP _let_8 _let_12 (hAPP _let_21 _let_18 (combb int _let_8 _let_2) (hAPP _let_19 _let_21 (combc _let_2 int int) _let_20)) _let_11))))))))))))))))))))))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_3 _let_3))) (let ((_let_5 (fun _let_1 _let_4))) (let ((_let_6 (fun _let_1 _let_2))) (let ((_let_7 (combb bool bool _let_1))) (let ((_let_8 (fun _let_1 _let_0))) (let ((_let_9 (fun _let_1 int))) (hAPP _let_6 _let_5 (hAPP (fun _let_2 _let_4) (fun _let_6 _let_5) (combb _let_2 _let_4 _let_1) _let_7) (hAPP _let_3 _let_6 (hAPP (fun bool _let_2) (fun _let_3 _let_6) (combb bool _let_2 _let_1) fconj) (hAPP _let_3 _let_3 (hAPP _let_2 _let_4 _let_7 fNot) (hAPP int _let_3 (hAPP _let_8 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_9 _let_8 (hAPP (fun int _let_0) (fun _let_9 _let_8) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))))))))))) ) 15.27/15.46 ( (let ((_let_0 (fun (product_prod int int) bool))) (fun (fun bool bool) (fun _let_0 _let_0))), (let ((_let_0 (fun (product_prod int int) bool))) (fun (product_prod int int) (fun _let_0 _let_0))), (fun (product_prod int int) (fun bool bool)), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 bool))) (combb (fun bool bool) (fun _let_1 _let_1) _let_0))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_1 _let_2))) (let ((_let_5 (fun _let_1 _let_0))) (let ((_let_6 (fun _let_1 int))) (hAPP _let_3 _let_4 (hAPP (fun bool _let_2) (fun _let_3 _let_4) (combb bool _let_2 _let_1) fconj) (hAPP _let_3 _let_3 (hAPP _let_2 (fun _let_3 _let_3) (combb bool bool _let_1) fNot) (hAPP int _let_3 (hAPP _let_5 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_6 _let_5 (hAPP (fun int _let_0) (fun _let_6 _let_5) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))))))), (combb bool bool (product_prod int int)) ) 15.27/15.46 ( (fun (product_prod int int) (fun int bool)), (fun (product_prod int int) bool), int, (combc (product_prod int int) int bool), (zero_zero int), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 _let_0))) (let ((_let_3 (fun _let_1 int))) (hAPP _let_3 _let_2 (hAPP (fun int _let_0) (fun _let_3 _let_2) (combb int _let_0 _let_1) (fequal int)) (product_snd int int)))))) ) 15.27/15.46 ( (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 (fun int bool)))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 (fun int bool)))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (let ((_let_0 (product_prod int int))) (combb (fun _let_0 int) (fun _let_0 (fun int bool)) _let_0)), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_2))) (let ((_let_4 (fun _let_2 _let_2))) (let ((_let_5 (fun _let_1 _let_4))) (let ((_let_6 (fun _let_1 _let_0))) (hAPP _let_2 _let_3 (hAPP _let_5 (fun _let_2 _let_3) (combc _let_1 _let_2 _let_2) (hAPP _let_6 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_6 _let_5) (combb _let_0 _let_4 _let_1) (combb int int _let_1)) (hAPP _let_2 _let_6 (hAPP (fun int _let_0) (fun _let_2 _let_6) (combb int _let_0 _let_1) (times_times int)) (product_fst int int)))) (product_snd int int))))))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (hAPP (fun int _let_0) (fun (fun _let_1 int) (fun _let_1 _let_0)) (combb int _let_0 _let_1) (fequal int)))) ) 15.27/15.46 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun (fun _let_0 int) (fun _let_0 bool)))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (let ((_let_0 (product_prod int int))) (combs _let_0 (fun _let_0 int) (fun _let_0 bool))), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_2))) (let ((_let_4 (fun _let_1 _let_0))) (let ((_let_5 (fun int _let_2))) (hAPP _let_2 _let_3 (hAPP _let_5 (fun _let_2 _let_3) (combb int _let_2 _let_1) (hAPP _let_4 _let_5 (combc _let_1 int int) (hAPP _let_2 _let_4 (hAPP (fun int _let_0) (fun _let_2 _let_4) (combb int _let_0 _let_1) (times_times int)) (product_fst int int)))) (product_snd int int)))))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun _let_2 _let_0))) (let ((_let_4 (fun _let_2 int))) (let ((_let_5 (fun _let_4 _let_3))) (let ((_let_6 (fun _let_2 _let_4))) (let ((_let_7 (fun _let_4 (fun _let_2 bool)))) (let ((_let_8 (fun _let_2 _let_7))) (let ((_let_9 (fun _let_2 _let_3))) (let ((_let_10 (fun _let_4 _let_4))) (let ((_let_11 (fun _let_2 _let_10))) (let ((_let_12 (fun _let_2 _let_1))) (hAPP _let_9 _let_8 (hAPP (fun _let_3 _let_7) (fun _let_9 _let_8) (combb _let_3 _let_7 _let_2) (combs _let_2 int bool)) (hAPP _let_6 _let_9 (hAPP _let_5 (fun _let_6 _let_9) (combb _let_4 _let_3 _let_2) (hAPP (fun int _let_0) _let_5 (combb int _let_0 _let_2) (fequal int))) (hAPP _let_4 _let_6 (hAPP _let_11 (fun _let_4 _let_6) (combc _let_2 _let_4 _let_4) (hAPP _let_12 _let_11 (hAPP (fun _let_1 _let_10) (fun _let_12 _let_11) (combb _let_1 _let_10 _let_2) (combb int int _let_2)) (hAPP _let_4 _let_12 (hAPP (fun int _let_1) (fun _let_4 _let_12) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (product_snd int int))))))))))))))))) ) 15.27/15.46 ( (let ((_let_0 (product_prod int int))) (fun (fun _let_0 (fun int bool)) (fun (fun _let_0 int) (fun _let_0 bool)))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun (fun _let_0 int) (fun _let_0 bool)))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 (fun int bool)))), (let ((_let_0 (product_prod int int))) (combb (fun _let_0 (fun int bool)) (fun (fun _let_0 int) (fun _let_0 bool)) _let_0)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun _let_2 _let_0))) (let ((_let_4 (fun _let_2 int))) (let ((_let_5 (fun _let_4 _let_3))) (let ((_let_6 (fun _let_2 _let_4))) (let ((_let_7 (fun _let_2 _let_3))) (let ((_let_8 (fun _let_4 _let_4))) (let ((_let_9 (fun _let_2 _let_8))) (let ((_let_10 (fun _let_2 _let_1))) (hAPP _let_6 _let_7 (hAPP _let_5 (fun _let_6 _let_7) (combb _let_4 _let_3 _let_2) (hAPP (fun int _let_0) _let_5 (combb int _let_0 _let_2) (fequal int))) (hAPP _let_4 _let_6 (hAPP _let_9 (fun _let_4 _let_6) (combc _let_2 _let_4 _let_4) (hAPP _let_10 _let_9 (hAPP (fun _let_1 _let_8) (fun _let_10 _let_9) (combb _let_1 _let_8 _let_2) (combb int int _let_2)) (hAPP _let_4 _let_10 (hAPP (fun int _let_1) (fun _let_4 _let_10) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (product_snd int int)))))))))))))), (combs (product_prod int int) int bool) ) 15.27/15.46 ( (let ((_let_0 (fun (product_prod int int) int))) (fun (product_prod int int) (fun _let_0 _let_0))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (fun (product_prod int int) int), (let ((_let_0 (fun (product_prod int int) int))) (combc (product_prod int int) _let_0 _let_0)), (product_snd int int), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_2 _let_2))) (let ((_let_4 (fun _let_1 _let_3))) (let ((_let_5 (fun _let_1 _let_0))) (hAPP _let_5 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_5 _let_4) (combb _let_0 _let_3 _let_1) (combb int int _let_1)) (hAPP _let_2 _let_5 (hAPP (fun int _let_0) (fun _let_2 _let_5) (combb int _let_0 _let_1) (times_times int)) (product_fst int int))))))))) ) 15.27/15.46 ( (let ((_let_0 (fun (product_prod int int) int))) (fun (fun int int) (fun _let_0 _let_0))), (let ((_let_0 (fun (product_prod int int) int))) (fun (product_prod int int) (fun _let_0 _let_0))), (fun (product_prod int int) (fun int int)), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 int))) (combb (fun int int) (fun _let_1 _let_1) _let_0))), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_0))) (hAPP _let_2 _let_3 (hAPP (fun int _let_0) (fun _let_2 _let_3) (combb int _let_0 _let_1) (times_times int)) (product_fst int int)))))), (combb int int (product_prod int int)) ) 15.27/15.46 ( (fun int (fun (product_prod int int) int)), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (fun (product_prod int int) int), (let ((_let_0 (product_prod int int))) (combb int (fun _let_0 int) _let_0)), (product_snd int int), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_0))) (hAPP _let_3 (fun int _let_2) (combc _let_1 int int) (hAPP _let_2 _let_3 (hAPP (fun int _let_0) (fun _let_2 _let_3) (combb int _let_0 _let_1) (times_times int)) (product_fst int int))))))) ) 15.27/15.46 ( (fun real (fun bool bool)), (fun real bool), (fun real bool), (combs real bool bool), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun real _let_0))) (hAPP real _let_0 (hAPP _let_2 _let_2 (combc real real bool) (hAPP _let_1 _let_2 (hAPP _let_2 (fun _let_1 _let_2) (combb real _let_0 real) (fequal real)) cos)) (zero_zero real))))), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun real (fun real bool)))) (let ((_let_2 (fun real _let_0))) (hAPP (fun real bool) _let_2 (hAPP (fun bool _let_0) (fun (fun real bool) _let_2) (combb bool _let_0 real) fconj) (hAPP real (fun real bool) (hAPP _let_1 _let_1 (combc real real bool) (ord_less_eq real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 15.27/15.46 ( (fun real (fun bool bool)), (fun real bool), (fun real bool), (combs real bool bool), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun real _let_0))) (let ((_let_4 (fun real _let_2))) (let ((_let_5 (combc real real bool))) (hAPP _let_0 _let_0 (hAPP _let_4 (fun _let_0 _let_0) (combs real bool bool) (hAPP _let_0 _let_4 (hAPP (fun bool _let_2) (fun _let_0 _let_4) (combb bool _let_2 real) fconj) (hAPP real _let_0 (hAPP _let_3 _let_3 _let_5 (ord_less_eq real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_3 _let_3 _let_5 (hAPP _let_1 _let_3 (hAPP _let_3 (fun _let_1 _let_3) (combb real _let_0 real) (fequal real)) cos)) (zero_zero real))))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun real _let_1))) (hAPP _let_0 _let_2 (hAPP (fun bool _let_1) (fun _let_0 _let_2) (combb bool _let_1 real) fconj) (hAPP real _let_0 (ord_less_eq real) (zero_zero real)))))) ) 15.27/15.46 ( (let ((_let_0 (fun int bool))) (fun (fun int (fun int (fun bool bool))) (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))), (fun real (fun int (fun int (fun bool bool)))), (let ((_let_0 (fun int bool))) (combb (fun int (fun int (fun bool bool))) (fun int (fun _let_0 _let_0)) real)), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun int _let_3))) (let ((_let_6 (fun (fun int bool) _let_5))) (let ((_let_7 (fun int real))) (let ((_let_8 (fun int _let_5))) (let ((_let_9 (fun (fun int (fun int bool)) _let_8))) (let ((_let_10 (fun real (fun int (fun int bool))))) (let ((_let_11 (fun real _let_8))) (let ((_let_12 (fun int _let_7))) (let ((_let_13 (fun _let_12 (fun int (fun int bool))))) (let ((_let_14 (fun real _let_13))) (let ((_let_15 (fun _let_7 (fun int bool)))) (let ((_let_16 (fun real _let_15))) (let ((_let_17 (fun _let_7 _let_7))) (let ((_let_18 (fun int _let_17))) (let ((_let_19 (fun int _let_1))) (hAPP _let_10 _let_11 (hAPP _let_9 (fun _let_10 _let_11) (combb (fun int (fun int bool)) _let_8 real) (hAPP _let_6 _let_9 (combb (fun int bool) _let_5 int) (hAPP (fun bool _let_3) _let_6 (combb bool _let_3 int) fconj))) (hAPP _let_12 _let_10 (hAPP _let_14 (fun _let_12 _let_10) (combc real _let_12 (fun int (fun int bool))) (hAPP _let_16 _let_14 (hAPP (fun _let_15 _let_13) (fun _let_16 _let_14) (combb _let_15 _let_13 real) (combb _let_7 (fun int bool) int)) (hAPP _let_4 _let_16 (hAPP (fun _let_0 _let_15) (fun _let_4 _let_16) (combb _let_0 _let_15 real) (combb real bool int)) (fequal real)))) (hAPP _let_7 _let_12 (hAPP _let_18 (fun _let_7 _let_12) (combc int _let_7 _let_7) (hAPP _let_19 _let_18 (hAPP (fun _let_1 _let_17) (fun _let_19 _let_18) (combb _let_1 _let_17 int) (combb real real int)) (hAPP _let_7 _let_19 (hAPP (fun real _let_1) (fun _let_7 _let_19) (combb real _let_1 int) (inverse_divide real)) _let_2))) _let_2))))))))))))))))))))))), (let ((_let_0 (fun int (fun bool bool)))) (let ((_let_1 (fun (fun int bool) (fun int bool)))) (hAPP (fun _let_0 _let_1) (fun (fun int _let_0) (fun int _let_1)) (combb _let_0 _let_1 int) (combs int bool bool)))) ) 15.27/15.46 ( (fun (fun int (fun int bool)) (fun int (fun int (fun bool bool)))), (fun real (fun int (fun int (fun bool bool)))), (fun real (fun int (fun int bool))), (combb (fun int (fun int bool)) (fun int (fun int (fun bool bool))) real), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun real _let_0))) (let ((_let_4 (fun int real))) (let ((_let_5 (fun real (fun int (fun int bool))))) (let ((_let_6 (fun int _let_4))) (let ((_let_7 (fun _let_6 (fun int (fun int bool))))) (let ((_let_8 (fun real _let_7))) (let ((_let_9 (fun _let_4 (fun int bool)))) (let ((_let_10 (fun real _let_9))) (let ((_let_11 (fun _let_4 _let_4))) (let ((_let_12 (fun int _let_11))) (let ((_let_13 (fun int _let_1))) (hAPP _let_6 _let_5 (hAPP _let_8 (fun _let_6 _let_5) (combc real _let_6 (fun int (fun int bool))) (hAPP _let_10 _let_8 (hAPP (fun _let_9 _let_7) (fun _let_10 _let_8) (combb _let_9 _let_7 real) (combb _let_4 (fun int bool) int)) (hAPP _let_3 _let_10 (hAPP (fun _let_0 _let_9) (fun _let_3 _let_10) (combb _let_0 _let_9 real) (combb real bool int)) (fequal real)))) (hAPP _let_4 _let_6 (hAPP _let_12 (fun _let_4 _let_6) (combc int _let_4 _let_4) (hAPP _let_13 _let_12 (hAPP (fun _let_1 _let_11) (fun _let_13 _let_12) (combb _let_1 _let_11 int) (combb real real int)) (hAPP _let_4 _let_13 (hAPP (fun real _let_1) (fun _let_4 _let_13) (combb real _let_1 int) (inverse_divide real)) _let_2))) _let_2)))))))))))))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (fun _let_0 _let_2))) (hAPP _let_3 (fun (fun int _let_0) (fun int _let_2)) (combb _let_0 _let_2 int) (hAPP (fun bool _let_1) _let_3 (combb bool _let_1 int) fconj)))))) ) 15.27/15.46 ( (fun int (fun nat int)), (fun int int), nat, (combc int nat int), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (power_power int) ) 15.27/15.46 ( (let ((_let_0 (fun int bool))) (fun real (fun _let_0 (fun int _let_0)))), (fun real (fun int (fun int bool))), (fun int bool), (let ((_let_0 (fun int bool))) (combc real _let_0 (fun int _let_0))), (let ((_let_0 (fun int (fun int bool)))) (hAPP (fun int bool) (fun int bool) (hAPP (fun bool bool) (fun (fun int bool) (fun int bool)) (combb bool bool int) fNot) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (fequal int)) (zero_zero int)))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun int _let_3))) (let ((_let_6 (fun (fun int bool) (fun int bool)))) (let ((_let_7 (fun (fun int bool) _let_5))) (let ((_let_8 (fun int real))) (let ((_let_9 (fun int _let_6))) (let ((_let_10 (fun (fun int bool) (fun int (fun int bool))))) (let ((_let_11 (fun int _let_5))) (let ((_let_12 (fun _let_11 _let_9))) (let ((_let_13 (fun (fun int (fun int bool)) _let_11))) (let ((_let_14 (fun real (fun int (fun int bool))))) (let ((_let_15 (fun real _let_10))) (let ((_let_16 (fun real _let_9))) (let ((_let_17 (fun real _let_11))) (let ((_let_18 (fun int _let_8))) (let ((_let_19 (fun _let_18 (fun int (fun int bool))))) (let ((_let_20 (fun real _let_19))) (let ((_let_21 (fun _let_8 (fun int bool)))) (let ((_let_22 (fun real _let_21))) (let ((_let_23 (fun _let_8 _let_8))) (let ((_let_24 (fun int _let_23))) (let ((_let_25 (fun int _let_1))) (hAPP _let_16 _let_15 (hAPP (fun _let_9 _let_10) (fun _let_16 _let_15) (combb _let_9 _let_10 real) (combc int (fun int bool) (fun int bool))) (hAPP _let_17 _let_16 (hAPP _let_12 (fun _let_17 _let_16) (combb _let_11 _let_9 real) (hAPP (fun _let_5 _let_6) _let_12 (combb _let_5 _let_6 int) (combs int bool bool))) (hAPP _let_14 _let_17 (hAPP _let_13 (fun _let_14 _let_17) (combb (fun int (fun int bool)) _let_11 real) (hAPP _let_7 _let_13 (combb (fun int bool) _let_5 int) (hAPP (fun bool _let_3) _let_7 (combb bool _let_3 int) fconj))) (hAPP _let_18 _let_14 (hAPP _let_20 (fun _let_18 _let_14) (combc real _let_18 (fun int (fun int bool))) (hAPP _let_22 _let_20 (hAPP (fun _let_21 _let_19) (fun _let_22 _let_20) (combb _let_21 _let_19 real) (combb _let_8 (fun int bool) int)) (hAPP _let_4 _let_22 (hAPP (fun _let_0 _let_21) (fun _let_4 _let_22) (combb _let_0 _let_21 real) (combb real bool int)) (fequal real)))) (hAPP _let_8 _let_18 (hAPP _let_24 (fun _let_8 _let_18) (combc int _let_8 _let_8) (hAPP _let_25 _let_24 (hAPP (fun _let_1 _let_23) (fun _let_25 _let_24) (combb _let_1 _let_23 int) (combb real real int)) (hAPP _let_8 _let_25 (hAPP (fun real _let_1) (fun _let_8 _let_25) (combb real _let_1 int) (inverse_divide real)) _let_2))) _let_2))))))))))))))))))))))))))))))) ) 15.27/15.47 ( (let ((_let_0 (fun int bool))) (fun (fun int (fun _let_0 _let_0)) (fun _let_0 (fun int _let_0)))), (let ((_let_0 (fun int bool))) (fun real (fun _let_0 (fun int _let_0)))), (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun int bool))) (combb (fun int (fun _let_0 _let_0)) (fun _let_0 (fun int _let_0)) real)), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun int _let_3))) (let ((_let_6 (fun (fun int bool) (fun int bool)))) (let ((_let_7 (fun (fun int bool) _let_5))) (let ((_let_8 (fun int real))) (let ((_let_9 (fun int _let_6))) (let ((_let_10 (fun int _let_5))) (let ((_let_11 (fun _let_10 _let_9))) (let ((_let_12 (fun (fun int (fun int bool)) _let_10))) (let ((_let_13 (fun real (fun int (fun int bool))))) (let ((_let_14 (fun real _let_9))) (let ((_let_15 (fun real _let_10))) (let ((_let_16 (fun int _let_8))) (let ((_let_17 (fun _let_16 (fun int (fun int bool))))) (let ((_let_18 (fun real _let_17))) (let ((_let_19 (fun _let_8 (fun int bool)))) (let ((_let_20 (fun real _let_19))) (let ((_let_21 (fun _let_8 _let_8))) (let ((_let_22 (fun int _let_21))) (let ((_let_23 (fun int _let_1))) (hAPP _let_15 _let_14 (hAPP _let_11 (fun _let_15 _let_14) (combb _let_10 _let_9 real) (hAPP (fun _let_5 _let_6) _let_11 (combb _let_5 _let_6 int) (combs int bool bool))) (hAPP _let_13 _let_15 (hAPP _let_12 (fun _let_13 _let_15) (combb (fun int (fun int bool)) _let_10 real) (hAPP _let_7 _let_12 (combb (fun int bool) _let_5 int) (hAPP (fun bool _let_3) _let_7 (combb bool _let_3 int) fconj))) (hAPP _let_16 _let_13 (hAPP _let_18 (fun _let_16 _let_13) (combc real _let_16 (fun int (fun int bool))) (hAPP _let_20 _let_18 (hAPP (fun _let_19 _let_17) (fun _let_20 _let_18) (combb _let_19 _let_17 real) (combb _let_8 (fun int bool) int)) (hAPP _let_4 _let_20 (hAPP (fun _let_0 _let_19) (fun _let_4 _let_20) (combb _let_0 _let_19 real) (combb real bool int)) (fequal real)))) (hAPP _let_8 _let_16 (hAPP _let_22 (fun _let_8 _let_16) (combc int _let_8 _let_8) (hAPP _let_23 _let_22 (hAPP (fun _let_1 _let_21) (fun _let_23 _let_22) (combb _let_1 _let_21 int) (combb real real int)) (hAPP _let_8 _let_23 (hAPP (fun real _let_1) (fun _let_8 _let_23) (combb real _let_1 int) (inverse_divide real)) _let_2))) _let_2)))))))))))))))))))))))))))), (let ((_let_0 (fun int bool))) (combc int _let_0 _let_0)) ) 15.27/15.47 ( (fun real (fun (fun int (fun int real)) (fun int (fun int bool)))), (fun real (fun int (fun int bool))), (fun int (fun int real)), (combc real (fun int (fun int real)) (fun int (fun int bool))), (let ((_let_0 (fun real real))) (let ((_let_1 (real_1 int))) (let ((_let_2 (fun int real))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun _let_2 _let_2))) (let ((_let_5 (fun int _let_4))) (let ((_let_6 (fun int _let_0))) (hAPP _let_2 _let_3 (hAPP _let_5 (fun _let_2 _let_3) (combc int _let_2 _let_2) (hAPP _let_6 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_6 _let_5) (combb _let_0 _let_4 int) (combb real real int)) (hAPP _let_2 _let_6 (hAPP (fun real _let_0) (fun _let_2 _let_6) (combb real _let_0 int) (inverse_divide real)) _let_1))) _let_1)))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun int (fun int real)) (fun int (fun int bool))))) (let ((_let_3 (fun real _let_2))) (let ((_let_4 (fun (fun int real) (fun int bool)))) (let ((_let_5 (fun real _let_4))) (hAPP _let_5 _let_3 (hAPP (fun _let_4 _let_2) (fun _let_5 _let_3) (combb _let_4 _let_2 real) (combb (fun int real) (fun int bool) int)) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_1 _let_5) (combb _let_0 _let_4 real) (combb real bool int)) (fequal real))))))))) ) 15.27/15.47 ( (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int real))) (fun (fun _let_1 _let_0) (fun (fun int _let_1) (fun int _let_0))))), (fun real (fun (fun int (fun int real)) (fun int (fun int bool)))), (fun real (fun (fun int real) (fun int bool))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int real))) (combb (fun _let_1 _let_0) (fun (fun int _let_1) (fun int _let_0)) real))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun int real) (fun int bool)))) (let ((_let_3 (fun real _let_2))) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 real) (combb real bool int)) (fequal real)))))), (combb (fun int real) (fun int bool) int) ) 15.27/15.47 ( (fun (fun real bool) (fun (fun int real) (fun int bool))), (fun real (fun (fun int real) (fun int bool))), (fun real (fun real bool)), (combb (fun real bool) (fun (fun int real) (fun int bool)) real), (fequal real), (combb real bool int) ) 15.27/15.47 ( (let ((_let_0 (fun int real))) (fun int (fun _let_0 _let_0))), (fun int (fun int real)), (fun int real), (let ((_let_0 (fun int real))) (combc int _let_0 _let_0)), (real_1 int), (let ((_let_0 (fun real real))) (let ((_let_1 (fun int real))) (let ((_let_2 (fun _let_1 _let_1))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int _let_0))) (hAPP _let_4 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_4 _let_3) (combb _let_0 _let_2 int) (combb real real int)) (hAPP _let_1 _let_4 (hAPP (fun real _let_0) (fun _let_1 _let_4) (combb real _let_0 int) (inverse_divide real)) (real_1 int)))))))) ) 15.27/15.47 ( (let ((_let_0 (fun int real))) (fun (fun real real) (fun _let_0 _let_0))), (let ((_let_0 (fun int real))) (fun int (fun _let_0 _let_0))), (fun int (fun real real)), (let ((_let_0 (fun int real))) (combb (fun real real) (fun _let_0 _let_0) int)), (let ((_let_0 (fun real real))) (let ((_let_1 (fun int real))) (let ((_let_2 (fun int _let_0))) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 int) (inverse_divide real)) (real_1 int))))), (combb real real int) ) 15.27/15.47 ( (let ((_let_0 (fun int (fun int bool)))) (fun _let_0 _let_0)), (fun int (fun int (fun int bool))), (fun int (fun int (fun int bool))), (let ((_let_0 (fun int (fun int bool)))) (combb _let_0 _let_0 int)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int _let_1))) (let ((_let_5 (fun _let_2 _let_1))) (hAPP _let_3 _let_4 (hAPP _let_5 (fun _let_3 _let_4) (combb _let_2 _let_1 int) (hAPP _let_1 _let_5 (combb int _let_0 int) (fequal int))) int_gcd))))))), (combc int int bool) ) 15.27/15.47 ( (fun (fun int (fun nat bool)) (fun int bool)), (fun real (fun int bool)), (fun real (fun int (fun nat bool))), (combb (fun int (fun nat bool)) (fun int bool) real), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat (fun nat bool)))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun (fun nat real) (fun nat real)))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun (fun nat bool) (fun nat bool)))) (let ((_let_7 (fun int real))) (let ((_let_8 (fun nat _let_3))) (let ((_let_9 (fun (fun nat bool) _let_8))) (let ((_let_10 (fun int _let_1))) (let ((_let_11 (fun real (fun int (fun nat bool))))) (let ((_let_12 (fun (fun nat bool) (fun int (fun nat bool))))) (let ((_let_13 (fun real _let_12))) (let ((_let_14 (fun int _let_6))) (let ((_let_15 (fun real _let_14))) (let ((_let_16 (fun int _let_8))) (let ((_let_17 (fun real _let_16))) (let ((_let_18 (fun _let_16 _let_14))) (let ((_let_19 (fun (fun int (fun nat bool)) _let_16))) (let ((_let_20 (fun int (fun nat real)))) (let ((_let_21 (fun _let_20 (fun int (fun nat bool))))) (let ((_let_22 (fun real _let_21))) (let ((_let_23 (fun (fun nat real) (fun nat bool)))) (let ((_let_24 (fun real _let_23))) (let ((_let_25 (fun int _let_4))) (hAPP (fun nat bool) _let_11 (hAPP _let_13 (fun (fun nat bool) _let_11) (combc real (fun nat bool) (fun int (fun nat bool))) (hAPP _let_15 _let_13 (hAPP (fun _let_14 _let_12) (fun _let_15 _let_13) (combb _let_14 _let_12 real) (combc int (fun nat bool) (fun nat bool))) (hAPP _let_17 _let_15 (hAPP _let_18 (fun _let_17 _let_15) (combb _let_16 _let_14 real) (hAPP (fun _let_8 _let_6) _let_18 (combb _let_8 _let_6 int) (combs nat bool bool))) (hAPP _let_11 _let_17 (hAPP _let_19 (fun _let_11 _let_17) (combb (fun int (fun nat bool)) _let_16 real) (hAPP _let_9 _let_19 (combb (fun nat bool) _let_8 int) (hAPP (fun bool _let_3) _let_9 (combb bool _let_3 nat) fconj))) (hAPP _let_20 _let_11 (hAPP _let_22 (fun _let_20 _let_11) (combc real _let_20 (fun int (fun nat bool))) (hAPP _let_24 _let_22 (hAPP (fun _let_23 _let_21) (fun _let_24 _let_22) (combb _let_23 _let_21 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_5 _let_24 (hAPP (fun _let_0 _let_23) (fun _let_5 _let_24) (combb _let_0 _let_23 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_20 (hAPP _let_25 (fun (fun nat real) _let_20) (combc int (fun nat real) (fun nat real)) (hAPP _let_10 _let_25 (hAPP (fun _let_1 _let_4) (fun _let_10 _let_25) (combb _let_1 _let_4 int) (combb real real nat)) (hAPP _let_7 _let_10 (hAPP (fun real _let_1) (fun _let_7 _let_10) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat))))))) (hAPP (fun nat bool) (fun nat bool) (hAPP _let_3 _let_6 (combb bool bool nat) fNot) (hAPP nat (fun nat bool) (hAPP _let_2 _let_2 (combc nat nat bool) (fequal nat)) (zero_zero nat)))))))))))))))))))))))))))))), (let ((_let_0 (fun nat bool))) (hAPP (fun _let_0 bool) (fun (fun int _let_0) (fun int bool)) (combb _let_0 bool int) (fEx nat))) ) 15.27/15.47 ( (let ((_let_0 (fun nat bool))) (fun real (fun _let_0 (fun int _let_0)))), (fun real (fun int (fun nat bool))), (fun nat bool), (let ((_let_0 (fun nat bool))) (combc real _let_0 (fun int _let_0))), (let ((_let_0 (fun nat (fun nat bool)))) (hAPP (fun nat bool) (fun nat bool) (hAPP (fun bool bool) (fun (fun nat bool) (fun nat bool)) (combb bool bool nat) fNot) (hAPP nat (fun nat bool) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat)) (zero_zero nat)))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun (fun nat real) (fun nat real)))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun (fun nat bool) (fun nat bool)))) (let ((_let_6 (fun int real))) (let ((_let_7 (fun nat _let_2))) (let ((_let_8 (fun (fun nat bool) _let_7))) (let ((_let_9 (fun int _let_1))) (let ((_let_10 (fun real (fun int (fun nat bool))))) (let ((_let_11 (fun (fun nat bool) (fun int (fun nat bool))))) (let ((_let_12 (fun real _let_11))) (let ((_let_13 (fun int _let_5))) (let ((_let_14 (fun real _let_13))) (let ((_let_15 (fun int _let_7))) (let ((_let_16 (fun real _let_15))) (let ((_let_17 (fun _let_15 _let_13))) (let ((_let_18 (fun (fun int (fun nat bool)) _let_15))) (let ((_let_19 (fun int (fun nat real)))) (let ((_let_20 (fun _let_19 (fun int (fun nat bool))))) (let ((_let_21 (fun real _let_20))) (let ((_let_22 (fun (fun nat real) (fun nat bool)))) (let ((_let_23 (fun real _let_22))) (let ((_let_24 (fun int _let_3))) (hAPP _let_14 _let_12 (hAPP (fun _let_13 _let_11) (fun _let_14 _let_12) (combb _let_13 _let_11 real) (combc int (fun nat bool) (fun nat bool))) (hAPP _let_16 _let_14 (hAPP _let_17 (fun _let_16 _let_14) (combb _let_15 _let_13 real) (hAPP (fun _let_7 _let_5) _let_17 (combb _let_7 _let_5 int) (combs nat bool bool))) (hAPP _let_10 _let_16 (hAPP _let_18 (fun _let_10 _let_16) (combb (fun int (fun nat bool)) _let_15 real) (hAPP _let_8 _let_18 (combb (fun nat bool) _let_7 int) (hAPP (fun bool _let_2) _let_8 (combb bool _let_2 nat) fconj))) (hAPP _let_19 _let_10 (hAPP _let_21 (fun _let_19 _let_10) (combc real _let_19 (fun int (fun nat bool))) (hAPP _let_23 _let_21 (hAPP (fun _let_22 _let_20) (fun _let_23 _let_21) (combb _let_22 _let_20 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_4 _let_23 (hAPP (fun _let_0 _let_22) (fun _let_4 _let_23) (combb _let_0 _let_22 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_19 (hAPP _let_24 (fun (fun nat real) _let_19) (combc int (fun nat real) (fun nat real)) (hAPP _let_9 _let_24 (hAPP (fun _let_1 _let_3) (fun _let_9 _let_24) (combb _let_1 _let_3 int) (combb real real nat)) (hAPP _let_6 _let_9 (hAPP (fun real _let_1) (fun _let_6 _let_9) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat))))))))))))))))))))))))))))))) ) 15.27/15.47 ( (let ((_let_0 (fun nat bool))) (fun (fun int (fun _let_0 _let_0)) (fun _let_0 (fun int _let_0)))), (let ((_let_0 (fun nat bool))) (fun real (fun _let_0 (fun int _let_0)))), (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun nat bool))) (combb (fun int (fun _let_0 _let_0)) (fun _let_0 (fun int _let_0)) real)), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun (fun nat real) (fun nat real)))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun (fun nat bool) (fun nat bool)))) (let ((_let_6 (fun int real))) (let ((_let_7 (fun nat _let_2))) (let ((_let_8 (fun (fun nat bool) _let_7))) (let ((_let_9 (fun int _let_1))) (let ((_let_10 (fun real (fun int (fun nat bool))))) (let ((_let_11 (fun int _let_5))) (let ((_let_12 (fun real _let_11))) (let ((_let_13 (fun int _let_7))) (let ((_let_14 (fun real _let_13))) (let ((_let_15 (fun _let_13 _let_11))) (let ((_let_16 (fun (fun int (fun nat bool)) _let_13))) (let ((_let_17 (fun int (fun nat real)))) (let ((_let_18 (fun _let_17 (fun int (fun nat bool))))) (let ((_let_19 (fun real _let_18))) (let ((_let_20 (fun (fun nat real) (fun nat bool)))) (let ((_let_21 (fun real _let_20))) (let ((_let_22 (fun int _let_3))) (hAPP _let_14 _let_12 (hAPP _let_15 (fun _let_14 _let_12) (combb _let_13 _let_11 real) (hAPP (fun _let_7 _let_5) _let_15 (combb _let_7 _let_5 int) (combs nat bool bool))) (hAPP _let_10 _let_14 (hAPP _let_16 (fun _let_10 _let_14) (combb (fun int (fun nat bool)) _let_13 real) (hAPP _let_8 _let_16 (combb (fun nat bool) _let_7 int) (hAPP (fun bool _let_2) _let_8 (combb bool _let_2 nat) fconj))) (hAPP _let_17 _let_10 (hAPP _let_19 (fun _let_17 _let_10) (combc real _let_17 (fun int (fun nat bool))) (hAPP _let_21 _let_19 (hAPP (fun _let_20 _let_18) (fun _let_21 _let_19) (combb _let_20 _let_18 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_4 _let_21 (hAPP (fun _let_0 _let_20) (fun _let_4 _let_21) (combb _let_0 _let_20 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_17 (hAPP _let_22 (fun (fun nat real) _let_17) (combc int (fun nat real) (fun nat real)) (hAPP _let_9 _let_22 (hAPP (fun _let_1 _let_3) (fun _let_9 _let_22) (combb _let_1 _let_3 int) (combb real real nat)) (hAPP _let_6 _let_9 (hAPP (fun real _let_1) (fun _let_6 _let_9) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat)))))))))))))))))))))))))))), (let ((_let_0 (fun nat bool))) (combc int _let_0 _let_0)) ) 15.27/15.47 ( (let ((_let_0 (fun nat bool))) (fun (fun int (fun nat (fun bool bool))) (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))), (fun real (fun int (fun nat (fun bool bool)))), (let ((_let_0 (fun nat bool))) (combb (fun int (fun nat (fun bool bool))) (fun int (fun _let_0 _let_0)) real)), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun (fun nat real) (fun nat real)))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun int real))) (let ((_let_6 (fun nat _let_2))) (let ((_let_7 (fun (fun nat bool) _let_6))) (let ((_let_8 (fun int _let_1))) (let ((_let_9 (fun real (fun int (fun nat bool))))) (let ((_let_10 (fun int _let_6))) (let ((_let_11 (fun real _let_10))) (let ((_let_12 (fun (fun int (fun nat bool)) _let_10))) (let ((_let_13 (fun int (fun nat real)))) (let ((_let_14 (fun _let_13 (fun int (fun nat bool))))) (let ((_let_15 (fun real _let_14))) (let ((_let_16 (fun (fun nat real) (fun nat bool)))) (let ((_let_17 (fun real _let_16))) (let ((_let_18 (fun int _let_3))) (hAPP _let_9 _let_11 (hAPP _let_12 (fun _let_9 _let_11) (combb (fun int (fun nat bool)) _let_10 real) (hAPP _let_7 _let_12 (combb (fun nat bool) _let_6 int) (hAPP (fun bool _let_2) _let_7 (combb bool _let_2 nat) fconj))) (hAPP _let_13 _let_9 (hAPP _let_15 (fun _let_13 _let_9) (combc real _let_13 (fun int (fun nat bool))) (hAPP _let_17 _let_15 (hAPP (fun _let_16 _let_14) (fun _let_17 _let_15) (combb _let_16 _let_14 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_4 _let_17 (hAPP (fun _let_0 _let_16) (fun _let_4 _let_17) (combb _let_0 _let_16 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_13 (hAPP _let_18 (fun (fun nat real) _let_13) (combc int (fun nat real) (fun nat real)) (hAPP _let_8 _let_18 (hAPP (fun _let_1 _let_3) (fun _let_8 _let_18) (combb _let_1 _let_3 int) (combb real real nat)) (hAPP _let_5 _let_8 (hAPP (fun real _let_1) (fun _let_5 _let_8) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat))))))))))))))))))))))), (let ((_let_0 (fun (fun nat bool) (fun nat bool)))) (let ((_let_1 (fun nat (fun bool bool)))) (hAPP (fun _let_1 _let_0) (fun (fun int _let_1) (fun int _let_0)) (combb _let_1 _let_0 int) (combs nat bool bool)))) ) 15.27/15.47 ( (fun (fun int (fun nat bool)) (fun int (fun nat (fun bool bool)))), (fun real (fun int (fun nat (fun bool bool)))), (fun real (fun int (fun nat bool))), (combb (fun int (fun nat bool)) (fun int (fun nat (fun bool bool))) real), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun (fun nat real) (fun nat real)))) (let ((_let_3 (fun real _let_0))) (let ((_let_4 (fun int real))) (let ((_let_5 (fun int _let_1))) (let ((_let_6 (fun real (fun int (fun nat bool))))) (let ((_let_7 (fun int (fun nat real)))) (let ((_let_8 (fun _let_7 (fun int (fun nat bool))))) (let ((_let_9 (fun real _let_8))) (let ((_let_10 (fun (fun nat real) (fun nat bool)))) (let ((_let_11 (fun real _let_10))) (let ((_let_12 (fun int _let_2))) (hAPP _let_7 _let_6 (hAPP _let_9 (fun _let_7 _let_6) (combc real _let_7 (fun int (fun nat bool))) (hAPP _let_11 _let_9 (hAPP (fun _let_10 _let_8) (fun _let_11 _let_9) (combb _let_10 _let_8 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_3 _let_11 (hAPP (fun _let_0 _let_10) (fun _let_3 _let_11) (combb _let_0 _let_10 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_7 (hAPP _let_12 (fun (fun nat real) _let_7) (combc int (fun nat real) (fun nat real)) (hAPP _let_5 _let_12 (hAPP (fun _let_1 _let_2) (fun _let_5 _let_12) (combb _let_1 _let_2 int) (combb real real nat)) (hAPP _let_4 _let_5 (hAPP (fun real _let_1) (fun _let_4 _let_5) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat)))))))))))))))), (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun nat _let_1))) (let ((_let_3 (fun _let_0 _let_2))) (hAPP _let_3 (fun (fun int _let_0) (fun int _let_2)) (combb _let_0 _let_2 int) (hAPP (fun bool _let_1) _let_3 (combb bool _let_1 nat) fconj)))))) ) 15.27/15.47 ( (fun real (fun (fun int (fun nat real)) (fun int (fun nat bool)))), (fun real (fun int (fun nat bool))), (fun int (fun nat real)), (combc real (fun int (fun nat real)) (fun int (fun nat bool))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun (fun nat real) (fun nat real)))) (let ((_let_2 (fun int real))) (let ((_let_3 (fun int _let_0))) (let ((_let_4 (fun int (fun nat real)))) (let ((_let_5 (fun int _let_1))) (hAPP (fun nat real) _let_4 (hAPP _let_5 (fun (fun nat real) _let_4) (combc int (fun nat real) (fun nat real)) (hAPP _let_3 _let_5 (hAPP (fun _let_0 _let_1) (fun _let_3 _let_5) (combb _let_0 _let_1 int) (combb real real nat)) (hAPP _let_2 _let_3 (hAPP (fun real _let_0) (fun _let_2 _let_3) (combb real _let_0 int) (inverse_divide real)) (real_1 int)))) (real_1 nat)))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun int (fun nat real)) (fun int (fun nat bool))))) (let ((_let_3 (fun real _let_2))) (let ((_let_4 (fun (fun nat real) (fun nat bool)))) (let ((_let_5 (fun real _let_4))) (hAPP _let_5 _let_3 (hAPP (fun _let_4 _let_2) (fun _let_5 _let_3) (combb _let_4 _let_2 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_1 _let_5) (combb _let_0 _let_4 real) (combb real bool nat)) (fequal real))))))))) ) 15.27/15.47 ( (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat real))) (fun (fun _let_1 _let_0) (fun (fun int _let_1) (fun int _let_0))))), (fun real (fun (fun int (fun nat real)) (fun int (fun nat bool)))), (fun real (fun (fun nat real) (fun nat bool))), (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat real))) (combb (fun _let_1 _let_0) (fun (fun int _let_1) (fun int _let_0)) real))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun nat real) (fun nat bool)))) (let ((_let_3 (fun real _let_2))) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 real) (combb real bool nat)) (fequal real)))))), (combb (fun nat real) (fun nat bool) int) ) 15.27/15.47 ( (fun (fun real bool) (fun (fun nat real) (fun nat bool))), (fun real (fun (fun nat real) (fun nat bool))), (fun real (fun real bool)), (combb (fun real bool) (fun (fun nat real) (fun nat bool)) real), (fequal real), (combb real bool nat) ) 15.27/15.47 ( (let ((_let_0 (fun nat real))) (fun int (fun _let_0 _let_0))), (fun int (fun nat real)), (fun nat real), (let ((_let_0 (fun nat real))) (combc int _let_0 _let_0)), (real_1 nat), (let ((_let_0 (fun real real))) (let ((_let_1 (fun (fun nat real) (fun nat real)))) (let ((_let_2 (fun int real))) (let ((_let_3 (fun int _let_0))) (let ((_let_4 (fun int _let_1))) (hAPP _let_3 _let_4 (hAPP (fun _let_0 _let_1) (fun _let_3 _let_4) (combb _let_0 _let_1 int) (combb real real nat)) (hAPP _let_2 _let_3 (hAPP (fun real _let_0) (fun _let_2 _let_3) (combb real _let_0 int) (inverse_divide real)) (real_1 int)))))))) ) 15.27/15.47 ( (let ((_let_0 (fun nat real))) (fun (fun real real) (fun _let_0 _let_0))), (let ((_let_0 (fun nat real))) (fun int (fun _let_0 _let_0))), (fun int (fun real real)), (let ((_let_0 (fun nat real))) (combb (fun real real) (fun _let_0 _let_0) int)), (let ((_let_0 (fun real real))) (let ((_let_1 (fun int real))) (let ((_let_2 (fun int _let_0))) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 int) (inverse_divide real)) (real_1 int))))), (combb real real nat) ) 15.27/15.47 ( (let ((_let_0 (fun int int))) (fun int (fun _let_0 _let_0))), (fun int (fun int int)), (fun int int), (let ((_let_0 (fun int int))) (combc int _let_0 _let_0)), (let ((_let_0 (fun int int))) (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun _let_0 _let_0))) (let ((_let_3 (fun int _let_2))) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 int) (combb int int int)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)) (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))))) ) 15.27/15.47 ( (let ((_let_0 (fun int int))) (fun _let_0 (fun _let_0 _let_0))), (let ((_let_0 (fun int int))) (fun int (fun _let_0 _let_0))), (fun int (fun int int)), (let ((_let_0 (fun int int))) (combb _let_0 (fun _let_0 _let_0) int)), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)) (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))), (combb int int int) ) 15.27/15.47 ) 15.27/15.47 (instantiation (forall ((K_4 $$unsorted)) (let ((_let_0 (product_prod int int))) (= (hAPP _let_0 rat frct (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) (hAPP int int (number_number_of int) K_4)) (one_one int))) (hAPP int rat (number_number_of rat) K_4))) ) 15.27/15.47 ( pls ) 15.27/15.47 ( (hAPP int int bit1 pls) ) 15.27/15.47 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.27/15.47 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.27/15.47 ( min_1 ) 15.27/15.47 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.47 ) 15.27/15.47 (instantiation (forall ((N_1 $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (one_one nat))) (= _let_1 (hAPP nat nat (hAPP nat _let_0 (gcd_gcd nat) (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) N_1) _let_1)) N_1)))) ) 15.27/15.47 ( (one_one nat) ) 15.27/15.47 ) 15.27/15.47 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_103810 $$unsorted)) (or (not (real_algebra_1 X_a)) (= (hAPP real X_a (of_real X_a) (hAPP int real (ring_1_of_int real) BOUND_VARIABLE_103810)) (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_103810))) ) 15.27/15.47 ( real, (one_one int) ) 15.27/15.47 ( real, (zero_zero int) ) 15.27/15.47 ) 15.27/15.47 (instantiation (forall ((A_2 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (let ((_let_3 (fun (filter nat) bool))) (or (not (hBOOL (hAPP (filter nat) bool (hAPP real _let_3 (hAPP _let_1 (fun real _let_3) (tendsto nat real) A_2) (zero_zero real)) sequentially))) (not (forall ((N_2 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) (hAPP nat real A_2 N_2))) )) (not (forall ((N_2 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP nat real A_2 (hAPP nat nat suc N_2))) (hAPP nat real A_2 N_2))) )) (hBOOL (hAPP _let_1 bool (summable real) (hAPP _let_1 _let_1 (hAPP _let_2 (fun _let_1 _let_1) (combs nat real real) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 nat) (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) A_2)))))))) ) 15.27/15.47 ( (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))) ) 15.27/15.47 ) 15.27/15.47 (instantiation (forall ((M $$unsorted)) (let ((_let_0 (fun nat nat))) (= M (hAPP nat nat (hAPP nat _let_0 (div_div nat) (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) M) M)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.27/15.47 ( (one_one nat) ) 15.27/15.47 ) 15.27/15.47 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_103902 $$unsorted)) (or (not (archim1804426504_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) BOUND_VARIABLE_103902))) (not (forall ((N_2 $$unsorted)) (or (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP X_a X_a (inverse_inverse X_a) (hAPP nat X_a (semiring_1_of_nat X_a) N_2))) BOUND_VARIABLE_103902))) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_2)))) ))) ) 15.27/15.47 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.47 ( int, (one_one int) ) 15.27/15.47 ( int, pls ) 15.27/15.47 ( int, min_1 ) 15.27/15.47 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.27/15.47 ( real, pi ) 15.27/15.47 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.47 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.47 ( real, skv_2 ) 15.27/15.47 ( real, skv_8 ) 15.27/15.47 ( real, skv_9 ) 15.27/15.47 ) 15.27/15.47 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_104004 $$unsorted) (BOUND_VARIABLE_104005 $$unsorted)) (or (not (monoid_mult X_a)) (not (linordered_ring X_a)) (not (hBOOL (hAPP nat bool (even_odd_even nat) BOUND_VARIABLE_104005))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)) (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_104004) BOUND_VARIABLE_104005)))) ) 15.27/15.47 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.47 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.47 ( int, skv_14, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.47 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.47 ) 15.27/15.47 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_104069 $$unsorted) (BOUND_VARIABLE_104070 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_104070) _let_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_104069) _let_2))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_104070) BOUND_VARIABLE_104069))))))) ) 15.27/15.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 15.27/15.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.27/15.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.27/15.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.27/15.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 15.27/15.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), pi ) 15.27/15.47 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (one_one real) ) 15.27/15.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))), pi ) 15.27/15.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 15.27/15.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))), (one_one real) ) 15.27/15.47 ) 15.27/15.47 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_104101 $$unsorted) (BOUND_VARIABLE_104102 $$unsorted) (BOUND_VARIABLE_104103 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_104102))) (or (not (preorder X_a)) (not (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_104103))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_104103) BOUND_VARIABLE_104101))) (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_104101)))))) ) 15.27/15.47 ( int, pls, pls, pls ) 15.27/15.47 ( int, pls, min_1, min_1 ) 15.27/15.47 ( int, min_1, pls, min_1 ) 15.27/15.47 ( int, min_1, min_1, pls ) 15.27/15.47 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (one_one int), t ) 15.27/15.47 ( int, t, pls, (one_one int) ) 15.27/15.47 ( real, (zero_zero real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 15.27/15.47 ( real, pi, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 15.27/15.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.47 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.27/15.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real), pi ) 15.27/15.47 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi, (zero_zero real) ) 15.27/15.47 ) 15.27/15.47 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_104171 $$unsorted)) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP nat X_a (semiring_1_of_nat X_a) BOUND_VARIABLE_104171)) (zero_zero X_a))))) ) 15.27/15.47 ( int, (zero_zero nat) ) 15.27/15.47 ( int, (hAPP nat nat suc (zero_zero nat)) ) 15.27/15.47 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.27/15.47 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.47 ( real, (zero_zero nat) ) 15.27/15.47 ( real, (hAPP nat nat suc (zero_zero nat)) ) 15.27/15.47 ) 15.27/15.47 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_104291 $$unsorted) (BOUND_VARIABLE_104292 $$unsorted) (BOUND_VARIABLE_104303 $$unsorted) (BOUND_VARIABLE_104304 $$unsorted)) (let ((_let_0 (even_odd_even nat))) (let ((_let_1 (fun nat X_a))) (let ((_let_2 (power_power X_a))) (let ((_let_3 (uminus_uminus X_a))) (or (not (comm_ring_1 X_a)) (and (or (hBOOL (hAPP nat bool _let_0 BOUND_VARIABLE_104292)) (= (hAPP X_a X_a _let_3 (hAPP nat X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_104291) BOUND_VARIABLE_104292)) (hAPP nat X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a _let_3 BOUND_VARIABLE_104291)) BOUND_VARIABLE_104292))) (or (not (hBOOL (hAPP nat bool _let_0 BOUND_VARIABLE_104304))) (= (hAPP nat X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_104303) BOUND_VARIABLE_104304) (hAPP nat X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a _let_3 BOUND_VARIABLE_104303)) BOUND_VARIABLE_104304))))))))) ) 15.27/15.47 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.47 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.47 ( int, skv_14, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_14, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.47 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.47 ) 15.27/15.47 (instantiation (forall ((Z_4 $$unsorted) (Z_1 $$unsorted)) (let ((_let_0 (uminus_uminus int))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) Z_1) (zero_zero int)))) (= (hAPP int nat nat_1 (hAPP int int (hAPP int (fun int int) (times_times int) Z_1) Z_4)) (hAPP nat nat (hAPP nat (fun nat nat) (times_times nat) (hAPP int nat nat_1 (hAPP int int _let_0 Z_1))) (hAPP int nat nat_1 (hAPP int int _let_0 Z_4)))))) ) 15.27/15.47 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.47 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.27/15.47 ( skv_13, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.27/15.47 ) 15.27/15.47 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_104328 $$unsorted)) (let ((_let_0 (filter X_a))) (let ((_let_1 (fun _let_0 bool))) (or (not (topological_space X_a)) (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 (hAPP (fun X_a X_a) (fun X_a _let_1) (tendsto X_a X_a) (combi X_a)) BOUND_VARIABLE_104328) (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_104328)))))) ) 15.27/15.47 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.47 ) 15.27/15.47 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_104380 $$unsorted) (BOUND_VARIABLE_104381 $$unsorted)) (let ((_let_0 (fun nat X_a))) (let ((_let_1 (cauchy X_a))) (let ((_let_2 (fun X_a X_a))) (let ((_let_3 (fun nat _let_2))) (or (not (real_normed_algebra X_a)) (not (hBOOL (hAPP _let_0 bool _let_1 BOUND_VARIABLE_104381))) (hBOOL (hAPP _let_0 bool _let_1 (hAPP X_a _let_0 (hAPP _let_3 (fun X_a _let_0) (combc nat X_a X_a) (hAPP _let_0 _let_3 (hAPP (fun X_a _let_2) (fun _let_0 _let_3) (combb X_a _let_2 nat) (times_times X_a)) BOUND_VARIABLE_104381)) BOUND_VARIABLE_104380)))))))) ) 15.27/15.47 ( real, (one_one real), (hAPP real (fun nat real) (power_power real) (hAPP int real (number_number_of real) min_1)) ) 15.27/15.47 ) 15.27/15.47 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (group_add X_a)) (= _let_0 (hAPP X_a X_a (uminus_uminus X_a) _let_0)))) ) 15.27/15.47 ( nat ) 15.27/15.47 ( int ) 15.27/15.47 ( real ) 15.27/15.47 ( rat ) 15.27/15.47 ( complex ) 15.27/15.47 ( quickcheck_code_int ) 15.27/15.47 ( code_code_numeral ) 15.27/15.47 ) 15.27/15.47 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_104426 $$unsorted)) (let ((_let_0 (fun (filter nat) bool))) (let ((_let_1 (fun nat X_a))) (or (not (real_normed_field X_a)) (not (hBOOL (hAPP _let_1 bool (summable X_a) BOUND_VARIABLE_104426))) (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_0 (hAPP _let_1 (fun X_a _let_0) (tendsto nat X_a) BOUND_VARIABLE_104426) (zero_zero X_a)) sequentially))))) ) 15.27/15.47 ( real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))) ) 15.27/15.47 ) 15.27/15.47 (instantiation (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= Y_1 (hAPP complex real im (hAPP real complex (hAPP real (fun real complex) complex_1 X_1) Y_1))) ) 15.27/15.47 ( (one_one real), (zero_zero real) ) 15.27/15.47 ( (zero_zero real), (one_one real) ) 15.27/15.47 ( (zero_zero real), (zero_zero real) ) 15.27/15.47 ) 15.27/15.47 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_104460 $$unsorted)) (or (not (linordered_idom X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)) (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_104460) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 15.27/15.47 ( int, s ) 15.27/15.47 ( int, s1 ) 15.27/15.47 ( int, skv_14 ) 15.27/15.47 ( real, (hAPP int real (number_number_of real) min_1) ) 15.27/15.47 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.47 ( complex, ii ) 15.27/15.47 ) 15.27/15.47 (instantiation (forall ((V $$unsorted) (V_2 $$unsorted)) (let ((_let_0 (number_number_of nat))) (let ((_let_1 (hAPP int (fun int bool) (ord_less_eq int) V))) (= (or (hBOOL (hAPP int bool _let_1 V_2)) (hBOOL (hAPP int bool _let_1 pls))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP int nat _let_0 V)) (hAPP int nat _let_0 V_2)))))) ) 15.27/15.47 ( (one_one int), t ) 15.27/15.47 ( (zero_zero int), (one_one int) ) 15.27/15.47 ( (zero_zero int), min_1 ) 15.27/15.47 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.47 ( (zero_zero int), s ) 15.27/15.47 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.27/15.47 ( (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.27/15.47 ( (zero_zero int), skv_4 ) 15.27/15.47 ( (zero_zero int), skv_10 ) 15.27/15.47 ( min_1, pls ) 15.27/15.47 ( min_1, min_1 ) 15.27/15.47 ) 15.27/15.47 (instantiation (forall ((N_1 $$unsorted) (M $$unsorted)) (let ((_let_0 (fun int int))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (dvd_dvd int) N_1) M))) (= (ti int M) (hAPP int int (hAPP int _let_0 (times_times int) N_1) (hAPP int int (hAPP int _let_0 (div_div int) M) N_1))))) ) 15.27/15.47 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 15.27/15.47 ) 15.27/15.47 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (one_one real))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_5 (abs_abs real))) (let ((_let_6 (hAPP int real (number_number_of real) _let_4))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 (hAPP real real _let_5 X_1)) (hAPP real real (hAPP real _let_3 (inverse_divide real) _let_1) _let_6)))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 (hAPP real real _let_5 (hAPP real real (hAPP real _let_3 (minus_minus real) (hAPP real real ln (hAPP real real (hAPP real _let_3 (plus_plus real) _let_1) X_1))) X_1))) (hAPP real real (hAPP real _let_3 (times_times real) _let_6) (hAPP nat real (hAPP real (fun nat real) (power_power real) X_1) (hAPP int nat (number_number_of nat) _let_4))))))))))))) ) 15.27/15.47 ( (hAPP int real (number_number_of real) min_1) ) 15.27/15.47 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.47 ) 15.27/15.47 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_104563 $$unsorted) (BOUND_VARIABLE_104564 $$unsorted)) (let ((_let_0 (filter X_a))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun X_a X_b))) (or (not (topological_space X_b)) (not (topological_space X_a)) (= (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (hAPP _let_2 (fun X_b _let_1) (tendsto X_a X_b) BOUND_VARIABLE_104563) (hAPP X_a X_b BOUND_VARIABLE_104563 BOUND_VARIABLE_104564)) (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_104564))) (hBOOL (hAPP X_a bool (hAPP _let_2 (fun X_a bool) (isCont X_a X_b) BOUND_VARIABLE_104563) BOUND_VARIABLE_104564))))))) ) 15.27/15.47 ( bool, nat, (even_odd_even nat), (zero_zero nat) ) 15.27/15.47 ( bool, nat, (even_odd_even nat), (one_one nat) ) 15.27/15.47 ( bool, nat, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.47 ( bool, nat, prime, (zero_zero nat) ) 15.27/15.47 ( bool, nat, prime, (hAPP nat nat suc (zero_zero nat)) ) 15.27/15.47 ( bool, nat, prime, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.47 ( bool, int, (hAPP int (fun int bool) (ord_less int) pls), pls ) 15.27/15.47 ( bool, int, (hAPP int (fun int bool) (ord_less int) pls), min_1 ) 15.27/15.47 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) pls), min_1 ) 15.27/15.47 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (one_one int)), t ) 15.27/15.47 ( bool, int, nat_neg, (one_one int) ) 15.27/15.47 ( bool, int, nat_neg, (hAPP int int (number_number_of int) min_1) ) 15.27/15.47 ( bool, int, nat_neg, (hAPP int int (number_number_of int) pls) ) 15.27/15.47 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (one_one int) ) 15.27/15.47 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.47 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), s ) 15.27/15.47 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.27/15.47 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) pls) ) 15.27/15.47 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_4 ) 15.27/15.47 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_10 ) 15.27/15.47 ( bool, int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (one_one int) ) 15.27/15.47 ( bool, int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.27/15.47 ( bool, int, zprime, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.47 ( bool, int, zprime, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.27/15.47 ( bool, int, (hAPP int (fun int bool) (ord_less int) s), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.27/15.47 ( bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) s)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.27/15.47 ( bool, int, (let ((_let_0 (fun int int))) (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 15.27/15.47 ( bool, int, (hAPP int (fun int bool) (ord_less int) (one_one int)), t ) 15.27/15.47 ( bool, int, (even_odd_even int), (one_one int) ) 15.27/15.47 ( bool, int, (even_odd_even int), (zero_zero int) ) 15.27/15.47 ( bool, int, twoSqu1091635170sum2sq, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) t))) ) 15.27/15.47 ( bool, int, nat_is_nat, (one_one int) ) 15.27/15.47 ( bool, int, nat_is_nat, (zero_zero int) ) 15.27/15.47 ( bool, int, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.47 ( bool, int, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.27/15.47 ( bool, int, (hAPP int (fun int bool) (ord_less int) min_1), pls ) 15.27/15.47 ( bool, int, (hAPP int (fun int bool) (ord_less int) min_1), min_1 ) 15.27/15.47 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) min_1), pls ) 15.27/15.47 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) min_1), min_1 ) 15.27/15.47 ( bool, int, (let ((_let_0 (fun int int))) (hAPP int (fun int bool) quadRes (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int int (number_number_of int) min_1) ) 15.27/15.47 ( bool, int, (let ((_let_0 (fun int bool))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (let ((_let_3 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int _let_1 _let_2 s) _let_3)) (hAPP nat int (hAPP int _let_1 _let_2 s1) _let_3)))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.27/15.47 ( bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.27/15.47 ( bool, int, (hAPP int (fun int bool) (ord_less int) t), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.27/15.47 ( bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.27/15.47 ( bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_4)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.27/15.47 ( bool, int, (hAPP int (fun int bool) (ord_less int) skv_4), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.27/15.47 ( bool, int, (hAPP int (fun int bool) (ord_less int) skv_10), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.27/15.47 ( bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_10)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.27/15.47 ( bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.27/15.47 ( bool, (fun int bool), (hAPP (fun int nat) (fun (fun int bool) bool) (nat_tr1645093318rphism int nat) nat_1), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 15.27/15.47 ( bool, (fun int bool), (hAPP int (fun (fun int bool) bool) (member int) (one_one int)), zEven ) 15.27/15.47 ( bool, (fun nat bool), (finite_finite_1 nat), (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 15.27/15.47 ( bool, (fun nat bool), (hAPP (fun nat int) (fun (fun nat bool) bool) (nat_tr1645093318rphism nat int) (semiring_1_of_nat int)), (hAPP bool (fun nat bool) (combk bool nat) fTrue) ) 15.27/15.47 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), pi ) 15.27/15.47 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.47 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.48 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_3 ) 15.27/15.48 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_5 ) 15.27/15.48 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_7 ) 15.27/15.48 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_12 ) 15.27/15.48 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), pi ) 15.27/15.48 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.48 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.48 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_2 ) 15.27/15.48 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_8 ) 15.27/15.48 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_9 ) 15.27/15.48 ( bool, real, (hAPP real (fun real bool) (ord_less real) (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))), (zero_zero real) ) 15.27/15.48 ( bool, real, (hAPP real (fun real bool) (ord_less real) (one_one real)), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.48 ( bool, real, (hAPP real (fun real bool) (ord_less real) pi), (zero_zero real) ) 15.27/15.48 ( bool, real, (hAPP real (fun real bool) (ord_less real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.48 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.48 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 15.27/15.48 ( bool, real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 (fun real bool) (sums real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (hAPP real _let_1 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc)))), (one_one real) ) 15.27/15.48 ( bool, real, (hAPP real (fun real bool) (ord_less real) (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi))), pi ) 15.27/15.48 ( bool, real, (hAPP real (fun real bool) (ord_less real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.48 ( bool, real, (hAPP real (fun real bool) (ord_less real) (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 15.27/15.48 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 15.27/15.48 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) skv_5), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.48 ( bool, (filter nat), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun (filter nat) bool))) (hAPP real _let_2 (hAPP _let_1 (fun real _let_2) (tendsto nat real) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))) (zero_zero real))))), sequentially ) 15.27/15.48 ( bool, (filter nat), (trivial_limit nat), sequentially ) 15.27/15.48 ( bool, (filter real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (filter real) bool))) (hAPP real _let_2 (hAPP _let_0 (fun real _let_2) (tendsto real real) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin)) (zero_zero real))))), (hAPP real (filter real) (at real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.27/15.48 ( nat, nat, suc, (zero_zero nat) ) 15.27/15.48 ( nat, nat, suc, (hAPP nat nat suc (zero_zero nat)) ) 15.27/15.48 ( nat, nat, suc, (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 15.27/15.48 ( nat, nat, (fact_fact nat), (zero_zero nat) ) 15.27/15.48 ( nat, nat, (fact_fact nat), (hAPP nat nat suc (zero_zero nat)) ) 15.27/15.48 ( nat, nat, fact, (zero_zero nat) ) 15.27/15.48 ( nat, nat, (hAPP nat (fun nat nat) (plus_plus nat) (one_one nat)), (one_one nat) ) 15.27/15.48 ( nat, nat, nat_size, (zero_zero nat) ) 15.27/15.48 ( nat, nat, (size_size nat), (zero_zero nat) ) 15.27/15.48 ( nat, int, (number_number_of nat), pls ) 15.27/15.48 ( nat, int, (number_number_of nat), (hAPP int int bit1 pls) ) 15.27/15.48 ( nat, int, (number_number_of nat), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.27/15.48 ( nat, int, (number_number_of nat), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.27/15.48 ( nat, int, nat_1, (one_one int) ) 15.27/15.48 ( nat, int, nat_1, (zero_zero int) ) 15.27/15.48 ( nat, int, nat_1, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.48 ( nat, int, nat_1, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.27/15.48 ( nat, real, natfloor, (one_one real) ) 15.27/15.48 ( nat, real, natfloor, (zero_zero real) ) 15.27/15.48 ( nat, real, natceiling, (one_one real) ) 15.27/15.48 ( nat, real, natceiling, (zero_zero real) ) 15.27/15.48 ( nat, code_code_numeral, (size_size code_code_numeral), (zero_zero code_code_numeral) ) 15.27/15.48 ( nat, code_code_numeral, code_c271388182l_size, (zero_zero code_code_numeral) ) 15.27/15.48 ( int, nat, (semiring_1_of_nat int), (zero_zero nat) ) 15.27/15.48 ( int, nat, (semiring_1_of_nat int), (hAPP nat nat suc (zero_zero nat)) ) 15.27/15.48 ( int, nat, (semiring_1_of_nat int), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.27/15.48 ( int, nat, (semiring_1_of_nat int), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.48 ( int, nat, (hAPP int (fun nat int) (power_power int) s), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.48 ( int, nat, (hAPP int (fun nat int) (power_power int) s1), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.48 ( int, nat, (hAPP int (fun nat int) (power_power int) skv_14), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.48 ( int, int, bit0, pls ) 15.27/15.48 ( int, int, bit0, (hAPP int int bit1 pls) ) 15.27/15.48 ( int, int, bit0, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.27/15.48 ( int, int, bit0, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.27/15.48 ( int, int, bit0, min_1 ) 15.27/15.48 ( int, int, bit0, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.27/15.48 ( int, int, bit1, pls ) 15.27/15.48 ( int, int, bit1, (hAPP int int bit1 pls) ) 15.27/15.48 ( int, int, bit1, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.27/15.48 ( int, int, bit1, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.27/15.48 ( int, int, bit1, min_1 ) 15.27/15.48 ( int, int, bit1, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.27/15.48 ( int, int, bit1, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.27/15.48 ( int, int, bit1, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 15.27/15.48 ( int, int, bit1, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 15.27/15.48 ( int, int, (number_number_of int), pls ) 15.27/15.48 ( int, int, (number_number_of int), (hAPP int int bit1 pls) ) 15.27/15.48 ( int, int, (number_number_of int), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.27/15.48 ( int, int, (number_number_of int), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.27/15.48 ( int, int, (number_number_of int), min_1 ) 15.27/15.48 ( int, int, (number_number_of int), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.27/15.48 ( int, int, (fact_fact int), (one_one int) ) 15.27/15.48 ( int, int, (fact_fact int), (zero_zero int) ) 15.27/15.48 ( int, int, (uminus_uminus int), (one_one int) ) 15.27/15.48 ( int, int, (uminus_uminus int), pls ) 15.27/15.48 ( int, int, (uminus_uminus int), min_1 ) 15.27/15.48 ( int, int, pred, pls ) 15.27/15.48 ( int, int, pred, min_1 ) 15.27/15.48 ( int, int, (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))), m ) 15.27/15.48 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m))), (one_one int) ) 15.27/15.48 ( int, int, (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (one_one int) ) 15.27/15.48 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))))), t ) 15.27/15.48 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))))), skv_13 ) 15.27/15.48 ( int, int, succ, pls ) 15.27/15.48 ( int, int, succ, min_1 ) 15.27/15.48 ( int, int, (hAPP int (fun int int) legendre (hAPP int int (number_number_of int) min_1)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.27/15.48 ( int, int, (hAPP int (fun int int) (minus_minus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1) ) 15.27/15.48 ( int, (product_prod int int), twoSqu1094008024sum2sq, (let ((_let_0 (product_prod int int))) (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) s) (one_one int))) ) 15.27/15.48 ( int, quickcheck_code_int, quickcheck_int_of, (zero_zero quickcheck_code_int) ) 15.27/15.48 ( int, code_code_numeral, code_int_of, (zero_zero code_code_numeral) ) 15.27/15.48 ( (fun int bool), int, (ord_less_eq int), (one_one int) ) 15.27/15.48 ( (fun int bool), int, (ord_less_eq int), (zero_zero int) ) 15.27/15.48 ( (fun int bool), int, (ord_less_eq int), min_1 ) 15.27/15.48 ( (fun int bool), int, (ord_less int), (one_one int) ) 15.27/15.48 ( (fun int bool), int, (ord_less int), pls ) 15.27/15.48 ( (fun int bool), int, (ord_less int), min_1 ) 15.27/15.48 ( (fun int bool), int, (ord_less int), s ) 15.27/15.48 ( (fun int bool), int, (ord_less int), t ) 15.27/15.48 ( (fun int bool), int, (ord_less int), skv_4 ) 15.27/15.48 ( (fun int bool), int, (ord_less int), skv_10 ) 15.27/15.48 ( (fun int bool), int, (dvd_dvd int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.27/15.48 ( (fun int bool), int, quadRes, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.27/15.48 ( (fun int bool), int, (let ((_let_0 (fun int (fun int bool)))) (hAPP _let_0 _let_0 (combc int int bool) (fequal int))), (zero_zero int) ) 15.27/15.48 ( (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong s1), s ) 15.27/15.48 ( (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong s1), skv_4 ) 15.27/15.48 ( (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong s1), skv_10 ) 15.27/15.48 ( (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1) ) 15.27/15.48 ( (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.27/15.48 ( (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1) ) 15.27/15.48 ( (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1) ) 15.27/15.48 ( (fun int bool), (fun int bool), (collect int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun _let_2 _let_0))) (let ((_let_4 (fun int _let_3))) (hAPP _let_1 _let_0 (hAPP (fun _let_0 bool) (fun _let_1 _let_0) (combb _let_0 bool int) (fEx int)) (hAPP _let_2 _let_1 (hAPP _let_4 (fun _let_2 _let_1) (combc int _let_2 _let_0) (hAPP _let_1 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_1 _let_4) (combb _let_0 _let_3 int) (combb int bool int)) (fequal int))) (hAPP int _let_2 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))))))))) ) 15.33/15.51 ( (fun int bool), (fun int bool), (collect int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun _let_2 _let_0))) (let ((_let_5 (fun int _let_4))) (hAPP _let_1 _let_0 (hAPP (fun _let_0 bool) (fun _let_1 _let_0) (combb _let_0 bool int) (fEx int)) (hAPP _let_2 _let_1 (hAPP _let_5 (fun _let_2 _let_1) (combc int _let_2 _let_0) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_1 _let_5) (combb _let_0 _let_4 int) (combb int bool int)) (fequal int))) (hAPP int _let_2 (hAPP _let_3 _let_3 (combc int int int) (hAPP _let_2 _let_3 (hAPP _let_3 (fun _let_2 _let_3) (combb int _let_2 int) (plus_plus int)) (hAPP int _let_2 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one int)))))))))) ) 15.33/15.51 ( (fun int bool), (fun int bool), (let ((_let_0 (fun int bool))) (hAPP (fun bool bool) (fun _let_0 _let_0) (combb bool bool int) fNot)), (let ((_let_0 (fun int (fun int bool)))) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (fequal int)) (zero_zero int))) ) 15.33/15.51 ( (fun int bool), (fun int (fun int bool)), (let ((_let_0 (fun int bool))) (hAPP (fun _let_0 bool) (fun (fun int _let_0) _let_0) (combb _let_0 bool int) (fEx int))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun _let_2 _let_0))) (let ((_let_4 (fun int _let_3))) (hAPP _let_2 _let_1 (hAPP _let_4 (fun _let_2 _let_1) (combc int _let_2 _let_0) (hAPP _let_1 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_1 _let_4) (combb _let_0 _let_3 int) (combb int bool int)) (fequal int))) (hAPP int _let_2 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))))))) ) 15.33/15.51 ( (fun int bool), (fun int (fun int bool)), (let ((_let_0 (fun int bool))) (hAPP (fun _let_0 bool) (fun (fun int _let_0) _let_0) (combb _let_0 bool int) (fEx int))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun _let_2 _let_0))) (let ((_let_5 (fun int _let_4))) (hAPP _let_2 _let_1 (hAPP _let_5 (fun _let_2 _let_1) (combc int _let_2 _let_0) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_1 _let_5) (combb _let_0 _let_4 int) (combb int bool int)) (fequal int))) (hAPP int _let_2 (hAPP _let_3 _let_3 (combc int int int) (hAPP _let_2 _let_3 (hAPP _let_3 (fun _let_2 _let_3) (combb int _let_2 int) (plus_plus int)) (hAPP int _let_2 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one int))))))))) ) 15.33/15.51 ( (fun int (fun int bool)), int, zcong, s1 ) 15.33/15.51 ( (fun int (fun int bool)), int, zcong, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.51 ( (fun int (fun int bool)), int, zcong, (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.51 ( (fun int (fun int bool)), int, zcong, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.51 ( (fun int (fun int bool)), int, (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int _let_1))) (let ((_let_5 (fun _let_2 _let_1))) (hAPP _let_4 _let_4 (combc int int _let_0) (hAPP _let_4 _let_4 (hAPP (fun _let_1 _let_1) (fun _let_4 _let_4) (combb _let_1 _let_1 int) (combc int int bool)) (hAPP _let_3 _let_4 (hAPP _let_5 (fun _let_3 _let_4) (combb _let_2 _let_1 int) (hAPP _let_1 _let_5 (combb int _let_0 int) (fequal int))) int_gcd))))))))), (one_one int) ) 15.33/15.51 ( (fun int (fun int bool)), (fun int (fun int bool)), (combc int int bool), (fequal int) ) 15.33/15.51 ( (fun int (fun int bool)), (fun int (fun int bool)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun _let_0 _let_0))) (hAPP _let_4 (fun _let_1 _let_1) (combb _let_0 _let_0 int) (hAPP _let_3 _let_4 (combs int bool bool) (hAPP _let_0 _let_3 (hAPP (fun bool _let_2) (fun _let_0 _let_3) (combb bool _let_2 int) fconj) (hAPP int _let_0 (ord_less int) (zero_zero int)))))))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int _let_1))) (let ((_let_5 (fun _let_2 _let_1))) (hAPP int _let_1 (hAPP _let_4 _let_4 (combc int int _let_0) (hAPP _let_4 _let_4 (hAPP (fun _let_1 _let_1) (fun _let_4 _let_4) (combb _let_1 _let_1 int) (combc int int bool)) (hAPP _let_3 _let_4 (hAPP _let_5 (fun _let_3 _let_4) (combb _let_2 _let_1 int) (hAPP _let_1 _let_5 (combb int _let_0 int) (fequal int))) int_gcd))) (one_one int)))))))) ) 15.33/15.51 ( (fun int (fun int bool)), (fun int int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun (fun int int) _let_0))) (let ((_let_3 (fun int _let_2))) (hAPP _let_3 (fun (fun int int) _let_1) (combc int (fun int int) _let_0) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 int) (combb int bool int)) (fequal int))))))), (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.51 ( (fun int (fun int bool)), (fun int int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun (fun int int) _let_0))) (let ((_let_3 (fun int _let_2))) (hAPP _let_3 (fun (fun int int) _let_1) (combc int (fun int int) _let_0) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 int) (combb int bool int)) (fequal int))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (hAPP int _let_0 (hAPP _let_1 _let_1 (combc int int int) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)) (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one int)))) ) 15.33/15.51 ( (fun int int), nat, (hAPP (fun int (fun nat int)) (fun nat (fun int int)) (combc int nat int) (power_power int)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.51 ( (fun int int), int, (times_times int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.51 ( (fun int int), int, (times_times int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.51 ( (fun int int), int, (times_times int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.33/15.51 ( (fun int int), int, (minus_minus int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.51 ( (fun int int), int, (plus_plus int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.33/15.51 ( (fun int int), int, (plus_plus int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.51 ( (fun int int), int, legendre, (hAPP int int (number_number_of int) min_1) ) 15.33/15.51 ( (fun int int), int, (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (hAPP _let_1 _let_1 (combc int int int) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)) (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))))), (one_one int) ) 15.33/15.51 ( (fun nat bool), bool, (combk bool nat), fTrue ) 15.33/15.51 ( (fun nat bool), nat, (ord_less nat), (zero_zero nat) ) 15.33/15.51 ( (fun nat bool), nat, (let ((_let_0 (fun nat (fun nat bool)))) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat))), (zero_zero nat) ) 15.33/15.51 ( (fun nat bool), (fun nat bool), (collect nat), prime ) 15.33/15.51 ( (fun nat bool), (fun nat bool), (let ((_let_0 (fun nat bool))) (hAPP (fun bool bool) (fun _let_0 _let_0) (combb bool bool nat) fNot)), (let ((_let_0 (fun nat (fun nat bool)))) (hAPP nat (fun nat bool) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat)) (zero_zero nat))) ) 15.33/15.51 ( (fun nat nat), nat, (plus_plus nat), (one_one nat) ) 15.33/15.51 ( (fun nat nat), nat, (let ((_let_0 (fun nat (fun nat nat)))) (hAPP _let_0 _let_0 (combc nat nat nat) (times_times nat))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.51 ( (fun nat nat), nat, (let ((_let_0 (fun nat (fun nat nat)))) (let ((_let_1 (combc nat nat nat))) (hAPP _let_0 _let_0 _let_1 (hAPP (fun nat nat) _let_0 (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_0 _let_0 _let_1 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))), (one_one nat) ) 15.33/15.51 ( (fun (product_prod nat nat) bool), (fun (product_prod nat nat) bool), (collect (product_prod nat nat)), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat (fun nat bool)))) (hAPP _let_1 (fun (product_prod nat nat) bool) (product_prod_case nat nat bool) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat (fun nat bool) nat) (hAPP _let_1 _let_1 (combc nat nat bool) (fequal nat))) suc)))) ) 15.33/15.51 ( (fun (product_prod nat nat) bool), (fun nat (fun nat bool)), (product_prod_case nat nat bool), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat (fun nat bool)))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat (fun nat bool) nat) (hAPP _let_1 _let_1 (combc nat nat bool) (fequal nat))) suc))) ) 15.33/15.51 ( real, nat, (real_1 nat), (zero_zero nat) ) 15.33/15.51 ( real, nat, (real_1 nat), (hAPP nat nat suc (zero_zero nat)) ) 15.33/15.51 ( real, int, (real_1 int), (one_one int) ) 15.33/15.51 ( real, int, (real_1 int), (zero_zero int) ) 15.33/15.51 ( real, int, (number_number_of real), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.33/15.51 ( real, int, (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.33/15.51 ( real, int, (number_number_of real), min_1 ) 15.33/15.51 ( real, int, (number_number_of real), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.51 ( real, int, (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.33/15.51 ( real, int, (number_number_of real), (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.51 ( real, int, (number_number_of real), (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 15.33/15.51 ( real, real, ln, (one_one real) ) 15.33/15.51 ( real, real, (uminus_uminus real), (one_one real) ) 15.33/15.51 ( real, real, (uminus_uminus real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.51 ( real, real, (uminus_uminus real), (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.33/15.51 ( real, real, cos, (zero_zero real) ) 15.33/15.51 ( real, real, cos, pi ) 15.33/15.51 ( real, real, cos, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.51 ( real, real, cos, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.51 ( real, real, cos, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.33/15.51 ( real, real, cos, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.33/15.51 ( real, real, cos, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.33/15.51 ( real, real, cos, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.33/15.51 ( real, real, cos, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.33/15.51 ( real, real, cos, skv_5 ) 15.33/15.51 ( real, real, sqrt, (one_one real) ) 15.33/15.51 ( real, real, sqrt, (zero_zero real) ) 15.33/15.51 ( real, real, sqrt, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.51 ( real, real, sqrt, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.33/15.51 ( real, real, sin, (zero_zero real) ) 15.33/15.51 ( real, real, sin, pi ) 15.33/15.51 ( real, real, sin, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.51 ( real, real, sin, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.33/15.51 ( real, real, sin, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.33/15.51 ( real, real, sin, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.33/15.51 ( real, real, sin, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.33/15.51 ( real, real, sin, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.33/15.51 ( real, real, (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.51 ( real, real, (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.51 ( real, real, (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.33/15.51 ( real, real, (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.33/15.51 ( real, real, tan, (zero_zero real) ) 15.33/15.51 ( real, real, tan, pi ) 15.33/15.51 ( real, real, tan, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.33/15.51 ( real, real, tan, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.33/15.51 ( real, real, tan, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.33/15.51 ( real, real, (hAPP real (fun real real) (inverse_divide real) (one_one real)), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.51 ( real, real, (hAPP real (fun real real) (inverse_divide real) (one_one real)), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.33/15.51 ( real, real, (hAPP real (fun real real) (inverse_divide real) (one_one real)), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.51 ( real, real, (hAPP real (fun real real) (inverse_divide real) (one_one real)), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 15.33/15.51 ( real, real, (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 15.33/15.51 ( real, real, (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.33/15.51 ( real, real, (inverse_inverse real), (zero_zero real) ) 15.33/15.51 ( real, real, arctan, (one_one real) ) 15.33/15.51 ( real, real, arctan, (zero_zero real) ) 15.33/15.51 ( real, real, arctan, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.33/15.51 ( real, real, arctan, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))))) ) 15.33/15.51 ( real, real, (hAPP real (fun real real) (inverse_divide real) (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.51 ( real, real, (sgn_sgn real), (zero_zero real) ) 15.33/15.51 ( real, real, (hAPP real (fun real real) (inverse_divide real) (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.51 ( real, real, (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.33/15.51 ( real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real _let_0 (minus_minus real) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1))))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 15.33/15.51 ( real, real, (hAPP real (fun real real) (inverse_divide real) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.51 ( real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1))))))), pi ) 15.33/15.51 ( real, (fun real bool), (the real), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3)))))))))))))) ) 15.33/15.51 ( real, rat, ratreal, (zero_zero rat) ) 15.33/15.51 ( real, rat, ratreal, (one_one rat) ) 15.33/15.51 ( real, complex, re, (one_one complex) ) 15.33/15.51 ( real, complex, re, ii ) 15.33/15.51 ( real, complex, re, (zero_zero complex) ) 15.33/15.51 ( real, complex, im, (one_one complex) ) 15.33/15.51 ( real, complex, im, ii ) 15.33/15.51 ( real, complex, im, (zero_zero complex) ) 15.33/15.51 ( real, (fun nat real), (suminf real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat (fun nat nat)))) (let ((_let_3 (fun nat _let_0))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun _let_1 _let_3))) (let ((_let_6 (combb real _let_0 nat))) (let ((_let_7 (combc nat nat nat))) (hAPP _let_1 _let_1 (hAPP _let_3 (fun _let_1 _let_1) (combs nat real real) (hAPP _let_1 _let_3 (hAPP _let_4 _let_5 _let_6 (inverse_divide real)) (hAPP real _let_1 (hAPP _let_3 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_3 (hAPP _let_4 _let_5 _let_6 (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) (one_one real)))) (hAPP (fun nat nat) _let_1 (hAPP _let_1 (fun (fun nat nat) _let_1) (combb nat real nat) (real_1 nat)) (hAPP nat (fun nat nat) (hAPP _let_2 _let_2 _let_7 (hAPP (fun nat nat) _let_2 (hAPP _let_2 (fun (fun nat nat) _let_2) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_2 _let_2 _let_7 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))))))))))) ) 15.33/15.51 ( (fun real bool), real, (ord_less real), (one_one real) ) 15.33/15.51 ( (fun real bool), real, (ord_less real), (zero_zero real) ) 15.33/15.51 ( (fun real bool), real, (ord_less real), pi ) 15.33/15.51 ( (fun real bool), real, (ord_less real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.51 ( (fun real bool), real, (ord_less real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.33/15.51 ( (fun real bool), real, (ord_less real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.51 ( (fun real bool), real, (ord_less real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 15.33/15.51 ( (fun real bool), real, (ord_less_eq real), (zero_zero real) ) 15.33/15.51 ( (fun real bool), real, (ord_less_eq real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.51 ( (fun real bool), real, (ord_less_eq real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.51 ( (fun real bool), real, (ord_less_eq real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.51 ( (fun real bool), real, (ord_less_eq real), skv_5 ) 15.33/15.51 ( (fun real bool), real, (let ((_let_0 (fun real (fun real bool)))) (hAPP _let_0 _let_0 (combc real real bool) (ord_less_eq real))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.51 ( (fun real bool), real, (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun real _let_0))) (hAPP _let_2 _let_2 (combc real real bool) (hAPP _let_1 _let_2 (hAPP _let_2 (fun _let_1 _let_2) (combb real _let_0 real) (fequal real)) cos))))), (zero_zero real) ) 15.33/15.51 ( (fun real bool), (fun real bool), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun real _let_1))) (hAPP _let_2 (fun _let_0 _let_0) (combs real bool bool) (hAPP _let_0 _let_2 (hAPP (fun bool _let_1) (fun _let_0 _let_2) (combb bool _let_1 real) fconj) (hAPP real _let_0 (ord_less_eq real) (zero_zero real))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun real _let_0))) (let ((_let_4 (fun real _let_2))) (let ((_let_5 (combc real real bool))) (hAPP _let_0 _let_0 (hAPP _let_4 (fun _let_0 _let_0) (combs real bool bool) (hAPP _let_0 _let_4 (hAPP (fun bool _let_2) (fun _let_0 _let_4) (combb bool _let_2 real) fconj) (hAPP real _let_0 (hAPP _let_3 _let_3 _let_5 (ord_less_eq real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_3 _let_3 _let_5 (hAPP _let_1 _let_3 (hAPP _let_3 (fun _let_1 _let_3) (combb real _let_0 real) (fequal real)) cos)) (zero_zero real))))))))) ) 15.33/15.51 ( (fun real bool), (fun real bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun real (fun real bool)))) (let ((_let_2 (fun real _let_0))) (hAPP _let_2 (fun (fun real bool) (fun real bool)) (combs real bool bool) (hAPP (fun real bool) _let_2 (hAPP (fun bool _let_0) (fun (fun real bool) _let_2) (combb bool _let_0 real) fconj) (hAPP real (fun real bool) (hAPP _let_1 _let_1 (combc real real bool) (ord_less_eq real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun real _let_0))) (hAPP real _let_0 (hAPP _let_2 _let_2 (combc real real bool) (hAPP _let_1 _let_2 (hAPP _let_2 (fun _let_1 _let_2) (combb real _let_0 real) (fequal real)) cos)) (zero_zero real))))) ) 15.33/15.51 ( (fun real bool), (fun real bool), (collect real), (let ((_let_0 (fun int (fun int bool)))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real real))) (let ((_let_3 (real_1 int))) (let ((_let_4 (fun (fun int bool) bool))) (let ((_let_5 (fun bool bool))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun int _let_5))) (let ((_let_8 (fun (fun int bool) (fun int bool)))) (let ((_let_9 (fun (fun int bool) _let_7))) (let ((_let_10 (fun _let_0 (fun int bool)))) (let ((_let_11 (fEx int))) (let ((_let_12 (fun int real))) (let ((_let_13 (fun int _let_8))) (let ((_let_14 (fun (fun int bool) _let_0))) (let ((_let_15 (fun int _let_7))) (let ((_let_16 (fun _let_15 _let_13))) (let ((_let_17 (fun _let_0 _let_15))) (let ((_let_18 (fun real (fun int bool)))) (let ((_let_19 (fun real _let_0))) (let ((_let_20 (fun real _let_14))) (let ((_let_21 (fun real _let_13))) (let ((_let_22 (fun real _let_15))) (let ((_let_23 (fun int _let_12))) (let ((_let_24 (fun _let_23 _let_0))) (let ((_let_25 (fun real _let_24))) (let ((_let_26 (fun _let_12 (fun int bool)))) (let ((_let_27 (fun real _let_26))) (let ((_let_28 (fun _let_12 _let_12))) (let ((_let_29 (fun int _let_28))) (let ((_let_30 (fun int _let_2))) (hAPP _let_18 _let_1 (hAPP _let_4 (fun _let_18 _let_1) (combb (fun int bool) bool real) _let_11) (hAPP _let_19 _let_18 (hAPP _let_10 (fun _let_19 _let_18) (combb _let_0 (fun int bool) real) (hAPP _let_4 _let_10 (combb (fun int bool) bool int) _let_11)) (hAPP (fun int bool) _let_19 (hAPP _let_20 (fun (fun int bool) _let_19) (combc real (fun int bool) _let_0) (hAPP _let_21 _let_20 (hAPP (fun _let_13 _let_14) (fun _let_21 _let_20) (combb _let_13 _let_14 real) (combc int (fun int bool) (fun int bool))) (hAPP _let_22 _let_21 (hAPP _let_16 (fun _let_22 _let_21) (combb _let_15 _let_13 real) (hAPP (fun _let_7 _let_8) _let_16 (combb _let_7 _let_8 int) (combs int bool bool))) (hAPP _let_19 _let_22 (hAPP _let_17 (fun _let_19 _let_22) (combb _let_0 _let_15 real) (hAPP _let_9 _let_17 (combb (fun int bool) _let_7 int) (hAPP (fun bool _let_5) _let_9 (combb bool _let_5 int) fconj))) (hAPP _let_23 _let_19 (hAPP _let_25 (fun _let_23 _let_19) (combc real _let_23 _let_0) (hAPP _let_27 _let_25 (hAPP (fun _let_26 _let_24) (fun _let_27 _let_25) (combb _let_26 _let_24 real) (combb _let_12 (fun int bool) int)) (hAPP _let_6 _let_27 (hAPP (fun _let_1 _let_26) (fun _let_6 _let_27) (combb _let_1 _let_26 real) (combb real bool int)) (fequal real)))) (hAPP _let_12 _let_23 (hAPP _let_29 (fun _let_12 _let_23) (combc int _let_12 _let_12) (hAPP _let_30 _let_29 (hAPP (fun _let_2 _let_28) (fun _let_30 _let_29) (combb _let_2 _let_28 int) (combb real real int)) (hAPP _let_12 _let_30 (hAPP (fun real _let_2) (fun _let_12 _let_30) (combb real _let_2 int) (inverse_divide real)) _let_3))) _let_3)))))) (hAPP (fun int bool) (fun int bool) (hAPP _let_5 _let_8 (combb bool bool int) fNot) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (fequal int)) (zero_zero int))))))))))))))))))))))))))))))))))))) ) 15.33/15.51 ( (fun real bool), (fun real bool), (collect real), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real real))) (let ((_let_3 (fun nat (fun nat bool)))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun (fun nat real) (fun nat real)))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun (fun nat bool) (fun nat bool)))) (let ((_let_8 (fun int real))) (let ((_let_9 (fun nat _let_4))) (let ((_let_10 (fun (fun nat bool) _let_9))) (let ((_let_11 (fun real _let_0))) (let ((_let_12 (fun int _let_2))) (let ((_let_13 (fun real (fun int (fun nat bool))))) (let ((_let_14 (fun (fun int (fun nat bool)) _let_0))) (let ((_let_15 (fun (fun nat bool) (fun int (fun nat bool))))) (let ((_let_16 (fun real _let_15))) (let ((_let_17 (fun int _let_7))) (let ((_let_18 (fun real _let_17))) (let ((_let_19 (fun int _let_9))) (let ((_let_20 (fun real _let_19))) (let ((_let_21 (fun _let_19 _let_17))) (let ((_let_22 (fun (fun int (fun nat bool)) _let_19))) (let ((_let_23 (fun int (fun nat real)))) (let ((_let_24 (fun _let_23 (fun int (fun nat bool))))) (let ((_let_25 (fun real _let_24))) (let ((_let_26 (fun (fun nat real) (fun nat bool)))) (let ((_let_27 (fun real _let_26))) (let ((_let_28 (fun int _let_5))) (hAPP _let_11 _let_1 (hAPP (fun _let_0 bool) (fun _let_11 _let_1) (combb _let_0 bool real) (fEx int)) (hAPP _let_13 _let_11 (hAPP _let_14 (fun _let_13 _let_11) (combb (fun int (fun nat bool)) _let_0 real) (hAPP (fun (fun nat bool) bool) _let_14 (combb (fun nat bool) bool int) (fEx nat))) (hAPP (fun nat bool) _let_13 (hAPP _let_16 (fun (fun nat bool) _let_13) (combc real (fun nat bool) (fun int (fun nat bool))) (hAPP _let_18 _let_16 (hAPP (fun _let_17 _let_15) (fun _let_18 _let_16) (combb _let_17 _let_15 real) (combc int (fun nat bool) (fun nat bool))) (hAPP _let_20 _let_18 (hAPP _let_21 (fun _let_20 _let_18) (combb _let_19 _let_17 real) (hAPP (fun _let_9 _let_7) _let_21 (combb _let_9 _let_7 int) (combs nat bool bool))) (hAPP _let_13 _let_20 (hAPP _let_22 (fun _let_13 _let_20) (combb (fun int (fun nat bool)) _let_19 real) (hAPP _let_10 _let_22 (combb (fun nat bool) _let_9 int) (hAPP (fun bool _let_4) _let_10 (combb bool _let_4 nat) fconj))) (hAPP _let_23 _let_13 (hAPP _let_25 (fun _let_23 _let_13) (combc real _let_23 (fun int (fun nat bool))) (hAPP _let_27 _let_25 (hAPP (fun _let_26 _let_24) (fun _let_27 _let_25) (combb _let_26 _let_24 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_6 _let_27 (hAPP (fun _let_1 _let_26) (fun _let_6 _let_27) (combb _let_1 _let_26 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_23 (hAPP _let_28 (fun (fun nat real) _let_23) (combc int (fun nat real) (fun nat real)) (hAPP _let_12 _let_28 (hAPP (fun _let_2 _let_5) (fun _let_12 _let_28) (combb _let_2 _let_5 int) (combb real real nat)) (hAPP _let_8 _let_12 (hAPP (fun real _let_2) (fun _let_8 _let_12) (combb real _let_2 int) (inverse_divide real)) (real_1 int)))) (real_1 nat))))))) (hAPP (fun nat bool) (fun nat bool) (hAPP _let_4 _let_7 (combb bool bool nat) fNot) (hAPP nat (fun nat bool) (hAPP _let_3 _let_3 (combc nat nat bool) (fequal nat)) (zero_zero nat))))))))))))))))))))))))))))))))))) ) 15.33/15.51 ( (fun real bool), (fun nat real), (sums real), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (hAPP real _let_1 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc))) ) 15.33/15.51 ( (fun real bool), (fun real (fun int bool)), (let ((_let_0 (fun int bool))) (hAPP (fun _let_0 bool) (fun (fun real _let_0) (fun real bool)) (combb _let_0 bool real) (fEx int))), (let ((_let_0 (fun int (fun int bool)))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real real))) (let ((_let_3 (real_1 int))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun int _let_4))) (let ((_let_7 (fun (fun int bool) (fun int bool)))) (let ((_let_8 (fun (fun int bool) _let_6))) (let ((_let_9 (fun _let_0 (fun int bool)))) (let ((_let_10 (fun int real))) (let ((_let_11 (fun int _let_7))) (let ((_let_12 (fun (fun int bool) _let_0))) (let ((_let_13 (fun int _let_6))) (let ((_let_14 (fun _let_13 _let_11))) (let ((_let_15 (fun _let_0 _let_13))) (let ((_let_16 (fun real (fun int bool)))) (let ((_let_17 (fun real _let_0))) (let ((_let_18 (fun real _let_12))) (let ((_let_19 (fun real _let_11))) (let ((_let_20 (fun real _let_13))) (let ((_let_21 (fun int _let_10))) (let ((_let_22 (fun _let_21 _let_0))) (let ((_let_23 (fun real _let_22))) (let ((_let_24 (fun _let_10 (fun int bool)))) (let ((_let_25 (fun real _let_24))) (let ((_let_26 (fun _let_10 _let_10))) (let ((_let_27 (fun int _let_26))) (let ((_let_28 (fun int _let_2))) (hAPP _let_17 _let_16 (hAPP _let_9 (fun _let_17 _let_16) (combb _let_0 (fun int bool) real) (hAPP (fun (fun int bool) bool) _let_9 (combb (fun int bool) bool int) (fEx int))) (hAPP (fun int bool) _let_17 (hAPP _let_18 (fun (fun int bool) _let_17) (combc real (fun int bool) _let_0) (hAPP _let_19 _let_18 (hAPP (fun _let_11 _let_12) (fun _let_19 _let_18) (combb _let_11 _let_12 real) (combc int (fun int bool) (fun int bool))) (hAPP _let_20 _let_19 (hAPP _let_14 (fun _let_20 _let_19) (combb _let_13 _let_11 real) (hAPP (fun _let_6 _let_7) _let_14 (combb _let_6 _let_7 int) (combs int bool bool))) (hAPP _let_17 _let_20 (hAPP _let_15 (fun _let_17 _let_20) (combb _let_0 _let_13 real) (hAPP _let_8 _let_15 (combb (fun int bool) _let_6 int) (hAPP (fun bool _let_4) _let_8 (combb bool _let_4 int) fconj))) (hAPP _let_21 _let_17 (hAPP _let_23 (fun _let_21 _let_17) (combc real _let_21 _let_0) (hAPP _let_25 _let_23 (hAPP (fun _let_24 _let_22) (fun _let_25 _let_23) (combb _let_24 _let_22 real) (combb _let_10 (fun int bool) int)) (hAPP _let_5 _let_25 (hAPP (fun _let_1 _let_24) (fun _let_5 _let_25) (combb _let_1 _let_24 real) (combb real bool int)) (fequal real)))) (hAPP _let_10 _let_21 (hAPP _let_27 (fun _let_10 _let_21) (combc int _let_10 _let_10) (hAPP _let_28 _let_27 (hAPP (fun _let_2 _let_26) (fun _let_28 _let_27) (combb _let_2 _let_26 int) (combb real real int)) (hAPP _let_10 _let_28 (hAPP (fun real _let_2) (fun _let_10 _let_28) (combb real _let_2 int) (inverse_divide real)) _let_3))) _let_3)))))) (hAPP (fun int bool) (fun int bool) (hAPP _let_4 _let_7 (combb bool bool int) fNot) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (fequal int)) (zero_zero int)))))))))))))))))))))))))))))))))) ) 15.33/15.51 ( (fun real bool), (fun real (fun int bool)), (let ((_let_0 (fun int bool))) (hAPP (fun _let_0 bool) (fun (fun real _let_0) (fun real bool)) (combb _let_0 bool real) (fEx int))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real real))) (let ((_let_3 (fun nat (fun nat bool)))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun (fun nat real) (fun nat real)))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun (fun nat bool) (fun nat bool)))) (let ((_let_8 (fun int real))) (let ((_let_9 (fun nat _let_4))) (let ((_let_10 (fun (fun nat bool) _let_9))) (let ((_let_11 (fun real _let_0))) (let ((_let_12 (fun int _let_2))) (let ((_let_13 (fun real (fun int (fun nat bool))))) (let ((_let_14 (fun (fun int (fun nat bool)) _let_0))) (let ((_let_15 (fun (fun nat bool) (fun int (fun nat bool))))) (let ((_let_16 (fun real _let_15))) (let ((_let_17 (fun int _let_7))) (let ((_let_18 (fun real _let_17))) (let ((_let_19 (fun int _let_9))) (let ((_let_20 (fun real _let_19))) (let ((_let_21 (fun _let_19 _let_17))) (let ((_let_22 (fun (fun int (fun nat bool)) _let_19))) (let ((_let_23 (fun int (fun nat real)))) (let ((_let_24 (fun _let_23 (fun int (fun nat bool))))) (let ((_let_25 (fun real _let_24))) (let ((_let_26 (fun (fun nat real) (fun nat bool)))) (let ((_let_27 (fun real _let_26))) (let ((_let_28 (fun int _let_5))) (hAPP _let_13 _let_11 (hAPP _let_14 (fun _let_13 _let_11) (combb (fun int (fun nat bool)) _let_0 real) (hAPP (fun (fun nat bool) bool) _let_14 (combb (fun nat bool) bool int) (fEx nat))) (hAPP (fun nat bool) _let_13 (hAPP _let_16 (fun (fun nat bool) _let_13) (combc real (fun nat bool) (fun int (fun nat bool))) (hAPP _let_18 _let_16 (hAPP (fun _let_17 _let_15) (fun _let_18 _let_16) (combb _let_17 _let_15 real) (combc int (fun nat bool) (fun nat bool))) (hAPP _let_20 _let_18 (hAPP _let_21 (fun _let_20 _let_18) (combb _let_19 _let_17 real) (hAPP (fun _let_9 _let_7) _let_21 (combb _let_9 _let_7 int) (combs nat bool bool))) (hAPP _let_13 _let_20 (hAPP _let_22 (fun _let_13 _let_20) (combb (fun int (fun nat bool)) _let_19 real) (hAPP _let_10 _let_22 (combb (fun nat bool) _let_9 int) (hAPP (fun bool _let_4) _let_10 (combb bool _let_4 nat) fconj))) (hAPP _let_23 _let_13 (hAPP _let_25 (fun _let_23 _let_13) (combc real _let_23 (fun int (fun nat bool))) (hAPP _let_27 _let_25 (hAPP (fun _let_26 _let_24) (fun _let_27 _let_25) (combb _let_26 _let_24 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_6 _let_27 (hAPP (fun _let_1 _let_26) (fun _let_6 _let_27) (combb _let_1 _let_26 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_23 (hAPP _let_28 (fun (fun nat real) _let_23) (combc int (fun nat real) (fun nat real)) (hAPP _let_12 _let_28 (hAPP (fun _let_2 _let_5) (fun _let_12 _let_28) (combb _let_2 _let_5 int) (combb real real nat)) (hAPP _let_8 _let_12 (hAPP (fun real _let_2) (fun _let_8 _let_12) (combb real _let_2 int) (inverse_divide real)) (real_1 int)))) (real_1 nat))))))) (hAPP (fun nat bool) (fun nat bool) (hAPP _let_4 _let_7 (combb bool bool nat) fNot) (hAPP nat (fun nat bool) (hAPP _let_3 _let_3 (combc nat nat bool) (fequal nat)) (zero_zero nat)))))))))))))))))))))))))))))))))) ) 15.33/15.51 ( (fun real real), nat, root, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.51 ( (fun real real), real, (minus_minus real), (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))) ) 15.33/15.51 ( (fun real real), real, (inverse_divide real), (one_one real) ) 15.33/15.51 ( (fun real real), real, (inverse_divide real), pi ) 15.33/15.51 ( (fun real real), real, (inverse_divide real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.33/15.51 ( (fun real real), real, (inverse_divide real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.33/15.52 ( (fun real real), real, (inverse_divide real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.52 ( (fun real real), real, (times_times real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.52 ( (fun real real), real, (times_times real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.52 ( (fun real real), real, (times_times real), (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 15.33/15.52 ( (fun real real), (fun real real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)))), sin ) 15.33/15.52 ( rat, int, (hAPP int (fun int rat) fract (zero_zero int)), (one_one int) ) 15.33/15.52 ( rat, int, (hAPP int (fun int rat) fract (one_one int)), (one_one int) ) 15.33/15.52 ( rat, rat, (sgn_sgn rat), (zero_zero rat) ) 15.33/15.52 ( rat, (product_prod int int), frct, (let ((_let_0 (one_one int))) (let ((_let_1 (product_prod int int))) (hAPP int _let_1 (hAPP int (fun int _let_1) (product_Pair int int) _let_0) _let_0))) ) 15.33/15.52 ( (fun int rat), int, fract, (one_one int) ) 15.33/15.52 ( (fun int rat), int, fract, (zero_zero int) ) 15.33/15.52 ( (fun nat (fun nat bool)), (fun nat nat), (let ((_let_0 (fun nat (fun nat bool)))) (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat (fun nat bool) nat) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat)))), suc ) 15.33/15.52 ( (fun nat (fun nat bool)), (fun nat (fun nat bool)), (combc nat nat bool), (fequal nat) ) 15.33/15.52 ( (fun nat int), int, (power_power int), s ) 15.33/15.52 ( (fun nat int), int, (power_power int), s1 ) 15.33/15.52 ( (fun nat int), int, (power_power int), skv_14 ) 15.33/15.52 ( complex, nat, (hAPP complex (fun nat complex) (power_power complex) ii), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.52 ( complex, int, (number_number_of complex), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.33/15.52 ( complex, int, (number_number_of complex), min_1 ) 15.33/15.52 ( complex, real, cis, (zero_zero real) ) 15.33/15.52 ( complex, real, (hAPP real (fun real complex) complex_1 (zero_zero real)), (one_one real) ) 15.33/15.52 ( complex, real, (hAPP real (fun real complex) complex_1 (zero_zero real)), (zero_zero real) ) 15.33/15.52 ( complex, real, (of_real complex), pi ) 15.33/15.52 ( complex, real, (of_real complex), (hAPP int real (number_number_of real) min_1) ) 15.33/15.52 ( complex, real, (of_real complex), (hAPP real real (uminus_uminus real) (one_one real)) ) 15.33/15.52 ( complex, real, (hAPP real (fun real complex) complex_1 (one_one real)), (zero_zero real) ) 15.33/15.52 ( complex, complex, (inverse_inverse complex), ii ) 15.33/15.52 ( complex, complex, expi, (zero_zero complex) ) 15.33/15.52 ( complex, complex, expi, (let ((_let_0 (fun complex complex))) (let ((_let_1 (times_times complex))) (hAPP complex complex (hAPP complex _let_0 _let_1 (hAPP complex complex (hAPP complex _let_0 _let_1 (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi))) ii))) ) 15.33/15.52 ( complex, complex, (uminus_uminus complex), (one_one complex) ) 15.33/15.52 ( complex, complex, (uminus_uminus complex), ii ) 15.33/15.52 ( complex, complex, cnj, (one_one complex) ) 15.33/15.52 ( complex, complex, cnj, ii ) 15.33/15.52 ( complex, complex, cnj, (zero_zero complex) ) 15.33/15.52 ( complex, complex, (hAPP complex (fun complex complex) (times_times complex) ii), ii ) 15.33/15.52 ( complex, complex, (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real complex (of_real complex) pi) ) 15.33/15.52 ( complex, complex, (let ((_let_0 (fun complex complex))) (let ((_let_1 (times_times complex))) (hAPP complex _let_0 _let_1 (hAPP complex complex (hAPP complex _let_0 _let_1 (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi))))), ii ) 15.33/15.52 ( (fun nat real), (fun nat nat), (let ((_let_0 (fun nat real))) (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat real nat) (real_1 nat))), suc ) 15.33/15.52 ( (fun nat real), (fun nat nat), (let ((_let_0 (fun nat real))) (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat real nat) (real_1 nat))), (let ((_let_0 (fun nat (fun nat nat)))) (let ((_let_1 (combc nat nat nat))) (hAPP nat (fun nat nat) (hAPP _let_0 _let_0 _let_1 (hAPP (fun nat nat) _let_0 (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_0 _let_0 _let_1 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))) ) 15.33/15.52 ( (fun nat real), (fun nat nat), (let ((_let_0 (fun nat real))) (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat real nat) (hAPP real _let_0 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))), suc ) 15.33/15.52 ( (fun nat real), real, (power_power real), (hAPP int real (number_number_of real) min_1) ) 15.33/15.52 ( (fun nat real), real, (power_power real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.52 ( (fun nat real), real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (hAPP _let_2 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 nat) (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1))))))), (one_one real) ) 15.33/15.52 ( (fun nat real), (fun nat real), (diffs real), sin_coeff ) 15.33/15.52 ( (fun nat real), (fun nat real), (let ((_let_0 (fun nat real))) (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real))), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))) ) 15.33/15.52 ( (fun nat real), (fun nat real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (let ((_let_3 (fun real _let_0))) (let ((_let_4 (fun _let_1 _let_2))) (let ((_let_5 (combb real _let_0 nat))) (hAPP _let_2 (fun _let_1 _let_1) (combs nat real real) (hAPP _let_1 _let_2 (hAPP _let_3 _let_4 _let_5 (inverse_divide real)) (hAPP real _let_1 (hAPP _let_2 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_2 (hAPP _let_3 _let_4 _let_5 (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) (one_one real)))))))))), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat (fun nat nat)))) (let ((_let_2 (combc nat nat nat))) (hAPP (fun nat nat) _let_0 (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat real nat) (real_1 nat)) (hAPP nat (fun nat nat) (hAPP _let_1 _let_1 _let_2 (hAPP (fun nat nat) _let_1 (hAPP _let_1 (fun (fun nat nat) _let_1) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_1 _let_1 _let_2 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))))) ) 15.33/15.52 ( (fun int (fun int int)), (fun int int), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)))), (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.52 ( (fun int (fun int int)), (fun int int), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)))), (let ((_let_0 (fun int int))) (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.33/15.52 ( (fun int (fun int int)), (fun int int), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun _let_0 _let_1))) (let ((_let_3 (fun _let_0 _let_0))) (let ((_let_4 (fun int _let_3))) (hAPP _let_4 _let_2 (combc int _let_0 _let_0) (hAPP _let_1 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_1 _let_4) (combb _let_0 _let_3 int) (combb int int int)) (hAPP _let_0 _let_1 (hAPP _let_1 _let_2 (combb int _let_0 int) (plus_plus int)) (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))))))), (let ((_let_0 (fun int int))) (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.33/15.52 ( (fun int (fun int int)), (fun int (fun int int)), (combc int int int), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)) (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 15.33/15.52 ( (fun complex complex), complex, (times_times complex), ii ) 15.33/15.52 ( (fun complex complex), complex, (times_times complex), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.52 ( (fun complex complex), complex, (times_times complex), (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 15.33/15.52 ( (fun real complex), real, complex_1, (one_one real) ) 15.33/15.52 ( (fun real complex), real, complex_1, (zero_zero real) ) 15.33/15.52 ( (product_prod int int), int, (hAPP int (fun int (product_prod int int)) (product_Pair int int) (zero_zero int)), (one_one int) ) 15.33/15.52 ( (product_prod int int), int, (hAPP int (fun int (product_prod int int)) (product_Pair int int) s), (one_one int) ) 15.33/15.52 ( (product_prod int int), int, (hAPP int (fun int (product_prod int int)) (product_Pair int int) (one_one int)), (one_one int) ) 15.33/15.52 ( (product_prod int int), rat, quotient_of, (zero_zero rat) ) 15.33/15.52 ( (product_prod int int), rat, quotient_of, (one_one rat) ) 15.33/15.52 ( (fun int (product_prod int int)), int, (product_Pair int int), (one_one int) ) 15.33/15.52 ( (fun int (product_prod int int)), int, (product_Pair int int), (zero_zero int) ) 15.33/15.52 ( (fun int (product_prod int int)), int, (product_Pair int int), s ) 15.33/15.52 ( (fun (fun nat bool) bool), (fun nat int), (nat_tr1645093318rphism nat int), (semiring_1_of_nat int) ) 15.33/15.52 ( (fun (fun int bool) bool), int, (member int), (one_one int) ) 15.33/15.52 ( (fun (fun int bool) bool), (fun int nat), (nat_tr1645093318rphism int nat), nat_1 ) 15.33/15.52 ( quickcheck_code_int, int, (number_number_of quickcheck_code_int), (hAPP int int bit1 pls) ) 15.33/15.52 ( quickcheck_code_int, int, quickcheck_of_int, (one_one int) ) 15.33/15.52 ( quickcheck_code_int, int, quickcheck_of_int, (zero_zero int) ) 15.33/15.52 ( (fun nat (fun nat nat)), (fun nat nat), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat _let_0))) (hAPP _let_1 (fun _let_0 _let_1) (combb nat _let_0 nat) (plus_plus nat)))), (let ((_let_0 (fun nat (fun nat nat)))) (hAPP nat (fun nat nat) (hAPP _let_0 _let_0 (combc nat nat nat) (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.33/15.52 ( (fun nat (fun nat nat)), (fun nat (fun nat nat)), (combc nat nat nat), (times_times nat) ) 15.33/15.52 ( (fun nat (fun nat nat)), (fun nat (fun nat nat)), (combc nat nat nat), (let ((_let_0 (fun nat (fun nat nat)))) (hAPP (fun nat nat) _let_0 (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_0 _let_0 (combc nat nat nat) (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.33/15.52 ( (fun nat complex), complex, (power_power complex), ii ) 15.33/15.52 ( (fun nat (fun real real)), (fun nat real), (let ((_let_0 (fun real real))) (hAPP (fun real _let_0) (fun (fun nat real) (fun nat _let_0)) (combb real _let_0 nat) (inverse_divide real))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (hAPP real _let_1 (hAPP _let_2 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 nat) (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) (one_one real))))) ) 15.33/15.52 ( (fun nat (fun real real)), (fun nat real), (let ((_let_0 (fun real real))) (hAPP (fun real _let_0) (fun (fun nat real) (fun nat _let_0)) (combb real _let_0 nat) (times_times real))), (hAPP real (fun nat real) (power_power real) (hAPP int real (number_number_of real) min_1)) ) 15.33/15.52 ( (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)), (fun real real), (combb real real nat), (inverse_inverse real) ) 15.33/15.52 ( (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)), (fun nat (fun real real)), (combs nat real real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (let ((_let_3 (fun real _let_0))) (let ((_let_4 (fun _let_1 _let_2))) (let ((_let_5 (combb real _let_0 nat))) (hAPP _let_1 _let_2 (hAPP _let_3 _let_4 _let_5 (inverse_divide real)) (hAPP real _let_1 (hAPP _let_2 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_2 (hAPP _let_3 _let_4 _let_5 (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) (one_one real))))))))) ) 15.33/15.52 ( (fun real (fun real real)), (fun real real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)))), cos ) 15.33/15.52 ( (fun (fun nat real) (fun nat (fun real real))), (fun real (fun real real)), (combb real (fun real real) nat), (inverse_divide real) ) 15.33/15.52 ( (fun (fun nat real) (fun nat (fun real real))), (fun real (fun real real)), (combb real (fun real real) nat), (times_times real) ) 15.33/15.52 ( (fun (fun nat nat) (fun nat real)), (fun nat real), (combb nat real nat), (real_1 nat) ) 15.33/15.52 ( (fun (fun nat nat) (fun nat real)), (fun nat real), (combb nat real nat), (hAPP real (fun nat real) (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.33/15.52 ( (fun (filter nat) bool), real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 (fun real (fun (filter nat) bool)) (tendsto nat real) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))))), (zero_zero real) ) 15.33/15.52 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), (fun int int), (product_apsnd int int int), (uminus_uminus int) ) 15.33/15.52 ( (let ((_let_0 (fun int int))) (fun _let_0 (fun int _let_0))), (fun int (fun int int)), (combb int (fun int int) int), (plus_plus int) ) 15.33/15.52 ( (let ((_let_0 (fun int int))) (fun _let_0 (fun int _let_0))), (let ((_let_0 (fun int int))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun int int))) (combc int _let_0 _let_0)), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun _let_0 _let_0))) (let ((_let_3 (fun int _let_2))) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 int) (combb int int int)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)) (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))))) ) 15.33/15.52 ( code_code_numeral, int, (number_number_of code_code_numeral), pls ) 15.33/15.52 ( code_code_numeral, int, (number_number_of code_code_numeral), (hAPP int int bit1 pls) ) 15.33/15.52 ( code_code_numeral, code_code_numeral, (hAPP code_code_numeral (fun code_code_numeral code_code_numeral) (minus_minus code_code_numeral) (zero_zero code_code_numeral)), (one_one code_code_numeral) ) 15.33/15.52 ( (fun int (fun int (fun int bool))), (fun int (fun int int)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun _let_2 _let_1))) (hAPP _let_3 (fun (fun int _let_2) (fun int _let_1)) (combb _let_2 _let_1 int) (hAPP _let_1 _let_3 (combb int _let_0 int) (fequal int))))))), int_gcd ) 15.33/15.52 ( (fun int (fun int (fun int bool))), (fun int (fun int (fun int bool))), (combc int int (fun int bool)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int _let_1))) (let ((_let_5 (fun _let_2 _let_1))) (hAPP _let_4 _let_4 (hAPP (fun _let_1 _let_1) (fun _let_4 _let_4) (combb _let_1 _let_1 int) (combc int int bool)) (hAPP _let_3 _let_4 (hAPP _let_5 (fun _let_3 _let_4) (combb _let_2 _let_1 int) (hAPP _let_1 _let_5 (combb int _let_0 int) (fequal int))) int_gcd)))))))) ) 15.33/15.52 ( (fun int (fun int (fun int bool))), (fun int (fun int (fun int bool))), (let ((_let_0 (fun int (fun int bool)))) (let ((_let_1 (fun int _let_0))) (hAPP (fun _let_0 _let_0) (fun _let_1 _let_1) (combb _let_0 _let_0 int) (combc int int bool)))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int _let_1))) (let ((_let_5 (fun _let_2 _let_1))) (hAPP _let_3 _let_4 (hAPP _let_5 (fun _let_3 _let_4) (combb _let_2 _let_1 int) (hAPP _let_1 _let_5 (combb int _let_0 int) (fequal int))) int_gcd))))))) ) 15.33/15.52 ( (fun real (fun real bool)), (fun real real), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (hAPP _let_1 (fun (fun real real) _let_1) (combb real _let_0 real) (fequal real)))), cos ) 15.33/15.52 ( (fun real (fun real bool)), (fun real (fun real bool)), (combc real real bool), (ord_less_eq real) ) 15.33/15.52 ( (fun real (fun real bool)), (fun real (fun real bool)), (combc real real bool), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun real _let_0))) (hAPP _let_1 _let_2 (hAPP _let_2 (fun _let_1 _let_2) (combb real _let_0 real) (fequal real)) cos)))) ) 15.33/15.52 ( (fun real (fun nat real)), (fun nat (fun real real)), (combc nat real real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 nat) (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))))) ) 15.33/15.52 ( (let ((_let_0 (fun real real))) (fun _let_0 _let_0)), (fun real (fun real real)), (combs real real real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos))) ) 15.33/15.52 ( (let ((_let_0 (fun real real))) (fun _let_0 (fun real _let_0))), (fun real (fun real real)), (combb real (fun real real) real), (inverse_divide real) ) 15.33/15.52 ( (fun (product_prod int int) bool), int, (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 _let_0))) (let ((_let_3 (fun _let_1 int))) (hAPP _let_2 (fun int (fun _let_1 bool)) (combc _let_1 int bool) (hAPP _let_3 _let_2 (hAPP (fun int _let_0) (fun _let_3 _let_2) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))))))), (zero_zero int) ) 15.33/15.52 ( (fun (product_prod int int) bool), (fun int (fun int bool)), (product_prod_case int int bool), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun int _let_1))) (let ((_let_6 (fun int _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (fun _let_2 _let_1))) (let ((_let_9 (fun _let_1 _let_1))) (hAPP _let_1 _let_1 (hAPP _let_7 _let_9 (combb _let_0 _let_0 int) (hAPP _let_6 _let_7 (combs int bool bool) (hAPP _let_0 _let_6 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 int) fconj) (hAPP int _let_0 (ord_less int) (zero_zero int))))) (hAPP int _let_1 (hAPP _let_5 _let_5 (combc int int _let_0) (hAPP _let_5 _let_5 (hAPP _let_9 (fun _let_5 _let_5) (combb _let_1 _let_1 int) (combc int int bool)) (hAPP _let_3 _let_5 (hAPP _let_8 (fun _let_3 _let_5) (combb _let_2 _let_1 int) (hAPP _let_1 _let_8 (combb int _let_0 int) (fequal int))) int_gcd))) (one_one int))))))))))))) ) 15.33/15.52 ( (fun (product_prod int int) bool), (fun (product_prod int int) bool), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 bool))) (hAPP (fun bool bool) (fun _let_1 _let_1) (combb bool bool _let_0) fNot))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun _let_1 _let_0))) (let ((_let_4 (fun _let_1 int))) (hAPP int _let_2 (hAPP _let_3 (fun int _let_2) (combc _let_1 int bool) (hAPP _let_4 _let_3 (hAPP (fun int _let_0) (fun _let_4 _let_3) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))) ) 15.33/15.52 ( (fun int (fun (product_prod int int) bool)), (fun (product_prod int int) (fun int bool)), (combc (product_prod int int) int bool), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 _let_0))) (let ((_let_3 (fun _let_1 int))) (hAPP _let_3 _let_2 (hAPP (fun int _let_0) (fun _let_3 _let_2) (combb int _let_0 _let_1) (fequal int)) (product_snd int int)))))) ) 15.33/15.52 ( (fun real (fun (filter nat) bool)), (fun nat real), (tendsto nat real), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))) ) 15.33/15.52 ( (fun code_code_numeral code_code_numeral), code_code_numeral, (minus_minus code_code_numeral), (zero_zero code_code_numeral) ) 15.33/15.52 ( (fun int (fun bool bool)), (fun int bool), (let ((_let_0 (fun bool bool))) (hAPP (fun bool _let_0) (fun (fun int bool) (fun int _let_0)) (combb bool _let_0 int) fconj)), (hAPP int (fun int bool) (ord_less int) (zero_zero int)) ) 15.33/15.52 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), (fun bool bool), (combb bool bool int), fNot ) 15.33/15.52 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), (fun int (fun bool bool)), (combs int bool bool), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun int _let_1))) (hAPP _let_0 _let_2 (hAPP (fun bool _let_1) (fun _let_0 _let_2) (combb bool _let_1 int) fconj) (hAPP int _let_0 (ord_less int) (zero_zero int)))))) ) 15.33/15.52 ( (fun (fun int bool) (fun int (fun bool bool))), (fun bool (fun bool bool)), (combb bool (fun bool bool) int), fconj ) 15.33/15.52 ( (let ((_let_0 (fun int bool))) (fun (fun int _let_0) _let_0)), (fun (fun int bool) bool), (combb (fun int bool) bool int), (fEx int) ) 15.33/15.52 ( (fun int (fun (fun int int) (fun int bool))), (fun int (fun int bool)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun (fun int int) _let_0))) (hAPP (fun _let_0 _let_1) (fun (fun int _let_0) (fun int _let_1)) (combb _let_0 _let_1 int) (combb int bool int)))), (fequal int) ) 15.33/15.52 ( (fun (fun int int) (fun int (fun int bool))), (fun int (fun int bool)), (combb int (fun int bool) int), (fequal int) ) 15.33/15.52 ( (fun (fun int int) (fun int (fun int bool))), (fun int (fun (fun int int) (fun int bool))), (combc int (fun int int) (fun int bool)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun (fun int int) _let_0))) (let ((_let_3 (fun int _let_2))) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 int) (combb int bool int)) (fequal int)))))) ) 15.33/15.52 ( (let ((_let_0 (fun int bool))) (fun (fun int _let_0) (fun int (fun (fun int int) _let_0)))), (let ((_let_0 (fun int bool))) (fun _let_0 (fun (fun int int) _let_0))), (let ((_let_0 (fun int bool))) (combb _let_0 (fun (fun int int) _let_0) int)), (combb int bool int) ) 15.33/15.52 ( (filter real), real, (at real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.52 ( (fun (filter real) bool), real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 (fun real (fun (filter real) bool)) (tendsto real real) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin)))), (zero_zero real) ) 15.33/15.52 ( (fun real (fun (filter real) bool)), (fun real real), (tendsto real real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))) ) 15.33/15.52 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), (let ((_let_0 (product_prod int int))) (collect (product_prod _let_0 _let_0))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun _let_2 (fun _let_2 bool)))) (let ((_let_5 (fun (fun _let_2 bool) (fun _let_2 bool)))) (let ((_let_6 (fun _let_2 _let_5))) (let ((_let_7 (fun _let_4 _let_4))) (let ((_let_8 (fun _let_2 _let_3))) (let ((_let_9 (fun _let_2 _let_0))) (let ((_let_10 (fun _let_2 int))) (let ((_let_11 (fun _let_10 _let_9))) (let ((_let_12 (hAPP (fun int _let_0) _let_11 (combb int _let_0 _let_2) (fequal int)))) (let ((_let_13 (product_snd int int))) (let ((_let_14 (hAPP (fun _let_2 bool) _let_8 (hAPP (fun bool _let_3) (fun (fun _let_2 bool) _let_8) (combb bool _let_3 _let_2) fconj) (hAPP (fun _let_2 bool) (fun _let_2 bool) (hAPP _let_3 _let_5 (combb bool bool _let_2) fNot) (hAPP int (fun _let_2 bool) (hAPP _let_9 (fun int (fun _let_2 bool)) (combc _let_2 int bool) (hAPP _let_10 _let_9 _let_12 _let_13)) (zero_zero int)))))) (let ((_let_15 (fun _let_2 _let_10))) (let ((_let_16 (fun _let_10 (fun _let_2 bool)))) (let ((_let_17 (fun _let_2 _let_16))) (let ((_let_18 (fun _let_2 _let_9))) (let ((_let_19 (fun _let_10 _let_10))) (let ((_let_20 (fun _let_2 _let_19))) (let ((_let_21 (fun _let_10 _let_15))) (let ((_let_22 (fun _let_2 _let_1))) (let ((_let_23 (hAPP _let_10 _let_22 (hAPP (fun int _let_1) (fun _let_10 _let_22) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (let ((_let_24 (fun int _let_10))) (hAPP _let_4 (fun (product_prod _let_2 _let_2) bool) (product_prod_case _let_2 _let_2 bool) (hAPP _let_4 _let_4 (hAPP _let_6 _let_7 (combs _let_2 (fun _let_2 bool) (fun _let_2 bool)) (hAPP _let_8 _let_6 (hAPP (fun _let_3 _let_5) (fun _let_8 _let_6) (combb _let_3 _let_5 _let_2) (combb bool bool _let_2)) _let_14)) (hAPP _let_4 _let_4 (hAPP _let_5 _let_7 (combb (fun _let_2 bool) (fun _let_2 bool) _let_2) (hAPP _let_8 _let_5 (combs _let_2 bool bool) _let_14)) (hAPP _let_15 _let_4 (hAPP _let_17 (fun _let_15 _let_4) (combs _let_2 _let_10 (fun _let_2 bool)) (hAPP _let_18 _let_17 (hAPP (fun _let_9 _let_16) (fun _let_18 _let_17) (combb _let_9 _let_16 _let_2) (combs _let_2 int bool)) (hAPP _let_15 _let_18 (hAPP _let_11 (fun _let_15 _let_18) (combb _let_10 _let_9 _let_2) _let_12) (hAPP _let_10 _let_15 (hAPP _let_20 _let_21 (combc _let_2 _let_10 _let_10) (hAPP _let_22 _let_20 (hAPP (fun _let_1 _let_19) (fun _let_22 _let_20) (combb _let_1 _let_19 _let_2) (combb int int _let_2)) _let_23)) _let_13)))) (hAPP _let_10 _let_15 (hAPP _let_24 _let_21 (combb int _let_10 _let_2) (hAPP _let_22 _let_24 (combc _let_2 int int) _let_23)) _let_13)))))))))))))))))))))))))))))) ) 15.33/15.52 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (product_prod_case _let_0 _let_0 bool)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun _let_2 (fun _let_2 bool)))) (let ((_let_5 (fun (fun _let_2 bool) (fun _let_2 bool)))) (let ((_let_6 (fun _let_2 _let_5))) (let ((_let_7 (fun _let_4 _let_4))) (let ((_let_8 (fun _let_2 _let_3))) (let ((_let_9 (fun _let_2 _let_0))) (let ((_let_10 (fun _let_2 int))) (let ((_let_11 (fun _let_10 _let_9))) (let ((_let_12 (hAPP (fun int _let_0) _let_11 (combb int _let_0 _let_2) (fequal int)))) (let ((_let_13 (product_snd int int))) (let ((_let_14 (hAPP (fun _let_2 bool) _let_8 (hAPP (fun bool _let_3) (fun (fun _let_2 bool) _let_8) (combb bool _let_3 _let_2) fconj) (hAPP (fun _let_2 bool) (fun _let_2 bool) (hAPP _let_3 _let_5 (combb bool bool _let_2) fNot) (hAPP int (fun _let_2 bool) (hAPP _let_9 (fun int (fun _let_2 bool)) (combc _let_2 int bool) (hAPP _let_10 _let_9 _let_12 _let_13)) (zero_zero int)))))) (let ((_let_15 (fun _let_2 _let_10))) (let ((_let_16 (fun _let_10 (fun _let_2 bool)))) (let ((_let_17 (fun _let_2 _let_16))) (let ((_let_18 (fun _let_2 _let_9))) (let ((_let_19 (fun _let_10 _let_10))) (let ((_let_20 (fun _let_2 _let_19))) (let ((_let_21 (fun _let_10 _let_15))) (let ((_let_22 (fun _let_2 _let_1))) (let ((_let_23 (hAPP _let_10 _let_22 (hAPP (fun int _let_1) (fun _let_10 _let_22) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (let ((_let_24 (fun int _let_10))) (hAPP _let_4 _let_4 (hAPP _let_6 _let_7 (combs _let_2 (fun _let_2 bool) (fun _let_2 bool)) (hAPP _let_8 _let_6 (hAPP (fun _let_3 _let_5) (fun _let_8 _let_6) (combb _let_3 _let_5 _let_2) (combb bool bool _let_2)) _let_14)) (hAPP _let_4 _let_4 (hAPP _let_5 _let_7 (combb (fun _let_2 bool) (fun _let_2 bool) _let_2) (hAPP _let_8 _let_5 (combs _let_2 bool bool) _let_14)) (hAPP _let_15 _let_4 (hAPP _let_17 (fun _let_15 _let_4) (combs _let_2 _let_10 (fun _let_2 bool)) (hAPP _let_18 _let_17 (hAPP (fun _let_9 _let_16) (fun _let_18 _let_17) (combb _let_9 _let_16 _let_2) (combs _let_2 int bool)) (hAPP _let_15 _let_18 (hAPP _let_11 (fun _let_15 _let_18) (combb _let_10 _let_9 _let_2) _let_12) (hAPP _let_10 _let_15 (hAPP _let_20 _let_21 (combc _let_2 _let_10 _let_10) (hAPP _let_22 _let_20 (hAPP (fun _let_1 _let_19) (fun _let_22 _let_20) (combb _let_1 _let_19 _let_2) (combb int int _let_2)) _let_23)) _let_13)))) (hAPP _let_10 _let_15 (hAPP _let_24 _let_21 (combb int _let_10 _let_2) (hAPP _let_22 _let_24 (combc _let_2 int int) _let_23)) _let_13))))))))))))))))))))))))))))) ) 15.33/15.52 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_1 _let_3))) (let ((_let_5 (fun _let_3 _let_3))) (let ((_let_6 (fun _let_1 _let_5))) (let ((_let_7 (fun _let_1 _let_2))) (let ((_let_8 (combb bool bool _let_1))) (let ((_let_9 (fun _let_1 _let_0))) (let ((_let_10 (fun _let_1 int))) (hAPP _let_6 (fun _let_4 _let_4) (combs _let_1 _let_3 _let_3) (hAPP _let_7 _let_6 (hAPP (fun _let_2 _let_5) (fun _let_7 _let_6) (combb _let_2 _let_5 _let_1) _let_8) (hAPP _let_3 _let_7 (hAPP (fun bool _let_2) (fun _let_3 _let_7) (combb bool _let_2 _let_1) fconj) (hAPP _let_3 _let_3 (hAPP _let_2 _let_5 _let_8 fNot) (hAPP int _let_3 (hAPP _let_9 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_10 _let_9 (hAPP (fun int _let_0) (fun _let_10 _let_9) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))))))))))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun _let_2 (fun _let_2 bool)))) (let ((_let_5 (fun (fun _let_2 bool) (fun _let_2 bool)))) (let ((_let_6 (fun _let_2 _let_3))) (let ((_let_7 (fun _let_2 _let_0))) (let ((_let_8 (fun _let_2 int))) (let ((_let_9 (fun _let_8 _let_7))) (let ((_let_10 (hAPP (fun int _let_0) _let_9 (combb int _let_0 _let_2) (fequal int)))) (let ((_let_11 (product_snd int int))) (let ((_let_12 (fun _let_2 _let_8))) (let ((_let_13 (fun _let_8 (fun _let_2 bool)))) (let ((_let_14 (fun _let_2 _let_13))) (let ((_let_15 (fun _let_2 _let_7))) (let ((_let_16 (fun _let_8 _let_8))) (let ((_let_17 (fun _let_2 _let_16))) (let ((_let_18 (fun _let_8 _let_12))) (let ((_let_19 (fun _let_2 _let_1))) (let ((_let_20 (hAPP _let_8 _let_19 (hAPP (fun int _let_1) (fun _let_8 _let_19) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (let ((_let_21 (fun int _let_8))) (hAPP _let_4 _let_4 (hAPP _let_5 (fun _let_4 _let_4) (combb (fun _let_2 bool) (fun _let_2 bool) _let_2) (hAPP _let_6 _let_5 (combs _let_2 bool bool) (hAPP (fun _let_2 bool) _let_6 (hAPP (fun bool _let_3) (fun (fun _let_2 bool) _let_6) (combb bool _let_3 _let_2) fconj) (hAPP (fun _let_2 bool) (fun _let_2 bool) (hAPP _let_3 _let_5 (combb bool bool _let_2) fNot) (hAPP int (fun _let_2 bool) (hAPP _let_7 (fun int (fun _let_2 bool)) (combc _let_2 int bool) (hAPP _let_8 _let_7 _let_10 _let_11)) (zero_zero int)))))) (hAPP _let_12 _let_4 (hAPP _let_14 (fun _let_12 _let_4) (combs _let_2 _let_8 (fun _let_2 bool)) (hAPP _let_15 _let_14 (hAPP (fun _let_7 _let_13) (fun _let_15 _let_14) (combb _let_7 _let_13 _let_2) (combs _let_2 int bool)) (hAPP _let_12 _let_15 (hAPP _let_9 (fun _let_12 _let_15) (combb _let_8 _let_7 _let_2) _let_10) (hAPP _let_8 _let_12 (hAPP _let_17 _let_18 (combc _let_2 _let_8 _let_8) (hAPP _let_19 _let_17 (hAPP (fun _let_1 _let_16) (fun _let_19 _let_17) (combb _let_1 _let_16 _let_2) (combb int int _let_2)) _let_20)) _let_11)))) (hAPP _let_8 _let_12 (hAPP _let_21 _let_18 (combb int _let_8 _let_2) (hAPP _let_19 _let_21 (combc _let_2 int int) _let_20)) _let_11))))))))))))))))))))))))) ) 15.33/15.52 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_1 _let_3))) (let ((_let_5 (fun _let_3 _let_3))) (let ((_let_6 (fun _let_1 _let_2))) (let ((_let_7 (fun _let_1 _let_0))) (let ((_let_8 (fun _let_1 int))) (hAPP _let_5 (fun _let_4 _let_4) (combb _let_3 _let_3 _let_1) (hAPP _let_6 _let_5 (combs _let_1 bool bool) (hAPP _let_3 _let_6 (hAPP (fun bool _let_2) (fun _let_3 _let_6) (combb bool _let_2 _let_1) fconj) (hAPP _let_3 _let_3 (hAPP _let_2 _let_5 (combb bool bool _let_1) fNot) (hAPP int _let_3 (hAPP _let_7 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_8 _let_7 (hAPP (fun int _let_0) (fun _let_8 _let_7) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))))))))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun _let_2 (fun _let_2 bool)))) (let ((_let_4 (fun _let_2 _let_0))) (let ((_let_5 (fun _let_2 int))) (let ((_let_6 (fun _let_5 _let_4))) (let ((_let_7 (product_snd int int))) (let ((_let_8 (fun _let_2 _let_5))) (let ((_let_9 (fun _let_5 (fun _let_2 bool)))) (let ((_let_10 (fun _let_2 _let_9))) (let ((_let_11 (fun _let_2 _let_4))) (let ((_let_12 (fun _let_5 _let_5))) (let ((_let_13 (fun _let_2 _let_12))) (let ((_let_14 (fun _let_5 _let_8))) (let ((_let_15 (fun _let_2 _let_1))) (let ((_let_16 (hAPP _let_5 _let_15 (hAPP (fun int _let_1) (fun _let_5 _let_15) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (let ((_let_17 (fun int _let_5))) (hAPP _let_8 _let_3 (hAPP _let_10 (fun _let_8 _let_3) (combs _let_2 _let_5 (fun _let_2 bool)) (hAPP _let_11 _let_10 (hAPP (fun _let_4 _let_9) (fun _let_11 _let_10) (combb _let_4 _let_9 _let_2) (combs _let_2 int bool)) (hAPP _let_8 _let_11 (hAPP _let_6 (fun _let_8 _let_11) (combb _let_5 _let_4 _let_2) (hAPP (fun int _let_0) _let_6 (combb int _let_0 _let_2) (fequal int))) (hAPP _let_5 _let_8 (hAPP _let_13 _let_14 (combc _let_2 _let_5 _let_5) (hAPP _let_15 _let_13 (hAPP (fun _let_1 _let_12) (fun _let_15 _let_13) (combb _let_1 _let_12 _let_2) (combb int int _let_2)) _let_16)) _let_7)))) (hAPP _let_5 _let_8 (hAPP _let_17 _let_14 (combb int _let_5 _let_2) (hAPP _let_15 _let_17 (combc _let_2 int int) _let_16)) _let_7)))))))))))))))))))) ) 15.33/15.52 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun _let_2 _let_0))) (let ((_let_4 (fun _let_2 int))) (let ((_let_5 (fun _let_4 _let_3))) (let ((_let_6 (fun _let_2 _let_4))) (let ((_let_7 (fun _let_4 (fun _let_2 bool)))) (let ((_let_8 (fun _let_2 _let_7))) (let ((_let_9 (fun _let_2 _let_3))) (let ((_let_10 (fun _let_4 _let_4))) (let ((_let_11 (fun _let_2 _let_10))) (let ((_let_12 (fun _let_2 _let_1))) (hAPP _let_8 (fun _let_6 (fun _let_2 (fun _let_2 bool))) (combs _let_2 _let_4 (fun _let_2 bool)) (hAPP _let_9 _let_8 (hAPP (fun _let_3 _let_7) (fun _let_9 _let_8) (combb _let_3 _let_7 _let_2) (combs _let_2 int bool)) (hAPP _let_6 _let_9 (hAPP _let_5 (fun _let_6 _let_9) (combb _let_4 _let_3 _let_2) (hAPP (fun int _let_0) _let_5 (combb int _let_0 _let_2) (fequal int))) (hAPP _let_4 _let_6 (hAPP _let_11 (fun _let_4 _let_6) (combc _let_2 _let_4 _let_4) (hAPP _let_12 _let_11 (hAPP (fun _let_1 _let_10) (fun _let_12 _let_11) (combb _let_1 _let_10 _let_2) (combb int int _let_2)) (hAPP _let_4 _let_12 (hAPP (fun int _let_1) (fun _let_4 _let_12) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (product_snd int int)))))))))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_2))) (let ((_let_4 (fun _let_1 _let_0))) (let ((_let_5 (fun int _let_2))) (hAPP _let_2 _let_3 (hAPP _let_5 (fun _let_2 _let_3) (combb int _let_2 _let_1) (hAPP _let_4 _let_5 (combc _let_1 int int) (hAPP _let_2 _let_4 (hAPP (fun int _let_0) (fun _let_2 _let_4) (combb int _let_0 _let_1) (times_times int)) (product_fst int int)))) (product_snd int int)))))))) ) 15.33/15.52 ( (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)), (fun bool bool), (combb bool bool (product_prod int int)), fNot ) 15.33/15.52 ( (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)), (fun (product_prod int int) (fun bool bool)), (combs (product_prod int int) bool bool), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_1 _let_2))) (let ((_let_5 (fun _let_1 _let_0))) (let ((_let_6 (fun _let_1 int))) (hAPP _let_3 _let_4 (hAPP (fun bool _let_2) (fun _let_3 _let_4) (combb bool _let_2 _let_1) fconj) (hAPP _let_3 _let_3 (hAPP _let_2 (fun _let_3 _let_3) (combb bool bool _let_1) fNot) (hAPP int _let_3 (hAPP _let_5 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_6 _let_5 (hAPP (fun int _let_0) (fun _let_6 _let_5) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))))))) ) 15.33/15.52 ( (let ((_let_0 (fun (product_prod int int) bool))) (fun (product_prod int int) (fun _let_0 _let_0))), (fun (product_prod int int) (fun bool bool)), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun (fun _let_0 bool) (fun _let_0 bool)))) (hAPP (fun _let_1 _let_2) (fun (fun _let_0 _let_1) (fun _let_0 _let_2)) (combb _let_1 _let_2 _let_0) (combb bool bool _let_0))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_1 _let_2))) (let ((_let_5 (fun _let_1 _let_0))) (let ((_let_6 (fun _let_1 int))) (hAPP _let_3 _let_4 (hAPP (fun bool _let_2) (fun _let_3 _let_4) (combb bool _let_2 _let_1) fconj) (hAPP _let_3 _let_3 (hAPP _let_2 (fun _let_3 _let_3) (combb bool bool _let_1) fNot) (hAPP int _let_3 (hAPP _let_5 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_6 _let_5 (hAPP (fun int _let_0) (fun _let_6 _let_5) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))))))) ) 15.33/15.52 ( (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (fun _let_1 _let_1))), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 bool))) (combb _let_1 _let_1 _let_0))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_3 _let_3))) (let ((_let_5 (fun _let_1 _let_2))) (let ((_let_6 (fun _let_1 _let_0))) (let ((_let_7 (fun _let_1 int))) (hAPP _let_5 _let_4 (combs _let_1 bool bool) (hAPP _let_3 _let_5 (hAPP (fun bool _let_2) (fun _let_3 _let_5) (combb bool _let_2 _let_1) fconj) (hAPP _let_3 _let_3 (hAPP _let_2 _let_4 (combb bool bool _let_1) fNot) (hAPP int _let_3 (hAPP _let_6 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_7 _let_6 (hAPP (fun int _let_0) (fun _let_7 _let_6) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))))))))) ) 15.33/15.52 ( (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (fun _let_1 _let_1))), (let ((_let_0 (fun (product_prod int int) bool))) (fun (product_prod int int) (fun _let_0 _let_0))), (let ((_let_0 (fun (product_prod int int) bool))) (combs (product_prod int int) _let_0 _let_0)), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_3 _let_3))) (let ((_let_5 (fun _let_1 _let_4))) (let ((_let_6 (fun _let_1 _let_2))) (let ((_let_7 (combb bool bool _let_1))) (let ((_let_8 (fun _let_1 _let_0))) (let ((_let_9 (fun _let_1 int))) (hAPP _let_6 _let_5 (hAPP (fun _let_2 _let_4) (fun _let_6 _let_5) (combb _let_2 _let_4 _let_1) _let_7) (hAPP _let_3 _let_6 (hAPP (fun bool _let_2) (fun _let_3 _let_6) (combb bool _let_2 _let_1) fconj) (hAPP _let_3 _let_3 (hAPP _let_2 _let_4 _let_7 fNot) (hAPP int _let_3 (hAPP _let_8 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_9 _let_8 (hAPP (fun int _let_0) (fun _let_9 _let_8) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))))))))))) ) 15.33/15.52 ( (fun (product_prod int int) (fun bool bool)), (fun (product_prod int int) bool), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun bool bool))) (hAPP (fun bool _let_1) (fun (fun _let_0 bool) (fun _let_0 _let_1)) (combb bool _let_1 _let_0) fconj))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun _let_1 _let_0))) (let ((_let_4 (fun _let_1 int))) (hAPP _let_2 _let_2 (hAPP (fun bool bool) (fun _let_2 _let_2) (combb bool bool _let_1) fNot) (hAPP int _let_2 (hAPP _let_3 (fun int _let_2) (combc _let_1 int bool) (hAPP _let_4 _let_3 (hAPP (fun int _let_0) (fun _let_4 _let_3) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int)))))))) ) 15.33/15.52 ( (let ((_let_0 (fun (product_prod int int) bool))) (fun (fun (product_prod int int) (fun bool bool)) (fun (product_prod int int) (fun _let_0 _let_0)))), (let ((_let_0 (fun (product_prod int int) bool))) (fun (fun bool bool) (fun _let_0 _let_0))), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 bool))) (combb (fun bool bool) (fun _let_1 _let_1) _let_0))), (combb bool bool (product_prod int int)) ) 15.33/15.52 ( (let ((_let_0 (product_prod int int))) (fun (fun _let_0 bool) (fun _let_0 (fun bool bool)))), (fun bool (fun bool bool)), (combb bool (fun bool bool) (product_prod int int)), fconj ) 15.33/15.52 ( (fun (product_prod int int) (fun int bool)), (fun (product_prod int int) int), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (hAPP (fun int _let_0) (fun (fun _let_1 int) (fun _let_1 _let_0)) (combb int _let_0 _let_1) (fequal int)))), (product_snd int int) ) 15.33/15.52 ( (fun (product_prod int int) int), (fun int (fun int int)), (product_prod_case int int int), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun _let_0 _let_1))) (let ((_let_3 (fun _let_0 _let_0))) (let ((_let_4 (fun int _let_3))) (let ((_let_5 (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP _let_0 _let_1 (hAPP _let_4 _let_2 (combc int _let_0 _let_0) (hAPP _let_1 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_1 _let_4) (combb _let_0 _let_3 int) (combb int int int)) (hAPP _let_0 _let_1 (hAPP _let_1 _let_2 (combb int _let_0 int) (plus_plus int)) _let_5))) _let_5))))))) ) 15.33/15.52 ( (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 (fun int bool)))), (fun int (fun int bool)), (combb int (fun int bool) (product_prod int int)), (fequal int) ) 15.33/15.52 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (fun (product_prod int int) int), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_2 _let_2))) (let ((_let_4 (fun _let_1 _let_3))) (let ((_let_5 (fun _let_1 _let_0))) (hAPP _let_4 (fun _let_2 (fun _let_1 _let_2)) (combc _let_1 _let_2 _let_2) (hAPP _let_5 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_5 _let_4) (combb _let_0 _let_3 _let_1) (combb int int _let_1)) (hAPP _let_2 _let_5 (hAPP (fun int _let_0) (fun _let_2 _let_5) (combb int _let_0 _let_1) (times_times int)) (product_fst int int)))))))))), (product_snd int int) ) 15.33/15.52 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (fun (product_prod int int) int), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_0))) (let ((_let_4 (fun int _let_2))) (hAPP _let_4 (fun _let_2 (fun _let_1 _let_2)) (combb int _let_2 _let_1) (hAPP _let_3 _let_4 (combc _let_1 int int) (hAPP _let_2 _let_3 (hAPP (fun int _let_0) (fun _let_2 _let_3) (combb int _let_0 _let_1) (times_times int)) (product_fst int int))))))))), (product_snd int int) ) 15.33/15.52 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun (fun _let_0 int) (fun _let_0 bool)))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 (fun int bool)))), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 (fun int bool)))) (let ((_let_2 (fun (fun _let_0 int) (fun _let_0 bool)))) (hAPP (fun _let_1 _let_2) (fun (fun _let_0 _let_1) (fun _let_0 _let_2)) (combb _let_1 _let_2 _let_0) (combs _let_0 int bool))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun _let_2 _let_0))) (let ((_let_4 (fun _let_2 int))) (let ((_let_5 (fun _let_4 _let_3))) (let ((_let_6 (fun _let_2 _let_4))) (let ((_let_7 (fun _let_2 _let_3))) (let ((_let_8 (fun _let_4 _let_4))) (let ((_let_9 (fun _let_2 _let_8))) (let ((_let_10 (fun _let_2 _let_1))) (hAPP _let_6 _let_7 (hAPP _let_5 (fun _let_6 _let_7) (combb _let_4 _let_3 _let_2) (hAPP (fun int _let_0) _let_5 (combb int _let_0 _let_2) (fequal int))) (hAPP _let_4 _let_6 (hAPP _let_9 (fun _let_4 _let_6) (combc _let_2 _let_4 _let_4) (hAPP _let_10 _let_9 (hAPP (fun _let_1 _let_8) (fun _let_10 _let_9) (combb _let_1 _let_8 _let_2) (combb int int _let_2)) (hAPP _let_4 _let_10 (hAPP (fun int _let_1) (fun _let_4 _let_10) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (product_snd int int)))))))))))))) ) 15.33/15.52 ( (let ((_let_0 (product_prod int int))) (fun (fun _let_0 (fun _let_0 int)) (fun _let_0 (fun _let_0 bool)))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun (fun _let_0 int) (fun _let_0 bool)))), (let ((_let_0 (product_prod int int))) (combs _let_0 (fun _let_0 int) (fun _let_0 bool))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun _let_2 _let_0))) (let ((_let_4 (fun _let_2 int))) (let ((_let_5 (fun _let_4 _let_3))) (let ((_let_6 (fun _let_2 _let_4))) (let ((_let_7 (fun _let_4 (fun _let_2 bool)))) (let ((_let_8 (fun _let_2 _let_7))) (let ((_let_9 (fun _let_2 _let_3))) (let ((_let_10 (fun _let_4 _let_4))) (let ((_let_11 (fun _let_2 _let_10))) (let ((_let_12 (fun _let_2 _let_1))) (hAPP _let_9 _let_8 (hAPP (fun _let_3 _let_7) (fun _let_9 _let_8) (combb _let_3 _let_7 _let_2) (combs _let_2 int bool)) (hAPP _let_6 _let_9 (hAPP _let_5 (fun _let_6 _let_9) (combb _let_4 _let_3 _let_2) (hAPP (fun int _let_0) _let_5 (combb int _let_0 _let_2) (fequal int))) (hAPP _let_4 _let_6 (hAPP _let_11 (fun _let_4 _let_6) (combc _let_2 _let_4 _let_4) (hAPP _let_12 _let_11 (hAPP (fun _let_1 _let_10) (fun _let_12 _let_11) (combb _let_1 _let_10 _let_2) (combb int int _let_2)) (hAPP _let_4 _let_12 (hAPP (fun int _let_1) (fun _let_4 _let_12) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (product_snd int int))))))))))))))))) ) 15.33/15.53 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 (fun int bool)))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 _let_0))) (let ((_let_3 (fun _let_1 int))) (let ((_let_4 (fun _let_3 _let_2))) (hAPP _let_4 (fun (fun _let_1 _let_3) (fun _let_1 _let_2)) (combb _let_3 _let_2 _let_1) (hAPP (fun int _let_0) _let_4 (combb int _let_0 _let_1) (fequal int)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_2))) (let ((_let_4 (fun _let_2 _let_2))) (let ((_let_5 (fun _let_1 _let_4))) (let ((_let_6 (fun _let_1 _let_0))) (hAPP _let_2 _let_3 (hAPP _let_5 (fun _let_2 _let_3) (combc _let_1 _let_2 _let_2) (hAPP _let_6 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_6 _let_5) (combb _let_0 _let_4 _let_1) (combb int int _let_1)) (hAPP _let_2 _let_6 (hAPP (fun int _let_0) (fun _let_2 _let_6) (combb int _let_0 _let_1) (times_times int)) (product_fst int int)))) (product_snd int int))))))))) ) 15.33/15.53 ( (let ((_let_0 (product_prod int int))) (fun (fun _let_0 (fun _let_0 (fun int bool))) (fun _let_0 (fun (fun _let_0 int) (fun _let_0 bool))))), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 (fun int bool)) (fun (fun _let_0 int) (fun _let_0 bool)))), (let ((_let_0 (product_prod int int))) (combb (fun _let_0 (fun int bool)) (fun (fun _let_0 int) (fun _let_0 bool)) _let_0)), (combs (product_prod int int) int bool) ) 15.33/15.53 ( (let ((_let_0 (product_prod int int))) (fun (fun _let_0 (fun _let_0 int)) (fun _let_0 (fun _let_0 (fun int bool))))), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 (fun int bool)))), (let ((_let_0 (product_prod int int))) (combb (fun _let_0 int) (fun _let_0 (fun int bool)) _let_0)), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (hAPP (fun int _let_0) (fun (fun _let_1 int) (fun _let_1 _let_0)) (combb int _let_0 _let_1) (fequal int)))) ) 15.33/15.53 ( (let ((_let_0 (fun (product_prod int int) int))) (fun (product_prod int int) (fun _let_0 _let_0))), (fun (product_prod int int) (fun int int)), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun (fun _let_1 int) (fun _let_1 int)))) (hAPP (fun _let_0 _let_2) (fun (fun _let_1 _let_0) (fun _let_1 _let_2)) (combb _let_0 _let_2 _let_1) (combb int int _let_1))))), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_0))) (hAPP _let_2 _let_3 (hAPP (fun int _let_0) (fun _let_2 _let_3) (combb int _let_0 _let_1) (times_times int)) (product_fst int int)))))) ) 15.33/15.53 ( (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 int))) (fun _let_1 (fun _let_0 _let_1)))), (let ((_let_0 (fun (product_prod int int) int))) (fun (product_prod int int) (fun _let_0 _let_0))), (let ((_let_0 (fun (product_prod int int) int))) (combc (product_prod int int) _let_0 _let_0)), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_2 _let_2))) (let ((_let_4 (fun _let_1 _let_3))) (let ((_let_5 (fun _let_1 _let_0))) (hAPP _let_5 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_5 _let_4) (combb _let_0 _let_3 _let_1) (combb int int _let_1)) (hAPP _let_2 _let_5 (hAPP (fun int _let_0) (fun _let_2 _let_5) (combb int _let_0 _let_1) (times_times int)) (product_fst int int))))))))) ) 15.33/15.53 ( (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 int))) (fun _let_1 (fun _let_0 _let_1)))), (fun int (fun (product_prod int int) int)), (let ((_let_0 (product_prod int int))) (combb int (fun _let_0 int) _let_0)), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_0))) (hAPP _let_3 (fun int _let_2) (combc _let_1 int int) (hAPP _let_2 _let_3 (hAPP (fun int _let_0) (fun _let_2 _let_3) (combb int _let_0 _let_1) (times_times int)) (product_fst int int))))))) ) 15.33/15.53 ( (fun (product_prod int int) (fun int int)), (fun (product_prod int int) int), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (hAPP (fun int _let_0) (fun (fun _let_1 int) (fun _let_1 _let_0)) (combb int _let_0 _let_1) (times_times int)))), (product_fst int int) ) 15.33/15.53 ( (let ((_let_0 (fun (product_prod int int) int))) (fun (fun (product_prod int int) (fun int int)) (fun (product_prod int int) (fun _let_0 _let_0)))), (let ((_let_0 (fun (product_prod int int) int))) (fun (fun int int) (fun _let_0 _let_0))), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 int))) (combb (fun int int) (fun _let_1 _let_1) _let_0))), (combb int int (product_prod int int)) ) 15.33/15.53 ( (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 (fun int int)))), (fun int (fun int int)), (combb int (fun int int) (product_prod int int)), (times_times int) ) 15.33/15.53 ( (fun int (fun (product_prod int int) int)), (fun (product_prod int int) (fun int int)), (combc (product_prod int int) int int), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_0))) (hAPP _let_2 _let_3 (hAPP (fun int _let_0) (fun _let_2 _let_3) (combb int _let_0 _let_1) (times_times int)) (product_fst int int)))))) ) 15.33/15.53 ( (fun (fun nat nat) (fun nat (fun nat bool))), (fun nat (fun nat bool)), (combb nat (fun nat bool) nat), (let ((_let_0 (fun nat (fun nat bool)))) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat))) ) 15.33/15.53 ( (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)), (fun bool bool), (combb bool bool nat), fNot ) 15.33/15.53 ( (let ((_let_0 (fun nat nat))) (fun _let_0 (fun nat _let_0))), (fun nat (fun nat nat)), (combb nat (fun nat nat) nat), (plus_plus nat) ) 15.33/15.53 ( (fun real (fun bool bool)), (fun real bool), (let ((_let_0 (fun bool bool))) (hAPP (fun bool _let_0) (fun (fun real bool) (fun real _let_0)) (combb bool _let_0 real) fconj)), (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) ) 15.33/15.53 ( (fun real (fun bool bool)), (fun real bool), (let ((_let_0 (fun bool bool))) (hAPP (fun bool _let_0) (fun (fun real bool) (fun real _let_0)) (combb bool _let_0 real) fconj)), (let ((_let_0 (fun real (fun real bool)))) (hAPP real (fun real bool) (hAPP _let_0 _let_0 (combc real real bool) (ord_less_eq real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.33/15.53 ( (let ((_let_0 (fun real bool))) (fun _let_0 _let_0)), (fun real (fun bool bool)), (combs real bool bool), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun real _let_1))) (hAPP _let_0 _let_2 (hAPP (fun bool _let_1) (fun _let_0 _let_2) (combb bool _let_1 real) fconj) (hAPP real _let_0 (ord_less_eq real) (zero_zero real)))))) ) 15.33/15.53 ( (let ((_let_0 (fun real bool))) (fun _let_0 _let_0)), (fun real (fun bool bool)), (combs real bool bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun real (fun real bool)))) (let ((_let_2 (fun real _let_0))) (hAPP (fun real bool) _let_2 (hAPP (fun bool _let_0) (fun (fun real bool) _let_2) (combb bool _let_0 real) fconj) (hAPP real (fun real bool) (hAPP _let_1 _let_1 (combc real real bool) (ord_less_eq real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 15.33/15.53 ( (fun (fun real bool) (fun real (fun bool bool))), (fun bool (fun bool bool)), (combb bool (fun bool bool) real), fconj ) 15.33/15.53 ( (fun (fun real real) (fun real (fun real bool))), (fun real (fun real bool)), (combb real (fun real bool) real), (fequal real) ) 15.33/15.53 ( (fun (fun nat bool) (fun nat (fun bool bool))), (fun bool (fun bool bool)), (combb bool (fun bool bool) nat), fconj ) 15.33/15.53 ( (let ((_let_0 (fun int bool))) (fun (fun int (fun int (fun bool bool))) (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun int bool))) (fun (fun int (fun bool bool)) (fun _let_0 _let_0))), (let ((_let_0 (fun int bool))) (combb (fun int (fun bool bool)) (fun _let_0 _let_0) int)), (combs int bool bool) ) 15.33/15.53 ( (fun (fun int (fun int bool)) (fun int (fun int (fun bool bool)))), (fun (fun int bool) (fun int (fun bool bool))), (combb (fun int bool) (fun int (fun bool bool)) int), (let ((_let_0 (fun bool bool))) (hAPP (fun bool _let_0) (fun (fun int bool) (fun int _let_0)) (combb bool _let_0 int) fconj)) ) 15.33/15.53 ( (fun nat (fun int int)), (fun int (fun nat int)), (combc int nat int), (power_power int) ) 15.33/15.53 ( (fun real (fun int bool)), (fun real (fun int (fun int bool))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun _let_1 _let_0))) (hAPP _let_2 (fun (fun real _let_1) (fun real _let_0)) (combb _let_1 _let_0 real) (hAPP (fun _let_0 bool) _let_2 (combb _let_0 bool int) (fEx int)))))), (let ((_let_0 (fun int (fun int bool)))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real real))) (let ((_let_3 (real_1 int))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun int _let_4))) (let ((_let_7 (fun (fun int bool) (fun int bool)))) (let ((_let_8 (fun (fun int bool) _let_6))) (let ((_let_9 (fun int real))) (let ((_let_10 (fun int _let_7))) (let ((_let_11 (fun (fun int bool) _let_0))) (let ((_let_12 (fun int _let_6))) (let ((_let_13 (fun _let_12 _let_10))) (let ((_let_14 (fun _let_0 _let_12))) (let ((_let_15 (fun real _let_0))) (let ((_let_16 (fun real _let_11))) (let ((_let_17 (fun real _let_10))) (let ((_let_18 (fun real _let_12))) (let ((_let_19 (fun int _let_9))) (let ((_let_20 (fun _let_19 _let_0))) (let ((_let_21 (fun real _let_20))) (let ((_let_22 (fun _let_9 (fun int bool)))) (let ((_let_23 (fun real _let_22))) (let ((_let_24 (fun _let_9 _let_9))) (let ((_let_25 (fun int _let_24))) (let ((_let_26 (fun int _let_2))) (hAPP (fun int bool) _let_15 (hAPP _let_16 (fun (fun int bool) _let_15) (combc real (fun int bool) _let_0) (hAPP _let_17 _let_16 (hAPP (fun _let_10 _let_11) (fun _let_17 _let_16) (combb _let_10 _let_11 real) (combc int (fun int bool) (fun int bool))) (hAPP _let_18 _let_17 (hAPP _let_13 (fun _let_18 _let_17) (combb _let_12 _let_10 real) (hAPP (fun _let_6 _let_7) _let_13 (combb _let_6 _let_7 int) (combs int bool bool))) (hAPP _let_15 _let_18 (hAPP _let_14 (fun _let_15 _let_18) (combb _let_0 _let_12 real) (hAPP _let_8 _let_14 (combb (fun int bool) _let_6 int) (hAPP (fun bool _let_4) _let_8 (combb bool _let_4 int) fconj))) (hAPP _let_19 _let_15 (hAPP _let_21 (fun _let_19 _let_15) (combc real _let_19 _let_0) (hAPP _let_23 _let_21 (hAPP (fun _let_22 _let_20) (fun _let_23 _let_21) (combb _let_22 _let_20 real) (combb _let_9 (fun int bool) int)) (hAPP _let_5 _let_23 (hAPP (fun _let_1 _let_22) (fun _let_5 _let_23) (combb _let_1 _let_22 real) (combb real bool int)) (fequal real)))) (hAPP _let_9 _let_19 (hAPP _let_25 (fun _let_9 _let_19) (combc int _let_9 _let_9) (hAPP _let_26 _let_25 (hAPP (fun _let_2 _let_24) (fun _let_26 _let_25) (combb _let_2 _let_24 int) (combb real real int)) (hAPP _let_9 _let_26 (hAPP (fun real _let_2) (fun _let_9 _let_26) (combb real _let_2 int) (inverse_divide real)) _let_3))) _let_3)))))) (hAPP (fun int bool) (fun int bool) (hAPP _let_4 _let_7 (combb bool bool int) fNot) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (fequal int)) (zero_zero int))))))))))))))))))))))))))))))) ) 15.33/15.53 ( (fun real (fun int bool)), (fun real (fun int (fun nat bool))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun nat bool))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (fun _let_2 _let_0))) (hAPP _let_3 (fun (fun real _let_2) (fun real _let_0)) (combb _let_2 _let_0 real) (hAPP (fun _let_1 bool) _let_3 (combb _let_1 bool int) (fEx nat))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat (fun nat bool)))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun (fun nat real) (fun nat real)))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun (fun nat bool) (fun nat bool)))) (let ((_let_7 (fun int real))) (let ((_let_8 (fun nat _let_3))) (let ((_let_9 (fun (fun nat bool) _let_8))) (let ((_let_10 (fun int _let_1))) (let ((_let_11 (fun real (fun int (fun nat bool))))) (let ((_let_12 (fun (fun nat bool) (fun int (fun nat bool))))) (let ((_let_13 (fun real _let_12))) (let ((_let_14 (fun int _let_6))) (let ((_let_15 (fun real _let_14))) (let ((_let_16 (fun int _let_8))) (let ((_let_17 (fun real _let_16))) (let ((_let_18 (fun _let_16 _let_14))) (let ((_let_19 (fun (fun int (fun nat bool)) _let_16))) (let ((_let_20 (fun int (fun nat real)))) (let ((_let_21 (fun _let_20 (fun int (fun nat bool))))) (let ((_let_22 (fun real _let_21))) (let ((_let_23 (fun (fun nat real) (fun nat bool)))) (let ((_let_24 (fun real _let_23))) (let ((_let_25 (fun int _let_4))) (hAPP (fun nat bool) _let_11 (hAPP _let_13 (fun (fun nat bool) _let_11) (combc real (fun nat bool) (fun int (fun nat bool))) (hAPP _let_15 _let_13 (hAPP (fun _let_14 _let_12) (fun _let_15 _let_13) (combb _let_14 _let_12 real) (combc int (fun nat bool) (fun nat bool))) (hAPP _let_17 _let_15 (hAPP _let_18 (fun _let_17 _let_15) (combb _let_16 _let_14 real) (hAPP (fun _let_8 _let_6) _let_18 (combb _let_8 _let_6 int) (combs nat bool bool))) (hAPP _let_11 _let_17 (hAPP _let_19 (fun _let_11 _let_17) (combb (fun int (fun nat bool)) _let_16 real) (hAPP _let_9 _let_19 (combb (fun nat bool) _let_8 int) (hAPP (fun bool _let_3) _let_9 (combb bool _let_3 nat) fconj))) (hAPP _let_20 _let_11 (hAPP _let_22 (fun _let_20 _let_11) (combc real _let_20 (fun int (fun nat bool))) (hAPP _let_24 _let_22 (hAPP (fun _let_23 _let_21) (fun _let_24 _let_22) (combb _let_23 _let_21 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_5 _let_24 (hAPP (fun _let_0 _let_23) (fun _let_5 _let_24) (combb _let_0 _let_23 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_20 (hAPP _let_25 (fun (fun nat real) _let_20) (combc int (fun nat real) (fun nat real)) (hAPP _let_10 _let_25 (hAPP (fun _let_1 _let_4) (fun _let_10 _let_25) (combb _let_1 _let_4 int) (combb real real nat)) (hAPP _let_7 _let_10 (hAPP (fun real _let_1) (fun _let_7 _let_10) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat))))))) (hAPP (fun nat bool) (fun nat bool) (hAPP _let_3 _let_6 (combb bool bool nat) fNot) (hAPP nat (fun nat bool) (hAPP _let_2 _let_2 (combc nat nat bool) (fequal nat)) (zero_zero nat)))))))))))))))))))))))))))))) ) 15.33/15.53 ( (fun (fun real (fun int bool)) (fun real bool)), (fun (fun int bool) bool), (combb (fun int bool) bool real), (fEx int) ) 15.33/15.53 ( (fun real (fun int (fun int bool))), (fun int bool), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun int _let_3))) (let ((_let_6 (fun (fun int bool) (fun int bool)))) (let ((_let_7 (fun (fun int bool) _let_5))) (let ((_let_8 (fun int real))) (let ((_let_9 (fun int _let_6))) (let ((_let_10 (fun (fun int bool) (fun int (fun int bool))))) (let ((_let_11 (fun int _let_5))) (let ((_let_12 (fun _let_11 _let_9))) (let ((_let_13 (fun (fun int (fun int bool)) _let_11))) (let ((_let_14 (fun real (fun int (fun int bool))))) (let ((_let_15 (fun real _let_10))) (let ((_let_16 (fun real _let_9))) (let ((_let_17 (fun real _let_11))) (let ((_let_18 (fun int _let_8))) (let ((_let_19 (fun _let_18 (fun int (fun int bool))))) (let ((_let_20 (fun real _let_19))) (let ((_let_21 (fun _let_8 (fun int bool)))) (let ((_let_22 (fun real _let_21))) (let ((_let_23 (fun _let_8 _let_8))) (let ((_let_24 (fun int _let_23))) (let ((_let_25 (fun int _let_1))) (hAPP _let_15 (fun (fun int bool) _let_14) (combc real (fun int bool) (fun int (fun int bool))) (hAPP _let_16 _let_15 (hAPP (fun _let_9 _let_10) (fun _let_16 _let_15) (combb _let_9 _let_10 real) (combc int (fun int bool) (fun int bool))) (hAPP _let_17 _let_16 (hAPP _let_12 (fun _let_17 _let_16) (combb _let_11 _let_9 real) (hAPP (fun _let_5 _let_6) _let_12 (combb _let_5 _let_6 int) (combs int bool bool))) (hAPP _let_14 _let_17 (hAPP _let_13 (fun _let_14 _let_17) (combb (fun int (fun int bool)) _let_11 real) (hAPP _let_7 _let_13 (combb (fun int bool) _let_5 int) (hAPP (fun bool _let_3) _let_7 (combb bool _let_3 int) fconj))) (hAPP _let_18 _let_14 (hAPP _let_20 (fun _let_18 _let_14) (combc real _let_18 (fun int (fun int bool))) (hAPP _let_22 _let_20 (hAPP (fun _let_21 _let_19) (fun _let_22 _let_20) (combb _let_21 _let_19 real) (combb _let_8 (fun int bool) int)) (hAPP _let_4 _let_22 (hAPP (fun _let_0 _let_21) (fun _let_4 _let_22) (combb _let_0 _let_21 real) (combb real bool int)) (fequal real)))) (hAPP _let_8 _let_18 (hAPP _let_24 (fun _let_8 _let_18) (combc int _let_8 _let_8) (hAPP _let_25 _let_24 (hAPP (fun _let_1 _let_23) (fun _let_25 _let_24) (combb _let_1 _let_23 int) (combb real real int)) (hAPP _let_8 _let_25 (hAPP (fun real _let_1) (fun _let_8 _let_25) (combb real _let_1 int) (inverse_divide real)) _let_2))) _let_2)))))))))))))))))))))))))))))))), (let ((_let_0 (fun int (fun int bool)))) (hAPP (fun int bool) (fun int bool) (hAPP (fun bool bool) (fun (fun int bool) (fun int bool)) (combb bool bool int) fNot) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (fequal int)) (zero_zero int)))) ) 15.33/15.53 ( (fun real (fun int (fun int bool))), (fun int (fun int real)), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun int (fun int real)) (fun int (fun int bool))))) (let ((_let_3 (fun real _let_2))) (let ((_let_4 (fun (fun int real) (fun int bool)))) (let ((_let_5 (fun real _let_4))) (hAPP _let_3 (fun (fun int (fun int real)) (fun real (fun int (fun int bool)))) (combc real (fun int (fun int real)) (fun int (fun int bool))) (hAPP _let_5 _let_3 (hAPP (fun _let_4 _let_2) (fun _let_5 _let_3) (combb _let_4 _let_2 real) (combb (fun int real) (fun int bool) int)) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_1 _let_5) (combb _let_0 _let_4 real) (combb real bool int)) (fequal real)))))))))), (let ((_let_0 (fun real real))) (let ((_let_1 (real_1 int))) (let ((_let_2 (fun int real))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun _let_2 _let_2))) (let ((_let_5 (fun int _let_4))) (let ((_let_6 (fun int _let_0))) (hAPP _let_2 _let_3 (hAPP _let_5 (fun _let_2 _let_3) (combc int _let_2 _let_2) (hAPP _let_6 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_6 _let_5) (combb _let_0 _let_4 int) (combb real real int)) (hAPP _let_2 _let_6 (hAPP (fun real _let_0) (fun _let_2 _let_6) (combb real _let_0 int) (inverse_divide real)) _let_1))) _let_1)))))))) ) 15.33/15.53 ( (let ((_let_0 (fun int bool))) (fun (fun real (fun int _let_0)) (fun real _let_0))), (let ((_let_0 (fun int bool))) (fun (fun int _let_0) _let_0)), (let ((_let_0 (fun int bool))) (combb (fun int _let_0) _let_0 real)), (let ((_let_0 (fun int bool))) (hAPP (fun _let_0 bool) (fun (fun int _let_0) _let_0) (combb _let_0 bool int) (fEx int))) ) 15.33/15.53 ( (let ((_let_0 (fun int bool))) (fun real (fun _let_0 (fun int _let_0)))), (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int (fun _let_0 _let_0)))) (let ((_let_2 (fun _let_0 (fun int _let_0)))) (hAPP (fun _let_1 _let_2) (fun (fun real _let_1) (fun real _let_2)) (combb _let_1 _let_2 real) (combc int _let_0 _let_0))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun int _let_3))) (let ((_let_6 (fun (fun int bool) (fun int bool)))) (let ((_let_7 (fun (fun int bool) _let_5))) (let ((_let_8 (fun int real))) (let ((_let_9 (fun int _let_6))) (let ((_let_10 (fun int _let_5))) (let ((_let_11 (fun _let_10 _let_9))) (let ((_let_12 (fun (fun int (fun int bool)) _let_10))) (let ((_let_13 (fun real (fun int (fun int bool))))) (let ((_let_14 (fun real _let_9))) (let ((_let_15 (fun real _let_10))) (let ((_let_16 (fun int _let_8))) (let ((_let_17 (fun _let_16 (fun int (fun int bool))))) (let ((_let_18 (fun real _let_17))) (let ((_let_19 (fun _let_8 (fun int bool)))) (let ((_let_20 (fun real _let_19))) (let ((_let_21 (fun _let_8 _let_8))) (let ((_let_22 (fun int _let_21))) (let ((_let_23 (fun int _let_1))) (hAPP _let_15 _let_14 (hAPP _let_11 (fun _let_15 _let_14) (combb _let_10 _let_9 real) (hAPP (fun _let_5 _let_6) _let_11 (combb _let_5 _let_6 int) (combs int bool bool))) (hAPP _let_13 _let_15 (hAPP _let_12 (fun _let_13 _let_15) (combb (fun int (fun int bool)) _let_10 real) (hAPP _let_7 _let_12 (combb (fun int bool) _let_5 int) (hAPP (fun bool _let_3) _let_7 (combb bool _let_3 int) fconj))) (hAPP _let_16 _let_13 (hAPP _let_18 (fun _let_16 _let_13) (combc real _let_16 (fun int (fun int bool))) (hAPP _let_20 _let_18 (hAPP (fun _let_19 _let_17) (fun _let_20 _let_18) (combb _let_19 _let_17 real) (combb _let_8 (fun int bool) int)) (hAPP _let_4 _let_20 (hAPP (fun _let_0 _let_19) (fun _let_4 _let_20) (combb _let_0 _let_19 real) (combb real bool int)) (fequal real)))) (hAPP _let_8 _let_16 (hAPP _let_22 (fun _let_8 _let_16) (combc int _let_8 _let_8) (hAPP _let_23 _let_22 (hAPP (fun _let_1 _let_21) (fun _let_23 _let_22) (combb _let_1 _let_21 int) (combb real real int)) (hAPP _let_8 _let_23 (hAPP (fun real _let_1) (fun _let_8 _let_23) (combb real _let_1 int) (inverse_divide real)) _let_2))) _let_2)))))))))))))))))))))))))))) ) 15.33/15.53 ( (let ((_let_0 (fun int bool))) (fun _let_0 (fun real (fun int _let_0)))), (let ((_let_0 (fun int bool))) (fun real (fun _let_0 (fun int _let_0)))), (let ((_let_0 (fun int bool))) (combc real _let_0 (fun int _let_0))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun int _let_3))) (let ((_let_6 (fun (fun int bool) (fun int bool)))) (let ((_let_7 (fun (fun int bool) _let_5))) (let ((_let_8 (fun int real))) (let ((_let_9 (fun int _let_6))) (let ((_let_10 (fun (fun int bool) (fun int (fun int bool))))) (let ((_let_11 (fun int _let_5))) (let ((_let_12 (fun _let_11 _let_9))) (let ((_let_13 (fun (fun int (fun int bool)) _let_11))) (let ((_let_14 (fun real (fun int (fun int bool))))) (let ((_let_15 (fun real _let_10))) (let ((_let_16 (fun real _let_9))) (let ((_let_17 (fun real _let_11))) (let ((_let_18 (fun int _let_8))) (let ((_let_19 (fun _let_18 (fun int (fun int bool))))) (let ((_let_20 (fun real _let_19))) (let ((_let_21 (fun _let_8 (fun int bool)))) (let ((_let_22 (fun real _let_21))) (let ((_let_23 (fun _let_8 _let_8))) (let ((_let_24 (fun int _let_23))) (let ((_let_25 (fun int _let_1))) (hAPP _let_16 _let_15 (hAPP (fun _let_9 _let_10) (fun _let_16 _let_15) (combb _let_9 _let_10 real) (combc int (fun int bool) (fun int bool))) (hAPP _let_17 _let_16 (hAPP _let_12 (fun _let_17 _let_16) (combb _let_11 _let_9 real) (hAPP (fun _let_5 _let_6) _let_12 (combb _let_5 _let_6 int) (combs int bool bool))) (hAPP _let_14 _let_17 (hAPP _let_13 (fun _let_14 _let_17) (combb (fun int (fun int bool)) _let_11 real) (hAPP _let_7 _let_13 (combb (fun int bool) _let_5 int) (hAPP (fun bool _let_3) _let_7 (combb bool _let_3 int) fconj))) (hAPP _let_18 _let_14 (hAPP _let_20 (fun _let_18 _let_14) (combc real _let_18 (fun int (fun int bool))) (hAPP _let_22 _let_20 (hAPP (fun _let_21 _let_19) (fun _let_22 _let_20) (combb _let_21 _let_19 real) (combb _let_8 (fun int bool) int)) (hAPP _let_4 _let_22 (hAPP (fun _let_0 _let_21) (fun _let_4 _let_22) (combb _let_0 _let_21 real) (combb real bool int)) (fequal real)))) (hAPP _let_8 _let_18 (hAPP _let_24 (fun _let_8 _let_18) (combc int _let_8 _let_8) (hAPP _let_25 _let_24 (hAPP (fun _let_1 _let_23) (fun _let_25 _let_24) (combb _let_1 _let_23 int) (combb real real int)) (hAPP _let_8 _let_25 (hAPP (fun real _let_1) (fun _let_8 _let_25) (combb real _let_1 int) (inverse_divide real)) _let_2))) _let_2))))))))))))))))))))))))))))))) ) 15.33/15.53 ( (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))), (fun real (fun int (fun int (fun bool bool)))), (let ((_let_0 (fun int (fun bool bool)))) (let ((_let_1 (fun (fun int bool) (fun int bool)))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (fun int _let_0))) (let ((_let_4 (fun _let_3 _let_2))) (hAPP _let_4 (fun (fun real _let_3) (fun real _let_2)) (combb _let_3 _let_2 real) (hAPP (fun _let_0 _let_1) _let_4 (combb _let_0 _let_1 int) (combs int bool bool)))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun int _let_3))) (let ((_let_6 (fun (fun int bool) _let_5))) (let ((_let_7 (fun int real))) (let ((_let_8 (fun int _let_5))) (let ((_let_9 (fun (fun int (fun int bool)) _let_8))) (let ((_let_10 (fun real (fun int (fun int bool))))) (let ((_let_11 (fun real _let_8))) (let ((_let_12 (fun int _let_7))) (let ((_let_13 (fun _let_12 (fun int (fun int bool))))) (let ((_let_14 (fun real _let_13))) (let ((_let_15 (fun _let_7 (fun int bool)))) (let ((_let_16 (fun real _let_15))) (let ((_let_17 (fun _let_7 _let_7))) (let ((_let_18 (fun int _let_17))) (let ((_let_19 (fun int _let_1))) (hAPP _let_10 _let_11 (hAPP _let_9 (fun _let_10 _let_11) (combb (fun int (fun int bool)) _let_8 real) (hAPP _let_6 _let_9 (combb (fun int bool) _let_5 int) (hAPP (fun bool _let_3) _let_6 (combb bool _let_3 int) fconj))) (hAPP _let_12 _let_10 (hAPP _let_14 (fun _let_12 _let_10) (combc real _let_12 (fun int (fun int bool))) (hAPP _let_16 _let_14 (hAPP (fun _let_15 _let_13) (fun _let_16 _let_14) (combb _let_15 _let_13 real) (combb _let_7 (fun int bool) int)) (hAPP _let_4 _let_16 (hAPP (fun _let_0 _let_15) (fun _let_4 _let_16) (combb _let_0 _let_15 real) (combb real bool int)) (fequal real)))) (hAPP _let_7 _let_12 (hAPP _let_18 (fun _let_7 _let_12) (combc int _let_7 _let_7) (hAPP _let_19 _let_18 (hAPP (fun _let_1 _let_17) (fun _let_19 _let_18) (combb _let_1 _let_17 int) (combb real real int)) (hAPP _let_7 _let_19 (hAPP (fun real _let_1) (fun _let_7 _let_19) (combb real _let_1 int) (inverse_divide real)) _let_2))) _let_2))))))))))))))))))))))) ) 15.33/15.53 ( (let ((_let_0 (fun int bool))) (fun (fun real (fun int (fun _let_0 _let_0))) (fun real (fun _let_0 (fun int _let_0))))), (let ((_let_0 (fun int bool))) (fun (fun int (fun _let_0 _let_0)) (fun _let_0 (fun int _let_0)))), (let ((_let_0 (fun int bool))) (combb (fun int (fun _let_0 _let_0)) (fun _let_0 (fun int _let_0)) real)), (let ((_let_0 (fun int bool))) (combc int _let_0 _let_0)) ) 15.33/15.53 ( (fun real (fun int (fun int (fun bool bool)))), (fun real (fun int (fun int bool))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun _let_0 _let_3))) (let ((_let_5 (fun int _let_3))) (let ((_let_6 (fun _let_1 _let_5))) (hAPP _let_6 (fun (fun real _let_1) (fun real _let_5)) (combb _let_1 _let_5 real) (hAPP _let_4 _let_6 (combb _let_0 _let_3 int) (hAPP (fun bool _let_2) _let_4 (combb bool _let_2 int) fconj)))))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun real _let_0))) (let ((_let_4 (fun int real))) (let ((_let_5 (fun real (fun int (fun int bool))))) (let ((_let_6 (fun int _let_4))) (let ((_let_7 (fun _let_6 (fun int (fun int bool))))) (let ((_let_8 (fun real _let_7))) (let ((_let_9 (fun _let_4 (fun int bool)))) (let ((_let_10 (fun real _let_9))) (let ((_let_11 (fun _let_4 _let_4))) (let ((_let_12 (fun int _let_11))) (let ((_let_13 (fun int _let_1))) (hAPP _let_6 _let_5 (hAPP _let_8 (fun _let_6 _let_5) (combc real _let_6 (fun int (fun int bool))) (hAPP _let_10 _let_8 (hAPP (fun _let_9 _let_7) (fun _let_10 _let_8) (combb _let_9 _let_7 real) (combb _let_4 (fun int bool) int)) (hAPP _let_3 _let_10 (hAPP (fun _let_0 _let_9) (fun _let_3 _let_10) (combb _let_0 _let_9 real) (combb real bool int)) (fequal real)))) (hAPP _let_4 _let_6 (hAPP _let_12 (fun _let_4 _let_6) (combc int _let_4 _let_4) (hAPP _let_13 _let_12 (hAPP (fun _let_1 _let_11) (fun _let_13 _let_12) (combb _let_1 _let_11 int) (combb real real int)) (hAPP _let_4 _let_13 (hAPP (fun real _let_1) (fun _let_4 _let_13) (combb real _let_1 int) (inverse_divide real)) _let_2))) _let_2)))))))))))))))) ) 15.33/15.53 ( (let ((_let_0 (fun int bool))) (fun (fun real (fun int (fun int (fun bool bool)))) (fun real (fun int (fun _let_0 _let_0))))), (let ((_let_0 (fun int bool))) (fun (fun int (fun int (fun bool bool))) (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun int bool))) (combb (fun int (fun int (fun bool bool))) (fun int (fun _let_0 _let_0)) real)), (let ((_let_0 (fun int (fun bool bool)))) (let ((_let_1 (fun (fun int bool) (fun int bool)))) (hAPP (fun _let_0 _let_1) (fun (fun int _let_0) (fun int _let_1)) (combb _let_0 _let_1 int) (combs int bool bool)))) ) 15.33/15.53 ( (fun (fun real (fun int (fun int bool))) (fun real (fun int (fun int (fun bool bool))))), (fun (fun int (fun int bool)) (fun int (fun int (fun bool bool)))), (combb (fun int (fun int bool)) (fun int (fun int (fun bool bool))) real), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (fun _let_0 _let_2))) (hAPP _let_3 (fun (fun int _let_0) (fun int _let_2)) (combb _let_0 _let_2 int) (hAPP (fun bool _let_1) _let_3 (combb bool _let_1 int) fconj)))))) ) 15.33/15.53 ( (fun int (fun int real)), (fun int real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun int real))) (let ((_let_2 (fun _let_1 _let_1))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int _let_0))) (hAPP _let_3 (fun _let_1 (fun int _let_1)) (combc int _let_1 _let_1) (hAPP _let_4 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_4 _let_3) (combb _let_0 _let_2 int) (combb real real int)) (hAPP _let_1 _let_4 (hAPP (fun real _let_0) (fun _let_1 _let_4) (combb real _let_0 int) (inverse_divide real)) (real_1 int))))))))), (real_1 int) ) 15.33/15.53 ( (fun real (fun (fun int (fun int real)) (fun int (fun int bool)))), (fun real (fun (fun int real) (fun int bool))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int real))) (let ((_let_2 (fun (fun int _let_1) (fun int _let_0)))) (let ((_let_3 (fun _let_1 _let_0))) (hAPP (fun _let_3 _let_2) (fun (fun real _let_3) (fun real _let_2)) (combb _let_3 _let_2 real) (combb _let_1 _let_0 int)))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun int real) (fun int bool)))) (let ((_let_3 (fun real _let_2))) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 real) (combb real bool int)) (fequal real)))))) ) 15.33/15.53 ( (fun (fun int (fun int real)) (fun real (fun int (fun int bool)))), (fun real (fun (fun int (fun int real)) (fun int (fun int bool)))), (combc real (fun int (fun int real)) (fun int (fun int bool))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun int (fun int real)) (fun int (fun int bool))))) (let ((_let_3 (fun real _let_2))) (let ((_let_4 (fun (fun int real) (fun int bool)))) (let ((_let_5 (fun real _let_4))) (hAPP _let_5 _let_3 (hAPP (fun _let_4 _let_2) (fun _let_5 _let_3) (combb _let_4 _let_2 real) (combb (fun int real) (fun int bool) int)) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_1 _let_5) (combb _let_0 _let_4 real) (combb real bool int)) (fequal real))))))))) ) 15.33/15.53 ( (fun real (fun (fun int real) (fun int bool))), (fun real (fun real bool)), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun (fun int real) (fun int bool)))) (hAPP (fun _let_0 _let_1) (fun (fun real _let_0) (fun real _let_1)) (combb _let_0 _let_1 real) (combb real bool int)))), (fequal real) ) 15.33/15.53 ( (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int real))) (fun (fun real (fun _let_1 _let_0)) (fun real (fun (fun int _let_1) (fun int _let_0)))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int real))) (fun (fun _let_1 _let_0) (fun (fun int _let_1) (fun int _let_0))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int real))) (combb (fun _let_1 _let_0) (fun (fun int _let_1) (fun int _let_0)) real))), (combb (fun int real) (fun int bool) int) ) 15.33/15.53 ( (fun (fun real (fun real bool)) (fun real (fun (fun int real) (fun int bool)))), (fun (fun real bool) (fun (fun int real) (fun int bool))), (combb (fun real bool) (fun (fun int real) (fun int bool)) real), (combb real bool int) ) 15.33/15.53 ( (let ((_let_0 (fun int real))) (fun int (fun _let_0 _let_0))), (fun int (fun real real)), (let ((_let_0 (fun real real))) (let ((_let_1 (fun (fun int real) (fun int real)))) (hAPP (fun _let_0 _let_1) (fun (fun int _let_0) (fun int _let_1)) (combb _let_0 _let_1 int) (combb real real int)))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun int real))) (let ((_let_2 (fun int _let_0))) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 int) (inverse_divide real)) (real_1 int))))) ) 15.33/15.53 ( (let ((_let_0 (fun int real))) (fun _let_0 (fun int _let_0))), (let ((_let_0 (fun int real))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun int real))) (combc int _let_0 _let_0)), (let ((_let_0 (fun real real))) (let ((_let_1 (fun int real))) (let ((_let_2 (fun _let_1 _let_1))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int _let_0))) (hAPP _let_4 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_4 _let_3) (combb _let_0 _let_2 int) (combb real real int)) (hAPP _let_1 _let_4 (hAPP (fun real _let_0) (fun _let_1 _let_4) (combb real _let_0 int) (inverse_divide real)) (real_1 int)))))))) ) 15.33/15.53 ( (fun int (fun real real)), (fun int real), (let ((_let_0 (fun real real))) (hAPP (fun real _let_0) (fun (fun int real) (fun int _let_0)) (combb real _let_0 int) (inverse_divide real))), (real_1 int) ) 15.33/15.53 ( (let ((_let_0 (fun int real))) (fun (fun int (fun real real)) (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun int real))) (fun (fun real real) (fun _let_0 _let_0))), (let ((_let_0 (fun int real))) (combb (fun real real) (fun _let_0 _let_0) int)), (combb real real int) ) 15.33/15.53 ( (fun (fun int real) (fun int (fun real real))), (fun real (fun real real)), (combb real (fun real real) int), (inverse_divide real) ) 15.33/15.53 ( (let ((_let_0 (fun int (fun int bool)))) (fun _let_0 _let_0)), (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), (let ((_let_0 (fun int bool))) (combb _let_0 _let_0 int)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun int _let_1))) (hAPP _let_2 (fun _let_0 _let_0) (combs int bool bool) (hAPP _let_0 _let_2 (hAPP (fun bool _let_1) (fun _let_0 _let_2) (combb bool _let_1 int) fconj) (hAPP int _let_0 (ord_less int) (zero_zero int))))))) ) 15.33/15.53 ( (fun real (fun int (fun nat bool))), (fun nat bool), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun (fun nat real) (fun nat real)))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun (fun nat bool) (fun nat bool)))) (let ((_let_6 (fun int real))) (let ((_let_7 (fun nat _let_2))) (let ((_let_8 (fun (fun nat bool) _let_7))) (let ((_let_9 (fun int _let_1))) (let ((_let_10 (fun real (fun int (fun nat bool))))) (let ((_let_11 (fun (fun nat bool) (fun int (fun nat bool))))) (let ((_let_12 (fun real _let_11))) (let ((_let_13 (fun int _let_5))) (let ((_let_14 (fun real _let_13))) (let ((_let_15 (fun int _let_7))) (let ((_let_16 (fun real _let_15))) (let ((_let_17 (fun _let_15 _let_13))) (let ((_let_18 (fun (fun int (fun nat bool)) _let_15))) (let ((_let_19 (fun int (fun nat real)))) (let ((_let_20 (fun _let_19 (fun int (fun nat bool))))) (let ((_let_21 (fun real _let_20))) (let ((_let_22 (fun (fun nat real) (fun nat bool)))) (let ((_let_23 (fun real _let_22))) (let ((_let_24 (fun int _let_3))) (hAPP _let_12 (fun (fun nat bool) _let_10) (combc real (fun nat bool) (fun int (fun nat bool))) (hAPP _let_14 _let_12 (hAPP (fun _let_13 _let_11) (fun _let_14 _let_12) (combb _let_13 _let_11 real) (combc int (fun nat bool) (fun nat bool))) (hAPP _let_16 _let_14 (hAPP _let_17 (fun _let_16 _let_14) (combb _let_15 _let_13 real) (hAPP (fun _let_7 _let_5) _let_17 (combb _let_7 _let_5 int) (combs nat bool bool))) (hAPP _let_10 _let_16 (hAPP _let_18 (fun _let_10 _let_16) (combb (fun int (fun nat bool)) _let_15 real) (hAPP _let_8 _let_18 (combb (fun nat bool) _let_7 int) (hAPP (fun bool _let_2) _let_8 (combb bool _let_2 nat) fconj))) (hAPP _let_19 _let_10 (hAPP _let_21 (fun _let_19 _let_10) (combc real _let_19 (fun int (fun nat bool))) (hAPP _let_23 _let_21 (hAPP (fun _let_22 _let_20) (fun _let_23 _let_21) (combb _let_22 _let_20 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_4 _let_23 (hAPP (fun _let_0 _let_22) (fun _let_4 _let_23) (combb _let_0 _let_22 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_19 (hAPP _let_24 (fun (fun nat real) _let_19) (combc int (fun nat real) (fun nat real)) (hAPP _let_9 _let_24 (hAPP (fun _let_1 _let_3) (fun _let_9 _let_24) (combb _let_1 _let_3 int) (combb real real nat)) (hAPP _let_6 _let_9 (hAPP (fun real _let_1) (fun _let_6 _let_9) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat)))))))))))))))))))))))))))))))), (let ((_let_0 (fun nat (fun nat bool)))) (hAPP (fun nat bool) (fun nat bool) (hAPP (fun bool bool) (fun (fun nat bool) (fun nat bool)) (combb bool bool nat) fNot) (hAPP nat (fun nat bool) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat)) (zero_zero nat)))) ) 15.33/15.53 ( (fun real (fun int (fun nat bool))), (fun int (fun nat real)), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun int (fun nat real)) (fun int (fun nat bool))))) (let ((_let_3 (fun real _let_2))) (let ((_let_4 (fun (fun nat real) (fun nat bool)))) (let ((_let_5 (fun real _let_4))) (hAPP _let_3 (fun (fun int (fun nat real)) (fun real (fun int (fun nat bool)))) (combc real (fun int (fun nat real)) (fun int (fun nat bool))) (hAPP _let_5 _let_3 (hAPP (fun _let_4 _let_2) (fun _let_5 _let_3) (combb _let_4 _let_2 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_1 _let_5) (combb _let_0 _let_4 real) (combb real bool nat)) (fequal real)))))))))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun (fun nat real) (fun nat real)))) (let ((_let_2 (fun int real))) (let ((_let_3 (fun int _let_0))) (let ((_let_4 (fun int (fun nat real)))) (let ((_let_5 (fun int _let_1))) (hAPP (fun nat real) _let_4 (hAPP _let_5 (fun (fun nat real) _let_4) (combc int (fun nat real) (fun nat real)) (hAPP _let_3 _let_5 (hAPP (fun _let_0 _let_1) (fun _let_3 _let_5) (combb _let_0 _let_1 int) (combb real real nat)) (hAPP _let_2 _let_3 (hAPP (fun real _let_0) (fun _let_2 _let_3) (combb real _let_0 int) (inverse_divide real)) (real_1 int)))) (real_1 nat)))))))) ) 15.33/15.53 ( (fun (fun int (fun nat bool)) (fun int bool)), (fun (fun nat bool) bool), (combb (fun nat bool) bool int), (fEx nat) ) 15.33/15.53 ( (fun (fun real (fun int (fun nat bool))) (fun real (fun int bool))), (fun (fun int (fun nat bool)) (fun int bool)), (combb (fun int (fun nat bool)) (fun int bool) real), (let ((_let_0 (fun nat bool))) (hAPP (fun _let_0 bool) (fun (fun int _let_0) (fun int bool)) (combb _let_0 bool int) (fEx nat))) ) 15.33/15.53 ( (let ((_let_0 (fun nat bool))) (fun real (fun _let_0 (fun int _let_0)))), (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun _let_0 (fun int _let_0)))) (let ((_let_2 (fun int (fun _let_0 _let_0)))) (hAPP (fun _let_2 _let_1) (fun (fun real _let_2) (fun real _let_1)) (combb _let_2 _let_1 real) (combc int _let_0 _let_0))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun (fun nat real) (fun nat real)))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun (fun nat bool) (fun nat bool)))) (let ((_let_6 (fun int real))) (let ((_let_7 (fun nat _let_2))) (let ((_let_8 (fun (fun nat bool) _let_7))) (let ((_let_9 (fun int _let_1))) (let ((_let_10 (fun real (fun int (fun nat bool))))) (let ((_let_11 (fun int _let_5))) (let ((_let_12 (fun real _let_11))) (let ((_let_13 (fun int _let_7))) (let ((_let_14 (fun real _let_13))) (let ((_let_15 (fun _let_13 _let_11))) (let ((_let_16 (fun (fun int (fun nat bool)) _let_13))) (let ((_let_17 (fun int (fun nat real)))) (let ((_let_18 (fun _let_17 (fun int (fun nat bool))))) (let ((_let_19 (fun real _let_18))) (let ((_let_20 (fun (fun nat real) (fun nat bool)))) (let ((_let_21 (fun real _let_20))) (let ((_let_22 (fun int _let_3))) (hAPP _let_14 _let_12 (hAPP _let_15 (fun _let_14 _let_12) (combb _let_13 _let_11 real) (hAPP (fun _let_7 _let_5) _let_15 (combb _let_7 _let_5 int) (combs nat bool bool))) (hAPP _let_10 _let_14 (hAPP _let_16 (fun _let_10 _let_14) (combb (fun int (fun nat bool)) _let_13 real) (hAPP _let_8 _let_16 (combb (fun nat bool) _let_7 int) (hAPP (fun bool _let_2) _let_8 (combb bool _let_2 nat) fconj))) (hAPP _let_17 _let_10 (hAPP _let_19 (fun _let_17 _let_10) (combc real _let_17 (fun int (fun nat bool))) (hAPP _let_21 _let_19 (hAPP (fun _let_20 _let_18) (fun _let_21 _let_19) (combb _let_20 _let_18 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_4 _let_21 (hAPP (fun _let_0 _let_20) (fun _let_4 _let_21) (combb _let_0 _let_20 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_17 (hAPP _let_22 (fun (fun nat real) _let_17) (combc int (fun nat real) (fun nat real)) (hAPP _let_9 _let_22 (hAPP (fun _let_1 _let_3) (fun _let_9 _let_22) (combb _let_1 _let_3 int) (combb real real nat)) (hAPP _let_6 _let_9 (hAPP (fun real _let_1) (fun _let_6 _let_9) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat)))))))))))))))))))))))))))) ) 15.33/15.53 ( (let ((_let_0 (fun nat bool))) (fun _let_0 (fun real (fun int _let_0)))), (let ((_let_0 (fun nat bool))) (fun real (fun _let_0 (fun int _let_0)))), (let ((_let_0 (fun nat bool))) (combc real _let_0 (fun int _let_0))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun (fun nat real) (fun nat real)))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun (fun nat bool) (fun nat bool)))) (let ((_let_6 (fun int real))) (let ((_let_7 (fun nat _let_2))) (let ((_let_8 (fun (fun nat bool) _let_7))) (let ((_let_9 (fun int _let_1))) (let ((_let_10 (fun real (fun int (fun nat bool))))) (let ((_let_11 (fun (fun nat bool) (fun int (fun nat bool))))) (let ((_let_12 (fun real _let_11))) (let ((_let_13 (fun int _let_5))) (let ((_let_14 (fun real _let_13))) (let ((_let_15 (fun int _let_7))) (let ((_let_16 (fun real _let_15))) (let ((_let_17 (fun _let_15 _let_13))) (let ((_let_18 (fun (fun int (fun nat bool)) _let_15))) (let ((_let_19 (fun int (fun nat real)))) (let ((_let_20 (fun _let_19 (fun int (fun nat bool))))) (let ((_let_21 (fun real _let_20))) (let ((_let_22 (fun (fun nat real) (fun nat bool)))) (let ((_let_23 (fun real _let_22))) (let ((_let_24 (fun int _let_3))) (hAPP _let_14 _let_12 (hAPP (fun _let_13 _let_11) (fun _let_14 _let_12) (combb _let_13 _let_11 real) (combc int (fun nat bool) (fun nat bool))) (hAPP _let_16 _let_14 (hAPP _let_17 (fun _let_16 _let_14) (combb _let_15 _let_13 real) (hAPP (fun _let_7 _let_5) _let_17 (combb _let_7 _let_5 int) (combs nat bool bool))) (hAPP _let_10 _let_16 (hAPP _let_18 (fun _let_10 _let_16) (combb (fun int (fun nat bool)) _let_15 real) (hAPP _let_8 _let_18 (combb (fun nat bool) _let_7 int) (hAPP (fun bool _let_2) _let_8 (combb bool _let_2 nat) fconj))) (hAPP _let_19 _let_10 (hAPP _let_21 (fun _let_19 _let_10) (combc real _let_19 (fun int (fun nat bool))) (hAPP _let_23 _let_21 (hAPP (fun _let_22 _let_20) (fun _let_23 _let_21) (combb _let_22 _let_20 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_4 _let_23 (hAPP (fun _let_0 _let_22) (fun _let_4 _let_23) (combb _let_0 _let_22 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_19 (hAPP _let_24 (fun (fun nat real) _let_19) (combc int (fun nat real) (fun nat real)) (hAPP _let_9 _let_24 (hAPP (fun _let_1 _let_3) (fun _let_9 _let_24) (combb _let_1 _let_3 int) (combb real real nat)) (hAPP _let_6 _let_9 (hAPP (fun real _let_1) (fun _let_6 _let_9) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat))))))))))))))))))))))))))))))) ) 15.33/15.53 ( (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))), (fun real (fun int (fun nat (fun bool bool)))), (let ((_let_0 (fun (fun nat bool) (fun nat bool)))) (let ((_let_1 (fun nat (fun bool bool)))) (let ((_let_2 (fun int _let_0))) (let ((_let_3 (fun int _let_1))) (let ((_let_4 (fun _let_3 _let_2))) (hAPP _let_4 (fun (fun real _let_3) (fun real _let_2)) (combb _let_3 _let_2 real) (hAPP (fun _let_1 _let_0) _let_4 (combb _let_1 _let_0 int) (combs nat bool bool)))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun (fun nat real) (fun nat real)))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun int real))) (let ((_let_6 (fun nat _let_2))) (let ((_let_7 (fun (fun nat bool) _let_6))) (let ((_let_8 (fun int _let_1))) (let ((_let_9 (fun real (fun int (fun nat bool))))) (let ((_let_10 (fun int _let_6))) (let ((_let_11 (fun real _let_10))) (let ((_let_12 (fun (fun int (fun nat bool)) _let_10))) (let ((_let_13 (fun int (fun nat real)))) (let ((_let_14 (fun _let_13 (fun int (fun nat bool))))) (let ((_let_15 (fun real _let_14))) (let ((_let_16 (fun (fun nat real) (fun nat bool)))) (let ((_let_17 (fun real _let_16))) (let ((_let_18 (fun int _let_3))) (hAPP _let_9 _let_11 (hAPP _let_12 (fun _let_9 _let_11) (combb (fun int (fun nat bool)) _let_10 real) (hAPP _let_7 _let_12 (combb (fun nat bool) _let_6 int) (hAPP (fun bool _let_2) _let_7 (combb bool _let_2 nat) fconj))) (hAPP _let_13 _let_9 (hAPP _let_15 (fun _let_13 _let_9) (combc real _let_13 (fun int (fun nat bool))) (hAPP _let_17 _let_15 (hAPP (fun _let_16 _let_14) (fun _let_17 _let_15) (combb _let_16 _let_14 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_4 _let_17 (hAPP (fun _let_0 _let_16) (fun _let_4 _let_17) (combb _let_0 _let_16 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_13 (hAPP _let_18 (fun (fun nat real) _let_13) (combc int (fun nat real) (fun nat real)) (hAPP _let_8 _let_18 (hAPP (fun _let_1 _let_3) (fun _let_8 _let_18) (combb _let_1 _let_3 int) (combb real real nat)) (hAPP _let_5 _let_8 (hAPP (fun real _let_1) (fun _let_5 _let_8) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat))))))))))))))))))))))) ) 15.33/15.53 ( (let ((_let_0 (fun nat bool))) (fun (fun real (fun int (fun _let_0 _let_0))) (fun real (fun _let_0 (fun int _let_0))))), (let ((_let_0 (fun nat bool))) (fun (fun int (fun _let_0 _let_0)) (fun _let_0 (fun int _let_0)))), (let ((_let_0 (fun nat bool))) (combb (fun int (fun _let_0 _let_0)) (fun _let_0 (fun int _let_0)) real)), (let ((_let_0 (fun nat bool))) (combc int _let_0 _let_0)) ) 15.33/15.54 ( (fun real (fun int (fun nat (fun bool bool)))), (fun real (fun int (fun nat bool))), (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun nat _let_1))) (let ((_let_3 (fun _let_0 _let_2))) (let ((_let_4 (fun int _let_0))) (let ((_let_5 (fun int _let_2))) (let ((_let_6 (fun _let_4 _let_5))) (hAPP _let_6 (fun (fun real _let_4) (fun real _let_5)) (combb _let_4 _let_5 real) (hAPP _let_3 _let_6 (combb _let_0 _let_2 int) (hAPP (fun bool _let_1) _let_3 (combb bool _let_1 nat) fconj)))))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun (fun nat real) (fun nat real)))) (let ((_let_3 (fun real _let_0))) (let ((_let_4 (fun int real))) (let ((_let_5 (fun int _let_1))) (let ((_let_6 (fun real (fun int (fun nat bool))))) (let ((_let_7 (fun int (fun nat real)))) (let ((_let_8 (fun _let_7 (fun int (fun nat bool))))) (let ((_let_9 (fun real _let_8))) (let ((_let_10 (fun (fun nat real) (fun nat bool)))) (let ((_let_11 (fun real _let_10))) (let ((_let_12 (fun int _let_2))) (hAPP _let_7 _let_6 (hAPP _let_9 (fun _let_7 _let_6) (combc real _let_7 (fun int (fun nat bool))) (hAPP _let_11 _let_9 (hAPP (fun _let_10 _let_8) (fun _let_11 _let_9) (combb _let_10 _let_8 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_3 _let_11 (hAPP (fun _let_0 _let_10) (fun _let_3 _let_11) (combb _let_0 _let_10 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_7 (hAPP _let_12 (fun (fun nat real) _let_7) (combc int (fun nat real) (fun nat real)) (hAPP _let_5 _let_12 (hAPP (fun _let_1 _let_2) (fun _let_5 _let_12) (combb _let_1 _let_2 int) (combb real real nat)) (hAPP _let_4 _let_5 (hAPP (fun real _let_1) (fun _let_4 _let_5) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat)))))))))))))))) ) 15.33/15.54 ( (let ((_let_0 (fun nat bool))) (fun (fun int (fun nat (fun bool bool))) (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun nat bool))) (fun (fun nat (fun bool bool)) (fun _let_0 _let_0))), (let ((_let_0 (fun nat bool))) (combb (fun nat (fun bool bool)) (fun _let_0 _let_0) int)), (combs nat bool bool) ) 15.33/15.54 ( (let ((_let_0 (fun nat bool))) (fun (fun real (fun int (fun nat (fun bool bool)))) (fun real (fun int (fun _let_0 _let_0))))), (let ((_let_0 (fun nat bool))) (fun (fun int (fun nat (fun bool bool))) (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun nat bool))) (combb (fun int (fun nat (fun bool bool))) (fun int (fun _let_0 _let_0)) real)), (let ((_let_0 (fun (fun nat bool) (fun nat bool)))) (let ((_let_1 (fun nat (fun bool bool)))) (hAPP (fun _let_1 _let_0) (fun (fun int _let_1) (fun int _let_0)) (combb _let_1 _let_0 int) (combs nat bool bool)))) ) 15.33/15.54 ( (fun (fun int (fun nat bool)) (fun int (fun nat (fun bool bool)))), (fun (fun nat bool) (fun nat (fun bool bool))), (combb (fun nat bool) (fun nat (fun bool bool)) int), (let ((_let_0 (fun bool bool))) (hAPP (fun bool _let_0) (fun (fun nat bool) (fun nat _let_0)) (combb bool _let_0 nat) fconj)) ) 15.33/15.54 ( (fun (fun real (fun int (fun nat bool))) (fun real (fun int (fun nat (fun bool bool))))), (fun (fun int (fun nat bool)) (fun int (fun nat (fun bool bool)))), (combb (fun int (fun nat bool)) (fun int (fun nat (fun bool bool))) real), (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun nat _let_1))) (let ((_let_3 (fun _let_0 _let_2))) (hAPP _let_3 (fun (fun int _let_0) (fun int _let_2)) (combb _let_0 _let_2 int) (hAPP (fun bool _let_1) _let_3 (combb bool _let_1 nat) fconj)))))) ) 15.33/15.54 ( (fun int (fun nat real)), (fun nat real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun (fun nat real) (fun nat real)))) (let ((_let_2 (fun int real))) (let ((_let_3 (fun int _let_0))) (let ((_let_4 (fun int _let_1))) (hAPP _let_4 (fun (fun nat real) (fun int (fun nat real))) (combc int (fun nat real) (fun nat real)) (hAPP _let_3 _let_4 (hAPP (fun _let_0 _let_1) (fun _let_3 _let_4) (combb _let_0 _let_1 int) (combb real real nat)) (hAPP _let_2 _let_3 (hAPP (fun real _let_0) (fun _let_2 _let_3) (combb real _let_0 int) (inverse_divide real)) (real_1 int))))))))), (real_1 nat) ) 15.33/15.54 ( (fun real (fun (fun int (fun nat real)) (fun int (fun nat bool)))), (fun real (fun (fun nat real) (fun nat bool))), (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun (fun int _let_1) (fun int _let_0)))) (let ((_let_3 (fun _let_1 _let_0))) (hAPP (fun _let_3 _let_2) (fun (fun real _let_3) (fun real _let_2)) (combb _let_3 _let_2 real) (combb _let_1 _let_0 int)))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun nat real) (fun nat bool)))) (let ((_let_3 (fun real _let_2))) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 real) (combb real bool nat)) (fequal real)))))) ) 15.33/15.54 ( (fun (fun int (fun nat real)) (fun real (fun int (fun nat bool)))), (fun real (fun (fun int (fun nat real)) (fun int (fun nat bool)))), (combc real (fun int (fun nat real)) (fun int (fun nat bool))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun int (fun nat real)) (fun int (fun nat bool))))) (let ((_let_3 (fun real _let_2))) (let ((_let_4 (fun (fun nat real) (fun nat bool)))) (let ((_let_5 (fun real _let_4))) (hAPP _let_5 _let_3 (hAPP (fun _let_4 _let_2) (fun _let_5 _let_3) (combb _let_4 _let_2 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_1 _let_5) (combb _let_0 _let_4 real) (combb real bool nat)) (fequal real))))))))) ) 15.33/15.54 ( (fun real (fun (fun nat real) (fun nat bool))), (fun real (fun real bool)), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun (fun nat real) (fun nat bool)))) (hAPP (fun _let_0 _let_1) (fun (fun real _let_0) (fun real _let_1)) (combb _let_0 _let_1 real) (combb real bool nat)))), (fequal real) ) 15.33/15.54 ( (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat real))) (fun (fun real (fun _let_1 _let_0)) (fun real (fun (fun int _let_1) (fun int _let_0)))))), (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat real))) (fun (fun _let_1 _let_0) (fun (fun int _let_1) (fun int _let_0))))), (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat real))) (combb (fun _let_1 _let_0) (fun (fun int _let_1) (fun int _let_0)) real))), (combb (fun nat real) (fun nat bool) int) ) 15.33/15.54 ( (fun (fun real (fun real bool)) (fun real (fun (fun nat real) (fun nat bool)))), (fun (fun real bool) (fun (fun nat real) (fun nat bool))), (combb (fun real bool) (fun (fun nat real) (fun nat bool)) real), (combb real bool nat) ) 15.33/15.54 ( (let ((_let_0 (fun nat real))) (fun int (fun _let_0 _let_0))), (fun int (fun real real)), (let ((_let_0 (fun real real))) (let ((_let_1 (fun (fun nat real) (fun nat real)))) (hAPP (fun _let_0 _let_1) (fun (fun int _let_0) (fun int _let_1)) (combb _let_0 _let_1 int) (combb real real nat)))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun int real))) (let ((_let_2 (fun int _let_0))) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 int) (inverse_divide real)) (real_1 int))))) ) 15.33/15.54 ( (let ((_let_0 (fun nat real))) (fun _let_0 (fun int _let_0))), (let ((_let_0 (fun nat real))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun nat real))) (combc int _let_0 _let_0)), (let ((_let_0 (fun real real))) (let ((_let_1 (fun (fun nat real) (fun nat real)))) (let ((_let_2 (fun int real))) (let ((_let_3 (fun int _let_0))) (let ((_let_4 (fun int _let_1))) (hAPP _let_3 _let_4 (hAPP (fun _let_0 _let_1) (fun _let_3 _let_4) (combb _let_0 _let_1 int) (combb real real nat)) (hAPP _let_2 _let_3 (hAPP (fun real _let_0) (fun _let_2 _let_3) (combb real _let_0 int) (inverse_divide real)) (real_1 int)))))))) ) 15.33/15.54 ( (let ((_let_0 (fun nat real))) (fun (fun int (fun real real)) (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun nat real))) (fun (fun real real) (fun _let_0 _let_0))), (let ((_let_0 (fun nat real))) (combb (fun real real) (fun _let_0 _let_0) int)), (combb real real nat) ) 15.33/15.54 ( (let ((_let_0 (fun int int))) (fun int (fun _let_0 _let_0))), (fun int (fun int int)), (let ((_let_0 (fun (fun int int) (fun int int)))) (hAPP (fun (fun int int) _let_0) (fun (fun int (fun int int)) (fun int _let_0)) (combb (fun int int) _let_0 int) (combb int int int))), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)) (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 15.33/15.54 ( (let ((_let_0 (fun int int))) (fun (fun int _let_0) (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun int int))) (fun _let_0 (fun _let_0 _let_0))), (let ((_let_0 (fun int int))) (combb _let_0 (fun _let_0 _let_0) int)), (combb int int int) ) 15.33/15.54 ( (let ((_let_0 (fun int (fun int (fun int bool))))) (fun _let_0 _let_0)), (let ((_let_0 (fun int (fun int bool)))) (fun _let_0 _let_0)), (let ((_let_0 (fun int (fun int bool)))) (combb _let_0 _let_0 int)), (combc int int bool) ) 15.33/15.54 ( (fun (fun int (fun int int)) (fun int (fun int (fun int bool)))), (fun (fun int int) (fun int (fun int bool))), (combb (fun int int) (fun int (fun int bool)) int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (hAPP _let_1 (fun (fun int int) _let_1) (combb int _let_0 int) (fequal int)))) ) 15.33/15.54 ) 15.33/15.54 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) _let_2))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real cos (hAPP real real (hAPP real (fun real real) (times_times real) _let_2) X_1))) (one_one real))))))) ) 15.33/15.54 ( pi ) 15.33/15.54 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.54 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.54 ( (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.33/15.54 ( skv_2 ) 15.33/15.54 ( skv_8 ) 15.33/15.54 ( skv_9 ) 15.33/15.54 ) 15.33/15.54 (instantiation (forall ((N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_1))) (not (forall ((M_2 $$unsorted)) (not (= N_1 (hAPP nat nat suc M_2))) ))) ) 15.33/15.54 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.54 ) 15.33/15.54 (instantiation (forall ((Z_1 $$unsorted)) (let ((_let_0 (fun complex complex))) (= (hAPP complex complex (hAPP complex _let_0 (times_times complex) (hAPP real complex (of_real complex) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP complex real im Z_1)))) ii) (hAPP complex complex (hAPP complex _let_0 (minus_minus complex) Z_1) (hAPP complex complex cnj Z_1)))) ) 15.33/15.54 ( (one_one complex) ) 15.33/15.54 ( ii ) 15.33/15.54 ( (zero_zero complex) ) 15.33/15.54 ) 15.33/15.54 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_104602 $$unsorted) (BOUND_VARIABLE_104603 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (times_times X_a))) (let ((_let_2 (uminus_uminus X_a))) (or (not (ring X_a)) (= (hAPP X_a X_a _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_104602) BOUND_VARIABLE_104603)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_104602)) BOUND_VARIABLE_104603)))))) ) 15.33/15.54 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 15.33/15.54 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.33/15.54 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13 ) 15.33/15.54 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.33/15.54 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.33/15.54 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.33/15.54 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 15.33/15.54 ( complex, ii, ii ) 15.33/15.54 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 15.33/15.54 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 15.33/15.54 ) 15.33/15.54 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_104621 $$unsorted) (BOUND_VARIABLE_104622 $$unsorted)) (let ((_let_0 (uminus_uminus X_a))) (let ((_let_1 (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_104621))) (or (not (ring X_a)) (= (hAPP X_a X_a _let_0 (hAPP X_a X_a _let_1 BOUND_VARIABLE_104622)) (hAPP X_a X_a _let_1 (hAPP X_a X_a _let_0 BOUND_VARIABLE_104622)))))) ) 15.33/15.54 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 15.33/15.54 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.33/15.54 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13 ) 15.33/15.54 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.33/15.54 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.33/15.54 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.33/15.54 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 15.33/15.54 ( complex, ii, ii ) 15.33/15.54 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 15.33/15.54 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 15.33/15.54 ) 15.33/15.54 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted) (F $$unsorted)) (let ((_let_0 (fun X_b X_c))) (let ((_let_1 (fun X_a _let_0))) (let ((_let_2 (product_prod X_a X_b))) (let ((_let_3 (fun _let_2 X_c))) (let ((_let_4 (fun X_b _let_2))) (let ((_let_5 (fun X_a _let_4))) (let ((_let_6 (fun _let_4 _let_0))) (= (ti _let_3 F) (hAPP _let_1 _let_3 (product_prod_case X_a X_b X_c) (hAPP _let_5 _let_1 (hAPP _let_6 (fun _let_5 _let_1) (combb _let_4 _let_0 X_a) (hAPP _let_3 _let_6 (combb _let_2 X_c X_b) F)) (product_Pair X_a X_b))))))))))) ) 15.33/15.54 ( nat, nat, bool, pred_nat ) 15.33/15.54 ( nat, nat, (fun (product_prod nat nat) bool), nat_gcd_rel ) 15.33/15.54 ( int, int, bool, frac_1 ) 15.33/15.54 ( int, int, int, twoSqu1094008024sum2sq ) 15.33/15.54 ( int, int, rat, frct ) 15.33/15.54 ( int, int, (product_prod int int), negateSnd ) 15.33/15.54 ( int, int, (product_prod int int), normalize ) 15.33/15.54 ( int, int, (fun (product_prod int int) bool), norm_frac_rel ) 15.33/15.54 ( int, int, (fun (product_prod int int) bool), posDivAlg_rel ) 15.33/15.54 ( int, int, (fun (product_prod int int) bool), lazy_small_lazy_rel ) 15.33/15.54 ( int, int, (fun (product_prod int int) bool), negDivAlg_rel ) 15.33/15.54 ( int, int, (fun (product_prod int int) bool), upto_rel ) 15.33/15.54 ( (product_prod nat nat), (product_prod nat nat), bool, pair_less ) 15.33/15.54 ( (product_prod nat nat), (product_prod nat nat), bool, pair_leq ) 15.33/15.54 ( (product_prod int int), (product_prod int int), bool, ratrel ) 15.33/15.54 ) 15.33/15.54 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_104642 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (group_add X_a)) (= (= _let_0 (ti X_a BOUND_VARIABLE_104642)) (= _let_0 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_104642))))) ) 15.33/15.54 ( bool, fFalse ) 15.33/15.54 ( bool, fTrue ) 15.33/15.54 ( int, (one_one int) ) 15.33/15.54 ( int, pls ) 15.33/15.54 ( int, min_1 ) 15.33/15.54 ( int, s ) 15.33/15.54 ( int, m ) 15.33/15.54 ( int, s1 ) 15.33/15.54 ( int, t ) 15.33/15.54 ( (fun int bool), nat_neg ) 15.33/15.54 ( (fun int bool), zprime ) 15.33/15.54 ( (fun int bool), zEven ) 15.33/15.54 ( (fun int bool), zOdd ) 15.33/15.54 ( (fun int bool), (even_odd_even int) ) 15.33/15.54 ( (fun int bool), twoSqu1091635170sum2sq ) 15.33/15.54 ( (fun int bool), nat_is_nat ) 15.33/15.54 ( (fun int (fun int bool)), norRRset ) 15.33/15.54 ( (fun int (fun int bool)), quadRes ) 15.33/15.54 ( (fun int (fun int bool)), sRStar ) 15.33/15.54 ( (fun int (fun int bool)), d22set ) 15.33/15.54 ( (fun int (fun int bool)), sr ) 15.33/15.54 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 15.33/15.54 ( (fun int int), zfact ) 15.33/15.54 ( (fun int int), bit0 ) 15.33/15.54 ( (fun int int), bit1 ) 15.33/15.54 ( (fun int int), (fact_fact int) ) 15.33/15.54 ( (fun int int), pred ) 15.33/15.54 ( (fun int int), succ ) 15.33/15.54 ( (fun nat bool), (even_odd_even nat) ) 15.33/15.54 ( (fun nat bool), prime ) 15.33/15.54 ( (fun nat nat), suc ) 15.33/15.54 ( (fun nat nat), (fact_fact nat) ) 15.33/15.54 ( (fun nat nat), fact ) 15.33/15.54 ( (fun nat nat), nat_size ) 15.33/15.54 ( (fun nat nat), (size_size nat) ) 15.33/15.54 ( (fun (product_prod nat nat) bool), pred_nat ) 15.33/15.54 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 15.33/15.54 ( real, (one_one real) ) 15.33/15.54 ( real, pi ) 15.33/15.54 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.54 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.33/15.54 ( (fun real real), ln ) 15.33/15.54 ( (fun real real), cos ) 15.33/15.54 ( (fun real real), sqrt ) 15.33/15.54 ( (fun real real), sin ) 15.33/15.54 ( (fun real real), arccos ) 15.33/15.54 ( (fun real real), arcsin ) 15.33/15.54 ( (fun real real), tan ) 15.33/15.54 ( (fun real real), arctan ) 15.33/15.54 ( (fun nat (fun nat bool)), coprime ) 15.33/15.54 ( complex, (one_one complex) ) 15.33/15.54 ( complex, ii ) 15.33/15.54 ( (fun nat real), (real_1 nat) ) 15.33/15.54 ( (fun nat real), sin_coeff ) 15.33/15.54 ( (fun nat real), cos_coeff ) 15.33/15.54 ( (filter nat), sequentially ) 15.33/15.54 ( (fun int (fun int int)), (gcd_gcd int) ) 15.33/15.54 ( (fun int (fun int int)), legendre ) 15.33/15.54 ( (fun int (fun int int)), legacy_zgcd ) 15.33/15.54 ( (fun int (fun int int)), standardRes ) 15.33/15.54 ( (fun int (fun int int)), nat_tsub ) 15.33/15.54 ( (fun int (fun int int)), multInv ) 15.33/15.54 ( (fun int (fun int int)), z3mod ) 15.33/15.54 ( (fun int (fun int int)), z3div ) 15.33/15.54 ( (fun int (fun int int)), int_gcd ) 15.33/15.54 ( (fun int (fun int int)), int_lcm ) 15.33/15.54 ( (fun int (fun int int)), inv ) 15.33/15.54 ( (fun complex complex), expi ) 15.33/15.54 ( (fun complex complex), cnj ) 15.33/15.54 ( (fun real complex), cis ) 15.33/15.54 ( (fun int nat), nat_1 ) 15.33/15.54 ( (fun int nat), phi ) 15.33/15.54 ( (fun (fun int bool) bool), nat_nat_set ) 15.33/15.54 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 15.33/15.54 ( (fun nat (fun nat nat)), nat_gcd ) 15.33/15.54 ( (fun nat (fun nat nat)), nat_lcm ) 15.33/15.54 ( (fun (fun int bool) int), (the int) ) 15.33/15.54 ( (fun complex real), re ) 15.33/15.54 ( (fun complex real), im ) 15.33/15.54 ( (fun complex real), arg ) 15.33/15.54 ( (fun bool bool), fNot ) 15.33/15.54 ( (fun nat (fun real real)), root ) 15.33/15.54 ( (fun real (fun real real)), log ) 15.33/15.54 ( (fun real (fun real real)), powr ) 15.33/15.54 ( (fun bool (fun bool bool)), fimplies ) 15.33/15.54 ( (fun bool (fun bool bool)), fconj ) 15.33/15.54 ( (fun bool (fun bool bool)), fdisj ) 15.33/15.54 ( (fun int (fun int (product_prod int int))), negDivAlg ) 15.33/15.54 ( (fun int (fun int (product_prod int int))), posDivAlg ) 15.33/15.54 ( (fun int (fun int (product_prod int int))), divmod_int ) 15.33/15.54 ( (fun int (fun int (product_prod int int))), pdivmod ) 15.33/15.54 ( (fun int (fun int (product_prod int int))), norm_frac ) 15.33/15.54 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 15.33/15.54 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 15.33/15.54 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 15.33/15.54 ( (fun int (fun int (fun int bool))), zcong ) 15.33/15.54 ( (fun int (fun int (fun int bool))), zcongm ) 15.33/15.54 ( (fun int (fun int (fun int bool))), noXRRset ) 15.33/15.54 ( (fun int (fun int (fun int bool))), bnorRset ) 15.33/15.54 ( (fun int (fun int (fun int bool))), wset ) 15.33/15.54 ( (fun (product_prod int int) bool), frac_1 ) 15.33/15.54 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 15.33/15.54 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 15.33/15.54 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 15.33/15.54 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 15.33/15.54 ( (fun (fun nat rat) bool), vanishes ) 15.33/15.54 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 15.33/15.54 ( (fun code_code_numeral nat), code_c271388182l_size ) 15.33/15.54 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 15.33/15.54 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 15.33/15.54 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 15.33/15.54 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 15.33/15.54 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 15.33/15.54 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 15.33/15.54 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 15.33/15.54 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 15.33/15.54 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 15.33/15.54 ( (fun complex nat), complex_size ) 15.33/15.54 ( (fun complex nat), (size_size complex) ) 15.33/15.54 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 15.33/15.54 ( (fun nat (fun nat (product_prod int int))), bezw ) 15.33/15.54 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 15.33/15.54 ( (fun int (fun nat nat)), nat_aux ) 15.33/15.54 ( (fun int (fun (fun int bool) bool)), rsetR ) 15.33/15.54 ( (fun int (fun (fun int bool) bool)), resSet ) 15.33/15.54 ( (fun int (list int)), quickc666637781d_zero ) 15.33/15.54 ( (fun (product_prod int int) rat), frct ) 15.33/15.54 ( (fun int (fun int rat)), fract ) 15.33/15.54 ( (fun real (fun real complex)), complex_1 ) 15.33/15.54 ( (fun real (fun real complex)), rcis ) 15.33/15.54 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 15.33/15.54 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 15.33/15.54 ( (fun int real), (real_1 int) ) 15.33/15.54 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 15.33/15.54 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 15.33/15.54 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 15.33/15.54 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 15.33/15.54 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 15.33/15.54 ( (fun real nat), natfloor ) 15.33/15.54 ( (fun real nat), natceiling ) 15.33/15.54 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 15.33/15.54 ( (fun quickcheck_code_int int), quickcheck_int_of ) 15.33/15.54 ( (fun rat (product_prod int int)), quotient_of ) 15.33/15.54 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 15.33/15.54 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 15.33/15.54 ( (fun rat real), ratreal ) 15.33/15.54 ( (fun code_code_numeral int), code_int_of ) 15.33/15.54 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 15.33/15.54 ( (fun int quickcheck_code_int), quickcheck_of_int ) 15.33/15.54 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 15.33/15.54 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 15.33/15.54 ) 15.33/15.54 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_104658 $$unsorted)) (or (not (linorder X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (ord_max X_a) BOUND_VARIABLE_104658) BOUND_VARIABLE_104658) (ti X_a BOUND_VARIABLE_104658))) ) 15.33/15.54 ( bool, fFalse ) 15.33/15.54 ( bool, fTrue ) 15.33/15.54 ( int, pls ) 15.33/15.54 ( int, min_1 ) 15.33/15.54 ( int, s ) 15.33/15.54 ( int, m ) 15.33/15.54 ( int, s1 ) 15.33/15.54 ( int, t ) 15.33/15.54 ( (fun int bool), nat_neg ) 15.33/15.54 ( (fun int bool), zprime ) 15.33/15.54 ( (fun int bool), zEven ) 15.33/15.54 ( (fun int bool), zOdd ) 15.33/15.54 ( (fun int bool), (even_odd_even int) ) 15.33/15.54 ( (fun int bool), twoSqu1091635170sum2sq ) 15.33/15.54 ( (fun int bool), nat_is_nat ) 15.33/15.54 ( (fun int (fun int bool)), norRRset ) 15.33/15.54 ( (fun int (fun int bool)), quadRes ) 15.33/15.54 ( (fun int (fun int bool)), sRStar ) 15.33/15.54 ( (fun int (fun int bool)), d22set ) 15.33/15.54 ( (fun int (fun int bool)), sr ) 15.33/15.54 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 15.33/15.54 ( (fun int int), zfact ) 15.33/15.54 ( (fun int int), bit0 ) 15.33/15.54 ( (fun int int), bit1 ) 15.33/15.54 ( (fun int int), (fact_fact int) ) 15.33/15.54 ( (fun int int), pred ) 15.33/15.54 ( (fun int int), succ ) 15.33/15.54 ( (fun nat bool), (even_odd_even nat) ) 15.33/15.54 ( (fun nat bool), prime ) 15.33/15.54 ( (fun nat nat), suc ) 15.33/15.54 ( (fun nat nat), (fact_fact nat) ) 15.33/15.54 ( (fun nat nat), fact ) 15.33/15.54 ( (fun nat nat), nat_size ) 15.33/15.54 ( (fun nat nat), (size_size nat) ) 15.33/15.54 ( (fun (product_prod nat nat) bool), pred_nat ) 15.33/15.54 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 15.33/15.54 ( real, pi ) 15.33/15.54 ( (fun real real), ln ) 15.33/15.54 ( (fun real real), cos ) 15.33/15.54 ( (fun real real), sqrt ) 15.33/15.54 ( (fun real real), sin ) 15.33/15.54 ( (fun real real), arccos ) 15.33/15.54 ( (fun real real), arcsin ) 15.33/15.54 ( (fun real real), tan ) 15.33/15.54 ( (fun real real), arctan ) 15.33/15.54 ( (fun nat (fun nat bool)), coprime ) 15.33/15.54 ( complex, ii ) 15.33/15.54 ( (fun nat real), (real_1 nat) ) 15.33/15.54 ( (fun nat real), sin_coeff ) 15.33/15.54 ( (fun nat real), cos_coeff ) 15.33/15.54 ( (filter nat), sequentially ) 15.33/15.54 ( (fun int (fun int int)), (gcd_gcd int) ) 15.33/15.54 ( (fun int (fun int int)), legendre ) 15.33/15.54 ( (fun int (fun int int)), legacy_zgcd ) 15.33/15.54 ( (fun int (fun int int)), standardRes ) 15.33/15.54 ( (fun int (fun int int)), nat_tsub ) 15.33/15.54 ( (fun int (fun int int)), multInv ) 15.33/15.54 ( (fun int (fun int int)), z3mod ) 15.33/15.54 ( (fun int (fun int int)), z3div ) 15.33/15.54 ( (fun int (fun int int)), int_gcd ) 15.33/15.54 ( (fun int (fun int int)), int_lcm ) 15.33/15.54 ( (fun int (fun int int)), inv ) 15.33/15.54 ( (fun complex complex), expi ) 15.33/15.54 ( (fun complex complex), cnj ) 15.33/15.54 ( (fun real complex), cis ) 15.33/15.54 ( (fun int nat), nat_1 ) 15.33/15.54 ( (fun int nat), phi ) 15.33/15.54 ( (fun (fun int bool) bool), nat_nat_set ) 15.33/15.54 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 15.33/15.54 ( (fun nat (fun nat nat)), nat_gcd ) 15.33/15.54 ( (fun nat (fun nat nat)), nat_lcm ) 15.33/15.54 ( (fun (fun int bool) int), (the int) ) 15.33/15.54 ( (fun complex real), re ) 15.33/15.54 ( (fun complex real), im ) 15.33/15.54 ( (fun complex real), arg ) 15.33/15.54 ( (fun bool bool), fNot ) 15.33/15.54 ( (fun nat (fun real real)), root ) 15.33/15.54 ( (fun real (fun real real)), log ) 15.33/15.54 ( (fun real (fun real real)), powr ) 15.33/15.54 ( (fun bool (fun bool bool)), fimplies ) 15.33/15.54 ( (fun bool (fun bool bool)), fconj ) 15.33/15.54 ( (fun bool (fun bool bool)), fdisj ) 15.33/15.54 ( (fun int (fun int (product_prod int int))), negDivAlg ) 15.33/15.54 ( (fun int (fun int (product_prod int int))), posDivAlg ) 15.33/15.54 ( (fun int (fun int (product_prod int int))), divmod_int ) 15.33/15.54 ( (fun int (fun int (product_prod int int))), pdivmod ) 15.33/15.54 ( (fun int (fun int (product_prod int int))), norm_frac ) 15.33/15.54 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 15.33/15.54 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 15.33/15.54 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 15.33/15.54 ( (fun int (fun int (fun int bool))), zcong ) 15.33/15.54 ( (fun int (fun int (fun int bool))), zcongm ) 15.33/15.54 ( (fun int (fun int (fun int bool))), noXRRset ) 15.33/15.54 ( (fun int (fun int (fun int bool))), bnorRset ) 15.33/15.54 ( (fun int (fun int (fun int bool))), wset ) 15.33/15.54 ( (fun (product_prod int int) bool), frac_1 ) 15.33/15.54 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 15.33/15.54 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 15.33/15.54 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 15.33/15.54 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 15.33/15.54 ( (fun (fun nat rat) bool), vanishes ) 15.33/15.54 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 15.33/15.54 ( (fun code_code_numeral nat), code_c271388182l_size ) 15.33/15.54 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 15.33/15.54 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 15.33/15.54 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 15.33/15.54 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 15.33/15.54 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 15.33/15.54 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 15.33/15.54 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 15.33/15.54 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 15.33/15.54 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 15.33/15.54 ( (fun complex nat), complex_size ) 15.33/15.54 ( (fun complex nat), (size_size complex) ) 15.33/15.54 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 15.33/15.54 ( (fun nat (fun nat (product_prod int int))), bezw ) 15.33/15.54 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 15.33/15.54 ( (fun int (fun nat nat)), nat_aux ) 15.33/15.54 ( (fun int (fun (fun int bool) bool)), rsetR ) 15.33/15.54 ( (fun int (fun (fun int bool) bool)), resSet ) 15.33/15.54 ( (fun int (list int)), quickc666637781d_zero ) 15.33/15.54 ( (fun (product_prod int int) rat), frct ) 15.33/15.54 ( (fun int (fun int rat)), fract ) 15.33/15.54 ( (fun real (fun real complex)), complex_1 ) 15.33/15.54 ( (fun real (fun real complex)), rcis ) 15.33/15.54 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 15.33/15.54 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 15.33/15.54 ( (fun int real), (real_1 int) ) 15.33/15.54 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 15.33/15.54 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 15.33/15.54 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 15.33/15.54 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 15.33/15.54 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 15.33/15.54 ( (fun real nat), natfloor ) 15.33/15.54 ( (fun real nat), natceiling ) 15.33/15.54 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 15.33/15.54 ( (fun quickcheck_code_int int), quickcheck_int_of ) 15.33/15.54 ( (fun rat (product_prod int int)), quotient_of ) 15.33/15.54 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 15.33/15.54 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 15.33/15.54 ( (fun rat real), ratreal ) 15.33/15.54 ( (fun code_code_numeral int), code_int_of ) 15.33/15.54 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 15.33/15.54 ( (fun int quickcheck_code_int), quickcheck_of_int ) 15.33/15.54 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 15.33/15.54 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 15.33/15.54 ) 15.33/15.54 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_104673 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) (hAPP X_a int (archim2085082626_floor X_a) BOUND_VARIABLE_104673))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (one_one X_a)) BOUND_VARIABLE_104673)))) ) 15.33/15.54 ( int, t ) 15.33/15.54 ) 15.33/15.54 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (hAPP real _let_0 _let_1 (zero_zero real)))) (or (not (hBOOL (hAPP real bool _let_2 X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))) (hBOOL (hAPP real bool _let_2 (hAPP real real tan X_1))))))) ) 15.33/15.54 ( (one_one real) ) 15.33/15.54 ( (zero_zero real) ) 15.33/15.54 ( pi ) 15.33/15.54 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.54 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.33/15.54 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.33/15.54 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.33/15.54 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.54 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 15.33/15.54 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.33/15.54 ) 15.33/15.54 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_104696 $$unsorted)) (let ((_let_0 (fun nat X_a))) (or (not (real_normed_field X_a)) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP X_a real (norm_norm X_a) BOUND_VARIABLE_104696)) (one_one real)))) (hBOOL (hAPP _let_0 bool (summable X_a) (hAPP X_a _let_0 (power_power X_a) BOUND_VARIABLE_104696))))) ) 15.33/15.54 ( int, s ) 15.33/15.54 ( int, s1 ) 15.33/15.54 ( int, skv_14 ) 15.33/15.54 ( real, (hAPP int real (number_number_of real) min_1) ) 15.33/15.54 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.54 ( complex, ii ) 15.33/15.54 ) 15.33/15.54 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_104790 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (real_normed_vector X_a)) (= (= _let_0 (hAPP X_a X_a (sgn_sgn X_a) BOUND_VARIABLE_104790)) (= _let_0 (ti X_a BOUND_VARIABLE_104790))))) ) 15.33/15.54 ( bool, fFalse ) 15.33/15.54 ( bool, fTrue ) 15.33/15.54 ( int, pls ) 15.33/15.54 ( int, min_1 ) 15.33/15.54 ( int, s ) 15.33/15.54 ( int, m ) 15.33/15.54 ( int, s1 ) 15.33/15.54 ( int, t ) 15.33/15.54 ( (fun int bool), nat_neg ) 15.33/15.54 ( (fun int bool), zprime ) 15.33/15.54 ( (fun int bool), zEven ) 15.33/15.54 ( (fun int bool), zOdd ) 15.33/15.54 ( (fun int bool), (even_odd_even int) ) 15.33/15.54 ( (fun int bool), twoSqu1091635170sum2sq ) 15.33/15.54 ( (fun int bool), nat_is_nat ) 15.33/15.54 ( (fun int (fun int bool)), norRRset ) 15.33/15.54 ( (fun int (fun int bool)), quadRes ) 15.33/15.54 ( (fun int (fun int bool)), sRStar ) 15.33/15.54 ( (fun int (fun int bool)), d22set ) 15.33/15.54 ( (fun int (fun int bool)), sr ) 15.33/15.54 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 15.33/15.54 ( (fun int int), zfact ) 15.33/15.54 ( (fun int int), bit0 ) 15.33/15.54 ( (fun int int), bit1 ) 15.33/15.54 ( (fun int int), (fact_fact int) ) 15.33/15.54 ( (fun int int), pred ) 15.33/15.54 ( (fun int int), succ ) 15.33/15.54 ( (fun nat bool), (even_odd_even nat) ) 15.33/15.54 ( (fun nat bool), prime ) 15.33/15.54 ( (fun nat nat), suc ) 15.33/15.54 ( (fun nat nat), (fact_fact nat) ) 15.33/15.54 ( (fun nat nat), fact ) 15.33/15.54 ( (fun nat nat), nat_size ) 15.33/15.54 ( (fun nat nat), (size_size nat) ) 15.33/15.54 ( (fun (product_prod nat nat) bool), pred_nat ) 15.33/15.54 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 15.33/15.54 ( real, (zero_zero real) ) 15.33/15.54 ( real, pi ) 15.33/15.54 ( (fun real real), ln ) 15.33/15.54 ( (fun real real), cos ) 15.33/15.54 ( (fun real real), sqrt ) 15.33/15.54 ( (fun real real), sin ) 15.33/15.54 ( (fun real real), arccos ) 15.33/15.54 ( (fun real real), arcsin ) 15.33/15.54 ( (fun real real), tan ) 15.33/15.54 ( (fun real real), arctan ) 15.33/15.54 ( rat, (zero_zero rat) ) 15.33/15.54 ( (fun nat (fun nat bool)), coprime ) 15.33/15.54 ( complex, ii ) 15.33/15.54 ( (fun nat real), (real_1 nat) ) 15.33/15.54 ( (fun nat real), sin_coeff ) 15.33/15.54 ( (fun nat real), cos_coeff ) 15.33/15.54 ( (filter nat), sequentially ) 15.33/15.54 ( (fun int (fun int int)), (gcd_gcd int) ) 15.33/15.54 ( (fun int (fun int int)), legendre ) 15.33/15.54 ( (fun int (fun int int)), legacy_zgcd ) 15.33/15.54 ( (fun int (fun int int)), standardRes ) 15.33/15.54 ( (fun int (fun int int)), nat_tsub ) 15.33/15.54 ( (fun int (fun int int)), multInv ) 15.33/15.54 ( (fun int (fun int int)), z3mod ) 15.33/15.54 ( (fun int (fun int int)), z3div ) 15.33/15.54 ( (fun int (fun int int)), int_gcd ) 15.33/15.54 ( (fun int (fun int int)), int_lcm ) 15.33/15.54 ( (fun int (fun int int)), inv ) 15.33/15.54 ( (fun complex complex), expi ) 15.33/15.54 ( (fun complex complex), cnj ) 15.33/15.54 ( (fun real complex), cis ) 15.33/15.54 ( (fun int nat), nat_1 ) 15.33/15.54 ( (fun int nat), phi ) 15.33/15.54 ( (fun (fun int bool) bool), nat_nat_set ) 15.33/15.54 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 15.33/15.54 ( (fun nat (fun nat nat)), nat_gcd ) 15.33/15.54 ( (fun nat (fun nat nat)), nat_lcm ) 15.33/15.54 ( (fun (fun int bool) int), (the int) ) 15.33/15.54 ( (fun complex real), re ) 15.33/15.54 ( (fun complex real), im ) 15.33/15.54 ( (fun complex real), arg ) 15.33/15.54 ( (fun bool bool), fNot ) 15.33/15.54 ( (fun nat (fun real real)), root ) 15.33/15.54 ( (fun real (fun real real)), log ) 15.33/15.54 ( (fun real (fun real real)), powr ) 15.33/15.54 ( (fun bool (fun bool bool)), fimplies ) 15.33/15.54 ( (fun bool (fun bool bool)), fconj ) 15.33/15.54 ( (fun bool (fun bool bool)), fdisj ) 15.33/15.54 ( (fun int (fun int (product_prod int int))), negDivAlg ) 15.33/15.54 ( (fun int (fun int (product_prod int int))), posDivAlg ) 15.33/15.54 ( (fun int (fun int (product_prod int int))), divmod_int ) 15.33/15.54 ( (fun int (fun int (product_prod int int))), pdivmod ) 15.33/15.54 ( (fun int (fun int (product_prod int int))), norm_frac ) 15.33/15.54 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 15.33/15.54 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 15.33/15.54 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 15.33/15.54 ( (fun int (fun int (fun int bool))), zcong ) 15.33/15.54 ( (fun int (fun int (fun int bool))), zcongm ) 15.33/15.54 ( (fun int (fun int (fun int bool))), noXRRset ) 15.33/15.54 ( (fun int (fun int (fun int bool))), bnorRset ) 15.33/15.54 ( (fun int (fun int (fun int bool))), wset ) 15.33/15.54 ( (fun (product_prod int int) bool), frac_1 ) 15.33/15.54 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 15.33/15.54 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 15.33/15.54 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 15.33/15.54 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 15.33/15.54 ( (fun (fun nat rat) bool), vanishes ) 15.33/15.54 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 15.33/15.54 ( (fun code_code_numeral nat), code_c271388182l_size ) 15.33/15.54 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 15.33/15.54 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 15.33/15.54 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 15.33/15.54 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 15.33/15.54 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 15.33/15.54 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 15.33/15.54 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 15.33/15.54 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 15.33/15.54 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 15.33/15.54 ( (fun complex nat), complex_size ) 15.33/15.54 ( (fun complex nat), (size_size complex) ) 15.33/15.54 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 15.33/15.54 ( (fun nat (fun nat (product_prod int int))), bezw ) 15.33/15.54 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 15.33/15.54 ( (fun int (fun nat nat)), nat_aux ) 15.33/15.54 ( (fun int (fun (fun int bool) bool)), rsetR ) 15.33/15.54 ( (fun int (fun (fun int bool) bool)), resSet ) 15.33/15.54 ( (fun int (list int)), quickc666637781d_zero ) 15.33/15.54 ( (fun (product_prod int int) rat), frct ) 15.33/15.54 ( (fun int (fun int rat)), fract ) 15.33/15.54 ( (fun real (fun real complex)), complex_1 ) 15.33/15.54 ( (fun real (fun real complex)), rcis ) 15.33/15.54 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 15.33/15.54 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 15.33/15.54 ( (fun int real), (real_1 int) ) 15.33/15.54 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 15.33/15.54 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 15.33/15.54 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 15.33/15.54 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 15.33/15.54 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 15.33/15.54 ( (fun real nat), natfloor ) 15.33/15.54 ( (fun real nat), natceiling ) 15.33/15.54 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 15.33/15.54 ( (fun quickcheck_code_int int), quickcheck_int_of ) 15.33/15.54 ( (fun rat (product_prod int int)), quotient_of ) 15.33/15.54 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 15.33/15.54 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 15.33/15.54 ( (fun rat real), ratreal ) 15.33/15.54 ( (fun code_code_numeral int), code_int_of ) 15.33/15.54 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 15.33/15.54 ( (fun int quickcheck_code_int), quickcheck_of_int ) 15.33/15.54 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 15.33/15.54 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 15.33/15.54 ) 15.33/15.54 (instantiation (forall ((N_1 $$unsorted)) (let ((_let_0 (zero_zero nat))) (or (= _let_0 N_1) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) _let_0) N_1)))) ) 15.33/15.54 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.54 ) 15.33/15.54 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_104820 $$unsorted) (BOUND_VARIABLE_104821 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member X_a))) (let ((_let_3 (ring_1_Ints X_a))) (or (not (ring_1 X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_104821) _let_3))) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_104820) _let_3))) (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_104821) BOUND_VARIABLE_104820)) _let_3))))))) ) 15.33/15.54 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.54 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.33/15.54 ( int, skv_13, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.33/15.54 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.54 ( real, pi, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 15.33/15.54 ( real, (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.54 ( real, (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.54 ( complex, ii, ii ) 15.33/15.54 ( complex, ii, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 15.33/15.54 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.54 ) 15.33/15.54 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_0 (zero_zero nat))) (let ((_let_1 (fun nat nat))) (let ((_let_2 (div_div nat))) (let ((_let_3 (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) M) N_1)))) (let ((_let_4 (hAPP nat nat (hAPP nat _let_1 _let_2 M) N_1))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) _let_0) N_1))) (and (or _let_3 (= _let_4 (hAPP nat nat suc (hAPP nat nat (hAPP nat _let_1 _let_2 (hAPP nat nat (hAPP nat _let_1 (minus_minus nat) M) N_1)) N_1)))) (or (not _let_3) (= _let_0 _let_4))))))))) ) 15.33/15.54 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.54 ) 15.33/15.54 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted)) (let ((_let_0 (product_prod_case X_a X_b X_c))) (= _let_0 (ti (fun (fun X_a (fun X_b X_c)) (fun (product_prod X_a X_b) X_c)) _let_0))) ) 15.33/15.54 ( nat, nat, bool ) 15.33/15.54 ( nat, nat, (fun (product_prod nat nat) bool) ) 15.33/15.54 ( int, int, bool ) 15.33/15.54 ( int, int, int ) 15.33/15.54 ( int, int, (fun int bool) ) 15.33/15.54 ( int, int, (fun int int) ) 15.33/15.54 ( int, int, rat ) 15.33/15.54 ( int, int, (product_prod int int) ) 15.33/15.54 ( int, int, (fun bool bool) ) 15.33/15.54 ( int, int, (fun (product_prod int int) bool) ) 15.33/15.54 ( int, int, (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 15.33/15.54 ( int, int, (fun (product_prod int int) (fun int bool)) ) 15.33/15.54 ( int, int, (fun (product_prod int int) int) ) 15.33/15.54 ( int, int, (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 15.33/15.54 ( int, int, (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 15.33/15.54 ( (product_prod nat nat), (product_prod nat nat), bool ) 15.33/15.54 ( real, real, bool ) 15.33/15.54 ( (product_prod int int), (product_prod int int), bool ) 15.33/15.54 ) 15.33/15.54 (instantiation (forall ((M $$unsorted)) (let ((_let_0 (one_one int))) (let ((_let_1 (hAPP int (fun int int) (minus_minus int) M))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) _let_0) M))) (= (hAPP nat nat suc (hAPP int nat nat_1 (hAPP int int _let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP int nat nat_1 (hAPP int int _let_1 _let_0)))))) ) 15.33/15.54 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.54 ( t ) 15.33/15.54 ) 15.33/15.54 (instantiation (forall ((N_1 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (fact_fact int))) (let ((_let_2 (hAPP int int (hAPP int _let_0 (plus_plus int) N_1) (one_one int)))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) N_1))) (= (hAPP int int _let_1 _let_2) (hAPP int int (hAPP int _let_0 (times_times int) _let_2) (hAPP int int _let_1 N_1))))))) ) 15.33/15.54 ( (one_one int) ) 15.33/15.54 ( min_1 ) 15.33/15.54 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.54 ( s ) 15.33/15.54 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.33/15.54 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.54 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.33/15.54 ( (hAPP int int (number_number_of int) pls) ) 15.33/15.54 ( skv_4 ) 15.33/15.54 ( skv_10 ) 15.33/15.54 ) 15.33/15.54 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real real))) (= (hAPP real real cos X_1) (hAPP real real sin (hAPP real real (hAPP real _let_0 (minus_minus real) (hAPP real real (hAPP real _let_0 (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) X_1)))) ) 15.33/15.54 ( (zero_zero real) ) 15.33/15.54 ( pi ) 15.33/15.54 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.54 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.54 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.33/15.54 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.33/15.54 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.33/15.54 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.33/15.54 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.33/15.54 ( skv_5 ) 15.33/15.54 ) 15.33/15.54 (instantiation (forall ((X_a $$unsorted)) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (one_one X_a)) (zero_zero X_a))))) ) 15.33/15.54 ( bool ) 15.33/15.54 ( nat ) 15.33/15.54 ( int ) 15.33/15.54 ( (fun int bool) ) 15.33/15.54 ( (fun nat bool) ) 15.33/15.54 ( (product_prod nat nat) ) 15.33/15.54 ( real ) 15.33/15.54 ( rat ) 15.33/15.54 ( complex ) 15.33/15.54 ( (filter nat) ) 15.33/15.54 ( (product_prod int int) ) 15.33/15.54 ( quickcheck_code_int ) 15.33/15.54 ( code_code_numeral ) 15.33/15.54 ( (product_prod real real) ) 15.33/15.54 ( (fun nat rat) ) 15.33/15.54 ( (filter real) ) 15.33/15.54 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 15.33/15.54 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 15.33/15.54 ) 15.33/15.54 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_105001 $$unsorted) (BOUND_VARIABLE_105002 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_105002))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_105001) _let_2))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_105002) BOUND_VARIABLE_105001)) _let_2)))))) ) 15.33/15.54 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 15.33/15.54 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.33/15.54 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.33/15.54 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.33/15.54 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.54 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 15.33/15.54 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), pi ) 15.33/15.54 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (one_one real) ) 15.33/15.54 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))), pi ) 15.33/15.54 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 15.33/15.54 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))), (one_one real) ) 15.33/15.54 ) 15.33/15.54 (instantiation (forall ((F $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 A_2) B_1))) (not (forall ((X $$unsorted)) (let ((_let_2 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 X) B_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 A_2) X))) (not (forall ((Y $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP (fun real real) (fun real _let_0) (deriv real) F) X) Y))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) Y)))) )))) )) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real F A_2)) (hAPP real real F B_1)))))) ) 15.33/15.54 ( cos, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_5 ) 15.33/15.54 ( sqrt, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.54 ( sqrt, (zero_zero real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.54 ) 15.33/15.54 (instantiation (forall ((N_1 $$unsorted) (M $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less nat))) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 (zero_zero nat)) M))) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 M) N_1))) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (dvd_dvd nat) N_1) M)))))) ) 15.33/15.54 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 15.33/15.54 ) 15.33/15.54 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int int (hAPP int (fun int int) (plus_plus int) K_4) K_4) (hAPP int int bit0 K_4)) ) 15.33/15.54 ( pls ) 15.33/15.55 ( (hAPP int int bit1 pls) ) 15.33/15.55 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.33/15.55 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.33/15.55 ( min_1 ) 15.33/15.55 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.33/15.55 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.55 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.33/15.55 ) 15.33/15.55 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (zero X_a)) (= _let_0 (ti X_a _let_0)))) ) 15.33/15.55 ( nat ) 15.33/15.55 ( int ) 15.33/15.55 ( real ) 15.33/15.55 ( rat ) 15.33/15.55 ( complex ) 15.33/15.55 ( quickcheck_code_int ) 15.33/15.55 ( code_code_numeral ) 15.33/15.55 ) 15.33/15.55 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_105215 $$unsorted) (BOUND_VARIABLE_105216 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (exp X_a))) (or (not (banach X_a)) (not (real_normed_field X_a)) (= (hAPP X_a X_a _let_1 (hAPP X_a X_a (hAPP X_a _let_0 (minus_minus X_a) BOUND_VARIABLE_105215) BOUND_VARIABLE_105216)) (hAPP X_a X_a (hAPP X_a _let_0 (inverse_divide X_a) (hAPP X_a X_a _let_1 BOUND_VARIABLE_105215)) (hAPP X_a X_a _let_1 BOUND_VARIABLE_105216)))))) ) 15.33/15.55 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.33/15.55 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 15.33/15.55 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 15.33/15.55 ) 15.33/15.55 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_105231 $$unsorted) (BOUND_VARIABLE_105232 $$unsorted)) (let ((_let_0 (semiring_1_of_nat X_a))) (or (not (linordered_semidom X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP nat X_a _let_0 BOUND_VARIABLE_105231)) (hAPP nat X_a _let_0 BOUND_VARIABLE_105232))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) BOUND_VARIABLE_105231) BOUND_VARIABLE_105232))))) ) 15.33/15.55 ( int, (zero_zero nat), (zero_zero nat) ) 15.33/15.55 ( int, (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 15.33/15.55 ) 15.33/15.55 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (lim X_a))) (or (not (metric_space X_a)) (= _let_0 (ti (fun (fun nat X_a) X_a) _let_0)))) ) 15.33/15.55 ( bool ) 15.33/15.55 ( nat ) 15.33/15.55 ( int ) 15.33/15.55 ( (fun int int) ) 15.33/15.55 ( (fun nat bool) ) 15.33/15.55 ( (fun nat nat) ) 15.33/15.55 ( (product_prod nat nat) ) 15.33/15.55 ( (fun (product_prod nat nat) bool) ) 15.33/15.55 ( (fun nat (fun (product_prod nat nat) bool)) ) 15.33/15.55 ( real ) 15.33/15.55 ( (fun real real) ) 15.33/15.55 ( rat ) 15.33/15.55 ( (fun nat (fun nat bool)) ) 15.33/15.55 ( complex ) 15.33/15.55 ( (product_prod int int) ) 15.33/15.55 ( (fun bool bool) ) 15.33/15.55 ( (product_prod real real) ) 15.33/15.55 ( (fun nat (product_prod nat nat)) ) 15.33/15.55 ( (fun nat (product_prod int int)) ) 15.33/15.55 ) 15.33/15.55 (instantiation (forall ((X_1 $$unsorted)) (or (not (= (one_one real) (hAPP real real cos X_1))) (= (zero_zero real) (hAPP real real sin X_1))) ) 15.33/15.55 ( (zero_zero real) ) 15.33/15.55 ( pi ) 15.33/15.55 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.55 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.55 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.33/15.55 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.33/15.55 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.33/15.55 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.33/15.55 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.33/15.55 ( skv_5 ) 15.33/15.55 ) 15.33/15.55 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (at X_a))) (or (not (topological_space X_a)) (= _let_0 (ti (fun X_a (filter X_a)) _let_0)))) ) 15.33/15.55 ( nat ) 15.33/15.55 ( real ) 15.33/15.55 ( complex ) 15.33/15.55 ) 15.33/15.55 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_105291 $$unsorted)) (let ((_let_0 (number_number_of X_a))) (or (not (number_ring X_a)) (= (hAPP X_a X_a (uminus_uminus X_a) (hAPP int X_a _let_0 BOUND_VARIABLE_105291)) (hAPP int X_a _let_0 (hAPP int int (uminus_uminus int) BOUND_VARIABLE_105291))))) ) 15.33/15.55 ( nat, pls ) 15.33/15.55 ( nat, min_1 ) 15.33/15.55 ( int, (one_one int) ) 15.33/15.55 ( int, pls ) 15.33/15.55 ( int, (hAPP int int bit1 pls) ) 15.33/15.55 ( int, min_1 ) 15.33/15.55 ( real, (one_one int) ) 15.33/15.55 ( complex, (one_one int) ) 15.33/15.55 ( quickcheck_code_int, pls ) 15.33/15.55 ( quickcheck_code_int, min_1 ) 15.33/15.55 ( code_code_numeral, pls ) 15.33/15.55 ( code_code_numeral, min_1 ) 15.33/15.55 ) 15.33/15.55 (instantiation (forall ((X_a $$unsorted) (F1 $$unsorted) (Real1 $$unsorted) (Real2 $$unsorted)) (let ((_let_0 (fun real X_a))) (= (hAPP real X_a (hAPP real _let_0 F1 Real1) Real2) (hAPP complex X_a (hAPP (fun real _let_0) (fun complex X_a) (complex_rec X_a) F1) (hAPP real complex (hAPP real (fun real complex) complex_1 Real1) Real2)))) ) 15.33/15.55 ( bool, (ord_less real), (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.55 ( bool, (ord_less real), (zero_zero real), pi ) 15.33/15.55 ( bool, (ord_less real), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.55 ( bool, (ord_less real), (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.55 ( bool, (ord_less real), (zero_zero real), skv_2 ) 15.33/15.55 ( bool, (ord_less real), (zero_zero real), skv_8 ) 15.33/15.55 ( bool, (ord_less real), (zero_zero real), skv_9 ) 15.33/15.55 ( bool, (ord_less real), pi, (zero_zero real) ) 15.33/15.55 ( bool, (ord_less real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.55 ( bool, (ord_less real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.55 ( bool, (ord_less real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 15.33/15.55 ( bool, (ord_less real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.33/15.55 ( bool, (ord_less real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 15.33/15.55 ( bool, (ord_less_eq real), (zero_zero real), pi ) 15.33/15.55 ( bool, (ord_less_eq real), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.55 ( bool, (ord_less_eq real), (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.55 ( bool, (ord_less_eq real), (zero_zero real), skv_3 ) 15.33/15.55 ( bool, (ord_less_eq real), (zero_zero real), skv_5 ) 15.33/15.55 ( bool, (ord_less_eq real), (zero_zero real), skv_7 ) 15.33/15.55 ( bool, (ord_less_eq real), (zero_zero real), skv_12 ) 15.33/15.55 ( bool, (ord_less_eq real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.33/15.55 ( bool, (ord_less_eq real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.55 ( bool, (ord_less_eq real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.33/15.55 ( bool, (ord_less_eq real), skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.55 ( real, (minus_minus real), (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 15.33/15.55 ( real, (inverse_divide real), (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.55 ( real, (inverse_divide real), (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.33/15.55 ( real, (inverse_divide real), (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.55 ( real, (inverse_divide real), (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 15.33/15.55 ( real, (inverse_divide real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.55 ( real, (inverse_divide real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.55 ( real, (inverse_divide real), pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.33/15.55 ( real, (inverse_divide real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.33/15.55 ( real, (inverse_divide real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.55 ( real, (inverse_divide real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.55 ( real, (inverse_divide real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.55 ( real, (times_times real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.33/15.55 ( real, (times_times real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.33/15.55 ( real, (times_times real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.33/15.55 ( real, (times_times real), (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 15.33/15.55 ( complex, complex_1, (one_one real), (zero_zero real) ) 15.33/15.55 ( complex, complex_1, (zero_zero real), (one_one real) ) 15.33/15.55 ( complex, complex_1, (zero_zero real), (zero_zero real) ) 15.33/15.55 ) 15.33/15.55 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_105394 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (one_one X_a))) (let ((_let_2 (number_number_of X_a))) (or (not (number_ring X_a)) (= (hAPP int X_a _let_2 (hAPP int int bit0 BOUND_VARIABLE_105394)) (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) (hAPP X_a X_a (hAPP X_a _let_0 (plus_plus X_a) _let_1) _let_1)) (hAPP int X_a _let_2 BOUND_VARIABLE_105394))))))) ) 15.33/15.55 ( nat, pls ) 15.33/15.55 ( nat, (hAPP int int bit1 pls) ) 15.33/15.55 ( int, pls ) 15.33/15.55 ( int, (hAPP int int bit1 pls) ) 15.33/15.55 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.33/15.55 ( real, (hAPP int int bit1 pls) ) 15.33/15.55 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.33/15.55 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.33/15.55 ( complex, (hAPP int int bit1 pls) ) 15.33/15.55 ( quickcheck_code_int, pls ) 15.33/15.55 ( code_code_numeral, pls ) 15.33/15.55 ) 15.33/15.55 (instantiation (forall ((N_1 $$unsorted)) (or (hBOOL (hAPP nat bool (even_odd_even nat) N_1)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_1))) ) 15.33/15.55 ( (zero_zero nat) ) 15.33/15.55 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.55 ( (one_one nat) ) 15.33/15.55 ) 15.33/15.55 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_105544 $$unsorted) (BOUND_VARIABLE_105545 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_105544))) (or (not (archim1727834104eiling X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) _let_1) BOUND_VARIABLE_105545))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_105545) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) _let_1) (one_one X_a))))) (= (hAPP X_a int (archim2085082626_floor X_a) BOUND_VARIABLE_105545) (ti int BOUND_VARIABLE_105544))))) ) 15.33/15.55 ( real, (zero_zero int), pi ) 15.33/15.55 ( real, (zero_zero int), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.55 ( real, (zero_zero int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.55 ( real, (zero_zero int), skv_3 ) 15.33/15.55 ( real, (zero_zero int), skv_5 ) 15.33/15.55 ( real, (zero_zero int), skv_7 ) 15.33/15.55 ( real, (zero_zero int), skv_12 ) 15.33/15.55 ) 15.33/15.55 (instantiation (forall ((F $$unsorted) (L $$unsorted) (C_1 $$unsorted)) (let ((_let_0 (filter real))) (let ((_let_1 (fun _let_0 bool))) (or (not (hBOOL (hAPP _let_0 bool (hAPP real _let_1 (hAPP (fun real real) (fun real _let_1) (tendsto real real) F) L) (hAPP real _let_0 (at real) C_1)))) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) L))) (not (forall ((R_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) R_2))) (not (forall ((X $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (or (= C_1 X) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (abs_abs real) (hAPP real real (hAPP real (fun real real) (minus_minus real) C_1) X))) R_2))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) (hAPP real real F X)))))) ))) ))))) ) 15.33/15.55 ( (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.55 ) 15.33/15.55 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_105670 $$unsorted) (BOUND_VARIABLE_105671 $$unsorted)) (or (not (linorder X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_105670) BOUND_VARIABLE_105671))) (= (ti X_a BOUND_VARIABLE_105671) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (ord_max X_a) BOUND_VARIABLE_105671) BOUND_VARIABLE_105670))) ) 15.33/15.55 ( int, (one_one int), t ) 15.33/15.55 ( int, (zero_zero int), (one_one int) ) 15.33/15.55 ( int, (zero_zero int), min_1 ) 15.33/15.55 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.55 ( int, (zero_zero int), s ) 15.33/15.55 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.33/15.55 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.33/15.55 ( int, (zero_zero int), skv_4 ) 15.33/15.55 ( int, (zero_zero int), skv_10 ) 15.33/15.55 ( int, min_1, pls ) 15.33/15.55 ( int, min_1, min_1 ) 15.33/15.55 ( real, (zero_zero real), pi ) 15.33/15.55 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.55 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.55 ( real, (zero_zero real), skv_3 ) 15.33/15.55 ( real, (zero_zero real), skv_5 ) 15.33/15.55 ( real, (zero_zero real), skv_7 ) 15.33/15.55 ( real, (zero_zero real), skv_12 ) 15.33/15.55 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.33/15.55 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.55 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.33/15.55 ( real, skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.55 ) 15.33/15.55 (instantiation (forall ((Z_1 $$unsorted) (W $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (times_times real))) (= (hAPP real real (hAPP real _let_0 _let_1 Z_1) W) (hAPP real real (hAPP real _let_0 _let_1 W) Z_1)))) ) 15.33/15.55 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.55 ( pi, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 15.33/15.55 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.33/15.55 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.33/15.55 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.33/15.55 ( (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.55 ( (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.55 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 15.33/15.55 ) 15.33/15.55 (instantiation (forall ((X_1 $$unsorted)) (or (= (zero_zero real) X_1) (= (one_one real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP real real (inverse_inverse real) X_1)) X_1))) ) 15.33/15.55 ( (zero_zero real) ) 15.33/15.55 ) 15.33/15.55 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (plus_plus nat))) (= (hAPP nat nat (hAPP nat _let_0 _let_1 (hAPP nat nat suc M)) N_1) (hAPP nat nat suc (hAPP nat nat (hAPP nat _let_0 _let_1 M) N_1))))) ) 15.33/15.55 ( (zero_zero nat), (one_one nat) ) 15.33/15.55 ( (one_one nat), (one_one nat) ) 15.33/15.55 ) 15.33/15.55 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_105840 $$unsorted) (BOUND_VARIABLE_105841 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (uminus_uminus X_a))) (or (not (ordered_ab_group_add X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_105841) (hAPP X_a X_a _let_2 BOUND_VARIABLE_105840))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_105840) (hAPP X_a X_a _let_2 BOUND_VARIABLE_105841)))))))) ) 15.33/15.55 ( int, (one_one int), pls ) 15.33/15.55 ( int, (one_one int), min_1 ) 15.33/15.55 ( int, pls, (one_one int) ) 15.33/15.55 ( int, pls, pls ) 15.33/15.55 ( int, pls, min_1 ) 15.33/15.55 ( int, min_1, (one_one int) ) 15.33/15.55 ( int, min_1, pls ) 15.33/15.55 ) 15.33/15.55 (instantiation (forall ((B $$unsorted)) (let ((_let_0 (hAPP int int (number_number_of int) min_1))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) B))) (= _let_0 (hAPP int int (hAPP int (fun int int) (div_div int) _let_0) B)))) ) 15.33/15.55 ( (one_one int) ) 15.33/15.55 ( pls ) 15.33/15.55 ( min_1 ) 15.33/15.55 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.33/15.55 ) 15.33/15.55 (instantiation (forall ((A_1 $$unsorted)) (let ((_let_0 (one_one real))) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) A_1))) (= _let_0 A_1) (= _let_0 (hAPP real real (hAPP real (fun real real) log A_1) A_1)))) ) 15.33/15.55 ( pi ) 15.33/15.55 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.55 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.55 ( skv_2 ) 15.33/15.55 ( skv_8 ) 15.33/15.55 ( skv_9 ) 15.33/15.55 ) 15.33/15.55 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_106080 $$unsorted) (BOUND_VARIABLE_106081 $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (one_one X_a))) (let ((_let_2 (fun nat X_a))) (let ((_let_3 (fun X_a X_a))) (let ((_let_4 (minus_minus X_a))) (let ((_let_5 (hAPP X_a _let_2 (power_power X_a) BOUND_VARIABLE_106081))) (or (not (field X_a)) (= _let_1 (ti X_a BOUND_VARIABLE_106081)) (= (hAPP X_a X_a (hAPP X_a _let_3 (inverse_divide X_a) (hAPP X_a X_a (hAPP X_a _let_3 _let_4 (hAPP nat X_a _let_5 BOUND_VARIABLE_106080)) _let_1)) (hAPP X_a X_a (hAPP X_a _let_3 _let_4 BOUND_VARIABLE_106081) _let_1)) (hAPP _let_0 X_a (hAPP _let_2 (fun _let_0 X_a) (big_co1399186613setsum nat X_a) _let_5) (hAPP nat _let_0 (hAPP nat (fun nat _let_0) (ord_atLeastLessThan nat) (zero_zero nat)) BOUND_VARIABLE_106080)))))))))) ) 15.33/15.55 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 15.33/15.55 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 15.33/15.55 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_14 ) 15.33/15.55 ( complex, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), ii ) 15.33/15.55 ) 15.33/15.55 (instantiation (forall ((X_c $$unsorted) (X_b $$unsorted) (X_a $$unsorted)) (let ((_let_0 (product_apsnd X_c X_b X_a))) (= _let_0 (ti (fun (fun X_c X_b) (fun (product_prod X_a X_c) (product_prod X_a X_b))) _let_0))) ) 15.33/15.55 ( int, int, int ) 15.33/15.55 ) 15.33/15.55 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (hAPP real (fun real bool) (ord_less_eq real) (one_one real)))) (or (not (hBOOL (hAPP real bool _let_0 X_1))) (hBOOL (hAPP real bool _let_0 (hAPP real real sqrt X_1))))) ) 15.33/15.55 ( (one_one real) ) 15.33/15.55 ( (zero_zero real) ) 15.33/15.55 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.55 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.33/15.55 ) 15.33/15.55 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (BOUND_VARIABLE_106190 $$unsorted) (BOUND_VARIABLE_106191 $$unsorted) (BOUND_VARIABLE_106192 $$unsorted)) (let ((_let_0 (fun X_a X_b))) (or (not (ord X_b)) (not (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) BOUND_VARIABLE_106191) BOUND_VARIABLE_106192))) (hBOOL (hAPP X_b bool (hAPP X_b (fun X_b bool) (ord_less_eq X_b) (hAPP X_a X_b BOUND_VARIABLE_106191 BOUND_VARIABLE_106190)) (hAPP X_a X_b BOUND_VARIABLE_106192 BOUND_VARIABLE_106190))))) ) 15.33/15.55 ( nat, int, (zero_zero nat), (semiring_1_of_nat int), (semiring_1_of_nat int) ) 15.33/15.55 ( int, int, (zero_zero int), (number_number_of int), (fact_fact int) ) 15.33/15.55 ( int, int, pls, pred, (number_number_of int) ) 15.33/15.55 ( int, int, min_1, bit1, bit1 ) 15.33/15.55 ( int, int, min_1, succ, bit1 ) 15.33/15.55 ( real, real, (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), cos, (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.55 ) 15.33/15.55 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_106216 $$unsorted) (BOUND_VARIABLE_106217 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (one_one X_a)))) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_106217))) (hBOOL (hAPP X_a bool _let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_106217) BOUND_VARIABLE_106216))))) ) 15.33/15.55 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 15.33/15.55 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 15.33/15.55 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_14 ) 15.33/15.55 ( complex, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), ii ) 15.33/15.55 ) 15.33/15.55 (instantiation (forall ((S $$unsorted)) (or (not (hBOOL (hAPP (fun nat bool) bool (finite_finite_1 nat) S))) (not (forall ((K_1 $$unsorted)) (let ((_let_0 (fun nat bool))) (not (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) S) (hAPP nat _let_0 (ord_lessThan nat) K_1))))) ))) ) 15.33/15.55 ( (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 15.33/15.55 ) 15.33/15.55 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_106291 $$unsorted)) (or (not (linordered_semidom X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)) (hAPP nat X_a (semiring_1_of_nat X_a) (hAPP nat nat (fact_fact nat) BOUND_VARIABLE_106291))))) ) 15.33/15.55 ( int, (hAPP nat nat suc (zero_zero nat)) ) 15.33/15.55 ( real, (hAPP nat nat suc (zero_zero nat)) ) 15.33/15.55 ) 15.33/15.55 (instantiation (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_0 (real_1 int))) (= (hAPP real real (hAPP real (fun real real) (minus_minus real) (hAPP int real _let_0 X_1)) (hAPP int real _let_0 Y_1)) (hAPP int real _let_0 (hAPP int int (hAPP int (fun int int) (minus_minus int) X_1) Y_1)))) ) 15.33/15.55 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.33/15.55 ) 15.33/15.55 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_0 (fun real complex))) (= (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP real complex (hAPP real _let_0 complex_1 A_1) B)) ii) (hAPP real complex (hAPP real _let_0 complex_1 (hAPP real real (uminus_uminus real) B)) A_1))) ) 15.33/15.55 ( (one_one real), (zero_zero real) ) 15.33/15.55 ( (zero_zero real), (one_one real) ) 15.33/15.55 ( (zero_zero real), (zero_zero real) ) 15.33/15.55 ) 15.33/15.55 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (div_mod nat))) (or (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) M) N_1)) (= (hAPP nat nat (hAPP nat _let_0 _let_1 (hAPP nat nat (hAPP nat _let_0 (minus_minus nat) M) N_1)) N_1) (hAPP nat nat (hAPP nat _let_0 _let_1 M) N_1))))) ) 15.33/15.55 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.55 ) 15.33/15.55 (instantiation (forall ((N_1 $$unsorted) (M $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (zero_zero int)) M))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 M) N_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (dvd_dvd int) N_1) M)))))) ) 15.33/15.55 ( (one_one int), pls ) 15.33/15.55 ( pls, pls ) 15.33/15.55 ( pls, min_1 ) 15.33/15.55 ( min_1, pls ) 15.33/15.55 ( min_1, min_1 ) 15.33/15.55 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), pls ) 15.33/15.55 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s ) 15.33/15.55 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 15.33/15.55 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.33/15.55 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_4 ) 15.33/15.55 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_10 ) 15.33/15.55 ( t, (one_one int) ) 15.33/15.55 ) 15.33/15.55 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (field_char_0_Rats X_a))) (or (not (field_char_0 X_a)) (= _let_0 (ti (fun X_a bool) _let_0)))) ) 15.33/15.55 ( bool ) 15.33/15.55 ( nat ) 15.33/15.55 ( int ) 15.33/15.55 ( (fun int bool) ) 15.33/15.55 ( (fun nat bool) ) 15.33/15.55 ( (product_prod nat nat) ) 15.33/15.55 ( real ) 15.33/15.55 ( rat ) 15.33/15.55 ( complex ) 15.33/15.55 ( (filter nat) ) 15.33/15.55 ( (product_prod int int) ) 15.33/15.55 ( (product_prod real real) ) 15.33/15.55 ( (fun nat rat) ) 15.33/15.55 ( (filter real) ) 15.33/15.55 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 15.33/15.55 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 15.33/15.55 ) 15.33/15.55 (instantiation (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member int))) (or (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP int int (hAPP int (fun int int) (plus_plus int) A_2) B_1)) zOdd))) (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 A_2) zEven))) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 B_1) zOdd)))))) ) 15.33/15.55 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 15.33/15.55 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 15.33/15.55 ) 15.33/15.55 (instantiation (forall ((F $$unsorted)) (let ((_let_0 (fun nat real))) (or (not (forall ((N_2 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) (hAPP nat real F N_2))) )) (not (hBOOL (hAPP _let_0 bool (summable real) F))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) (hAPP _let_0 real (suminf real) F))))) ) 15.33/15.55 ( (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat (fun nat nat)))) (let ((_let_3 (fun nat _let_0))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun _let_1 _let_3))) (let ((_let_6 (combb real _let_0 nat))) (let ((_let_7 (combc nat nat nat))) (hAPP _let_1 _let_1 (hAPP _let_3 (fun _let_1 _let_1) (combs nat real real) (hAPP _let_1 _let_3 (hAPP _let_4 _let_5 _let_6 (inverse_divide real)) (hAPP real _let_1 (hAPP _let_3 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_3 (hAPP _let_4 _let_5 _let_6 (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) (one_one real)))) (hAPP (fun nat nat) _let_1 (hAPP _let_1 (fun (fun nat nat) _let_1) (combb nat real nat) (real_1 nat)) (hAPP nat (fun nat nat) (hAPP _let_2 _let_2 _let_7 (hAPP (fun nat nat) _let_2 (hAPP _let_2 (fun (fun nat nat) _let_2) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_2 _let_2 _let_7 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))))))))))) ) 15.33/15.55 ) 15.33/15.55 (instantiation (forall ((X_a $$unsorted)) (or (not (ord X_a)) (= (ord_max X_a) (hAPP (fun X_a (fun X_a bool)) (fun X_a (fun X_a X_a)) (max X_a) (ord_less_eq X_a)))) ) 15.33/15.55 ( bool ) 15.33/15.55 ( nat ) 15.33/15.55 ( int ) 15.33/15.55 ( (fun int bool) ) 15.33/15.55 ( (fun int (fun int bool)) ) 15.33/15.55 ( (fun int int) ) 15.33/15.55 ( (fun nat bool) ) 15.33/15.55 ( (product_prod nat nat) ) 15.33/15.55 ( real ) 15.33/15.55 ( (fun real bool) ) 15.33/15.55 ( (fun real real) ) 15.33/15.55 ( rat ) 15.33/15.55 ( complex ) 15.33/15.55 ( (fun nat real) ) 15.33/15.55 ( (filter nat) ) 15.33/15.55 ( (product_prod int int) ) 15.33/15.55 ( quickcheck_code_int ) 15.33/15.55 ( code_code_numeral ) 15.33/15.55 ( (fun int (fun int (fun int bool))) ) 15.33/15.55 ( (product_prod real real) ) 15.33/15.55 ( (fun (product_prod int int) bool) ) 15.33/15.55 ( (fun nat rat) ) 15.33/15.55 ( (filter real) ) 15.33/15.55 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 15.33/15.55 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 15.33/15.55 ( (fun (product_prod int int) int) ) 15.33/15.55 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 15.33/15.55 ( (fun int real) ) 15.33/15.55 ) 15.33/15.55 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_106440 $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (ring_1 X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) BOUND_VARIABLE_106440) (ring_1_Ints X_a)))) (not (forall ((Z_2 $$unsorted)) (not (= (hAPP int X_a (ring_1_of_int X_a) Z_2) (ti X_a BOUND_VARIABLE_106440))) )))) ) 15.33/15.55 ( int, (one_one int) ) 15.33/15.55 ) 15.33/15.55 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_106476 $$unsorted) (BOUND_VARIABLE_106477 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (times_times X_a))) (let ((_let_2 (ti X_a BOUND_VARIABLE_106476))) (or (not (idom X_a)) (= (or (= (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_106477) _let_2) (= _let_2 (ti X_a BOUND_VARIABLE_106477))) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_106477) BOUND_VARIABLE_106477) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_106476) BOUND_VARIABLE_106476))))))) ) 15.33/15.55 ( int, pls, (one_one int) ) 15.33/15.55 ( int, s, min_1 ) 15.33/15.55 ( int, s1, pls ) 15.33/15.55 ( real, pi, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.55 ( complex, ii, (one_one complex) ) 15.33/15.55 ( complex, ii, ii ) 15.33/15.55 ) 15.33/15.55 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (uminus_uminus real) _let_2)) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) _let_2))) (= X_1 (hAPP real real arctan (hAPP real real tan X_1))))))) ) 15.33/15.55 ( (one_one real) ) 15.33/15.55 ( (zero_zero real) ) 15.33/15.55 ( pi ) 15.33/15.55 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.55 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.33/15.55 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.33/15.55 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.33/15.55 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.55 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 15.33/15.55 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.33/15.55 ) 15.33/15.55 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (refl X_a))) (= _let_0 (ti (fun (fun (product_prod X_a X_a) bool) bool) _let_0))) ) 15.33/15.55 ( nat ) 15.33/15.55 ( int ) 15.33/15.55 ( (product_prod nat nat) ) 15.33/15.55 ( real ) 15.33/15.55 ( (product_prod int int) ) 15.33/15.55 ( quickcheck_code_int ) 15.33/15.55 ( code_code_numeral ) 15.33/15.55 ) 15.33/15.55 (instantiation (forall ((M $$unsorted)) (let ((_let_0 (zero_zero int))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) M) _let_0))) (= _let_0 (hAPP int int (fact_fact int) M)))) ) 15.33/15.55 ( (one_one int) ) 15.33/15.55 ( (zero_zero int) ) 15.33/15.55 ( pls ) 15.33/15.55 ( min_1 ) 15.33/15.55 ( s ) 15.33/15.55 ( t ) 15.33/15.55 ( skv_4 ) 15.33/15.55 ( skv_10 ) 15.33/15.55 ) 15.33/15.55 (instantiation (forall ((B_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member int))) (or (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 A_2) zEven))) (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 B_1) zOdd))) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP int int (hAPP int (fun int int) (plus_plus int) A_2) B_1)) zOdd)))))) ) 15.33/15.55 ( (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.33/15.55 ( (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.55 ) 15.33/15.55 (instantiation (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_0 (even_odd_even int))) (or (hBOOL (hAPP int bool _let_0 X_1)) (hBOOL (hAPP int bool _let_0 Y_1)) (not (hBOOL (hAPP int bool _let_0 (hAPP int int (hAPP int (fun int int) (times_times int) X_1) Y_1)))))) ) 15.33/15.55 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.55 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.33/15.55 ( skv_13, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.33/15.55 ) 15.33/15.55 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (inverse_inverse real))) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) X_1))) (= (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP real real _let_0 (hAPP real real sqrt X_1))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real _let_0 X_1)))) ) 15.33/15.55 ( (one_one real) ) 15.33/15.55 ( (zero_zero real) ) 15.33/15.55 ( pi ) 15.33/15.55 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.55 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.55 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.33/15.55 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.55 ( skv_2 ) 15.33/15.55 ( skv_8 ) 15.33/15.55 ( skv_9 ) 15.33/15.55 ) 15.33/15.55 (instantiation (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted) (F1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (product_prod X_b X_c))) (let ((_let_1 (fun X_c X_a))) (= (hAPP X_c X_a (hAPP X_b _let_1 F1 A_2) B_1) (hAPP _let_0 X_a (hAPP (fun X_b _let_1) (fun _let_0 X_a) (product_prod_case X_b X_c X_a) F1) (hAPP X_c _let_0 (hAPP X_b (fun X_c _let_0) (product_Pair X_b X_c) A_2) B_1))))) ) 15.33/15.55 ( nat, nat, bool, (ord_less nat), (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.55 ( nat, nat, nat, (plus_plus nat), (one_one nat), (one_one nat) ) 15.33/15.55 ( nat, real, real, root, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 15.33/15.55 ( nat, real, real, root, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real) ) 15.33/15.55 ( nat, real, real, root, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.55 ( nat, real, real, root, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.33/15.55 ( int, nat, int, (power_power int), s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.55 ( int, nat, int, (power_power int), s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.55 ( int, nat, int, (power_power int), skv_14, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.55 ( int, int, bool, (ord_less_eq int), (one_one int), t ) 15.33/15.55 ( int, int, bool, (ord_less_eq int), (zero_zero int), (one_one int) ) 15.33/15.55 ( int, int, bool, (ord_less_eq int), (zero_zero int), min_1 ) 15.33/15.55 ( int, int, bool, (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.55 ( int, int, bool, (ord_less_eq int), (zero_zero int), s ) 15.33/15.55 ( int, int, bool, (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.33/15.55 ( int, int, bool, (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.33/15.55 ( int, int, bool, (ord_less_eq int), (zero_zero int), skv_4 ) 15.33/15.55 ( int, int, bool, (ord_less_eq int), (zero_zero int), skv_10 ) 15.33/15.55 ( int, int, bool, (ord_less_eq int), min_1, pls ) 15.33/15.55 ( int, int, bool, (ord_less_eq int), min_1, min_1 ) 15.33/15.55 ( int, int, bool, (ord_less int), (one_one int), t ) 15.33/15.55 ( int, int, bool, (ord_less int), pls, (one_one int) ) 15.33/15.55 ( int, int, bool, (ord_less int), pls, pls ) 15.33/15.55 ( int, int, bool, (ord_less int), pls, min_1 ) 15.33/15.55 ( int, int, bool, (ord_less int), pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.33/15.55 ( int, int, bool, (ord_less int), min_1, pls ) 15.33/15.55 ( int, int, bool, (ord_less int), min_1, min_1 ) 15.33/15.55 ( int, int, bool, (ord_less int), s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.33/15.55 ( int, int, bool, (ord_less int), t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.33/15.55 ( int, int, bool, (ord_less int), skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.33/15.55 ( int, int, bool, (ord_less int), skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.33/15.55 ( int, int, bool, (dvd_dvd int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 15.33/15.55 ( int, int, bool, quadRes, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (number_number_of int) min_1) ) 15.33/15.55 ( int, int, bool, (hAPP int (fun int (fun int bool)) zcong s1), s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.33/15.55 ( int, int, bool, (hAPP int (fun int (fun int bool)) zcong s1), skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.33/15.55 ( int, int, bool, (hAPP int (fun int (fun int bool)) zcong s1), skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.33/15.55 ( int, int, bool, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.33/15.55 ( int, int, bool, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.33/15.55 ( int, int, bool, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.33/15.55 ( int, int, bool, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.33/15.55 ( int, int, int, (times_times int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 15.33/15.55 ( int, int, int, (times_times int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.33/15.55 ( int, int, int, (times_times int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13 ) 15.33/15.55 ( int, int, int, (minus_minus int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.33/15.55 ( int, int, int, (plus_plus int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 15.33/15.55 ( int, int, int, (plus_plus int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 15.33/15.55 ( int, int, int, legendre, (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.33/15.55 ( int, int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun _let_0 _let_1))) (let ((_let_3 (fun _let_0 _let_0))) (let ((_let_4 (fun int _let_3))) (let ((_let_5 (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP _let_0 _let_1 (hAPP _let_4 _let_2 (combc int _let_0 _let_0) (hAPP _let_1 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_1 _let_4) (combb _let_0 _let_3 int) (combb int int int)) (hAPP _let_0 _let_1 (hAPP _let_1 _let_2 (combb int _let_0 int) (plus_plus int)) _let_5))) _let_5))))))), s, (one_one int) ) 15.33/15.55 ( int, int, (fun int bool), zcong, s1, s ) 15.33/15.55 ( int, int, (fun int bool), zcong, s1, skv_4 ) 15.33/15.55 ( int, int, (fun int bool), zcong, s1, skv_10 ) 15.33/15.55 ( int, int, (fun int bool), zcong, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.33/15.55 ( int, int, (fun int bool), zcong, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.55 ( int, int, (fun int bool), zcong, (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.33/15.55 ( int, int, (fun int bool), zcong, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.33/15.55 ( int, int, rat, fract, (one_one int), (one_one int) ) 15.33/15.55 ( int, int, rat, fract, (zero_zero int), (one_one int) ) 15.33/15.55 ( int, int, (product_prod int int), (product_Pair int int), (one_one int), (one_one int) ) 15.33/15.55 ( int, int, (product_prod int int), (product_Pair int int), (zero_zero int), (one_one int) ) 15.33/15.55 ( int, int, (product_prod int int), (product_Pair int int), s, (one_one int) ) 15.33/15.55 ( int, (fun int bool), bool, (member int), (one_one int), zEven ) 15.33/15.55 ( (fun int (fun int bool)), int, (fun int bool), (combc int int bool), (fequal int), (zero_zero int) ) 15.33/15.55 ( (fun int (fun int bool)), (fun (product_prod int int) int), (fun (product_prod int int) (fun int bool)), (combb int (fun int bool) (product_prod int int)), (fequal int), (product_snd int int) ) 15.33/15.55 ( real, real, bool, (ord_less real), (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.55 ( real, real, bool, (ord_less real), (zero_zero real), pi ) 15.33/15.55 ( real, real, bool, (ord_less real), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.55 ( real, real, bool, (ord_less real), (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.55 ( real, real, bool, (ord_less real), (zero_zero real), skv_2 ) 15.33/15.55 ( real, real, bool, (ord_less real), (zero_zero real), skv_8 ) 15.33/15.55 ( real, real, bool, (ord_less real), (zero_zero real), skv_9 ) 15.33/15.55 ( real, real, bool, (ord_less real), pi, (zero_zero real) ) 15.33/15.55 ( real, real, bool, (ord_less real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.55 ( real, real, bool, (ord_less real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.55 ( real, real, bool, (ord_less real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 15.33/15.55 ( real, real, bool, (ord_less real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.33/15.55 ( real, real, bool, (ord_less real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 15.33/15.55 ( real, real, bool, (ord_less_eq real), (zero_zero real), pi ) 15.33/15.55 ( real, real, bool, (ord_less_eq real), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.56 ( real, real, bool, (ord_less_eq real), (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.56 ( real, real, bool, (ord_less_eq real), (zero_zero real), skv_3 ) 15.33/15.56 ( real, real, bool, (ord_less_eq real), (zero_zero real), skv_5 ) 15.33/15.56 ( real, real, bool, (ord_less_eq real), (zero_zero real), skv_7 ) 15.33/15.56 ( real, real, bool, (ord_less_eq real), (zero_zero real), skv_12 ) 15.33/15.56 ( real, real, bool, (ord_less_eq real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.33/15.56 ( real, real, bool, (ord_less_eq real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.56 ( real, real, bool, (ord_less_eq real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.33/15.56 ( real, real, bool, (ord_less_eq real), skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.56 ( real, real, real, (minus_minus real), (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 15.33/15.56 ( real, real, real, (inverse_divide real), (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.56 ( real, real, real, (inverse_divide real), (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.33/15.56 ( real, real, real, (inverse_divide real), (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.56 ( real, real, real, (inverse_divide real), (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 15.33/15.56 ( real, real, real, (inverse_divide real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.56 ( real, real, real, (inverse_divide real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.56 ( real, real, real, (inverse_divide real), pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.33/15.56 ( real, real, real, (inverse_divide real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.33/15.56 ( real, real, real, (inverse_divide real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.56 ( real, real, real, (inverse_divide real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.56 ( real, real, real, (inverse_divide real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.56 ( real, real, real, (times_times real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.33/15.56 ( real, real, real, (times_times real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.33/15.56 ( real, real, real, (times_times real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.33/15.56 ( real, real, real, (times_times real), (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 15.33/15.56 ( real, real, complex, complex_1, (one_one real), (zero_zero real) ) 15.33/15.56 ( real, real, complex, complex_1, (zero_zero real), (one_one real) ) 15.33/15.56 ( real, real, complex, complex_1, (zero_zero real), (zero_zero real) ) 15.33/15.56 ( real, (filter nat), bool, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 (fun real (fun (filter nat) bool)) (tendsto nat real) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))))), (zero_zero real), sequentially ) 15.33/15.56 ( real, (filter real), bool, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 (fun real (fun (filter real) bool)) (tendsto real real) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin)))), (zero_zero real), (hAPP real (filter real) (at real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.33/15.56 ( (fun real real), real, (fun (filter real) bool), (tendsto real real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real) ) 15.33/15.56 ( (fun real real), (fun nat real), (fun nat real), (combb real real nat), (inverse_inverse real), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))) ) 15.33/15.56 ( (fun nat (fun nat bool)), nat, (fun nat bool), (combc nat nat bool), (fequal nat), (zero_zero nat) ) 15.33/15.56 ( (fun nat (fun nat bool)), (fun nat nat), (fun nat (fun nat bool)), (combb nat (fun nat bool) nat), (let ((_let_0 (fun nat (fun nat bool)))) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat))), suc ) 15.33/15.56 ( (fun nat int), (fun nat bool), bool, (nat_tr1645093318rphism nat int), (semiring_1_of_nat int), (hAPP bool (fun nat bool) (combk bool nat) fTrue) ) 15.33/15.56 ( complex, nat, complex, (power_power complex), ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.56 ( complex, complex, complex, (times_times complex), ii, ii ) 15.33/15.56 ( complex, complex, complex, (times_times complex), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 15.33/15.56 ( complex, complex, complex, (times_times complex), (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 15.33/15.56 ( (fun nat real), (fun nat nat), (fun nat real), (combb nat real nat), (real_1 nat), suc ) 15.33/15.56 ( (fun nat real), (fun nat nat), (fun nat real), (combb nat real nat), (real_1 nat), (let ((_let_0 (fun nat (fun nat nat)))) (let ((_let_1 (combc nat nat nat))) (hAPP nat (fun nat nat) (hAPP _let_0 _let_0 _let_1 (hAPP (fun nat nat) _let_0 (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_0 _let_0 _let_1 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))) ) 15.33/15.56 ( (fun nat real), (fun nat nat), (fun nat real), (combb nat real nat), (hAPP real (fun nat real) (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), suc ) 15.33/15.56 ( (fun nat real), real, bool, (sums real), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (hAPP real _let_1 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc))), (one_one real) ) 15.33/15.56 ( (fun nat real), real, (fun (filter nat) bool), (tendsto nat real), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real) ) 15.33/15.56 ( (fun int (fun int int)), int, (fun int int), (combc int int int), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)) (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))))), (one_one int) ) 15.33/15.56 ( (fun int (fun int int)), (fun int int), (fun int (fun int int)), (combb int (fun int int) int), (plus_plus int), (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.33/15.56 ( (fun int (fun int int)), (fun int int), (fun int (fun int int)), (combb int (fun int int) int), (plus_plus int), (let ((_let_0 (fun int int))) (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.33/15.56 ( (fun int (fun int int)), (product_prod int int), int, (product_prod_case int int int), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun _let_0 _let_1))) (let ((_let_3 (fun _let_0 _let_0))) (let ((_let_4 (fun int _let_3))) (let ((_let_5 (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP _let_0 _let_1 (hAPP _let_4 _let_2 (combc int _let_0 _let_0) (hAPP _let_1 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_1 _let_4) (combb _let_0 _let_3 int) (combb int int int)) (hAPP _let_0 _let_1 (hAPP _let_1 _let_2 (combb int _let_0 int) (plus_plus int)) _let_5))) _let_5))))))), (let ((_let_0 (product_prod int int))) (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) s) (one_one int))) ) 15.33/15.56 ( (fun int (fun int int)), (fun (product_prod int int) int), (fun (product_prod int int) (fun int int)), (combb int (fun int int) (product_prod int int)), (times_times int), (product_fst int int) ) 15.33/15.56 ( (fun int nat), (fun int bool), bool, (nat_tr1645093318rphism int nat), nat_1, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 15.33/15.56 ( (fun (fun int bool) bool), (fun int (fun int bool)), (fun int bool), (combb (fun int bool) bool int), (fEx int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun _let_2 _let_0))) (let ((_let_4 (fun int _let_3))) (hAPP _let_2 _let_1 (hAPP _let_4 (fun _let_2 _let_1) (combc int _let_2 _let_0) (hAPP _let_1 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_1 _let_4) (combb _let_0 _let_3 int) (combb int bool int)) (fequal int))) (hAPP int _let_2 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))))))) ) 15.33/15.56 ( (fun (fun int bool) bool), (fun int (fun int bool)), (fun int bool), (combb (fun int bool) bool int), (fEx int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun _let_2 _let_0))) (let ((_let_5 (fun int _let_4))) (hAPP _let_2 _let_1 (hAPP _let_5 (fun _let_2 _let_1) (combc int _let_2 _let_0) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_1 _let_5) (combb _let_0 _let_4 int) (combb int bool int)) (fequal int))) (hAPP int _let_2 (hAPP _let_3 _let_3 (combc int int int) (hAPP _let_2 _let_3 (hAPP _let_3 (fun _let_2 _let_3) (combb int _let_2 int) (plus_plus int)) (hAPP int _let_2 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one int))))))))) ) 15.33/15.56 ( (fun (fun int bool) bool), (fun real (fun int bool)), (fun real bool), (combb (fun int bool) bool real), (fEx int), (let ((_let_0 (fun int (fun int bool)))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real real))) (let ((_let_3 (real_1 int))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun int _let_4))) (let ((_let_7 (fun (fun int bool) (fun int bool)))) (let ((_let_8 (fun (fun int bool) _let_6))) (let ((_let_9 (fun _let_0 (fun int bool)))) (let ((_let_10 (fun int real))) (let ((_let_11 (fun int _let_7))) (let ((_let_12 (fun (fun int bool) _let_0))) (let ((_let_13 (fun int _let_6))) (let ((_let_14 (fun _let_13 _let_11))) (let ((_let_15 (fun _let_0 _let_13))) (let ((_let_16 (fun real (fun int bool)))) (let ((_let_17 (fun real _let_0))) (let ((_let_18 (fun real _let_12))) (let ((_let_19 (fun real _let_11))) (let ((_let_20 (fun real _let_13))) (let ((_let_21 (fun int _let_10))) (let ((_let_22 (fun _let_21 _let_0))) (let ((_let_23 (fun real _let_22))) (let ((_let_24 (fun _let_10 (fun int bool)))) (let ((_let_25 (fun real _let_24))) (let ((_let_26 (fun _let_10 _let_10))) (let ((_let_27 (fun int _let_26))) (let ((_let_28 (fun int _let_2))) (hAPP _let_17 _let_16 (hAPP _let_9 (fun _let_17 _let_16) (combb _let_0 (fun int bool) real) (hAPP (fun (fun int bool) bool) _let_9 (combb (fun int bool) bool int) (fEx int))) (hAPP (fun int bool) _let_17 (hAPP _let_18 (fun (fun int bool) _let_17) (combc real (fun int bool) _let_0) (hAPP _let_19 _let_18 (hAPP (fun _let_11 _let_12) (fun _let_19 _let_18) (combb _let_11 _let_12 real) (combc int (fun int bool) (fun int bool))) (hAPP _let_20 _let_19 (hAPP _let_14 (fun _let_20 _let_19) (combb _let_13 _let_11 real) (hAPP (fun _let_6 _let_7) _let_14 (combb _let_6 _let_7 int) (combs int bool bool))) (hAPP _let_17 _let_20 (hAPP _let_15 (fun _let_17 _let_20) (combb _let_0 _let_13 real) (hAPP _let_8 _let_15 (combb (fun int bool) _let_6 int) (hAPP (fun bool _let_4) _let_8 (combb bool _let_4 int) fconj))) (hAPP _let_21 _let_17 (hAPP _let_23 (fun _let_21 _let_17) (combc real _let_21 _let_0) (hAPP _let_25 _let_23 (hAPP (fun _let_24 _let_22) (fun _let_25 _let_23) (combb _let_24 _let_22 real) (combb _let_10 (fun int bool) int)) (hAPP _let_5 _let_25 (hAPP (fun _let_1 _let_24) (fun _let_5 _let_25) (combb _let_1 _let_24 real) (combb real bool int)) (fequal real)))) (hAPP _let_10 _let_21 (hAPP _let_27 (fun _let_10 _let_21) (combc int _let_10 _let_10) (hAPP _let_28 _let_27 (hAPP (fun _let_2 _let_26) (fun _let_28 _let_27) (combb _let_2 _let_26 int) (combb real real int)) (hAPP _let_10 _let_28 (hAPP (fun real _let_2) (fun _let_10 _let_28) (combb real _let_2 int) (inverse_divide real)) _let_3))) _let_3)))))) (hAPP (fun int bool) (fun int bool) (hAPP _let_4 _let_7 (combb bool bool int) fNot) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (fequal int)) (zero_zero int)))))))))))))))))))))))))))))))))) ) 15.33/15.56 ( (fun (fun int bool) bool), (fun real (fun int bool)), (fun real bool), (combb (fun int bool) bool real), (fEx int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real real))) (let ((_let_3 (fun nat (fun nat bool)))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun (fun nat real) (fun nat real)))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun (fun nat bool) (fun nat bool)))) (let ((_let_8 (fun int real))) (let ((_let_9 (fun nat _let_4))) (let ((_let_10 (fun (fun nat bool) _let_9))) (let ((_let_11 (fun real _let_0))) (let ((_let_12 (fun int _let_2))) (let ((_let_13 (fun real (fun int (fun nat bool))))) (let ((_let_14 (fun (fun int (fun nat bool)) _let_0))) (let ((_let_15 (fun (fun nat bool) (fun int (fun nat bool))))) (let ((_let_16 (fun real _let_15))) (let ((_let_17 (fun int _let_7))) (let ((_let_18 (fun real _let_17))) (let ((_let_19 (fun int _let_9))) (let ((_let_20 (fun real _let_19))) (let ((_let_21 (fun _let_19 _let_17))) (let ((_let_22 (fun (fun int (fun nat bool)) _let_19))) (let ((_let_23 (fun int (fun nat real)))) (let ((_let_24 (fun _let_23 (fun int (fun nat bool))))) (let ((_let_25 (fun real _let_24))) (let ((_let_26 (fun (fun nat real) (fun nat bool)))) (let ((_let_27 (fun real _let_26))) (let ((_let_28 (fun int _let_5))) (hAPP _let_13 _let_11 (hAPP _let_14 (fun _let_13 _let_11) (combb (fun int (fun nat bool)) _let_0 real) (hAPP (fun (fun nat bool) bool) _let_14 (combb (fun nat bool) bool int) (fEx nat))) (hAPP (fun nat bool) _let_13 (hAPP _let_16 (fun (fun nat bool) _let_13) (combc real (fun nat bool) (fun int (fun nat bool))) (hAPP _let_18 _let_16 (hAPP (fun _let_17 _let_15) (fun _let_18 _let_16) (combb _let_17 _let_15 real) (combc int (fun nat bool) (fun nat bool))) (hAPP _let_20 _let_18 (hAPP _let_21 (fun _let_20 _let_18) (combb _let_19 _let_17 real) (hAPP (fun _let_9 _let_7) _let_21 (combb _let_9 _let_7 int) (combs nat bool bool))) (hAPP _let_13 _let_20 (hAPP _let_22 (fun _let_13 _let_20) (combb (fun int (fun nat bool)) _let_19 real) (hAPP _let_10 _let_22 (combb (fun nat bool) _let_9 int) (hAPP (fun bool _let_4) _let_10 (combb bool _let_4 nat) fconj))) (hAPP _let_23 _let_13 (hAPP _let_25 (fun _let_23 _let_13) (combc real _let_23 (fun int (fun nat bool))) (hAPP _let_27 _let_25 (hAPP (fun _let_26 _let_24) (fun _let_27 _let_25) (combb _let_26 _let_24 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_6 _let_27 (hAPP (fun _let_1 _let_26) (fun _let_6 _let_27) (combb _let_1 _let_26 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_23 (hAPP _let_28 (fun (fun nat real) _let_23) (combc int (fun nat real) (fun nat real)) (hAPP _let_12 _let_28 (hAPP (fun _let_2 _let_5) (fun _let_12 _let_28) (combb _let_2 _let_5 int) (combb real real nat)) (hAPP _let_8 _let_12 (hAPP (fun real _let_2) (fun _let_8 _let_12) (combb real _let_2 int) (inverse_divide real)) (real_1 int)))) (real_1 nat))))))) (hAPP (fun nat bool) (fun nat bool) (hAPP _let_4 _let_7 (combb bool bool nat) fNot) (hAPP nat (fun nat bool) (hAPP _let_3 _let_3 (combc nat nat bool) (fequal nat)) (zero_zero nat)))))))))))))))))))))))))))))))))) ) 15.33/15.56 ( (fun nat (fun nat nat)), nat, (fun nat nat), (combc nat nat nat), (times_times nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.33/15.56 ( (fun nat (fun nat nat)), nat, (fun nat nat), (combc nat nat nat), (let ((_let_0 (fun nat (fun nat nat)))) (hAPP (fun nat nat) _let_0 (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_0 _let_0 (combc nat nat nat) (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))), (one_one nat) ) 15.33/15.56 ( (fun nat (fun nat nat)), (fun nat nat), (fun nat (fun nat nat)), (combb nat (fun nat nat) nat), (plus_plus nat), (let ((_let_0 (fun nat (fun nat nat)))) (hAPP nat (fun nat nat) (hAPP _let_0 _let_0 (combc nat nat nat) (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.33/15.56 ( (fun bool bool), (fun int bool), (fun int bool), (combb bool bool int), fNot, (let ((_let_0 (fun int (fun int bool)))) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (fequal int)) (zero_zero int))) ) 15.33/15.56 ( (fun bool bool), (fun nat bool), (fun nat bool), (combb bool bool nat), fNot, (let ((_let_0 (fun nat (fun nat bool)))) (hAPP nat (fun nat bool) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat)) (zero_zero nat))) ) 15.33/15.56 ( (fun bool bool), (fun (product_prod int int) bool), (fun (product_prod int int) bool), (combb bool bool (product_prod int int)), fNot, (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun _let_1 _let_0))) (let ((_let_4 (fun _let_1 int))) (hAPP int _let_2 (hAPP _let_3 (fun int _let_2) (combc _let_1 int bool) (hAPP _let_4 _let_3 (hAPP (fun int _let_0) (fun _let_4 _let_3) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))) ) 15.33/15.56 ( (fun nat (fun real real)), real, (fun nat real), (combc nat real real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 nat) (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))))), (one_one real) ) 15.33/15.56 ( (fun nat (fun real real)), (fun nat real), (fun nat real), (combs nat real real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (let ((_let_3 (fun real _let_0))) (let ((_let_4 (fun _let_1 _let_2))) (let ((_let_5 (combb real _let_0 nat))) (hAPP _let_1 _let_2 (hAPP _let_3 _let_4 _let_5 (inverse_divide real)) (hAPP real _let_1 (hAPP _let_2 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_2 (hAPP _let_3 _let_4 _let_5 (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) (one_one real))))))))), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat (fun nat nat)))) (let ((_let_2 (combc nat nat nat))) (hAPP (fun nat nat) _let_0 (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat real nat) (real_1 nat)) (hAPP nat (fun nat nat) (hAPP _let_1 _let_1 _let_2 (hAPP (fun nat nat) _let_1 (hAPP _let_1 (fun (fun nat nat) _let_1) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_1 _let_1 _let_2 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))))) ) 15.33/15.56 ( (fun real (fun real real)), (fun real real), (fun real real), (combs real real real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos))), sin ) 15.33/15.56 ( (fun real (fun real real)), (fun real real), (fun real (fun real real)), (combb real (fun real real) real), (inverse_divide real), cos ) 15.33/15.56 ( (fun real (fun real real)), (fun nat real), (fun nat (fun real real)), (combb real (fun real real) nat), (inverse_divide real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (hAPP real _let_1 (hAPP _let_2 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 nat) (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) (one_one real))))) ) 15.33/15.56 ( (fun real (fun real real)), (fun nat real), (fun nat (fun real real)), (combb real (fun real real) nat), (times_times real), (hAPP real (fun nat real) (power_power real) (hAPP int real (number_number_of real) min_1)) ) 15.33/15.56 ( (fun real (fun real real)), (fun int real), (fun int (fun real real)), (combb real (fun real real) int), (inverse_divide real), (real_1 int) ) 15.33/15.56 ( (fun bool (fun bool bool)), (fun int bool), (fun int (fun bool bool)), (combb bool (fun bool bool) int), fconj, (hAPP int (fun int bool) (ord_less int) (zero_zero int)) ) 15.33/15.56 ( (fun bool (fun bool bool)), (fun real bool), (fun real (fun bool bool)), (combb bool (fun bool bool) real), fconj, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) ) 15.33/15.56 ( (fun bool (fun bool bool)), (fun real bool), (fun real (fun bool bool)), (combb bool (fun bool bool) real), fconj, (let ((_let_0 (fun real (fun real bool)))) (hAPP real (fun real bool) (hAPP _let_0 _let_0 (combc real real bool) (ord_less_eq real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.39/15.56 ( (fun bool (fun bool bool)), (fun (product_prod int int) bool), (fun (product_prod int int) (fun bool bool)), (combb bool (fun bool bool) (product_prod int int)), fconj, (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun _let_1 _let_0))) (let ((_let_4 (fun _let_1 int))) (hAPP _let_2 _let_2 (hAPP (fun bool bool) (fun _let_2 _let_2) (combb bool bool _let_1) fNot) (hAPP int _let_2 (hAPP _let_3 (fun int _let_2) (combc _let_1 int bool) (hAPP _let_4 _let_3 (hAPP (fun int _let_0) (fun _let_4 _let_3) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int)))))))) ) 15.39/15.56 ( code_code_numeral, code_code_numeral, code_code_numeral, (minus_minus code_code_numeral), (zero_zero code_code_numeral), (one_one code_code_numeral) ) 15.39/15.56 ( (fun int (fun int (fun int bool))), int, (fun int (fun int bool)), (combc int int (fun int bool)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int _let_1))) (let ((_let_5 (fun _let_2 _let_1))) (hAPP _let_4 _let_4 (hAPP (fun _let_1 _let_1) (fun _let_4 _let_4) (combb _let_1 _let_1 int) (combc int int bool)) (hAPP _let_3 _let_4 (hAPP _let_5 (fun _let_3 _let_4) (combb _let_2 _let_1 int) (hAPP _let_1 _let_5 (combb int _let_0 int) (fequal int))) int_gcd)))))))), (one_one int) ) 15.39/15.56 ( (fun real (fun real bool)), real, (fun real bool), (combc real real bool), (ord_less_eq real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.56 ( (fun real (fun real bool)), real, (fun real bool), (combc real real bool), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun real _let_0))) (hAPP _let_1 _let_2 (hAPP _let_2 (fun _let_1 _let_2) (combb real _let_0 real) (fequal real)) cos)))), (zero_zero real) ) 15.39/15.56 ( (fun real (fun real bool)), (fun real real), (fun real (fun real bool)), (combb real (fun real bool) real), (fequal real), cos ) 15.39/15.56 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), (fun int (fun int bool)), (fun int (fun int bool)), (let ((_let_0 (fun int bool))) (combb _let_0 _let_0 int)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun int _let_1))) (hAPP _let_2 (fun _let_0 _let_0) (combs int bool bool) (hAPP _let_0 _let_2 (hAPP (fun bool _let_1) (fun _let_0 _let_2) (combb bool _let_1 int) fconj) (hAPP int _let_0 (ord_less int) (zero_zero int))))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int _let_1))) (let ((_let_5 (fun _let_2 _let_1))) (hAPP int _let_1 (hAPP _let_4 _let_4 (combc int int _let_0) (hAPP _let_4 _let_4 (hAPP (fun _let_1 _let_1) (fun _let_4 _let_4) (combb _let_1 _let_1 int) (combc int int bool)) (hAPP _let_3 _let_4 (hAPP _let_5 (fun _let_3 _let_4) (combb _let_2 _let_1 int) (hAPP _let_1 _let_5 (combb int _let_0 int) (fequal int))) int_gcd))) (one_one int)))))))) ) 15.39/15.56 ( (let ((_let_0 (fun int bool))) (fun (fun int _let_0) _let_0)), (fun real (fun int (fun int bool))), (fun real (fun int bool)), (let ((_let_0 (fun int bool))) (combb (fun int _let_0) _let_0 real)), (let ((_let_0 (fun int bool))) (hAPP (fun _let_0 bool) (fun (fun int _let_0) _let_0) (combb _let_0 bool int) (fEx int))), (let ((_let_0 (fun int (fun int bool)))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real real))) (let ((_let_3 (real_1 int))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun int _let_4))) (let ((_let_7 (fun (fun int bool) (fun int bool)))) (let ((_let_8 (fun (fun int bool) _let_6))) (let ((_let_9 (fun int real))) (let ((_let_10 (fun int _let_7))) (let ((_let_11 (fun (fun int bool) _let_0))) (let ((_let_12 (fun int _let_6))) (let ((_let_13 (fun _let_12 _let_10))) (let ((_let_14 (fun _let_0 _let_12))) (let ((_let_15 (fun real _let_0))) (let ((_let_16 (fun real _let_11))) (let ((_let_17 (fun real _let_10))) (let ((_let_18 (fun real _let_12))) (let ((_let_19 (fun int _let_9))) (let ((_let_20 (fun _let_19 _let_0))) (let ((_let_21 (fun real _let_20))) (let ((_let_22 (fun _let_9 (fun int bool)))) (let ((_let_23 (fun real _let_22))) (let ((_let_24 (fun _let_9 _let_9))) (let ((_let_25 (fun int _let_24))) (let ((_let_26 (fun int _let_2))) (hAPP (fun int bool) _let_15 (hAPP _let_16 (fun (fun int bool) _let_15) (combc real (fun int bool) _let_0) (hAPP _let_17 _let_16 (hAPP (fun _let_10 _let_11) (fun _let_17 _let_16) (combb _let_10 _let_11 real) (combc int (fun int bool) (fun int bool))) (hAPP _let_18 _let_17 (hAPP _let_13 (fun _let_18 _let_17) (combb _let_12 _let_10 real) (hAPP (fun _let_6 _let_7) _let_13 (combb _let_6 _let_7 int) (combs int bool bool))) (hAPP _let_15 _let_18 (hAPP _let_14 (fun _let_15 _let_18) (combb _let_0 _let_12 real) (hAPP _let_8 _let_14 (combb (fun int bool) _let_6 int) (hAPP (fun bool _let_4) _let_8 (combb bool _let_4 int) fconj))) (hAPP _let_19 _let_15 (hAPP _let_21 (fun _let_19 _let_15) (combc real _let_19 _let_0) (hAPP _let_23 _let_21 (hAPP (fun _let_22 _let_20) (fun _let_23 _let_21) (combb _let_22 _let_20 real) (combb _let_9 (fun int bool) int)) (hAPP _let_5 _let_23 (hAPP (fun _let_1 _let_22) (fun _let_5 _let_23) (combb _let_1 _let_22 real) (combb real bool int)) (fequal real)))) (hAPP _let_9 _let_19 (hAPP _let_25 (fun _let_9 _let_19) (combc int _let_9 _let_9) (hAPP _let_26 _let_25 (hAPP (fun _let_2 _let_24) (fun _let_26 _let_25) (combb _let_2 _let_24 int) (combb real real int)) (hAPP _let_9 _let_26 (hAPP (fun real _let_2) (fun _let_9 _let_26) (combb real _let_2 int) (inverse_divide real)) _let_3))) _let_3)))))) (hAPP (fun int bool) (fun int bool) (hAPP _let_4 _let_7 (combb bool bool int) fNot) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (fequal int)) (zero_zero int))))))))))))))))))))))))))))))) ) 15.39/15.56 ( (fun int (fun (fun int int) (fun int bool))), (fun int int), (fun int (fun int bool)), (combc int (fun int int) (fun int bool)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun (fun int int) _let_0))) (let ((_let_3 (fun int _let_2))) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 int) (combb int bool int)) (fequal int)))))), (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.56 ( (fun int (fun (fun int int) (fun int bool))), (fun int int), (fun int (fun int bool)), (combc int (fun int int) (fun int bool)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun (fun int int) _let_0))) (let ((_let_3 (fun int _let_2))) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 int) (combb int bool int)) (fequal int)))))), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (hAPP int _let_0 (hAPP _let_1 _let_1 (combc int int int) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)) (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one int)))) ) 15.39/15.56 ( (fun (fun int int) (fun int (fun int bool))), (fun int (fun int int)), (fun int (fun int (fun int bool))), (combb (fun int int) (fun int (fun int bool)) int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (hAPP _let_1 (fun (fun int int) _let_1) (combb int _let_0 int) (fequal int)))), int_gcd ) 15.39/15.56 ( (let ((_let_0 (fun int bool))) (fun _let_0 (fun (fun int int) _let_0))), (fun int (fun int bool)), (fun int (fun (fun int int) (fun int bool))), (let ((_let_0 (fun int bool))) (combb _let_0 (fun (fun int int) _let_0) int)), (combb int bool int), (fequal int) ) 15.39/15.56 ( (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 bool))) (combb _let_1 _let_1 _let_0))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_3 _let_3))) (let ((_let_5 (fun _let_1 _let_2))) (let ((_let_6 (fun _let_1 _let_0))) (let ((_let_7 (fun _let_1 int))) (hAPP _let_5 _let_4 (combs _let_1 bool bool) (hAPP _let_3 _let_5 (hAPP (fun bool _let_2) (fun _let_3 _let_5) (combb bool _let_2 _let_1) fconj) (hAPP _let_3 _let_3 (hAPP _let_2 _let_4 (combb bool bool _let_1) fNot) (hAPP int _let_3 (hAPP _let_6 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_7 _let_6 (hAPP (fun int _let_0) (fun _let_7 _let_6) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))))))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun _let_2 (fun _let_2 bool)))) (let ((_let_4 (fun _let_2 _let_0))) (let ((_let_5 (fun _let_2 int))) (let ((_let_6 (fun _let_5 _let_4))) (let ((_let_7 (product_snd int int))) (let ((_let_8 (fun _let_2 _let_5))) (let ((_let_9 (fun _let_5 (fun _let_2 bool)))) (let ((_let_10 (fun _let_2 _let_9))) (let ((_let_11 (fun _let_2 _let_4))) (let ((_let_12 (fun _let_5 _let_5))) (let ((_let_13 (fun _let_2 _let_12))) (let ((_let_14 (fun _let_5 _let_8))) (let ((_let_15 (fun _let_2 _let_1))) (let ((_let_16 (hAPP _let_5 _let_15 (hAPP (fun int _let_1) (fun _let_5 _let_15) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (let ((_let_17 (fun int _let_5))) (hAPP _let_8 _let_3 (hAPP _let_10 (fun _let_8 _let_3) (combs _let_2 _let_5 (fun _let_2 bool)) (hAPP _let_11 _let_10 (hAPP (fun _let_4 _let_9) (fun _let_11 _let_10) (combb _let_4 _let_9 _let_2) (combs _let_2 int bool)) (hAPP _let_8 _let_11 (hAPP _let_6 (fun _let_8 _let_11) (combb _let_5 _let_4 _let_2) (hAPP (fun int _let_0) _let_6 (combb int _let_0 _let_2) (fequal int))) (hAPP _let_5 _let_8 (hAPP _let_13 _let_14 (combc _let_2 _let_5 _let_5) (hAPP _let_15 _let_13 (hAPP (fun _let_1 _let_12) (fun _let_15 _let_13) (combb _let_1 _let_12 _let_2) (combb int int _let_2)) _let_16)) _let_7)))) (hAPP _let_5 _let_8 (hAPP _let_17 _let_14 (combb int _let_5 _let_2) (hAPP _let_15 _let_17 (combc _let_2 int int) _let_16)) _let_7)))))))))))))))))))) ) 15.39/15.56 ( (let ((_let_0 (fun (product_prod int int) bool))) (fun (product_prod int int) (fun _let_0 _let_0))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (fun (product_prod int int) bool))) (combs (product_prod int int) _let_0 _let_0)), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_3 _let_3))) (let ((_let_5 (fun _let_1 _let_4))) (let ((_let_6 (fun _let_1 _let_2))) (let ((_let_7 (combb bool bool _let_1))) (let ((_let_8 (fun _let_1 _let_0))) (let ((_let_9 (fun _let_1 int))) (hAPP _let_6 _let_5 (hAPP (fun _let_2 _let_4) (fun _let_6 _let_5) (combb _let_2 _let_4 _let_1) _let_7) (hAPP _let_3 _let_6 (hAPP (fun bool _let_2) (fun _let_3 _let_6) (combb bool _let_2 _let_1) fconj) (hAPP _let_3 _let_3 (hAPP _let_2 _let_4 _let_7 fNot) (hAPP int _let_3 (hAPP _let_8 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_9 _let_8 (hAPP (fun int _let_0) (fun _let_9 _let_8) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))))))))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun _let_2 (fun _let_2 bool)))) (let ((_let_5 (fun (fun _let_2 bool) (fun _let_2 bool)))) (let ((_let_6 (fun _let_2 _let_3))) (let ((_let_7 (fun _let_2 _let_0))) (let ((_let_8 (fun _let_2 int))) (let ((_let_9 (fun _let_8 _let_7))) (let ((_let_10 (hAPP (fun int _let_0) _let_9 (combb int _let_0 _let_2) (fequal int)))) (let ((_let_11 (product_snd int int))) (let ((_let_12 (fun _let_2 _let_8))) (let ((_let_13 (fun _let_8 (fun _let_2 bool)))) (let ((_let_14 (fun _let_2 _let_13))) (let ((_let_15 (fun _let_2 _let_7))) (let ((_let_16 (fun _let_8 _let_8))) (let ((_let_17 (fun _let_2 _let_16))) (let ((_let_18 (fun _let_8 _let_12))) (let ((_let_19 (fun _let_2 _let_1))) (let ((_let_20 (hAPP _let_8 _let_19 (hAPP (fun int _let_1) (fun _let_8 _let_19) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (let ((_let_21 (fun int _let_8))) (hAPP _let_4 _let_4 (hAPP _let_5 (fun _let_4 _let_4) (combb (fun _let_2 bool) (fun _let_2 bool) _let_2) (hAPP _let_6 _let_5 (combs _let_2 bool bool) (hAPP (fun _let_2 bool) _let_6 (hAPP (fun bool _let_3) (fun (fun _let_2 bool) _let_6) (combb bool _let_3 _let_2) fconj) (hAPP (fun _let_2 bool) (fun _let_2 bool) (hAPP _let_3 _let_5 (combb bool bool _let_2) fNot) (hAPP int (fun _let_2 bool) (hAPP _let_7 (fun int (fun _let_2 bool)) (combc _let_2 int bool) (hAPP _let_8 _let_7 _let_10 _let_11)) (zero_zero int)))))) (hAPP _let_12 _let_4 (hAPP _let_14 (fun _let_12 _let_4) (combs _let_2 _let_8 (fun _let_2 bool)) (hAPP _let_15 _let_14 (hAPP (fun _let_7 _let_13) (fun _let_15 _let_14) (combb _let_7 _let_13 _let_2) (combs _let_2 int bool)) (hAPP _let_12 _let_15 (hAPP _let_9 (fun _let_12 _let_15) (combb _let_8 _let_7 _let_2) _let_10) (hAPP _let_8 _let_12 (hAPP _let_17 _let_18 (combc _let_2 _let_8 _let_8) (hAPP _let_19 _let_17 (hAPP (fun _let_1 _let_16) (fun _let_19 _let_17) (combb _let_1 _let_16 _let_2) (combb int int _let_2)) _let_20)) _let_11)))) (hAPP _let_8 _let_12 (hAPP _let_21 _let_18 (combb int _let_8 _let_2) (hAPP _let_19 _let_21 (combc _let_2 int int) _let_20)) _let_11))))))))))))))))))))))))) ) 15.39/15.56 ( (let ((_let_0 (fun (product_prod int int) bool))) (fun (fun bool bool) (fun _let_0 _let_0))), (fun (product_prod int int) (fun bool bool)), (let ((_let_0 (fun (product_prod int int) bool))) (fun (product_prod int int) (fun _let_0 _let_0))), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 bool))) (combb (fun bool bool) (fun _let_1 _let_1) _let_0))), (combb bool bool (product_prod int int)), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_1 _let_2))) (let ((_let_5 (fun _let_1 _let_0))) (let ((_let_6 (fun _let_1 int))) (hAPP _let_3 _let_4 (hAPP (fun bool _let_2) (fun _let_3 _let_4) (combb bool _let_2 _let_1) fconj) (hAPP _let_3 _let_3 (hAPP _let_2 (fun _let_3 _let_3) (combb bool bool _let_1) fNot) (hAPP int _let_3 (hAPP _let_5 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_6 _let_5 (hAPP (fun int _let_0) (fun _let_6 _let_5) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))))))) ) 15.39/15.56 ( (fun (product_prod int int) (fun int bool)), int, (fun (product_prod int int) bool), (combc (product_prod int int) int bool), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 _let_0))) (let ((_let_3 (fun _let_1 int))) (hAPP _let_3 _let_2 (hAPP (fun int _let_0) (fun _let_3 _let_2) (combb int _let_0 _let_1) (fequal int)) (product_snd int int)))))), (zero_zero int) ) 15.39/15.56 ( (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 (fun int bool)))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 (fun int bool)))), (let ((_let_0 (product_prod int int))) (combb (fun _let_0 int) (fun _let_0 (fun int bool)) _let_0)), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (hAPP (fun int _let_0) (fun (fun _let_1 int) (fun _let_1 _let_0)) (combb int _let_0 _let_1) (fequal int)))), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_2))) (let ((_let_4 (fun _let_2 _let_2))) (let ((_let_5 (fun _let_1 _let_4))) (let ((_let_6 (fun _let_1 _let_0))) (hAPP _let_2 _let_3 (hAPP _let_5 (fun _let_2 _let_3) (combc _let_1 _let_2 _let_2) (hAPP _let_6 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_6 _let_5) (combb _let_0 _let_4 _let_1) (combb int int _let_1)) (hAPP _let_2 _let_6 (hAPP (fun int _let_0) (fun _let_2 _let_6) (combb int _let_0 _let_1) (times_times int)) (product_fst int int)))) (product_snd int int))))))))) ) 15.39/15.56 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun (fun _let_0 int) (fun _let_0 bool)))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (combs _let_0 (fun _let_0 int) (fun _let_0 bool))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun _let_2 _let_0))) (let ((_let_4 (fun _let_2 int))) (let ((_let_5 (fun _let_4 _let_3))) (let ((_let_6 (fun _let_2 _let_4))) (let ((_let_7 (fun _let_4 (fun _let_2 bool)))) (let ((_let_8 (fun _let_2 _let_7))) (let ((_let_9 (fun _let_2 _let_3))) (let ((_let_10 (fun _let_4 _let_4))) (let ((_let_11 (fun _let_2 _let_10))) (let ((_let_12 (fun _let_2 _let_1))) (hAPP _let_9 _let_8 (hAPP (fun _let_3 _let_7) (fun _let_9 _let_8) (combb _let_3 _let_7 _let_2) (combs _let_2 int bool)) (hAPP _let_6 _let_9 (hAPP _let_5 (fun _let_6 _let_9) (combb _let_4 _let_3 _let_2) (hAPP (fun int _let_0) _let_5 (combb int _let_0 _let_2) (fequal int))) (hAPP _let_4 _let_6 (hAPP _let_11 (fun _let_4 _let_6) (combc _let_2 _let_4 _let_4) (hAPP _let_12 _let_11 (hAPP (fun _let_1 _let_10) (fun _let_12 _let_11) (combb _let_1 _let_10 _let_2) (combb int int _let_2)) (hAPP _let_4 _let_12 (hAPP (fun int _let_1) (fun _let_4 _let_12) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (product_snd int int))))))))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_2))) (let ((_let_4 (fun _let_1 _let_0))) (let ((_let_5 (fun int _let_2))) (hAPP _let_2 _let_3 (hAPP _let_5 (fun _let_2 _let_3) (combb int _let_2 _let_1) (hAPP _let_4 _let_5 (combc _let_1 int int) (hAPP _let_2 _let_4 (hAPP (fun int _let_0) (fun _let_2 _let_4) (combb int _let_0 _let_1) (times_times int)) (product_fst int int)))) (product_snd int int)))))))) ) 15.39/15.56 ( (let ((_let_0 (product_prod int int))) (fun (fun _let_0 (fun int bool)) (fun (fun _let_0 int) (fun _let_0 bool)))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 (fun int bool)))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun (fun _let_0 int) (fun _let_0 bool)))), (let ((_let_0 (product_prod int int))) (combb (fun _let_0 (fun int bool)) (fun (fun _let_0 int) (fun _let_0 bool)) _let_0)), (combs (product_prod int int) int bool), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun _let_2 _let_0))) (let ((_let_4 (fun _let_2 int))) (let ((_let_5 (fun _let_4 _let_3))) (let ((_let_6 (fun _let_2 _let_4))) (let ((_let_7 (fun _let_2 _let_3))) (let ((_let_8 (fun _let_4 _let_4))) (let ((_let_9 (fun _let_2 _let_8))) (let ((_let_10 (fun _let_2 _let_1))) (hAPP _let_6 _let_7 (hAPP _let_5 (fun _let_6 _let_7) (combb _let_4 _let_3 _let_2) (hAPP (fun int _let_0) _let_5 (combb int _let_0 _let_2) (fequal int))) (hAPP _let_4 _let_6 (hAPP _let_9 (fun _let_4 _let_6) (combc _let_2 _let_4 _let_4) (hAPP _let_10 _let_9 (hAPP (fun _let_1 _let_8) (fun _let_10 _let_9) (combb _let_1 _let_8 _let_2) (combb int int _let_2)) (hAPP _let_4 _let_10 (hAPP (fun int _let_1) (fun _let_4 _let_10) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (product_snd int int)))))))))))))) ) 15.39/15.56 ( (let ((_let_0 (fun (product_prod int int) int))) (fun (product_prod int int) (fun _let_0 _let_0))), (fun (product_prod int int) int), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (let ((_let_0 (fun (product_prod int int) int))) (combc (product_prod int int) _let_0 _let_0)), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_2 _let_2))) (let ((_let_4 (fun _let_1 _let_3))) (let ((_let_5 (fun _let_1 _let_0))) (hAPP _let_5 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_5 _let_4) (combb _let_0 _let_3 _let_1) (combb int int _let_1)) (hAPP _let_2 _let_5 (hAPP (fun int _let_0) (fun _let_2 _let_5) (combb int _let_0 _let_1) (times_times int)) (product_fst int int))))))))), (product_snd int int) ) 15.39/15.56 ( (let ((_let_0 (fun (product_prod int int) int))) (fun (fun int int) (fun _let_0 _let_0))), (fun (product_prod int int) (fun int int)), (let ((_let_0 (fun (product_prod int int) int))) (fun (product_prod int int) (fun _let_0 _let_0))), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 int))) (combb (fun int int) (fun _let_1 _let_1) _let_0))), (combb int int (product_prod int int)), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_0))) (hAPP _let_2 _let_3 (hAPP (fun int _let_0) (fun _let_2 _let_3) (combb int _let_0 _let_1) (times_times int)) (product_fst int int)))))) ) 15.39/15.56 ( (fun int (fun (product_prod int int) int)), (fun (product_prod int int) int), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (let ((_let_0 (product_prod int int))) (combb int (fun _let_0 int) _let_0)), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_0))) (hAPP _let_3 (fun int _let_2) (combc _let_1 int int) (hAPP _let_2 _let_3 (hAPP (fun int _let_0) (fun _let_2 _let_3) (combb int _let_0 _let_1) (times_times int)) (product_fst int int))))))), (product_snd int int) ) 15.39/15.56 ( (fun real (fun bool bool)), (fun real bool), (fun real bool), (combs real bool bool), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun real _let_1))) (hAPP _let_0 _let_2 (hAPP (fun bool _let_1) (fun _let_0 _let_2) (combb bool _let_1 real) fconj) (hAPP real _let_0 (ord_less_eq real) (zero_zero real)))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun real _let_0))) (let ((_let_4 (fun real _let_2))) (let ((_let_5 (combc real real bool))) (hAPP _let_0 _let_0 (hAPP _let_4 (fun _let_0 _let_0) (combs real bool bool) (hAPP _let_0 _let_4 (hAPP (fun bool _let_2) (fun _let_0 _let_4) (combb bool _let_2 real) fconj) (hAPP real _let_0 (hAPP _let_3 _let_3 _let_5 (ord_less_eq real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_3 _let_3 _let_5 (hAPP _let_1 _let_3 (hAPP _let_3 (fun _let_1 _let_3) (combb real _let_0 real) (fequal real)) cos)) (zero_zero real))))))))) ) 15.39/15.56 ( (fun real (fun bool bool)), (fun real bool), (fun real bool), (combs real bool bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun real (fun real bool)))) (let ((_let_2 (fun real _let_0))) (hAPP (fun real bool) _let_2 (hAPP (fun bool _let_0) (fun (fun real bool) _let_2) (combb bool _let_0 real) fconj) (hAPP real (fun real bool) (hAPP _let_1 _let_1 (combc real real bool) (ord_less_eq real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun real _let_0))) (hAPP real _let_0 (hAPP _let_2 _let_2 (combc real real bool) (hAPP _let_1 _let_2 (hAPP _let_2 (fun _let_1 _let_2) (combb real _let_0 real) (fequal real)) cos)) (zero_zero real))))) ) 15.39/15.57 ( (let ((_let_0 (fun int bool))) (fun (fun int (fun int (fun bool bool))) (fun int (fun _let_0 _let_0)))), (fun real (fun int (fun int (fun bool bool)))), (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun int bool))) (combb (fun int (fun int (fun bool bool))) (fun int (fun _let_0 _let_0)) real)), (let ((_let_0 (fun int (fun bool bool)))) (let ((_let_1 (fun (fun int bool) (fun int bool)))) (hAPP (fun _let_0 _let_1) (fun (fun int _let_0) (fun int _let_1)) (combb _let_0 _let_1 int) (combs int bool bool)))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun int _let_3))) (let ((_let_6 (fun (fun int bool) _let_5))) (let ((_let_7 (fun int real))) (let ((_let_8 (fun int _let_5))) (let ((_let_9 (fun (fun int (fun int bool)) _let_8))) (let ((_let_10 (fun real (fun int (fun int bool))))) (let ((_let_11 (fun real _let_8))) (let ((_let_12 (fun int _let_7))) (let ((_let_13 (fun _let_12 (fun int (fun int bool))))) (let ((_let_14 (fun real _let_13))) (let ((_let_15 (fun _let_7 (fun int bool)))) (let ((_let_16 (fun real _let_15))) (let ((_let_17 (fun _let_7 _let_7))) (let ((_let_18 (fun int _let_17))) (let ((_let_19 (fun int _let_1))) (hAPP _let_10 _let_11 (hAPP _let_9 (fun _let_10 _let_11) (combb (fun int (fun int bool)) _let_8 real) (hAPP _let_6 _let_9 (combb (fun int bool) _let_5 int) (hAPP (fun bool _let_3) _let_6 (combb bool _let_3 int) fconj))) (hAPP _let_12 _let_10 (hAPP _let_14 (fun _let_12 _let_10) (combc real _let_12 (fun int (fun int bool))) (hAPP _let_16 _let_14 (hAPP (fun _let_15 _let_13) (fun _let_16 _let_14) (combb _let_15 _let_13 real) (combb _let_7 (fun int bool) int)) (hAPP _let_4 _let_16 (hAPP (fun _let_0 _let_15) (fun _let_4 _let_16) (combb _let_0 _let_15 real) (combb real bool int)) (fequal real)))) (hAPP _let_7 _let_12 (hAPP _let_18 (fun _let_7 _let_12) (combc int _let_7 _let_7) (hAPP _let_19 _let_18 (hAPP (fun _let_1 _let_17) (fun _let_19 _let_18) (combb _let_1 _let_17 int) (combb real real int)) (hAPP _let_7 _let_19 (hAPP (fun real _let_1) (fun _let_7 _let_19) (combb real _let_1 int) (inverse_divide real)) _let_2))) _let_2))))))))))))))))))))))) ) 15.39/15.57 ( (fun (fun int (fun int bool)) (fun int (fun int (fun bool bool)))), (fun real (fun int (fun int bool))), (fun real (fun int (fun int (fun bool bool)))), (combb (fun int (fun int bool)) (fun int (fun int (fun bool bool))) real), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (fun _let_0 _let_2))) (hAPP _let_3 (fun (fun int _let_0) (fun int _let_2)) (combb _let_0 _let_2 int) (hAPP (fun bool _let_1) _let_3 (combb bool _let_1 int) fconj)))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun real _let_0))) (let ((_let_4 (fun int real))) (let ((_let_5 (fun real (fun int (fun int bool))))) (let ((_let_6 (fun int _let_4))) (let ((_let_7 (fun _let_6 (fun int (fun int bool))))) (let ((_let_8 (fun real _let_7))) (let ((_let_9 (fun _let_4 (fun int bool)))) (let ((_let_10 (fun real _let_9))) (let ((_let_11 (fun _let_4 _let_4))) (let ((_let_12 (fun int _let_11))) (let ((_let_13 (fun int _let_1))) (hAPP _let_6 _let_5 (hAPP _let_8 (fun _let_6 _let_5) (combc real _let_6 (fun int (fun int bool))) (hAPP _let_10 _let_8 (hAPP (fun _let_9 _let_7) (fun _let_10 _let_8) (combb _let_9 _let_7 real) (combb _let_4 (fun int bool) int)) (hAPP _let_3 _let_10 (hAPP (fun _let_0 _let_9) (fun _let_3 _let_10) (combb _let_0 _let_9 real) (combb real bool int)) (fequal real)))) (hAPP _let_4 _let_6 (hAPP _let_12 (fun _let_4 _let_6) (combc int _let_4 _let_4) (hAPP _let_13 _let_12 (hAPP (fun _let_1 _let_11) (fun _let_13 _let_12) (combb _let_1 _let_11 int) (combb real real int)) (hAPP _let_4 _let_13 (hAPP (fun real _let_1) (fun _let_4 _let_13) (combb real _let_1 int) (inverse_divide real)) _let_2))) _let_2)))))))))))))))) ) 15.39/15.57 ( (fun int (fun nat int)), nat, (fun int int), (combc int nat int), (power_power int), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.57 ( (let ((_let_0 (fun int bool))) (fun real (fun _let_0 (fun int _let_0)))), (fun int bool), (fun real (fun int (fun int bool))), (let ((_let_0 (fun int bool))) (combc real _let_0 (fun int _let_0))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun int _let_3))) (let ((_let_6 (fun (fun int bool) (fun int bool)))) (let ((_let_7 (fun (fun int bool) _let_5))) (let ((_let_8 (fun int real))) (let ((_let_9 (fun int _let_6))) (let ((_let_10 (fun (fun int bool) (fun int (fun int bool))))) (let ((_let_11 (fun int _let_5))) (let ((_let_12 (fun _let_11 _let_9))) (let ((_let_13 (fun (fun int (fun int bool)) _let_11))) (let ((_let_14 (fun real (fun int (fun int bool))))) (let ((_let_15 (fun real _let_10))) (let ((_let_16 (fun real _let_9))) (let ((_let_17 (fun real _let_11))) (let ((_let_18 (fun int _let_8))) (let ((_let_19 (fun _let_18 (fun int (fun int bool))))) (let ((_let_20 (fun real _let_19))) (let ((_let_21 (fun _let_8 (fun int bool)))) (let ((_let_22 (fun real _let_21))) (let ((_let_23 (fun _let_8 _let_8))) (let ((_let_24 (fun int _let_23))) (let ((_let_25 (fun int _let_1))) (hAPP _let_16 _let_15 (hAPP (fun _let_9 _let_10) (fun _let_16 _let_15) (combb _let_9 _let_10 real) (combc int (fun int bool) (fun int bool))) (hAPP _let_17 _let_16 (hAPP _let_12 (fun _let_17 _let_16) (combb _let_11 _let_9 real) (hAPP (fun _let_5 _let_6) _let_12 (combb _let_5 _let_6 int) (combs int bool bool))) (hAPP _let_14 _let_17 (hAPP _let_13 (fun _let_14 _let_17) (combb (fun int (fun int bool)) _let_11 real) (hAPP _let_7 _let_13 (combb (fun int bool) _let_5 int) (hAPP (fun bool _let_3) _let_7 (combb bool _let_3 int) fconj))) (hAPP _let_18 _let_14 (hAPP _let_20 (fun _let_18 _let_14) (combc real _let_18 (fun int (fun int bool))) (hAPP _let_22 _let_20 (hAPP (fun _let_21 _let_19) (fun _let_22 _let_20) (combb _let_21 _let_19 real) (combb _let_8 (fun int bool) int)) (hAPP _let_4 _let_22 (hAPP (fun _let_0 _let_21) (fun _let_4 _let_22) (combb _let_0 _let_21 real) (combb real bool int)) (fequal real)))) (hAPP _let_8 _let_18 (hAPP _let_24 (fun _let_8 _let_18) (combc int _let_8 _let_8) (hAPP _let_25 _let_24 (hAPP (fun _let_1 _let_23) (fun _let_25 _let_24) (combb _let_1 _let_23 int) (combb real real int)) (hAPP _let_8 _let_25 (hAPP (fun real _let_1) (fun _let_8 _let_25) (combb real _let_1 int) (inverse_divide real)) _let_2))) _let_2))))))))))))))))))))))))))))))), (let ((_let_0 (fun int (fun int bool)))) (hAPP (fun int bool) (fun int bool) (hAPP (fun bool bool) (fun (fun int bool) (fun int bool)) (combb bool bool int) fNot) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (fequal int)) (zero_zero int)))) ) 15.39/15.57 ( (let ((_let_0 (fun int bool))) (fun (fun int (fun _let_0 _let_0)) (fun _let_0 (fun int _let_0)))), (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun int bool))) (fun real (fun _let_0 (fun int _let_0)))), (let ((_let_0 (fun int bool))) (combb (fun int (fun _let_0 _let_0)) (fun _let_0 (fun int _let_0)) real)), (let ((_let_0 (fun int bool))) (combc int _let_0 _let_0)), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun int _let_3))) (let ((_let_6 (fun (fun int bool) (fun int bool)))) (let ((_let_7 (fun (fun int bool) _let_5))) (let ((_let_8 (fun int real))) (let ((_let_9 (fun int _let_6))) (let ((_let_10 (fun int _let_5))) (let ((_let_11 (fun _let_10 _let_9))) (let ((_let_12 (fun (fun int (fun int bool)) _let_10))) (let ((_let_13 (fun real (fun int (fun int bool))))) (let ((_let_14 (fun real _let_9))) (let ((_let_15 (fun real _let_10))) (let ((_let_16 (fun int _let_8))) (let ((_let_17 (fun _let_16 (fun int (fun int bool))))) (let ((_let_18 (fun real _let_17))) (let ((_let_19 (fun _let_8 (fun int bool)))) (let ((_let_20 (fun real _let_19))) (let ((_let_21 (fun _let_8 _let_8))) (let ((_let_22 (fun int _let_21))) (let ((_let_23 (fun int _let_1))) (hAPP _let_15 _let_14 (hAPP _let_11 (fun _let_15 _let_14) (combb _let_10 _let_9 real) (hAPP (fun _let_5 _let_6) _let_11 (combb _let_5 _let_6 int) (combs int bool bool))) (hAPP _let_13 _let_15 (hAPP _let_12 (fun _let_13 _let_15) (combb (fun int (fun int bool)) _let_10 real) (hAPP _let_7 _let_12 (combb (fun int bool) _let_5 int) (hAPP (fun bool _let_3) _let_7 (combb bool _let_3 int) fconj))) (hAPP _let_16 _let_13 (hAPP _let_18 (fun _let_16 _let_13) (combc real _let_16 (fun int (fun int bool))) (hAPP _let_20 _let_18 (hAPP (fun _let_19 _let_17) (fun _let_20 _let_18) (combb _let_19 _let_17 real) (combb _let_8 (fun int bool) int)) (hAPP _let_4 _let_20 (hAPP (fun _let_0 _let_19) (fun _let_4 _let_20) (combb _let_0 _let_19 real) (combb real bool int)) (fequal real)))) (hAPP _let_8 _let_16 (hAPP _let_22 (fun _let_8 _let_16) (combc int _let_8 _let_8) (hAPP _let_23 _let_22 (hAPP (fun _let_1 _let_21) (fun _let_23 _let_22) (combb _let_1 _let_21 int) (combb real real int)) (hAPP _let_8 _let_23 (hAPP (fun real _let_1) (fun _let_8 _let_23) (combb real _let_1 int) (inverse_divide real)) _let_2))) _let_2)))))))))))))))))))))))))))) ) 15.39/15.57 ( (fun real (fun (fun int (fun int real)) (fun int (fun int bool)))), (fun int (fun int real)), (fun real (fun int (fun int bool))), (combc real (fun int (fun int real)) (fun int (fun int bool))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun int (fun int real)) (fun int (fun int bool))))) (let ((_let_3 (fun real _let_2))) (let ((_let_4 (fun (fun int real) (fun int bool)))) (let ((_let_5 (fun real _let_4))) (hAPP _let_5 _let_3 (hAPP (fun _let_4 _let_2) (fun _let_5 _let_3) (combb _let_4 _let_2 real) (combb (fun int real) (fun int bool) int)) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_1 _let_5) (combb _let_0 _let_4 real) (combb real bool int)) (fequal real))))))))), (let ((_let_0 (fun real real))) (let ((_let_1 (real_1 int))) (let ((_let_2 (fun int real))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun _let_2 _let_2))) (let ((_let_5 (fun int _let_4))) (let ((_let_6 (fun int _let_0))) (hAPP _let_2 _let_3 (hAPP _let_5 (fun _let_2 _let_3) (combc int _let_2 _let_2) (hAPP _let_6 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_6 _let_5) (combb _let_0 _let_4 int) (combb real real int)) (hAPP _let_2 _let_6 (hAPP (fun real _let_0) (fun _let_2 _let_6) (combb real _let_0 int) (inverse_divide real)) _let_1))) _let_1)))))))) ) 15.39/15.57 ( (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int real))) (fun (fun _let_1 _let_0) (fun (fun int _let_1) (fun int _let_0))))), (fun real (fun (fun int real) (fun int bool))), (fun real (fun (fun int (fun int real)) (fun int (fun int bool)))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int real))) (combb (fun _let_1 _let_0) (fun (fun int _let_1) (fun int _let_0)) real))), (combb (fun int real) (fun int bool) int), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun int real) (fun int bool)))) (let ((_let_3 (fun real _let_2))) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 real) (combb real bool int)) (fequal real)))))) ) 15.39/15.57 ( (fun (fun real bool) (fun (fun int real) (fun int bool))), (fun real (fun real bool)), (fun real (fun (fun int real) (fun int bool))), (combb (fun real bool) (fun (fun int real) (fun int bool)) real), (combb real bool int), (fequal real) ) 15.39/15.57 ( (let ((_let_0 (fun int real))) (fun int (fun _let_0 _let_0))), (fun int real), (fun int (fun int real)), (let ((_let_0 (fun int real))) (combc int _let_0 _let_0)), (let ((_let_0 (fun real real))) (let ((_let_1 (fun int real))) (let ((_let_2 (fun _let_1 _let_1))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int _let_0))) (hAPP _let_4 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_4 _let_3) (combb _let_0 _let_2 int) (combb real real int)) (hAPP _let_1 _let_4 (hAPP (fun real _let_0) (fun _let_1 _let_4) (combb real _let_0 int) (inverse_divide real)) (real_1 int)))))))), (real_1 int) ) 15.39/15.57 ( (let ((_let_0 (fun int real))) (fun (fun real real) (fun _let_0 _let_0))), (fun int (fun real real)), (let ((_let_0 (fun int real))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun int real))) (combb (fun real real) (fun _let_0 _let_0) int)), (combb real real int), (let ((_let_0 (fun real real))) (let ((_let_1 (fun int real))) (let ((_let_2 (fun int _let_0))) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 int) (inverse_divide real)) (real_1 int))))) ) 15.39/15.57 ( (let ((_let_0 (fun int (fun int bool)))) (fun _let_0 _let_0)), (fun int (fun int (fun int bool))), (fun int (fun int (fun int bool))), (let ((_let_0 (fun int (fun int bool)))) (combb _let_0 _let_0 int)), (combc int int bool), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int _let_1))) (let ((_let_5 (fun _let_2 _let_1))) (hAPP _let_3 _let_4 (hAPP _let_5 (fun _let_3 _let_4) (combb _let_2 _let_1 int) (hAPP _let_1 _let_5 (combb int _let_0 int) (fequal int))) int_gcd))))))) ) 15.39/15.57 ( (fun (fun int (fun nat bool)) (fun int bool)), (fun real (fun int (fun nat bool))), (fun real (fun int bool)), (combb (fun int (fun nat bool)) (fun int bool) real), (let ((_let_0 (fun nat bool))) (hAPP (fun _let_0 bool) (fun (fun int _let_0) (fun int bool)) (combb _let_0 bool int) (fEx nat))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat (fun nat bool)))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun (fun nat real) (fun nat real)))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun (fun nat bool) (fun nat bool)))) (let ((_let_7 (fun int real))) (let ((_let_8 (fun nat _let_3))) (let ((_let_9 (fun (fun nat bool) _let_8))) (let ((_let_10 (fun int _let_1))) (let ((_let_11 (fun real (fun int (fun nat bool))))) (let ((_let_12 (fun (fun nat bool) (fun int (fun nat bool))))) (let ((_let_13 (fun real _let_12))) (let ((_let_14 (fun int _let_6))) (let ((_let_15 (fun real _let_14))) (let ((_let_16 (fun int _let_8))) (let ((_let_17 (fun real _let_16))) (let ((_let_18 (fun _let_16 _let_14))) (let ((_let_19 (fun (fun int (fun nat bool)) _let_16))) (let ((_let_20 (fun int (fun nat real)))) (let ((_let_21 (fun _let_20 (fun int (fun nat bool))))) (let ((_let_22 (fun real _let_21))) (let ((_let_23 (fun (fun nat real) (fun nat bool)))) (let ((_let_24 (fun real _let_23))) (let ((_let_25 (fun int _let_4))) (hAPP (fun nat bool) _let_11 (hAPP _let_13 (fun (fun nat bool) _let_11) (combc real (fun nat bool) (fun int (fun nat bool))) (hAPP _let_15 _let_13 (hAPP (fun _let_14 _let_12) (fun _let_15 _let_13) (combb _let_14 _let_12 real) (combc int (fun nat bool) (fun nat bool))) (hAPP _let_17 _let_15 (hAPP _let_18 (fun _let_17 _let_15) (combb _let_16 _let_14 real) (hAPP (fun _let_8 _let_6) _let_18 (combb _let_8 _let_6 int) (combs nat bool bool))) (hAPP _let_11 _let_17 (hAPP _let_19 (fun _let_11 _let_17) (combb (fun int (fun nat bool)) _let_16 real) (hAPP _let_9 _let_19 (combb (fun nat bool) _let_8 int) (hAPP (fun bool _let_3) _let_9 (combb bool _let_3 nat) fconj))) (hAPP _let_20 _let_11 (hAPP _let_22 (fun _let_20 _let_11) (combc real _let_20 (fun int (fun nat bool))) (hAPP _let_24 _let_22 (hAPP (fun _let_23 _let_21) (fun _let_24 _let_22) (combb _let_23 _let_21 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_5 _let_24 (hAPP (fun _let_0 _let_23) (fun _let_5 _let_24) (combb _let_0 _let_23 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_20 (hAPP _let_25 (fun (fun nat real) _let_20) (combc int (fun nat real) (fun nat real)) (hAPP _let_10 _let_25 (hAPP (fun _let_1 _let_4) (fun _let_10 _let_25) (combb _let_1 _let_4 int) (combb real real nat)) (hAPP _let_7 _let_10 (hAPP (fun real _let_1) (fun _let_7 _let_10) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat))))))) (hAPP (fun nat bool) (fun nat bool) (hAPP _let_3 _let_6 (combb bool bool nat) fNot) (hAPP nat (fun nat bool) (hAPP _let_2 _let_2 (combc nat nat bool) (fequal nat)) (zero_zero nat)))))))))))))))))))))))))))))) ) 15.39/15.57 ( (let ((_let_0 (fun nat bool))) (fun real (fun _let_0 (fun int _let_0)))), (fun nat bool), (fun real (fun int (fun nat bool))), (let ((_let_0 (fun nat bool))) (combc real _let_0 (fun int _let_0))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun (fun nat real) (fun nat real)))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun (fun nat bool) (fun nat bool)))) (let ((_let_6 (fun int real))) (let ((_let_7 (fun nat _let_2))) (let ((_let_8 (fun (fun nat bool) _let_7))) (let ((_let_9 (fun int _let_1))) (let ((_let_10 (fun real (fun int (fun nat bool))))) (let ((_let_11 (fun (fun nat bool) (fun int (fun nat bool))))) (let ((_let_12 (fun real _let_11))) (let ((_let_13 (fun int _let_5))) (let ((_let_14 (fun real _let_13))) (let ((_let_15 (fun int _let_7))) (let ((_let_16 (fun real _let_15))) (let ((_let_17 (fun _let_15 _let_13))) (let ((_let_18 (fun (fun int (fun nat bool)) _let_15))) (let ((_let_19 (fun int (fun nat real)))) (let ((_let_20 (fun _let_19 (fun int (fun nat bool))))) (let ((_let_21 (fun real _let_20))) (let ((_let_22 (fun (fun nat real) (fun nat bool)))) (let ((_let_23 (fun real _let_22))) (let ((_let_24 (fun int _let_3))) (hAPP _let_14 _let_12 (hAPP (fun _let_13 _let_11) (fun _let_14 _let_12) (combb _let_13 _let_11 real) (combc int (fun nat bool) (fun nat bool))) (hAPP _let_16 _let_14 (hAPP _let_17 (fun _let_16 _let_14) (combb _let_15 _let_13 real) (hAPP (fun _let_7 _let_5) _let_17 (combb _let_7 _let_5 int) (combs nat bool bool))) (hAPP _let_10 _let_16 (hAPP _let_18 (fun _let_10 _let_16) (combb (fun int (fun nat bool)) _let_15 real) (hAPP _let_8 _let_18 (combb (fun nat bool) _let_7 int) (hAPP (fun bool _let_2) _let_8 (combb bool _let_2 nat) fconj))) (hAPP _let_19 _let_10 (hAPP _let_21 (fun _let_19 _let_10) (combc real _let_19 (fun int (fun nat bool))) (hAPP _let_23 _let_21 (hAPP (fun _let_22 _let_20) (fun _let_23 _let_21) (combb _let_22 _let_20 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_4 _let_23 (hAPP (fun _let_0 _let_22) (fun _let_4 _let_23) (combb _let_0 _let_22 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_19 (hAPP _let_24 (fun (fun nat real) _let_19) (combc int (fun nat real) (fun nat real)) (hAPP _let_9 _let_24 (hAPP (fun _let_1 _let_3) (fun _let_9 _let_24) (combb _let_1 _let_3 int) (combb real real nat)) (hAPP _let_6 _let_9 (hAPP (fun real _let_1) (fun _let_6 _let_9) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat))))))))))))))))))))))))))))))), (let ((_let_0 (fun nat (fun nat bool)))) (hAPP (fun nat bool) (fun nat bool) (hAPP (fun bool bool) (fun (fun nat bool) (fun nat bool)) (combb bool bool nat) fNot) (hAPP nat (fun nat bool) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat)) (zero_zero nat)))) ) 15.39/15.57 ( (let ((_let_0 (fun nat bool))) (fun (fun int (fun _let_0 _let_0)) (fun _let_0 (fun int _let_0)))), (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun nat bool))) (fun real (fun _let_0 (fun int _let_0)))), (let ((_let_0 (fun nat bool))) (combb (fun int (fun _let_0 _let_0)) (fun _let_0 (fun int _let_0)) real)), (let ((_let_0 (fun nat bool))) (combc int _let_0 _let_0)), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun (fun nat real) (fun nat real)))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun (fun nat bool) (fun nat bool)))) (let ((_let_6 (fun int real))) (let ((_let_7 (fun nat _let_2))) (let ((_let_8 (fun (fun nat bool) _let_7))) (let ((_let_9 (fun int _let_1))) (let ((_let_10 (fun real (fun int (fun nat bool))))) (let ((_let_11 (fun int _let_5))) (let ((_let_12 (fun real _let_11))) (let ((_let_13 (fun int _let_7))) (let ((_let_14 (fun real _let_13))) (let ((_let_15 (fun _let_13 _let_11))) (let ((_let_16 (fun (fun int (fun nat bool)) _let_13))) (let ((_let_17 (fun int (fun nat real)))) (let ((_let_18 (fun _let_17 (fun int (fun nat bool))))) (let ((_let_19 (fun real _let_18))) (let ((_let_20 (fun (fun nat real) (fun nat bool)))) (let ((_let_21 (fun real _let_20))) (let ((_let_22 (fun int _let_3))) (hAPP _let_14 _let_12 (hAPP _let_15 (fun _let_14 _let_12) (combb _let_13 _let_11 real) (hAPP (fun _let_7 _let_5) _let_15 (combb _let_7 _let_5 int) (combs nat bool bool))) (hAPP _let_10 _let_14 (hAPP _let_16 (fun _let_10 _let_14) (combb (fun int (fun nat bool)) _let_13 real) (hAPP _let_8 _let_16 (combb (fun nat bool) _let_7 int) (hAPP (fun bool _let_2) _let_8 (combb bool _let_2 nat) fconj))) (hAPP _let_17 _let_10 (hAPP _let_19 (fun _let_17 _let_10) (combc real _let_17 (fun int (fun nat bool))) (hAPP _let_21 _let_19 (hAPP (fun _let_20 _let_18) (fun _let_21 _let_19) (combb _let_20 _let_18 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_4 _let_21 (hAPP (fun _let_0 _let_20) (fun _let_4 _let_21) (combb _let_0 _let_20 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_17 (hAPP _let_22 (fun (fun nat real) _let_17) (combc int (fun nat real) (fun nat real)) (hAPP _let_9 _let_22 (hAPP (fun _let_1 _let_3) (fun _let_9 _let_22) (combb _let_1 _let_3 int) (combb real real nat)) (hAPP _let_6 _let_9 (hAPP (fun real _let_1) (fun _let_6 _let_9) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat)))))))))))))))))))))))))))) ) 15.39/15.57 ( (let ((_let_0 (fun nat bool))) (fun (fun int (fun nat (fun bool bool))) (fun int (fun _let_0 _let_0)))), (fun real (fun int (fun nat (fun bool bool)))), (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun nat bool))) (combb (fun int (fun nat (fun bool bool))) (fun int (fun _let_0 _let_0)) real)), (let ((_let_0 (fun (fun nat bool) (fun nat bool)))) (let ((_let_1 (fun nat (fun bool bool)))) (hAPP (fun _let_1 _let_0) (fun (fun int _let_1) (fun int _let_0)) (combb _let_1 _let_0 int) (combs nat bool bool)))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun (fun nat real) (fun nat real)))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun int real))) (let ((_let_6 (fun nat _let_2))) (let ((_let_7 (fun (fun nat bool) _let_6))) (let ((_let_8 (fun int _let_1))) (let ((_let_9 (fun real (fun int (fun nat bool))))) (let ((_let_10 (fun int _let_6))) (let ((_let_11 (fun real _let_10))) (let ((_let_12 (fun (fun int (fun nat bool)) _let_10))) (let ((_let_13 (fun int (fun nat real)))) (let ((_let_14 (fun _let_13 (fun int (fun nat bool))))) (let ((_let_15 (fun real _let_14))) (let ((_let_16 (fun (fun nat real) (fun nat bool)))) (let ((_let_17 (fun real _let_16))) (let ((_let_18 (fun int _let_3))) (hAPP _let_9 _let_11 (hAPP _let_12 (fun _let_9 _let_11) (combb (fun int (fun nat bool)) _let_10 real) (hAPP _let_7 _let_12 (combb (fun nat bool) _let_6 int) (hAPP (fun bool _let_2) _let_7 (combb bool _let_2 nat) fconj))) (hAPP _let_13 _let_9 (hAPP _let_15 (fun _let_13 _let_9) (combc real _let_13 (fun int (fun nat bool))) (hAPP _let_17 _let_15 (hAPP (fun _let_16 _let_14) (fun _let_17 _let_15) (combb _let_16 _let_14 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_4 _let_17 (hAPP (fun _let_0 _let_16) (fun _let_4 _let_17) (combb _let_0 _let_16 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_13 (hAPP _let_18 (fun (fun nat real) _let_13) (combc int (fun nat real) (fun nat real)) (hAPP _let_8 _let_18 (hAPP (fun _let_1 _let_3) (fun _let_8 _let_18) (combb _let_1 _let_3 int) (combb real real nat)) (hAPP _let_5 _let_8 (hAPP (fun real _let_1) (fun _let_5 _let_8) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat))))))))))))))))))))))) ) 15.39/15.57 ( (fun (fun int (fun nat bool)) (fun int (fun nat (fun bool bool)))), (fun real (fun int (fun nat bool))), (fun real (fun int (fun nat (fun bool bool)))), (combb (fun int (fun nat bool)) (fun int (fun nat (fun bool bool))) real), (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun nat _let_1))) (let ((_let_3 (fun _let_0 _let_2))) (hAPP _let_3 (fun (fun int _let_0) (fun int _let_2)) (combb _let_0 _let_2 int) (hAPP (fun bool _let_1) _let_3 (combb bool _let_1 nat) fconj)))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun (fun nat real) (fun nat real)))) (let ((_let_3 (fun real _let_0))) (let ((_let_4 (fun int real))) (let ((_let_5 (fun int _let_1))) (let ((_let_6 (fun real (fun int (fun nat bool))))) (let ((_let_7 (fun int (fun nat real)))) (let ((_let_8 (fun _let_7 (fun int (fun nat bool))))) (let ((_let_9 (fun real _let_8))) (let ((_let_10 (fun (fun nat real) (fun nat bool)))) (let ((_let_11 (fun real _let_10))) (let ((_let_12 (fun int _let_2))) (hAPP _let_7 _let_6 (hAPP _let_9 (fun _let_7 _let_6) (combc real _let_7 (fun int (fun nat bool))) (hAPP _let_11 _let_9 (hAPP (fun _let_10 _let_8) (fun _let_11 _let_9) (combb _let_10 _let_8 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_3 _let_11 (hAPP (fun _let_0 _let_10) (fun _let_3 _let_11) (combb _let_0 _let_10 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_7 (hAPP _let_12 (fun (fun nat real) _let_7) (combc int (fun nat real) (fun nat real)) (hAPP _let_5 _let_12 (hAPP (fun _let_1 _let_2) (fun _let_5 _let_12) (combb _let_1 _let_2 int) (combb real real nat)) (hAPP _let_4 _let_5 (hAPP (fun real _let_1) (fun _let_4 _let_5) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat)))))))))))))))) ) 15.39/15.57 ( (fun real (fun (fun int (fun nat real)) (fun int (fun nat bool)))), (fun int (fun nat real)), (fun real (fun int (fun nat bool))), (combc real (fun int (fun nat real)) (fun int (fun nat bool))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun int (fun nat real)) (fun int (fun nat bool))))) (let ((_let_3 (fun real _let_2))) (let ((_let_4 (fun (fun nat real) (fun nat bool)))) (let ((_let_5 (fun real _let_4))) (hAPP _let_5 _let_3 (hAPP (fun _let_4 _let_2) (fun _let_5 _let_3) (combb _let_4 _let_2 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_1 _let_5) (combb _let_0 _let_4 real) (combb real bool nat)) (fequal real))))))))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun (fun nat real) (fun nat real)))) (let ((_let_2 (fun int real))) (let ((_let_3 (fun int _let_0))) (let ((_let_4 (fun int (fun nat real)))) (let ((_let_5 (fun int _let_1))) (hAPP (fun nat real) _let_4 (hAPP _let_5 (fun (fun nat real) _let_4) (combc int (fun nat real) (fun nat real)) (hAPP _let_3 _let_5 (hAPP (fun _let_0 _let_1) (fun _let_3 _let_5) (combb _let_0 _let_1 int) (combb real real nat)) (hAPP _let_2 _let_3 (hAPP (fun real _let_0) (fun _let_2 _let_3) (combb real _let_0 int) (inverse_divide real)) (real_1 int)))) (real_1 nat)))))))) ) 15.39/15.57 ( (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat real))) (fun (fun _let_1 _let_0) (fun (fun int _let_1) (fun int _let_0))))), (fun real (fun (fun nat real) (fun nat bool))), (fun real (fun (fun int (fun nat real)) (fun int (fun nat bool)))), (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat real))) (combb (fun _let_1 _let_0) (fun (fun int _let_1) (fun int _let_0)) real))), (combb (fun nat real) (fun nat bool) int), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun nat real) (fun nat bool)))) (let ((_let_3 (fun real _let_2))) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 real) (combb real bool nat)) (fequal real)))))) ) 15.39/15.57 ( (fun (fun real bool) (fun (fun nat real) (fun nat bool))), (fun real (fun real bool)), (fun real (fun (fun nat real) (fun nat bool))), (combb (fun real bool) (fun (fun nat real) (fun nat bool)) real), (combb real bool nat), (fequal real) ) 15.39/15.57 ( (let ((_let_0 (fun nat real))) (fun int (fun _let_0 _let_0))), (fun nat real), (fun int (fun nat real)), (let ((_let_0 (fun nat real))) (combc int _let_0 _let_0)), (let ((_let_0 (fun real real))) (let ((_let_1 (fun (fun nat real) (fun nat real)))) (let ((_let_2 (fun int real))) (let ((_let_3 (fun int _let_0))) (let ((_let_4 (fun int _let_1))) (hAPP _let_3 _let_4 (hAPP (fun _let_0 _let_1) (fun _let_3 _let_4) (combb _let_0 _let_1 int) (combb real real nat)) (hAPP _let_2 _let_3 (hAPP (fun real _let_0) (fun _let_2 _let_3) (combb real _let_0 int) (inverse_divide real)) (real_1 int)))))))), (real_1 nat) ) 15.39/15.57 ( (let ((_let_0 (fun nat real))) (fun (fun real real) (fun _let_0 _let_0))), (fun int (fun real real)), (let ((_let_0 (fun nat real))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun nat real))) (combb (fun real real) (fun _let_0 _let_0) int)), (combb real real nat), (let ((_let_0 (fun real real))) (let ((_let_1 (fun int real))) (let ((_let_2 (fun int _let_0))) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 int) (inverse_divide real)) (real_1 int))))) ) 15.39/15.57 ( (let ((_let_0 (fun int int))) (fun int (fun _let_0 _let_0))), (fun int int), (fun int (fun int int)), (let ((_let_0 (fun int int))) (combc int _let_0 _let_0)), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun _let_0 _let_0))) (let ((_let_3 (fun int _let_2))) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 int) (combb int int int)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)) (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))))), (let ((_let_0 (fun int int))) (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.39/15.57 ( (let ((_let_0 (fun int int))) (fun _let_0 (fun _let_0 _let_0))), (fun int (fun int int)), (let ((_let_0 (fun int int))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun int int))) (combb _let_0 (fun _let_0 _let_0) int)), (combb int int int), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)) (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 15.39/15.57 ) 15.39/15.57 (instantiation (forall ((A_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (one_one int)) A_1))) (not (forall ((P_6 $$unsorted)) (or (not (hBOOL (hAPP int bool zprime P_6))) (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (dvd_dvd int) P_6) A_1)))) ))) ) 15.39/15.57 ( t ) 15.39/15.57 ) 15.39/15.57 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_106732 $$unsorted)) (let ((_let_0 (archim2085082626_floor X_a))) (or (not (archim1727834104eiling X_a)) (= (hAPP X_a int _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) BOUND_VARIABLE_106732) (one_one X_a))) (hAPP int int (hAPP int (fun int int) (minus_minus int) (hAPP X_a int _let_0 BOUND_VARIABLE_106732)) (one_one int))))) ) 15.39/15.57 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.57 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))) ) 15.39/15.57 ( code_code_numeral, (zero_zero code_code_numeral) ) 15.39/15.57 ) 15.39/15.57 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_0 (real_1 nat))) (= (hAPP nat real _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) M) N_1)) (hAPP real real (hAPP real (fun real real) (plus_plus real) (hAPP nat real _let_0 M)) (hAPP nat real _let_0 N_1)))) ) 15.39/15.57 ( (one_one nat), (one_one nat) ) 15.39/15.57 ) 15.39/15.57 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (semiri532925092at_aux X_a))) (or (not (semiring_1 X_a)) (= _let_1 (ti (fun _let_0 (fun nat _let_0)) _let_1))))) ) 15.39/15.57 ( bool ) 15.39/15.57 ( nat ) 15.39/15.57 ( int ) 15.39/15.57 ( (fun int bool) ) 15.39/15.57 ( (fun int (fun int bool)) ) 15.39/15.57 ( (fun int int) ) 15.39/15.57 ( (fun nat bool) ) 15.39/15.57 ( real ) 15.39/15.57 ( (fun real bool) ) 15.39/15.57 ( (fun real real) ) 15.39/15.57 ( rat ) 15.39/15.57 ( complex ) 15.39/15.57 ( (fun nat real) ) 15.39/15.57 ( (product_prod int int) ) 15.39/15.57 ( quickcheck_code_int ) 15.39/15.57 ( code_code_numeral ) 15.39/15.57 ( (fun int (fun int (fun int bool))) ) 15.39/15.57 ( (fun (product_prod int int) bool) ) 15.39/15.57 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 15.39/15.57 ( (fun (product_prod int int) int) ) 15.39/15.57 ( (fun int real) ) 15.39/15.57 ) 15.39/15.57 (instantiation (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (one_one int)) B_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) B_1) A_2))) (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) B_1) (hAPP int _let_0 d22set A_2))))) ) 15.39/15.57 ( (one_one int), (zero_zero int) ) 15.39/15.57 ( pls, min_1 ) 15.39/15.57 ( min_1, (zero_zero int) ) 15.39/15.57 ( min_1, min_1 ) 15.39/15.57 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 15.39/15.57 ( s, (zero_zero int) ) 15.39/15.57 ( t, (one_one int) ) 15.39/15.57 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 15.39/15.57 ( (hAPP int int (number_number_of int) pls), (zero_zero int) ) 15.39/15.57 ( skv_4, (zero_zero int) ) 15.39/15.57 ( skv_10, (zero_zero int) ) 15.39/15.57 ) 15.39/15.57 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_106900 $$unsorted)) (let ((_let_0 (hAPP int X_b (number_number_of X_b) BOUND_VARIABLE_106900))) (or (not (division_ring X_b)) (not (number X_b)) (= (hAPP X_b X_b (hAPP X_b (fun X_b X_b) (inverse_divide X_b) (one_one X_b)) _let_0) (hAPP X_b X_b (inverse_inverse X_b) _let_0)))) ) 15.39/15.57 ( nat, pls ) 15.39/15.57 ( nat, (hAPP int int bit1 pls) ) 15.39/15.57 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.39/15.57 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.39/15.57 ( int, pls ) 15.39/15.57 ( int, (hAPP int int bit1 pls) ) 15.39/15.57 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.39/15.57 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.39/15.57 ( int, min_1 ) 15.39/15.57 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.57 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.39/15.57 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.39/15.57 ( real, min_1 ) 15.39/15.57 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.57 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.39/15.57 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.57 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 15.39/15.57 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.39/15.57 ( complex, min_1 ) 15.39/15.57 ( quickcheck_code_int, (one_one int) ) 15.39/15.57 ( quickcheck_code_int, (zero_zero int) ) 15.39/15.57 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 15.39/15.57 ( code_code_numeral, pls ) 15.39/15.57 ( code_code_numeral, (hAPP int int bit1 pls) ) 15.39/15.57 ) 15.39/15.57 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (hAPP int (fun int _let_1) posDivAlg A_1))) (or (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) B) (zero_zero int))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) A_1) B)) (= (hAPP _let_1 _let_1 (hAPP int (fun _let_1 _let_1) adjust B) (hAPP int _let_1 _let_2 (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) B))) (hAPP int _let_1 _let_2 B)))))) ) 15.39/15.57 ( (one_one int), t ) 15.39/15.57 ( pls, (one_one int) ) 15.39/15.57 ( pls, pls ) 15.39/15.57 ( pls, min_1 ) 15.39/15.57 ( pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.39/15.57 ( min_1, pls ) 15.39/15.57 ( min_1, min_1 ) 15.39/15.57 ( s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.39/15.57 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.39/15.57 ( skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.39/15.57 ( skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.39/15.57 ) 15.39/15.57 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun int _let_2))) (or (and (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) A_1) B))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) B) _let_1)))) (= (hAPP int _let_2 (hAPP int _let_3 posDivAlg A_1) B) (hAPP int _let_2 (hAPP int _let_3 (product_Pair int int) _let_1) A_1))))))) ) 15.39/15.57 ( (one_one int), t ) 15.39/15.57 ( pls, (one_one int) ) 15.39/15.57 ( pls, pls ) 15.39/15.57 ( pls, min_1 ) 15.39/15.57 ( pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.39/15.57 ( min_1, pls ) 15.39/15.57 ( min_1, min_1 ) 15.39/15.57 ( s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.39/15.57 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.39/15.57 ( skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.39/15.57 ( skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.39/15.57 ) 15.39/15.57 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_106928 $$unsorted) (BOUND_VARIABLE_106929 $$unsorted)) (let ((_let_0 (norm_norm X_a))) (or (not (real_n2089651433ebra_1 X_a)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP X_a real _let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_106928) BOUND_VARIABLE_106929))) (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP X_a real _let_0 BOUND_VARIABLE_106928)) BOUND_VARIABLE_106929))))) ) 15.39/15.57 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.57 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.57 ( int, skv_14, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.57 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.57 ) 15.39/15.57 (instantiation (forall ((V_1 $$unsorted)) (let ((_let_0 (one_one nat))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) V_1) pls))) (= _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) _let_0) (hAPP int nat (number_number_of nat) V_1))))) ) 15.39/15.57 ( (one_one int) ) 15.39/15.57 ( pls ) 15.39/15.57 ( (hAPP int int bit1 pls) ) 15.39/15.57 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.39/15.57 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.39/15.57 ( min_1 ) 15.39/15.57 ( s ) 15.39/15.57 ( t ) 15.39/15.57 ( skv_4 ) 15.39/15.57 ( skv_10 ) 15.39/15.57 ) 15.39/15.57 (instantiation (forall ((V_1 $$unsorted)) (let ((_let_0 (number_number_of nat))) (or (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) V_1) pls)) (= (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (one_one nat)) (hAPP int nat _let_0 V_1)) (hAPP int nat _let_0 (hAPP int int succ V_1))))) ) 15.39/15.57 ( (one_one int) ) 15.39/15.57 ( pls ) 15.39/15.57 ( (hAPP int int bit1 pls) ) 15.39/15.57 ( min_1 ) 15.39/15.57 ( s ) 15.39/15.57 ( t ) 15.39/15.57 ( skv_4 ) 15.39/15.57 ( skv_10 ) 15.39/15.57 ) 15.39/15.57 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_107093 $$unsorted)) (or (not (division_ring X_a)) (= (ti X_a BOUND_VARIABLE_107093) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_107093) (one_one X_a)))) ) 15.39/15.57 ( bool, fFalse ) 15.39/15.57 ( bool, fTrue ) 15.39/15.57 ( int, pls ) 15.39/15.57 ( int, min_1 ) 15.39/15.57 ( int, s ) 15.39/15.57 ( int, m ) 15.39/15.57 ( int, s1 ) 15.39/15.57 ( int, t ) 15.39/15.57 ( (fun int bool), nat_neg ) 15.39/15.57 ( (fun int bool), zprime ) 15.39/15.57 ( (fun int bool), zEven ) 15.39/15.57 ( (fun int bool), zOdd ) 15.39/15.57 ( (fun int bool), (even_odd_even int) ) 15.39/15.57 ( (fun int bool), twoSqu1091635170sum2sq ) 15.39/15.57 ( (fun int bool), nat_is_nat ) 15.39/15.57 ( (fun int (fun int bool)), norRRset ) 15.39/15.57 ( (fun int (fun int bool)), quadRes ) 15.39/15.57 ( (fun int (fun int bool)), sRStar ) 15.39/15.57 ( (fun int (fun int bool)), d22set ) 15.39/15.57 ( (fun int (fun int bool)), sr ) 15.39/15.57 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 15.39/15.57 ( (fun int int), zfact ) 15.39/15.57 ( (fun int int), bit0 ) 15.39/15.57 ( (fun int int), bit1 ) 15.39/15.57 ( (fun int int), (fact_fact int) ) 15.39/15.57 ( (fun int int), pred ) 15.39/15.57 ( (fun int int), succ ) 15.39/15.57 ( (fun nat bool), (even_odd_even nat) ) 15.39/15.57 ( (fun nat bool), prime ) 15.39/15.57 ( (fun nat nat), suc ) 15.39/15.57 ( (fun nat nat), (fact_fact nat) ) 15.39/15.57 ( (fun nat nat), fact ) 15.39/15.57 ( (fun nat nat), nat_size ) 15.39/15.57 ( (fun nat nat), (size_size nat) ) 15.39/15.57 ( (fun (product_prod nat nat) bool), pred_nat ) 15.39/15.57 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 15.39/15.57 ( real, (one_one real) ) 15.39/15.57 ( real, pi ) 15.39/15.57 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.39/15.57 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.39/15.57 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.57 ( (fun real real), ln ) 15.39/15.57 ( (fun real real), cos ) 15.39/15.57 ( (fun real real), sqrt ) 15.39/15.57 ( (fun real real), sin ) 15.39/15.57 ( (fun real real), arccos ) 15.39/15.57 ( (fun real real), arcsin ) 15.39/15.57 ( (fun real real), tan ) 15.39/15.57 ( (fun real real), arctan ) 15.39/15.57 ( (fun nat (fun nat bool)), coprime ) 15.39/15.57 ( complex, ii ) 15.39/15.57 ( (fun nat real), (real_1 nat) ) 15.39/15.57 ( (fun nat real), sin_coeff ) 15.39/15.57 ( (fun nat real), cos_coeff ) 15.39/15.57 ( (filter nat), sequentially ) 15.39/15.57 ( (fun int (fun int int)), (gcd_gcd int) ) 15.39/15.57 ( (fun int (fun int int)), legendre ) 15.39/15.57 ( (fun int (fun int int)), legacy_zgcd ) 15.39/15.57 ( (fun int (fun int int)), standardRes ) 15.39/15.57 ( (fun int (fun int int)), nat_tsub ) 15.39/15.57 ( (fun int (fun int int)), multInv ) 15.39/15.57 ( (fun int (fun int int)), z3mod ) 15.39/15.57 ( (fun int (fun int int)), z3div ) 15.39/15.57 ( (fun int (fun int int)), int_gcd ) 15.39/15.57 ( (fun int (fun int int)), int_lcm ) 15.39/15.57 ( (fun int (fun int int)), inv ) 15.39/15.57 ( (fun complex complex), expi ) 15.39/15.57 ( (fun complex complex), cnj ) 15.39/15.57 ( (fun real complex), cis ) 15.39/15.57 ( (fun int nat), nat_1 ) 15.39/15.57 ( (fun int nat), phi ) 15.39/15.57 ( (fun (fun int bool) bool), nat_nat_set ) 15.39/15.57 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 15.39/15.57 ( (fun nat (fun nat nat)), nat_gcd ) 15.39/15.57 ( (fun nat (fun nat nat)), nat_lcm ) 15.39/15.57 ( (fun (fun int bool) int), (the int) ) 15.39/15.57 ( (fun complex real), re ) 15.39/15.57 ( (fun complex real), im ) 15.39/15.57 ( (fun complex real), arg ) 15.39/15.57 ( (fun bool bool), fNot ) 15.39/15.57 ( (fun nat (fun real real)), root ) 15.39/15.57 ( (fun real (fun real real)), log ) 15.39/15.57 ( (fun real (fun real real)), powr ) 15.39/15.57 ( (fun bool (fun bool bool)), fimplies ) 15.39/15.57 ( (fun bool (fun bool bool)), fconj ) 15.39/15.57 ( (fun bool (fun bool bool)), fdisj ) 15.39/15.57 ( (fun int (fun int (product_prod int int))), negDivAlg ) 15.39/15.57 ( (fun int (fun int (product_prod int int))), posDivAlg ) 15.39/15.57 ( (fun int (fun int (product_prod int int))), divmod_int ) 15.39/15.57 ( (fun int (fun int (product_prod int int))), pdivmod ) 15.39/15.57 ( (fun int (fun int (product_prod int int))), norm_frac ) 15.39/15.57 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 15.39/15.57 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 15.39/15.57 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 15.39/15.57 ( (fun int (fun int (fun int bool))), zcong ) 15.39/15.57 ( (fun int (fun int (fun int bool))), zcongm ) 15.39/15.57 ( (fun int (fun int (fun int bool))), noXRRset ) 15.39/15.57 ( (fun int (fun int (fun int bool))), bnorRset ) 15.39/15.57 ( (fun int (fun int (fun int bool))), wset ) 15.39/15.57 ( (fun (product_prod int int) bool), frac_1 ) 15.39/15.57 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 15.39/15.57 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 15.39/15.57 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 15.39/15.57 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 15.39/15.57 ( (fun (fun nat rat) bool), vanishes ) 15.39/15.57 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 15.39/15.57 ( (fun code_code_numeral nat), code_c271388182l_size ) 15.39/15.57 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 15.39/15.57 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 15.39/15.57 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 15.39/15.57 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 15.39/15.57 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 15.39/15.57 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 15.39/15.57 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 15.39/15.57 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 15.39/15.57 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 15.39/15.57 ( (fun complex nat), complex_size ) 15.39/15.57 ( (fun complex nat), (size_size complex) ) 15.39/15.57 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 15.39/15.57 ( (fun nat (fun nat (product_prod int int))), bezw ) 15.39/15.57 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 15.39/15.57 ( (fun int (fun nat nat)), nat_aux ) 15.39/15.57 ( (fun int (fun (fun int bool) bool)), rsetR ) 15.39/15.57 ( (fun int (fun (fun int bool) bool)), resSet ) 15.39/15.57 ( (fun int (list int)), quickc666637781d_zero ) 15.39/15.57 ( (fun (product_prod int int) rat), frct ) 15.39/15.57 ( (fun int (fun int rat)), fract ) 15.39/15.57 ( (fun real (fun real complex)), complex_1 ) 15.39/15.57 ( (fun real (fun real complex)), rcis ) 15.39/15.57 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 15.39/15.57 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 15.39/15.57 ( (fun int real), (real_1 int) ) 15.39/15.57 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 15.39/15.57 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 15.39/15.57 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 15.39/15.57 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 15.39/15.57 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 15.39/15.57 ( (fun real nat), natfloor ) 15.39/15.57 ( (fun real nat), natceiling ) 15.39/15.57 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 15.39/15.57 ( (fun quickcheck_code_int int), quickcheck_int_of ) 15.39/15.57 ( (fun rat (product_prod int int)), quotient_of ) 15.39/15.57 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 15.39/15.57 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 15.39/15.57 ( (fun rat real), ratreal ) 15.39/15.57 ( (fun code_code_numeral int), code_int_of ) 15.39/15.57 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 15.39/15.57 ( (fun int quickcheck_code_int), quickcheck_of_int ) 15.39/15.57 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 15.39/15.57 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 15.39/15.57 ) 15.39/15.57 (instantiation (forall ((Y_2 $$unsorted) (X_2 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (hAPP int _let_0 (ord_less_eq int) (zero_zero int)))) (or (not (hBOOL (hAPP int bool _let_1 X_2))) (not (hBOOL (hAPP int bool _let_1 Y_2))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) X_2) Y_2)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (hAPP int nat nat_1 X_2)) (hAPP int nat nat_1 Y_2))))))) ) 15.39/15.57 ( (one_one int), pls ) 15.39/15.57 ( pls, pls ) 15.39/15.57 ( pls, min_1 ) 15.39/15.57 ( min_1, pls ) 15.39/15.57 ( min_1, min_1 ) 15.39/15.58 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 15.39/15.58 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), pls ) 15.39/15.58 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s ) 15.39/15.58 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.39/15.58 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_4 ) 15.39/15.58 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_10 ) 15.39/15.58 ( t, (one_one int) ) 15.39/15.58 ) 15.39/15.58 (instantiation (forall ((X_a $$unsorted)) (or (not (semiring_1 X_a)) (hBOOL (hAPP X_a bool (iszero X_a) (zero_zero X_a)))) ) 15.39/15.58 ( nat ) 15.39/15.58 ( int ) 15.39/15.58 ( real ) 15.39/15.58 ( rat ) 15.39/15.58 ( complex ) 15.39/15.58 ( quickcheck_code_int ) 15.39/15.58 ( code_code_numeral ) 15.39/15.58 ) 15.39/15.58 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_107204 $$unsorted) (BOUND_VARIABLE_107205 $$unsorted) (BOUND_VARIABLE_107206 $$unsorted) (BOUND_VARIABLE_107207 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (minus_minus X_a))) (or (not (ab_group_add X_a)) (not (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_107204) BOUND_VARIABLE_107205) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_107206) BOUND_VARIABLE_107207))) (= (= (ti X_a BOUND_VARIABLE_107207) (ti X_a BOUND_VARIABLE_107206)) (= (ti X_a BOUND_VARIABLE_107204) (ti X_a BOUND_VARIABLE_107205)))))) ) 15.39/15.58 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.39/15.58 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))), (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 15.39/15.58 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral), (zero_zero code_code_numeral), (one_one code_code_numeral) ) 15.39/15.58 ) 15.39/15.58 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_107236 $$unsorted) (BOUND_VARIABLE_107237 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)))) (or (not (linordered_idom X_a)) (= (hBOOL (hAPP X_a bool _let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_107236) BOUND_VARIABLE_107237))) (or (hBOOL (hAPP nat bool (even_odd_even nat) BOUND_VARIABLE_107237)) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_107236)))))) ) 15.39/15.58 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.58 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.58 ( int, skv_14, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.58 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.58 ) 15.39/15.58 (instantiation (forall ((N_1 $$unsorted)) (not (= N_1 (hAPP nat nat suc N_1))) ) 15.39/15.58 ( (zero_zero nat) ) 15.39/15.58 ( (hAPP nat nat suc (zero_zero nat)) ) 15.39/15.58 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 15.39/15.58 ) 15.39/15.58 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_107261 $$unsorted)) (or (not (field X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) (one_one X_a)) BOUND_VARIABLE_107261) (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_107261))) ) 15.39/15.58 ( real, (zero_zero real) ) 15.39/15.58 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.58 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.39/15.58 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.58 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 15.39/15.58 ( complex, ii ) 15.39/15.58 ) 15.39/15.58 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_107276 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member X_a))) (let ((_let_3 (field_char_0_Rats X_a))) (or (not (field_char_0 X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_107276) _let_3))) (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_107276)) _let_3))))))) ) 15.39/15.58 ( int, (one_one int) ) 15.39/15.58 ( int, pls ) 15.39/15.58 ( int, min_1 ) 15.39/15.58 ( real, (one_one real) ) 15.39/15.58 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.58 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.39/15.58 ( complex, (one_one complex) ) 15.39/15.58 ( complex, ii ) 15.39/15.58 ) 15.39/15.58 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_107369 $$unsorted) (BOUND_VARIABLE_107376 $$unsorted)) (let ((_let_0 (one_one X_a))) (let ((_let_1 (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) BOUND_VARIABLE_107376)))) (let ((_let_2 (hAPP X_a X_a (sgn_sgn X_a) BOUND_VARIABLE_107376))) (or (not (sgn_if X_a)) (and (or (not (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_107369))) (= (zero_zero X_a) (hAPP X_a X_a (sgn_sgn X_a) BOUND_VARIABLE_107369))) (or (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_107376)) (and (or _let_1 (= (hAPP X_a X_a (uminus_uminus X_a) _let_0) _let_2)) (or (not _let_1) (= _let_0 _let_2))))))))) ) 15.39/15.58 ( bool, fFalse, fFalse ) 15.39/15.58 ( bool, fTrue, fTrue ) 15.39/15.58 ( int, pls, pls ) 15.39/15.58 ( int, min_1, min_1 ) 15.39/15.58 ( int, s, s ) 15.39/15.58 ( int, m, m ) 15.39/15.58 ( int, s1, s1 ) 15.39/15.58 ( int, t, t ) 15.39/15.58 ( (fun int bool), nat_neg, nat_neg ) 15.39/15.58 ( (fun int bool), zprime, zprime ) 15.39/15.58 ( (fun int bool), zEven, zEven ) 15.39/15.58 ( (fun int bool), zOdd, zOdd ) 15.39/15.58 ( (fun int bool), (even_odd_even int), (even_odd_even int) ) 15.39/15.58 ( (fun int bool), twoSqu1091635170sum2sq, twoSqu1091635170sum2sq ) 15.39/15.58 ( (fun int bool), nat_is_nat, nat_is_nat ) 15.39/15.58 ( (fun int (fun int bool)), norRRset, norRRset ) 15.39/15.58 ( (fun int (fun int bool)), quadRes, quadRes ) 15.39/15.58 ( (fun int (fun int bool)), sRStar, sRStar ) 15.39/15.58 ( (fun int (fun int bool)), d22set, d22set ) 15.39/15.58 ( (fun int (fun int bool)), sr, sr ) 15.39/15.58 ( (fun int (fun int bool)), quickc1265749348ro_rel, quickc1265749348ro_rel ) 15.39/15.58 ( (fun int int), zfact, zfact ) 15.39/15.58 ( (fun int int), bit0, bit0 ) 15.39/15.58 ( (fun int int), bit1, bit1 ) 15.39/15.58 ( (fun int int), (fact_fact int), (fact_fact int) ) 15.39/15.58 ( (fun int int), pred, pred ) 15.39/15.58 ( (fun int int), succ, succ ) 15.39/15.58 ( (fun nat bool), (even_odd_even nat), (even_odd_even nat) ) 15.39/15.58 ( (fun nat bool), prime, prime ) 15.39/15.58 ( (fun nat nat), suc, suc ) 15.39/15.58 ( (fun nat nat), (fact_fact nat), (fact_fact nat) ) 15.39/15.58 ( (fun nat nat), fact, fact ) 15.39/15.58 ( (fun nat nat), nat_size, nat_size ) 15.39/15.58 ( (fun nat nat), (size_size nat), (size_size nat) ) 15.39/15.58 ( (fun (product_prod nat nat) bool), pred_nat, pred_nat ) 15.39/15.58 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel, divmod_nat_rel ) 15.39/15.58 ( real, pi, pi ) 15.39/15.58 ( (fun real real), ln, ln ) 15.39/15.58 ( (fun real real), cos, cos ) 15.39/15.58 ( (fun real real), sqrt, sqrt ) 15.39/15.58 ( (fun real real), sin, sin ) 15.39/15.58 ( (fun real real), arccos, arccos ) 15.39/15.58 ( (fun real real), arcsin, arcsin ) 15.39/15.58 ( (fun real real), tan, tan ) 15.39/15.58 ( (fun real real), arctan, arctan ) 15.39/15.58 ( (fun nat (fun nat bool)), coprime, coprime ) 15.39/15.58 ( complex, ii, ii ) 15.39/15.58 ( (fun nat real), (real_1 nat), (real_1 nat) ) 15.39/15.58 ( (fun nat real), sin_coeff, sin_coeff ) 15.39/15.58 ( (fun nat real), cos_coeff, cos_coeff ) 15.39/15.58 ( (filter nat), sequentially, sequentially ) 15.39/15.58 ( (fun int (fun int int)), (gcd_gcd int), (gcd_gcd int) ) 15.39/15.58 ( (fun int (fun int int)), legendre, legendre ) 15.39/15.58 ( (fun int (fun int int)), legacy_zgcd, legacy_zgcd ) 15.39/15.58 ( (fun int (fun int int)), standardRes, standardRes ) 15.39/15.58 ( (fun int (fun int int)), nat_tsub, nat_tsub ) 15.39/15.58 ( (fun int (fun int int)), multInv, multInv ) 15.39/15.58 ( (fun int (fun int int)), z3mod, z3mod ) 15.39/15.58 ( (fun int (fun int int)), z3div, z3div ) 15.39/15.58 ( (fun int (fun int int)), int_gcd, int_gcd ) 15.39/15.58 ( (fun int (fun int int)), int_lcm, int_lcm ) 15.39/15.58 ( (fun int (fun int int)), inv, inv ) 15.39/15.58 ( (fun complex complex), expi, expi ) 15.39/15.58 ( (fun complex complex), cnj, cnj ) 15.39/15.58 ( (fun real complex), cis, cis ) 15.39/15.58 ( (fun int nat), nat_1, nat_1 ) 15.39/15.58 ( (fun int nat), phi, phi ) 15.39/15.58 ( (fun (fun int bool) bool), nat_nat_set, nat_nat_set ) 15.39/15.58 ( (fun nat (fun nat nat)), (gcd_gcd nat), (gcd_gcd nat) ) 15.39/15.58 ( (fun nat (fun nat nat)), nat_gcd, nat_gcd ) 15.39/15.58 ( (fun nat (fun nat nat)), nat_lcm, nat_lcm ) 15.39/15.58 ( (fun (fun int bool) int), (the int), (the int) ) 15.39/15.58 ( (fun complex real), re, re ) 15.39/15.58 ( (fun complex real), im, im ) 15.39/15.58 ( (fun complex real), arg, arg ) 15.39/15.58 ( (fun bool bool), fNot, fNot ) 15.39/15.58 ( (fun nat (fun real real)), root, root ) 15.39/15.58 ( (fun real (fun real real)), log, log ) 15.39/15.58 ( (fun real (fun real real)), powr, powr ) 15.39/15.58 ( (fun bool (fun bool bool)), fimplies, fimplies ) 15.39/15.58 ( (fun bool (fun bool bool)), fconj, fconj ) 15.39/15.58 ( (fun bool (fun bool bool)), fdisj, fdisj ) 15.39/15.58 ( (fun int (fun int (product_prod int int))), negDivAlg, negDivAlg ) 15.39/15.58 ( (fun int (fun int (product_prod int int))), posDivAlg, posDivAlg ) 15.39/15.58 ( (fun int (fun int (product_prod int int))), divmod_int, divmod_int ) 15.39/15.58 ( (fun int (fun int (product_prod int int))), pdivmod, pdivmod ) 15.39/15.58 ( (fun int (fun int (product_prod int int))), norm_frac, norm_frac ) 15.39/15.58 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd, negateSnd ) 15.39/15.58 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize, normalize ) 15.39/15.58 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust, adjust ) 15.39/15.58 ( (fun int (fun int (fun int bool))), zcong, zcong ) 15.39/15.58 ( (fun int (fun int (fun int bool))), zcongm, zcongm ) 15.39/15.58 ( (fun int (fun int (fun int bool))), noXRRset, noXRRset ) 15.39/15.58 ( (fun int (fun int (fun int bool))), bnorRset, bnorRset ) 15.39/15.58 ( (fun int (fun int (fun int bool))), wset, wset ) 15.39/15.58 ( (fun (product_prod int int) bool), frac_1, frac_1 ) 15.39/15.58 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than, int_ge_less_than ) 15.39/15.58 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2, int_ge_less_than2 ) 15.39/15.58 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral, code_S1047413653umeral ) 15.39/15.58 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset, is_RRset ) 15.39/15.58 ( (fun (fun nat rat) bool), vanishes, vanishes ) 15.39/15.58 ( (fun code_code_numeral nat), (size_size code_code_numeral), (size_size code_code_numeral) ) 15.39/15.58 ( (fun code_code_numeral nat), code_c271388182l_size, code_c271388182l_size ) 15.39/15.58 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel, ratrel ) 15.39/15.58 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel, norm_frac_rel ) 15.39/15.58 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel, posDivAlg_rel ) 15.39/15.58 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel, lazy_small_lazy_rel ) 15.39/15.58 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel, negDivAlg_rel ) 15.39/15.58 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel, upto_rel ) 15.39/15.58 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq, twoSqu1094008024sum2sq ) 15.39/15.58 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less, pair_less ) 15.39/15.58 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq, pair_leq ) 15.39/15.58 ( (fun complex nat), complex_size, complex_size ) 15.39/15.58 ( (fun complex nat), (size_size complex), (size_size complex) ) 15.39/15.58 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel, nat_gcd_rel ) 15.39/15.58 ( (fun nat (fun nat (product_prod int int))), bezw, bezw ) 15.39/15.58 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd, xzgcd ) 15.39/15.58 ( (fun int (fun nat nat)), nat_aux, nat_aux ) 15.39/15.58 ( (fun int (fun (fun int bool) bool)), rsetR, rsetR ) 15.39/15.58 ( (fun int (fun (fun int bool) bool)), resSet, resSet ) 15.39/15.58 ( (fun int (list int)), quickc666637781d_zero, quickc666637781d_zero ) 15.39/15.58 ( (fun (product_prod int int) rat), frct, frct ) 15.39/15.58 ( (fun int (fun int rat)), fract, fract ) 15.39/15.58 ( (fun real (fun real complex)), complex_1, complex_1 ) 15.39/15.58 ( (fun real (fun real complex)), rcis, rcis ) 15.39/15.58 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat), (ord_gr676655987ssThan nat) ) 15.39/15.58 ( (fun quickcheck_code_int nat), quickcheck_nat_of, quickcheck_nat_of ) 15.39/15.58 ( (fun int real), (real_1 int), (real_1 int) ) 15.39/15.58 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect, bolzano_bisect ) 15.39/15.58 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR, rRset2norRR ) 15.39/15.58 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int, quickc495462417de_int ) 15.39/15.58 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda, xzgcda ) 15.39/15.58 ( (fun int (fun int (fun int (fun int bool)))), multInvPair, multInvPair ) 15.39/15.58 ( (fun real nat), natfloor, natfloor ) 15.39/15.58 ( (fun real nat), natceiling, natceiling ) 15.39/15.58 ( (fun (fun real bool) real), (complete_Sup_Sup real), (complete_Sup_Sup real) ) 15.39/15.58 ( (fun quickcheck_code_int int), quickcheck_int_of, quickcheck_int_of ) 15.39/15.58 ( (fun rat (product_prod int int)), quotient_of, quotient_of ) 15.39/15.58 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral, code_d418564891umeral ) 15.39/15.58 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat, divmod_nat ) 15.39/15.58 ( (fun rat real), ratreal, ratreal ) 15.39/15.58 ( (fun code_code_numeral int), code_int_of, code_int_of ) 15.39/15.58 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel, divmod_int_rel ) 15.39/15.58 ( (fun int quickcheck_code_int), quickcheck_of_int, quickcheck_of_int ) 15.39/15.58 ( (fun int (fun int (fun (fun int bool) bool))), setS, setS ) 15.39/15.58 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux, code_nat_of_aux ) 15.39/15.58 ) 15.39/15.58 (instantiation (forall ((V_3 $$unsorted)) (let ((_let_0 (hAPP int int (number_number_of int) V_3))) (or (hBOOL (hAPP int bool nat_neg _let_0)) (= (hAPP int nat nat_1 (hAPP int int (hAPP int (fun int int) (div_mod int) (one_one int)) _let_0)) (hAPP nat nat (hAPP nat (fun nat nat) (div_mod nat) (hAPP nat nat suc (zero_zero nat))) (hAPP int nat (number_number_of nat) V_3))))) ) 15.39/15.58 ( pls ) 15.39/15.58 ( (hAPP int int bit1 pls) ) 15.39/15.58 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.39/15.58 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.39/15.58 ( min_1 ) 15.39/15.58 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.58 ) 15.39/15.58 (instantiation (forall ((V_3 $$unsorted)) (let ((_let_0 (hAPP nat nat suc (zero_zero nat)))) (or (not (hBOOL (hAPP int bool nat_neg (hAPP int int (number_number_of int) V_3)))) (= _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (div_mod nat) _let_0) (hAPP int nat (number_number_of nat) V_3))))) ) 15.39/15.58 ( pls ) 15.39/15.58 ( (hAPP int int bit1 pls) ) 15.39/15.58 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.39/15.58 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.39/15.58 ( min_1 ) 15.39/15.58 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.58 ) 15.39/15.58 (instantiation (forall ((C_1 $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (fun (filter nat) bool))) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP real real (abs_abs real) C_1)) (one_one real)))) (hBOOL (hAPP (filter nat) bool (hAPP real _let_1 (hAPP _let_0 (fun real _let_1) (tendsto nat real) (hAPP real _let_0 (power_power real) C_1)) (zero_zero real)) sequentially))))) ) 15.39/15.58 ( (hAPP int real (number_number_of real) min_1) ) 15.39/15.58 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.58 ) 15.39/15.58 (instantiation (forall ((K_4 $$unsorted) (I_1 $$unsorted) (J_2 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int (fun int bool) (dvd_dvd int) I_1))) (or (not (= (one_one int) (hAPP int int (hAPP int _let_0 legacy_zgcd I_1) J_2))) (not (hBOOL (hAPP int bool _let_1 (hAPP int int (hAPP int _let_0 (times_times int) K_4) J_2)))) (hBOOL (hAPP int bool _let_1 K_4))))) ) 15.39/15.58 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.39/15.58 ) 15.39/15.58 (instantiation (forall ((X_1 $$unsorted) (M $$unsorted) (Y_1 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (div_mod int))) (or (not (= (hAPP int int (hAPP int _let_1 _let_2 X_1) M) (hAPP int int (hAPP int _let_1 _let_2 Y_1) M))) (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong X_1) Y_1) M)))))) ) 15.39/15.58 ( s1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s ) 15.39/15.58 ( s1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_4 ) 15.39/15.58 ( s1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_10 ) 15.39/15.58 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (number_number_of int) min_1) ) 15.39/15.58 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.58 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (number_number_of int) min_1) ) 15.39/15.58 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (number_number_of int) min_1) ) 15.39/15.58 ) 15.39/15.58 (instantiation (forall ((X_1 $$unsorted)) (= (hAPP rat int (archim2085082626_floor rat) X_1) (hAPP real int (archim2085082626_floor real) (hAPP rat real ratreal X_1))) ) 15.39/15.58 ( (zero_zero rat) ) 15.39/15.58 ( (one_one rat) ) 15.39/15.58 ) 15.39/15.58 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP int real (number_number_of real) min_1)) X_2))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_2) (one_one real)))) (hBOOL (hAPP real bool (hAPP (fun real real) _let_0 (isCont real real) arcsin) X_2))))) ) 15.39/15.58 ( (one_one real) ) 15.39/15.58 ( (zero_zero real) ) 15.39/15.58 ( pi ) 15.39/15.58 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.58 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.39/15.58 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.58 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 15.39/15.58 ) 15.39/15.58 (instantiation (forall ((X_5 $$unsorted) (N_6 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (zero_zero real))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_6))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) _let_1) X_5))) (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) _let_1) (hAPP real real (hAPP nat (fun real real) root N_6) X_5)))))) ) 15.39/15.58 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.58 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.58 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.58 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.58 ) 15.39/15.58 (instantiation (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) X_1) (zero_zero int)))) (not (forall ((N_2 $$unsorted)) (not (= (ti int X_1) (hAPP int int (uminus_uminus int) (hAPP nat int (semiring_1_of_nat int) (hAPP nat nat suc N_2))))) ))) ) 15.39/15.58 ( (one_one int) ) 15.39/15.58 ( pls ) 15.39/15.58 ( min_1 ) 15.39/15.58 ( s ) 15.39/15.58 ( t ) 15.39/15.58 ( skv_4 ) 15.39/15.58 ( skv_10 ) 15.39/15.58 ) 15.39/15.58 (instantiation (forall ((T_5 $$unsorted)) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) T_5) T_5))) ) 15.39/15.58 ( (zero_zero nat) ) 15.39/15.58 ) 15.39/15.58 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) (zero_zero real)) X_1))) (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) (hAPP real real ln X_1)) (hAPP real real (hAPP real (fun real real) (minus_minus real) X_1) (one_one real)))))) ) 15.39/15.58 ( (one_one real) ) 15.39/15.58 ( pi ) 15.39/15.58 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.58 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.58 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))) ) 15.39/15.58 ( skv_2 ) 15.39/15.58 ( skv_8 ) 15.39/15.58 ( skv_9 ) 15.39/15.58 ) 15.39/15.58 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (times_times X_a))) (or (not (mult_zero X_a)) (= _let_0 (ti (fun X_a (fun X_a X_a)) _let_0)))) ) 15.39/15.58 ( bool ) 15.39/15.58 ( nat ) 15.39/15.58 ( int ) 15.39/15.58 ( (fun int bool) ) 15.39/15.58 ( (fun int (fun int bool)) ) 15.39/15.58 ( (fun int int) ) 15.39/15.58 ( (fun nat bool) ) 15.39/15.58 ( real ) 15.39/15.58 ( (fun real bool) ) 15.39/15.58 ( (fun real real) ) 15.39/15.58 ( rat ) 15.39/15.58 ( complex ) 15.39/15.58 ( (fun nat real) ) 15.39/15.58 ( (product_prod int int) ) 15.39/15.58 ( quickcheck_code_int ) 15.39/15.58 ( code_code_numeral ) 15.39/15.58 ( (fun int (fun int (fun int bool))) ) 15.39/15.58 ( (fun (product_prod int int) bool) ) 15.39/15.58 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 15.39/15.58 ( (fun (product_prod int int) int) ) 15.39/15.58 ( (fun int real) ) 15.39/15.58 ) 15.39/15.58 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_107803 $$unsorted) (BOUND_VARIABLE_107804 $$unsorted)) (let ((_let_0 (norm_norm X_a))) (or (not (field_inverse_zero X_a)) (not (real_normed_field X_a)) (= (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP X_a real _let_0 BOUND_VARIABLE_107803)) (hAPP X_a real _let_0 BOUND_VARIABLE_107804)) (hAPP X_a real _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_107803) BOUND_VARIABLE_107804))))) ) 15.39/15.58 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.58 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.39/15.58 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.58 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 15.39/15.58 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.58 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.58 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.39/15.58 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.39/15.58 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.58 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.58 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.58 ) 15.39/15.58 (instantiation (forall ((M $$unsorted) (A_1 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) _let_1) A_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) A_1) M))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong A_1) _let_1) M))) (= _let_1 (ti int A_1))))) ) 15.39/15.58 ( (one_one int), pls ) 15.39/15.58 ( pls, pls ) 15.39/15.58 ( pls, min_1 ) 15.39/15.58 ( min_1, pls ) 15.39/15.58 ( min_1, min_1 ) 15.39/15.58 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), pls ) 15.39/15.58 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s ) 15.39/15.58 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.39/15.58 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_4 ) 15.39/15.58 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_10 ) 15.39/15.58 ( t, (one_one int) ) 15.39/15.58 ) 15.39/15.58 (instantiation (forall ((Y_1 $$unsorted)) (let ((_let_0 (zero_zero real))) (or (= _let_0 Y_1) (= _let_0 (hAPP real real cos (hAPP complex real arg (hAPP real complex (hAPP real (fun real complex) complex_1 _let_0) Y_1)))))) ) 15.39/15.58 ( (one_one real) ) 15.39/15.58 ( (zero_zero real) ) 15.39/15.58 ) 15.39/15.58 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_107974 $$unsorted) (BOUND_VARIABLE_107975 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (div_mod X_a))) (or (not (semiring_div X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_107974) BOUND_VARIABLE_107975) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_0 (plus_plus X_a) BOUND_VARIABLE_107974) BOUND_VARIABLE_107975)) BOUND_VARIABLE_107975))))) ) 15.39/15.58 ( nat, (one_one nat), (one_one nat) ) 15.39/15.58 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 15.39/15.58 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 15.39/15.58 ) 15.39/15.58 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_108005 $$unsorted) (BOUND_VARIABLE_108015 $$unsorted)) (let ((_let_0 (abs_abs X_a))) (let ((_let_1 (fun X_a bool))) (let ((_let_2 (ord_less X_a))) (let ((_let_3 (zero_zero X_a))) (let ((_let_4 (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_108005))) (let ((_let_5 (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_108015))) (or (not (number_ring X_a)) (not (linordered_idom X_a)) (and (or (not (hBOOL (hAPP X_a bool (hAPP X_a _let_1 _let_2 _let_4) _let_3))) (= (hAPP X_a X_a (uminus_uminus X_a) _let_4) (hAPP X_a X_a _let_0 _let_4))) (or (hBOOL (hAPP X_a bool (hAPP X_a _let_1 _let_2 _let_5) _let_3)) (= _let_5 (hAPP X_a X_a _let_0 _let_5))))))))))) ) 15.39/15.58 ( nat, pls, pls ) 15.39/15.58 ( nat, (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 15.39/15.58 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.39/15.58 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.39/15.58 ( int, pls, pls ) 15.39/15.58 ( int, (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 15.39/15.58 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.39/15.58 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.39/15.58 ( int, min_1, min_1 ) 15.39/15.58 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.58 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.39/15.58 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.39/15.58 ( real, min_1, min_1 ) 15.39/15.58 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.58 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.39/15.58 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.58 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))), (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 15.39/15.58 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.39/15.58 ( complex, min_1, min_1 ) 15.39/15.58 ( quickcheck_code_int, (one_one int), (one_one int) ) 15.39/15.58 ( quickcheck_code_int, (zero_zero int), (zero_zero int) ) 15.39/15.58 ( quickcheck_code_int, (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 15.39/15.58 ( code_code_numeral, pls, pls ) 15.39/15.58 ( code_code_numeral, (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 15.39/15.58 ) 15.39/15.58 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_108053 $$unsorted) (BOUND_VARIABLE_108054 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (or (not (preorder X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_108053) BOUND_VARIABLE_108054))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_108054) BOUND_VARIABLE_108053)))))) ) 15.39/15.58 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.58 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 15.39/15.58 ( int, (one_one int), pls ) 15.39/15.58 ( int, (one_one int), t ) 15.39/15.58 ( int, pls, (one_one int) ) 15.39/15.58 ( int, pls, pls ) 15.39/15.58 ( int, pls, min_1 ) 15.39/15.58 ( int, pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.39/15.58 ( int, min_1, pls ) 15.39/15.58 ( int, min_1, min_1 ) 15.39/15.58 ( int, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.39/15.58 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), pls ) 15.39/15.58 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s ) 15.39/15.58 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.39/15.58 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_4 ) 15.39/15.58 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_10 ) 15.39/15.58 ( int, t, (one_one int) ) 15.39/15.58 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.39/15.58 ( int, skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.39/15.58 ( int, skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.39/15.58 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.58 ( real, (zero_zero real), pi ) 15.39/15.58 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.58 ( real, (zero_zero real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.39/15.58 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.58 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.58 ( real, (zero_zero real), skv_2 ) 15.39/15.58 ( real, (zero_zero real), skv_8 ) 15.39/15.58 ( real, (zero_zero real), skv_9 ) 15.39/15.58 ( real, pi, (zero_zero real) ) 15.39/15.58 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.58 ( real, pi, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 15.39/15.58 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.58 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.39/15.58 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.58 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 15.39/15.58 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 15.39/15.58 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 15.39/15.58 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.39/15.58 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.39/15.58 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 15.39/15.58 ( real, skv_2, (zero_zero real) ) 15.39/15.58 ( real, skv_8, (zero_zero real) ) 15.39/15.58 ( real, skv_9, (zero_zero real) ) 15.39/15.58 ) 15.39/15.58 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_0 (one_one int))) (let ((_let_1 (abs_abs int))) (or (not (= _let_0 (hAPP int int _let_1 (hAPP int int (hAPP int (fun int int) (times_times int) M) N_1)))) (= _let_0 (hAPP int int _let_1 M))))) ) 15.39/15.58 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 15.39/15.58 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.39/15.58 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13 ) 15.39/15.58 ) 15.39/15.58 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_108106 $$unsorted) (BOUND_VARIABLE_108107 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (zero_zero X_a))) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_108107) _let_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_108106) _let_2))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_108107) BOUND_VARIABLE_108106))))))) ) 15.39/15.58 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 15.39/15.58 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.39/15.58 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.39/15.58 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.39/15.58 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.58 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 15.39/15.58 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), pi ) 15.39/15.58 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (one_one real) ) 15.39/15.58 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))), pi ) 15.39/15.58 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 15.39/15.58 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))), (one_one real) ) 15.39/15.58 ) 15.39/15.58 (instantiation (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_0 (fun int int))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) Y_1) X_1))) (= (hAPP int int (hAPP int _let_0 (minus_minus int) X_1) Y_1) (hAPP int int (hAPP int _let_0 nat_tsub X_1) Y_1)))) ) 15.39/15.58 ( (one_one int), t ) 15.39/15.58 ( (zero_zero int), (one_one int) ) 15.39/15.58 ( (zero_zero int), min_1 ) 15.39/15.58 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.58 ( (zero_zero int), s ) 15.39/15.58 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.39/15.58 ( (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.39/15.58 ( (zero_zero int), skv_4 ) 15.39/15.58 ( (zero_zero int), skv_10 ) 15.39/15.58 ( min_1, pls ) 15.39/15.58 ( min_1, min_1 ) 15.39/15.58 ( (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.58 ) 15.39/15.58 (instantiation (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (dvd_dvd int) X_1) Y_1))) (= (hAPP int int (hAPP int (fun int int) (gcd_gcd int) X_1) Y_1) (hAPP int int (abs_abs int) X_1))) ) 15.39/15.58 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 15.39/15.58 ) 15.39/15.58 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP rat real ratreal (hAPP int rat (number_number_of rat) K_4)) (hAPP int real (number_number_of real) K_4)) ) 15.39/15.58 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.39/15.58 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.39/15.58 ( min_1 ) 15.39/15.58 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.58 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.39/15.58 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.58 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 15.39/15.58 ) 15.39/15.58 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_108194 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (or (not (number_semiring X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 (plus_plus X_a) BOUND_VARIABLE_108194) BOUND_VARIABLE_108194) (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) (hAPP int X_a (number_number_of X_a) (hAPP int int bit0 (hAPP int int bit1 pls)))) BOUND_VARIABLE_108194)))) ) 15.39/15.58 ( nat, (one_one nat) ) 15.39/15.58 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.39/15.58 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.58 ( real, pi ) 15.39/15.58 ( real, (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.39/15.58 ( complex, (hAPP real complex (of_real complex) pi) ) 15.39/15.58 ) 15.39/15.58 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_108205 $$unsorted)) (or (not (linordered_ring X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_108205) BOUND_VARIABLE_108205)) (zero_zero X_a))))) ) 15.39/15.58 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.58 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.58 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.39/15.58 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.58 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.58 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 15.39/15.58 ( complex, ii ) 15.39/15.58 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.58 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 15.39/15.58 ) 15.39/15.58 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_108225 $$unsorted) (BOUND_VARIABLE_108226 $$unsorted) (BOUND_VARIABLE_108227 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (fun X_a X_a))) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_108227))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_108225) (hAPP X_a X_a (hAPP X_a _let_2 (times_times X_a) BOUND_VARIABLE_108226) BOUND_VARIABLE_108227)))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_2 (inverse_divide X_a) BOUND_VARIABLE_108225) BOUND_VARIABLE_108227)) BOUND_VARIABLE_108226)))))) ) 15.39/15.58 ( real, (zero_zero real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.39/15.58 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.58 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.39/15.58 ) 15.39/15.58 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_108313 $$unsorted) (BOUND_VARIABLE_108314 $$unsorted) (BOUND_VARIABLE_108315 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_108313))) (or (not (order X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_108314) BOUND_VARIABLE_108315))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_108314))) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_108315)))) ) 15.39/15.58 ( int, (one_one int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.58 ( int, pls, (zero_zero int), s ) 15.39/15.58 ( int, min_1, min_1, pls ) 15.39/15.58 ( int, s, (zero_zero int), (one_one int) ) 15.39/15.58 ( int, t, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.39/15.58 ( int, skv_4, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.39/15.58 ( int, skv_10, (zero_zero int), min_1 ) 15.39/15.58 ( real, (one_one real), (zero_zero real), skv_3 ) 15.39/15.58 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.39/15.58 ( real, pi, (zero_zero real), pi ) 15.39/15.58 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.39/15.58 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.58 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.58 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.58 ) 15.39/15.58 (instantiation (forall ((Z1 $$unsorted) (Z2 $$unsorted) (W $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (plus_plus int))) (= (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 Z1) W)) (hAPP int int (hAPP int _let_0 _let_1 Z2) W)) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 Z1) Z2)) W))))) ) 15.39/15.58 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int), t ) 15.39/15.58 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int), skv_13 ) 15.39/15.58 ) 15.39/15.58 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_108424 $$unsorted) (BOUND_VARIABLE_108425 $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (preorder X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_108424) BOUND_VARIABLE_108425))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_108424) BOUND_VARIABLE_108425)))) ) 15.39/15.58 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.58 ( int, (one_one int), t ) 15.39/15.58 ( int, (zero_zero int), (one_one int) ) 15.39/15.58 ( int, (zero_zero int), min_1 ) 15.39/15.58 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.58 ( int, (zero_zero int), s ) 15.39/15.58 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.39/15.58 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.39/15.58 ( int, (zero_zero int), skv_4 ) 15.39/15.58 ( int, (zero_zero int), skv_10 ) 15.39/15.58 ( int, pls, (one_one int) ) 15.39/15.58 ( int, pls, pls ) 15.39/15.58 ( int, pls, min_1 ) 15.39/15.58 ( int, pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.39/15.58 ( int, min_1, pls ) 15.39/15.58 ( int, min_1, min_1 ) 15.39/15.58 ( int, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.39/15.58 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.39/15.58 ( int, skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.39/15.58 ( int, skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.39/15.58 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.58 ( real, (zero_zero real), pi ) 15.39/15.58 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.58 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.58 ( real, (zero_zero real), skv_2 ) 15.39/15.58 ( real, (zero_zero real), skv_3 ) 15.39/15.58 ( real, (zero_zero real), skv_5 ) 15.39/15.58 ( real, (zero_zero real), skv_7 ) 15.39/15.58 ( real, (zero_zero real), skv_8 ) 15.39/15.58 ( real, (zero_zero real), skv_9 ) 15.39/15.58 ( real, (zero_zero real), skv_12 ) 15.39/15.58 ( real, pi, (zero_zero real) ) 15.39/15.58 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.58 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.39/15.58 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.58 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 15.39/15.58 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.39/15.58 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 15.39/15.58 ( real, skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.58 ) 15.39/15.58 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (div_mod X_a))) (or (not (semiring_div X_a)) (= _let_0 (ti (fun X_a (fun X_a X_a)) _let_0)))) ) 15.39/15.58 ( bool ) 15.39/15.58 ( nat ) 15.39/15.58 ( int ) 15.39/15.58 ( (fun int bool) ) 15.39/15.58 ( (fun int (fun int bool)) ) 15.39/15.58 ( (fun int int) ) 15.39/15.58 ( (fun nat bool) ) 15.39/15.58 ( real ) 15.39/15.58 ( (fun real bool) ) 15.39/15.58 ( (fun real real) ) 15.39/15.58 ( complex ) 15.39/15.58 ( (fun nat real) ) 15.39/15.58 ( (product_prod int int) ) 15.39/15.58 ( quickcheck_code_int ) 15.39/15.58 ( code_code_numeral ) 15.39/15.58 ( (fun int (fun int (fun int bool))) ) 15.39/15.59 ( (fun (product_prod int int) bool) ) 15.39/15.59 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 15.39/15.59 ( (fun (product_prod int int) int) ) 15.39/15.59 ( (fun int real) ) 15.39/15.59 ) 15.39/15.59 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (fun nat X_a))) (let ((_let_1 (nat_case X_a))) (= _let_1 (ti (fun X_a (fun _let_0 _let_0)) _let_1)))) ) 15.39/15.59 ( bool ) 15.39/15.59 ( nat ) 15.39/15.59 ( int ) 15.39/15.59 ( (fun int int) ) 15.39/15.59 ( (fun nat bool) ) 15.39/15.59 ( (fun nat nat) ) 15.39/15.59 ( (product_prod nat nat) ) 15.39/15.59 ( (fun (product_prod nat nat) bool) ) 15.39/15.59 ( (fun nat (fun (product_prod nat nat) bool)) ) 15.39/15.59 ( real ) 15.39/15.59 ( (fun real real) ) 15.39/15.59 ( rat ) 15.39/15.59 ( (fun nat (fun nat bool)) ) 15.39/15.59 ( complex ) 15.39/15.59 ( (product_prod int int) ) 15.39/15.59 ( (fun bool bool) ) 15.39/15.59 ( (product_prod real real) ) 15.39/15.59 ( (fun nat (product_prod nat nat)) ) 15.39/15.59 ( (fun nat (product_prod int int)) ) 15.39/15.59 ) 15.39/15.59 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_108514 $$unsorted) (BOUND_VARIABLE_108515 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (or (not (semiring_div X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_108515)) (= (ti X_a BOUND_VARIABLE_108514) (hAPP X_a X_a (hAPP X_a _let_0 (div_div X_a) (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_108515) BOUND_VARIABLE_108514)) BOUND_VARIABLE_108515)))) ) 15.39/15.59 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.59 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.39/15.59 ( int, skv_13, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.39/15.59 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.59 ( real, pi, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 15.39/15.59 ( real, (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.59 ( real, (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.59 ( complex, ii, ii ) 15.39/15.59 ( complex, ii, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 15.39/15.59 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.59 ) 15.39/15.59 (instantiation (forall ((M $$unsorted) (K_4 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (let ((_let_2 (fact_fact int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (zero_zero int)) K_4))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int _let_2 M)) (hAPP int int _let_2 (hAPP int int (hAPP int (fun int int) (plus_plus int) M) K_4)))))))) ) 15.39/15.59 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 15.39/15.59 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 15.39/15.59 ) 15.39/15.59 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_108558 $$unsorted) (BOUND_VARIABLE_108559 $$unsorted) (BOUND_VARIABLE_108560 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (times_times X_a))) (let ((_let_2 (plus_plus X_a))) (or (not (comm_semiring_1 X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_108558) BOUND_VARIABLE_108559)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_108560) BOUND_VARIABLE_108559)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_108558) BOUND_VARIABLE_108560)) BOUND_VARIABLE_108559)))))) ) 15.39/15.59 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), t, (one_one int) ) 15.39/15.59 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), skv_13, (one_one int) ) 15.39/15.59 ) 15.39/15.59 (instantiation (forall ((P_4 $$unsorted)) (let ((_let_0 (product_prod int int))) (= (hAPP _let_0 int (hAPP (fun int (fun int int)) (fun _let_0 int) (product_prod_case int int int) (div_div int)) (hAPP rat _let_0 quotient_of P_4)) (hAPP rat int (archim2085082626_floor rat) P_4))) ) 15.39/15.59 ( (zero_zero rat) ) 15.39/15.59 ( (one_one rat) ) 15.39/15.59 ) 15.39/15.59 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (one_one X_a))) (or (not (semiring_1 X_a)) (= _let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) _let_0) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 15.39/15.59 ( bool ) 15.39/15.59 ( nat ) 15.39/15.59 ( int ) 15.39/15.59 ( (fun int int) ) 15.39/15.59 ( (fun nat bool) ) 15.39/15.59 ( (fun nat nat) ) 15.39/15.59 ( (product_prod nat nat) ) 15.39/15.59 ( (fun (product_prod nat nat) bool) ) 15.39/15.59 ( (fun nat (fun (product_prod nat nat) bool)) ) 15.39/15.59 ( real ) 15.39/15.59 ( (fun real real) ) 15.39/15.59 ( rat ) 15.39/15.59 ( (fun nat (fun nat bool)) ) 15.39/15.59 ( complex ) 15.39/15.59 ( (product_prod int int) ) 15.39/15.59 ( quickcheck_code_int ) 15.39/15.59 ( (fun bool bool) ) 15.39/15.59 ( code_code_numeral ) 15.39/15.59 ( (product_prod real real) ) 15.39/15.59 ( (fun nat (product_prod nat nat)) ) 15.39/15.59 ( (fun nat (product_prod int int)) ) 15.39/15.59 ) 15.39/15.59 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_108663 $$unsorted) (BOUND_VARIABLE_108664 $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (order X_a)) (= (ti X_a BOUND_VARIABLE_108664) (ti X_a BOUND_VARIABLE_108663)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_108664) BOUND_VARIABLE_108663))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_108664) BOUND_VARIABLE_108663)))) ) 15.39/15.59 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 15.39/15.59 ( int, (one_one int), (zero_zero int) ) 15.39/15.59 ( int, (one_one int), pls ) 15.39/15.59 ( int, pls, pls ) 15.39/15.59 ( int, pls, min_1 ) 15.39/15.59 ( int, min_1, (zero_zero int) ) 15.39/15.59 ( int, min_1, pls ) 15.39/15.59 ( int, min_1, min_1 ) 15.39/15.59 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 15.39/15.59 ( int, s, (zero_zero int) ) 15.39/15.59 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), pls ) 15.39/15.59 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s ) 15.39/15.59 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.39/15.59 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_4 ) 15.39/15.59 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_10 ) 15.39/15.59 ( int, t, (one_one int) ) 15.39/15.59 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 15.39/15.59 ( int, (hAPP int int (number_number_of int) pls), (zero_zero int) ) 15.39/15.59 ( int, skv_4, (zero_zero int) ) 15.39/15.59 ( int, skv_10, (zero_zero int) ) 15.39/15.59 ( real, (zero_zero real), pi ) 15.39/15.59 ( real, (zero_zero real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.39/15.59 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.59 ( real, pi, (zero_zero real) ) 15.39/15.59 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.59 ( real, pi, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 15.39/15.59 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.59 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_5 ) 15.39/15.59 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.39/15.59 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 15.39/15.59 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 15.39/15.59 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.39/15.59 ( real, skv_2, (zero_zero real) ) 15.39/15.59 ( real, skv_3, (zero_zero real) ) 15.39/15.59 ( real, skv_5, (zero_zero real) ) 15.39/15.59 ( real, skv_7, (zero_zero real) ) 15.39/15.59 ( real, skv_8, (zero_zero real) ) 15.39/15.59 ( real, skv_9, (zero_zero real) ) 15.39/15.59 ( real, skv_12, (zero_zero real) ) 15.39/15.59 ) 15.39/15.59 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_108705 $$unsorted) (BOUND_VARIABLE_108706 $$unsorted) (BOUND_VARIABLE_108707 $$unsorted)) (let ((_let_0 (fun nat X_a))) (let ((_let_1 (power_power X_a))) (let ((_let_2 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)))) (let ((_let_3 (hAPP nat nat suc BOUND_VARIABLE_108706))) (or (not (linordered_semidom X_a)) (not (= (hAPP nat X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_108705) _let_3) (hAPP nat X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_108707) _let_3))) (not (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_108705))) (not (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_108707))) (= (ti X_a BOUND_VARIABLE_108707) (ti X_a BOUND_VARIABLE_108705))))))) ) 15.39/15.59 ( int, s, (zero_zero nat), s ) 15.39/15.59 ( int, s, (zero_zero nat), s1 ) 15.39/15.59 ( int, s, (hAPP nat nat suc (zero_zero nat)), s ) 15.39/15.59 ( int, s, (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))), s ) 15.39/15.59 ( int, s1, (hAPP nat nat suc (zero_zero nat)), s ) 15.39/15.59 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))), (hAPP int real (number_number_of real) min_1) ) 15.39/15.59 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.59 ) 15.39/15.59 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_108764 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)))) (or (not (linord1117847801e_zero X_a)) (not (number_ring X_a)) (= (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_108764)) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_108764) (hAPP int X_a (number_number_of X_a) (hAPP int int bit0 (hAPP int int bit1 pls))))))))) ) 15.39/15.59 ( real, (one_one real) ) 15.39/15.59 ( real, pi ) 15.39/15.59 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.39/15.59 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.39/15.59 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.59 ) 15.39/15.59 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (uminus_uminus real) _let_2)) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) _let_2))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) (hAPP real real cos X_1))))))) ) 15.39/15.59 ( (zero_zero real) ) 15.39/15.59 ( pi ) 15.39/15.59 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.59 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.59 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.39/15.59 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.39/15.59 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.39/15.59 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.59 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.39/15.59 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.39/15.59 ( skv_5 ) 15.39/15.59 ) 15.39/15.59 (instantiation (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_1))) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) X_1))) (= X_1 (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP real real (hAPP nat (fun real real) root N_1) X_1)) N_1))) ) 15.39/15.59 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.59 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.59 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.59 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.59 ) 15.39/15.59 (instantiation (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 (zero_zero real)) Y_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Y_1) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 X_1) pi))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real cos X_1)) (hAPP real real cos Y_1))))))) ) 15.39/15.59 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_5 ) 15.39/15.59 ) 15.39/15.59 (instantiation (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (or (hBOOL (hAPP nat bool (even_odd_even nat) N_1)) (= X_1 (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP real real (hAPP nat (fun real real) root N_1) X_1)) N_1))) ) 15.39/15.59 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.59 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.59 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.59 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.59 ) 15.39/15.59 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (inverse_divide X_a))) (or (not (real_normed_vector X_a)) (not (inverse X_a)) (= _let_0 (ti (fun X_a (fun X_a X_a)) _let_0)))) ) 15.39/15.59 ( bool ) 15.39/15.59 ( nat ) 15.39/15.59 ( int ) 15.39/15.59 ( (fun int bool) ) 15.39/15.59 ( (fun int (fun int bool)) ) 15.39/15.59 ( (fun int int) ) 15.39/15.59 ( (fun nat bool) ) 15.39/15.59 ( real ) 15.39/15.59 ( (fun real bool) ) 15.39/15.59 ( (fun real real) ) 15.39/15.59 ( rat ) 15.39/15.59 ( complex ) 15.39/15.59 ( (fun nat real) ) 15.39/15.59 ( (product_prod int int) ) 15.39/15.59 ( code_code_numeral ) 15.39/15.59 ( (fun int (fun int (fun int bool))) ) 15.39/15.59 ( (fun (product_prod int int) bool) ) 15.39/15.59 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 15.39/15.59 ( (fun (product_prod int int) int) ) 15.39/15.59 ( (fun int real) ) 15.39/15.59 ) 15.39/15.59 (instantiation (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (times_times real))) (= (hAPP complex real im (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) X_1) Y_1)) (hAPP real real (hAPP real _let_0 (plus_plus real) (hAPP real real (hAPP real _let_0 _let_1 (hAPP complex real re X_1)) (hAPP complex real im Y_1))) (hAPP real real (hAPP real _let_0 _let_1 (hAPP complex real im X_1)) (hAPP complex real re Y_1)))))) ) 15.39/15.59 ( ii, ii ) 15.39/15.59 ( (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 15.39/15.59 ( (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 15.39/15.59 ) 15.39/15.59 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted) (K_4 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (hAPP int _let_0 (dvd_dvd int) K_4))) (or (not (= (one_one int) (hAPP int int (hAPP int _let_1 legacy_zgcd N_1) K_4))) (not (hBOOL (hAPP int bool _let_2 (hAPP int int (hAPP int _let_1 (times_times int) M) N_1)))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (zero_zero int)) M))) (hBOOL (hAPP int bool _let_2 M)))))) ) 15.39/15.59 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.39/15.59 ) 15.39/15.59 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (hAPP real real sqrt X_1))) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) X_1))) (= (hAPP real real (inverse_inverse real) _let_0) (hAPP real real (hAPP real (fun real real) (inverse_divide real) _let_0) X_1)))) ) 15.39/15.59 ( (one_one real) ) 15.39/15.59 ( (zero_zero real) ) 15.39/15.59 ( pi ) 15.39/15.59 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.59 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.59 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.39/15.59 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.59 ( skv_3 ) 15.39/15.59 ( skv_5 ) 15.39/15.59 ( skv_7 ) 15.39/15.59 ( skv_12 ) 15.39/15.59 ) 15.39/15.59 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_109050 $$unsorted) (BOUND_VARIABLE_109051 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (or (not (ordere142940540dd_abs X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_109050)) BOUND_VARIABLE_109051))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_109050) BOUND_VARIABLE_109051))))) ) 15.39/15.59 ( int, (one_one int), t ) 15.39/15.59 ( int, (zero_zero int), (one_one int) ) 15.39/15.59 ( int, (zero_zero int), min_1 ) 15.39/15.59 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.59 ( int, (zero_zero int), s ) 15.39/15.59 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.39/15.59 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.39/15.59 ( int, (zero_zero int), skv_4 ) 15.39/15.59 ( int, (zero_zero int), skv_10 ) 15.39/15.59 ( int, min_1, pls ) 15.39/15.59 ( int, min_1, min_1 ) 15.39/15.59 ( real, (zero_zero real), pi ) 15.39/15.59 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.59 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.59 ( real, (zero_zero real), skv_3 ) 15.39/15.59 ( real, (zero_zero real), skv_5 ) 15.39/15.59 ( real, (zero_zero real), skv_7 ) 15.39/15.59 ( real, (zero_zero real), skv_12 ) 15.39/15.59 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.39/15.59 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.59 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.39/15.59 ( real, skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.59 ) 15.39/15.59 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_109093 $$unsorted) (BOUND_VARIABLE_109094 $$unsorted)) (let ((_let_0 (fun X_b X_a))) (or (not (uminus X_a)) (= (hAPP X_a X_a (uminus_uminus X_a) (hAPP X_b X_a BOUND_VARIABLE_109093 BOUND_VARIABLE_109094)) (hAPP X_b X_a (hAPP _let_0 _let_0 (uminus_uminus _let_0) BOUND_VARIABLE_109093) BOUND_VARIABLE_109094)))) ) 15.39/15.59 ( nat, int, (semiring_1_of_nat int), (zero_zero nat) ) 15.39/15.59 ( int, int, bit1, min_1 ) 15.39/15.59 ( int, int, (fact_fact int), (one_one int) ) 15.39/15.59 ( real, real, cos, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.39/15.59 ( real, real, (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.59 ( real, real, (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 15.39/15.59 ( real, complex, (hAPP real (fun real complex) complex_1 (zero_zero real)), (one_one real) ) 15.39/15.59 ( complex, complex, expi, (let ((_let_0 (fun complex complex))) (let ((_let_1 (times_times complex))) (hAPP complex complex (hAPP complex _let_0 _let_1 (hAPP complex complex (hAPP complex _let_0 _let_1 (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi))) ii))) ) 15.39/15.59 ) 15.39/15.59 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (suminf X_a))) (or (not (topological_space X_a)) (not (comm_monoid_add X_a)) (= _let_0 (ti (fun (fun nat X_a) X_a) _let_0)))) ) 15.39/15.59 ( bool ) 15.39/15.59 ( nat ) 15.39/15.59 ( int ) 15.39/15.59 ( (fun int int) ) 15.39/15.59 ( (fun nat bool) ) 15.39/15.59 ( (fun nat nat) ) 15.39/15.59 ( (product_prod nat nat) ) 15.39/15.59 ( (fun (product_prod nat nat) bool) ) 15.39/15.59 ( (fun nat (fun (product_prod nat nat) bool)) ) 15.39/15.59 ( real ) 15.39/15.59 ( (fun real real) ) 15.39/15.59 ( rat ) 15.39/15.59 ( (fun nat (fun nat bool)) ) 15.39/15.59 ( complex ) 15.39/15.59 ( (product_prod int int) ) 15.39/15.59 ( quickcheck_code_int ) 15.39/15.59 ( (fun bool bool) ) 15.39/15.59 ( code_code_numeral ) 15.39/15.59 ( (product_prod real real) ) 15.39/15.59 ( (fun nat (product_prod nat nat)) ) 15.39/15.59 ( (fun nat (product_prod int int)) ) 15.39/15.59 ) 15.39/15.59 (instantiation (forall ((B_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member int))) (or (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 A_2) zOdd))) (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 B_1) zOdd))) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP int int (hAPP int (fun int int) (plus_plus int) A_2) B_1)) zEven)))))) ) 15.39/15.59 ( (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.39/15.59 ( (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.59 ) 15.39/15.59 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_109126 $$unsorted)) (or (not (ordere142940540dd_abs X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_109126) (zero_zero X_a)))) (= (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_109126) (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_109126))) ) 15.39/15.59 ( nat, (zero_zero nat) ) 15.39/15.59 ( int, (one_one int) ) 15.39/15.59 ( int, pls ) 15.39/15.59 ( int, min_1 ) 15.39/15.59 ( int, s ) 15.39/15.59 ( int, t ) 15.39/15.59 ( int, skv_4 ) 15.39/15.59 ( int, skv_10 ) 15.39/15.59 ( real, (one_one real) ) 15.39/15.59 ( real, (zero_zero real) ) 15.39/15.59 ( real, pi ) 15.39/15.59 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.59 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.39/15.59 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.39/15.59 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.59 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 15.39/15.59 ( complex, (one_one complex) ) 15.39/15.59 ( complex, ii ) 15.39/15.59 ) 15.39/15.59 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_109146 $$unsorted) (BOUND_VARIABLE_109147 $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat _let_0))) (let ((_let_2 (fun (filter nat) bool))) (let ((_let_3 (fun nat X_a))) (let ((_let_4 (fun _let_0 X_a))) (or (not (topological_space X_a)) (not (comm_monoid_add X_a)) (= (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_2 (hAPP _let_3 (fun X_a _let_2) (tendsto nat X_a) (hAPP _let_1 _let_3 (hAPP _let_4 (fun _let_1 _let_3) (combb _let_0 X_a nat) (hAPP _let_3 _let_4 (big_co1399186613setsum nat X_a) BOUND_VARIABLE_109146)) (hAPP nat _let_1 (ord_atLeastLessThan nat) (zero_zero nat)))) BOUND_VARIABLE_109147) sequentially)) (hBOOL (hAPP X_a bool (hAPP _let_3 (fun X_a bool) (sums X_a) BOUND_VARIABLE_109146) BOUND_VARIABLE_109147))))))))) ) 15.39/15.59 ( real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (hAPP real _let_1 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc))), (one_one real) ) 15.39/15.59 ) 15.39/15.59 (instantiation (forall ((X_a $$unsorted)) (or (not (number_ring X_a)) (hBOOL (hAPP X_a bool (iszero X_a) (hAPP int X_a (number_number_of X_a) pls)))) ) 15.39/15.59 ( nat ) 15.39/15.59 ( int ) 15.39/15.59 ( real ) 15.39/15.59 ( rat ) 15.39/15.59 ( complex ) 15.39/15.59 ( quickcheck_code_int ) 15.39/15.59 ( code_code_numeral ) 15.39/15.59 ) 15.39/15.59 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_109212 $$unsorted) (BOUND_VARIABLE_109213 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (or (not (linorder X_a)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_109212) BOUND_VARIABLE_109213)) (= (= (ti X_a BOUND_VARIABLE_109213) (ti X_a BOUND_VARIABLE_109212)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_109213) BOUND_VARIABLE_109212))))))) ) 15.39/15.59 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.59 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 15.39/15.59 ( int, (one_one int), pls ) 15.39/15.59 ( int, (one_one int), t ) 15.39/15.59 ( int, pls, (one_one int) ) 15.39/15.59 ( int, pls, pls ) 15.39/15.59 ( int, pls, min_1 ) 15.39/15.59 ( int, pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.39/15.59 ( int, min_1, pls ) 15.39/15.59 ( int, min_1, min_1 ) 15.39/15.59 ( int, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.39/15.59 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), pls ) 15.39/15.59 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s ) 15.39/15.59 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.39/15.59 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_4 ) 15.39/15.59 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_10 ) 15.39/15.59 ( int, t, (one_one int) ) 15.39/15.59 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.39/15.59 ( int, skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.39/15.59 ( int, skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.39/15.59 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.59 ( real, (zero_zero real), pi ) 15.39/15.59 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.59 ( real, (zero_zero real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.39/15.59 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.59 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.59 ( real, (zero_zero real), skv_2 ) 15.39/15.59 ( real, (zero_zero real), skv_8 ) 15.39/15.59 ( real, (zero_zero real), skv_9 ) 15.39/15.59 ( real, pi, (zero_zero real) ) 15.39/15.59 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.59 ( real, pi, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 15.39/15.59 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.59 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.39/15.59 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.59 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 15.39/15.59 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 15.39/15.59 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 15.39/15.59 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.39/15.59 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.39/15.59 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 15.39/15.59 ( real, skv_2, (zero_zero real) ) 15.39/15.59 ( real, skv_8, (zero_zero real) ) 15.39/15.59 ( real, skv_9, (zero_zero real) ) 15.39/15.59 ) 15.39/15.59 (instantiation (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted) (X_2 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (hAPP int nat nat_1 X_2))) (or (not (= (hAPP nat int (hAPP int (fun nat int) (power_power int) C_1) _let_2) (hAPP int int (hAPP int _let_1 (times_times int) A_2) B_1))) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (one_one nat)) _let_2))) (not (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) X_2) zOdd))) (not (= (one_one int) (hAPP int int (hAPP int _let_1 legacy_zgcd A_2) B_1))) (not (forall ((K_1 $$unsorted)) (not (= (ti int A_2) (hAPP nat int (hAPP int (fun nat int) (power_power int) K_1) _let_2))) )))))) ) 15.39/15.59 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m, s, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.59 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t, s1, (zero_zero int) ) 15.39/15.59 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13, skv_14, (one_one int) ) 15.39/15.59 ) 15.39/15.59 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_109260 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (let ((_let_3 (fun X_a X_a))) (let ((_let_4 (plus_plus X_a))) (or (not (linordered_idom X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) BOUND_VARIABLE_109260) (ring_1_Ints X_a)))) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_109260) _let_2)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_3 _let_4 (hAPP X_a X_a (hAPP X_a _let_3 _let_4 (one_one X_a)) BOUND_VARIABLE_109260)) BOUND_VARIABLE_109260)) _let_2))))))))) ) 15.39/15.59 ( nat, (one_one nat) ) 15.39/15.59 ( int, (one_one int) ) 15.39/15.59 ( int, pls ) 15.39/15.59 ( int, min_1 ) 15.39/15.59 ( real, pi ) 15.39/15.59 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.39/15.59 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.59 ) 15.39/15.59 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_109299 $$unsorted) (BOUND_VARIABLE_109300 $$unsorted)) (let ((_let_0 (abs_abs X_a))) (let ((_let_1 (fun nat X_a))) (let ((_let_2 (power_power X_a))) (or (not (linordered_idom X_a)) (= (hAPP X_a X_a _let_0 (hAPP nat X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_109299) BOUND_VARIABLE_109300)) (hAPP X_a X_a _let_0 (hAPP nat X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_109299)) BOUND_VARIABLE_109300))))))) ) 15.39/15.59 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.59 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.59 ( int, skv_14, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.59 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.59 ) 15.39/15.59 (instantiation (forall ((X_2 $$unsorted) (N $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member int))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N))) (= (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 X_2) zEven)) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP nat int (hAPP int (fun nat int) (power_power int) X_2) N)) zEven))))))) ) 15.39/15.59 ( s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.59 ( s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.59 ( skv_14, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.59 ) 15.39/15.59 (instantiation (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP real (fun real bool) (ord_less real) (zero_zero real)))) (or (not (hBOOL (hAPP real bool _let_1 X_1))) (not (hBOOL (hAPP real bool _let_1 Y_1))) (= (hAPP real real (hAPP real _let_0 (minus_minus real) (hAPP real real ln X_1)) (hAPP real real ln Y_1)) (hAPP real real ln (hAPP real real (hAPP real _let_0 (inverse_divide real) X_1) Y_1)))))) ) 15.39/15.59 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 15.39/15.59 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.39/15.59 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.39/15.59 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.39/15.59 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.59 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 15.39/15.59 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), pi ) 15.39/15.59 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (one_one real) ) 15.39/15.59 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))), pi ) 15.39/15.59 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 15.39/15.59 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))), (one_one real) ) 15.39/15.59 ) 15.39/15.59 (instantiation (forall ((N_1 $$unsorted) (V_1 $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (plus_plus nat))) (or (not (hBOOL (hAPP int bool nat_neg (hAPP int int (number_number_of int) V_1)))) (= (hAPP nat nat (hAPP nat _let_0 _let_1 (one_one nat)) N_1) (hAPP nat nat suc (hAPP nat nat (hAPP nat _let_0 _let_1 (hAPP int nat (number_number_of nat) V_1)) N_1)))))) ) 15.39/15.59 ( (one_one nat), (hAPP int int bit1 pls) ) 15.39/15.59 ) 15.39/15.59 (instantiation (forall ((N_1 $$unsorted) (V_1 $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (number_number_of nat))) (let ((_let_2 (plus_plus nat))) (or (hBOOL (hAPP int bool nat_neg (hAPP int int (number_number_of int) V_1))) (= (hAPP nat nat suc (hAPP nat nat (hAPP nat _let_0 _let_2 (hAPP int nat _let_1 V_1)) N_1)) (hAPP nat nat (hAPP nat _let_0 _let_2 (hAPP int nat _let_1 (hAPP int int succ V_1))) N_1)))))) ) 15.39/15.59 ( (one_one nat), pls ) 15.39/15.59 ( (one_one nat), (hAPP int int bit1 pls) ) 15.39/15.59 ) 15.39/15.59 (instantiation (forall ((I_1 $$unsorted) (J_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) I_1) J_2))) (not (forall ((K_1 $$unsorted)) (or (not (= J_2 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) I_1) K_1))) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) K_1)))) ))) ) 15.39/15.59 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.59 ) 15.39/15.59 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (BOUND_VARIABLE_109489 $$unsorted) (BOUND_VARIABLE_109490 $$unsorted) (BOUND_VARIABLE_109491 $$unsorted) (BOUND_VARIABLE_109492 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_109490))) (or (not (order X_a)) (not (order X_b)) (not (hBOOL (hAPP X_a bool _let_0 (hAPP X_b X_a BOUND_VARIABLE_109491 BOUND_VARIABLE_109492)))) (not (hBOOL (hAPP X_b bool (hAPP X_b (fun X_b bool) (ord_less_eq X_b) BOUND_VARIABLE_109492) BOUND_VARIABLE_109489))) (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (hBOOL (hAPP X_b bool (hAPP X_b (fun X_b bool) (ord_less_eq X_b) X) Y))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (hAPP X_b X_a BOUND_VARIABLE_109491 X)) (hAPP X_b X_a BOUND_VARIABLE_109491 Y)))) )) (hBOOL (hAPP X_a bool _let_0 (hAPP X_b X_a BOUND_VARIABLE_109491 BOUND_VARIABLE_109489))))) ) 15.39/15.59 ( nat, real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero nat), natceiling, (zero_zero real) ) 15.39/15.59 ( int, int, min_1, pls, (uminus_uminus int), min_1 ) 15.39/15.59 ( int, int, min_1, skv_10, (number_number_of int), pls ) 15.39/15.59 ( int, int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one int), (fact_fact int), (zero_zero int) ) 15.39/15.59 ( int, int, s, s, bit1, pls ) 15.39/15.59 ( int, int, t, min_1, (let ((_let_0 (fun int int))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m))), (one_one int) ) 15.39/15.59 ( int, int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), t, (uminus_uminus int), pls ) 15.39/15.59 ( int, int, (hAPP int int (number_number_of int) pls), skv_4, pred, pls ) 15.39/15.59 ( real, int, (one_one int), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (real_1 int), (zero_zero int) ) 15.39/15.59 ( real, int, pls, pi, (number_number_of real), min_1 ) 15.39/15.59 ( real, real, pi, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.59 ( real, real, pi, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), sqrt, (zero_zero real) ) 15.39/15.59 ( real, real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real), cos, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.59 ( real, real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (inverse_inverse real), (zero_zero real) ) 15.39/15.59 ( real, real, skv_3, (one_one real), arctan, (zero_zero real) ) 15.39/15.59 ) 15.39/15.59 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_109531 $$unsorted) (BOUND_VARIABLE_109532 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (inverse_inverse X_a))) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_109531) BOUND_VARIABLE_109532))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) (zero_zero X_a)) BOUND_VARIABLE_109531))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_109532)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_109531))))))) ) 15.39/15.59 ( int, (one_one int), t ) 15.39/15.59 ( int, (zero_zero int), (one_one int) ) 15.39/15.59 ( int, (zero_zero int), min_1 ) 15.39/15.59 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.59 ( int, (zero_zero int), s ) 15.39/15.59 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.39/15.59 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.39/15.59 ( int, (zero_zero int), skv_4 ) 15.39/15.59 ( int, (zero_zero int), skv_10 ) 15.39/15.59 ( int, min_1, pls ) 15.39/15.59 ( int, min_1, min_1 ) 15.39/15.59 ( real, (zero_zero real), pi ) 15.39/15.59 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.59 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.59 ( real, (zero_zero real), skv_3 ) 15.39/15.59 ( real, (zero_zero real), skv_5 ) 15.39/15.59 ( real, (zero_zero real), skv_7 ) 15.39/15.59 ( real, (zero_zero real), skv_12 ) 15.39/15.59 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.39/15.59 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.59 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.39/15.59 ( real, skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.59 ) 15.39/15.59 (instantiation (forall ((A_2 $$unsorted) (P_4 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (fun (fun int bool) bool))) (let ((_let_2 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))) (or (not (hBOOL (hAPP int bool zprime P_4))) (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) _let_2) P_4))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (hAPP int (fun int (fun int bool)) zcong A_2) (zero_zero int)) P_4)) (hBOOL (hAPP int bool (hAPP int (fun int bool) quadRes P_4) A_2)) (= (hAPP int int (hAPP int _let_0 (div_div int) (hAPP int int (hAPP int _let_0 (minus_minus int) P_4) (one_one int))) _let_2) (hAPP nat int (semiring_1_of_nat int) (hAPP _let_1 nat (finite_card (fun int bool)) (hAPP int _let_1 (hAPP int (fun int _let_1) setS A_2) P_4)))))))) ) 15.39/15.59 ( (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.39/15.59 ) 15.39/15.59 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_109570 $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (field_char_0 X_a)) (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_109570)) (field_char_0_Rats X_a))))) ) 15.39/15.59 ( real, (one_one int) ) 15.39/15.59 ( real, (zero_zero int) ) 15.39/15.59 ) 15.39/15.59 (instantiation (forall ((S $$unsorted)) (= (forall ((M_2 $$unsorted)) (not (forall ((N_2 $$unsorted)) (let ((_let_0 (fun nat bool))) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) M_2) N_2))) (not (hBOOL (hAPP _let_0 bool (hAPP nat (fun _let_0 bool) (member nat) N_2) S))))) )) ) (not (hBOOL (hAPP (fun nat bool) bool (finite_finite_1 nat) S)))) ) 15.39/15.59 ( (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 15.39/15.59 ) 15.39/15.59 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_109599 $$unsorted) (BOUND_VARIABLE_109600 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)))) (or (not (linord20386208strict X_a)) (not (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_109599) BOUND_VARIABLE_109600)))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_109600))) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_109599)))) ) 15.39/15.59 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 15.39/15.59 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.39/15.59 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13 ) 15.39/15.59 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.39/15.59 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.39/15.59 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.39/15.59 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 15.39/15.59 ( complex, ii, ii ) 15.39/15.59 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 15.39/15.59 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 15.39/15.59 ) 15.39/15.59 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (minus T_1)) (minus (fun T_2 T_1))) ) 15.39/15.59 ( bool, bool ) 15.39/15.59 ( bool, (fun bool bool) ) 15.39/15.59 ( nat, bool ) 15.39/15.59 ( nat, nat ) 15.39/15.59 ( nat, int ) 15.39/15.59 ( nat, (fun int int) ) 15.39/15.59 ( nat, (fun nat bool) ) 15.39/15.59 ( nat, (fun nat nat) ) 15.39/15.59 ( nat, (product_prod nat nat) ) 15.39/15.59 ( nat, (fun (product_prod nat nat) bool) ) 15.39/15.59 ( nat, (fun nat (fun (product_prod nat nat) bool)) ) 15.39/15.59 ( nat, real ) 15.39/15.59 ( nat, (fun real real) ) 15.39/15.59 ( nat, rat ) 15.39/15.59 ( nat, (fun nat (fun nat bool)) ) 15.39/15.59 ( nat, complex ) 15.39/15.59 ( nat, (product_prod int int) ) 15.39/15.59 ( nat, (fun bool bool) ) 15.39/15.59 ( nat, (product_prod real real) ) 15.39/15.59 ( nat, (fun nat (product_prod nat nat)) ) 15.39/15.59 ( nat, (fun nat (product_prod int int)) ) 15.39/15.59 ( int, bool ) 15.39/15.59 ( int, nat ) 15.39/15.59 ( int, int ) 15.39/15.59 ( int, (fun int bool) ) 15.39/15.59 ( int, (fun int (fun int bool)) ) 15.39/15.59 ( int, (fun int int) ) 15.39/15.59 ( int, (fun nat bool) ) 15.39/15.59 ( int, (fun nat nat) ) 15.39/15.59 ( int, real ) 15.39/15.59 ( int, (fun real real) ) 15.39/15.59 ( int, rat ) 15.39/15.59 ( int, (fun int rat) ) 15.39/15.59 ( int, (fun nat int) ) 15.39/15.59 ( int, (fun nat real) ) 15.39/15.59 ( int, (product_prod int int) ) 15.39/15.59 ( int, (fun int (product_prod int int)) ) 15.39/15.59 ( int, (fun (fun int bool) bool) ) 15.39/15.59 ( int, quickcheck_code_int ) 15.39/15.59 ( int, (fun bool bool) ) 15.39/15.59 ( int, (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 15.39/15.59 ( int, (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)) ) 15.39/15.59 ( int, (fun int (fun int (fun int bool))) ) 15.39/15.59 ( int, (fun (product_prod int int) bool) ) 15.39/15.59 ( int, (fun int (fun (product_prod int int) bool)) ) 15.39/15.59 ( int, (fun int (fun bool bool)) ) 15.39/15.59 ( int, (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 15.39/15.59 ( int, (fun (fun int int) (fun int bool)) ) 15.39/15.59 ( int, (fun (product_prod int int) int) ) 15.39/15.59 ( int, (product_prod int (product_prod int int)) ) 15.39/15.59 ( int, (fun int (product_prod int (product_prod int int))) ) 15.39/15.59 ( int, (fun int (fun int (product_prod int (product_prod int int)))) ) 15.39/15.59 ( int, (fun int (fun int (fun int (product_prod int (product_prod int int))))) ) 15.39/15.59 ( int, (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))) ) 15.39/15.59 ( int, (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))) ) 15.39/15.59 ( int, (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))) ) 15.39/15.59 ( int, (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))))) ) 15.39/15.59 ( int, (fun int (fun (fun int bool) bool)) ) 15.39/15.59 ( int, (list int) ) 15.39/15.59 ( int, (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 15.39/15.59 ( int, (fun int real) ) 15.39/15.59 ( int, (fun nat (fun bool bool)) ) 15.39/15.59 ( int, (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 15.39/15.59 ( int, (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 15.39/15.59 ( (fun int bool), bool ) 15.39/15.59 ( (fun int bool), int ) 15.39/15.59 ( (fun int bool), (fun int bool) ) 15.39/15.59 ( (fun int bool), (fun int (fun int bool)) ) 15.39/15.59 ( (fun int bool), (fun int (fun int int)) ) 15.39/15.59 ( (fun int bool), (fun int (fun bool bool)) ) 15.39/15.59 ( (fun int bool), (fun (fun int int) (fun int bool)) ) 15.39/15.59 ( (fun int bool), (fun real (fun int (fun int bool))) ) 15.39/15.59 ( (fun int (fun int bool)), (fun int bool) ) 15.39/15.59 ( (fun int (fun int bool)), (fun int (fun int bool)) ) 15.39/15.59 ( (fun int (fun int bool)), (fun int (fun (fun int int) (fun int bool))) ) 15.39/15.59 ( (fun int (fun int bool)), (fun int (fun int (fun bool bool))) ) 15.39/15.59 ( (fun int int), (fun int bool) ) 15.39/15.59 ( (fun int int), (fun int (fun int bool)) ) 15.39/15.59 ( (fun int int), (fun int int) ) 15.39/15.59 ( (fun int int), (fun int (fun int int)) ) 15.39/15.59 ( (fun int int), (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 15.39/15.59 ( (fun int int), (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 15.39/15.59 ( (fun nat bool), bool ) 15.39/15.59 ( (fun nat bool), (fun nat bool) ) 15.39/15.59 ( (fun nat bool), (fun nat (fun bool bool)) ) 15.39/15.59 ( (fun nat bool), (fun int (fun nat bool)) ) 15.39/15.59 ( (fun nat bool), (fun real (fun int (fun nat bool))) ) 15.39/15.59 ( (fun nat nat), (fun nat (fun nat bool)) ) 15.39/15.59 ( (fun nat nat), (fun nat real) ) 15.39/15.59 ( (fun nat nat), (fun nat (fun nat nat)) ) 15.39/15.59 ( (product_prod nat nat), bool ) 15.39/15.59 ( (product_prod nat nat), (fun (product_prod nat nat) bool) ) 15.39/15.59 ( real, bool ) 15.39/15.59 ( real, nat ) 15.39/15.59 ( real, (fun int bool) ) 15.39/15.59 ( real, (fun int (fun int bool)) ) 15.39/15.59 ( real, real ) 15.39/15.59 ( real, (fun real bool) ) 15.39/15.59 ( real, (fun real real) ) 15.39/15.59 ( real, complex ) 15.39/15.59 ( real, (fun nat real) ) 15.39/15.59 ( real, (fun real complex) ) 15.39/15.59 ( real, (fun bool bool) ) 15.39/15.59 ( real, (fun (filter nat) bool) ) 15.39/15.59 ( real, (fun nat (product_prod real real)) ) 15.39/15.59 ( real, (fun real (fun nat (product_prod real real))) ) 15.39/15.59 ( real, (fun (filter real) bool) ) 15.39/15.59 ( real, (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 15.39/15.59 ( real, (let ((_let_0 (fun int bool))) (fun _let_0 (fun int _let_0))) ) 15.39/15.59 ( real, (fun int (fun int (fun bool bool))) ) 15.39/15.59 ( real, (fun (fun int (fun int real)) (fun int (fun int bool))) ) 15.39/15.59 ( real, (fun (fun int real) (fun int bool)) ) 15.39/15.59 ( real, (fun int (fun nat bool)) ) 15.39/15.59 ( real, (let ((_let_0 (fun nat bool))) (fun _let_0 (fun int _let_0))) ) 15.39/15.59 ( real, (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 15.39/15.59 ( real, (fun int (fun nat (fun bool bool))) ) 15.39/15.59 ( real, (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 15.39/15.59 ( real, (fun (fun nat real) (fun nat bool)) ) 15.39/15.59 ( (fun real bool), real ) 15.39/15.59 ( (fun real bool), (fun real bool) ) 15.39/15.59 ( (fun real bool), (fun real (fun bool bool)) ) 15.39/15.59 ( (fun real bool), (fun (fun int real) (fun int bool)) ) 15.39/15.59 ( (fun real bool), (fun (fun nat real) (fun nat bool)) ) 15.39/15.59 ( (fun real real), (fun real real) ) 15.39/15.59 ( (fun real real), (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 15.39/15.59 ( (fun real real), (fun real (fun real real)) ) 15.39/15.59 ( (fun real real), (fun real (fun real bool)) ) 15.39/15.59 ( (fun real real), (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 15.39/15.59 ( rat, real ) 15.39/15.59 ( rat, (product_prod int int) ) 15.39/15.59 ( complex, nat ) 15.39/15.59 ( complex, real ) 15.39/15.59 ( complex, complex ) 15.39/15.59 ( (fun nat real), (fun nat bool) ) 15.39/15.59 ( (fun nat real), (fun nat real) ) 15.39/15.60 ( (fun nat real), (fun nat (fun real real)) ) 15.39/15.60 ( (fun nat real), (fun int (fun nat real)) ) 15.39/15.60 ( (filter nat), bool ) 15.39/15.60 ( (fun int (fun int int)), (fun int (fun int (fun int bool))) ) 15.39/15.60 ( (fun int (fun int int)), (let ((_let_0 (fun int int))) (fun int (fun _let_0 _let_0))) ) 15.39/15.60 ( (product_prod int int), bool ) 15.39/15.60 ( (product_prod int int), int ) 15.39/15.60 ( (product_prod int int), (fun int bool) ) 15.39/15.60 ( (product_prod int int), (fun int int) ) 15.39/15.60 ( (product_prod int int), rat ) 15.39/15.60 ( (product_prod int int), (product_prod int int) ) 15.39/15.60 ( (product_prod int int), (fun bool bool) ) 15.39/15.60 ( (product_prod int int), (fun (product_prod int int) bool) ) 15.39/15.60 ( (product_prod int int), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 15.39/15.60 ( (product_prod int int), (fun (product_prod int int) (fun int bool)) ) 15.39/15.60 ( (product_prod int int), (fun (product_prod int int) int) ) 15.39/15.60 ( (product_prod int int), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 15.39/15.60 ( (product_prod int int), (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 15.39/15.60 ( quickcheck_code_int, nat ) 15.39/15.60 ( quickcheck_code_int, int ) 15.39/15.60 ( quickcheck_code_int, (product_prod quickcheck_code_int quickcheck_code_int) ) 15.39/15.60 ( quickcheck_code_int, (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int)) ) 15.39/15.60 ( (fun bool bool), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 15.39/15.60 ( code_code_numeral, nat ) 15.39/15.60 ( code_code_numeral, int ) 15.39/15.60 ( code_code_numeral, (fun nat nat) ) 15.39/15.60 ( code_code_numeral, code_code_numeral ) 15.39/15.60 ( code_code_numeral, (product_prod code_code_numeral code_code_numeral) ) 15.39/15.60 ( code_code_numeral, (fun code_code_numeral (product_prod code_code_numeral code_code_numeral)) ) 15.39/15.60 ( (fun int (fun int (fun int bool))), (fun int (fun int (fun int bool))) ) 15.39/15.60 ( (fun real (fun real bool)), (fun real (fun (fun int real) (fun int bool))) ) 15.39/15.60 ( (fun real (fun real bool)), (fun real (fun (fun nat real) (fun nat bool))) ) 15.39/15.60 ( (product_prod real real), bool ) 15.39/15.60 ( (fun (product_prod real real) bool), (fun real (fun real (fun nat (product_prod real real)))) ) 15.39/15.60 ( (fun (product_prod int int) bool), (fun (product_prod int int) bool) ) 15.39/15.60 ( (fun (product_prod int int) bool), (fun (product_prod int int) (fun bool bool)) ) 15.39/15.60 ( (fun int (fun bool bool)), (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 15.39/15.60 ( (fun nat rat), bool ) 15.39/15.60 ( (filter real), bool ) 15.39/15.60 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)), bool ) 15.39/15.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 15.39/15.60 ( (fun (product_prod int int) (fun bool bool)), (let ((_let_0 (fun (product_prod int int) bool))) (fun (product_prod int int) (fun _let_0 _let_0))) ) 15.39/15.60 ( (fun (product_prod int int) (fun int bool)), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 15.39/15.60 ( (fun (product_prod int int) int), (fun (product_prod int int) bool) ) 15.39/15.60 ( (fun (product_prod int int) int), (fun (product_prod int int) (fun int bool)) ) 15.39/15.60 ( (fun (product_prod int int) int), (fun (product_prod int int) int) ) 15.39/15.60 ( (fun (product_prod int int) int), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))) ) 15.39/15.60 ( (fun (product_prod int int) int), (fun (product_prod int int) (fun int int)) ) 15.39/15.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 15.39/15.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 (fun int bool)))) ) 15.39/15.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 (fun int bool)))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun (fun _let_0 int) (fun _let_0 bool)))) ) 15.39/15.60 ( (fun (product_prod int int) (fun int int)), (let ((_let_0 (fun (product_prod int int) int))) (fun (product_prod int int) (fun _let_0 _let_0))) ) 15.39/15.60 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), bool ) 15.39/15.60 ( (fun int real), (fun int bool) ) 15.39/15.60 ( (fun int real), (fun int real) ) 15.39/15.60 ( (fun int real), (fun int (fun int real)) ) 15.39/15.60 ( (fun int real), (fun int (fun real real)) ) 15.39/15.60 ( (fun nat (fun bool bool)), (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 15.39/15.60 ( (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun int bool))) (fun _let_0 (fun int _let_0))) ) 15.39/15.60 ( (fun int (fun int (fun bool bool))), (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 15.39/15.60 ( (fun real (fun int bool)), (fun real bool) ) 15.39/15.60 ( (fun real (fun int (fun int bool))), (fun real (fun int bool)) ) 15.39/15.60 ( (fun real (fun int (fun int bool))), (fun real (fun int (fun int (fun bool bool)))) ) 15.39/15.60 ( (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun int bool))) (fun real (fun _let_0 (fun int _let_0)))) ) 15.39/15.60 ( (fun real (fun int (fun int (fun bool bool)))), (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))) ) 15.39/15.60 ( (fun int (fun int real)), (fun int (fun int bool)) ) 15.39/15.60 ( (fun int (fun int real)), (fun real (fun int (fun int bool))) ) 15.39/15.60 ( (fun (fun int real) (fun int bool)), (fun (fun int (fun int real)) (fun int (fun int bool))) ) 15.39/15.60 ( (fun real (fun (fun int real) (fun int bool))), (fun real (fun (fun int (fun int real)) (fun int (fun int bool)))) ) 15.39/15.60 ( (fun int (fun real real)), (let ((_let_0 (fun int real))) (fun int (fun _let_0 _let_0))) ) 15.39/15.60 ( (fun int (fun real real)), (let ((_let_0 (fun nat real))) (fun int (fun _let_0 _let_0))) ) 15.39/15.60 ( (fun int (fun nat bool)), (fun int bool) ) 15.39/15.60 ( (fun int (fun nat bool)), (fun int (fun nat (fun bool bool))) ) 15.39/15.60 ( (fun real (fun int (fun nat bool))), (fun real (fun int bool)) ) 15.39/15.60 ( (fun real (fun int (fun nat bool))), (fun real (fun int (fun nat (fun bool bool)))) ) 15.39/15.60 ( (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun nat bool))) (fun _let_0 (fun int _let_0))) ) 15.39/15.60 ( (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun nat bool))) (fun real (fun _let_0 (fun int _let_0)))) ) 15.39/15.60 ( (fun int (fun nat (fun bool bool))), (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 15.39/15.60 ( (fun real (fun int (fun nat (fun bool bool)))), (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))) ) 15.39/15.60 ( (fun int (fun nat real)), (fun int (fun nat bool)) ) 15.39/15.60 ( (fun int (fun nat real)), (fun real (fun int (fun nat bool))) ) 15.39/15.60 ( (fun (fun nat real) (fun nat bool)), (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 15.39/15.60 ( (fun real (fun (fun nat real) (fun nat bool))), (fun real (fun (fun int (fun nat real)) (fun int (fun nat bool)))) ) 15.39/15.60 ) 15.39/15.60 (instantiation (forall ((N_1 $$unsorted)) (= (hAPP real real cos (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP nat real (real_1 nat) N_1)) pi)) (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP int real (number_number_of real) min_1)) N_1)) ) 15.39/15.60 ( (zero_zero nat) ) 15.39/15.60 ( (hAPP nat nat suc (zero_zero nat)) ) 15.39/15.60 ) 15.39/15.60 (instantiation (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) Y_1))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real sqrt X_1)) (hAPP real real sqrt Y_1)))))) ) 15.39/15.60 ( (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.60 ( (zero_zero real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.60 ) 15.39/15.60 (instantiation (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun int bool))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong A_2) B_1) (zero_zero int))) (= (ti int B_1) (ti int A_2)))) ) 15.39/15.60 ( s1, s ) 15.39/15.60 ( s1, skv_4 ) 15.39/15.60 ( s1, skv_10 ) 15.39/15.60 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.39/15.60 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.60 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.39/15.60 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.39/15.60 ) 15.39/15.60 (instantiation (forall ((W $$unsorted)) (not (= ii (hAPP int complex (number_number_of complex) W))) ) 15.39/15.60 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.39/15.60 ( min_1 ) 15.39/15.60 ) 15.39/15.60 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_109682 $$unsorted) (BOUND_VARIABLE_109683 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (or (not (ab_group_add X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 (plus_plus X_a) BOUND_VARIABLE_109682) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_109683)) (hAPP X_a X_a (hAPP X_a _let_0 (minus_minus X_a) BOUND_VARIABLE_109682) BOUND_VARIABLE_109683)))) ) 15.39/15.60 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.39/15.60 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 15.39/15.60 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 15.39/15.60 ) 15.39/15.60 (instantiation (forall ((Q_3 $$unsorted)) (let ((_let_0 (hAPP rat rat (sgn_sgn rat) Q_3))) (let ((_let_1 (hBOOL (hAPP rat bool (hAPP rat (fun rat bool) (ord_less rat) (zero_zero rat)) Q_3)))) (let ((_let_2 (one_one rat))) (or (= (zero_zero rat) Q_3) (and (or (not _let_1) (= _let_0 _let_2)) (or _let_1 (= _let_0 (hAPP rat rat (uminus_uminus rat) _let_2)))))))) ) 15.39/15.60 ( (zero_zero rat) ) 15.39/15.60 ) 15.39/15.60 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_109732 $$unsorted)) (or (not (comm_semiring_1 X_a)) (= (ti X_a BOUND_VARIABLE_109732) (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_109732) (one_one nat)))) ) 15.39/15.60 ( bool, fFalse ) 15.39/15.60 ( bool, fTrue ) 15.39/15.60 ( int, pls ) 15.39/15.60 ( int, min_1 ) 15.39/15.60 ( int, s ) 15.39/15.60 ( int, m ) 15.39/15.60 ( int, s1 ) 15.39/15.60 ( int, t ) 15.39/15.60 ( int, skv_14 ) 15.39/15.60 ( (fun int bool), nat_neg ) 15.39/15.60 ( (fun int bool), zprime ) 15.39/15.60 ( (fun int bool), zEven ) 15.39/15.60 ( (fun int bool), zOdd ) 15.39/15.60 ( (fun int bool), (even_odd_even int) ) 15.39/15.60 ( (fun int bool), twoSqu1091635170sum2sq ) 15.39/15.60 ( (fun int bool), nat_is_nat ) 15.39/15.60 ( (fun int (fun int bool)), norRRset ) 15.39/15.60 ( (fun int (fun int bool)), quadRes ) 15.39/15.60 ( (fun int (fun int bool)), sRStar ) 15.39/15.60 ( (fun int (fun int bool)), d22set ) 15.39/15.60 ( (fun int (fun int bool)), sr ) 15.39/15.60 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 15.39/15.60 ( (fun int int), zfact ) 15.39/15.60 ( (fun int int), bit0 ) 15.39/15.60 ( (fun int int), bit1 ) 15.39/15.60 ( (fun int int), (fact_fact int) ) 15.39/15.60 ( (fun int int), pred ) 15.39/15.60 ( (fun int int), succ ) 15.39/15.60 ( (fun nat bool), (even_odd_even nat) ) 15.39/15.60 ( (fun nat bool), prime ) 15.39/15.60 ( (fun nat nat), suc ) 15.39/15.60 ( (fun nat nat), (fact_fact nat) ) 15.39/15.60 ( (fun nat nat), fact ) 15.39/15.60 ( (fun nat nat), nat_size ) 15.39/15.60 ( (fun nat nat), (size_size nat) ) 15.39/15.60 ( (fun (product_prod nat nat) bool), pred_nat ) 15.39/15.60 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 15.39/15.60 ( real, pi ) 15.39/15.60 ( real, (hAPP int real (number_number_of real) min_1) ) 15.39/15.60 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.60 ( (fun real real), ln ) 15.39/15.60 ( (fun real real), cos ) 15.39/15.60 ( (fun real real), sqrt ) 15.39/15.60 ( (fun real real), sin ) 15.39/15.60 ( (fun real real), arccos ) 15.39/15.60 ( (fun real real), arcsin ) 15.39/15.60 ( (fun real real), tan ) 15.39/15.60 ( (fun real real), arctan ) 15.39/15.60 ( (fun nat (fun nat bool)), coprime ) 15.39/15.60 ( complex, ii ) 15.39/15.60 ( (fun nat real), (real_1 nat) ) 15.39/15.60 ( (fun nat real), sin_coeff ) 15.39/15.60 ( (fun nat real), cos_coeff ) 15.39/15.60 ( (filter nat), sequentially ) 15.39/15.60 ( (fun int (fun int int)), (gcd_gcd int) ) 15.39/15.60 ( (fun int (fun int int)), legendre ) 15.39/15.60 ( (fun int (fun int int)), legacy_zgcd ) 15.39/15.60 ( (fun int (fun int int)), standardRes ) 15.39/15.60 ( (fun int (fun int int)), nat_tsub ) 15.39/15.60 ( (fun int (fun int int)), multInv ) 15.39/15.60 ( (fun int (fun int int)), z3mod ) 15.39/15.60 ( (fun int (fun int int)), z3div ) 15.39/15.60 ( (fun int (fun int int)), int_gcd ) 15.39/15.60 ( (fun int (fun int int)), int_lcm ) 15.39/15.60 ( (fun int (fun int int)), inv ) 15.39/15.60 ( (fun complex complex), expi ) 15.39/15.60 ( (fun complex complex), cnj ) 15.39/15.60 ( (fun real complex), cis ) 15.39/15.60 ( (fun int nat), nat_1 ) 15.39/15.60 ( (fun int nat), phi ) 15.39/15.60 ( (fun (fun int bool) bool), nat_nat_set ) 15.39/15.60 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 15.39/15.60 ( (fun nat (fun nat nat)), nat_gcd ) 15.39/15.60 ( (fun nat (fun nat nat)), nat_lcm ) 15.39/15.60 ( (fun (fun int bool) int), (the int) ) 15.39/15.60 ( (fun complex real), re ) 15.39/15.60 ( (fun complex real), im ) 15.39/15.60 ( (fun complex real), arg ) 15.39/15.60 ( (fun bool bool), fNot ) 15.39/15.60 ( (fun nat (fun real real)), root ) 15.39/15.60 ( (fun real (fun real real)), log ) 15.39/15.60 ( (fun real (fun real real)), powr ) 15.39/15.60 ( (fun bool (fun bool bool)), fimplies ) 15.39/15.60 ( (fun bool (fun bool bool)), fconj ) 15.39/15.60 ( (fun bool (fun bool bool)), fdisj ) 15.39/15.60 ( (fun int (fun int (product_prod int int))), negDivAlg ) 15.39/15.60 ( (fun int (fun int (product_prod int int))), posDivAlg ) 15.39/15.60 ( (fun int (fun int (product_prod int int))), divmod_int ) 15.39/15.60 ( (fun int (fun int (product_prod int int))), pdivmod ) 15.39/15.60 ( (fun int (fun int (product_prod int int))), norm_frac ) 15.39/15.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 15.39/15.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 15.39/15.60 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 15.39/15.60 ( (fun int (fun int (fun int bool))), zcong ) 15.39/15.60 ( (fun int (fun int (fun int bool))), zcongm ) 15.39/15.60 ( (fun int (fun int (fun int bool))), noXRRset ) 15.39/15.60 ( (fun int (fun int (fun int bool))), bnorRset ) 15.39/15.60 ( (fun int (fun int (fun int bool))), wset ) 15.39/15.60 ( (fun (product_prod int int) bool), frac_1 ) 15.39/15.60 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 15.39/15.60 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 15.39/15.60 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 15.39/15.60 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 15.39/15.60 ( (fun (fun nat rat) bool), vanishes ) 15.39/15.60 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 15.39/15.60 ( (fun code_code_numeral nat), code_c271388182l_size ) 15.39/15.60 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 15.39/15.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 15.39/15.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 15.39/15.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 15.39/15.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 15.39/15.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 15.39/15.60 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 15.39/15.60 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 15.39/15.60 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 15.39/15.60 ( (fun complex nat), complex_size ) 15.39/15.60 ( (fun complex nat), (size_size complex) ) 15.39/15.60 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 15.39/15.60 ( (fun nat (fun nat (product_prod int int))), bezw ) 15.39/15.60 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 15.39/15.60 ( (fun int (fun nat nat)), nat_aux ) 15.39/15.60 ( (fun int (fun (fun int bool) bool)), rsetR ) 15.39/15.60 ( (fun int (fun (fun int bool) bool)), resSet ) 15.39/15.60 ( (fun int (list int)), quickc666637781d_zero ) 15.39/15.60 ( (fun (product_prod int int) rat), frct ) 15.39/15.60 ( (fun int (fun int rat)), fract ) 15.39/15.60 ( (fun real (fun real complex)), complex_1 ) 15.39/15.60 ( (fun real (fun real complex)), rcis ) 15.39/15.60 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 15.39/15.60 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 15.39/15.60 ( (fun int real), (real_1 int) ) 15.39/15.60 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 15.39/15.60 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 15.39/15.60 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 15.39/15.60 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 15.39/15.60 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 15.39/15.60 ( (fun real nat), natfloor ) 15.39/15.60 ( (fun real nat), natceiling ) 15.39/15.60 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 15.39/15.60 ( (fun quickcheck_code_int int), quickcheck_int_of ) 15.39/15.60 ( (fun rat (product_prod int int)), quotient_of ) 15.39/15.60 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 15.39/15.60 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 15.39/15.60 ( (fun rat real), ratreal ) 15.39/15.60 ( (fun code_code_numeral int), code_int_of ) 15.39/15.60 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 15.39/15.60 ( (fun int quickcheck_code_int), quickcheck_of_int ) 15.39/15.60 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 15.39/15.60 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 15.39/15.60 ) 15.39/15.60 (instantiation (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (inverse_divide real))) (let ((_let_2 (hAPP nat _let_0 root N_1))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_1))) (= (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real _let_2 X_1)) (hAPP real real _let_2 Y_1)) (hAPP real real _let_2 (hAPP real real (hAPP real _let_0 _let_1 X_1) Y_1))))))) ) 15.39/15.60 ( (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.60 ) 15.39/15.60 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (hAPP real (fun real bool) (ord_less real) (zero_zero real)))) (or (not (hBOOL (hAPP real bool _let_0 X_1))) (hBOOL (hAPP real bool _let_0 (hAPP real real sqrt X_1))))) ) 15.39/15.60 ( (one_one real) ) 15.39/15.60 ( (zero_zero real) ) 15.39/15.60 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.60 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.39/15.60 ) 15.39/15.60 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_109829 $$unsorted) (BOUND_VARIABLE_109830 $$unsorted)) (or (not (semiring_div X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_109829) BOUND_VARIABLE_109830))) (= (zero_zero X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (div_mod X_a) BOUND_VARIABLE_109830) BOUND_VARIABLE_109829))) ) 15.39/15.60 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 15.39/15.60 ) 15.39/15.60 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_109849 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (mult_zero X_a)) (= _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_109849) _let_0)))) ) 15.39/15.60 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.60 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.60 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.39/15.60 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.60 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.60 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 15.39/15.60 ( complex, ii ) 15.39/15.60 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.39/15.60 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 15.39/15.60 ) 15.39/15.60 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_109859 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (or (not (ordered_ab_group_add X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_109859)) _let_2)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_109859))))))) ) 15.39/15.60 ( int, (one_one int) ) 15.39/15.60 ( int, pls ) 15.39/15.60 ( int, min_1 ) 15.39/15.60 ( real, (one_one real) ) 15.39/15.60 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.39/15.60 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.39/15.60 ( complex, (one_one complex) ) 15.39/15.60 ( complex, ii ) 15.39/15.60 ) 15.44/15.60 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_109892 $$unsorted) (BOUND_VARIABLE_109893 $$unsorted) (BOUND_VARIABLE_109894 $$unsorted) (BOUND_VARIABLE_109895 $$unsorted)) (let ((_let_0 (fun X_b bool))) (or (not (order X_a)) (not (order X_b)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_109894) BOUND_VARIABLE_109895))) (not (hBOOL (hAPP X_b bool (hAPP X_b _let_0 (ord_less_eq X_b) BOUND_VARIABLE_109892) (hAPP X_a X_b BOUND_VARIABLE_109893 BOUND_VARIABLE_109894)))) (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) Y) X))) (hBOOL (hAPP X_b bool (hAPP X_b _let_0 (ord_less X_b) (hAPP X_a X_b BOUND_VARIABLE_109893 Y)) (hAPP X_a X_b BOUND_VARIABLE_109893 X)))) )) (hBOOL (hAPP X_b bool (hAPP X_b _let_0 (ord_less X_b) BOUND_VARIABLE_109892) (hAPP X_a X_b BOUND_VARIABLE_109893 BOUND_VARIABLE_109895))))) ) 15.44/15.60 ( int, int, (one_one int), (let ((_let_0 (fun int int))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m))), (one_one int), t ) 15.44/15.60 ( int, int, (zero_zero int), (uminus_uminus int), min_1, min_1 ) 15.44/15.60 ( int, int, min_1, bit1, pls, pls ) 15.44/15.60 ( real, int, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (number_number_of real), min_1, pls ) 15.44/15.60 ( real, real, (zero_zero real), cos, pi, (zero_zero real) ) 15.44/15.60 ( real, real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), cos, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.60 ( real, real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), sin, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.44/15.60 ( real, real, skv_5, sqrt, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.44/15.60 ) 15.44/15.60 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int int (hAPP int (fun int int) (plus_plus int) pls) K_4) (ti int K_4)) ) 15.44/15.60 ( pls ) 15.44/15.60 ( min_1 ) 15.44/15.60 ( s ) 15.44/15.60 ( m ) 15.44/15.60 ( s1 ) 15.44/15.60 ( t ) 15.44/15.60 ) 15.44/15.60 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_109932 $$unsorted) (BOUND_VARIABLE_109933 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (inverse_divide X_a))) (let ((_let_2 (uminus_uminus X_a))) (or (not (division_ring X_a)) (= (hAPP X_a X_a _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_109932) BOUND_VARIABLE_109933)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_109932)) BOUND_VARIABLE_109933)))))) ) 15.44/15.60 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.60 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.44/15.60 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.44/15.60 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 15.44/15.60 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.60 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.44/15.60 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.44/15.60 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.44/15.60 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.60 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.60 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.60 ) 15.44/15.60 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_109991 $$unsorted) (BOUND_VARIABLE_109992 $$unsorted) (BOUND_VARIABLE_109993 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_109991))) (or (not (cancel146912293up_add X_a)) (not (= (hAPP X_a X_a _let_0 BOUND_VARIABLE_109992) (hAPP X_a X_a _let_0 BOUND_VARIABLE_109993))) (= (ti X_a BOUND_VARIABLE_109993) (ti X_a BOUND_VARIABLE_109992)))) ) 15.44/15.60 ( nat, (one_one nat), (one_one nat), (one_one nat) ) 15.44/15.60 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int), (one_one int) ) 15.44/15.60 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int), (one_one int) ) 15.44/15.60 ) 15.44/15.60 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_110017 $$unsorted) (BOUND_VARIABLE_110018 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (one_one X_a)))) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_110018))) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_110018) (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_110018) BOUND_VARIABLE_110017)))))) ) 15.44/15.60 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 15.44/15.60 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 15.44/15.60 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_14 ) 15.44/15.60 ( complex, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), ii ) 15.44/15.60 ) 15.44/15.60 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_110098 $$unsorted)) (or (not (linordered_idom X_a)) (not (number_ring X_a)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) BOUND_VARIABLE_110098) (hAPP int int bit1 pls))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_110098)) (one_one X_a))))) ) 15.44/15.60 ( nat, pls ) 15.44/15.60 ( nat, (hAPP int int bit1 pls) ) 15.44/15.60 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.44/15.60 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.44/15.60 ( int, pls ) 15.44/15.60 ( int, (hAPP int int bit1 pls) ) 15.44/15.60 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.44/15.60 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.44/15.60 ( int, min_1 ) 15.44/15.60 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.60 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.44/15.60 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.44/15.60 ( real, min_1 ) 15.44/15.60 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.60 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.44/15.60 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.60 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 15.44/15.60 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.44/15.60 ( complex, min_1 ) 15.44/15.60 ( quickcheck_code_int, (one_one int) ) 15.44/15.60 ( quickcheck_code_int, (zero_zero int) ) 15.44/15.60 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 15.44/15.60 ( code_code_numeral, pls ) 15.44/15.60 ( code_code_numeral, (hAPP int int bit1 pls) ) 15.44/15.60 ) 15.44/15.60 (instantiation (forall ((Z_3 $$unsorted) (Z $$unsorted)) (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)))) (or (not (hBOOL (hAPP int bool _let_0 Z))) (not (hBOOL (hAPP int bool _let_0 Z_3))) (= (= (ti int Z) (ti int Z_3)) (= (hAPP int nat nat_1 Z_3) (hAPP int nat nat_1 Z))))) ) 15.44/15.60 ( (one_one int), s ) 15.44/15.60 ( min_1, (hAPP int int (number_number_of int) pls) ) 15.44/15.60 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.44/15.60 ( s, (one_one int) ) 15.44/15.60 ( s, s ) 15.44/15.60 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.60 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.44/15.60 ( (hAPP int int (number_number_of int) pls), min_1 ) 15.44/15.60 ( (hAPP int int (number_number_of int) pls), (hAPP int int (number_number_of int) pls) ) 15.44/15.60 ( skv_4, skv_4 ) 15.44/15.60 ( skv_4, skv_10 ) 15.44/15.60 ( skv_10, skv_4 ) 15.44/15.60 ) 15.44/15.60 (instantiation (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (dvd_dvd int) Y_1) X_1))) (= (hAPP int int (hAPP int (fun int int) (gcd_gcd int) X_1) Y_1) (hAPP int int (abs_abs int) Y_1))) ) 15.44/15.60 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 15.44/15.60 ) 15.44/15.60 (instantiation (forall ((W $$unsorted)) (let ((_let_0 (number_number_of int))) (let ((_let_1 (uminus_uminus int))) (= (hAPP int int _let_1 (hAPP int int _let_0 W)) (hAPP int int _let_0 (hAPP int int _let_1 W))))) ) 15.44/15.60 ( (one_one int) ) 15.44/15.60 ( pls ) 15.44/15.60 ( (hAPP int int bit1 pls) ) 15.44/15.60 ( min_1 ) 15.44/15.60 ) 15.44/15.60 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_110220 $$unsorted) (BOUND_VARIABLE_110221 $$unsorted)) (or (not (group_add X_a)) (= (= (zero_zero X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_110220) BOUND_VARIABLE_110221)) (= (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_110221) (ti X_a BOUND_VARIABLE_110220)))) ) 15.44/15.60 ( nat, (one_one nat), (one_one nat) ) 15.44/15.60 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 15.44/15.60 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 15.44/15.60 ) 15.44/15.60 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (ord_less_eq int))) (let ((_let_3 (zero_zero int))) (let ((_let_4 (product_prod int int))) (let ((_let_5 (hAPP int (fun int _let_4) negDivAlg A_1))) (or (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 _let_3) (hAPP int int (hAPP int _let_1 (plus_plus int) A_1) B))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 B) _let_3)) (= (hAPP _let_4 _let_4 (hAPP int (fun _let_4 _let_4) adjust B) (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_1 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) B))) (hAPP int _let_4 _let_5 B))))))))) ) 15.44/15.60 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 15.44/15.60 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 15.44/15.60 ) 15.44/15.60 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (let ((_let_2 (zero_zero int))) (let ((_let_3 (product_prod int int))) (let ((_let_4 (fun int _let_3))) (let ((_let_5 (hAPP int int (hAPP int (fun int int) (plus_plus int) A_1) B))) (or (and (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 B) _let_2))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 _let_2) _let_5)))) (= (hAPP int _let_3 (hAPP int _let_4 negDivAlg A_1) B) (hAPP int _let_3 (hAPP int _let_4 (product_Pair int int) (hAPP int int (number_number_of int) min_1)) _let_5))))))))) ) 15.44/15.60 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 15.44/15.60 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 15.44/15.60 ) 15.44/15.60 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_110262 $$unsorted) (BOUND_VARIABLE_110263 $$unsorted)) (let ((_let_0 (norm_norm X_a))) (or (not (real_n1866405975lgebra X_a)) (= (hAPP X_a real _let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_110262) BOUND_VARIABLE_110263)) (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP X_a real _let_0 BOUND_VARIABLE_110262)) BOUND_VARIABLE_110263)))) ) 15.44/15.60 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.60 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.60 ( int, skv_14, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.60 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.60 ) 15.44/15.60 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (plus_plus X_a))) (or (not (monoid_add X_a)) (= _let_0 (ti (fun X_a (fun X_a X_a)) _let_0)))) ) 15.44/15.60 ( bool ) 15.44/15.60 ( nat ) 15.44/15.60 ( int ) 15.44/15.60 ( (fun int bool) ) 15.44/15.60 ( (fun int (fun int bool)) ) 15.44/15.60 ( (fun int int) ) 15.44/15.60 ( (fun nat bool) ) 15.44/15.60 ( real ) 15.44/15.60 ( (fun real bool) ) 15.44/15.60 ( (fun real real) ) 15.44/15.60 ( rat ) 15.44/15.60 ( complex ) 15.44/15.60 ( (fun nat real) ) 15.44/15.60 ( (product_prod int int) ) 15.44/15.60 ( quickcheck_code_int ) 15.44/15.60 ( code_code_numeral ) 15.44/15.60 ( (fun int (fun int (fun int bool))) ) 15.44/15.60 ( (fun (product_prod int int) bool) ) 15.44/15.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 15.44/15.60 ( (fun (product_prod int int) int) ) 15.44/15.60 ( (fun int real) ) 15.44/15.60 ) 15.44/15.60 (instantiation (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted) (P_1 $$unsorted) (Z $$unsorted)) (let ((_let_0 (fun X_c X_a))) (let ((_let_1 (product_prod X_b X_c))) (= (hAPP _let_1 X_a (hAPP (fun X_b _let_0) (fun _let_1 X_a) (product_prod_case X_b X_c X_a) P_1) Z) (hAPP X_c X_a (hAPP X_b _let_0 P_1 (hAPP _let_1 X_b (product_fst X_b X_c) Z)) (hAPP _let_1 X_c (product_snd X_b X_c) Z))))) ) 15.44/15.60 ( int, int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun _let_0 _let_1))) (let ((_let_3 (fun _let_0 _let_0))) (let ((_let_4 (fun int _let_3))) (let ((_let_5 (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP _let_0 _let_1 (hAPP _let_4 _let_2 (combc int _let_0 _let_0) (hAPP _let_1 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_1 _let_4) (combb _let_0 _let_3 int) (combb int int int)) (hAPP _let_0 _let_1 (hAPP _let_1 _let_2 (combb int _let_0 int) (plus_plus int)) _let_5))) _let_5))))))), (let ((_let_0 (product_prod int int))) (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) s) (one_one int))) ) 15.44/15.60 ) 15.44/15.60 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_110292 $$unsorted)) (or (not (real_n2089651433ebra_1 X_a)) (= (hAPP real real (abs_abs real) BOUND_VARIABLE_110292) (hAPP X_a real (norm_norm X_a) (hAPP real X_a (of_real X_a) BOUND_VARIABLE_110292)))) ) 15.44/15.60 ( complex, pi ) 15.44/15.60 ( complex, (hAPP int real (number_number_of real) min_1) ) 15.44/15.60 ( complex, (hAPP real real (uminus_uminus real) (one_one real)) ) 15.44/15.60 ) 15.44/15.60 (instantiation (forall ((V $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less nat))) (let ((_let_2 (hAPP int int (number_number_of int) (hAPP int int pred V)))) (= (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 (hAPP int nat (number_number_of nat) V)) (hAPP nat nat suc N))) (or (hBOOL (hAPP int bool nat_neg _let_2)) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 (hAPP int nat nat_1 _let_2)) N))))))) ) 15.44/15.60 ( pls, (hAPP nat nat suc (zero_zero nat)) ) 15.44/15.60 ) 15.44/15.60 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (hAPP real _let_0 _let_1 (zero_zero real)))) (or (not (hBOOL (hAPP real bool _let_2 X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))) (hBOOL (hAPP real bool _let_2 (hAPP real real cos X_1))))))) ) 15.44/15.60 ( (one_one real) ) 15.44/15.60 ( (zero_zero real) ) 15.44/15.60 ( pi ) 15.44/15.60 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.60 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.44/15.60 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.44/15.60 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.44/15.60 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.44/15.60 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.44/15.60 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.44/15.60 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 15.44/15.60 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.44/15.60 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.44/15.60 ( skv_5 ) 15.44/15.60 ) 15.44/15.60 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) X_1))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (one_one real)) (hAPP real real (exp real) X_1)))))) ) 15.44/15.60 ( pi ) 15.44/15.60 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.44/15.60 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.44/15.60 ( skv_2 ) 15.44/15.60 ( skv_8 ) 15.44/15.60 ( skv_9 ) 15.44/15.60 ) 15.44/15.60 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_110571 $$unsorted)) (or (not (real_normed_vector X_a)) (= (= (zero_zero real) (hAPP X_a real (norm_norm X_a) BOUND_VARIABLE_110571)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_110571)))) ) 15.44/15.60 ( bool, fFalse ) 15.44/15.60 ( bool, fTrue ) 15.44/15.60 ( int, pls ) 15.44/15.60 ( int, min_1 ) 15.44/15.60 ( int, s ) 15.44/15.60 ( int, m ) 15.44/15.60 ( int, s1 ) 15.44/15.60 ( int, t ) 15.44/15.60 ( (fun int bool), nat_neg ) 15.44/15.60 ( (fun int bool), zprime ) 15.44/15.60 ( (fun int bool), zEven ) 15.44/15.60 ( (fun int bool), zOdd ) 15.44/15.60 ( (fun int bool), (even_odd_even int) ) 15.44/15.60 ( (fun int bool), twoSqu1091635170sum2sq ) 15.44/15.60 ( (fun int bool), nat_is_nat ) 15.44/15.60 ( (fun int (fun int bool)), norRRset ) 15.44/15.60 ( (fun int (fun int bool)), quadRes ) 15.44/15.60 ( (fun int (fun int bool)), sRStar ) 15.44/15.60 ( (fun int (fun int bool)), d22set ) 15.44/15.60 ( (fun int (fun int bool)), sr ) 15.44/15.60 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 15.44/15.60 ( (fun int int), zfact ) 15.44/15.60 ( (fun int int), bit0 ) 15.44/15.60 ( (fun int int), bit1 ) 15.44/15.60 ( (fun int int), (fact_fact int) ) 15.44/15.60 ( (fun int int), pred ) 15.44/15.60 ( (fun int int), succ ) 15.44/15.60 ( (fun nat bool), (even_odd_even nat) ) 15.44/15.60 ( (fun nat bool), prime ) 15.44/15.60 ( (fun nat nat), suc ) 15.44/15.60 ( (fun nat nat), (fact_fact nat) ) 15.44/15.60 ( (fun nat nat), fact ) 15.44/15.60 ( (fun nat nat), nat_size ) 15.44/15.60 ( (fun nat nat), (size_size nat) ) 15.44/15.60 ( (fun (product_prod nat nat) bool), pred_nat ) 15.44/15.60 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 15.44/15.60 ( real, pi ) 15.44/15.60 ( (fun real real), ln ) 15.44/15.60 ( (fun real real), cos ) 15.44/15.60 ( (fun real real), sqrt ) 15.44/15.60 ( (fun real real), sin ) 15.44/15.60 ( (fun real real), arccos ) 15.44/15.60 ( (fun real real), arcsin ) 15.44/15.60 ( (fun real real), tan ) 15.44/15.60 ( (fun real real), arctan ) 15.44/15.60 ( (fun nat (fun nat bool)), coprime ) 15.44/15.60 ( complex, ii ) 15.44/15.60 ( (fun nat real), (real_1 nat) ) 15.44/15.60 ( (fun nat real), sin_coeff ) 15.44/15.60 ( (fun nat real), cos_coeff ) 15.44/15.60 ( (filter nat), sequentially ) 15.44/15.60 ( (fun int (fun int int)), (gcd_gcd int) ) 15.44/15.60 ( (fun int (fun int int)), legendre ) 15.44/15.60 ( (fun int (fun int int)), legacy_zgcd ) 15.44/15.60 ( (fun int (fun int int)), standardRes ) 15.44/15.60 ( (fun int (fun int int)), nat_tsub ) 15.44/15.60 ( (fun int (fun int int)), multInv ) 15.44/15.60 ( (fun int (fun int int)), z3mod ) 15.44/15.60 ( (fun int (fun int int)), z3div ) 15.44/15.60 ( (fun int (fun int int)), int_gcd ) 15.44/15.60 ( (fun int (fun int int)), int_lcm ) 15.44/15.60 ( (fun int (fun int int)), inv ) 15.44/15.60 ( (fun complex complex), expi ) 15.44/15.60 ( (fun complex complex), cnj ) 15.44/15.60 ( (fun real complex), cis ) 15.44/15.60 ( (fun int nat), nat_1 ) 15.44/15.60 ( (fun int nat), phi ) 15.44/15.60 ( (fun (fun int bool) bool), nat_nat_set ) 15.44/15.60 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 15.44/15.60 ( (fun nat (fun nat nat)), nat_gcd ) 15.44/15.60 ( (fun nat (fun nat nat)), nat_lcm ) 15.44/15.60 ( (fun (fun int bool) int), (the int) ) 15.44/15.60 ( (fun complex real), re ) 15.44/15.60 ( (fun complex real), im ) 15.44/15.60 ( (fun complex real), arg ) 15.44/15.60 ( (fun bool bool), fNot ) 15.44/15.60 ( (fun nat (fun real real)), root ) 15.44/15.60 ( (fun real (fun real real)), log ) 15.44/15.60 ( (fun real (fun real real)), powr ) 15.44/15.60 ( (fun bool (fun bool bool)), fimplies ) 15.44/15.60 ( (fun bool (fun bool bool)), fconj ) 15.44/15.60 ( (fun bool (fun bool bool)), fdisj ) 15.44/15.60 ( (fun int (fun int (product_prod int int))), negDivAlg ) 15.44/15.60 ( (fun int (fun int (product_prod int int))), posDivAlg ) 15.44/15.60 ( (fun int (fun int (product_prod int int))), divmod_int ) 15.44/15.60 ( (fun int (fun int (product_prod int int))), pdivmod ) 15.44/15.60 ( (fun int (fun int (product_prod int int))), norm_frac ) 15.44/15.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 15.44/15.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 15.44/15.60 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 15.44/15.60 ( (fun int (fun int (fun int bool))), zcong ) 15.44/15.60 ( (fun int (fun int (fun int bool))), zcongm ) 15.44/15.60 ( (fun int (fun int (fun int bool))), noXRRset ) 15.44/15.60 ( (fun int (fun int (fun int bool))), bnorRset ) 15.44/15.60 ( (fun int (fun int (fun int bool))), wset ) 15.44/15.60 ( (fun (product_prod int int) bool), frac_1 ) 15.44/15.60 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 15.44/15.60 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 15.44/15.60 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 15.44/15.60 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 15.44/15.60 ( (fun (fun nat rat) bool), vanishes ) 15.44/15.60 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 15.44/15.60 ( (fun code_code_numeral nat), code_c271388182l_size ) 15.44/15.60 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 15.44/15.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 15.44/15.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 15.44/15.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 15.44/15.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 15.44/15.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 15.44/15.60 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 15.44/15.60 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 15.44/15.60 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 15.44/15.60 ( (fun complex nat), complex_size ) 15.44/15.60 ( (fun complex nat), (size_size complex) ) 15.44/15.60 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 15.44/15.60 ( (fun nat (fun nat (product_prod int int))), bezw ) 15.44/15.60 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 15.44/15.60 ( (fun int (fun nat nat)), nat_aux ) 15.44/15.60 ( (fun int (fun (fun int bool) bool)), rsetR ) 15.44/15.60 ( (fun int (fun (fun int bool) bool)), resSet ) 15.44/15.60 ( (fun int (list int)), quickc666637781d_zero ) 15.44/15.60 ( (fun (product_prod int int) rat), frct ) 15.44/15.60 ( (fun int (fun int rat)), fract ) 15.44/15.60 ( (fun real (fun real complex)), complex_1 ) 15.44/15.60 ( (fun real (fun real complex)), rcis ) 15.44/15.60 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 15.44/15.60 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 15.44/15.60 ( (fun int real), (real_1 int) ) 15.44/15.60 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 15.44/15.60 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 15.44/15.60 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 15.44/15.60 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 15.44/15.60 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 15.44/15.60 ( (fun real nat), natfloor ) 15.44/15.60 ( (fun real nat), natceiling ) 15.44/15.60 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 15.44/15.60 ( (fun quickcheck_code_int int), quickcheck_int_of ) 15.44/15.60 ( (fun rat (product_prod int int)), quotient_of ) 15.44/15.60 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 15.44/15.60 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 15.44/15.60 ( (fun rat real), ratreal ) 15.44/15.60 ( (fun code_code_numeral int), code_int_of ) 15.44/15.60 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 15.44/15.60 ( (fun int quickcheck_code_int), quickcheck_of_int ) 15.44/15.60 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 15.44/15.60 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 15.44/15.60 ) 15.44/15.60 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_110588 $$unsorted)) (or (not (semiring_char_0 X_a)) (not (= (zero_zero X_a) (hAPP nat X_a (semiring_1_of_nat X_a) (hAPP nat nat (fact_fact nat) BOUND_VARIABLE_110588))))) ) 15.44/15.60 ( int, (hAPP nat nat suc (zero_zero nat)) ) 15.44/15.60 ( real, (hAPP nat nat suc (zero_zero nat)) ) 15.44/15.60 ) 15.44/15.60 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_110603 $$unsorted) (BOUND_VARIABLE_110604 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (let ((_let_3 (hAPP int nat (number_number_of nat) BOUND_VARIABLE_110604))) (or (not (linordered_idom X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_110603) _let_3)) _let_2)) (and (not (hBOOL (hAPP nat bool (even_odd_even nat) _let_3))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_110603) _let_2))))))))) ) 15.44/15.60 ( int, s, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.44/15.60 ( int, s1, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.44/15.60 ( int, skv_14, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.44/15.60 ( complex, ii, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.44/15.60 ) 15.44/15.60 (instantiation (forall ((V_3 $$unsorted)) (= (hAPP int nat nat_1 (hAPP int int (hAPP int (fun int int) (div_div int) (one_one int)) (hAPP int int (number_number_of int) V_3))) (hAPP nat nat (hAPP nat (fun nat nat) (div_div nat) (hAPP nat nat suc (zero_zero nat))) (hAPP int nat (number_number_of nat) V_3))) ) 15.44/15.60 ( pls ) 15.44/15.60 ( (hAPP int int bit1 pls) ) 15.44/15.60 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.44/15.60 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.44/15.60 ( min_1 ) 15.44/15.60 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.60 ) 15.44/15.60 (instantiation (forall ((M $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (one_one int))) (let ((_let_2 (number_number_of int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int _let_2 (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) M)) _let_1))) (or (not (hBOOL (hAPP int bool zprime _let_3))) (= _let_1 (hAPP int int (hAPP int _let_0 legendre (hAPP int int _let_2 min_1)) _let_3))))))) ) 15.44/15.60 ( m ) 15.44/15.60 ) 15.44/15.60 (instantiation (forall ((N $$unsorted)) (= (= (zero_zero nat) N) (= (zero_zero real) (hAPP nat real (real_1 nat) N))) ) 15.44/15.60 ( (zero_zero nat) ) 15.44/15.60 ( (hAPP nat nat suc (zero_zero nat)) ) 15.44/15.60 ) 15.44/15.60 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_110654 $$unsorted) (BOUND_VARIABLE_110661 $$unsorted)) (let ((_let_0 (norm_norm X_a))) (let ((_let_1 (sgn_sgn X_a))) (let ((_let_2 (zero_zero X_a))) (or (not (real_normed_vector X_a)) (and (or (= _let_2 (ti X_a BOUND_VARIABLE_110654)) (= (one_one real) (hAPP X_a real _let_0 (hAPP X_a X_a _let_1 BOUND_VARIABLE_110654)))) (or (not (= _let_2 (ti X_a BOUND_VARIABLE_110661))) (= (zero_zero real) (hAPP X_a real _let_0 (hAPP X_a X_a _let_1 BOUND_VARIABLE_110661))))))))) ) 15.44/15.60 ( bool, fFalse, fFalse ) 15.44/15.60 ( bool, fTrue, fTrue ) 15.44/15.60 ( int, pls, pls ) 15.44/15.60 ( int, min_1, min_1 ) 15.44/15.60 ( int, s, s ) 15.44/15.60 ( int, m, m ) 15.44/15.60 ( int, s1, s1 ) 15.44/15.60 ( int, t, t ) 15.44/15.60 ( (fun int bool), nat_neg, nat_neg ) 15.44/15.60 ( (fun int bool), zprime, zprime ) 15.44/15.60 ( (fun int bool), zEven, zEven ) 15.44/15.60 ( (fun int bool), zOdd, zOdd ) 15.44/15.60 ( (fun int bool), (even_odd_even int), (even_odd_even int) ) 15.44/15.60 ( (fun int bool), twoSqu1091635170sum2sq, twoSqu1091635170sum2sq ) 15.44/15.60 ( (fun int bool), nat_is_nat, nat_is_nat ) 15.44/15.60 ( (fun int (fun int bool)), norRRset, norRRset ) 15.44/15.60 ( (fun int (fun int bool)), quadRes, quadRes ) 15.44/15.60 ( (fun int (fun int bool)), sRStar, sRStar ) 15.44/15.60 ( (fun int (fun int bool)), d22set, d22set ) 15.44/15.60 ( (fun int (fun int bool)), sr, sr ) 15.44/15.60 ( (fun int (fun int bool)), quickc1265749348ro_rel, quickc1265749348ro_rel ) 15.44/15.60 ( (fun int int), zfact, zfact ) 15.44/15.60 ( (fun int int), bit0, bit0 ) 15.44/15.60 ( (fun int int), bit1, bit1 ) 15.44/15.60 ( (fun int int), (fact_fact int), (fact_fact int) ) 15.44/15.60 ( (fun int int), pred, pred ) 15.44/15.60 ( (fun int int), succ, succ ) 15.44/15.60 ( (fun nat bool), (even_odd_even nat), (even_odd_even nat) ) 15.44/15.60 ( (fun nat bool), prime, prime ) 15.44/15.60 ( (fun nat nat), suc, suc ) 15.44/15.60 ( (fun nat nat), (fact_fact nat), (fact_fact nat) ) 15.44/15.60 ( (fun nat nat), fact, fact ) 15.44/15.60 ( (fun nat nat), nat_size, nat_size ) 15.44/15.60 ( (fun nat nat), (size_size nat), (size_size nat) ) 15.44/15.60 ( (fun (product_prod nat nat) bool), pred_nat, pred_nat ) 15.44/15.60 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel, divmod_nat_rel ) 15.44/15.60 ( real, pi, pi ) 15.44/15.60 ( (fun real real), ln, ln ) 15.44/15.60 ( (fun real real), cos, cos ) 15.44/15.60 ( (fun real real), sqrt, sqrt ) 15.44/15.60 ( (fun real real), sin, sin ) 15.44/15.60 ( (fun real real), arccos, arccos ) 15.44/15.60 ( (fun real real), arcsin, arcsin ) 15.44/15.60 ( (fun real real), tan, tan ) 15.44/15.60 ( (fun real real), arctan, arctan ) 15.44/15.60 ( (fun nat (fun nat bool)), coprime, coprime ) 15.44/15.60 ( complex, ii, ii ) 15.44/15.60 ( (fun nat real), (real_1 nat), (real_1 nat) ) 15.44/15.60 ( (fun nat real), sin_coeff, sin_coeff ) 15.44/15.60 ( (fun nat real), cos_coeff, cos_coeff ) 15.44/15.60 ( (filter nat), sequentially, sequentially ) 15.44/15.60 ( (fun int (fun int int)), (gcd_gcd int), (gcd_gcd int) ) 15.44/15.60 ( (fun int (fun int int)), legendre, legendre ) 15.44/15.60 ( (fun int (fun int int)), legacy_zgcd, legacy_zgcd ) 15.44/15.60 ( (fun int (fun int int)), standardRes, standardRes ) 15.44/15.60 ( (fun int (fun int int)), nat_tsub, nat_tsub ) 15.44/15.60 ( (fun int (fun int int)), multInv, multInv ) 15.44/15.60 ( (fun int (fun int int)), z3mod, z3mod ) 15.44/15.60 ( (fun int (fun int int)), z3div, z3div ) 15.44/15.60 ( (fun int (fun int int)), int_gcd, int_gcd ) 15.44/15.60 ( (fun int (fun int int)), int_lcm, int_lcm ) 15.44/15.60 ( (fun int (fun int int)), inv, inv ) 15.44/15.60 ( (fun complex complex), expi, expi ) 15.44/15.60 ( (fun complex complex), cnj, cnj ) 15.44/15.60 ( (fun real complex), cis, cis ) 15.44/15.60 ( (fun int nat), nat_1, nat_1 ) 15.44/15.60 ( (fun int nat), phi, phi ) 15.44/15.60 ( (fun (fun int bool) bool), nat_nat_set, nat_nat_set ) 15.44/15.60 ( (fun nat (fun nat nat)), (gcd_gcd nat), (gcd_gcd nat) ) 15.44/15.60 ( (fun nat (fun nat nat)), nat_gcd, nat_gcd ) 15.44/15.60 ( (fun nat (fun nat nat)), nat_lcm, nat_lcm ) 15.44/15.60 ( (fun (fun int bool) int), (the int), (the int) ) 15.44/15.60 ( (fun complex real), re, re ) 15.44/15.60 ( (fun complex real), im, im ) 15.44/15.60 ( (fun complex real), arg, arg ) 15.44/15.60 ( (fun bool bool), fNot, fNot ) 15.44/15.60 ( (fun nat (fun real real)), root, root ) 15.44/15.60 ( (fun real (fun real real)), log, log ) 15.44/15.60 ( (fun real (fun real real)), powr, powr ) 15.44/15.60 ( (fun bool (fun bool bool)), fimplies, fimplies ) 15.44/15.60 ( (fun bool (fun bool bool)), fconj, fconj ) 15.44/15.60 ( (fun bool (fun bool bool)), fdisj, fdisj ) 15.44/15.60 ( (fun int (fun int (product_prod int int))), negDivAlg, negDivAlg ) 15.44/15.60 ( (fun int (fun int (product_prod int int))), posDivAlg, posDivAlg ) 15.44/15.60 ( (fun int (fun int (product_prod int int))), divmod_int, divmod_int ) 15.44/15.60 ( (fun int (fun int (product_prod int int))), pdivmod, pdivmod ) 15.44/15.60 ( (fun int (fun int (product_prod int int))), norm_frac, norm_frac ) 15.44/15.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd, negateSnd ) 15.44/15.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize, normalize ) 15.44/15.60 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust, adjust ) 15.44/15.60 ( (fun int (fun int (fun int bool))), zcong, zcong ) 15.44/15.60 ( (fun int (fun int (fun int bool))), zcongm, zcongm ) 15.44/15.60 ( (fun int (fun int (fun int bool))), noXRRset, noXRRset ) 15.44/15.60 ( (fun int (fun int (fun int bool))), bnorRset, bnorRset ) 15.44/15.60 ( (fun int (fun int (fun int bool))), wset, wset ) 15.44/15.60 ( (fun (product_prod int int) bool), frac_1, frac_1 ) 15.44/15.60 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than, int_ge_less_than ) 15.44/15.60 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2, int_ge_less_than2 ) 15.44/15.60 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral, code_S1047413653umeral ) 15.44/15.60 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset, is_RRset ) 15.44/15.60 ( (fun (fun nat rat) bool), vanishes, vanishes ) 15.44/15.60 ( (fun code_code_numeral nat), (size_size code_code_numeral), (size_size code_code_numeral) ) 15.44/15.60 ( (fun code_code_numeral nat), code_c271388182l_size, code_c271388182l_size ) 15.44/15.60 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel, ratrel ) 15.44/15.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel, norm_frac_rel ) 15.44/15.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel, posDivAlg_rel ) 15.44/15.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel, lazy_small_lazy_rel ) 15.44/15.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel, negDivAlg_rel ) 15.44/15.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel, upto_rel ) 15.44/15.60 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq, twoSqu1094008024sum2sq ) 15.44/15.60 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less, pair_less ) 15.44/15.60 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq, pair_leq ) 15.44/15.60 ( (fun complex nat), complex_size, complex_size ) 15.44/15.60 ( (fun complex nat), (size_size complex), (size_size complex) ) 15.44/15.60 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel, nat_gcd_rel ) 15.44/15.60 ( (fun nat (fun nat (product_prod int int))), bezw, bezw ) 15.44/15.60 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd, xzgcd ) 15.44/15.60 ( (fun int (fun nat nat)), nat_aux, nat_aux ) 15.44/15.60 ( (fun int (fun (fun int bool) bool)), rsetR, rsetR ) 15.44/15.60 ( (fun int (fun (fun int bool) bool)), resSet, resSet ) 15.44/15.60 ( (fun int (list int)), quickc666637781d_zero, quickc666637781d_zero ) 15.44/15.60 ( (fun (product_prod int int) rat), frct, frct ) 15.44/15.60 ( (fun int (fun int rat)), fract, fract ) 15.44/15.60 ( (fun real (fun real complex)), complex_1, complex_1 ) 15.44/15.60 ( (fun real (fun real complex)), rcis, rcis ) 15.44/15.60 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat), (ord_gr676655987ssThan nat) ) 15.44/15.60 ( (fun quickcheck_code_int nat), quickcheck_nat_of, quickcheck_nat_of ) 15.44/15.60 ( (fun int real), (real_1 int), (real_1 int) ) 15.44/15.60 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect, bolzano_bisect ) 15.44/15.60 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR, rRset2norRR ) 15.44/15.60 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int, quickc495462417de_int ) 15.44/15.60 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda, xzgcda ) 15.44/15.60 ( (fun int (fun int (fun int (fun int bool)))), multInvPair, multInvPair ) 15.44/15.60 ( (fun real nat), natfloor, natfloor ) 15.44/15.60 ( (fun real nat), natceiling, natceiling ) 15.44/15.60 ( (fun (fun real bool) real), (complete_Sup_Sup real), (complete_Sup_Sup real) ) 15.44/15.60 ( (fun quickcheck_code_int int), quickcheck_int_of, quickcheck_int_of ) 15.44/15.60 ( (fun rat (product_prod int int)), quotient_of, quotient_of ) 15.44/15.60 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral, code_d418564891umeral ) 15.44/15.60 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat, divmod_nat ) 15.44/15.60 ( (fun rat real), ratreal, ratreal ) 15.44/15.60 ( (fun code_code_numeral int), code_int_of, code_int_of ) 15.44/15.60 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel, divmod_int_rel ) 15.44/15.60 ( (fun int quickcheck_code_int), quickcheck_of_int, quickcheck_of_int ) 15.44/15.60 ( (fun int (fun int (fun (fun int bool) bool))), setS, setS ) 15.44/15.60 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux, code_nat_of_aux ) 15.44/15.60 ) 15.44/15.61 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_110739 $$unsorted) (BOUND_VARIABLE_110740 $$unsorted) (BOUND_VARIABLE_110741 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (zero_zero X_a))) (let ((_let_2 (ord_less_eq X_a))) (let ((_let_3 (fun X_a X_a))) (let ((_let_4 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) _let_1) BOUND_VARIABLE_110741)))) (let ((_let_5 (hAPP X_a X_a (hAPP X_a _let_3 (times_times X_a) BOUND_VARIABLE_110739) BOUND_VARIABLE_110741))) (let ((_let_6 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_110741) _let_1)))) (let ((_let_7 (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_110739))) (or (not (linord1117847801e_zero X_a)) (= (and (or (not _let_4) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 _let_5) BOUND_VARIABLE_110740))) (or _let_4 (and (or _let_6 (hBOOL (hAPP X_a bool _let_7 _let_1))) (or (not _let_6) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_110740) _let_5)))))) (hBOOL (hAPP X_a bool _let_7 (hAPP X_a X_a (hAPP X_a _let_3 (inverse_divide X_a) BOUND_VARIABLE_110740) BOUND_VARIABLE_110741))))))))))))) ) 15.44/15.61 ( real, (zero_zero real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.61 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.44/15.61 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.44/15.61 ) 15.44/15.61 (instantiation (forall ((X_a $$unsorted)) (or (not (real_normed_algebra X_a)) (not (forall ((K_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) K_2))) (not (forall ((A_4 $$unsorted) (B_4 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (times_times real))) (let ((_let_2 (norm_norm X_a))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP X_a real _let_2 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) A_4) B_4))) (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real (hAPP real _let_0 _let_1 (hAPP X_a real _let_2 A_4)) (hAPP X_a real _let_2 B_4))) K_2)))))) ))) ))) ) 15.44/15.61 ( real ) 15.44/15.61 ( complex ) 15.44/15.61 ) 15.44/15.61 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_110837 $$unsorted) (BOUND_VARIABLE_110838 $$unsorted)) (let ((_let_0 (uminus_uminus X_a))) (let ((_let_1 (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_110837))) (or (not (division_ring X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_110838)) (= (hAPP X_a X_a _let_1 (hAPP X_a X_a _let_0 BOUND_VARIABLE_110838)) (hAPP X_a X_a _let_0 (hAPP X_a X_a _let_1 BOUND_VARIABLE_110838)))))) ) 15.44/15.61 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.61 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.44/15.61 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.44/15.61 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 15.44/15.61 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.61 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.44/15.61 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.44/15.61 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.44/15.61 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.61 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.61 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.61 ) 15.44/15.61 (instantiation (forall ((N_1 $$unsorted)) (= (hAPP nat nat suc (hAPP nat nat suc (hAPP nat nat suc N_1))) (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls)))) N_1)) ) 15.44/15.61 ( (zero_zero nat) ) 15.44/15.61 ) 15.44/15.61 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (= (hAPP _let_1 real (suminf real) (hAPP _let_1 _let_1 (hAPP _let_2 (fun _let_1 _let_1) (combs nat real real) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 nat) (times_times real)) sin_coeff)) (hAPP real _let_1 (power_power real) X_2))) (hAPP real real sin X_2))))) ) 15.44/15.61 ( (zero_zero real) ) 15.44/15.61 ( pi ) 15.44/15.61 ( (hAPP int real (number_number_of real) min_1) ) 15.44/15.61 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.44/15.61 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.44/15.61 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.44/15.61 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.44/15.61 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.44/15.61 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.44/15.61 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.44/15.61 ) 15.44/15.61 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_110883 $$unsorted) (BOUND_VARIABLE_110884 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (uminus_uminus X_a))) (or (not (ordered_ab_group_add X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_110883)) BOUND_VARIABLE_110884)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_110884)) BOUND_VARIABLE_110883))))))) ) 15.44/15.61 ( int, (one_one int), pls ) 15.44/15.61 ( int, (one_one int), min_1 ) 15.44/15.61 ( int, pls, (one_one int) ) 15.44/15.61 ( int, pls, pls ) 15.44/15.61 ( int, pls, min_1 ) 15.44/15.61 ( int, pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.44/15.61 ( int, min_1, (one_one int) ) 15.44/15.61 ( int, min_1, pls ) 15.44/15.61 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), pls ) 15.44/15.61 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.44/15.61 ( real, pi, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.44/15.61 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.44/15.61 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi), pi ) 15.44/15.61 ) 15.44/15.61 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (zero_zero real))) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) _let_0) X_1))) (not (= _let_0 (hAPP real real sqrt X_1))))) ) 15.44/15.61 ( (one_one real) ) 15.44/15.61 ( (zero_zero real) ) 15.44/15.61 ( pi ) 15.44/15.61 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.61 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.44/15.61 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.44/15.61 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.44/15.61 ( skv_2 ) 15.44/15.61 ( skv_8 ) 15.44/15.61 ( skv_9 ) 15.44/15.61 ) 15.44/15.61 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_110941 $$unsorted) (BOUND_VARIABLE_110942 $$unsorted) (BOUND_VARIABLE_110943 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (fun X_a X_a))) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) (zero_zero X_a)) BOUND_VARIABLE_110943))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_2 (times_times X_a) BOUND_VARIABLE_110941) BOUND_VARIABLE_110943)) BOUND_VARIABLE_110942))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_110941) (hAPP X_a X_a (hAPP X_a _let_2 (inverse_divide X_a) BOUND_VARIABLE_110942) BOUND_VARIABLE_110943))))))) ) 15.44/15.61 ( real, (zero_zero real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.61 ) 15.44/15.61 (instantiation (forall ((Z_1 $$unsorted)) (= (hAPP real complex (hAPP real (fun real complex) complex_1 (hAPP complex real re Z_1)) (hAPP real real (uminus_uminus real) (hAPP complex real im Z_1))) (hAPP complex complex cnj Z_1)) ) 15.44/15.61 ( (one_one complex) ) 15.44/15.61 ( ii ) 15.44/15.61 ( (zero_zero complex) ) 15.44/15.61 ) 15.44/15.61 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int _let_0 (gcd_gcd int) M))) (= (hAPP int int _let_1 N_1) (hAPP int int _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) M) N_1))))) ) 15.44/15.61 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 15.44/15.61 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 15.44/15.61 ) 15.44/15.61 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (BOUND_VARIABLE_111076 $$unsorted) (BOUND_VARIABLE_111077 $$unsorted) (BOUND_VARIABLE_111078 $$unsorted)) (let ((_let_0 (fun (filter X_a) bool))) (let ((_let_1 (fun X_a X_b))) (let ((_let_2 (fun X_a real))) (let ((_let_3 (norm_norm X_b))) (or (not (real_normed_vector X_b)) (not (hBOOL (hAPP (filter X_a) bool (hAPP X_b _let_0 (hAPP _let_1 (fun X_b _let_0) (tendsto X_a X_b) BOUND_VARIABLE_111076) BOUND_VARIABLE_111077) BOUND_VARIABLE_111078))) (hBOOL (hAPP (filter X_a) bool (hAPP real _let_0 (hAPP _let_2 (fun real _let_0) (tendsto X_a real) (hAPP _let_1 _let_2 (hAPP (fun X_b real) (fun _let_1 _let_2) (combb X_b real X_a) _let_3) BOUND_VARIABLE_111076)) (hAPP X_b real _let_3 BOUND_VARIABLE_111077)) BOUND_VARIABLE_111078))))))) ) 15.44/15.61 ( nat, real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real), sequentially ) 15.44/15.61 ( real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (hAPP real (filter real) (at real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.44/15.61 ) 15.44/15.61 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_111238 $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat X_a))) (let ((_let_3 (fun X_a X_a))) (let ((_let_4 (fun nat _let_3))) (or (not (banach X_a)) (not (real_n2089651433ebra_1 X_a)) (hBOOL (hAPP _let_1 bool (summable real) (hAPP _let_2 _let_1 (hAPP (fun X_a real) (fun _let_2 _let_1) (combb X_a real nat) (norm_norm X_a)) (hAPP _let_2 _let_2 (hAPP _let_4 (fun _let_2 _let_2) (combs nat X_a X_a) (hAPP _let_1 _let_4 (hAPP (fun real _let_3) (fun _let_1 _let_4) (combb real _let_3 nat) (scaleR_scaleR X_a)) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) (fact_fact nat))))) (hAPP X_a _let_2 (power_power X_a) BOUND_VARIABLE_111238))))))))))) ) 15.44/15.61 ( int, s ) 15.44/15.61 ( int, s1 ) 15.44/15.61 ( int, skv_14 ) 15.44/15.61 ( real, (hAPP int real (number_number_of real) min_1) ) 15.44/15.61 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.44/15.61 ( complex, ii ) 15.44/15.61 ) 15.44/15.61 (instantiation (forall ((X_2 $$unsorted) (N $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (or (hBOOL (hAPP int bool nat_neg (hAPP int int (number_number_of int) N))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) X_2))) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP int nat (number_number_of nat) N)) (hAPP real nat natfloor X_2))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP int real (number_number_of real) N)) X_2)))))) ) 15.44/15.61 ( pi, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.44/15.61 ) 15.44/15.61 (instantiation (forall ((N_1 $$unsorted)) (= (hAPP nat nat suc (hAPP nat nat suc N_1)) (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) N_1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.44/15.61 ( (zero_zero nat) ) 15.44/15.61 ( (hAPP nat nat suc (zero_zero nat)) ) 15.44/15.61 ( (one_one nat) ) 15.44/15.61 ) 15.44/15.61 (instantiation (forall ((W $$unsorted) (Z_1 $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) W) Z_1))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (hAPP int int (hAPP int (fun int int) (plus_plus int) W) (one_one int))) Z_1)))) ) 15.44/15.61 ( (one_one int), t ) 15.44/15.61 ( pls, (one_one int) ) 15.44/15.61 ( pls, pls ) 15.44/15.61 ( pls, min_1 ) 15.44/15.61 ( pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.44/15.61 ( min_1, pls ) 15.44/15.61 ( min_1, min_1 ) 15.44/15.61 ( s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.44/15.61 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.44/15.61 ( skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.44/15.61 ( skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.44/15.61 ) 15.44/15.61 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_111320 $$unsorted)) (or (not (comm_semiring_1 X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_111320) (one_one X_a)) (ti X_a BOUND_VARIABLE_111320))) ) 15.44/15.61 ( bool, fFalse ) 15.44/15.61 ( bool, fTrue ) 15.44/15.61 ( int, pls ) 15.44/15.61 ( int, min_1 ) 15.44/15.61 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.61 ( int, s ) 15.44/15.61 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.44/15.61 ( int, m ) 15.44/15.61 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.44/15.61 ( int, s1 ) 15.44/15.61 ( int, t ) 15.44/15.61 ( (fun int bool), nat_neg ) 15.44/15.61 ( (fun int bool), zprime ) 15.44/15.61 ( (fun int bool), zEven ) 15.44/15.61 ( (fun int bool), zOdd ) 15.44/15.61 ( (fun int bool), (even_odd_even int) ) 15.44/15.61 ( (fun int bool), twoSqu1091635170sum2sq ) 15.44/15.61 ( (fun int bool), nat_is_nat ) 15.44/15.61 ( (fun int (fun int bool)), norRRset ) 15.44/15.61 ( (fun int (fun int bool)), quadRes ) 15.44/15.61 ( (fun int (fun int bool)), sRStar ) 15.44/15.61 ( (fun int (fun int bool)), d22set ) 15.44/15.61 ( (fun int (fun int bool)), sr ) 15.44/15.61 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 15.44/15.61 ( (fun int int), zfact ) 15.44/15.61 ( (fun int int), bit0 ) 15.44/15.61 ( (fun int int), bit1 ) 15.44/15.61 ( (fun int int), (fact_fact int) ) 15.44/15.61 ( (fun int int), pred ) 15.44/15.61 ( (fun int int), succ ) 15.44/15.61 ( (fun nat bool), (even_odd_even nat) ) 15.44/15.61 ( (fun nat bool), prime ) 15.44/15.61 ( (fun nat nat), suc ) 15.44/15.61 ( (fun nat nat), (fact_fact nat) ) 15.44/15.61 ( (fun nat nat), fact ) 15.44/15.61 ( (fun nat nat), nat_size ) 15.44/15.61 ( (fun nat nat), (size_size nat) ) 15.44/15.61 ( (fun (product_prod nat nat) bool), pred_nat ) 15.44/15.61 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 15.44/15.61 ( real, pi ) 15.44/15.61 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.61 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.44/15.61 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 15.44/15.61 ( (fun real real), ln ) 15.44/15.61 ( (fun real real), cos ) 15.44/15.61 ( (fun real real), sqrt ) 15.44/15.61 ( (fun real real), sin ) 15.44/15.61 ( (fun real real), arccos ) 15.44/15.61 ( (fun real real), arcsin ) 15.44/15.61 ( (fun real real), tan ) 15.44/15.61 ( (fun real real), arctan ) 15.44/15.61 ( (fun nat (fun nat bool)), coprime ) 15.44/15.61 ( complex, ii ) 15.44/15.61 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.61 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 15.44/15.61 ( (fun nat real), (real_1 nat) ) 15.44/15.61 ( (fun nat real), sin_coeff ) 15.44/15.61 ( (fun nat real), cos_coeff ) 15.44/15.61 ( (filter nat), sequentially ) 15.44/15.61 ( (fun int (fun int int)), (gcd_gcd int) ) 15.44/15.61 ( (fun int (fun int int)), legendre ) 15.44/15.61 ( (fun int (fun int int)), legacy_zgcd ) 15.44/15.61 ( (fun int (fun int int)), standardRes ) 15.44/15.61 ( (fun int (fun int int)), nat_tsub ) 15.44/15.61 ( (fun int (fun int int)), multInv ) 15.44/15.61 ( (fun int (fun int int)), z3mod ) 15.44/15.61 ( (fun int (fun int int)), z3div ) 15.44/15.61 ( (fun int (fun int int)), int_gcd ) 15.44/15.61 ( (fun int (fun int int)), int_lcm ) 15.44/15.61 ( (fun int (fun int int)), inv ) 15.44/15.61 ( (fun complex complex), expi ) 15.44/15.61 ( (fun complex complex), cnj ) 15.44/15.61 ( (fun real complex), cis ) 15.44/15.61 ( (fun int nat), nat_1 ) 15.44/15.61 ( (fun int nat), phi ) 15.44/15.61 ( (fun (fun int bool) bool), nat_nat_set ) 15.44/15.61 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 15.44/15.61 ( (fun nat (fun nat nat)), nat_gcd ) 15.44/15.61 ( (fun nat (fun nat nat)), nat_lcm ) 15.44/15.61 ( (fun (fun int bool) int), (the int) ) 15.44/15.61 ( (fun complex real), re ) 15.44/15.61 ( (fun complex real), im ) 15.44/15.61 ( (fun complex real), arg ) 15.44/15.61 ( (fun bool bool), fNot ) 15.44/15.61 ( (fun nat (fun real real)), root ) 15.44/15.61 ( (fun real (fun real real)), log ) 15.44/15.61 ( (fun real (fun real real)), powr ) 15.44/15.61 ( (fun bool (fun bool bool)), fimplies ) 15.44/15.61 ( (fun bool (fun bool bool)), fconj ) 15.44/15.61 ( (fun bool (fun bool bool)), fdisj ) 15.44/15.61 ( (fun int (fun int (product_prod int int))), negDivAlg ) 15.44/15.61 ( (fun int (fun int (product_prod int int))), posDivAlg ) 15.44/15.61 ( (fun int (fun int (product_prod int int))), divmod_int ) 15.44/15.61 ( (fun int (fun int (product_prod int int))), pdivmod ) 15.44/15.61 ( (fun int (fun int (product_prod int int))), norm_frac ) 15.44/15.61 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 15.44/15.61 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 15.44/15.61 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 15.44/15.61 ( (fun int (fun int (fun int bool))), zcong ) 15.44/15.61 ( (fun int (fun int (fun int bool))), zcongm ) 15.44/15.61 ( (fun int (fun int (fun int bool))), noXRRset ) 15.44/15.61 ( (fun int (fun int (fun int bool))), bnorRset ) 15.44/15.61 ( (fun int (fun int (fun int bool))), wset ) 15.44/15.61 ( (fun (product_prod int int) bool), frac_1 ) 15.44/15.61 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 15.44/15.61 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 15.44/15.61 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 15.44/15.61 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 15.44/15.61 ( (fun (fun nat rat) bool), vanishes ) 15.44/15.61 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 15.44/15.61 ( (fun code_code_numeral nat), code_c271388182l_size ) 15.44/15.61 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 15.44/15.61 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 15.44/15.61 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 15.44/15.61 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 15.44/15.61 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 15.44/15.61 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 15.44/15.61 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 15.44/15.61 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 15.44/15.61 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 15.44/15.61 ( (fun complex nat), complex_size ) 15.44/15.61 ( (fun complex nat), (size_size complex) ) 15.44/15.61 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 15.44/15.61 ( (fun nat (fun nat (product_prod int int))), bezw ) 15.44/15.61 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 15.44/15.61 ( (fun int (fun nat nat)), nat_aux ) 15.44/15.61 ( (fun int (fun (fun int bool) bool)), rsetR ) 15.44/15.61 ( (fun int (fun (fun int bool) bool)), resSet ) 15.44/15.61 ( (fun int (list int)), quickc666637781d_zero ) 15.44/15.61 ( (fun (product_prod int int) rat), frct ) 15.44/15.61 ( (fun int (fun int rat)), fract ) 15.44/15.61 ( (fun real (fun real complex)), complex_1 ) 15.44/15.61 ( (fun real (fun real complex)), rcis ) 15.44/15.61 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 15.44/15.61 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 15.44/15.61 ( (fun int real), (real_1 int) ) 15.44/15.61 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 15.44/15.61 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 15.44/15.61 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 15.44/15.61 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 15.44/15.61 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 15.44/15.61 ( (fun real nat), natfloor ) 15.44/15.61 ( (fun real nat), natceiling ) 15.44/15.61 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 15.44/15.61 ( (fun quickcheck_code_int int), quickcheck_int_of ) 15.44/15.61 ( (fun rat (product_prod int int)), quotient_of ) 15.44/15.61 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 15.44/15.61 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 15.44/15.61 ( (fun rat real), ratreal ) 15.44/15.61 ( (fun code_code_numeral int), code_int_of ) 15.44/15.61 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 15.44/15.61 ( (fun int quickcheck_code_int), quickcheck_of_int ) 15.44/15.61 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 15.44/15.61 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 15.44/15.61 ) 15.44/15.61 (instantiation (forall ((X_1 $$unsorted) (N_1 $$unsorted) (M $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)))) (or (not (hBOOL (hAPP nat bool _let_1 M))) (not (hBOOL (hAPP nat bool _let_1 N_1))) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) X_1))) (= (hAPP real real (hAPP nat _let_0 root (hAPP nat nat (hAPP nat (fun nat nat) (times_times nat) M) N_1)) X_1) (hAPP real real (hAPP nat _let_0 root M) (hAPP real real (hAPP nat _let_0 root N_1) X_1)))))) ) 15.44/15.61 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.61 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.61 ) 15.44/15.61 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_111345 $$unsorted)) (or (not (linordered_field X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)) (hAPP X_a X_a (inverse_inverse X_a) (hAPP nat X_a (semiring_1_of_nat X_a) (hAPP nat nat (fact_fact nat) BOUND_VARIABLE_111345)))))) ) 15.44/15.61 ( int, (hAPP nat nat suc (zero_zero nat)) ) 15.44/15.61 ( real, (hAPP nat nat suc (zero_zero nat)) ) 15.44/15.61 ) 15.44/15.61 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_111360 $$unsorted)) (or (not (linordered_idom X_a)) (not (number_ring X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (one_one X_a)) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_111360))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP int int bit1 pls)) BOUND_VARIABLE_111360)))) ) 15.44/15.61 ( nat, pls ) 15.44/15.61 ( nat, (hAPP int int bit1 pls) ) 15.44/15.61 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.44/15.61 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.44/15.61 ( int, pls ) 15.44/15.61 ( int, (hAPP int int bit1 pls) ) 15.44/15.61 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.44/15.61 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.44/15.61 ( int, min_1 ) 15.44/15.61 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.61 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.44/15.61 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.44/15.61 ( real, min_1 ) 15.44/15.61 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.61 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.44/15.61 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.61 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 15.44/15.61 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.44/15.61 ( complex, min_1 ) 15.44/15.61 ( quickcheck_code_int, (one_one int) ) 15.44/15.61 ( quickcheck_code_int, (zero_zero int) ) 15.44/15.61 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 15.44/15.61 ( code_code_numeral, pls ) 15.44/15.61 ( code_code_numeral, (hAPP int int bit1 pls) ) 15.44/15.61 ) 15.44/15.61 (instantiation (forall ((X_c $$unsorted) (X_a $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (let ((_let_0 (hAPP X_a X_c B_1_1 B_2_1))) (= _let_0 (ti X_c _let_0))) ) 15.44/15.61 ( bool, nat, (even_odd_even nat), (zero_zero nat) ) 15.44/15.61 ( bool, nat, (even_odd_even nat), (one_one nat) ) 15.44/15.61 ( bool, nat, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.61 ( bool, nat, prime, (zero_zero nat) ) 15.44/15.61 ( bool, nat, prime, (hAPP nat nat suc (zero_zero nat)) ) 15.44/15.61 ( bool, nat, prime, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.61 ( bool, int, (hAPP int (fun int bool) (ord_less int) pls), pls ) 15.44/15.61 ( bool, int, (hAPP int (fun int bool) (ord_less int) pls), min_1 ) 15.44/15.61 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) pls), min_1 ) 15.44/15.61 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (one_one int)), t ) 15.44/15.61 ( bool, int, nat_neg, (one_one int) ) 15.44/15.61 ( bool, int, nat_neg, (hAPP int int (number_number_of int) min_1) ) 15.44/15.61 ( bool, int, nat_neg, (hAPP int int (number_number_of int) pls) ) 15.44/15.61 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (one_one int) ) 15.44/15.61 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.61 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), s ) 15.44/15.61 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.44/15.61 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) pls) ) 15.44/15.61 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_4 ) 15.44/15.61 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_10 ) 15.44/15.61 ( bool, int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (one_one int) ) 15.44/15.61 ( bool, int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.44/15.61 ( bool, int, zprime, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.61 ( bool, int, zprime, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.44/15.61 ( bool, int, (hAPP int (fun int bool) (ord_less int) s), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.44/15.61 ( bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) s)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.44/15.61 ( bool, int, (let ((_let_0 (fun int int))) (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 15.44/15.61 ( bool, int, (hAPP int (fun int bool) (ord_less int) (one_one int)), t ) 15.44/15.61 ( bool, int, (even_odd_even int), (one_one int) ) 15.44/15.61 ( bool, int, (even_odd_even int), (zero_zero int) ) 15.44/15.61 ( bool, int, twoSqu1091635170sum2sq, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) t))) ) 15.44/15.61 ( bool, int, nat_is_nat, (one_one int) ) 15.44/15.61 ( bool, int, nat_is_nat, (zero_zero int) ) 15.44/15.61 ( bool, int, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.61 ( bool, int, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.44/15.61 ( bool, int, (hAPP int (fun int bool) (ord_less int) min_1), pls ) 15.44/15.61 ( bool, int, (hAPP int (fun int bool) (ord_less int) min_1), min_1 ) 15.44/15.61 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) min_1), pls ) 15.44/15.61 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) min_1), min_1 ) 15.44/15.61 ( bool, int, (let ((_let_0 (fun int int))) (hAPP int (fun int bool) quadRes (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int int (number_number_of int) min_1) ) 15.44/15.61 ( bool, int, (let ((_let_0 (fun int bool))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (let ((_let_3 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int _let_1 _let_2 s) _let_3)) (hAPP nat int (hAPP int _let_1 _let_2 s1) _let_3)))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.44/15.61 ( bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.44/15.61 ( bool, int, (hAPP int (fun int bool) (ord_less int) t), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.44/15.61 ( bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.44/15.61 ( bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_4)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.44/15.61 ( bool, int, (hAPP int (fun int bool) (ord_less int) skv_4), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.44/15.61 ( bool, int, (hAPP int (fun int bool) (ord_less int) skv_10), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.44/15.61 ( bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_10)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.44/15.61 ( bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.44/15.61 ( bool, (fun int bool), (hAPP (fun int nat) (fun (fun int bool) bool) (nat_tr1645093318rphism int nat) nat_1), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 15.44/15.61 ( bool, (fun int bool), (hAPP int (fun (fun int bool) bool) (member int) (one_one int)), zEven ) 15.44/15.61 ( bool, (fun nat bool), (finite_finite_1 nat), (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 15.44/15.61 ( bool, (fun nat bool), (hAPP (fun nat int) (fun (fun nat bool) bool) (nat_tr1645093318rphism nat int) (semiring_1_of_nat int)), (hAPP bool (fun nat bool) (combk bool nat) fTrue) ) 15.44/15.61 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), pi ) 15.44/15.61 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.44/15.61 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.44/15.61 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_3 ) 15.44/15.61 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_5 ) 15.44/15.61 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_7 ) 15.44/15.61 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_12 ) 15.44/15.61 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), pi ) 15.44/15.61 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.44/15.61 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.44/15.61 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_2 ) 15.44/15.61 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_8 ) 15.44/15.61 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_9 ) 15.44/15.61 ( bool, real, (hAPP real (fun real bool) (ord_less real) (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))), (zero_zero real) ) 15.44/15.61 ( bool, real, (hAPP real (fun real bool) (ord_less real) (one_one real)), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.44/15.61 ( bool, real, (hAPP real (fun real bool) (ord_less real) pi), (zero_zero real) ) 15.44/15.61 ( bool, real, (hAPP real (fun real bool) (ord_less real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.44/15.61 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.61 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 15.44/15.61 ( bool, real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 (fun real bool) (sums real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (hAPP real _let_1 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc)))), (one_one real) ) 15.44/15.61 ( bool, real, (hAPP real (fun real bool) (ord_less real) (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi))), pi ) 15.44/15.61 ( bool, real, (hAPP real (fun real bool) (ord_less real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.61 ( bool, real, (hAPP real (fun real bool) (ord_less real) (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 15.44/15.61 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 15.44/15.61 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) skv_5), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.61 ( bool, (filter nat), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun (filter nat) bool))) (hAPP real _let_2 (hAPP _let_1 (fun real _let_2) (tendsto nat real) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))) (zero_zero real))))), sequentially ) 15.44/15.61 ( bool, (filter nat), (trivial_limit nat), sequentially ) 15.44/15.61 ( bool, (filter real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (filter real) bool))) (hAPP real _let_2 (hAPP _let_0 (fun real _let_2) (tendsto real real) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin)) (zero_zero real))))), (hAPP real (filter real) (at real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.44/15.61 ( nat, nat, suc, (zero_zero nat) ) 15.44/15.61 ( nat, nat, suc, (hAPP nat nat suc (zero_zero nat)) ) 15.44/15.61 ( nat, nat, suc, (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 15.44/15.61 ( nat, nat, (fact_fact nat), (zero_zero nat) ) 15.44/15.61 ( nat, nat, (fact_fact nat), (hAPP nat nat suc (zero_zero nat)) ) 15.44/15.61 ( nat, nat, fact, (zero_zero nat) ) 15.44/15.61 ( nat, nat, (hAPP nat (fun nat nat) (plus_plus nat) (one_one nat)), (one_one nat) ) 15.44/15.61 ( nat, nat, nat_size, (zero_zero nat) ) 15.44/15.61 ( nat, nat, (size_size nat), (zero_zero nat) ) 15.44/15.61 ( nat, int, (number_number_of nat), pls ) 15.44/15.61 ( nat, int, (number_number_of nat), (hAPP int int bit1 pls) ) 15.44/15.61 ( nat, int, (number_number_of nat), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.44/15.61 ( nat, int, (number_number_of nat), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.44/15.61 ( nat, int, nat_1, (one_one int) ) 15.44/15.61 ( nat, int, nat_1, (zero_zero int) ) 15.44/15.61 ( nat, int, nat_1, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.61 ( nat, int, nat_1, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.44/15.61 ( nat, real, natfloor, (one_one real) ) 15.44/15.61 ( nat, real, natfloor, (zero_zero real) ) 15.44/15.61 ( nat, real, natceiling, (one_one real) ) 15.44/15.61 ( nat, real, natceiling, (zero_zero real) ) 15.44/15.61 ( nat, code_code_numeral, (size_size code_code_numeral), (zero_zero code_code_numeral) ) 15.44/15.61 ( nat, code_code_numeral, code_c271388182l_size, (zero_zero code_code_numeral) ) 15.44/15.61 ( int, nat, (semiring_1_of_nat int), (zero_zero nat) ) 15.44/15.61 ( int, nat, (semiring_1_of_nat int), (hAPP nat nat suc (zero_zero nat)) ) 15.44/15.61 ( int, nat, (semiring_1_of_nat int), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.44/15.61 ( int, nat, (semiring_1_of_nat int), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.61 ( int, nat, (hAPP int (fun nat int) (power_power int) s), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.61 ( int, nat, (hAPP int (fun nat int) (power_power int) s1), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.61 ( int, nat, (hAPP int (fun nat int) (power_power int) skv_14), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.61 ( int, int, bit0, pls ) 15.44/15.61 ( int, int, bit0, (hAPP int int bit1 pls) ) 15.44/15.61 ( int, int, bit0, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.44/15.61 ( int, int, bit0, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.44/15.61 ( int, int, bit0, min_1 ) 15.44/15.61 ( int, int, bit0, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.44/15.61 ( int, int, bit1, pls ) 15.44/15.61 ( int, int, bit1, (hAPP int int bit1 pls) ) 15.44/15.61 ( int, int, bit1, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.44/15.61 ( int, int, bit1, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.44/15.61 ( int, int, bit1, min_1 ) 15.44/15.61 ( int, int, bit1, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.44/15.61 ( int, int, bit1, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.44/15.61 ( int, int, bit1, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 15.44/15.61 ( int, int, bit1, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 15.44/15.61 ( int, int, (number_number_of int), pls ) 15.44/15.61 ( int, int, (number_number_of int), (hAPP int int bit1 pls) ) 15.44/15.61 ( int, int, (number_number_of int), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.44/15.61 ( int, int, (number_number_of int), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.44/15.61 ( int, int, (number_number_of int), min_1 ) 15.44/15.61 ( int, int, (number_number_of int), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.61 ( int, int, (fact_fact int), (one_one int) ) 15.44/15.61 ( int, int, (fact_fact int), (zero_zero int) ) 15.44/15.61 ( int, int, (uminus_uminus int), (one_one int) ) 15.44/15.61 ( int, int, (uminus_uminus int), pls ) 15.44/15.61 ( int, int, (uminus_uminus int), min_1 ) 15.44/15.61 ( int, int, pred, pls ) 15.44/15.61 ( int, int, pred, min_1 ) 15.44/15.61 ( int, int, (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))), m ) 15.44/15.61 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m))), (one_one int) ) 15.44/15.61 ( int, int, (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (one_one int) ) 15.44/15.61 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))))), t ) 15.44/15.61 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))))), skv_13 ) 15.44/15.61 ( int, int, succ, pls ) 15.44/15.61 ( int, int, succ, min_1 ) 15.44/15.61 ( int, int, (hAPP int (fun int int) legendre (hAPP int int (number_number_of int) min_1)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.44/15.61 ( int, int, (hAPP int (fun int int) (minus_minus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1) ) 15.44/15.61 ( int, (product_prod int int), twoSqu1094008024sum2sq, (let ((_let_0 (product_prod int int))) (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) s) (one_one int))) ) 15.44/15.61 ( int, quickcheck_code_int, quickcheck_int_of, (zero_zero quickcheck_code_int) ) 15.44/15.61 ( int, code_code_numeral, code_int_of, (zero_zero code_code_numeral) ) 15.44/15.61 ( (fun int bool), int, (ord_less_eq int), (one_one int) ) 15.44/15.61 ( (fun int bool), int, (ord_less_eq int), (zero_zero int) ) 15.44/15.61 ( (fun int bool), int, (ord_less_eq int), min_1 ) 15.44/15.61 ( (fun int bool), int, (ord_less int), (one_one int) ) 15.44/15.61 ( (fun int bool), int, (ord_less int), pls ) 15.44/15.61 ( (fun int bool), int, (ord_less int), min_1 ) 15.44/15.61 ( (fun int bool), int, (ord_less int), s ) 15.44/15.61 ( (fun int bool), int, (ord_less int), t ) 15.44/15.61 ( (fun int bool), int, (ord_less int), skv_4 ) 15.44/15.61 ( (fun int bool), int, (ord_less int), skv_10 ) 15.44/15.61 ( (fun int bool), int, (dvd_dvd int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.44/15.61 ( (fun int bool), int, quadRes, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.44/15.61 ( (fun int bool), int, (let ((_let_0 (fun int (fun int bool)))) (hAPP _let_0 _let_0 (combc int int bool) (fequal int))), (zero_zero int) ) 15.44/15.61 ( (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong s1), s ) 15.44/15.61 ( (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong s1), skv_4 ) 15.44/15.61 ( (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong s1), skv_10 ) 15.44/15.61 ( (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1) ) 15.44/15.61 ( (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.44/15.61 ( (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1) ) 15.44/15.61 ( (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1) ) 15.44/15.61 ( (fun int bool), (fun int bool), (collect int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun _let_2 _let_0))) (let ((_let_4 (fun int _let_3))) (hAPP _let_1 _let_0 (hAPP (fun _let_0 bool) (fun _let_1 _let_0) (combb _let_0 bool int) (fEx int)) (hAPP _let_2 _let_1 (hAPP _let_4 (fun _let_2 _let_1) (combc int _let_2 _let_0) (hAPP _let_1 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_1 _let_4) (combb _let_0 _let_3 int) (combb int bool int)) (fequal int))) (hAPP int _let_2 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))))))))) ) 15.44/15.61 ( (fun int bool), (fun int bool), (collect int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun _let_2 _let_0))) (let ((_let_5 (fun int _let_4))) (hAPP _let_1 _let_0 (hAPP (fun _let_0 bool) (fun _let_1 _let_0) (combb _let_0 bool int) (fEx int)) (hAPP _let_2 _let_1 (hAPP _let_5 (fun _let_2 _let_1) (combc int _let_2 _let_0) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_1 _let_5) (combb _let_0 _let_4 int) (combb int bool int)) (fequal int))) (hAPP int _let_2 (hAPP _let_3 _let_3 (combc int int int) (hAPP _let_2 _let_3 (hAPP _let_3 (fun _let_2 _let_3) (combb int _let_2 int) (plus_plus int)) (hAPP int _let_2 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one int)))))))))) ) 15.44/15.61 ( (fun int bool), (fun int bool), (let ((_let_0 (fun int bool))) (hAPP (fun bool bool) (fun _let_0 _let_0) (combb bool bool int) fNot)), (let ((_let_0 (fun int (fun int bool)))) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (fequal int)) (zero_zero int))) ) 15.44/15.61 ( (fun int bool), (fun int (fun int bool)), (let ((_let_0 (fun int bool))) (hAPP (fun _let_0 bool) (fun (fun int _let_0) _let_0) (combb _let_0 bool int) (fEx int))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun _let_2 _let_0))) (let ((_let_4 (fun int _let_3))) (hAPP _let_2 _let_1 (hAPP _let_4 (fun _let_2 _let_1) (combc int _let_2 _let_0) (hAPP _let_1 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_1 _let_4) (combb _let_0 _let_3 int) (combb int bool int)) (fequal int))) (hAPP int _let_2 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))))))) ) 15.44/15.61 ( (fun int bool), (fun int (fun int bool)), (let ((_let_0 (fun int bool))) (hAPP (fun _let_0 bool) (fun (fun int _let_0) _let_0) (combb _let_0 bool int) (fEx int))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun _let_2 _let_0))) (let ((_let_5 (fun int _let_4))) (hAPP _let_2 _let_1 (hAPP _let_5 (fun _let_2 _let_1) (combc int _let_2 _let_0) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_1 _let_5) (combb _let_0 _let_4 int) (combb int bool int)) (fequal int))) (hAPP int _let_2 (hAPP _let_3 _let_3 (combc int int int) (hAPP _let_2 _let_3 (hAPP _let_3 (fun _let_2 _let_3) (combb int _let_2 int) (plus_plus int)) (hAPP int _let_2 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one int))))))))) ) 15.44/15.61 ( (fun int (fun int bool)), int, zcong, s1 ) 15.44/15.61 ( (fun int (fun int bool)), int, zcong, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.44/15.61 ( (fun int (fun int bool)), int, zcong, (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.44/15.61 ( (fun int (fun int bool)), int, zcong, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.44/15.61 ( (fun int (fun int bool)), int, (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int _let_1))) (let ((_let_5 (fun _let_2 _let_1))) (hAPP _let_4 _let_4 (combc int int _let_0) (hAPP _let_4 _let_4 (hAPP (fun _let_1 _let_1) (fun _let_4 _let_4) (combb _let_1 _let_1 int) (combc int int bool)) (hAPP _let_3 _let_4 (hAPP _let_5 (fun _let_3 _let_4) (combb _let_2 _let_1 int) (hAPP _let_1 _let_5 (combb int _let_0 int) (fequal int))) int_gcd))))))))), (one_one int) ) 15.44/15.61 ( (fun int (fun int bool)), (fun int (fun int bool)), (combc int int bool), (fequal int) ) 15.44/15.61 ( (fun int (fun int bool)), (fun int (fun int bool)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun _let_0 _let_0))) (hAPP _let_4 (fun _let_1 _let_1) (combb _let_0 _let_0 int) (hAPP _let_3 _let_4 (combs int bool bool) (hAPP _let_0 _let_3 (hAPP (fun bool _let_2) (fun _let_0 _let_3) (combb bool _let_2 int) fconj) (hAPP int _let_0 (ord_less int) (zero_zero int)))))))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int _let_1))) (let ((_let_5 (fun _let_2 _let_1))) (hAPP int _let_1 (hAPP _let_4 _let_4 (combc int int _let_0) (hAPP _let_4 _let_4 (hAPP (fun _let_1 _let_1) (fun _let_4 _let_4) (combb _let_1 _let_1 int) (combc int int bool)) (hAPP _let_3 _let_4 (hAPP _let_5 (fun _let_3 _let_4) (combb _let_2 _let_1 int) (hAPP _let_1 _let_5 (combb int _let_0 int) (fequal int))) int_gcd))) (one_one int)))))))) ) 15.44/15.61 ( (fun int (fun int bool)), (fun int int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun (fun int int) _let_0))) (let ((_let_3 (fun int _let_2))) (hAPP _let_3 (fun (fun int int) _let_1) (combc int (fun int int) _let_0) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 int) (combb int bool int)) (fequal int))))))), (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.44/15.62 ( (fun int (fun int bool)), (fun int int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun (fun int int) _let_0))) (let ((_let_3 (fun int _let_2))) (hAPP _let_3 (fun (fun int int) _let_1) (combc int (fun int int) _let_0) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 int) (combb int bool int)) (fequal int))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (hAPP int _let_0 (hAPP _let_1 _let_1 (combc int int int) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)) (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one int)))) ) 15.44/15.62 ( (fun int int), nat, (hAPP (fun int (fun nat int)) (fun nat (fun int int)) (combc int nat int) (power_power int)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.62 ( (fun int int), int, (times_times int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.62 ( (fun int int), int, (times_times int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.44/15.62 ( (fun int int), int, (times_times int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.44/15.62 ( (fun int int), int, (minus_minus int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.44/15.62 ( (fun int int), int, (plus_plus int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.44/15.62 ( (fun int int), int, (plus_plus int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.44/15.62 ( (fun int int), int, legendre, (hAPP int int (number_number_of int) min_1) ) 15.44/15.62 ( (fun int int), int, (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (hAPP _let_1 _let_1 (combc int int int) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)) (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))))), (one_one int) ) 15.44/15.62 ( (fun nat bool), bool, (combk bool nat), fTrue ) 15.44/15.62 ( (fun nat bool), nat, (ord_less nat), (zero_zero nat) ) 15.44/15.62 ( (fun nat bool), nat, (let ((_let_0 (fun nat (fun nat bool)))) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat))), (zero_zero nat) ) 15.44/15.62 ( (fun nat bool), (fun nat bool), (collect nat), prime ) 15.44/15.62 ( (fun nat bool), (fun nat bool), (let ((_let_0 (fun nat bool))) (hAPP (fun bool bool) (fun _let_0 _let_0) (combb bool bool nat) fNot)), (let ((_let_0 (fun nat (fun nat bool)))) (hAPP nat (fun nat bool) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat)) (zero_zero nat))) ) 15.44/15.62 ( (fun nat nat), nat, (plus_plus nat), (one_one nat) ) 15.44/15.62 ( (fun nat nat), nat, (let ((_let_0 (fun nat (fun nat nat)))) (hAPP _let_0 _let_0 (combc nat nat nat) (times_times nat))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.62 ( (fun nat nat), nat, (let ((_let_0 (fun nat (fun nat nat)))) (let ((_let_1 (combc nat nat nat))) (hAPP _let_0 _let_0 _let_1 (hAPP (fun nat nat) _let_0 (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_0 _let_0 _let_1 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))), (one_one nat) ) 15.44/15.62 ( (fun (product_prod nat nat) bool), (fun (product_prod nat nat) bool), (collect (product_prod nat nat)), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat (fun nat bool)))) (hAPP _let_1 (fun (product_prod nat nat) bool) (product_prod_case nat nat bool) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat (fun nat bool) nat) (hAPP _let_1 _let_1 (combc nat nat bool) (fequal nat))) suc)))) ) 15.44/15.62 ( (fun (product_prod nat nat) bool), (fun nat (fun nat bool)), (product_prod_case nat nat bool), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat (fun nat bool)))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat (fun nat bool) nat) (hAPP _let_1 _let_1 (combc nat nat bool) (fequal nat))) suc))) ) 15.44/15.62 ( real, nat, (real_1 nat), (zero_zero nat) ) 15.44/15.62 ( real, nat, (real_1 nat), (hAPP nat nat suc (zero_zero nat)) ) 15.44/15.62 ( real, int, (real_1 int), (one_one int) ) 15.44/15.62 ( real, int, (real_1 int), (zero_zero int) ) 15.44/15.62 ( real, int, (number_number_of real), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.44/15.62 ( real, int, (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.44/15.62 ( real, int, (number_number_of real), min_1 ) 15.44/15.62 ( real, int, (number_number_of real), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.62 ( real, int, (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.44/15.62 ( real, int, (number_number_of real), (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.62 ( real, int, (number_number_of real), (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 15.44/15.62 ( real, real, ln, (one_one real) ) 15.44/15.62 ( real, real, (uminus_uminus real), (one_one real) ) 15.44/15.62 ( real, real, (uminus_uminus real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.44/15.62 ( real, real, (uminus_uminus real), (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.44/15.62 ( real, real, cos, (zero_zero real) ) 15.44/15.62 ( real, real, cos, pi ) 15.44/15.62 ( real, real, cos, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.62 ( real, real, cos, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.44/15.62 ( real, real, cos, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.44/15.62 ( real, real, cos, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.44/15.62 ( real, real, cos, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.44/15.62 ( real, real, cos, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.44/15.62 ( real, real, cos, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.44/15.62 ( real, real, cos, skv_5 ) 15.44/15.62 ( real, real, sqrt, (one_one real) ) 15.44/15.62 ( real, real, sqrt, (zero_zero real) ) 15.44/15.62 ( real, real, sqrt, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.62 ( real, real, sqrt, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.44/15.62 ( real, real, sin, (zero_zero real) ) 15.44/15.62 ( real, real, sin, pi ) 15.44/15.62 ( real, real, sin, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.44/15.62 ( real, real, sin, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.44/15.62 ( real, real, sin, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.44/15.62 ( real, real, sin, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.44/15.62 ( real, real, sin, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.44/15.62 ( real, real, sin, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.44/15.62 ( real, real, (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.62 ( real, real, (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.44/15.62 ( real, real, (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.44/15.62 ( real, real, (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.44/15.62 ( real, real, tan, (zero_zero real) ) 15.44/15.62 ( real, real, tan, pi ) 15.44/15.62 ( real, real, tan, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.44/15.62 ( real, real, tan, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.44/15.62 ( real, real, tan, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.44/15.62 ( real, real, (hAPP real (fun real real) (inverse_divide real) (one_one real)), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.62 ( real, real, (hAPP real (fun real real) (inverse_divide real) (one_one real)), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.44/15.62 ( real, real, (hAPP real (fun real real) (inverse_divide real) (one_one real)), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.44/15.62 ( real, real, (hAPP real (fun real real) (inverse_divide real) (one_one real)), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 15.44/15.62 ( real, real, (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 15.44/15.62 ( real, real, (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.44/15.62 ( real, real, (inverse_inverse real), (zero_zero real) ) 15.44/15.62 ( real, real, arctan, (one_one real) ) 15.44/15.62 ( real, real, arctan, (zero_zero real) ) 15.44/15.62 ( real, real, arctan, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.44/15.62 ( real, real, arctan, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))))) ) 15.44/15.62 ( real, real, (hAPP real (fun real real) (inverse_divide real) (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.62 ( real, real, (sgn_sgn real), (zero_zero real) ) 15.44/15.62 ( real, real, (hAPP real (fun real real) (inverse_divide real) (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.62 ( real, real, (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.44/15.62 ( real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real _let_0 (minus_minus real) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1))))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 15.44/15.62 ( real, real, (hAPP real (fun real real) (inverse_divide real) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.62 ( real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1))))))), pi ) 15.44/15.62 ( real, (fun real bool), (the real), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3)))))))))))))) ) 15.44/15.62 ( real, rat, ratreal, (zero_zero rat) ) 15.44/15.62 ( real, rat, ratreal, (one_one rat) ) 15.44/15.62 ( real, complex, re, (one_one complex) ) 15.44/15.62 ( real, complex, re, ii ) 15.44/15.62 ( real, complex, re, (zero_zero complex) ) 15.44/15.62 ( real, complex, im, (one_one complex) ) 15.44/15.62 ( real, complex, im, ii ) 15.44/15.62 ( real, complex, im, (zero_zero complex) ) 15.44/15.62 ( real, (fun nat real), (suminf real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat (fun nat nat)))) (let ((_let_3 (fun nat _let_0))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun _let_1 _let_3))) (let ((_let_6 (combb real _let_0 nat))) (let ((_let_7 (combc nat nat nat))) (hAPP _let_1 _let_1 (hAPP _let_3 (fun _let_1 _let_1) (combs nat real real) (hAPP _let_1 _let_3 (hAPP _let_4 _let_5 _let_6 (inverse_divide real)) (hAPP real _let_1 (hAPP _let_3 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_3 (hAPP _let_4 _let_5 _let_6 (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) (one_one real)))) (hAPP (fun nat nat) _let_1 (hAPP _let_1 (fun (fun nat nat) _let_1) (combb nat real nat) (real_1 nat)) (hAPP nat (fun nat nat) (hAPP _let_2 _let_2 _let_7 (hAPP (fun nat nat) _let_2 (hAPP _let_2 (fun (fun nat nat) _let_2) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_2 _let_2 _let_7 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))))))))))) ) 15.44/15.62 ( (fun real bool), real, (ord_less real), (one_one real) ) 15.44/15.62 ( (fun real bool), real, (ord_less real), (zero_zero real) ) 15.44/15.62 ( (fun real bool), real, (ord_less real), pi ) 15.44/15.62 ( (fun real bool), real, (ord_less real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.44/15.62 ( (fun real bool), real, (ord_less real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.44/15.62 ( (fun real bool), real, (ord_less real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.44/15.62 ( (fun real bool), real, (ord_less real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 15.44/15.62 ( (fun real bool), real, (ord_less_eq real), (zero_zero real) ) 15.44/15.62 ( (fun real bool), real, (ord_less_eq real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.62 ( (fun real bool), real, (ord_less_eq real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.44/15.62 ( (fun real bool), real, (ord_less_eq real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.44/15.62 ( (fun real bool), real, (ord_less_eq real), skv_5 ) 15.44/15.62 ( (fun real bool), real, (let ((_let_0 (fun real (fun real bool)))) (hAPP _let_0 _let_0 (combc real real bool) (ord_less_eq real))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.62 ( (fun real bool), real, (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun real _let_0))) (hAPP _let_2 _let_2 (combc real real bool) (hAPP _let_1 _let_2 (hAPP _let_2 (fun _let_1 _let_2) (combb real _let_0 real) (fequal real)) cos))))), (zero_zero real) ) 15.44/15.62 ( (fun real bool), (fun real bool), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun real _let_1))) (hAPP _let_2 (fun _let_0 _let_0) (combs real bool bool) (hAPP _let_0 _let_2 (hAPP (fun bool _let_1) (fun _let_0 _let_2) (combb bool _let_1 real) fconj) (hAPP real _let_0 (ord_less_eq real) (zero_zero real))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun real _let_0))) (let ((_let_4 (fun real _let_2))) (let ((_let_5 (combc real real bool))) (hAPP _let_0 _let_0 (hAPP _let_4 (fun _let_0 _let_0) (combs real bool bool) (hAPP _let_0 _let_4 (hAPP (fun bool _let_2) (fun _let_0 _let_4) (combb bool _let_2 real) fconj) (hAPP real _let_0 (hAPP _let_3 _let_3 _let_5 (ord_less_eq real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_3 _let_3 _let_5 (hAPP _let_1 _let_3 (hAPP _let_3 (fun _let_1 _let_3) (combb real _let_0 real) (fequal real)) cos)) (zero_zero real))))))))) ) 15.44/15.62 ( (fun real bool), (fun real bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun real (fun real bool)))) (let ((_let_2 (fun real _let_0))) (hAPP _let_2 (fun (fun real bool) (fun real bool)) (combs real bool bool) (hAPP (fun real bool) _let_2 (hAPP (fun bool _let_0) (fun (fun real bool) _let_2) (combb bool _let_0 real) fconj) (hAPP real (fun real bool) (hAPP _let_1 _let_1 (combc real real bool) (ord_less_eq real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun real _let_0))) (hAPP real _let_0 (hAPP _let_2 _let_2 (combc real real bool) (hAPP _let_1 _let_2 (hAPP _let_2 (fun _let_1 _let_2) (combb real _let_0 real) (fequal real)) cos)) (zero_zero real))))) ) 15.44/15.62 ( (fun real bool), (fun real bool), (collect real), (let ((_let_0 (fun int (fun int bool)))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real real))) (let ((_let_3 (real_1 int))) (let ((_let_4 (fun (fun int bool) bool))) (let ((_let_5 (fun bool bool))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun int _let_5))) (let ((_let_8 (fun (fun int bool) (fun int bool)))) (let ((_let_9 (fun (fun int bool) _let_7))) (let ((_let_10 (fun _let_0 (fun int bool)))) (let ((_let_11 (fEx int))) (let ((_let_12 (fun int real))) (let ((_let_13 (fun int _let_8))) (let ((_let_14 (fun (fun int bool) _let_0))) (let ((_let_15 (fun int _let_7))) (let ((_let_16 (fun _let_15 _let_13))) (let ((_let_17 (fun _let_0 _let_15))) (let ((_let_18 (fun real (fun int bool)))) (let ((_let_19 (fun real _let_0))) (let ((_let_20 (fun real _let_14))) (let ((_let_21 (fun real _let_13))) (let ((_let_22 (fun real _let_15))) (let ((_let_23 (fun int _let_12))) (let ((_let_24 (fun _let_23 _let_0))) (let ((_let_25 (fun real _let_24))) (let ((_let_26 (fun _let_12 (fun int bool)))) (let ((_let_27 (fun real _let_26))) (let ((_let_28 (fun _let_12 _let_12))) (let ((_let_29 (fun int _let_28))) (let ((_let_30 (fun int _let_2))) (hAPP _let_18 _let_1 (hAPP _let_4 (fun _let_18 _let_1) (combb (fun int bool) bool real) _let_11) (hAPP _let_19 _let_18 (hAPP _let_10 (fun _let_19 _let_18) (combb _let_0 (fun int bool) real) (hAPP _let_4 _let_10 (combb (fun int bool) bool int) _let_11)) (hAPP (fun int bool) _let_19 (hAPP _let_20 (fun (fun int bool) _let_19) (combc real (fun int bool) _let_0) (hAPP _let_21 _let_20 (hAPP (fun _let_13 _let_14) (fun _let_21 _let_20) (combb _let_13 _let_14 real) (combc int (fun int bool) (fun int bool))) (hAPP _let_22 _let_21 (hAPP _let_16 (fun _let_22 _let_21) (combb _let_15 _let_13 real) (hAPP (fun _let_7 _let_8) _let_16 (combb _let_7 _let_8 int) (combs int bool bool))) (hAPP _let_19 _let_22 (hAPP _let_17 (fun _let_19 _let_22) (combb _let_0 _let_15 real) (hAPP _let_9 _let_17 (combb (fun int bool) _let_7 int) (hAPP (fun bool _let_5) _let_9 (combb bool _let_5 int) fconj))) (hAPP _let_23 _let_19 (hAPP _let_25 (fun _let_23 _let_19) (combc real _let_23 _let_0) (hAPP _let_27 _let_25 (hAPP (fun _let_26 _let_24) (fun _let_27 _let_25) (combb _let_26 _let_24 real) (combb _let_12 (fun int bool) int)) (hAPP _let_6 _let_27 (hAPP (fun _let_1 _let_26) (fun _let_6 _let_27) (combb _let_1 _let_26 real) (combb real bool int)) (fequal real)))) (hAPP _let_12 _let_23 (hAPP _let_29 (fun _let_12 _let_23) (combc int _let_12 _let_12) (hAPP _let_30 _let_29 (hAPP (fun _let_2 _let_28) (fun _let_30 _let_29) (combb _let_2 _let_28 int) (combb real real int)) (hAPP _let_12 _let_30 (hAPP (fun real _let_2) (fun _let_12 _let_30) (combb real _let_2 int) (inverse_divide real)) _let_3))) _let_3)))))) (hAPP (fun int bool) (fun int bool) (hAPP _let_5 _let_8 (combb bool bool int) fNot) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (fequal int)) (zero_zero int))))))))))))))))))))))))))))))))))))) ) 15.44/15.62 ( (fun real bool), (fun real bool), (collect real), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real real))) (let ((_let_3 (fun nat (fun nat bool)))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun (fun nat real) (fun nat real)))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun (fun nat bool) (fun nat bool)))) (let ((_let_8 (fun int real))) (let ((_let_9 (fun nat _let_4))) (let ((_let_10 (fun (fun nat bool) _let_9))) (let ((_let_11 (fun real _let_0))) (let ((_let_12 (fun int _let_2))) (let ((_let_13 (fun real (fun int (fun nat bool))))) (let ((_let_14 (fun (fun int (fun nat bool)) _let_0))) (let ((_let_15 (fun (fun nat bool) (fun int (fun nat bool))))) (let ((_let_16 (fun real _let_15))) (let ((_let_17 (fun int _let_7))) (let ((_let_18 (fun real _let_17))) (let ((_let_19 (fun int _let_9))) (let ((_let_20 (fun real _let_19))) (let ((_let_21 (fun _let_19 _let_17))) (let ((_let_22 (fun (fun int (fun nat bool)) _let_19))) (let ((_let_23 (fun int (fun nat real)))) (let ((_let_24 (fun _let_23 (fun int (fun nat bool))))) (let ((_let_25 (fun real _let_24))) (let ((_let_26 (fun (fun nat real) (fun nat bool)))) (let ((_let_27 (fun real _let_26))) (let ((_let_28 (fun int _let_5))) (hAPP _let_11 _let_1 (hAPP (fun _let_0 bool) (fun _let_11 _let_1) (combb _let_0 bool real) (fEx int)) (hAPP _let_13 _let_11 (hAPP _let_14 (fun _let_13 _let_11) (combb (fun int (fun nat bool)) _let_0 real) (hAPP (fun (fun nat bool) bool) _let_14 (combb (fun nat bool) bool int) (fEx nat))) (hAPP (fun nat bool) _let_13 (hAPP _let_16 (fun (fun nat bool) _let_13) (combc real (fun nat bool) (fun int (fun nat bool))) (hAPP _let_18 _let_16 (hAPP (fun _let_17 _let_15) (fun _let_18 _let_16) (combb _let_17 _let_15 real) (combc int (fun nat bool) (fun nat bool))) (hAPP _let_20 _let_18 (hAPP _let_21 (fun _let_20 _let_18) (combb _let_19 _let_17 real) (hAPP (fun _let_9 _let_7) _let_21 (combb _let_9 _let_7 int) (combs nat bool bool))) (hAPP _let_13 _let_20 (hAPP _let_22 (fun _let_13 _let_20) (combb (fun int (fun nat bool)) _let_19 real) (hAPP _let_10 _let_22 (combb (fun nat bool) _let_9 int) (hAPP (fun bool _let_4) _let_10 (combb bool _let_4 nat) fconj))) (hAPP _let_23 _let_13 (hAPP _let_25 (fun _let_23 _let_13) (combc real _let_23 (fun int (fun nat bool))) (hAPP _let_27 _let_25 (hAPP (fun _let_26 _let_24) (fun _let_27 _let_25) (combb _let_26 _let_24 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_6 _let_27 (hAPP (fun _let_1 _let_26) (fun _let_6 _let_27) (combb _let_1 _let_26 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_23 (hAPP _let_28 (fun (fun nat real) _let_23) (combc int (fun nat real) (fun nat real)) (hAPP _let_12 _let_28 (hAPP (fun _let_2 _let_5) (fun _let_12 _let_28) (combb _let_2 _let_5 int) (combb real real nat)) (hAPP _let_8 _let_12 (hAPP (fun real _let_2) (fun _let_8 _let_12) (combb real _let_2 int) (inverse_divide real)) (real_1 int)))) (real_1 nat))))))) (hAPP (fun nat bool) (fun nat bool) (hAPP _let_4 _let_7 (combb bool bool nat) fNot) (hAPP nat (fun nat bool) (hAPP _let_3 _let_3 (combc nat nat bool) (fequal nat)) (zero_zero nat))))))))))))))))))))))))))))))))))) ) 15.44/15.62 ( (fun real bool), (fun nat real), (sums real), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (hAPP real _let_1 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc))) ) 15.44/15.62 ( (fun real bool), (fun real (fun int bool)), (let ((_let_0 (fun int bool))) (hAPP (fun _let_0 bool) (fun (fun real _let_0) (fun real bool)) (combb _let_0 bool real) (fEx int))), (let ((_let_0 (fun int (fun int bool)))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real real))) (let ((_let_3 (real_1 int))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun int _let_4))) (let ((_let_7 (fun (fun int bool) (fun int bool)))) (let ((_let_8 (fun (fun int bool) _let_6))) (let ((_let_9 (fun _let_0 (fun int bool)))) (let ((_let_10 (fun int real))) (let ((_let_11 (fun int _let_7))) (let ((_let_12 (fun (fun int bool) _let_0))) (let ((_let_13 (fun int _let_6))) (let ((_let_14 (fun _let_13 _let_11))) (let ((_let_15 (fun _let_0 _let_13))) (let ((_let_16 (fun real (fun int bool)))) (let ((_let_17 (fun real _let_0))) (let ((_let_18 (fun real _let_12))) (let ((_let_19 (fun real _let_11))) (let ((_let_20 (fun real _let_13))) (let ((_let_21 (fun int _let_10))) (let ((_let_22 (fun _let_21 _let_0))) (let ((_let_23 (fun real _let_22))) (let ((_let_24 (fun _let_10 (fun int bool)))) (let ((_let_25 (fun real _let_24))) (let ((_let_26 (fun _let_10 _let_10))) (let ((_let_27 (fun int _let_26))) (let ((_let_28 (fun int _let_2))) (hAPP _let_17 _let_16 (hAPP _let_9 (fun _let_17 _let_16) (combb _let_0 (fun int bool) real) (hAPP (fun (fun int bool) bool) _let_9 (combb (fun int bool) bool int) (fEx int))) (hAPP (fun int bool) _let_17 (hAPP _let_18 (fun (fun int bool) _let_17) (combc real (fun int bool) _let_0) (hAPP _let_19 _let_18 (hAPP (fun _let_11 _let_12) (fun _let_19 _let_18) (combb _let_11 _let_12 real) (combc int (fun int bool) (fun int bool))) (hAPP _let_20 _let_19 (hAPP _let_14 (fun _let_20 _let_19) (combb _let_13 _let_11 real) (hAPP (fun _let_6 _let_7) _let_14 (combb _let_6 _let_7 int) (combs int bool bool))) (hAPP _let_17 _let_20 (hAPP _let_15 (fun _let_17 _let_20) (combb _let_0 _let_13 real) (hAPP _let_8 _let_15 (combb (fun int bool) _let_6 int) (hAPP (fun bool _let_4) _let_8 (combb bool _let_4 int) fconj))) (hAPP _let_21 _let_17 (hAPP _let_23 (fun _let_21 _let_17) (combc real _let_21 _let_0) (hAPP _let_25 _let_23 (hAPP (fun _let_24 _let_22) (fun _let_25 _let_23) (combb _let_24 _let_22 real) (combb _let_10 (fun int bool) int)) (hAPP _let_5 _let_25 (hAPP (fun _let_1 _let_24) (fun _let_5 _let_25) (combb _let_1 _let_24 real) (combb real bool int)) (fequal real)))) (hAPP _let_10 _let_21 (hAPP _let_27 (fun _let_10 _let_21) (combc int _let_10 _let_10) (hAPP _let_28 _let_27 (hAPP (fun _let_2 _let_26) (fun _let_28 _let_27) (combb _let_2 _let_26 int) (combb real real int)) (hAPP _let_10 _let_28 (hAPP (fun real _let_2) (fun _let_10 _let_28) (combb real _let_2 int) (inverse_divide real)) _let_3))) _let_3)))))) (hAPP (fun int bool) (fun int bool) (hAPP _let_4 _let_7 (combb bool bool int) fNot) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (fequal int)) (zero_zero int)))))))))))))))))))))))))))))))))) ) 15.44/15.62 ( (fun real bool), (fun real (fun int bool)), (let ((_let_0 (fun int bool))) (hAPP (fun _let_0 bool) (fun (fun real _let_0) (fun real bool)) (combb _let_0 bool real) (fEx int))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real real))) (let ((_let_3 (fun nat (fun nat bool)))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun (fun nat real) (fun nat real)))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun (fun nat bool) (fun nat bool)))) (let ((_let_8 (fun int real))) (let ((_let_9 (fun nat _let_4))) (let ((_let_10 (fun (fun nat bool) _let_9))) (let ((_let_11 (fun real _let_0))) (let ((_let_12 (fun int _let_2))) (let ((_let_13 (fun real (fun int (fun nat bool))))) (let ((_let_14 (fun (fun int (fun nat bool)) _let_0))) (let ((_let_15 (fun (fun nat bool) (fun int (fun nat bool))))) (let ((_let_16 (fun real _let_15))) (let ((_let_17 (fun int _let_7))) (let ((_let_18 (fun real _let_17))) (let ((_let_19 (fun int _let_9))) (let ((_let_20 (fun real _let_19))) (let ((_let_21 (fun _let_19 _let_17))) (let ((_let_22 (fun (fun int (fun nat bool)) _let_19))) (let ((_let_23 (fun int (fun nat real)))) (let ((_let_24 (fun _let_23 (fun int (fun nat bool))))) (let ((_let_25 (fun real _let_24))) (let ((_let_26 (fun (fun nat real) (fun nat bool)))) (let ((_let_27 (fun real _let_26))) (let ((_let_28 (fun int _let_5))) (hAPP _let_13 _let_11 (hAPP _let_14 (fun _let_13 _let_11) (combb (fun int (fun nat bool)) _let_0 real) (hAPP (fun (fun nat bool) bool) _let_14 (combb (fun nat bool) bool int) (fEx nat))) (hAPP (fun nat bool) _let_13 (hAPP _let_16 (fun (fun nat bool) _let_13) (combc real (fun nat bool) (fun int (fun nat bool))) (hAPP _let_18 _let_16 (hAPP (fun _let_17 _let_15) (fun _let_18 _let_16) (combb _let_17 _let_15 real) (combc int (fun nat bool) (fun nat bool))) (hAPP _let_20 _let_18 (hAPP _let_21 (fun _let_20 _let_18) (combb _let_19 _let_17 real) (hAPP (fun _let_9 _let_7) _let_21 (combb _let_9 _let_7 int) (combs nat bool bool))) (hAPP _let_13 _let_20 (hAPP _let_22 (fun _let_13 _let_20) (combb (fun int (fun nat bool)) _let_19 real) (hAPP _let_10 _let_22 (combb (fun nat bool) _let_9 int) (hAPP (fun bool _let_4) _let_10 (combb bool _let_4 nat) fconj))) (hAPP _let_23 _let_13 (hAPP _let_25 (fun _let_23 _let_13) (combc real _let_23 (fun int (fun nat bool))) (hAPP _let_27 _let_25 (hAPP (fun _let_26 _let_24) (fun _let_27 _let_25) (combb _let_26 _let_24 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_6 _let_27 (hAPP (fun _let_1 _let_26) (fun _let_6 _let_27) (combb _let_1 _let_26 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_23 (hAPP _let_28 (fun (fun nat real) _let_23) (combc int (fun nat real) (fun nat real)) (hAPP _let_12 _let_28 (hAPP (fun _let_2 _let_5) (fun _let_12 _let_28) (combb _let_2 _let_5 int) (combb real real nat)) (hAPP _let_8 _let_12 (hAPP (fun real _let_2) (fun _let_8 _let_12) (combb real _let_2 int) (inverse_divide real)) (real_1 int)))) (real_1 nat))))))) (hAPP (fun nat bool) (fun nat bool) (hAPP _let_4 _let_7 (combb bool bool nat) fNot) (hAPP nat (fun nat bool) (hAPP _let_3 _let_3 (combc nat nat bool) (fequal nat)) (zero_zero nat)))))))))))))))))))))))))))))))))) ) 15.44/15.62 ( (fun real real), nat, root, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.62 ( (fun real real), real, (minus_minus real), (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))) ) 15.44/15.62 ( (fun real real), real, (inverse_divide real), (one_one real) ) 15.44/15.62 ( (fun real real), real, (inverse_divide real), pi ) 15.44/15.62 ( (fun real real), real, (inverse_divide real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.44/15.62 ( (fun real real), real, (inverse_divide real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.44/15.62 ( (fun real real), real, (inverse_divide real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.44/15.62 ( (fun real real), real, (times_times real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.62 ( (fun real real), real, (times_times real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.44/15.62 ( (fun real real), real, (times_times real), (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 15.44/15.62 ( (fun real real), (fun real real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)))), sin ) 15.44/15.62 ( rat, int, (hAPP int (fun int rat) fract (zero_zero int)), (one_one int) ) 15.44/15.62 ( rat, int, (hAPP int (fun int rat) fract (one_one int)), (one_one int) ) 15.44/15.62 ( rat, rat, (sgn_sgn rat), (zero_zero rat) ) 15.44/15.62 ( rat, (product_prod int int), frct, (let ((_let_0 (one_one int))) (let ((_let_1 (product_prod int int))) (hAPP int _let_1 (hAPP int (fun int _let_1) (product_Pair int int) _let_0) _let_0))) ) 15.44/15.62 ( (fun int rat), int, fract, (one_one int) ) 15.44/15.62 ( (fun int rat), int, fract, (zero_zero int) ) 15.44/15.62 ( (fun nat (fun nat bool)), (fun nat nat), (let ((_let_0 (fun nat (fun nat bool)))) (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat (fun nat bool) nat) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat)))), suc ) 15.44/15.62 ( (fun nat (fun nat bool)), (fun nat (fun nat bool)), (combc nat nat bool), (fequal nat) ) 15.44/15.62 ( (fun nat int), int, (power_power int), s ) 15.44/15.62 ( (fun nat int), int, (power_power int), s1 ) 15.44/15.62 ( (fun nat int), int, (power_power int), skv_14 ) 15.44/15.62 ( complex, nat, (hAPP complex (fun nat complex) (power_power complex) ii), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.62 ( complex, int, (number_number_of complex), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.44/15.62 ( complex, int, (number_number_of complex), min_1 ) 15.44/15.62 ( complex, real, cis, (zero_zero real) ) 15.44/15.62 ( complex, real, (hAPP real (fun real complex) complex_1 (zero_zero real)), (one_one real) ) 15.44/15.62 ( complex, real, (hAPP real (fun real complex) complex_1 (zero_zero real)), (zero_zero real) ) 15.44/15.62 ( complex, real, (of_real complex), pi ) 15.44/15.62 ( complex, real, (of_real complex), (hAPP int real (number_number_of real) min_1) ) 15.44/15.62 ( complex, real, (of_real complex), (hAPP real real (uminus_uminus real) (one_one real)) ) 15.44/15.62 ( complex, real, (hAPP real (fun real complex) complex_1 (one_one real)), (zero_zero real) ) 15.44/15.62 ( complex, complex, (inverse_inverse complex), ii ) 15.44/15.62 ( complex, complex, expi, (zero_zero complex) ) 15.44/15.62 ( complex, complex, expi, (let ((_let_0 (fun complex complex))) (let ((_let_1 (times_times complex))) (hAPP complex complex (hAPP complex _let_0 _let_1 (hAPP complex complex (hAPP complex _let_0 _let_1 (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi))) ii))) ) 15.44/15.62 ( complex, complex, (uminus_uminus complex), (one_one complex) ) 15.44/15.62 ( complex, complex, (uminus_uminus complex), ii ) 15.44/15.62 ( complex, complex, cnj, (one_one complex) ) 15.44/15.62 ( complex, complex, cnj, ii ) 15.44/15.62 ( complex, complex, cnj, (zero_zero complex) ) 15.44/15.62 ( complex, complex, (hAPP complex (fun complex complex) (times_times complex) ii), ii ) 15.44/15.62 ( complex, complex, (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real complex (of_real complex) pi) ) 15.44/15.62 ( complex, complex, (let ((_let_0 (fun complex complex))) (let ((_let_1 (times_times complex))) (hAPP complex _let_0 _let_1 (hAPP complex complex (hAPP complex _let_0 _let_1 (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi))))), ii ) 15.44/15.62 ( (fun nat real), (fun nat nat), (let ((_let_0 (fun nat real))) (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat real nat) (real_1 nat))), suc ) 15.44/15.62 ( (fun nat real), (fun nat nat), (let ((_let_0 (fun nat real))) (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat real nat) (real_1 nat))), (let ((_let_0 (fun nat (fun nat nat)))) (let ((_let_1 (combc nat nat nat))) (hAPP nat (fun nat nat) (hAPP _let_0 _let_0 _let_1 (hAPP (fun nat nat) _let_0 (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_0 _let_0 _let_1 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))) ) 15.44/15.62 ( (fun nat real), (fun nat nat), (let ((_let_0 (fun nat real))) (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat real nat) (hAPP real _let_0 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))), suc ) 15.44/15.62 ( (fun nat real), real, (power_power real), (hAPP int real (number_number_of real) min_1) ) 15.44/15.62 ( (fun nat real), real, (power_power real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.44/15.62 ( (fun nat real), real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (hAPP _let_2 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 nat) (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1))))))), (one_one real) ) 15.44/15.62 ( (fun nat real), (fun nat real), (diffs real), sin_coeff ) 15.44/15.62 ( (fun nat real), (fun nat real), (let ((_let_0 (fun nat real))) (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real))), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))) ) 15.44/15.62 ( (fun nat real), (fun nat real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (let ((_let_3 (fun real _let_0))) (let ((_let_4 (fun _let_1 _let_2))) (let ((_let_5 (combb real _let_0 nat))) (hAPP _let_2 (fun _let_1 _let_1) (combs nat real real) (hAPP _let_1 _let_2 (hAPP _let_3 _let_4 _let_5 (inverse_divide real)) (hAPP real _let_1 (hAPP _let_2 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_2 (hAPP _let_3 _let_4 _let_5 (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) (one_one real)))))))))), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat (fun nat nat)))) (let ((_let_2 (combc nat nat nat))) (hAPP (fun nat nat) _let_0 (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat real nat) (real_1 nat)) (hAPP nat (fun nat nat) (hAPP _let_1 _let_1 _let_2 (hAPP (fun nat nat) _let_1 (hAPP _let_1 (fun (fun nat nat) _let_1) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_1 _let_1 _let_2 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))))) ) 15.44/15.62 ( (fun int (fun int int)), (fun int int), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)))), (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.44/15.62 ( (fun int (fun int int)), (fun int int), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)))), (let ((_let_0 (fun int int))) (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.44/15.62 ( (fun int (fun int int)), (fun int int), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun _let_0 _let_1))) (let ((_let_3 (fun _let_0 _let_0))) (let ((_let_4 (fun int _let_3))) (hAPP _let_4 _let_2 (combc int _let_0 _let_0) (hAPP _let_1 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_1 _let_4) (combb _let_0 _let_3 int) (combb int int int)) (hAPP _let_0 _let_1 (hAPP _let_1 _let_2 (combb int _let_0 int) (plus_plus int)) (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))))))), (let ((_let_0 (fun int int))) (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.44/15.62 ( (fun int (fun int int)), (fun int (fun int int)), (combc int int int), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)) (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 15.44/15.62 ( (fun complex complex), complex, (times_times complex), ii ) 15.44/15.62 ( (fun complex complex), complex, (times_times complex), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.44/15.62 ( (fun complex complex), complex, (times_times complex), (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 15.44/15.62 ( (fun real complex), real, complex_1, (one_one real) ) 15.44/15.62 ( (fun real complex), real, complex_1, (zero_zero real) ) 15.44/15.62 ( (product_prod int int), int, (hAPP int (fun int (product_prod int int)) (product_Pair int int) (zero_zero int)), (one_one int) ) 15.44/15.62 ( (product_prod int int), int, (hAPP int (fun int (product_prod int int)) (product_Pair int int) s), (one_one int) ) 15.44/15.62 ( (product_prod int int), int, (hAPP int (fun int (product_prod int int)) (product_Pair int int) (one_one int)), (one_one int) ) 15.44/15.62 ( (product_prod int int), rat, quotient_of, (zero_zero rat) ) 15.44/15.62 ( (product_prod int int), rat, quotient_of, (one_one rat) ) 15.44/15.62 ( (fun int (product_prod int int)), int, (product_Pair int int), (one_one int) ) 15.44/15.62 ( (fun int (product_prod int int)), int, (product_Pair int int), (zero_zero int) ) 15.44/15.62 ( (fun int (product_prod int int)), int, (product_Pair int int), s ) 15.44/15.62 ( (fun (fun nat bool) bool), (fun nat int), (nat_tr1645093318rphism nat int), (semiring_1_of_nat int) ) 15.44/15.62 ( (fun (fun int bool) bool), int, (member int), (one_one int) ) 15.44/15.62 ( (fun (fun int bool) bool), (fun int nat), (nat_tr1645093318rphism int nat), nat_1 ) 15.44/15.62 ( quickcheck_code_int, int, (number_number_of quickcheck_code_int), (hAPP int int bit1 pls) ) 15.44/15.62 ( quickcheck_code_int, int, quickcheck_of_int, (one_one int) ) 15.44/15.62 ( quickcheck_code_int, int, quickcheck_of_int, (zero_zero int) ) 15.44/15.62 ( (fun nat (fun nat nat)), (fun nat nat), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat _let_0))) (hAPP _let_1 (fun _let_0 _let_1) (combb nat _let_0 nat) (plus_plus nat)))), (let ((_let_0 (fun nat (fun nat nat)))) (hAPP nat (fun nat nat) (hAPP _let_0 _let_0 (combc nat nat nat) (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.44/15.62 ( (fun nat (fun nat nat)), (fun nat (fun nat nat)), (combc nat nat nat), (times_times nat) ) 15.44/15.62 ( (fun nat (fun nat nat)), (fun nat (fun nat nat)), (combc nat nat nat), (let ((_let_0 (fun nat (fun nat nat)))) (hAPP (fun nat nat) _let_0 (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_0 _let_0 (combc nat nat nat) (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.44/15.62 ( (fun nat complex), complex, (power_power complex), ii ) 15.44/15.62 ( (fun nat (fun real real)), (fun nat real), (let ((_let_0 (fun real real))) (hAPP (fun real _let_0) (fun (fun nat real) (fun nat _let_0)) (combb real _let_0 nat) (inverse_divide real))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (hAPP real _let_1 (hAPP _let_2 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 nat) (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) (one_one real))))) ) 15.44/15.62 ( (fun nat (fun real real)), (fun nat real), (let ((_let_0 (fun real real))) (hAPP (fun real _let_0) (fun (fun nat real) (fun nat _let_0)) (combb real _let_0 nat) (times_times real))), (hAPP real (fun nat real) (power_power real) (hAPP int real (number_number_of real) min_1)) ) 15.44/15.62 ( (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)), (fun real real), (combb real real nat), (inverse_inverse real) ) 15.44/15.62 ( (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)), (fun nat (fun real real)), (combs nat real real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (let ((_let_3 (fun real _let_0))) (let ((_let_4 (fun _let_1 _let_2))) (let ((_let_5 (combb real _let_0 nat))) (hAPP _let_1 _let_2 (hAPP _let_3 _let_4 _let_5 (inverse_divide real)) (hAPP real _let_1 (hAPP _let_2 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_2 (hAPP _let_3 _let_4 _let_5 (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) (one_one real))))))))) ) 15.44/15.62 ( (fun real (fun real real)), (fun real real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)))), cos ) 15.44/15.62 ( (fun (fun nat real) (fun nat (fun real real))), (fun real (fun real real)), (combb real (fun real real) nat), (inverse_divide real) ) 15.44/15.62 ( (fun (fun nat real) (fun nat (fun real real))), (fun real (fun real real)), (combb real (fun real real) nat), (times_times real) ) 15.44/15.62 ( (fun (fun nat nat) (fun nat real)), (fun nat real), (combb nat real nat), (real_1 nat) ) 15.44/15.62 ( (fun (fun nat nat) (fun nat real)), (fun nat real), (combb nat real nat), (hAPP real (fun nat real) (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.44/15.62 ( (fun (filter nat) bool), real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 (fun real (fun (filter nat) bool)) (tendsto nat real) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))))), (zero_zero real) ) 15.44/15.62 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), (fun int int), (product_apsnd int int int), (uminus_uminus int) ) 15.44/15.62 ( (let ((_let_0 (fun int int))) (fun _let_0 (fun int _let_0))), (fun int (fun int int)), (combb int (fun int int) int), (plus_plus int) ) 15.44/15.62 ( (let ((_let_0 (fun int int))) (fun _let_0 (fun int _let_0))), (let ((_let_0 (fun int int))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun int int))) (combc int _let_0 _let_0)), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun _let_0 _let_0))) (let ((_let_3 (fun int _let_2))) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 int) (combb int int int)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)) (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))))) ) 15.44/15.62 ( code_code_numeral, int, (number_number_of code_code_numeral), pls ) 15.44/15.62 ( code_code_numeral, int, (number_number_of code_code_numeral), (hAPP int int bit1 pls) ) 15.44/15.62 ( code_code_numeral, code_code_numeral, (hAPP code_code_numeral (fun code_code_numeral code_code_numeral) (minus_minus code_code_numeral) (zero_zero code_code_numeral)), (one_one code_code_numeral) ) 15.44/15.62 ( (fun int (fun int (fun int bool))), (fun int (fun int int)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun _let_2 _let_1))) (hAPP _let_3 (fun (fun int _let_2) (fun int _let_1)) (combb _let_2 _let_1 int) (hAPP _let_1 _let_3 (combb int _let_0 int) (fequal int))))))), int_gcd ) 15.44/15.62 ( (fun int (fun int (fun int bool))), (fun int (fun int (fun int bool))), (combc int int (fun int bool)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int _let_1))) (let ((_let_5 (fun _let_2 _let_1))) (hAPP _let_4 _let_4 (hAPP (fun _let_1 _let_1) (fun _let_4 _let_4) (combb _let_1 _let_1 int) (combc int int bool)) (hAPP _let_3 _let_4 (hAPP _let_5 (fun _let_3 _let_4) (combb _let_2 _let_1 int) (hAPP _let_1 _let_5 (combb int _let_0 int) (fequal int))) int_gcd)))))))) ) 15.44/15.62 ( (fun int (fun int (fun int bool))), (fun int (fun int (fun int bool))), (let ((_let_0 (fun int (fun int bool)))) (let ((_let_1 (fun int _let_0))) (hAPP (fun _let_0 _let_0) (fun _let_1 _let_1) (combb _let_0 _let_0 int) (combc int int bool)))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int _let_1))) (let ((_let_5 (fun _let_2 _let_1))) (hAPP _let_3 _let_4 (hAPP _let_5 (fun _let_3 _let_4) (combb _let_2 _let_1 int) (hAPP _let_1 _let_5 (combb int _let_0 int) (fequal int))) int_gcd))))))) ) 15.44/15.62 ( (fun real (fun real bool)), (fun real real), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (hAPP _let_1 (fun (fun real real) _let_1) (combb real _let_0 real) (fequal real)))), cos ) 15.44/15.62 ( (fun real (fun real bool)), (fun real (fun real bool)), (combc real real bool), (ord_less_eq real) ) 15.44/15.62 ( (fun real (fun real bool)), (fun real (fun real bool)), (combc real real bool), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun real _let_0))) (hAPP _let_1 _let_2 (hAPP _let_2 (fun _let_1 _let_2) (combb real _let_0 real) (fequal real)) cos)))) ) 15.44/15.62 ( (fun real (fun nat real)), (fun nat (fun real real)), (combc nat real real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 nat) (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))))) ) 15.44/15.62 ( (let ((_let_0 (fun real real))) (fun _let_0 _let_0)), (fun real (fun real real)), (combs real real real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos))) ) 15.44/15.62 ( (let ((_let_0 (fun real real))) (fun _let_0 (fun real _let_0))), (fun real (fun real real)), (combb real (fun real real) real), (inverse_divide real) ) 15.44/15.62 ( (fun (product_prod int int) bool), int, (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 _let_0))) (let ((_let_3 (fun _let_1 int))) (hAPP _let_2 (fun int (fun _let_1 bool)) (combc _let_1 int bool) (hAPP _let_3 _let_2 (hAPP (fun int _let_0) (fun _let_3 _let_2) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))))))), (zero_zero int) ) 15.44/15.62 ( (fun (product_prod int int) bool), (fun int (fun int bool)), (product_prod_case int int bool), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun int _let_1))) (let ((_let_6 (fun int _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (fun _let_2 _let_1))) (let ((_let_9 (fun _let_1 _let_1))) (hAPP _let_1 _let_1 (hAPP _let_7 _let_9 (combb _let_0 _let_0 int) (hAPP _let_6 _let_7 (combs int bool bool) (hAPP _let_0 _let_6 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 int) fconj) (hAPP int _let_0 (ord_less int) (zero_zero int))))) (hAPP int _let_1 (hAPP _let_5 _let_5 (combc int int _let_0) (hAPP _let_5 _let_5 (hAPP _let_9 (fun _let_5 _let_5) (combb _let_1 _let_1 int) (combc int int bool)) (hAPP _let_3 _let_5 (hAPP _let_8 (fun _let_3 _let_5) (combb _let_2 _let_1 int) (hAPP _let_1 _let_8 (combb int _let_0 int) (fequal int))) int_gcd))) (one_one int))))))))))))) ) 15.44/15.63 ( (fun (product_prod int int) bool), (fun (product_prod int int) bool), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 bool))) (hAPP (fun bool bool) (fun _let_1 _let_1) (combb bool bool _let_0) fNot))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun _let_1 _let_0))) (let ((_let_4 (fun _let_1 int))) (hAPP int _let_2 (hAPP _let_3 (fun int _let_2) (combc _let_1 int bool) (hAPP _let_4 _let_3 (hAPP (fun int _let_0) (fun _let_4 _let_3) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))) ) 15.44/15.63 ( (fun int (fun (product_prod int int) bool)), (fun (product_prod int int) (fun int bool)), (combc (product_prod int int) int bool), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 _let_0))) (let ((_let_3 (fun _let_1 int))) (hAPP _let_3 _let_2 (hAPP (fun int _let_0) (fun _let_3 _let_2) (combb int _let_0 _let_1) (fequal int)) (product_snd int int)))))) ) 15.44/15.63 ( (fun real (fun (filter nat) bool)), (fun nat real), (tendsto nat real), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))) ) 15.44/15.63 ( (fun code_code_numeral code_code_numeral), code_code_numeral, (minus_minus code_code_numeral), (zero_zero code_code_numeral) ) 15.44/15.63 ( (fun int (fun bool bool)), (fun int bool), (let ((_let_0 (fun bool bool))) (hAPP (fun bool _let_0) (fun (fun int bool) (fun int _let_0)) (combb bool _let_0 int) fconj)), (hAPP int (fun int bool) (ord_less int) (zero_zero int)) ) 15.44/15.63 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), (fun bool bool), (combb bool bool int), fNot ) 15.44/15.63 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), (fun int (fun bool bool)), (combs int bool bool), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun int _let_1))) (hAPP _let_0 _let_2 (hAPP (fun bool _let_1) (fun _let_0 _let_2) (combb bool _let_1 int) fconj) (hAPP int _let_0 (ord_less int) (zero_zero int)))))) ) 15.44/15.63 ( (fun (fun int bool) (fun int (fun bool bool))), (fun bool (fun bool bool)), (combb bool (fun bool bool) int), fconj ) 15.44/15.63 ( (let ((_let_0 (fun int bool))) (fun (fun int _let_0) _let_0)), (fun (fun int bool) bool), (combb (fun int bool) bool int), (fEx int) ) 15.44/15.63 ( (fun int (fun (fun int int) (fun int bool))), (fun int (fun int bool)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun (fun int int) _let_0))) (hAPP (fun _let_0 _let_1) (fun (fun int _let_0) (fun int _let_1)) (combb _let_0 _let_1 int) (combb int bool int)))), (fequal int) ) 15.44/15.63 ( (fun (fun int int) (fun int (fun int bool))), (fun int (fun int bool)), (combb int (fun int bool) int), (fequal int) ) 15.44/15.63 ( (fun (fun int int) (fun int (fun int bool))), (fun int (fun (fun int int) (fun int bool))), (combc int (fun int int) (fun int bool)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun (fun int int) _let_0))) (let ((_let_3 (fun int _let_2))) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 int) (combb int bool int)) (fequal int)))))) ) 15.44/15.63 ( (let ((_let_0 (fun int bool))) (fun (fun int _let_0) (fun int (fun (fun int int) _let_0)))), (let ((_let_0 (fun int bool))) (fun _let_0 (fun (fun int int) _let_0))), (let ((_let_0 (fun int bool))) (combb _let_0 (fun (fun int int) _let_0) int)), (combb int bool int) ) 15.44/15.63 ( (filter real), real, (at real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.44/15.63 ( (fun (filter real) bool), real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 (fun real (fun (filter real) bool)) (tendsto real real) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin)))), (zero_zero real) ) 15.44/15.63 ( (fun real (fun (filter real) bool)), (fun real real), (tendsto real real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))) ) 15.44/15.63 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), (let ((_let_0 (product_prod int int))) (collect (product_prod _let_0 _let_0))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun _let_2 (fun _let_2 bool)))) (let ((_let_5 (fun (fun _let_2 bool) (fun _let_2 bool)))) (let ((_let_6 (fun _let_2 _let_5))) (let ((_let_7 (fun _let_4 _let_4))) (let ((_let_8 (fun _let_2 _let_3))) (let ((_let_9 (fun _let_2 _let_0))) (let ((_let_10 (fun _let_2 int))) (let ((_let_11 (fun _let_10 _let_9))) (let ((_let_12 (hAPP (fun int _let_0) _let_11 (combb int _let_0 _let_2) (fequal int)))) (let ((_let_13 (product_snd int int))) (let ((_let_14 (hAPP (fun _let_2 bool) _let_8 (hAPP (fun bool _let_3) (fun (fun _let_2 bool) _let_8) (combb bool _let_3 _let_2) fconj) (hAPP (fun _let_2 bool) (fun _let_2 bool) (hAPP _let_3 _let_5 (combb bool bool _let_2) fNot) (hAPP int (fun _let_2 bool) (hAPP _let_9 (fun int (fun _let_2 bool)) (combc _let_2 int bool) (hAPP _let_10 _let_9 _let_12 _let_13)) (zero_zero int)))))) (let ((_let_15 (fun _let_2 _let_10))) (let ((_let_16 (fun _let_10 (fun _let_2 bool)))) (let ((_let_17 (fun _let_2 _let_16))) (let ((_let_18 (fun _let_2 _let_9))) (let ((_let_19 (fun _let_10 _let_10))) (let ((_let_20 (fun _let_2 _let_19))) (let ((_let_21 (fun _let_10 _let_15))) (let ((_let_22 (fun _let_2 _let_1))) (let ((_let_23 (hAPP _let_10 _let_22 (hAPP (fun int _let_1) (fun _let_10 _let_22) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (let ((_let_24 (fun int _let_10))) (hAPP _let_4 (fun (product_prod _let_2 _let_2) bool) (product_prod_case _let_2 _let_2 bool) (hAPP _let_4 _let_4 (hAPP _let_6 _let_7 (combs _let_2 (fun _let_2 bool) (fun _let_2 bool)) (hAPP _let_8 _let_6 (hAPP (fun _let_3 _let_5) (fun _let_8 _let_6) (combb _let_3 _let_5 _let_2) (combb bool bool _let_2)) _let_14)) (hAPP _let_4 _let_4 (hAPP _let_5 _let_7 (combb (fun _let_2 bool) (fun _let_2 bool) _let_2) (hAPP _let_8 _let_5 (combs _let_2 bool bool) _let_14)) (hAPP _let_15 _let_4 (hAPP _let_17 (fun _let_15 _let_4) (combs _let_2 _let_10 (fun _let_2 bool)) (hAPP _let_18 _let_17 (hAPP (fun _let_9 _let_16) (fun _let_18 _let_17) (combb _let_9 _let_16 _let_2) (combs _let_2 int bool)) (hAPP _let_15 _let_18 (hAPP _let_11 (fun _let_15 _let_18) (combb _let_10 _let_9 _let_2) _let_12) (hAPP _let_10 _let_15 (hAPP _let_20 _let_21 (combc _let_2 _let_10 _let_10) (hAPP _let_22 _let_20 (hAPP (fun _let_1 _let_19) (fun _let_22 _let_20) (combb _let_1 _let_19 _let_2) (combb int int _let_2)) _let_23)) _let_13)))) (hAPP _let_10 _let_15 (hAPP _let_24 _let_21 (combb int _let_10 _let_2) (hAPP _let_22 _let_24 (combc _let_2 int int) _let_23)) _let_13)))))))))))))))))))))))))))))) ) 15.44/15.63 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (product_prod_case _let_0 _let_0 bool)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun _let_2 (fun _let_2 bool)))) (let ((_let_5 (fun (fun _let_2 bool) (fun _let_2 bool)))) (let ((_let_6 (fun _let_2 _let_5))) (let ((_let_7 (fun _let_4 _let_4))) (let ((_let_8 (fun _let_2 _let_3))) (let ((_let_9 (fun _let_2 _let_0))) (let ((_let_10 (fun _let_2 int))) (let ((_let_11 (fun _let_10 _let_9))) (let ((_let_12 (hAPP (fun int _let_0) _let_11 (combb int _let_0 _let_2) (fequal int)))) (let ((_let_13 (product_snd int int))) (let ((_let_14 (hAPP (fun _let_2 bool) _let_8 (hAPP (fun bool _let_3) (fun (fun _let_2 bool) _let_8) (combb bool _let_3 _let_2) fconj) (hAPP (fun _let_2 bool) (fun _let_2 bool) (hAPP _let_3 _let_5 (combb bool bool _let_2) fNot) (hAPP int (fun _let_2 bool) (hAPP _let_9 (fun int (fun _let_2 bool)) (combc _let_2 int bool) (hAPP _let_10 _let_9 _let_12 _let_13)) (zero_zero int)))))) (let ((_let_15 (fun _let_2 _let_10))) (let ((_let_16 (fun _let_10 (fun _let_2 bool)))) (let ((_let_17 (fun _let_2 _let_16))) (let ((_let_18 (fun _let_2 _let_9))) (let ((_let_19 (fun _let_10 _let_10))) (let ((_let_20 (fun _let_2 _let_19))) (let ((_let_21 (fun _let_10 _let_15))) (let ((_let_22 (fun _let_2 _let_1))) (let ((_let_23 (hAPP _let_10 _let_22 (hAPP (fun int _let_1) (fun _let_10 _let_22) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (let ((_let_24 (fun int _let_10))) (hAPP _let_4 _let_4 (hAPP _let_6 _let_7 (combs _let_2 (fun _let_2 bool) (fun _let_2 bool)) (hAPP _let_8 _let_6 (hAPP (fun _let_3 _let_5) (fun _let_8 _let_6) (combb _let_3 _let_5 _let_2) (combb bool bool _let_2)) _let_14)) (hAPP _let_4 _let_4 (hAPP _let_5 _let_7 (combb (fun _let_2 bool) (fun _let_2 bool) _let_2) (hAPP _let_8 _let_5 (combs _let_2 bool bool) _let_14)) (hAPP _let_15 _let_4 (hAPP _let_17 (fun _let_15 _let_4) (combs _let_2 _let_10 (fun _let_2 bool)) (hAPP _let_18 _let_17 (hAPP (fun _let_9 _let_16) (fun _let_18 _let_17) (combb _let_9 _let_16 _let_2) (combs _let_2 int bool)) (hAPP _let_15 _let_18 (hAPP _let_11 (fun _let_15 _let_18) (combb _let_10 _let_9 _let_2) _let_12) (hAPP _let_10 _let_15 (hAPP _let_20 _let_21 (combc _let_2 _let_10 _let_10) (hAPP _let_22 _let_20 (hAPP (fun _let_1 _let_19) (fun _let_22 _let_20) (combb _let_1 _let_19 _let_2) (combb int int _let_2)) _let_23)) _let_13)))) (hAPP _let_10 _let_15 (hAPP _let_24 _let_21 (combb int _let_10 _let_2) (hAPP _let_22 _let_24 (combc _let_2 int int) _let_23)) _let_13))))))))))))))))))))))))))))) ) 15.44/15.63 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_1 _let_3))) (let ((_let_5 (fun _let_3 _let_3))) (let ((_let_6 (fun _let_1 _let_5))) (let ((_let_7 (fun _let_1 _let_2))) (let ((_let_8 (combb bool bool _let_1))) (let ((_let_9 (fun _let_1 _let_0))) (let ((_let_10 (fun _let_1 int))) (hAPP _let_6 (fun _let_4 _let_4) (combs _let_1 _let_3 _let_3) (hAPP _let_7 _let_6 (hAPP (fun _let_2 _let_5) (fun _let_7 _let_6) (combb _let_2 _let_5 _let_1) _let_8) (hAPP _let_3 _let_7 (hAPP (fun bool _let_2) (fun _let_3 _let_7) (combb bool _let_2 _let_1) fconj) (hAPP _let_3 _let_3 (hAPP _let_2 _let_5 _let_8 fNot) (hAPP int _let_3 (hAPP _let_9 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_10 _let_9 (hAPP (fun int _let_0) (fun _let_10 _let_9) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))))))))))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun _let_2 (fun _let_2 bool)))) (let ((_let_5 (fun (fun _let_2 bool) (fun _let_2 bool)))) (let ((_let_6 (fun _let_2 _let_3))) (let ((_let_7 (fun _let_2 _let_0))) (let ((_let_8 (fun _let_2 int))) (let ((_let_9 (fun _let_8 _let_7))) (let ((_let_10 (hAPP (fun int _let_0) _let_9 (combb int _let_0 _let_2) (fequal int)))) (let ((_let_11 (product_snd int int))) (let ((_let_12 (fun _let_2 _let_8))) (let ((_let_13 (fun _let_8 (fun _let_2 bool)))) (let ((_let_14 (fun _let_2 _let_13))) (let ((_let_15 (fun _let_2 _let_7))) (let ((_let_16 (fun _let_8 _let_8))) (let ((_let_17 (fun _let_2 _let_16))) (let ((_let_18 (fun _let_8 _let_12))) (let ((_let_19 (fun _let_2 _let_1))) (let ((_let_20 (hAPP _let_8 _let_19 (hAPP (fun int _let_1) (fun _let_8 _let_19) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (let ((_let_21 (fun int _let_8))) (hAPP _let_4 _let_4 (hAPP _let_5 (fun _let_4 _let_4) (combb (fun _let_2 bool) (fun _let_2 bool) _let_2) (hAPP _let_6 _let_5 (combs _let_2 bool bool) (hAPP (fun _let_2 bool) _let_6 (hAPP (fun bool _let_3) (fun (fun _let_2 bool) _let_6) (combb bool _let_3 _let_2) fconj) (hAPP (fun _let_2 bool) (fun _let_2 bool) (hAPP _let_3 _let_5 (combb bool bool _let_2) fNot) (hAPP int (fun _let_2 bool) (hAPP _let_7 (fun int (fun _let_2 bool)) (combc _let_2 int bool) (hAPP _let_8 _let_7 _let_10 _let_11)) (zero_zero int)))))) (hAPP _let_12 _let_4 (hAPP _let_14 (fun _let_12 _let_4) (combs _let_2 _let_8 (fun _let_2 bool)) (hAPP _let_15 _let_14 (hAPP (fun _let_7 _let_13) (fun _let_15 _let_14) (combb _let_7 _let_13 _let_2) (combs _let_2 int bool)) (hAPP _let_12 _let_15 (hAPP _let_9 (fun _let_12 _let_15) (combb _let_8 _let_7 _let_2) _let_10) (hAPP _let_8 _let_12 (hAPP _let_17 _let_18 (combc _let_2 _let_8 _let_8) (hAPP _let_19 _let_17 (hAPP (fun _let_1 _let_16) (fun _let_19 _let_17) (combb _let_1 _let_16 _let_2) (combb int int _let_2)) _let_20)) _let_11)))) (hAPP _let_8 _let_12 (hAPP _let_21 _let_18 (combb int _let_8 _let_2) (hAPP _let_19 _let_21 (combc _let_2 int int) _let_20)) _let_11))))))))))))))))))))))))) ) 15.44/15.63 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_1 _let_3))) (let ((_let_5 (fun _let_3 _let_3))) (let ((_let_6 (fun _let_1 _let_2))) (let ((_let_7 (fun _let_1 _let_0))) (let ((_let_8 (fun _let_1 int))) (hAPP _let_5 (fun _let_4 _let_4) (combb _let_3 _let_3 _let_1) (hAPP _let_6 _let_5 (combs _let_1 bool bool) (hAPP _let_3 _let_6 (hAPP (fun bool _let_2) (fun _let_3 _let_6) (combb bool _let_2 _let_1) fconj) (hAPP _let_3 _let_3 (hAPP _let_2 _let_5 (combb bool bool _let_1) fNot) (hAPP int _let_3 (hAPP _let_7 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_8 _let_7 (hAPP (fun int _let_0) (fun _let_8 _let_7) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))))))))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun _let_2 (fun _let_2 bool)))) (let ((_let_4 (fun _let_2 _let_0))) (let ((_let_5 (fun _let_2 int))) (let ((_let_6 (fun _let_5 _let_4))) (let ((_let_7 (product_snd int int))) (let ((_let_8 (fun _let_2 _let_5))) (let ((_let_9 (fun _let_5 (fun _let_2 bool)))) (let ((_let_10 (fun _let_2 _let_9))) (let ((_let_11 (fun _let_2 _let_4))) (let ((_let_12 (fun _let_5 _let_5))) (let ((_let_13 (fun _let_2 _let_12))) (let ((_let_14 (fun _let_5 _let_8))) (let ((_let_15 (fun _let_2 _let_1))) (let ((_let_16 (hAPP _let_5 _let_15 (hAPP (fun int _let_1) (fun _let_5 _let_15) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (let ((_let_17 (fun int _let_5))) (hAPP _let_8 _let_3 (hAPP _let_10 (fun _let_8 _let_3) (combs _let_2 _let_5 (fun _let_2 bool)) (hAPP _let_11 _let_10 (hAPP (fun _let_4 _let_9) (fun _let_11 _let_10) (combb _let_4 _let_9 _let_2) (combs _let_2 int bool)) (hAPP _let_8 _let_11 (hAPP _let_6 (fun _let_8 _let_11) (combb _let_5 _let_4 _let_2) (hAPP (fun int _let_0) _let_6 (combb int _let_0 _let_2) (fequal int))) (hAPP _let_5 _let_8 (hAPP _let_13 _let_14 (combc _let_2 _let_5 _let_5) (hAPP _let_15 _let_13 (hAPP (fun _let_1 _let_12) (fun _let_15 _let_13) (combb _let_1 _let_12 _let_2) (combb int int _let_2)) _let_16)) _let_7)))) (hAPP _let_5 _let_8 (hAPP _let_17 _let_14 (combb int _let_5 _let_2) (hAPP _let_15 _let_17 (combc _let_2 int int) _let_16)) _let_7)))))))))))))))))))) ) 15.44/15.63 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun _let_2 _let_0))) (let ((_let_4 (fun _let_2 int))) (let ((_let_5 (fun _let_4 _let_3))) (let ((_let_6 (fun _let_2 _let_4))) (let ((_let_7 (fun _let_4 (fun _let_2 bool)))) (let ((_let_8 (fun _let_2 _let_7))) (let ((_let_9 (fun _let_2 _let_3))) (let ((_let_10 (fun _let_4 _let_4))) (let ((_let_11 (fun _let_2 _let_10))) (let ((_let_12 (fun _let_2 _let_1))) (hAPP _let_8 (fun _let_6 (fun _let_2 (fun _let_2 bool))) (combs _let_2 _let_4 (fun _let_2 bool)) (hAPP _let_9 _let_8 (hAPP (fun _let_3 _let_7) (fun _let_9 _let_8) (combb _let_3 _let_7 _let_2) (combs _let_2 int bool)) (hAPP _let_6 _let_9 (hAPP _let_5 (fun _let_6 _let_9) (combb _let_4 _let_3 _let_2) (hAPP (fun int _let_0) _let_5 (combb int _let_0 _let_2) (fequal int))) (hAPP _let_4 _let_6 (hAPP _let_11 (fun _let_4 _let_6) (combc _let_2 _let_4 _let_4) (hAPP _let_12 _let_11 (hAPP (fun _let_1 _let_10) (fun _let_12 _let_11) (combb _let_1 _let_10 _let_2) (combb int int _let_2)) (hAPP _let_4 _let_12 (hAPP (fun int _let_1) (fun _let_4 _let_12) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (product_snd int int)))))))))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_2))) (let ((_let_4 (fun _let_1 _let_0))) (let ((_let_5 (fun int _let_2))) (hAPP _let_2 _let_3 (hAPP _let_5 (fun _let_2 _let_3) (combb int _let_2 _let_1) (hAPP _let_4 _let_5 (combc _let_1 int int) (hAPP _let_2 _let_4 (hAPP (fun int _let_0) (fun _let_2 _let_4) (combb int _let_0 _let_1) (times_times int)) (product_fst int int)))) (product_snd int int)))))))) ) 15.44/15.63 ( (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)), (fun bool bool), (combb bool bool (product_prod int int)), fNot ) 15.44/15.63 ( (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)), (fun (product_prod int int) (fun bool bool)), (combs (product_prod int int) bool bool), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_1 _let_2))) (let ((_let_5 (fun _let_1 _let_0))) (let ((_let_6 (fun _let_1 int))) (hAPP _let_3 _let_4 (hAPP (fun bool _let_2) (fun _let_3 _let_4) (combb bool _let_2 _let_1) fconj) (hAPP _let_3 _let_3 (hAPP _let_2 (fun _let_3 _let_3) (combb bool bool _let_1) fNot) (hAPP int _let_3 (hAPP _let_5 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_6 _let_5 (hAPP (fun int _let_0) (fun _let_6 _let_5) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))))))) ) 15.44/15.63 ( (let ((_let_0 (fun (product_prod int int) bool))) (fun (product_prod int int) (fun _let_0 _let_0))), (fun (product_prod int int) (fun bool bool)), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun (fun _let_0 bool) (fun _let_0 bool)))) (hAPP (fun _let_1 _let_2) (fun (fun _let_0 _let_1) (fun _let_0 _let_2)) (combb _let_1 _let_2 _let_0) (combb bool bool _let_0))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_1 _let_2))) (let ((_let_5 (fun _let_1 _let_0))) (let ((_let_6 (fun _let_1 int))) (hAPP _let_3 _let_4 (hAPP (fun bool _let_2) (fun _let_3 _let_4) (combb bool _let_2 _let_1) fconj) (hAPP _let_3 _let_3 (hAPP _let_2 (fun _let_3 _let_3) (combb bool bool _let_1) fNot) (hAPP int _let_3 (hAPP _let_5 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_6 _let_5 (hAPP (fun int _let_0) (fun _let_6 _let_5) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))))))) ) 15.44/15.63 ( (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (fun _let_1 _let_1))), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 bool))) (combb _let_1 _let_1 _let_0))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_3 _let_3))) (let ((_let_5 (fun _let_1 _let_2))) (let ((_let_6 (fun _let_1 _let_0))) (let ((_let_7 (fun _let_1 int))) (hAPP _let_5 _let_4 (combs _let_1 bool bool) (hAPP _let_3 _let_5 (hAPP (fun bool _let_2) (fun _let_3 _let_5) (combb bool _let_2 _let_1) fconj) (hAPP _let_3 _let_3 (hAPP _let_2 _let_4 (combb bool bool _let_1) fNot) (hAPP int _let_3 (hAPP _let_6 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_7 _let_6 (hAPP (fun int _let_0) (fun _let_7 _let_6) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))))))))) ) 15.44/15.63 ( (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (fun _let_1 _let_1))), (let ((_let_0 (fun (product_prod int int) bool))) (fun (product_prod int int) (fun _let_0 _let_0))), (let ((_let_0 (fun (product_prod int int) bool))) (combs (product_prod int int) _let_0 _let_0)), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_3 _let_3))) (let ((_let_5 (fun _let_1 _let_4))) (let ((_let_6 (fun _let_1 _let_2))) (let ((_let_7 (combb bool bool _let_1))) (let ((_let_8 (fun _let_1 _let_0))) (let ((_let_9 (fun _let_1 int))) (hAPP _let_6 _let_5 (hAPP (fun _let_2 _let_4) (fun _let_6 _let_5) (combb _let_2 _let_4 _let_1) _let_7) (hAPP _let_3 _let_6 (hAPP (fun bool _let_2) (fun _let_3 _let_6) (combb bool _let_2 _let_1) fconj) (hAPP _let_3 _let_3 (hAPP _let_2 _let_4 _let_7 fNot) (hAPP int _let_3 (hAPP _let_8 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_9 _let_8 (hAPP (fun int _let_0) (fun _let_9 _let_8) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))))))))))) ) 15.44/15.63 ( (fun (product_prod int int) (fun bool bool)), (fun (product_prod int int) bool), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun bool bool))) (hAPP (fun bool _let_1) (fun (fun _let_0 bool) (fun _let_0 _let_1)) (combb bool _let_1 _let_0) fconj))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun _let_1 _let_0))) (let ((_let_4 (fun _let_1 int))) (hAPP _let_2 _let_2 (hAPP (fun bool bool) (fun _let_2 _let_2) (combb bool bool _let_1) fNot) (hAPP int _let_2 (hAPP _let_3 (fun int _let_2) (combc _let_1 int bool) (hAPP _let_4 _let_3 (hAPP (fun int _let_0) (fun _let_4 _let_3) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int)))))))) ) 15.44/15.63 ( (let ((_let_0 (fun (product_prod int int) bool))) (fun (fun (product_prod int int) (fun bool bool)) (fun (product_prod int int) (fun _let_0 _let_0)))), (let ((_let_0 (fun (product_prod int int) bool))) (fun (fun bool bool) (fun _let_0 _let_0))), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 bool))) (combb (fun bool bool) (fun _let_1 _let_1) _let_0))), (combb bool bool (product_prod int int)) ) 15.44/15.63 ( (let ((_let_0 (product_prod int int))) (fun (fun _let_0 bool) (fun _let_0 (fun bool bool)))), (fun bool (fun bool bool)), (combb bool (fun bool bool) (product_prod int int)), fconj ) 15.44/15.63 ( (fun (product_prod int int) (fun int bool)), (fun (product_prod int int) int), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (hAPP (fun int _let_0) (fun (fun _let_1 int) (fun _let_1 _let_0)) (combb int _let_0 _let_1) (fequal int)))), (product_snd int int) ) 15.44/15.63 ( (fun (product_prod int int) int), (fun int (fun int int)), (product_prod_case int int int), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun _let_0 _let_1))) (let ((_let_3 (fun _let_0 _let_0))) (let ((_let_4 (fun int _let_3))) (let ((_let_5 (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP _let_0 _let_1 (hAPP _let_4 _let_2 (combc int _let_0 _let_0) (hAPP _let_1 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_1 _let_4) (combb _let_0 _let_3 int) (combb int int int)) (hAPP _let_0 _let_1 (hAPP _let_1 _let_2 (combb int _let_0 int) (plus_plus int)) _let_5))) _let_5))))))) ) 15.44/15.63 ( (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 (fun int bool)))), (fun int (fun int bool)), (combb int (fun int bool) (product_prod int int)), (fequal int) ) 15.44/15.63 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (fun (product_prod int int) int), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_2 _let_2))) (let ((_let_4 (fun _let_1 _let_3))) (let ((_let_5 (fun _let_1 _let_0))) (hAPP _let_4 (fun _let_2 (fun _let_1 _let_2)) (combc _let_1 _let_2 _let_2) (hAPP _let_5 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_5 _let_4) (combb _let_0 _let_3 _let_1) (combb int int _let_1)) (hAPP _let_2 _let_5 (hAPP (fun int _let_0) (fun _let_2 _let_5) (combb int _let_0 _let_1) (times_times int)) (product_fst int int)))))))))), (product_snd int int) ) 15.44/15.63 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (fun (product_prod int int) int), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_0))) (let ((_let_4 (fun int _let_2))) (hAPP _let_4 (fun _let_2 (fun _let_1 _let_2)) (combb int _let_2 _let_1) (hAPP _let_3 _let_4 (combc _let_1 int int) (hAPP _let_2 _let_3 (hAPP (fun int _let_0) (fun _let_2 _let_3) (combb int _let_0 _let_1) (times_times int)) (product_fst int int))))))))), (product_snd int int) ) 15.44/15.63 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun (fun _let_0 int) (fun _let_0 bool)))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 (fun int bool)))), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 (fun int bool)))) (let ((_let_2 (fun (fun _let_0 int) (fun _let_0 bool)))) (hAPP (fun _let_1 _let_2) (fun (fun _let_0 _let_1) (fun _let_0 _let_2)) (combb _let_1 _let_2 _let_0) (combs _let_0 int bool))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun _let_2 _let_0))) (let ((_let_4 (fun _let_2 int))) (let ((_let_5 (fun _let_4 _let_3))) (let ((_let_6 (fun _let_2 _let_4))) (let ((_let_7 (fun _let_2 _let_3))) (let ((_let_8 (fun _let_4 _let_4))) (let ((_let_9 (fun _let_2 _let_8))) (let ((_let_10 (fun _let_2 _let_1))) (hAPP _let_6 _let_7 (hAPP _let_5 (fun _let_6 _let_7) (combb _let_4 _let_3 _let_2) (hAPP (fun int _let_0) _let_5 (combb int _let_0 _let_2) (fequal int))) (hAPP _let_4 _let_6 (hAPP _let_9 (fun _let_4 _let_6) (combc _let_2 _let_4 _let_4) (hAPP _let_10 _let_9 (hAPP (fun _let_1 _let_8) (fun _let_10 _let_9) (combb _let_1 _let_8 _let_2) (combb int int _let_2)) (hAPP _let_4 _let_10 (hAPP (fun int _let_1) (fun _let_4 _let_10) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (product_snd int int)))))))))))))) ) 15.44/15.63 ( (let ((_let_0 (product_prod int int))) (fun (fun _let_0 (fun _let_0 int)) (fun _let_0 (fun _let_0 bool)))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun (fun _let_0 int) (fun _let_0 bool)))), (let ((_let_0 (product_prod int int))) (combs _let_0 (fun _let_0 int) (fun _let_0 bool))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun _let_2 _let_0))) (let ((_let_4 (fun _let_2 int))) (let ((_let_5 (fun _let_4 _let_3))) (let ((_let_6 (fun _let_2 _let_4))) (let ((_let_7 (fun _let_4 (fun _let_2 bool)))) (let ((_let_8 (fun _let_2 _let_7))) (let ((_let_9 (fun _let_2 _let_3))) (let ((_let_10 (fun _let_4 _let_4))) (let ((_let_11 (fun _let_2 _let_10))) (let ((_let_12 (fun _let_2 _let_1))) (hAPP _let_9 _let_8 (hAPP (fun _let_3 _let_7) (fun _let_9 _let_8) (combb _let_3 _let_7 _let_2) (combs _let_2 int bool)) (hAPP _let_6 _let_9 (hAPP _let_5 (fun _let_6 _let_9) (combb _let_4 _let_3 _let_2) (hAPP (fun int _let_0) _let_5 (combb int _let_0 _let_2) (fequal int))) (hAPP _let_4 _let_6 (hAPP _let_11 (fun _let_4 _let_6) (combc _let_2 _let_4 _let_4) (hAPP _let_12 _let_11 (hAPP (fun _let_1 _let_10) (fun _let_12 _let_11) (combb _let_1 _let_10 _let_2) (combb int int _let_2)) (hAPP _let_4 _let_12 (hAPP (fun int _let_1) (fun _let_4 _let_12) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (product_snd int int))))))))))))))))) ) 15.44/15.63 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 (fun int bool)))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 _let_0))) (let ((_let_3 (fun _let_1 int))) (let ((_let_4 (fun _let_3 _let_2))) (hAPP _let_4 (fun (fun _let_1 _let_3) (fun _let_1 _let_2)) (combb _let_3 _let_2 _let_1) (hAPP (fun int _let_0) _let_4 (combb int _let_0 _let_1) (fequal int)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_2))) (let ((_let_4 (fun _let_2 _let_2))) (let ((_let_5 (fun _let_1 _let_4))) (let ((_let_6 (fun _let_1 _let_0))) (hAPP _let_2 _let_3 (hAPP _let_5 (fun _let_2 _let_3) (combc _let_1 _let_2 _let_2) (hAPP _let_6 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_6 _let_5) (combb _let_0 _let_4 _let_1) (combb int int _let_1)) (hAPP _let_2 _let_6 (hAPP (fun int _let_0) (fun _let_2 _let_6) (combb int _let_0 _let_1) (times_times int)) (product_fst int int)))) (product_snd int int))))))))) ) 15.44/15.63 ( (let ((_let_0 (product_prod int int))) (fun (fun _let_0 (fun _let_0 (fun int bool))) (fun _let_0 (fun (fun _let_0 int) (fun _let_0 bool))))), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 (fun int bool)) (fun (fun _let_0 int) (fun _let_0 bool)))), (let ((_let_0 (product_prod int int))) (combb (fun _let_0 (fun int bool)) (fun (fun _let_0 int) (fun _let_0 bool)) _let_0)), (combs (product_prod int int) int bool) ) 15.44/15.63 ( (let ((_let_0 (product_prod int int))) (fun (fun _let_0 (fun _let_0 int)) (fun _let_0 (fun _let_0 (fun int bool))))), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 (fun int bool)))), (let ((_let_0 (product_prod int int))) (combb (fun _let_0 int) (fun _let_0 (fun int bool)) _let_0)), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (hAPP (fun int _let_0) (fun (fun _let_1 int) (fun _let_1 _let_0)) (combb int _let_0 _let_1) (fequal int)))) ) 15.44/15.63 ( (let ((_let_0 (fun (product_prod int int) int))) (fun (product_prod int int) (fun _let_0 _let_0))), (fun (product_prod int int) (fun int int)), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun (fun _let_1 int) (fun _let_1 int)))) (hAPP (fun _let_0 _let_2) (fun (fun _let_1 _let_0) (fun _let_1 _let_2)) (combb _let_0 _let_2 _let_1) (combb int int _let_1))))), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_0))) (hAPP _let_2 _let_3 (hAPP (fun int _let_0) (fun _let_2 _let_3) (combb int _let_0 _let_1) (times_times int)) (product_fst int int)))))) ) 15.44/15.63 ( (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 int))) (fun _let_1 (fun _let_0 _let_1)))), (let ((_let_0 (fun (product_prod int int) int))) (fun (product_prod int int) (fun _let_0 _let_0))), (let ((_let_0 (fun (product_prod int int) int))) (combc (product_prod int int) _let_0 _let_0)), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_2 _let_2))) (let ((_let_4 (fun _let_1 _let_3))) (let ((_let_5 (fun _let_1 _let_0))) (hAPP _let_5 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_5 _let_4) (combb _let_0 _let_3 _let_1) (combb int int _let_1)) (hAPP _let_2 _let_5 (hAPP (fun int _let_0) (fun _let_2 _let_5) (combb int _let_0 _let_1) (times_times int)) (product_fst int int))))))))) ) 15.44/15.63 ( (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 int))) (fun _let_1 (fun _let_0 _let_1)))), (fun int (fun (product_prod int int) int)), (let ((_let_0 (product_prod int int))) (combb int (fun _let_0 int) _let_0)), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_0))) (hAPP _let_3 (fun int _let_2) (combc _let_1 int int) (hAPP _let_2 _let_3 (hAPP (fun int _let_0) (fun _let_2 _let_3) (combb int _let_0 _let_1) (times_times int)) (product_fst int int))))))) ) 15.47/15.63 ( (fun (product_prod int int) (fun int int)), (fun (product_prod int int) int), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (hAPP (fun int _let_0) (fun (fun _let_1 int) (fun _let_1 _let_0)) (combb int _let_0 _let_1) (times_times int)))), (product_fst int int) ) 15.47/15.63 ( (let ((_let_0 (fun (product_prod int int) int))) (fun (fun (product_prod int int) (fun int int)) (fun (product_prod int int) (fun _let_0 _let_0)))), (let ((_let_0 (fun (product_prod int int) int))) (fun (fun int int) (fun _let_0 _let_0))), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 int))) (combb (fun int int) (fun _let_1 _let_1) _let_0))), (combb int int (product_prod int int)) ) 15.47/15.63 ( (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 (fun int int)))), (fun int (fun int int)), (combb int (fun int int) (product_prod int int)), (times_times int) ) 15.47/15.63 ( (fun int (fun (product_prod int int) int)), (fun (product_prod int int) (fun int int)), (combc (product_prod int int) int int), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_0))) (hAPP _let_2 _let_3 (hAPP (fun int _let_0) (fun _let_2 _let_3) (combb int _let_0 _let_1) (times_times int)) (product_fst int int)))))) ) 15.47/15.63 ( (fun (fun nat nat) (fun nat (fun nat bool))), (fun nat (fun nat bool)), (combb nat (fun nat bool) nat), (let ((_let_0 (fun nat (fun nat bool)))) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat))) ) 15.47/15.63 ( (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)), (fun bool bool), (combb bool bool nat), fNot ) 15.47/15.63 ( (let ((_let_0 (fun nat nat))) (fun _let_0 (fun nat _let_0))), (fun nat (fun nat nat)), (combb nat (fun nat nat) nat), (plus_plus nat) ) 15.47/15.63 ( (fun real (fun bool bool)), (fun real bool), (let ((_let_0 (fun bool bool))) (hAPP (fun bool _let_0) (fun (fun real bool) (fun real _let_0)) (combb bool _let_0 real) fconj)), (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) ) 15.47/15.63 ( (fun real (fun bool bool)), (fun real bool), (let ((_let_0 (fun bool bool))) (hAPP (fun bool _let_0) (fun (fun real bool) (fun real _let_0)) (combb bool _let_0 real) fconj)), (let ((_let_0 (fun real (fun real bool)))) (hAPP real (fun real bool) (hAPP _let_0 _let_0 (combc real real bool) (ord_less_eq real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.47/15.63 ( (let ((_let_0 (fun real bool))) (fun _let_0 _let_0)), (fun real (fun bool bool)), (combs real bool bool), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun real _let_1))) (hAPP _let_0 _let_2 (hAPP (fun bool _let_1) (fun _let_0 _let_2) (combb bool _let_1 real) fconj) (hAPP real _let_0 (ord_less_eq real) (zero_zero real)))))) ) 15.47/15.63 ( (let ((_let_0 (fun real bool))) (fun _let_0 _let_0)), (fun real (fun bool bool)), (combs real bool bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun real (fun real bool)))) (let ((_let_2 (fun real _let_0))) (hAPP (fun real bool) _let_2 (hAPP (fun bool _let_0) (fun (fun real bool) _let_2) (combb bool _let_0 real) fconj) (hAPP real (fun real bool) (hAPP _let_1 _let_1 (combc real real bool) (ord_less_eq real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 15.47/15.63 ( (fun (fun real bool) (fun real (fun bool bool))), (fun bool (fun bool bool)), (combb bool (fun bool bool) real), fconj ) 15.47/15.63 ( (fun (fun real real) (fun real (fun real bool))), (fun real (fun real bool)), (combb real (fun real bool) real), (fequal real) ) 15.47/15.63 ( (fun (fun nat bool) (fun nat (fun bool bool))), (fun bool (fun bool bool)), (combb bool (fun bool bool) nat), fconj ) 15.47/15.63 ( (let ((_let_0 (fun int bool))) (fun (fun int (fun int (fun bool bool))) (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun int bool))) (fun (fun int (fun bool bool)) (fun _let_0 _let_0))), (let ((_let_0 (fun int bool))) (combb (fun int (fun bool bool)) (fun _let_0 _let_0) int)), (combs int bool bool) ) 15.47/15.63 ( (fun (fun int (fun int bool)) (fun int (fun int (fun bool bool)))), (fun (fun int bool) (fun int (fun bool bool))), (combb (fun int bool) (fun int (fun bool bool)) int), (let ((_let_0 (fun bool bool))) (hAPP (fun bool _let_0) (fun (fun int bool) (fun int _let_0)) (combb bool _let_0 int) fconj)) ) 15.47/15.63 ( (fun nat (fun int int)), (fun int (fun nat int)), (combc int nat int), (power_power int) ) 15.47/15.63 ( (fun real (fun int bool)), (fun real (fun int (fun int bool))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun _let_1 _let_0))) (hAPP _let_2 (fun (fun real _let_1) (fun real _let_0)) (combb _let_1 _let_0 real) (hAPP (fun _let_0 bool) _let_2 (combb _let_0 bool int) (fEx int)))))), (let ((_let_0 (fun int (fun int bool)))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real real))) (let ((_let_3 (real_1 int))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun int _let_4))) (let ((_let_7 (fun (fun int bool) (fun int bool)))) (let ((_let_8 (fun (fun int bool) _let_6))) (let ((_let_9 (fun int real))) (let ((_let_10 (fun int _let_7))) (let ((_let_11 (fun (fun int bool) _let_0))) (let ((_let_12 (fun int _let_6))) (let ((_let_13 (fun _let_12 _let_10))) (let ((_let_14 (fun _let_0 _let_12))) (let ((_let_15 (fun real _let_0))) (let ((_let_16 (fun real _let_11))) (let ((_let_17 (fun real _let_10))) (let ((_let_18 (fun real _let_12))) (let ((_let_19 (fun int _let_9))) (let ((_let_20 (fun _let_19 _let_0))) (let ((_let_21 (fun real _let_20))) (let ((_let_22 (fun _let_9 (fun int bool)))) (let ((_let_23 (fun real _let_22))) (let ((_let_24 (fun _let_9 _let_9))) (let ((_let_25 (fun int _let_24))) (let ((_let_26 (fun int _let_2))) (hAPP (fun int bool) _let_15 (hAPP _let_16 (fun (fun int bool) _let_15) (combc real (fun int bool) _let_0) (hAPP _let_17 _let_16 (hAPP (fun _let_10 _let_11) (fun _let_17 _let_16) (combb _let_10 _let_11 real) (combc int (fun int bool) (fun int bool))) (hAPP _let_18 _let_17 (hAPP _let_13 (fun _let_18 _let_17) (combb _let_12 _let_10 real) (hAPP (fun _let_6 _let_7) _let_13 (combb _let_6 _let_7 int) (combs int bool bool))) (hAPP _let_15 _let_18 (hAPP _let_14 (fun _let_15 _let_18) (combb _let_0 _let_12 real) (hAPP _let_8 _let_14 (combb (fun int bool) _let_6 int) (hAPP (fun bool _let_4) _let_8 (combb bool _let_4 int) fconj))) (hAPP _let_19 _let_15 (hAPP _let_21 (fun _let_19 _let_15) (combc real _let_19 _let_0) (hAPP _let_23 _let_21 (hAPP (fun _let_22 _let_20) (fun _let_23 _let_21) (combb _let_22 _let_20 real) (combb _let_9 (fun int bool) int)) (hAPP _let_5 _let_23 (hAPP (fun _let_1 _let_22) (fun _let_5 _let_23) (combb _let_1 _let_22 real) (combb real bool int)) (fequal real)))) (hAPP _let_9 _let_19 (hAPP _let_25 (fun _let_9 _let_19) (combc int _let_9 _let_9) (hAPP _let_26 _let_25 (hAPP (fun _let_2 _let_24) (fun _let_26 _let_25) (combb _let_2 _let_24 int) (combb real real int)) (hAPP _let_9 _let_26 (hAPP (fun real _let_2) (fun _let_9 _let_26) (combb real _let_2 int) (inverse_divide real)) _let_3))) _let_3)))))) (hAPP (fun int bool) (fun int bool) (hAPP _let_4 _let_7 (combb bool bool int) fNot) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (fequal int)) (zero_zero int))))))))))))))))))))))))))))))) ) 15.47/15.63 ( (fun real (fun int bool)), (fun real (fun int (fun nat bool))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun nat bool))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (fun _let_2 _let_0))) (hAPP _let_3 (fun (fun real _let_2) (fun real _let_0)) (combb _let_2 _let_0 real) (hAPP (fun _let_1 bool) _let_3 (combb _let_1 bool int) (fEx nat))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat (fun nat bool)))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun (fun nat real) (fun nat real)))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun (fun nat bool) (fun nat bool)))) (let ((_let_7 (fun int real))) (let ((_let_8 (fun nat _let_3))) (let ((_let_9 (fun (fun nat bool) _let_8))) (let ((_let_10 (fun int _let_1))) (let ((_let_11 (fun real (fun int (fun nat bool))))) (let ((_let_12 (fun (fun nat bool) (fun int (fun nat bool))))) (let ((_let_13 (fun real _let_12))) (let ((_let_14 (fun int _let_6))) (let ((_let_15 (fun real _let_14))) (let ((_let_16 (fun int _let_8))) (let ((_let_17 (fun real _let_16))) (let ((_let_18 (fun _let_16 _let_14))) (let ((_let_19 (fun (fun int (fun nat bool)) _let_16))) (let ((_let_20 (fun int (fun nat real)))) (let ((_let_21 (fun _let_20 (fun int (fun nat bool))))) (let ((_let_22 (fun real _let_21))) (let ((_let_23 (fun (fun nat real) (fun nat bool)))) (let ((_let_24 (fun real _let_23))) (let ((_let_25 (fun int _let_4))) (hAPP (fun nat bool) _let_11 (hAPP _let_13 (fun (fun nat bool) _let_11) (combc real (fun nat bool) (fun int (fun nat bool))) (hAPP _let_15 _let_13 (hAPP (fun _let_14 _let_12) (fun _let_15 _let_13) (combb _let_14 _let_12 real) (combc int (fun nat bool) (fun nat bool))) (hAPP _let_17 _let_15 (hAPP _let_18 (fun _let_17 _let_15) (combb _let_16 _let_14 real) (hAPP (fun _let_8 _let_6) _let_18 (combb _let_8 _let_6 int) (combs nat bool bool))) (hAPP _let_11 _let_17 (hAPP _let_19 (fun _let_11 _let_17) (combb (fun int (fun nat bool)) _let_16 real) (hAPP _let_9 _let_19 (combb (fun nat bool) _let_8 int) (hAPP (fun bool _let_3) _let_9 (combb bool _let_3 nat) fconj))) (hAPP _let_20 _let_11 (hAPP _let_22 (fun _let_20 _let_11) (combc real _let_20 (fun int (fun nat bool))) (hAPP _let_24 _let_22 (hAPP (fun _let_23 _let_21) (fun _let_24 _let_22) (combb _let_23 _let_21 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_5 _let_24 (hAPP (fun _let_0 _let_23) (fun _let_5 _let_24) (combb _let_0 _let_23 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_20 (hAPP _let_25 (fun (fun nat real) _let_20) (combc int (fun nat real) (fun nat real)) (hAPP _let_10 _let_25 (hAPP (fun _let_1 _let_4) (fun _let_10 _let_25) (combb _let_1 _let_4 int) (combb real real nat)) (hAPP _let_7 _let_10 (hAPP (fun real _let_1) (fun _let_7 _let_10) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat))))))) (hAPP (fun nat bool) (fun nat bool) (hAPP _let_3 _let_6 (combb bool bool nat) fNot) (hAPP nat (fun nat bool) (hAPP _let_2 _let_2 (combc nat nat bool) (fequal nat)) (zero_zero nat)))))))))))))))))))))))))))))) ) 15.47/15.63 ( (fun (fun real (fun int bool)) (fun real bool)), (fun (fun int bool) bool), (combb (fun int bool) bool real), (fEx int) ) 15.47/15.64 ( (fun real (fun int (fun int bool))), (fun int bool), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun int _let_3))) (let ((_let_6 (fun (fun int bool) (fun int bool)))) (let ((_let_7 (fun (fun int bool) _let_5))) (let ((_let_8 (fun int real))) (let ((_let_9 (fun int _let_6))) (let ((_let_10 (fun (fun int bool) (fun int (fun int bool))))) (let ((_let_11 (fun int _let_5))) (let ((_let_12 (fun _let_11 _let_9))) (let ((_let_13 (fun (fun int (fun int bool)) _let_11))) (let ((_let_14 (fun real (fun int (fun int bool))))) (let ((_let_15 (fun real _let_10))) (let ((_let_16 (fun real _let_9))) (let ((_let_17 (fun real _let_11))) (let ((_let_18 (fun int _let_8))) (let ((_let_19 (fun _let_18 (fun int (fun int bool))))) (let ((_let_20 (fun real _let_19))) (let ((_let_21 (fun _let_8 (fun int bool)))) (let ((_let_22 (fun real _let_21))) (let ((_let_23 (fun _let_8 _let_8))) (let ((_let_24 (fun int _let_23))) (let ((_let_25 (fun int _let_1))) (hAPP _let_15 (fun (fun int bool) _let_14) (combc real (fun int bool) (fun int (fun int bool))) (hAPP _let_16 _let_15 (hAPP (fun _let_9 _let_10) (fun _let_16 _let_15) (combb _let_9 _let_10 real) (combc int (fun int bool) (fun int bool))) (hAPP _let_17 _let_16 (hAPP _let_12 (fun _let_17 _let_16) (combb _let_11 _let_9 real) (hAPP (fun _let_5 _let_6) _let_12 (combb _let_5 _let_6 int) (combs int bool bool))) (hAPP _let_14 _let_17 (hAPP _let_13 (fun _let_14 _let_17) (combb (fun int (fun int bool)) _let_11 real) (hAPP _let_7 _let_13 (combb (fun int bool) _let_5 int) (hAPP (fun bool _let_3) _let_7 (combb bool _let_3 int) fconj))) (hAPP _let_18 _let_14 (hAPP _let_20 (fun _let_18 _let_14) (combc real _let_18 (fun int (fun int bool))) (hAPP _let_22 _let_20 (hAPP (fun _let_21 _let_19) (fun _let_22 _let_20) (combb _let_21 _let_19 real) (combb _let_8 (fun int bool) int)) (hAPP _let_4 _let_22 (hAPP (fun _let_0 _let_21) (fun _let_4 _let_22) (combb _let_0 _let_21 real) (combb real bool int)) (fequal real)))) (hAPP _let_8 _let_18 (hAPP _let_24 (fun _let_8 _let_18) (combc int _let_8 _let_8) (hAPP _let_25 _let_24 (hAPP (fun _let_1 _let_23) (fun _let_25 _let_24) (combb _let_1 _let_23 int) (combb real real int)) (hAPP _let_8 _let_25 (hAPP (fun real _let_1) (fun _let_8 _let_25) (combb real _let_1 int) (inverse_divide real)) _let_2))) _let_2)))))))))))))))))))))))))))))))), (let ((_let_0 (fun int (fun int bool)))) (hAPP (fun int bool) (fun int bool) (hAPP (fun bool bool) (fun (fun int bool) (fun int bool)) (combb bool bool int) fNot) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (fequal int)) (zero_zero int)))) ) 15.47/15.64 ( (fun real (fun int (fun int bool))), (fun int (fun int real)), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun int (fun int real)) (fun int (fun int bool))))) (let ((_let_3 (fun real _let_2))) (let ((_let_4 (fun (fun int real) (fun int bool)))) (let ((_let_5 (fun real _let_4))) (hAPP _let_3 (fun (fun int (fun int real)) (fun real (fun int (fun int bool)))) (combc real (fun int (fun int real)) (fun int (fun int bool))) (hAPP _let_5 _let_3 (hAPP (fun _let_4 _let_2) (fun _let_5 _let_3) (combb _let_4 _let_2 real) (combb (fun int real) (fun int bool) int)) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_1 _let_5) (combb _let_0 _let_4 real) (combb real bool int)) (fequal real)))))))))), (let ((_let_0 (fun real real))) (let ((_let_1 (real_1 int))) (let ((_let_2 (fun int real))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun _let_2 _let_2))) (let ((_let_5 (fun int _let_4))) (let ((_let_6 (fun int _let_0))) (hAPP _let_2 _let_3 (hAPP _let_5 (fun _let_2 _let_3) (combc int _let_2 _let_2) (hAPP _let_6 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_6 _let_5) (combb _let_0 _let_4 int) (combb real real int)) (hAPP _let_2 _let_6 (hAPP (fun real _let_0) (fun _let_2 _let_6) (combb real _let_0 int) (inverse_divide real)) _let_1))) _let_1)))))))) ) 15.47/15.64 ( (let ((_let_0 (fun int bool))) (fun (fun real (fun int _let_0)) (fun real _let_0))), (let ((_let_0 (fun int bool))) (fun (fun int _let_0) _let_0)), (let ((_let_0 (fun int bool))) (combb (fun int _let_0) _let_0 real)), (let ((_let_0 (fun int bool))) (hAPP (fun _let_0 bool) (fun (fun int _let_0) _let_0) (combb _let_0 bool int) (fEx int))) ) 15.47/15.64 ( (let ((_let_0 (fun int bool))) (fun real (fun _let_0 (fun int _let_0)))), (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int (fun _let_0 _let_0)))) (let ((_let_2 (fun _let_0 (fun int _let_0)))) (hAPP (fun _let_1 _let_2) (fun (fun real _let_1) (fun real _let_2)) (combb _let_1 _let_2 real) (combc int _let_0 _let_0))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun int _let_3))) (let ((_let_6 (fun (fun int bool) (fun int bool)))) (let ((_let_7 (fun (fun int bool) _let_5))) (let ((_let_8 (fun int real))) (let ((_let_9 (fun int _let_6))) (let ((_let_10 (fun int _let_5))) (let ((_let_11 (fun _let_10 _let_9))) (let ((_let_12 (fun (fun int (fun int bool)) _let_10))) (let ((_let_13 (fun real (fun int (fun int bool))))) (let ((_let_14 (fun real _let_9))) (let ((_let_15 (fun real _let_10))) (let ((_let_16 (fun int _let_8))) (let ((_let_17 (fun _let_16 (fun int (fun int bool))))) (let ((_let_18 (fun real _let_17))) (let ((_let_19 (fun _let_8 (fun int bool)))) (let ((_let_20 (fun real _let_19))) (let ((_let_21 (fun _let_8 _let_8))) (let ((_let_22 (fun int _let_21))) (let ((_let_23 (fun int _let_1))) (hAPP _let_15 _let_14 (hAPP _let_11 (fun _let_15 _let_14) (combb _let_10 _let_9 real) (hAPP (fun _let_5 _let_6) _let_11 (combb _let_5 _let_6 int) (combs int bool bool))) (hAPP _let_13 _let_15 (hAPP _let_12 (fun _let_13 _let_15) (combb (fun int (fun int bool)) _let_10 real) (hAPP _let_7 _let_12 (combb (fun int bool) _let_5 int) (hAPP (fun bool _let_3) _let_7 (combb bool _let_3 int) fconj))) (hAPP _let_16 _let_13 (hAPP _let_18 (fun _let_16 _let_13) (combc real _let_16 (fun int (fun int bool))) (hAPP _let_20 _let_18 (hAPP (fun _let_19 _let_17) (fun _let_20 _let_18) (combb _let_19 _let_17 real) (combb _let_8 (fun int bool) int)) (hAPP _let_4 _let_20 (hAPP (fun _let_0 _let_19) (fun _let_4 _let_20) (combb _let_0 _let_19 real) (combb real bool int)) (fequal real)))) (hAPP _let_8 _let_16 (hAPP _let_22 (fun _let_8 _let_16) (combc int _let_8 _let_8) (hAPP _let_23 _let_22 (hAPP (fun _let_1 _let_21) (fun _let_23 _let_22) (combb _let_1 _let_21 int) (combb real real int)) (hAPP _let_8 _let_23 (hAPP (fun real _let_1) (fun _let_8 _let_23) (combb real _let_1 int) (inverse_divide real)) _let_2))) _let_2)))))))))))))))))))))))))))) ) 15.47/15.64 ( (let ((_let_0 (fun int bool))) (fun _let_0 (fun real (fun int _let_0)))), (let ((_let_0 (fun int bool))) (fun real (fun _let_0 (fun int _let_0)))), (let ((_let_0 (fun int bool))) (combc real _let_0 (fun int _let_0))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun int _let_3))) (let ((_let_6 (fun (fun int bool) (fun int bool)))) (let ((_let_7 (fun (fun int bool) _let_5))) (let ((_let_8 (fun int real))) (let ((_let_9 (fun int _let_6))) (let ((_let_10 (fun (fun int bool) (fun int (fun int bool))))) (let ((_let_11 (fun int _let_5))) (let ((_let_12 (fun _let_11 _let_9))) (let ((_let_13 (fun (fun int (fun int bool)) _let_11))) (let ((_let_14 (fun real (fun int (fun int bool))))) (let ((_let_15 (fun real _let_10))) (let ((_let_16 (fun real _let_9))) (let ((_let_17 (fun real _let_11))) (let ((_let_18 (fun int _let_8))) (let ((_let_19 (fun _let_18 (fun int (fun int bool))))) (let ((_let_20 (fun real _let_19))) (let ((_let_21 (fun _let_8 (fun int bool)))) (let ((_let_22 (fun real _let_21))) (let ((_let_23 (fun _let_8 _let_8))) (let ((_let_24 (fun int _let_23))) (let ((_let_25 (fun int _let_1))) (hAPP _let_16 _let_15 (hAPP (fun _let_9 _let_10) (fun _let_16 _let_15) (combb _let_9 _let_10 real) (combc int (fun int bool) (fun int bool))) (hAPP _let_17 _let_16 (hAPP _let_12 (fun _let_17 _let_16) (combb _let_11 _let_9 real) (hAPP (fun _let_5 _let_6) _let_12 (combb _let_5 _let_6 int) (combs int bool bool))) (hAPP _let_14 _let_17 (hAPP _let_13 (fun _let_14 _let_17) (combb (fun int (fun int bool)) _let_11 real) (hAPP _let_7 _let_13 (combb (fun int bool) _let_5 int) (hAPP (fun bool _let_3) _let_7 (combb bool _let_3 int) fconj))) (hAPP _let_18 _let_14 (hAPP _let_20 (fun _let_18 _let_14) (combc real _let_18 (fun int (fun int bool))) (hAPP _let_22 _let_20 (hAPP (fun _let_21 _let_19) (fun _let_22 _let_20) (combb _let_21 _let_19 real) (combb _let_8 (fun int bool) int)) (hAPP _let_4 _let_22 (hAPP (fun _let_0 _let_21) (fun _let_4 _let_22) (combb _let_0 _let_21 real) (combb real bool int)) (fequal real)))) (hAPP _let_8 _let_18 (hAPP _let_24 (fun _let_8 _let_18) (combc int _let_8 _let_8) (hAPP _let_25 _let_24 (hAPP (fun _let_1 _let_23) (fun _let_25 _let_24) (combb _let_1 _let_23 int) (combb real real int)) (hAPP _let_8 _let_25 (hAPP (fun real _let_1) (fun _let_8 _let_25) (combb real _let_1 int) (inverse_divide real)) _let_2))) _let_2))))))))))))))))))))))))))))))) ) 15.47/15.64 ( (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))), (fun real (fun int (fun int (fun bool bool)))), (let ((_let_0 (fun int (fun bool bool)))) (let ((_let_1 (fun (fun int bool) (fun int bool)))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (fun int _let_0))) (let ((_let_4 (fun _let_3 _let_2))) (hAPP _let_4 (fun (fun real _let_3) (fun real _let_2)) (combb _let_3 _let_2 real) (hAPP (fun _let_0 _let_1) _let_4 (combb _let_0 _let_1 int) (combs int bool bool)))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun int _let_3))) (let ((_let_6 (fun (fun int bool) _let_5))) (let ((_let_7 (fun int real))) (let ((_let_8 (fun int _let_5))) (let ((_let_9 (fun (fun int (fun int bool)) _let_8))) (let ((_let_10 (fun real (fun int (fun int bool))))) (let ((_let_11 (fun real _let_8))) (let ((_let_12 (fun int _let_7))) (let ((_let_13 (fun _let_12 (fun int (fun int bool))))) (let ((_let_14 (fun real _let_13))) (let ((_let_15 (fun _let_7 (fun int bool)))) (let ((_let_16 (fun real _let_15))) (let ((_let_17 (fun _let_7 _let_7))) (let ((_let_18 (fun int _let_17))) (let ((_let_19 (fun int _let_1))) (hAPP _let_10 _let_11 (hAPP _let_9 (fun _let_10 _let_11) (combb (fun int (fun int bool)) _let_8 real) (hAPP _let_6 _let_9 (combb (fun int bool) _let_5 int) (hAPP (fun bool _let_3) _let_6 (combb bool _let_3 int) fconj))) (hAPP _let_12 _let_10 (hAPP _let_14 (fun _let_12 _let_10) (combc real _let_12 (fun int (fun int bool))) (hAPP _let_16 _let_14 (hAPP (fun _let_15 _let_13) (fun _let_16 _let_14) (combb _let_15 _let_13 real) (combb _let_7 (fun int bool) int)) (hAPP _let_4 _let_16 (hAPP (fun _let_0 _let_15) (fun _let_4 _let_16) (combb _let_0 _let_15 real) (combb real bool int)) (fequal real)))) (hAPP _let_7 _let_12 (hAPP _let_18 (fun _let_7 _let_12) (combc int _let_7 _let_7) (hAPP _let_19 _let_18 (hAPP (fun _let_1 _let_17) (fun _let_19 _let_18) (combb _let_1 _let_17 int) (combb real real int)) (hAPP _let_7 _let_19 (hAPP (fun real _let_1) (fun _let_7 _let_19) (combb real _let_1 int) (inverse_divide real)) _let_2))) _let_2))))))))))))))))))))))) ) 15.47/15.64 ( (let ((_let_0 (fun int bool))) (fun (fun real (fun int (fun _let_0 _let_0))) (fun real (fun _let_0 (fun int _let_0))))), (let ((_let_0 (fun int bool))) (fun (fun int (fun _let_0 _let_0)) (fun _let_0 (fun int _let_0)))), (let ((_let_0 (fun int bool))) (combb (fun int (fun _let_0 _let_0)) (fun _let_0 (fun int _let_0)) real)), (let ((_let_0 (fun int bool))) (combc int _let_0 _let_0)) ) 15.47/15.67 ( (fun real (fun int (fun int (fun bool bool)))), (fun real (fun int (fun int bool))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun _let_0 _let_3))) (let ((_let_5 (fun int _let_3))) (let ((_let_6 (fun _let_1 _let_5))) (hAPP _let_6 (fun (fun real _let_1) (fun real _let_5)) (combb _let_1 _let_5 real) (hAPP _let_4 _let_6 (combb _let_0 _let_3 int) (hAPP (fun bool _let_2) _let_4 (combb bool _let_2 int) fconj)))))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun real _let_0))) (let ((_let_4 (fun int real))) (let ((_let_5 (fun real (fun int (fun int bool))))) (let ((_let_6 (fun int _let_4))) (let ((_let_7 (fun _let_6 (fun int (fun int bool))))) (let ((_let_8 (fun real _let_7))) (let ((_let_9 (fun _let_4 (fun int bool)))) (let ((_let_10 (fun real _let_9))) (let ((_let_11 (fun _let_4 _let_4))) (let ((_let_12 (fun int _let_11))) (let ((_let_13 (fun int _let_1))) (hAPP _let_6 _let_5 (hAPP _let_8 (fun _let_6 _let_5) (combc real _let_6 (fun int (fun int bool))) (hAPP _let_10 _let_8 (hAPP (fun _let_9 _let_7) (fun _let_10 _let_8) (combb _let_9 _let_7 real) (combb _let_4 (fun int bool) int)) (hAPP _let_3 _let_10 (hAPP (fun _let_0 _let_9) (fun _let_3 _let_10) (combb _let_0 _let_9 real) (combb real bool int)) (fequal real)))) (hAPP _let_4 _let_6 (hAPP _let_12 (fun _let_4 _let_6) (combc int _let_4 _let_4) (hAPP _let_13 _let_12 (hAPP (fun _let_1 _let_11) (fun _let_13 _let_12) (combb _let_1 _let_11 int) (combb real real int)) (hAPP _let_4 _let_13 (hAPP (fun real _let_1) (fun _let_4 _let_13) (combb real _let_1 int) (inverse_divide real)) _let_2))) _let_2)))))))))))))))) ) 15.47/15.67 ( (let ((_let_0 (fun int bool))) (fun (fun real (fun int (fun int (fun bool bool)))) (fun real (fun int (fun _let_0 _let_0))))), (let ((_let_0 (fun int bool))) (fun (fun int (fun int (fun bool bool))) (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun int bool))) (combb (fun int (fun int (fun bool bool))) (fun int (fun _let_0 _let_0)) real)), (let ((_let_0 (fun int (fun bool bool)))) (let ((_let_1 (fun (fun int bool) (fun int bool)))) (hAPP (fun _let_0 _let_1) (fun (fun int _let_0) (fun int _let_1)) (combb _let_0 _let_1 int) (combs int bool bool)))) ) 15.47/15.67 ( (fun (fun real (fun int (fun int bool))) (fun real (fun int (fun int (fun bool bool))))), (fun (fun int (fun int bool)) (fun int (fun int (fun bool bool)))), (combb (fun int (fun int bool)) (fun int (fun int (fun bool bool))) real), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (fun _let_0 _let_2))) (hAPP _let_3 (fun (fun int _let_0) (fun int _let_2)) (combb _let_0 _let_2 int) (hAPP (fun bool _let_1) _let_3 (combb bool _let_1 int) fconj)))))) ) 15.47/15.67 ( (fun int (fun int real)), (fun int real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun int real))) (let ((_let_2 (fun _let_1 _let_1))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int _let_0))) (hAPP _let_3 (fun _let_1 (fun int _let_1)) (combc int _let_1 _let_1) (hAPP _let_4 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_4 _let_3) (combb _let_0 _let_2 int) (combb real real int)) (hAPP _let_1 _let_4 (hAPP (fun real _let_0) (fun _let_1 _let_4) (combb real _let_0 int) (inverse_divide real)) (real_1 int))))))))), (real_1 int) ) 15.47/15.67 ( (fun real (fun (fun int (fun int real)) (fun int (fun int bool)))), (fun real (fun (fun int real) (fun int bool))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int real))) (let ((_let_2 (fun (fun int _let_1) (fun int _let_0)))) (let ((_let_3 (fun _let_1 _let_0))) (hAPP (fun _let_3 _let_2) (fun (fun real _let_3) (fun real _let_2)) (combb _let_3 _let_2 real) (combb _let_1 _let_0 int)))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun int real) (fun int bool)))) (let ((_let_3 (fun real _let_2))) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 real) (combb real bool int)) (fequal real)))))) ) 15.47/15.67 ( (fun (fun int (fun int real)) (fun real (fun int (fun int bool)))), (fun real (fun (fun int (fun int real)) (fun int (fun int bool)))), (combc real (fun int (fun int real)) (fun int (fun int bool))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun int (fun int real)) (fun int (fun int bool))))) (let ((_let_3 (fun real _let_2))) (let ((_let_4 (fun (fun int real) (fun int bool)))) (let ((_let_5 (fun real _let_4))) (hAPP _let_5 _let_3 (hAPP (fun _let_4 _let_2) (fun _let_5 _let_3) (combb _let_4 _let_2 real) (combb (fun int real) (fun int bool) int)) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_1 _let_5) (combb _let_0 _let_4 real) (combb real bool int)) (fequal real))))))))) ) 15.47/15.67 ( (fun real (fun (fun int real) (fun int bool))), (fun real (fun real bool)), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun (fun int real) (fun int bool)))) (hAPP (fun _let_0 _let_1) (fun (fun real _let_0) (fun real _let_1)) (combb _let_0 _let_1 real) (combb real bool int)))), (fequal real) ) 15.47/15.67 ( (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int real))) (fun (fun real (fun _let_1 _let_0)) (fun real (fun (fun int _let_1) (fun int _let_0)))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int real))) (fun (fun _let_1 _let_0) (fun (fun int _let_1) (fun int _let_0))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int real))) (combb (fun _let_1 _let_0) (fun (fun int _let_1) (fun int _let_0)) real))), (combb (fun int real) (fun int bool) int) ) 15.47/15.67 ( (fun (fun real (fun real bool)) (fun real (fun (fun int real) (fun int bool)))), (fun (fun real bool) (fun (fun int real) (fun int bool))), (combb (fun real bool) (fun (fun int real) (fun int bool)) real), (combb real bool int) ) 15.47/15.67 ( (let ((_let_0 (fun int real))) (fun int (fun _let_0 _let_0))), (fun int (fun real real)), (let ((_let_0 (fun real real))) (let ((_let_1 (fun (fun int real) (fun int real)))) (hAPP (fun _let_0 _let_1) (fun (fun int _let_0) (fun int _let_1)) (combb _let_0 _let_1 int) (combb real real int)))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun int real))) (let ((_let_2 (fun int _let_0))) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 int) (inverse_divide real)) (real_1 int))))) ) 15.47/15.67 ( (let ((_let_0 (fun int real))) (fun _let_0 (fun int _let_0))), (let ((_let_0 (fun int real))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun int real))) (combc int _let_0 _let_0)), (let ((_let_0 (fun real real))) (let ((_let_1 (fun int real))) (let ((_let_2 (fun _let_1 _let_1))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int _let_0))) (hAPP _let_4 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_4 _let_3) (combb _let_0 _let_2 int) (combb real real int)) (hAPP _let_1 _let_4 (hAPP (fun real _let_0) (fun _let_1 _let_4) (combb real _let_0 int) (inverse_divide real)) (real_1 int)))))))) ) 15.47/15.67 ( (fun int (fun real real)), (fun int real), (let ((_let_0 (fun real real))) (hAPP (fun real _let_0) (fun (fun int real) (fun int _let_0)) (combb real _let_0 int) (inverse_divide real))), (real_1 int) ) 15.47/15.67 ( (let ((_let_0 (fun int real))) (fun (fun int (fun real real)) (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun int real))) (fun (fun real real) (fun _let_0 _let_0))), (let ((_let_0 (fun int real))) (combb (fun real real) (fun _let_0 _let_0) int)), (combb real real int) ) 15.47/15.67 ( (fun (fun int real) (fun int (fun real real))), (fun real (fun real real)), (combb real (fun real real) int), (inverse_divide real) ) 15.47/15.67 ( (let ((_let_0 (fun int (fun int bool)))) (fun _let_0 _let_0)), (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), (let ((_let_0 (fun int bool))) (combb _let_0 _let_0 int)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun int _let_1))) (hAPP _let_2 (fun _let_0 _let_0) (combs int bool bool) (hAPP _let_0 _let_2 (hAPP (fun bool _let_1) (fun _let_0 _let_2) (combb bool _let_1 int) fconj) (hAPP int _let_0 (ord_less int) (zero_zero int))))))) ) 15.47/15.67 ( (fun real (fun int (fun nat bool))), (fun nat bool), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun (fun nat real) (fun nat real)))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun (fun nat bool) (fun nat bool)))) (let ((_let_6 (fun int real))) (let ((_let_7 (fun nat _let_2))) (let ((_let_8 (fun (fun nat bool) _let_7))) (let ((_let_9 (fun int _let_1))) (let ((_let_10 (fun real (fun int (fun nat bool))))) (let ((_let_11 (fun (fun nat bool) (fun int (fun nat bool))))) (let ((_let_12 (fun real _let_11))) (let ((_let_13 (fun int _let_5))) (let ((_let_14 (fun real _let_13))) (let ((_let_15 (fun int _let_7))) (let ((_let_16 (fun real _let_15))) (let ((_let_17 (fun _let_15 _let_13))) (let ((_let_18 (fun (fun int (fun nat bool)) _let_15))) (let ((_let_19 (fun int (fun nat real)))) (let ((_let_20 (fun _let_19 (fun int (fun nat bool))))) (let ((_let_21 (fun real _let_20))) (let ((_let_22 (fun (fun nat real) (fun nat bool)))) (let ((_let_23 (fun real _let_22))) (let ((_let_24 (fun int _let_3))) (hAPP _let_12 (fun (fun nat bool) _let_10) (combc real (fun nat bool) (fun int (fun nat bool))) (hAPP _let_14 _let_12 (hAPP (fun _let_13 _let_11) (fun _let_14 _let_12) (combb _let_13 _let_11 real) (combc int (fun nat bool) (fun nat bool))) (hAPP _let_16 _let_14 (hAPP _let_17 (fun _let_16 _let_14) (combb _let_15 _let_13 real) (hAPP (fun _let_7 _let_5) _let_17 (combb _let_7 _let_5 int) (combs nat bool bool))) (hAPP _let_10 _let_16 (hAPP _let_18 (fun _let_10 _let_16) (combb (fun int (fun nat bool)) _let_15 real) (hAPP _let_8 _let_18 (combb (fun nat bool) _let_7 int) (hAPP (fun bool _let_2) _let_8 (combb bool _let_2 nat) fconj))) (hAPP _let_19 _let_10 (hAPP _let_21 (fun _let_19 _let_10) (combc real _let_19 (fun int (fun nat bool))) (hAPP _let_23 _let_21 (hAPP (fun _let_22 _let_20) (fun _let_23 _let_21) (combb _let_22 _let_20 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_4 _let_23 (hAPP (fun _let_0 _let_22) (fun _let_4 _let_23) (combb _let_0 _let_22 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_19 (hAPP _let_24 (fun (fun nat real) _let_19) (combc int (fun nat real) (fun nat real)) (hAPP _let_9 _let_24 (hAPP (fun _let_1 _let_3) (fun _let_9 _let_24) (combb _let_1 _let_3 int) (combb real real nat)) (hAPP _let_6 _let_9 (hAPP (fun real _let_1) (fun _let_6 _let_9) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat)))))))))))))))))))))))))))))))), (let ((_let_0 (fun nat (fun nat bool)))) (hAPP (fun nat bool) (fun nat bool) (hAPP (fun bool bool) (fun (fun nat bool) (fun nat bool)) (combb bool bool nat) fNot) (hAPP nat (fun nat bool) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat)) (zero_zero nat)))) ) 15.47/15.67 ( (fun real (fun int (fun nat bool))), (fun int (fun nat real)), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun int (fun nat real)) (fun int (fun nat bool))))) (let ((_let_3 (fun real _let_2))) (let ((_let_4 (fun (fun nat real) (fun nat bool)))) (let ((_let_5 (fun real _let_4))) (hAPP _let_3 (fun (fun int (fun nat real)) (fun real (fun int (fun nat bool)))) (combc real (fun int (fun nat real)) (fun int (fun nat bool))) (hAPP _let_5 _let_3 (hAPP (fun _let_4 _let_2) (fun _let_5 _let_3) (combb _let_4 _let_2 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_1 _let_5) (combb _let_0 _let_4 real) (combb real bool nat)) (fequal real)))))))))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun (fun nat real) (fun nat real)))) (let ((_let_2 (fun int real))) (let ((_let_3 (fun int _let_0))) (let ((_let_4 (fun int (fun nat real)))) (let ((_let_5 (fun int _let_1))) (hAPP (fun nat real) _let_4 (hAPP _let_5 (fun (fun nat real) _let_4) (combc int (fun nat real) (fun nat real)) (hAPP _let_3 _let_5 (hAPP (fun _let_0 _let_1) (fun _let_3 _let_5) (combb _let_0 _let_1 int) (combb real real nat)) (hAPP _let_2 _let_3 (hAPP (fun real _let_0) (fun _let_2 _let_3) (combb real _let_0 int) (inverse_divide real)) (real_1 int)))) (real_1 nat)))))))) ) 15.47/15.67 ( (fun (fun int (fun nat bool)) (fun int bool)), (fun (fun nat bool) bool), (combb (fun nat bool) bool int), (fEx nat) ) 15.47/15.67 ( (fun (fun real (fun int (fun nat bool))) (fun real (fun int bool))), (fun (fun int (fun nat bool)) (fun int bool)), (combb (fun int (fun nat bool)) (fun int bool) real), (let ((_let_0 (fun nat bool))) (hAPP (fun _let_0 bool) (fun (fun int _let_0) (fun int bool)) (combb _let_0 bool int) (fEx nat))) ) 15.47/15.67 ( (let ((_let_0 (fun nat bool))) (fun real (fun _let_0 (fun int _let_0)))), (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun _let_0 (fun int _let_0)))) (let ((_let_2 (fun int (fun _let_0 _let_0)))) (hAPP (fun _let_2 _let_1) (fun (fun real _let_2) (fun real _let_1)) (combb _let_2 _let_1 real) (combc int _let_0 _let_0))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun (fun nat real) (fun nat real)))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun (fun nat bool) (fun nat bool)))) (let ((_let_6 (fun int real))) (let ((_let_7 (fun nat _let_2))) (let ((_let_8 (fun (fun nat bool) _let_7))) (let ((_let_9 (fun int _let_1))) (let ((_let_10 (fun real (fun int (fun nat bool))))) (let ((_let_11 (fun int _let_5))) (let ((_let_12 (fun real _let_11))) (let ((_let_13 (fun int _let_7))) (let ((_let_14 (fun real _let_13))) (let ((_let_15 (fun _let_13 _let_11))) (let ((_let_16 (fun (fun int (fun nat bool)) _let_13))) (let ((_let_17 (fun int (fun nat real)))) (let ((_let_18 (fun _let_17 (fun int (fun nat bool))))) (let ((_let_19 (fun real _let_18))) (let ((_let_20 (fun (fun nat real) (fun nat bool)))) (let ((_let_21 (fun real _let_20))) (let ((_let_22 (fun int _let_3))) (hAPP _let_14 _let_12 (hAPP _let_15 (fun _let_14 _let_12) (combb _let_13 _let_11 real) (hAPP (fun _let_7 _let_5) _let_15 (combb _let_7 _let_5 int) (combs nat bool bool))) (hAPP _let_10 _let_14 (hAPP _let_16 (fun _let_10 _let_14) (combb (fun int (fun nat bool)) _let_13 real) (hAPP _let_8 _let_16 (combb (fun nat bool) _let_7 int) (hAPP (fun bool _let_2) _let_8 (combb bool _let_2 nat) fconj))) (hAPP _let_17 _let_10 (hAPP _let_19 (fun _let_17 _let_10) (combc real _let_17 (fun int (fun nat bool))) (hAPP _let_21 _let_19 (hAPP (fun _let_20 _let_18) (fun _let_21 _let_19) (combb _let_20 _let_18 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_4 _let_21 (hAPP (fun _let_0 _let_20) (fun _let_4 _let_21) (combb _let_0 _let_20 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_17 (hAPP _let_22 (fun (fun nat real) _let_17) (combc int (fun nat real) (fun nat real)) (hAPP _let_9 _let_22 (hAPP (fun _let_1 _let_3) (fun _let_9 _let_22) (combb _let_1 _let_3 int) (combb real real nat)) (hAPP _let_6 _let_9 (hAPP (fun real _let_1) (fun _let_6 _let_9) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat)))))))))))))))))))))))))))) ) 15.47/15.67 ( (let ((_let_0 (fun nat bool))) (fun _let_0 (fun real (fun int _let_0)))), (let ((_let_0 (fun nat bool))) (fun real (fun _let_0 (fun int _let_0)))), (let ((_let_0 (fun nat bool))) (combc real _let_0 (fun int _let_0))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun (fun nat real) (fun nat real)))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun (fun nat bool) (fun nat bool)))) (let ((_let_6 (fun int real))) (let ((_let_7 (fun nat _let_2))) (let ((_let_8 (fun (fun nat bool) _let_7))) (let ((_let_9 (fun int _let_1))) (let ((_let_10 (fun real (fun int (fun nat bool))))) (let ((_let_11 (fun (fun nat bool) (fun int (fun nat bool))))) (let ((_let_12 (fun real _let_11))) (let ((_let_13 (fun int _let_5))) (let ((_let_14 (fun real _let_13))) (let ((_let_15 (fun int _let_7))) (let ((_let_16 (fun real _let_15))) (let ((_let_17 (fun _let_15 _let_13))) (let ((_let_18 (fun (fun int (fun nat bool)) _let_15))) (let ((_let_19 (fun int (fun nat real)))) (let ((_let_20 (fun _let_19 (fun int (fun nat bool))))) (let ((_let_21 (fun real _let_20))) (let ((_let_22 (fun (fun nat real) (fun nat bool)))) (let ((_let_23 (fun real _let_22))) (let ((_let_24 (fun int _let_3))) (hAPP _let_14 _let_12 (hAPP (fun _let_13 _let_11) (fun _let_14 _let_12) (combb _let_13 _let_11 real) (combc int (fun nat bool) (fun nat bool))) (hAPP _let_16 _let_14 (hAPP _let_17 (fun _let_16 _let_14) (combb _let_15 _let_13 real) (hAPP (fun _let_7 _let_5) _let_17 (combb _let_7 _let_5 int) (combs nat bool bool))) (hAPP _let_10 _let_16 (hAPP _let_18 (fun _let_10 _let_16) (combb (fun int (fun nat bool)) _let_15 real) (hAPP _let_8 _let_18 (combb (fun nat bool) _let_7 int) (hAPP (fun bool _let_2) _let_8 (combb bool _let_2 nat) fconj))) (hAPP _let_19 _let_10 (hAPP _let_21 (fun _let_19 _let_10) (combc real _let_19 (fun int (fun nat bool))) (hAPP _let_23 _let_21 (hAPP (fun _let_22 _let_20) (fun _let_23 _let_21) (combb _let_22 _let_20 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_4 _let_23 (hAPP (fun _let_0 _let_22) (fun _let_4 _let_23) (combb _let_0 _let_22 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_19 (hAPP _let_24 (fun (fun nat real) _let_19) (combc int (fun nat real) (fun nat real)) (hAPP _let_9 _let_24 (hAPP (fun _let_1 _let_3) (fun _let_9 _let_24) (combb _let_1 _let_3 int) (combb real real nat)) (hAPP _let_6 _let_9 (hAPP (fun real _let_1) (fun _let_6 _let_9) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat))))))))))))))))))))))))))))))) ) 15.47/15.67 ( (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))), (fun real (fun int (fun nat (fun bool bool)))), (let ((_let_0 (fun (fun nat bool) (fun nat bool)))) (let ((_let_1 (fun nat (fun bool bool)))) (let ((_let_2 (fun int _let_0))) (let ((_let_3 (fun int _let_1))) (let ((_let_4 (fun _let_3 _let_2))) (hAPP _let_4 (fun (fun real _let_3) (fun real _let_2)) (combb _let_3 _let_2 real) (hAPP (fun _let_1 _let_0) _let_4 (combb _let_1 _let_0 int) (combs nat bool bool)))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun (fun nat real) (fun nat real)))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun int real))) (let ((_let_6 (fun nat _let_2))) (let ((_let_7 (fun (fun nat bool) _let_6))) (let ((_let_8 (fun int _let_1))) (let ((_let_9 (fun real (fun int (fun nat bool))))) (let ((_let_10 (fun int _let_6))) (let ((_let_11 (fun real _let_10))) (let ((_let_12 (fun (fun int (fun nat bool)) _let_10))) (let ((_let_13 (fun int (fun nat real)))) (let ((_let_14 (fun _let_13 (fun int (fun nat bool))))) (let ((_let_15 (fun real _let_14))) (let ((_let_16 (fun (fun nat real) (fun nat bool)))) (let ((_let_17 (fun real _let_16))) (let ((_let_18 (fun int _let_3))) (hAPP _let_9 _let_11 (hAPP _let_12 (fun _let_9 _let_11) (combb (fun int (fun nat bool)) _let_10 real) (hAPP _let_7 _let_12 (combb (fun nat bool) _let_6 int) (hAPP (fun bool _let_2) _let_7 (combb bool _let_2 nat) fconj))) (hAPP _let_13 _let_9 (hAPP _let_15 (fun _let_13 _let_9) (combc real _let_13 (fun int (fun nat bool))) (hAPP _let_17 _let_15 (hAPP (fun _let_16 _let_14) (fun _let_17 _let_15) (combb _let_16 _let_14 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_4 _let_17 (hAPP (fun _let_0 _let_16) (fun _let_4 _let_17) (combb _let_0 _let_16 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_13 (hAPP _let_18 (fun (fun nat real) _let_13) (combc int (fun nat real) (fun nat real)) (hAPP _let_8 _let_18 (hAPP (fun _let_1 _let_3) (fun _let_8 _let_18) (combb _let_1 _let_3 int) (combb real real nat)) (hAPP _let_5 _let_8 (hAPP (fun real _let_1) (fun _let_5 _let_8) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat))))))))))))))))))))))) ) 15.47/15.67 ( (let ((_let_0 (fun nat bool))) (fun (fun real (fun int (fun _let_0 _let_0))) (fun real (fun _let_0 (fun int _let_0))))), (let ((_let_0 (fun nat bool))) (fun (fun int (fun _let_0 _let_0)) (fun _let_0 (fun int _let_0)))), (let ((_let_0 (fun nat bool))) (combb (fun int (fun _let_0 _let_0)) (fun _let_0 (fun int _let_0)) real)), (let ((_let_0 (fun nat bool))) (combc int _let_0 _let_0)) ) 15.47/15.67 ( (fun real (fun int (fun nat (fun bool bool)))), (fun real (fun int (fun nat bool))), (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun nat _let_1))) (let ((_let_3 (fun _let_0 _let_2))) (let ((_let_4 (fun int _let_0))) (let ((_let_5 (fun int _let_2))) (let ((_let_6 (fun _let_4 _let_5))) (hAPP _let_6 (fun (fun real _let_4) (fun real _let_5)) (combb _let_4 _let_5 real) (hAPP _let_3 _let_6 (combb _let_0 _let_2 int) (hAPP (fun bool _let_1) _let_3 (combb bool _let_1 nat) fconj)))))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun (fun nat real) (fun nat real)))) (let ((_let_3 (fun real _let_0))) (let ((_let_4 (fun int real))) (let ((_let_5 (fun int _let_1))) (let ((_let_6 (fun real (fun int (fun nat bool))))) (let ((_let_7 (fun int (fun nat real)))) (let ((_let_8 (fun _let_7 (fun int (fun nat bool))))) (let ((_let_9 (fun real _let_8))) (let ((_let_10 (fun (fun nat real) (fun nat bool)))) (let ((_let_11 (fun real _let_10))) (let ((_let_12 (fun int _let_2))) (hAPP _let_7 _let_6 (hAPP _let_9 (fun _let_7 _let_6) (combc real _let_7 (fun int (fun nat bool))) (hAPP _let_11 _let_9 (hAPP (fun _let_10 _let_8) (fun _let_11 _let_9) (combb _let_10 _let_8 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_3 _let_11 (hAPP (fun _let_0 _let_10) (fun _let_3 _let_11) (combb _let_0 _let_10 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_7 (hAPP _let_12 (fun (fun nat real) _let_7) (combc int (fun nat real) (fun nat real)) (hAPP _let_5 _let_12 (hAPP (fun _let_1 _let_2) (fun _let_5 _let_12) (combb _let_1 _let_2 int) (combb real real nat)) (hAPP _let_4 _let_5 (hAPP (fun real _let_1) (fun _let_4 _let_5) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat)))))))))))))))) ) 15.47/15.67 ( (let ((_let_0 (fun nat bool))) (fun (fun int (fun nat (fun bool bool))) (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun nat bool))) (fun (fun nat (fun bool bool)) (fun _let_0 _let_0))), (let ((_let_0 (fun nat bool))) (combb (fun nat (fun bool bool)) (fun _let_0 _let_0) int)), (combs nat bool bool) ) 15.47/15.67 ( (let ((_let_0 (fun nat bool))) (fun (fun real (fun int (fun nat (fun bool bool)))) (fun real (fun int (fun _let_0 _let_0))))), (let ((_let_0 (fun nat bool))) (fun (fun int (fun nat (fun bool bool))) (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun nat bool))) (combb (fun int (fun nat (fun bool bool))) (fun int (fun _let_0 _let_0)) real)), (let ((_let_0 (fun (fun nat bool) (fun nat bool)))) (let ((_let_1 (fun nat (fun bool bool)))) (hAPP (fun _let_1 _let_0) (fun (fun int _let_1) (fun int _let_0)) (combb _let_1 _let_0 int) (combs nat bool bool)))) ) 15.47/15.67 ( (fun (fun int (fun nat bool)) (fun int (fun nat (fun bool bool)))), (fun (fun nat bool) (fun nat (fun bool bool))), (combb (fun nat bool) (fun nat (fun bool bool)) int), (let ((_let_0 (fun bool bool))) (hAPP (fun bool _let_0) (fun (fun nat bool) (fun nat _let_0)) (combb bool _let_0 nat) fconj)) ) 15.47/15.67 ( (fun (fun real (fun int (fun nat bool))) (fun real (fun int (fun nat (fun bool bool))))), (fun (fun int (fun nat bool)) (fun int (fun nat (fun bool bool)))), (combb (fun int (fun nat bool)) (fun int (fun nat (fun bool bool))) real), (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun nat _let_1))) (let ((_let_3 (fun _let_0 _let_2))) (hAPP _let_3 (fun (fun int _let_0) (fun int _let_2)) (combb _let_0 _let_2 int) (hAPP (fun bool _let_1) _let_3 (combb bool _let_1 nat) fconj)))))) ) 15.47/15.67 ( (fun int (fun nat real)), (fun nat real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun (fun nat real) (fun nat real)))) (let ((_let_2 (fun int real))) (let ((_let_3 (fun int _let_0))) (let ((_let_4 (fun int _let_1))) (hAPP _let_4 (fun (fun nat real) (fun int (fun nat real))) (combc int (fun nat real) (fun nat real)) (hAPP _let_3 _let_4 (hAPP (fun _let_0 _let_1) (fun _let_3 _let_4) (combb _let_0 _let_1 int) (combb real real nat)) (hAPP _let_2 _let_3 (hAPP (fun real _let_0) (fun _let_2 _let_3) (combb real _let_0 int) (inverse_divide real)) (real_1 int))))))))), (real_1 nat) ) 15.47/15.67 ( (fun real (fun (fun int (fun nat real)) (fun int (fun nat bool)))), (fun real (fun (fun nat real) (fun nat bool))), (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun (fun int _let_1) (fun int _let_0)))) (let ((_let_3 (fun _let_1 _let_0))) (hAPP (fun _let_3 _let_2) (fun (fun real _let_3) (fun real _let_2)) (combb _let_3 _let_2 real) (combb _let_1 _let_0 int)))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun nat real) (fun nat bool)))) (let ((_let_3 (fun real _let_2))) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 real) (combb real bool nat)) (fequal real)))))) ) 15.47/15.67 ( (fun (fun int (fun nat real)) (fun real (fun int (fun nat bool)))), (fun real (fun (fun int (fun nat real)) (fun int (fun nat bool)))), (combc real (fun int (fun nat real)) (fun int (fun nat bool))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun int (fun nat real)) (fun int (fun nat bool))))) (let ((_let_3 (fun real _let_2))) (let ((_let_4 (fun (fun nat real) (fun nat bool)))) (let ((_let_5 (fun real _let_4))) (hAPP _let_5 _let_3 (hAPP (fun _let_4 _let_2) (fun _let_5 _let_3) (combb _let_4 _let_2 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_1 _let_5) (combb _let_0 _let_4 real) (combb real bool nat)) (fequal real))))))))) ) 15.47/15.67 ( (fun real (fun (fun nat real) (fun nat bool))), (fun real (fun real bool)), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun (fun nat real) (fun nat bool)))) (hAPP (fun _let_0 _let_1) (fun (fun real _let_0) (fun real _let_1)) (combb _let_0 _let_1 real) (combb real bool nat)))), (fequal real) ) 15.47/15.67 ( (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat real))) (fun (fun real (fun _let_1 _let_0)) (fun real (fun (fun int _let_1) (fun int _let_0)))))), (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat real))) (fun (fun _let_1 _let_0) (fun (fun int _let_1) (fun int _let_0))))), (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat real))) (combb (fun _let_1 _let_0) (fun (fun int _let_1) (fun int _let_0)) real))), (combb (fun nat real) (fun nat bool) int) ) 15.47/15.67 ( (fun (fun real (fun real bool)) (fun real (fun (fun nat real) (fun nat bool)))), (fun (fun real bool) (fun (fun nat real) (fun nat bool))), (combb (fun real bool) (fun (fun nat real) (fun nat bool)) real), (combb real bool nat) ) 15.47/15.67 ( (let ((_let_0 (fun nat real))) (fun int (fun _let_0 _let_0))), (fun int (fun real real)), (let ((_let_0 (fun real real))) (let ((_let_1 (fun (fun nat real) (fun nat real)))) (hAPP (fun _let_0 _let_1) (fun (fun int _let_0) (fun int _let_1)) (combb _let_0 _let_1 int) (combb real real nat)))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun int real))) (let ((_let_2 (fun int _let_0))) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 int) (inverse_divide real)) (real_1 int))))) ) 15.47/15.67 ( (let ((_let_0 (fun nat real))) (fun _let_0 (fun int _let_0))), (let ((_let_0 (fun nat real))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun nat real))) (combc int _let_0 _let_0)), (let ((_let_0 (fun real real))) (let ((_let_1 (fun (fun nat real) (fun nat real)))) (let ((_let_2 (fun int real))) (let ((_let_3 (fun int _let_0))) (let ((_let_4 (fun int _let_1))) (hAPP _let_3 _let_4 (hAPP (fun _let_0 _let_1) (fun _let_3 _let_4) (combb _let_0 _let_1 int) (combb real real nat)) (hAPP _let_2 _let_3 (hAPP (fun real _let_0) (fun _let_2 _let_3) (combb real _let_0 int) (inverse_divide real)) (real_1 int)))))))) ) 15.47/15.67 ( (let ((_let_0 (fun nat real))) (fun (fun int (fun real real)) (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun nat real))) (fun (fun real real) (fun _let_0 _let_0))), (let ((_let_0 (fun nat real))) (combb (fun real real) (fun _let_0 _let_0) int)), (combb real real nat) ) 15.47/15.67 ( (let ((_let_0 (fun int int))) (fun int (fun _let_0 _let_0))), (fun int (fun int int)), (let ((_let_0 (fun (fun int int) (fun int int)))) (hAPP (fun (fun int int) _let_0) (fun (fun int (fun int int)) (fun int _let_0)) (combb (fun int int) _let_0 int) (combb int int int))), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)) (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 15.47/15.67 ( (let ((_let_0 (fun int int))) (fun (fun int _let_0) (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun int int))) (fun _let_0 (fun _let_0 _let_0))), (let ((_let_0 (fun int int))) (combb _let_0 (fun _let_0 _let_0) int)), (combb int int int) ) 15.47/15.67 ( (let ((_let_0 (fun int (fun int (fun int bool))))) (fun _let_0 _let_0)), (let ((_let_0 (fun int (fun int bool)))) (fun _let_0 _let_0)), (let ((_let_0 (fun int (fun int bool)))) (combb _let_0 _let_0 int)), (combc int int bool) ) 15.47/15.67 ( (fun (fun int (fun int int)) (fun int (fun int (fun int bool)))), (fun (fun int int) (fun int (fun int bool))), (combb (fun int int) (fun int (fun int bool)) int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (hAPP _let_1 (fun (fun int int) _let_1) (combb int _let_0 int) (fequal int)))) ) 15.47/15.67 ) 15.47/15.67 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_111409 $$unsorted) (BOUND_VARIABLE_111410 $$unsorted) (BOUND_VARIABLE_111411 $$unsorted)) (let ((_let_0 (filter real))) (let ((_let_1 (fun _let_0 bool))) (or (not (metric_space X_a)) (= (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 (hAPP (fun real X_a) (fun X_a _let_1) (tendsto real X_a) BOUND_VARIABLE_111409) BOUND_VARIABLE_111410) (hAPP real _let_0 (at real) BOUND_VARIABLE_111411))) (forall ((S_2 $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (fun (filter nat) bool))) (let ((_let_2 (fun nat X_a))) (or (not (hBOOL (hAPP (filter nat) bool (hAPP real _let_1 (hAPP _let_0 (fun real _let_1) (tendsto nat real) S_2) BOUND_VARIABLE_111411) sequentially))) (not (forall ((N_2 $$unsorted)) (not (= (hAPP nat real S_2 N_2) BOUND_VARIABLE_111411)) )) (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_1 (hAPP _let_2 (fun X_a _let_1) (tendsto nat X_a) (hAPP _let_0 _let_2 (hAPP (fun real X_a) (fun _let_0 _let_2) (combb real X_a nat) BOUND_VARIABLE_111409) S_2)) BOUND_VARIABLE_111410) sequentially)))))) ))))) ) 15.47/15.67 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.67 ) 15.47/15.67 (instantiation (forall ((Ma $$unsorted)) (let ((_let_0 (fun int bool))) (= (hAPP int _let_0 norRRset Ma) (hAPP int _let_0 (hAPP int (fun int _let_0) bnorRset (hAPP int int (hAPP int (fun int int) (minus_minus int) Ma) (one_one int))) Ma))) ) 15.47/15.67 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.67 ) 15.47/15.67 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_111512 $$unsorted) (BOUND_VARIABLE_111513 $$unsorted)) (or (not (linorder X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_111512) BOUND_VARIABLE_111513))) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (ord_max X_a) BOUND_VARIABLE_111512) BOUND_VARIABLE_111513) (ti X_a BOUND_VARIABLE_111513))) ) 15.47/15.67 ( int, (one_one int), t ) 15.47/15.67 ( int, (zero_zero int), (one_one int) ) 15.47/15.67 ( int, (zero_zero int), min_1 ) 15.47/15.67 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.67 ( int, (zero_zero int), s ) 15.47/15.67 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.47/15.67 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.47/15.67 ( int, (zero_zero int), skv_4 ) 15.47/15.67 ( int, (zero_zero int), skv_10 ) 15.47/15.68 ( int, min_1, pls ) 15.47/15.68 ( int, min_1, min_1 ) 15.47/15.68 ( real, (zero_zero real), pi ) 15.47/15.68 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.68 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.68 ( real, (zero_zero real), skv_3 ) 15.47/15.68 ( real, (zero_zero real), skv_5 ) 15.47/15.68 ( real, (zero_zero real), skv_7 ) 15.47/15.68 ( real, (zero_zero real), skv_12 ) 15.47/15.68 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.47/15.68 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.68 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.47/15.68 ( real, skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.68 ) 15.47/15.68 (instantiation (forall ((A_1 $$unsorted)) (= (one_one real) (hAPP complex real (norm_norm complex) (hAPP real complex (hAPP real (fun real complex) complex_1 (hAPP real real cos A_1)) (hAPP real real sin A_1)))) ) 15.47/15.68 ( (zero_zero real) ) 15.47/15.68 ( pi ) 15.47/15.68 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.68 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.68 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.47/15.68 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.47/15.68 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.47/15.68 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.47/15.68 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.47/15.68 ( skv_5 ) 15.47/15.68 ) 15.47/15.68 (instantiation (forall ((Z_4 $$unsorted) (Z_1 $$unsorted)) (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)))) (or (not (hBOOL (hAPP int bool _let_0 Z_1))) (not (hBOOL (hAPP int bool _let_0 Z_4))) (= (hAPP int nat nat_1 (hAPP int int (hAPP int (fun int int) (plus_plus int) Z_1) Z_4)) (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP int nat nat_1 Z_1)) (hAPP int nat nat_1 Z_4))))) ) 15.47/15.68 ( (one_one int), (one_one int) ) 15.47/15.68 ( (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.47/15.68 ( (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.68 ) 15.47/15.68 (instantiation (forall ((K_4 $$unsorted)) (let ((_let_0 (product_prod int int))) (= (hAPP rat _let_0 quotient_of (hAPP int rat (number_number_of rat) K_4)) (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) (hAPP int int (number_number_of int) K_4)) (one_one int)))) ) 15.47/15.68 ( pls ) 15.47/15.68 ( (hAPP int int bit1 pls) ) 15.47/15.68 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.47/15.68 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.47/15.68 ( min_1 ) 15.47/15.68 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.68 ) 15.47/15.68 (instantiation (forall ((X_a $$unsorted) (Y_3 $$unsorted)) (let ((_let_0 (fun X_a bool))) (= (hAPP _let_0 _let_0 (hAPP (fun X_a X_a) (fun _let_0 _let_0) (image X_a X_a) (combi X_a)) Y_3) (ti _let_0 Y_3))) ) 15.47/15.68 ( bool, fNot ) 15.47/15.68 ( nat, (even_odd_even nat) ) 15.47/15.68 ( nat, prime ) 15.47/15.68 ( int, nat_neg ) 15.47/15.68 ( int, zprime ) 15.47/15.68 ( int, zEven ) 15.47/15.68 ( int, zOdd ) 15.47/15.68 ( int, (even_odd_even int) ) 15.47/15.68 ( int, twoSqu1091635170sum2sq ) 15.47/15.68 ( int, nat_is_nat ) 15.47/15.68 ( (fun int bool), nat_nat_set ) 15.47/15.68 ( (product_prod nat nat), pred_nat ) 15.47/15.68 ( (product_prod int int), frac_1 ) 15.47/15.68 ( (fun nat rat), vanishes ) 15.47/15.68 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)), ratrel ) 15.47/15.68 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), pair_less ) 15.47/15.68 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), pair_leq ) 15.47/15.68 ) 15.47/15.68 (instantiation (forall ((K_4 $$unsorted)) (let ((_let_0 (uminus_uminus int))) (= (hAPP int int bit1 (hAPP int int pred (hAPP int int _let_0 K_4))) (hAPP int int _let_0 (hAPP int int bit1 K_4)))) ) 15.47/15.68 ( (one_one int) ) 15.47/15.68 ( pls ) 15.47/15.68 ( min_1 ) 15.47/15.68 ) 15.47/15.68 (instantiation (forall ((N_1 $$unsorted) (P_5 $$unsorted) (M $$unsorted)) (let ((_let_0 (hAPP int (fun int bool) (dvd_dvd int) P_5))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) M))) (not (hBOOL (hAPP int bool zprime P_5))) (not (hBOOL (hAPP int bool _let_0 (hAPP int int (hAPP int (fun int int) (times_times int) M) N_1)))) (hBOOL (hAPP int bool _let_0 N_1)) (hBOOL (hAPP int bool _let_0 M)))) ) 15.47/15.68 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.68 ) 15.47/15.68 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted) (F $$unsorted)) (or (not (forall ((X $$unsorted)) (let ((_let_0 (fun real bool))) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP (fun real real) (fun real _let_0) (deriv real) F) X) (zero_zero real)))) )) (= (hAPP real real F Y_2) (hAPP real real F X_2))) ) 15.47/15.68 ( (one_one real), (one_one real), ln ) 15.47/15.68 ( (one_one real), (one_one real), sqrt ) 15.47/15.68 ( (one_one real), (one_one real), arctan ) 15.47/15.68 ( (one_one real), (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi), (uminus_uminus real) ) 15.47/15.68 ( (zero_zero real), (zero_zero real), sqrt ) 15.47/15.68 ( (zero_zero real), (zero_zero real), (inverse_inverse real) ) 15.47/15.68 ( (zero_zero real), (zero_zero real), arctan ) 15.47/15.68 ( (zero_zero real), (zero_zero real), (sgn_sgn real) ) 15.47/15.68 ( (zero_zero real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), cos ) 15.47/15.68 ( (zero_zero real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), sqrt ) 15.47/15.68 ( (zero_zero real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), sqrt ) 15.47/15.68 ( (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))), tan ) 15.47/15.68 ( (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))))), arctan ) 15.47/15.68 ( (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))))), arctan ) 15.47/15.68 ( (zero_zero real), (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))), sin ) 15.47/15.68 ( pi, pi, cos ) 15.47/15.68 ( pi, pi, sin ) 15.47/15.68 ( pi, pi, tan ) 15.47/15.68 ( pi, pi, (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.68 ( pi, pi, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1))))))) ) 15.47/15.68 ( pi, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), cos ) 15.47/15.68 ( pi, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi), sin ) 15.47/15.68 ( pi, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), cos ) 15.47/15.68 ( pi, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), sin ) 15.47/15.68 ( pi, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), tan ) 15.47/15.68 ( pi, (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.68 ( pi, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))), tan ) 15.47/15.68 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real (fun real real) (inverse_divide real) pi) ) 15.47/15.68 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real (fun real real) (inverse_divide real) (one_one real)) ) 15.47/15.68 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real (fun real real) (inverse_divide real) (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.47/15.68 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real (fun real real) (inverse_divide real) (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.47/15.68 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real (fun real real) (inverse_divide real) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.47/15.68 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real (fun real real) (inverse_divide real) pi) ) 15.47/15.68 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), sqrt ) 15.47/15.68 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP real (fun real real) (inverse_divide real) pi) ) 15.47/15.68 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))), cos ) 15.47/15.68 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real (fun real real) (inverse_divide real) (one_one real)) ) 15.47/15.68 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))), (hAPP real (fun real real) (inverse_divide real) (one_one real)) ) 15.47/15.68 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real), (uminus_uminus real) ) 15.47/15.68 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi, cos ) 15.47/15.68 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (uminus_uminus real) ) 15.47/15.68 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi), (uminus_uminus real) ) 15.47/15.68 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))), sin ) 15.47/15.68 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP real (fun real real) (inverse_divide real) pi) ) 15.47/15.68 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi), pi, sin ) 15.47/15.68 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (uminus_uminus real) ) 15.47/15.68 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi), (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))), cos ) 15.47/15.68 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero real), sqrt ) 15.47/15.68 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real (fun real real) (inverse_divide real) pi) ) 15.47/15.68 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP real (fun real real) (inverse_divide real) (one_one real)) ) 15.47/15.68 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), pi, tan ) 15.47/15.68 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), cos ) 15.47/15.68 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi), sin ) 15.47/15.68 ( (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), pi, (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.68 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real), cos ) 15.47/15.68 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), cos ) 15.47/15.68 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), tan ) 15.47/15.68 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))), cos ) 15.47/15.68 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))), sin ) 15.47/15.68 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP real (fun real real) (inverse_divide real) pi) ) 15.47/15.68 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))), (zero_zero real), tan ) 15.47/15.68 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), sin ) 15.47/15.68 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))), (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi), cos ) 15.47/15.68 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))), sin ) 15.47/15.68 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))), cos ) 15.47/15.68 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))), sin ) 15.47/15.68 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))), tan ) 15.47/15.68 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))), (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))), cos ) 15.47/15.68 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))), (hAPP real (fun real real) (inverse_divide real) (one_one real)) ) 15.47/15.68 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))))), arctan ) 15.47/15.68 ( (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.47/15.68 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real (fun real real) (inverse_divide real) (one_one real)) ) 15.47/15.68 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))))), (zero_zero real), arctan ) 15.47/15.68 ( (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))), (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real _let_0 (minus_minus real) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1))))))))) ) 15.47/15.68 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))), (zero_zero real), sin ) 15.47/15.68 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))), cos ) 15.47/15.68 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))), (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))), sin ) 15.47/15.68 ( skv_5, skv_5, cos ) 15.47/15.68 ) 15.47/15.68 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)))) (or (not (hBOOL (hAPP real bool _let_0 X_1))) (hBOOL (hAPP real bool _let_0 (hAPP real real sqrt X_1))))) ) 15.47/15.68 ( (one_one real) ) 15.47/15.68 ( (zero_zero real) ) 15.47/15.68 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.68 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.47/15.68 ) 15.47/15.68 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (zero_zero real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) _let_2) X_2))) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (one_one real)) X_2)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 _let_2) (hAPP real real ln X_2)))))))) ) 15.47/15.68 ( (one_one real) ) 15.47/15.68 ( pi ) 15.47/15.68 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.68 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.68 ( skv_2 ) 15.47/15.68 ( skv_8 ) 15.47/15.68 ( skv_9 ) 15.47/15.68 ) 15.47/15.68 (instantiation (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted)) (let ((_let_0 (hAPP real (fun real real) (times_times real) C_1))) (or (= (zero_zero real) C_1) (= (= A_2 B_1) (= (hAPP real real _let_0 A_2) (hAPP real real _let_0 B_1))))) ) 15.47/15.68 ( pi, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.68 ( pi, pi, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 15.47/15.68 ( pi, (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.68 ( (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.68 ( (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.68 ) 15.47/15.68 (instantiation (forall ((Z $$unsorted) (W_1 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (let ((_let_2 (zero_zero int))) (or (and (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) _let_2) W_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 _let_2) Z)))) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP int nat nat_1 W_1)) (hAPP int nat nat_1 Z))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 W_1) Z))))))) ) 15.47/15.68 ( (one_one int), (zero_zero int) ) 15.47/15.68 ( pls, min_1 ) 15.47/15.68 ( min_1, (zero_zero int) ) 15.47/15.68 ( min_1, min_1 ) 15.47/15.68 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 15.47/15.68 ( s, (zero_zero int) ) 15.47/15.68 ( t, (one_one int) ) 15.47/15.68 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 15.47/15.68 ( (hAPP int int (number_number_of int) pls), (zero_zero int) ) 15.47/15.68 ( skv_4, (zero_zero int) ) 15.47/15.68 ( skv_10, (zero_zero int) ) 15.47/15.68 ) 15.47/15.68 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (ord_atLeastAtMost X_a))) (or (not (order X_a)) (= _let_0 (ti (fun X_a (fun X_a (fun X_a bool))) _let_0)))) ) 15.47/15.68 ( bool ) 15.47/15.68 ( nat ) 15.47/15.68 ( int ) 15.47/15.68 ( (fun int bool) ) 15.47/15.68 ( (fun nat bool) ) 15.47/15.68 ( (product_prod nat nat) ) 15.47/15.68 ( real ) 15.47/15.68 ( rat ) 15.47/15.68 ( (filter nat) ) 15.47/15.68 ( (product_prod int int) ) 15.47/15.68 ( quickcheck_code_int ) 15.47/15.68 ( code_code_numeral ) 15.47/15.68 ( (product_prod real real) ) 15.47/15.68 ( (fun nat rat) ) 15.47/15.68 ( (filter real) ) 15.47/15.68 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 15.47/15.68 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 15.47/15.68 ) 15.47/15.68 (instantiation (forall ((W $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (number_number_of int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (hAPP int (fun int _let_2) negDivAlg (one_one int)))) (let ((_let_4 (hAPP int int _let_1 W))) (let ((_let_5 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) _let_4))) (let ((_let_6 (hAPP int _let_2 _let_3 _let_4))) (let ((_let_7 (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) _let_5)))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) _let_4))) (and (or (not _let_7) (= (hAPP int _let_2 (hAPP int (fun int _let_2) (product_Pair int int) (hAPP int int _let_1 min_1)) _let_5) _let_6)) (or _let_7 (= _let_6 (hAPP _let_2 _let_2 (hAPP int (fun _let_2 _let_2) adjust _let_4) (hAPP int _let_2 _let_3 (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int _let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) _let_4))))))))))))))) ) 15.47/15.68 ( pls ) 15.47/15.68 ( (hAPP int int bit1 pls) ) 15.47/15.68 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.47/15.68 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.47/15.68 ( min_1 ) 15.47/15.68 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.68 ) 15.47/15.68 (instantiation (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (or (not (hBOOL (hAPP int bool nat_is_nat X_1))) (not (hBOOL (hAPP int bool nat_is_nat Y_1))) (hBOOL (hAPP int bool nat_is_nat (hAPP int int (hAPP int (fun int int) (times_times int) X_1) Y_1)))) ) 15.47/15.68 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.68 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.68 ( skv_13, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.68 ) 15.47/15.68 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (ord_atMost X_a))) (or (not (ord X_a)) (= _let_0 (ti (fun X_a (fun X_a bool)) _let_0)))) ) 15.47/15.68 ( bool ) 15.47/15.68 ( nat ) 15.47/15.68 ( int ) 15.47/15.68 ( (fun int bool) ) 15.47/15.68 ( (fun nat bool) ) 15.47/15.68 ( (product_prod nat nat) ) 15.47/15.68 ( real ) 15.47/15.68 ( rat ) 15.47/15.68 ( (filter nat) ) 15.47/15.68 ( (product_prod int int) ) 15.47/15.68 ( quickcheck_code_int ) 15.47/15.68 ( code_code_numeral ) 15.47/15.68 ( (product_prod real real) ) 15.47/15.68 ( (fun nat rat) ) 15.47/15.68 ( (filter real) ) 15.47/15.68 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 15.47/15.68 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 15.47/15.68 ) 15.47/15.68 (instantiation (forall ((N $$unsorted) (P_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool P_1 (zero_zero nat)))) (not (forall ((N_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool P_1 N_2))) (hBOOL (hAPP nat bool P_1 (hAPP nat nat suc N_2)))) )) (hBOOL (hAPP nat bool P_1 N))) ) 15.47/15.68 ( (zero_zero nat), (even_odd_even nat) ) 15.47/15.68 ( (zero_zero nat), prime ) 15.47/15.68 ( (hAPP nat nat suc (zero_zero nat)), prime ) 15.47/15.68 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) ) 15.47/15.68 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), prime ) 15.47/15.68 ( (one_one nat), (even_odd_even nat) ) 15.47/15.68 ) 15.47/15.68 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_111932 $$unsorted) (BOUND_VARIABLE_111933 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (zero_zero X_a))) (or (not (ordered_ring X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_111933) _let_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_111932) _let_2))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_111933) BOUND_VARIABLE_111932))))))) ) 15.47/15.68 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.68 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.68 ( int, skv_13, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.68 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.68 ( real, pi, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 15.47/15.68 ( real, (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.68 ( real, (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.68 ( complex, ii, ii ) 15.47/15.68 ( complex, ii, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 15.47/15.68 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.68 ) 15.47/15.68 (instantiation (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) _let_1) A_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) A_1) B))) (= _let_1 (hAPP int int (hAPP int (fun int int) (div_div int) A_1) B))))) ) 15.47/15.68 ( (one_one int), pls ) 15.47/15.68 ( pls, pls ) 15.47/15.68 ( pls, min_1 ) 15.47/15.68 ( min_1, pls ) 15.47/15.68 ( min_1, min_1 ) 15.47/15.68 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), pls ) 15.47/15.68 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s ) 15.47/15.68 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.47/15.68 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_4 ) 15.47/15.68 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_10 ) 15.47/15.68 ( t, (one_one int) ) 15.47/15.68 ) 15.47/15.68 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_111989 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (zero_zero X_a))) (or (not (linord219039673up_add X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_111989) BOUND_VARIABLE_111989)) _let_2)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_111989) _let_2))))))) ) 15.47/15.68 ( nat, (one_one nat) ) 15.47/15.68 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.47/15.68 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.68 ) 15.47/15.68 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_112016 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member X_a))) (let ((_let_3 (field_char_0_Rats X_a))) (or (not (field_char_0 X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_112016) _let_3))) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_112016)) (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_112016)) _let_3))))))) ) 15.47/15.68 ( bool, fFalse ) 15.47/15.68 ( bool, fTrue ) 15.47/15.68 ( int, pls ) 15.47/15.68 ( int, min_1 ) 15.47/15.68 ( int, s ) 15.47/15.68 ( int, m ) 15.47/15.68 ( int, s1 ) 15.47/15.68 ( int, t ) 15.47/15.68 ( (fun int bool), nat_neg ) 15.47/15.68 ( (fun int bool), zprime ) 15.47/15.68 ( (fun int bool), zEven ) 15.47/15.68 ( (fun int bool), zOdd ) 15.47/15.68 ( (fun int bool), (even_odd_even int) ) 15.47/15.68 ( (fun int bool), twoSqu1091635170sum2sq ) 15.47/15.68 ( (fun int bool), nat_is_nat ) 15.47/15.68 ( (fun int (fun int bool)), norRRset ) 15.47/15.68 ( (fun int (fun int bool)), quadRes ) 15.47/15.68 ( (fun int (fun int bool)), sRStar ) 15.47/15.68 ( (fun int (fun int bool)), d22set ) 15.47/15.68 ( (fun int (fun int bool)), sr ) 15.47/15.68 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 15.47/15.68 ( (fun int int), zfact ) 15.47/15.68 ( (fun int int), bit0 ) 15.47/15.68 ( (fun int int), bit1 ) 15.47/15.68 ( (fun int int), (fact_fact int) ) 15.47/15.68 ( (fun int int), pred ) 15.47/15.68 ( (fun int int), succ ) 15.47/15.68 ( (fun nat bool), (even_odd_even nat) ) 15.47/15.68 ( (fun nat bool), prime ) 15.47/15.68 ( (fun nat nat), suc ) 15.47/15.68 ( (fun nat nat), (fact_fact nat) ) 15.47/15.68 ( (fun nat nat), fact ) 15.47/15.68 ( (fun nat nat), nat_size ) 15.47/15.68 ( (fun nat nat), (size_size nat) ) 15.47/15.68 ( (fun (product_prod nat nat) bool), pred_nat ) 15.47/15.68 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 15.47/15.68 ( real, (zero_zero real) ) 15.47/15.68 ( real, pi ) 15.47/15.68 ( (fun real real), ln ) 15.47/15.68 ( (fun real real), cos ) 15.47/15.68 ( (fun real real), sqrt ) 15.47/15.68 ( (fun real real), sin ) 15.47/15.68 ( (fun real real), arccos ) 15.47/15.68 ( (fun real real), arcsin ) 15.47/15.68 ( (fun real real), tan ) 15.47/15.68 ( (fun real real), arctan ) 15.47/15.68 ( (fun nat (fun nat bool)), coprime ) 15.47/15.68 ( complex, ii ) 15.47/15.68 ( (fun nat real), (real_1 nat) ) 15.47/15.68 ( (fun nat real), sin_coeff ) 15.47/15.68 ( (fun nat real), cos_coeff ) 15.47/15.68 ( (filter nat), sequentially ) 15.47/15.68 ( (fun int (fun int int)), (gcd_gcd int) ) 15.47/15.68 ( (fun int (fun int int)), legendre ) 15.47/15.68 ( (fun int (fun int int)), legacy_zgcd ) 15.47/15.68 ( (fun int (fun int int)), standardRes ) 15.47/15.68 ( (fun int (fun int int)), nat_tsub ) 15.47/15.68 ( (fun int (fun int int)), multInv ) 15.47/15.68 ( (fun int (fun int int)), z3mod ) 15.47/15.68 ( (fun int (fun int int)), z3div ) 15.47/15.68 ( (fun int (fun int int)), int_gcd ) 15.47/15.68 ( (fun int (fun int int)), int_lcm ) 15.47/15.68 ( (fun int (fun int int)), inv ) 15.47/15.68 ( (fun complex complex), expi ) 15.47/15.68 ( (fun complex complex), cnj ) 15.47/15.68 ( (fun real complex), cis ) 15.47/15.68 ( (fun int nat), nat_1 ) 15.47/15.68 ( (fun int nat), phi ) 15.47/15.68 ( (fun (fun int bool) bool), nat_nat_set ) 15.47/15.68 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 15.47/15.68 ( (fun nat (fun nat nat)), nat_gcd ) 15.47/15.68 ( (fun nat (fun nat nat)), nat_lcm ) 15.47/15.68 ( (fun (fun int bool) int), (the int) ) 15.47/15.68 ( (fun complex real), re ) 15.47/15.68 ( (fun complex real), im ) 15.47/15.68 ( (fun complex real), arg ) 15.47/15.68 ( (fun bool bool), fNot ) 15.47/15.68 ( (fun nat (fun real real)), root ) 15.47/15.68 ( (fun real (fun real real)), log ) 15.47/15.68 ( (fun real (fun real real)), powr ) 15.47/15.68 ( (fun bool (fun bool bool)), fimplies ) 15.47/15.68 ( (fun bool (fun bool bool)), fconj ) 15.47/15.68 ( (fun bool (fun bool bool)), fdisj ) 15.47/15.68 ( (fun int (fun int (product_prod int int))), negDivAlg ) 15.47/15.68 ( (fun int (fun int (product_prod int int))), posDivAlg ) 15.47/15.68 ( (fun int (fun int (product_prod int int))), divmod_int ) 15.47/15.68 ( (fun int (fun int (product_prod int int))), pdivmod ) 15.47/15.68 ( (fun int (fun int (product_prod int int))), norm_frac ) 15.47/15.68 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 15.47/15.68 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 15.47/15.68 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 15.47/15.68 ( (fun int (fun int (fun int bool))), zcong ) 15.47/15.68 ( (fun int (fun int (fun int bool))), zcongm ) 15.47/15.68 ( (fun int (fun int (fun int bool))), noXRRset ) 15.47/15.68 ( (fun int (fun int (fun int bool))), bnorRset ) 15.47/15.68 ( (fun int (fun int (fun int bool))), wset ) 15.47/15.68 ( (fun (product_prod int int) bool), frac_1 ) 15.47/15.68 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 15.47/15.68 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 15.47/15.68 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 15.47/15.68 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 15.47/15.68 ( (fun (fun nat rat) bool), vanishes ) 15.47/15.68 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 15.47/15.68 ( (fun code_code_numeral nat), code_c271388182l_size ) 15.47/15.68 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 15.47/15.68 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 15.47/15.68 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 15.47/15.68 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 15.47/15.68 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 15.47/15.68 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 15.47/15.68 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 15.47/15.68 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 15.47/15.68 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 15.47/15.68 ( (fun complex nat), complex_size ) 15.47/15.68 ( (fun complex nat), (size_size complex) ) 15.47/15.68 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 15.47/15.68 ( (fun nat (fun nat (product_prod int int))), bezw ) 15.47/15.68 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 15.47/15.68 ( (fun int (fun nat nat)), nat_aux ) 15.47/15.68 ( (fun int (fun (fun int bool) bool)), rsetR ) 15.47/15.68 ( (fun int (fun (fun int bool) bool)), resSet ) 15.47/15.68 ( (fun int (list int)), quickc666637781d_zero ) 15.47/15.68 ( (fun (product_prod int int) rat), frct ) 15.47/15.68 ( (fun int (fun int rat)), fract ) 15.47/15.68 ( (fun real (fun real complex)), complex_1 ) 15.47/15.68 ( (fun real (fun real complex)), rcis ) 15.47/15.68 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 15.47/15.68 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 15.47/15.68 ( (fun int real), (real_1 int) ) 15.47/15.68 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 15.47/15.68 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 15.47/15.68 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 15.47/15.68 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 15.47/15.68 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 15.47/15.68 ( (fun real nat), natfloor ) 15.47/15.68 ( (fun real nat), natceiling ) 15.47/15.68 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 15.47/15.68 ( (fun quickcheck_code_int int), quickcheck_int_of ) 15.47/15.68 ( (fun rat (product_prod int int)), quotient_of ) 15.47/15.68 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 15.47/15.68 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 15.47/15.68 ( (fun rat real), ratreal ) 15.47/15.68 ( (fun code_code_numeral int), code_int_of ) 15.47/15.68 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 15.47/15.68 ( (fun int quickcheck_code_int), quickcheck_of_int ) 15.47/15.68 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 15.47/15.68 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 15.47/15.68 ) 15.47/15.68 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_112040 $$unsorted)) (let ((_let_0 (ring_1_of_int X_a))) (or (not (ring_1 X_a)) (= (hAPP int X_a _let_0 (hAPP int int (uminus_uminus int) BOUND_VARIABLE_112040)) (hAPP X_a X_a (uminus_uminus X_a) (hAPP int X_a _let_0 BOUND_VARIABLE_112040))))) ) 15.47/15.68 ( real, (one_one int) ) 15.47/15.68 ( real, pls ) 15.47/15.68 ) 15.47/15.68 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_112065 $$unsorted) (BOUND_VARIABLE_112066 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (plus_plus X_a))) (or (not (group_add X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_112065)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_112065) BOUND_VARIABLE_112066)) (ti X_a BOUND_VARIABLE_112066))))) ) 15.47/15.68 ( nat, (one_one nat), (one_one nat) ) 15.47/15.68 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 15.47/15.68 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 15.47/15.68 ) 15.47/15.68 (instantiation (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) X_1) (zero_zero real)))) (= (hAPP int real (number_number_of real) min_1) (hAPP real real (sgn_sgn real) X_1))) ) 15.47/15.68 ( (one_one real) ) 15.47/15.68 ( (zero_zero real) ) 15.47/15.68 ( pi ) 15.47/15.68 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.68 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.47/15.68 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.68 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 15.47/15.68 ) 15.47/15.68 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (zero_zero real))) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) _let_0) X_1))) (not (= _let_0 (hAPP real real sqrt X_1))) (= _let_0 X_1))) ) 15.47/15.68 ( (one_one real) ) 15.47/15.68 ( (zero_zero real) ) 15.47/15.68 ( pi ) 15.47/15.68 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.68 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.68 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.47/15.68 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.68 ( skv_3 ) 15.47/15.68 ( skv_5 ) 15.47/15.68 ( skv_7 ) 15.47/15.68 ( skv_12 ) 15.47/15.68 ) 15.47/15.68 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_112124 $$unsorted) (BOUND_VARIABLE_112125 $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (linorder X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_112125) BOUND_VARIABLE_112124)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_112124) BOUND_VARIABLE_112125)))))) ) 15.47/15.68 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 15.47/15.68 ( int, (one_one int), pls ) 15.47/15.68 ( int, (one_one int), t ) 15.47/15.68 ( int, (zero_zero int), (one_one int) ) 15.47/15.68 ( int, (zero_zero int), min_1 ) 15.47/15.68 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.68 ( int, (zero_zero int), s ) 15.47/15.68 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.47/15.68 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.47/15.68 ( int, (zero_zero int), skv_4 ) 15.47/15.68 ( int, (zero_zero int), skv_10 ) 15.47/15.68 ( int, pls, pls ) 15.47/15.68 ( int, pls, min_1 ) 15.47/15.68 ( int, min_1, pls ) 15.47/15.68 ( int, min_1, min_1 ) 15.47/15.68 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), pls ) 15.47/15.68 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s ) 15.47/15.68 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.47/15.68 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_4 ) 15.47/15.68 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_10 ) 15.47/15.68 ( int, t, (one_one int) ) 15.47/15.68 ( real, (zero_zero real), pi ) 15.47/15.68 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.68 ( real, (zero_zero real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.47/15.68 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.68 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.68 ( real, (zero_zero real), skv_3 ) 15.47/15.68 ( real, (zero_zero real), skv_5 ) 15.47/15.68 ( real, (zero_zero real), skv_7 ) 15.47/15.68 ( real, (zero_zero real), skv_12 ) 15.47/15.68 ( real, pi, (zero_zero real) ) 15.47/15.68 ( real, pi, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 15.47/15.68 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.47/15.68 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.68 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.47/15.68 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.68 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 15.47/15.68 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 15.47/15.68 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.47/15.68 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.47/15.68 ( real, skv_2, (zero_zero real) ) 15.47/15.68 ( real, skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.68 ( real, skv_8, (zero_zero real) ) 15.47/15.68 ( real, skv_9, (zero_zero real) ) 15.47/15.68 ) 15.47/15.68 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_112180 $$unsorted) (BOUND_VARIABLE_112181 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (uminus_uminus X_a))) (or (not (boolean_algebra X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_112180)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_112181))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_112181) BOUND_VARIABLE_112180))))))) ) 15.47/15.68 ( int, (one_one int), (one_one int) ) 15.47/15.68 ( int, (one_one int), (zero_zero int) ) 15.47/15.68 ( int, (one_one int), pls ) 15.47/15.68 ( int, pls, (one_one int) ) 15.47/15.68 ( int, pls, pls ) 15.47/15.68 ( int, pls, min_1 ) 15.47/15.68 ( int, min_1, (zero_zero int) ) 15.47/15.68 ( int, min_1, min_1 ) 15.47/15.68 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 15.47/15.68 ( int, s, (zero_zero int) ) 15.47/15.68 ( int, t, (one_one int) ) 15.47/15.68 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 15.47/15.68 ( int, (hAPP int int (number_number_of int) pls), (zero_zero int) ) 15.47/15.68 ( int, skv_4, (zero_zero int) ) 15.47/15.68 ( int, skv_10, (zero_zero int) ) 15.47/15.68 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.68 ( real, pi, (zero_zero real) ) 15.47/15.68 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.68 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.68 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_5 ) 15.47/15.68 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.47/15.68 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.47/15.68 ( real, skv_3, (zero_zero real) ) 15.47/15.68 ( real, skv_5, (zero_zero real) ) 15.47/15.68 ( real, skv_7, (zero_zero real) ) 15.47/15.68 ( real, skv_12, (zero_zero real) ) 15.47/15.68 ) 15.47/15.68 (instantiation (forall ((X_a $$unsorted)) (or (not (semiring_1 X_a)) (= (hAPP nat X_a (semiring_1_of_nat X_a) (zero_zero nat)) (zero_zero X_a))) ) 15.47/15.68 ( nat ) 15.47/15.68 ( int ) 15.47/15.68 ( real ) 15.47/15.68 ( rat ) 15.47/15.68 ( complex ) 15.47/15.68 ( quickcheck_code_int ) 15.47/15.68 ( code_code_numeral ) 15.47/15.68 ) 15.47/15.68 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_112242 $$unsorted) (BOUND_VARIABLE_112243 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (no_zero_divisors X_a)) (not (= _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_112242) BOUND_VARIABLE_112243))) (= _let_0 (ti X_a BOUND_VARIABLE_112243)) (= _let_0 (ti X_a BOUND_VARIABLE_112242)))) ) 15.47/15.68 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 15.47/15.68 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.47/15.68 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13 ) 15.47/15.68 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.47/15.69 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.47/15.69 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.47/15.69 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 15.47/15.69 ( complex, ii, ii ) 15.47/15.69 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 15.47/15.69 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 15.47/15.69 ) 15.47/15.69 (instantiation (forall ((U $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) U))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (hAPP real (fun real real) (inverse_divide real) U) (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) U))))) ) 15.47/15.69 ( (one_one real) ) 15.47/15.69 ( pi ) 15.47/15.69 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.69 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.47/15.69 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.47/15.69 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.69 ( skv_2 ) 15.47/15.69 ( skv_8 ) 15.47/15.69 ( skv_9 ) 15.47/15.69 ) 15.47/15.69 (instantiation (forall ((N $$unsorted)) (= (not (hBOOL (hAPP nat bool (even_odd_even nat) N))) (not (forall ((M_2 $$unsorted)) (not (= N (hAPP nat nat suc (hAPP nat nat (hAPP nat (fun nat nat) (times_times nat) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) M_2)))) ))) ) 15.47/15.69 ( (zero_zero nat) ) 15.47/15.69 ( (one_one nat) ) 15.47/15.69 ) 15.47/15.69 (instantiation (forall ((N_1 $$unsorted)) (let ((_let_0 (number_number_of int))) (let ((_let_1 (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)))) (or (not (hBOOL (hAPP int bool _let_1 (hAPP int int _let_0 N_1)))) (and (hBOOL (hAPP int bool _let_1 (hAPP int int _let_0 (hAPP int int bit1 N_1)))) (hBOOL (hAPP int bool _let_1 (hAPP int int _let_0 (hAPP int int bit0 N_1)))))))) ) 15.47/15.69 ( pls ) 15.47/15.69 ( (hAPP int int bit1 pls) ) 15.47/15.69 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.47/15.69 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.47/15.69 ( min_1 ) 15.47/15.69 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.47/15.69 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.47/15.69 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.47/15.69 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 15.47/15.69 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 15.47/15.69 ) 15.47/15.69 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_112330 $$unsorted) (BOUND_VARIABLE_112331 $$unsorted)) (let ((_let_0 (semiring_1_of_nat X_a))) (or (not (semiring_1 X_a)) (= (hAPP nat X_a _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) BOUND_VARIABLE_112330) BOUND_VARIABLE_112331)) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (hAPP nat X_a _let_0 BOUND_VARIABLE_112330)) (hAPP nat X_a _let_0 BOUND_VARIABLE_112331))))) ) 15.47/15.69 ( int, (one_one nat), (one_one nat) ) 15.47/15.69 ) 15.47/15.69 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_112390 $$unsorted)) (or (not (field X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_112390)) (= (one_one X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_112390)) BOUND_VARIABLE_112390))) ) 15.47/15.69 ( bool, fFalse ) 15.47/15.69 ( bool, fTrue ) 15.47/15.69 ( int, pls ) 15.47/15.69 ( int, min_1 ) 15.47/15.69 ( int, s ) 15.47/15.69 ( int, m ) 15.47/15.69 ( int, s1 ) 15.47/15.69 ( int, t ) 15.47/15.69 ( (fun int bool), nat_neg ) 15.47/15.69 ( (fun int bool), zprime ) 15.47/15.69 ( (fun int bool), zEven ) 15.47/15.69 ( (fun int bool), zOdd ) 15.47/15.69 ( (fun int bool), (even_odd_even int) ) 15.47/15.69 ( (fun int bool), twoSqu1091635170sum2sq ) 15.47/15.69 ( (fun int bool), nat_is_nat ) 15.47/15.69 ( (fun int (fun int bool)), norRRset ) 15.47/15.69 ( (fun int (fun int bool)), quadRes ) 15.47/15.69 ( (fun int (fun int bool)), sRStar ) 15.47/15.69 ( (fun int (fun int bool)), d22set ) 15.47/15.69 ( (fun int (fun int bool)), sr ) 15.47/15.69 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 15.47/15.69 ( (fun int int), zfact ) 15.47/15.69 ( (fun int int), bit0 ) 15.47/15.69 ( (fun int int), bit1 ) 15.47/15.69 ( (fun int int), (fact_fact int) ) 15.47/15.69 ( (fun int int), pred ) 15.47/15.69 ( (fun int int), succ ) 15.47/15.69 ( (fun nat bool), (even_odd_even nat) ) 15.47/15.69 ( (fun nat bool), prime ) 15.47/15.69 ( (fun nat nat), suc ) 15.47/15.69 ( (fun nat nat), (fact_fact nat) ) 15.47/15.69 ( (fun nat nat), fact ) 15.47/15.69 ( (fun nat nat), nat_size ) 15.47/15.69 ( (fun nat nat), (size_size nat) ) 15.47/15.69 ( (fun (product_prod nat nat) bool), pred_nat ) 15.47/15.69 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 15.47/15.69 ( real, (zero_zero real) ) 15.47/15.69 ( real, pi ) 15.47/15.69 ( (fun real real), ln ) 15.47/15.69 ( (fun real real), cos ) 15.47/15.69 ( (fun real real), sqrt ) 15.47/15.69 ( (fun real real), sin ) 15.47/15.69 ( (fun real real), arccos ) 15.47/15.69 ( (fun real real), arcsin ) 15.47/15.69 ( (fun real real), tan ) 15.47/15.69 ( (fun real real), arctan ) 15.47/15.69 ( (fun nat (fun nat bool)), coprime ) 15.47/15.69 ( complex, ii ) 15.47/15.69 ( (fun nat real), (real_1 nat) ) 15.47/15.69 ( (fun nat real), sin_coeff ) 15.47/15.69 ( (fun nat real), cos_coeff ) 15.47/15.69 ( (filter nat), sequentially ) 15.47/15.69 ( (fun int (fun int int)), (gcd_gcd int) ) 15.47/15.69 ( (fun int (fun int int)), legendre ) 15.47/15.69 ( (fun int (fun int int)), legacy_zgcd ) 15.47/15.69 ( (fun int (fun int int)), standardRes ) 15.47/15.69 ( (fun int (fun int int)), nat_tsub ) 15.47/15.69 ( (fun int (fun int int)), multInv ) 15.47/15.69 ( (fun int (fun int int)), z3mod ) 15.47/15.69 ( (fun int (fun int int)), z3div ) 15.47/15.69 ( (fun int (fun int int)), int_gcd ) 15.47/15.69 ( (fun int (fun int int)), int_lcm ) 15.47/15.69 ( (fun int (fun int int)), inv ) 15.47/15.69 ( (fun complex complex), expi ) 15.47/15.69 ( (fun complex complex), cnj ) 15.47/15.69 ( (fun real complex), cis ) 15.47/15.69 ( (fun int nat), nat_1 ) 15.47/15.69 ( (fun int nat), phi ) 15.47/15.69 ( (fun (fun int bool) bool), nat_nat_set ) 15.47/15.69 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 15.47/15.69 ( (fun nat (fun nat nat)), nat_gcd ) 15.47/15.69 ( (fun nat (fun nat nat)), nat_lcm ) 15.47/15.69 ( (fun (fun int bool) int), (the int) ) 15.47/15.69 ( (fun complex real), re ) 15.47/15.69 ( (fun complex real), im ) 15.47/15.69 ( (fun complex real), arg ) 15.47/15.69 ( (fun bool bool), fNot ) 15.47/15.69 ( (fun nat (fun real real)), root ) 15.47/15.69 ( (fun real (fun real real)), log ) 15.47/15.69 ( (fun real (fun real real)), powr ) 15.47/15.69 ( (fun bool (fun bool bool)), fimplies ) 15.47/15.69 ( (fun bool (fun bool bool)), fconj ) 15.47/15.69 ( (fun bool (fun bool bool)), fdisj ) 15.47/15.69 ( (fun int (fun int (product_prod int int))), negDivAlg ) 15.47/15.69 ( (fun int (fun int (product_prod int int))), posDivAlg ) 15.47/15.69 ( (fun int (fun int (product_prod int int))), divmod_int ) 15.47/15.69 ( (fun int (fun int (product_prod int int))), pdivmod ) 15.47/15.69 ( (fun int (fun int (product_prod int int))), norm_frac ) 15.47/15.69 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 15.47/15.69 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 15.47/15.69 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 15.47/15.69 ( (fun int (fun int (fun int bool))), zcong ) 15.47/15.69 ( (fun int (fun int (fun int bool))), zcongm ) 15.47/15.69 ( (fun int (fun int (fun int bool))), noXRRset ) 15.47/15.69 ( (fun int (fun int (fun int bool))), bnorRset ) 15.47/15.69 ( (fun int (fun int (fun int bool))), wset ) 15.47/15.69 ( (fun (product_prod int int) bool), frac_1 ) 15.47/15.69 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 15.47/15.69 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 15.47/15.69 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 15.47/15.69 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 15.47/15.69 ( (fun (fun nat rat) bool), vanishes ) 15.47/15.69 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 15.47/15.69 ( (fun code_code_numeral nat), code_c271388182l_size ) 15.47/15.69 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 15.47/15.69 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 15.47/15.69 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 15.47/15.69 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 15.47/15.69 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 15.47/15.69 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 15.47/15.69 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 15.47/15.69 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 15.47/15.69 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 15.47/15.69 ( (fun complex nat), complex_size ) 15.47/15.69 ( (fun complex nat), (size_size complex) ) 15.47/15.69 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 15.47/15.69 ( (fun nat (fun nat (product_prod int int))), bezw ) 15.47/15.69 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 15.47/15.69 ( (fun int (fun nat nat)), nat_aux ) 15.47/15.69 ( (fun int (fun (fun int bool) bool)), rsetR ) 15.47/15.69 ( (fun int (fun (fun int bool) bool)), resSet ) 15.47/15.69 ( (fun int (list int)), quickc666637781d_zero ) 15.47/15.69 ( (fun (product_prod int int) rat), frct ) 15.47/15.69 ( (fun int (fun int rat)), fract ) 15.47/15.69 ( (fun real (fun real complex)), complex_1 ) 15.47/15.69 ( (fun real (fun real complex)), rcis ) 15.47/15.69 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 15.47/15.69 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 15.47/15.69 ( (fun int real), (real_1 int) ) 15.47/15.69 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 15.47/15.69 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 15.47/15.69 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 15.47/15.69 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 15.47/15.69 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 15.47/15.69 ( (fun real nat), natfloor ) 15.47/15.69 ( (fun real nat), natceiling ) 15.47/15.69 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 15.47/15.69 ( (fun quickcheck_code_int int), quickcheck_int_of ) 15.47/15.69 ( (fun rat (product_prod int int)), quotient_of ) 15.47/15.69 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 15.47/15.69 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 15.47/15.69 ( (fun rat real), ratreal ) 15.47/15.69 ( (fun code_code_numeral int), code_int_of ) 15.47/15.69 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 15.47/15.69 ( (fun int quickcheck_code_int), quickcheck_of_int ) 15.47/15.69 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 15.47/15.69 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 15.47/15.69 ) 15.47/15.69 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (fun int rat))) (let ((_let_3 (product_prod int int))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun _let_3 bool))) (let ((_let_6 (product_fst int int))) (let ((_let_7 (fun _let_5 _let_5))) (let ((_let_8 (fun _let_3 _let_4))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_5 _let_8) (combb bool _let_4 _let_3) fconj))) (let ((_let_10 (fun _let_3 _let_0))) (let ((_let_11 (fun _let_3 int))) (let ((_let_12 (product_snd int int))) (let ((_let_13 (combs _let_3 bool bool))) (let ((_let_14 (fun _let_3 _let_1))) (let ((_let_15 (fun rat bool))) (let ((_let_16 (fun _let_3 rat))) (let ((_let_17 (fun _let_3 _let_2))) (= (hAPP rat _let_3 quotient_of X_2) (hAPP _let_5 _let_3 (the _let_3) (hAPP _let_5 _let_5 (hAPP _let_8 _let_7 _let_13 (hAPP _let_5 _let_8 _let_9 (hAPP _let_16 _let_5 (hAPP _let_15 (fun _let_16 _let_5) (combb rat bool _let_3) (hAPP rat _let_15 (fequal rat) X_2)) (hAPP _let_11 _let_16 (hAPP _let_17 (fun _let_11 _let_16) (combs _let_3 int rat) (hAPP _let_11 _let_17 (hAPP (fun int _let_2) (fun _let_11 _let_17) (combb int _let_2 _let_3) fract) _let_6)) _let_12)))) (hAPP _let_5 _let_5 (hAPP _let_8 _let_7 _let_13 (hAPP _let_5 _let_8 _let_9 (hAPP _let_11 _let_5 (hAPP _let_0 (fun _let_11 _let_5) (combb int bool _let_3) (hAPP int _let_0 (ord_less int) (zero_zero int))) _let_12))) (hAPP int _let_5 (hAPP _let_10 (fun int _let_5) (combc _let_3 int bool) (hAPP _let_11 _let_10 (hAPP (fun int _let_0) (fun _let_11 _let_10) (combb int _let_0 _let_3) (fequal int)) (hAPP _let_11 _let_11 (hAPP _let_14 (fun _let_11 _let_11) (combs _let_3 int int) (hAPP _let_11 _let_14 (hAPP (fun int _let_1) (fun _let_11 _let_14) (combb int _let_1 _let_3) (gcd_gcd int)) _let_6)) _let_12))) (one_one int)))))))))))))))))))))))) ) 15.47/15.69 ( (zero_zero rat) ) 15.47/15.69 ( (one_one rat) ) 15.47/15.69 ) 15.47/15.69 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_112414 $$unsorted)) (or (not (division_ring X_a)) (= (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_112414) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) (one_one X_a)) BOUND_VARIABLE_112414))) ) 15.47/15.69 ( real, (zero_zero real) ) 15.47/15.69 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.69 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.47/15.69 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.69 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 15.47/15.69 ( complex, ii ) 15.47/15.69 ) 15.47/15.69 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_112429 $$unsorted) (BOUND_VARIABLE_112430 $$unsorted) (BOUND_VARIABLE_112431 $$unsorted)) (let ((_let_0 (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_112429))) (or (not (comm_semiring_1 X_a)) (= (hAPP nat X_a _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) BOUND_VARIABLE_112430) BOUND_VARIABLE_112431)) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) (hAPP nat X_a _let_0 BOUND_VARIABLE_112430)) (hAPP nat X_a _let_0 BOUND_VARIABLE_112431))))) ) 15.47/15.69 ( int, s, (one_one nat), (one_one nat) ) 15.47/15.69 ( int, s1, (one_one nat), (one_one nat) ) 15.47/15.69 ( int, skv_14, (one_one nat), (one_one nat) ) 15.47/15.69 ( complex, ii, (one_one nat), (one_one nat) ) 15.47/15.69 ) 15.47/15.69 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int rat (hAPP int (fun int rat) fract (hAPP int int (number_number_of int) K_4)) (one_one int)) (hAPP int rat (number_number_of rat) K_4)) ) 15.47/15.69 ( pls ) 15.47/15.69 ( (hAPP int int bit1 pls) ) 15.47/15.69 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.47/15.69 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.47/15.69 ( min_1 ) 15.47/15.69 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.69 ) 15.47/15.69 (instantiation (forall ((X_1 $$unsorted)) (= (hAPP real real (abs_abs real) X_1) (hAPP real real sqrt (hAPP nat real (hAPP real (fun nat real) (power_power real) X_1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.47/15.69 ( (hAPP int real (number_number_of real) min_1) ) 15.47/15.69 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.69 ) 15.47/15.69 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_112622 $$unsorted) (BOUND_VARIABLE_112623 $$unsorted)) (let ((_let_0 (archim2085082626_floor X_a))) (or (not (archim1727834104eiling X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_112622) BOUND_VARIABLE_112623))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP X_a int _let_0 BOUND_VARIABLE_112622)) (hAPP X_a int _let_0 BOUND_VARIABLE_112623))))) ) 15.47/15.69 ( int, (one_one int), t ) 15.47/15.69 ( int, (zero_zero int), (one_one int) ) 15.47/15.69 ( int, (zero_zero int), min_1 ) 15.47/15.69 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.69 ( int, (zero_zero int), s ) 15.47/15.69 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.47/15.69 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.47/15.69 ( int, (zero_zero int), skv_4 ) 15.47/15.69 ( int, (zero_zero int), skv_10 ) 15.47/15.69 ( int, min_1, pls ) 15.47/15.69 ( int, min_1, min_1 ) 15.47/15.69 ( real, (zero_zero real), pi ) 15.47/15.69 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.69 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.69 ( real, (zero_zero real), skv_3 ) 15.47/15.69 ( real, (zero_zero real), skv_5 ) 15.47/15.69 ( real, (zero_zero real), skv_7 ) 15.47/15.69 ( real, (zero_zero real), skv_12 ) 15.47/15.69 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.47/15.69 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.69 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.47/15.69 ( real, skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.69 ) 15.47/15.69 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted) (N_1 $$unsorted)) (let ((_let_0 (fun int int))) (or (not (= (hAPP nat int (hAPP int (fun nat int) (power_power int) C) N_1) (hAPP int int (hAPP int _let_0 (times_times int) A_1) B))) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (one_one nat)) N_1))) (not (= (one_one int) (hAPP int int (hAPP int _let_0 legacy_zgcd A_1) B))) (not (forall ((K_1 $$unsorted)) (not (= (hAPP int int (abs_abs int) A_1) (hAPP nat int (hAPP int (fun nat int) (power_power int) K_1) N_1))) )))) ) 15.47/15.69 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.69 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.69 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13, skv_14, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.69 ) 15.47/15.69 (instantiation (forall ((L $$unsorted)) (= (= pls (ti int L)) (= pls (hAPP int int bit0 L))) ) 15.47/15.69 ( pls ) 15.47/15.69 ( (hAPP int int bit1 pls) ) 15.47/15.69 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.47/15.69 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.47/15.69 ( min_1 ) 15.47/15.69 ( s ) 15.47/15.69 ( m ) 15.47/15.69 ( s1 ) 15.47/15.69 ( t ) 15.47/15.69 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.47/15.69 ) 15.47/15.69 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_112714 $$unsorted) (BOUND_VARIABLE_112715 $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (linorder X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_112715) BOUND_VARIABLE_112714)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_112714) BOUND_VARIABLE_112715)))))) ) 15.47/15.69 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.69 ( int, (one_one int), (zero_zero int) ) 15.47/15.69 ( int, (one_one int), t ) 15.47/15.69 ( int, pls, (one_one int) ) 15.47/15.69 ( int, pls, pls ) 15.47/15.69 ( int, pls, min_1 ) 15.47/15.69 ( int, pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.69 ( int, min_1, (zero_zero int) ) 15.47/15.69 ( int, min_1, pls ) 15.47/15.69 ( int, min_1, min_1 ) 15.47/15.69 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 15.47/15.69 ( int, s, (zero_zero int) ) 15.47/15.69 ( int, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.69 ( int, t, (one_one int) ) 15.47/15.69 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.69 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 15.47/15.69 ( int, (hAPP int int (number_number_of int) pls), (zero_zero int) ) 15.47/15.69 ( int, skv_4, (zero_zero int) ) 15.47/15.69 ( int, skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.69 ( int, skv_10, (zero_zero int) ) 15.47/15.69 ( int, skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.69 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.69 ( real, (zero_zero real), pi ) 15.47/15.69 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.69 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.69 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.69 ( real, (zero_zero real), skv_2 ) 15.47/15.69 ( real, (zero_zero real), skv_8 ) 15.47/15.69 ( real, (zero_zero real), skv_9 ) 15.47/15.69 ( real, pi, (zero_zero real) ) 15.47/15.69 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.69 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.69 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.69 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_5 ) 15.47/15.69 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.47/15.69 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.69 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 15.47/15.69 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.47/15.69 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.47/15.69 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 15.47/15.69 ( real, skv_3, (zero_zero real) ) 15.47/15.69 ( real, skv_5, (zero_zero real) ) 15.47/15.69 ( real, skv_7, (zero_zero real) ) 15.47/15.69 ( real, skv_12, (zero_zero real) ) 15.47/15.69 ) 15.47/15.69 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_112755 $$unsorted) (BOUND_VARIABLE_112756 $$unsorted) (BOUND_VARIABLE_112757 $$unsorted)) (let ((_let_0 (zero_zero real))) (let ((_let_1 (filter X_a))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun X_a real))) (let ((_let_4 (fun real _let_2))) (let ((_let_5 (tendsto X_a real))) (let ((_let_6 (hAPP X_a _let_1 (at X_a) BOUND_VARIABLE_112757))) (or (not (topological_space X_a)) (not (hBOOL (hAPP _let_1 bool (hAPP real _let_2 (hAPP _let_3 _let_4 _let_5 BOUND_VARIABLE_112756) _let_0) _let_6))) (not (forall ((X $$unsorted)) (or (= (ti X_a X) (ti X_a BOUND_VARIABLE_112757)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) _let_0) (hAPP X_a real BOUND_VARIABLE_112755 X)))) )) (not (forall ((X $$unsorted)) (or (= (ti X_a X) (ti X_a BOUND_VARIABLE_112757)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP X_a real BOUND_VARIABLE_112755 X)) (hAPP X_a real BOUND_VARIABLE_112756 X)))) )) (hBOOL (hAPP _let_1 bool (hAPP real _let_2 (hAPP _let_3 _let_4 _let_5 BOUND_VARIABLE_112755) _let_0) _let_6)))))))))) ) 15.47/15.69 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.69 ) 15.47/15.69 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_112805 $$unsorted) (BOUND_VARIABLE_112806 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (or (not (linorder X_a)) (= (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_112805) BOUND_VARIABLE_112806))) (or (= (ti X_a BOUND_VARIABLE_112805) (ti X_a BOUND_VARIABLE_112806)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_112806) BOUND_VARIABLE_112805))))))) ) 15.47/15.69 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.69 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 15.47/15.69 ( int, (one_one int), pls ) 15.47/15.69 ( int, (one_one int), t ) 15.47/15.69 ( int, pls, (one_one int) ) 15.47/15.69 ( int, pls, pls ) 15.47/15.69 ( int, pls, min_1 ) 15.47/15.69 ( int, pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.69 ( int, min_1, pls ) 15.47/15.69 ( int, min_1, min_1 ) 15.47/15.69 ( int, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.69 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), pls ) 15.47/15.69 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s ) 15.47/15.69 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.47/15.69 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_4 ) 15.47/15.69 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_10 ) 15.47/15.69 ( int, t, (one_one int) ) 15.47/15.69 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.69 ( int, skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.69 ( int, skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.69 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.69 ( real, (zero_zero real), pi ) 15.47/15.69 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.69 ( real, (zero_zero real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.47/15.69 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.69 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.69 ( real, (zero_zero real), skv_2 ) 15.47/15.69 ( real, (zero_zero real), skv_8 ) 15.47/15.69 ( real, (zero_zero real), skv_9 ) 15.47/15.69 ( real, pi, (zero_zero real) ) 15.47/15.69 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.69 ( real, pi, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 15.47/15.69 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.69 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.47/15.69 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.69 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 15.47/15.69 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 15.47/15.69 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 15.47/15.69 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.47/15.69 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.47/15.69 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 15.47/15.69 ( real, skv_2, (zero_zero real) ) 15.47/15.69 ( real, skv_8, (zero_zero real) ) 15.47/15.69 ( real, skv_9, (zero_zero real) ) 15.47/15.69 ) 15.47/15.69 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_112829 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (ti int BOUND_VARIABLE_112829) (hAPP X_a int (archim2085082626_floor X_a) (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_112829)))) ) 15.47/15.69 ( real, (one_one int) ) 15.47/15.69 ( real, (zero_zero int) ) 15.47/15.69 ) 15.47/15.69 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_112847 $$unsorted) (BOUND_VARIABLE_112848 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (one_one X_a)))) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_112848))) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) BOUND_VARIABLE_112847))) (hBOOL (hAPP X_a bool _let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_112848) BOUND_VARIABLE_112847))))) ) 15.47/15.69 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 15.47/15.69 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 15.47/15.69 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_14 ) 15.47/15.69 ( complex, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), ii ) 15.47/15.69 ) 15.47/15.69 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_112877 $$unsorted) (BOUND_VARIABLE_112878 $$unsorted) (BOUND_VARIABLE_112879 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (times_times X_a))) (let ((_let_2 (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_112877))) (or (not (comm_semiring_1 X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_112878)) BOUND_VARIABLE_112879) (hAPP X_a X_a _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_112878) BOUND_VARIABLE_112879))))))) ) 15.47/15.69 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.47/15.69 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.47/15.69 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi), ii ) 15.47/15.69 ) 15.47/15.69 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_112898 $$unsorted) (BOUND_VARIABLE_112899 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_112898))) (let ((_let_1 (hAPP X_a X_a _let_0 BOUND_VARIABLE_112899))) (or (not (ab_sem1668676832m_mult X_a)) (= _let_1 (hAPP X_a X_a _let_0 _let_1))))) ) 15.47/15.69 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 15.47/15.69 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.47/15.69 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13 ) 15.47/15.69 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.47/15.69 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.47/15.69 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.47/15.69 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 15.47/15.69 ( complex, ii, ii ) 15.47/15.69 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 15.47/15.69 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 15.47/15.69 ) 15.47/15.69 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_0 (fun nat nat))) (= M (hAPP nat nat (hAPP nat _let_0 (minus_minus nat) (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) M) N_1)) N_1))) ) 15.47/15.69 ( (one_one nat), (one_one nat) ) 15.47/15.69 ) 15.47/15.69 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_112967 $$unsorted)) (or (not (monoid_mult X_a)) (= (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_112967) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_112967) BOUND_VARIABLE_112967))) ) 15.47/15.69 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.69 ( int, s ) 15.47/15.69 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.69 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.69 ( int, s1 ) 15.47/15.69 ( int, skv_14 ) 15.47/15.69 ( real, (hAPP int real (number_number_of real) min_1) ) 15.47/15.69 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.69 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.69 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.69 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 15.47/15.69 ( complex, ii ) 15.47/15.69 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.69 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 15.47/15.69 ) 15.47/15.69 (instantiation (forall ((X_2 $$unsorted)) (= (hBOOL (hAPP int bool twoSqu1091635170sum2sq X_2)) (not (forall ((A_4 $$unsorted) (B_4 $$unsorted)) (let ((_let_0 (product_prod int int))) (not (= (ti int X_2) (hAPP _let_0 int twoSqu1094008024sum2sq (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) A_4) B_4))))) ))) ) 15.47/15.69 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) t))) ) 15.47/15.69 ) 15.47/15.69 (instantiation (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (zero_zero int)) B_1))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) B_1) A_2)) (hBOOL (hAPP rat bool (hAPP rat (fun rat bool) (ord_less_eq rat) (one_one rat)) (hAPP int rat (hAPP int (fun int rat) fract A_2) B_1)))))) ) 15.47/15.69 ( (one_one int), (one_one int) ) 15.47/15.69 ( (one_one int), (zero_zero int) ) 15.47/15.69 ( (zero_zero int), (one_one int) ) 15.47/15.69 ( pls, min_1 ) 15.47/15.69 ( min_1, (zero_zero int) ) 15.47/15.69 ( min_1, min_1 ) 15.47/15.69 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 15.47/15.69 ( s, (zero_zero int) ) 15.47/15.69 ( t, (one_one int) ) 15.47/15.69 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 15.47/15.69 ( (hAPP int int (number_number_of int) pls), (zero_zero int) ) 15.47/15.69 ( skv_4, (zero_zero int) ) 15.47/15.69 ( skv_10, (zero_zero int) ) 15.47/15.69 ) 15.47/15.69 (instantiation (forall ((P_1 $$unsorted) (K $$unsorted) (I $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) K) I))) (not (hBOOL (hAPP int bool P_1 K))) (not (forall ((I_2 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) K) I_2))) (not (hBOOL (hAPP int bool P_1 I_2))) (hBOOL (hAPP int bool P_1 (hAPP int int (hAPP int (fun int int) (plus_plus int) I_2) (one_one int))))) )) (hBOOL (hAPP int bool P_1 I))) ) 15.47/15.69 ( (hAPP int (fun int bool) (ord_less int) pls), (zero_zero int), s ) 15.47/15.69 ( (hAPP int (fun int bool) (ord_less_eq int) pls), min_1, min_1 ) 15.47/15.69 ( nat_neg, (zero_zero int), skv_4 ) 15.47/15.69 ( (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (zero_zero int), min_1 ) 15.47/15.69 ( (even_odd_even int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.47/15.69 ( nat_is_nat, (one_one int), t ) 15.47/15.69 ( nat_is_nat, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.47/15.69 ( (hAPP int (fun int bool) (ord_less int) min_1), (zero_zero int), (one_one int) ) 15.47/15.69 ( (hAPP int (fun int bool) (ord_less int) min_1), min_1, pls ) 15.47/15.69 ( (hAPP int (fun int bool) (ord_less_eq int) min_1), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.69 ) 15.47/15.69 (instantiation (forall ((Z_1 $$unsorted) (W $$unsorted)) (let ((_let_0 (hAPP nat int (hAPP int (fun nat int) (power_power int) Z_1) (hAPP int nat (number_number_of nat) W)))) (= (hAPP nat int (hAPP int (fun nat int) (power_power int) Z_1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 W))) (hAPP int int (hAPP int (fun int int) (times_times int) _let_0) _let_0))) ) 15.47/15.69 ( s, (hAPP int int bit1 pls) ) 15.47/15.69 ( s1, (hAPP int int bit1 pls) ) 15.47/15.69 ( skv_14, (hAPP int int bit1 pls) ) 15.47/15.69 ) 15.47/15.69 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_113209 $$unsorted) (BOUND_VARIABLE_113210 $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (linorder X_a)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_113209) BOUND_VARIABLE_113210)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_113210) BOUND_VARIABLE_113209)))) ) 15.47/15.69 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.69 ( int, (one_one int), (zero_zero int) ) 15.47/15.69 ( int, (one_one int), t ) 15.47/15.69 ( int, pls, (one_one int) ) 15.47/15.69 ( int, pls, pls ) 15.47/15.69 ( int, pls, min_1 ) 15.47/15.69 ( int, pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.69 ( int, min_1, (zero_zero int) ) 15.47/15.69 ( int, min_1, pls ) 15.47/15.69 ( int, min_1, min_1 ) 15.47/15.69 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 15.47/15.69 ( int, s, (zero_zero int) ) 15.47/15.69 ( int, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.69 ( int, t, (one_one int) ) 15.47/15.69 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.69 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 15.47/15.69 ( int, (hAPP int int (number_number_of int) pls), (zero_zero int) ) 15.47/15.69 ( int, skv_4, (zero_zero int) ) 15.47/15.69 ( int, skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.69 ( int, skv_10, (zero_zero int) ) 15.47/15.69 ( int, skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.69 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.69 ( real, (zero_zero real), pi ) 15.47/15.69 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.69 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.69 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.69 ( real, (zero_zero real), skv_2 ) 15.47/15.69 ( real, (zero_zero real), skv_8 ) 15.47/15.69 ( real, (zero_zero real), skv_9 ) 15.47/15.69 ( real, pi, (zero_zero real) ) 15.47/15.69 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.69 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.69 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.69 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_5 ) 15.47/15.69 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.47/15.69 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.69 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 15.47/15.69 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.47/15.69 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.47/15.69 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 15.47/15.69 ( real, skv_3, (zero_zero real) ) 15.47/15.69 ( real, skv_5, (zero_zero real) ) 15.47/15.69 ( real, skv_7, (zero_zero real) ) 15.47/15.69 ( real, skv_12, (zero_zero real) ) 15.47/15.69 ) 15.47/15.69 (instantiation (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP real (fun real bool) (ord_less real) (zero_zero real)))) (or (not (hBOOL (hAPP real bool _let_1 X_1))) (not (hBOOL (hAPP real bool _let_1 Y_1))) (= (hAPP real real (hAPP real _let_0 (plus_plus real) (hAPP real real ln X_1)) (hAPP real real ln Y_1)) (hAPP real real ln (hAPP real real (hAPP real _let_0 (times_times real) X_1) Y_1)))))) ) 15.47/15.69 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.69 ( pi, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 15.47/15.69 ( (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.69 ( (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.69 ) 15.47/15.69 (instantiation (forall ((A_1 $$unsorted) (X_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP int real (real_1 int) A_1)) X_1))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) A_1) (hAPP real int (archim2085082626_floor real) X_1)))) ) 15.47/15.69 ( (zero_zero int), pi ) 15.47/15.69 ( (zero_zero int), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.69 ( (zero_zero int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.69 ( (zero_zero int), skv_3 ) 15.47/15.69 ( (zero_zero int), skv_5 ) 15.47/15.69 ( (zero_zero int), skv_7 ) 15.47/15.69 ( (zero_zero int), skv_12 ) 15.47/15.69 ) 15.47/15.69 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_113253 $$unsorted) (BOUND_VARIABLE_113254 $$unsorted) (BOUND_VARIABLE_113255 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (zero_zero X_a))) (let ((_let_2 (ti X_a BOUND_VARIABLE_113255))) (let ((_let_3 (= _let_1 (ti X_a BOUND_VARIABLE_113254)))) (or (not (field_inverse_zero X_a)) (= (= _let_2 (hAPP X_a X_a (hAPP X_a _let_0 (inverse_divide X_a) BOUND_VARIABLE_113253) BOUND_VARIABLE_113254)) (and (or (not _let_3) (= _let_1 _let_2)) (or _let_3 (= (ti X_a BOUND_VARIABLE_113253) (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_113255) BOUND_VARIABLE_113254)))))))))) ) 15.47/15.69 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.47/15.69 ) 15.47/15.69 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (inverse_inverse real))) (= (hAPP real real sqrt (hAPP real real _let_0 X_1)) (hAPP real real _let_0 (hAPP real real sqrt X_1)))) ) 15.47/15.69 ( (zero_zero real) ) 15.47/15.69 ) 15.47/15.69 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_113344 $$unsorted) (BOUND_VARIABLE_113345 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)))) (let ((_let_1 (hBOOL (hAPP nat bool (even_odd_even nat) BOUND_VARIABLE_113345)))) (or (not (linordered_idom X_a)) (= (or (= (zero_zero nat) BOUND_VARIABLE_113345) (and _let_1 (not (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_113344)))) (and (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_113344)) (not _let_1))) (hBOOL (hAPP X_a bool _let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_113344) BOUND_VARIABLE_113345))))))) ) 15.47/15.69 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.69 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.69 ( int, skv_14, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.69 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.69 ) 15.47/15.69 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_113382 $$unsorted) (BOUND_VARIABLE_113383 $$unsorted)) (or (not (group_add X_a)) (= (= (ti X_a BOUND_VARIABLE_113383) (ti X_a BOUND_VARIABLE_113382)) (= (zero_zero X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) BOUND_VARIABLE_113382) BOUND_VARIABLE_113383)))) ) 15.47/15.69 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.47/15.69 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 15.47/15.69 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 15.47/15.69 ) 15.47/15.69 (instantiation (forall ((X_a $$unsorted)) (or (not (number_ring X_a)) (= (zero_zero X_a) (hAPP int X_a (number_number_of X_a) pls))) ) 15.47/15.69 ( nat ) 15.47/15.69 ( int ) 15.47/15.69 ( real ) 15.47/15.69 ( rat ) 15.47/15.69 ( complex ) 15.47/15.69 ( quickcheck_code_int ) 15.47/15.69 ( code_code_numeral ) 15.47/15.69 ) 15.47/15.69 (instantiation (forall ((A_9 $$unsorted) (B_8 $$unsorted) (Y_1 $$unsorted) (R_6 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (ord_less_eq int))) (let ((_let_3 (zero_zero int))) (let ((_let_4 (ord_less int))) (let ((_let_5 (hBOOL (hAPP int bool (hAPP int _let_0 _let_4 _let_3) B_8)))) (or (not (= (hAPP int int (hAPP int _let_1 (plus_plus int) (hAPP int int (hAPP int _let_1 (times_times int) B_8) Y_1)) R_6) (ti int A_9))) (and _let_5 (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 _let_3) R_6))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_4 R_6) B_8))))) (and (not _let_5) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 R_6) _let_3))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_4 B_8) R_6))))) (= _let_3 (ti int B_8)) (= (ti int Y_1) (hAPP int int (hAPP int _let_1 (div_div int) A_9) B_8))))))))) ) 15.47/15.69 ( s, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m, (one_one int) ) 15.47/15.69 ) 15.47/15.69 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_113503 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP X_a int (archimedean_ceiling X_a) BOUND_VARIABLE_113503)) (one_one int))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_113503) (zero_zero X_a))))) ) 15.47/15.69 ( int, (one_one int) ) 15.47/15.69 ( int, (zero_zero int) ) 15.47/15.69 ( int, min_1 ) 15.47/15.69 ( real, (zero_zero real) ) 15.47/15.70 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.70 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.70 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.70 ( real, skv_5 ) 15.47/15.70 ) 15.47/15.70 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_113554 $$unsorted) (BOUND_VARIABLE_113555 $$unsorted) (BOUND_VARIABLE_113556 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (fun X_a X_a))) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_113556))) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_113554) (hAPP X_a X_a (hAPP X_a _let_2 (times_times X_a) BOUND_VARIABLE_113555) BOUND_VARIABLE_113556))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_2 (inverse_divide X_a) BOUND_VARIABLE_113554) BOUND_VARIABLE_113556)) BOUND_VARIABLE_113555))))))) ) 15.47/15.70 ( real, (zero_zero real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.47/15.70 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.70 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.47/15.70 ) 15.47/15.70 (instantiation (forall ((N_1 $$unsorted)) (= N_1 (hAPP real nat natceiling (hAPP nat real (real_1 nat) N_1))) ) 15.47/15.70 ( (zero_zero nat) ) 15.47/15.70 ( (hAPP nat nat suc (zero_zero nat)) ) 15.47/15.70 ) 15.47/15.70 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) X_1))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP nat real (real_1 nat) (hAPP real nat natfloor X_1))) X_1))))) ) 15.47/15.70 ( (one_one real) ) 15.47/15.70 ( (zero_zero real) ) 15.47/15.70 ( pi ) 15.47/15.70 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.70 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.70 ( skv_3 ) 15.47/15.70 ( skv_5 ) 15.47/15.70 ( skv_7 ) 15.47/15.70 ( skv_12 ) 15.47/15.70 ) 15.47/15.70 (instantiation (forall ((L $$unsorted) (U_1 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (= (hAPP int nat nat_1 (hAPP int int (hAPP int _let_1 (plus_plus int) (hAPP int int (hAPP int _let_1 (minus_minus int) U_1) L)) (one_one int))) (hAPP _let_0 nat (finite_card int) (hAPP int _let_0 (hAPP int (fun int _let_0) (ord_atLeastAtMost int) L) U_1))))) ) 15.47/15.70 ( (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.70 ) 15.47/15.70 (instantiation (forall ((X_a $$unsorted)) (or (not (number_ring X_a)) (= (one_one X_a) (hAPP int X_a (number_number_of X_a) (hAPP int int bit1 pls)))) ) 15.47/15.70 ( nat ) 15.47/15.70 ( int ) 15.47/15.70 ( real ) 15.47/15.70 ( rat ) 15.47/15.70 ( complex ) 15.47/15.70 ( quickcheck_code_int ) 15.47/15.70 ( code_code_numeral ) 15.47/15.70 ) 15.47/15.70 (instantiation (forall ((K $$unsorted) (L $$unsorted)) (= (= (ti int L) (ti int K)) (= (hAPP int int bit0 K) (hAPP int int bit0 L))) ) 15.47/15.70 ( pls, s1 ) 15.47/15.70 ( min_1, t ) 15.47/15.70 ( s, pls ) 15.47/15.70 ( s, s ) 15.47/15.70 ( s, s1 ) 15.47/15.70 ( m, min_1 ) 15.47/15.70 ( m, m ) 15.47/15.70 ( m, t ) 15.47/15.70 ( s1, s ) 15.47/15.70 ( t, m ) 15.47/15.70 ) 15.47/15.70 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP int real (number_number_of real) min_1)) X_2))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_2) (one_one real)))) (hBOOL (hAPP real bool (hAPP (fun real real) _let_0 (isCont real real) arccos) X_2))))) ) 15.47/15.70 ( (one_one real) ) 15.47/15.70 ( (zero_zero real) ) 15.47/15.70 ( pi ) 15.47/15.70 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.70 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.47/15.70 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.70 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 15.47/15.70 ) 15.47/15.70 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_113783 $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat X_a))) (let ((_let_3 (fun X_a X_a))) (let ((_let_4 (fun nat _let_3))) (or (not (real_normed_field X_a)) (not (banach X_a)) (= (hAPP _let_2 X_a (suminf X_a) (hAPP _let_2 _let_2 (hAPP _let_4 (fun _let_2 _let_2) (combs nat X_a X_a) (hAPP _let_1 _let_4 (hAPP (fun real _let_3) (fun _let_1 _let_4) (combb real _let_3 nat) (scaleR_scaleR X_a)) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) (fact_fact nat))))) (hAPP X_a _let_2 (power_power X_a) BOUND_VARIABLE_113783))) (hAPP X_a X_a (exp X_a) BOUND_VARIABLE_113783)))))))) ) 15.47/15.70 ( int, s ) 15.47/15.70 ( int, s1 ) 15.47/15.70 ( int, skv_14 ) 15.47/15.70 ( real, (hAPP int real (number_number_of real) min_1) ) 15.47/15.70 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.70 ( complex, ii ) 15.47/15.70 ) 15.47/15.70 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_113849 $$unsorted)) (let ((_let_0 (number_number_of X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (plus_plus X_a))) (let ((_let_3 (hAPP int X_a _let_0 BOUND_VARIABLE_113849))) (or (not (number_ring X_a)) (= (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (one_one X_a)) _let_3)) _let_3) (hAPP int X_a _let_0 (hAPP int int bit1 BOUND_VARIABLE_113849)))))))) ) 15.47/15.70 ( nat, pls ) 15.47/15.70 ( nat, (hAPP int int bit1 pls) ) 15.47/15.70 ( int, pls ) 15.47/15.70 ( int, (hAPP int int bit1 pls) ) 15.47/15.70 ( int, min_1 ) 15.47/15.70 ( real, (hAPP int int bit1 pls) ) 15.47/15.70 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.47/15.70 ( real, min_1 ) 15.47/15.70 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 15.47/15.70 ( complex, min_1 ) 15.47/15.70 ( quickcheck_code_int, pls ) 15.47/15.70 ( code_code_numeral, pls ) 15.47/15.70 ) 15.47/15.70 (instantiation (forall ((N_1 $$unsorted)) (let ((_let_0 (real_1 nat))) (= (hAPP nat real _let_0 (hAPP nat nat suc N_1)) (hAPP real real (hAPP real (fun real real) (plus_plus real) (hAPP nat real _let_0 N_1)) (one_one real)))) ) 15.47/15.70 ( (zero_zero nat) ) 15.47/15.70 ( (hAPP nat nat suc (zero_zero nat)) ) 15.47/15.70 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 15.47/15.70 ) 15.47/15.70 (instantiation (forall ((N_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_0 (even_odd_even int))) (or (hBOOL (hAPP int bool _let_0 X_1)) (not (hBOOL (hAPP int bool _let_0 (hAPP nat int (hAPP int (fun nat int) (power_power int) X_1) N_1)))))) ) 15.47/15.70 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 15.47/15.70 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 15.47/15.70 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_14 ) 15.47/15.70 ) 15.47/15.70 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_113882 $$unsorted) (BOUND_VARIABLE_113883 $$unsorted)) (let ((_let_0 (number_number_of X_a))) (or (not (number_ring X_a)) (= (hAPP int X_a _let_0 (hAPP int int (hAPP int (fun int int) (plus_plus int) BOUND_VARIABLE_113882) (hAPP int int (uminus_uminus int) BOUND_VARIABLE_113883))) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) (hAPP int X_a _let_0 BOUND_VARIABLE_113882)) (hAPP int X_a _let_0 BOUND_VARIABLE_113883))))) ) 15.47/15.70 ( code_code_numeral, pls, (hAPP int int bit1 pls) ) 15.47/15.70 ) 15.47/15.70 (instantiation (forall ((P_2 $$unsorted) (P_1 $$unsorted) (X_2 $$unsorted)) (let ((_let_0 (hBOOL P_1))) (let ((_let_1 (hBOOL P_2))) (let ((_let_2 (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) X_2)))) (or (and _let_2 (= (not _let_0) _let_1)) (= (and _let_1 _let_2) (and _let_0 _let_2)))))) ) 15.47/15.70 ( (hAPP int bool (hAPP int (fun int bool) (ord_less int) pls) pls), (hAPP int bool (hAPP int (fun int bool) (ord_less int) pls) pls), s ) 15.47/15.70 ( (hAPP int bool (hAPP int (fun int bool) (ord_less int) pls) pls), (let ((_let_0 (fun int int))) (hAPP int bool (hAPP int (fun int bool) (ord_less int) s) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (one_one int) ) 15.47/15.70 ( (let ((_let_0 (fun int int))) (hAPP int bool (hAPP int (fun int bool) (ord_less int) s) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int bool (hAPP int (fun int bool) (ord_less int) pls) pls), s ) 15.47/15.70 ( (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) s) (hAPP int int (hAPP int _let_1 (plus_plus int) (hAPP int int (hAPP int _let_1 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) s) (hAPP int int (hAPP int _let_1 (plus_plus int) (hAPP int int (hAPP int _let_1 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))))), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.47/15.70 ( (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) s) (hAPP int int (hAPP int _let_1 (plus_plus int) (hAPP int int (hAPP int _let_1 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))))), (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) s), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.70 ( (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) s), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) s) (hAPP int int (hAPP int _let_1 (plus_plus int) (hAPP int int (hAPP int _let_1 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))))), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.47/15.70 ( (let ((_let_0 (fun int int))) (let ((_let_1 (one_one int))) (let ((_let_2 (plus_plus int))) (let ((_let_3 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int bool (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 _let_3))) m)) _let_1)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) _let_3))) _let_1)))))), (let ((_let_0 (fun int int))) (let ((_let_1 (one_one int))) (let ((_let_2 (plus_plus int))) (let ((_let_3 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int bool (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 _let_3))) m)) _let_1)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) _let_3))) _let_1)))))), (hAPP int int (number_number_of int) pls) ) 15.47/15.70 ( (let ((_let_0 (fun int int))) (let ((_let_1 (one_one int))) (let ((_let_2 (plus_plus int))) (let ((_let_3 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int bool (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 _let_3))) m)) _let_1)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) _let_3))) _let_1)))))), (hAPP nat bool prime (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), min_1 ) 15.47/15.70 ( (hAPP nat bool prime (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (let ((_let_1 (one_one int))) (let ((_let_2 (plus_plus int))) (let ((_let_3 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int bool (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 _let_3))) m)) _let_1)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) _let_3))) _let_1)))))), (hAPP int int (number_number_of int) pls) ) 15.47/15.70 ( (let ((_let_0 (fun real real))) (let ((_let_1 (inverse_divide real))) (let ((_let_2 (fun real _let_0))) (let ((_let_3 (filter real))) (let ((_let_4 (fun _let_3 bool))) (hAPP _let_3 bool (hAPP real _let_4 (hAPP _let_0 (fun real _let_4) (tendsto real real) (hAPP _let_0 _let_0 (hAPP _let_2 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_2 (hAPP _let_2 (fun _let_0 _let_2) (combb real _let_0 real) _let_1) cos)) sin)) (zero_zero real)) (hAPP real _let_3 (at real) (hAPP real real (hAPP real _let_0 _let_1 pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))))))), (let ((_let_0 (fun real real))) (let ((_let_1 (inverse_divide real))) (let ((_let_2 (fun real _let_0))) (let ((_let_3 (filter real))) (let ((_let_4 (fun _let_3 bool))) (hAPP _let_3 bool (hAPP real _let_4 (hAPP _let_0 (fun real _let_4) (tendsto real real) (hAPP _let_0 _let_0 (hAPP _let_2 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_2 (hAPP _let_2 (fun _let_0 _let_2) (combb real _let_0 real) _let_1) cos)) sin)) (zero_zero real)) (hAPP real _let_3 (at real) (hAPP real real (hAPP real _let_0 _let_1 pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))))))), skv_4 ) 15.47/15.70 ( (let ((_let_0 (fun real real))) (let ((_let_1 (inverse_divide real))) (let ((_let_2 (fun real _let_0))) (let ((_let_3 (filter real))) (let ((_let_4 (fun _let_3 bool))) (hAPP _let_3 bool (hAPP real _let_4 (hAPP _let_0 (fun real _let_4) (tendsto real real) (hAPP _let_0 _let_0 (hAPP _let_2 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_2 (hAPP _let_2 (fun _let_0 _let_2) (combb real _let_0 real) _let_1) cos)) sin)) (zero_zero real)) (hAPP real _let_3 (at real) (hAPP real real (hAPP real _let_0 _let_1 pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))))))), (hAPP nat bool (even_odd_even nat) (zero_zero nat)), skv_10 ) 15.47/15.70 ( (hAPP nat bool (even_odd_even nat) (zero_zero nat)), (let ((_let_0 (fun real real))) (let ((_let_1 (inverse_divide real))) (let ((_let_2 (fun real _let_0))) (let ((_let_3 (filter real))) (let ((_let_4 (fun _let_3 bool))) (hAPP _let_3 bool (hAPP real _let_4 (hAPP _let_0 (fun real _let_4) (tendsto real real) (hAPP _let_0 _let_0 (hAPP _let_2 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_2 (hAPP _let_2 (fun _let_0 _let_2) (combb real _let_0 real) _let_1) cos)) sin)) (zero_zero real)) (hAPP real _let_3 (at real) (hAPP real real (hAPP real _let_0 _let_1 pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))))))), skv_4 ) 15.47/15.70 ) 15.47/15.70 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_113981 $$unsorted) (BOUND_VARIABLE_113982 $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (order X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_113981) BOUND_VARIABLE_113982))) (= (ti X_a BOUND_VARIABLE_113982) (ti X_a BOUND_VARIABLE_113981)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_113981) BOUND_VARIABLE_113982)))) ) 15.47/15.70 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.70 ( int, (one_one int), t ) 15.47/15.70 ( int, (zero_zero int), (one_one int) ) 15.47/15.70 ( int, (zero_zero int), min_1 ) 15.47/15.70 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.70 ( int, (zero_zero int), s ) 15.47/15.70 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.47/15.70 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.47/15.70 ( int, (zero_zero int), skv_4 ) 15.47/15.70 ( int, (zero_zero int), skv_10 ) 15.47/15.70 ( int, pls, (one_one int) ) 15.47/15.70 ( int, pls, pls ) 15.47/15.70 ( int, pls, min_1 ) 15.47/15.70 ( int, pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.70 ( int, min_1, pls ) 15.47/15.70 ( int, min_1, min_1 ) 15.47/15.70 ( int, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.70 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.70 ( int, skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.70 ( int, skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.70 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.70 ( real, (zero_zero real), pi ) 15.47/15.70 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.70 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.70 ( real, (zero_zero real), skv_2 ) 15.47/15.70 ( real, (zero_zero real), skv_3 ) 15.47/15.70 ( real, (zero_zero real), skv_5 ) 15.47/15.70 ( real, (zero_zero real), skv_7 ) 15.47/15.70 ( real, (zero_zero real), skv_8 ) 15.47/15.70 ( real, (zero_zero real), skv_9 ) 15.47/15.70 ( real, (zero_zero real), skv_12 ) 15.47/15.70 ( real, pi, (zero_zero real) ) 15.47/15.70 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.70 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.47/15.70 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.70 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 15.47/15.70 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.47/15.70 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 15.47/15.70 ( real, skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.70 ) 15.47/15.70 (instantiation (forall ((Z $$unsorted) (W_1 $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (zero_zero int)) W_1))) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (hAPP int nat nat_1 W_1)) (hAPP int nat nat_1 Z))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) W_1) Z))))) ) 15.47/15.70 ( (one_one int), pls ) 15.47/15.70 ( pls, pls ) 15.47/15.70 ( pls, min_1 ) 15.47/15.70 ( min_1, pls ) 15.47/15.70 ( min_1, min_1 ) 15.47/15.70 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 15.47/15.70 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), pls ) 15.47/15.70 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s ) 15.47/15.70 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.47/15.70 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_4 ) 15.47/15.70 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_10 ) 15.47/15.70 ( t, (one_one int) ) 15.47/15.70 ) 15.47/15.70 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_114138 $$unsorted) (BOUND_VARIABLE_114145 $$unsorted)) (let ((_let_0 (zero_zero nat))) (let ((_let_1 (zero_zero X_a))) (let ((_let_2 (hAPP X_a (fun nat X_a) (power_power X_a) _let_1))) (let ((_let_3 (hAPP int nat (number_number_of nat) BOUND_VARIABLE_114138))) (let ((_let_4 (hAPP int nat (number_number_of nat) BOUND_VARIABLE_114145))) (or (not (semiring_0 X_a)) (not (power X_a)) (and (or (not (= _let_0 _let_3)) (= (one_one X_a) (hAPP nat X_a _let_2 _let_3))) (or (= _let_0 _let_4) (= _let_1 (hAPP nat X_a _let_2 _let_4)))))))))) ) 15.47/15.70 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.47/15.70 ( rat, (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.47/15.70 ( complex, pls, pls ) 15.47/15.70 ( code_code_numeral, (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 15.47/15.70 ) 15.47/15.70 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_114187 $$unsorted) (BOUND_VARIABLE_114188 $$unsorted) (BOUND_VARIABLE_114189 $$unsorted)) (let ((_let_0 (fun (filter nat) bool))) (or (not (metric_space X_a)) (not (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_0 (hAPP (fun nat X_a) (fun X_a _let_0) (tendsto nat X_a) BOUND_VARIABLE_114188) BOUND_VARIABLE_114189) sequentially))) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) BOUND_VARIABLE_114187))) (not (forall ((No $$unsorted)) (not (forall ((N_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) No) N_2))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP X_a real (hAPP X_a (fun X_a real) (dist_dist X_a) (hAPP nat X_a BOUND_VARIABLE_114188 N_2)) BOUND_VARIABLE_114189)) BOUND_VARIABLE_114187))) )) )))) ) 15.47/15.70 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real) ) 15.47/15.70 ) 15.47/15.70 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_114231 $$unsorted) (BOUND_VARIABLE_114232 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member X_a))) (let ((_let_3 (field_char_0_Rats X_a))) (or (not (field_inverse_zero X_a)) (not (field_char_0 X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_114232) _let_3))) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_114231) _let_3))) (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_114232) BOUND_VARIABLE_114231)) _let_3))))))) ) 15.47/15.70 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 15.47/15.70 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.47/15.70 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.47/15.70 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.47/15.70 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.70 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 15.47/15.70 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), pi ) 15.47/15.70 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (one_one real) ) 15.47/15.70 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))), pi ) 15.47/15.70 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 15.47/15.70 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))), (one_one real) ) 15.47/15.70 ) 15.47/15.70 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_114259 $$unsorted)) (or (not (group_add X_a)) (= (zero_zero X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_114259) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_114259)))) ) 15.47/15.70 ( nat, (one_one nat) ) 15.47/15.70 ( int, (one_one int) ) 15.47/15.70 ( int, pls ) 15.47/15.70 ( int, min_1 ) 15.47/15.70 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.47/15.70 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.70 ( real, (one_one real) ) 15.47/15.70 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.70 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.47/15.70 ( complex, (one_one complex) ) 15.47/15.70 ( complex, ii ) 15.47/15.70 ) 15.47/15.70 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_114270 $$unsorted) (BOUND_VARIABLE_114271 $$unsorted)) (let ((_let_0 (norm_norm X_a))) (or (not (real_normed_vector X_a)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (hAPP real (fun real real) (minus_minus real) (hAPP X_a real _let_0 BOUND_VARIABLE_114270)) (hAPP X_a real _let_0 BOUND_VARIABLE_114271))) (hAPP X_a real _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) BOUND_VARIABLE_114270) BOUND_VARIABLE_114271)))))) ) 15.47/15.70 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.47/15.70 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 15.47/15.70 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 15.47/15.70 ) 15.47/15.70 (instantiation (forall ((A_2 $$unsorted) (X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) X_2))) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) A_2) (hAPP real nat natfloor X_2))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP nat real (real_1 nat) A_2)) X_2)))))) ) 15.47/15.70 ( (zero_zero nat), pi ) 15.47/15.70 ( (zero_zero nat), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.70 ( (zero_zero nat), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.70 ( (zero_zero nat), skv_3 ) 15.47/15.70 ( (zero_zero nat), skv_5 ) 15.47/15.70 ( (zero_zero nat), skv_7 ) 15.47/15.70 ( (zero_zero nat), skv_12 ) 15.47/15.70 ) 15.47/15.70 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int int (hAPP int (fun int int) (plus_plus int) K_4) (one_one int)) (hAPP int int succ K_4)) ) 15.47/15.70 ( pls ) 15.47/15.70 ( min_1 ) 15.47/15.70 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.47/15.70 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.70 ) 15.47/15.70 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_0 (product_prod X_a X_b))) (let ((_let_1 (lex_prod X_a X_b))) (= _let_1 (ti (fun (fun (product_prod X_a X_a) bool) (fun (fun (product_prod X_b X_b) bool) (fun (product_prod _let_0 _let_0) bool))) _let_1)))) ) 15.47/15.70 ( nat, nat ) 15.47/15.70 ( int, int ) 15.47/15.70 ) 15.47/15.70 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (scaleR_scaleR X_a))) (or (not (real_vector X_a)) (= _let_0 (ti (fun real (fun X_a X_a)) _let_0)))) ) 15.47/15.70 ( bool ) 15.47/15.70 ( nat ) 15.47/15.70 ( int ) 15.47/15.70 ( (fun int bool) ) 15.47/15.70 ( (fun int (fun int bool)) ) 15.47/15.70 ( (fun int int) ) 15.47/15.70 ( (fun nat bool) ) 15.47/15.70 ( real ) 15.47/15.70 ( (fun real bool) ) 15.47/15.70 ( (fun real real) ) 15.47/15.70 ( complex ) 15.47/15.70 ( (fun nat real) ) 15.47/15.70 ( (product_prod int int) ) 15.47/15.70 ( code_code_numeral ) 15.47/15.70 ( (fun int (fun int (fun int bool))) ) 15.47/15.70 ( (fun (product_prod int int) bool) ) 15.47/15.70 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 15.47/15.70 ( (fun (product_prod int int) int) ) 15.47/15.70 ( (fun int real) ) 15.47/15.70 ) 15.47/15.70 (instantiation (forall ((P_1 $$unsorted) (I $$unsorted)) (= (and (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) I) (zero_zero int)))) (hBOOL (hAPP nat bool P_1 (zero_zero nat)))) (forall ((N_2 $$unsorted)) (or (not (= (ti int I) (hAPP nat int (semiring_1_of_nat int) N_2))) (hBOOL (hAPP nat bool P_1 N_2))) )) (hBOOL (hAPP nat bool P_1 (hAPP int nat nat_1 I)))) ) 15.47/15.70 ( (even_odd_even nat), (one_one int) ) 15.47/15.70 ( (even_odd_even nat), (zero_zero int) ) 15.47/15.70 ( (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.70 ( prime, (one_one int) ) 15.47/15.70 ( prime, (zero_zero int) ) 15.47/15.70 ( prime, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.70 ) 15.47/15.70 (instantiation (forall ((A_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_4 (hAPP int int (hAPP int _let_2 (minus_minus int) P_5) (one_one int)))) (or (not (hBOOL (hAPP int bool zprime P_5))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) _let_3) P_5))) (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int _let_1 zcong A_1) (zero_zero int)) P_5)) (hBOOL (hAPP int bool (hAPP int _let_0 quadRes P_5) A_1)) (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int _let_1 zcong (hAPP int int zfact _let_4)) (hAPP nat int (hAPP int (fun nat int) (power_power int) A_1) (hAPP int nat nat_1 (hAPP int int (hAPP int _let_2 (div_div int) _let_4) _let_3)))) P_5)))))))) ) 15.47/15.70 ( (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.70 ) 15.47/15.70 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_114437 $$unsorted)) (or (not (monoid_mult X_a)) (= (ti X_a BOUND_VARIABLE_114437) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) (one_one X_a)) BOUND_VARIABLE_114437))) ) 15.47/15.70 ( bool, fFalse ) 15.47/15.70 ( bool, fTrue ) 15.47/15.70 ( int, pls ) 15.47/15.70 ( int, min_1 ) 15.47/15.70 ( int, s ) 15.47/15.70 ( int, m ) 15.47/15.70 ( int, s1 ) 15.47/15.70 ( int, t ) 15.47/15.70 ( (fun int bool), nat_neg ) 15.47/15.70 ( (fun int bool), zprime ) 15.47/15.70 ( (fun int bool), zEven ) 15.47/15.70 ( (fun int bool), zOdd ) 15.47/15.70 ( (fun int bool), (even_odd_even int) ) 15.47/15.70 ( (fun int bool), twoSqu1091635170sum2sq ) 15.47/15.70 ( (fun int bool), nat_is_nat ) 15.47/15.70 ( (fun int (fun int bool)), norRRset ) 15.47/15.70 ( (fun int (fun int bool)), quadRes ) 15.47/15.70 ( (fun int (fun int bool)), sRStar ) 15.47/15.70 ( (fun int (fun int bool)), d22set ) 15.47/15.70 ( (fun int (fun int bool)), sr ) 15.47/15.70 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 15.47/15.70 ( (fun int int), zfact ) 15.47/15.70 ( (fun int int), bit0 ) 15.47/15.70 ( (fun int int), bit1 ) 15.47/15.70 ( (fun int int), (fact_fact int) ) 15.47/15.70 ( (fun int int), pred ) 15.47/15.70 ( (fun int int), succ ) 15.47/15.70 ( (fun nat bool), (even_odd_even nat) ) 15.47/15.70 ( (fun nat bool), prime ) 15.47/15.70 ( (fun nat nat), suc ) 15.47/15.70 ( (fun nat nat), (fact_fact nat) ) 15.47/15.70 ( (fun nat nat), fact ) 15.47/15.70 ( (fun nat nat), nat_size ) 15.47/15.70 ( (fun nat nat), (size_size nat) ) 15.47/15.70 ( (fun (product_prod nat nat) bool), pred_nat ) 15.47/15.70 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 15.47/15.70 ( real, pi ) 15.47/15.70 ( (fun real real), ln ) 15.47/15.70 ( (fun real real), cos ) 15.47/15.70 ( (fun real real), sqrt ) 15.47/15.70 ( (fun real real), sin ) 15.47/15.70 ( (fun real real), arccos ) 15.47/15.70 ( (fun real real), arcsin ) 15.47/15.70 ( (fun real real), tan ) 15.47/15.70 ( (fun real real), arctan ) 15.47/15.70 ( (fun nat (fun nat bool)), coprime ) 15.47/15.70 ( complex, ii ) 15.47/15.70 ( (fun nat real), (real_1 nat) ) 15.47/15.70 ( (fun nat real), sin_coeff ) 15.47/15.70 ( (fun nat real), cos_coeff ) 15.47/15.70 ( (filter nat), sequentially ) 15.47/15.70 ( (fun int (fun int int)), (gcd_gcd int) ) 15.47/15.70 ( (fun int (fun int int)), legendre ) 15.47/15.70 ( (fun int (fun int int)), legacy_zgcd ) 15.47/15.70 ( (fun int (fun int int)), standardRes ) 15.47/15.70 ( (fun int (fun int int)), nat_tsub ) 15.47/15.70 ( (fun int (fun int int)), multInv ) 15.47/15.70 ( (fun int (fun int int)), z3mod ) 15.47/15.70 ( (fun int (fun int int)), z3div ) 15.47/15.70 ( (fun int (fun int int)), int_gcd ) 15.47/15.70 ( (fun int (fun int int)), int_lcm ) 15.47/15.70 ( (fun int (fun int int)), inv ) 15.47/15.70 ( (fun complex complex), expi ) 15.47/15.70 ( (fun complex complex), cnj ) 15.47/15.70 ( (fun real complex), cis ) 15.47/15.70 ( (fun int nat), nat_1 ) 15.47/15.70 ( (fun int nat), phi ) 15.47/15.70 ( (fun (fun int bool) bool), nat_nat_set ) 15.47/15.70 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 15.47/15.70 ( (fun nat (fun nat nat)), nat_gcd ) 15.47/15.70 ( (fun nat (fun nat nat)), nat_lcm ) 15.47/15.70 ( (fun (fun int bool) int), (the int) ) 15.47/15.70 ( (fun complex real), re ) 15.47/15.70 ( (fun complex real), im ) 15.47/15.70 ( (fun complex real), arg ) 15.47/15.70 ( (fun bool bool), fNot ) 15.47/15.70 ( (fun nat (fun real real)), root ) 15.47/15.70 ( (fun real (fun real real)), log ) 15.47/15.70 ( (fun real (fun real real)), powr ) 15.47/15.70 ( (fun bool (fun bool bool)), fimplies ) 15.47/15.70 ( (fun bool (fun bool bool)), fconj ) 15.47/15.70 ( (fun bool (fun bool bool)), fdisj ) 15.47/15.70 ( (fun int (fun int (product_prod int int))), negDivAlg ) 15.47/15.70 ( (fun int (fun int (product_prod int int))), posDivAlg ) 15.47/15.70 ( (fun int (fun int (product_prod int int))), divmod_int ) 15.47/15.70 ( (fun int (fun int (product_prod int int))), pdivmod ) 15.47/15.70 ( (fun int (fun int (product_prod int int))), norm_frac ) 15.47/15.70 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 15.47/15.70 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 15.47/15.70 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 15.47/15.70 ( (fun int (fun int (fun int bool))), zcong ) 15.47/15.70 ( (fun int (fun int (fun int bool))), zcongm ) 15.47/15.70 ( (fun int (fun int (fun int bool))), noXRRset ) 15.47/15.70 ( (fun int (fun int (fun int bool))), bnorRset ) 15.47/15.70 ( (fun int (fun int (fun int bool))), wset ) 15.47/15.70 ( (fun (product_prod int int) bool), frac_1 ) 15.47/15.70 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 15.47/15.70 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 15.47/15.70 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 15.47/15.70 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 15.47/15.70 ( (fun (fun nat rat) bool), vanishes ) 15.47/15.70 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 15.47/15.70 ( (fun code_code_numeral nat), code_c271388182l_size ) 15.47/15.70 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 15.47/15.70 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 15.47/15.70 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 15.47/15.70 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 15.47/15.70 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 15.47/15.70 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 15.47/15.70 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 15.47/15.70 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 15.47/15.70 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 15.47/15.70 ( (fun complex nat), complex_size ) 15.47/15.70 ( (fun complex nat), (size_size complex) ) 15.47/15.70 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 15.47/15.70 ( (fun nat (fun nat (product_prod int int))), bezw ) 15.47/15.70 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 15.47/15.70 ( (fun int (fun nat nat)), nat_aux ) 15.47/15.70 ( (fun int (fun (fun int bool) bool)), rsetR ) 15.47/15.70 ( (fun int (fun (fun int bool) bool)), resSet ) 15.47/15.70 ( (fun int (list int)), quickc666637781d_zero ) 15.47/15.70 ( (fun (product_prod int int) rat), frct ) 15.47/15.70 ( (fun int (fun int rat)), fract ) 15.47/15.70 ( (fun real (fun real complex)), complex_1 ) 15.47/15.70 ( (fun real (fun real complex)), rcis ) 15.47/15.70 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 15.47/15.70 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 15.47/15.70 ( (fun int real), (real_1 int) ) 15.47/15.70 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 15.47/15.70 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 15.47/15.70 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 15.47/15.70 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 15.47/15.70 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 15.47/15.70 ( (fun real nat), natfloor ) 15.47/15.70 ( (fun real nat), natceiling ) 15.47/15.70 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 15.47/15.70 ( (fun quickcheck_code_int int), quickcheck_int_of ) 15.47/15.70 ( (fun rat (product_prod int int)), quotient_of ) 15.47/15.70 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 15.47/15.70 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 15.47/15.70 ( (fun rat real), ratreal ) 15.47/15.70 ( (fun code_code_numeral int), code_int_of ) 15.47/15.70 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 15.47/15.70 ( (fun int quickcheck_code_int), quickcheck_of_int ) 15.47/15.70 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 15.47/15.70 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 15.47/15.70 ) 15.47/15.70 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_114515 $$unsorted)) (or (not (real_n2089651433ebra_1 X_a)) (= (hAPP real real (abs_abs real) (hAPP int real (ring_1_of_int real) BOUND_VARIABLE_114515)) (hAPP X_a real (norm_norm X_a) (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_114515)))) ) 15.47/15.70 ( real, (one_one int) ) 15.47/15.70 ( real, (zero_zero int) ) 15.47/15.70 ) 15.47/15.70 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_114538 $$unsorted) (BOUND_VARIABLE_114545 $$unsorted)) (let ((_let_0 (even_odd_even nat))) (let ((_let_1 (hAPP X_a X_a (uminus_uminus X_a) (one_one X_a)))) (let ((_let_2 (hAPP X_a (fun nat X_a) (power_power X_a) _let_1))) (or (not (comm_ring_1 X_a)) (and (or (not (hBOOL (hAPP nat bool _let_0 BOUND_VARIABLE_114538))) (= (one_one X_a) (hAPP nat X_a _let_2 BOUND_VARIABLE_114538))) (or (hBOOL (hAPP nat bool _let_0 BOUND_VARIABLE_114545)) (= _let_1 (hAPP nat X_a _let_2 BOUND_VARIABLE_114545)))))))) ) 15.47/15.70 ( int, (zero_zero nat), (zero_zero nat) ) 15.47/15.70 ( rat, (one_one nat), (one_one nat) ) 15.47/15.70 ) 15.47/15.70 (instantiation (forall ((N_1 $$unsorted)) (= (hAPP int nat (number_number_of nat) N_1) (hAPP real nat natfloor (hAPP int real (number_number_of real) N_1))) ) 15.47/15.70 ( pls ) 15.47/15.70 ( (hAPP int int bit1 pls) ) 15.47/15.70 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.47/15.70 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.47/15.70 ( min_1 ) 15.47/15.70 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.70 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.47/15.70 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.70 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 15.47/15.70 ) 15.47/15.70 (instantiation (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_0 (real_1 int))) (= (hAPP int real _let_0 (hAPP int int (hAPP int (fun int int) (plus_plus int) X_1) Y_1)) (hAPP real real (hAPP real (fun real real) (plus_plus real) (hAPP int real _let_0 X_1)) (hAPP int real _let_0 Y_1)))) ) 15.47/15.70 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 15.47/15.70 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 15.47/15.70 ) 15.47/15.70 (instantiation (forall ((Z_1 $$unsorted) (W $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (= (hAPP int int (hAPP int _let_0 _let_1 W) Z_1) (hAPP int int (hAPP int _let_0 _let_1 Z_1) W)))) ) 15.47/15.70 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 15.47/15.70 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.70 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.47/15.70 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13 ) 15.47/15.70 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.70 ( skv_13, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.70 ) 15.47/15.70 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_114649 $$unsorted) (BOUND_VARIABLE_114650 $$unsorted) (BOUND_VARIABLE_114651 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_114649))) (or (not (comple44059174attice X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) BOUND_VARIABLE_114650) BOUND_VARIABLE_114651))) (not (hBOOL (hAPP X_a bool _let_1 BOUND_VARIABLE_114650))) (hBOOL (hAPP X_a bool _let_1 (hAPP _let_0 X_a (complete_Sup_Sup X_a) BOUND_VARIABLE_114651)))))) ) 15.47/15.70 ( int, (zero_zero int), (one_one int), zEven ) 15.47/15.70 ) 15.47/15.70 (instantiation (forall ((Ma $$unsorted) (N $$unsorted)) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) Ma) N)) (not (forall ((K_1 $$unsorted)) (not (= N (hAPP nat nat suc (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) Ma) K_1)))) ))) ) 15.47/15.70 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.70 ) 15.47/15.70 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (uminus_uminus real))) (= (hAPP real real _let_0 (hAPP real real sqrt X_1)) (hAPP real real sqrt (hAPP real real _let_0 X_1)))) ) 15.47/15.70 ( (one_one real) ) 15.47/15.70 ) 15.47/15.70 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_114703 $$unsorted) (BOUND_VARIABLE_114704 $$unsorted) (BOUND_VARIABLE_114722 $$unsorted) (BOUND_VARIABLE_114723 $$unsorted)) (let ((_let_0 (number_number_of int))) (let ((_let_1 (number_number_of nat))) (let ((_let_2 (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)))) (let ((_let_3 (fun nat X_b))) (let ((_let_4 (power_power X_b))) (let ((_let_5 (number_number_of X_b))) (let ((_let_6 (fun X_b X_b))) (let ((_let_7 (times_times X_b))) (let ((_let_8 (hAPP X_b _let_3 _let_4 (hAPP int X_b _let_5 BOUND_VARIABLE_114703)))) (let ((_let_9 (hAPP nat X_b _let_8 (hAPP int nat _let_1 BOUND_VARIABLE_114704)))) (or (not (number X_b)) (not (monoid_mult X_b)) (and (or (not (hBOOL (hAPP int bool _let_2 (hAPP int int _let_0 BOUND_VARIABLE_114704)))) (= (hAPP X_b X_b (hAPP X_b _let_6 _let_7 (hAPP X_b X_b (hAPP X_b _let_6 _let_7 (hAPP int X_b _let_5 BOUND_VARIABLE_114703)) _let_9)) _let_9) (hAPP nat X_b _let_8 (hAPP int nat _let_1 (hAPP int int bit1 BOUND_VARIABLE_114704))))) (or (hBOOL (hAPP int bool _let_2 (hAPP int int _let_0 BOUND_VARIABLE_114723))) (= (one_one X_b) (hAPP nat X_b (hAPP X_b _let_3 _let_4 (hAPP int X_b _let_5 BOUND_VARIABLE_114722)) (hAPP int nat _let_1 (hAPP int int bit1 BOUND_VARIABLE_114723))))))))))))))))) ) 15.47/15.70 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit1 pls), (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit1 pls) ) 15.47/15.70 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)), min_1, (hAPP int int bit0 (hAPP int int bit1 pls)), min_1 ) 15.47/15.70 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.47/15.70 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.47/15.70 ( real, min_1, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))), min_1, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.70 ( quickcheck_code_int, (hAPP int int bit1 pls), pls, (hAPP int int bit1 pls), pls ) 15.47/15.70 ) 15.47/15.70 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_114800 $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat X_a))) (let ((_let_3 (fun X_a X_a))) (let ((_let_4 (fun nat _let_3))) (or (not (banach X_a)) (not (real_normed_field X_a)) (hBOOL (hAPP X_a bool (hAPP _let_2 (fun X_a bool) (sums X_a) (hAPP _let_2 _let_2 (hAPP _let_4 (fun _let_2 _let_2) (combs nat X_a X_a) (hAPP _let_1 _let_4 (hAPP (fun real _let_3) (fun _let_1 _let_4) (combb real _let_3 nat) (scaleR_scaleR X_a)) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) (fact_fact nat))))) (hAPP X_a _let_2 (power_power X_a) BOUND_VARIABLE_114800))) (hAPP X_a X_a (exp X_a) BOUND_VARIABLE_114800))))))))) ) 15.47/15.70 ( int, s ) 15.47/15.70 ( int, s1 ) 15.47/15.70 ( int, skv_14 ) 15.47/15.70 ( real, (hAPP int real (number_number_of real) min_1) ) 15.47/15.70 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.70 ( complex, ii ) 15.47/15.70 ) 15.47/15.70 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (of_real X_a))) (or (not (real_algebra_1 X_a)) (= _let_0 (ti (fun real X_a) _let_0)))) ) 15.47/15.70 ( bool ) 15.47/15.70 ( nat ) 15.47/15.70 ( (fun int bool) ) 15.47/15.70 ( (fun int (fun int bool)) ) 15.47/15.70 ( real ) 15.47/15.70 ( (fun real bool) ) 15.47/15.70 ( (fun real real) ) 15.47/15.70 ( complex ) 15.47/15.70 ( (fun nat real) ) 15.47/15.70 ( (fun real complex) ) 15.47/15.70 ( (fun bool bool) ) 15.47/15.70 ( (fun (filter nat) bool) ) 15.47/15.70 ( (fun nat (product_prod real real)) ) 15.47/15.70 ( (fun real (fun nat (product_prod real real))) ) 15.47/15.70 ( (fun (filter real) bool) ) 15.47/15.70 ( (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 15.47/15.70 ( (let ((_let_0 (fun int bool))) (fun _let_0 (fun int _let_0))) ) 15.47/15.70 ( (fun int (fun int (fun bool bool))) ) 15.47/15.70 ( (fun (fun int (fun int real)) (fun int (fun int bool))) ) 15.47/15.70 ( (fun (fun int real) (fun int bool)) ) 15.47/15.70 ( (fun int (fun nat bool)) ) 15.47/15.70 ( (let ((_let_0 (fun nat bool))) (fun _let_0 (fun int _let_0))) ) 15.47/15.70 ( (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 15.47/15.70 ( (fun int (fun nat (fun bool bool))) ) 15.47/15.70 ( (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 15.47/15.70 ( (fun (fun nat real) (fun nat bool)) ) 15.47/15.70 ) 15.47/15.70 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_114849 $$unsorted) (BOUND_VARIABLE_114850 $$unsorted)) (let ((_let_0 (semiring_1_of_nat X_a))) (or (not (semiring_char_0 X_a)) (= (= (hAPP nat X_a _let_0 BOUND_VARIABLE_114850) (hAPP nat X_a _let_0 BOUND_VARIABLE_114849)) (= BOUND_VARIABLE_114849 BOUND_VARIABLE_114850)))) ) 15.47/15.70 ( int, (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 15.47/15.70 ( int, (hAPP nat nat suc (zero_zero nat)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.70 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.47/15.70 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 15.47/15.70 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP nat nat suc (zero_zero nat)) ) 15.47/15.70 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.70 ( real, (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 15.47/15.70 ( real, (hAPP nat nat suc (zero_zero nat)), (zero_zero nat) ) 15.47/15.70 ( real, (hAPP nat nat suc (zero_zero nat)), (hAPP nat nat suc (zero_zero nat)) ) 15.47/15.70 ) 15.47/15.70 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_114866 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (or (not (number_semiring X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_114866) (hAPP int X_a (number_number_of X_a) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP X_a X_a (hAPP X_a _let_0 (plus_plus X_a) BOUND_VARIABLE_114866) BOUND_VARIABLE_114866)))) ) 15.47/15.70 ( nat, (one_one nat) ) 15.47/15.70 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.70 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.70 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.47/15.70 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.70 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.70 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.70 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.70 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 15.47/15.70 ( complex, ii ) 15.47/15.70 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.70 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 15.47/15.70 ) 15.47/15.71 (instantiation (forall ((Y_2 $$unsorted) (X_2 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member int))) (or (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 X_2) zOdd))) (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 Y_2) zOdd))) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP int int (hAPP int (fun int int) (minus_minus int) X_2) Y_2)) zEven)))))) ) 15.47/15.71 ( (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.71 ) 15.47/15.71 (instantiation (forall ((Y_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) Y_1))) (not (forall ((X $$unsorted)) (let ((_let_0 (fun real bool))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) X) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))) (not (= Y_1 (hAPP real real tan X))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) (zero_zero real)) X))))) ))) ) 15.47/15.71 ( pi ) 15.47/15.71 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.71 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.71 ( skv_3 ) 15.47/15.71 ( skv_5 ) 15.47/15.71 ( skv_7 ) 15.47/15.71 ( skv_12 ) 15.47/15.71 ) 15.47/15.71 (instantiation (forall ((Ma $$unsorted) (V $$unsorted)) (let ((_let_0 (hAPP int int (number_number_of int) V))) (= (= (hAPP nat int (semiring_1_of_nat int) Ma) _let_0) (and (= Ma (hAPP int nat nat_1 _let_0)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) _let_0))))) ) 15.47/15.71 ( (zero_zero nat), (hAPP int int bit1 pls) ) 15.47/15.71 ( (hAPP nat nat suc (zero_zero nat)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.47/15.71 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))), min_1 ) 15.47/15.71 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.71 ) 15.47/15.71 (instantiation (forall ((Z_1 $$unsorted)) (= (hAPP int int (hAPP int (fun int int) (times_times int) Z_1) (one_one int)) (ti int Z_1)) ) 15.47/15.71 ( pls ) 15.47/15.71 ( min_1 ) 15.47/15.71 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.71 ( s ) 15.47/15.71 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.71 ( m ) 15.47/15.71 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.71 ( s1 ) 15.47/15.71 ( t ) 15.47/15.71 ) 15.47/15.71 (instantiation (forall ((A_2 $$unsorted) (Ma $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun _let_0 bool))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) A_2) Ma))) (hBOOL (hAPP _let_1 bool (hAPP _let_0 (fun _let_1 bool) (member _let_0) (hAPP int _let_0 (hAPP int (fun int _let_0) bnorRset A_2) Ma)) (hAPP int _let_1 rsetR Ma)))))) ) 15.47/15.71 ( (one_one int), t ) 15.47/15.71 ( pls, (one_one int) ) 15.47/15.71 ( pls, pls ) 15.47/15.71 ( pls, min_1 ) 15.47/15.71 ( pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.71 ( min_1, pls ) 15.47/15.71 ( min_1, min_1 ) 15.47/15.71 ( s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.71 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.71 ( skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.71 ( skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.71 ) 15.47/15.71 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_115105 $$unsorted) (BOUND_VARIABLE_115106 $$unsorted) (BOUND_VARIABLE_115107 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_115105))) (or (not (ordere216010020id_add X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)) BOUND_VARIABLE_115107))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_115106))) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_115107) BOUND_VARIABLE_115106))))) ) 15.47/15.71 ( nat, (zero_zero nat), (one_one nat), (one_one nat) ) 15.47/15.71 ( int, pls, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.47/15.71 ( int, s, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.47/15.71 ( int, t, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.47/15.71 ( int, skv_4, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.47/15.71 ( int, skv_10, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.47/15.71 ) 15.47/15.71 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_115133 $$unsorted)) (or (not (real_normed_vector X_a)) (= (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_115133)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP X_a real (norm_norm X_a) BOUND_VARIABLE_115133)) (zero_zero real))))) ) 15.47/15.71 ( bool, fFalse ) 15.47/15.71 ( bool, fTrue ) 15.47/15.71 ( int, pls ) 15.47/15.71 ( int, min_1 ) 15.47/15.71 ( int, s ) 15.47/15.71 ( int, m ) 15.47/15.71 ( int, s1 ) 15.47/15.71 ( int, t ) 15.47/15.71 ( (fun int bool), nat_neg ) 15.47/15.71 ( (fun int bool), zprime ) 15.47/15.71 ( (fun int bool), zEven ) 15.47/15.71 ( (fun int bool), zOdd ) 15.47/15.71 ( (fun int bool), (even_odd_even int) ) 15.47/15.71 ( (fun int bool), twoSqu1091635170sum2sq ) 15.47/15.71 ( (fun int bool), nat_is_nat ) 15.47/15.71 ( (fun int (fun int bool)), norRRset ) 15.47/15.71 ( (fun int (fun int bool)), quadRes ) 15.47/15.71 ( (fun int (fun int bool)), sRStar ) 15.47/15.71 ( (fun int (fun int bool)), d22set ) 15.47/15.71 ( (fun int (fun int bool)), sr ) 15.47/15.71 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 15.47/15.71 ( (fun int int), zfact ) 15.47/15.71 ( (fun int int), bit0 ) 15.47/15.71 ( (fun int int), bit1 ) 15.47/15.71 ( (fun int int), (fact_fact int) ) 15.47/15.71 ( (fun int int), pred ) 15.47/15.71 ( (fun int int), succ ) 15.47/15.71 ( (fun nat bool), (even_odd_even nat) ) 15.47/15.71 ( (fun nat bool), prime ) 15.47/15.71 ( (fun nat nat), suc ) 15.47/15.71 ( (fun nat nat), (fact_fact nat) ) 15.47/15.71 ( (fun nat nat), fact ) 15.47/15.71 ( (fun nat nat), nat_size ) 15.47/15.71 ( (fun nat nat), (size_size nat) ) 15.47/15.71 ( (fun (product_prod nat nat) bool), pred_nat ) 15.47/15.71 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 15.47/15.71 ( real, pi ) 15.47/15.71 ( (fun real real), ln ) 15.47/15.71 ( (fun real real), cos ) 15.47/15.71 ( (fun real real), sqrt ) 15.47/15.71 ( (fun real real), sin ) 15.47/15.71 ( (fun real real), arccos ) 15.47/15.71 ( (fun real real), arcsin ) 15.47/15.71 ( (fun real real), tan ) 15.47/15.71 ( (fun real real), arctan ) 15.47/15.71 ( (fun nat (fun nat bool)), coprime ) 15.47/15.71 ( complex, ii ) 15.47/15.71 ( (fun nat real), (real_1 nat) ) 15.47/15.71 ( (fun nat real), sin_coeff ) 15.47/15.71 ( (fun nat real), cos_coeff ) 15.47/15.71 ( (filter nat), sequentially ) 15.47/15.71 ( (fun int (fun int int)), (gcd_gcd int) ) 15.47/15.71 ( (fun int (fun int int)), legendre ) 15.47/15.71 ( (fun int (fun int int)), legacy_zgcd ) 15.47/15.71 ( (fun int (fun int int)), standardRes ) 15.47/15.71 ( (fun int (fun int int)), nat_tsub ) 15.47/15.71 ( (fun int (fun int int)), multInv ) 15.47/15.71 ( (fun int (fun int int)), z3mod ) 15.47/15.71 ( (fun int (fun int int)), z3div ) 15.47/15.71 ( (fun int (fun int int)), int_gcd ) 15.47/15.71 ( (fun int (fun int int)), int_lcm ) 15.47/15.71 ( (fun int (fun int int)), inv ) 15.47/15.71 ( (fun complex complex), expi ) 15.47/15.71 ( (fun complex complex), cnj ) 15.47/15.71 ( (fun real complex), cis ) 15.47/15.71 ( (fun int nat), nat_1 ) 15.47/15.71 ( (fun int nat), phi ) 15.47/15.71 ( (fun (fun int bool) bool), nat_nat_set ) 15.47/15.71 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 15.47/15.71 ( (fun nat (fun nat nat)), nat_gcd ) 15.47/15.71 ( (fun nat (fun nat nat)), nat_lcm ) 15.47/15.71 ( (fun (fun int bool) int), (the int) ) 15.47/15.71 ( (fun complex real), re ) 15.47/15.71 ( (fun complex real), im ) 15.47/15.71 ( (fun complex real), arg ) 15.47/15.71 ( (fun bool bool), fNot ) 15.47/15.71 ( (fun nat (fun real real)), root ) 15.47/15.71 ( (fun real (fun real real)), log ) 15.47/15.71 ( (fun real (fun real real)), powr ) 15.47/15.71 ( (fun bool (fun bool bool)), fimplies ) 15.47/15.71 ( (fun bool (fun bool bool)), fconj ) 15.47/15.71 ( (fun bool (fun bool bool)), fdisj ) 15.47/15.71 ( (fun int (fun int (product_prod int int))), negDivAlg ) 15.47/15.71 ( (fun int (fun int (product_prod int int))), posDivAlg ) 15.47/15.71 ( (fun int (fun int (product_prod int int))), divmod_int ) 15.47/15.71 ( (fun int (fun int (product_prod int int))), pdivmod ) 15.47/15.71 ( (fun int (fun int (product_prod int int))), norm_frac ) 15.47/15.71 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 15.47/15.71 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 15.47/15.71 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 15.47/15.71 ( (fun int (fun int (fun int bool))), zcong ) 15.47/15.71 ( (fun int (fun int (fun int bool))), zcongm ) 15.47/15.71 ( (fun int (fun int (fun int bool))), noXRRset ) 15.47/15.71 ( (fun int (fun int (fun int bool))), bnorRset ) 15.47/15.71 ( (fun int (fun int (fun int bool))), wset ) 15.47/15.71 ( (fun (product_prod int int) bool), frac_1 ) 15.47/15.71 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 15.47/15.71 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 15.47/15.71 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 15.47/15.71 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 15.47/15.71 ( (fun (fun nat rat) bool), vanishes ) 15.47/15.71 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 15.47/15.71 ( (fun code_code_numeral nat), code_c271388182l_size ) 15.47/15.71 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 15.47/15.71 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 15.47/15.71 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 15.47/15.71 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 15.47/15.71 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 15.47/15.71 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 15.47/15.71 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 15.47/15.71 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 15.47/15.71 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 15.47/15.71 ( (fun complex nat), complex_size ) 15.47/15.71 ( (fun complex nat), (size_size complex) ) 15.47/15.71 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 15.47/15.71 ( (fun nat (fun nat (product_prod int int))), bezw ) 15.47/15.71 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 15.47/15.71 ( (fun int (fun nat nat)), nat_aux ) 15.47/15.71 ( (fun int (fun (fun int bool) bool)), rsetR ) 15.47/15.71 ( (fun int (fun (fun int bool) bool)), resSet ) 15.47/15.71 ( (fun int (list int)), quickc666637781d_zero ) 15.47/15.71 ( (fun (product_prod int int) rat), frct ) 15.47/15.71 ( (fun int (fun int rat)), fract ) 15.47/15.71 ( (fun real (fun real complex)), complex_1 ) 15.47/15.71 ( (fun real (fun real complex)), rcis ) 15.47/15.71 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 15.47/15.71 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 15.47/15.71 ( (fun int real), (real_1 int) ) 15.47/15.71 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 15.47/15.71 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 15.47/15.71 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 15.47/15.71 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 15.47/15.71 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 15.47/15.71 ( (fun real nat), natfloor ) 15.47/15.71 ( (fun real nat), natceiling ) 15.47/15.71 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 15.47/15.71 ( (fun quickcheck_code_int int), quickcheck_int_of ) 15.47/15.71 ( (fun rat (product_prod int int)), quotient_of ) 15.47/15.71 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 15.47/15.71 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 15.47/15.71 ( (fun rat real), ratreal ) 15.47/15.71 ( (fun code_code_numeral int), code_int_of ) 15.47/15.71 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 15.47/15.71 ( (fun int quickcheck_code_int), quickcheck_of_int ) 15.47/15.71 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 15.47/15.71 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 15.47/15.71 ) 15.47/15.71 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_115154 $$unsorted)) (let ((_let_0 (one_one X_a))) (let ((_let_1 (ti X_a BOUND_VARIABLE_115154))) (or (not (ring_11004092258visors X_a)) (= (= _let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_115154) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (or (= _let_0 _let_1) (= (hAPP X_a X_a (uminus_uminus X_a) _let_0) _let_1)))))) ) 15.47/15.71 ( bool, fFalse ) 15.47/15.71 ( bool, fTrue ) 15.47/15.71 ( int, pls ) 15.47/15.71 ( int, min_1 ) 15.47/15.71 ( int, s ) 15.47/15.71 ( int, m ) 15.47/15.71 ( int, s1 ) 15.47/15.71 ( int, t ) 15.47/15.71 ( int, skv_14 ) 15.47/15.71 ( (fun int bool), nat_neg ) 15.47/15.71 ( (fun int bool), zprime ) 15.47/15.71 ( (fun int bool), zEven ) 15.47/15.71 ( (fun int bool), zOdd ) 15.47/15.71 ( (fun int bool), (even_odd_even int) ) 15.47/15.71 ( (fun int bool), twoSqu1091635170sum2sq ) 15.47/15.71 ( (fun int bool), nat_is_nat ) 15.47/15.71 ( (fun int (fun int bool)), norRRset ) 15.47/15.71 ( (fun int (fun int bool)), quadRes ) 15.47/15.71 ( (fun int (fun int bool)), sRStar ) 15.47/15.71 ( (fun int (fun int bool)), d22set ) 15.47/15.71 ( (fun int (fun int bool)), sr ) 15.47/15.71 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 15.47/15.71 ( (fun int int), zfact ) 15.47/15.71 ( (fun int int), bit0 ) 15.47/15.71 ( (fun int int), bit1 ) 15.47/15.71 ( (fun int int), (fact_fact int) ) 15.47/15.71 ( (fun int int), pred ) 15.47/15.71 ( (fun int int), succ ) 15.47/15.71 ( (fun nat bool), (even_odd_even nat) ) 15.47/15.71 ( (fun nat bool), prime ) 15.47/15.71 ( (fun nat nat), suc ) 15.47/15.71 ( (fun nat nat), (fact_fact nat) ) 15.47/15.71 ( (fun nat nat), fact ) 15.47/15.71 ( (fun nat nat), nat_size ) 15.47/15.71 ( (fun nat nat), (size_size nat) ) 15.47/15.71 ( (fun (product_prod nat nat) bool), pred_nat ) 15.47/15.71 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 15.47/15.71 ( real, pi ) 15.47/15.71 ( real, (hAPP int real (number_number_of real) min_1) ) 15.47/15.71 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.71 ( (fun real real), ln ) 15.47/15.71 ( (fun real real), cos ) 15.47/15.71 ( (fun real real), sqrt ) 15.47/15.71 ( (fun real real), sin ) 15.47/15.71 ( (fun real real), arccos ) 15.47/15.71 ( (fun real real), arcsin ) 15.47/15.71 ( (fun real real), tan ) 15.47/15.71 ( (fun real real), arctan ) 15.47/15.71 ( (fun nat (fun nat bool)), coprime ) 15.47/15.71 ( complex, ii ) 15.47/15.71 ( (fun nat real), (real_1 nat) ) 15.47/15.71 ( (fun nat real), sin_coeff ) 15.47/15.71 ( (fun nat real), cos_coeff ) 15.47/15.71 ( (filter nat), sequentially ) 15.47/15.71 ( (fun int (fun int int)), (gcd_gcd int) ) 15.47/15.71 ( (fun int (fun int int)), legendre ) 15.47/15.71 ( (fun int (fun int int)), legacy_zgcd ) 15.47/15.71 ( (fun int (fun int int)), standardRes ) 15.47/15.71 ( (fun int (fun int int)), nat_tsub ) 15.47/15.71 ( (fun int (fun int int)), multInv ) 15.47/15.71 ( (fun int (fun int int)), z3mod ) 15.47/15.71 ( (fun int (fun int int)), z3div ) 15.47/15.71 ( (fun int (fun int int)), int_gcd ) 15.47/15.71 ( (fun int (fun int int)), int_lcm ) 15.47/15.71 ( (fun int (fun int int)), inv ) 15.47/15.71 ( (fun complex complex), expi ) 15.47/15.71 ( (fun complex complex), cnj ) 15.47/15.71 ( (fun real complex), cis ) 15.47/15.71 ( (fun int nat), nat_1 ) 15.47/15.71 ( (fun int nat), phi ) 15.47/15.71 ( (fun (fun int bool) bool), nat_nat_set ) 15.47/15.71 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 15.47/15.71 ( (fun nat (fun nat nat)), nat_gcd ) 15.47/15.71 ( (fun nat (fun nat nat)), nat_lcm ) 15.47/15.71 ( (fun (fun int bool) int), (the int) ) 15.47/15.71 ( (fun complex real), re ) 15.47/15.71 ( (fun complex real), im ) 15.47/15.71 ( (fun complex real), arg ) 15.47/15.71 ( (fun bool bool), fNot ) 15.47/15.71 ( (fun nat (fun real real)), root ) 15.47/15.71 ( (fun real (fun real real)), log ) 15.47/15.71 ( (fun real (fun real real)), powr ) 15.47/15.71 ( (fun bool (fun bool bool)), fimplies ) 15.47/15.71 ( (fun bool (fun bool bool)), fconj ) 15.47/15.71 ( (fun bool (fun bool bool)), fdisj ) 15.47/15.71 ( (fun int (fun int (product_prod int int))), negDivAlg ) 15.47/15.71 ( (fun int (fun int (product_prod int int))), posDivAlg ) 15.47/15.71 ( (fun int (fun int (product_prod int int))), divmod_int ) 15.47/15.71 ( (fun int (fun int (product_prod int int))), pdivmod ) 15.47/15.71 ( (fun int (fun int (product_prod int int))), norm_frac ) 15.47/15.71 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 15.47/15.71 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 15.47/15.71 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 15.47/15.71 ( (fun int (fun int (fun int bool))), zcong ) 15.47/15.71 ( (fun int (fun int (fun int bool))), zcongm ) 15.47/15.71 ( (fun int (fun int (fun int bool))), noXRRset ) 15.47/15.71 ( (fun int (fun int (fun int bool))), bnorRset ) 15.47/15.71 ( (fun int (fun int (fun int bool))), wset ) 15.47/15.71 ( (fun (product_prod int int) bool), frac_1 ) 15.47/15.71 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 15.47/15.71 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 15.47/15.71 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 15.47/15.71 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 15.47/15.71 ( (fun (fun nat rat) bool), vanishes ) 15.47/15.71 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 15.47/15.71 ( (fun code_code_numeral nat), code_c271388182l_size ) 15.47/15.71 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 15.47/15.71 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 15.47/15.71 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 15.47/15.71 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 15.47/15.71 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 15.47/15.71 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 15.47/15.71 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 15.47/15.71 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 15.47/15.71 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 15.47/15.71 ( (fun complex nat), complex_size ) 15.47/15.71 ( (fun complex nat), (size_size complex) ) 15.47/15.71 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 15.47/15.71 ( (fun nat (fun nat (product_prod int int))), bezw ) 15.47/15.71 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 15.47/15.71 ( (fun int (fun nat nat)), nat_aux ) 15.47/15.71 ( (fun int (fun (fun int bool) bool)), rsetR ) 15.47/15.71 ( (fun int (fun (fun int bool) bool)), resSet ) 15.47/15.71 ( (fun int (list int)), quickc666637781d_zero ) 15.47/15.71 ( (fun (product_prod int int) rat), frct ) 15.47/15.71 ( (fun int (fun int rat)), fract ) 15.47/15.71 ( (fun real (fun real complex)), complex_1 ) 15.47/15.71 ( (fun real (fun real complex)), rcis ) 15.47/15.71 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 15.47/15.71 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 15.47/15.71 ( (fun int real), (real_1 int) ) 15.47/15.71 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 15.47/15.71 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 15.47/15.71 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 15.47/15.71 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 15.47/15.71 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 15.47/15.71 ( (fun real nat), natfloor ) 15.47/15.71 ( (fun real nat), natceiling ) 15.47/15.71 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 15.47/15.71 ( (fun quickcheck_code_int int), quickcheck_int_of ) 15.47/15.71 ( (fun rat (product_prod int int)), quotient_of ) 15.47/15.71 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 15.47/15.71 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 15.47/15.71 ( (fun rat real), ratreal ) 15.47/15.71 ( (fun code_code_numeral int), code_int_of ) 15.47/15.71 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 15.47/15.71 ( (fun int quickcheck_code_int), quickcheck_of_int ) 15.47/15.71 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 15.47/15.71 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 15.47/15.71 ) 15.47/15.71 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_115212 $$unsorted) (BOUND_VARIABLE_115213 $$unsorted)) (let ((_let_0 (inverse_inverse X_a))) (let ((_let_1 (fun nat X_a))) (let ((_let_2 (power_power X_a))) (or (not (divisi14063676e_zero X_a)) (= (hAPP nat X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a _let_0 BOUND_VARIABLE_115212)) BOUND_VARIABLE_115213) (hAPP X_a X_a _let_0 (hAPP nat X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_115212) BOUND_VARIABLE_115213))))))) ) 15.47/15.71 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.71 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.71 ( int, skv_14, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.71 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.71 ) 15.47/15.71 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (one_one real)) X_1))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) (hAPP real real ln X_1)))))) ) 15.47/15.71 ( (one_one real) ) 15.47/15.71 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.71 ) 15.47/15.71 (instantiation (forall ((X_a $$unsorted)) (or (not (real_algebra_1 X_a)) (not (real_normed_vector X_a)) (= (zero_zero X_a) (hAPP real X_a (of_real X_a) (zero_zero real)))) ) 15.47/15.71 ( nat ) 15.47/15.71 ( int ) 15.47/15.71 ( real ) 15.47/15.71 ( rat ) 15.47/15.71 ( complex ) 15.47/15.71 ( quickcheck_code_int ) 15.47/15.71 ( code_code_numeral ) 15.47/15.71 ) 15.47/15.71 (instantiation (forall ((K $$unsorted) (F $$unsorted) (N $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (or (not (forall ((I_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) I_2) N))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int (abs_abs int) (hAPP int int (hAPP int (fun int int) (minus_minus int) (hAPP nat int F (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) I_2) (one_one nat)))) (hAPP nat int F I_2)))) (one_one int)))) )) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP nat int F (zero_zero nat))) K))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) (hAPP nat int F N)))) (not (forall ((I_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) I_2) N))) (not (= (ti int K) (hAPP nat int F I_2)))) ))))) ) 15.47/15.71 ( (zero_zero int), (semiring_1_of_nat int), (zero_zero nat) ) 15.47/15.71 ( (zero_zero int), (semiring_1_of_nat int), (hAPP nat nat suc (zero_zero nat)) ) 15.47/15.71 ( (zero_zero int), (semiring_1_of_nat int), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.47/15.71 ( (zero_zero int), (semiring_1_of_nat int), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.71 ( min_1, (semiring_1_of_nat int), (zero_zero nat) ) 15.47/15.71 ) 15.47/15.71 (instantiation (forall ((X_a $$unsorted) (A_2 $$unsorted) (R_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (hAPP (fun X_a _let_0) _let_0 (accp X_a) R_1))) (or (not (hBOOL (hAPP X_a bool _let_1 B_1))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 R_1 A_2) B_1))) (hBOOL (hAPP X_a bool _let_1 A_2))))) ) 15.47/15.71 ( nat, (zero_zero nat), (ord_less nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.71 ( int, (one_one int), (ord_less_eq int), t ) 15.47/15.71 ( int, (one_one int), (ord_less int), t ) 15.47/15.71 ( int, (zero_zero int), (ord_less_eq int), (one_one int) ) 15.47/15.71 ( int, (zero_zero int), (ord_less_eq int), min_1 ) 15.47/15.71 ( int, (zero_zero int), (ord_less_eq int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.71 ( int, (zero_zero int), (ord_less_eq int), s ) 15.47/15.71 ( int, (zero_zero int), (ord_less_eq int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.47/15.71 ( int, (zero_zero int), (ord_less_eq int), (hAPP int int (number_number_of int) pls) ) 15.47/15.71 ( int, (zero_zero int), (ord_less_eq int), skv_4 ) 15.47/15.71 ( int, (zero_zero int), (ord_less_eq int), skv_10 ) 15.47/15.71 ( int, pls, (ord_less int), (one_one int) ) 15.47/15.71 ( int, pls, (ord_less int), pls ) 15.47/15.71 ( int, pls, (ord_less int), min_1 ) 15.47/15.71 ( int, pls, (ord_less int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.71 ( int, min_1, (ord_less_eq int), pls ) 15.47/15.71 ( int, min_1, (ord_less_eq int), min_1 ) 15.47/15.71 ( int, min_1, (ord_less int), pls ) 15.47/15.71 ( int, min_1, (ord_less int), min_1 ) 15.47/15.71 ( int, (hAPP int int (number_number_of int) min_1), (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.71 ( int, (hAPP int int (number_number_of int) min_1), (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.71 ( int, (hAPP int int (number_number_of int) min_1), (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.71 ( int, s, (ord_less int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.71 ( int, s, (hAPP int (fun int (fun int bool)) zcong s1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.71 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (dvd_dvd int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 15.47/15.71 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), quadRes, (hAPP int int (number_number_of int) min_1) ) 15.47/15.71 ( int, t, (ord_less int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.71 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.71 ( int, skv_4, (ord_less int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.71 ( int, skv_4, (hAPP int (fun int (fun int bool)) zcong s1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.71 ( int, skv_10, (ord_less int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.71 ( int, skv_10, (hAPP int (fun int (fun int bool)) zcong s1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.71 ( real, (one_one real), (ord_less real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.71 ( real, (zero_zero real), (ord_less real), pi ) 15.47/15.71 ( real, (zero_zero real), (ord_less real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.71 ( real, (zero_zero real), (ord_less real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.71 ( real, (zero_zero real), (ord_less real), skv_2 ) 15.47/15.71 ( real, (zero_zero real), (ord_less real), skv_8 ) 15.47/15.71 ( real, (zero_zero real), (ord_less real), skv_9 ) 15.47/15.71 ( real, (zero_zero real), (ord_less_eq real), pi ) 15.47/15.71 ( real, (zero_zero real), (ord_less_eq real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.71 ( real, (zero_zero real), (ord_less_eq real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.71 ( real, (zero_zero real), (ord_less_eq real), skv_3 ) 15.47/15.71 ( real, (zero_zero real), (ord_less_eq real), skv_5 ) 15.47/15.71 ( real, (zero_zero real), (ord_less_eq real), skv_7 ) 15.47/15.71 ( real, (zero_zero real), (ord_less_eq real), skv_12 ) 15.47/15.71 ( real, pi, (ord_less real), (zero_zero real) ) 15.47/15.71 ( real, pi, (ord_less real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.71 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (ord_less_eq real), pi ) 15.47/15.71 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (ord_less real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.71 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (ord_less_eq real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.71 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (ord_less real), (zero_zero real) ) 15.47/15.71 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (ord_less real), (zero_zero real) ) 15.47/15.71 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (ord_less_eq real), (zero_zero real) ) 15.47/15.71 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), (ord_less real), pi ) 15.47/15.71 ( real, skv_5, (ord_less_eq real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.71 ) 15.47/15.71 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (pow X_a))) (= _let_1 (ti (fun _let_0 (fun _let_0 bool)) _let_1)))) ) 15.47/15.71 ( nat ) 15.47/15.71 ( int ) 15.47/15.71 ) 15.47/15.71 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_115401 $$unsorted)) (or (not (number_ring X_a)) (not (linordered_idom X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (one_one X_a)) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_115401))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP int int bit1 pls)) BOUND_VARIABLE_115401)))) ) 15.47/15.71 ( nat, pls ) 15.47/15.71 ( nat, (hAPP int int bit1 pls) ) 15.47/15.71 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.47/15.71 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.47/15.71 ( int, pls ) 15.47/15.71 ( int, (hAPP int int bit1 pls) ) 15.47/15.71 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.47/15.71 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.47/15.71 ( int, min_1 ) 15.47/15.71 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.71 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.47/15.71 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.47/15.71 ( real, min_1 ) 15.47/15.71 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.71 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.47/15.71 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.71 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 15.47/15.71 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.47/15.71 ( complex, min_1 ) 15.47/15.71 ( quickcheck_code_int, (one_one int) ) 15.47/15.71 ( quickcheck_code_int, (zero_zero int) ) 15.47/15.71 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 15.47/15.71 ( code_code_numeral, pls ) 15.47/15.71 ( code_code_numeral, (hAPP int int bit1 pls) ) 15.47/15.71 ) 15.47/15.71 (instantiation (forall ((Y_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) Y_1))) (not (forall ((X $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Y_1) (hAPP real real tan X)))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) X)))))) ))) ) 15.47/15.71 ( pi ) 15.47/15.71 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.71 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.71 ( skv_2 ) 15.47/15.71 ( skv_8 ) 15.47/15.71 ( skv_9 ) 15.47/15.71 ) 15.47/15.71 (instantiation (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (or (not (hBOOL (hAPP int bool twoSqu1091635170sum2sq X_1))) (not (hBOOL (hAPP int bool twoSqu1091635170sum2sq Y_1))) (hBOOL (hAPP int bool twoSqu1091635170sum2sq (hAPP int int (hAPP int (fun int int) (times_times int) X_1) Y_1)))) ) 15.47/15.71 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.71 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.71 ( skv_13, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.71 ) 15.47/15.71 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_115476 $$unsorted)) (or (not (division_ring X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_115476)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) (one_one X_a)) BOUND_VARIABLE_115476) (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_115476))) ) 15.47/15.71 ( bool, fFalse ) 15.47/15.71 ( bool, fTrue ) 15.47/15.71 ( int, pls ) 15.47/15.71 ( int, min_1 ) 15.47/15.71 ( int, s ) 15.47/15.71 ( int, m ) 15.47/15.71 ( int, s1 ) 15.47/15.71 ( int, t ) 15.47/15.71 ( (fun int bool), nat_neg ) 15.47/15.71 ( (fun int bool), zprime ) 15.47/15.71 ( (fun int bool), zEven ) 15.47/15.71 ( (fun int bool), zOdd ) 15.47/15.71 ( (fun int bool), (even_odd_even int) ) 15.47/15.71 ( (fun int bool), twoSqu1091635170sum2sq ) 15.47/15.71 ( (fun int bool), nat_is_nat ) 15.47/15.71 ( (fun int (fun int bool)), norRRset ) 15.47/15.71 ( (fun int (fun int bool)), quadRes ) 15.47/15.71 ( (fun int (fun int bool)), sRStar ) 15.47/15.71 ( (fun int (fun int bool)), d22set ) 15.47/15.71 ( (fun int (fun int bool)), sr ) 15.47/15.71 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 15.47/15.71 ( (fun int int), zfact ) 15.47/15.71 ( (fun int int), bit0 ) 15.47/15.71 ( (fun int int), bit1 ) 15.47/15.71 ( (fun int int), (fact_fact int) ) 15.47/15.71 ( (fun int int), pred ) 15.47/15.71 ( (fun int int), succ ) 15.47/15.71 ( (fun nat bool), (even_odd_even nat) ) 15.47/15.71 ( (fun nat bool), prime ) 15.47/15.71 ( (fun nat nat), suc ) 15.47/15.71 ( (fun nat nat), (fact_fact nat) ) 15.47/15.71 ( (fun nat nat), fact ) 15.47/15.71 ( (fun nat nat), nat_size ) 15.47/15.71 ( (fun nat nat), (size_size nat) ) 15.47/15.71 ( (fun (product_prod nat nat) bool), pred_nat ) 15.47/15.71 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 15.47/15.71 ( real, (zero_zero real) ) 15.47/15.71 ( real, pi ) 15.47/15.71 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.71 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.47/15.71 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.71 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 15.47/15.71 ( (fun real real), ln ) 15.47/15.71 ( (fun real real), cos ) 15.47/15.71 ( (fun real real), sqrt ) 15.47/15.71 ( (fun real real), sin ) 15.47/15.71 ( (fun real real), arccos ) 15.47/15.71 ( (fun real real), arcsin ) 15.47/15.71 ( (fun real real), tan ) 15.47/15.71 ( (fun real real), arctan ) 15.47/15.71 ( (fun nat (fun nat bool)), coprime ) 15.47/15.71 ( complex, ii ) 15.47/15.71 ( (fun nat real), (real_1 nat) ) 15.47/15.71 ( (fun nat real), sin_coeff ) 15.47/15.71 ( (fun nat real), cos_coeff ) 15.47/15.71 ( (filter nat), sequentially ) 15.47/15.71 ( (fun int (fun int int)), (gcd_gcd int) ) 15.47/15.71 ( (fun int (fun int int)), legendre ) 15.47/15.71 ( (fun int (fun int int)), legacy_zgcd ) 15.47/15.71 ( (fun int (fun int int)), standardRes ) 15.47/15.71 ( (fun int (fun int int)), nat_tsub ) 15.47/15.71 ( (fun int (fun int int)), multInv ) 15.47/15.71 ( (fun int (fun int int)), z3mod ) 15.47/15.71 ( (fun int (fun int int)), z3div ) 15.47/15.71 ( (fun int (fun int int)), int_gcd ) 15.47/15.71 ( (fun int (fun int int)), int_lcm ) 15.47/15.71 ( (fun int (fun int int)), inv ) 15.47/15.71 ( (fun complex complex), expi ) 15.47/15.71 ( (fun complex complex), cnj ) 15.47/15.71 ( (fun real complex), cis ) 15.47/15.71 ( (fun int nat), nat_1 ) 15.47/15.71 ( (fun int nat), phi ) 15.47/15.71 ( (fun (fun int bool) bool), nat_nat_set ) 15.47/15.71 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 15.47/15.71 ( (fun nat (fun nat nat)), nat_gcd ) 15.47/15.71 ( (fun nat (fun nat nat)), nat_lcm ) 15.47/15.71 ( (fun (fun int bool) int), (the int) ) 15.47/15.71 ( (fun complex real), re ) 15.47/15.71 ( (fun complex real), im ) 15.47/15.71 ( (fun complex real), arg ) 15.47/15.71 ( (fun bool bool), fNot ) 15.47/15.71 ( (fun nat (fun real real)), root ) 15.47/15.71 ( (fun real (fun real real)), log ) 15.47/15.71 ( (fun real (fun real real)), powr ) 15.47/15.71 ( (fun bool (fun bool bool)), fimplies ) 15.47/15.71 ( (fun bool (fun bool bool)), fconj ) 15.47/15.71 ( (fun bool (fun bool bool)), fdisj ) 15.47/15.71 ( (fun int (fun int (product_prod int int))), negDivAlg ) 15.47/15.71 ( (fun int (fun int (product_prod int int))), posDivAlg ) 15.47/15.71 ( (fun int (fun int (product_prod int int))), divmod_int ) 15.47/15.71 ( (fun int (fun int (product_prod int int))), pdivmod ) 15.47/15.71 ( (fun int (fun int (product_prod int int))), norm_frac ) 15.47/15.71 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 15.47/15.71 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 15.47/15.71 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 15.47/15.71 ( (fun int (fun int (fun int bool))), zcong ) 15.47/15.71 ( (fun int (fun int (fun int bool))), zcongm ) 15.47/15.71 ( (fun int (fun int (fun int bool))), noXRRset ) 15.47/15.71 ( (fun int (fun int (fun int bool))), bnorRset ) 15.47/15.71 ( (fun int (fun int (fun int bool))), wset ) 15.47/15.71 ( (fun (product_prod int int) bool), frac_1 ) 15.47/15.71 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 15.47/15.71 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 15.47/15.71 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 15.47/15.71 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 15.47/15.71 ( (fun (fun nat rat) bool), vanishes ) 15.47/15.71 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 15.47/15.71 ( (fun code_code_numeral nat), code_c271388182l_size ) 15.47/15.71 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 15.47/15.71 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 15.47/15.71 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 15.47/15.71 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 15.47/15.71 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 15.47/15.71 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 15.47/15.71 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 15.47/15.71 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 15.47/15.71 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 15.47/15.71 ( (fun complex nat), complex_size ) 15.47/15.71 ( (fun complex nat), (size_size complex) ) 15.47/15.71 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 15.47/15.71 ( (fun nat (fun nat (product_prod int int))), bezw ) 15.47/15.71 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 15.47/15.71 ( (fun int (fun nat nat)), nat_aux ) 15.47/15.71 ( (fun int (fun (fun int bool) bool)), rsetR ) 15.47/15.71 ( (fun int (fun (fun int bool) bool)), resSet ) 15.47/15.71 ( (fun int (list int)), quickc666637781d_zero ) 15.47/15.71 ( (fun (product_prod int int) rat), frct ) 15.47/15.71 ( (fun int (fun int rat)), fract ) 15.47/15.71 ( (fun real (fun real complex)), complex_1 ) 15.47/15.71 ( (fun real (fun real complex)), rcis ) 15.47/15.71 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 15.47/15.71 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 15.47/15.71 ( (fun int real), (real_1 int) ) 15.47/15.71 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 15.47/15.71 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 15.47/15.71 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 15.47/15.71 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 15.47/15.71 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 15.47/15.71 ( (fun real nat), natfloor ) 15.47/15.71 ( (fun real nat), natceiling ) 15.47/15.71 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 15.47/15.71 ( (fun quickcheck_code_int int), quickcheck_int_of ) 15.47/15.71 ( (fun rat (product_prod int int)), quotient_of ) 15.47/15.71 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 15.47/15.71 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 15.47/15.71 ( (fun rat real), ratreal ) 15.47/15.71 ( (fun code_code_numeral int), code_int_of ) 15.47/15.71 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 15.47/15.71 ( (fun int quickcheck_code_int), quickcheck_of_int ) 15.47/15.71 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 15.47/15.71 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 15.47/15.71 ) 15.47/15.71 (instantiation (forall ((Y_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP real real arctan Y_1)) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.47/15.71 ( (one_one real) ) 15.47/15.71 ( (zero_zero real) ) 15.47/15.71 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.47/15.71 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))))) ) 15.47/15.71 ) 15.47/15.71 (instantiation (forall ((Y_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real real arctan Y_1))) ) 15.47/15.71 ( (one_one real) ) 15.47/15.71 ( (zero_zero real) ) 15.47/15.71 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.47/15.71 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))))) ) 15.47/15.71 ) 15.47/15.71 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_115518 $$unsorted) (BOUND_VARIABLE_115519 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (minus_minus X_a))) (let ((_let_2 (uminus_uminus X_a))) (or (not (ab_group_add X_a)) (= (hAPP X_a X_a _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_115518) BOUND_VARIABLE_115519)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_115518)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_115519))))))) ) 15.47/15.71 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.47/15.71 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 15.47/15.71 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 15.47/15.71 ) 15.47/15.71 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int int pred K_4) (hAPP int int (hAPP int (fun int int) (plus_plus int) K_4) min_1)) ) 15.47/15.71 ( pls ) 15.47/15.71 ( min_1 ) 15.47/15.71 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.47/15.71 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.71 ) 15.47/15.71 (instantiation (forall ((X_a $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (hBOOL (hAPP _let_0 bool (finite_finite_1 X_a) A_3)) (= (zero_zero nat) (hAPP _let_0 nat (finite_card X_a) A_3)))) ) 15.47/15.71 ( nat, (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 15.47/15.71 ) 15.47/15.71 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (one_one int))) (= (= _let_0 (hAPP int int (abs_abs int) X_2)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (dvd_dvd int) X_2) _let_0)))) ) 15.47/15.71 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.71 ) 15.47/15.71 (instantiation (forall ((P_5 $$unsorted)) (or (not (hBOOL (hAPP nat bool prime P_5))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) P_5))) ) 15.47/15.71 ( (zero_zero nat) ) 15.47/15.71 ( (hAPP nat nat suc (zero_zero nat)) ) 15.47/15.71 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.71 ) 15.47/15.71 (instantiation (forall ((R_4 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) R_4))) (not (forall ((N_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (real_1 nat))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) R_4) (hAPP nat real _let_1 (hAPP nat nat suc N_2))))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) (hAPP nat real _let_1 N_2)) R_4)))))) ))) ) 15.47/15.71 ( pi ) 15.47/15.71 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.71 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.71 ( skv_3 ) 15.47/15.71 ( skv_5 ) 15.47/15.71 ( skv_7 ) 15.47/15.71 ( skv_12 ) 15.47/15.71 ) 15.47/15.71 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_115753 $$unsorted) (BOUND_VARIABLE_115754 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_115753)) BOUND_VARIABLE_115754)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP int int (number_number_of int) BOUND_VARIABLE_115753)) (hAPP X_a int (archimedean_ceiling X_a) BOUND_VARIABLE_115754))))) ) 15.47/15.71 ( nat, pls, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.71 ( int, pls, (one_one int) ) 15.47/15.71 ( int, pls, pls ) 15.47/15.71 ( int, pls, min_1 ) 15.47/15.71 ( int, pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.71 ( int, (hAPP int int bit1 pls), t ) 15.47/15.71 ) 15.47/15.71 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (BOUND_VARIABLE_115810 $$unsorted) (BOUND_VARIABLE_115811 $$unsorted) (BOUND_VARIABLE_115812 $$unsorted)) (let ((_let_0 (fun (filter X_a) bool))) (let ((_let_1 (fun X_a X_b))) (let ((_let_2 (fun X_b _let_0))) (let ((_let_3 (tendsto X_a X_b))) (let ((_let_4 (inverse_inverse X_b))) (or (not (real_n1866405975lgebra X_b)) (not (hBOOL (hAPP (filter X_a) bool (hAPP X_b _let_0 (hAPP _let_1 _let_2 _let_3 BOUND_VARIABLE_115810) BOUND_VARIABLE_115811) BOUND_VARIABLE_115812))) (= (zero_zero X_b) (ti X_b BOUND_VARIABLE_115811)) (hBOOL (hAPP (filter X_a) bool (hAPP X_b _let_0 (hAPP _let_1 _let_2 _let_3 (hAPP _let_1 _let_1 (hAPP (fun X_b X_b) (fun _let_1 _let_1) (combb X_b X_b X_a) _let_4) BOUND_VARIABLE_115810)) (hAPP X_b X_b _let_4 BOUND_VARIABLE_115811)) BOUND_VARIABLE_115812)))))))) ) 15.47/15.71 ( nat, real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))), (zero_zero real), sequentially ) 15.47/15.71 ) 15.47/15.71 (instantiation (forall ((X_1 $$unsorted)) (= (hAPP real real sqrt (hAPP real real (hAPP real (fun real real) (times_times real) X_1) X_1)) (hAPP real real (abs_abs real) X_1)) ) 15.47/15.71 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.71 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.71 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 15.47/15.71 ) 15.47/15.71 (instantiation (forall ((Y_2 $$unsorted) (X_2 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member int))) (or (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 X_2) zEven))) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP int int (hAPP int (fun int int) (times_times int) X_2) Y_2)) zEven)))))) ) 15.47/15.71 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.71 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.71 ( skv_13, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.71 ) 15.47/15.71 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int int bit1 K_4) (hAPP int int succ (hAPP int int bit0 K_4))) ) 15.47/15.71 ( pls ) 15.47/15.71 ( (hAPP int int bit1 pls) ) 15.47/15.71 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.47/15.71 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.47/15.71 ( min_1 ) 15.47/15.71 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.47/15.71 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.47/15.71 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.47/15.71 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 15.47/15.71 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 15.47/15.71 ) 15.47/15.71 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_115859 $$unsorted) (BOUND_VARIABLE_115860 $$unsorted)) (let ((_let_0 (fun nat X_a))) (or (not (comm_monoid_add X_a)) (not (t2_space X_a)) (= (and (hBOOL (hAPP _let_0 bool (summable X_a) BOUND_VARIABLE_115859)) (= (hAPP _let_0 X_a (suminf X_a) BOUND_VARIABLE_115859) (ti X_a BOUND_VARIABLE_115860))) (hBOOL (hAPP X_a bool (hAPP _let_0 (fun X_a bool) (sums X_a) BOUND_VARIABLE_115859) BOUND_VARIABLE_115860))))) ) 15.47/15.71 ( real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (hAPP real _let_1 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc))), (one_one real) ) 15.47/15.71 ) 15.47/15.71 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (fun X_a (fun X_a bool)))) (or (not (linorder X_a)) (= (hAPP _let_0 (fun X_a (fun X_a X_a)) (max X_a) (hAPP _let_0 _let_0 (combc X_a X_a bool) (ord_less_eq X_a))) (ord_min X_a)))) ) 15.47/15.71 ( bool ) 15.47/15.71 ( nat ) 15.47/15.71 ( int ) 15.47/15.71 ( (fun int bool) ) 15.47/15.71 ( (fun int (fun int bool)) ) 15.47/15.71 ( (fun int int) ) 15.47/15.71 ( (fun nat bool) ) 15.47/15.71 ( (product_prod nat nat) ) 15.47/15.71 ( real ) 15.47/15.71 ( (fun real bool) ) 15.47/15.71 ( (fun real real) ) 15.47/15.71 ( rat ) 15.47/15.71 ( complex ) 15.47/15.71 ( (fun nat real) ) 15.47/15.71 ( (filter nat) ) 15.47/15.71 ( (product_prod int int) ) 15.47/15.71 ( quickcheck_code_int ) 15.47/15.71 ( code_code_numeral ) 15.47/15.71 ( (fun int (fun int (fun int bool))) ) 15.47/15.71 ( (product_prod real real) ) 15.47/15.71 ( (fun (product_prod int int) bool) ) 15.47/15.71 ( (fun nat rat) ) 15.47/15.71 ( (filter real) ) 15.47/15.71 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 15.47/15.71 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 15.47/15.71 ( (fun (product_prod int int) int) ) 15.47/15.71 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 15.47/15.71 ( (fun int real) ) 15.47/15.71 ) 15.47/15.71 (instantiation (forall ((Ma $$unsorted) (W_1 $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (zero_zero int)) W_1))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) W_1) (hAPP nat int (semiring_1_of_nat int) Ma))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (hAPP int nat nat_1 W_1)) Ma))))) ) 15.47/15.71 ( (zero_zero nat), pls ) 15.47/15.71 ( (zero_zero nat), min_1 ) 15.47/15.71 ( (hAPP nat nat suc (zero_zero nat)), pls ) 15.47/15.71 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 15.47/15.71 ) 15.47/15.71 (instantiation (forall ((B_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) B_1) (hAPP int _let_0 d22set A_2)))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) B_1) A_2)))) ) 15.47/15.71 ( (one_one int), t ) 15.47/15.71 ( (zero_zero int), (one_one int) ) 15.47/15.71 ( (zero_zero int), min_1 ) 15.47/15.71 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.71 ( (zero_zero int), s ) 15.47/15.71 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.47/15.71 ( (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.47/15.71 ( (zero_zero int), skv_4 ) 15.47/15.71 ( (zero_zero int), skv_10 ) 15.47/15.71 ( min_1, pls ) 15.47/15.71 ( min_1, min_1 ) 15.47/15.71 ) 15.47/15.72 (instantiation (forall ((V $$unsorted) (V_2 $$unsorted)) (let ((_let_0 (zero_zero int))) (let ((_let_1 (number_number_of int))) (let ((_let_2 (number_number_of nat))) (let ((_let_3 (hAPP int int _let_1 V_2))) (let ((_let_4 (hBOOL (hAPP int bool nat_neg _let_3)))) (let ((_let_5 (hAPP int int _let_1 V))) (let ((_let_6 (hBOOL (hAPP int bool nat_neg _let_5)))) (= (and (or _let_6 (and (or _let_4 (= (ti int V_2) (ti int V))) (or (not _let_4) (= _let_0 _let_5)))) (or (not _let_6) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) _let_3) _let_0)))) (= (hAPP int nat _let_2 V_2) (hAPP int nat _let_2 V)))))))))) ) 15.47/15.72 ( pls, pls ) 15.47/15.72 ( (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 15.47/15.72 ( (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.47/15.72 ( (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.47/15.72 ( min_1, min_1 ) 15.47/15.72 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.72 ) 15.47/15.72 (instantiation (forall ((X_1 $$unsorted)) (= (hAPP real real (uminus_uminus real) (hAPP complex real im X_1)) (hAPP complex real im (hAPP complex complex (uminus_uminus complex) X_1))) ) 15.47/15.72 ( (one_one complex) ) 15.47/15.72 ( ii ) 15.47/15.72 ) 15.47/15.72 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (plus_plus real))) (let ((_let_2 (fun nat real))) (let ((_let_3 (power_power real))) (let ((_let_4 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_5 (hAPP real real (uminus_uminus real) X_1))) (= (zero_zero real) (hAPP real real (hAPP real _let_0 _let_1 (hAPP nat real (hAPP real _let_2 _let_3 (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real sin _let_5)) (hAPP real real sin X_1))) _let_4)) (hAPP nat real (hAPP real _let_2 _let_3 (hAPP real real (hAPP real _let_0 (minus_minus real) (hAPP real real cos _let_5)) (hAPP real real cos X_1))) _let_4))))))))) ) 15.47/15.72 ( (one_one real) ) 15.47/15.72 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.72 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.47/15.72 ) 15.47/15.72 (instantiation (forall ((X_1 $$unsorted)) (= (hAPP real real (uminus_uminus real) (hAPP real real sin X_1)) (hAPP real real sin (hAPP real real (hAPP real (fun real real) (plus_plus real) pi) X_1))) ) 15.47/15.72 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.72 ) 15.47/15.72 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_115991 $$unsorted)) (let ((_let_0 (abs_abs X_a))) (or (not (ordere142940540dd_abs X_a)) (= (hAPP X_a X_a _let_0 BOUND_VARIABLE_115991) (hAPP X_a X_a _let_0 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_115991))))) ) 15.47/15.72 ( int, (one_one int) ) 15.47/15.72 ( int, pls ) 15.47/15.72 ( int, min_1 ) 15.47/15.72 ( real, (one_one real) ) 15.47/15.72 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.72 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.47/15.72 ( complex, (one_one complex) ) 15.47/15.72 ( complex, ii ) 15.47/15.72 ) 15.47/15.72 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_116038 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (linord219039673up_add X_a)) (= (= _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_116038) BOUND_VARIABLE_116038)) (= _let_0 (ti X_a BOUND_VARIABLE_116038))))) ) 15.47/15.72 ( bool, fFalse ) 15.47/15.72 ( bool, fTrue ) 15.47/15.72 ( nat, (one_one nat) ) 15.47/15.72 ( int, pls ) 15.47/15.72 ( int, min_1 ) 15.47/15.72 ( int, s ) 15.47/15.72 ( int, m ) 15.47/15.72 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.47/15.72 ( int, s1 ) 15.47/15.72 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.72 ( int, t ) 15.47/15.72 ( (fun int bool), nat_neg ) 15.47/15.72 ( (fun int bool), zprime ) 15.47/15.72 ( (fun int bool), zEven ) 15.47/15.72 ( (fun int bool), zOdd ) 15.47/15.72 ( (fun int bool), (even_odd_even int) ) 15.47/15.72 ( (fun int bool), twoSqu1091635170sum2sq ) 15.47/15.72 ( (fun int bool), nat_is_nat ) 15.47/15.72 ( (fun int (fun int bool)), norRRset ) 15.47/15.72 ( (fun int (fun int bool)), quadRes ) 15.47/15.72 ( (fun int (fun int bool)), sRStar ) 15.47/15.72 ( (fun int (fun int bool)), d22set ) 15.47/15.72 ( (fun int (fun int bool)), sr ) 15.47/15.72 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 15.47/15.72 ( (fun int int), zfact ) 15.47/15.72 ( (fun int int), bit0 ) 15.47/15.72 ( (fun int int), bit1 ) 15.47/15.72 ( (fun int int), (fact_fact int) ) 15.47/15.72 ( (fun int int), pred ) 15.47/15.72 ( (fun int int), succ ) 15.47/15.72 ( (fun nat bool), (even_odd_even nat) ) 15.47/15.72 ( (fun nat bool), prime ) 15.47/15.72 ( (fun nat nat), suc ) 15.47/15.72 ( (fun nat nat), (fact_fact nat) ) 15.47/15.72 ( (fun nat nat), fact ) 15.47/15.72 ( (fun nat nat), nat_size ) 15.47/15.72 ( (fun nat nat), (size_size nat) ) 15.47/15.72 ( (fun (product_prod nat nat) bool), pred_nat ) 15.47/15.72 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 15.47/15.72 ( real, pi ) 15.47/15.72 ( (fun real real), ln ) 15.47/15.72 ( (fun real real), cos ) 15.47/15.72 ( (fun real real), sqrt ) 15.47/15.72 ( (fun real real), sin ) 15.47/15.72 ( (fun real real), arccos ) 15.47/15.72 ( (fun real real), arcsin ) 15.47/15.72 ( (fun real real), tan ) 15.47/15.72 ( (fun real real), arctan ) 15.47/15.72 ( (fun nat (fun nat bool)), coprime ) 15.47/15.72 ( complex, ii ) 15.47/15.72 ( (fun nat real), (real_1 nat) ) 15.47/15.72 ( (fun nat real), sin_coeff ) 15.47/15.72 ( (fun nat real), cos_coeff ) 15.47/15.72 ( (filter nat), sequentially ) 15.47/15.72 ( (fun int (fun int int)), (gcd_gcd int) ) 15.47/15.72 ( (fun int (fun int int)), legendre ) 15.47/15.72 ( (fun int (fun int int)), legacy_zgcd ) 15.47/15.72 ( (fun int (fun int int)), standardRes ) 15.47/15.72 ( (fun int (fun int int)), nat_tsub ) 15.47/15.72 ( (fun int (fun int int)), multInv ) 15.47/15.72 ( (fun int (fun int int)), z3mod ) 15.47/15.72 ( (fun int (fun int int)), z3div ) 15.47/15.72 ( (fun int (fun int int)), int_gcd ) 15.47/15.72 ( (fun int (fun int int)), int_lcm ) 15.47/15.72 ( (fun int (fun int int)), inv ) 15.47/15.72 ( (fun complex complex), expi ) 15.47/15.72 ( (fun complex complex), cnj ) 15.47/15.72 ( (fun real complex), cis ) 15.47/15.72 ( (fun int nat), nat_1 ) 15.47/15.72 ( (fun int nat), phi ) 15.47/15.72 ( (fun (fun int bool) bool), nat_nat_set ) 15.47/15.72 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 15.47/15.72 ( (fun nat (fun nat nat)), nat_gcd ) 15.47/15.72 ( (fun nat (fun nat nat)), nat_lcm ) 15.47/15.72 ( (fun (fun int bool) int), (the int) ) 15.47/15.72 ( (fun complex real), re ) 15.47/15.72 ( (fun complex real), im ) 15.47/15.72 ( (fun complex real), arg ) 15.47/15.72 ( (fun bool bool), fNot ) 15.47/15.72 ( (fun nat (fun real real)), root ) 15.47/15.72 ( (fun real (fun real real)), log ) 15.47/15.72 ( (fun real (fun real real)), powr ) 15.47/15.72 ( (fun bool (fun bool bool)), fimplies ) 15.47/15.72 ( (fun bool (fun bool bool)), fconj ) 15.47/15.72 ( (fun bool (fun bool bool)), fdisj ) 15.47/15.72 ( (fun int (fun int (product_prod int int))), negDivAlg ) 15.47/15.72 ( (fun int (fun int (product_prod int int))), posDivAlg ) 15.47/15.72 ( (fun int (fun int (product_prod int int))), divmod_int ) 15.47/15.72 ( (fun int (fun int (product_prod int int))), pdivmod ) 15.47/15.72 ( (fun int (fun int (product_prod int int))), norm_frac ) 15.47/15.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 15.47/15.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 15.47/15.72 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 15.47/15.72 ( (fun int (fun int (fun int bool))), zcong ) 15.47/15.72 ( (fun int (fun int (fun int bool))), zcongm ) 15.47/15.72 ( (fun int (fun int (fun int bool))), noXRRset ) 15.47/15.72 ( (fun int (fun int (fun int bool))), bnorRset ) 15.47/15.72 ( (fun int (fun int (fun int bool))), wset ) 15.47/15.72 ( (fun (product_prod int int) bool), frac_1 ) 15.47/15.72 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 15.47/15.72 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 15.47/15.72 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 15.47/15.72 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 15.47/15.72 ( (fun (fun nat rat) bool), vanishes ) 15.47/15.72 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 15.47/15.72 ( (fun code_code_numeral nat), code_c271388182l_size ) 15.47/15.72 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 15.47/15.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 15.47/15.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 15.47/15.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 15.47/15.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 15.47/15.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 15.47/15.72 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 15.47/15.72 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 15.47/15.72 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 15.47/15.72 ( (fun complex nat), complex_size ) 15.47/15.72 ( (fun complex nat), (size_size complex) ) 15.47/15.72 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 15.47/15.72 ( (fun nat (fun nat (product_prod int int))), bezw ) 15.47/15.72 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 15.47/15.72 ( (fun int (fun nat nat)), nat_aux ) 15.47/15.72 ( (fun int (fun (fun int bool) bool)), rsetR ) 15.47/15.72 ( (fun int (fun (fun int bool) bool)), resSet ) 15.47/15.72 ( (fun int (list int)), quickc666637781d_zero ) 15.47/15.72 ( (fun (product_prod int int) rat), frct ) 15.47/15.72 ( (fun int (fun int rat)), fract ) 15.47/15.72 ( (fun real (fun real complex)), complex_1 ) 15.47/15.72 ( (fun real (fun real complex)), rcis ) 15.47/15.72 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 15.47/15.72 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 15.47/15.72 ( (fun int real), (real_1 int) ) 15.47/15.72 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 15.47/15.72 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 15.47/15.72 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 15.47/15.72 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 15.47/15.72 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 15.47/15.72 ( (fun real nat), natfloor ) 15.47/15.72 ( (fun real nat), natceiling ) 15.47/15.72 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 15.47/15.72 ( (fun quickcheck_code_int int), quickcheck_int_of ) 15.47/15.72 ( (fun rat (product_prod int int)), quotient_of ) 15.47/15.72 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 15.47/15.72 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 15.47/15.72 ( (fun rat real), ratreal ) 15.47/15.72 ( (fun code_code_numeral int), code_int_of ) 15.47/15.72 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 15.47/15.72 ( (fun int quickcheck_code_int), quickcheck_of_int ) 15.47/15.72 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 15.47/15.72 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 15.47/15.72 ) 15.47/15.72 (instantiation (forall ((W $$unsorted)) (let ((_let_0 (one_one int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (uminus_uminus int))) (let ((_let_3 (hAPP int int (number_number_of int) W))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) _let_3) (zero_zero int)))) (= (hAPP _let_1 int (product_snd int int) (hAPP _let_1 _let_1 negateSnd (hAPP int _let_1 (hAPP int (fun int _let_1) negDivAlg (hAPP int int _let_2 _let_0)) (hAPP int int _let_2 _let_3)))) (hAPP int int (hAPP int (fun int int) (div_mod int) _let_0) _let_3))))))) ) 15.47/15.72 ( pls ) 15.47/15.72 ( (hAPP int int bit1 pls) ) 15.47/15.72 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.47/15.72 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.47/15.72 ( min_1 ) 15.47/15.72 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.72 ) 15.47/15.72 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_116069 $$unsorted) (BOUND_VARIABLE_116070 $$unsorted)) (let ((_let_0 (fun nat X_a))) (or (not (comm_monoid_add X_a)) (not (topological_space X_a)) (not (hBOOL (hAPP X_a bool (hAPP _let_0 (fun X_a bool) (sums X_a) BOUND_VARIABLE_116069) BOUND_VARIABLE_116070))) (hBOOL (hAPP _let_0 bool (summable X_a) BOUND_VARIABLE_116069)))) ) 15.47/15.72 ( real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (hAPP real _let_1 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc))), (one_one real) ) 15.47/15.72 ) 15.47/15.72 (instantiation (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (inverse_divide real))) (= (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real sqrt X_1)) (hAPP real real sqrt Y_1)) (hAPP real real sqrt (hAPP real real (hAPP real _let_0 _let_1 X_1) Y_1))))) ) 15.47/15.72 ( (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.47/15.72 ) 15.47/15.72 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_116100 $$unsorted) (BOUND_VARIABLE_116101 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (or (not (linorder X_a)) (= (ti X_a BOUND_VARIABLE_116100) (ti X_a BOUND_VARIABLE_116101)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_116100) BOUND_VARIABLE_116101)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_116101) BOUND_VARIABLE_116100))))) ) 15.47/15.72 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.72 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 15.47/15.72 ( int, (one_one int), pls ) 15.47/15.72 ( int, (one_one int), t ) 15.47/15.72 ( int, pls, (one_one int) ) 15.47/15.72 ( int, pls, pls ) 15.47/15.72 ( int, pls, min_1 ) 15.47/15.72 ( int, pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.72 ( int, min_1, pls ) 15.47/15.72 ( int, min_1, min_1 ) 15.47/15.72 ( int, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.72 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), pls ) 15.47/15.72 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s ) 15.47/15.72 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.47/15.72 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_4 ) 15.47/15.72 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_10 ) 15.47/15.72 ( int, t, (one_one int) ) 15.47/15.72 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.72 ( int, skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.72 ( int, skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.72 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.72 ( real, (zero_zero real), pi ) 15.47/15.72 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.72 ( real, (zero_zero real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.47/15.72 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.72 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.72 ( real, (zero_zero real), skv_2 ) 15.47/15.72 ( real, (zero_zero real), skv_8 ) 15.47/15.72 ( real, (zero_zero real), skv_9 ) 15.47/15.72 ( real, pi, (zero_zero real) ) 15.47/15.72 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.72 ( real, pi, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 15.47/15.72 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.72 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.47/15.72 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.72 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 15.47/15.72 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 15.47/15.72 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 15.47/15.72 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.47/15.72 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.47/15.72 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 15.47/15.72 ( real, skv_2, (zero_zero real) ) 15.47/15.72 ( real, skv_8, (zero_zero real) ) 15.47/15.72 ( real, skv_9, (zero_zero real) ) 15.47/15.72 ) 15.47/15.72 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (frac X_a))) (= _let_0 (ti (fun int (fun int X_a)) _let_0))) ) 15.47/15.72 ( bool ) 15.47/15.72 ( int ) 15.47/15.72 ( (fun int bool) ) 15.47/15.72 ( (fun int (fun int bool)) ) 15.47/15.72 ( real ) 15.47/15.72 ( rat ) 15.47/15.72 ( (product_prod int int) ) 15.47/15.72 ( (fun (fun int bool) bool) ) 15.47/15.72 ( (fun bool bool) ) 15.47/15.72 ( (fun (product_prod int int) bool) ) 15.47/15.72 ( (product_prod int (product_prod int int)) ) 15.47/15.72 ( (fun int (product_prod int (product_prod int int))) ) 15.47/15.72 ( (fun int (fun int (product_prod int (product_prod int int)))) ) 15.47/15.72 ( (fun int (fun int (fun int (product_prod int (product_prod int int))))) ) 15.47/15.72 ( (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))) ) 15.47/15.72 ( (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))) ) 15.47/15.72 ( (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))) ) 15.47/15.72 ) 15.47/15.72 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_116189 $$unsorted) (BOUND_VARIABLE_116190 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (let ((_let_1 (hAPP X_a (fun X_a bool) (ord_less X_a) _let_0))) (let ((_let_2 (hAPP int nat (number_number_of nat) BOUND_VARIABLE_116190))) (let ((_let_3 (hBOOL (hAPP nat bool (even_odd_even nat) _let_2)))) (or (not (linordered_idom X_a)) (= (hBOOL (hAPP X_a bool _let_1 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_116189) _let_2))) (or (and (not (= _let_0 (ti X_a BOUND_VARIABLE_116189))) _let_3) (and (hBOOL (hAPP X_a bool _let_1 BOUND_VARIABLE_116189)) (not _let_3)) (= (zero_zero nat) _let_2)))))))) ) 15.47/15.72 ( int, s, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.47/15.72 ( int, s1, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.47/15.72 ( int, skv_14, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.47/15.72 ( complex, ii, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.47/15.72 ) 15.47/15.72 (instantiation (forall ((Y_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (number_number_of real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP int real _let_2 min_1)) Y_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Y_1) (one_one real)))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real _let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real real arcsin Y_1))))))) ) 15.47/15.72 ( (zero_zero real) ) 15.47/15.72 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.72 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.72 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.72 ( skv_5 ) 15.47/15.72 ) 15.47/15.72 (instantiation (forall ((N $$unsorted)) (let ((_let_0 (fun nat bool))) (= (hAPP _let_0 nat (hAPP (fun nat nat) (fun _let_0 nat) (big_co302546470etprod nat nat) (combi nat)) (hAPP nat _let_0 (hAPP nat (fun nat _let_0) (ord_atLeastAtMost nat) (one_one nat)) N)) (hAPP nat nat (fact_fact nat) N))) ) 15.47/15.72 ( (zero_zero nat) ) 15.47/15.72 ( (hAPP nat nat suc (zero_zero nat)) ) 15.47/15.72 ) 15.47/15.72 (instantiation (forall ((N_1 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (zero_zero real))) (let ((_let_2 (fun nat real))) (let ((_let_3 (power_power real))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_1))) (= _let_1 (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP nat real (hAPP real _let_2 _let_3 (hAPP int real (number_number_of real) min_1)) (hAPP nat nat (hAPP nat (fun nat nat) (div_div nat) N_1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP nat real (real_1 nat) (hAPP nat nat (fact_fact nat) N_1)))) (hAPP nat real (hAPP real _let_2 _let_3 _let_1) N_1)))))))) ) 15.47/15.72 ( (zero_zero nat) ) 15.47/15.72 ( (hAPP nat nat suc (zero_zero nat)) ) 15.47/15.72 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.72 ) 15.47/15.72 (instantiation (forall ((Y_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP int real (number_number_of real) min_1)) Y_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Y_1) (one_one real)))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) (hAPP real real arccos Y_1)))))) ) 15.47/15.72 ( (zero_zero real) ) 15.47/15.72 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.72 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.72 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.72 ( skv_5 ) 15.47/15.72 ) 15.47/15.72 (instantiation (forall ((Z_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) Z_1))) (= (hAPP nat nat suc (hAPP int nat nat_1 Z_1)) (hAPP int nat nat_1 (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) Z_1)))) ) 15.47/15.72 ( (one_one int) ) 15.47/15.72 ( (zero_zero int) ) 15.47/15.72 ( min_1 ) 15.47/15.72 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.72 ( s ) 15.47/15.72 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.47/15.72 ( (hAPP int int (number_number_of int) pls) ) 15.47/15.72 ( skv_4 ) 15.47/15.72 ( skv_10 ) 15.47/15.72 ) 15.47/15.72 (instantiation (forall ((Y_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (fun real real))) (let ((_let_3 (hAPP real real (hAPP real _let_2 (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (= (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 (hAPP real real (uminus_uminus real) _let_3)))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) _let_3))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) tan)) Y_2)))) (hAPP real real arctan Y_2))))))))))))) ) 15.47/15.72 ( (one_one real) ) 15.47/15.72 ( (zero_zero real) ) 15.47/15.72 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.47/15.72 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))))) ) 15.47/15.72 ) 15.47/15.72 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_116526 $$unsorted) (BOUND_VARIABLE_116527 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member X_a))) (let ((_let_3 (field_char_0_Rats X_a))) (or (not (field_char_0 X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_116527) _let_3))) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_116526) _let_3))) (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) BOUND_VARIABLE_116527) BOUND_VARIABLE_116526)) _let_3))))))) ) 15.47/15.72 ( int, (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.72 ( real, (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))), (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))) ) 15.47/15.72 ( code_code_numeral, (one_one code_code_numeral), (zero_zero code_code_numeral) ) 15.47/15.72 ) 15.47/15.72 (instantiation (forall ((V_1 $$unsorted)) (= (hAPP int nat (number_number_of nat) V_1) (hAPP int nat nat_1 (hAPP int int (number_number_of int) V_1))) ) 15.47/15.72 ( pls ) 15.47/15.72 ( (hAPP int int bit1 pls) ) 15.47/15.72 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.47/15.72 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.47/15.72 ( min_1 ) 15.47/15.72 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.72 ) 15.47/15.72 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (div_div int))) (or (not (hBOOL (hAPP int bool (even_odd_even int) X_1))) (= (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 (plus_plus int) X_1) (one_one int))) _let_1) (hAPP int int (hAPP int _let_0 _let_2 X_1) _let_1)))))) ) 15.47/15.72 ( (one_one int) ) 15.47/15.72 ( (zero_zero int) ) 15.47/15.72 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.47/15.72 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.72 ) 15.47/15.72 (instantiation (forall ((X_b $$unsorted)) (let ((_let_0 (minus_minus X_b))) (or (not (minus X_b)) (= _let_0 (ti (fun X_b (fun X_b X_b)) _let_0)))) ) 15.47/15.72 ( bool ) 15.47/15.72 ( nat ) 15.47/15.72 ( int ) 15.47/15.72 ( (fun int bool) ) 15.47/15.72 ( (fun int (fun int bool)) ) 15.47/15.72 ( (fun int int) ) 15.47/15.72 ( (fun nat bool) ) 15.47/15.72 ( real ) 15.47/15.72 ( (fun real bool) ) 15.47/15.72 ( (fun real real) ) 15.47/15.72 ( rat ) 15.47/15.72 ( complex ) 15.47/15.72 ( (fun nat real) ) 15.47/15.72 ( (product_prod int int) ) 15.47/15.72 ( quickcheck_code_int ) 15.47/15.72 ( code_code_numeral ) 15.47/15.72 ( (fun int (fun int (fun int bool))) ) 15.47/15.72 ( (fun (product_prod int int) bool) ) 15.47/15.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 15.47/15.72 ( (fun (product_prod int int) int) ) 15.47/15.72 ( (fun int real) ) 15.47/15.72 ) 15.47/15.72 (instantiation (forall ((N_1 $$unsorted)) (= (hAPP real nat natceiling (hAPP int real (number_number_of real) N_1)) (hAPP int nat (number_number_of nat) N_1)) ) 15.47/15.72 ( pls ) 15.47/15.72 ( (hAPP int int bit1 pls) ) 15.47/15.72 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.47/15.72 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.47/15.72 ( min_1 ) 15.47/15.72 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.72 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.47/15.72 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.72 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 15.47/15.72 ) 15.47/15.72 (instantiation (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)))) (or (not (hBOOL (hAPP int bool _let_0 X_1))) (not (hBOOL (hAPP int bool _let_0 Y_1))) (= (hAPP int nat nat_1 (hAPP int int (hAPP int (fun int int) (times_times int) X_1) Y_1)) (hAPP nat nat (hAPP nat (fun nat nat) (times_times nat) (hAPP int nat nat_1 X_1)) (hAPP int nat nat_1 Y_1))))) ) 15.47/15.72 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.72 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.72 ( skv_13, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.72 ) 15.47/15.72 (instantiation (forall ((N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (even_odd_even nat) N_1))) (not (forall ((X $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (number_number_of nat))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (not (= (hAPP nat nat (hAPP nat _let_0 (times_times nat) (hAPP int nat _let_1 (hAPP int int bit0 _let_2))) X) (hAPP nat nat (hAPP nat _let_0 (power_power nat) N_1) (hAPP int nat _let_1 _let_2))))))) ))) ) 15.47/15.72 ( (zero_zero nat) ) 15.47/15.72 ( (one_one nat) ) 15.47/15.72 ) 15.47/15.72 (instantiation (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (minus_minus real))) (let ((_let_2 (times_times real))) (= (hAPP real real sin (hAPP real real (hAPP real _let_0 _let_1 X_1) Y_1)) (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real (hAPP real _let_0 _let_2 (hAPP real real cos Y_1)) (hAPP real real sin X_1))) (hAPP real real (hAPP real _let_0 _let_2 (hAPP real real sin Y_1)) (hAPP real real cos X_1))))))) ) 15.47/15.72 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 15.47/15.72 ) 15.47/15.72 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_116633 $$unsorted) (BOUND_VARIABLE_116634 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (inverse_divide X_a))) (let ((_let_2 (uminus_uminus X_a))) (or (not (field_inverse_zero X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_116633)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_116634)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_116633) BOUND_VARIABLE_116634)))))) ) 15.47/15.72 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.72 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.47/15.72 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.72 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 15.47/15.72 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.72 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.72 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.47/15.72 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.47/15.72 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.72 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.72 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.72 ) 15.47/15.72 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_116652 $$unsorted) (BOUND_VARIABLE_116653 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (inverse_divide X_a))) (let ((_let_2 (uminus_uminus X_a))) (or (not (real_normed_field X_a)) (= (hAPP X_a X_a _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_116652) BOUND_VARIABLE_116653)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_116652)) BOUND_VARIABLE_116653)))))) ) 15.47/15.72 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.72 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.47/15.72 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.72 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 15.47/15.72 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.72 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.72 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.47/15.72 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.47/15.72 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.72 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.72 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.72 ) 15.47/15.72 (instantiation (forall ((N $$unsorted) (V $$unsorted)) (let ((_let_0 (hAPP int int (number_number_of int) (hAPP int int pred V)))) (let ((_let_1 (hBOOL (hAPP int bool nat_neg _let_0)))) (= (= (hAPP nat nat suc N) (hAPP int nat (number_number_of nat) V)) (and (or _let_1 (= N (hAPP int nat nat_1 _let_0))) (not _let_1))))) ) 15.47/15.72 ( (zero_zero nat), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.47/15.72 ( (hAPP nat nat suc (zero_zero nat)), (hAPP int int bit1 pls) ) 15.47/15.72 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.47/15.72 ) 15.47/15.72 (instantiation (forall ((W $$unsorted)) (let ((_let_0 (hAPP int complex (number_number_of complex) W))) (= _let_0 (hAPP complex complex cnj _let_0))) ) 15.47/15.72 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.47/15.72 ( min_1 ) 15.47/15.72 ) 15.47/15.72 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_116867 $$unsorted) (BOUND_VARIABLE_116868 $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (order X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_116867) BOUND_VARIABLE_116868)) (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_116867) BOUND_VARIABLE_116868)) (not (= (ti X_a BOUND_VARIABLE_116867) (ti X_a BOUND_VARIABLE_116868))))))) ) 15.47/15.72 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.72 ( int, (one_one int), t ) 15.47/15.72 ( int, (zero_zero int), (one_one int) ) 15.47/15.72 ( int, (zero_zero int), min_1 ) 15.47/15.72 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.72 ( int, (zero_zero int), s ) 15.47/15.72 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.47/15.72 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.47/15.72 ( int, (zero_zero int), skv_4 ) 15.47/15.72 ( int, (zero_zero int), skv_10 ) 15.47/15.72 ( int, pls, (one_one int) ) 15.47/15.72 ( int, pls, pls ) 15.47/15.72 ( int, pls, min_1 ) 15.47/15.72 ( int, pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.72 ( int, min_1, pls ) 15.47/15.72 ( int, min_1, min_1 ) 15.47/15.72 ( int, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.72 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.72 ( int, skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.72 ( int, skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.72 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.72 ( real, (zero_zero real), pi ) 15.47/15.72 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.72 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.72 ( real, (zero_zero real), skv_2 ) 15.47/15.72 ( real, (zero_zero real), skv_3 ) 15.47/15.72 ( real, (zero_zero real), skv_5 ) 15.47/15.72 ( real, (zero_zero real), skv_7 ) 15.47/15.72 ( real, (zero_zero real), skv_8 ) 15.47/15.72 ( real, (zero_zero real), skv_9 ) 15.47/15.72 ( real, (zero_zero real), skv_12 ) 15.47/15.72 ( real, pi, (zero_zero real) ) 15.47/15.72 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.72 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.47/15.72 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.72 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 15.47/15.72 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.47/15.72 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 15.47/15.72 ( real, skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.72 ) 15.47/15.72 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_116900 $$unsorted) (BOUND_VARIABLE_116901 $$unsorted)) (let ((_let_0 (norm_norm X_a))) (or (not (real_normed_algebra X_a)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP X_a real _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_116900) BOUND_VARIABLE_116901))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP X_a real _let_0 BOUND_VARIABLE_116900)) (hAPP X_a real _let_0 BOUND_VARIABLE_116901)))))) ) 15.47/15.72 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 15.47/15.72 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.47/15.72 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13 ) 15.47/15.72 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.47/15.72 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.47/15.72 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.47/15.72 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 15.47/15.72 ( complex, ii, ii ) 15.47/15.72 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 15.47/15.72 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 15.47/15.72 ) 15.47/15.72 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_116966 $$unsorted)) (let ((_let_0 (fun (filter nat) bool))) (let ((_let_1 (fun nat X_a))) (or (not (real_n2089651433ebra_1 X_a)) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP X_a real (norm_norm X_a) BOUND_VARIABLE_116966)) (one_one real)))) (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_0 (hAPP _let_1 (fun X_a _let_0) (tendsto nat X_a) (hAPP X_a _let_1 (power_power X_a) BOUND_VARIABLE_116966)) (zero_zero X_a)) sequentially))))) ) 15.47/15.72 ( int, s ) 15.47/15.72 ( int, s1 ) 15.47/15.72 ( int, skv_14 ) 15.47/15.72 ( real, (hAPP int real (number_number_of real) min_1) ) 15.47/15.72 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.72 ( complex, ii ) 15.47/15.72 ) 15.47/15.72 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_116993 $$unsorted) (BOUND_VARIABLE_116994 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (inverse_inverse X_a))) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_116993) BOUND_VARIABLE_116994))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_116994) (zero_zero X_a)))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_116994)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_116993))))))) ) 15.47/15.72 ( int, (one_one int), t ) 15.47/15.72 ( int, (zero_zero int), (one_one int) ) 15.47/15.72 ( int, (zero_zero int), min_1 ) 15.47/15.72 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.72 ( int, (zero_zero int), s ) 15.47/15.72 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.47/15.72 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.47/15.72 ( int, (zero_zero int), skv_4 ) 15.47/15.72 ( int, (zero_zero int), skv_10 ) 15.47/15.72 ( int, min_1, pls ) 15.47/15.72 ( int, min_1, min_1 ) 15.47/15.72 ( real, (zero_zero real), pi ) 15.47/15.72 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.72 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.72 ( real, (zero_zero real), skv_3 ) 15.47/15.72 ( real, (zero_zero real), skv_5 ) 15.47/15.72 ( real, (zero_zero real), skv_7 ) 15.47/15.72 ( real, (zero_zero real), skv_12 ) 15.47/15.72 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.47/15.72 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.72 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.47/15.72 ( real, skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.72 ) 15.47/15.72 (instantiation (forall ((X_a $$unsorted)) (or (not (zero_neq_one X_a)) (not (= (zero_zero X_a) (one_one X_a)))) ) 15.47/15.72 ( nat ) 15.47/15.72 ( int ) 15.47/15.72 ( real ) 15.47/15.72 ( rat ) 15.47/15.72 ( complex ) 15.47/15.72 ( quickcheck_code_int ) 15.47/15.72 ( code_code_numeral ) 15.47/15.72 ) 15.47/15.72 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_117046 $$unsorted) (BOUND_VARIABLE_117047 $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat X_a))) (let ((_let_2 (fun X_a bool))) (let ((_let_3 (sums X_a))) (or (not (topological_space X_a)) (not (comm_monoid_add X_a)) (not (= (zero_zero X_a) (hAPP nat X_a BOUND_VARIABLE_117047 (zero_zero nat)))) (not (hBOOL (hAPP X_a bool (hAPP _let_1 _let_2 _let_3 (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat X_a nat) BOUND_VARIABLE_117047) suc)) BOUND_VARIABLE_117046))) (hBOOL (hAPP X_a bool (hAPP _let_1 _let_2 _let_3 BOUND_VARIABLE_117047) BOUND_VARIABLE_117046))))))) ) 15.47/15.72 ( real, (one_one real), (hAPP real (fun nat real) (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.47/15.72 ) 15.47/15.72 (instantiation (forall ((W $$unsorted)) (let ((_let_0 (one_one int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (hAPP int int (number_number_of int) W))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) _let_2))) (= (hAPP int int (hAPP int (fun int int) (div_div int) _let_0) _let_2) (hAPP _let_1 int (product_fst int int) (hAPP int _let_1 (hAPP int (fun int _let_1) posDivAlg _let_0) _let_2))))))) ) 15.47/15.72 ( pls ) 15.47/15.72 ( (hAPP int int bit1 pls) ) 15.47/15.72 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.47/15.72 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.47/15.72 ( min_1 ) 15.47/15.72 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.72 ) 15.47/15.72 (instantiation (forall ((P_1 $$unsorted) (A0 $$unsorted) (A1 $$unsorted)) (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 bool))) (or (not (hBOOL (hAPP _let_0 bool (hAPP (fun _let_0 _let_1) _let_1 (accp _let_0) posDivAlg_rel) (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) A0) A1)))) (not (forall ((A_4 $$unsorted) (B_4 $$unsorted)) (let ((_let_2 (hAPP int (fun int bool) P_1 A_4))) (or (not (hBOOL (hAPP _let_0 bool (hAPP (fun _let_0 _let_1) _let_1 (accp _let_0) posDivAlg_rel) (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) A_4) B_4)))) (and (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) B_4) (zero_zero int)))) (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) A_4) B_4))) (not (hBOOL (hAPP int bool _let_2 (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) B_4))))) (hBOOL (hAPP int bool _let_2 B_4)))) )) (hBOOL (hAPP int bool (hAPP int (fun int bool) P_1 A0) A1))))) ) 15.47/15.72 ( (ord_less_eq int), (one_one int), t ) 15.47/15.72 ( (ord_less_eq int), (zero_zero int), (one_one int) ) 15.47/15.72 ( (ord_less_eq int), (zero_zero int), min_1 ) 15.47/15.72 ( (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.72 ( (ord_less_eq int), (zero_zero int), s ) 15.47/15.72 ( (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.47/15.72 ( (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.47/15.72 ( (ord_less_eq int), (zero_zero int), skv_4 ) 15.47/15.72 ( (ord_less_eq int), (zero_zero int), skv_10 ) 15.47/15.72 ( (ord_less_eq int), min_1, pls ) 15.47/15.72 ( (ord_less_eq int), min_1, min_1 ) 15.47/15.72 ( (ord_less int), (one_one int), t ) 15.47/15.72 ( (ord_less int), pls, (one_one int) ) 15.47/15.72 ( (ord_less int), pls, pls ) 15.47/15.72 ( (ord_less int), pls, min_1 ) 15.47/15.72 ( (ord_less int), pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.72 ( (ord_less int), min_1, pls ) 15.47/15.72 ( (ord_less int), min_1, min_1 ) 15.47/15.72 ( (ord_less int), s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.72 ( (ord_less int), t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.72 ( (ord_less int), skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.72 ( (ord_less int), skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.72 ( (dvd_dvd int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 15.47/15.72 ( quadRes, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (number_number_of int) min_1) ) 15.47/15.72 ( (hAPP int (fun int (fun int bool)) zcong s1), s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.72 ( (hAPP int (fun int (fun int bool)) zcong s1), skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.72 ( (hAPP int (fun int (fun int bool)) zcong s1), skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.72 ( (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.72 ( (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.72 ( (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.72 ( (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.72 ) 15.47/15.73 (instantiation (forall ((N $$unsorted)) (let ((_let_0 (fun int (fun int bool)))) (let ((_let_1 (ord_less_eq int))) (let ((_let_2 (zero_zero int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun int _let_3))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) _let_1 _let_2) N))) (= (hAPP nat int (semiring_1_of_nat int) (hAPP (fun int bool) nat (finite_card int) (hAPP (fun int bool) (fun int bool) (collect int) (hAPP (fun int bool) (fun int bool) (hAPP _let_4 (fun (fun int bool) (fun int bool)) (combs int bool bool) (hAPP (fun int bool) _let_4 (hAPP (fun bool _let_3) (fun (fun int bool) _let_4) (combb bool _let_3 int) fconj) (hAPP int (fun int bool) (ord_less int) _let_2))) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) _let_1) N))))) (ti int N)))))))) ) 15.47/15.73 ( (one_one int) ) 15.47/15.73 ( pls ) 15.47/15.73 ( min_1 ) 15.47/15.73 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.73 ( s ) 15.47/15.73 ( m ) 15.47/15.73 ( s1 ) 15.47/15.73 ( t ) 15.47/15.73 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.47/15.73 ( (hAPP int int (number_number_of int) pls) ) 15.47/15.73 ( skv_4 ) 15.47/15.73 ( skv_10 ) 15.47/15.73 ) 15.47/15.73 (instantiation (forall ((I $$unsorted) (K $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (let ((_let_2 (zero_zero int))) (let ((_let_3 (ord_less int))) (= (or (= _let_2 (ti int K)) (and (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 I) _let_2)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_3 K) I))) (and (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 _let_2) I)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_3 I) K)))) (= _let_2 (hAPP int int (hAPP int (fun int int) (div_div int) I) K))))))) ) 15.47/15.73 ( (one_one int), pls ) 15.47/15.73 ( (one_one int), t ) 15.47/15.73 ( pls, (one_one int) ) 15.47/15.73 ( pls, pls ) 15.47/15.73 ( pls, min_1 ) 15.47/15.73 ( pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.73 ( min_1, pls ) 15.47/15.73 ( min_1, min_1 ) 15.47/15.73 ( s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.73 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), pls ) 15.47/15.73 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s ) 15.47/15.73 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.47/15.73 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_4 ) 15.47/15.73 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_10 ) 15.47/15.73 ( t, (one_one int) ) 15.47/15.73 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.73 ( skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.73 ( skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.73 ) 15.47/15.73 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_117119 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (zero_zero X_a))) (or (not (ring_char_0 X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) BOUND_VARIABLE_117119) (ring_1_Ints X_a)))) (= (= _let_1 (ti X_a BOUND_VARIABLE_117119)) (= _let_1 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_117119) BOUND_VARIABLE_117119)))))) ) 15.47/15.73 ( bool, fFalse ) 15.47/15.73 ( bool, fTrue ) 15.47/15.73 ( nat, (one_one nat) ) 15.47/15.73 ( int, (one_one int) ) 15.47/15.73 ( int, pls ) 15.47/15.73 ( int, min_1 ) 15.47/15.73 ( int, s ) 15.47/15.73 ( int, m ) 15.47/15.73 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.47/15.73 ( int, s1 ) 15.47/15.73 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.73 ( int, t ) 15.47/15.73 ( (fun int bool), nat_neg ) 15.47/15.73 ( (fun int bool), zprime ) 15.47/15.73 ( (fun int bool), zEven ) 15.47/15.73 ( (fun int bool), zOdd ) 15.47/15.73 ( (fun int bool), (even_odd_even int) ) 15.47/15.73 ( (fun int bool), twoSqu1091635170sum2sq ) 15.47/15.73 ( (fun int bool), nat_is_nat ) 15.47/15.73 ( (fun int (fun int bool)), norRRset ) 15.47/15.73 ( (fun int (fun int bool)), quadRes ) 15.47/15.73 ( (fun int (fun int bool)), sRStar ) 15.47/15.73 ( (fun int (fun int bool)), d22set ) 15.47/15.73 ( (fun int (fun int bool)), sr ) 15.47/15.73 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 15.47/15.73 ( (fun int int), zfact ) 15.47/15.73 ( (fun int int), bit0 ) 15.47/15.73 ( (fun int int), bit1 ) 15.47/15.73 ( (fun int int), (fact_fact int) ) 15.47/15.73 ( (fun int int), pred ) 15.47/15.73 ( (fun int int), succ ) 15.47/15.73 ( (fun nat bool), (even_odd_even nat) ) 15.47/15.73 ( (fun nat bool), prime ) 15.47/15.73 ( (fun nat nat), suc ) 15.47/15.73 ( (fun nat nat), (fact_fact nat) ) 15.47/15.73 ( (fun nat nat), fact ) 15.47/15.73 ( (fun nat nat), nat_size ) 15.47/15.73 ( (fun nat nat), (size_size nat) ) 15.47/15.73 ( (fun (product_prod nat nat) bool), pred_nat ) 15.47/15.73 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 15.47/15.73 ( real, pi ) 15.47/15.73 ( (fun real real), ln ) 15.47/15.73 ( (fun real real), cos ) 15.47/15.73 ( (fun real real), sqrt ) 15.47/15.73 ( (fun real real), sin ) 15.47/15.73 ( (fun real real), arccos ) 15.47/15.73 ( (fun real real), arcsin ) 15.47/15.73 ( (fun real real), tan ) 15.47/15.73 ( (fun real real), arctan ) 15.47/15.73 ( (fun nat (fun nat bool)), coprime ) 15.47/15.73 ( complex, ii ) 15.47/15.73 ( (fun nat real), (real_1 nat) ) 15.47/15.73 ( (fun nat real), sin_coeff ) 15.47/15.73 ( (fun nat real), cos_coeff ) 15.47/15.73 ( (filter nat), sequentially ) 15.47/15.73 ( (fun int (fun int int)), (gcd_gcd int) ) 15.47/15.73 ( (fun int (fun int int)), legendre ) 15.47/15.73 ( (fun int (fun int int)), legacy_zgcd ) 15.47/15.73 ( (fun int (fun int int)), standardRes ) 15.47/15.73 ( (fun int (fun int int)), nat_tsub ) 15.47/15.73 ( (fun int (fun int int)), multInv ) 15.47/15.73 ( (fun int (fun int int)), z3mod ) 15.47/15.73 ( (fun int (fun int int)), z3div ) 15.47/15.73 ( (fun int (fun int int)), int_gcd ) 15.47/15.73 ( (fun int (fun int int)), int_lcm ) 15.47/15.73 ( (fun int (fun int int)), inv ) 15.47/15.73 ( (fun complex complex), expi ) 15.47/15.73 ( (fun complex complex), cnj ) 15.47/15.73 ( (fun real complex), cis ) 15.47/15.73 ( (fun int nat), nat_1 ) 15.47/15.73 ( (fun int nat), phi ) 15.47/15.73 ( (fun (fun int bool) bool), nat_nat_set ) 15.47/15.73 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 15.47/15.73 ( (fun nat (fun nat nat)), nat_gcd ) 15.47/15.73 ( (fun nat (fun nat nat)), nat_lcm ) 15.47/15.73 ( (fun (fun int bool) int), (the int) ) 15.47/15.73 ( (fun complex real), re ) 15.47/15.73 ( (fun complex real), im ) 15.47/15.73 ( (fun complex real), arg ) 15.47/15.73 ( (fun bool bool), fNot ) 15.47/15.73 ( (fun nat (fun real real)), root ) 15.47/15.73 ( (fun real (fun real real)), log ) 15.47/15.73 ( (fun real (fun real real)), powr ) 15.47/15.73 ( (fun bool (fun bool bool)), fimplies ) 15.47/15.73 ( (fun bool (fun bool bool)), fconj ) 15.47/15.73 ( (fun bool (fun bool bool)), fdisj ) 15.47/15.73 ( (fun int (fun int (product_prod int int))), negDivAlg ) 15.47/15.73 ( (fun int (fun int (product_prod int int))), posDivAlg ) 15.47/15.73 ( (fun int (fun int (product_prod int int))), divmod_int ) 15.47/15.73 ( (fun int (fun int (product_prod int int))), pdivmod ) 15.47/15.73 ( (fun int (fun int (product_prod int int))), norm_frac ) 15.47/15.73 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 15.47/15.73 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 15.47/15.73 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 15.47/15.73 ( (fun int (fun int (fun int bool))), zcong ) 15.47/15.73 ( (fun int (fun int (fun int bool))), zcongm ) 15.47/15.73 ( (fun int (fun int (fun int bool))), noXRRset ) 15.47/15.73 ( (fun int (fun int (fun int bool))), bnorRset ) 15.47/15.73 ( (fun int (fun int (fun int bool))), wset ) 15.47/15.73 ( (fun (product_prod int int) bool), frac_1 ) 15.47/15.73 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 15.47/15.73 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 15.47/15.73 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 15.47/15.73 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 15.47/15.73 ( (fun (fun nat rat) bool), vanishes ) 15.47/15.73 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 15.47/15.73 ( (fun code_code_numeral nat), code_c271388182l_size ) 15.47/15.73 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 15.47/15.73 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 15.47/15.73 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 15.47/15.73 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 15.47/15.73 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 15.47/15.73 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 15.47/15.73 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 15.47/15.73 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 15.47/15.73 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 15.47/15.73 ( (fun complex nat), complex_size ) 15.47/15.73 ( (fun complex nat), (size_size complex) ) 15.47/15.73 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 15.47/15.73 ( (fun nat (fun nat (product_prod int int))), bezw ) 15.47/15.73 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 15.47/15.73 ( (fun int (fun nat nat)), nat_aux ) 15.47/15.73 ( (fun int (fun (fun int bool) bool)), rsetR ) 15.47/15.73 ( (fun int (fun (fun int bool) bool)), resSet ) 15.47/15.73 ( (fun int (list int)), quickc666637781d_zero ) 15.47/15.73 ( (fun (product_prod int int) rat), frct ) 15.47/15.73 ( (fun int (fun int rat)), fract ) 15.47/15.73 ( (fun real (fun real complex)), complex_1 ) 15.47/15.73 ( (fun real (fun real complex)), rcis ) 15.47/15.73 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 15.47/15.73 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 15.47/15.73 ( (fun int real), (real_1 int) ) 15.47/15.73 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 15.47/15.73 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 15.47/15.73 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 15.47/15.73 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 15.47/15.73 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 15.47/15.73 ( (fun real nat), natfloor ) 15.47/15.73 ( (fun real nat), natceiling ) 15.47/15.73 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 15.47/15.73 ( (fun quickcheck_code_int int), quickcheck_int_of ) 15.47/15.73 ( (fun rat (product_prod int int)), quotient_of ) 15.47/15.73 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 15.47/15.73 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 15.47/15.73 ( (fun rat real), ratreal ) 15.47/15.73 ( (fun code_code_numeral int), code_int_of ) 15.47/15.73 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 15.47/15.73 ( (fun int quickcheck_code_int), quickcheck_of_int ) 15.47/15.73 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 15.47/15.73 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 15.47/15.73 ) 15.47/15.73 (instantiation (forall ((N_1 $$unsorted)) (= (hAPP real int (archim2085082626_floor real) (hAPP nat real (real_1 nat) N_1)) (hAPP nat int (semiring_1_of_nat int) N_1)) ) 15.47/15.73 ( (zero_zero nat) ) 15.47/15.73 ( (hAPP nat nat suc (zero_zero nat)) ) 15.47/15.73 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.47/15.73 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.73 ) 15.47/15.73 (instantiation (forall ((X_c $$unsorted) (X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_117250 $$unsorted) (BOUND_VARIABLE_117251 $$unsorted) (BOUND_VARIABLE_117252 $$unsorted) (BOUND_VARIABLE_117253 $$unsorted) (BOUND_VARIABLE_117254 $$unsorted) (BOUND_VARIABLE_117255 $$unsorted)) (let ((_let_0 (filter X_b))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun X_b X_c))) (let ((_let_3 (filter X_a))) (let ((_let_4 (fun _let_3 bool))) (let ((_let_5 (fun X_a X_c))) (let ((_let_6 (fun X_a X_b))) (let ((_let_7 (hAPP X_a _let_3 (at X_a) BOUND_VARIABLE_117254))) (or (not (topological_space X_c)) (not (topological_space X_b)) (not (real_normed_vector X_a)) (not (hBOOL (hAPP _let_3 bool (hAPP X_b _let_4 (hAPP _let_6 (fun X_b _let_4) (tendsto X_a X_b) BOUND_VARIABLE_117252) BOUND_VARIABLE_117253) _let_7))) (not (hBOOL (hAPP _let_0 bool (hAPP X_c _let_1 (hAPP _let_2 (fun X_c _let_1) (tendsto X_b X_c) BOUND_VARIABLE_117250) BOUND_VARIABLE_117251) (hAPP X_b _let_0 (at X_b) BOUND_VARIABLE_117253)))) (hBOOL (hAPP _let_3 bool (hAPP X_c _let_4 (hAPP _let_5 (fun X_c _let_4) (tendsto X_a X_c) (hAPP _let_6 _let_5 (hAPP _let_2 (fun _let_6 _let_5) (combb X_b X_c X_a) BOUND_VARIABLE_117250) BOUND_VARIABLE_117252)) BOUND_VARIABLE_117251) _let_7)) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) BOUND_VARIABLE_117255))) (not (forall ((X $$unsorted)) (or (= (ti X_a X) (ti X_a BOUND_VARIABLE_117254)) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP X_a real (norm_norm X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) X) BOUND_VARIABLE_117254))) BOUND_VARIABLE_117255))) (not (= (ti X_b BOUND_VARIABLE_117253) (hAPP X_a X_b BOUND_VARIABLE_117252 X)))) ))))))))))) ) 15.47/15.73 ( real, real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.73 ) 15.47/15.73 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_117305 $$unsorted)) (let ((_let_0 (number_number_of X_a))) (or (not (number_ring X_a)) (= (hAPP int X_a _let_0 (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP int int bit1 pls)) BOUND_VARIABLE_117305)) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (one_one X_a)) (hAPP int X_a _let_0 BOUND_VARIABLE_117305))))) ) 15.47/15.73 ( nat, (hAPP int int bit1 pls) ) 15.47/15.73 ) 15.47/15.73 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (times_times X_a))) (or (not (semiring X_a)) (= _let_0 (ti (fun X_a (fun X_a X_a)) _let_0)))) ) 15.47/15.73 ( bool ) 15.47/15.73 ( nat ) 15.47/15.73 ( int ) 15.47/15.73 ( (fun int bool) ) 15.47/15.73 ( (fun int (fun int bool)) ) 15.47/15.73 ( (fun int int) ) 15.47/15.73 ( (fun nat bool) ) 15.47/15.73 ( real ) 15.47/15.73 ( (fun real bool) ) 15.47/15.73 ( (fun real real) ) 15.47/15.73 ( rat ) 15.47/15.73 ( complex ) 15.47/15.73 ( (fun nat real) ) 15.47/15.73 ( (product_prod int int) ) 15.47/15.73 ( quickcheck_code_int ) 15.47/15.73 ( code_code_numeral ) 15.47/15.73 ( (fun int (fun int (fun int bool))) ) 15.47/15.73 ( (fun (product_prod int int) bool) ) 15.47/15.73 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 15.47/15.73 ( (fun (product_prod int int) int) ) 15.47/15.73 ( (fun int real) ) 15.47/15.73 ) 15.47/15.73 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_117336 $$unsorted) (BOUND_VARIABLE_117337 $$unsorted) (BOUND_VARIABLE_117338 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (zero_zero X_a))) (let ((_let_3 (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_117337))) (let ((_let_4 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) _let_2) _let_3)))) (let ((_let_5 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_117338) _let_3))) (let ((_let_6 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) _let_3) _let_2)))) (or (not (number X_a)) (not (linord1117847801e_zero X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_117336) _let_3)) BOUND_VARIABLE_117338)) (and (or (not _let_4) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_117336) _let_5))) (or _let_4 (and (or _let_6 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_117338))) (or (not _let_6) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_5) BOUND_VARIABLE_117336))))))))))))))) ) 15.47/15.73 ( real, pi, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.73 ) 15.47/15.73 (instantiation (forall ((I_1 $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (list int))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) I_1))) (= (hAPP _let_1 nat (size_size _let_1) (hAPP int _let_1 quickc666637781d_zero I_1)) (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) (hAPP nat nat (hAPP nat _let_0 (times_times nat) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int nat nat_1 I_1))) (one_one nat)))))) ) 15.47/15.73 ( (one_one int) ) 15.47/15.73 ( (zero_zero int) ) 15.47/15.73 ( min_1 ) 15.47/15.73 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.73 ( s ) 15.47/15.73 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.47/15.73 ( (hAPP int int (number_number_of int) pls) ) 15.47/15.73 ( skv_4 ) 15.47/15.73 ( skv_10 ) 15.47/15.73 ) 15.47/15.73 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (uminus_uminus real) _let_2)) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) _let_2))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) (hAPP real real cos X_1))))))) ) 15.47/15.73 ( (one_one real) ) 15.47/15.73 ( (zero_zero real) ) 15.47/15.73 ( pi ) 15.47/15.73 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.73 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.73 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.47/15.73 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.47/15.73 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.47/15.73 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.47/15.73 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.73 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 15.47/15.73 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.47/15.73 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.47/15.73 ( skv_5 ) 15.47/15.73 ) 15.47/15.73 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_117405 $$unsorted) (BOUND_VARIABLE_117406 $$unsorted)) (let ((_let_0 (fun (filter nat) bool))) (or (not (metric_space X_a)) (not (forall ((R_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) R_2))) (not (forall ((No $$unsorted)) (not (forall ((N_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) No) N_2))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP X_a real (hAPP X_a (fun X_a real) (dist_dist X_a) (hAPP nat X_a BOUND_VARIABLE_117405 N_2)) BOUND_VARIABLE_117406)) R_2))) )) ))) )) (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_0 (hAPP (fun nat X_a) (fun X_a _let_0) (tendsto nat X_a) BOUND_VARIABLE_117405) BOUND_VARIABLE_117406) sequentially)))) ) 15.47/15.73 ( real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real) ) 15.47/15.73 ) 15.47/15.73 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_117446 $$unsorted)) (or (not (ab_group_add X_a)) (= (zero_zero X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_117446)) BOUND_VARIABLE_117446))) ) 15.47/15.73 ( int, (one_one int) ) 15.47/15.73 ( int, pls ) 15.47/15.73 ( int, min_1 ) 15.47/15.73 ( real, (one_one real) ) 15.47/15.73 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.47/15.73 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.47/15.73 ( complex, (one_one complex) ) 15.47/15.73 ( complex, ii ) 15.47/15.73 ) 15.47/15.73 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_117566 $$unsorted) (BOUND_VARIABLE_117567 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (or (not (order X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_117566) BOUND_VARIABLE_117567))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_117567) BOUND_VARIABLE_117566)))))) ) 15.47/15.73 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.47/15.73 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 15.47/15.73 ( int, (one_one int), pls ) 15.47/15.73 ( int, (one_one int), t ) 15.47/15.73 ( int, pls, (one_one int) ) 15.47/15.73 ( int, pls, pls ) 15.47/15.73 ( int, pls, min_1 ) 15.47/15.73 ( int, pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.73 ( int, min_1, pls ) 15.47/15.73 ( int, min_1, min_1 ) 15.47/15.73 ( int, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.47/15.73 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), pls ) 15.47/15.73 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s ) 15.47/15.73 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.56/15.73 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_4 ) 15.56/15.73 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_10 ) 15.56/15.73 ( int, t, (one_one int) ) 15.56/15.73 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.56/15.73 ( int, skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.56/15.73 ( int, skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.56/15.73 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.73 ( real, (zero_zero real), pi ) 15.56/15.73 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.73 ( real, (zero_zero real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.56/15.73 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.73 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.73 ( real, (zero_zero real), skv_2 ) 15.56/15.73 ( real, (zero_zero real), skv_8 ) 15.56/15.73 ( real, (zero_zero real), skv_9 ) 15.56/15.73 ( real, pi, (zero_zero real) ) 15.56/15.73 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.73 ( real, pi, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 15.56/15.73 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.73 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.56/15.73 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.73 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 15.56/15.73 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 15.56/15.73 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 15.56/15.73 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.56/15.73 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.56/15.73 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 15.56/15.73 ( real, skv_2, (zero_zero real) ) 15.56/15.73 ( real, skv_8, (zero_zero real) ) 15.56/15.73 ( real, skv_9, (zero_zero real) ) 15.56/15.73 ) 15.56/15.73 (instantiation (forall ((N_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (hAPP int real (real_1 int) N_1))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 _let_2) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) (hAPP real real (hAPP real (fun real real) (plus_plus real) _let_2) (one_one real))))) (= (ti int N_1) (hAPP real int (archim2085082626_floor real) X_1)))))) ) 15.56/15.73 ( (one_one int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.73 ( (zero_zero int), pi ) 15.56/15.73 ( (zero_zero int), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.73 ( (zero_zero int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.73 ( (zero_zero int), skv_2 ) 15.56/15.73 ( (zero_zero int), skv_8 ) 15.56/15.73 ( (zero_zero int), skv_9 ) 15.56/15.73 ) 15.56/15.73 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_117620 $$unsorted) (BOUND_VARIABLE_117621 $$unsorted) (BOUND_VARIABLE_117622 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (or (not (semiring_div X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_117622)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_117622) BOUND_VARIABLE_117621))) (= (= (ti X_a BOUND_VARIABLE_117621) (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_117620) BOUND_VARIABLE_117622)) (= (hAPP X_a X_a (hAPP X_a _let_0 (div_div X_a) BOUND_VARIABLE_117621) BOUND_VARIABLE_117622) (ti X_a BOUND_VARIABLE_117620))))) ) 15.56/15.73 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.56/15.73 ) 15.56/15.73 (instantiation (forall ((N_1 $$unsorted) (M $$unsorted)) (let ((_let_0 (hAPP nat (fun nat bool) (ord_less nat) N_1))) (or (hBOOL (hAPP nat bool _let_0 M)) (not (hBOOL (hAPP nat bool _let_0 (hAPP nat nat suc M)))) (= N_1 M))) ) 15.56/15.73 ( (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 15.56/15.73 ) 15.56/15.73 (instantiation (forall ((L $$unsorted) (U_1 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (ord_atLeastLessThan int))) (= (hAPP int _let_0 (hAPP int _let_1 _let_4 L) U_1) (hAPP _let_0 _let_0 (hAPP _let_2 (fun _let_0 _let_0) (image int int) (hAPP int _let_2 (hAPP _let_3 _let_3 (combc int int int) (plus_plus int)) L)) (hAPP int _let_0 (hAPP int _let_1 _let_4 (zero_zero int)) (hAPP int int (hAPP int _let_2 (minus_minus int) U_1) L))))))))) ) 15.56/15.73 ( (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.73 ) 15.56/15.73 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_117659 $$unsorted) (BOUND_VARIABLE_117660 $$unsorted) (BOUND_VARIABLE_117661 $$unsorted) (BOUND_VARIABLE_117662 $$unsorted) (BOUND_VARIABLE_117663 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (plus_plus X_a))) (let ((_let_2 (times_times X_a))) (or (not (ring X_a)) (= (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_117659) BOUND_VARIABLE_117660)) BOUND_VARIABLE_117661) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_117662) BOUND_VARIABLE_117660)) BOUND_VARIABLE_117663)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_0 _let_2 (hAPP X_a X_a (hAPP X_a _let_0 (minus_minus X_a) BOUND_VARIABLE_117659) BOUND_VARIABLE_117662)) BOUND_VARIABLE_117660)) BOUND_VARIABLE_117661) (ti X_a BOUND_VARIABLE_117663))))))) ) 15.56/15.73 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m, (one_one int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 15.56/15.73 ) 15.56/15.73 (instantiation (forall ((R_4 $$unsorted)) (or (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) R_4) (zero_zero real))) (= R_4 (hAPP real real (abs_abs real) R_4))) ) 15.56/15.73 ( (one_one real) ) 15.56/15.73 ( (zero_zero real) ) 15.56/15.73 ( pi ) 15.56/15.73 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.73 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.56/15.73 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.73 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 15.56/15.73 ) 15.56/15.73 (instantiation (forall ((R_4 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) R_4) (zero_zero real)))) (= (hAPP real real (abs_abs real) R_4) (hAPP real real (uminus_uminus real) R_4))) ) 15.56/15.73 ( (one_one real) ) 15.56/15.73 ( (zero_zero real) ) 15.56/15.73 ( pi ) 15.56/15.73 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.73 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.56/15.73 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.56/15.73 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.73 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 15.56/15.73 ) 15.56/15.73 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (fun nat bool))) (= (hAPP nat _let_0 (ord_less_eq nat) (hAPP nat nat suc X)) (hAPP nat _let_0 (ord_less nat) X))) ) 15.56/15.73 ( (zero_zero nat) ) 15.56/15.73 ( (hAPP nat nat suc (zero_zero nat)) ) 15.56/15.73 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 15.56/15.73 ) 15.56/15.73 (instantiation (forall ((A_1 $$unsorted)) (= (hAPP int int (hAPP int (fun int int) (div_div int) A_1) (hAPP int int (number_number_of int) min_1)) (hAPP int int (uminus_uminus int) A_1)) ) 15.56/15.73 ( (one_one int) ) 15.56/15.73 ( pls ) 15.56/15.73 ( min_1 ) 15.56/15.73 ) 15.56/15.73 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_117816 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (one_one X_a))) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) (zero_zero X_a)) BOUND_VARIABLE_117816))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_117816) _let_2))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_117816))))))) ) 15.56/15.73 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.73 ( int, (one_one int) ) 15.56/15.73 ( int, (zero_zero int) ) 15.56/15.73 ( int, pls ) 15.56/15.73 ( int, min_1 ) 15.56/15.73 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.56/15.73 ( real, (zero_zero real) ) 15.56/15.73 ( real, pi ) 15.56/15.73 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.73 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.73 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.73 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.73 ( real, skv_2 ) 15.56/15.73 ( real, skv_5 ) 15.56/15.73 ( real, skv_8 ) 15.56/15.73 ( real, skv_9 ) 15.56/15.73 ( complex, ii ) 15.56/15.73 ) 15.56/15.73 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real real))) (= (hAPP real real cos (hAPP real real (hAPP real _let_0 (plus_plus real) X_1) (hAPP real real (hAPP real _let_0 (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real real (uminus_uminus real) (hAPP real real sin X_1)))) ) 15.56/15.73 ( (zero_zero real) ) 15.56/15.73 ( pi ) 15.56/15.73 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.73 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.56/15.73 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.56/15.73 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.56/15.73 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.56/15.73 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.56/15.73 ) 15.56/15.73 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_117859 $$unsorted)) (let ((_let_0 (fun nat X_a))) (or (not (banach X_a)) (not (real_n2089651433ebra_1 X_a)) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP X_a real (norm_norm X_a) BOUND_VARIABLE_117859)) (one_one real)))) (hBOOL (hAPP _let_0 bool (summable X_a) (hAPP X_a _let_0 (power_power X_a) BOUND_VARIABLE_117859))))) ) 15.56/15.73 ( int, s ) 15.56/15.73 ( int, s1 ) 15.56/15.73 ( int, skv_14 ) 15.56/15.73 ( real, (hAPP int real (number_number_of real) min_1) ) 15.56/15.73 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.73 ( complex, ii ) 15.56/15.73 ) 15.56/15.73 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_117900 $$unsorted) (BOUND_VARIABLE_117901 $$unsorted)) (let ((_let_0 (number_number_of X_a))) (or (not (number_ring X_a)) (not (linordered_idom X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (hAPP int X_a _let_0 BOUND_VARIABLE_117900)) (hAPP int X_a _let_0 BOUND_VARIABLE_117901))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) BOUND_VARIABLE_117900) BOUND_VARIABLE_117901))))) ) 15.56/15.73 ( int, pls, pls ) 15.56/15.73 ( int, pls, (hAPP int int bit1 pls) ) 15.56/15.73 ( int, pls, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.56/15.73 ( int, pls, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.56/15.73 ) 15.56/15.73 (instantiation (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (minus_minus nat))) (let ((_let_3 (power_power nat))) (= (hAPP nat nat (hAPP nat _let_0 (times_times nat) (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) X_1) Y_1)) (hAPP nat nat (hAPP nat _let_0 _let_2 X_1) Y_1)) (hAPP nat nat (hAPP nat _let_0 _let_2 (hAPP nat nat (hAPP nat _let_0 _let_3 X_1) _let_1)) (hAPP nat nat (hAPP nat _let_0 _let_3 Y_1) _let_1))))))) ) 15.56/15.73 ( (one_one nat), (one_one nat) ) 15.56/15.73 ) 15.56/15.73 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_117968 $$unsorted)) (let ((_let_0 (number_number_of X_a))) (or (not (number_ring X_a)) (= (hAPP int X_a _let_0 (hAPP int int succ BOUND_VARIABLE_117968)) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (one_one X_a)) (hAPP int X_a _let_0 BOUND_VARIABLE_117968))))) ) 15.56/15.73 ( nat, pls ) 15.56/15.73 ( nat, (hAPP int int bit1 pls) ) 15.56/15.73 ( nat, min_1 ) 15.56/15.73 ( int, pls ) 15.56/15.73 ( int, min_1 ) 15.56/15.73 ( quickcheck_code_int, pls ) 15.56/15.73 ( quickcheck_code_int, min_1 ) 15.56/15.73 ( code_code_numeral, pls ) 15.56/15.73 ( code_code_numeral, min_1 ) 15.56/15.73 ) 15.56/15.73 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_118024 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (or (not (ordered_ab_group_add X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_118024))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_118024) _let_2))))))) ) 15.56/15.73 ( nat, (zero_zero nat) ) 15.56/15.73 ( int, (one_one int) ) 15.56/15.73 ( int, pls ) 15.56/15.73 ( int, min_1 ) 15.56/15.73 ( int, s ) 15.56/15.73 ( int, t ) 15.56/15.73 ( int, skv_4 ) 15.56/15.73 ( int, skv_10 ) 15.56/15.73 ( real, (one_one real) ) 15.56/15.73 ( real, (zero_zero real) ) 15.56/15.73 ( real, pi ) 15.56/15.73 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.73 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.56/15.73 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.56/15.73 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.73 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 15.56/15.73 ( complex, (one_one complex) ) 15.56/15.73 ( complex, ii ) 15.56/15.73 ) 15.56/15.73 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) X_1))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (hAPP real (fun real real) (plus_plus real) (one_one real)) X_1)) (hAPP real real (exp real) X_1)))))) ) 15.56/15.73 ( pi ) 15.56/15.73 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.73 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.73 ( skv_3 ) 15.56/15.73 ( skv_5 ) 15.56/15.73 ( skv_7 ) 15.56/15.73 ( skv_12 ) 15.56/15.73 ) 15.56/15.73 (instantiation (forall ((X_2 $$unsorted) (F $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) A_2) B_1))) (not (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 A_2) X))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X) B_1))) (hBOOL (hAPP real bool (hAPP (fun real real) _let_0 (isCont real real) F) X))) )) (not (forall ((X $$unsorted)) (let ((_let_1 (ord_less real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X) B_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 A_2) X))) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP (fun real real) (fun real _let_0) (deriv real) F) X) (zero_zero real))))) )) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 A_2) X_2))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_2) B_1))) (= (hAPP real real F X_2) (hAPP real real F A_2))))) ) 15.56/15.73 ( (zero_zero real), sqrt, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.73 ( (zero_zero real), (inverse_inverse real), (zero_zero real), skv_9 ) 15.56/15.73 ( pi, cos, pi, (zero_zero real) ) 15.56/15.73 ( pi, cos, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 15.56/15.73 ( pi, sin, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.73 ( pi, tan, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 15.56/15.73 ( pi, (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.56/15.73 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real (fun real real) (inverse_divide real) pi), pi, (zero_zero real) ) 15.56/15.73 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real (fun real real) (inverse_divide real) (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))))), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.73 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), cos, (zero_zero real), pi ) 15.56/15.73 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), cos, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.73 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi), sin, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.73 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), sqrt, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.73 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP real (fun real real) (inverse_divide real) pi), (zero_zero real), skv_2 ) 15.56/15.73 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), cos, (zero_zero real), skv_9 ) 15.56/15.73 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), sin, (zero_zero real), skv_8 ) 15.56/15.73 ) 15.56/15.73 (instantiation (forall ((M $$unsorted) (X_1 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (let ((_let_2 (ord_less int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 _let_1) X_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 X_1) M))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong X_1) _let_1) M))))))) ) 15.56/15.73 ( (one_one int), pls ) 15.56/15.73 ( pls, pls ) 15.56/15.73 ( pls, min_1 ) 15.56/15.73 ( min_1, pls ) 15.56/15.73 ( min_1, min_1 ) 15.56/15.73 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), pls ) 15.56/15.73 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s ) 15.56/15.73 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.56/15.73 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_4 ) 15.56/15.73 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_10 ) 15.56/15.73 ( t, (one_one int) ) 15.56/15.73 ) 15.56/15.73 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (power_power real))) (let ((_let_3 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_4 (hAPP complex real im X_1))) (= (hAPP complex real im (hAPP complex complex (inverse_inverse complex) X_1)) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP real real (uminus_uminus real) _let_4)) (hAPP real real (hAPP real _let_0 (plus_plus real) (hAPP nat real (hAPP real _let_1 _let_2 (hAPP complex real re X_1)) _let_3)) (hAPP nat real (hAPP real _let_1 _let_2 _let_4) _let_3))))))))) ) 15.56/15.73 ( (one_one complex) ) 15.56/15.73 ( ii ) 15.56/15.73 ( (zero_zero complex) ) 15.56/15.73 ) 15.56/15.73 (instantiation (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (hAPP nat (fun real real) root N_1))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) Y_1))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real _let_2 X_1)) (hAPP real real _let_2 Y_1))))))) ) 15.56/15.73 ( (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.73 ( (zero_zero real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.73 ) 15.56/15.73 (instantiation (forall ((N $$unsorted)) (let ((_let_0 (fun real real))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N))) (hBOOL (hAPP real bool (hAPP _let_0 (fun real bool) (isCont real real) (hAPP nat _let_0 root N)) (zero_zero real))))) ) 15.56/15.73 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.73 ) 15.56/15.73 (instantiation (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) X_1))) (not (forall ((N_2 $$unsorted)) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP real real (inverse_inverse real) (hAPP nat real (real_1 nat) (hAPP nat nat suc N_2)))) X_1))) ))) ) 15.56/15.73 ( pi ) 15.56/15.73 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.73 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.73 ( skv_2 ) 15.56/15.73 ( skv_8 ) 15.56/15.73 ( skv_9 ) 15.56/15.73 ) 15.56/15.73 (instantiation (forall ((N_4 $$unsorted)) (= (not (forall ((M_2 $$unsorted)) (not (forall ((X $$unsorted)) (let ((_let_0 (fun nat bool))) (or (not (hBOOL (hAPP _let_0 bool (hAPP nat (fun _let_0 bool) (member nat) X) N_4))) (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) X) M_2)))) )) )) (hBOOL (hAPP (fun nat bool) bool (finite_finite_1 nat) N_4))) ) 15.56/15.73 ( (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 15.56/15.73 ) 15.56/15.73 (instantiation (forall ((M $$unsorted)) (= M (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) M) (zero_zero nat))) ) 15.56/15.73 ( (one_one nat) ) 15.56/15.73 ) 15.56/15.73 (instantiation (forall ((V_1 $$unsorted)) (let ((_let_0 (hAPP int nat (number_number_of nat) V_1))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) _let_0))) (= _let_0 (hAPP nat nat suc (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) _let_0) (one_one nat)))))) ) 15.56/15.73 ( pls ) 15.56/15.73 ( (hAPP int int bit1 pls) ) 15.56/15.73 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.56/15.73 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.56/15.73 ) 15.56/15.73 (instantiation (forall ((X_a $$unsorted)) (or (not (number_semiring X_a)) (= (zero_zero X_a) (hAPP int X_a (number_number_of X_a) pls))) ) 15.56/15.73 ( nat ) 15.56/15.73 ( int ) 15.56/15.73 ( real ) 15.56/15.73 ( rat ) 15.56/15.73 ( complex ) 15.56/15.73 ( quickcheck_code_int ) 15.56/15.73 ( code_code_numeral ) 15.56/15.73 ) 15.56/15.73 (instantiation (forall ((X_a $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (one_one int) (hAPP X_a int (archimedean_ceiling X_a) (one_one X_a)))) ) 15.56/15.73 ( nat ) 15.56/15.73 ( int ) 15.56/15.73 ( real ) 15.56/15.73 ( rat ) 15.56/15.73 ( complex ) 15.56/15.73 ( quickcheck_code_int ) 15.56/15.73 ( code_code_numeral ) 15.56/15.73 ) 15.56/15.73 (instantiation (forall ((X_2 $$unsorted)) (= (= (zero_zero real) (hAPP real real sin X_2)) (or (not (forall ((N_2 $$unsorted)) (let ((_let_0 (fun real real))) (or (not (= X_2 (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP nat real (real_1 nat) N_2)) (hAPP real real (hAPP real _let_0 (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) (not (hBOOL (hAPP nat bool (even_odd_even nat) N_2))))) )) (not (forall ((N_2 $$unsorted)) (let ((_let_0 (fun real real))) (or (not (hBOOL (hAPP nat bool (even_odd_even nat) N_2))) (not (= X_2 (hAPP real real (hAPP real _let_0 (times_times real) (hAPP nat real (real_1 nat) N_2)) (hAPP real real (hAPP real _let_0 (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))))) )))) ) 15.56/15.73 ( (zero_zero real) ) 15.56/15.73 ( pi ) 15.56/15.73 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.73 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.56/15.73 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.56/15.73 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.56/15.73 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.56/15.73 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.56/15.73 ) 15.56/15.73 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (uminus_uminus real))) (let ((_let_2 (fun nat real))) (let ((_let_3 (fun nat _let_0))) (let ((_let_4 (fun _let_2 _let_2))) (= (hAPP _let_2 real (suminf real) (hAPP _let_2 _let_2 (hAPP _let_0 _let_4 (combb real real nat) _let_1) (hAPP _let_2 _let_2 (hAPP _let_3 _let_4 (combs nat real real) (hAPP _let_2 _let_3 (hAPP (fun real _let_0) (fun _let_2 _let_3) (combb real _let_0 nat) (times_times real)) sin_coeff)) (hAPP real _let_2 (power_power real) X_2)))) (hAPP real real _let_1 (hAPP real real sin X_2)))))))) ) 15.56/15.73 ( (zero_zero real) ) 15.56/15.73 ( pi ) 15.56/15.73 ( (hAPP int real (number_number_of real) min_1) ) 15.56/15.73 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.73 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.73 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.56/15.73 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.56/15.74 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.56/15.74 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.56/15.74 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.56/15.74 ) 15.56/15.74 (instantiation (forall ((Z_1 $$unsorted)) (= (ti int Z_1) (hAPP int int (hAPP int (fun int int) (plus_plus int) (zero_zero int)) Z_1)) ) 15.56/15.74 ( pls ) 15.56/15.74 ( min_1 ) 15.56/15.74 ( s ) 15.56/15.74 ( m ) 15.56/15.74 ( s1 ) 15.56/15.74 ( t ) 15.56/15.74 ) 15.56/15.74 (instantiation (forall ((N_1 $$unsorted)) (= (hAPP real int (archim2085082626_floor real) (hAPP int real (real_1 int) N_1)) (ti int N_1)) ) 15.56/15.74 ( (one_one int) ) 15.56/15.74 ( (zero_zero int) ) 15.56/15.74 ( pls ) 15.56/15.74 ( min_1 ) 15.56/15.74 ( s ) 15.56/15.74 ( m ) 15.56/15.74 ( s1 ) 15.56/15.74 ( t ) 15.56/15.74 ) 15.56/15.74 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (fun (filter nat) bool))) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (one_one real)) X_2))) (hBOOL (hAPP (filter nat) bool (hAPP real _let_1 (hAPP _let_0 (fun real _let_1) (tendsto nat real) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)) (hAPP real _let_0 (power_power real) X_2))) (zero_zero real)) sequentially))))) ) 15.56/15.74 ( (hAPP int real (number_number_of real) min_1) ) 15.56/15.74 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.74 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.74 ) 15.56/15.74 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_118372 $$unsorted)) (or (not (linordered_semidom X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)) (hAPP nat X_a (semiring_1_of_nat X_a) BOUND_VARIABLE_118372)))) ) 15.56/15.74 ( int, (zero_zero nat) ) 15.56/15.74 ( int, (hAPP nat nat suc (zero_zero nat)) ) 15.56/15.74 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.56/15.74 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.74 ( real, (zero_zero nat) ) 15.56/15.74 ( real, (hAPP nat nat suc (zero_zero nat)) ) 15.56/15.74 ) 15.56/15.74 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (gcd_gcd int))) (= (hAPP int int (hAPP int _let_0 _let_1 M) N_1) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) M) N_1)) N_1)))) ) 15.56/15.74 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 15.56/15.74 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 15.56/15.74 ) 15.56/15.74 (instantiation (forall ((X_1 $$unsorted)) (= (hAPP int real (ring_1_of_int real) X_1) (hAPP int real (number_number_of real) X_1)) ) 15.56/15.74 ( (one_one int) ) 15.56/15.74 ( (zero_zero int) ) 15.56/15.74 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.56/15.74 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.56/15.74 ( min_1 ) 15.56/15.74 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.74 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.56/15.74 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.74 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 15.56/15.74 ) 15.56/15.74 (instantiation (forall ((V_1 $$unsorted)) (= (hAPP int real (number_number_of real) V_1) (hAPP int real (real_1 int) (hAPP int int (number_number_of int) V_1))) ) 15.56/15.74 ( pls ) 15.56/15.74 ( (hAPP int int bit1 pls) ) 15.56/15.74 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.56/15.74 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.56/15.74 ( min_1 ) 15.56/15.74 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.74 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.56/15.74 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.74 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 15.56/15.74 ) 15.56/15.74 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_118428 $$unsorted) (BOUND_VARIABLE_118429 $$unsorted)) (let ((_let_0 (uminus_uminus X_a))) (let ((_let_1 (hAPP X_a (fun X_a X_a) (div_div X_a) BOUND_VARIABLE_118429))) (or (not (ring_div X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_118428) BOUND_VARIABLE_118429))) (= (hAPP X_a X_a _let_1 (hAPP X_a X_a _let_0 BOUND_VARIABLE_118428)) (hAPP X_a X_a _let_0 (hAPP X_a X_a _let_1 BOUND_VARIABLE_118428)))))) ) 15.56/15.74 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 15.56/15.74 ) 15.56/15.74 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))))) (let ((_let_1 (fun nat nat))) (let ((_let_2 (div_div nat))) (or (hBOOL (hAPP nat bool (even_odd_even nat) X_1)) (= (hAPP nat nat (hAPP nat _let_1 _let_2 (hAPP nat nat suc X_1)) _let_0) (hAPP nat nat suc (hAPP nat nat (hAPP nat _let_1 _let_2 X_1) _let_0))))))) ) 15.56/15.74 ( (zero_zero nat) ) 15.56/15.74 ( (one_one nat) ) 15.56/15.74 ) 15.56/15.74 (instantiation (forall ((X_a $$unsorted)) (or (not (ring_1 X_a)) (= (one_one X_a) (hAPP int X_a (ring_1_of_int X_a) (one_one int)))) ) 15.56/15.74 ( nat ) 15.56/15.74 ( int ) 15.56/15.74 ( real ) 15.56/15.74 ( rat ) 15.56/15.74 ( complex ) 15.56/15.74 ( quickcheck_code_int ) 15.56/15.74 ( code_code_numeral ) 15.56/15.74 ) 15.56/15.74 (instantiation (forall ((K $$unsorted)) (let ((_let_0 (fun nat bool))) (= (hAPP nat _let_0 (ord_atMost nat) K) (hAPP nat _let_0 (ord_lessThan nat) (hAPP nat nat suc K)))) ) 15.56/15.74 ( (zero_zero nat) ) 15.56/15.74 ( (hAPP nat nat suc (zero_zero nat)) ) 15.56/15.74 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 15.56/15.74 ) 15.56/15.74 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_118628 $$unsorted) (BOUND_VARIABLE_118629 $$unsorted)) (let ((_let_0 (filter X_a))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun X_a X_a))) (let ((_let_3 (fun X_a _let_2))) (let ((_let_4 (times_times X_a))) (or (not (real_normed_algebra X_a)) (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 (hAPP _let_2 (fun X_a _let_1) (tendsto X_a X_a) (hAPP X_a _let_2 (hAPP _let_3 _let_3 (combc X_a X_a X_a) _let_4) BOUND_VARIABLE_118628)) (hAPP X_a X_a (hAPP X_a _let_2 _let_4 BOUND_VARIABLE_118629) BOUND_VARIABLE_118628)) (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_118629))))))))) ) 15.56/15.74 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.74 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.56/15.74 ( int, skv_13, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.56/15.74 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.74 ( real, pi, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 15.56/15.74 ( real, (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.74 ( real, (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.74 ( complex, ii, ii ) 15.56/15.74 ( complex, ii, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 15.56/15.74 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.74 ) 15.56/15.74 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_118651 $$unsorted) (BOUND_VARIABLE_118652 $$unsorted)) (let ((_let_0 (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))))) (let ((_let_1 (fun nat X_a))) (let ((_let_2 (power_power X_a))) (let ((_let_3 (ti X_a BOUND_VARIABLE_118651))) (or (not (idom X_a)) (= (= (hAPP nat X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_118651) _let_0) (hAPP nat X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_118652) _let_0)) (or (= (ti X_a BOUND_VARIABLE_118652) _let_3) (= _let_3 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_118652))))))))) ) 15.56/15.74 ( int, s, s ) 15.56/15.74 ( int, s, s1 ) 15.56/15.74 ( int, s1, s ) 15.56/15.74 ( int, skv_14, skv_14 ) 15.56/15.74 ( real, (hAPP int real (number_number_of real) min_1), (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.74 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) min_1) ) 15.56/15.74 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.74 ( complex, ii, ii ) 15.56/15.74 ) 15.56/15.74 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (the X_a))) (or (not (topological_space X_a)) (not (comm_monoid_add X_a)) (= _let_0 (ti (fun (fun X_a bool) X_a) _let_0)))) ) 15.56/15.74 ( bool ) 15.56/15.74 ( nat ) 15.56/15.74 ( int ) 15.56/15.74 ( (fun int bool) ) 15.56/15.74 ( (fun nat bool) ) 15.56/15.74 ( (product_prod nat nat) ) 15.56/15.74 ( real ) 15.56/15.74 ( rat ) 15.56/15.74 ( complex ) 15.56/15.74 ( (filter nat) ) 15.56/15.74 ( (product_prod int int) ) 15.56/15.74 ( quickcheck_code_int ) 15.56/15.74 ( code_code_numeral ) 15.56/15.74 ( (product_prod real real) ) 15.56/15.74 ( (fun nat rat) ) 15.56/15.74 ( (filter real) ) 15.56/15.74 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 15.56/15.74 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 15.56/15.74 ) 15.56/15.74 (instantiation (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) X_1))) (= (hAPP int real (real_1 int) X_1) (hAPP nat real (real_1 nat) (hAPP int nat nat_1 X_1)))) ) 15.56/15.74 ( (one_one int) ) 15.56/15.74 ( (zero_zero int) ) 15.56/15.74 ( min_1 ) 15.56/15.74 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.74 ( s ) 15.56/15.74 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.56/15.74 ( (hAPP int int (number_number_of int) pls) ) 15.56/15.74 ( skv_4 ) 15.56/15.74 ( skv_10 ) 15.56/15.74 ) 15.56/15.74 (instantiation (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member int))) (or (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP int int (hAPP int (fun int int) (plus_plus int) A_2) B_1)) zOdd))) (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 A_2) zOdd))) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 B_1) zEven)))))) ) 15.56/15.74 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 15.56/15.74 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 15.56/15.74 ) 15.56/15.74 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (= (= X_2 Y_2) (= (hAPP real real sqrt Y_2) (hAPP real real sqrt X_2))) ) 15.56/15.74 ( (one_one real), (one_one real) ) 15.56/15.74 ( (zero_zero real), (zero_zero real) ) 15.56/15.74 ( (zero_zero real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.74 ( (zero_zero real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.56/15.74 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.56/15.74 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero real) ) 15.56/15.74 ) 15.56/15.74 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_118831 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (hAPP int X_a (number_number_of X_a) (hAPP int int bit0 (hAPP int int bit1 pls)))) BOUND_VARIABLE_118831)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (one_one int)) (hAPP X_a int (archim2085082626_floor X_a) BOUND_VARIABLE_118831))))) ) 15.56/15.74 ( real, pi ) 15.56/15.74 ) 15.56/15.74 (instantiation (forall ((Ta $$unsorted) (B_2 $$unsorted) (D_2 $$unsorted) (BOUND_VARIABLE_118925 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ti int Ta))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (zero_zero int)) D_2))) (not (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) Ta) B_2))) (not (forall ((Xa $$unsorted) (BOUND_VARIABLE_118891 $$unsorted)) (let ((_let_1 (member int))) (let ((_let_2 (fun _let_0 bool))) (or (not (hBOOL (hAPP _let_0 bool (hAPP int _let_2 _let_1 Xa) (hAPP int _let_0 (hAPP int (fun int _let_0) (ord_atLeastAtMost int) (one_one int)) D_2)))) (not (hBOOL (hAPP _let_0 bool (hAPP int _let_2 _let_1 BOUND_VARIABLE_118891) B_2))) (not (= (hAPP int int (hAPP int (fun int int) (plus_plus int) BOUND_VARIABLE_118891) Xa) (ti int BOUND_VARIABLE_118925)))))) )) (= _let_1 (ti int BOUND_VARIABLE_118925)) (not (= _let_1 (hAPP int int (hAPP int (fun int int) (minus_minus int) BOUND_VARIABLE_118925) D_2)))))) ) 15.56/15.74 ( (one_one int), zEven, pls, s ) 15.56/15.74 ) 15.56/15.74 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_119002 $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat X_a))) (let ((_let_3 (fun X_a X_a))) (let ((_let_4 (fun nat _let_3))) (or (not (real_n2089651433ebra_1 X_a)) (not (banach X_a)) (hBOOL (hAPP _let_2 bool (summable X_a) (hAPP _let_2 _let_2 (hAPP _let_4 (fun _let_2 _let_2) (combs nat X_a X_a) (hAPP _let_1 _let_4 (hAPP (fun real _let_3) (fun _let_1 _let_4) (combb real _let_3 nat) (scaleR_scaleR X_a)) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) (fact_fact nat))))) (hAPP X_a _let_2 (power_power X_a) BOUND_VARIABLE_119002)))))))))) ) 15.56/15.74 ( int, s ) 15.56/15.74 ( int, s1 ) 15.56/15.74 ( int, skv_14 ) 15.56/15.74 ( real, (hAPP int real (number_number_of real) min_1) ) 15.56/15.74 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.74 ( complex, ii ) 15.56/15.74 ) 15.56/15.74 (instantiation (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_0 (real_1 int))) (= (hAPP int real _let_0 (hAPP nat int (hAPP int (fun nat int) (power_power int) X_1) N_1)) (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP int real _let_0 X_1)) N_1))) ) 15.56/15.74 ( s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.74 ( s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.74 ( skv_14, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.74 ) 15.56/15.74 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_119061 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) (hAPP X_a int (archim2085082626_floor X_a) BOUND_VARIABLE_119061))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)) BOUND_VARIABLE_119061)))) ) 15.56/15.74 ( int, (one_one int) ) 15.56/15.74 ( int, min_1 ) 15.56/15.74 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.74 ( int, s ) 15.56/15.74 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.56/15.74 ( int, (hAPP int int (number_number_of int) pls) ) 15.56/15.74 ( int, skv_4 ) 15.56/15.74 ( int, skv_10 ) 15.56/15.74 ( real, pi ) 15.56/15.74 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.74 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.74 ( real, skv_3 ) 15.56/15.74 ( real, skv_5 ) 15.56/15.74 ( real, skv_7 ) 15.56/15.74 ( real, skv_12 ) 15.56/15.74 ) 15.56/15.74 (instantiation (forall ((X_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less nat))) (or (not (hBOOL (hAPP nat bool prime P_5))) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 (zero_zero nat)) X_1))) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 X_1) P_5))) (hBOOL (hAPP nat bool (hAPP nat _let_0 coprime X_1) P_5))))) ) 15.56/15.74 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.74 ) 15.56/15.74 (instantiation (forall ((X_a $$unsorted) (P_1 $$unsorted)) (let ((_let_0 (fun X_a bool))) (= (hAPP _let_0 _let_0 (collect X_a) P_1) (ti _let_0 P_1))) ) 15.56/15.74 ( bool, fNot ) 15.56/15.74 ( nat, (even_odd_even nat) ) 15.56/15.74 ( nat, prime ) 15.56/15.74 ( int, nat_neg ) 15.56/15.74 ( int, zprime ) 15.56/15.74 ( int, (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun _let_2 _let_0))) (let ((_let_4 (fun int _let_3))) (hAPP _let_1 _let_0 (hAPP (fun _let_0 bool) (fun _let_1 _let_0) (combb _let_0 bool int) (fEx int)) (hAPP _let_2 _let_1 (hAPP _let_4 (fun _let_2 _let_1) (combc int _let_2 _let_0) (hAPP _let_1 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_1 _let_4) (combb _let_0 _let_3 int) (combb int bool int)) (fequal int))) (hAPP int _let_2 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))))))))) ) 15.56/15.74 ( int, zEven ) 15.56/15.74 ( int, zOdd ) 15.56/15.74 ( int, (even_odd_even int) ) 15.56/15.74 ( int, twoSqu1091635170sum2sq ) 15.56/15.74 ( int, nat_is_nat ) 15.56/15.74 ( int, (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun _let_2 _let_0))) (let ((_let_5 (fun int _let_4))) (hAPP _let_1 _let_0 (hAPP (fun _let_0 bool) (fun _let_1 _let_0) (combb _let_0 bool int) (fEx int)) (hAPP _let_2 _let_1 (hAPP _let_5 (fun _let_2 _let_1) (combc int _let_2 _let_0) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_1 _let_5) (combb _let_0 _let_4 int) (combb int bool int)) (fequal int))) (hAPP int _let_2 (hAPP _let_3 _let_3 (combc int int int) (hAPP _let_2 _let_3 (hAPP _let_3 (fun _let_2 _let_3) (combb int _let_2 int) (plus_plus int)) (hAPP int _let_2 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one int)))))))))) ) 15.56/15.74 ( (fun int bool), nat_nat_set ) 15.56/15.74 ( (product_prod nat nat), pred_nat ) 15.56/15.74 ( (product_prod nat nat), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat (fun nat bool)))) (hAPP _let_1 (fun (product_prod nat nat) bool) (product_prod_case nat nat bool) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat (fun nat bool) nat) (hAPP _let_1 _let_1 (combc nat nat bool) (fequal nat))) suc)))) ) 15.56/15.74 ( real, (let ((_let_0 (fun int (fun int bool)))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real real))) (let ((_let_3 (real_1 int))) (let ((_let_4 (fun (fun int bool) bool))) (let ((_let_5 (fun bool bool))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun int _let_5))) (let ((_let_8 (fun (fun int bool) (fun int bool)))) (let ((_let_9 (fun (fun int bool) _let_7))) (let ((_let_10 (fun _let_0 (fun int bool)))) (let ((_let_11 (fEx int))) (let ((_let_12 (fun int real))) (let ((_let_13 (fun int _let_8))) (let ((_let_14 (fun (fun int bool) _let_0))) (let ((_let_15 (fun int _let_7))) (let ((_let_16 (fun _let_15 _let_13))) (let ((_let_17 (fun _let_0 _let_15))) (let ((_let_18 (fun real (fun int bool)))) (let ((_let_19 (fun real _let_0))) (let ((_let_20 (fun real _let_14))) (let ((_let_21 (fun real _let_13))) (let ((_let_22 (fun real _let_15))) (let ((_let_23 (fun int _let_12))) (let ((_let_24 (fun _let_23 _let_0))) (let ((_let_25 (fun real _let_24))) (let ((_let_26 (fun _let_12 (fun int bool)))) (let ((_let_27 (fun real _let_26))) (let ((_let_28 (fun _let_12 _let_12))) (let ((_let_29 (fun int _let_28))) (let ((_let_30 (fun int _let_2))) (hAPP _let_18 _let_1 (hAPP _let_4 (fun _let_18 _let_1) (combb (fun int bool) bool real) _let_11) (hAPP _let_19 _let_18 (hAPP _let_10 (fun _let_19 _let_18) (combb _let_0 (fun int bool) real) (hAPP _let_4 _let_10 (combb (fun int bool) bool int) _let_11)) (hAPP (fun int bool) _let_19 (hAPP _let_20 (fun (fun int bool) _let_19) (combc real (fun int bool) _let_0) (hAPP _let_21 _let_20 (hAPP (fun _let_13 _let_14) (fun _let_21 _let_20) (combb _let_13 _let_14 real) (combc int (fun int bool) (fun int bool))) (hAPP _let_22 _let_21 (hAPP _let_16 (fun _let_22 _let_21) (combb _let_15 _let_13 real) (hAPP (fun _let_7 _let_8) _let_16 (combb _let_7 _let_8 int) (combs int bool bool))) (hAPP _let_19 _let_22 (hAPP _let_17 (fun _let_19 _let_22) (combb _let_0 _let_15 real) (hAPP _let_9 _let_17 (combb (fun int bool) _let_7 int) (hAPP (fun bool _let_5) _let_9 (combb bool _let_5 int) fconj))) (hAPP _let_23 _let_19 (hAPP _let_25 (fun _let_23 _let_19) (combc real _let_23 _let_0) (hAPP _let_27 _let_25 (hAPP (fun _let_26 _let_24) (fun _let_27 _let_25) (combb _let_26 _let_24 real) (combb _let_12 (fun int bool) int)) (hAPP _let_6 _let_27 (hAPP (fun _let_1 _let_26) (fun _let_6 _let_27) (combb _let_1 _let_26 real) (combb real bool int)) (fequal real)))) (hAPP _let_12 _let_23 (hAPP _let_29 (fun _let_12 _let_23) (combc int _let_12 _let_12) (hAPP _let_30 _let_29 (hAPP (fun _let_2 _let_28) (fun _let_30 _let_29) (combb _let_2 _let_28 int) (combb real real int)) (hAPP _let_12 _let_30 (hAPP (fun real _let_2) (fun _let_12 _let_30) (combb real _let_2 int) (inverse_divide real)) _let_3))) _let_3)))))) (hAPP (fun int bool) (fun int bool) (hAPP _let_5 _let_8 (combb bool bool int) fNot) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (fequal int)) (zero_zero int))))))))))))))))))))))))))))))))))))) ) 15.56/15.74 ( real, (let ((_let_0 (fun int bool))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real real))) (let ((_let_3 (fun nat (fun nat bool)))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun (fun nat real) (fun nat real)))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun (fun nat bool) (fun nat bool)))) (let ((_let_8 (fun int real))) (let ((_let_9 (fun nat _let_4))) (let ((_let_10 (fun (fun nat bool) _let_9))) (let ((_let_11 (fun real _let_0))) (let ((_let_12 (fun int _let_2))) (let ((_let_13 (fun real (fun int (fun nat bool))))) (let ((_let_14 (fun (fun int (fun nat bool)) _let_0))) (let ((_let_15 (fun (fun nat bool) (fun int (fun nat bool))))) (let ((_let_16 (fun real _let_15))) (let ((_let_17 (fun int _let_7))) (let ((_let_18 (fun real _let_17))) (let ((_let_19 (fun int _let_9))) (let ((_let_20 (fun real _let_19))) (let ((_let_21 (fun _let_19 _let_17))) (let ((_let_22 (fun (fun int (fun nat bool)) _let_19))) (let ((_let_23 (fun int (fun nat real)))) (let ((_let_24 (fun _let_23 (fun int (fun nat bool))))) (let ((_let_25 (fun real _let_24))) (let ((_let_26 (fun (fun nat real) (fun nat bool)))) (let ((_let_27 (fun real _let_26))) (let ((_let_28 (fun int _let_5))) (hAPP _let_11 _let_1 (hAPP (fun _let_0 bool) (fun _let_11 _let_1) (combb _let_0 bool real) (fEx int)) (hAPP _let_13 _let_11 (hAPP _let_14 (fun _let_13 _let_11) (combb (fun int (fun nat bool)) _let_0 real) (hAPP (fun (fun nat bool) bool) _let_14 (combb (fun nat bool) bool int) (fEx nat))) (hAPP (fun nat bool) _let_13 (hAPP _let_16 (fun (fun nat bool) _let_13) (combc real (fun nat bool) (fun int (fun nat bool))) (hAPP _let_18 _let_16 (hAPP (fun _let_17 _let_15) (fun _let_18 _let_16) (combb _let_17 _let_15 real) (combc int (fun nat bool) (fun nat bool))) (hAPP _let_20 _let_18 (hAPP _let_21 (fun _let_20 _let_18) (combb _let_19 _let_17 real) (hAPP (fun _let_9 _let_7) _let_21 (combb _let_9 _let_7 int) (combs nat bool bool))) (hAPP _let_13 _let_20 (hAPP _let_22 (fun _let_13 _let_20) (combb (fun int (fun nat bool)) _let_19 real) (hAPP _let_10 _let_22 (combb (fun nat bool) _let_9 int) (hAPP (fun bool _let_4) _let_10 (combb bool _let_4 nat) fconj))) (hAPP _let_23 _let_13 (hAPP _let_25 (fun _let_23 _let_13) (combc real _let_23 (fun int (fun nat bool))) (hAPP _let_27 _let_25 (hAPP (fun _let_26 _let_24) (fun _let_27 _let_25) (combb _let_26 _let_24 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_6 _let_27 (hAPP (fun _let_1 _let_26) (fun _let_6 _let_27) (combb _let_1 _let_26 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_23 (hAPP _let_28 (fun (fun nat real) _let_23) (combc int (fun nat real) (fun nat real)) (hAPP _let_12 _let_28 (hAPP (fun _let_2 _let_5) (fun _let_12 _let_28) (combb _let_2 _let_5 int) (combb real real nat)) (hAPP _let_8 _let_12 (hAPP (fun real _let_2) (fun _let_8 _let_12) (combb real _let_2 int) (inverse_divide real)) (real_1 int)))) (real_1 nat))))))) (hAPP (fun nat bool) (fun nat bool) (hAPP _let_4 _let_7 (combb bool bool nat) fNot) (hAPP nat (fun nat bool) (hAPP _let_3 _let_3 (combc nat nat bool) (fequal nat)) (zero_zero nat))))))))))))))))))))))))))))))))))) ) 15.56/15.74 ( (product_prod int int), frac_1 ) 15.56/15.74 ( (fun nat rat), vanishes ) 15.56/15.74 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun _let_2 (fun _let_2 bool)))) (let ((_let_5 (fun (fun _let_2 bool) (fun _let_2 bool)))) (let ((_let_6 (fun _let_2 _let_5))) (let ((_let_7 (fun _let_4 _let_4))) (let ((_let_8 (fun _let_2 _let_3))) (let ((_let_9 (fun _let_2 _let_0))) (let ((_let_10 (fun _let_2 int))) (let ((_let_11 (fun _let_10 _let_9))) (let ((_let_12 (hAPP (fun int _let_0) _let_11 (combb int _let_0 _let_2) (fequal int)))) (let ((_let_13 (product_snd int int))) (let ((_let_14 (hAPP (fun _let_2 bool) _let_8 (hAPP (fun bool _let_3) (fun (fun _let_2 bool) _let_8) (combb bool _let_3 _let_2) fconj) (hAPP (fun _let_2 bool) (fun _let_2 bool) (hAPP _let_3 _let_5 (combb bool bool _let_2) fNot) (hAPP int (fun _let_2 bool) (hAPP _let_9 (fun int (fun _let_2 bool)) (combc _let_2 int bool) (hAPP _let_10 _let_9 _let_12 _let_13)) (zero_zero int)))))) (let ((_let_15 (fun _let_2 _let_10))) (let ((_let_16 (fun _let_10 (fun _let_2 bool)))) (let ((_let_17 (fun _let_2 _let_16))) (let ((_let_18 (fun _let_2 _let_9))) (let ((_let_19 (fun _let_10 _let_10))) (let ((_let_20 (fun _let_2 _let_19))) (let ((_let_21 (fun _let_10 _let_15))) (let ((_let_22 (fun _let_2 _let_1))) (let ((_let_23 (hAPP _let_10 _let_22 (hAPP (fun int _let_1) (fun _let_10 _let_22) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (let ((_let_24 (fun int _let_10))) (hAPP _let_4 (fun (product_prod _let_2 _let_2) bool) (product_prod_case _let_2 _let_2 bool) (hAPP _let_4 _let_4 (hAPP _let_6 _let_7 (combs _let_2 (fun _let_2 bool) (fun _let_2 bool)) (hAPP _let_8 _let_6 (hAPP (fun _let_3 _let_5) (fun _let_8 _let_6) (combb _let_3 _let_5 _let_2) (combb bool bool _let_2)) _let_14)) (hAPP _let_4 _let_4 (hAPP _let_5 _let_7 (combb (fun _let_2 bool) (fun _let_2 bool) _let_2) (hAPP _let_8 _let_5 (combs _let_2 bool bool) _let_14)) (hAPP _let_15 _let_4 (hAPP _let_17 (fun _let_15 _let_4) (combs _let_2 _let_10 (fun _let_2 bool)) (hAPP _let_18 _let_17 (hAPP (fun _let_9 _let_16) (fun _let_18 _let_17) (combb _let_9 _let_16 _let_2) (combs _let_2 int bool)) (hAPP _let_15 _let_18 (hAPP _let_11 (fun _let_15 _let_18) (combb _let_10 _let_9 _let_2) _let_12) (hAPP _let_10 _let_15 (hAPP _let_20 _let_21 (combc _let_2 _let_10 _let_10) (hAPP _let_22 _let_20 (hAPP (fun _let_1 _let_19) (fun _let_22 _let_20) (combb _let_1 _let_19 _let_2) (combb int int _let_2)) _let_23)) _let_13)))) (hAPP _let_10 _let_15 (hAPP _let_24 _let_21 (combb int _let_10 _let_2) (hAPP _let_22 _let_24 (combc _let_2 int int) _let_23)) _let_13)))))))))))))))))))))))))))))) ) 15.56/15.74 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)), ratrel ) 15.56/15.74 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), pair_less ) 15.56/15.74 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), pair_leq ) 15.56/15.74 ) 15.56/15.74 (instantiation (forall ((Z_1 $$unsorted)) (= (ti int Z_1) (hAPP int int (hAPP int (fun int int) (times_times int) (one_one int)) Z_1)) ) 15.56/15.74 ( pls ) 15.56/15.74 ( min_1 ) 15.56/15.74 ( s ) 15.56/15.74 ( m ) 15.56/15.74 ( s1 ) 15.56/15.74 ( t ) 15.56/15.74 ) 15.56/15.74 (instantiation (forall ((A_2 $$unsorted) (P_4 $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP int bool zprime P_4))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) A_2) P_4))) (= (hAPP int nat nat_1 A_2) (hAPP _let_0 nat (finite_card int) (hAPP int _let_0 (hAPP int (fun int _let_0) bnorRset A_2) P_4))))) ) 15.56/15.74 ( (one_one int), t ) 15.56/15.74 ( pls, (one_one int) ) 15.56/15.74 ( pls, pls ) 15.56/15.74 ( pls, min_1 ) 15.56/15.74 ( pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.56/15.74 ( min_1, pls ) 15.56/15.74 ( min_1, min_1 ) 15.56/15.74 ( s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.56/15.74 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.56/15.74 ( skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.56/15.74 ( skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.56/15.74 ) 15.56/15.74 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (one_one real))) (let ((_let_3 (fun real real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP int real (number_number_of real) min_1)) X_2))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_2) _let_2))) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP _let_3 (fun real _let_0) (deriv real) arccos) X_2) (hAPP real real (inverse_inverse real) (hAPP real real (uminus_uminus real) (hAPP real real sqrt (hAPP real real (hAPP real _let_3 (minus_minus real) _let_2) (hAPP nat real (hAPP real (fun nat real) (power_power real) X_2) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))))))))))) ) 15.56/15.74 ( (one_one real) ) 15.56/15.74 ( (zero_zero real) ) 15.56/15.74 ( pi ) 15.56/15.74 ( (hAPP int real (number_number_of real) min_1) ) 15.56/15.74 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.74 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.56/15.74 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.74 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.74 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 15.56/15.74 ) 15.56/15.74 (instantiation (forall ((X_a $$unsorted) (Q_1 $$unsorted) (P_1 $$unsorted)) (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun X_a bool))) (let ((_let_2 (finite_finite_1 X_a))) (let ((_let_3 (collect X_a))) (let ((_let_4 (fun X_a _let_0))) (or (and (not (hBOOL (hAPP _let_1 bool _let_2 (hAPP _let_1 _let_1 _let_3 Q_1)))) (not (hBOOL (hAPP _let_1 bool _let_2 (hAPP _let_1 _let_1 _let_3 P_1))))) (hBOOL (hAPP _let_1 bool _let_2 (hAPP _let_1 _let_1 _let_3 (hAPP _let_1 _let_1 (hAPP _let_4 (fun _let_1 _let_1) (combs X_a bool bool) (hAPP _let_1 _let_4 (hAPP (fun bool _let_0) (fun _let_1 _let_4) (combb bool _let_0 X_a) fconj) P_1)) Q_1)))))))))) ) 15.56/15.74 ( real, (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun real _let_0))) (hAPP real _let_0 (hAPP _let_2 _let_2 (combc real real bool) (hAPP _let_1 _let_2 (hAPP _let_2 (fun _let_1 _let_2) (combb real _let_0 real) (fequal real)) cos)) (zero_zero real))))), (let ((_let_0 (fun real (fun real bool)))) (hAPP real (fun real bool) (hAPP _let_0 _let_0 (combc real real bool) (ord_less_eq real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.56/15.74 ( real, (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun real _let_0))) (let ((_let_4 (fun real _let_2))) (let ((_let_5 (combc real real bool))) (hAPP _let_0 _let_0 (hAPP _let_4 (fun _let_0 _let_0) (combs real bool bool) (hAPP _let_0 _let_4 (hAPP (fun bool _let_2) (fun _let_0 _let_4) (combb bool _let_2 real) fconj) (hAPP real _let_0 (hAPP _let_3 _let_3 _let_5 (ord_less_eq real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_3 _let_3 _let_5 (hAPP _let_1 _let_3 (hAPP _let_3 (fun _let_1 _let_3) (combb real _let_0 real) (fequal real)) cos)) (zero_zero real))))))))), (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) ) 15.56/15.74 ) 15.56/15.74 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (hAPP int (fun _let_0 bool) (member int) X_2))) (or (hBOOL (hAPP _let_0 bool _let_1 zOdd)) (hBOOL (hAPP _let_0 bool _let_1 zEven))))) ) 15.56/15.74 ( (one_one int) ) 15.56/15.74 ) 15.56/15.74 (instantiation (forall ((K_4 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) K_4))) (not (forall ((N_2 $$unsorted)) (or (not (= (ti int K_4) (hAPP nat int (semiring_1_of_nat int) N_2))) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_2)))) ))) ) 15.56/15.74 ( (one_one int) ) 15.56/15.74 ( pls ) 15.56/15.74 ( min_1 ) 15.56/15.74 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.56/15.74 ) 15.56/15.74 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_119223 $$unsorted)) (or (not (number_ring X_a)) (not (field_inverse_zero X_a)) (= (zero_zero X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_119223) (hAPP int X_a (number_number_of X_a) pls)))) ) 15.56/15.74 ( real, (one_one real) ) 15.56/15.74 ( real, pi ) 15.56/15.74 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.56/15.74 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.56/15.74 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.74 ) 15.56/15.74 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_0 (product_fst X_a X_b))) (= _let_0 (ti (fun (product_prod X_a X_b) X_a) _let_0))) ) 15.56/15.74 ( nat, nat ) 15.56/15.74 ( int, int ) 15.56/15.74 ( int, (product_prod int int) ) 15.56/15.74 ( (product_prod nat nat), (product_prod nat nat) ) 15.56/15.74 ( real, real ) 15.56/15.74 ( (product_prod int int), (product_prod int int) ) 15.56/15.74 ( quickcheck_code_int, quickcheck_code_int ) 15.56/15.74 ( code_code_numeral, code_code_numeral ) 15.56/15.74 ) 15.56/15.74 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_119256 $$unsorted) (BOUND_VARIABLE_119257 $$unsorted) (BOUND_VARIABLE_119258 $$unsorted) (BOUND_VARIABLE_119259 $$unsorted) (BOUND_VARIABLE_119260 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (plus_plus X_a))) (let ((_let_2 (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_119260))) (or (not (semiri456707255roduct X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_119260)) (not (= (ti X_a BOUND_VARIABLE_119259) (ti X_a BOUND_VARIABLE_119258))) (= (ti X_a BOUND_VARIABLE_119256) (ti X_a BOUND_VARIABLE_119257)) (not (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_119259) (hAPP X_a X_a _let_2 BOUND_VARIABLE_119257)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_119258) (hAPP X_a X_a _let_2 BOUND_VARIABLE_119256)))))))) ) 15.56/15.74 ( bool, fFalse, fFalse, fFalse, fFalse, fFalse ) 15.56/15.74 ( bool, fFalse, fTrue, fFalse, fFalse, fFalse ) 15.56/15.74 ( bool, fTrue, fFalse, fTrue, fTrue, fTrue ) 15.56/15.74 ( int, pls, pls, pls, pls, pls ) 15.56/15.74 ( int, pls, m, pls, pls, pls ) 15.56/15.74 ( int, min_1, t, min_1, min_1, min_1 ) 15.56/15.74 ( int, s, s, s, s, s ) 15.56/15.74 ( int, s, s1, s, s, s ) 15.56/15.74 ( int, m, pls, m, m, m ) 15.56/15.74 ( int, s1, s, s1, s1, s1 ) 15.56/15.74 ( int, t, min_1, t, t, t ) 15.56/15.74 ( int, t, t, t, t, t ) 15.56/15.74 ( (fun int bool), nat_neg, nat_neg, nat_neg, nat_neg, nat_neg ) 15.56/15.74 ( (fun int bool), nat_neg, zprime, nat_neg, nat_neg, nat_neg ) 15.56/15.74 ( (fun int bool), zprime, nat_neg, zprime, zprime, zprime ) 15.56/15.74 ( (fun int bool), zEven, twoSqu1091635170sum2sq, zEven, zEven, zEven ) 15.56/15.74 ( (fun int bool), zOdd, zOdd, zOdd, zOdd, zOdd ) 15.56/15.74 ( (fun int bool), (even_odd_even int), nat_is_nat, (even_odd_even int), (even_odd_even int), (even_odd_even int) ) 15.56/15.74 ( (fun int bool), twoSqu1091635170sum2sq, zEven, twoSqu1091635170sum2sq, twoSqu1091635170sum2sq, twoSqu1091635170sum2sq ) 15.56/15.74 ( (fun int bool), twoSqu1091635170sum2sq, twoSqu1091635170sum2sq, twoSqu1091635170sum2sq, twoSqu1091635170sum2sq, twoSqu1091635170sum2sq ) 15.56/15.74 ( (fun int bool), nat_is_nat, (even_odd_even int), nat_is_nat, nat_is_nat, nat_is_nat ) 15.56/15.74 ( (fun int bool), nat_is_nat, nat_is_nat, nat_is_nat, nat_is_nat, nat_is_nat ) 15.56/15.74 ( (fun int (fun int bool)), norRRset, norRRset, norRRset, norRRset, norRRset ) 15.56/15.74 ( (fun int (fun int bool)), norRRset, sr, norRRset, norRRset, norRRset ) 15.56/15.74 ( (fun int (fun int bool)), quadRes, d22set, quadRes, quadRes, quadRes ) 15.56/15.74 ( (fun int (fun int bool)), sRStar, sRStar, sRStar, sRStar, sRStar ) 15.56/15.74 ( (fun int (fun int bool)), sRStar, quickc1265749348ro_rel, sRStar, sRStar, sRStar ) 15.56/15.74 ( (fun int (fun int bool)), d22set, quadRes, d22set, d22set, d22set ) 15.56/15.74 ( (fun int (fun int bool)), d22set, d22set, d22set, d22set, d22set ) 15.56/15.74 ( (fun int (fun int bool)), sr, norRRset, sr, sr, sr ) 15.56/15.74 ( (fun int (fun int bool)), quickc1265749348ro_rel, sRStar, quickc1265749348ro_rel, quickc1265749348ro_rel, quickc1265749348ro_rel ) 15.56/15.74 ( (fun int int), zfact, zfact, zfact, zfact, zfact ) 15.56/15.74 ( (fun int int), zfact, (fact_fact int), zfact, zfact, zfact ) 15.56/15.74 ( (fun int int), bit0, bit0, bit0, bit0, bit0 ) 15.56/15.74 ( (fun int int), bit0, succ, bit0, bit0, bit0 ) 15.56/15.74 ( (fun int int), bit1, bit1, bit1, bit1, bit1 ) 15.56/15.74 ( (fun int int), bit1, pred, bit1, bit1, bit1 ) 15.56/15.74 ( (fun int int), (fact_fact int), zfact, (fact_fact int), (fact_fact int), (fact_fact int) ) 15.56/15.74 ( (fun int int), pred, bit1, pred, pred, pred ) 15.56/15.74 ( (fun int int), succ, bit0, succ, succ, succ ) 15.56/15.74 ( (fun nat bool), (even_odd_even nat), (even_odd_even nat), (even_odd_even nat), (even_odd_even nat), (even_odd_even nat) ) 15.56/15.74 ( (fun nat bool), (even_odd_even nat), prime, (even_odd_even nat), (even_odd_even nat), (even_odd_even nat) ) 15.56/15.74 ( (fun nat bool), prime, (even_odd_even nat), prime, prime, prime ) 15.56/15.74 ( (fun nat nat), suc, suc, suc, suc, suc ) 15.56/15.74 ( (fun nat nat), (fact_fact nat), (fact_fact nat), (fact_fact nat), (fact_fact nat), (fact_fact nat) ) 15.56/15.74 ( (fun nat nat), (fact_fact nat), fact, (fact_fact nat), (fact_fact nat), (fact_fact nat) ) 15.56/15.74 ( (fun nat nat), fact, (fact_fact nat), fact, fact, fact ) 15.56/15.74 ( (fun nat nat), nat_size, nat_size, nat_size, nat_size, nat_size ) 15.56/15.74 ( (fun nat nat), nat_size, (size_size nat), nat_size, nat_size, nat_size ) 15.56/15.74 ( (fun nat nat), (size_size nat), nat_size, (size_size nat), (size_size nat), (size_size nat) ) 15.56/15.74 ( (fun (product_prod nat nat) bool), pred_nat, pred_nat, pred_nat, pred_nat, pred_nat ) 15.56/15.74 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel, divmod_nat_rel, divmod_nat_rel, divmod_nat_rel, divmod_nat_rel ) 15.56/15.74 ( real, pi, pi, pi, pi, pi ) 15.56/15.74 ( (fun real real), ln, sqrt, ln, ln, ln ) 15.56/15.74 ( (fun real real), cos, cos, cos, cos, cos ) 15.56/15.74 ( (fun real real), cos, tan, cos, cos, cos ) 15.56/15.74 ( (fun real real), sqrt, ln, sqrt, sqrt, sqrt ) 15.56/15.74 ( (fun real real), sqrt, sqrt, sqrt, sqrt, sqrt ) 15.56/15.74 ( (fun real real), sin, sin, sin, sin, sin ) 15.56/15.74 ( (fun real real), sin, arctan, sin, sin, sin ) 15.56/15.74 ( (fun real real), arccos, arccos, arccos, arccos, arccos ) 15.56/15.74 ( (fun real real), arccos, arcsin, arccos, arccos, arccos ) 15.56/15.74 ( (fun real real), arcsin, arccos, arcsin, arcsin, arcsin ) 15.56/15.74 ( (fun real real), tan, cos, tan, tan, tan ) 15.56/15.74 ( (fun real real), arctan, sin, arctan, arctan, arctan ) 15.56/15.74 ( (fun nat (fun nat bool)), coprime, coprime, coprime, coprime, coprime ) 15.56/15.74 ( complex, ii, ii, ii, ii, ii ) 15.56/15.74 ( (fun nat real), (real_1 nat), sin_coeff, (real_1 nat), (real_1 nat), (real_1 nat) ) 15.56/15.74 ( (fun nat real), sin_coeff, (real_1 nat), sin_coeff, sin_coeff, sin_coeff ) 15.56/15.74 ( (fun nat real), sin_coeff, sin_coeff, sin_coeff, sin_coeff, sin_coeff ) 15.56/15.74 ( (fun nat real), cos_coeff, cos_coeff, cos_coeff, cos_coeff, cos_coeff ) 15.56/15.74 ( (filter nat), sequentially, sequentially, sequentially, sequentially, sequentially ) 15.56/15.74 ( (fun int (fun int int)), (gcd_gcd int), inv, (gcd_gcd int), (gcd_gcd int), (gcd_gcd int) ) 15.56/15.74 ( (fun int (fun int int)), legendre, legendre, legendre, legendre, legendre ) 15.56/15.74 ( (fun int (fun int int)), legendre, legacy_zgcd, legendre, legendre, legendre ) 15.56/15.74 ( (fun int (fun int int)), legacy_zgcd, legendre, legacy_zgcd, legacy_zgcd, legacy_zgcd ) 15.56/15.74 ( (fun int (fun int int)), standardRes, multInv, standardRes, standardRes, standardRes ) 15.56/15.74 ( (fun int (fun int int)), nat_tsub, z3mod, nat_tsub, nat_tsub, nat_tsub ) 15.56/15.74 ( (fun int (fun int int)), multInv, standardRes, multInv, multInv, multInv ) 15.56/15.74 ( (fun int (fun int int)), multInv, multInv, multInv, multInv, multInv ) 15.56/15.74 ( (fun int (fun int int)), z3mod, nat_tsub, z3mod, z3mod, z3mod ) 15.56/15.74 ( (fun int (fun int int)), z3mod, z3mod, z3mod, z3mod, z3mod ) 15.56/15.74 ( (fun int (fun int int)), z3div, int_lcm, z3div, z3div, z3div ) 15.56/15.74 ( (fun int (fun int int)), int_gcd, int_gcd, int_gcd, int_gcd, int_gcd ) 15.56/15.74 ( (fun int (fun int int)), int_lcm, z3div, int_lcm, int_lcm, int_lcm ) 15.56/15.74 ( (fun int (fun int int)), int_lcm, int_lcm, int_lcm, int_lcm, int_lcm ) 15.56/15.74 ( (fun int (fun int int)), inv, (gcd_gcd int), inv, inv, inv ) 15.56/15.74 ( (fun int (fun int int)), inv, inv, inv, inv, inv ) 15.56/15.74 ( (fun complex complex), expi, expi, expi, expi, expi ) 15.56/15.74 ( (fun complex complex), expi, cnj, expi, expi, expi ) 15.56/15.74 ( (fun complex complex), cnj, expi, cnj, cnj, cnj ) 15.56/15.74 ( (fun real complex), cis, cis, cis, cis, cis ) 15.56/15.74 ( (fun int nat), nat_1, phi, nat_1, nat_1, nat_1 ) 15.56/15.74 ( (fun int nat), phi, nat_1, phi, phi, phi ) 15.56/15.74 ( (fun int nat), phi, phi, phi, phi, phi ) 15.56/15.74 ( (fun (fun int bool) bool), nat_nat_set, nat_nat_set, nat_nat_set, nat_nat_set, nat_nat_set ) 15.56/15.74 ( (fun nat (fun nat nat)), (gcd_gcd nat), (gcd_gcd nat), (gcd_gcd nat), (gcd_gcd nat), (gcd_gcd nat) ) 15.56/15.74 ( (fun nat (fun nat nat)), (gcd_gcd nat), nat_gcd, (gcd_gcd nat), (gcd_gcd nat), (gcd_gcd nat) ) 15.56/15.74 ( (fun nat (fun nat nat)), nat_gcd, (gcd_gcd nat), nat_gcd, nat_gcd, nat_gcd ) 15.56/15.74 ( (fun nat (fun nat nat)), nat_lcm, nat_lcm, nat_lcm, nat_lcm, nat_lcm ) 15.56/15.74 ( (fun (fun int bool) int), (the int), (the int), (the int), (the int), (the int) ) 15.56/15.74 ( (fun complex real), re, re, re, re, re ) 15.56/15.74 ( (fun complex real), im, im, im, im, im ) 15.56/15.74 ( (fun complex real), im, arg, im, im, im ) 15.56/15.74 ( (fun complex real), arg, im, arg, arg, arg ) 15.56/15.74 ( (fun bool bool), fNot, fNot, fNot, fNot, fNot ) 15.56/15.74 ( (fun nat (fun real real)), root, root, root, root, root ) 15.56/15.74 ( (fun real (fun real real)), log, log, log, log, log ) 15.56/15.74 ( (fun real (fun real real)), log, powr, log, log, log ) 15.56/15.74 ( (fun real (fun real real)), powr, log, powr, powr, powr ) 15.56/15.74 ( (fun bool (fun bool bool)), fimplies, fimplies, fimplies, fimplies, fimplies ) 15.56/15.74 ( (fun bool (fun bool bool)), fimplies, fconj, fimplies, fimplies, fimplies ) 15.56/15.74 ( (fun bool (fun bool bool)), fconj, fimplies, fconj, fconj, fconj ) 15.56/15.74 ( (fun bool (fun bool bool)), fdisj, fdisj, fdisj, fdisj, fdisj ) 15.56/15.74 ( (fun int (fun int (product_prod int int))), negDivAlg, norm_frac, negDivAlg, negDivAlg, negDivAlg ) 15.56/15.74 ( (fun int (fun int (product_prod int int))), posDivAlg, posDivAlg, posDivAlg, posDivAlg, posDivAlg ) 15.56/15.74 ( (fun int (fun int (product_prod int int))), divmod_int, pdivmod, divmod_int, divmod_int, divmod_int ) 15.56/15.74 ( (fun int (fun int (product_prod int int))), pdivmod, divmod_int, pdivmod, pdivmod, pdivmod ) 15.56/15.74 ( (fun int (fun int (product_prod int int))), pdivmod, pdivmod, pdivmod, pdivmod, pdivmod ) 15.56/15.74 ( (fun int (fun int (product_prod int int))), norm_frac, negDivAlg, norm_frac, norm_frac, norm_frac ) 15.56/15.74 ( (fun int (fun int (product_prod int int))), norm_frac, norm_frac, norm_frac, norm_frac, norm_frac ) 15.56/15.74 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd, negateSnd, negateSnd, negateSnd, negateSnd ) 15.56/15.74 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd, normalize, negateSnd, negateSnd, negateSnd ) 15.56/15.74 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize, negateSnd, normalize, normalize, normalize ) 15.56/15.74 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust, adjust, adjust, adjust, adjust ) 15.56/15.74 ( (fun int (fun int (fun int bool))), zcong, noXRRset, zcong, zcong, zcong ) 15.56/15.74 ( (fun int (fun int (fun int bool))), zcongm, zcongm, zcongm, zcongm, zcongm ) 15.56/15.74 ( (fun int (fun int (fun int bool))), zcongm, bnorRset, zcongm, zcongm, zcongm ) 15.56/15.74 ( (fun int (fun int (fun int bool))), noXRRset, zcong, noXRRset, noXRRset, noXRRset ) 15.56/15.74 ( (fun int (fun int (fun int bool))), noXRRset, noXRRset, noXRRset, noXRRset, noXRRset ) 15.56/15.74 ( (fun int (fun int (fun int bool))), bnorRset, zcongm, bnorRset, bnorRset, bnorRset ) 15.56/15.74 ( (fun int (fun int (fun int bool))), wset, wset, wset, wset, wset ) 15.56/15.74 ( (fun (product_prod int int) bool), frac_1, frac_1, frac_1, frac_1, frac_1 ) 15.56/15.74 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than, int_ge_less_than, int_ge_less_than, int_ge_less_than, int_ge_less_than ) 15.56/15.74 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than, int_ge_less_than2, int_ge_less_than, int_ge_less_than, int_ge_less_than ) 15.56/15.74 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2, int_ge_less_than, int_ge_less_than2, int_ge_less_than2, int_ge_less_than2 ) 15.56/15.74 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral, code_S1047413653umeral, code_S1047413653umeral, code_S1047413653umeral, code_S1047413653umeral ) 15.56/15.74 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset, is_RRset, is_RRset, is_RRset, is_RRset ) 15.56/15.74 ( (fun (fun nat rat) bool), vanishes, vanishes, vanishes, vanishes, vanishes ) 15.56/15.74 ( (fun code_code_numeral nat), (size_size code_code_numeral), (size_size code_code_numeral), (size_size code_code_numeral), (size_size code_code_numeral), (size_size code_code_numeral) ) 15.56/15.74 ( (fun code_code_numeral nat), (size_size code_code_numeral), code_c271388182l_size, (size_size code_code_numeral), (size_size code_code_numeral), (size_size code_code_numeral) ) 15.56/15.74 ( (fun code_code_numeral nat), code_c271388182l_size, (size_size code_code_numeral), code_c271388182l_size, code_c271388182l_size, code_c271388182l_size ) 15.56/15.74 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel, ratrel, ratrel, ratrel, ratrel ) 15.56/15.74 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel, norm_frac_rel, norm_frac_rel, norm_frac_rel, norm_frac_rel ) 15.56/15.74 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel, lazy_small_lazy_rel, norm_frac_rel, norm_frac_rel, norm_frac_rel ) 15.56/15.74 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel, negDivAlg_rel, posDivAlg_rel, posDivAlg_rel, posDivAlg_rel ) 15.56/15.74 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel, norm_frac_rel, lazy_small_lazy_rel, lazy_small_lazy_rel, lazy_small_lazy_rel ) 15.56/15.74 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel, posDivAlg_rel, negDivAlg_rel, negDivAlg_rel, negDivAlg_rel ) 15.56/15.74 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel, negDivAlg_rel, negDivAlg_rel, negDivAlg_rel, negDivAlg_rel ) 15.56/15.74 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel, upto_rel, upto_rel, upto_rel, upto_rel ) 15.56/15.74 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq, twoSqu1094008024sum2sq, twoSqu1094008024sum2sq, twoSqu1094008024sum2sq, twoSqu1094008024sum2sq ) 15.56/15.74 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less, pair_less, pair_less, pair_less, pair_less ) 15.56/15.74 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less, pair_leq, pair_less, pair_less, pair_less ) 15.56/15.74 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq, pair_less, pair_leq, pair_leq, pair_leq ) 15.56/15.74 ( (fun complex nat), complex_size, complex_size, complex_size, complex_size, complex_size ) 15.56/15.74 ( (fun complex nat), complex_size, (size_size complex), complex_size, complex_size, complex_size ) 15.56/15.74 ( (fun complex nat), (size_size complex), complex_size, (size_size complex), (size_size complex), (size_size complex) ) 15.56/15.74 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel, nat_gcd_rel, nat_gcd_rel, nat_gcd_rel, nat_gcd_rel ) 15.56/15.74 ( (fun nat (fun nat (product_prod int int))), bezw, bezw, bezw, bezw, bezw ) 15.56/15.74 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd, xzgcd, xzgcd, xzgcd, xzgcd ) 15.56/15.74 ( (fun int (fun nat nat)), nat_aux, nat_aux, nat_aux, nat_aux, nat_aux ) 15.56/15.74 ( (fun int (fun (fun int bool) bool)), rsetR, resSet, rsetR, rsetR, rsetR ) 15.56/15.74 ( (fun int (fun (fun int bool) bool)), resSet, rsetR, resSet, resSet, resSet ) 15.56/15.74 ( (fun int (fun (fun int bool) bool)), resSet, resSet, resSet, resSet, resSet ) 15.56/15.74 ( (fun int (list int)), quickc666637781d_zero, quickc666637781d_zero, quickc666637781d_zero, quickc666637781d_zero, quickc666637781d_zero ) 15.56/15.74 ( (fun (product_prod int int) rat), frct, frct, frct, frct, frct ) 15.56/15.74 ( (fun int (fun int rat)), fract, fract, fract, fract, fract ) 15.56/15.74 ( (fun real (fun real complex)), complex_1, rcis, complex_1, complex_1, complex_1 ) 15.56/15.74 ( (fun real (fun real complex)), rcis, complex_1, rcis, rcis, rcis ) 15.56/15.74 ( (fun real (fun real complex)), rcis, rcis, rcis, rcis, rcis ) 15.56/15.74 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat), (ord_gr676655987ssThan nat), (ord_gr676655987ssThan nat), (ord_gr676655987ssThan nat), (ord_gr676655987ssThan nat) ) 15.56/15.74 ( (fun quickcheck_code_int nat), quickcheck_nat_of, quickcheck_nat_of, quickcheck_nat_of, quickcheck_nat_of, quickcheck_nat_of ) 15.56/15.74 ( (fun int real), (real_1 int), (real_1 int), (real_1 int), (real_1 int), (real_1 int) ) 15.56/15.74 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect, bolzano_bisect, bolzano_bisect, bolzano_bisect, bolzano_bisect ) 15.56/15.74 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR, rRset2norRR, rRset2norRR, rRset2norRR, rRset2norRR ) 15.56/15.74 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int, quickc495462417de_int, quickc495462417de_int, quickc495462417de_int, quickc495462417de_int ) 15.56/15.74 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda, xzgcda, xzgcda, xzgcda, xzgcda ) 15.56/15.74 ( (fun int (fun int (fun int (fun int bool)))), multInvPair, multInvPair, multInvPair, multInvPair, multInvPair ) 15.56/15.74 ( (fun real nat), natfloor, natceiling, natfloor, natfloor, natfloor ) 15.56/15.74 ( (fun real nat), natceiling, natfloor, natceiling, natceiling, natceiling ) 15.56/15.74 ( (fun real nat), natceiling, natceiling, natceiling, natceiling, natceiling ) 15.56/15.74 ( (fun (fun real bool) real), (complete_Sup_Sup real), (complete_Sup_Sup real), (complete_Sup_Sup real), (complete_Sup_Sup real), (complete_Sup_Sup real) ) 15.56/15.74 ( (fun quickcheck_code_int int), quickcheck_int_of, quickcheck_int_of, quickcheck_int_of, quickcheck_int_of, quickcheck_int_of ) 15.56/15.74 ( (fun rat (product_prod int int)), quotient_of, quotient_of, quotient_of, quotient_of, quotient_of ) 15.56/15.74 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral, code_d418564891umeral, code_d418564891umeral, code_d418564891umeral, code_d418564891umeral ) 15.56/15.74 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat, divmod_nat, divmod_nat, divmod_nat, divmod_nat ) 15.56/15.74 ( (fun rat real), ratreal, ratreal, ratreal, ratreal, ratreal ) 15.56/15.74 ( (fun code_code_numeral int), code_int_of, code_int_of, code_int_of, code_int_of, code_int_of ) 15.56/15.74 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel, divmod_int_rel, divmod_int_rel, divmod_int_rel, divmod_int_rel ) 15.56/15.74 ( (fun int quickcheck_code_int), quickcheck_of_int, quickcheck_of_int, quickcheck_of_int, quickcheck_of_int, quickcheck_of_int ) 15.56/15.74 ( (fun int (fun int (fun (fun int bool) bool))), setS, setS, setS, setS, setS ) 15.56/15.74 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux, code_nat_of_aux, code_nat_of_aux, code_nat_of_aux, code_nat_of_aux ) 15.56/15.74 ) 15.56/15.74 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_119393 $$unsorted)) (let ((_let_0 (number_number_of X_a))) (or (not (number_semiring X_a)) (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) pls) BOUND_VARIABLE_119393))) (= (hAPP int X_a _let_0 (hAPP int int succ BOUND_VARIABLE_119393)) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (one_one X_a)) (hAPP int X_a _let_0 BOUND_VARIABLE_119393))))) ) 15.56/15.74 ( nat, pls ) 15.56/15.74 ( nat, (hAPP int int bit1 pls) ) 15.56/15.74 ( nat, min_1 ) 15.56/15.74 ( int, pls ) 15.56/15.74 ( int, min_1 ) 15.56/15.74 ( quickcheck_code_int, pls ) 15.56/15.74 ( quickcheck_code_int, min_1 ) 15.56/15.74 ( code_code_numeral, pls ) 15.56/15.74 ( code_code_numeral, min_1 ) 15.56/15.74 ) 15.56/15.74 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_119411 $$unsorted) (BOUND_VARIABLE_119412 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (let ((_let_3 (hAPP X_a _let_0 _let_1 _let_2))) (or (not (linord1117847801e_zero X_a)) (= (or (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_119412) _let_2)) (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_119411))) (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_119411) _let_2)) (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_119412)))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_119411) BOUND_VARIABLE_119412)) _let_2)))))))) ) 15.56/15.74 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.74 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.56/15.74 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.74 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 15.56/15.74 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.74 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.74 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.56/15.74 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.56/15.74 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.74 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.74 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.74 ) 15.56/15.74 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_119474 $$unsorted) (BOUND_VARIABLE_119475 $$unsorted) (BOUND_VARIABLE_119476 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (plus_plus X_a))) (or (not (cancel_semigroup_add X_a)) (not (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_119474) BOUND_VARIABLE_119475) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_119476) BOUND_VARIABLE_119475))) (= (ti X_a BOUND_VARIABLE_119474) (ti X_a BOUND_VARIABLE_119476))))) ) 15.56/15.74 ( nat, (one_one nat), (one_one nat), (one_one nat) ) 15.56/15.75 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.56/15.75 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.75 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.56/15.75 ) 15.56/15.75 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_119503 $$unsorted) (BOUND_VARIABLE_119504 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (zero_zero X_a))) (let ((_let_3 (hAPP int nat (number_number_of nat) BOUND_VARIABLE_119504))) (let ((_let_4 (hBOOL (hAPP nat bool (even_odd_even nat) _let_3)))) (or (not (linordered_idom X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_119503) _let_3)) _let_2)) (and (or (and (not _let_4) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_119503) _let_2))) (and _let_4 (= _let_2 (ti X_a BOUND_VARIABLE_119503)))) (not (= (zero_zero nat) _let_3)))))))))) ) 15.56/15.75 ( int, s, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.56/15.75 ( int, s1, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.56/15.75 ( int, skv_14, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.56/15.75 ( complex, ii, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.56/15.75 ) 15.56/15.75 (instantiation (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (let ((_let_0 (fun X_b X_c))) (let ((_let_1 (fun X_a X_b))) (let ((_let_2 (fun X_a X_c))) (= (hAPP X_a X_c (hAPP _let_1 _let_2 (hAPP (fun X_a _let_0) (fun _let_1 _let_2) (combs X_a X_b X_c) P) Q) R) (hAPP X_b X_c (hAPP X_a _let_0 P R) (hAPP X_a X_b Q R)))))) ) 15.56/15.75 ( nat, nat, nat, (plus_plus nat), (fact_fact nat), (one_one nat) ) 15.56/15.75 ( int, bool, int, (ord_less_eq int), bit1, min_1 ) 15.56/15.75 ( int, bool, int, (ord_less_eq int), (number_number_of int), (zero_zero int) ) 15.56/15.75 ( int, bool, int, (ord_less_eq int), (fact_fact int), (zero_zero int) ) 15.56/15.75 ( int, bool, int, (ord_less_eq int), pred, (zero_zero int) ) 15.56/15.75 ( int, bool, int, (ord_less_eq int), succ, min_1 ) 15.56/15.75 ( int, bool, int, (ord_less int), bit1, min_1 ) 15.56/15.75 ( int, bool, int, (ord_less int), (number_number_of int), pls ) 15.56/15.75 ( int, bool, int, (ord_less int), (fact_fact int), pls ) 15.56/15.75 ( int, bool, int, (ord_less int), pred, pls ) 15.56/15.75 ( int, bool, int, (ord_less int), succ, min_1 ) 15.56/15.75 ( int, rat, int, fract, (fact_fact int), (one_one int) ) 15.56/15.75 ( int, rat, int, fract, (fact_fact int), (zero_zero int) ) 15.56/15.75 ( int, (product_prod int int), int, (product_Pair int int), (fact_fact int), (one_one int) ) 15.56/15.75 ( int, (product_prod int int), int, (product_Pair int int), (fact_fact int), (zero_zero int) ) 15.56/15.75 ( real, bool, real, (ord_less real), tan, pi ) 15.56/15.75 ( real, real, real, (times_times real), (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.75 ( real, complex, real, complex_1, ln, (one_one real) ) 15.56/15.75 ( real, complex, real, complex_1, cos, (zero_zero real) ) 15.56/15.75 ( real, complex, real, complex_1, tan, (zero_zero real) ) 15.56/15.75 ) 15.56/15.75 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_119609 $$unsorted) (BOUND_VARIABLE_119610 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (uminus_uminus X_a))) (or (not (boolean_algebra X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_119610) BOUND_VARIABLE_119609)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_119609)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_119610)))))))) ) 15.56/15.75 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 15.56/15.75 ( int, (one_one int), (one_one int) ) 15.56/15.75 ( int, (one_one int), pls ) 15.56/15.75 ( int, pls, (one_one int) ) 15.56/15.75 ( int, pls, pls ) 15.56/15.75 ( int, pls, min_1 ) 15.56/15.75 ( int, min_1, pls ) 15.56/15.75 ( int, min_1, min_1 ) 15.56/15.75 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), pls ) 15.56/15.75 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s ) 15.56/15.75 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.56/15.75 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_4 ) 15.56/15.75 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_10 ) 15.56/15.75 ( int, t, (one_one int) ) 15.56/15.75 ( real, (zero_zero real), pi ) 15.56/15.75 ( real, (zero_zero real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.56/15.75 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.75 ( real, pi, (zero_zero real) ) 15.56/15.75 ( real, pi, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 15.56/15.75 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.75 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.56/15.75 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 15.56/15.75 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 15.56/15.75 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.56/15.75 ( real, skv_2, (zero_zero real) ) 15.56/15.75 ( real, skv_8, (zero_zero real) ) 15.56/15.75 ( real, skv_9, (zero_zero real) ) 15.56/15.75 ) 15.56/15.75 (instantiation (forall ((D $$unsorted) (C $$unsorted) (A_1 $$unsorted) (B $$unsorted) (M $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (hAPP int _let_1 zcong A_1))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 B) M))) (not (= (ti int C) (ti int B))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int _let_1 zcong C) D) M))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 D) M)))))) ) 15.56/15.75 ( (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.56/15.75 ( (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.56/15.75 ( (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.56/15.75 ( s, s1, s1, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.56/15.75 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.56/15.75 ( skv_4, s1, s1, skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.56/15.75 ( skv_10, s1, s1, skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.56/15.75 ) 15.56/15.75 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_119656 $$unsorted) (BOUND_VARIABLE_119657 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (plus_plus X_a))) (let ((_let_2 (div_div X_a))) (or (not (semiring_div X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_119657)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_119656) BOUND_VARIABLE_119657)) BOUND_VARIABLE_119657) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_119656) BOUND_VARIABLE_119657)) (one_one X_a))))))) ) 15.56/15.75 ( nat, (one_one nat), (one_one nat) ) 15.56/15.75 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 15.56/15.75 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 15.56/15.75 ) 15.56/15.75 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_119685 $$unsorted) (BOUND_VARIABLE_119686 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (zero_zero X_a))) (let ((_let_2 (ord_less X_a))) (or (not (ordere216010020id_add X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_119686) _let_1))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_119685) _let_1))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_119686) BOUND_VARIABLE_119685)) _let_1)))))) ) 15.56/15.75 ( nat, (one_one nat), (one_one nat) ) 15.56/15.75 ( int, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.56/15.75 ( int, (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.75 ) 15.56/15.75 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_0 (fun nat bool))) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) (hAPP nat nat suc M)) N_1))) (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) M) N_1)))) ) 15.56/15.75 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.75 ) 15.56/15.75 (instantiation (forall ((X_a $$unsorted) (X_c $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (hAPP X_a X_c (ti (fun X_a X_c) B_1_1) B_2_1) (hAPP X_a X_c B_1_1 B_2_1)) ) 15.56/15.75 ( nat, bool, (even_odd_even nat), (zero_zero nat) ) 15.56/15.75 ( nat, bool, (even_odd_even nat), (one_one nat) ) 15.56/15.75 ( nat, bool, prime, (zero_zero nat) ) 15.56/15.75 ( nat, bool, prime, (hAPP nat nat suc (zero_zero nat)) ) 15.56/15.75 ( nat, bool, prime, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.75 ( nat, nat, suc, (zero_zero nat) ) 15.56/15.75 ( nat, nat, suc, (hAPP nat nat suc (zero_zero nat)) ) 15.56/15.75 ( nat, nat, suc, (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 15.56/15.75 ( nat, nat, (fact_fact nat), (zero_zero nat) ) 15.56/15.75 ( nat, nat, (fact_fact nat), (hAPP nat nat suc (zero_zero nat)) ) 15.56/15.75 ( nat, nat, fact, (zero_zero nat) ) 15.56/15.75 ( nat, nat, nat_size, (zero_zero nat) ) 15.56/15.75 ( nat, nat, (size_size nat), (zero_zero nat) ) 15.56/15.75 ( nat, real, (real_1 nat), (zero_zero nat) ) 15.56/15.75 ( nat, real, (real_1 nat), (hAPP nat nat suc (zero_zero nat)) ) 15.56/15.75 ( nat, (fun real real), root, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.75 ( int, bool, nat_neg, (one_one int) ) 15.56/15.75 ( int, bool, nat_neg, (hAPP int int (number_number_of int) min_1) ) 15.56/15.75 ( int, bool, nat_neg, (hAPP int int (number_number_of int) pls) ) 15.56/15.75 ( int, bool, zprime, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.75 ( int, bool, zprime, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.56/15.75 ( int, bool, (even_odd_even int), (one_one int) ) 15.56/15.75 ( int, bool, (even_odd_even int), (zero_zero int) ) 15.56/15.75 ( int, bool, twoSqu1091635170sum2sq, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) t))) ) 15.56/15.75 ( int, bool, nat_is_nat, (one_one int) ) 15.56/15.75 ( int, bool, nat_is_nat, (zero_zero int) ) 15.56/15.75 ( int, bool, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.75 ( int, bool, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.56/15.75 ( int, nat, nat_1, (one_one int) ) 15.56/15.75 ( int, nat, nat_1, (zero_zero int) ) 15.56/15.75 ( int, nat, nat_1, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.75 ( int, nat, nat_1, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.56/15.75 ( int, int, bit0, pls ) 15.56/15.75 ( int, int, bit0, (hAPP int int bit1 pls) ) 15.56/15.75 ( int, int, bit0, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.56/15.75 ( int, int, bit0, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.56/15.75 ( int, int, bit0, min_1 ) 15.56/15.75 ( int, int, bit0, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.56/15.75 ( int, int, bit1, pls ) 15.56/15.75 ( int, int, bit1, (hAPP int int bit1 pls) ) 15.56/15.75 ( int, int, bit1, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.56/15.75 ( int, int, bit1, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.56/15.75 ( int, int, bit1, min_1 ) 15.56/15.75 ( int, int, bit1, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.56/15.75 ( int, int, bit1, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.56/15.75 ( int, int, bit1, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 15.56/15.75 ( int, int, bit1, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 15.56/15.75 ( int, int, (fact_fact int), (one_one int) ) 15.56/15.75 ( int, int, (fact_fact int), (zero_zero int) ) 15.56/15.75 ( int, int, pred, pls ) 15.56/15.75 ( int, int, pred, min_1 ) 15.56/15.75 ( int, int, succ, pls ) 15.56/15.75 ( int, int, succ, min_1 ) 15.56/15.75 ( int, (fun int bool), quadRes, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.56/15.75 ( int, (fun int (fun int bool)), zcong, s1 ) 15.56/15.75 ( int, (fun int (fun int bool)), zcong, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.75 ( int, (fun int (fun int bool)), zcong, (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.75 ( int, (fun int (fun int bool)), zcong, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.75 ( int, (fun int int), legendre, (hAPP int int (number_number_of int) min_1) ) 15.56/15.75 ( int, real, (real_1 int), (one_one int) ) 15.56/15.75 ( int, real, (real_1 int), (zero_zero int) ) 15.56/15.75 ( int, (fun int rat), fract, (one_one int) ) 15.56/15.75 ( int, (fun int rat), fract, (zero_zero int) ) 15.56/15.75 ( int, quickcheck_code_int, quickcheck_of_int, (one_one int) ) 15.56/15.75 ( int, quickcheck_code_int, quickcheck_of_int, (zero_zero int) ) 15.56/15.75 ( int, quickcheck_code_int, quickcheck_of_int, (hAPP int int bit1 pls) ) 15.56/15.75 ( real, nat, natfloor, (one_one real) ) 15.56/15.75 ( real, nat, natfloor, (zero_zero real) ) 15.56/15.75 ( real, nat, natceiling, (one_one real) ) 15.56/15.75 ( real, nat, natceiling, (zero_zero real) ) 15.56/15.75 ( real, real, ln, (one_one real) ) 15.56/15.75 ( real, real, cos, (zero_zero real) ) 15.56/15.75 ( real, real, cos, pi ) 15.56/15.75 ( real, real, cos, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.75 ( real, real, cos, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.75 ( real, real, cos, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.56/15.75 ( real, real, cos, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.56/15.75 ( real, real, cos, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.56/15.75 ( real, real, cos, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.56/15.75 ( real, real, cos, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.56/15.75 ( real, real, cos, skv_5 ) 15.56/15.75 ( real, real, sqrt, (one_one real) ) 15.56/15.75 ( real, real, sqrt, (zero_zero real) ) 15.56/15.75 ( real, real, sqrt, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.75 ( real, real, sqrt, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.56/15.75 ( real, real, sin, (zero_zero real) ) 15.56/15.75 ( real, real, sin, pi ) 15.56/15.75 ( real, real, sin, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.75 ( real, real, sin, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.56/15.75 ( real, real, sin, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.56/15.75 ( real, real, sin, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.56/15.75 ( real, real, sin, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.56/15.75 ( real, real, sin, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.56/15.75 ( real, real, tan, (zero_zero real) ) 15.56/15.75 ( real, real, tan, pi ) 15.56/15.75 ( real, real, tan, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.56/15.75 ( real, real, tan, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.56/15.75 ( real, real, tan, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.56/15.75 ( real, real, arctan, (one_one real) ) 15.56/15.75 ( real, real, arctan, (zero_zero real) ) 15.56/15.75 ( real, real, arctan, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.56/15.75 ( real, real, arctan, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))))) ) 15.56/15.75 ( real, complex, cis, (zero_zero real) ) 15.56/15.75 ( real, (fun real complex), complex_1, (one_one real) ) 15.56/15.75 ( real, (fun real complex), complex_1, (zero_zero real) ) 15.56/15.75 ( rat, real, ratreal, (zero_zero rat) ) 15.56/15.75 ( rat, real, ratreal, (one_one rat) ) 15.56/15.75 ( rat, (product_prod int int), quotient_of, (zero_zero rat) ) 15.56/15.75 ( rat, (product_prod int int), quotient_of, (one_one rat) ) 15.56/15.75 ( complex, real, re, (one_one complex) ) 15.56/15.75 ( complex, real, re, ii ) 15.56/15.75 ( complex, real, re, (zero_zero complex) ) 15.56/15.75 ( complex, real, im, (one_one complex) ) 15.56/15.75 ( complex, real, im, ii ) 15.56/15.75 ( complex, real, im, (zero_zero complex) ) 15.56/15.75 ( complex, complex, expi, (zero_zero complex) ) 15.56/15.75 ( complex, complex, expi, (let ((_let_0 (fun complex complex))) (let ((_let_1 (times_times complex))) (hAPP complex complex (hAPP complex _let_0 _let_1 (hAPP complex complex (hAPP complex _let_0 _let_1 (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi))) ii))) ) 15.56/15.75 ( complex, complex, cnj, (one_one complex) ) 15.56/15.75 ( complex, complex, cnj, ii ) 15.56/15.75 ( complex, complex, cnj, (zero_zero complex) ) 15.56/15.75 ( (product_prod int int), int, twoSqu1094008024sum2sq, (let ((_let_0 (product_prod int int))) (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) s) (one_one int))) ) 15.56/15.75 ( (product_prod int int), rat, frct, (let ((_let_0 (one_one int))) (let ((_let_1 (product_prod int int))) (hAPP int _let_1 (hAPP int (fun int _let_1) (product_Pair int int) _let_0) _let_0))) ) 15.56/15.75 ( quickcheck_code_int, int, quickcheck_int_of, (zero_zero quickcheck_code_int) ) 15.56/15.75 ( code_code_numeral, nat, (size_size code_code_numeral), (zero_zero code_code_numeral) ) 15.56/15.75 ( code_code_numeral, nat, code_c271388182l_size, (zero_zero code_code_numeral) ) 15.56/15.75 ( code_code_numeral, int, code_int_of, (zero_zero code_code_numeral) ) 15.56/15.75 ) 15.56/15.75 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_119716 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (zero_zero X_a))) (or (not (linord1117847801e_zero X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_119716) _let_2)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_119716)) _let_2))))))) ) 15.56/15.75 ( int, (zero_zero int) ) 15.56/15.75 ( int, min_1 ) 15.56/15.75 ( real, (zero_zero real) ) 15.56/15.75 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.75 ( complex, ii ) 15.56/15.75 ) 15.56/15.75 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_119736 $$unsorted) (BOUND_VARIABLE_119737 $$unsorted) (BOUND_VARIABLE_119738 $$unsorted)) (or (not (order X_a)) (not (forall ((N_2 $$unsorted)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP nat X_a BOUND_VARIABLE_119738 N_2)) (hAPP nat X_a BOUND_VARIABLE_119738 (hAPP nat nat suc N_2)))) )) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP nat X_a BOUND_VARIABLE_119738 BOUND_VARIABLE_119736)) (hAPP nat X_a BOUND_VARIABLE_119738 BOUND_VARIABLE_119737))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) BOUND_VARIABLE_119736) BOUND_VARIABLE_119737)))) ) 15.56/15.75 ( int, (zero_zero nat), (zero_zero nat), (semiring_1_of_nat int) ) 15.56/15.75 ( int, (zero_zero nat), (hAPP nat nat suc (zero_zero nat)), (semiring_1_of_nat int) ) 15.56/15.75 ) 15.56/15.75 (instantiation (forall ((X_a $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (number_number_of int) min_1)) (hAPP (fun X_a bool) nat (finite_card X_a) A_3)))) (or (not (hBOOL (hAPP (fun X_a bool) bool (finite_finite_1 X_a) A_3))) (= (one_one int) (hAPP int int (hAPP int (fun int int) (times_times int) _let_0) _let_0)))) ) 15.56/15.75 ( nat, (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 15.56/15.75 ) 15.56/15.75 (instantiation (forall ((R_4 $$unsorted)) (= (hAPP real complex (of_real complex) R_4) (hAPP real complex (hAPP real (fun real complex) complex_1 R_4) (zero_zero real))) ) 15.56/15.75 ( (one_one real) ) 15.56/15.75 ( (zero_zero real) ) 15.56/15.75 ( pi ) 15.56/15.75 ( (hAPP int real (number_number_of real) min_1) ) 15.56/15.75 ( (hAPP real real (uminus_uminus real) (one_one real)) ) 15.56/15.75 ) 15.56/15.75 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (boolean_algebra T_1)) (boolean_algebra (fun T_2 T_1))) ) 15.56/15.75 ( bool, bool ) 15.56/15.75 ( bool, (fun bool bool) ) 15.56/15.75 ( nat, bool ) 15.56/15.75 ( nat, nat ) 15.56/15.75 ( nat, int ) 15.56/15.75 ( nat, (fun int int) ) 15.56/15.75 ( nat, (fun nat bool) ) 15.56/15.75 ( nat, (fun nat nat) ) 15.56/15.75 ( nat, (product_prod nat nat) ) 15.56/15.75 ( nat, (fun (product_prod nat nat) bool) ) 15.56/15.75 ( nat, (fun nat (fun (product_prod nat nat) bool)) ) 15.56/15.75 ( nat, real ) 15.56/15.75 ( nat, (fun real real) ) 15.56/15.75 ( nat, rat ) 15.56/15.75 ( nat, (fun nat (fun nat bool)) ) 15.56/15.75 ( nat, complex ) 15.56/15.75 ( nat, (product_prod int int) ) 15.56/15.75 ( nat, (fun bool bool) ) 15.56/15.75 ( nat, (product_prod real real) ) 15.56/15.75 ( nat, (fun nat (product_prod nat nat)) ) 15.56/15.75 ( nat, (fun nat (product_prod int int)) ) 15.56/15.75 ( int, bool ) 15.56/15.75 ( int, nat ) 15.56/15.75 ( int, int ) 15.56/15.75 ( int, (fun int bool) ) 15.56/15.75 ( int, (fun int (fun int bool)) ) 15.56/15.75 ( int, (fun int int) ) 15.56/15.75 ( int, (fun nat bool) ) 15.56/15.75 ( int, (fun nat nat) ) 15.56/15.75 ( int, real ) 15.56/15.75 ( int, (fun real real) ) 15.56/15.75 ( int, rat ) 15.56/15.75 ( int, (fun int rat) ) 15.56/15.75 ( int, (fun nat int) ) 15.56/15.75 ( int, (fun nat real) ) 15.56/15.75 ( int, (product_prod int int) ) 15.56/15.75 ( int, (fun int (product_prod int int)) ) 15.56/15.75 ( int, (fun (fun int bool) bool) ) 15.56/15.75 ( int, quickcheck_code_int ) 15.56/15.75 ( int, (fun bool bool) ) 15.56/15.75 ( int, (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 15.56/15.75 ( int, (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)) ) 15.56/15.75 ( int, (fun int (fun int (fun int bool))) ) 15.56/15.75 ( int, (fun (product_prod int int) bool) ) 15.56/15.75 ( int, (fun int (fun (product_prod int int) bool)) ) 15.56/15.75 ( int, (fun int (fun bool bool)) ) 15.56/15.75 ( int, (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 15.56/15.75 ( int, (fun (fun int int) (fun int bool)) ) 15.56/15.75 ( int, (fun (product_prod int int) int) ) 15.56/15.75 ( int, (product_prod int (product_prod int int)) ) 15.56/15.75 ( int, (fun int (product_prod int (product_prod int int))) ) 15.56/15.75 ( int, (fun int (fun int (product_prod int (product_prod int int)))) ) 15.56/15.75 ( int, (fun int (fun int (fun int (product_prod int (product_prod int int))))) ) 15.56/15.75 ( int, (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))) ) 15.56/15.75 ( int, (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))) ) 15.56/15.75 ( int, (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))) ) 15.56/15.75 ( int, (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))))) ) 15.56/15.75 ( int, (fun int (fun (fun int bool) bool)) ) 15.56/15.75 ( int, (list int) ) 15.56/15.75 ( int, (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 15.56/15.75 ( int, (fun int real) ) 15.56/15.75 ( int, (fun nat (fun bool bool)) ) 15.56/15.75 ( int, (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 15.56/15.75 ( int, (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 15.56/15.75 ( (fun int bool), bool ) 15.56/15.75 ( (fun int bool), int ) 15.56/15.75 ( (fun int bool), (fun int bool) ) 15.56/15.75 ( (fun int bool), (fun int (fun int bool)) ) 15.56/15.75 ( (fun int bool), (fun int (fun int int)) ) 15.56/15.75 ( (fun int bool), (fun int (fun bool bool)) ) 15.56/15.75 ( (fun int bool), (fun (fun int int) (fun int bool)) ) 15.56/15.75 ( (fun int bool), (fun real (fun int (fun int bool))) ) 15.56/15.75 ( (fun int (fun int bool)), (fun int bool) ) 15.56/15.75 ( (fun int (fun int bool)), (fun int (fun int bool)) ) 15.56/15.75 ( (fun int (fun int bool)), (fun int (fun (fun int int) (fun int bool))) ) 15.56/15.75 ( (fun int (fun int bool)), (fun int (fun int (fun bool bool))) ) 15.56/15.75 ( (fun int int), (fun int bool) ) 15.56/15.75 ( (fun int int), (fun int (fun int bool)) ) 15.56/15.75 ( (fun int int), (fun int int) ) 15.56/15.75 ( (fun int int), (fun int (fun int int)) ) 15.56/15.75 ( (fun int int), (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 15.56/15.75 ( (fun int int), (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 15.56/15.75 ( (fun nat bool), bool ) 15.56/15.75 ( (fun nat bool), (fun nat bool) ) 15.56/15.75 ( (fun nat bool), (fun nat (fun bool bool)) ) 15.56/15.75 ( (fun nat bool), (fun int (fun nat bool)) ) 15.56/15.75 ( (fun nat bool), (fun real (fun int (fun nat bool))) ) 15.56/15.75 ( (fun nat nat), (fun nat (fun nat bool)) ) 15.56/15.75 ( (fun nat nat), (fun nat real) ) 15.56/15.75 ( (fun nat nat), (fun nat (fun nat nat)) ) 15.56/15.75 ( (product_prod nat nat), bool ) 15.56/15.75 ( (product_prod nat nat), (fun (product_prod nat nat) bool) ) 15.56/15.75 ( real, bool ) 15.56/15.75 ( real, nat ) 15.56/15.75 ( real, (fun int bool) ) 15.56/15.75 ( real, (fun int (fun int bool)) ) 15.56/15.75 ( real, real ) 15.56/15.75 ( real, (fun real bool) ) 15.56/15.75 ( real, (fun real real) ) 15.56/15.75 ( real, complex ) 15.56/15.75 ( real, (fun nat real) ) 15.56/15.75 ( real, (fun real complex) ) 15.56/15.75 ( real, (fun bool bool) ) 15.56/15.75 ( real, (fun (filter nat) bool) ) 15.56/15.75 ( real, (fun nat (product_prod real real)) ) 15.56/15.75 ( real, (fun real (fun nat (product_prod real real))) ) 15.56/15.75 ( real, (fun (filter real) bool) ) 15.56/15.75 ( real, (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 15.56/15.75 ( real, (let ((_let_0 (fun int bool))) (fun _let_0 (fun int _let_0))) ) 15.56/15.75 ( real, (fun int (fun int (fun bool bool))) ) 15.56/15.75 ( real, (fun (fun int (fun int real)) (fun int (fun int bool))) ) 15.56/15.75 ( real, (fun (fun int real) (fun int bool)) ) 15.56/15.75 ( real, (fun int (fun nat bool)) ) 15.56/15.75 ( real, (let ((_let_0 (fun nat bool))) (fun _let_0 (fun int _let_0))) ) 15.56/15.75 ( real, (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 15.56/15.75 ( real, (fun int (fun nat (fun bool bool))) ) 15.56/15.75 ( real, (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 15.56/15.75 ( real, (fun (fun nat real) (fun nat bool)) ) 15.56/15.75 ( (fun real bool), real ) 15.56/15.75 ( (fun real bool), (fun real bool) ) 15.56/15.75 ( (fun real bool), (fun real (fun bool bool)) ) 15.56/15.75 ( (fun real bool), (fun (fun int real) (fun int bool)) ) 15.56/15.75 ( (fun real bool), (fun (fun nat real) (fun nat bool)) ) 15.56/15.75 ( (fun real real), (fun real real) ) 15.56/15.75 ( (fun real real), (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 15.56/15.75 ( (fun real real), (fun real (fun real real)) ) 15.56/15.75 ( (fun real real), (fun real (fun real bool)) ) 15.56/15.75 ( (fun real real), (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 15.56/15.75 ( rat, real ) 15.56/15.75 ( rat, (product_prod int int) ) 15.56/15.75 ( complex, nat ) 15.56/15.75 ( complex, real ) 15.56/15.75 ( complex, complex ) 15.56/15.75 ( (fun nat real), (fun nat bool) ) 15.56/15.75 ( (fun nat real), (fun nat real) ) 15.56/15.75 ( (fun nat real), (fun nat (fun real real)) ) 15.56/15.75 ( (fun nat real), (fun int (fun nat real)) ) 15.56/15.75 ( (filter nat), bool ) 15.56/15.75 ( (fun int (fun int int)), (fun int (fun int (fun int bool))) ) 15.56/15.75 ( (fun int (fun int int)), (let ((_let_0 (fun int int))) (fun int (fun _let_0 _let_0))) ) 15.56/15.75 ( (product_prod int int), bool ) 15.56/15.75 ( (product_prod int int), int ) 15.56/15.75 ( (product_prod int int), (fun int bool) ) 15.56/15.75 ( (product_prod int int), (fun int int) ) 15.56/15.75 ( (product_prod int int), rat ) 15.56/15.75 ( (product_prod int int), (product_prod int int) ) 15.56/15.75 ( (product_prod int int), (fun bool bool) ) 15.56/15.75 ( (product_prod int int), (fun (product_prod int int) bool) ) 15.56/15.75 ( (product_prod int int), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 15.56/15.75 ( (product_prod int int), (fun (product_prod int int) (fun int bool)) ) 15.56/15.75 ( (product_prod int int), (fun (product_prod int int) int) ) 15.56/15.75 ( (product_prod int int), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 15.56/15.75 ( (product_prod int int), (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 15.56/15.75 ( quickcheck_code_int, nat ) 15.56/15.75 ( quickcheck_code_int, int ) 15.56/15.75 ( quickcheck_code_int, (product_prod quickcheck_code_int quickcheck_code_int) ) 15.56/15.75 ( quickcheck_code_int, (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int)) ) 15.56/15.75 ( (fun bool bool), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 15.56/15.75 ( code_code_numeral, nat ) 15.56/15.75 ( code_code_numeral, int ) 15.56/15.75 ( code_code_numeral, (fun nat nat) ) 15.56/15.75 ( code_code_numeral, code_code_numeral ) 15.56/15.75 ( code_code_numeral, (product_prod code_code_numeral code_code_numeral) ) 15.56/15.75 ( code_code_numeral, (fun code_code_numeral (product_prod code_code_numeral code_code_numeral)) ) 15.56/15.75 ( (fun int (fun int (fun int bool))), (fun int (fun int (fun int bool))) ) 15.56/15.75 ( (fun real (fun real bool)), (fun real (fun (fun int real) (fun int bool))) ) 15.56/15.75 ( (fun real (fun real bool)), (fun real (fun (fun nat real) (fun nat bool))) ) 15.56/15.75 ( (product_prod real real), bool ) 15.56/15.75 ( (fun (product_prod real real) bool), (fun real (fun real (fun nat (product_prod real real)))) ) 15.56/15.75 ( (fun (product_prod int int) bool), (fun (product_prod int int) bool) ) 15.56/15.75 ( (fun (product_prod int int) bool), (fun (product_prod int int) (fun bool bool)) ) 15.56/15.75 ( (fun int (fun bool bool)), (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 15.56/15.75 ( (fun nat rat), bool ) 15.56/15.75 ( (filter real), bool ) 15.56/15.75 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)), bool ) 15.56/15.75 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 15.56/15.75 ( (fun (product_prod int int) (fun bool bool)), (let ((_let_0 (fun (product_prod int int) bool))) (fun (product_prod int int) (fun _let_0 _let_0))) ) 15.56/15.75 ( (fun (product_prod int int) (fun int bool)), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 15.56/15.75 ( (fun (product_prod int int) int), (fun (product_prod int int) bool) ) 15.56/15.75 ( (fun (product_prod int int) int), (fun (product_prod int int) (fun int bool)) ) 15.56/15.75 ( (fun (product_prod int int) int), (fun (product_prod int int) int) ) 15.56/15.75 ( (fun (product_prod int int) int), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))) ) 15.56/15.75 ( (fun (product_prod int int) int), (fun (product_prod int int) (fun int int)) ) 15.56/15.75 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 15.56/15.75 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 (fun int bool)))) ) 15.56/15.75 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 (fun int bool)))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun (fun _let_0 int) (fun _let_0 bool)))) ) 15.56/15.75 ( (fun (product_prod int int) (fun int int)), (let ((_let_0 (fun (product_prod int int) int))) (fun (product_prod int int) (fun _let_0 _let_0))) ) 15.56/15.75 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), bool ) 15.56/15.75 ( (fun int real), (fun int bool) ) 15.56/15.75 ( (fun int real), (fun int real) ) 15.56/15.75 ( (fun int real), (fun int (fun int real)) ) 15.56/15.75 ( (fun int real), (fun int (fun real real)) ) 15.56/15.75 ( (fun nat (fun bool bool)), (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 15.56/15.75 ( (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun int bool))) (fun _let_0 (fun int _let_0))) ) 15.56/15.75 ( (fun int (fun int (fun bool bool))), (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 15.56/15.75 ( (fun real (fun int bool)), (fun real bool) ) 15.56/15.75 ( (fun real (fun int (fun int bool))), (fun real (fun int bool)) ) 15.56/15.75 ( (fun real (fun int (fun int bool))), (fun real (fun int (fun int (fun bool bool)))) ) 15.56/15.75 ( (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun int bool))) (fun real (fun _let_0 (fun int _let_0)))) ) 15.56/15.75 ( (fun real (fun int (fun int (fun bool bool)))), (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))) ) 15.56/15.75 ( (fun int (fun int real)), (fun int (fun int bool)) ) 15.56/15.75 ( (fun int (fun int real)), (fun real (fun int (fun int bool))) ) 15.56/15.75 ( (fun (fun int real) (fun int bool)), (fun (fun int (fun int real)) (fun int (fun int bool))) ) 15.56/15.75 ( (fun real (fun (fun int real) (fun int bool))), (fun real (fun (fun int (fun int real)) (fun int (fun int bool)))) ) 15.56/15.75 ( (fun int (fun real real)), (let ((_let_0 (fun int real))) (fun int (fun _let_0 _let_0))) ) 15.56/15.75 ( (fun int (fun real real)), (let ((_let_0 (fun nat real))) (fun int (fun _let_0 _let_0))) ) 15.56/15.75 ( (fun int (fun nat bool)), (fun int bool) ) 15.56/15.75 ( (fun int (fun nat bool)), (fun int (fun nat (fun bool bool))) ) 15.56/15.75 ( (fun real (fun int (fun nat bool))), (fun real (fun int bool)) ) 15.56/15.75 ( (fun real (fun int (fun nat bool))), (fun real (fun int (fun nat (fun bool bool)))) ) 15.56/15.75 ( (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun nat bool))) (fun _let_0 (fun int _let_0))) ) 15.56/15.75 ( (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun nat bool))) (fun real (fun _let_0 (fun int _let_0)))) ) 15.56/15.75 ( (fun int (fun nat (fun bool bool))), (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 15.56/15.75 ( (fun real (fun int (fun nat (fun bool bool)))), (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))) ) 15.56/15.75 ( (fun int (fun nat real)), (fun int (fun nat bool)) ) 15.56/15.75 ( (fun int (fun nat real)), (fun real (fun int (fun nat bool))) ) 15.56/15.75 ( (fun (fun nat real) (fun nat bool)), (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 15.56/15.75 ( (fun real (fun (fun nat real) (fun nat bool))), (fun real (fun (fun int (fun nat real)) (fun int (fun nat bool)))) ) 15.56/15.75 ) 15.56/15.75 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (P_1 $$unsorted)) (let ((_let_0 (product_prod X_a X_b))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (the _let_0))) (let ((_let_3 (fun _let_0 X_b))) (let ((_let_4 (fun X_b bool))) (let ((_let_5 (fun _let_0 _let_4))) (let ((_let_6 (fun _let_0 X_a))) (let ((_let_7 (fun X_a _let_4))) (= (hAPP _let_1 _let_0 _let_2 (hAPP _let_7 _let_1 (product_prod_case X_a X_b bool) P_1)) (hAPP _let_1 _let_0 _let_2 (hAPP _let_3 _let_1 (hAPP _let_5 (fun _let_3 _let_1) (combs _let_0 X_b bool) (hAPP _let_6 _let_5 (hAPP _let_7 (fun _let_6 _let_5) (combb X_a _let_4 _let_0) P_1) (product_fst X_a X_b))) (product_snd X_a X_b)))))))))))) ) 15.56/15.75 ( nat, nat, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat (fun nat bool)))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat (fun nat bool) nat) (hAPP _let_1 _let_1 (combc nat nat bool) (fequal nat))) suc))) ) 15.56/15.75 ( int, int, (fequal int) ) 15.56/15.75 ( int, int, (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun int _let_1))) (let ((_let_6 (fun int _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (fun _let_2 _let_1))) (let ((_let_9 (fun _let_1 _let_1))) (hAPP _let_1 _let_1 (hAPP _let_7 _let_9 (combb _let_0 _let_0 int) (hAPP _let_6 _let_7 (combs int bool bool) (hAPP _let_0 _let_6 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 int) fconj) (hAPP int _let_0 (ord_less int) (zero_zero int))))) (hAPP int _let_1 (hAPP _let_5 _let_5 (combc int int _let_0) (hAPP _let_5 _let_5 (hAPP _let_9 (fun _let_5 _let_5) (combb _let_1 _let_1 int) (combc int int bool)) (hAPP _let_3 _let_5 (hAPP _let_8 (fun _let_3 _let_5) (combb _let_2 _let_1 int) (hAPP _let_1 _let_8 (combb int _let_0 int) (fequal int))) int_gcd))) (one_one int))))))))))))) ) 15.56/15.78 ( (product_prod int int), (product_prod int int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun _let_2 (fun _let_2 bool)))) (let ((_let_5 (fun (fun _let_2 bool) (fun _let_2 bool)))) (let ((_let_6 (fun _let_2 _let_5))) (let ((_let_7 (fun _let_4 _let_4))) (let ((_let_8 (fun _let_2 _let_3))) (let ((_let_9 (fun _let_2 _let_0))) (let ((_let_10 (fun _let_2 int))) (let ((_let_11 (fun _let_10 _let_9))) (let ((_let_12 (hAPP (fun int _let_0) _let_11 (combb int _let_0 _let_2) (fequal int)))) (let ((_let_13 (product_snd int int))) (let ((_let_14 (hAPP (fun _let_2 bool) _let_8 (hAPP (fun bool _let_3) (fun (fun _let_2 bool) _let_8) (combb bool _let_3 _let_2) fconj) (hAPP (fun _let_2 bool) (fun _let_2 bool) (hAPP _let_3 _let_5 (combb bool bool _let_2) fNot) (hAPP int (fun _let_2 bool) (hAPP _let_9 (fun int (fun _let_2 bool)) (combc _let_2 int bool) (hAPP _let_10 _let_9 _let_12 _let_13)) (zero_zero int)))))) (let ((_let_15 (fun _let_2 _let_10))) (let ((_let_16 (fun _let_10 (fun _let_2 bool)))) (let ((_let_17 (fun _let_2 _let_16))) (let ((_let_18 (fun _let_2 _let_9))) (let ((_let_19 (fun _let_10 _let_10))) (let ((_let_20 (fun _let_2 _let_19))) (let ((_let_21 (fun _let_10 _let_15))) (let ((_let_22 (fun _let_2 _let_1))) (let ((_let_23 (hAPP _let_10 _let_22 (hAPP (fun int _let_1) (fun _let_10 _let_22) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (let ((_let_24 (fun int _let_10))) (hAPP _let_4 _let_4 (hAPP _let_6 _let_7 (combs _let_2 (fun _let_2 bool) (fun _let_2 bool)) (hAPP _let_8 _let_6 (hAPP (fun _let_3 _let_5) (fun _let_8 _let_6) (combb _let_3 _let_5 _let_2) (combb bool bool _let_2)) _let_14)) (hAPP _let_4 _let_4 (hAPP _let_5 _let_7 (combb (fun _let_2 bool) (fun _let_2 bool) _let_2) (hAPP _let_8 _let_5 (combs _let_2 bool bool) _let_14)) (hAPP _let_15 _let_4 (hAPP _let_17 (fun _let_15 _let_4) (combs _let_2 _let_10 (fun _let_2 bool)) (hAPP _let_18 _let_17 (hAPP (fun _let_9 _let_16) (fun _let_18 _let_17) (combb _let_9 _let_16 _let_2) (combs _let_2 int bool)) (hAPP _let_15 _let_18 (hAPP _let_11 (fun _let_15 _let_18) (combb _let_10 _let_9 _let_2) _let_12) (hAPP _let_10 _let_15 (hAPP _let_20 _let_21 (combc _let_2 _let_10 _let_10) (hAPP _let_22 _let_20 (hAPP (fun _let_1 _let_19) (fun _let_22 _let_20) (combb _let_1 _let_19 _let_2) (combb int int _let_2)) _let_23)) _let_13)))) (hAPP _let_10 _let_15 (hAPP _let_24 _let_21 (combb int _let_10 _let_2) (hAPP _let_22 _let_24 (combc _let_2 int int) _let_23)) _let_13))))))))))))))))))))))))))))) ) 15.56/15.78 ) 15.56/15.78 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_119925 $$unsorted) (BOUND_VARIABLE_119926 $$unsorted)) (let ((_let_0 (norm_norm X_a))) (or (not (real_n1866405975lgebra X_a)) (= (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP X_a real _let_0 BOUND_VARIABLE_119925)) (hAPP X_a real _let_0 BOUND_VARIABLE_119926)) (hAPP X_a real _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_119925) BOUND_VARIABLE_119926))))) ) 15.56/15.78 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 15.56/15.78 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.56/15.78 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13 ) 15.56/15.78 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.56/15.78 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.56/15.78 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.56/15.78 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 15.56/15.78 ( complex, ii, ii ) 15.56/15.78 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 15.56/15.78 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 15.56/15.78 ) 15.56/15.79 (instantiation (forall ((B $$unsorted) (A_1 $$unsorted) (M $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (one_one int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (zero_zero int)) M))) (not (= _let_2 (hAPP int int (hAPP int _let_1 legacy_zgcd A_1) M))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong A_1) B) M))) (= _let_2 (hAPP int int (hAPP int _let_1 legacy_zgcd B) M)))))) ) 15.56/15.79 ( (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.56/15.79 ( (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.56/15.79 ( (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.56/15.79 ( s, s1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.56/15.79 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.56/15.79 ( skv_4, s1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.56/15.79 ( skv_10, s1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.56/15.79 ) 15.56/15.79 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (BOUND_VARIABLE_119982 $$unsorted) (BOUND_VARIABLE_119983 $$unsorted) (BOUND_VARIABLE_119984 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (zero_zero X_b))) (or (not (comm_semiring_1 X_b)) (not (hBOOL (hAPP _let_0 bool (finite_finite_1 X_a) BOUND_VARIABLE_119983))) (= _let_1 (hAPP _let_0 X_b (hAPP (fun X_a X_b) (fun _let_0 X_b) (big_co302546470etprod X_a X_b) BOUND_VARIABLE_119982) BOUND_VARIABLE_119983)) (not (= _let_1 (hAPP X_a X_b BOUND_VARIABLE_119982 BOUND_VARIABLE_119984))) (not (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) BOUND_VARIABLE_119984) BOUND_VARIABLE_119983)))))) ) 15.56/15.79 ( nat, int, (hAPP int (fun nat int) (power_power int) s), (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.79 ) 15.56/15.79 (instantiation (forall ((Y_2 $$unsorted) (X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) (zero_zero real)) X_2))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) X_2) Y_2))) (not (forall ((X $$unsorted)) (let ((_let_1 (ord_less real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_2) X))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X) Y_2))) (not (hBOOL (hAPP _let_0 bool (hAPP real (fun _let_0 bool) (member real) X) (field_char_0_Rats real)))))) )))) ) 15.56/15.79 ( (zero_zero real), pi ) 15.56/15.79 ( (zero_zero real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.56/15.79 ( (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.79 ( pi, (zero_zero real) ) 15.56/15.79 ( pi, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 15.56/15.79 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.79 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.56/15.79 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 15.56/15.79 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 15.56/15.79 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.56/15.79 ( skv_2, (zero_zero real) ) 15.56/15.79 ( skv_8, (zero_zero real) ) 15.56/15.79 ( skv_9, (zero_zero real) ) 15.56/15.79 ) 15.56/15.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_120056 $$unsorted) (BOUND_VARIABLE_120057 $$unsorted) (BOUND_VARIABLE_120058 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (or (not (order X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_120057) BOUND_VARIABLE_120058))) (not (= (ti X_a BOUND_VARIABLE_120057) (ti X_a BOUND_VARIABLE_120056))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_120056) BOUND_VARIABLE_120058))))) ) 15.56/15.79 ( int, pls, min_1, pls ) 15.56/15.79 ( int, min_1, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.56/15.79 ( int, s, (zero_zero int), s ) 15.56/15.79 ( int, m, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.56/15.79 ( int, s1, (zero_zero int), (one_one int) ) 15.56/15.79 ( int, t, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.79 ( real, pi, (zero_zero real), pi ) 15.56/15.79 ) 15.56/15.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_120087 $$unsorted) (BOUND_VARIABLE_120088 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (fun X_a X_a))) (let ((_let_3 (plus_plus X_a))) (let ((_let_4 (one_one X_a))) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_120087) BOUND_VARIABLE_120088))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_2 (inverse_divide X_a) (hAPP X_a X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_120087) BOUND_VARIABLE_120088)) (hAPP X_a X_a (hAPP X_a _let_2 _let_3 _let_4) _let_4))) BOUND_VARIABLE_120088)))))))) ) 15.56/15.79 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.79 ( nat, (one_one nat), (one_one nat) ) 15.56/15.79 ( int, (one_one int), t ) 15.56/15.79 ( int, pls, (one_one int) ) 15.56/15.79 ( int, pls, pls ) 15.56/15.79 ( int, pls, min_1 ) 15.56/15.79 ( int, pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.56/15.79 ( int, min_1, pls ) 15.56/15.79 ( int, min_1, min_1 ) 15.56/15.79 ( int, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.56/15.79 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 15.56/15.79 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 15.56/15.79 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.56/15.79 ( int, skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.56/15.79 ( int, skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.56/15.79 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.79 ( real, (zero_zero real), pi ) 15.56/15.79 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.79 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.79 ( real, (zero_zero real), skv_2 ) 15.56/15.79 ( real, (zero_zero real), skv_8 ) 15.56/15.79 ( real, (zero_zero real), skv_9 ) 15.56/15.79 ( real, pi, (zero_zero real) ) 15.56/15.79 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.79 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.79 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 15.56/15.79 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.56/15.79 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 15.56/15.79 ) 15.56/15.79 (instantiation (forall ((Z_1 $$unsorted)) (= (hAPP complex real re (hAPP int complex (ring_1_of_int complex) Z_1)) (hAPP int real (ring_1_of_int real) Z_1)) ) 15.56/15.79 ( (one_one int) ) 15.56/15.79 ( (zero_zero int) ) 15.56/15.79 ) 15.56/15.79 (instantiation (forall ((Y_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP int real (number_number_of real) min_1)) Y_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Y_1) (one_one real)))) (not (forall ((X $$unsorted)) (let ((_let_2 (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (or (not (forall ((Y $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Y) _let_2))) (not (= Y_1 (hAPP real real sin Y))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (uminus_uminus real) _let_2)) Y))) (= X Y)) )) (not (= Y_1 (hAPP real real sin X))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X) _let_2))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (uminus_uminus real) _let_2)) X))))) ))))) ) 15.56/15.79 ( (zero_zero real) ) 15.56/15.79 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.79 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.79 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.79 ( skv_5 ) 15.56/15.79 ) 15.56/15.79 (instantiation (forall ((N $$unsorted) (Ma $$unsorted)) (let ((_let_0 (hAPP nat (fun nat bool) (ord_less nat) N))) (or (hBOOL (hAPP nat bool _let_0 Ma)) (= (hBOOL (hAPP nat bool _let_0 (hAPP nat nat suc Ma))) (= N Ma)))) ) 15.56/15.79 ( (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 15.56/15.79 ) 15.56/15.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_120184 $$unsorted) (BOUND_VARIABLE_120185 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (times_times X_a))) (let ((_let_2 (abs_abs X_a))) (or (not (linordered_idom X_a)) (= (hAPP X_a X_a _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_120184) BOUND_VARIABLE_120185)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_120184)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_120185))))))) ) 15.56/15.79 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 15.56/15.79 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.56/15.79 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13 ) 15.56/15.79 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.56/15.79 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.56/15.79 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.56/15.79 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 15.56/15.79 ( complex, ii, ii ) 15.56/15.79 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 15.56/15.79 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 15.56/15.79 ) 15.56/15.79 (instantiation (forall ((N_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (hAPP int real (real_1 int) N_1))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) (hAPP real real (hAPP real (fun real real) (minus_minus real) _let_1) (one_one real))) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) X_1) _let_1))) (= (ti int N_1) (hAPP real int (archimedean_ceiling real) X_1))))) ) 15.56/15.79 ( (zero_zero int), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.79 ) 15.56/15.79 (instantiation (forall ((Y_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP int real (number_number_of real) min_1)) Y_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Y_1) (one_one real)))) (not (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X) pi))) (not (= Y_1 (hAPP real real cos X))) (not (forall ((Y $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) Y))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Y) pi))) (not (= Y_1 (hAPP real real cos Y))) (= X Y)) )) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) X)))) ))))) ) 15.56/15.79 ( (zero_zero real) ) 15.56/15.79 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.79 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.79 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.79 ( skv_5 ) 15.56/15.79 ) 15.56/15.79 (instantiation (forall ((Z_1 $$unsorted) (W $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (= (hAPP int int (hAPP int _let_0 _let_1 W) Z_1) (hAPP int int (hAPP int _let_0 _let_1 Z_1) W)))) ) 15.56/15.79 ( (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.56/15.79 ( (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.79 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 15.56/15.79 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 15.56/15.79 ) 15.56/15.79 (instantiation (forall ((N_1 $$unsorted)) (= N_1 (hAPP real nat natfloor (hAPP nat real (real_1 nat) N_1))) ) 15.56/15.79 ( (zero_zero nat) ) 15.56/15.79 ( (hAPP nat nat suc (zero_zero nat)) ) 15.56/15.79 ) 15.56/15.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_120299 $$unsorted) (BOUND_VARIABLE_120300 $$unsorted) (BOUND_VARIABLE_120301 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (or (not (division_ring X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_120301)) (= (= (hAPP X_a X_a (hAPP X_a _let_0 (inverse_divide X_a) BOUND_VARIABLE_120299) BOUND_VARIABLE_120301) (ti X_a BOUND_VARIABLE_120300)) (= (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_120300) BOUND_VARIABLE_120301) (ti X_a BOUND_VARIABLE_120299))))) ) 15.56/15.79 ( real, pi, pi, pi ) 15.56/15.79 ) 15.56/15.79 (instantiation (forall ((X_a $$unsorted)) (or (not (real_normed_vector X_a)) (not (forall ((K_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) K_2))) (not (forall ((A_4 $$unsorted) (B_4 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (times_times real))) (let ((_let_2 (norm_norm X_a))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP X_a real _let_2 (hAPP X_a X_a (hAPP real (fun X_a X_a) (scaleR_scaleR X_a) A_4) B_4))) (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real (norm_norm real) A_4)) (hAPP X_a real _let_2 B_4))) K_2)))))) ))) ))) ) 15.56/15.79 ( real ) 15.56/15.79 ( complex ) 15.56/15.79 ) 15.56/15.79 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (one_one real))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 (zero_zero real)) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 X_1) _let_1))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 (hAPP real real (hAPP real _let_3 (minus_minus real) X_1) (hAPP nat real (hAPP real (fun nat real) (power_power real) X_1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real real ln (hAPP real real (hAPP real _let_3 (plus_plus real) _let_1) X_1))))))))) ) 15.56/15.79 ( pi ) 15.56/15.79 ( (hAPP int real (number_number_of real) min_1) ) 15.56/15.79 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.79 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.79 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.79 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))) ) 15.56/15.79 ( skv_3 ) 15.56/15.79 ( skv_5 ) 15.56/15.79 ( skv_7 ) 15.56/15.79 ( skv_12 ) 15.56/15.79 ) 15.56/15.79 (instantiation (forall ((X_1 $$unsorted)) (= (hAPP real real (uminus_uminus real) (hAPP real real sin X_1)) (hAPP real real sin (hAPP real real (hAPP real (fun real real) (plus_plus real) X_1) pi))) ) 15.56/15.79 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.79 ) 15.56/15.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_120369 $$unsorted) (BOUND_VARIABLE_120370 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (plus_plus X_a))) (let ((_let_2 (times_times X_a))) (or (not (comm_semiring_1 X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_120369) (one_one X_a))) BOUND_VARIABLE_120370) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_120369) BOUND_VARIABLE_120370)) BOUND_VARIABLE_120370)))))) ) 15.56/15.79 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 15.56/15.79 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), t ) 15.56/15.79 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), skv_13 ) 15.56/15.79 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.56/15.79 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13 ) 15.56/15.79 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.56/15.79 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.56/15.79 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.56/15.79 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 15.56/15.79 ( complex, ii, ii ) 15.56/15.79 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 15.56/15.79 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 15.56/15.79 ) 15.56/15.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_120395 $$unsorted)) (or (not (division_ring X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_120395)) (= (one_one X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_120395) (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_120395)))) ) 15.56/15.79 ( bool, fFalse ) 15.56/15.79 ( bool, fTrue ) 15.56/15.79 ( int, pls ) 15.56/15.79 ( int, min_1 ) 15.56/15.79 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.79 ( int, s ) 15.56/15.79 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.79 ( int, m ) 15.56/15.79 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.56/15.79 ( int, s1 ) 15.56/15.79 ( int, t ) 15.56/15.79 ( (fun int bool), nat_neg ) 15.56/15.79 ( (fun int bool), zprime ) 15.56/15.79 ( (fun int bool), zEven ) 15.56/15.79 ( (fun int bool), zOdd ) 15.56/15.79 ( (fun int bool), (even_odd_even int) ) 15.56/15.79 ( (fun int bool), twoSqu1091635170sum2sq ) 15.56/15.79 ( (fun int bool), nat_is_nat ) 15.56/15.79 ( (fun int (fun int bool)), norRRset ) 15.56/15.79 ( (fun int (fun int bool)), quadRes ) 15.56/15.79 ( (fun int (fun int bool)), sRStar ) 15.56/15.79 ( (fun int (fun int bool)), d22set ) 15.56/15.79 ( (fun int (fun int bool)), sr ) 15.56/15.79 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 15.56/15.79 ( (fun int int), zfact ) 15.56/15.79 ( (fun int int), bit0 ) 15.56/15.79 ( (fun int int), bit1 ) 15.56/15.79 ( (fun int int), (fact_fact int) ) 15.56/15.79 ( (fun int int), pred ) 15.56/15.79 ( (fun int int), succ ) 15.56/15.79 ( (fun nat bool), (even_odd_even nat) ) 15.56/15.79 ( (fun nat bool), prime ) 15.56/15.79 ( (fun nat nat), suc ) 15.56/15.79 ( (fun nat nat), (fact_fact nat) ) 15.56/15.79 ( (fun nat nat), fact ) 15.56/15.79 ( (fun nat nat), nat_size ) 15.56/15.79 ( (fun nat nat), (size_size nat) ) 15.56/15.79 ( (fun (product_prod nat nat) bool), pred_nat ) 15.56/15.79 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 15.56/15.79 ( real, (zero_zero real) ) 15.56/15.79 ( real, pi ) 15.56/15.79 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.79 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.56/15.79 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 15.56/15.79 ( (fun real real), ln ) 15.56/15.79 ( (fun real real), cos ) 15.56/15.79 ( (fun real real), sqrt ) 15.56/15.79 ( (fun real real), sin ) 15.56/15.79 ( (fun real real), arccos ) 15.56/15.79 ( (fun real real), arcsin ) 15.56/15.79 ( (fun real real), tan ) 15.56/15.79 ( (fun real real), arctan ) 15.56/15.79 ( (fun nat (fun nat bool)), coprime ) 15.56/15.79 ( complex, ii ) 15.56/15.79 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.79 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 15.56/15.79 ( (fun nat real), (real_1 nat) ) 15.56/15.79 ( (fun nat real), sin_coeff ) 15.56/15.79 ( (fun nat real), cos_coeff ) 15.56/15.79 ( (filter nat), sequentially ) 15.56/15.79 ( (fun int (fun int int)), (gcd_gcd int) ) 15.56/15.79 ( (fun int (fun int int)), legendre ) 15.56/15.79 ( (fun int (fun int int)), legacy_zgcd ) 15.56/15.79 ( (fun int (fun int int)), standardRes ) 15.56/15.79 ( (fun int (fun int int)), nat_tsub ) 15.56/15.79 ( (fun int (fun int int)), multInv ) 15.56/15.79 ( (fun int (fun int int)), z3mod ) 15.56/15.79 ( (fun int (fun int int)), z3div ) 15.56/15.79 ( (fun int (fun int int)), int_gcd ) 15.56/15.79 ( (fun int (fun int int)), int_lcm ) 15.56/15.79 ( (fun int (fun int int)), inv ) 15.56/15.79 ( (fun complex complex), expi ) 15.56/15.79 ( (fun complex complex), cnj ) 15.56/15.79 ( (fun real complex), cis ) 15.56/15.79 ( (fun int nat), nat_1 ) 15.56/15.79 ( (fun int nat), phi ) 15.56/15.79 ( (fun (fun int bool) bool), nat_nat_set ) 15.56/15.79 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 15.56/15.79 ( (fun nat (fun nat nat)), nat_gcd ) 15.56/15.79 ( (fun nat (fun nat nat)), nat_lcm ) 15.56/15.79 ( (fun (fun int bool) int), (the int) ) 15.56/15.79 ( (fun complex real), re ) 15.56/15.79 ( (fun complex real), im ) 15.56/15.79 ( (fun complex real), arg ) 15.56/15.79 ( (fun bool bool), fNot ) 15.56/15.79 ( (fun nat (fun real real)), root ) 15.56/15.79 ( (fun real (fun real real)), log ) 15.56/15.79 ( (fun real (fun real real)), powr ) 15.56/15.79 ( (fun bool (fun bool bool)), fimplies ) 15.56/15.79 ( (fun bool (fun bool bool)), fconj ) 15.56/15.79 ( (fun bool (fun bool bool)), fdisj ) 15.56/15.79 ( (fun int (fun int (product_prod int int))), negDivAlg ) 15.56/15.79 ( (fun int (fun int (product_prod int int))), posDivAlg ) 15.56/15.79 ( (fun int (fun int (product_prod int int))), divmod_int ) 15.56/15.79 ( (fun int (fun int (product_prod int int))), pdivmod ) 15.56/15.79 ( (fun int (fun int (product_prod int int))), norm_frac ) 15.56/15.79 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 15.56/15.79 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 15.56/15.79 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 15.56/15.79 ( (fun int (fun int (fun int bool))), zcong ) 15.56/15.79 ( (fun int (fun int (fun int bool))), zcongm ) 15.56/15.79 ( (fun int (fun int (fun int bool))), noXRRset ) 15.56/15.79 ( (fun int (fun int (fun int bool))), bnorRset ) 15.56/15.79 ( (fun int (fun int (fun int bool))), wset ) 15.56/15.79 ( (fun (product_prod int int) bool), frac_1 ) 15.56/15.79 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 15.56/15.79 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 15.56/15.79 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 15.56/15.79 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 15.56/15.79 ( (fun (fun nat rat) bool), vanishes ) 15.56/15.79 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 15.56/15.79 ( (fun code_code_numeral nat), code_c271388182l_size ) 15.56/15.79 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 15.56/15.79 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 15.56/15.79 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 15.56/15.79 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 15.56/15.79 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 15.56/15.79 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 15.56/15.79 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 15.56/15.79 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 15.56/15.79 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 15.56/15.79 ( (fun complex nat), complex_size ) 15.56/15.79 ( (fun complex nat), (size_size complex) ) 15.56/15.79 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 15.56/15.79 ( (fun nat (fun nat (product_prod int int))), bezw ) 15.56/15.79 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 15.56/15.79 ( (fun int (fun nat nat)), nat_aux ) 15.56/15.79 ( (fun int (fun (fun int bool) bool)), rsetR ) 15.56/15.79 ( (fun int (fun (fun int bool) bool)), resSet ) 15.56/15.79 ( (fun int (list int)), quickc666637781d_zero ) 15.56/15.79 ( (fun (product_prod int int) rat), frct ) 15.56/15.79 ( (fun int (fun int rat)), fract ) 15.56/15.79 ( (fun real (fun real complex)), complex_1 ) 15.56/15.79 ( (fun real (fun real complex)), rcis ) 15.56/15.79 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 15.56/15.79 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 15.56/15.79 ( (fun int real), (real_1 int) ) 15.56/15.79 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 15.56/15.79 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 15.56/15.79 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 15.56/15.79 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 15.56/15.79 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 15.56/15.79 ( (fun real nat), natfloor ) 15.56/15.79 ( (fun real nat), natceiling ) 15.56/15.79 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 15.56/15.79 ( (fun quickcheck_code_int int), quickcheck_int_of ) 15.56/15.79 ( (fun rat (product_prod int int)), quotient_of ) 15.56/15.79 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 15.56/15.79 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 15.56/15.79 ( (fun rat real), ratreal ) 15.56/15.79 ( (fun code_code_numeral int), code_int_of ) 15.56/15.79 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 15.56/15.79 ( (fun int quickcheck_code_int), quickcheck_of_int ) 15.56/15.79 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 15.56/15.79 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 15.56/15.79 ) 15.56/15.79 (instantiation (forall ((N_1 $$unsorted)) (= (hAPP real int (archim2085082626_floor real) (hAPP real real (uminus_uminus real) (hAPP nat real (real_1 nat) N_1))) (hAPP int int (uminus_uminus int) (hAPP nat int (semiring_1_of_nat int) N_1))) ) 15.56/15.79 ( (zero_zero nat) ) 15.56/15.79 ( (hAPP nat nat suc (zero_zero nat)) ) 15.56/15.79 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.56/15.79 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.79 ) 15.56/15.79 (instantiation (forall ((W_1 $$unsorted) (Ma $$unsorted)) (let ((_let_0 (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) W_1)))) (= (= Ma (hAPP int nat nat_1 W_1)) (and (or (not _let_0) (= (ti int W_1) (hAPP nat int (semiring_1_of_nat int) Ma))) (or _let_0 (= (zero_zero nat) Ma))))) ) 15.56/15.79 ( (one_one int), (zero_zero nat) ) 15.56/15.79 ( (zero_zero int), (hAPP nat nat suc (zero_zero nat)) ) 15.56/15.79 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.79 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.56/15.79 ) 15.56/15.79 (instantiation (forall ((X_a $$unsorted)) (or (not (number_ring X_a)) (not (hBOOL (hAPP X_a bool (iszero X_a) (hAPP int X_a (number_number_of X_a) min_1))))) ) 15.56/15.79 ( nat ) 15.56/15.79 ( int ) 15.56/15.79 ( real ) 15.56/15.79 ( rat ) 15.56/15.79 ( complex ) 15.56/15.79 ( quickcheck_code_int ) 15.56/15.79 ( code_code_numeral ) 15.56/15.79 ) 15.56/15.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_120492 $$unsorted)) (or (not (finite_finite X_a)) (hBOOL (hAPP (fun X_a bool) bool (finite_finite_1 X_a) BOUND_VARIABLE_120492))) ) 15.56/15.79 ( nat, (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 15.56/15.79 ) 15.56/15.79 (instantiation (forall ((A_2 $$unsorted) (C_1 $$unsorted) (D_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (zero_zero int))) (let ((_let_3 (fun int rat))) (or (= _let_2 (ti int B_1)) (= _let_2 (ti int D_1)) (= (= (hAPP int int (hAPP int _let_0 _let_1 C_1) B_1) (hAPP int int (hAPP int _let_0 _let_1 A_2) D_1)) (= (hAPP int rat (hAPP int _let_3 fract C_1) D_1) (hAPP int rat (hAPP int _let_3 fract A_2) B_1)))))))) ) 15.56/15.79 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), s, s ) 15.56/15.79 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), s1, s1 ) 15.56/15.79 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), s, s ) 15.56/15.79 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), m, m ) 15.56/15.79 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t, m ) 15.56/15.79 ) 15.56/15.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_120541 $$unsorted) (BOUND_VARIABLE_120542 $$unsorted)) (let ((_let_0 (fun nat X_a))) (let ((_let_1 (power_power X_a))) (let ((_let_2 (abs_abs X_a))) (or (not (linordered_idom X_a)) (= (hAPP X_a X_a _let_2 (hAPP nat X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_120541) BOUND_VARIABLE_120542)) (hAPP nat X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_120541)) BOUND_VARIABLE_120542)))))) ) 15.56/15.79 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.79 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.79 ( int, skv_14, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.79 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.79 ) 15.56/15.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_120565 $$unsorted) (BOUND_VARIABLE_120566 $$unsorted)) (or (not (group_add X_a)) (not (= (zero_zero X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_120565) BOUND_VARIABLE_120566))) (= (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_120565) (ti X_a BOUND_VARIABLE_120566))) ) 15.56/15.79 ( nat, (one_one nat), (one_one nat) ) 15.56/15.79 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 15.56/15.79 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 15.56/15.79 ) 15.56/15.79 (instantiation (forall ((Y_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun _let_0 _let_0))) (let ((_let_7 (combs real bool bool))) (let ((_let_8 (hAPP (fun bool _let_3) (fun _let_0 _let_5) (combb bool _let_3 real) fconj))) (let ((_let_9 (combc real real bool))) (= (hAPP real real arccos Y_2) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_5 _let_6 _let_7 (hAPP _let_0 _let_5 _let_8 (hAPP real _let_0 _let_1 (zero_zero real)))) (hAPP _let_0 _let_0 (hAPP _let_5 _let_6 _let_7 (hAPP _let_0 _let_5 _let_8 (hAPP real _let_0 (hAPP _let_4 _let_4 _let_9 _let_1) pi))) (hAPP real _let_0 (hAPP _let_4 _let_4 _let_9 (hAPP _let_2 _let_4 (hAPP _let_4 (fun _let_2 _let_4) (combb real _let_0 real) (fequal real)) cos)) Y_2))))))))))))))) ) 15.56/15.79 ( (zero_zero real) ) 15.56/15.79 ) 15.56/15.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_120591 $$unsorted) (BOUND_VARIABLE_120592 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (or (not (linorder X_a)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_120591) BOUND_VARIABLE_120592)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_120592) BOUND_VARIABLE_120591))))) ) 15.56/15.79 ( int, (one_one int), (zero_zero int) ) 15.56/15.79 ( int, (one_one int), t ) 15.56/15.79 ( int, (zero_zero int), (one_one int) ) 15.56/15.79 ( int, (zero_zero int), min_1 ) 15.56/15.79 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.56/15.79 ( int, (zero_zero int), s ) 15.56/15.79 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.56/15.79 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.56/15.79 ( int, (zero_zero int), skv_4 ) 15.56/15.79 ( int, (zero_zero int), skv_10 ) 15.56/15.79 ( int, pls, min_1 ) 15.56/15.79 ( int, min_1, (zero_zero int) ) 15.56/15.79 ( int, min_1, pls ) 15.56/15.79 ( int, min_1, min_1 ) 15.56/15.79 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 15.56/15.79 ( int, s, (zero_zero int) ) 15.56/15.79 ( int, t, (one_one int) ) 15.63/15.79 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 15.63/15.79 ( int, (hAPP int int (number_number_of int) pls), (zero_zero int) ) 15.63/15.79 ( int, skv_4, (zero_zero int) ) 15.63/15.79 ( int, skv_10, (zero_zero int) ) 15.63/15.79 ( real, (zero_zero real), pi ) 15.63/15.79 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.79 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.79 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.79 ( real, (zero_zero real), skv_3 ) 15.63/15.79 ( real, (zero_zero real), skv_5 ) 15.63/15.79 ( real, (zero_zero real), skv_7 ) 15.63/15.79 ( real, (zero_zero real), skv_12 ) 15.63/15.79 ( real, pi, (zero_zero real) ) 15.63/15.79 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.79 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.63/15.79 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.79 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_5 ) 15.63/15.79 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.63/15.79 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.79 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.63/15.79 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.63/15.79 ( real, skv_3, (zero_zero real) ) 15.63/15.79 ( real, skv_5, (zero_zero real) ) 15.63/15.79 ( real, skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.79 ( real, skv_7, (zero_zero real) ) 15.63/15.79 ( real, skv_12, (zero_zero real) ) 15.63/15.79 ) 15.63/15.79 (instantiation (forall ((A_1 $$unsorted)) (= (ti int A_1) (hAPP int int (hAPP int (fun int int) (div_mod int) A_1) (zero_zero int))) ) 15.63/15.79 ( pls ) 15.63/15.79 ( min_1 ) 15.63/15.79 ( s ) 15.63/15.79 ( m ) 15.63/15.79 ( s1 ) 15.63/15.79 ( t ) 15.63/15.79 ) 15.63/15.79 (instantiation (forall ((N_1 $$unsorted) (K_4 $$unsorted)) (let ((_let_0 (fun int int))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) K_4))) (= (ti int K_4) (hAPP int int (hAPP int _let_0 legacy_zgcd K_4) (hAPP int int (hAPP int _let_0 (times_times int) K_4) N_1))))) ) 15.63/15.79 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.79 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.79 ( skv_13, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.79 ) 15.63/15.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_120682 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP X_a int (archim2085082626_floor X_a) BOUND_VARIABLE_120682)) (one_one int))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_120682) (one_one X_a))))) ) 15.63/15.79 ( nat, (zero_zero nat) ) 15.63/15.79 ( int, (one_one int) ) 15.63/15.79 ( int, pls ) 15.63/15.79 ( int, min_1 ) 15.63/15.79 ( int, s ) 15.63/15.79 ( int, t ) 15.63/15.79 ( int, skv_4 ) 15.63/15.79 ( int, skv_10 ) 15.63/15.79 ( real, (one_one real) ) 15.63/15.79 ( real, (zero_zero real) ) 15.63/15.79 ( real, pi ) 15.63/15.79 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.79 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.63/15.79 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.79 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 15.63/15.79 ) 15.63/15.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_120701 $$unsorted) (BOUND_VARIABLE_120702 $$unsorted)) (let ((_let_0 (uminus_uminus X_a))) (let ((_let_1 (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_120701))) (or (not (field_inverse_zero X_a)) (= (hAPP X_a X_a _let_1 (hAPP X_a X_a _let_0 BOUND_VARIABLE_120702)) (hAPP X_a X_a _let_0 (hAPP X_a X_a _let_1 BOUND_VARIABLE_120702)))))) ) 15.63/15.79 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.79 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.63/15.79 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.79 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 15.63/15.79 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.79 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.79 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.63/15.79 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.63/15.79 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.79 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.79 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.79 ) 15.63/15.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_120764 $$unsorted) (BOUND_VARIABLE_120765 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (or (not (order X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_120764) BOUND_VARIABLE_120765))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_120765) BOUND_VARIABLE_120764))) (= (ti X_a BOUND_VARIABLE_120764) (ti X_a BOUND_VARIABLE_120765))))) ) 15.63/15.79 ( int, (one_one int), (zero_zero int) ) 15.63/15.79 ( int, (one_one int), t ) 15.63/15.79 ( int, (zero_zero int), (one_one int) ) 15.63/15.79 ( int, (zero_zero int), min_1 ) 15.63/15.79 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.79 ( int, (zero_zero int), s ) 15.63/15.79 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.63/15.79 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.63/15.79 ( int, (zero_zero int), skv_4 ) 15.63/15.79 ( int, (zero_zero int), skv_10 ) 15.63/15.79 ( int, pls, min_1 ) 15.63/15.79 ( int, min_1, (zero_zero int) ) 15.63/15.79 ( int, min_1, pls ) 15.63/15.79 ( int, min_1, min_1 ) 15.63/15.79 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 15.63/15.79 ( int, s, (zero_zero int) ) 15.63/15.79 ( int, t, (one_one int) ) 15.63/15.79 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 15.63/15.79 ( int, (hAPP int int (number_number_of int) pls), (zero_zero int) ) 15.63/15.79 ( int, skv_4, (zero_zero int) ) 15.63/15.79 ( int, skv_10, (zero_zero int) ) 15.63/15.79 ( real, (zero_zero real), pi ) 15.63/15.79 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.79 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.79 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.79 ( real, (zero_zero real), skv_3 ) 15.63/15.79 ( real, (zero_zero real), skv_5 ) 15.63/15.79 ( real, (zero_zero real), skv_7 ) 15.63/15.79 ( real, (zero_zero real), skv_12 ) 15.63/15.79 ( real, pi, (zero_zero real) ) 15.63/15.79 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.79 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.63/15.79 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.79 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_5 ) 15.63/15.79 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.63/15.79 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.79 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.63/15.79 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.63/15.79 ( real, skv_3, (zero_zero real) ) 15.63/15.79 ( real, skv_5, (zero_zero real) ) 15.63/15.79 ( real, skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.79 ( real, skv_7, (zero_zero real) ) 15.63/15.79 ( real, skv_12, (zero_zero real) ) 15.63/15.79 ) 15.63/15.79 (instantiation (forall ((X_a $$unsorted)) (or (not (real_algebra_1 X_a)) (not (real_normed_vector X_a)) (not (forall ((K_2 $$unsorted)) (not (forall ((X $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP X_a real (norm_norm X_a) (hAPP real X_a (of_real X_a) X))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP real real (norm_norm real) X)) K_2))) )) ))) ) 15.63/15.79 ( real ) 15.63/15.79 ( complex ) 15.63/15.79 ) 15.63/15.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_120828 $$unsorted) (BOUND_VARIABLE_120829 $$unsorted)) (or (not (linorder X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_120828) BOUND_VARIABLE_120829))) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (ord_min X_a) BOUND_VARIABLE_120829) BOUND_VARIABLE_120828) (ti X_a BOUND_VARIABLE_120828))) ) 15.63/15.79 ( int, (one_one int), t ) 15.63/15.79 ( int, (zero_zero int), (one_one int) ) 15.63/15.79 ( int, (zero_zero int), min_1 ) 15.63/15.79 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.79 ( int, (zero_zero int), s ) 15.63/15.79 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.63/15.79 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.63/15.79 ( int, (zero_zero int), skv_4 ) 15.63/15.79 ( int, (zero_zero int), skv_10 ) 15.63/15.79 ( int, min_1, pls ) 15.63/15.79 ( int, min_1, min_1 ) 15.63/15.79 ( real, (zero_zero real), pi ) 15.63/15.79 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.79 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.79 ( real, (zero_zero real), skv_3 ) 15.63/15.79 ( real, (zero_zero real), skv_5 ) 15.63/15.79 ( real, (zero_zero real), skv_7 ) 15.63/15.79 ( real, (zero_zero real), skv_12 ) 15.63/15.79 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.63/15.79 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.79 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.63/15.79 ( real, skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.79 ) 15.63/15.79 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (BOUND_VARIABLE_120847 $$unsorted) (BOUND_VARIABLE_120848 $$unsorted)) (let ((_let_0 (fun (filter X_a) bool))) (let ((_let_1 (fun X_a real))) (let ((_let_2 (fun X_a X_b))) (or (not (real_normed_vector X_b)) (= (hBOOL (hAPP (filter X_a) bool (hAPP real _let_0 (hAPP _let_1 (fun real _let_0) (tendsto X_a real) (hAPP _let_2 _let_1 (hAPP (fun X_b real) (fun _let_2 _let_1) (combb X_b real X_a) (norm_norm X_b)) BOUND_VARIABLE_120847)) (zero_zero real)) BOUND_VARIABLE_120848)) (hBOOL (hAPP (filter X_a) bool (hAPP X_b _let_0 (hAPP _let_2 (fun X_b _let_0) (tendsto X_a X_b) BOUND_VARIABLE_120847) (zero_zero X_b)) BOUND_VARIABLE_120848))))))) ) 15.63/15.79 ( nat, real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))), sequentially ) 15.63/15.79 ( real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (hAPP real (filter real) (at real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.63/15.79 ) 15.63/15.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_120905 $$unsorted)) (or (not (ordere142940540dd_abs X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_120905) (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_120905)))) ) 15.63/15.79 ( int, (one_one int) ) 15.63/15.79 ( int, (zero_zero int) ) 15.63/15.79 ( int, min_1 ) 15.63/15.79 ( real, (zero_zero real) ) 15.63/15.79 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.79 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.79 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.79 ( real, skv_5 ) 15.63/15.79 ) 15.63/15.80 (instantiation (forall ((F $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted) (BOUND_VARIABLE_120945 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) A_2) B_1))) (not (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 A_2) X))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X) B_1))) (hBOOL (hAPP real bool (hAPP (fun real real) _let_0 (isCont real real) F) X))) )) (not (forall ((X $$unsorted)) (let ((_let_1 (ord_less real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X) B_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 A_2) X))) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP (fun real real) (fun real _let_0) (deriv real) F) X) (zero_zero real))))) )) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 BOUND_VARIABLE_120945) B_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 A_2) BOUND_VARIABLE_120945))) (= (hAPP real real F A_2) (hAPP real real F BOUND_VARIABLE_120945))))) ) 15.63/15.80 ( cos, pi, (zero_zero real), (zero_zero real) ) 15.63/15.80 ( cos, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.80 ( sqrt, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.80 ( (inverse_inverse real), (zero_zero real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.80 ( arctan, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), skv_5 ) 15.63/15.80 ) 15.63/15.80 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (ord_atLeastLessThan X_a))) (or (not (ord X_a)) (= _let_0 (ti (fun X_a (fun X_a (fun X_a bool))) _let_0)))) ) 15.63/15.80 ( bool ) 15.63/15.80 ( nat ) 15.63/15.80 ( int ) 15.63/15.80 ( (fun int bool) ) 15.63/15.80 ( (fun nat bool) ) 15.63/15.80 ( (product_prod nat nat) ) 15.63/15.80 ( real ) 15.63/15.80 ( rat ) 15.63/15.80 ( (filter nat) ) 15.63/15.80 ( (product_prod int int) ) 15.63/15.80 ( quickcheck_code_int ) 15.63/15.80 ( code_code_numeral ) 15.63/15.80 ( (product_prod real real) ) 15.63/15.80 ( (fun nat rat) ) 15.63/15.80 ( (filter real) ) 15.63/15.80 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 15.63/15.80 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 15.63/15.80 ) 15.63/15.80 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_121007 $$unsorted)) (or (not (number_ring X_a)) (not (linordered_idom X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP nat X_a (semiring_1_of_nat X_a) BOUND_VARIABLE_121007)) (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) (hAPP int X_a (number_number_of X_a) (hAPP int int bit0 (hAPP int int bit1 pls)))) BOUND_VARIABLE_121007)))) ) 15.63/15.80 ( int, (zero_zero nat) ) 15.63/15.80 ( int, (hAPP nat nat suc (zero_zero nat)) ) 15.63/15.80 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.63/15.80 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.80 ( real, (zero_zero nat) ) 15.63/15.80 ( real, (hAPP nat nat suc (zero_zero nat)) ) 15.63/15.80 ) 15.63/15.80 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_121033 $$unsorted) (BOUND_VARIABLE_121034 $$unsorted) (BOUND_VARIABLE_121035 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (or (not (division_ring X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_121035)) (not (= (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_121033) BOUND_VARIABLE_121035) (ti X_a BOUND_VARIABLE_121034))) (= (ti X_a BOUND_VARIABLE_121033) (hAPP X_a X_a (hAPP X_a _let_0 (inverse_divide X_a) BOUND_VARIABLE_121034) BOUND_VARIABLE_121035)))) ) 15.63/15.80 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), s1, s1 ) 15.63/15.80 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), s, s ) 15.63/15.80 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), pls, pls ) 15.63/15.80 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi, pi ) 15.63/15.80 ( complex, ii, ii, ii ) 15.63/15.80 ) 15.63/15.80 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_121063 $$unsorted) (BOUND_VARIABLE_121064 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (or (not (semiring_div X_a)) (= (zero_zero X_a) (hAPP X_a X_a (hAPP X_a _let_0 (div_mod X_a) (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_121063) BOUND_VARIABLE_121064)) BOUND_VARIABLE_121063)))) ) 15.63/15.80 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 15.63/15.80 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.63/15.80 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13 ) 15.63/15.80 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.63/15.80 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.63/15.80 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.63/15.80 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 15.63/15.80 ( complex, ii, ii ) 15.63/15.80 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 15.63/15.80 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 15.63/15.80 ) 15.63/15.80 (instantiation (forall ((Y_2 $$unsorted) (N $$unsorted)) (let ((_let_0 (hAPP real (fun real bool) (ord_less real) (zero_zero real)))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N))) (= (hBOOL (hAPP real bool _let_0 Y_2)) (hBOOL (hAPP real bool _let_0 (hAPP real real (hAPP nat (fun real real) root N) Y_2)))))) ) 15.63/15.80 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.80 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.80 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.80 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.80 ) 15.63/15.80 (instantiation (forall ((A_1 $$unsorted)) (let ((_let_0 (zero_zero int))) (let ((_let_1 (fun int rat))) (= (hAPP int rat (hAPP int _let_1 fract _let_0) (one_one int)) (hAPP int rat (hAPP int _let_1 fract A_1) _let_0)))) ) 15.63/15.80 ( (one_one int) ) 15.63/15.80 ( (zero_zero int) ) 15.63/15.80 ) 15.63/15.80 (instantiation (forall ((N $$unsorted) (Ma $$unsorted)) (let ((_let_0 (zero_zero nat))) (let ((_let_1 (semiring_1_of_nat int))) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP nat int _let_1 N)) (hAPP int int (uminus_uminus int) (hAPP nat int _let_1 Ma)))) (and (= _let_0 Ma) (= _let_0 N))))) ) 15.63/15.80 ( (zero_zero nat), (zero_zero nat) ) 15.63/15.80 ( (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 15.63/15.80 ) 15.63/15.80 (instantiation (forall ((P_1 $$unsorted) (I $$unsorted) (K $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) I) K))) (not (hBOOL (hAPP int bool P_1 K))) (not (forall ((I_2 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) I_2) K))) (not (hBOOL (hAPP int bool P_1 I_2))) (hBOOL (hAPP int bool P_1 (hAPP int int (hAPP int (fun int int) (minus_minus int) I_2) (one_one int))))) )) (hBOOL (hAPP int bool P_1 I))) ) 15.63/15.80 ( (hAPP int (fun int bool) (ord_less int) pls), min_1, pls ) 15.63/15.80 ( (hAPP int (fun int bool) (ord_less_eq int) pls), min_1, min_1 ) 15.63/15.80 ( (hAPP int (fun int bool) (ord_less_eq int) (one_one int)), (one_one int), t ) 15.63/15.80 ( (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (zero_zero int), s ) 15.63/15.80 ( (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (zero_zero int), skv_4 ) 15.63/15.80 ( (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (zero_zero int), skv_10 ) 15.63/15.80 ( zprime, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.80 ( nat_is_nat, (zero_zero int), (one_one int) ) 15.63/15.80 ( nat_is_nat, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.63/15.80 ( (hAPP int (fun int bool) (ord_less int) min_1), (zero_zero int), min_1 ) 15.63/15.80 ( (hAPP int (fun int bool) (ord_less int) min_1), (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.63/15.80 ) 15.63/15.80 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (hAPP real real cos X_2))) (or (= (zero_zero real) _let_1) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP (fun real real) (fun real _let_0) (deriv real) tan) X_2) (hAPP real real (inverse_inverse real) (hAPP nat real (hAPP real (fun nat real) (power_power real) _let_1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))))) ) 15.63/15.80 ( (zero_zero real) ) 15.63/15.80 ( pi ) 15.63/15.80 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.80 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.63/15.80 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.63/15.80 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.63/15.80 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.63/15.80 ) 15.63/15.80 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) A_1) (hAPP int int (hAPP int (fun int int) (minus_minus int) B) (one_one int))))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) A_1) B)))) ) 15.63/15.80 ( (one_one int), t ) 15.63/15.80 ( pls, (one_one int) ) 15.63/15.80 ( pls, pls ) 15.63/15.80 ( pls, min_1 ) 15.63/15.80 ( pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.80 ( min_1, pls ) 15.63/15.80 ( min_1, min_1 ) 15.63/15.80 ( s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.80 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.80 ( skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.80 ( skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.80 ) 15.63/15.80 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_121268 $$unsorted) (BOUND_VARIABLE_121269 $$unsorted)) (let ((_let_0 (abs_abs X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (minus_minus X_a))) (or (not (ordere142940540dd_abs X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (hAPP X_a X_a _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a _let_0 BOUND_VARIABLE_121268)) (hAPP X_a X_a _let_0 BOUND_VARIABLE_121269)))) (hAPP X_a X_a _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_121268) BOUND_VARIABLE_121269)))))))) ) 15.63/15.80 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.63/15.80 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 15.63/15.80 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 15.63/15.80 ) 15.63/15.80 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_121287 $$unsorted) (BOUND_VARIABLE_121288 $$unsorted)) (let ((_let_0 (norm_norm X_a))) (or (not (real_normed_vector X_a)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (hAPP real (fun real real) (minus_minus real) (hAPP X_a real _let_0 BOUND_VARIABLE_121287)) (hAPP X_a real _let_0 BOUND_VARIABLE_121288))) (hAPP X_a real _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_121287) BOUND_VARIABLE_121288)))))) ) 15.63/15.80 ( nat, (one_one nat), (one_one nat) ) 15.63/15.80 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 15.63/15.80 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 15.63/15.80 ) 15.63/15.83 (instantiation (forall ((A_2 $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat nat))) (let ((_let_2 (fun real real))) (let ((_let_3 (fun nat _let_0))) (let ((_let_4 (fun nat real))) (let ((_let_5 (fun nat _let_1))) (let ((_let_6 (fun _let_0 real))) (let ((_let_7 (fun nat _let_2))) (let ((_let_8 (fun (filter nat) bool))) (let ((_let_9 (fun real _let_8))) (let ((_let_10 (tendsto nat real))) (let ((_let_11 (hAPP _let_4 _let_4 (hAPP _let_7 (fun _let_4 _let_4) (combs nat real real) (hAPP _let_4 _let_7 (hAPP (fun real _let_2) (fun _let_4 _let_7) (combb real _let_2 nat) (times_times real)) (hAPP real _let_4 (power_power real) (hAPP int real (number_number_of real) min_1)))) A_2))) (or (not (hBOOL (hAPP (filter nat) bool (hAPP real _let_8 (hAPP _let_4 _let_9 _let_10 A_2) (zero_zero real)) sequentially))) (not (hBOOL (hAPP _let_4 bool (monoseq real) A_2))) (hBOOL (hAPP (filter nat) bool (hAPP real _let_8 (hAPP _let_4 _let_9 _let_10 (hAPP _let_3 _let_4 (hAPP _let_6 (fun _let_3 _let_4) (combb _let_0 real nat) (hAPP _let_4 _let_6 (big_co1399186613setsum nat real) _let_11)) (hAPP _let_1 _let_3 (hAPP _let_3 (fun _let_1 _let_3) (combb nat _let_0 nat) (hAPP nat _let_3 (ord_atLeastLessThan nat) (zero_zero nat))) (hAPP nat _let_1 (hAPP _let_5 _let_5 (combc nat nat nat) (hAPP _let_1 _let_5 (hAPP _let_5 (fun _let_1 _let_5) (combb nat _let_1 nat) (plus_plus nat)) (hAPP nat _let_1 (times_times nat) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat))))) (hAPP _let_4 real (suminf real) _let_11)) sequentially))))))))))))))) ) 15.63/15.83 ( (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))) ) 15.63/15.83 ) 15.63/15.83 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_121319 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (divisi14063676e_zero X_a)) (= (= _let_0 (ti X_a BOUND_VARIABLE_121319)) (= _let_0 (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_121319))))) ) 15.63/15.83 ( bool, fFalse ) 15.63/15.83 ( bool, fTrue ) 15.63/15.83 ( int, pls ) 15.63/15.83 ( int, min_1 ) 15.63/15.83 ( int, s ) 15.63/15.83 ( int, m ) 15.63/15.83 ( int, s1 ) 15.63/15.83 ( int, t ) 15.63/15.83 ( (fun int bool), nat_neg ) 15.63/15.83 ( (fun int bool), zprime ) 15.63/15.83 ( (fun int bool), zEven ) 15.63/15.83 ( (fun int bool), zOdd ) 15.63/15.83 ( (fun int bool), (even_odd_even int) ) 15.63/15.83 ( (fun int bool), twoSqu1091635170sum2sq ) 15.63/15.83 ( (fun int bool), nat_is_nat ) 15.63/15.83 ( (fun int (fun int bool)), norRRset ) 15.63/15.83 ( (fun int (fun int bool)), quadRes ) 15.63/15.83 ( (fun int (fun int bool)), sRStar ) 15.63/15.83 ( (fun int (fun int bool)), d22set ) 15.63/15.83 ( (fun int (fun int bool)), sr ) 15.63/15.83 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 15.63/15.83 ( (fun int int), zfact ) 15.63/15.83 ( (fun int int), bit0 ) 15.63/15.83 ( (fun int int), bit1 ) 15.63/15.83 ( (fun int int), (fact_fact int) ) 15.63/15.83 ( (fun int int), pred ) 15.63/15.83 ( (fun int int), succ ) 15.63/15.83 ( (fun nat bool), (even_odd_even nat) ) 15.63/15.83 ( (fun nat bool), prime ) 15.63/15.83 ( (fun nat nat), suc ) 15.63/15.83 ( (fun nat nat), (fact_fact nat) ) 15.63/15.83 ( (fun nat nat), fact ) 15.63/15.83 ( (fun nat nat), nat_size ) 15.63/15.83 ( (fun nat nat), (size_size nat) ) 15.63/15.83 ( (fun (product_prod nat nat) bool), pred_nat ) 15.63/15.83 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 15.63/15.83 ( real, (zero_zero real) ) 15.63/15.83 ( real, pi ) 15.63/15.83 ( (fun real real), ln ) 15.63/15.83 ( (fun real real), cos ) 15.63/15.83 ( (fun real real), sqrt ) 15.63/15.83 ( (fun real real), sin ) 15.63/15.83 ( (fun real real), arccos ) 15.63/15.83 ( (fun real real), arcsin ) 15.63/15.83 ( (fun real real), tan ) 15.63/15.83 ( (fun real real), arctan ) 15.63/15.83 ( (fun nat (fun nat bool)), coprime ) 15.63/15.83 ( complex, ii ) 15.63/15.83 ( (fun nat real), (real_1 nat) ) 15.63/15.83 ( (fun nat real), sin_coeff ) 15.63/15.83 ( (fun nat real), cos_coeff ) 15.63/15.83 ( (filter nat), sequentially ) 15.63/15.83 ( (fun int (fun int int)), (gcd_gcd int) ) 15.63/15.83 ( (fun int (fun int int)), legendre ) 15.63/15.83 ( (fun int (fun int int)), legacy_zgcd ) 15.63/15.83 ( (fun int (fun int int)), standardRes ) 15.63/15.83 ( (fun int (fun int int)), nat_tsub ) 15.63/15.83 ( (fun int (fun int int)), multInv ) 15.63/15.83 ( (fun int (fun int int)), z3mod ) 15.63/15.83 ( (fun int (fun int int)), z3div ) 15.63/15.83 ( (fun int (fun int int)), int_gcd ) 15.63/15.83 ( (fun int (fun int int)), int_lcm ) 15.63/15.83 ( (fun int (fun int int)), inv ) 15.63/15.83 ( (fun complex complex), expi ) 15.63/15.83 ( (fun complex complex), cnj ) 15.63/15.83 ( (fun real complex), cis ) 15.63/15.83 ( (fun int nat), nat_1 ) 15.63/15.83 ( (fun int nat), phi ) 15.63/15.83 ( (fun (fun int bool) bool), nat_nat_set ) 15.63/15.83 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 15.63/15.83 ( (fun nat (fun nat nat)), nat_gcd ) 15.63/15.83 ( (fun nat (fun nat nat)), nat_lcm ) 15.63/15.83 ( (fun (fun int bool) int), (the int) ) 15.63/15.83 ( (fun complex real), re ) 15.63/15.83 ( (fun complex real), im ) 15.63/15.83 ( (fun complex real), arg ) 15.63/15.83 ( (fun bool bool), fNot ) 15.63/15.83 ( (fun nat (fun real real)), root ) 15.63/15.83 ( (fun real (fun real real)), log ) 15.63/15.83 ( (fun real (fun real real)), powr ) 15.63/15.83 ( (fun bool (fun bool bool)), fimplies ) 15.63/15.83 ( (fun bool (fun bool bool)), fconj ) 15.63/15.83 ( (fun bool (fun bool bool)), fdisj ) 15.63/15.83 ( (fun int (fun int (product_prod int int))), negDivAlg ) 15.63/15.83 ( (fun int (fun int (product_prod int int))), posDivAlg ) 15.63/15.83 ( (fun int (fun int (product_prod int int))), divmod_int ) 15.63/15.83 ( (fun int (fun int (product_prod int int))), pdivmod ) 15.63/15.83 ( (fun int (fun int (product_prod int int))), norm_frac ) 15.63/15.83 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 15.63/15.83 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 15.63/15.83 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 15.63/15.83 ( (fun int (fun int (fun int bool))), zcong ) 15.63/15.83 ( (fun int (fun int (fun int bool))), zcongm ) 15.63/15.83 ( (fun int (fun int (fun int bool))), noXRRset ) 15.63/15.83 ( (fun int (fun int (fun int bool))), bnorRset ) 15.63/15.83 ( (fun int (fun int (fun int bool))), wset ) 15.63/15.83 ( (fun (product_prod int int) bool), frac_1 ) 15.63/15.83 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 15.63/15.83 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 15.63/15.83 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 15.63/15.83 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 15.63/15.83 ( (fun (fun nat rat) bool), vanishes ) 15.63/15.83 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 15.63/15.83 ( (fun code_code_numeral nat), code_c271388182l_size ) 15.63/15.83 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 15.63/15.83 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 15.63/15.83 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 15.63/15.83 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 15.63/15.83 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 15.63/15.83 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 15.63/15.83 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 15.63/15.83 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 15.63/15.83 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 15.63/15.83 ( (fun complex nat), complex_size ) 15.63/15.83 ( (fun complex nat), (size_size complex) ) 15.63/15.83 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 15.63/15.83 ( (fun nat (fun nat (product_prod int int))), bezw ) 15.63/15.83 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 15.63/15.83 ( (fun int (fun nat nat)), nat_aux ) 15.63/15.83 ( (fun int (fun (fun int bool) bool)), rsetR ) 15.63/15.83 ( (fun int (fun (fun int bool) bool)), resSet ) 15.63/15.83 ( (fun int (list int)), quickc666637781d_zero ) 15.63/15.83 ( (fun (product_prod int int) rat), frct ) 15.63/15.83 ( (fun int (fun int rat)), fract ) 15.63/15.83 ( (fun real (fun real complex)), complex_1 ) 15.63/15.83 ( (fun real (fun real complex)), rcis ) 15.63/15.83 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 15.63/15.83 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 15.63/15.83 ( (fun int real), (real_1 int) ) 15.63/15.83 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 15.63/15.83 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 15.63/15.83 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 15.63/15.83 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 15.63/15.83 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 15.63/15.83 ( (fun real nat), natfloor ) 15.63/15.83 ( (fun real nat), natceiling ) 15.63/15.83 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 15.63/15.83 ( (fun quickcheck_code_int int), quickcheck_int_of ) 15.63/15.83 ( (fun rat (product_prod int int)), quotient_of ) 15.63/15.83 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 15.63/15.83 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 15.63/15.83 ( (fun rat real), ratreal ) 15.63/15.83 ( (fun code_code_numeral int), code_int_of ) 15.63/15.83 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 15.63/15.83 ( (fun int quickcheck_code_int), quickcheck_of_int ) 15.63/15.83 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 15.63/15.83 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 15.63/15.83 ) 15.63/15.83 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (zero_zero real))) (let ((_let_2 (fun nat real))) (let ((_let_3 (fun (filter nat) bool))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) _let_1) X_2))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) X_2) (one_one real)))) (hBOOL (hAPP (filter nat) bool (hAPP real _let_3 (hAPP _let_2 (fun real _let_3) (tendsto nat real) (hAPP real _let_2 (power_power real) X_2)) _let_1) sequentially))))))) ) 15.63/15.83 ( (one_one real) ) 15.63/15.83 ( (zero_zero real) ) 15.63/15.83 ( pi ) 15.63/15.83 ( (hAPP int real (number_number_of real) min_1) ) 15.63/15.83 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.83 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.63/15.83 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.83 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.83 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.83 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 15.63/15.83 ( skv_3 ) 15.63/15.83 ( skv_5 ) 15.63/15.83 ( skv_7 ) 15.63/15.83 ( skv_12 ) 15.63/15.83 ) 15.63/15.83 (instantiation (forall ((A_1 $$unsorted)) (= (hAPP complex real im (hAPP real complex cis A_1)) (hAPP real real sin A_1)) ) 15.63/15.83 ( (zero_zero real) ) 15.63/15.83 ( pi ) 15.63/15.83 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.83 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.63/15.83 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.63/15.83 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.63/15.83 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.63/15.83 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.63/15.83 ) 15.63/15.83 (instantiation (forall ((X_a $$unsorted) (P_1 $$unsorted) (X_2 $$unsorted)) (or (not (hBOOL (hAPP X_a bool P_1 X_2))) (hBOOL (hAPP X_a bool P_1 (hAPP (fun X_a bool) X_a (hilbert_Eps X_a) P_1)))) ) 15.63/15.83 ( nat, (even_odd_even nat), (zero_zero nat) ) 15.63/15.83 ( nat, (even_odd_even nat), (one_one nat) ) 15.63/15.83 ( nat, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.83 ( nat, prime, (zero_zero nat) ) 15.63/15.83 ( nat, prime, (hAPP nat nat suc (zero_zero nat)) ) 15.63/15.83 ( nat, prime, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.83 ( int, (hAPP int (fun int bool) (ord_less int) pls), pls ) 15.63/15.83 ( int, (hAPP int (fun int bool) (ord_less int) pls), min_1 ) 15.63/15.83 ( int, (hAPP int (fun int bool) (ord_less_eq int) pls), min_1 ) 15.63/15.83 ( int, (hAPP int (fun int bool) (ord_less_eq int) (one_one int)), t ) 15.63/15.83 ( int, nat_neg, (one_one int) ) 15.63/15.83 ( int, nat_neg, (hAPP int int (number_number_of int) min_1) ) 15.63/15.83 ( int, nat_neg, (hAPP int int (number_number_of int) pls) ) 15.63/15.83 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (one_one int) ) 15.63/15.83 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.83 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), s ) 15.63/15.83 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.63/15.83 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) pls) ) 15.63/15.83 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_4 ) 15.63/15.83 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_10 ) 15.63/15.83 ( int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (one_one int) ) 15.63/15.83 ( int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.83 ( int, zprime, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.83 ( int, zprime, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.83 ( int, (hAPP int (fun int bool) (ord_less int) s), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.83 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) s)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.83 ( int, (let ((_let_0 (fun int int))) (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 15.63/15.83 ( int, (hAPP int (fun int bool) (ord_less int) (one_one int)), t ) 15.63/15.83 ( int, (even_odd_even int), (one_one int) ) 15.63/15.83 ( int, (even_odd_even int), (zero_zero int) ) 15.63/15.83 ( int, twoSqu1091635170sum2sq, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) t))) ) 15.63/15.83 ( int, nat_is_nat, (one_one int) ) 15.63/15.83 ( int, nat_is_nat, (zero_zero int) ) 15.63/15.83 ( int, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.83 ( int, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.63/15.83 ( int, (hAPP int (fun int bool) (ord_less int) min_1), pls ) 15.63/15.83 ( int, (hAPP int (fun int bool) (ord_less int) min_1), min_1 ) 15.63/15.83 ( int, (hAPP int (fun int bool) (ord_less_eq int) min_1), pls ) 15.63/15.83 ( int, (hAPP int (fun int bool) (ord_less_eq int) min_1), min_1 ) 15.63/15.83 ( int, (let ((_let_0 (fun int int))) (hAPP int (fun int bool) quadRes (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int int (number_number_of int) min_1) ) 15.63/15.83 ( int, (let ((_let_0 (fun int bool))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (let ((_let_3 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int _let_1 _let_2 s) _let_3)) (hAPP nat int (hAPP int _let_1 _let_2 s1) _let_3)))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.83 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.83 ( int, (hAPP int (fun int bool) (ord_less int) t), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.83 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.83 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_4)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.83 ( int, (hAPP int (fun int bool) (ord_less int) skv_4), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.83 ( int, (hAPP int (fun int bool) (ord_less int) skv_10), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.83 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_10)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.83 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.83 ( (fun int bool), (hAPP (fun int nat) (fun (fun int bool) bool) (nat_tr1645093318rphism int nat) nat_1), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 15.63/15.83 ( (fun int bool), (hAPP int (fun (fun int bool) bool) (member int) (one_one int)), zEven ) 15.63/15.83 ( (fun nat bool), (finite_finite_1 nat), (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 15.63/15.83 ( (fun nat bool), (hAPP (fun nat int) (fun (fun nat bool) bool) (nat_tr1645093318rphism nat int) (semiring_1_of_nat int)), (hAPP bool (fun nat bool) (combk bool nat) fTrue) ) 15.63/15.83 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), pi ) 15.63/15.83 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.83 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.83 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_3 ) 15.63/15.83 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_5 ) 15.63/15.83 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_7 ) 15.63/15.83 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_12 ) 15.63/15.83 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), pi ) 15.63/15.83 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.83 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.83 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_2 ) 15.63/15.83 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_8 ) 15.63/15.83 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_9 ) 15.63/15.83 ( real, (hAPP real (fun real bool) (ord_less real) (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))), (zero_zero real) ) 15.63/15.83 ( real, (hAPP real (fun real bool) (ord_less real) (one_one real)), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.83 ( real, (hAPP real (fun real bool) (ord_less real) pi), (zero_zero real) ) 15.63/15.83 ( real, (hAPP real (fun real bool) (ord_less real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.83 ( real, (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.83 ( real, (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 15.63/15.83 ( real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 (fun real bool) (sums real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (hAPP real _let_1 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc)))), (one_one real) ) 15.63/15.83 ( real, (hAPP real (fun real bool) (ord_less real) (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi))), pi ) 15.63/15.83 ( real, (hAPP real (fun real bool) (ord_less real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.83 ( real, (hAPP real (fun real bool) (ord_less real) (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 15.63/15.83 ( real, (hAPP real (fun real bool) (ord_less_eq real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 15.63/15.83 ( real, (hAPP real (fun real bool) (ord_less_eq real) skv_5), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.83 ( (filter nat), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun (filter nat) bool))) (hAPP real _let_2 (hAPP _let_1 (fun real _let_2) (tendsto nat real) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))) (zero_zero real))))), sequentially ) 15.63/15.83 ( (filter nat), (trivial_limit nat), sequentially ) 15.63/15.83 ( (filter real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (filter real) bool))) (hAPP real _let_2 (hAPP _let_0 (fun real _let_2) (tendsto real real) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin)) (zero_zero real))))), (hAPP real (filter real) (at real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.63/15.83 ) 15.63/15.83 (instantiation (forall ((X_b $$unsorted)) (let ((_let_0 (ord_less_eq X_b))) (or (not (ord X_b)) (= _let_0 (ti (fun X_b (fun X_b bool)) _let_0)))) ) 15.63/15.83 ( bool ) 15.63/15.83 ( nat ) 15.63/15.83 ( int ) 15.63/15.83 ( (fun int bool) ) 15.63/15.83 ( (fun nat bool) ) 15.63/15.83 ( (product_prod nat nat) ) 15.63/15.83 ( real ) 15.63/15.83 ( rat ) 15.63/15.84 ( (filter nat) ) 15.63/15.84 ( (product_prod int int) ) 15.63/15.84 ( quickcheck_code_int ) 15.63/15.84 ( code_code_numeral ) 15.63/15.84 ( (product_prod real real) ) 15.63/15.84 ( (fun nat rat) ) 15.63/15.84 ( (filter real) ) 15.63/15.84 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 15.63/15.84 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 15.63/15.84 ) 15.63/15.84 (instantiation (forall ((N $$unsorted) (X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP real _let_0 (ord_less real) (zero_zero real)))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun real _let_3))) (or (not (hBOOL (hAPP real bool _let_2 X_2))) (= (hAPP real real (hAPP nat _let_1 root N) X_2) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_5 (fun _let_0 _let_0) (combs real bool bool) (hAPP _let_0 _let_5 (hAPP (fun bool _let_3) (fun _let_0 _let_5) (combb bool _let_3 real) fconj) _let_2)) (hAPP real _let_0 (hAPP _let_4 _let_4 (combc real real bool) (hAPP _let_1 _let_4 (hAPP _let_4 (fun _let_1 _let_4) (combb real _let_0 real) (fequal real)) (hAPP nat _let_1 (hAPP (fun real (fun nat real)) (fun nat _let_1) (combc real nat real) (power_power real)) N))) X_2))))))))))) ) 15.63/15.84 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 15.63/15.84 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real) ) 15.63/15.84 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.84 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.63/15.84 ) 15.63/15.84 (instantiation (forall ((N $$unsorted) (X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (fun real real))) (let ((_let_3 (uminus_uminus real))) (let ((_let_4 (zero_zero real))) (let ((_let_5 (hAPP real _let_0 _let_1 _let_4))) (let ((_let_6 (fun bool bool))) (let ((_let_7 (fun real _let_0))) (let ((_let_8 (fun real _let_6))) (let ((_let_9 (hAPP real real (hAPP nat _let_2 root N) X_2))) (let ((_let_10 (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_2) _let_4)))) (or (hBOOL (hAPP real bool _let_5 X_2)) (and (or _let_10 (= _let_4 _let_9)) (or (not _let_10) (= _let_9 (hAPP real real _let_3 (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_8 (fun _let_0 _let_0) (combs real bool bool) (hAPP _let_0 _let_8 (hAPP (fun bool _let_6) (fun _let_0 _let_8) (combb bool _let_6 real) fconj) _let_5)) (hAPP real _let_0 (hAPP _let_7 _let_7 (combc real real bool) (hAPP _let_2 _let_7 (hAPP _let_7 (fun _let_2 _let_7) (combb real _let_0 real) (fequal real)) (hAPP nat _let_2 (hAPP (fun real (fun nat real)) (fun nat _let_2) (combc real nat real) (power_power real)) N))) (hAPP real real _let_3 X_2)))))))))))))))))))) ) 15.63/15.84 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 15.63/15.84 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real) ) 15.63/15.84 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.84 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.63/15.84 ) 15.63/15.84 (instantiation (forall ((N $$unsorted) (Ma $$unsorted)) (let ((_let_0 (real_1 nat))) (= (= (hAPP nat real _let_0 Ma) (hAPP nat real _let_0 N)) (= N Ma))) ) 15.63/15.84 ( (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 15.63/15.84 ( (hAPP nat nat suc (zero_zero nat)), (zero_zero nat) ) 15.63/15.84 ( (hAPP nat nat suc (zero_zero nat)), (hAPP nat nat suc (zero_zero nat)) ) 15.63/15.84 ) 15.63/15.84 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_121539 $$unsorted)) (or (not (number_ring X_a)) (not (ring_char_0 X_a)) (not (hBOOL (hAPP X_a bool (iszero X_a) (hAPP int X_a (number_number_of X_a) (hAPP int int bit1 BOUND_VARIABLE_121539)))))) ) 15.63/15.84 ( nat, pls ) 15.63/15.84 ( nat, (hAPP int int bit1 pls) ) 15.63/15.84 ( int, pls ) 15.63/15.84 ( int, (hAPP int int bit1 pls) ) 15.63/15.84 ( int, min_1 ) 15.63/15.84 ( real, (hAPP int int bit1 pls) ) 15.63/15.84 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.63/15.84 ( real, min_1 ) 15.63/15.84 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 15.63/15.84 ( complex, min_1 ) 15.63/15.84 ( quickcheck_code_int, pls ) 15.63/15.84 ( code_code_numeral, pls ) 15.63/15.84 ) 15.63/15.84 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (uminus_uminus complex))) (= (hAPP complex complex cnj (hAPP complex complex _let_0 X_1)) (hAPP complex complex _let_0 (hAPP complex complex cnj X_1)))) ) 15.63/15.84 ( (one_one complex) ) 15.63/15.84 ) 15.63/15.84 (instantiation (forall ((W_1 $$unsorted) (Z $$unsorted)) (let ((_let_0 (hAPP int (fun int bool) (ord_less int) W_1))) (= (hBOOL (hAPP int bool _let_0 (hAPP int int (hAPP int (fun int int) (plus_plus int) Z) (one_one int)))) (or (= (ti int Z) (ti int W_1)) (hBOOL (hAPP int bool _let_0 Z))))) ) 15.63/15.84 ( pls, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.63/15.84 ( s, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.63/15.84 ( t, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.63/15.84 ( skv_4, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.63/15.84 ( skv_10, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.63/15.84 ) 15.63/15.84 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_121611 $$unsorted) (BOUND_VARIABLE_121612 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (or (not (order X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_121611) BOUND_VARIABLE_121612))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_121612) BOUND_VARIABLE_121611))) (= (ti X_a BOUND_VARIABLE_121612) (ti X_a BOUND_VARIABLE_121611))))) ) 15.63/15.84 ( int, (one_one int), (zero_zero int) ) 15.63/15.84 ( int, (one_one int), t ) 15.63/15.84 ( int, (zero_zero int), (one_one int) ) 15.63/15.84 ( int, (zero_zero int), min_1 ) 15.63/15.84 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.84 ( int, (zero_zero int), s ) 15.63/15.84 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.63/15.84 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.63/15.84 ( int, (zero_zero int), skv_4 ) 15.63/15.84 ( int, (zero_zero int), skv_10 ) 15.63/15.84 ( int, pls, min_1 ) 15.63/15.84 ( int, min_1, (zero_zero int) ) 15.63/15.84 ( int, min_1, pls ) 15.63/15.84 ( int, min_1, min_1 ) 15.63/15.84 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 15.63/15.84 ( int, s, (zero_zero int) ) 15.63/15.84 ( int, t, (one_one int) ) 15.63/15.84 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 15.63/15.84 ( int, (hAPP int int (number_number_of int) pls), (zero_zero int) ) 15.63/15.84 ( int, skv_4, (zero_zero int) ) 15.63/15.84 ( int, skv_10, (zero_zero int) ) 15.63/15.84 ( real, (zero_zero real), pi ) 15.63/15.84 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.84 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.84 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.84 ( real, (zero_zero real), skv_3 ) 15.63/15.84 ( real, (zero_zero real), skv_5 ) 15.63/15.84 ( real, (zero_zero real), skv_7 ) 15.63/15.84 ( real, (zero_zero real), skv_12 ) 15.63/15.84 ( real, pi, (zero_zero real) ) 15.63/15.84 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.84 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.63/15.84 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.84 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_5 ) 15.63/15.84 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.63/15.84 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.84 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.63/15.84 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.63/15.84 ( real, skv_3, (zero_zero real) ) 15.63/15.84 ( real, skv_5, (zero_zero real) ) 15.63/15.84 ( real, skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.84 ( real, skv_7, (zero_zero real) ) 15.63/15.84 ( real, skv_12, (zero_zero real) ) 15.63/15.84 ) 15.63/15.84 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_121640 $$unsorted) (BOUND_VARIABLE_121641 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (zero_zero X_a))) (or (not (ordere453448008miring X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_121641))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_121640) _let_2))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_121640) BOUND_VARIABLE_121641)) _let_2)))))) ) 15.63/15.84 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 15.63/15.84 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.63/15.84 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13 ) 15.63/15.84 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.63/15.84 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.63/15.84 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.63/15.84 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 15.63/15.84 ( complex, ii, ii ) 15.63/15.84 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 15.63/15.84 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 15.63/15.84 ) 15.63/15.84 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_121679 $$unsorted)) (or (not (comm_semiring_1 X_a)) (= (ti X_a BOUND_VARIABLE_121679) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_121679) (zero_zero X_a)))) ) 15.63/15.84 ( bool, fFalse ) 15.63/15.84 ( bool, fTrue ) 15.63/15.84 ( nat, (one_one nat) ) 15.63/15.84 ( int, pls ) 15.63/15.84 ( int, min_1 ) 15.63/15.84 ( int, s ) 15.63/15.84 ( int, m ) 15.63/15.84 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.63/15.84 ( int, s1 ) 15.63/15.84 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.84 ( int, t ) 15.63/15.84 ( (fun int bool), nat_neg ) 15.63/15.84 ( (fun int bool), zprime ) 15.63/15.84 ( (fun int bool), zEven ) 15.63/15.84 ( (fun int bool), zOdd ) 15.63/15.84 ( (fun int bool), (even_odd_even int) ) 15.63/15.84 ( (fun int bool), twoSqu1091635170sum2sq ) 15.63/15.84 ( (fun int bool), nat_is_nat ) 15.63/15.84 ( (fun int (fun int bool)), norRRset ) 15.63/15.84 ( (fun int (fun int bool)), quadRes ) 15.63/15.84 ( (fun int (fun int bool)), sRStar ) 15.63/15.84 ( (fun int (fun int bool)), d22set ) 15.63/15.84 ( (fun int (fun int bool)), sr ) 15.63/15.84 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 15.63/15.84 ( (fun int int), zfact ) 15.63/15.84 ( (fun int int), bit0 ) 15.63/15.84 ( (fun int int), bit1 ) 15.63/15.84 ( (fun int int), (fact_fact int) ) 15.63/15.84 ( (fun int int), pred ) 15.63/15.84 ( (fun int int), succ ) 15.63/15.84 ( (fun nat bool), (even_odd_even nat) ) 15.63/15.84 ( (fun nat bool), prime ) 15.63/15.84 ( (fun nat nat), suc ) 15.63/15.84 ( (fun nat nat), (fact_fact nat) ) 15.63/15.84 ( (fun nat nat), fact ) 15.63/15.84 ( (fun nat nat), nat_size ) 15.63/15.84 ( (fun nat nat), (size_size nat) ) 15.63/15.84 ( (fun (product_prod nat nat) bool), pred_nat ) 15.63/15.84 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 15.63/15.84 ( real, pi ) 15.63/15.84 ( (fun real real), ln ) 15.63/15.84 ( (fun real real), cos ) 15.63/15.84 ( (fun real real), sqrt ) 15.63/15.84 ( (fun real real), sin ) 15.63/15.84 ( (fun real real), arccos ) 15.63/15.84 ( (fun real real), arcsin ) 15.63/15.84 ( (fun real real), tan ) 15.63/15.84 ( (fun real real), arctan ) 15.63/15.84 ( (fun nat (fun nat bool)), coprime ) 15.63/15.84 ( complex, ii ) 15.63/15.84 ( (fun nat real), (real_1 nat) ) 15.63/15.84 ( (fun nat real), sin_coeff ) 15.63/15.84 ( (fun nat real), cos_coeff ) 15.63/15.84 ( (filter nat), sequentially ) 15.63/15.84 ( (fun int (fun int int)), (gcd_gcd int) ) 15.63/15.84 ( (fun int (fun int int)), legendre ) 15.63/15.84 ( (fun int (fun int int)), legacy_zgcd ) 15.63/15.84 ( (fun int (fun int int)), standardRes ) 15.63/15.84 ( (fun int (fun int int)), nat_tsub ) 15.63/15.84 ( (fun int (fun int int)), multInv ) 15.63/15.84 ( (fun int (fun int int)), z3mod ) 15.63/15.84 ( (fun int (fun int int)), z3div ) 15.63/15.84 ( (fun int (fun int int)), int_gcd ) 15.63/15.84 ( (fun int (fun int int)), int_lcm ) 15.63/15.84 ( (fun int (fun int int)), inv ) 15.63/15.84 ( (fun complex complex), expi ) 15.63/15.84 ( (fun complex complex), cnj ) 15.63/15.84 ( (fun real complex), cis ) 15.63/15.84 ( (fun int nat), nat_1 ) 15.63/15.84 ( (fun int nat), phi ) 15.63/15.84 ( (fun (fun int bool) bool), nat_nat_set ) 15.63/15.84 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 15.63/15.84 ( (fun nat (fun nat nat)), nat_gcd ) 15.63/15.84 ( (fun nat (fun nat nat)), nat_lcm ) 15.63/15.84 ( (fun (fun int bool) int), (the int) ) 15.63/15.84 ( (fun complex real), re ) 15.63/15.84 ( (fun complex real), im ) 15.63/15.84 ( (fun complex real), arg ) 15.63/15.84 ( (fun bool bool), fNot ) 15.63/15.84 ( (fun nat (fun real real)), root ) 15.63/15.84 ( (fun real (fun real real)), log ) 15.63/15.84 ( (fun real (fun real real)), powr ) 15.63/15.84 ( (fun bool (fun bool bool)), fimplies ) 15.63/15.84 ( (fun bool (fun bool bool)), fconj ) 15.63/15.84 ( (fun bool (fun bool bool)), fdisj ) 15.63/15.84 ( (fun int (fun int (product_prod int int))), negDivAlg ) 15.63/15.84 ( (fun int (fun int (product_prod int int))), posDivAlg ) 15.63/15.84 ( (fun int (fun int (product_prod int int))), divmod_int ) 15.63/15.84 ( (fun int (fun int (product_prod int int))), pdivmod ) 15.63/15.84 ( (fun int (fun int (product_prod int int))), norm_frac ) 15.63/15.84 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 15.63/15.84 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 15.63/15.84 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 15.63/15.84 ( (fun int (fun int (fun int bool))), zcong ) 15.63/15.84 ( (fun int (fun int (fun int bool))), zcongm ) 15.63/15.84 ( (fun int (fun int (fun int bool))), noXRRset ) 15.63/15.84 ( (fun int (fun int (fun int bool))), bnorRset ) 15.63/15.84 ( (fun int (fun int (fun int bool))), wset ) 15.63/15.84 ( (fun (product_prod int int) bool), frac_1 ) 15.63/15.84 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 15.63/15.84 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 15.63/15.84 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 15.63/15.84 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 15.63/15.84 ( (fun (fun nat rat) bool), vanishes ) 15.63/15.84 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 15.63/15.84 ( (fun code_code_numeral nat), code_c271388182l_size ) 15.63/15.84 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 15.63/15.84 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 15.63/15.84 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 15.63/15.84 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 15.63/15.84 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 15.63/15.84 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 15.63/15.84 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 15.63/15.84 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 15.63/15.84 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 15.63/15.84 ( (fun complex nat), complex_size ) 15.63/15.84 ( (fun complex nat), (size_size complex) ) 15.63/15.84 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 15.63/15.84 ( (fun nat (fun nat (product_prod int int))), bezw ) 15.63/15.84 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 15.63/15.84 ( (fun int (fun nat nat)), nat_aux ) 15.63/15.84 ( (fun int (fun (fun int bool) bool)), rsetR ) 15.63/15.84 ( (fun int (fun (fun int bool) bool)), resSet ) 15.63/15.84 ( (fun int (list int)), quickc666637781d_zero ) 15.63/15.84 ( (fun (product_prod int int) rat), frct ) 15.63/15.84 ( (fun int (fun int rat)), fract ) 15.63/15.84 ( (fun real (fun real complex)), complex_1 ) 15.63/15.84 ( (fun real (fun real complex)), rcis ) 15.63/15.84 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 15.63/15.84 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 15.63/15.84 ( (fun int real), (real_1 int) ) 15.63/15.84 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 15.63/15.84 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 15.63/15.84 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 15.63/15.84 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 15.63/15.84 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 15.63/15.84 ( (fun real nat), natfloor ) 15.63/15.84 ( (fun real nat), natceiling ) 15.63/15.84 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 15.63/15.84 ( (fun quickcheck_code_int int), quickcheck_int_of ) 15.63/15.84 ( (fun rat (product_prod int int)), quotient_of ) 15.63/15.84 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 15.63/15.84 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 15.63/15.84 ( (fun rat real), ratreal ) 15.63/15.84 ( (fun code_code_numeral int), code_int_of ) 15.63/15.84 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 15.63/15.84 ( (fun int quickcheck_code_int), quickcheck_of_int ) 15.63/15.84 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 15.63/15.84 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 15.63/15.84 ) 15.63/15.84 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_121694 $$unsorted)) (or (not (group_add X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) (zero_zero X_a)) BOUND_VARIABLE_121694) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_121694))) ) 15.63/15.84 ( int, (one_one int) ) 15.63/15.84 ( int, pls ) 15.63/15.84 ( int, min_1 ) 15.63/15.84 ( real, (one_one real) ) 15.63/15.84 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.84 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.63/15.84 ( complex, (one_one complex) ) 15.63/15.84 ( complex, ii ) 15.63/15.84 ( code_code_numeral, (one_one code_code_numeral) ) 15.63/15.84 ) 15.63/15.84 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_121704 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP X_a int (archimedean_ceiling X_a) BOUND_VARIABLE_121704)) (zero_zero int))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_121704) (zero_zero X_a))))) ) 15.63/15.84 ( int, (one_one int) ) 15.63/15.84 ( int, (zero_zero int) ) 15.63/15.84 ( int, min_1 ) 15.63/15.84 ( real, (zero_zero real) ) 15.63/15.84 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.84 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.84 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.84 ( real, skv_5 ) 15.63/15.84 ) 15.63/15.84 (instantiation (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_0 (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_1))) (not (hBOOL (hAPP real bool _let_0 X_1))) (hBOOL (hAPP real bool _let_0 (hAPP real real (hAPP nat (fun real real) root N_1) X_1))))) ) 15.63/15.84 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.84 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.84 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.84 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.84 ) 15.63/15.84 (instantiation (forall ((X_2 $$unsorted) (N $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (or (hBOOL (hAPP int bool nat_neg (hAPP int int (number_number_of int) N))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) X_2))) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP real nat natceiling X_2)) (hAPP int nat (number_number_of nat) N))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_2) (hAPP int real (number_number_of real) N))))))) ) 15.63/15.84 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.63/15.84 ( skv_5, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.63/15.84 ) 15.63/15.84 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_121775 $$unsorted)) (or (not (real_algebra_1 X_a)) (= (hAPP real X_a (of_real X_a) BOUND_VARIABLE_121775) (hAPP X_a X_a (hAPP real (fun X_a X_a) (scaleR_scaleR X_a) BOUND_VARIABLE_121775) (one_one X_a)))) ) 15.63/15.84 ( complex, pi ) 15.63/15.84 ( complex, (hAPP int real (number_number_of real) min_1) ) 15.63/15.84 ( complex, (hAPP real real (uminus_uminus real) (one_one real)) ) 15.63/15.84 ) 15.63/15.84 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))) (or (hBOOL (hAPP int bool (even_odd_even int) X_1)) (= (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) _let_1) (hAPP int int (hAPP int _let_0 (div_div int) X_1) _let_1))) (one_one int)) (ti int X_1))))) ) 15.63/15.84 ( (one_one int) ) 15.63/15.84 ( (zero_zero int) ) 15.63/15.84 ( pls ) 15.63/15.84 ( min_1 ) 15.63/15.84 ( s ) 15.63/15.84 ( m ) 15.63/15.84 ( s1 ) 15.63/15.84 ( t ) 15.63/15.84 ) 15.63/15.84 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (= (hAPP real real cos X) (hAPP _let_1 real (suminf real) (hAPP _let_1 _let_1 (hAPP _let_2 (fun _let_1 _let_1) (combs nat real real) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 nat) (times_times real)) cos_coeff)) (hAPP real _let_1 (power_power real) X))))))) ) 15.63/15.84 ( (zero_zero real) ) 15.63/15.84 ( pi ) 15.63/15.84 ( (hAPP int real (number_number_of real) min_1) ) 15.63/15.84 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.84 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.84 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.84 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.63/15.84 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.63/15.84 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.63/15.84 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.63/15.84 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.63/15.84 ( skv_5 ) 15.63/15.84 ) 15.63/15.84 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_121824 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (one_one X_a))) (or (not (linord1117847801e_zero X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_121824))) (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) (zero_zero X_a)) BOUND_VARIABLE_121824)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_121824) _let_2)))))))) ) 15.63/15.84 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.84 ( int, (one_one int) ) 15.63/15.84 ( int, (zero_zero int) ) 15.63/15.84 ( int, pls ) 15.63/15.84 ( int, min_1 ) 15.63/15.84 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.84 ( real, (zero_zero real) ) 15.63/15.84 ( real, pi ) 15.63/15.84 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.84 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.84 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.84 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.84 ( real, skv_2 ) 15.63/15.84 ( real, skv_5 ) 15.63/15.84 ( real, skv_8 ) 15.63/15.84 ( real, skv_9 ) 15.63/15.84 ( complex, ii ) 15.63/15.84 ) 15.63/15.84 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_121841 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (divisi14063676e_zero X_a)) (= _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_121841) _let_0)))) ) 15.63/15.84 ( real, (one_one real) ) 15.63/15.84 ( real, pi ) 15.63/15.84 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.63/15.84 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.63/15.84 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.84 ) 15.63/15.84 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_121865 $$unsorted) (BOUND_VARIABLE_121866 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (let ((_let_1 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) _let_0))) (or (not (ordere216010020id_add X_a)) (not (hBOOL (hAPP X_a bool _let_1 BOUND_VARIABLE_121866))) (not (hBOOL (hAPP X_a bool _let_1 BOUND_VARIABLE_121865))) (= (= _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_121866) BOUND_VARIABLE_121865)) (and (= _let_0 (ti X_a BOUND_VARIABLE_121865)) (= _let_0 (ti X_a BOUND_VARIABLE_121866))))))) ) 15.63/15.84 ( nat, (one_one nat), (one_one nat) ) 15.63/15.84 ( int, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.63/15.84 ( int, (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.84 ) 15.63/15.84 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_121959 $$unsorted)) (let ((_let_0 (uminus_uminus X_a))) (or (not (boolean_algebra X_a)) (= (ti X_a BOUND_VARIABLE_121959) (hAPP X_a X_a _let_0 (hAPP X_a X_a _let_0 BOUND_VARIABLE_121959))))) ) 15.63/15.84 ( bool, fFalse ) 15.63/15.84 ( bool, fTrue ) 15.63/15.84 ( int, (one_one int) ) 15.63/15.84 ( int, pls ) 15.63/15.84 ( int, min_1 ) 15.63/15.84 ( int, s ) 15.63/15.84 ( int, m ) 15.63/15.84 ( int, s1 ) 15.63/15.84 ( int, t ) 15.63/15.84 ( (fun int bool), nat_neg ) 15.63/15.84 ( (fun int bool), zprime ) 15.63/15.84 ( (fun int bool), zEven ) 15.63/15.84 ( (fun int bool), zOdd ) 15.63/15.84 ( (fun int bool), (even_odd_even int) ) 15.63/15.84 ( (fun int bool), twoSqu1091635170sum2sq ) 15.63/15.84 ( (fun int bool), nat_is_nat ) 15.63/15.84 ( (fun int (fun int bool)), norRRset ) 15.63/15.84 ( (fun int (fun int bool)), quadRes ) 15.63/15.84 ( (fun int (fun int bool)), sRStar ) 15.63/15.84 ( (fun int (fun int bool)), d22set ) 15.63/15.84 ( (fun int (fun int bool)), sr ) 15.63/15.84 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 15.63/15.84 ( (fun int int), zfact ) 15.63/15.84 ( (fun int int), bit0 ) 15.63/15.84 ( (fun int int), bit1 ) 15.63/15.84 ( (fun int int), (fact_fact int) ) 15.63/15.84 ( (fun int int), pred ) 15.63/15.84 ( (fun int int), succ ) 15.63/15.84 ( (fun nat bool), (even_odd_even nat) ) 15.63/15.84 ( (fun nat bool), prime ) 15.63/15.84 ( (fun nat nat), suc ) 15.63/15.84 ( (fun nat nat), (fact_fact nat) ) 15.63/15.84 ( (fun nat nat), fact ) 15.63/15.84 ( (fun nat nat), nat_size ) 15.63/15.84 ( (fun nat nat), (size_size nat) ) 15.63/15.84 ( (fun (product_prod nat nat) bool), pred_nat ) 15.63/15.84 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 15.63/15.84 ( real, (one_one real) ) 15.63/15.84 ( real, pi ) 15.63/15.84 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.84 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.63/15.84 ( (fun real real), ln ) 15.63/15.84 ( (fun real real), cos ) 15.63/15.84 ( (fun real real), sqrt ) 15.63/15.84 ( (fun real real), sin ) 15.63/15.84 ( (fun real real), arccos ) 15.63/15.84 ( (fun real real), arcsin ) 15.63/15.84 ( (fun real real), tan ) 15.63/15.84 ( (fun real real), arctan ) 15.63/15.84 ( (fun nat (fun nat bool)), coprime ) 15.63/15.84 ( complex, (one_one complex) ) 15.63/15.84 ( complex, ii ) 15.63/15.84 ( (fun nat real), (real_1 nat) ) 15.63/15.84 ( (fun nat real), sin_coeff ) 15.63/15.84 ( (fun nat real), cos_coeff ) 15.63/15.84 ( (filter nat), sequentially ) 15.63/15.84 ( (fun int (fun int int)), (gcd_gcd int) ) 15.63/15.84 ( (fun int (fun int int)), legendre ) 15.63/15.84 ( (fun int (fun int int)), legacy_zgcd ) 15.63/15.84 ( (fun int (fun int int)), standardRes ) 15.63/15.84 ( (fun int (fun int int)), nat_tsub ) 15.63/15.84 ( (fun int (fun int int)), multInv ) 15.63/15.84 ( (fun int (fun int int)), z3mod ) 15.63/15.84 ( (fun int (fun int int)), z3div ) 15.63/15.84 ( (fun int (fun int int)), int_gcd ) 15.63/15.84 ( (fun int (fun int int)), int_lcm ) 15.63/15.84 ( (fun int (fun int int)), inv ) 15.63/15.84 ( (fun complex complex), expi ) 15.63/15.84 ( (fun complex complex), cnj ) 15.63/15.84 ( (fun real complex), cis ) 15.63/15.84 ( (fun int nat), nat_1 ) 15.63/15.84 ( (fun int nat), phi ) 15.63/15.84 ( (fun (fun int bool) bool), nat_nat_set ) 15.63/15.84 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 15.63/15.84 ( (fun nat (fun nat nat)), nat_gcd ) 15.63/15.84 ( (fun nat (fun nat nat)), nat_lcm ) 15.63/15.84 ( (fun (fun int bool) int), (the int) ) 15.63/15.84 ( (fun complex real), re ) 15.63/15.84 ( (fun complex real), im ) 15.63/15.84 ( (fun complex real), arg ) 15.63/15.84 ( (fun bool bool), fNot ) 15.63/15.84 ( (fun nat (fun real real)), root ) 15.63/15.84 ( (fun real (fun real real)), log ) 15.63/15.84 ( (fun real (fun real real)), powr ) 15.63/15.84 ( (fun bool (fun bool bool)), fimplies ) 15.63/15.84 ( (fun bool (fun bool bool)), fconj ) 15.63/15.84 ( (fun bool (fun bool bool)), fdisj ) 15.63/15.84 ( (fun int (fun int (product_prod int int))), negDivAlg ) 15.63/15.84 ( (fun int (fun int (product_prod int int))), posDivAlg ) 15.63/15.84 ( (fun int (fun int (product_prod int int))), divmod_int ) 15.63/15.84 ( (fun int (fun int (product_prod int int))), pdivmod ) 15.63/15.84 ( (fun int (fun int (product_prod int int))), norm_frac ) 15.63/15.84 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 15.63/15.84 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 15.63/15.84 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 15.63/15.84 ( (fun int (fun int (fun int bool))), zcong ) 15.63/15.84 ( (fun int (fun int (fun int bool))), zcongm ) 15.63/15.84 ( (fun int (fun int (fun int bool))), noXRRset ) 15.63/15.84 ( (fun int (fun int (fun int bool))), bnorRset ) 15.63/15.84 ( (fun int (fun int (fun int bool))), wset ) 15.63/15.84 ( (fun (product_prod int int) bool), frac_1 ) 15.63/15.84 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 15.63/15.84 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 15.63/15.84 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 15.63/15.84 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 15.63/15.84 ( (fun (fun nat rat) bool), vanishes ) 15.63/15.84 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 15.63/15.84 ( (fun code_code_numeral nat), code_c271388182l_size ) 15.63/15.84 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 15.63/15.84 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 15.63/15.84 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 15.63/15.84 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 15.63/15.84 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 15.63/15.84 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 15.63/15.84 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 15.63/15.84 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 15.63/15.84 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 15.63/15.84 ( (fun complex nat), complex_size ) 15.63/15.84 ( (fun complex nat), (size_size complex) ) 15.63/15.84 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 15.63/15.84 ( (fun nat (fun nat (product_prod int int))), bezw ) 15.63/15.84 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 15.63/15.84 ( (fun int (fun nat nat)), nat_aux ) 15.63/15.84 ( (fun int (fun (fun int bool) bool)), rsetR ) 15.63/15.84 ( (fun int (fun (fun int bool) bool)), resSet ) 15.63/15.84 ( (fun int (list int)), quickc666637781d_zero ) 15.63/15.84 ( (fun (product_prod int int) rat), frct ) 15.63/15.84 ( (fun int (fun int rat)), fract ) 15.63/15.84 ( (fun real (fun real complex)), complex_1 ) 15.63/15.84 ( (fun real (fun real complex)), rcis ) 15.63/15.84 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 15.63/15.84 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 15.63/15.84 ( (fun int real), (real_1 int) ) 15.63/15.84 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 15.63/15.84 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 15.63/15.84 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 15.63/15.84 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 15.63/15.84 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 15.63/15.84 ( (fun real nat), natfloor ) 15.63/15.84 ( (fun real nat), natceiling ) 15.63/15.84 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 15.63/15.84 ( (fun quickcheck_code_int int), quickcheck_int_of ) 15.63/15.84 ( (fun rat (product_prod int int)), quotient_of ) 15.63/15.84 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 15.63/15.84 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 15.63/15.84 ( (fun rat real), ratreal ) 15.63/15.84 ( (fun code_code_numeral int), code_int_of ) 15.63/15.84 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 15.63/15.84 ( (fun int quickcheck_code_int), quickcheck_of_int ) 15.63/15.84 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 15.63/15.84 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 15.63/15.84 ) 15.63/15.84 (instantiation (forall ((X_a $$unsorted) (X_c $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (hAPP X_a X_c B_1_1 B_2_1) (hAPP X_a X_c B_1_1 (ti X_a B_2_1))) ) 15.63/15.84 ( bool, (fun nat bool), (combk bool nat), fTrue ) 15.63/15.84 ( int, bool, (hAPP int (fun int bool) (ord_less int) pls), pls ) 15.63/15.84 ( int, bool, (hAPP int (fun int bool) (ord_less int) pls), min_1 ) 15.63/15.84 ( int, bool, (hAPP int (fun int bool) (ord_less_eq int) pls), min_1 ) 15.63/15.84 ( int, bool, (hAPP int (fun int bool) (ord_less_eq int) (one_one int)), t ) 15.63/15.84 ( int, bool, nat_neg, pls ) 15.63/15.84 ( int, bool, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), pls ) 15.63/15.84 ( int, bool, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), s ) 15.63/15.84 ( int, bool, (hAPP int (fun int bool) (ord_less int) (one_one int)), t ) 15.63/15.84 ( int, bool, (even_odd_even int), pls ) 15.63/15.84 ( int, bool, nat_is_nat, pls ) 15.63/15.84 ( int, bool, (hAPP int (fun int bool) (ord_less int) min_1), pls ) 15.63/15.84 ( int, bool, (hAPP int (fun int bool) (ord_less int) min_1), min_1 ) 15.63/15.84 ( int, bool, (hAPP int (fun int bool) (ord_less_eq int) min_1), pls ) 15.63/15.84 ( int, bool, (hAPP int (fun int bool) (ord_less_eq int) min_1), min_1 ) 15.63/15.84 ( int, nat, (number_number_of nat), pls ) 15.63/15.84 ( int, nat, nat_1, pls ) 15.63/15.84 ( int, int, bit0, pls ) 15.63/15.84 ( int, int, bit0, min_1 ) 15.63/15.84 ( int, int, bit1, pls ) 15.63/15.84 ( int, int, bit1, min_1 ) 15.63/15.84 ( int, int, (number_number_of int), pls ) 15.63/15.84 ( int, int, (number_number_of int), min_1 ) 15.63/15.84 ( int, int, (fact_fact int), pls ) 15.63/15.84 ( int, int, (uminus_uminus int), pls ) 15.63/15.84 ( int, int, (uminus_uminus int), min_1 ) 15.63/15.84 ( int, int, pred, pls ) 15.63/15.84 ( int, int, pred, min_1 ) 15.63/15.84 ( int, int, (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))), m ) 15.63/15.84 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))))), t ) 15.63/15.84 ( int, int, succ, pls ) 15.63/15.84 ( int, int, succ, min_1 ) 15.63/15.84 ( int, (fun int bool), (ord_less_eq int), pls ) 15.63/15.84 ( int, (fun int bool), (ord_less_eq int), min_1 ) 15.63/15.84 ( int, (fun int bool), (ord_less int), pls ) 15.63/15.84 ( int, (fun int bool), (ord_less int), min_1 ) 15.63/15.84 ( int, (fun int bool), (ord_less int), s ) 15.63/15.84 ( int, (fun int bool), (ord_less int), t ) 15.63/15.84 ( int, (fun int bool), (let ((_let_0 (fun int (fun int bool)))) (hAPP _let_0 _let_0 (combc int int bool) (fequal int))), pls ) 15.63/15.84 ( int, (fun int bool), (hAPP int (fun int (fun int bool)) zcong s1), s ) 15.63/15.84 ( int, (fun int (fun int bool)), zcong, s1 ) 15.63/15.84 ( int, real, (real_1 int), pls ) 15.63/15.84 ( int, real, (number_number_of real), min_1 ) 15.63/15.84 ( int, (fun int rat), fract, pls ) 15.63/15.84 ( int, (fun nat int), (power_power int), s ) 15.63/15.84 ( int, (fun nat int), (power_power int), s1 ) 15.63/15.84 ( int, complex, (number_number_of complex), min_1 ) 15.63/15.84 ( int, (fun int (product_prod int int)), (product_Pair int int), pls ) 15.63/15.84 ( int, (fun int (product_prod int int)), (product_Pair int int), s ) 15.63/15.84 ( int, quickcheck_code_int, quickcheck_of_int, pls ) 15.63/15.84 ( int, code_code_numeral, (number_number_of code_code_numeral), pls ) 15.63/15.84 ( int, (fun (product_prod int int) bool), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 _let_0))) (let ((_let_3 (fun _let_1 int))) (hAPP _let_2 (fun int (fun _let_1 bool)) (combc _let_1 int bool) (hAPP _let_3 _let_2 (hAPP (fun int _let_0) (fun _let_3 _let_2) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))))))), pls ) 15.63/15.84 ( (fun int bool), bool, (hAPP int (fun (fun int bool) bool) (member int) (one_one int)), zEven ) 15.63/15.84 ( (fun nat bool), (fun nat bool), (collect nat), prime ) 15.63/15.84 ( (fun nat nat), (fun nat (fun nat bool)), (let ((_let_0 (fun nat (fun nat bool)))) (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat (fun nat bool) nat) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat)))), suc ) 15.63/15.84 ( (fun nat nat), (fun nat real), (let ((_let_0 (fun nat real))) (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat real nat) (real_1 nat))), suc ) 15.63/15.84 ( (fun nat nat), (fun nat real), (let ((_let_0 (fun nat real))) (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat real nat) (hAPP real _let_0 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))), suc ) 15.63/15.84 ( real, bool, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), pi ) 15.63/15.84 ( real, bool, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), pi ) 15.63/15.84 ( real, bool, (hAPP real (fun real bool) (ord_less real) (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi))), pi ) 15.63/15.84 ( real, bool, (hAPP real (fun real bool) (ord_less_eq real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 15.63/15.84 ( real, real, cos, pi ) 15.63/15.84 ( real, real, sin, pi ) 15.63/15.84 ( real, real, tan, pi ) 15.63/15.84 ( real, real, (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 15.63/15.84 ( real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1))))))), pi ) 15.63/15.84 ( real, (fun real bool), (ord_less real), pi ) 15.63/15.84 ( real, (fun real real), (inverse_divide real), pi ) 15.63/15.84 ( real, complex, (of_real complex), pi ) 15.63/15.84 ( (fun real real), (fun real real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)))), sin ) 15.63/15.84 ( (fun real real), (fun real (fun real real)), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)))), cos ) 15.63/15.84 ( (fun real real), (fun real (fun real bool)), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (hAPP _let_1 (fun (fun real real) _let_1) (combb real _let_0 real) (fequal real)))), cos ) 15.63/15.84 ( complex, real, re, ii ) 15.63/15.84 ( complex, real, im, ii ) 15.63/15.84 ( complex, complex, (inverse_inverse complex), ii ) 15.63/15.84 ( complex, complex, (uminus_uminus complex), ii ) 15.63/15.84 ( complex, complex, cnj, ii ) 15.63/15.84 ( complex, complex, (hAPP complex (fun complex complex) (times_times complex) ii), ii ) 15.63/15.84 ( complex, complex, (let ((_let_0 (fun complex complex))) (let ((_let_1 (times_times complex))) (hAPP complex _let_0 _let_1 (hAPP complex complex (hAPP complex _let_0 _let_1 (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi))))), ii ) 15.63/15.84 ( complex, (fun complex complex), (times_times complex), ii ) 15.63/15.84 ( complex, (fun nat complex), (power_power complex), ii ) 15.63/15.84 ( (fun nat real), (fun nat real), (diffs real), sin_coeff ) 15.63/15.84 ( (fun nat real), (fun (fun nat nat) (fun nat real)), (combb nat real nat), (real_1 nat) ) 15.63/15.84 ( (fun nat real), (fun int (fun nat real)), (let ((_let_0 (fun real real))) (let ((_let_1 (fun (fun nat real) (fun nat real)))) (let ((_let_2 (fun int real))) (let ((_let_3 (fun int _let_0))) (let ((_let_4 (fun int _let_1))) (hAPP _let_4 (fun (fun nat real) (fun int (fun nat real))) (combc int (fun nat real) (fun nat real)) (hAPP _let_3 _let_4 (hAPP (fun _let_0 _let_1) (fun _let_3 _let_4) (combb _let_0 _let_1 int) (combb real real nat)) (hAPP _let_2 _let_3 (hAPP (fun real _let_0) (fun _let_2 _let_3) (combb real _let_0 int) (inverse_divide real)) (real_1 int))))))))), (real_1 nat) ) 15.63/15.84 ( (filter nat), bool, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun (filter nat) bool))) (hAPP real _let_2 (hAPP _let_1 (fun real _let_2) (tendsto nat real) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))) (zero_zero real))))), sequentially ) 15.63/15.84 ( (filter nat), bool, (trivial_limit nat), sequentially ) 15.63/15.84 ( (fun int (fun int int)), (fun int (fun int (fun int bool))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun _let_2 _let_1))) (hAPP _let_3 (fun (fun int _let_2) (fun int _let_1)) (combb _let_2 _let_1 int) (hAPP _let_1 _let_3 (combb int _let_0 int) (fequal int))))))), int_gcd ) 15.63/15.84 ( (fun int nat), (fun (fun int bool) bool), (nat_tr1645093318rphism int nat), nat_1 ) 15.63/15.84 ( (fun bool bool), (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), (combb bool bool int), fNot ) 15.63/15.84 ( (fun bool bool), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)), (combb bool bool (product_prod int int)), fNot ) 15.63/15.84 ( (fun bool bool), (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)), (combb bool bool nat), fNot ) 15.63/15.84 ( (fun bool (fun bool bool)), (fun (fun int bool) (fun int (fun bool bool))), (combb bool (fun bool bool) int), fconj ) 15.63/15.84 ( (fun bool (fun bool bool)), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 bool) (fun _let_0 (fun bool bool)))), (combb bool (fun bool bool) (product_prod int int)), fconj ) 15.63/15.84 ( (fun bool (fun bool bool)), (fun (fun real bool) (fun real (fun bool bool))), (combb bool (fun bool bool) real), fconj ) 15.63/15.84 ( (fun bool (fun bool bool)), (fun (fun nat bool) (fun nat (fun bool bool))), (combb bool (fun bool bool) nat), fconj ) 15.63/15.84 ( (fun int real), (fun int (fun int real)), (let ((_let_0 (fun real real))) (let ((_let_1 (fun int real))) (let ((_let_2 (fun _let_1 _let_1))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int _let_0))) (hAPP _let_3 (fun _let_1 (fun int _let_1)) (combc int _let_1 _let_1) (hAPP _let_4 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_4 _let_3) (combb _let_0 _let_2 int) (combb real real int)) (hAPP _let_1 _let_4 (hAPP (fun real _let_0) (fun _let_1 _let_4) (combb real _let_0 int) (inverse_divide real)) (real_1 int))))))))), (real_1 int) ) 15.63/15.84 ( (fun int real), (fun int (fun real real)), (let ((_let_0 (fun real real))) (hAPP (fun real _let_0) (fun (fun int real) (fun int _let_0)) (combb real _let_0 int) (inverse_divide real))), (real_1 int) ) 15.63/15.84 ) 15.63/15.84 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_121977 $$unsorted) (BOUND_VARIABLE_121978 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_121978) BOUND_VARIABLE_121977))) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (one_one X_a)) BOUND_VARIABLE_121978))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_121978) _let_2))))))) ) 15.63/15.84 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 15.63/15.84 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 15.63/15.84 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_14 ) 15.63/15.84 ( complex, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), ii ) 15.63/15.84 ) 15.63/15.84 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_122014 $$unsorted) (BOUND_VARIABLE_122015 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)))) (or (not (ordere216010020id_add X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_122015))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_122014))) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_122015) BOUND_VARIABLE_122014))))) ) 15.63/15.84 ( nat, (one_one nat), (one_one nat) ) 15.63/15.84 ( int, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.63/15.84 ( int, (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.84 ) 15.63/15.84 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_122067 $$unsorted) (BOUND_VARIABLE_122068 $$unsorted) (BOUND_VARIABLE_122069 $$unsorted)) (let ((_let_0 (filter X_a))) (let ((_let_1 (fun _let_0 bool))) (or (not (metric_space X_a)) (not (metric_space X_b)) (= (forall ((R_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) R_2))) (not (forall ((S_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) S_1))) (not (forall ((X $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (or (= (ti X_a X) (ti X_a BOUND_VARIABLE_122069)) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP X_a real (hAPP X_a (fun X_a real) (dist_dist X_a) X) BOUND_VARIABLE_122069)) S_1))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP X_b real (hAPP X_b (fun X_b real) (dist_dist X_b) (hAPP X_a X_b BOUND_VARIABLE_122067 X)) BOUND_VARIABLE_122068)) R_2))))) ))) ))) ) (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (hAPP (fun X_a X_b) (fun X_b _let_1) (tendsto X_a X_b) BOUND_VARIABLE_122067) BOUND_VARIABLE_122068) (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_122069))))))) ) 15.63/15.84 ( real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.84 ) 15.63/15.84 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_122174 $$unsorted) (BOUND_VARIABLE_122175 $$unsorted) (BOUND_VARIABLE_122176 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_122174))) (or (not (order X_a)) (not (= (ti X_a BOUND_VARIABLE_122176) (ti X_a BOUND_VARIABLE_122175))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_122176))) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_122175)))) ) 15.63/15.84 ( int, (one_one int), pls, pls ) 15.63/15.84 ( int, (zero_zero int), s, s ) 15.63/15.84 ( int, min_1, s1, s1 ) 15.63/15.84 ( real, (zero_zero real), pi, pi ) 15.63/15.84 ) 15.63/15.84 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (fun nat nat))) (or (hBOOL (hAPP nat bool (even_odd_even nat) X)) (= (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP int real (number_number_of real) min_1)) (hAPP nat nat (hAPP nat _let_0 (div_div nat) (hAPP nat nat (hAPP nat _let_0 (minus_minus nat) X) (hAPP nat nat suc (zero_zero nat)))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP nat real (real_1 nat) (hAPP nat nat (fact_fact nat) X))) (hAPP nat real sin_coeff X)))) ) 15.63/15.84 ( (zero_zero nat) ) 15.63/15.84 ( (hAPP nat nat suc (zero_zero nat)) ) 15.63/15.84 ( (one_one nat) ) 15.63/15.84 ) 15.63/15.84 (instantiation (forall ((X $$unsorted)) (or (not (hBOOL (hAPP nat bool (even_odd_even nat) X))) (= (zero_zero real) (hAPP nat real sin_coeff X))) ) 15.63/15.84 ( (zero_zero nat) ) 15.63/15.84 ( (one_one nat) ) 15.63/15.84 ) 15.63/15.84 (instantiation (forall ((X_a $$unsorted)) (or (not (real_algebra_1 X_a)) (= (hAPP real X_a (of_real X_a) (zero_zero real)) (zero_zero X_a))) ) 15.63/15.84 ( nat ) 15.63/15.84 ( int ) 15.63/15.84 ( real ) 15.63/15.84 ( rat ) 15.63/15.84 ( complex ) 15.63/15.84 ( quickcheck_code_int ) 15.63/15.84 ( code_code_numeral ) 15.63/15.84 ) 15.63/15.84 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_122238 $$unsorted) (BOUND_VARIABLE_122239 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (number_number_of X_a))) (let ((_let_2 (hAPP int X_a _let_1 BOUND_VARIABLE_122239))) (let ((_let_3 (hAPP int X_a _let_1 BOUND_VARIABLE_122238))) (or (not (number X_a)) (not (linorder X_a)) (= (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) _let_2) _let_3))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) _let_3) _let_2)))))))) ) 15.63/15.84 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)), pls ) 15.63/15.84 ( int, pls, pls ) 15.63/15.84 ( int, pls, (hAPP int int bit1 pls) ) 15.63/15.84 ( int, pls, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.63/15.84 ( int, pls, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.63/15.84 ( int, (hAPP int int bit1 pls), pls ) 15.63/15.84 ) 15.63/15.84 (instantiation (forall ((Z $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP int int (abs_abs int) Z)) (one_one int))) (= (zero_zero int) (ti int Z))) ) 15.63/15.84 ( pls ) 15.63/15.84 ( min_1 ) 15.63/15.84 ( s ) 15.63/15.84 ( m ) 15.63/15.84 ( s1 ) 15.63/15.84 ( t ) 15.63/15.84 ) 15.63/15.84 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_122301 $$unsorted) (BOUND_VARIABLE_122302 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)))) (or (not (ordere216010020id_add X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)) BOUND_VARIABLE_122302))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_122301))) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_122302) BOUND_VARIABLE_122301))))) ) 15.63/15.84 ( nat, (one_one nat), (one_one nat) ) 15.63/15.84 ( int, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.63/15.84 ( int, (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.84 ) 15.63/15.84 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (norm_norm X_a))) (or (not (dist_norm X_a)) (= _let_0 (ti (fun X_a real) _let_0)))) ) 15.63/15.84 ( nat ) 15.63/15.84 ( int ) 15.63/15.84 ( real ) 15.63/15.84 ( (fun real bool) ) 15.63/15.84 ( rat ) 15.63/15.84 ( complex ) 15.63/15.84 ) 15.63/15.84 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_122363 $$unsorted) (BOUND_VARIABLE_122364 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (or (not (linord20386208strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_122364))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_122363) _let_2))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_122363) BOUND_VARIABLE_122364)) _let_2)))))) ) 15.63/15.84 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 15.63/15.84 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.63/15.84 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13 ) 15.63/15.84 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.63/15.85 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.63/15.85 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.63/15.85 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 15.63/15.85 ( complex, ii, ii ) 15.63/15.85 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 15.63/15.85 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 15.63/15.85 ) 15.63/15.85 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_122390 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hAPP X_a int (archimedean_ceiling X_a) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_122390)) (hAPP int int (number_number_of int) BOUND_VARIABLE_122390))) ) 15.63/15.85 ( nat, pls ) 15.63/15.85 ( nat, (hAPP int int bit1 pls) ) 15.63/15.85 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.63/15.85 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.63/15.85 ( int, pls ) 15.63/15.85 ( int, (hAPP int int bit1 pls) ) 15.63/15.85 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.63/15.85 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.63/15.85 ( int, min_1 ) 15.63/15.85 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.85 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.63/15.85 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.63/15.85 ( real, min_1 ) 15.63/15.85 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.85 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.63/15.85 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.85 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 15.63/15.85 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.63/15.85 ( complex, min_1 ) 15.63/15.85 ( quickcheck_code_int, (one_one int) ) 15.63/15.85 ( quickcheck_code_int, (zero_zero int) ) 15.63/15.85 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 15.63/15.85 ( code_code_numeral, pls ) 15.63/15.85 ( code_code_numeral, (hAPP int int bit1 pls) ) 15.63/15.85 ) 15.63/15.85 (instantiation (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_0 (inverse_inverse real))) (let ((_let_1 (hAPP nat (fun real real) root N_1))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_1))) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) X_1))) (= (hAPP real real _let_1 (hAPP real real _let_0 X_1)) (hAPP real real _let_0 (hAPP real real _let_1 X_1)))))) ) 15.63/15.85 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.85 ) 15.63/15.85 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_122447 $$unsorted) (BOUND_VARIABLE_122448 $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (order X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_122447) BOUND_VARIABLE_122448)) (or (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_122447) BOUND_VARIABLE_122448)) (= (ti X_a BOUND_VARIABLE_122447) (ti X_a BOUND_VARIABLE_122448)))))) ) 15.63/15.85 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.85 ( int, (one_one int), t ) 15.63/15.85 ( int, (zero_zero int), (one_one int) ) 15.63/15.85 ( int, (zero_zero int), min_1 ) 15.63/15.85 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.85 ( int, (zero_zero int), s ) 15.63/15.85 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.63/15.85 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.63/15.85 ( int, (zero_zero int), skv_4 ) 15.63/15.85 ( int, (zero_zero int), skv_10 ) 15.63/15.85 ( int, pls, (one_one int) ) 15.63/15.85 ( int, pls, pls ) 15.63/15.85 ( int, pls, min_1 ) 15.63/15.85 ( int, pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.85 ( int, min_1, pls ) 15.63/15.85 ( int, min_1, min_1 ) 15.63/15.85 ( int, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.85 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.85 ( int, skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.85 ( int, skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.85 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.85 ( real, (zero_zero real), pi ) 15.63/15.85 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.85 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.85 ( real, (zero_zero real), skv_2 ) 15.63/15.85 ( real, (zero_zero real), skv_3 ) 15.63/15.85 ( real, (zero_zero real), skv_5 ) 15.63/15.85 ( real, (zero_zero real), skv_7 ) 15.63/15.85 ( real, (zero_zero real), skv_8 ) 15.63/15.85 ( real, (zero_zero real), skv_9 ) 15.63/15.85 ( real, (zero_zero real), skv_12 ) 15.63/15.85 ( real, pi, (zero_zero real) ) 15.63/15.85 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.85 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.63/15.85 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.85 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 15.63/15.85 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.63/15.85 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 15.63/15.85 ( real, skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.85 ) 15.63/15.85 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_122500 $$unsorted) (BOUND_VARIABLE_122501 $$unsorted)) (let ((_let_0 (fun nat X_a))) (let ((_let_1 (summable X_a))) (let ((_let_2 (fun X_a X_a))) (let ((_let_3 (fun nat _let_2))) (or (not (real_normed_algebra X_a)) (not (hBOOL (hAPP _let_0 bool _let_1 BOUND_VARIABLE_122501))) (hBOOL (hAPP _let_0 bool _let_1 (hAPP X_a _let_0 (hAPP _let_3 (fun X_a _let_0) (combc nat X_a X_a) (hAPP _let_0 _let_3 (hAPP (fun X_a _let_2) (fun _let_0 _let_3) (combb X_a _let_2 nat) (times_times X_a)) BOUND_VARIABLE_122501)) BOUND_VARIABLE_122500)))))))) ) 15.63/15.85 ( real, (one_one real), (hAPP real (fun nat real) (power_power real) (hAPP int real (number_number_of real) min_1)) ) 15.63/15.85 ) 15.63/15.85 (instantiation (forall ((N_1 $$unsorted)) (= (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (one_one nat)) N_1) (hAPP nat nat suc N_1)) ) 15.63/15.85 ( (zero_zero nat) ) 15.63/15.85 ( (hAPP nat nat suc (zero_zero nat)) ) 15.63/15.85 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 15.63/15.85 ( (one_one nat) ) 15.63/15.85 ) 15.63/15.85 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_0 (uminus_uminus real))) (let ((_let_1 (fun real complex))) (= (hAPP real complex (hAPP real _let_1 complex_1 (hAPP real real _let_0 A_1)) (hAPP real real _let_0 B)) (hAPP complex complex (uminus_uminus complex) (hAPP real complex (hAPP real _let_1 complex_1 A_1) B))))) ) 15.63/15.85 ( (one_one real), (zero_zero real) ) 15.63/15.85 ( (zero_zero real), (one_one real) ) 15.63/15.85 ) 15.63/15.85 (instantiation (forall ((B $$unsorted) (A_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 A_1) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) B))) (not (forall ((D_3 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) D_3))) (not (forall ((Y $$unsorted)) (let ((_let_2 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (abs_abs real) (hAPP real real (hAPP real (fun real real) (minus_minus real) X_1) Y))) D_3))) (and (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 Y) B)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 A_1) Y))))) ))) ))))) ) 15.63/15.85 ( (zero_zero real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 15.63/15.85 ( pi, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 15.63/15.85 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.85 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.63/15.85 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real), pi ) 15.63/15.85 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi, (zero_zero real) ) 15.63/15.85 ) 15.63/15.85 (instantiation (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) Y_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Y_1) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) pi))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real cos X_1)) (hAPP real real cos Y_1)))))) ) 15.63/15.85 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_5 ) 15.63/15.85 ) 15.63/15.85 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_122612 $$unsorted) (BOUND_VARIABLE_122613 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (plus_plus X_a))) (let ((_let_2 (uminus_uminus X_a))) (or (not (ab_group_add X_a)) (= (hAPP X_a X_a _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_122612) BOUND_VARIABLE_122613)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_122612)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_122613))))))) ) 15.63/15.85 ( nat, (one_one nat), (one_one nat) ) 15.63/15.85 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 15.63/15.85 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 15.63/15.85 ) 15.63/15.85 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_122632 $$unsorted) (BOUND_VARIABLE_122633 $$unsorted) (BOUND_VARIABLE_122634 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (inverse_divide X_a))) (let ((_let_2 (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_122632))) (or (not (division_ring X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_122633)) BOUND_VARIABLE_122634) (hAPP X_a X_a _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_122633) BOUND_VARIABLE_122634))))))) ) 15.63/15.85 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.85 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.85 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.85 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.63/15.85 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.63/15.85 ) 15.63/15.85 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_122657 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (inverse_inverse X_a))) (or (not (real_normed_field X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_122657)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (hAPP (fun X_a X_a) (fun X_a _let_0) (deriv X_a) _let_1) BOUND_VARIABLE_122657) (hAPP X_a X_a (uminus_uminus X_a) (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) (hAPP X_a X_a _let_1 BOUND_VARIABLE_122657)) (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat)))))))))) ) 15.63/15.85 ( bool, fFalse ) 15.63/15.85 ( bool, fTrue ) 15.63/15.85 ( int, pls ) 15.63/15.85 ( int, min_1 ) 15.63/15.85 ( int, s ) 15.63/15.85 ( int, m ) 15.63/15.85 ( int, s1 ) 15.63/15.85 ( int, t ) 15.63/15.85 ( (fun int bool), nat_neg ) 15.63/15.85 ( (fun int bool), zprime ) 15.63/15.85 ( (fun int bool), zEven ) 15.63/15.85 ( (fun int bool), zOdd ) 15.63/15.85 ( (fun int bool), (even_odd_even int) ) 15.63/15.85 ( (fun int bool), twoSqu1091635170sum2sq ) 15.63/15.85 ( (fun int bool), nat_is_nat ) 15.63/15.85 ( (fun int (fun int bool)), norRRset ) 15.63/15.85 ( (fun int (fun int bool)), quadRes ) 15.63/15.85 ( (fun int (fun int bool)), sRStar ) 15.63/15.85 ( (fun int (fun int bool)), d22set ) 15.63/15.85 ( (fun int (fun int bool)), sr ) 15.63/15.85 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 15.63/15.85 ( (fun int int), zfact ) 15.63/15.85 ( (fun int int), bit0 ) 15.63/15.85 ( (fun int int), bit1 ) 15.63/15.85 ( (fun int int), (fact_fact int) ) 15.63/15.85 ( (fun int int), pred ) 15.63/15.85 ( (fun int int), succ ) 15.63/15.85 ( (fun nat bool), (even_odd_even nat) ) 15.63/15.85 ( (fun nat bool), prime ) 15.63/15.85 ( (fun nat nat), suc ) 15.63/15.85 ( (fun nat nat), (fact_fact nat) ) 15.63/15.85 ( (fun nat nat), fact ) 15.63/15.85 ( (fun nat nat), nat_size ) 15.63/15.85 ( (fun nat nat), (size_size nat) ) 15.63/15.85 ( (fun (product_prod nat nat) bool), pred_nat ) 15.63/15.85 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 15.63/15.85 ( real, (zero_zero real) ) 15.63/15.85 ( real, pi ) 15.63/15.85 ( (fun real real), ln ) 15.63/15.85 ( (fun real real), cos ) 15.63/15.85 ( (fun real real), sqrt ) 15.63/15.85 ( (fun real real), sin ) 15.63/15.85 ( (fun real real), arccos ) 15.63/15.85 ( (fun real real), arcsin ) 15.63/15.85 ( (fun real real), tan ) 15.63/15.85 ( (fun real real), arctan ) 15.63/15.85 ( (fun nat (fun nat bool)), coprime ) 15.63/15.85 ( complex, ii ) 15.63/15.85 ( (fun nat real), (real_1 nat) ) 15.63/15.85 ( (fun nat real), sin_coeff ) 15.63/15.85 ( (fun nat real), cos_coeff ) 15.63/15.85 ( (filter nat), sequentially ) 15.63/15.85 ( (fun int (fun int int)), (gcd_gcd int) ) 15.63/15.85 ( (fun int (fun int int)), legendre ) 15.63/15.85 ( (fun int (fun int int)), legacy_zgcd ) 15.63/15.85 ( (fun int (fun int int)), standardRes ) 15.63/15.85 ( (fun int (fun int int)), nat_tsub ) 15.63/15.85 ( (fun int (fun int int)), multInv ) 15.63/15.85 ( (fun int (fun int int)), z3mod ) 15.63/15.85 ( (fun int (fun int int)), z3div ) 15.63/15.85 ( (fun int (fun int int)), int_gcd ) 15.63/15.85 ( (fun int (fun int int)), int_lcm ) 15.63/15.85 ( (fun int (fun int int)), inv ) 15.63/15.85 ( (fun complex complex), expi ) 15.63/15.85 ( (fun complex complex), cnj ) 15.63/15.85 ( (fun real complex), cis ) 15.63/15.85 ( (fun int nat), nat_1 ) 15.63/15.85 ( (fun int nat), phi ) 15.63/15.85 ( (fun (fun int bool) bool), nat_nat_set ) 15.63/15.85 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 15.63/15.85 ( (fun nat (fun nat nat)), nat_gcd ) 15.63/15.85 ( (fun nat (fun nat nat)), nat_lcm ) 15.63/15.85 ( (fun (fun int bool) int), (the int) ) 15.63/15.85 ( (fun complex real), re ) 15.63/15.85 ( (fun complex real), im ) 15.63/15.85 ( (fun complex real), arg ) 15.63/15.85 ( (fun bool bool), fNot ) 15.63/15.85 ( (fun nat (fun real real)), root ) 15.63/15.85 ( (fun real (fun real real)), log ) 15.63/15.85 ( (fun real (fun real real)), powr ) 15.63/15.85 ( (fun bool (fun bool bool)), fimplies ) 15.63/15.85 ( (fun bool (fun bool bool)), fconj ) 15.63/15.85 ( (fun bool (fun bool bool)), fdisj ) 15.63/15.85 ( (fun int (fun int (product_prod int int))), negDivAlg ) 15.63/15.85 ( (fun int (fun int (product_prod int int))), posDivAlg ) 15.63/15.85 ( (fun int (fun int (product_prod int int))), divmod_int ) 15.63/15.85 ( (fun int (fun int (product_prod int int))), pdivmod ) 15.63/15.85 ( (fun int (fun int (product_prod int int))), norm_frac ) 15.63/15.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 15.63/15.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 15.63/15.85 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 15.63/15.85 ( (fun int (fun int (fun int bool))), zcong ) 15.63/15.85 ( (fun int (fun int (fun int bool))), zcongm ) 15.63/15.85 ( (fun int (fun int (fun int bool))), noXRRset ) 15.63/15.85 ( (fun int (fun int (fun int bool))), bnorRset ) 15.63/15.85 ( (fun int (fun int (fun int bool))), wset ) 15.63/15.85 ( (fun (product_prod int int) bool), frac_1 ) 15.63/15.85 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 15.63/15.85 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 15.63/15.85 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 15.63/15.85 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 15.63/15.85 ( (fun (fun nat rat) bool), vanishes ) 15.63/15.85 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 15.63/15.85 ( (fun code_code_numeral nat), code_c271388182l_size ) 15.63/15.85 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 15.63/15.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 15.63/15.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 15.63/15.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 15.63/15.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 15.63/15.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 15.63/15.85 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 15.63/15.85 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 15.63/15.85 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 15.63/15.85 ( (fun complex nat), complex_size ) 15.63/15.85 ( (fun complex nat), (size_size complex) ) 15.63/15.85 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 15.63/15.85 ( (fun nat (fun nat (product_prod int int))), bezw ) 15.63/15.85 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 15.63/15.85 ( (fun int (fun nat nat)), nat_aux ) 15.63/15.85 ( (fun int (fun (fun int bool) bool)), rsetR ) 15.63/15.85 ( (fun int (fun (fun int bool) bool)), resSet ) 15.63/15.85 ( (fun int (list int)), quickc666637781d_zero ) 15.63/15.85 ( (fun (product_prod int int) rat), frct ) 15.63/15.85 ( (fun int (fun int rat)), fract ) 15.63/15.85 ( (fun real (fun real complex)), complex_1 ) 15.63/15.85 ( (fun real (fun real complex)), rcis ) 15.63/15.85 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 15.63/15.85 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 15.63/15.85 ( (fun int real), (real_1 int) ) 15.63/15.85 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 15.63/15.85 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 15.63/15.85 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 15.63/15.85 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 15.63/15.85 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 15.63/15.85 ( (fun real nat), natfloor ) 15.63/15.85 ( (fun real nat), natceiling ) 15.63/15.85 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 15.63/15.85 ( (fun quickcheck_code_int int), quickcheck_int_of ) 15.63/15.85 ( (fun rat (product_prod int int)), quotient_of ) 15.63/15.85 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 15.63/15.85 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 15.63/15.85 ( (fun rat real), ratreal ) 15.63/15.85 ( (fun code_code_numeral int), code_int_of ) 15.63/15.85 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 15.63/15.85 ( (fun int quickcheck_code_int), quickcheck_of_int ) 15.63/15.85 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 15.63/15.85 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 15.63/15.85 ) 15.63/15.85 (instantiation (forall ((K_4 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (= (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) K_4)) K_4) (hAPP int int bit1 K_4)))) ) 15.63/15.85 ( pls ) 15.63/15.85 ( (hAPP int int bit1 pls) ) 15.63/15.85 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.63/15.85 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.63/15.85 ( min_1 ) 15.63/15.85 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.63/15.85 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.63/15.85 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 15.63/15.85 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 15.63/15.85 ) 15.63/15.85 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP nat rat (semiring_1_of_nat rat) K_4) (hAPP int rat (hAPP int (fun int rat) fract (hAPP nat int (semiring_1_of_nat int) K_4)) (one_one int))) ) 15.63/15.85 ( (zero_zero nat) ) 15.63/15.85 ( (hAPP nat nat suc (zero_zero nat)) ) 15.63/15.85 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.63/15.85 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.85 ) 15.63/15.85 (instantiation (forall ((Y_2 $$unsorted) (X_2 $$unsorted)) (let ((_let_0 (hAPP real (fun real bool) (ord_less real) (zero_zero real)))) (or (not (hBOOL (hAPP real bool _let_0 X_2))) (not (hBOOL (hAPP real bool _let_0 Y_2))) (= (= (hAPP real real ln X_2) (hAPP real real ln Y_2)) (= Y_2 X_2)))) ) 15.63/15.85 ( pi, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.85 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.85 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), skv_2 ) 15.63/15.85 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 15.63/15.85 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.85 ( skv_2, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.85 ( skv_8, skv_8 ) 15.63/15.85 ( skv_8, skv_9 ) 15.63/15.85 ( skv_9, skv_8 ) 15.63/15.85 ) 15.63/15.85 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_122723 $$unsorted) (BOUND_VARIABLE_122724 $$unsorted) (BOUND_VARIABLE_122725 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (or (not (preorder X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_122724) BOUND_VARIABLE_122725))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_122725) BOUND_VARIABLE_122723))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_122724) BOUND_VARIABLE_122723))))) ) 15.63/15.85 ( int, pls, (zero_zero int), min_1 ) 15.63/15.85 ( int, pls, min_1, pls ) 15.63/15.85 ( int, min_1, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.63/15.85 ( int, min_1, min_1, min_1 ) 15.63/15.85 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (one_one int), t ) 15.63/15.85 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (zero_zero int), s ) 15.63/15.85 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (zero_zero int), skv_4 ) 15.63/15.85 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (zero_zero int), skv_10 ) 15.63/15.85 ( int, t, (zero_zero int), (one_one int) ) 15.63/15.85 ( real, (zero_zero real), (zero_zero real), pi ) 15.63/15.85 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.85 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.63/15.85 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.63/15.85 ) 15.63/15.85 (instantiation (forall ((Y_1 $$unsorted) (X_1 $$unsorted) (Z_1 $$unsorted)) (let ((_let_0 (hAPP nat (fun nat bool) (ord_less nat) X_1))) (or (not (hBOOL (hAPP nat bool _let_0 Z_1))) (hBOOL (hAPP nat bool _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) Y_1) Z_1))))) ) 15.63/15.85 ( (one_one nat), (zero_zero nat), (one_one nat) ) 15.63/15.85 ) 15.63/15.85 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_122877 $$unsorted) (BOUND_VARIABLE_122878 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (zero_zero X_a))) (let ((_let_3 (hAPP X_a _let_0 _let_1 _let_2))) (or (not (ordere453448008miring X_a)) (and (or (not (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_122877))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_122878) _let_2)))) (or (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_122877) _let_2))) (not (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_122878))))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_122878) BOUND_VARIABLE_122877)) _let_2))))))) ) 15.63/15.85 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.85 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.85 ( int, skv_13, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.85 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.85 ( real, pi, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 15.63/15.85 ( real, (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.85 ( real, (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.85 ( complex, ii, ii ) 15.63/15.85 ( complex, ii, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 15.63/15.85 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.85 ) 15.63/15.85 (instantiation (forall ((N_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) (zero_zero real)) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) X_1) (hAPP nat real (real_1 nat) N_1)))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (hAPP real nat natfloor X_1)) N_1)))) ) 15.63/15.85 ( (zero_zero nat), pi ) 15.63/15.85 ( (zero_zero nat), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.63/15.85 ( (zero_zero nat), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.85 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real) ) 15.63/15.85 ) 15.63/15.85 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_122968 $$unsorted)) (or (not (number_ring X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (hAPP int X_a (number_number_of X_a) pls)) BOUND_VARIABLE_122968) (ti X_a BOUND_VARIABLE_122968))) ) 15.63/15.85 ( bool, fFalse ) 15.63/15.85 ( bool, fTrue ) 15.63/15.85 ( int, pls ) 15.63/15.85 ( int, min_1 ) 15.63/15.85 ( int, s ) 15.63/15.85 ( int, m ) 15.63/15.85 ( int, s1 ) 15.63/15.85 ( int, t ) 15.63/15.85 ( (fun int bool), nat_neg ) 15.63/15.85 ( (fun int bool), zprime ) 15.63/15.85 ( (fun int bool), zEven ) 15.63/15.85 ( (fun int bool), zOdd ) 15.63/15.85 ( (fun int bool), (even_odd_even int) ) 15.63/15.85 ( (fun int bool), twoSqu1091635170sum2sq ) 15.63/15.85 ( (fun int bool), nat_is_nat ) 15.63/15.85 ( (fun int (fun int bool)), norRRset ) 15.63/15.85 ( (fun int (fun int bool)), quadRes ) 15.63/15.85 ( (fun int (fun int bool)), sRStar ) 15.63/15.85 ( (fun int (fun int bool)), d22set ) 15.63/15.85 ( (fun int (fun int bool)), sr ) 15.63/15.85 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 15.63/15.85 ( (fun int int), zfact ) 15.63/15.85 ( (fun int int), bit0 ) 15.63/15.85 ( (fun int int), bit1 ) 15.63/15.85 ( (fun int int), (fact_fact int) ) 15.63/15.85 ( (fun int int), pred ) 15.63/15.85 ( (fun int int), succ ) 15.63/15.85 ( (fun nat bool), (even_odd_even nat) ) 15.63/15.85 ( (fun nat bool), prime ) 15.63/15.85 ( (fun nat nat), suc ) 15.63/15.85 ( (fun nat nat), (fact_fact nat) ) 15.63/15.85 ( (fun nat nat), fact ) 15.63/15.85 ( (fun nat nat), nat_size ) 15.63/15.85 ( (fun nat nat), (size_size nat) ) 15.63/15.85 ( (fun (product_prod nat nat) bool), pred_nat ) 15.63/15.85 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 15.63/15.85 ( real, pi ) 15.63/15.85 ( (fun real real), ln ) 15.63/15.85 ( (fun real real), cos ) 15.63/15.85 ( (fun real real), sqrt ) 15.63/15.85 ( (fun real real), sin ) 15.63/15.85 ( (fun real real), arccos ) 15.63/15.85 ( (fun real real), arcsin ) 15.63/15.85 ( (fun real real), tan ) 15.63/15.85 ( (fun real real), arctan ) 15.63/15.85 ( (fun nat (fun nat bool)), coprime ) 15.63/15.85 ( complex, ii ) 15.63/15.85 ( (fun nat real), (real_1 nat) ) 15.63/15.85 ( (fun nat real), sin_coeff ) 15.63/15.85 ( (fun nat real), cos_coeff ) 15.63/15.85 ( (filter nat), sequentially ) 15.63/15.85 ( (fun int (fun int int)), (gcd_gcd int) ) 15.63/15.85 ( (fun int (fun int int)), legendre ) 15.63/15.85 ( (fun int (fun int int)), legacy_zgcd ) 15.63/15.85 ( (fun int (fun int int)), standardRes ) 15.63/15.85 ( (fun int (fun int int)), nat_tsub ) 15.63/15.85 ( (fun int (fun int int)), multInv ) 15.63/15.85 ( (fun int (fun int int)), z3mod ) 15.63/15.85 ( (fun int (fun int int)), z3div ) 15.63/15.85 ( (fun int (fun int int)), int_gcd ) 15.63/15.85 ( (fun int (fun int int)), int_lcm ) 15.63/15.85 ( (fun int (fun int int)), inv ) 15.63/15.85 ( (fun complex complex), expi ) 15.63/15.85 ( (fun complex complex), cnj ) 15.63/15.85 ( (fun real complex), cis ) 15.63/15.85 ( (fun int nat), nat_1 ) 15.63/15.85 ( (fun int nat), phi ) 15.63/15.85 ( (fun (fun int bool) bool), nat_nat_set ) 15.63/15.85 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 15.63/15.85 ( (fun nat (fun nat nat)), nat_gcd ) 15.63/15.85 ( (fun nat (fun nat nat)), nat_lcm ) 15.63/15.85 ( (fun (fun int bool) int), (the int) ) 15.63/15.85 ( (fun complex real), re ) 15.63/15.85 ( (fun complex real), im ) 15.63/15.85 ( (fun complex real), arg ) 15.63/15.85 ( (fun bool bool), fNot ) 15.63/15.85 ( (fun nat (fun real real)), root ) 15.63/15.85 ( (fun real (fun real real)), log ) 15.63/15.85 ( (fun real (fun real real)), powr ) 15.63/15.85 ( (fun bool (fun bool bool)), fimplies ) 15.63/15.85 ( (fun bool (fun bool bool)), fconj ) 15.63/15.85 ( (fun bool (fun bool bool)), fdisj ) 15.63/15.85 ( (fun int (fun int (product_prod int int))), negDivAlg ) 15.63/15.85 ( (fun int (fun int (product_prod int int))), posDivAlg ) 15.63/15.85 ( (fun int (fun int (product_prod int int))), divmod_int ) 15.63/15.85 ( (fun int (fun int (product_prod int int))), pdivmod ) 15.63/15.85 ( (fun int (fun int (product_prod int int))), norm_frac ) 15.63/15.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 15.63/15.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 15.63/15.85 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 15.63/15.85 ( (fun int (fun int (fun int bool))), zcong ) 15.63/15.85 ( (fun int (fun int (fun int bool))), zcongm ) 15.63/15.85 ( (fun int (fun int (fun int bool))), noXRRset ) 15.63/15.85 ( (fun int (fun int (fun int bool))), bnorRset ) 15.63/15.85 ( (fun int (fun int (fun int bool))), wset ) 15.63/15.85 ( (fun (product_prod int int) bool), frac_1 ) 15.63/15.85 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 15.63/15.85 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 15.63/15.85 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 15.63/15.85 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 15.63/15.85 ( (fun (fun nat rat) bool), vanishes ) 15.63/15.85 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 15.63/15.85 ( (fun code_code_numeral nat), code_c271388182l_size ) 15.63/15.85 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 15.63/15.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 15.63/15.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 15.63/15.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 15.63/15.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 15.63/15.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 15.63/15.85 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 15.63/15.85 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 15.63/15.85 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 15.63/15.85 ( (fun complex nat), complex_size ) 15.63/15.85 ( (fun complex nat), (size_size complex) ) 15.63/15.85 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 15.63/15.85 ( (fun nat (fun nat (product_prod int int))), bezw ) 15.63/15.85 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 15.63/15.85 ( (fun int (fun nat nat)), nat_aux ) 15.63/15.85 ( (fun int (fun (fun int bool) bool)), rsetR ) 15.63/15.85 ( (fun int (fun (fun int bool) bool)), resSet ) 15.63/15.85 ( (fun int (list int)), quickc666637781d_zero ) 15.63/15.85 ( (fun (product_prod int int) rat), frct ) 15.63/15.85 ( (fun int (fun int rat)), fract ) 15.63/15.85 ( (fun real (fun real complex)), complex_1 ) 15.63/15.85 ( (fun real (fun real complex)), rcis ) 15.63/15.85 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 15.63/15.85 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 15.63/15.85 ( (fun int real), (real_1 int) ) 15.63/15.85 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 15.63/15.85 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 15.63/15.85 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 15.63/15.85 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 15.63/15.85 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 15.63/15.85 ( (fun real nat), natfloor ) 15.63/15.85 ( (fun real nat), natceiling ) 15.63/15.85 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 15.63/15.85 ( (fun quickcheck_code_int int), quickcheck_int_of ) 15.63/15.85 ( (fun rat (product_prod int int)), quotient_of ) 15.63/15.85 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 15.63/15.85 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 15.63/15.85 ( (fun rat real), ratreal ) 15.63/15.85 ( (fun code_code_numeral int), code_int_of ) 15.63/15.85 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 15.63/15.85 ( (fun int quickcheck_code_int), quickcheck_of_int ) 15.63/15.85 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 15.63/15.85 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 15.63/15.85 ) 15.63/15.85 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (= (and (= (one_one real) Y_2) (= (zero_zero real) X_2)) (= ii (hAPP real complex (hAPP real (fun real complex) complex_1 X_2) Y_2))) ) 15.63/15.85 ( (one_one real), (zero_zero real) ) 15.63/15.85 ( (zero_zero real), (one_one real) ) 15.63/15.85 ( (zero_zero real), (zero_zero real) ) 15.63/15.85 ) 15.63/15.85 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_122991 $$unsorted) (BOUND_VARIABLE_122992 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (or (not (linordered_idom X_a)) (= (ti X_a BOUND_VARIABLE_122991) (ti X_a BOUND_VARIABLE_122992)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_122991) BOUND_VARIABLE_122992)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_122992) BOUND_VARIABLE_122991))))) ) 15.63/15.85 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.85 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 15.63/15.85 ( int, (one_one int), pls ) 15.63/15.85 ( int, (one_one int), t ) 15.63/15.85 ( int, pls, (one_one int) ) 15.63/15.85 ( int, pls, pls ) 15.63/15.85 ( int, pls, min_1 ) 15.63/15.85 ( int, pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.85 ( int, min_1, pls ) 15.63/15.85 ( int, min_1, min_1 ) 15.63/15.85 ( int, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.85 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), pls ) 15.63/15.85 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s ) 15.63/15.85 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.63/15.85 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_4 ) 15.63/15.85 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_10 ) 15.63/15.85 ( int, t, (one_one int) ) 15.63/15.85 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.85 ( int, skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.85 ( int, skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.85 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.85 ( real, (zero_zero real), pi ) 15.63/15.85 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.85 ( real, (zero_zero real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.63/15.85 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.85 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.85 ( real, (zero_zero real), skv_2 ) 15.63/15.85 ( real, (zero_zero real), skv_8 ) 15.63/15.85 ( real, (zero_zero real), skv_9 ) 15.63/15.85 ( real, pi, (zero_zero real) ) 15.63/15.85 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.85 ( real, pi, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 15.63/15.85 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.85 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.63/15.85 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.85 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 15.63/15.85 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 15.63/15.85 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 15.63/15.85 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.63/15.85 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.63/15.85 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 15.63/15.85 ( real, skv_2, (zero_zero real) ) 15.63/15.85 ( real, skv_8, (zero_zero real) ) 15.63/15.85 ( real, skv_9, (zero_zero real) ) 15.63/15.85 ) 15.63/15.85 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (zero_zero real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 _let_2) X_2))) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_2) (one_one real))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real ln X_2)) _let_2))))))) ) 15.63/15.85 ( (one_one real) ) 15.63/15.85 ( pi ) 15.63/15.85 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.85 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.85 ( skv_2 ) 15.63/15.85 ( skv_8 ) 15.63/15.85 ( skv_9 ) 15.63/15.85 ) 15.63/15.85 (instantiation (forall ((Z_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) Z_1))) (= (hAPP nat int (semiring_1_of_nat int) (hAPP int nat nat_1 Z_1)) (ti int Z_1))) ) 15.63/15.85 ( (one_one int) ) 15.63/15.85 ( (zero_zero int) ) 15.63/15.85 ( pls ) 15.63/15.85 ( min_1 ) 15.63/15.85 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.85 ( s ) 15.63/15.85 ( m ) 15.63/15.85 ( s1 ) 15.63/15.85 ( t ) 15.63/15.85 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.63/15.85 ( (hAPP int int (number_number_of int) pls) ) 15.63/15.85 ( skv_4 ) 15.63/15.85 ( skv_10 ) 15.63/15.85 ) 15.63/15.85 (instantiation (forall ((Z $$unsorted) (Z_3 $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (hAPP int int (hAPP int (fun int int) (minus_minus int) Z) Z_3))) (or (hBOOL (hAPP int bool nat_neg Z_3)) (= (hAPP nat nat (hAPP nat _let_0 (minus_minus nat) (hAPP int nat nat_1 Z)) (hAPP int nat nat_1 Z_3)) (hAPP nat nat (hAPP nat _let_0 (hAPP bool (fun nat _let_0) (if nat) (hAPP int bool nat_neg _let_1)) (zero_zero nat)) (hAPP int nat nat_1 _let_1)))))) ) 15.63/15.85 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.63/15.85 ) 15.63/15.85 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_123090 $$unsorted) (BOUND_VARIABLE_123091 $$unsorted)) (let ((_let_0 (filter X_a))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_123090))) (or (not (real_normed_algebra X_a)) (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 (hAPP (fun X_a X_a) (fun X_a _let_1) (tendsto X_a X_a) _let_2) (hAPP X_a X_a _let_2 BOUND_VARIABLE_123091)) (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_123091))))))) ) 15.63/15.85 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 15.63/15.85 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.63/15.85 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13 ) 15.63/15.85 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.63/15.85 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.63/15.85 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.63/15.85 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 15.63/15.85 ( complex, ii, ii ) 15.63/15.85 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 15.63/15.85 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 15.63/15.85 ) 15.63/15.85 (instantiation (forall ((N $$unsorted) (Ma $$unsorted)) (let ((_let_0 (one_one int))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) Ma))) (= (= _let_0 (hAPP int int (hAPP int (fun int int) (times_times int) Ma) N)) (and (= _let_0 (ti int Ma)) (= _let_0 (ti int N)))))) ) 15.63/15.85 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.85 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.85 ( skv_13, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.85 ) 15.63/15.85 (instantiation (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) X_1) (zero_zero real)))) (= (zero_zero nat) (hAPP real nat natfloor X_1))) ) 15.63/15.85 ( (one_one real) ) 15.63/15.85 ( (zero_zero real) ) 15.63/15.85 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.85 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.85 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.85 ( skv_5 ) 15.63/15.85 ) 15.63/15.85 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_123216 $$unsorted)) (or (not (linordered_idom X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)) (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_123216))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) BOUND_VARIABLE_123216)))) ) 15.63/15.85 ( real, (one_one int) ) 15.63/15.85 ( real, (zero_zero int) ) 15.63/15.85 ) 15.63/15.85 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_0 (product_prod X_b X_a))) (= (ti X_a B) (hAPP _let_0 X_a (product_snd X_b X_a) (hAPP X_a _let_0 (hAPP X_b (fun X_a _let_0) (product_Pair X_b X_a) A_1) B)))) ) 15.63/15.85 ( int, int, (one_one int), (one_one int) ) 15.63/15.85 ( int, int, (zero_zero int), (one_one int) ) 15.63/15.85 ( int, int, s, (one_one int) ) 15.63/15.85 ) 15.63/15.85 (instantiation (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_0 (even_odd_even int))) (or (not (hBOOL (hAPP int bool _let_0 X_1))) (not (hBOOL (hAPP int bool _let_0 Y_1))) (hBOOL (hAPP int bool _let_0 (hAPP int int (hAPP int (fun int int) (plus_plus int) X_1) Y_1))))) ) 15.63/15.85 ( (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.63/15.85 ( (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.85 ) 15.63/15.86 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_123317 $$unsorted)) (let ((_let_0 (archim2085082626_floor X_a))) (or (not (archim1727834104eiling X_a)) (= (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP X_a int _let_0 BOUND_VARIABLE_123317)) (one_one int)) (hAPP X_a int _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_123317) (one_one X_a)))))) ) 15.63/15.86 ( nat, (one_one nat) ) 15.63/15.86 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.63/15.86 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.86 ) 15.63/15.86 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (exp X_a))) (or (not (banach X_a)) (not (real_normed_field X_a)) (= _let_0 (ti (fun X_a X_a) _let_0)))) ) 15.63/15.86 ( bool ) 15.63/15.86 ( nat ) 15.63/15.86 ( int ) 15.63/15.86 ( (fun int bool) ) 15.63/15.86 ( (fun int (fun int bool)) ) 15.63/15.86 ( (fun int int) ) 15.63/15.86 ( (fun nat bool) ) 15.63/15.86 ( real ) 15.63/15.86 ( (fun real bool) ) 15.63/15.86 ( (fun real real) ) 15.63/15.86 ( complex ) 15.63/15.86 ( (fun nat real) ) 15.63/15.86 ( (product_prod int int) ) 15.63/15.86 ( code_code_numeral ) 15.63/15.86 ( (fun int (fun int (fun int bool))) ) 15.63/15.86 ( (fun (product_prod int int) bool) ) 15.63/15.86 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 15.63/15.86 ( (fun (product_prod int int) int) ) 15.63/15.86 ( (fun int real) ) 15.63/15.86 ) 15.63/15.86 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_123346 $$unsorted) (BOUND_VARIABLE_123347 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)))) (or (not (linord1117847801e_zero X_a)) (= (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_123346) BOUND_VARIABLE_123347))) (or (and (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_123347) (zero_zero X_a))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_123346) (zero_zero X_a)))) (and (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_123346)) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_123347))))))) ) 15.63/15.86 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.86 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.63/15.86 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.86 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 15.63/15.86 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.86 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.86 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.63/15.86 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.63/15.86 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.86 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.86 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.86 ) 15.63/15.86 (instantiation (forall ((V $$unsorted)) (= (= (zero_zero nat) (hAPP int nat (number_number_of nat) V)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) V) pls))) ) 15.63/15.86 ( (one_one int) ) 15.63/15.86 ( (zero_zero int) ) 15.63/15.86 ( pls ) 15.63/15.86 ( (hAPP int int bit1 pls) ) 15.63/15.86 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.63/15.86 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.63/15.86 ( min_1 ) 15.63/15.86 ) 15.63/15.86 (instantiation (forall ((P_4 $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP int bool zprime P_4))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) P_4)) (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) P_4) zOdd))))) ) 15.63/15.86 ( (one_one int) ) 15.63/15.86 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.86 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.86 ) 15.63/15.86 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (P_1 $$unsorted)) (let ((_let_0 (product_prod X_a X_b))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (hilbert_Eps _let_0))) (let ((_let_3 (fun _let_0 X_b))) (let ((_let_4 (fun X_b bool))) (let ((_let_5 (fun _let_0 _let_4))) (let ((_let_6 (fun _let_0 X_a))) (let ((_let_7 (fun X_a _let_4))) (= (hAPP _let_1 _let_0 _let_2 (hAPP _let_7 _let_1 (product_prod_case X_a X_b bool) P_1)) (hAPP _let_1 _let_0 _let_2 (hAPP _let_3 _let_1 (hAPP _let_5 (fun _let_3 _let_1) (combs _let_0 X_b bool) (hAPP _let_6 _let_5 (hAPP _let_7 (fun _let_6 _let_5) (combb X_a _let_4 _let_0) P_1) (product_fst X_a X_b))) (product_snd X_a X_b)))))))))))) ) 15.63/15.86 ( nat, nat, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat (fun nat bool)))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat (fun nat bool) nat) (hAPP _let_1 _let_1 (combc nat nat bool) (fequal nat))) suc))) ) 15.63/15.86 ( int, int, (fequal int) ) 15.63/15.86 ( int, int, (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun int _let_1))) (let ((_let_6 (fun int _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (fun _let_2 _let_1))) (let ((_let_9 (fun _let_1 _let_1))) (hAPP _let_1 _let_1 (hAPP _let_7 _let_9 (combb _let_0 _let_0 int) (hAPP _let_6 _let_7 (combs int bool bool) (hAPP _let_0 _let_6 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 int) fconj) (hAPP int _let_0 (ord_less int) (zero_zero int))))) (hAPP int _let_1 (hAPP _let_5 _let_5 (combc int int _let_0) (hAPP _let_5 _let_5 (hAPP _let_9 (fun _let_5 _let_5) (combb _let_1 _let_1 int) (combc int int bool)) (hAPP _let_3 _let_5 (hAPP _let_8 (fun _let_3 _let_5) (combb _let_2 _let_1 int) (hAPP _let_1 _let_8 (combb int _let_0 int) (fequal int))) int_gcd))) (one_one int))))))))))))) ) 15.63/15.86 ( (product_prod int int), (product_prod int int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun _let_2 (fun _let_2 bool)))) (let ((_let_5 (fun (fun _let_2 bool) (fun _let_2 bool)))) (let ((_let_6 (fun _let_2 _let_5))) (let ((_let_7 (fun _let_4 _let_4))) (let ((_let_8 (fun _let_2 _let_3))) (let ((_let_9 (fun _let_2 _let_0))) (let ((_let_10 (fun _let_2 int))) (let ((_let_11 (fun _let_10 _let_9))) (let ((_let_12 (hAPP (fun int _let_0) _let_11 (combb int _let_0 _let_2) (fequal int)))) (let ((_let_13 (product_snd int int))) (let ((_let_14 (hAPP (fun _let_2 bool) _let_8 (hAPP (fun bool _let_3) (fun (fun _let_2 bool) _let_8) (combb bool _let_3 _let_2) fconj) (hAPP (fun _let_2 bool) (fun _let_2 bool) (hAPP _let_3 _let_5 (combb bool bool _let_2) fNot) (hAPP int (fun _let_2 bool) (hAPP _let_9 (fun int (fun _let_2 bool)) (combc _let_2 int bool) (hAPP _let_10 _let_9 _let_12 _let_13)) (zero_zero int)))))) (let ((_let_15 (fun _let_2 _let_10))) (let ((_let_16 (fun _let_10 (fun _let_2 bool)))) (let ((_let_17 (fun _let_2 _let_16))) (let ((_let_18 (fun _let_2 _let_9))) (let ((_let_19 (fun _let_10 _let_10))) (let ((_let_20 (fun _let_2 _let_19))) (let ((_let_21 (fun _let_10 _let_15))) (let ((_let_22 (fun _let_2 _let_1))) (let ((_let_23 (hAPP _let_10 _let_22 (hAPP (fun int _let_1) (fun _let_10 _let_22) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (let ((_let_24 (fun int _let_10))) (hAPP _let_4 _let_4 (hAPP _let_6 _let_7 (combs _let_2 (fun _let_2 bool) (fun _let_2 bool)) (hAPP _let_8 _let_6 (hAPP (fun _let_3 _let_5) (fun _let_8 _let_6) (combb _let_3 _let_5 _let_2) (combb bool bool _let_2)) _let_14)) (hAPP _let_4 _let_4 (hAPP _let_5 _let_7 (combb (fun _let_2 bool) (fun _let_2 bool) _let_2) (hAPP _let_8 _let_5 (combs _let_2 bool bool) _let_14)) (hAPP _let_15 _let_4 (hAPP _let_17 (fun _let_15 _let_4) (combs _let_2 _let_10 (fun _let_2 bool)) (hAPP _let_18 _let_17 (hAPP (fun _let_9 _let_16) (fun _let_18 _let_17) (combb _let_9 _let_16 _let_2) (combs _let_2 int bool)) (hAPP _let_15 _let_18 (hAPP _let_11 (fun _let_15 _let_18) (combb _let_10 _let_9 _let_2) _let_12) (hAPP _let_10 _let_15 (hAPP _let_20 _let_21 (combc _let_2 _let_10 _let_10) (hAPP _let_22 _let_20 (hAPP (fun _let_1 _let_19) (fun _let_22 _let_20) (combb _let_1 _let_19 _let_2) (combb int int _let_2)) _let_23)) _let_13)))) (hAPP _let_10 _let_15 (hAPP _let_24 _let_21 (combb int _let_10 _let_2) (hAPP _let_22 _let_24 (combc _let_2 int int) _let_23)) _let_13))))))))))))))))))))))))))))) ) 15.63/15.86 ) 15.63/15.86 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted)) (let ((_let_0 (image X_b X_a))) (= _let_0 (ti (fun (fun X_b X_a) (fun (fun X_b bool) (fun X_a bool))) _let_0))) ) 15.63/15.86 ( nat, nat ) 15.63/15.86 ( int, int ) 15.63/15.86 ( real, real ) 15.63/15.86 ( (product_prod int int), (product_prod int int) ) 15.63/15.86 ) 15.63/15.86 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_123547 $$unsorted) (BOUND_VARIABLE_123548 $$unsorted) (BOUND_VARIABLE_123549 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (or (not (order X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_123548) BOUND_VARIABLE_123549))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_123547) BOUND_VARIABLE_123548))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_123547) BOUND_VARIABLE_123549))))) ) 15.63/15.86 ( int, (one_one int), min_1, pls ) 15.63/15.86 ( int, (zero_zero int), pls, pls ) 15.63/15.86 ( int, min_1, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.86 ( real, (zero_zero real), pi, (zero_zero real) ) 15.63/15.86 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 15.63/15.86 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 15.63/15.86 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.86 ( real, skv_5, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.86 ) 15.63/15.86 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_123573 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (one_one X_a))) (or (not (linord1117847801e_zero X_a)) (= (or (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_123573) (zero_zero X_a))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_123573))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_123573)) _let_2))))))) ) 15.63/15.86 ( int, (one_one int) ) 15.63/15.86 ( int, (zero_zero int) ) 15.63/15.86 ( int, min_1 ) 15.63/15.86 ( int, t ) 15.63/15.86 ( real, (zero_zero real) ) 15.63/15.86 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.86 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.86 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.86 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.86 ( real, skv_5 ) 15.63/15.86 ( complex, ii ) 15.63/15.86 ) 15.63/15.86 (instantiation (forall ((K_4 $$unsorted) (L_4 $$unsorted)) (let ((_let_0 (number_number_of int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (number_number_of rat))) (= (hAPP _let_1 rat frct (hAPP int _let_1 (hAPP int (fun int _let_1) (product_Pair int int) (hAPP int int _let_0 K_4)) (hAPP int int _let_0 L_4))) (hAPP rat rat (hAPP rat (fun rat rat) (inverse_divide rat) (hAPP int rat _let_2 K_4)) (hAPP int rat _let_2 L_4)))))) ) 15.63/15.86 ( pls, (hAPP int int bit1 pls) ) 15.63/15.86 ( (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 15.63/15.86 ) 15.63/15.86 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (plus_plus real))) (let ((_let_2 (fun nat real))) (let ((_let_3 (fun nat _let_0))) (let ((_let_4 (fun _let_2 _let_2))) (let ((_let_5 (fun (fun nat nat) _let_2))) (let ((_let_6 (combb nat real nat))) (let ((_let_7 (hAPP nat (fun nat nat) (hAPP (fun nat (fun nat nat)) (fun nat (fun nat nat)) (combc nat nat nat) (plus_plus nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (= (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real (hAPP real _let_0 _let_1 (one_one real)) X_2)) (hAPP _let_2 real (suminf real) (hAPP _let_2 _let_2 (hAPP _let_3 _let_4 (combs nat real real) (hAPP _let_2 _let_3 (hAPP (fun real _let_0) (fun _let_2 _let_3) (combb real _let_0 nat) (times_times real)) (hAPP _let_2 _let_2 (hAPP _let_0 _let_4 (combb real real nat) (inverse_inverse real)) (hAPP (fun nat nat) _let_2 (hAPP _let_2 _let_5 _let_6 (real_1 nat)) (hAPP (fun nat nat) (fun nat nat) (hAPP (fun nat nat) (fun (fun nat nat) (fun nat nat)) (combb nat nat nat) (fact_fact nat)) _let_7))))) (hAPP (fun nat nat) _let_2 (hAPP _let_2 _let_5 _let_6 (hAPP real _let_2 (power_power real) X_2)) _let_7)))) (hAPP real real (exp real) X_2)))))))))) ) 15.63/15.86 ( (hAPP int real (number_number_of real) min_1) ) 15.63/15.86 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.86 ) 15.63/15.86 (instantiation (forall ((N_1 $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)))) (or (not (hBOOL (hAPP nat bool _let_1 N_1))) (hBOOL (hAPP nat bool _let_1 (hAPP nat nat (hAPP nat _let_0 (div_div nat) (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) N_1) (one_one nat))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))))) ) 15.63/15.86 ( (one_one nat) ) 15.63/15.86 ) 15.63/15.86 (instantiation (forall ((N_1 $$unsorted) (X_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) X_1))) (= (hAPP int nat nat_1 (hAPP nat int (hAPP int (fun nat int) (power_power int) X_1) N_1)) (hAPP nat nat (hAPP nat (fun nat nat) (power_power nat) (hAPP int nat nat_1 X_1)) N_1))) ) 15.63/15.86 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 15.63/15.86 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 15.63/15.86 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_14 ) 15.63/15.86 ) 15.63/15.86 (instantiation (forall ((P_1 $$unsorted) (A0 $$unsorted) (A1 $$unsorted)) (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 bool))) (or (not (hBOOL (hAPP _let_0 bool (hAPP (fun _let_0 _let_1) _let_1 (accp _let_0) negDivAlg_rel) (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) A0) A1)))) (not (forall ((A_4 $$unsorted) (B_4 $$unsorted)) (let ((_let_2 (fun int int))) (let ((_let_3 (ord_less_eq int))) (let ((_let_4 (zero_zero int))) (let ((_let_5 (hAPP int (fun int bool) P_1 A_4))) (or (not (hBOOL (hAPP _let_0 bool (hAPP (fun _let_0 _let_1) _let_1 (accp _let_0) negDivAlg_rel) (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) A_4) B_4)))) (and (not (hBOOL (hAPP int bool (hAPP int (fun int bool) _let_3 B_4) _let_4))) (not (hBOOL (hAPP int bool (hAPP int (fun int bool) _let_3 _let_4) (hAPP int int (hAPP int _let_2 (plus_plus int) A_4) B_4)))) (not (hBOOL (hAPP int bool _let_5 (hAPP int int (hAPP int _let_2 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) B_4))))) (hBOOL (hAPP int bool _let_5 B_4))))))) )) (hBOOL (hAPP int bool (hAPP int (fun int bool) P_1 A0) A1))))) ) 15.63/15.86 ( (ord_less_eq int), (one_one int), t ) 15.63/15.86 ( (ord_less_eq int), (zero_zero int), (one_one int) ) 15.63/15.86 ( (ord_less_eq int), (zero_zero int), min_1 ) 15.63/15.86 ( (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.86 ( (ord_less_eq int), (zero_zero int), s ) 15.63/15.86 ( (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.63/15.86 ( (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.63/15.86 ( (ord_less_eq int), (zero_zero int), skv_4 ) 15.63/15.86 ( (ord_less_eq int), (zero_zero int), skv_10 ) 15.63/15.86 ( (ord_less_eq int), min_1, pls ) 15.63/15.86 ( (ord_less_eq int), min_1, min_1 ) 15.63/15.86 ( (ord_less int), (one_one int), t ) 15.63/15.86 ( (ord_less int), pls, (one_one int) ) 15.63/15.86 ( (ord_less int), pls, pls ) 15.63/15.86 ( (ord_less int), pls, min_1 ) 15.63/15.86 ( (ord_less int), pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.86 ( (ord_less int), min_1, pls ) 15.63/15.86 ( (ord_less int), min_1, min_1 ) 15.63/15.86 ( (ord_less int), s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.86 ( (ord_less int), t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.86 ( (ord_less int), skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.86 ( (ord_less int), skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.86 ( (dvd_dvd int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 15.63/15.86 ( quadRes, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (number_number_of int) min_1) ) 15.63/15.86 ( (hAPP int (fun int (fun int bool)) zcong s1), s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.86 ( (hAPP int (fun int (fun int bool)) zcong s1), skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.86 ( (hAPP int (fun int (fun int bool)) zcong s1), skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.86 ( (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.86 ( (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.86 ( (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.86 ( (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.63/15.86 ) 15.63/15.86 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (fun X_a (fun X_a bool)))) (or (not (linorder X_a)) (= (hAPP _let_0 (fun X_a (fun X_a X_a)) (min X_a) (hAPP _let_0 _let_0 (combc X_a X_a bool) (ord_less_eq X_a))) (ord_max X_a)))) ) 15.63/15.86 ( bool ) 15.63/15.86 ( nat ) 15.63/15.86 ( int ) 15.63/15.86 ( (fun int bool) ) 15.63/15.86 ( (fun int (fun int bool)) ) 15.63/15.86 ( (fun int int) ) 15.63/15.86 ( (fun nat bool) ) 15.63/15.86 ( (product_prod nat nat) ) 15.63/15.86 ( real ) 15.63/15.86 ( (fun real bool) ) 15.63/15.86 ( (fun real real) ) 15.63/15.86 ( rat ) 15.63/15.86 ( complex ) 15.63/15.86 ( (fun nat real) ) 15.63/15.86 ( (filter nat) ) 15.63/15.86 ( (product_prod int int) ) 15.63/15.86 ( quickcheck_code_int ) 15.63/15.86 ( code_code_numeral ) 15.63/15.86 ( (fun int (fun int (fun int bool))) ) 15.63/15.86 ( (product_prod real real) ) 15.63/15.86 ( (fun (product_prod int int) bool) ) 15.63/15.86 ( (fun nat rat) ) 15.63/15.86 ( (filter real) ) 15.63/15.86 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 15.63/15.86 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 15.63/15.86 ( (fun (product_prod int int) int) ) 15.63/15.86 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 15.63/15.86 ( (fun int real) ) 15.63/15.86 ) 15.63/15.86 (instantiation (forall ((X_1 $$unsorted) (A_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP real int (archimedean_ceiling real) X_1)) A_1))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) X_1) (hAPP int real (real_1 int) A_1)))) ) 15.63/15.86 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero int) ) 15.63/15.86 ) 15.63/15.86 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_123756 $$unsorted) (BOUND_VARIABLE_123757 $$unsorted) (BOUND_VARIABLE_123758 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_123757))) (or (not (preorder X_a)) (not (hBOOL (hAPP X_a bool _let_1 BOUND_VARIABLE_123758))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_123758) BOUND_VARIABLE_123756))) (hBOOL (hAPP X_a bool _let_1 BOUND_VARIABLE_123756))))) ) 15.63/15.86 ( int, (one_one int), min_1, pls ) 15.63/15.86 ( int, pls, min_1, min_1 ) 15.63/15.86 ( int, min_1, pls, min_1 ) 15.63/15.86 ( int, s, pls, pls ) 15.63/15.86 ( int, t, pls, (one_one int) ) 15.63/15.86 ( real, pi, pi, (zero_zero real) ) 15.63/15.86 ( real, pi, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.86 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.86 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.63/15.86 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 15.63/15.86 ) 15.63/15.86 (instantiation (forall ((R_4 $$unsorted) (S_3 $$unsorted)) (let ((_let_0 (fun real real))) (= (hAPP real real (hAPP real _let_0 (minus_minus real) R_4) S_3) (hAPP real real (hAPP real _let_0 (plus_plus real) R_4) (hAPP real real (uminus_uminus real) S_3)))) ) 15.63/15.86 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 15.63/15.86 ) 15.63/15.86 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_123829 $$unsorted) (BOUND_VARIABLE_123830 $$unsorted) (BOUND_VARIABLE_123831 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (times_times X_a))) (let ((_let_2 (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_123829))) (or (not (comm_semiring_1 X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_123830)) BOUND_VARIABLE_123831) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_123831)) BOUND_VARIABLE_123830)))))) ) 15.63/15.86 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), ii, (hAPP real complex (of_real complex) pi) ) 15.63/15.86 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi), ii ) 15.63/15.86 ) 15.63/15.86 (instantiation (forall ((Z_1 $$unsorted)) (let ((_let_0 (zero_zero int))) (or (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) _let_0) Z_1)) (= _let_0 (hAPP nat int (semiring_1_of_nat int) (hAPP int nat nat_1 Z_1))))) ) 15.63/15.86 ( (one_one int) ) 15.63/15.86 ( (zero_zero int) ) 15.63/15.86 ( min_1 ) 15.63/15.86 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.86 ( s ) 15.63/15.86 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.63/15.86 ( (hAPP int int (number_number_of int) pls) ) 15.63/15.86 ( skv_4 ) 15.63/15.86 ( skv_10 ) 15.63/15.86 ) 15.63/15.86 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_123886 $$unsorted)) (let ((_let_0 (of_real X_a))) (or (not (real_normed_vector X_a)) (not (real_algebra_1 X_a)) (= (hAPP real X_a _let_0 (hAPP real real (uminus_uminus real) BOUND_VARIABLE_123886)) (hAPP X_a X_a (uminus_uminus X_a) (hAPP real X_a _let_0 BOUND_VARIABLE_123886))))) ) 15.63/15.86 ( complex, (one_one real) ) 15.63/15.86 ) 15.63/15.86 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_123939 $$unsorted)) (let ((_let_0 (archimedean_ceiling X_a))) (or (not (archim1727834104eiling X_a)) (= (hAPP X_a int _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) BOUND_VARIABLE_123939) (one_one X_a))) (hAPP int int (hAPP int (fun int int) (minus_minus int) (hAPP X_a int _let_0 BOUND_VARIABLE_123939)) (one_one int))))) ) 15.63/15.86 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.86 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))) ) 15.63/15.86 ( code_code_numeral, (zero_zero code_code_numeral) ) 15.63/15.86 ) 15.63/15.86 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (zero_zero real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP real real (uminus_uminus real) pi)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) _let_2))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real sin X_1)) _let_2)))))) ) 15.63/15.86 ( (zero_zero real) ) 15.63/15.86 ( pi ) 15.63/15.86 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.86 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.63/15.86 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.63/15.86 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.63/15.86 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.63/15.86 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.63/15.86 ) 15.63/15.86 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_123963 $$unsorted) (BOUND_VARIABLE_123964 $$unsorted) (BOUND_VARIABLE_123965 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (fun X_a X_a))) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_123965))) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_2 (times_times X_a) BOUND_VARIABLE_123963) BOUND_VARIABLE_123965)) BOUND_VARIABLE_123964)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_123963) (hAPP X_a X_a (hAPP X_a _let_2 (inverse_divide X_a) BOUND_VARIABLE_123964) BOUND_VARIABLE_123965)))))))) ) 15.63/15.86 ( real, (zero_zero real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.86 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.63/15.86 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.63/15.86 ) 15.63/15.86 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_124026 $$unsorted) (BOUND_VARIABLE_124027 $$unsorted) (BOUND_VARIABLE_124028 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (zero_zero X_a))) (let ((_let_2 (ti X_a BOUND_VARIABLE_124026))) (let ((_let_3 (= _let_1 (ti X_a BOUND_VARIABLE_124028)))) (or (not (field_inverse_zero X_a)) (= (= _let_2 (hAPP X_a X_a (hAPP X_a _let_0 (inverse_divide X_a) BOUND_VARIABLE_124027) BOUND_VARIABLE_124028)) (and (or _let_3 (= (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_124026) BOUND_VARIABLE_124028) (ti X_a BOUND_VARIABLE_124027))) (or (not _let_3) (= _let_1 _let_2))))))))) ) 15.63/15.86 ( real, pi, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.86 ) 15.63/15.86 (instantiation (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (let ((_let_0 (fun X_a X_b))) (let ((_let_1 (fun X_a X_c))) (= (hAPP X_a X_c (hAPP _let_0 _let_1 (hAPP (fun X_b X_c) (fun _let_0 _let_1) (combb X_b X_c X_a) P) Q) R) (hAPP X_b X_c P (hAPP X_a X_b Q R))))) ) 15.63/15.86 ( bool, bool, (fun nat bool), (hAPP (fun nat int) (fun (fun nat bool) bool) (nat_tr1645093318rphism nat int) (semiring_1_of_nat int)), (combk bool nat), fTrue ) 15.63/15.86 ( nat, bool, nat, (even_odd_even nat), fact, (zero_zero nat) ) 15.63/15.86 ( nat, bool, nat, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), suc, (hAPP nat nat suc (zero_zero nat)) ) 15.63/15.86 ( nat, bool, nat, prime, suc, (hAPP nat nat suc (zero_zero nat)) ) 15.63/15.86 ( nat, bool, nat, prime, fact, (zero_zero nat) ) 15.63/15.86 ( nat, bool, int, (hAPP int (fun int bool) (ord_less int) pls), (semiring_1_of_nat int), (zero_zero nat) ) 15.63/15.86 ( nat, bool, int, nat_neg, (semiring_1_of_nat int), (zero_zero nat) ) 15.63/15.86 ( nat, bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (semiring_1_of_nat int), (zero_zero nat) ) 15.63/15.86 ( nat, bool, int, (even_odd_even int), (semiring_1_of_nat int), (zero_zero nat) ) 15.63/15.86 ( nat, bool, int, nat_is_nat, (semiring_1_of_nat int), (zero_zero nat) ) 15.63/15.86 ( nat, bool, int, (hAPP int (fun int bool) (ord_less int) min_1), (semiring_1_of_nat int), (zero_zero nat) ) 15.63/15.86 ( nat, bool, int, (hAPP int (fun int bool) (ord_less_eq int) min_1), (semiring_1_of_nat int), (zero_zero nat) ) 15.63/15.86 ( nat, nat, nat, suc, suc, (hAPP nat nat suc (zero_zero nat)) ) 15.63/15.86 ( nat, nat, nat, suc, fact, (zero_zero nat) ) 15.63/15.86 ( nat, nat, nat, (fact_fact nat), fact, (zero_zero nat) ) 15.63/15.86 ( nat, nat, nat, (hAPP nat (fun nat nat) (plus_plus nat) (one_one nat)), fact, (zero_zero nat) ) 15.63/15.86 ( nat, nat, int, (number_number_of nat), (semiring_1_of_nat int), (zero_zero nat) ) 15.63/15.86 ( nat, nat, int, nat_1, (semiring_1_of_nat int), (zero_zero nat) ) 15.63/15.86 ( nat, int, nat, (semiring_1_of_nat int), suc, (hAPP nat nat suc (zero_zero nat)) ) 15.63/15.86 ( nat, int, nat, (semiring_1_of_nat int), fact, (zero_zero nat) ) 15.63/15.86 ( nat, int, nat, (hAPP int (fun nat int) (power_power int) s), suc, (hAPP nat nat suc (zero_zero nat)) ) 15.63/15.86 ( nat, int, nat, (hAPP int (fun nat int) (power_power int) s1), suc, (hAPP nat nat suc (zero_zero nat)) ) 15.63/15.86 ( nat, int, nat, (hAPP int (fun nat int) (power_power int) skv_14), suc, (hAPP nat nat suc (zero_zero nat)) ) 15.63/15.86 ( nat, int, int, bit0, (semiring_1_of_nat int), (zero_zero nat) ) 15.63/15.86 ( nat, int, int, bit1, (semiring_1_of_nat int), (zero_zero nat) ) 15.63/15.86 ( nat, int, int, (number_number_of int), (semiring_1_of_nat int), (zero_zero nat) ) 15.63/15.86 ( nat, int, int, (fact_fact int), (semiring_1_of_nat int), (zero_zero nat) ) 15.63/15.86 ( nat, int, int, (uminus_uminus int), (semiring_1_of_nat int), (zero_zero nat) ) 15.63/15.86 ( nat, int, int, pred, (semiring_1_of_nat int), (zero_zero nat) ) 15.63/15.86 ( nat, int, int, succ, (semiring_1_of_nat int), (zero_zero nat) ) 15.63/15.86 ( nat, (fun int bool), int, (ord_less_eq int), (semiring_1_of_nat int), (zero_zero nat) ) 15.63/15.86 ( nat, (fun int bool), int, (ord_less int), (semiring_1_of_nat int), (zero_zero nat) ) 15.63/15.86 ( nat, (fun int bool), int, (let ((_let_0 (fun int (fun int bool)))) (hAPP _let_0 _let_0 (combc int int bool) (fequal int))), (semiring_1_of_nat int), (zero_zero nat) ) 15.63/15.86 ( nat, (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int (fun nat int) (power_power int) s1), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.86 ( nat, (fun int (fun int bool)), int, zcong, (hAPP int (fun nat int) (power_power int) s), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.86 ( nat, (fun int (fun int bool)), int, zcong, (hAPP int (fun nat int) (power_power int) s1), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.86 ( nat, (fun int (fun int bool)), int, zcong, (hAPP int (fun nat int) (power_power int) skv_14), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.86 ( nat, (fun int int), nat, (hAPP (fun int (fun nat int)) (fun nat (fun int int)) (combc int nat int) (power_power int)), suc, (hAPP nat nat suc (zero_zero nat)) ) 15.63/15.86 ( nat, (fun int int), int, (minus_minus int), (hAPP int (fun nat int) (power_power int) s), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.86 ( nat, (fun int int), int, (plus_plus int), (hAPP int (fun nat int) (power_power int) s), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.86 ( nat, (fun nat bool), (fun nat bool), (let ((_let_0 (fun nat bool))) (hAPP (fun bool bool) (fun _let_0 _let_0) (combb bool bool nat) fNot)), (let ((_let_0 (fun nat (fun nat bool)))) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat))), (zero_zero nat) ) 15.63/15.86 ( nat, (fun nat nat), nat, (plus_plus nat), fact, (zero_zero nat) ) 15.63/15.86 ( nat, (fun nat nat), nat, (let ((_let_0 (fun nat (fun nat nat)))) (hAPP _let_0 _let_0 (combc nat nat nat) (times_times nat))), suc, (hAPP nat nat suc (zero_zero nat)) ) 15.63/15.86 ( nat, (fun nat nat), nat, (let ((_let_0 (fun nat (fun nat nat)))) (let ((_let_1 (combc nat nat nat))) (hAPP _let_0 _let_0 _let_1 (hAPP (fun nat nat) _let_0 (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_0 _let_0 _let_1 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))), fact, (zero_zero nat) ) 15.63/15.86 ( nat, real, nat, (real_1 nat), fact, (zero_zero nat) ) 15.63/15.86 ( nat, real, int, (real_1 int), (semiring_1_of_nat int), (zero_zero nat) ) 15.63/15.86 ( nat, (fun real real), nat, root, suc, (hAPP nat nat suc (zero_zero nat)) ) 15.63/15.86 ( nat, (fun int rat), int, fract, (semiring_1_of_nat int), (zero_zero nat) ) 15.63/15.86 ( nat, complex, nat, (hAPP complex (fun nat complex) (power_power complex) ii), suc, (hAPP nat nat suc (zero_zero nat)) ) 15.63/15.86 ( nat, (fun nat real), (fun nat nat), (let ((_let_0 (fun nat real))) (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat real nat) (real_1 nat))), (let ((_let_0 (fun nat (fun nat nat)))) (let ((_let_1 (combc nat nat nat))) (hAPP _let_0 _let_0 _let_1 (hAPP (fun nat nat) _let_0 (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_0 _let_0 _let_1 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))), (one_one nat) ) 15.63/15.86 ( nat, (fun int (fun int int)), (fun int int), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)))), (hAPP (fun int (fun nat int)) (fun nat (fun int int)) (combc int nat int) (power_power int)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.86 ( nat, (fun int (fun int int)), (fun int int), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun _let_0 _let_1))) (let ((_let_3 (fun _let_0 _let_0))) (let ((_let_4 (fun int _let_3))) (hAPP _let_4 _let_2 (combc int _let_0 _let_0) (hAPP _let_1 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_1 _let_4) (combb _let_0 _let_3 int) (combb int int int)) (hAPP _let_0 _let_1 (hAPP _let_1 _let_2 (combb int _let_0 int) (plus_plus int)) (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))))))), (hAPP (fun int (fun nat int)) (fun nat (fun int int)) (combc int nat int) (power_power int)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.86 ( nat, (fun int (product_prod int int)), int, (product_Pair int int), (semiring_1_of_nat int), (zero_zero nat) ) 15.63/15.86 ( nat, quickcheck_code_int, int, quickcheck_of_int, (semiring_1_of_nat int), (zero_zero nat) ) 15.63/15.86 ( nat, (fun nat (fun nat nat)), (fun nat nat), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat _let_0))) (hAPP _let_1 (fun _let_0 _let_1) (combb nat _let_0 nat) (plus_plus nat)))), (let ((_let_0 (fun nat (fun nat nat)))) (hAPP _let_0 _let_0 (combc nat nat nat) (times_times nat))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.86 ( nat, code_code_numeral, int, (number_number_of code_code_numeral), (semiring_1_of_nat int), (zero_zero nat) ) 15.63/15.86 ( nat, (fun (product_prod int int) bool), int, (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 _let_0))) (let ((_let_3 (fun _let_1 int))) (hAPP _let_2 (fun int (fun _let_1 bool)) (combc _let_1 int bool) (hAPP _let_3 _let_2 (hAPP (fun int _let_0) (fun _let_3 _let_2) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))))))), (semiring_1_of_nat int), (zero_zero nat) ) 15.63/15.86 ( int, bool, int, (hAPP int (fun int bool) (ord_less int) pls), bit1, min_1 ) 15.63/15.86 ( int, bool, int, (hAPP int (fun int bool) (ord_less_eq int) pls), bit1, min_1 ) 15.63/15.86 ( int, bool, int, nat_neg, (number_number_of int), min_1 ) 15.63/15.86 ( int, bool, int, nat_neg, (fact_fact int), (one_one int) ) 15.63/15.86 ( int, bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (number_number_of int), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.63/15.86 ( int, bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (number_number_of int), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.63/15.86 ( int, bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (fact_fact int), (one_one int) ) 15.63/15.86 ( int, bool, int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (fact_fact int), (one_one int) ) 15.63/15.86 ( int, bool, int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (let ((_let_0 (fun int int))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m))), (one_one int) ) 15.63/15.86 ( int, bool, int, zprime, (number_number_of int), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.63/15.86 ( int, bool, int, zprime, (let ((_let_0 (fun int int))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m))), (one_one int) ) 15.63/15.86 ( int, bool, int, (hAPP int (fun int bool) (ord_less int) s), (let ((_let_0 (fun int int))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m))), (one_one int) ) 15.63/15.86 ( int, bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) s)), (let ((_let_0 (fun int int))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m))), (one_one int) ) 15.63/15.86 ( int, bool, int, (let ((_let_0 (fun int int))) (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))))), t ) 15.63/15.86 ( int, bool, int, (even_odd_even int), (fact_fact int), (one_one int) ) 15.63/15.86 ( int, bool, int, twoSqu1091635170sum2sq, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))))), t ) 15.63/15.86 ( int, bool, int, nat_is_nat, (number_number_of int), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.63/15.86 ( int, bool, int, nat_is_nat, (number_number_of int), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.63/15.86 ( int, bool, int, nat_is_nat, (fact_fact int), (one_one int) ) 15.63/15.86 ( int, bool, int, (hAPP int (fun int bool) (ord_less int) min_1), bit1, min_1 ) 15.63/15.86 ( int, bool, int, (hAPP int (fun int bool) (ord_less_eq int) min_1), bit1, min_1 ) 15.63/15.86 ( int, bool, int, (let ((_let_0 (fun int int))) (hAPP int (fun int bool) quadRes (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (number_number_of int), min_1 ) 15.63/15.86 ( int, bool, int, (let ((_let_0 (fun int bool))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (let ((_let_3 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int _let_1 _let_2 s) _let_3)) (hAPP nat int (hAPP int _let_1 _let_2 s1) _let_3)))))), (let ((_let_0 (fun int int))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m))), (one_one int) ) 15.63/15.86 ( int, bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m))), (one_one int) ) 15.63/15.86 ( int, bool, int, (hAPP int (fun int bool) (ord_less int) t), (let ((_let_0 (fun int int))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m))), (one_one int) ) 15.63/15.86 ( int, bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m))), (one_one int) ) 15.63/15.86 ( int, bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_4)), (let ((_let_0 (fun int int))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m))), (one_one int) ) 15.63/15.86 ( int, bool, int, (hAPP int (fun int bool) (ord_less int) skv_4), (let ((_let_0 (fun int int))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m))), (one_one int) ) 15.63/15.86 ( int, bool, int, (hAPP int (fun int bool) (ord_less int) skv_10), (let ((_let_0 (fun int int))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m))), (one_one int) ) 15.63/15.86 ( int, bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_10)), (let ((_let_0 (fun int int))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m))), (one_one int) ) 15.63/15.86 ( int, bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m))), (one_one int) ) 15.63/15.86 ( int, bool, (fun int bool), (hAPP (fun int nat) (fun (fun int bool) bool) (nat_tr1645093318rphism int nat) nat_1), (ord_less_eq int), (zero_zero int) ) 15.63/15.86 ( int, bool, real, (hAPP real (fun real bool) (ord_less real) pi), (number_number_of real), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.86 ( int, bool, real, (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.63/15.86 ( int, bool, real, (hAPP real (fun real bool) (ord_less real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.63/15.86 ( int, bool, real, (hAPP real (fun real bool) (ord_less_eq real) skv_5), (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.63/15.86 ( int, nat, int, (number_number_of nat), bit0, (hAPP int int bit1 pls) ) 15.63/15.86 ( int, nat, int, (number_number_of nat), bit1, pls ) 15.63/15.86 ( int, nat, int, (number_number_of nat), bit1, (hAPP int int bit1 pls) ) 15.63/15.86 ( int, nat, int, nat_1, (number_number_of int), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.63/15.86 ( int, nat, int, nat_1, (number_number_of int), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.63/15.86 ( int, nat, int, nat_1, (fact_fact int), (one_one int) ) 15.63/15.86 ( int, int, nat, (semiring_1_of_nat int), (number_number_of nat), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.63/15.86 ( int, int, int, bit0, bit0, (hAPP int int bit1 pls) ) 15.63/15.86 ( int, int, int, bit0, bit1, pls ) 15.63/15.86 ( int, int, int, bit0, bit1, (hAPP int int bit1 pls) ) 15.63/15.86 ( int, int, int, bit0, bit1, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.63/15.87 ( int, int, int, bit0, bit1, min_1 ) 15.63/15.87 ( int, int, int, bit1, bit0, (hAPP int int bit1 pls) ) 15.63/15.87 ( int, int, int, bit1, bit0, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.63/15.87 ( int, int, int, bit1, bit1, pls ) 15.63/15.87 ( int, int, int, bit1, bit1, (hAPP int int bit1 pls) ) 15.63/15.87 ( int, int, int, bit1, bit1, min_1 ) 15.63/15.87 ( int, int, int, bit1, bit1, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.63/15.87 ( int, int, int, bit1, bit1, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.63/15.87 ( int, int, int, bit1, bit1, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 15.63/15.87 ( int, int, int, (number_number_of int), bit0, (hAPP int int bit1 pls) ) 15.63/15.87 ( int, int, int, (number_number_of int), bit0, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.63/15.87 ( int, int, int, (number_number_of int), bit1, pls ) 15.63/15.87 ( int, int, int, (number_number_of int), bit1, (hAPP int int bit1 pls) ) 15.63/15.87 ( int, int, int, (number_number_of int), bit1, min_1 ) 15.63/15.87 ( int, int, int, (fact_fact int), (fact_fact int), (one_one int) ) 15.63/15.87 ( int, int, int, (uminus_uminus int), bit1, min_1 ) 15.63/15.87 ( int, int, int, (uminus_uminus int), (fact_fact int), (one_one int) ) 15.63/15.87 ( int, int, int, pred, bit1, min_1 ) 15.63/15.87 ( int, int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m))), (fact_fact int), (one_one int) ) 15.63/15.87 ( int, int, int, (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (fact_fact int), (one_one int) ) 15.63/15.87 ( int, int, int, succ, bit1, min_1 ) 15.63/15.87 ( int, int, int, (hAPP int (fun int int) legendre (hAPP int int (number_number_of int) min_1)), (let ((_let_0 (fun int int))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m))), (one_one int) ) 15.63/15.87 ( int, int, int, (hAPP int (fun int int) (minus_minus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (number_number_of int), min_1 ) 15.63/15.87 ( int, int, (product_prod int int), twoSqu1094008024sum2sq, (hAPP int (fun int (product_prod int int)) (product_Pair int int) s), (one_one int) ) 15.63/15.87 ( int, int, quickcheck_code_int, quickcheck_int_of, quickcheck_of_int, (zero_zero int) ) 15.63/15.87 ( int, (fun int bool), int, (ord_less_eq int), bit1, min_1 ) 15.63/15.87 ( int, (fun int bool), int, (ord_less_eq int), (fact_fact int), (one_one int) ) 15.63/15.87 ( int, (fun int bool), int, (ord_less int), bit1, min_1 ) 15.63/15.87 ( int, (fun int bool), int, (ord_less int), (fact_fact int), (one_one int) ) 15.63/15.87 ( int, (fun int bool), int, (dvd_dvd int), (let ((_let_0 (fun int int))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m))), (one_one int) ) 15.63/15.87 ( int, (fun int bool), int, quadRes, (let ((_let_0 (fun int int))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m))), (one_one int) ) 15.63/15.87 ( int, (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (number_number_of int), min_1 ) 15.63/15.87 ( int, (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (number_number_of int), min_1 ) 15.63/15.87 ( int, (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (number_number_of int), min_1 ) 15.63/15.87 ( int, (fun int bool), (fun int bool), (let ((_let_0 (fun int bool))) (hAPP (fun bool bool) (fun _let_0 _let_0) (combb bool bool int) fNot)), (let ((_let_0 (fun int (fun int bool)))) (hAPP _let_0 _let_0 (combc int int bool) (fequal int))), (zero_zero int) ) 15.63/15.87 ( int, (fun int (fun int bool)), int, (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int _let_1))) (let ((_let_5 (fun _let_2 _let_1))) (hAPP _let_4 _let_4 (combc int int _let_0) (hAPP _let_4 _let_4 (hAPP (fun _let_1 _let_1) (fun _let_4 _let_4) (combb _let_1 _let_1 int) (combc int int bool)) (hAPP _let_3 _let_4 (hAPP _let_5 (fun _let_3 _let_4) (combb _let_2 _let_1 int) (hAPP _let_1 _let_5 (combb int _let_0 int) (fequal int))) int_gcd))))))))), (fact_fact int), (one_one int) ) 15.63/15.87 ( int, (fun int (fun int bool)), (fun int (fun int bool)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun _let_0 _let_0))) (hAPP _let_4 (fun _let_1 _let_1) (combb _let_0 _let_0 int) (hAPP _let_3 _let_4 (combs int bool bool) (hAPP _let_0 _let_3 (hAPP (fun bool _let_2) (fun _let_0 _let_3) (combb bool _let_2 int) fconj) (hAPP int _let_0 (ord_less int) (zero_zero int)))))))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int _let_1))) (let ((_let_5 (fun _let_2 _let_1))) (hAPP _let_4 _let_4 (combc int int _let_0) (hAPP _let_4 _let_4 (hAPP (fun _let_1 _let_1) (fun _let_4 _let_4) (combb _let_1 _let_1 int) (combc int int bool)) (hAPP _let_3 _let_4 (hAPP _let_5 (fun _let_3 _let_4) (combb _let_2 _let_1 int) (hAPP _let_1 _let_5 (combb int _let_0 int) (fequal int))) int_gcd))))))))), (one_one int) ) 15.63/15.87 ( int, (fun int (fun int bool)), (fun int int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun (fun int int) _let_0))) (let ((_let_3 (fun int _let_2))) (hAPP _let_3 (fun (fun int int) _let_1) (combc int (fun int int) _let_0) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 int) (combb int bool int)) (fequal int))))))), (times_times int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.87 ( int, (fun int (fun int bool)), (fun int int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun (fun int int) _let_0))) (let ((_let_3 (fun int _let_2))) (hAPP _let_3 (fun (fun int int) _let_1) (combc int (fun int int) _let_0) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 int) (combb int bool int)) (fequal int))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (hAPP _let_1 _let_1 (combc int int int) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)) (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))))), (one_one int) ) 15.63/15.87 ( int, (fun int int), int, (times_times int), (number_number_of int), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.63/15.87 ( int, (fun int int), int, (times_times int), (number_number_of int), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.87 ( int, (fun int int), int, (times_times int), (let ((_let_0 (fun int int))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m))), (one_one int) ) 15.63/15.87 ( int, (fun int int), int, (plus_plus int), (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))), m ) 15.63/15.87 ( int, (fun int int), int, legendre, (number_number_of int), min_1 ) 15.63/15.87 ( int, (fun int int), int, (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (hAPP _let_1 _let_1 (combc int int int) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)) (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))))), (fact_fact int), (one_one int) ) 15.63/15.87 ( int, real, int, (real_1 int), (fact_fact int), (one_one int) ) 15.63/15.87 ( int, real, int, (number_number_of real), bit0, (hAPP int int bit1 pls) ) 15.63/15.87 ( int, real, int, (number_number_of real), bit0, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.63/15.87 ( int, real, int, (number_number_of real), bit0, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.63/15.87 ( int, real, int, (number_number_of real), bit1, (hAPP int int bit1 pls) ) 15.63/15.87 ( int, real, int, (number_number_of real), bit1, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.63/15.87 ( int, real, int, (number_number_of real), bit1, min_1 ) 15.63/15.87 ( int, real, int, (number_number_of real), bit1, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 15.63/15.87 ( int, real, real, cos, (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.63/15.87 ( int, real, real, sqrt, (number_number_of real), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.63/15.87 ( int, real, real, sqrt, (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.63/15.87 ( int, real, real, (hAPP real (fun real real) (inverse_divide real) pi), (number_number_of real), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.63/15.87 ( int, real, real, (hAPP real (fun real real) (inverse_divide real) pi), (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.63/15.87 ( int, real, real, (hAPP real (fun real real) (inverse_divide real) pi), (number_number_of real), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.87 ( int, real, real, (hAPP real (fun real real) (inverse_divide real) pi), (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.63/15.87 ( int, real, real, (hAPP real (fun real real) (inverse_divide real) (one_one real)), (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.63/15.87 ( int, real, real, (hAPP real (fun real real) (inverse_divide real) (one_one real)), (number_number_of real), (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.87 ( int, real, real, (hAPP real (fun real real) (inverse_divide real) (one_one real)), (number_number_of real), (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 15.63/15.87 ( int, real, real, (hAPP real (fun real real) (inverse_divide real) (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))))), (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.63/15.87 ( int, real, real, (hAPP real (fun real real) (inverse_divide real) (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.63/15.87 ( int, real, real, (hAPP real (fun real real) (inverse_divide real) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.63/15.87 ( int, real, rat, ratreal, (hAPP int (fun int rat) fract (zero_zero int)), (one_one int) ) 15.63/15.87 ( int, real, rat, ratreal, (hAPP int (fun int rat) fract (one_one int)), (one_one int) ) 15.63/15.87 ( int, (fun real bool), real, (ord_less_eq real), (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.63/15.87 ( int, (fun real bool), real, (let ((_let_0 (fun real (fun real bool)))) (hAPP _let_0 _let_0 (combc real real bool) (ord_less_eq real))), (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.63/15.87 ( int, (fun real real), real, (inverse_divide real), (number_number_of real), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.63/15.87 ( int, (fun real real), real, (times_times real), (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.63/15.87 ( int, (fun real real), real, (times_times real), (number_number_of real), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.87 ( int, rat, int, (hAPP int (fun int rat) fract (zero_zero int)), (fact_fact int), (one_one int) ) 15.63/15.87 ( int, rat, int, (hAPP int (fun int rat) fract (one_one int)), (fact_fact int), (one_one int) ) 15.63/15.87 ( int, rat, rat, (sgn_sgn rat), (hAPP int (fun int rat) fract (zero_zero int)), (one_one int) ) 15.63/15.87 ( int, rat, (product_prod int int), frct, (hAPP int (fun int (product_prod int int)) (product_Pair int int) (one_one int)), (one_one int) ) 15.63/15.87 ( int, (fun int rat), int, fract, (fact_fact int), (one_one int) ) 15.63/15.87 ( int, complex, int, (number_number_of complex), bit0, (hAPP int int bit1 pls) ) 15.63/15.87 ( int, complex, int, (number_number_of complex), bit1, min_1 ) 15.63/15.87 ( int, complex, real, (of_real complex), (number_number_of real), min_1 ) 15.63/15.87 ( int, (fun nat real), real, (power_power real), (number_number_of real), min_1 ) 15.63/15.87 ( int, (fun int (fun int int)), (fun int int), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)))), (times_times int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.87 ( int, (fun complex complex), complex, (times_times complex), (number_number_of complex), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.63/15.87 ( int, (product_prod int int), int, (hAPP int (fun int (product_prod int int)) (product_Pair int int) (zero_zero int)), (fact_fact int), (one_one int) ) 15.63/15.87 ( int, (product_prod int int), int, (hAPP int (fun int (product_prod int int)) (product_Pair int int) s), (fact_fact int), (one_one int) ) 15.63/15.87 ( int, (product_prod int int), int, (hAPP int (fun int (product_prod int int)) (product_Pair int int) (one_one int)), (fact_fact int), (one_one int) ) 15.63/15.87 ( int, (product_prod int int), rat, quotient_of, (hAPP int (fun int rat) fract (zero_zero int)), (one_one int) ) 15.63/15.87 ( int, (product_prod int int), rat, quotient_of, (hAPP int (fun int rat) fract (one_one int)), (one_one int) ) 15.63/15.87 ( int, (fun int (product_prod int int)), int, (product_Pair int int), (fact_fact int), (one_one int) ) 15.63/15.87 ( int, (fun (fun int bool) bool), int, (member int), (fact_fact int), (one_one int) ) 15.63/15.87 ( int, quickcheck_code_int, int, (number_number_of quickcheck_code_int), bit1, pls ) 15.63/15.87 ( int, quickcheck_code_int, int, quickcheck_of_int, (fact_fact int), (one_one int) ) 15.63/15.87 ( int, code_code_numeral, int, (number_number_of code_code_numeral), bit1, pls ) 15.63/15.87 ( int, code_code_numeral, code_code_numeral, (hAPP code_code_numeral (fun code_code_numeral code_code_numeral) (minus_minus code_code_numeral) (zero_zero code_code_numeral)), (number_number_of code_code_numeral), (hAPP int int bit1 pls) ) 15.63/15.87 ( int, (fun (product_prod int int) bool), (fun (product_prod int int) bool), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 bool))) (hAPP (fun bool bool) (fun _let_1 _let_1) (combb bool bool _let_0) fNot))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 _let_0))) (let ((_let_3 (fun _let_1 int))) (hAPP _let_2 (fun int (fun _let_1 bool)) (combc _let_1 int bool) (hAPP _let_3 _let_2 (hAPP (fun int _let_0) (fun _let_3 _let_2) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))))))), (zero_zero int) ) 15.63/15.87 ( int, (fun int (fun bool bool)), (fun int bool), (let ((_let_0 (fun bool bool))) (hAPP (fun bool _let_0) (fun (fun int bool) (fun int _let_0)) (combb bool _let_0 int) fconj)), (ord_less int), pls ) 15.63/15.87 ( (fun int bool), bool, (fun int bool), (hAPP int (fun (fun int bool) bool) (member int) (one_one int)), (collect int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun _let_2 _let_0))) (let ((_let_4 (fun int _let_3))) (hAPP _let_1 _let_0 (hAPP (fun _let_0 bool) (fun _let_1 _let_0) (combb _let_0 bool int) (fEx int)) (hAPP _let_2 _let_1 (hAPP _let_4 (fun _let_2 _let_1) (combc int _let_2 _let_0) (hAPP _let_1 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_1 _let_4) (combb _let_0 _let_3 int) (combb int bool int)) (fequal int))) (hAPP int _let_2 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))))))))) ) 15.63/15.87 ( (fun int bool), (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), (fun int (fun bool bool)), (combs int bool bool), (let ((_let_0 (fun bool bool))) (hAPP (fun bool _let_0) (fun (fun int bool) (fun int _let_0)) (combb bool _let_0 int) fconj)), (hAPP int (fun int bool) (ord_less int) (zero_zero int)) ) 15.63/15.87 ( (fun int bool), (fun real (fun int bool)), (fun real (fun int (fun int bool))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun _let_1 _let_0))) (hAPP _let_2 (fun (fun real _let_1) (fun real _let_0)) (combb _let_1 _let_0 real) (hAPP (fun _let_0 bool) _let_2 (combb _let_0 bool int) (fEx int)))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun int _let_3))) (let ((_let_6 (fun (fun int bool) (fun int bool)))) (let ((_let_7 (fun (fun int bool) _let_5))) (let ((_let_8 (fun int real))) (let ((_let_9 (fun int _let_6))) (let ((_let_10 (fun (fun int bool) (fun int (fun int bool))))) (let ((_let_11 (fun int _let_5))) (let ((_let_12 (fun _let_11 _let_9))) (let ((_let_13 (fun (fun int (fun int bool)) _let_11))) (let ((_let_14 (fun real (fun int (fun int bool))))) (let ((_let_15 (fun real _let_10))) (let ((_let_16 (fun real _let_9))) (let ((_let_17 (fun real _let_11))) (let ((_let_18 (fun int _let_8))) (let ((_let_19 (fun _let_18 (fun int (fun int bool))))) (let ((_let_20 (fun real _let_19))) (let ((_let_21 (fun _let_8 (fun int bool)))) (let ((_let_22 (fun real _let_21))) (let ((_let_23 (fun _let_8 _let_8))) (let ((_let_24 (fun int _let_23))) (let ((_let_25 (fun int _let_1))) (hAPP _let_15 (fun (fun int bool) _let_14) (combc real (fun int bool) (fun int (fun int bool))) (hAPP _let_16 _let_15 (hAPP (fun _let_9 _let_10) (fun _let_16 _let_15) (combb _let_9 _let_10 real) (combc int (fun int bool) (fun int bool))) (hAPP _let_17 _let_16 (hAPP _let_12 (fun _let_17 _let_16) (combb _let_11 _let_9 real) (hAPP (fun _let_5 _let_6) _let_12 (combb _let_5 _let_6 int) (combs int bool bool))) (hAPP _let_14 _let_17 (hAPP _let_13 (fun _let_14 _let_17) (combb (fun int (fun int bool)) _let_11 real) (hAPP _let_7 _let_13 (combb (fun int bool) _let_5 int) (hAPP (fun bool _let_3) _let_7 (combb bool _let_3 int) fconj))) (hAPP _let_18 _let_14 (hAPP _let_20 (fun _let_18 _let_14) (combc real _let_18 (fun int (fun int bool))) (hAPP _let_22 _let_20 (hAPP (fun _let_21 _let_19) (fun _let_22 _let_20) (combb _let_21 _let_19 real) (combb _let_8 (fun int bool) int)) (hAPP _let_4 _let_22 (hAPP (fun _let_0 _let_21) (fun _let_4 _let_22) (combb _let_0 _let_21 real) (combb real bool int)) (fequal real)))) (hAPP _let_8 _let_18 (hAPP _let_24 (fun _let_8 _let_18) (combc int _let_8 _let_8) (hAPP _let_25 _let_24 (hAPP (fun _let_1 _let_23) (fun _let_25 _let_24) (combb _let_1 _let_23 int) (combb real real int)) (hAPP _let_8 _let_25 (hAPP (fun real _let_1) (fun _let_8 _let_25) (combb real _let_1 int) (inverse_divide real)) _let_2))) _let_2)))))))))))))))))))))))))))))))), (let ((_let_0 (fun int (fun int bool)))) (hAPP (fun int bool) (fun int bool) (hAPP (fun bool bool) (fun (fun int bool) (fun int bool)) (combb bool bool int) fNot) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (fequal int)) (zero_zero int)))) ) 15.63/15.87 ( (fun int bool), (fun real (fun int (fun int bool))), (fun int bool), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun int _let_3))) (let ((_let_6 (fun (fun int bool) (fun int bool)))) (let ((_let_7 (fun (fun int bool) _let_5))) (let ((_let_8 (fun int real))) (let ((_let_9 (fun int _let_6))) (let ((_let_10 (fun (fun int bool) (fun int (fun int bool))))) (let ((_let_11 (fun int _let_5))) (let ((_let_12 (fun _let_11 _let_9))) (let ((_let_13 (fun (fun int (fun int bool)) _let_11))) (let ((_let_14 (fun real (fun int (fun int bool))))) (let ((_let_15 (fun real _let_10))) (let ((_let_16 (fun real _let_9))) (let ((_let_17 (fun real _let_11))) (let ((_let_18 (fun int _let_8))) (let ((_let_19 (fun _let_18 (fun int (fun int bool))))) (let ((_let_20 (fun real _let_19))) (let ((_let_21 (fun _let_8 (fun int bool)))) (let ((_let_22 (fun real _let_21))) (let ((_let_23 (fun _let_8 _let_8))) (let ((_let_24 (fun int _let_23))) (let ((_let_25 (fun int _let_1))) (hAPP _let_15 (fun (fun int bool) _let_14) (combc real (fun int bool) (fun int (fun int bool))) (hAPP _let_16 _let_15 (hAPP (fun _let_9 _let_10) (fun _let_16 _let_15) (combb _let_9 _let_10 real) (combc int (fun int bool) (fun int bool))) (hAPP _let_17 _let_16 (hAPP _let_12 (fun _let_17 _let_16) (combb _let_11 _let_9 real) (hAPP (fun _let_5 _let_6) _let_12 (combb _let_5 _let_6 int) (combs int bool bool))) (hAPP _let_14 _let_17 (hAPP _let_13 (fun _let_14 _let_17) (combb (fun int (fun int bool)) _let_11 real) (hAPP _let_7 _let_13 (combb (fun int bool) _let_5 int) (hAPP (fun bool _let_3) _let_7 (combb bool _let_3 int) fconj))) (hAPP _let_18 _let_14 (hAPP _let_20 (fun _let_18 _let_14) (combc real _let_18 (fun int (fun int bool))) (hAPP _let_22 _let_20 (hAPP (fun _let_21 _let_19) (fun _let_22 _let_20) (combb _let_21 _let_19 real) (combb _let_8 (fun int bool) int)) (hAPP _let_4 _let_22 (hAPP (fun _let_0 _let_21) (fun _let_4 _let_22) (combb _let_0 _let_21 real) (combb real bool int)) (fequal real)))) (hAPP _let_8 _let_18 (hAPP _let_24 (fun _let_8 _let_18) (combc int _let_8 _let_8) (hAPP _let_25 _let_24 (hAPP (fun _let_1 _let_23) (fun _let_25 _let_24) (combb _let_1 _let_23 int) (combb real real int)) (hAPP _let_8 _let_25 (hAPP (fun real _let_1) (fun _let_8 _let_25) (combb real _let_1 int) (inverse_divide real)) _let_2))) _let_2)))))))))))))))))))))))))))))))), (let ((_let_0 (fun int bool))) (hAPP (fun bool bool) (fun _let_0 _let_0) (combb bool bool int) fNot)), (let ((_let_0 (fun int (fun int bool)))) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (fequal int)) (zero_zero int))) ) 15.63/15.87 ( (fun int (fun int bool)), (fun int bool), (fun int bool), (collect int), (let ((_let_0 (fun int bool))) (hAPP (fun _let_0 bool) (fun (fun int _let_0) _let_0) (combb _let_0 bool int) (fEx int))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun _let_2 _let_0))) (let ((_let_4 (fun int _let_3))) (hAPP _let_2 _let_1 (hAPP _let_4 (fun _let_2 _let_1) (combc int _let_2 _let_0) (hAPP _let_1 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_1 _let_4) (combb _let_0 _let_3 int) (combb int bool int)) (fequal int))) (hAPP int _let_2 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))))))) ) 15.63/15.87 ( (fun int (fun int bool)), (fun int bool), (fun int bool), (collect int), (let ((_let_0 (fun int bool))) (hAPP (fun _let_0 bool) (fun (fun int _let_0) _let_0) (combb _let_0 bool int) (fEx int))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun _let_2 _let_0))) (let ((_let_5 (fun int _let_4))) (hAPP _let_2 _let_1 (hAPP _let_5 (fun _let_2 _let_1) (combc int _let_2 _let_0) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_1 _let_5) (combb _let_0 _let_4 int) (combb int bool int)) (fequal int))) (hAPP int _let_2 (hAPP _let_3 _let_3 (combc int int int) (hAPP _let_2 _let_3 (hAPP _let_3 (fun _let_2 _let_3) (combb int _let_2 int) (plus_plus int)) (hAPP int _let_2 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one int))))))))) ) 15.63/15.87 ( (fun int (fun int bool)), (fun (product_prod int int) bool), (fun int (fun int bool)), (product_prod_case int int bool), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun _let_0 _let_0))) (hAPP _let_4 (fun _let_1 _let_1) (combb _let_0 _let_0 int) (hAPP _let_3 _let_4 (combs int bool bool) (hAPP _let_0 _let_3 (hAPP (fun bool _let_2) (fun _let_0 _let_3) (combb bool _let_2 int) fconj) (hAPP int _let_0 (ord_less int) (zero_zero int)))))))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int _let_1))) (let ((_let_5 (fun _let_2 _let_1))) (hAPP int _let_1 (hAPP _let_4 _let_4 (combc int int _let_0) (hAPP _let_4 _let_4 (hAPP (fun _let_1 _let_1) (fun _let_4 _let_4) (combb _let_1 _let_1 int) (combc int int bool)) (hAPP _let_3 _let_4 (hAPP _let_5 (fun _let_3 _let_4) (combb _let_2 _let_1 int) (hAPP _let_1 _let_5 (combb int _let_0 int) (fequal int))) int_gcd))) (one_one int)))))))) ) 15.63/15.87 ( (fun int (fun int bool)), (fun (fun int int) (fun int (fun int bool))), (fun int (fun (fun int int) (fun int bool))), (combc int (fun int int) (fun int bool)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun (fun int int) _let_0))) (hAPP (fun _let_0 _let_1) (fun (fun int _let_0) (fun int _let_1)) (combb _let_0 _let_1 int) (combb int bool int)))), (fequal int) ) 15.63/15.87 ( (fun int (fun int bool)), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 (fun _let_0 int)) (fun _let_0 (fun _let_0 (fun int bool))))), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 (fun int bool)))), (let ((_let_0 (product_prod int int))) (combb (fun _let_0 int) (fun _let_0 (fun int bool)) _let_0)), (combb int (fun int bool) (product_prod int int)), (fequal int) ) 15.63/15.87 ( (fun int (fun int bool)), (fun (fun int (fun int int)) (fun int (fun int (fun int bool)))), (fun (fun int int) (fun int (fun int bool))), (combb (fun int int) (fun int (fun int bool)) int), (combb int (fun int bool) int), (fequal int) ) 15.63/15.87 ( (fun int int), (fun int bool), (fun int (fun int bool)), (let ((_let_0 (fun int bool))) (hAPP (fun _let_0 bool) (fun (fun int _let_0) _let_0) (combb _let_0 bool int) (fEx int))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun (fun int int) _let_0))) (let ((_let_3 (fun int _let_2))) (hAPP _let_3 (fun (fun int int) _let_1) (combc int (fun int int) _let_0) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 int) (combb int bool int)) (fequal int))))))), (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.87 ( (fun int int), (fun int bool), (fun int (fun int bool)), (let ((_let_0 (fun int bool))) (hAPP (fun _let_0 bool) (fun (fun int _let_0) _let_0) (combb _let_0 bool int) (fEx int))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun (fun int int) _let_0))) (let ((_let_3 (fun int _let_2))) (hAPP _let_3 (fun (fun int int) _let_1) (combc int (fun int int) _let_0) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 int) (combb int bool int)) (fequal int))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (hAPP int _let_0 (hAPP _let_1 _let_1 (combc int int int) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)) (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one int)))) ) 15.63/15.87 ( (fun int int), (fun int (fun int int)), (fun int (fun int int)), (combc int int int), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)))), (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.63/15.87 ( (fun int int), (fun (product_prod int int) int), (fun int (fun int int)), (product_prod_case int int int), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun _let_0 _let_1))) (let ((_let_3 (fun _let_0 _let_0))) (let ((_let_4 (fun int _let_3))) (hAPP _let_4 _let_2 (combc int _let_0 _let_0) (hAPP _let_1 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_1 _let_4) (combb _let_0 _let_3 int) (combb int int int)) (hAPP _let_0 _let_1 (hAPP _let_1 _let_2 (combb int _let_0 int) (plus_plus int)) (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))))))), (let ((_let_0 (fun int int))) (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.63/15.87 ( (fun int int), (let ((_let_0 (fun int int))) (fun int (fun _let_0 _let_0))), (fun int (fun int int)), (let ((_let_0 (fun (fun int int) (fun int int)))) (hAPP (fun (fun int int) _let_0) (fun (fun int (fun int int)) (fun int _let_0)) (combb (fun int int) _let_0 int) (combb int int int))), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)))), (let ((_let_0 (fun int int))) (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.63/15.87 ( (fun nat bool), bool, (fun nat bool), (finite_finite_1 nat), (collect nat), prime ) 15.63/15.87 ( (fun nat bool), (fun real (fun int bool)), (fun real (fun int (fun nat bool))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun nat bool))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (fun _let_2 _let_0))) (hAPP _let_3 (fun (fun real _let_2) (fun real _let_0)) (combb _let_2 _let_0 real) (hAPP (fun _let_1 bool) _let_3 (combb _let_1 bool int) (fEx nat))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun (fun nat real) (fun nat real)))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun (fun nat bool) (fun nat bool)))) (let ((_let_6 (fun int real))) (let ((_let_7 (fun nat _let_2))) (let ((_let_8 (fun (fun nat bool) _let_7))) (let ((_let_9 (fun int _let_1))) (let ((_let_10 (fun real (fun int (fun nat bool))))) (let ((_let_11 (fun (fun nat bool) (fun int (fun nat bool))))) (let ((_let_12 (fun real _let_11))) (let ((_let_13 (fun int _let_5))) (let ((_let_14 (fun real _let_13))) (let ((_let_15 (fun int _let_7))) (let ((_let_16 (fun real _let_15))) (let ((_let_17 (fun _let_15 _let_13))) (let ((_let_18 (fun (fun int (fun nat bool)) _let_15))) (let ((_let_19 (fun int (fun nat real)))) (let ((_let_20 (fun _let_19 (fun int (fun nat bool))))) (let ((_let_21 (fun real _let_20))) (let ((_let_22 (fun (fun nat real) (fun nat bool)))) (let ((_let_23 (fun real _let_22))) (let ((_let_24 (fun int _let_3))) (hAPP _let_12 (fun (fun nat bool) _let_10) (combc real (fun nat bool) (fun int (fun nat bool))) (hAPP _let_14 _let_12 (hAPP (fun _let_13 _let_11) (fun _let_14 _let_12) (combb _let_13 _let_11 real) (combc int (fun nat bool) (fun nat bool))) (hAPP _let_16 _let_14 (hAPP _let_17 (fun _let_16 _let_14) (combb _let_15 _let_13 real) (hAPP (fun _let_7 _let_5) _let_17 (combb _let_7 _let_5 int) (combs nat bool bool))) (hAPP _let_10 _let_16 (hAPP _let_18 (fun _let_10 _let_16) (combb (fun int (fun nat bool)) _let_15 real) (hAPP _let_8 _let_18 (combb (fun nat bool) _let_7 int) (hAPP (fun bool _let_2) _let_8 (combb bool _let_2 nat) fconj))) (hAPP _let_19 _let_10 (hAPP _let_21 (fun _let_19 _let_10) (combc real _let_19 (fun int (fun nat bool))) (hAPP _let_23 _let_21 (hAPP (fun _let_22 _let_20) (fun _let_23 _let_21) (combb _let_22 _let_20 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_4 _let_23 (hAPP (fun _let_0 _let_22) (fun _let_4 _let_23) (combb _let_0 _let_22 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_19 (hAPP _let_24 (fun (fun nat real) _let_19) (combc int (fun nat real) (fun nat real)) (hAPP _let_9 _let_24 (hAPP (fun _let_1 _let_3) (fun _let_9 _let_24) (combb _let_1 _let_3 int) (combb real real nat)) (hAPP _let_6 _let_9 (hAPP (fun real _let_1) (fun _let_6 _let_9) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat)))))))))))))))))))))))))))))))), (let ((_let_0 (fun nat (fun nat bool)))) (hAPP (fun nat bool) (fun nat bool) (hAPP (fun bool bool) (fun (fun nat bool) (fun nat bool)) (combb bool bool nat) fNot) (hAPP nat (fun nat bool) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat)) (zero_zero nat)))) ) 15.63/15.87 ( (fun nat bool), (fun real (fun int (fun nat bool))), (fun nat bool), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun (fun nat real) (fun nat real)))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun (fun nat bool) (fun nat bool)))) (let ((_let_6 (fun int real))) (let ((_let_7 (fun nat _let_2))) (let ((_let_8 (fun (fun nat bool) _let_7))) (let ((_let_9 (fun int _let_1))) (let ((_let_10 (fun real (fun int (fun nat bool))))) (let ((_let_11 (fun (fun nat bool) (fun int (fun nat bool))))) (let ((_let_12 (fun real _let_11))) (let ((_let_13 (fun int _let_5))) (let ((_let_14 (fun real _let_13))) (let ((_let_15 (fun int _let_7))) (let ((_let_16 (fun real _let_15))) (let ((_let_17 (fun _let_15 _let_13))) (let ((_let_18 (fun (fun int (fun nat bool)) _let_15))) (let ((_let_19 (fun int (fun nat real)))) (let ((_let_20 (fun _let_19 (fun int (fun nat bool))))) (let ((_let_21 (fun real _let_20))) (let ((_let_22 (fun (fun nat real) (fun nat bool)))) (let ((_let_23 (fun real _let_22))) (let ((_let_24 (fun int _let_3))) (hAPP _let_12 (fun (fun nat bool) _let_10) (combc real (fun nat bool) (fun int (fun nat bool))) (hAPP _let_14 _let_12 (hAPP (fun _let_13 _let_11) (fun _let_14 _let_12) (combb _let_13 _let_11 real) (combc int (fun nat bool) (fun nat bool))) (hAPP _let_16 _let_14 (hAPP _let_17 (fun _let_16 _let_14) (combb _let_15 _let_13 real) (hAPP (fun _let_7 _let_5) _let_17 (combb _let_7 _let_5 int) (combs nat bool bool))) (hAPP _let_10 _let_16 (hAPP _let_18 (fun _let_10 _let_16) (combb (fun int (fun nat bool)) _let_15 real) (hAPP _let_8 _let_18 (combb (fun nat bool) _let_7 int) (hAPP (fun bool _let_2) _let_8 (combb bool _let_2 nat) fconj))) (hAPP _let_19 _let_10 (hAPP _let_21 (fun _let_19 _let_10) (combc real _let_19 (fun int (fun nat bool))) (hAPP _let_23 _let_21 (hAPP (fun _let_22 _let_20) (fun _let_23 _let_21) (combb _let_22 _let_20 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_4 _let_23 (hAPP (fun _let_0 _let_22) (fun _let_4 _let_23) (combb _let_0 _let_22 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_19 (hAPP _let_24 (fun (fun nat real) _let_19) (combc int (fun nat real) (fun nat real)) (hAPP _let_9 _let_24 (hAPP (fun _let_1 _let_3) (fun _let_9 _let_24) (combb _let_1 _let_3 int) (combb real real nat)) (hAPP _let_6 _let_9 (hAPP (fun real _let_1) (fun _let_6 _let_9) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat)))))))))))))))))))))))))))))))), (let ((_let_0 (fun nat bool))) (hAPP (fun bool bool) (fun _let_0 _let_0) (combb bool bool nat) fNot)), (let ((_let_0 (fun nat (fun nat bool)))) (hAPP nat (fun nat bool) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat)) (zero_zero nat))) ) 15.63/15.87 ( (fun nat nat), (fun (product_prod nat nat) bool), (fun nat (fun nat bool)), (product_prod_case nat nat bool), (let ((_let_0 (fun nat (fun nat bool)))) (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat (fun nat bool) nat) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat)))), suc ) 15.63/15.87 ( (fun nat nat), (fun real bool), (fun nat real), (sums real), (let ((_let_0 (fun nat real))) (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat real nat) (hAPP real _let_0 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))), suc ) 15.63/15.87 ( (fun nat nat), (fun nat real), (fun nat real), (let ((_let_0 (fun nat real))) (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real))), (let ((_let_0 (fun nat real))) (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat real nat) (real_1 nat))), suc ) 15.63/15.87 ( (fun nat nat), (fun nat real), (fun nat real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (let ((_let_3 (fun real _let_0))) (let ((_let_4 (fun _let_1 _let_2))) (let ((_let_5 (combb real _let_0 nat))) (hAPP _let_2 (fun _let_1 _let_1) (combs nat real real) (hAPP _let_1 _let_2 (hAPP _let_3 _let_4 _let_5 (inverse_divide real)) (hAPP real _let_1 (hAPP _let_2 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_2 (hAPP _let_3 _let_4 _let_5 (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) (one_one real)))))))))), (let ((_let_0 (fun nat real))) (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat real nat) (real_1 nat))), (let ((_let_0 (fun nat (fun nat nat)))) (let ((_let_1 (combc nat nat nat))) (hAPP nat (fun nat nat) (hAPP _let_0 _let_0 _let_1 (hAPP (fun nat nat) _let_0 (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_0 _let_0 _let_1 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))) ) 15.63/15.87 ( (fun nat nat), (fun nat (fun nat nat)), (fun nat (fun nat nat)), (combc nat nat nat), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat _let_0))) (hAPP _let_1 (fun _let_0 _let_1) (combb nat _let_0 nat) (plus_plus nat)))), (let ((_let_0 (fun nat (fun nat nat)))) (hAPP nat (fun nat nat) (hAPP _let_0 _let_0 (combc nat nat nat) (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.63/15.87 ( real, bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), sqrt, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.87 ( real, bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.87 ( real, bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.63/15.87 ( real, bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), sqrt, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.87 ( real, bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.87 ( real, bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.63/15.87 ( real, bool, real, (hAPP real (fun real bool) (ord_less real) (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))), cos, skv_5 ) 15.63/15.87 ( real, bool, real, (hAPP real (fun real bool) (ord_less real) (one_one real)), sqrt, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.63/15.87 ( real, bool, real, (hAPP real (fun real bool) (ord_less real) pi), cos, skv_5 ) 15.63/15.87 ( real, bool, real, (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), cos, skv_5 ) 15.63/15.87 ( real, bool, real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 (fun real bool) (sums real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (hAPP real _let_1 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc)))), cos, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.78/15.91 ( real, bool, real, (hAPP real (fun real bool) (ord_less real) (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi))), (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.78/15.91 ( real, bool, real, (hAPP real (fun real bool) (ord_less real) (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), cos, skv_5 ) 15.78/15.91 ( real, bool, real, (hAPP real (fun real bool) (ord_less_eq real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.78/15.91 ( real, bool, (filter real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (filter real) bool))) (hAPP real _let_2 (hAPP _let_0 (fun real _let_2) (tendsto real real) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin)) (zero_zero real))))), (at real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.78/15.91 ( real, nat, real, natfloor, cos, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.78/15.91 ( real, nat, real, natfloor, cos, skv_5 ) 15.78/15.91 ( real, nat, real, natceiling, cos, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.78/15.91 ( real, nat, real, natceiling, cos, skv_5 ) 15.78/15.91 ( real, real, real, ln, cos, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.78/15.91 ( real, real, real, (uminus_uminus real), cos, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.78/15.91 ( real, real, real, (uminus_uminus real), (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.78/15.91 ( real, real, real, (uminus_uminus real), (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 15.78/15.91 ( real, real, real, cos, cos, skv_5 ) 15.78/15.91 ( real, real, real, cos, (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.78/15.91 ( real, real, real, cos, (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.78/15.91 ( real, real, real, cos, (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.78/15.91 ( real, real, real, cos, (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.78/15.91 ( real, real, real, cos, (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 15.78/15.91 ( real, real, real, cos, (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.78/15.91 ( real, real, real, cos, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1))))))), pi ) 15.78/15.91 ( real, real, real, sqrt, cos, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.78/15.91 ( real, real, real, sqrt, cos, skv_5 ) 15.78/15.91 ( real, real, real, sin, cos, skv_5 ) 15.78/15.91 ( real, real, real, sin, (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.78/15.91 ( real, real, real, sin, (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.78/15.91 ( real, real, real, sin, (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.78/15.91 ( real, real, real, sin, (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.78/15.91 ( real, real, real, sin, (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 15.78/15.91 ( real, real, real, sin, (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.78/15.91 ( real, real, real, sin, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1))))))), pi ) 15.78/15.91 ( real, real, real, tan, cos, skv_5 ) 15.78/15.91 ( real, real, real, tan, (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.78/15.91 ( real, real, real, tan, (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.78/15.91 ( real, real, real, tan, (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.78/15.91 ( real, real, real, tan, (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.78/15.91 ( real, real, real, (hAPP real (fun real real) (inverse_divide real) (one_one real)), sqrt, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.78/15.91 ( real, real, real, (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.78/15.91 ( real, real, real, (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.78/15.91 ( real, real, real, (inverse_inverse real), cos, skv_5 ) 15.78/15.91 ( real, real, real, arctan, cos, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.78/15.91 ( real, real, real, arctan, cos, skv_5 ) 15.78/15.91 ( real, real, real, arctan, (hAPP real (fun real real) (inverse_divide real) (one_one real)), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.78/15.91 ( real, real, real, arctan, (hAPP real (fun real real) (inverse_divide real) (one_one real)), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 15.78/15.91 ( real, real, real, (sgn_sgn real), cos, skv_5 ) 15.78/15.91 ( real, real, real, (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))), arctan, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.78/15.91 ( real, real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real _let_0 (minus_minus real) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1))))))))), arctan, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))))) ) 15.78/15.91 ( real, real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1))))))), (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.78/15.91 ( real, real, complex, re, (hAPP real (fun real complex) complex_1 (zero_zero real)), (one_one real) ) 15.78/15.91 ( real, real, complex, re, (hAPP real (fun real complex) complex_1 (zero_zero real)), (zero_zero real) ) 15.78/15.91 ( real, real, complex, im, (hAPP real (fun real complex) complex_1 (zero_zero real)), (one_one real) ) 15.78/15.91 ( real, real, complex, im, (hAPP real (fun real complex) complex_1 (zero_zero real)), (zero_zero real) ) 15.78/15.91 ( real, (fun real bool), real, (ord_less real), (uminus_uminus real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.78/15.91 ( real, (fun real bool), real, (ord_less real), (uminus_uminus real), (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.78/15.91 ( real, (fun real bool), real, (ord_less real), cos, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.78/15.91 ( real, (fun real bool), real, (ord_less real), cos, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.78/15.91 ( real, (fun real bool), real, (ord_less real), cos, skv_5 ) 15.78/15.91 ( real, (fun real bool), real, (ord_less real), (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.78/15.91 ( real, (fun real bool), real, (ord_less real), (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.78/15.91 ( real, (fun real bool), real, (ord_less_eq real), cos, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.78/15.91 ( real, (fun real bool), real, (ord_less_eq real), cos, skv_5 ) 15.78/15.91 ( real, (fun real bool), real, (ord_less_eq real), (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.78/15.91 ( real, (fun real bool), real, (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun real _let_0))) (hAPP _let_2 _let_2 (combc real real bool) (hAPP _let_1 _let_2 (hAPP _let_2 (fun _let_1 _let_2) (combb real _let_0 real) (fequal real)) cos))))), cos, skv_5 ) 15.78/15.91 ( real, (fun real bool), (fun real bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun real (fun real bool)))) (let ((_let_2 (fun real _let_0))) (hAPP _let_2 (fun (fun real bool) (fun real bool)) (combs real bool bool) (hAPP (fun real bool) _let_2 (hAPP (fun bool _let_0) (fun (fun real bool) _let_2) (combb bool _let_0 real) fconj) (hAPP real (fun real bool) (hAPP _let_1 _let_1 (combc real real bool) (ord_less_eq real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun real _let_0))) (hAPP _let_2 _let_2 (combc real real bool) (hAPP _let_1 _let_2 (hAPP _let_2 (fun _let_1 _let_2) (combb real _let_0 real) (fequal real)) cos))))), (zero_zero real) ) 15.78/15.91 ( real, (fun real real), real, (minus_minus real), (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.78/15.91 ( real, (fun real real), real, (inverse_divide real), cos, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.78/15.91 ( real, (fun real real), real, (inverse_divide real), sqrt, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.78/15.91 ( real, (fun real real), real, (inverse_divide real), sqrt, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.78/15.91 ( real, (fun real real), real, (inverse_divide real), (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.78/15.91 ( real, (fun real real), real, (times_times real), (hAPP real (fun real real) (inverse_divide real) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.78/15.91 ( real, complex, real, cis, cos, skv_5 ) 15.78/15.91 ( real, complex, real, (hAPP real (fun real complex) complex_1 (zero_zero real)), cos, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.78/15.91 ( real, complex, real, (hAPP real (fun real complex) complex_1 (zero_zero real)), cos, skv_5 ) 15.78/15.91 ( real, complex, real, (of_real complex), (uminus_uminus real), (one_one real) ) 15.78/15.91 ( real, complex, real, (of_real complex), (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.78/15.91 ( real, complex, real, (hAPP real (fun real complex) complex_1 (one_one real)), cos, skv_5 ) 15.78/15.91 ( real, complex, complex, (inverse_inverse complex), (hAPP real (fun real complex) complex_1 (zero_zero real)), (one_one real) ) 15.78/15.91 ( real, complex, complex, expi, (hAPP real (fun real complex) complex_1 (zero_zero real)), (zero_zero real) ) 15.78/15.91 ( real, complex, complex, (uminus_uminus complex), (hAPP real (fun real complex) complex_1 (zero_zero real)), (one_one real) ) 15.78/15.91 ( real, complex, complex, cnj, (hAPP real (fun real complex) complex_1 (zero_zero real)), (one_one real) ) 15.78/15.91 ( real, complex, complex, cnj, (hAPP real (fun real complex) complex_1 (zero_zero real)), (zero_zero real) ) 15.78/15.91 ( real, complex, complex, (hAPP complex (fun complex complex) (times_times complex) ii), (hAPP real (fun real complex) complex_1 (zero_zero real)), (one_one real) ) 15.78/15.91 ( real, complex, complex, (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))), (of_real complex), pi ) 15.78/15.91 ( real, complex, complex, (let ((_let_0 (fun complex complex))) (let ((_let_1 (times_times complex))) (hAPP complex _let_0 _let_1 (hAPP complex complex (hAPP complex _let_0 _let_1 (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi))))), (hAPP real (fun real complex) complex_1 (zero_zero real)), (one_one real) ) 15.78/15.91 ( real, (fun nat real), real, (power_power real), (hAPP real (fun real real) (inverse_divide real) (one_one real)), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.78/15.91 ( real, (fun nat real), real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (hAPP _let_2 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 nat) (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1))))))), cos, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.78/15.91 ( real, (fun complex complex), complex, (times_times complex), (hAPP real (fun real complex) complex_1 (zero_zero real)), (one_one real) ) 15.78/15.91 ( real, (fun real complex), real, complex_1, cos, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.78/15.91 ( real, (fun real complex), real, complex_1, cos, skv_5 ) 15.78/15.91 ( real, (fun nat complex), complex, (power_power complex), (hAPP real (fun real complex) complex_1 (zero_zero real)), (one_one real) ) 15.78/15.91 ( real, (fun nat (fun real real)), (fun nat real), (let ((_let_0 (fun real real))) (hAPP (fun real _let_0) (fun (fun nat real) (fun nat _let_0)) (combb real _let_0 nat) (inverse_divide real))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (hAPP _let_2 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 nat) (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1))))))), (one_one real) ) 15.78/15.91 ( real, (fun nat (fun real real)), (fun nat real), (let ((_let_0 (fun real real))) (hAPP (fun real _let_0) (fun (fun nat real) (fun nat _let_0)) (combb real _let_0 nat) (times_times real))), (power_power real), (hAPP int real (number_number_of real) min_1) ) 15.78/15.91 ( real, (fun (fun nat nat) (fun nat real)), (fun nat real), (combb nat real nat), (power_power real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.78/15.91 ( real, (fun (filter nat) bool), real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 (fun real (fun (filter nat) bool)) (tendsto nat real) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))))), cos, skv_5 ) 15.78/15.91 ( real, (filter real), real, (at real), (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.78/15.91 ( real, (fun (filter real) bool), real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 (fun real (fun (filter real) bool)) (tendsto real real) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin)))), cos, skv_5 ) 15.78/15.91 ( real, (fun real (fun bool bool)), (fun real bool), (let ((_let_0 (fun bool bool))) (hAPP (fun bool _let_0) (fun (fun real bool) (fun real _let_0)) (combb bool _let_0 real) fconj)), (ord_less_eq real), (zero_zero real) ) 15.78/15.91 ( real, (fun real (fun bool bool)), (fun real bool), (let ((_let_0 (fun bool bool))) (hAPP (fun bool _let_0) (fun (fun real bool) (fun real _let_0)) (combb bool _let_0 real) fconj)), (let ((_let_0 (fun real (fun real bool)))) (hAPP _let_0 _let_0 (combc real real bool) (ord_less_eq real))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.78/15.91 ( (fun real bool), real, (fun real bool), (the real), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun real _let_1))) (hAPP _let_2 (fun _let_0 _let_0) (combs real bool bool) (hAPP _let_0 _let_2 (hAPP (fun bool _let_1) (fun _let_0 _let_2) (combb bool _let_1 real) fconj) (hAPP real _let_0 (ord_less_eq real) (zero_zero real))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun real _let_0))) (let ((_let_4 (fun real _let_2))) (let ((_let_5 (combc real real bool))) (hAPP _let_0 _let_0 (hAPP _let_4 (fun _let_0 _let_0) (combs real bool bool) (hAPP _let_0 _let_4 (hAPP (fun bool _let_2) (fun _let_0 _let_4) (combb bool _let_2 real) fconj) (hAPP real _let_0 (hAPP _let_3 _let_3 _let_5 (ord_less_eq real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_3 _let_3 _let_5 (hAPP _let_1 _let_3 (hAPP _let_3 (fun _let_1 _let_3) (combb real _let_0 real) (fequal real)) cos)) (zero_zero real))))))))) ) 15.78/15.91 ( (fun real bool), (fun real bool), (fun real bool), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun real _let_1))) (hAPP _let_2 (fun _let_0 _let_0) (combs real bool bool) (hAPP _let_0 _let_2 (hAPP (fun bool _let_1) (fun _let_0 _let_2) (combb bool _let_1 real) fconj) (hAPP real _let_0 (ord_less_eq real) (zero_zero real))))))), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun real (fun real bool)))) (let ((_let_2 (fun real _let_0))) (hAPP _let_2 (fun (fun real bool) (fun real bool)) (combs real bool bool) (hAPP (fun real bool) _let_2 (hAPP (fun bool _let_0) (fun (fun real bool) _let_2) (combb bool _let_0 real) fconj) (hAPP real (fun real bool) (hAPP _let_1 _let_1 (combc real real bool) (ord_less_eq real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun real _let_0))) (hAPP real _let_0 (hAPP _let_2 _let_2 (combc real real bool) (hAPP _let_1 _let_2 (hAPP _let_2 (fun _let_1 _let_2) (combb real _let_0 real) (fequal real)) cos)) (zero_zero real))))) ) 15.78/15.91 ( (fun real bool), (let ((_let_0 (fun real bool))) (fun _let_0 _let_0)), (fun real (fun bool bool)), (combs real bool bool), (let ((_let_0 (fun bool bool))) (hAPP (fun bool _let_0) (fun (fun real bool) (fun real _let_0)) (combb bool _let_0 real) fconj)), (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) ) 15.78/15.91 ( (fun real bool), (let ((_let_0 (fun real bool))) (fun _let_0 _let_0)), (fun real (fun bool bool)), (combs real bool bool), (let ((_let_0 (fun bool bool))) (hAPP (fun bool _let_0) (fun (fun real bool) (fun real _let_0)) (combb bool _let_0 real) fconj)), (let ((_let_0 (fun real (fun real bool)))) (hAPP real (fun real bool) (hAPP _let_0 _let_0 (combc real real bool) (ord_less_eq real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.78/15.91 ( (fun real real), (fun real (fun real bool)), (fun real (fun real bool)), (combc real real bool), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (hAPP _let_1 (fun (fun real real) _let_1) (combb real _let_0 real) (fequal real)))), cos ) 15.78/15.91 ( (fun real real), (let ((_let_0 (fun real real))) (fun _let_0 _let_0)), (fun real (fun real real)), (combs real real real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)))), cos ) 15.78/15.91 ( (fun real real), (fun real (fun (filter real) bool)), (fun real real), (tendsto real real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)))), sin ) 15.78/15.91 ( (fun nat (fun nat bool)), (fun (product_prod nat nat) bool), (fun (product_prod nat nat) bool), (collect (product_prod nat nat)), (product_prod_case nat nat bool), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat (fun nat bool)))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat (fun nat bool) nat) (hAPP _let_1 _let_1 (combc nat nat bool) (fequal nat))) suc))) ) 15.78/15.91 ( (fun nat (fun nat bool)), (fun (fun nat nat) (fun nat (fun nat bool))), (fun nat (fun nat bool)), (combb nat (fun nat bool) nat), (combc nat nat bool), (fequal nat) ) 15.78/15.91 ( complex, real, complex, re, expi, (let ((_let_0 (fun complex complex))) (let ((_let_1 (times_times complex))) (hAPP complex complex (hAPP complex _let_0 _let_1 (hAPP complex complex (hAPP complex _let_0 _let_1 (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi))) ii))) ) 15.78/15.91 ( complex, real, complex, im, expi, (let ((_let_0 (fun complex complex))) (let ((_let_1 (times_times complex))) (hAPP complex complex (hAPP complex _let_0 _let_1 (hAPP complex complex (hAPP complex _let_0 _let_1 (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi))) ii))) ) 15.78/15.91 ( complex, complex, complex, expi, (let ((_let_0 (fun complex complex))) (let ((_let_1 (times_times complex))) (hAPP complex _let_0 _let_1 (hAPP complex complex (hAPP complex _let_0 _let_1 (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi))))), ii ) 15.78/15.91 ( complex, complex, complex, (uminus_uminus complex), expi, (let ((_let_0 (fun complex complex))) (let ((_let_1 (times_times complex))) (hAPP complex complex (hAPP complex _let_0 _let_1 (hAPP complex complex (hAPP complex _let_0 _let_1 (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi))) ii))) ) 15.78/15.91 ( complex, complex, complex, cnj, expi, (let ((_let_0 (fun complex complex))) (let ((_let_1 (times_times complex))) (hAPP complex complex (hAPP complex _let_0 _let_1 (hAPP complex complex (hAPP complex _let_0 _let_1 (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi))) ii))) ) 15.78/15.91 ( complex, (fun complex complex), complex, (times_times complex), (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real complex (of_real complex) pi) ) 15.78/15.91 ( (fun nat real), real, (fun nat real), (suminf real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (let ((_let_3 (fun real _let_0))) (let ((_let_4 (fun _let_1 _let_2))) (let ((_let_5 (combb real _let_0 nat))) (hAPP _let_2 (fun _let_1 _let_1) (combs nat real real) (hAPP _let_1 _let_2 (hAPP _let_3 _let_4 _let_5 (inverse_divide real)) (hAPP real _let_1 (hAPP _let_2 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_2 (hAPP _let_3 _let_4 _let_5 (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) (one_one real)))))))))), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat (fun nat nat)))) (let ((_let_2 (combc nat nat nat))) (hAPP (fun nat nat) _let_0 (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat real nat) (real_1 nat)) (hAPP nat (fun nat nat) (hAPP _let_1 _let_1 _let_2 (hAPP (fun nat nat) _let_1 (hAPP _let_1 (fun (fun nat nat) _let_1) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_1 _let_1 _let_2 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))))) ) 15.78/15.91 ( (fun nat real), (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)), (fun nat (fun real real)), (combs nat real real), (let ((_let_0 (fun real real))) (hAPP (fun real _let_0) (fun (fun nat real) (fun nat _let_0)) (combb real _let_0 nat) (inverse_divide real))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (hAPP real _let_1 (hAPP _let_2 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 nat) (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) (one_one real))))) ) 15.78/15.91 ( (fun nat real), (fun real (fun nat real)), (fun nat (fun real real)), (combc nat real real), (let ((_let_0 (fun real real))) (hAPP (fun real _let_0) (fun (fun nat real) (fun nat _let_0)) (combb real _let_0 nat) (times_times real))), (hAPP real (fun nat real) (power_power real) (hAPP int real (number_number_of real) min_1)) ) 15.78/15.91 ( (fun nat real), (fun real (fun (filter nat) bool)), (fun nat real), (tendsto nat real), (let ((_let_0 (fun nat real))) (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real))), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))) ) 15.78/15.91 ( (fun nat real), (fun real (fun int (fun nat bool))), (fun int (fun nat real)), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun int (fun nat real)) (fun int (fun nat bool))))) (let ((_let_3 (fun real _let_2))) (let ((_let_4 (fun (fun nat real) (fun nat bool)))) (let ((_let_5 (fun real _let_4))) (hAPP _let_3 (fun (fun int (fun nat real)) (fun real (fun int (fun nat bool)))) (combc real (fun int (fun nat real)) (fun int (fun nat bool))) (hAPP _let_5 _let_3 (hAPP (fun _let_4 _let_2) (fun _let_5 _let_3) (combb _let_4 _let_2 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_1 _let_5) (combb _let_0 _let_4 real) (combb real bool nat)) (fequal real)))))))))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun (fun nat real) (fun nat real)))) (let ((_let_2 (fun int real))) (let ((_let_3 (fun int _let_0))) (let ((_let_4 (fun int _let_1))) (hAPP _let_4 (fun (fun nat real) (fun int (fun nat real))) (combc int (fun nat real) (fun nat real)) (hAPP _let_3 _let_4 (hAPP (fun _let_0 _let_1) (fun _let_3 _let_4) (combb _let_0 _let_1 int) (combb real real nat)) (hAPP _let_2 _let_3 (hAPP (fun real _let_0) (fun _let_2 _let_3) (combb real _let_0 int) (inverse_divide real)) (real_1 int))))))))), (real_1 nat) ) 15.78/15.91 ( (fun int (fun int int)), (let ((_let_0 (fun int int))) (fun _let_0 (fun int _let_0))), (let ((_let_0 (fun int int))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun int int))) (combc int _let_0 _let_0)), (let ((_let_0 (fun (fun int int) (fun int int)))) (hAPP (fun (fun int int) _let_0) (fun (fun int (fun int int)) (fun int _let_0)) (combb (fun int int) _let_0 int) (combb int int int))), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)) (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 15.78/15.91 ( (fun int (fun int int)), (fun int (fun int (fun int bool))), (fun int (fun int (fun int bool))), (let ((_let_0 (fun int (fun int bool)))) (let ((_let_1 (fun int _let_0))) (hAPP (fun _let_0 _let_0) (fun _let_1 _let_1) (combb _let_0 _let_0 int) (combc int int bool)))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun _let_2 _let_1))) (hAPP _let_3 (fun (fun int _let_2) (fun int _let_1)) (combb _let_2 _let_1 int) (hAPP _let_1 _let_3 (combb int _let_0 int) (fequal int))))))), int_gcd ) 15.78/15.91 ( (fun (fun nat bool) bool), (fun (fun real (fun int (fun nat bool))) (fun real (fun int bool))), (fun (fun int (fun nat bool)) (fun int bool)), (combb (fun int (fun nat bool)) (fun int bool) real), (combb (fun nat bool) bool int), (fEx nat) ) 15.78/15.91 ( (fun (fun int bool) bool), (let ((_let_0 (fun int bool))) (fun (fun real (fun int _let_0)) (fun real _let_0))), (let ((_let_0 (fun int bool))) (fun (fun int _let_0) _let_0)), (let ((_let_0 (fun int bool))) (combb (fun int _let_0) _let_0 real)), (combb (fun int bool) bool int), (fEx int) ) 15.78/15.91 ( (fun bool (fun bool bool)), (fun (fun int (fun int bool)) (fun int (fun int (fun bool bool)))), (fun (fun int bool) (fun int (fun bool bool))), (combb (fun int bool) (fun int (fun bool bool)) int), (combb bool (fun bool bool) int), fconj ) 15.78/15.91 ( (fun bool (fun bool bool)), (fun (fun int (fun nat bool)) (fun int (fun nat (fun bool bool)))), (fun (fun nat bool) (fun nat (fun bool bool))), (combb (fun nat bool) (fun nat (fun bool bool)) int), (combb bool (fun bool bool) nat), fconj ) 15.78/15.91 ( code_code_numeral, bool, nat, (even_odd_even nat), code_c271388182l_size, (zero_zero code_code_numeral) ) 15.78/15.91 ( code_code_numeral, bool, nat, prime, code_c271388182l_size, (zero_zero code_code_numeral) ) 15.78/15.91 ( code_code_numeral, nat, nat, suc, code_c271388182l_size, (zero_zero code_code_numeral) ) 15.78/15.91 ( code_code_numeral, nat, nat, (fact_fact nat), code_c271388182l_size, (zero_zero code_code_numeral) ) 15.78/15.91 ( code_code_numeral, nat, nat, fact, code_c271388182l_size, (zero_zero code_code_numeral) ) 15.78/15.91 ( code_code_numeral, nat, nat, nat_size, code_c271388182l_size, (zero_zero code_code_numeral) ) 15.78/15.91 ( code_code_numeral, nat, nat, (size_size nat), code_c271388182l_size, (zero_zero code_code_numeral) ) 15.78/15.91 ( code_code_numeral, nat, code_code_numeral, (size_size code_code_numeral), (hAPP code_code_numeral (fun code_code_numeral code_code_numeral) (minus_minus code_code_numeral) (zero_zero code_code_numeral)), (one_one code_code_numeral) ) 15.78/15.91 ( code_code_numeral, nat, code_code_numeral, code_c271388182l_size, (hAPP code_code_numeral (fun code_code_numeral code_code_numeral) (minus_minus code_code_numeral) (zero_zero code_code_numeral)), (one_one code_code_numeral) ) 15.78/15.91 ( code_code_numeral, int, nat, (semiring_1_of_nat int), code_c271388182l_size, (zero_zero code_code_numeral) ) 15.78/15.91 ( code_code_numeral, int, code_code_numeral, code_int_of, (hAPP code_code_numeral (fun code_code_numeral code_code_numeral) (minus_minus code_code_numeral) (zero_zero code_code_numeral)), (one_one code_code_numeral) ) 15.78/15.91 ( code_code_numeral, (fun nat bool), nat, (ord_less nat), code_c271388182l_size, (zero_zero code_code_numeral) ) 15.78/15.91 ( code_code_numeral, (fun nat bool), nat, (let ((_let_0 (fun nat (fun nat bool)))) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat))), code_c271388182l_size, (zero_zero code_code_numeral) ) 15.78/15.91 ( code_code_numeral, real, nat, (real_1 nat), code_c271388182l_size, (zero_zero code_code_numeral) ) 15.78/15.91 ( code_code_numeral, (fun code_code_numeral code_code_numeral), code_code_numeral, (minus_minus code_code_numeral), (hAPP code_code_numeral (fun code_code_numeral code_code_numeral) (minus_minus code_code_numeral) (zero_zero code_code_numeral)), (one_one code_code_numeral) ) 15.78/15.91 ( (fun int (fun int (fun int bool))), (fun int (fun int (fun int bool))), (fun int (fun int (fun int bool))), (combc int int (fun int bool)), (let ((_let_0 (fun int (fun int bool)))) (let ((_let_1 (fun int _let_0))) (hAPP (fun _let_0 _let_0) (fun _let_1 _let_1) (combb _let_0 _let_0 int) (combc int int bool)))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int _let_1))) (let ((_let_5 (fun _let_2 _let_1))) (hAPP _let_3 _let_4 (hAPP _let_5 (fun _let_3 _let_4) (combb _let_2 _let_1 int) (hAPP _let_1 _let_5 (combb int _let_0 int) (fequal int))) int_gcd))))))) ) 15.78/15.91 ( (fun real (fun real bool)), (fun real (fun (fun int (fun int real)) (fun int (fun int bool)))), (fun real (fun (fun int real) (fun int bool))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int real))) (let ((_let_2 (fun (fun int _let_1) (fun int _let_0)))) (let ((_let_3 (fun _let_1 _let_0))) (hAPP (fun _let_3 _let_2) (fun (fun real _let_3) (fun real _let_2)) (combb _let_3 _let_2 real) (combb _let_1 _let_0 int)))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun (fun int real) (fun int bool)))) (hAPP (fun _let_0 _let_1) (fun (fun real _let_0) (fun real _let_1)) (combb _let_0 _let_1 real) (combb real bool int)))), (fequal real) ) 15.78/15.91 ( (fun real (fun real bool)), (fun real (fun (fun int (fun nat real)) (fun int (fun nat bool)))), (fun real (fun (fun nat real) (fun nat bool))), (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun (fun int _let_1) (fun int _let_0)))) (let ((_let_3 (fun _let_1 _let_0))) (hAPP (fun _let_3 _let_2) (fun (fun real _let_3) (fun real _let_2)) (combb _let_3 _let_2 real) (combb _let_1 _let_0 int)))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun (fun nat real) (fun nat bool)))) (hAPP (fun _let_0 _let_1) (fun (fun real _let_0) (fun real _let_1)) (combb _let_0 _let_1 real) (combb real bool nat)))), (fequal real) ) 15.78/15.91 ( (fun (product_prod int int) bool), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)), (fun (product_prod int int) (fun bool bool)), (combs (product_prod int int) bool bool), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun bool bool))) (hAPP (fun bool _let_1) (fun (fun _let_0 bool) (fun _let_0 _let_1)) (combb bool _let_1 _let_0) fconj))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun _let_1 _let_0))) (let ((_let_4 (fun _let_1 int))) (hAPP _let_2 _let_2 (hAPP (fun bool bool) (fun _let_2 _let_2) (combb bool bool _let_1) fNot) (hAPP int _let_2 (hAPP _let_3 (fun int _let_2) (combc _let_1 int bool) (hAPP _let_4 _let_3 (hAPP (fun int _let_0) (fun _let_4 _let_3) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int)))))))) ) 15.78/15.91 ( (fun (product_prod int int) bool), (let ((_let_0 (fun (product_prod int int) bool))) (fun (product_prod int int) (fun _let_0 _let_0))), (fun (product_prod int int) (fun bool bool)), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun (fun _let_0 bool) (fun _let_0 bool)))) (hAPP (fun _let_1 _let_2) (fun (fun _let_0 _let_1) (fun _let_0 _let_2)) (combb _let_1 _let_2 _let_0) (combb bool bool _let_0))))), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun bool bool))) (hAPP (fun bool _let_1) (fun (fun _let_0 bool) (fun _let_0 _let_1)) (combb bool _let_1 _let_0) fconj))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun _let_1 _let_0))) (let ((_let_4 (fun _let_1 int))) (hAPP _let_2 _let_2 (hAPP (fun bool bool) (fun _let_2 _let_2) (combb bool bool _let_1) fNot) (hAPP int _let_2 (hAPP _let_3 (fun int _let_2) (combc _let_1 int bool) (hAPP _let_4 _let_3 (hAPP (fun int _let_0) (fun _let_4 _let_3) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int)))))))) ) 15.78/15.91 ( (fun (product_prod int int) bool), (fun (product_prod int int) (fun bool bool)), (fun (product_prod int int) bool), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun bool bool))) (hAPP (fun bool _let_1) (fun (fun _let_0 bool) (fun _let_0 _let_1)) (combb bool _let_1 _let_0) fconj))), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 bool))) (hAPP (fun bool bool) (fun _let_1 _let_1) (combb bool bool _let_0) fNot))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun _let_1 _let_0))) (let ((_let_4 (fun _let_1 int))) (hAPP int _let_2 (hAPP _let_3 (fun int _let_2) (combc _let_1 int bool) (hAPP _let_4 _let_3 (hAPP (fun int _let_0) (fun _let_4 _let_3) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))) ) 15.78/15.91 ( (fun int (fun bool bool)), (let ((_let_0 (fun int (fun int bool)))) (fun _let_0 _let_0)), (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), (let ((_let_0 (fun int bool))) (combb _let_0 _let_0 int)), (combs int bool bool), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun int _let_1))) (hAPP _let_0 _let_2 (hAPP (fun bool _let_1) (fun _let_0 _let_2) (combb bool _let_1 int) fconj) (hAPP int _let_0 (ord_less int) (zero_zero int)))))) ) 15.78/15.91 ( (fun (fun int bool) (fun int (fun bool bool))), (fun (fun real (fun int (fun int bool))) (fun real (fun int (fun int (fun bool bool))))), (fun (fun int (fun int bool)) (fun int (fun int (fun bool bool)))), (combb (fun int (fun int bool)) (fun int (fun int (fun bool bool))) real), (combb (fun int bool) (fun int (fun bool bool)) int), (let ((_let_0 (fun bool bool))) (hAPP (fun bool _let_0) (fun (fun int bool) (fun int _let_0)) (combb bool _let_0 int) fconj)) ) 15.78/15.92 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), (let ((_let_0 (product_prod int int))) (collect (product_prod _let_0 _let_0))), (let ((_let_0 (product_prod int int))) (product_prod_case _let_0 _let_0 bool)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun _let_2 (fun _let_2 bool)))) (let ((_let_5 (fun (fun _let_2 bool) (fun _let_2 bool)))) (let ((_let_6 (fun _let_2 _let_5))) (let ((_let_7 (fun _let_4 _let_4))) (let ((_let_8 (fun _let_2 _let_3))) (let ((_let_9 (fun _let_2 _let_0))) (let ((_let_10 (fun _let_2 int))) (let ((_let_11 (fun _let_10 _let_9))) (let ((_let_12 (hAPP (fun int _let_0) _let_11 (combb int _let_0 _let_2) (fequal int)))) (let ((_let_13 (product_snd int int))) (let ((_let_14 (hAPP (fun _let_2 bool) _let_8 (hAPP (fun bool _let_3) (fun (fun _let_2 bool) _let_8) (combb bool _let_3 _let_2) fconj) (hAPP (fun _let_2 bool) (fun _let_2 bool) (hAPP _let_3 _let_5 (combb bool bool _let_2) fNot) (hAPP int (fun _let_2 bool) (hAPP _let_9 (fun int (fun _let_2 bool)) (combc _let_2 int bool) (hAPP _let_10 _let_9 _let_12 _let_13)) (zero_zero int)))))) (let ((_let_15 (fun _let_2 _let_10))) (let ((_let_16 (fun _let_10 (fun _let_2 bool)))) (let ((_let_17 (fun _let_2 _let_16))) (let ((_let_18 (fun _let_2 _let_9))) (let ((_let_19 (fun _let_10 _let_10))) (let ((_let_20 (fun _let_2 _let_19))) (let ((_let_21 (fun _let_10 _let_15))) (let ((_let_22 (fun _let_2 _let_1))) (let ((_let_23 (hAPP _let_10 _let_22 (hAPP (fun int _let_1) (fun _let_10 _let_22) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (let ((_let_24 (fun int _let_10))) (hAPP _let_4 _let_4 (hAPP _let_6 _let_7 (combs _let_2 (fun _let_2 bool) (fun _let_2 bool)) (hAPP _let_8 _let_6 (hAPP (fun _let_3 _let_5) (fun _let_8 _let_6) (combb _let_3 _let_5 _let_2) (combb bool bool _let_2)) _let_14)) (hAPP _let_4 _let_4 (hAPP _let_5 _let_7 (combb (fun _let_2 bool) (fun _let_2 bool) _let_2) (hAPP _let_8 _let_5 (combs _let_2 bool bool) _let_14)) (hAPP _let_15 _let_4 (hAPP _let_17 (fun _let_15 _let_4) (combs _let_2 _let_10 (fun _let_2 bool)) (hAPP _let_18 _let_17 (hAPP (fun _let_9 _let_16) (fun _let_18 _let_17) (combb _let_9 _let_16 _let_2) (combs _let_2 int bool)) (hAPP _let_15 _let_18 (hAPP _let_11 (fun _let_15 _let_18) (combb _let_10 _let_9 _let_2) _let_12) (hAPP _let_10 _let_15 (hAPP _let_20 _let_21 (combc _let_2 _let_10 _let_10) (hAPP _let_22 _let_20 (hAPP (fun _let_1 _let_19) (fun _let_22 _let_20) (combb _let_1 _let_19 _let_2) (combb int int _let_2)) _let_23)) _let_13)))) (hAPP _let_10 _let_15 (hAPP _let_24 _let_21 (combb int _let_10 _let_2) (hAPP _let_22 _let_24 (combc _let_2 int int) _let_23)) _let_13))))))))))))))))))))))))))))) ) 15.81/15.92 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (product_prod_case _let_0 _let_0 bool)), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_1 _let_3))) (let ((_let_5 (fun _let_3 _let_3))) (let ((_let_6 (fun _let_1 _let_5))) (let ((_let_7 (fun _let_1 _let_2))) (let ((_let_8 (combb bool bool _let_1))) (let ((_let_9 (fun _let_1 _let_0))) (let ((_let_10 (fun _let_1 int))) (hAPP _let_6 (fun _let_4 _let_4) (combs _let_1 _let_3 _let_3) (hAPP _let_7 _let_6 (hAPP (fun _let_2 _let_5) (fun _let_7 _let_6) (combb _let_2 _let_5 _let_1) _let_8) (hAPP _let_3 _let_7 (hAPP (fun bool _let_2) (fun _let_3 _let_7) (combb bool _let_2 _let_1) fconj) (hAPP _let_3 _let_3 (hAPP _let_2 _let_5 _let_8 fNot) (hAPP int _let_3 (hAPP _let_9 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_10 _let_9 (hAPP (fun int _let_0) (fun _let_10 _let_9) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))))))))))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun _let_2 (fun _let_2 bool)))) (let ((_let_5 (fun (fun _let_2 bool) (fun _let_2 bool)))) (let ((_let_6 (fun _let_2 _let_3))) (let ((_let_7 (fun _let_2 _let_0))) (let ((_let_8 (fun _let_2 int))) (let ((_let_9 (fun _let_8 _let_7))) (let ((_let_10 (hAPP (fun int _let_0) _let_9 (combb int _let_0 _let_2) (fequal int)))) (let ((_let_11 (product_snd int int))) (let ((_let_12 (fun _let_2 _let_8))) (let ((_let_13 (fun _let_8 (fun _let_2 bool)))) (let ((_let_14 (fun _let_2 _let_13))) (let ((_let_15 (fun _let_2 _let_7))) (let ((_let_16 (fun _let_8 _let_8))) (let ((_let_17 (fun _let_2 _let_16))) (let ((_let_18 (fun _let_8 _let_12))) (let ((_let_19 (fun _let_2 _let_1))) (let ((_let_20 (hAPP _let_8 _let_19 (hAPP (fun int _let_1) (fun _let_8 _let_19) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (let ((_let_21 (fun int _let_8))) (hAPP _let_4 _let_4 (hAPP _let_5 (fun _let_4 _let_4) (combb (fun _let_2 bool) (fun _let_2 bool) _let_2) (hAPP _let_6 _let_5 (combs _let_2 bool bool) (hAPP (fun _let_2 bool) _let_6 (hAPP (fun bool _let_3) (fun (fun _let_2 bool) _let_6) (combb bool _let_3 _let_2) fconj) (hAPP (fun _let_2 bool) (fun _let_2 bool) (hAPP _let_3 _let_5 (combb bool bool _let_2) fNot) (hAPP int (fun _let_2 bool) (hAPP _let_7 (fun int (fun _let_2 bool)) (combc _let_2 int bool) (hAPP _let_8 _let_7 _let_10 _let_11)) (zero_zero int)))))) (hAPP _let_12 _let_4 (hAPP _let_14 (fun _let_12 _let_4) (combs _let_2 _let_8 (fun _let_2 bool)) (hAPP _let_15 _let_14 (hAPP (fun _let_7 _let_13) (fun _let_15 _let_14) (combb _let_7 _let_13 _let_2) (combs _let_2 int bool)) (hAPP _let_12 _let_15 (hAPP _let_9 (fun _let_12 _let_15) (combb _let_8 _let_7 _let_2) _let_10) (hAPP _let_8 _let_12 (hAPP _let_17 _let_18 (combc _let_2 _let_8 _let_8) (hAPP _let_19 _let_17 (hAPP (fun _let_1 _let_16) (fun _let_19 _let_17) (combb _let_1 _let_16 _let_2) (combb int int _let_2)) _let_20)) _let_11)))) (hAPP _let_8 _let_12 (hAPP _let_21 _let_18 (combb int _let_8 _let_2) (hAPP _let_19 _let_21 (combc _let_2 int int) _let_20)) _let_11))))))))))))))))))))))))) ) 15.81/15.92 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_1 _let_3))) (let ((_let_5 (fun _let_3 _let_3))) (let ((_let_6 (fun _let_1 _let_5))) (let ((_let_7 (fun _let_1 _let_2))) (let ((_let_8 (combb bool bool _let_1))) (let ((_let_9 (fun _let_1 _let_0))) (let ((_let_10 (fun _let_1 int))) (hAPP _let_6 (fun _let_4 _let_4) (combs _let_1 _let_3 _let_3) (hAPP _let_7 _let_6 (hAPP (fun _let_2 _let_5) (fun _let_7 _let_6) (combb _let_2 _let_5 _let_1) _let_8) (hAPP _let_3 _let_7 (hAPP (fun bool _let_2) (fun _let_3 _let_7) (combb bool _let_2 _let_1) fconj) (hAPP _let_3 _let_3 (hAPP _let_2 _let_5 _let_8 fNot) (hAPP int _let_3 (hAPP _let_9 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_10 _let_9 (hAPP (fun int _let_0) (fun _let_10 _let_9) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))))))))))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_1 _let_3))) (let ((_let_5 (fun _let_3 _let_3))) (let ((_let_6 (fun _let_1 _let_2))) (let ((_let_7 (fun _let_1 _let_0))) (let ((_let_8 (fun _let_1 int))) (hAPP _let_5 (fun _let_4 _let_4) (combb _let_3 _let_3 _let_1) (hAPP _let_6 _let_5 (combs _let_1 bool bool) (hAPP _let_3 _let_6 (hAPP (fun bool _let_2) (fun _let_3 _let_6) (combb bool _let_2 _let_1) fconj) (hAPP _let_3 _let_3 (hAPP _let_2 _let_5 (combb bool bool _let_1) fNot) (hAPP int _let_3 (hAPP _let_7 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_8 _let_7 (hAPP (fun int _let_0) (fun _let_8 _let_7) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))))))))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun _let_2 (fun _let_2 bool)))) (let ((_let_4 (fun _let_2 _let_0))) (let ((_let_5 (fun _let_2 int))) (let ((_let_6 (fun _let_5 _let_4))) (let ((_let_7 (product_snd int int))) (let ((_let_8 (fun _let_2 _let_5))) (let ((_let_9 (fun _let_5 (fun _let_2 bool)))) (let ((_let_10 (fun _let_2 _let_9))) (let ((_let_11 (fun _let_2 _let_4))) (let ((_let_12 (fun _let_5 _let_5))) (let ((_let_13 (fun _let_2 _let_12))) (let ((_let_14 (fun _let_5 _let_8))) (let ((_let_15 (fun _let_2 _let_1))) (let ((_let_16 (hAPP _let_5 _let_15 (hAPP (fun int _let_1) (fun _let_5 _let_15) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (let ((_let_17 (fun int _let_5))) (hAPP _let_8 _let_3 (hAPP _let_10 (fun _let_8 _let_3) (combs _let_2 _let_5 (fun _let_2 bool)) (hAPP _let_11 _let_10 (hAPP (fun _let_4 _let_9) (fun _let_11 _let_10) (combb _let_4 _let_9 _let_2) (combs _let_2 int bool)) (hAPP _let_8 _let_11 (hAPP _let_6 (fun _let_8 _let_11) (combb _let_5 _let_4 _let_2) (hAPP (fun int _let_0) _let_6 (combb int _let_0 _let_2) (fequal int))) (hAPP _let_5 _let_8 (hAPP _let_13 _let_14 (combc _let_2 _let_5 _let_5) (hAPP _let_15 _let_13 (hAPP (fun _let_1 _let_12) (fun _let_15 _let_13) (combb _let_1 _let_12 _let_2) (combb int int _let_2)) _let_16)) _let_7)))) (hAPP _let_5 _let_8 (hAPP _let_17 _let_14 (combb int _let_5 _let_2) (hAPP _let_15 _let_17 (combc _let_2 int int) _let_16)) _let_7)))))))))))))))))))) ) 15.81/15.92 ( (fun (product_prod int int) (fun bool bool)), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (fun _let_1 _let_1))), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 bool))) (combb _let_1 _let_1 _let_0))), (combs (product_prod int int) bool bool), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_1 _let_2))) (let ((_let_5 (fun _let_1 _let_0))) (let ((_let_6 (fun _let_1 int))) (hAPP _let_3 _let_4 (hAPP (fun bool _let_2) (fun _let_3 _let_4) (combb bool _let_2 _let_1) fconj) (hAPP _let_3 _let_3 (hAPP _let_2 (fun _let_3 _let_3) (combb bool bool _let_1) fNot) (hAPP int _let_3 (hAPP _let_5 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_6 _let_5 (hAPP (fun int _let_0) (fun _let_6 _let_5) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))))))) ) 15.81/15.92 ( (fun (product_prod int int) (fun bool bool)), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (fun _let_1 _let_1))), (let ((_let_0 (fun (product_prod int int) bool))) (fun (product_prod int int) (fun _let_0 _let_0))), (let ((_let_0 (fun (product_prod int int) bool))) (combs (product_prod int int) _let_0 _let_0)), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun (fun _let_0 bool) (fun _let_0 bool)))) (hAPP (fun _let_1 _let_2) (fun (fun _let_0 _let_1) (fun _let_0 _let_2)) (combb _let_1 _let_2 _let_0) (combb bool bool _let_0))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_1 _let_2))) (let ((_let_5 (fun _let_1 _let_0))) (let ((_let_6 (fun _let_1 int))) (hAPP _let_3 _let_4 (hAPP (fun bool _let_2) (fun _let_3 _let_4) (combb bool _let_2 _let_1) fconj) (hAPP _let_3 _let_3 (hAPP _let_2 (fun _let_3 _let_3) (combb bool bool _let_1) fNot) (hAPP int _let_3 (hAPP _let_5 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_6 _let_5 (hAPP (fun int _let_0) (fun _let_6 _let_5) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))))))) ) 15.81/15.92 ( (fun (product_prod int int) int), (fun int (fun (product_prod int int) bool)), (fun (product_prod int int) (fun int bool)), (combc (product_prod int int) int bool), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (hAPP (fun int _let_0) (fun (fun _let_1 int) (fun _let_1 _let_0)) (combb int _let_0 _let_1) (fequal int)))), (product_snd int int) ) 15.81/15.92 ( (fun (product_prod int int) int), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun _let_2 _let_0))) (let ((_let_4 (fun _let_2 int))) (let ((_let_5 (fun _let_4 _let_3))) (let ((_let_6 (fun _let_2 _let_4))) (let ((_let_7 (fun _let_4 (fun _let_2 bool)))) (let ((_let_8 (fun _let_2 _let_7))) (let ((_let_9 (fun _let_2 _let_3))) (let ((_let_10 (fun _let_4 _let_4))) (let ((_let_11 (fun _let_2 _let_10))) (let ((_let_12 (fun _let_2 _let_1))) (hAPP _let_8 (fun _let_6 (fun _let_2 (fun _let_2 bool))) (combs _let_2 _let_4 (fun _let_2 bool)) (hAPP _let_9 _let_8 (hAPP (fun _let_3 _let_7) (fun _let_9 _let_8) (combb _let_3 _let_7 _let_2) (combs _let_2 int bool)) (hAPP _let_6 _let_9 (hAPP _let_5 (fun _let_6 _let_9) (combb _let_4 _let_3 _let_2) (hAPP (fun int _let_0) _let_5 (combb int _let_0 _let_2) (fequal int))) (hAPP _let_4 _let_6 (hAPP _let_11 (fun _let_4 _let_6) (combc _let_2 _let_4 _let_4) (hAPP _let_12 _let_11 (hAPP (fun _let_1 _let_10) (fun _let_12 _let_11) (combb _let_1 _let_10 _let_2) (combb int int _let_2)) (hAPP _let_4 _let_12 (hAPP (fun int _let_1) (fun _let_4 _let_12) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (product_snd int int)))))))))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_0))) (let ((_let_4 (fun int _let_2))) (hAPP _let_4 (fun _let_2 (fun _let_1 _let_2)) (combb int _let_2 _let_1) (hAPP _let_3 _let_4 (combc _let_1 int int) (hAPP _let_2 _let_3 (hAPP (fun int _let_0) (fun _let_2 _let_3) (combb int _let_0 _let_1) (times_times int)) (product_fst int int))))))))), (product_snd int int) ) 15.81/15.92 ( (fun (product_prod int int) int), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 (fun int bool)))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 _let_0))) (let ((_let_3 (fun _let_1 int))) (let ((_let_4 (fun _let_3 _let_2))) (hAPP _let_4 (fun (fun _let_1 _let_3) (fun _let_1 _let_2)) (combb _let_3 _let_2 _let_1) (hAPP (fun int _let_0) _let_4 (combb int _let_0 _let_1) (fequal int)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_2 _let_2))) (let ((_let_4 (fun _let_1 _let_3))) (let ((_let_5 (fun _let_1 _let_0))) (hAPP _let_4 (fun _let_2 (fun _let_1 _let_2)) (combc _let_1 _let_2 _let_2) (hAPP _let_5 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_5 _let_4) (combb _let_0 _let_3 _let_1) (combb int int _let_1)) (hAPP _let_2 _let_5 (hAPP (fun int _let_0) (fun _let_2 _let_5) (combb int _let_0 _let_1) (times_times int)) (product_fst int int)))))))))), (product_snd int int) ) 15.81/15.92 ( (fun (product_prod int int) int), (let ((_let_0 (fun (product_prod int int) int))) (fun (product_prod int int) (fun _let_0 _let_0))), (fun (product_prod int int) (fun int int)), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun (fun _let_1 int) (fun _let_1 int)))) (hAPP (fun _let_0 _let_2) (fun (fun _let_1 _let_0) (fun _let_1 _let_2)) (combb _let_0 _let_2 _let_1) (combb int int _let_1))))), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (hAPP (fun int _let_0) (fun (fun _let_1 int) (fun _let_1 _let_0)) (combb int _let_0 _let_1) (times_times int)))), (product_fst int int) ) 15.81/15.92 ( (fun (product_prod int int) int), (fun int (fun (product_prod int int) int)), (fun (product_prod int int) (fun int int)), (combc (product_prod int int) int int), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (hAPP (fun int _let_0) (fun (fun _let_1 int) (fun _let_1 _let_0)) (combb int _let_0 _let_1) (times_times int)))), (product_fst int int) ) 15.81/15.92 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_1 _let_3))) (let ((_let_5 (fun _let_3 _let_3))) (let ((_let_6 (fun _let_1 _let_2))) (let ((_let_7 (fun _let_1 _let_0))) (let ((_let_8 (fun _let_1 int))) (hAPP _let_5 (fun _let_4 _let_4) (combb _let_3 _let_3 _let_1) (hAPP _let_6 _let_5 (combs _let_1 bool bool) (hAPP _let_3 _let_6 (hAPP (fun bool _let_2) (fun _let_3 _let_6) (combb bool _let_2 _let_1) fconj) (hAPP _let_3 _let_3 (hAPP _let_2 _let_5 (combb bool bool _let_1) fNot) (hAPP int _let_3 (hAPP _let_7 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_8 _let_7 (hAPP (fun int _let_0) (fun _let_8 _let_7) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))))))))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun _let_2 _let_0))) (let ((_let_4 (fun _let_2 int))) (let ((_let_5 (fun _let_4 _let_3))) (let ((_let_6 (fun _let_2 _let_4))) (let ((_let_7 (fun _let_4 (fun _let_2 bool)))) (let ((_let_8 (fun _let_2 _let_7))) (let ((_let_9 (fun _let_2 _let_3))) (let ((_let_10 (fun _let_4 _let_4))) (let ((_let_11 (fun _let_2 _let_10))) (let ((_let_12 (fun _let_2 _let_1))) (hAPP _let_8 (fun _let_6 (fun _let_2 (fun _let_2 bool))) (combs _let_2 _let_4 (fun _let_2 bool)) (hAPP _let_9 _let_8 (hAPP (fun _let_3 _let_7) (fun _let_9 _let_8) (combb _let_3 _let_7 _let_2) (combs _let_2 int bool)) (hAPP _let_6 _let_9 (hAPP _let_5 (fun _let_6 _let_9) (combb _let_4 _let_3 _let_2) (hAPP (fun int _let_0) _let_5 (combb int _let_0 _let_2) (fequal int))) (hAPP _let_4 _let_6 (hAPP _let_11 (fun _let_4 _let_6) (combc _let_2 _let_4 _let_4) (hAPP _let_12 _let_11 (hAPP (fun _let_1 _let_10) (fun _let_12 _let_11) (combb _let_1 _let_10 _let_2) (combb int int _let_2)) (hAPP _let_4 _let_12 (hAPP (fun int _let_1) (fun _let_4 _let_12) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (product_snd int int)))))))))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_2))) (let ((_let_4 (fun _let_1 _let_0))) (let ((_let_5 (fun int _let_2))) (hAPP _let_2 _let_3 (hAPP _let_5 (fun _let_2 _let_3) (combb int _let_2 _let_1) (hAPP _let_4 _let_5 (combc _let_1 int int) (hAPP _let_2 _let_4 (hAPP (fun int _let_0) (fun _let_2 _let_4) (combb int _let_0 _let_1) (times_times int)) (product_fst int int)))) (product_snd int int)))))))) ) 15.81/15.92 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun (fun _let_0 int) (fun _let_0 bool)))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 (fun int bool)))), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 (fun int bool)))) (let ((_let_2 (fun (fun _let_0 int) (fun _let_0 bool)))) (hAPP (fun _let_1 _let_2) (fun (fun _let_0 _let_1) (fun _let_0 _let_2)) (combb _let_1 _let_2 _let_0) (combs _let_0 int bool))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 _let_0))) (let ((_let_3 (fun _let_1 int))) (let ((_let_4 (fun _let_3 _let_2))) (hAPP _let_4 (fun (fun _let_1 _let_3) (fun _let_1 _let_2)) (combb _let_3 _let_2 _let_1) (hAPP (fun int _let_0) _let_4 (combb int _let_0 _let_1) (fequal int)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_2))) (let ((_let_4 (fun _let_2 _let_2))) (let ((_let_5 (fun _let_1 _let_4))) (let ((_let_6 (fun _let_1 _let_0))) (hAPP _let_2 _let_3 (hAPP _let_5 (fun _let_2 _let_3) (combc _let_1 _let_2 _let_2) (hAPP _let_6 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_6 _let_5) (combb _let_0 _let_4 _let_1) (combb int int _let_1)) (hAPP _let_2 _let_6 (hAPP (fun int _let_0) (fun _let_2 _let_6) (combb int _let_0 _let_1) (times_times int)) (product_fst int int)))) (product_snd int int))))))))) ) 15.81/15.92 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 (fun int bool)))), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 (fun _let_0 int)) (fun _let_0 (fun _let_0 bool)))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun (fun _let_0 int) (fun _let_0 bool)))), (let ((_let_0 (product_prod int int))) (combs _let_0 (fun _let_0 int) (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 (fun int bool)))) (let ((_let_2 (fun (fun _let_0 int) (fun _let_0 bool)))) (hAPP (fun _let_1 _let_2) (fun (fun _let_0 _let_1) (fun _let_0 _let_2)) (combb _let_1 _let_2 _let_0) (combs _let_0 int bool))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun _let_2 _let_0))) (let ((_let_4 (fun _let_2 int))) (let ((_let_5 (fun _let_4 _let_3))) (let ((_let_6 (fun _let_2 _let_4))) (let ((_let_7 (fun _let_2 _let_3))) (let ((_let_8 (fun _let_4 _let_4))) (let ((_let_9 (fun _let_2 _let_8))) (let ((_let_10 (fun _let_2 _let_1))) (hAPP _let_6 _let_7 (hAPP _let_5 (fun _let_6 _let_7) (combb _let_4 _let_3 _let_2) (hAPP (fun int _let_0) _let_5 (combb int _let_0 _let_2) (fequal int))) (hAPP _let_4 _let_6 (hAPP _let_9 (fun _let_4 _let_6) (combc _let_2 _let_4 _let_4) (hAPP _let_10 _let_9 (hAPP (fun _let_1 _let_8) (fun _let_10 _let_9) (combb _let_1 _let_8 _let_2) (combb int int _let_2)) (hAPP _let_4 _let_10 (hAPP (fun int _let_1) (fun _let_4 _let_10) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (product_snd int int)))))))))))))) ) 15.81/15.92 ( (fun (product_prod int int) (fun int int)), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 int))) (fun _let_1 (fun _let_0 _let_1)))), (let ((_let_0 (fun (product_prod int int) int))) (fun (product_prod int int) (fun _let_0 _let_0))), (let ((_let_0 (fun (product_prod int int) int))) (combc (product_prod int int) _let_0 _let_0)), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun (fun _let_1 int) (fun _let_1 int)))) (hAPP (fun _let_0 _let_2) (fun (fun _let_1 _let_0) (fun _let_1 _let_2)) (combb _let_0 _let_2 _let_1) (combb int int _let_1))))), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_0))) (hAPP _let_2 _let_3 (hAPP (fun int _let_0) (fun _let_2 _let_3) (combb int _let_0 _let_1) (times_times int)) (product_fst int int)))))) ) 15.81/15.92 ( (fun (product_prod int int) (fun int int)), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 int))) (fun _let_1 (fun _let_0 _let_1)))), (fun int (fun (product_prod int int) int)), (let ((_let_0 (product_prod int int))) (combb int (fun _let_0 int) _let_0)), (combc (product_prod int int) int int), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_0))) (hAPP _let_2 _let_3 (hAPP (fun int _let_0) (fun _let_2 _let_3) (combb int _let_0 _let_1) (times_times int)) (product_fst int int)))))) ) 15.81/15.92 ( (fun int real), (fun real (fun int (fun int bool))), (fun int (fun int real)), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun int (fun int real)) (fun int (fun int bool))))) (let ((_let_3 (fun real _let_2))) (let ((_let_4 (fun (fun int real) (fun int bool)))) (let ((_let_5 (fun real _let_4))) (hAPP _let_3 (fun (fun int (fun int real)) (fun real (fun int (fun int bool)))) (combc real (fun int (fun int real)) (fun int (fun int bool))) (hAPP _let_5 _let_3 (hAPP (fun _let_4 _let_2) (fun _let_5 _let_3) (combb _let_4 _let_2 real) (combb (fun int real) (fun int bool) int)) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_1 _let_5) (combb _let_0 _let_4 real) (combb real bool int)) (fequal real)))))))))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun int real))) (let ((_let_2 (fun _let_1 _let_1))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int _let_0))) (hAPP _let_3 (fun _let_1 (fun int _let_1)) (combc int _let_1 _let_1) (hAPP _let_4 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_4 _let_3) (combb _let_0 _let_2 int) (combb real real int)) (hAPP _let_1 _let_4 (hAPP (fun real _let_0) (fun _let_1 _let_4) (combb real _let_0 int) (inverse_divide real)) (real_1 int))))))))), (real_1 int) ) 15.81/15.92 ( (fun int real), (let ((_let_0 (fun int real))) (fun int (fun _let_0 _let_0))), (fun int (fun real real)), (let ((_let_0 (fun real real))) (let ((_let_1 (fun (fun int real) (fun int real)))) (hAPP (fun _let_0 _let_1) (fun (fun int _let_0) (fun int _let_1)) (combb _let_0 _let_1 int) (combb real real int)))), (let ((_let_0 (fun real real))) (hAPP (fun real _let_0) (fun (fun int real) (fun int _let_0)) (combb real _let_0 int) (inverse_divide real))), (real_1 int) ) 15.81/15.92 ( (fun int real), (let ((_let_0 (fun nat real))) (fun int (fun _let_0 _let_0))), (fun int (fun real real)), (let ((_let_0 (fun real real))) (let ((_let_1 (fun (fun nat real) (fun nat real)))) (hAPP (fun _let_0 _let_1) (fun (fun int _let_0) (fun int _let_1)) (combb _let_0 _let_1 int) (combb real real nat)))), (let ((_let_0 (fun real real))) (hAPP (fun real _let_0) (fun (fun int real) (fun int _let_0)) (combb real _let_0 int) (inverse_divide real))), (real_1 int) ) 15.81/15.92 ( (let ((_let_0 (fun nat bool))) (fun (fun nat (fun bool bool)) (fun _let_0 _let_0))), (let ((_let_0 (fun nat bool))) (fun (fun real (fun int (fun nat (fun bool bool)))) (fun real (fun int (fun _let_0 _let_0))))), (let ((_let_0 (fun nat bool))) (fun (fun int (fun nat (fun bool bool))) (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun nat bool))) (combb (fun int (fun nat (fun bool bool))) (fun int (fun _let_0 _let_0)) real)), (let ((_let_0 (fun nat bool))) (combb (fun nat (fun bool bool)) (fun _let_0 _let_0) int)), (combs nat bool bool) ) 15.81/15.92 ( (fun (fun nat bool) (fun nat (fun bool bool))), (fun (fun real (fun int (fun nat bool))) (fun real (fun int (fun nat (fun bool bool))))), (fun (fun int (fun nat bool)) (fun int (fun nat (fun bool bool)))), (combb (fun int (fun nat bool)) (fun int (fun nat (fun bool bool))) real), (combb (fun nat bool) (fun nat (fun bool bool)) int), (let ((_let_0 (fun bool bool))) (hAPP (fun bool _let_0) (fun (fun nat bool) (fun nat _let_0)) (combb bool _let_0 nat) fconj)) ) 15.81/15.92 ( (let ((_let_0 (fun int bool))) (fun (fun int (fun bool bool)) (fun _let_0 _let_0))), (let ((_let_0 (fun int bool))) (fun (fun real (fun int (fun int (fun bool bool)))) (fun real (fun int (fun _let_0 _let_0))))), (let ((_let_0 (fun int bool))) (fun (fun int (fun int (fun bool bool))) (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun int bool))) (combb (fun int (fun int (fun bool bool))) (fun int (fun _let_0 _let_0)) real)), (let ((_let_0 (fun int bool))) (combb (fun int (fun bool bool)) (fun _let_0 _let_0) int)), (combs int bool bool) ) 15.81/15.92 ( (fun real (fun int bool)), (fun real bool), (fun real bool), (collect real), (let ((_let_0 (fun int bool))) (hAPP (fun _let_0 bool) (fun (fun real _let_0) (fun real bool)) (combb _let_0 bool real) (fEx int))), (let ((_let_0 (fun int (fun int bool)))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real real))) (let ((_let_3 (real_1 int))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun int _let_4))) (let ((_let_7 (fun (fun int bool) (fun int bool)))) (let ((_let_8 (fun (fun int bool) _let_6))) (let ((_let_9 (fun _let_0 (fun int bool)))) (let ((_let_10 (fun int real))) (let ((_let_11 (fun int _let_7))) (let ((_let_12 (fun (fun int bool) _let_0))) (let ((_let_13 (fun int _let_6))) (let ((_let_14 (fun _let_13 _let_11))) (let ((_let_15 (fun _let_0 _let_13))) (let ((_let_16 (fun real (fun int bool)))) (let ((_let_17 (fun real _let_0))) (let ((_let_18 (fun real _let_12))) (let ((_let_19 (fun real _let_11))) (let ((_let_20 (fun real _let_13))) (let ((_let_21 (fun int _let_10))) (let ((_let_22 (fun _let_21 _let_0))) (let ((_let_23 (fun real _let_22))) (let ((_let_24 (fun _let_10 (fun int bool)))) (let ((_let_25 (fun real _let_24))) (let ((_let_26 (fun _let_10 _let_10))) (let ((_let_27 (fun int _let_26))) (let ((_let_28 (fun int _let_2))) (hAPP _let_17 _let_16 (hAPP _let_9 (fun _let_17 _let_16) (combb _let_0 (fun int bool) real) (hAPP (fun (fun int bool) bool) _let_9 (combb (fun int bool) bool int) (fEx int))) (hAPP (fun int bool) _let_17 (hAPP _let_18 (fun (fun int bool) _let_17) (combc real (fun int bool) _let_0) (hAPP _let_19 _let_18 (hAPP (fun _let_11 _let_12) (fun _let_19 _let_18) (combb _let_11 _let_12 real) (combc int (fun int bool) (fun int bool))) (hAPP _let_20 _let_19 (hAPP _let_14 (fun _let_20 _let_19) (combb _let_13 _let_11 real) (hAPP (fun _let_6 _let_7) _let_14 (combb _let_6 _let_7 int) (combs int bool bool))) (hAPP _let_17 _let_20 (hAPP _let_15 (fun _let_17 _let_20) (combb _let_0 _let_13 real) (hAPP _let_8 _let_15 (combb (fun int bool) _let_6 int) (hAPP (fun bool _let_4) _let_8 (combb bool _let_4 int) fconj))) (hAPP _let_21 _let_17 (hAPP _let_23 (fun _let_21 _let_17) (combc real _let_21 _let_0) (hAPP _let_25 _let_23 (hAPP (fun _let_24 _let_22) (fun _let_25 _let_23) (combb _let_24 _let_22 real) (combb _let_10 (fun int bool) int)) (hAPP _let_5 _let_25 (hAPP (fun _let_1 _let_24) (fun _let_5 _let_25) (combb _let_1 _let_24 real) (combb real bool int)) (fequal real)))) (hAPP _let_10 _let_21 (hAPP _let_27 (fun _let_10 _let_21) (combc int _let_10 _let_10) (hAPP _let_28 _let_27 (hAPP (fun _let_2 _let_26) (fun _let_28 _let_27) (combb _let_2 _let_26 int) (combb real real int)) (hAPP _let_10 _let_28 (hAPP (fun real _let_2) (fun _let_10 _let_28) (combb real _let_2 int) (inverse_divide real)) _let_3))) _let_3)))))) (hAPP (fun int bool) (fun int bool) (hAPP _let_4 _let_7 (combb bool bool int) fNot) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (fequal int)) (zero_zero int)))))))))))))))))))))))))))))))))) ) 15.81/15.92 ( (fun real (fun int bool)), (fun real bool), (fun real bool), (collect real), (let ((_let_0 (fun int bool))) (hAPP (fun _let_0 bool) (fun (fun real _let_0) (fun real bool)) (combb _let_0 bool real) (fEx int))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real real))) (let ((_let_3 (fun nat (fun nat bool)))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun (fun nat real) (fun nat real)))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun (fun nat bool) (fun nat bool)))) (let ((_let_8 (fun int real))) (let ((_let_9 (fun nat _let_4))) (let ((_let_10 (fun (fun nat bool) _let_9))) (let ((_let_11 (fun real _let_0))) (let ((_let_12 (fun int _let_2))) (let ((_let_13 (fun real (fun int (fun nat bool))))) (let ((_let_14 (fun (fun int (fun nat bool)) _let_0))) (let ((_let_15 (fun (fun nat bool) (fun int (fun nat bool))))) (let ((_let_16 (fun real _let_15))) (let ((_let_17 (fun int _let_7))) (let ((_let_18 (fun real _let_17))) (let ((_let_19 (fun int _let_9))) (let ((_let_20 (fun real _let_19))) (let ((_let_21 (fun _let_19 _let_17))) (let ((_let_22 (fun (fun int (fun nat bool)) _let_19))) (let ((_let_23 (fun int (fun nat real)))) (let ((_let_24 (fun _let_23 (fun int (fun nat bool))))) (let ((_let_25 (fun real _let_24))) (let ((_let_26 (fun (fun nat real) (fun nat bool)))) (let ((_let_27 (fun real _let_26))) (let ((_let_28 (fun int _let_5))) (hAPP _let_13 _let_11 (hAPP _let_14 (fun _let_13 _let_11) (combb (fun int (fun nat bool)) _let_0 real) (hAPP (fun (fun nat bool) bool) _let_14 (combb (fun nat bool) bool int) (fEx nat))) (hAPP (fun nat bool) _let_13 (hAPP _let_16 (fun (fun nat bool) _let_13) (combc real (fun nat bool) (fun int (fun nat bool))) (hAPP _let_18 _let_16 (hAPP (fun _let_17 _let_15) (fun _let_18 _let_16) (combb _let_17 _let_15 real) (combc int (fun nat bool) (fun nat bool))) (hAPP _let_20 _let_18 (hAPP _let_21 (fun _let_20 _let_18) (combb _let_19 _let_17 real) (hAPP (fun _let_9 _let_7) _let_21 (combb _let_9 _let_7 int) (combs nat bool bool))) (hAPP _let_13 _let_20 (hAPP _let_22 (fun _let_13 _let_20) (combb (fun int (fun nat bool)) _let_19 real) (hAPP _let_10 _let_22 (combb (fun nat bool) _let_9 int) (hAPP (fun bool _let_4) _let_10 (combb bool _let_4 nat) fconj))) (hAPP _let_23 _let_13 (hAPP _let_25 (fun _let_23 _let_13) (combc real _let_23 (fun int (fun nat bool))) (hAPP _let_27 _let_25 (hAPP (fun _let_26 _let_24) (fun _let_27 _let_25) (combb _let_26 _let_24 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_6 _let_27 (hAPP (fun _let_1 _let_26) (fun _let_6 _let_27) (combb _let_1 _let_26 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_23 (hAPP _let_28 (fun (fun nat real) _let_23) (combc int (fun nat real) (fun nat real)) (hAPP _let_12 _let_28 (hAPP (fun _let_2 _let_5) (fun _let_12 _let_28) (combb _let_2 _let_5 int) (combb real real nat)) (hAPP _let_8 _let_12 (hAPP (fun real _let_2) (fun _let_8 _let_12) (combb real _let_2 int) (inverse_divide real)) (real_1 int)))) (real_1 nat))))))) (hAPP (fun nat bool) (fun nat bool) (hAPP _let_4 _let_7 (combb bool bool nat) fNot) (hAPP nat (fun nat bool) (hAPP _let_3 _let_3 (combc nat nat bool) (fequal nat)) (zero_zero nat)))))))))))))))))))))))))))))))))) ) 15.81/15.92 ( (fun real (fun int (fun int bool))), (fun real bool), (fun real (fun int bool)), (let ((_let_0 (fun int bool))) (hAPP (fun _let_0 bool) (fun (fun real _let_0) (fun real bool)) (combb _let_0 bool real) (fEx int))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun _let_1 _let_0))) (hAPP _let_2 (fun (fun real _let_1) (fun real _let_0)) (combb _let_1 _let_0 real) (hAPP (fun _let_0 bool) _let_2 (combb _let_0 bool int) (fEx int)))))), (let ((_let_0 (fun int (fun int bool)))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real real))) (let ((_let_3 (real_1 int))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun int _let_4))) (let ((_let_7 (fun (fun int bool) (fun int bool)))) (let ((_let_8 (fun (fun int bool) _let_6))) (let ((_let_9 (fun int real))) (let ((_let_10 (fun int _let_7))) (let ((_let_11 (fun (fun int bool) _let_0))) (let ((_let_12 (fun int _let_6))) (let ((_let_13 (fun _let_12 _let_10))) (let ((_let_14 (fun _let_0 _let_12))) (let ((_let_15 (fun real _let_0))) (let ((_let_16 (fun real _let_11))) (let ((_let_17 (fun real _let_10))) (let ((_let_18 (fun real _let_12))) (let ((_let_19 (fun int _let_9))) (let ((_let_20 (fun _let_19 _let_0))) (let ((_let_21 (fun real _let_20))) (let ((_let_22 (fun _let_9 (fun int bool)))) (let ((_let_23 (fun real _let_22))) (let ((_let_24 (fun _let_9 _let_9))) (let ((_let_25 (fun int _let_24))) (let ((_let_26 (fun int _let_2))) (hAPP (fun int bool) _let_15 (hAPP _let_16 (fun (fun int bool) _let_15) (combc real (fun int bool) _let_0) (hAPP _let_17 _let_16 (hAPP (fun _let_10 _let_11) (fun _let_17 _let_16) (combb _let_10 _let_11 real) (combc int (fun int bool) (fun int bool))) (hAPP _let_18 _let_17 (hAPP _let_13 (fun _let_18 _let_17) (combb _let_12 _let_10 real) (hAPP (fun _let_6 _let_7) _let_13 (combb _let_6 _let_7 int) (combs int bool bool))) (hAPP _let_15 _let_18 (hAPP _let_14 (fun _let_15 _let_18) (combb _let_0 _let_12 real) (hAPP _let_8 _let_14 (combb (fun int bool) _let_6 int) (hAPP (fun bool _let_4) _let_8 (combb bool _let_4 int) fconj))) (hAPP _let_19 _let_15 (hAPP _let_21 (fun _let_19 _let_15) (combc real _let_19 _let_0) (hAPP _let_23 _let_21 (hAPP (fun _let_22 _let_20) (fun _let_23 _let_21) (combb _let_22 _let_20 real) (combb _let_9 (fun int bool) int)) (hAPP _let_5 _let_23 (hAPP (fun _let_1 _let_22) (fun _let_5 _let_23) (combb _let_1 _let_22 real) (combb real bool int)) (fequal real)))) (hAPP _let_9 _let_19 (hAPP _let_25 (fun _let_9 _let_19) (combc int _let_9 _let_9) (hAPP _let_26 _let_25 (hAPP (fun _let_2 _let_24) (fun _let_26 _let_25) (combb _let_2 _let_24 int) (combb real real int)) (hAPP _let_9 _let_26 (hAPP (fun real _let_2) (fun _let_9 _let_26) (combb real _let_2 int) (inverse_divide real)) _let_3))) _let_3)))))) (hAPP (fun int bool) (fun int bool) (hAPP _let_4 _let_7 (combb bool bool int) fNot) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (fequal int)) (zero_zero int))))))))))))))))))))))))))))))) ) 15.81/15.92 ( (fun real (fun int (fun int bool))), (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))), (fun real (fun int (fun int (fun bool bool)))), (let ((_let_0 (fun int (fun bool bool)))) (let ((_let_1 (fun (fun int bool) (fun int bool)))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (fun int _let_0))) (let ((_let_4 (fun _let_3 _let_2))) (hAPP _let_4 (fun (fun real _let_3) (fun real _let_2)) (combb _let_3 _let_2 real) (hAPP (fun _let_0 _let_1) _let_4 (combb _let_0 _let_1 int) (combs int bool bool)))))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun _let_0 _let_3))) (let ((_let_5 (fun int _let_3))) (let ((_let_6 (fun _let_1 _let_5))) (hAPP _let_6 (fun (fun real _let_1) (fun real _let_5)) (combb _let_1 _let_5 real) (hAPP _let_4 _let_6 (combb _let_0 _let_3 int) (hAPP (fun bool _let_2) _let_4 (combb bool _let_2 int) fconj)))))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun real _let_0))) (let ((_let_4 (fun int real))) (let ((_let_5 (fun real (fun int (fun int bool))))) (let ((_let_6 (fun int _let_4))) (let ((_let_7 (fun _let_6 (fun int (fun int bool))))) (let ((_let_8 (fun real _let_7))) (let ((_let_9 (fun _let_4 (fun int bool)))) (let ((_let_10 (fun real _let_9))) (let ((_let_11 (fun _let_4 _let_4))) (let ((_let_12 (fun int _let_11))) (let ((_let_13 (fun int _let_1))) (hAPP _let_6 _let_5 (hAPP _let_8 (fun _let_6 _let_5) (combc real _let_6 (fun int (fun int bool))) (hAPP _let_10 _let_8 (hAPP (fun _let_9 _let_7) (fun _let_10 _let_8) (combb _let_9 _let_7 real) (combb _let_4 (fun int bool) int)) (hAPP _let_3 _let_10 (hAPP (fun _let_0 _let_9) (fun _let_3 _let_10) (combb _let_0 _let_9 real) (combb real bool int)) (fequal real)))) (hAPP _let_4 _let_6 (hAPP _let_12 (fun _let_4 _let_6) (combc int _let_4 _let_4) (hAPP _let_13 _let_12 (hAPP (fun _let_1 _let_11) (fun _let_13 _let_12) (combb _let_1 _let_11 int) (combb real real int)) (hAPP _let_4 _let_13 (hAPP (fun real _let_1) (fun _let_4 _let_13) (combb real _let_1 int) (inverse_divide real)) _let_2))) _let_2)))))))))))))))) ) 15.81/15.92 ( (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun int bool))) (fun _let_0 (fun real (fun int _let_0)))), (let ((_let_0 (fun int bool))) (fun real (fun _let_0 (fun int _let_0)))), (let ((_let_0 (fun int bool))) (combc real _let_0 (fun int _let_0))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int (fun _let_0 _let_0)))) (let ((_let_2 (fun _let_0 (fun int _let_0)))) (hAPP (fun _let_1 _let_2) (fun (fun real _let_1) (fun real _let_2)) (combb _let_1 _let_2 real) (combc int _let_0 _let_0))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun int _let_3))) (let ((_let_6 (fun (fun int bool) (fun int bool)))) (let ((_let_7 (fun (fun int bool) _let_5))) (let ((_let_8 (fun int real))) (let ((_let_9 (fun int _let_6))) (let ((_let_10 (fun int _let_5))) (let ((_let_11 (fun _let_10 _let_9))) (let ((_let_12 (fun (fun int (fun int bool)) _let_10))) (let ((_let_13 (fun real (fun int (fun int bool))))) (let ((_let_14 (fun real _let_9))) (let ((_let_15 (fun real _let_10))) (let ((_let_16 (fun int _let_8))) (let ((_let_17 (fun _let_16 (fun int (fun int bool))))) (let ((_let_18 (fun real _let_17))) (let ((_let_19 (fun _let_8 (fun int bool)))) (let ((_let_20 (fun real _let_19))) (let ((_let_21 (fun _let_8 _let_8))) (let ((_let_22 (fun int _let_21))) (let ((_let_23 (fun int _let_1))) (hAPP _let_15 _let_14 (hAPP _let_11 (fun _let_15 _let_14) (combb _let_10 _let_9 real) (hAPP (fun _let_5 _let_6) _let_11 (combb _let_5 _let_6 int) (combs int bool bool))) (hAPP _let_13 _let_15 (hAPP _let_12 (fun _let_13 _let_15) (combb (fun int (fun int bool)) _let_10 real) (hAPP _let_7 _let_12 (combb (fun int bool) _let_5 int) (hAPP (fun bool _let_3) _let_7 (combb bool _let_3 int) fconj))) (hAPP _let_16 _let_13 (hAPP _let_18 (fun _let_16 _let_13) (combc real _let_16 (fun int (fun int bool))) (hAPP _let_20 _let_18 (hAPP (fun _let_19 _let_17) (fun _let_20 _let_18) (combb _let_19 _let_17 real) (combb _let_8 (fun int bool) int)) (hAPP _let_4 _let_20 (hAPP (fun _let_0 _let_19) (fun _let_4 _let_20) (combb _let_0 _let_19 real) (combb real bool int)) (fequal real)))) (hAPP _let_8 _let_16 (hAPP _let_22 (fun _let_8 _let_16) (combc int _let_8 _let_8) (hAPP _let_23 _let_22 (hAPP (fun _let_1 _let_21) (fun _let_23 _let_22) (combb _let_1 _let_21 int) (combb real real int)) (hAPP _let_8 _let_23 (hAPP (fun real _let_1) (fun _let_8 _let_23) (combb real _let_1 int) (inverse_divide real)) _let_2))) _let_2)))))))))))))))))))))))))))) ) 15.81/15.92 ( (fun real (fun int (fun int (fun bool bool)))), (let ((_let_0 (fun int bool))) (fun real (fun _let_0 (fun int _let_0)))), (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int (fun _let_0 _let_0)))) (let ((_let_2 (fun _let_0 (fun int _let_0)))) (hAPP (fun _let_1 _let_2) (fun (fun real _let_1) (fun real _let_2)) (combb _let_1 _let_2 real) (combc int _let_0 _let_0))))), (let ((_let_0 (fun int (fun bool bool)))) (let ((_let_1 (fun (fun int bool) (fun int bool)))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (fun int _let_0))) (let ((_let_4 (fun _let_3 _let_2))) (hAPP _let_4 (fun (fun real _let_3) (fun real _let_2)) (combb _let_3 _let_2 real) (hAPP (fun _let_0 _let_1) _let_4 (combb _let_0 _let_1 int) (combs int bool bool)))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun int _let_3))) (let ((_let_6 (fun (fun int bool) _let_5))) (let ((_let_7 (fun int real))) (let ((_let_8 (fun int _let_5))) (let ((_let_9 (fun (fun int (fun int bool)) _let_8))) (let ((_let_10 (fun real (fun int (fun int bool))))) (let ((_let_11 (fun real _let_8))) (let ((_let_12 (fun int _let_7))) (let ((_let_13 (fun _let_12 (fun int (fun int bool))))) (let ((_let_14 (fun real _let_13))) (let ((_let_15 (fun _let_7 (fun int bool)))) (let ((_let_16 (fun real _let_15))) (let ((_let_17 (fun _let_7 _let_7))) (let ((_let_18 (fun int _let_17))) (let ((_let_19 (fun int _let_1))) (hAPP _let_10 _let_11 (hAPP _let_9 (fun _let_10 _let_11) (combb (fun int (fun int bool)) _let_8 real) (hAPP _let_6 _let_9 (combb (fun int bool) _let_5 int) (hAPP (fun bool _let_3) _let_6 (combb bool _let_3 int) fconj))) (hAPP _let_12 _let_10 (hAPP _let_14 (fun _let_12 _let_10) (combc real _let_12 (fun int (fun int bool))) (hAPP _let_16 _let_14 (hAPP (fun _let_15 _let_13) (fun _let_16 _let_14) (combb _let_15 _let_13 real) (combb _let_7 (fun int bool) int)) (hAPP _let_4 _let_16 (hAPP (fun _let_0 _let_15) (fun _let_4 _let_16) (combb _let_0 _let_15 real) (combb real bool int)) (fequal real)))) (hAPP _let_7 _let_12 (hAPP _let_18 (fun _let_7 _let_12) (combc int _let_7 _let_7) (hAPP _let_19 _let_18 (hAPP (fun _let_1 _let_17) (fun _let_19 _let_18) (combb _let_1 _let_17 int) (combb real real int)) (hAPP _let_7 _let_19 (hAPP (fun real _let_1) (fun _let_7 _let_19) (combb real _let_1 int) (inverse_divide real)) _let_2))) _let_2))))))))))))))))))))))) ) 15.81/15.93 ( (fun int (fun int real)), (fun real (fun int (fun int (fun bool bool)))), (fun real (fun int (fun int bool))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun _let_0 _let_3))) (let ((_let_5 (fun int _let_3))) (let ((_let_6 (fun _let_1 _let_5))) (hAPP _let_6 (fun (fun real _let_1) (fun real _let_5)) (combb _let_1 _let_5 real) (hAPP _let_4 _let_6 (combb _let_0 _let_3 int) (hAPP (fun bool _let_2) _let_4 (combb bool _let_2 int) fconj)))))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun int (fun int real)) (fun int (fun int bool))))) (let ((_let_3 (fun real _let_2))) (let ((_let_4 (fun (fun int real) (fun int bool)))) (let ((_let_5 (fun real _let_4))) (hAPP _let_3 (fun (fun int (fun int real)) (fun real (fun int (fun int bool)))) (combc real (fun int (fun int real)) (fun int (fun int bool))) (hAPP _let_5 _let_3 (hAPP (fun _let_4 _let_2) (fun _let_5 _let_3) (combb _let_4 _let_2 real) (combb (fun int real) (fun int bool) int)) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_1 _let_5) (combb _let_0 _let_4 real) (combb real bool int)) (fequal real)))))))))), (let ((_let_0 (fun real real))) (let ((_let_1 (real_1 int))) (let ((_let_2 (fun int real))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun _let_2 _let_2))) (let ((_let_5 (fun int _let_4))) (let ((_let_6 (fun int _let_0))) (hAPP _let_2 _let_3 (hAPP _let_5 (fun _let_2 _let_3) (combc int _let_2 _let_2) (hAPP _let_6 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_6 _let_5) (combb _let_0 _let_4 int) (combb real real int)) (hAPP _let_2 _let_6 (hAPP (fun real _let_0) (fun _let_2 _let_6) (combb real _let_0 int) (inverse_divide real)) _let_1))) _let_1)))))))) ) 15.81/15.93 ( (fun real (fun (fun int real) (fun int bool))), (fun (fun int (fun int real)) (fun real (fun int (fun int bool)))), (fun real (fun (fun int (fun int real)) (fun int (fun int bool)))), (combc real (fun int (fun int real)) (fun int (fun int bool))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int real))) (let ((_let_2 (fun (fun int _let_1) (fun int _let_0)))) (let ((_let_3 (fun _let_1 _let_0))) (hAPP (fun _let_3 _let_2) (fun (fun real _let_3) (fun real _let_2)) (combb _let_3 _let_2 real) (combb _let_1 _let_0 int)))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun int real) (fun int bool)))) (let ((_let_3 (fun real _let_2))) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 real) (combb real bool int)) (fequal real)))))) ) 15.81/15.93 ( (fun int (fun real real)), (let ((_let_0 (fun int real))) (fun _let_0 (fun int _let_0))), (let ((_let_0 (fun int real))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun int real))) (combc int _let_0 _let_0)), (let ((_let_0 (fun real real))) (let ((_let_1 (fun (fun int real) (fun int real)))) (hAPP (fun _let_0 _let_1) (fun (fun int _let_0) (fun int _let_1)) (combb _let_0 _let_1 int) (combb real real int)))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun int real))) (let ((_let_2 (fun int _let_0))) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 int) (inverse_divide real)) (real_1 int))))) ) 15.81/15.93 ( (fun int (fun real real)), (let ((_let_0 (fun nat real))) (fun _let_0 (fun int _let_0))), (let ((_let_0 (fun nat real))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun nat real))) (combc int _let_0 _let_0)), (let ((_let_0 (fun real real))) (let ((_let_1 (fun (fun nat real) (fun nat real)))) (hAPP (fun _let_0 _let_1) (fun (fun int _let_0) (fun int _let_1)) (combb _let_0 _let_1 int) (combb real real nat)))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun int real))) (let ((_let_2 (fun int _let_0))) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 int) (inverse_divide real)) (real_1 int))))) ) 15.81/15.93 ( (fun real (fun int (fun nat bool))), (fun real bool), (fun real (fun int bool)), (let ((_let_0 (fun int bool))) (hAPP (fun _let_0 bool) (fun (fun real _let_0) (fun real bool)) (combb _let_0 bool real) (fEx int))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun nat bool))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (fun _let_2 _let_0))) (hAPP _let_3 (fun (fun real _let_2) (fun real _let_0)) (combb _let_2 _let_0 real) (hAPP (fun _let_1 bool) _let_3 (combb _let_1 bool int) (fEx nat))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat (fun nat bool)))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun (fun nat real) (fun nat real)))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun (fun nat bool) (fun nat bool)))) (let ((_let_7 (fun int real))) (let ((_let_8 (fun nat _let_3))) (let ((_let_9 (fun (fun nat bool) _let_8))) (let ((_let_10 (fun int _let_1))) (let ((_let_11 (fun real (fun int (fun nat bool))))) (let ((_let_12 (fun (fun nat bool) (fun int (fun nat bool))))) (let ((_let_13 (fun real _let_12))) (let ((_let_14 (fun int _let_6))) (let ((_let_15 (fun real _let_14))) (let ((_let_16 (fun int _let_8))) (let ((_let_17 (fun real _let_16))) (let ((_let_18 (fun _let_16 _let_14))) (let ((_let_19 (fun (fun int (fun nat bool)) _let_16))) (let ((_let_20 (fun int (fun nat real)))) (let ((_let_21 (fun _let_20 (fun int (fun nat bool))))) (let ((_let_22 (fun real _let_21))) (let ((_let_23 (fun (fun nat real) (fun nat bool)))) (let ((_let_24 (fun real _let_23))) (let ((_let_25 (fun int _let_4))) (hAPP (fun nat bool) _let_11 (hAPP _let_13 (fun (fun nat bool) _let_11) (combc real (fun nat bool) (fun int (fun nat bool))) (hAPP _let_15 _let_13 (hAPP (fun _let_14 _let_12) (fun _let_15 _let_13) (combb _let_14 _let_12 real) (combc int (fun nat bool) (fun nat bool))) (hAPP _let_17 _let_15 (hAPP _let_18 (fun _let_17 _let_15) (combb _let_16 _let_14 real) (hAPP (fun _let_8 _let_6) _let_18 (combb _let_8 _let_6 int) (combs nat bool bool))) (hAPP _let_11 _let_17 (hAPP _let_19 (fun _let_11 _let_17) (combb (fun int (fun nat bool)) _let_16 real) (hAPP _let_9 _let_19 (combb (fun nat bool) _let_8 int) (hAPP (fun bool _let_3) _let_9 (combb bool _let_3 nat) fconj))) (hAPP _let_20 _let_11 (hAPP _let_22 (fun _let_20 _let_11) (combc real _let_20 (fun int (fun nat bool))) (hAPP _let_24 _let_22 (hAPP (fun _let_23 _let_21) (fun _let_24 _let_22) (combb _let_23 _let_21 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_5 _let_24 (hAPP (fun _let_0 _let_23) (fun _let_5 _let_24) (combb _let_0 _let_23 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_20 (hAPP _let_25 (fun (fun nat real) _let_20) (combc int (fun nat real) (fun nat real)) (hAPP _let_10 _let_25 (hAPP (fun _let_1 _let_4) (fun _let_10 _let_25) (combb _let_1 _let_4 int) (combb real real nat)) (hAPP _let_7 _let_10 (hAPP (fun real _let_1) (fun _let_7 _let_10) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat))))))) (hAPP (fun nat bool) (fun nat bool) (hAPP _let_3 _let_6 (combb bool bool nat) fNot) (hAPP nat (fun nat bool) (hAPP _let_2 _let_2 (combc nat nat bool) (fequal nat)) (zero_zero nat)))))))))))))))))))))))))))))) ) 15.81/15.93 ( (fun real (fun int (fun nat bool))), (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))), (fun real (fun int (fun nat (fun bool bool)))), (let ((_let_0 (fun (fun nat bool) (fun nat bool)))) (let ((_let_1 (fun nat (fun bool bool)))) (let ((_let_2 (fun int _let_0))) (let ((_let_3 (fun int _let_1))) (let ((_let_4 (fun _let_3 _let_2))) (hAPP _let_4 (fun (fun real _let_3) (fun real _let_2)) (combb _let_3 _let_2 real) (hAPP (fun _let_1 _let_0) _let_4 (combb _let_1 _let_0 int) (combs nat bool bool)))))))), (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun nat _let_1))) (let ((_let_3 (fun _let_0 _let_2))) (let ((_let_4 (fun int _let_0))) (let ((_let_5 (fun int _let_2))) (let ((_let_6 (fun _let_4 _let_5))) (hAPP _let_6 (fun (fun real _let_4) (fun real _let_5)) (combb _let_4 _let_5 real) (hAPP _let_3 _let_6 (combb _let_0 _let_2 int) (hAPP (fun bool _let_1) _let_3 (combb bool _let_1 nat) fconj)))))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun (fun nat real) (fun nat real)))) (let ((_let_3 (fun real _let_0))) (let ((_let_4 (fun int real))) (let ((_let_5 (fun int _let_1))) (let ((_let_6 (fun real (fun int (fun nat bool))))) (let ((_let_7 (fun int (fun nat real)))) (let ((_let_8 (fun _let_7 (fun int (fun nat bool))))) (let ((_let_9 (fun real _let_8))) (let ((_let_10 (fun (fun nat real) (fun nat bool)))) (let ((_let_11 (fun real _let_10))) (let ((_let_12 (fun int _let_2))) (hAPP _let_7 _let_6 (hAPP _let_9 (fun _let_7 _let_6) (combc real _let_7 (fun int (fun nat bool))) (hAPP _let_11 _let_9 (hAPP (fun _let_10 _let_8) (fun _let_11 _let_9) (combb _let_10 _let_8 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_3 _let_11 (hAPP (fun _let_0 _let_10) (fun _let_3 _let_11) (combb _let_0 _let_10 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_7 (hAPP _let_12 (fun (fun nat real) _let_7) (combc int (fun nat real) (fun nat real)) (hAPP _let_5 _let_12 (hAPP (fun _let_1 _let_2) (fun _let_5 _let_12) (combb _let_1 _let_2 int) (combb real real nat)) (hAPP _let_4 _let_5 (hAPP (fun real _let_1) (fun _let_4 _let_5) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat)))))))))))))))) ) 15.81/15.93 ( (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun nat bool))) (fun _let_0 (fun real (fun int _let_0)))), (let ((_let_0 (fun nat bool))) (fun real (fun _let_0 (fun int _let_0)))), (let ((_let_0 (fun nat bool))) (combc real _let_0 (fun int _let_0))), (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun _let_0 (fun int _let_0)))) (let ((_let_2 (fun int (fun _let_0 _let_0)))) (hAPP (fun _let_2 _let_1) (fun (fun real _let_2) (fun real _let_1)) (combb _let_2 _let_1 real) (combc int _let_0 _let_0))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun (fun nat real) (fun nat real)))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun (fun nat bool) (fun nat bool)))) (let ((_let_6 (fun int real))) (let ((_let_7 (fun nat _let_2))) (let ((_let_8 (fun (fun nat bool) _let_7))) (let ((_let_9 (fun int _let_1))) (let ((_let_10 (fun real (fun int (fun nat bool))))) (let ((_let_11 (fun int _let_5))) (let ((_let_12 (fun real _let_11))) (let ((_let_13 (fun int _let_7))) (let ((_let_14 (fun real _let_13))) (let ((_let_15 (fun _let_13 _let_11))) (let ((_let_16 (fun (fun int (fun nat bool)) _let_13))) (let ((_let_17 (fun int (fun nat real)))) (let ((_let_18 (fun _let_17 (fun int (fun nat bool))))) (let ((_let_19 (fun real _let_18))) (let ((_let_20 (fun (fun nat real) (fun nat bool)))) (let ((_let_21 (fun real _let_20))) (let ((_let_22 (fun int _let_3))) (hAPP _let_14 _let_12 (hAPP _let_15 (fun _let_14 _let_12) (combb _let_13 _let_11 real) (hAPP (fun _let_7 _let_5) _let_15 (combb _let_7 _let_5 int) (combs nat bool bool))) (hAPP _let_10 _let_14 (hAPP _let_16 (fun _let_10 _let_14) (combb (fun int (fun nat bool)) _let_13 real) (hAPP _let_8 _let_16 (combb (fun nat bool) _let_7 int) (hAPP (fun bool _let_2) _let_8 (combb bool _let_2 nat) fconj))) (hAPP _let_17 _let_10 (hAPP _let_19 (fun _let_17 _let_10) (combc real _let_17 (fun int (fun nat bool))) (hAPP _let_21 _let_19 (hAPP (fun _let_20 _let_18) (fun _let_21 _let_19) (combb _let_20 _let_18 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_4 _let_21 (hAPP (fun _let_0 _let_20) (fun _let_4 _let_21) (combb _let_0 _let_20 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_17 (hAPP _let_22 (fun (fun nat real) _let_17) (combc int (fun nat real) (fun nat real)) (hAPP _let_9 _let_22 (hAPP (fun _let_1 _let_3) (fun _let_9 _let_22) (combb _let_1 _let_3 int) (combb real real nat)) (hAPP _let_6 _let_9 (hAPP (fun real _let_1) (fun _let_6 _let_9) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat)))))))))))))))))))))))))))) ) 15.81/15.93 ( (fun real (fun int (fun nat (fun bool bool)))), (let ((_let_0 (fun nat bool))) (fun real (fun _let_0 (fun int _let_0)))), (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun _let_0 (fun int _let_0)))) (let ((_let_2 (fun int (fun _let_0 _let_0)))) (hAPP (fun _let_2 _let_1) (fun (fun real _let_2) (fun real _let_1)) (combb _let_2 _let_1 real) (combc int _let_0 _let_0))))), (let ((_let_0 (fun (fun nat bool) (fun nat bool)))) (let ((_let_1 (fun nat (fun bool bool)))) (let ((_let_2 (fun int _let_0))) (let ((_let_3 (fun int _let_1))) (let ((_let_4 (fun _let_3 _let_2))) (hAPP _let_4 (fun (fun real _let_3) (fun real _let_2)) (combb _let_3 _let_2 real) (hAPP (fun _let_1 _let_0) _let_4 (combb _let_1 _let_0 int) (combs nat bool bool)))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun (fun nat real) (fun nat real)))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun int real))) (let ((_let_6 (fun nat _let_2))) (let ((_let_7 (fun (fun nat bool) _let_6))) (let ((_let_8 (fun int _let_1))) (let ((_let_9 (fun real (fun int (fun nat bool))))) (let ((_let_10 (fun int _let_6))) (let ((_let_11 (fun real _let_10))) (let ((_let_12 (fun (fun int (fun nat bool)) _let_10))) (let ((_let_13 (fun int (fun nat real)))) (let ((_let_14 (fun _let_13 (fun int (fun nat bool))))) (let ((_let_15 (fun real _let_14))) (let ((_let_16 (fun (fun nat real) (fun nat bool)))) (let ((_let_17 (fun real _let_16))) (let ((_let_18 (fun int _let_3))) (hAPP _let_9 _let_11 (hAPP _let_12 (fun _let_9 _let_11) (combb (fun int (fun nat bool)) _let_10 real) (hAPP _let_7 _let_12 (combb (fun nat bool) _let_6 int) (hAPP (fun bool _let_2) _let_7 (combb bool _let_2 nat) fconj))) (hAPP _let_13 _let_9 (hAPP _let_15 (fun _let_13 _let_9) (combc real _let_13 (fun int (fun nat bool))) (hAPP _let_17 _let_15 (hAPP (fun _let_16 _let_14) (fun _let_17 _let_15) (combb _let_16 _let_14 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_4 _let_17 (hAPP (fun _let_0 _let_16) (fun _let_4 _let_17) (combb _let_0 _let_16 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_13 (hAPP _let_18 (fun (fun nat real) _let_13) (combc int (fun nat real) (fun nat real)) (hAPP _let_8 _let_18 (hAPP (fun _let_1 _let_3) (fun _let_8 _let_18) (combb _let_1 _let_3 int) (combb real real nat)) (hAPP _let_5 _let_8 (hAPP (fun real _let_1) (fun _let_5 _let_8) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat))))))))))))))))))))))) ) 15.81/15.93 ( (fun int (fun nat real)), (fun real (fun int (fun nat (fun bool bool)))), (fun real (fun int (fun nat bool))), (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun nat _let_1))) (let ((_let_3 (fun _let_0 _let_2))) (let ((_let_4 (fun int _let_0))) (let ((_let_5 (fun int _let_2))) (let ((_let_6 (fun _let_4 _let_5))) (hAPP _let_6 (fun (fun real _let_4) (fun real _let_5)) (combb _let_4 _let_5 real) (hAPP _let_3 _let_6 (combb _let_0 _let_2 int) (hAPP (fun bool _let_1) _let_3 (combb bool _let_1 nat) fconj)))))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun int (fun nat real)) (fun int (fun nat bool))))) (let ((_let_3 (fun real _let_2))) (let ((_let_4 (fun (fun nat real) (fun nat bool)))) (let ((_let_5 (fun real _let_4))) (hAPP _let_3 (fun (fun int (fun nat real)) (fun real (fun int (fun nat bool)))) (combc real (fun int (fun nat real)) (fun int (fun nat bool))) (hAPP _let_5 _let_3 (hAPP (fun _let_4 _let_2) (fun _let_5 _let_3) (combb _let_4 _let_2 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_1 _let_5) (combb _let_0 _let_4 real) (combb real bool nat)) (fequal real)))))))))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun (fun nat real) (fun nat real)))) (let ((_let_2 (fun int real))) (let ((_let_3 (fun int _let_0))) (let ((_let_4 (fun int (fun nat real)))) (let ((_let_5 (fun int _let_1))) (hAPP (fun nat real) _let_4 (hAPP _let_5 (fun (fun nat real) _let_4) (combc int (fun nat real) (fun nat real)) (hAPP _let_3 _let_5 (hAPP (fun _let_0 _let_1) (fun _let_3 _let_5) (combb _let_0 _let_1 int) (combb real real nat)) (hAPP _let_2 _let_3 (hAPP (fun real _let_0) (fun _let_2 _let_3) (combb real _let_0 int) (inverse_divide real)) (real_1 int)))) (real_1 nat)))))))) ) 15.81/15.93 ( (fun real (fun (fun nat real) (fun nat bool))), (fun (fun int (fun nat real)) (fun real (fun int (fun nat bool)))), (fun real (fun (fun int (fun nat real)) (fun int (fun nat bool)))), (combc real (fun int (fun nat real)) (fun int (fun nat bool))), (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun (fun int _let_1) (fun int _let_0)))) (let ((_let_3 (fun _let_1 _let_0))) (hAPP (fun _let_3 _let_2) (fun (fun real _let_3) (fun real _let_2)) (combb _let_3 _let_2 real) (combb _let_1 _let_0 int)))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun nat real) (fun nat bool)))) (let ((_let_3 (fun real _let_2))) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 real) (combb real bool nat)) (fequal real)))))) ) 15.81/15.93 ) 15.81/15.93 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_124093 $$unsorted) (BOUND_VARIABLE_124094 $$unsorted) (BOUND_VARIABLE_124095 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_124094))) (or (not (preorder X_a)) (not (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_124095))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_124095) BOUND_VARIABLE_124093))) (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_124093)))))) ) 15.81/15.93 ( int, (one_one int), (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.81/15.93 ( int, pls, (zero_zero int), min_1 ) 15.81/15.93 ( int, min_1, min_1, min_1 ) 15.81/15.93 ( int, s, min_1, pls ) 15.81/15.93 ( int, t, (zero_zero int), (one_one int) ) 15.81/15.93 ( real, pi, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.81/15.93 ( real, pi, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.81/15.93 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.81/15.93 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real), skv_5 ) 15.81/15.93 ) 15.81/15.93 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_124175 $$unsorted)) (or (not (ordere142940540dd_abs X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_124175)) (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_124175)))) ) 15.81/15.93 ( int, (one_one int) ) 15.81/15.93 ( int, pls ) 15.81/15.93 ( int, min_1 ) 15.81/15.93 ( real, (one_one real) ) 15.81/15.93 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.81/15.93 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.81/15.93 ( complex, (one_one complex) ) 15.81/15.93 ( complex, ii ) 15.81/15.93 ) 15.81/15.93 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_124196 $$unsorted) (BOUND_VARIABLE_124197 $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (linorder X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_124196) BOUND_VARIABLE_124197))) (= (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_124196) BOUND_VARIABLE_124197))) (= (ti X_a BOUND_VARIABLE_124196) (ti X_a BOUND_VARIABLE_124197))))) ) 15.81/15.93 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.81/15.93 ( int, (one_one int), t ) 15.81/15.93 ( int, (zero_zero int), (one_one int) ) 15.81/15.93 ( int, (zero_zero int), min_1 ) 15.81/15.93 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.81/15.93 ( int, (zero_zero int), s ) 15.81/15.93 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.81/15.93 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.81/15.93 ( int, (zero_zero int), skv_4 ) 15.81/15.93 ( int, (zero_zero int), skv_10 ) 15.81/15.93 ( int, pls, (one_one int) ) 15.81/15.93 ( int, pls, pls ) 15.81/15.93 ( int, pls, min_1 ) 15.81/15.93 ( int, pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.81/15.93 ( int, min_1, pls ) 15.81/15.93 ( int, min_1, min_1 ) 15.81/15.93 ( int, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.81/15.93 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.81/15.93 ( int, skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.81/15.93 ( int, skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.81/15.93 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.81/15.93 ( real, (zero_zero real), pi ) 15.81/15.93 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.81/15.93 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.81/15.93 ( real, (zero_zero real), skv_2 ) 15.81/15.93 ( real, (zero_zero real), skv_3 ) 15.81/15.93 ( real, (zero_zero real), skv_5 ) 15.81/15.93 ( real, (zero_zero real), skv_7 ) 15.81/15.93 ( real, (zero_zero real), skv_8 ) 15.81/15.93 ( real, (zero_zero real), skv_9 ) 15.81/15.93 ( real, (zero_zero real), skv_12 ) 15.81/15.93 ( real, pi, (zero_zero real) ) 15.81/15.93 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.81/15.93 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.81/15.93 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.81/15.93 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 15.81/15.93 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.81/15.93 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 15.81/15.93 ( real, skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.81/15.93 ) 15.81/15.93 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_124227 $$unsorted)) (let ((_let_0 (fun nat X_a))) (or (not (t2_space X_a)) (not (comm_monoid_add X_a)) (not (hBOOL (hAPP _let_0 bool (summable X_a) BOUND_VARIABLE_124227))) (hBOOL (hAPP X_a bool (hAPP _let_0 (fun X_a bool) (sums X_a) BOUND_VARIABLE_124227) (hAPP _let_0 X_a (suminf X_a) BOUND_VARIABLE_124227))))) ) 15.81/15.93 ( real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (hAPP real _let_1 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc))) ) 15.81/15.93 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat (fun nat nat)))) (let ((_let_3 (fun nat _let_0))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun _let_1 _let_3))) (let ((_let_6 (combb real _let_0 nat))) (let ((_let_7 (combc nat nat nat))) (hAPP _let_1 _let_1 (hAPP _let_3 (fun _let_1 _let_1) (combs nat real real) (hAPP _let_1 _let_3 (hAPP _let_4 _let_5 _let_6 (inverse_divide real)) (hAPP real _let_1 (hAPP _let_3 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_3 (hAPP _let_4 _let_5 _let_6 (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) (one_one real)))) (hAPP (fun nat nat) _let_1 (hAPP _let_1 (fun (fun nat nat) _let_1) (combb nat real nat) (real_1 nat)) (hAPP nat (fun nat nat) (hAPP _let_2 _let_2 _let_7 (hAPP (fun nat nat) _let_2 (hAPP _let_2 (fun (fun nat nat) _let_2) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_2 _let_2 _let_7 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))))))))))) ) 15.81/15.93 ) 15.81/15.93 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_124267 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_124267))) (or (not (linord219039673up_add X_a)) (= (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_124267))) (hBOOL (hAPP X_a bool _let_0 (zero_zero X_a)))))) ) 15.81/15.93 ( int, (one_one int) ) 15.81/15.93 ( int, (zero_zero int) ) 15.81/15.93 ( int, pls ) 15.81/15.93 ( int, min_1 ) 15.81/15.93 ( real, (one_one real) ) 15.81/15.93 ( real, (zero_zero real) ) 15.81/15.93 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.81/15.93 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.81/15.93 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.81/15.93 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.81/15.93 ( real, skv_5 ) 15.81/15.93 ( complex, (one_one complex) ) 15.81/15.93 ( complex, ii ) 15.81/15.93 ) 15.81/15.93 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_0 (product_snd X_a X_b))) (= _let_0 (ti (fun (product_prod X_a X_b) X_b) _let_0))) ) 15.81/15.93 ( nat, nat ) 15.81/15.93 ( int, int ) 15.81/15.93 ( int, (product_prod int int) ) 15.81/15.93 ( (product_prod nat nat), (product_prod nat nat) ) 15.81/15.93 ( real, real ) 15.81/15.93 ( (product_prod int int), (product_prod int int) ) 15.81/15.93 ( quickcheck_code_int, quickcheck_code_int ) 15.81/15.93 ( code_code_numeral, code_code_numeral ) 15.81/15.93 ) 15.81/15.93 (instantiation (forall ((N_1 $$unsorted) (M $$unsorted) (R_4 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (real_1 int))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) (hAPP int real _let_1 M)) R_4))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) R_4) (hAPP real real (hAPP real (fun real real) (plus_plus real) (hAPP int real _let_1 N_1)) (one_one real))))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) M) N_1))))) ) 15.81/15.93 ( (one_one int), (zero_zero int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.81/15.93 ( (zero_zero int), (zero_zero int), pi ) 15.81/15.93 ) 15.81/15.93 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_124293 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP X_a int (archim2085082626_floor X_a) BOUND_VARIABLE_124293)) (one_one int))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_124293) (hAPP int X_a (number_number_of X_a) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 15.81/15.93 ( nat, (zero_zero nat) ) 15.81/15.93 ( int, (one_one int) ) 15.81/15.93 ( int, pls ) 15.81/15.93 ( int, min_1 ) 15.81/15.93 ( int, s ) 15.81/15.93 ( int, t ) 15.81/15.93 ( int, skv_4 ) 15.81/15.93 ( int, skv_10 ) 15.81/15.93 ( real, (one_one real) ) 15.81/15.93 ( real, (zero_zero real) ) 15.81/15.93 ( real, pi ) 15.81/15.93 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.81/15.93 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.81/15.93 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.81/15.93 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 15.81/15.93 ) 15.81/15.93 (instantiation (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (= (and (= (zero_zero real) B_1) (= (one_one real) A_2)) (= (one_one complex) (hAPP real complex (hAPP real (fun real complex) complex_1 A_2) B_1))) ) 15.81/15.93 ( (one_one real), (zero_zero real) ) 15.81/15.93 ( (zero_zero real), (one_one real) ) 15.81/15.93 ( (zero_zero real), (zero_zero real) ) 15.81/15.93 ) 15.81/15.93 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_124386 $$unsorted) (BOUND_VARIABLE_124387 $$unsorted) (BOUND_VARIABLE_124388 $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (dense_linorder X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_124387) BOUND_VARIABLE_124388))) (not (forall ((W_2 $$unsorted)) (let ((_let_1 (ord_less X_a))) (or (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_124387) W_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 W_2) BOUND_VARIABLE_124388))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) W_2) BOUND_VARIABLE_124386)))) )) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_124388) BOUND_VARIABLE_124386)))) ) 15.81/15.93 ( int, (one_one int), min_1, pls ) 15.81/15.93 ( int, pls, min_1, min_1 ) 15.81/15.93 ( int, min_1, pls, min_1 ) 15.81/15.93 ( int, s, pls, pls ) 15.81/15.93 ( int, t, pls, (one_one int) ) 15.81/15.93 ( real, pi, pi, (zero_zero real) ) 15.81/15.93 ( real, pi, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.81/15.93 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.81/15.93 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.81/15.93 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 15.81/15.93 ) 15.81/15.93 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_124480 $$unsorted) (BOUND_VARIABLE_124481 $$unsorted) (BOUND_VARIABLE_124482 $$unsorted) (BOUND_VARIABLE_124483 $$unsorted)) (let ((_let_0 (hAPP X_b (fun X_b bool) (ord_less X_b) BOUND_VARIABLE_124480))) (or (not (order X_a)) (not (order X_b)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_124482) BOUND_VARIABLE_124483))) (not (hBOOL (hAPP X_b bool _let_0 (hAPP X_a X_b BOUND_VARIABLE_124481 BOUND_VARIABLE_124482)))) (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) Y) X))) (hBOOL (hAPP X_b bool (hAPP X_b (fun X_b bool) (ord_less_eq X_b) (hAPP X_a X_b BOUND_VARIABLE_124481 Y)) (hAPP X_a X_b BOUND_VARIABLE_124481 X)))) )) (hBOOL (hAPP X_b bool _let_0 (hAPP X_a X_b BOUND_VARIABLE_124481 BOUND_VARIABLE_124483))))) ) 15.81/15.93 ( nat, real, (zero_zero nat), natceiling, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.81/15.93 ( int, int, (one_one int), (fact_fact int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.81/15.93 ( int, int, pls, (uminus_uminus int), min_1, min_1 ) 15.81/15.93 ( int, int, min_1, (let ((_let_0 (fun int int))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m))), (one_one int), t ) 15.81/15.93 ( int, int, s, bit1, pls, s ) 15.81/15.93 ( int, int, t, (uminus_uminus int), pls, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.81/15.93 ( int, int, skv_4, pred, pls, (hAPP int int (number_number_of int) pls) ) 15.81/15.93 ( int, int, skv_10, (number_number_of int), pls, min_1 ) 15.81/15.93 ( real, int, pi, (number_number_of real), min_1, pls ) 15.81/15.93 ( real, int, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (real_1 int), (zero_zero int), (one_one int) ) 15.81/15.93 ( real, real, (one_one real), arctan, (zero_zero real), skv_3 ) 15.81/15.93 ( real, real, (zero_zero real), cos, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.81/15.93 ( real, real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.81/15.93 ( real, real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (inverse_inverse real), (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.81/15.93 ( real, real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), sqrt, (zero_zero real), pi ) 15.81/15.93 ) 15.81/15.93 (instantiation (forall ((X_2 $$unsorted) (N $$unsorted)) (let ((_let_0 (zero_zero real))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N))) (= (= _let_0 (hAPP real real (hAPP nat (fun real real) root N) X_2)) (= _let_0 X_2)))) ) 15.81/15.93 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.81/15.93 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.81/15.93 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.81/15.93 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.81/15.93 ) 15.83/15.93 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (inverse_divide real))) (let ((_let_2 (fun nat real))) (let ((_let_3 (power_power real))) (let ((_let_4 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_5 (hAPP complex real im X_1))) (let ((_let_6 (hAPP real real (hAPP real _let_0 (plus_plus real) (hAPP nat real (hAPP real _let_2 _let_3 (hAPP complex real re X_1)) _let_4)) (hAPP nat real (hAPP real _let_2 _let_3 _let_5) _let_4)))) (= (hAPP real complex (hAPP real (fun real complex) complex_1 (hAPP real real (hAPP real _let_0 _let_1 (hAPP complex real re X_1)) _let_6)) (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real (uminus_uminus real) _let_5)) _let_6)) (hAPP complex complex (inverse_inverse complex) X_1))))))))) ) 15.83/15.93 ( (one_one complex) ) 15.83/15.93 ( ii ) 15.83/15.93 ( (zero_zero complex) ) 15.83/15.93 ) 15.83/15.93 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_0 (tendsto X_a X_b))) (or (not (topological_space X_b)) (= _let_0 (ti (fun (fun X_a X_b) (fun X_b (fun (filter X_a) bool))) _let_0)))) ) 15.83/15.93 ( nat, real ) 15.83/15.93 ( real, real ) 15.83/15.93 ) 15.83/15.93 (instantiation (forall ((X_2 $$unsorted)) (or (= (zero_zero real) (hAPP real real cos X_2)) (hBOOL (hAPP real bool (hAPP (fun real real) (fun real bool) (isCont real real) tan) X_2))) ) 15.83/15.93 ( (zero_zero real) ) 15.83/15.93 ( pi ) 15.83/15.93 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/15.93 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.83/15.93 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.83/15.93 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.83/15.93 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.83/15.93 ) 15.83/15.93 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_124613 $$unsorted) (BOUND_VARIABLE_124614 $$unsorted) (BOUND_VARIABLE_124615 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (zero_zero X_a))) (let ((_let_3 (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_124613))) (let ((_let_4 (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_124615))) (let ((_let_5 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) _let_2) _let_4)))) (let ((_let_6 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_124613) _let_4))) (let ((_let_7 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) _let_4) _let_2)))) (or (not (number X_a)) (not (linord1117847801e_zero X_a)) (= (hBOOL (hAPP X_a bool _let_3 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_124614) _let_4))) (and (or (not _let_5) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_6) BOUND_VARIABLE_124614))) (or _let_5 (and (or _let_7 (hBOOL (hAPP X_a bool _let_3 _let_2))) (or (not _let_7) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_124614) _let_6)))))))))))))))) ) 15.83/15.93 ( real, (zero_zero real), pi, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.83/15.93 ) 15.83/15.93 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_124688 $$unsorted) (BOUND_VARIABLE_124689 $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_atMost nat))) (let ((_let_2 (hAPP (fun nat X_a) (fun _let_0 X_a) (big_co1399186613setsum nat X_a) BOUND_VARIABLE_124688))) (let ((_let_3 (hAPP nat nat suc BOUND_VARIABLE_124689))) (or (not (comm_monoid_add X_a)) (= (hAPP _let_0 X_a _let_2 (hAPP nat _let_0 _let_1 _let_3)) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (hAPP _let_0 X_a _let_2 (hAPP nat _let_0 _let_1 BOUND_VARIABLE_124689))) (hAPP nat X_a BOUND_VARIABLE_124688 _let_3)))))))) ) 15.83/15.93 ( bool, (even_odd_even nat), (zero_zero nat) ) 15.83/15.93 ( bool, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), (hAPP nat nat suc (zero_zero nat)) ) 15.83/15.93 ( bool, prime, (zero_zero nat) ) 15.83/15.93 ( bool, prime, (hAPP nat nat suc (zero_zero nat)) ) 15.83/15.93 ( nat, suc, (zero_zero nat) ) 15.83/15.93 ( nat, suc, (hAPP nat nat suc (zero_zero nat)) ) 15.83/15.93 ( nat, (fact_fact nat), (zero_zero nat) ) 15.83/15.93 ( nat, (hAPP nat (fun nat nat) (plus_plus nat) (one_one nat)), (zero_zero nat) ) 15.83/15.93 ( int, (semiring_1_of_nat int), (zero_zero nat) ) 15.83/15.93 ( int, (semiring_1_of_nat int), (hAPP nat nat suc (zero_zero nat)) ) 15.83/15.93 ( int, (semiring_1_of_nat int), (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 15.83/15.93 ( int, (hAPP int (fun nat int) (power_power int) s), (hAPP nat nat suc (zero_zero nat)) ) 15.83/15.93 ( int, (hAPP int (fun nat int) (power_power int) s1), (hAPP nat nat suc (zero_zero nat)) ) 15.83/15.93 ( int, (hAPP int (fun nat int) (power_power int) skv_14), (hAPP nat nat suc (zero_zero nat)) ) 15.83/15.93 ( (fun int int), (hAPP (fun int (fun nat int)) (fun nat (fun int int)) (combc int nat int) (power_power int)), (hAPP nat nat suc (zero_zero nat)) ) 15.83/15.93 ( (fun nat nat), (plus_plus nat), (zero_zero nat) ) 15.83/15.93 ( (fun nat nat), (let ((_let_0 (fun nat (fun nat nat)))) (hAPP _let_0 _let_0 (combc nat nat nat) (times_times nat))), (hAPP nat nat suc (zero_zero nat)) ) 15.83/15.93 ( (fun nat nat), (let ((_let_0 (fun nat (fun nat nat)))) (let ((_let_1 (combc nat nat nat))) (hAPP _let_0 _let_0 _let_1 (hAPP (fun nat nat) _let_0 (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_0 _let_0 _let_1 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))), (zero_zero nat) ) 15.83/15.93 ( real, (real_1 nat), (zero_zero nat) ) 15.83/15.93 ( (fun real real), root, (hAPP nat nat suc (zero_zero nat)) ) 15.83/15.93 ( complex, (hAPP complex (fun nat complex) (power_power complex) ii), (hAPP nat nat suc (zero_zero nat)) ) 15.83/15.93 ) 15.83/15.93 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_124711 $$unsorted) (BOUND_VARIABLE_124712 $$unsorted)) (let ((_let_0 (of_real X_a))) (or (not (real_algebra_1 X_a)) (= (= (hAPP real X_a _let_0 BOUND_VARIABLE_124712) (hAPP real X_a _let_0 BOUND_VARIABLE_124711)) (= BOUND_VARIABLE_124711 BOUND_VARIABLE_124712)))) ) 15.83/15.93 ( complex, pi, (hAPP real real (uminus_uminus real) (one_one real)) ) 15.83/15.93 ( complex, (hAPP int real (number_number_of real) min_1), pi ) 15.83/15.93 ( complex, (hAPP int real (number_number_of real) min_1), (hAPP int real (number_number_of real) min_1) ) 15.83/15.93 ( complex, (hAPP int real (number_number_of real) min_1), (hAPP real real (uminus_uminus real) (one_one real)) ) 15.83/15.93 ( complex, (hAPP real real (uminus_uminus real) (one_one real)), (hAPP int real (number_number_of real) min_1) ) 15.83/15.93 ) 15.83/15.93 (instantiation (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (hAPP int (fun int bool) (ord_less int) (zero_zero int)))) (or (not (hBOOL (hAPP int bool _let_0 B_1))) (= (hBOOL (hAPP int bool _let_0 A_2)) (hBOOL (hAPP rat bool (hAPP rat (fun rat bool) (ord_less rat) (zero_zero rat)) (hAPP int rat (hAPP int (fun int rat) fract A_2) B_1)))))) ) 15.83/15.93 ( (one_one int), (one_one int) ) 15.83/15.93 ( (zero_zero int), (one_one int) ) 15.83/15.93 ) 15.83/15.93 (instantiation (forall ((K_4 $$unsorted) (L_4 $$unsorted)) (let ((_let_0 (ring_1_of_int rat))) (= (hAPP int rat (hAPP int (fun int rat) fract K_4) L_4) (hAPP rat rat (hAPP rat (fun rat rat) (inverse_divide rat) (hAPP int rat _let_0 K_4)) (hAPP int rat _let_0 L_4)))) ) 15.83/15.93 ( (one_one int), (one_one int) ) 15.83/15.93 ( (zero_zero int), (one_one int) ) 15.83/15.93 ) 15.83/15.93 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_124797 $$unsorted) (BOUND_VARIABLE_124798 $$unsorted)) (let ((_let_0 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_1 (hAPP int nat (number_number_of nat) _let_0))) (let ((_let_2 (fun nat X_a))) (let ((_let_3 (power_power X_a))) (let ((_let_4 (fun X_a X_a))) (let ((_let_5 (plus_plus X_a))) (let ((_let_6 (times_times X_a))) (or (not (number_semiring X_a)) (= (hAPP X_a X_a (hAPP X_a _let_4 _let_5 (hAPP X_a X_a (hAPP X_a _let_4 _let_5 (hAPP nat X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_124797) _let_1)) (hAPP nat X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_124798) _let_1))) (hAPP X_a X_a (hAPP X_a _let_4 _let_6 (hAPP X_a X_a (hAPP X_a _let_4 _let_6 (hAPP int X_a (number_number_of X_a) _let_0)) BOUND_VARIABLE_124797)) BOUND_VARIABLE_124798)) (hAPP nat X_a (hAPP X_a _let_2 _let_3 (hAPP X_a X_a (hAPP X_a _let_4 _let_5 BOUND_VARIABLE_124797) BOUND_VARIABLE_124798)) _let_1)))))))))) ) 15.83/15.93 ( nat, (one_one nat), (one_one nat) ) 15.83/15.93 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 15.83/15.93 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 15.83/15.93 ( complex, (hAPP real complex (of_real complex) pi), ii ) 15.83/15.93 ) 15.83/15.93 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_124842 $$unsorted) (BOUND_VARIABLE_124843 $$unsorted) (BOUND_VARIABLE_124844 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (fun X_a X_a))) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_124844) (zero_zero X_a)))) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_124842) (hAPP X_a X_a (hAPP X_a _let_2 (inverse_divide X_a) BOUND_VARIABLE_124843) BOUND_VARIABLE_124844))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_124843) (hAPP X_a X_a (hAPP X_a _let_2 (times_times X_a) BOUND_VARIABLE_124842) BOUND_VARIABLE_124844)))))))) ) 15.83/15.93 ( real, (zero_zero real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/15.93 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.83/15.93 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.83/15.93 ) 15.83/15.93 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (sgn_sgn X_a))) (or (not (sgn_if X_a)) (= _let_0 (ti (fun X_a X_a) _let_0)))) ) 15.83/15.93 ( bool ) 15.83/15.93 ( nat ) 15.83/15.93 ( int ) 15.83/15.93 ( (fun int bool) ) 15.83/15.93 ( (fun int (fun int bool)) ) 15.83/15.93 ( (fun int int) ) 15.83/15.93 ( (fun nat bool) ) 15.83/15.93 ( real ) 15.83/15.93 ( (fun real bool) ) 15.83/15.93 ( (fun real real) ) 15.83/15.93 ( rat ) 15.83/15.93 ( complex ) 15.83/15.93 ( (fun nat real) ) 15.83/15.93 ( (product_prod int int) ) 15.83/15.93 ( code_code_numeral ) 15.83/15.93 ( (fun int (fun int (fun int bool))) ) 15.83/15.93 ( (fun (product_prod int int) bool) ) 15.83/15.93 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 15.83/15.93 ( (fun (product_prod int int) int) ) 15.83/15.93 ( (fun int real) ) 15.83/15.93 ) 15.83/15.93 (instantiation (forall ((A_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool prime A_1))) (hBOOL (hAPP int bool zprime (hAPP nat int (semiring_1_of_nat int) A_1)))) ) 15.83/15.93 ( (zero_zero nat) ) 15.83/15.93 ( (hAPP nat nat suc (zero_zero nat)) ) 15.83/15.93 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.83/15.93 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/15.93 ) 15.83/15.93 (instantiation (forall ((Ma $$unsorted) (N $$unsorted)) (let ((_let_0 (zero_zero nat))) (let ((_let_1 (hAPP nat nat suc _let_0))) (= (= _let_1 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) Ma) N)) (or (and (= _let_1 N) (= _let_0 Ma)) (and (= _let_0 N) (= _let_1 Ma)))))) ) 15.83/15.93 ( (one_one nat), (one_one nat) ) 15.83/15.93 ) 15.83/15.93 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_124950 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (or (not (number_ring X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) (hAPP int X_a (number_number_of X_a) (hAPP int int bit0 (hAPP int int bit1 pls)))) BOUND_VARIABLE_124950) (hAPP X_a X_a (hAPP X_a _let_0 (plus_plus X_a) BOUND_VARIABLE_124950) BOUND_VARIABLE_124950)))) ) 15.83/15.93 ( nat, (one_one nat) ) 15.83/15.93 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.83/15.93 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/15.93 ( real, pi ) 15.83/15.94 ( real, (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.83/15.94 ( complex, (hAPP real complex (of_real complex) pi) ) 15.83/15.94 ) 15.83/15.94 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_124967 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (let ((_let_1 (hAPP X_a (fun X_a bool) (ord_less X_a) _let_0))) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool _let_1 (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_124967)))) (= _let_0 (ti X_a BOUND_VARIABLE_124967)) (hBOOL (hAPP X_a bool _let_1 BOUND_VARIABLE_124967))))) ) 15.83/15.94 ( bool, fFalse ) 15.83/15.94 ( bool, fTrue ) 15.83/15.94 ( int, pls ) 15.83/15.94 ( int, min_1 ) 15.83/15.94 ( int, s ) 15.83/15.94 ( int, m ) 15.83/15.94 ( int, s1 ) 15.83/15.94 ( int, t ) 15.83/15.94 ( (fun int bool), nat_neg ) 15.83/15.94 ( (fun int bool), zprime ) 15.83/15.94 ( (fun int bool), zEven ) 15.83/15.94 ( (fun int bool), zOdd ) 15.83/15.94 ( (fun int bool), (even_odd_even int) ) 15.83/15.94 ( (fun int bool), twoSqu1091635170sum2sq ) 15.83/15.94 ( (fun int bool), nat_is_nat ) 15.83/15.94 ( (fun int (fun int bool)), norRRset ) 15.83/15.94 ( (fun int (fun int bool)), quadRes ) 15.83/15.94 ( (fun int (fun int bool)), sRStar ) 15.83/15.94 ( (fun int (fun int bool)), d22set ) 15.83/15.94 ( (fun int (fun int bool)), sr ) 15.83/15.94 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 15.83/15.94 ( (fun int int), zfact ) 15.83/15.94 ( (fun int int), bit0 ) 15.83/15.94 ( (fun int int), bit1 ) 15.83/15.94 ( (fun int int), (fact_fact int) ) 15.83/15.94 ( (fun int int), pred ) 15.83/15.94 ( (fun int int), succ ) 15.83/15.94 ( (fun nat bool), (even_odd_even nat) ) 15.83/15.94 ( (fun nat bool), prime ) 15.83/15.94 ( (fun nat nat), suc ) 15.83/15.94 ( (fun nat nat), (fact_fact nat) ) 15.83/15.94 ( (fun nat nat), fact ) 15.83/15.94 ( (fun nat nat), nat_size ) 15.83/15.94 ( (fun nat nat), (size_size nat) ) 15.83/15.94 ( (fun (product_prod nat nat) bool), pred_nat ) 15.83/15.94 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 15.83/15.94 ( real, (zero_zero real) ) 15.83/15.94 ( real, pi ) 15.83/15.94 ( (fun real real), ln ) 15.83/15.94 ( (fun real real), cos ) 15.83/15.94 ( (fun real real), sqrt ) 15.83/15.94 ( (fun real real), sin ) 15.83/15.94 ( (fun real real), arccos ) 15.83/15.94 ( (fun real real), arcsin ) 15.83/15.94 ( (fun real real), tan ) 15.83/15.94 ( (fun real real), arctan ) 15.83/15.94 ( (fun nat (fun nat bool)), coprime ) 15.83/15.94 ( complex, ii ) 15.83/15.94 ( (fun nat real), (real_1 nat) ) 15.83/15.94 ( (fun nat real), sin_coeff ) 15.83/15.94 ( (fun nat real), cos_coeff ) 15.83/15.94 ( (filter nat), sequentially ) 15.83/15.94 ( (fun int (fun int int)), (gcd_gcd int) ) 15.83/15.94 ( (fun int (fun int int)), legendre ) 15.83/15.94 ( (fun int (fun int int)), legacy_zgcd ) 15.83/15.94 ( (fun int (fun int int)), standardRes ) 15.83/15.94 ( (fun int (fun int int)), nat_tsub ) 15.83/15.94 ( (fun int (fun int int)), multInv ) 15.83/15.94 ( (fun int (fun int int)), z3mod ) 15.83/15.94 ( (fun int (fun int int)), z3div ) 15.83/15.94 ( (fun int (fun int int)), int_gcd ) 15.83/15.94 ( (fun int (fun int int)), int_lcm ) 15.83/15.94 ( (fun int (fun int int)), inv ) 15.83/15.94 ( (fun complex complex), expi ) 15.83/15.94 ( (fun complex complex), cnj ) 15.83/15.94 ( (fun real complex), cis ) 15.83/15.94 ( (fun int nat), nat_1 ) 15.83/15.94 ( (fun int nat), phi ) 15.83/15.94 ( (fun (fun int bool) bool), nat_nat_set ) 15.83/15.94 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 15.83/15.94 ( (fun nat (fun nat nat)), nat_gcd ) 15.83/15.94 ( (fun nat (fun nat nat)), nat_lcm ) 15.83/15.94 ( (fun (fun int bool) int), (the int) ) 15.83/15.94 ( (fun complex real), re ) 15.83/15.94 ( (fun complex real), im ) 15.83/15.94 ( (fun complex real), arg ) 15.83/15.94 ( (fun bool bool), fNot ) 15.83/15.94 ( (fun nat (fun real real)), root ) 15.83/15.94 ( (fun real (fun real real)), log ) 15.83/15.94 ( (fun real (fun real real)), powr ) 15.83/15.94 ( (fun bool (fun bool bool)), fimplies ) 15.83/15.94 ( (fun bool (fun bool bool)), fconj ) 15.83/15.94 ( (fun bool (fun bool bool)), fdisj ) 15.83/15.94 ( (fun int (fun int (product_prod int int))), negDivAlg ) 15.83/15.94 ( (fun int (fun int (product_prod int int))), posDivAlg ) 15.83/15.94 ( (fun int (fun int (product_prod int int))), divmod_int ) 15.83/15.94 ( (fun int (fun int (product_prod int int))), pdivmod ) 15.83/15.94 ( (fun int (fun int (product_prod int int))), norm_frac ) 15.83/15.94 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 15.83/15.94 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 15.83/15.94 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 15.83/15.94 ( (fun int (fun int (fun int bool))), zcong ) 15.83/15.94 ( (fun int (fun int (fun int bool))), zcongm ) 15.83/15.94 ( (fun int (fun int (fun int bool))), noXRRset ) 15.83/15.94 ( (fun int (fun int (fun int bool))), bnorRset ) 15.83/15.94 ( (fun int (fun int (fun int bool))), wset ) 15.83/15.94 ( (fun (product_prod int int) bool), frac_1 ) 15.83/15.94 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 15.83/15.94 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 15.83/15.94 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 15.83/15.94 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 15.83/15.94 ( (fun (fun nat rat) bool), vanishes ) 15.83/15.94 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 15.83/15.94 ( (fun code_code_numeral nat), code_c271388182l_size ) 15.83/15.94 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 15.83/15.94 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 15.83/15.94 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 15.83/15.94 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 15.83/15.94 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 15.83/15.94 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 15.83/15.94 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 15.83/15.94 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 15.83/15.94 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 15.83/15.94 ( (fun complex nat), complex_size ) 15.83/15.94 ( (fun complex nat), (size_size complex) ) 15.83/15.94 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 15.83/15.94 ( (fun nat (fun nat (product_prod int int))), bezw ) 15.83/15.94 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 15.83/15.94 ( (fun int (fun nat nat)), nat_aux ) 15.83/15.94 ( (fun int (fun (fun int bool) bool)), rsetR ) 15.83/15.94 ( (fun int (fun (fun int bool) bool)), resSet ) 15.83/15.94 ( (fun int (list int)), quickc666637781d_zero ) 15.83/15.94 ( (fun (product_prod int int) rat), frct ) 15.83/15.94 ( (fun int (fun int rat)), fract ) 15.83/15.94 ( (fun real (fun real complex)), complex_1 ) 15.83/15.94 ( (fun real (fun real complex)), rcis ) 15.83/15.94 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 15.83/15.94 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 15.83/15.94 ( (fun int real), (real_1 int) ) 15.83/15.94 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 15.83/15.94 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 15.83/15.94 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 15.83/15.94 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 15.83/15.94 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 15.83/15.94 ( (fun real nat), natfloor ) 15.83/15.94 ( (fun real nat), natceiling ) 15.83/15.94 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 15.83/15.94 ( (fun quickcheck_code_int int), quickcheck_int_of ) 15.83/15.94 ( (fun rat (product_prod int int)), quotient_of ) 15.83/15.94 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 15.83/15.94 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 15.83/15.94 ( (fun rat real), ratreal ) 15.83/15.94 ( (fun code_code_numeral int), code_int_of ) 15.83/15.94 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 15.83/15.94 ( (fun int quickcheck_code_int), quickcheck_of_int ) 15.83/15.94 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 15.83/15.94 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 15.83/15.94 ) 15.83/15.94 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) X_2) zEven))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (zero_zero int)) X_2))) (= (one_one int) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (number_number_of int) min_1)) (hAPP int nat nat_1 X_2))))) ) 15.83/15.94 ( (one_one int) ) 15.83/15.94 ( (zero_zero int) ) 15.83/15.94 ( min_1 ) 15.83/15.94 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/15.94 ( s ) 15.83/15.94 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.83/15.94 ( (hAPP int int (number_number_of int) pls) ) 15.83/15.94 ( skv_4 ) 15.83/15.94 ( skv_10 ) 15.83/15.94 ) 15.83/15.94 (instantiation (forall ((M $$unsorted)) (let ((_let_0 (semiring_1_of_nat int))) (= (hAPP nat int _let_0 (hAPP nat nat suc M)) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int _let_0 M)))) ) 15.83/15.94 ( (zero_zero nat) ) 15.83/15.94 ( (hAPP nat nat suc (zero_zero nat)) ) 15.83/15.94 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 15.83/15.94 ) 15.83/15.94 (instantiation (forall ((X_a $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (fun _let_0 bool))) (or (not (hBOOL (hAPP _let_0 bool (finite_finite_1 X_a) A_3))) (= (hAPP nat nat (hAPP nat (fun nat nat) (power_power nat) (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat)))) (hAPP _let_0 nat (finite_card X_a) A_3)) (hAPP _let_1 nat (finite_card _let_0) (hAPP _let_0 _let_1 (pow X_a) A_3)))))) ) 15.83/15.94 ( nat, (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 15.83/15.94 ) 15.83/15.94 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_125085 $$unsorted) (BOUND_VARIABLE_125086 $$unsorted)) (let ((_let_0 (abs_abs X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (times_times X_a))) (or (not (linordered_idom X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)) BOUND_VARIABLE_125086))) (= (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a _let_0 BOUND_VARIABLE_125085)) BOUND_VARIABLE_125086) (hAPP X_a X_a _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_125085) BOUND_VARIABLE_125086))))))) ) 15.83/15.94 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 15.83/15.94 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.83/15.94 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13 ) 15.83/15.94 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.83/15.94 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.83/15.94 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.83/15.94 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 15.83/15.94 ( complex, ii, ii ) 15.83/15.94 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 15.83/15.94 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 15.83/15.94 ) 15.83/15.94 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_125113 $$unsorted) (BOUND_VARIABLE_125114 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (zero_zero X_a))) (let ((_let_2 (hAPP X_a _let_0 (ord_less X_a) _let_1))) (or (not (ordere216010020id_add X_a)) (not (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_125114))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) _let_1) BOUND_VARIABLE_125113))) (hBOOL (hAPP X_a bool _let_2 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_125114) BOUND_VARIABLE_125113))))))) ) 15.83/15.94 ( nat, (one_one nat), (one_one nat) ) 15.83/15.94 ( int, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.83/15.94 ( int, (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/15.94 ) 15.83/15.94 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_125150 $$unsorted) (BOUND_VARIABLE_125151 $$unsorted)) (let ((_let_0 (fun (filter nat) bool))) (or (not (real_normed_vector X_a)) (= (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_0 (hAPP (fun nat X_a) (fun X_a _let_0) (tendsto nat X_a) BOUND_VARIABLE_125150) BOUND_VARIABLE_125151) sequentially)) (forall ((R_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) R_2))) (not (forall ((No $$unsorted)) (not (forall ((N_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) No) N_2))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP X_a real (norm_norm X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) (hAPP nat X_a BOUND_VARIABLE_125150 N_2)) BOUND_VARIABLE_125151))) R_2))) )) ))) )))) ) 15.83/15.94 ( real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real) ) 15.83/15.94 ) 15.83/15.94 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_125182 $$unsorted)) (let ((_let_0 (ti X_a BOUND_VARIABLE_125182))) (or (not (linord219039673up_add X_a)) (= (= _let_0 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_125182)) (= (zero_zero X_a) _let_0)))) ) 15.83/15.94 ( bool, fFalse ) 15.83/15.94 ( bool, fTrue ) 15.83/15.94 ( int, (one_one int) ) 15.83/15.94 ( int, pls ) 15.83/15.94 ( int, min_1 ) 15.83/15.94 ( int, s ) 15.83/15.94 ( int, m ) 15.83/15.94 ( int, s1 ) 15.83/15.94 ( int, t ) 15.83/15.94 ( (fun int bool), nat_neg ) 15.83/15.94 ( (fun int bool), zprime ) 15.83/15.94 ( (fun int bool), zEven ) 15.83/15.94 ( (fun int bool), zOdd ) 15.83/15.94 ( (fun int bool), (even_odd_even int) ) 15.83/15.94 ( (fun int bool), twoSqu1091635170sum2sq ) 15.83/15.94 ( (fun int bool), nat_is_nat ) 15.83/15.94 ( (fun int (fun int bool)), norRRset ) 15.83/15.94 ( (fun int (fun int bool)), quadRes ) 15.83/15.94 ( (fun int (fun int bool)), sRStar ) 15.83/15.94 ( (fun int (fun int bool)), d22set ) 15.83/15.94 ( (fun int (fun int bool)), sr ) 15.83/15.94 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 15.83/15.94 ( (fun int int), zfact ) 15.83/15.94 ( (fun int int), bit0 ) 15.83/15.94 ( (fun int int), bit1 ) 15.83/15.94 ( (fun int int), (fact_fact int) ) 15.83/15.94 ( (fun int int), pred ) 15.83/15.94 ( (fun int int), succ ) 15.83/15.94 ( (fun nat bool), (even_odd_even nat) ) 15.83/15.94 ( (fun nat bool), prime ) 15.83/15.94 ( (fun nat nat), suc ) 15.83/15.94 ( (fun nat nat), (fact_fact nat) ) 15.83/15.94 ( (fun nat nat), fact ) 15.83/15.94 ( (fun nat nat), nat_size ) 15.83/15.94 ( (fun nat nat), (size_size nat) ) 15.83/15.94 ( (fun (product_prod nat nat) bool), pred_nat ) 15.83/15.94 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 15.83/15.94 ( real, (one_one real) ) 15.83/15.94 ( real, pi ) 15.83/15.94 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/15.94 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.83/15.94 ( (fun real real), ln ) 15.83/15.94 ( (fun real real), cos ) 15.83/15.94 ( (fun real real), sqrt ) 15.83/15.94 ( (fun real real), sin ) 15.83/15.94 ( (fun real real), arccos ) 15.83/15.94 ( (fun real real), arcsin ) 15.83/15.94 ( (fun real real), tan ) 15.83/15.94 ( (fun real real), arctan ) 15.83/15.94 ( (fun nat (fun nat bool)), coprime ) 15.83/15.94 ( complex, (one_one complex) ) 15.83/15.94 ( complex, ii ) 15.83/15.94 ( (fun nat real), (real_1 nat) ) 15.83/15.94 ( (fun nat real), sin_coeff ) 15.83/15.94 ( (fun nat real), cos_coeff ) 15.83/15.94 ( (filter nat), sequentially ) 15.83/15.94 ( (fun int (fun int int)), (gcd_gcd int) ) 15.83/15.94 ( (fun int (fun int int)), legendre ) 15.83/15.94 ( (fun int (fun int int)), legacy_zgcd ) 15.83/15.94 ( (fun int (fun int int)), standardRes ) 15.83/15.94 ( (fun int (fun int int)), nat_tsub ) 15.83/15.94 ( (fun int (fun int int)), multInv ) 15.83/15.94 ( (fun int (fun int int)), z3mod ) 15.83/15.94 ( (fun int (fun int int)), z3div ) 15.83/15.94 ( (fun int (fun int int)), int_gcd ) 15.83/15.94 ( (fun int (fun int int)), int_lcm ) 15.83/15.94 ( (fun int (fun int int)), inv ) 15.83/15.94 ( (fun complex complex), expi ) 15.83/15.94 ( (fun complex complex), cnj ) 15.83/15.94 ( (fun real complex), cis ) 15.83/15.94 ( (fun int nat), nat_1 ) 15.83/15.94 ( (fun int nat), phi ) 15.83/15.94 ( (fun (fun int bool) bool), nat_nat_set ) 15.83/15.94 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 15.83/15.94 ( (fun nat (fun nat nat)), nat_gcd ) 15.83/15.94 ( (fun nat (fun nat nat)), nat_lcm ) 15.83/15.94 ( (fun (fun int bool) int), (the int) ) 15.83/15.94 ( (fun complex real), re ) 15.83/15.94 ( (fun complex real), im ) 15.83/15.94 ( (fun complex real), arg ) 15.83/15.94 ( (fun bool bool), fNot ) 15.83/15.94 ( (fun nat (fun real real)), root ) 15.83/15.94 ( (fun real (fun real real)), log ) 15.83/15.94 ( (fun real (fun real real)), powr ) 15.83/15.94 ( (fun bool (fun bool bool)), fimplies ) 15.83/15.94 ( (fun bool (fun bool bool)), fconj ) 15.83/15.94 ( (fun bool (fun bool bool)), fdisj ) 15.83/15.94 ( (fun int (fun int (product_prod int int))), negDivAlg ) 15.83/15.94 ( (fun int (fun int (product_prod int int))), posDivAlg ) 15.83/15.94 ( (fun int (fun int (product_prod int int))), divmod_int ) 15.83/15.94 ( (fun int (fun int (product_prod int int))), pdivmod ) 15.83/15.94 ( (fun int (fun int (product_prod int int))), norm_frac ) 15.83/15.94 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 15.83/15.94 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 15.83/15.94 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 15.83/15.94 ( (fun int (fun int (fun int bool))), zcong ) 15.83/15.94 ( (fun int (fun int (fun int bool))), zcongm ) 15.83/15.94 ( (fun int (fun int (fun int bool))), noXRRset ) 15.83/15.94 ( (fun int (fun int (fun int bool))), bnorRset ) 15.83/15.94 ( (fun int (fun int (fun int bool))), wset ) 15.83/15.94 ( (fun (product_prod int int) bool), frac_1 ) 15.83/15.94 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 15.83/15.94 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 15.83/15.94 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 15.83/15.94 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 15.83/15.94 ( (fun (fun nat rat) bool), vanishes ) 15.83/15.94 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 15.83/15.94 ( (fun code_code_numeral nat), code_c271388182l_size ) 15.83/15.94 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 15.83/15.94 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 15.83/15.94 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 15.83/15.94 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 15.83/15.94 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 15.83/15.94 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 15.83/15.94 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 15.83/15.94 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 15.83/15.94 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 15.83/15.94 ( (fun complex nat), complex_size ) 15.83/15.94 ( (fun complex nat), (size_size complex) ) 15.83/15.94 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 15.83/15.94 ( (fun nat (fun nat (product_prod int int))), bezw ) 15.83/15.94 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 15.83/15.94 ( (fun int (fun nat nat)), nat_aux ) 15.83/15.94 ( (fun int (fun (fun int bool) bool)), rsetR ) 15.83/15.94 ( (fun int (fun (fun int bool) bool)), resSet ) 15.83/15.94 ( (fun int (list int)), quickc666637781d_zero ) 15.83/15.94 ( (fun (product_prod int int) rat), frct ) 15.83/15.94 ( (fun int (fun int rat)), fract ) 15.83/15.94 ( (fun real (fun real complex)), complex_1 ) 15.83/15.94 ( (fun real (fun real complex)), rcis ) 15.83/15.94 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 15.83/15.94 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 15.83/15.94 ( (fun int real), (real_1 int) ) 15.83/15.94 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 15.83/15.94 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 15.83/15.94 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 15.83/15.94 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 15.83/15.94 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 15.83/15.94 ( (fun real nat), natfloor ) 15.83/15.94 ( (fun real nat), natceiling ) 15.83/15.94 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 15.83/15.94 ( (fun quickcheck_code_int int), quickcheck_int_of ) 15.83/15.94 ( (fun rat (product_prod int int)), quotient_of ) 15.83/15.94 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 15.83/15.94 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 15.83/15.94 ( (fun rat real), ratreal ) 15.83/15.94 ( (fun code_code_numeral int), code_int_of ) 15.83/15.94 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 15.83/15.94 ( (fun int quickcheck_code_int), quickcheck_of_int ) 15.83/15.94 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 15.83/15.94 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 15.83/15.94 ) 15.83/15.94 (instantiation (forall ((K_4 $$unsorted)) (let ((_let_0 (uminus_uminus int))) (= (hAPP int int bit0 (hAPP int int _let_0 K_4)) (hAPP int int _let_0 (hAPP int int bit0 K_4)))) ) 15.83/15.94 ( (one_one int) ) 15.83/15.94 ( pls ) 15.83/15.94 ( min_1 ) 15.83/15.94 ) 15.83/15.94 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_125354 $$unsorted) (BOUND_VARIABLE_125355 $$unsorted)) (let ((_let_0 (fun (filter nat) bool))) (or (not (metric_space X_a)) (= (forall ((R_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) R_2))) (not (forall ((No $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) No))) (not (forall ((N_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) No) N_2))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP X_a real (hAPP X_a (fun X_a real) (dist_dist X_a) (hAPP nat X_a BOUND_VARIABLE_125354 N_2)) BOUND_VARIABLE_125355)) R_2))) ))) ))) ) (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_0 (hAPP (fun nat X_a) (fun X_a _let_0) (tendsto nat X_a) BOUND_VARIABLE_125354) BOUND_VARIABLE_125355) sequentially))))) ) 15.83/15.94 ( real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real) ) 15.83/15.94 ) 15.83/15.94 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (one_one real))) (let ((_let_2 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 (hAPP int real (number_number_of real) min_1)) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 X_1) _let_1))) (= (hAPP real real sqrt (hAPP real real (hAPP real (fun real real) (minus_minus real) _let_1) (hAPP nat real (hAPP real (fun nat real) (power_power real) X_1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real real cos (hAPP real real arcsin X_1))))))) ) 15.83/15.94 ( (zero_zero real) ) 15.83/15.94 ( (hAPP int real (number_number_of real) min_1) ) 15.83/15.94 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/15.94 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/15.94 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/15.94 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/15.94 ( skv_5 ) 15.83/15.94 ) 15.83/15.94 (instantiation (forall ((Y_1 $$unsorted) (X_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (hAPP nat (fun real real) root N_1))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) (zero_zero real)) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) Y_1))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real _let_2 X_1)) (hAPP real real _let_2 Y_1))))))) ) 15.83/15.94 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/15.94 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/15.94 ) 15.83/15.94 (instantiation (forall ((A_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) _let_2) P_5))) (not (hBOOL (hAPP int bool zprime P_5))) (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP int int (hAPP int _let_1 legendre A_1) P_5)) (hAPP nat int (hAPP int (fun nat int) (power_power int) A_1) (hAPP int nat nat_1 (hAPP int int (hAPP int _let_1 (div_div int) (hAPP int int (hAPP int _let_1 (minus_minus int) P_5) (one_one int))) _let_2)))) P_5)))))) ) 15.83/15.94 ( (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.83/15.94 ) 15.83/15.94 (instantiation (forall ((X_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP _let_0 bool nat_nat_set A_3))) (not (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) X_2) A_3))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (zero_zero int)) X_2)))) ) 15.83/15.94 ( (one_one int), zEven ) 15.83/15.94 ) 15.83/15.94 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_125500 $$unsorted) (BOUND_VARIABLE_125501 $$unsorted)) (let ((_let_0 (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_125500))) (or (not (power X_a)) (= (hAPP nat X_a _let_0 (hAPP nat nat suc BOUND_VARIABLE_125501)) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_125500) (hAPP nat X_a _let_0 BOUND_VARIABLE_125501))))) ) 15.83/15.94 ( int, s, (hAPP nat nat suc (zero_zero nat)) ) 15.83/15.94 ( int, s1, (hAPP nat nat suc (zero_zero nat)) ) 15.83/15.94 ( int, skv_14, (hAPP nat nat suc (zero_zero nat)) ) 15.83/15.94 ( complex, ii, (hAPP nat nat suc (zero_zero nat)) ) 15.83/15.94 ) 15.83/15.94 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted)) (hBOOL (hAPP rat bool (hAPP rat (fun rat bool) (ord_less_eq rat) (hAPP int rat (ring_1_of_int rat) (hAPP int int (hAPP int (fun int int) (div_div int) A_1) B))) (hAPP int rat (hAPP int (fun int rat) fract A_1) B))) ) 15.83/15.94 ( (one_one int), (one_one int) ) 15.83/15.94 ( (zero_zero int), (one_one int) ) 15.83/15.94 ) 15.83/15.94 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_0 (fun int int))) (hBOOL (hAPP rat bool (hAPP rat (fun rat bool) (ord_less rat) (hAPP int rat (hAPP int (fun int rat) fract A_1) B)) (hAPP int rat (ring_1_of_int rat) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (div_div int) A_1) B)) (one_one int)))))) ) 15.83/15.94 ( (one_one int), (one_one int) ) 15.83/15.94 ( (zero_zero int), (one_one int) ) 15.83/15.94 ) 15.83/15.94 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_125542 $$unsorted) (BOUND_VARIABLE_125543 $$unsorted)) (let ((_let_0 (uminus_uminus X_a))) (or (not (group_add X_a)) (= (= (ti X_a BOUND_VARIABLE_125542) (hAPP X_a X_a _let_0 BOUND_VARIABLE_125543)) (= (ti X_a BOUND_VARIABLE_125543) (hAPP X_a X_a _let_0 BOUND_VARIABLE_125542))))) ) 15.83/15.94 ( int, pls, (one_one int) ) 15.83/15.94 ( int, s, min_1 ) 15.83/15.94 ( int, s1, pls ) 15.83/15.94 ( real, pi, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/15.94 ( complex, ii, (one_one complex) ) 15.83/15.94 ( complex, ii, ii ) 15.83/15.94 ) 15.83/15.94 (instantiation (forall ((Y_2 $$unsorted) (X_2 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (let ((_let_2 (hAPP int _let_0 _let_1 (zero_zero int)))) (or (not (hBOOL (hAPP int bool _let_2 X_2))) (not (hBOOL (hAPP int bool _let_2 Y_2))) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 X_2) Y_2)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP int nat nat_1 X_2)) (hAPP int nat nat_1 Y_2)))))))) ) 15.83/15.94 ( (one_one int), (zero_zero int) ) 15.83/15.94 ( pls, min_1 ) 15.83/15.94 ( min_1, (zero_zero int) ) 15.83/15.94 ( min_1, min_1 ) 15.83/15.94 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 15.83/15.94 ( s, (zero_zero int) ) 15.83/15.94 ( t, (one_one int) ) 15.83/15.94 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 15.83/15.94 ( (hAPP int int (number_number_of int) pls), (zero_zero int) ) 15.83/15.94 ( skv_4, (zero_zero int) ) 15.83/15.94 ( skv_10, (zero_zero int) ) 15.83/15.94 ) 15.83/15.94 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_125598 $$unsorted)) (let ((_let_0 (archimedean_ceiling X_a))) (or (not (archim1727834104eiling X_a)) (= (hAPP X_a int _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_125598) (one_one X_a))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP X_a int _let_0 BOUND_VARIABLE_125598)) (one_one int))))) ) 15.83/15.94 ( nat, (one_one nat) ) 15.83/15.94 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.83/15.94 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/15.94 ) 15.83/15.94 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_125623 $$unsorted) (BOUND_VARIABLE_125624 $$unsorted)) (let ((_let_0 (fun nat X_a))) (let ((_let_1 (power_power X_a))) (or (not (linordered_idom X_a)) (not (hBOOL (hAPP nat bool (even_odd_even nat) BOUND_VARIABLE_125624))) (= (hAPP nat X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_125623) BOUND_VARIABLE_125624) (hAPP nat X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_125623)) BOUND_VARIABLE_125624))))) ) 15.83/15.94 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/15.94 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/15.94 ( int, skv_14, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/15.94 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/15.94 ) 15.83/15.94 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_125654 $$unsorted) (BOUND_VARIABLE_125655 $$unsorted) (BOUND_VARIABLE_125656 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_125655))) (or (not (ord X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_125656))) (not (= (ti X_a BOUND_VARIABLE_125654) (ti X_a BOUND_VARIABLE_125656))) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_125654)))) ) 15.83/15.94 ( int, pls, min_1, pls ) 15.83/15.94 ( int, min_1, pls, (one_one int) ) 15.83/15.94 ( int, s, pls, pls ) 15.83/15.94 ( int, m, min_1, min_1 ) 15.83/15.94 ( int, s1, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.83/15.94 ( int, t, pls, min_1 ) 15.83/15.94 ( real, pi, pi, (zero_zero real) ) 15.83/15.94 ) 15.83/15.94 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_125676 $$unsorted)) (let ((_let_0 (hAPP nat X_a (semiring_1_of_nat X_a) BOUND_VARIABLE_125676))) (or (not (linordered_idom X_a)) (= _let_0 (hAPP X_a X_a (abs_abs X_a) _let_0)))) ) 15.83/15.94 ( int, (zero_zero nat) ) 15.83/15.94 ( int, (hAPP nat nat suc (zero_zero nat)) ) 15.83/15.94 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.83/15.94 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/15.94 ( real, (zero_zero nat) ) 15.83/15.94 ( real, (hAPP nat nat suc (zero_zero nat)) ) 15.83/15.94 ) 15.83/15.94 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_125690 $$unsorted)) (or (not (number_ring X_a)) (= (hAPP int X_a (ring_1_of_int X_a) (hAPP int int (number_number_of int) BOUND_VARIABLE_125690)) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_125690))) ) 15.83/15.94 ( nat, pls ) 15.83/15.94 ( nat, (hAPP int int bit1 pls) ) 15.83/15.94 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.83/15.94 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.83/15.94 ( int, pls ) 15.83/15.94 ( int, (hAPP int int bit1 pls) ) 15.83/15.94 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.83/15.94 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.83/15.94 ( int, min_1 ) 15.83/15.94 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/15.94 ( real, pls ) 15.83/15.94 ( real, (hAPP int int bit1 pls) ) 15.83/15.94 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.83/15.94 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.83/15.94 ( real, min_1 ) 15.83/15.94 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/15.94 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.83/15.94 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/15.94 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 15.83/15.94 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.83/15.94 ( complex, min_1 ) 15.83/15.94 ( quickcheck_code_int, (one_one int) ) 15.83/15.94 ( quickcheck_code_int, (zero_zero int) ) 15.83/15.94 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 15.83/15.94 ( code_code_numeral, pls ) 15.83/15.94 ( code_code_numeral, (hAPP int int bit1 pls) ) 15.83/15.94 ) 15.83/15.94 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (times_times X_a))) (or (not (no_zero_divisors X_a)) (= _let_0 (ti (fun X_a (fun X_a X_a)) _let_0)))) ) 15.83/15.94 ( bool ) 15.83/15.94 ( nat ) 15.83/15.94 ( int ) 15.83/15.94 ( (fun int bool) ) 15.83/15.94 ( (fun int (fun int bool)) ) 15.83/15.94 ( (fun int int) ) 15.83/15.94 ( (fun nat bool) ) 15.83/15.94 ( real ) 15.83/15.94 ( (fun real bool) ) 15.83/15.94 ( (fun real real) ) 15.83/15.94 ( rat ) 15.83/15.94 ( complex ) 15.83/15.94 ( (fun nat real) ) 15.83/15.94 ( (product_prod int int) ) 15.83/15.94 ( quickcheck_code_int ) 15.83/15.94 ( code_code_numeral ) 15.83/15.94 ( (fun int (fun int (fun int bool))) ) 15.83/15.94 ( (fun (product_prod int int) bool) ) 15.83/15.94 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 15.83/15.94 ( (fun (product_prod int int) int) ) 15.83/15.94 ( (fun int real) ) 15.83/15.94 ) 15.83/15.94 (instantiation (forall ((N $$unsorted) (P_1 $$unsorted)) (or (hBOOL (hAPP nat bool P_1 (zero_zero nat))) (not (hBOOL (hAPP nat bool P_1 N))) (not (forall ((K_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) K_1) N))) (not (hBOOL (hAPP nat bool P_1 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) K_1) (one_one nat))))) (not (forall ((I_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) I_2) K_1))) (not (hBOOL (hAPP nat bool P_1 I_2)))) ))) ))) ) 15.83/15.94 ( (zero_zero nat), (even_odd_even nat) ) 15.83/15.94 ( (zero_zero nat), prime ) 15.83/15.94 ( (hAPP nat nat suc (zero_zero nat)), prime ) 15.83/15.94 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) ) 15.83/15.94 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), prime ) 15.83/15.94 ( (one_one nat), (even_odd_even nat) ) 15.83/15.94 ) 15.83/15.94 (instantiation (forall ((X_1 $$unsorted)) (= (hAPP rat real ratreal (hAPP rat rat (inverse_inverse rat) X_1)) (hAPP real real (inverse_inverse real) (hAPP rat real ratreal X_1))) ) 15.83/15.94 ( (zero_zero rat) ) 15.83/15.94 ) 15.83/15.94 (instantiation (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (or (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) Y_1) X_1)) (= (zero_zero int) (hAPP int int (hAPP int (fun int int) nat_tsub X_1) Y_1))) ) 15.83/15.94 ( (one_one int), t ) 15.83/15.94 ( (zero_zero int), (one_one int) ) 15.83/15.94 ( (zero_zero int), min_1 ) 15.83/15.94 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/15.94 ( (zero_zero int), s ) 15.83/15.94 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.83/15.94 ( (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.83/15.94 ( (zero_zero int), skv_4 ) 15.83/15.94 ( (zero_zero int), skv_10 ) 15.83/15.94 ( min_1, pls ) 15.83/15.94 ( min_1, min_1 ) 15.83/15.94 ) 15.83/15.94 (instantiation (forall ((N_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (hAPP int real (real_1 int) N_1))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) _let_1) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) X_1) (hAPP real real (hAPP real (fun real real) (plus_plus real) _let_1) (one_one real))))) (= (hAPP int int (hAPP int (fun int int) (plus_plus int) N_1) (one_one int)) (hAPP real int (archimedean_ceiling real) X_1))))) ) 15.83/15.94 ( (one_one int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/15.94 ( (zero_zero int), pi ) 15.83/15.94 ( (zero_zero int), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/15.94 ( (zero_zero int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/15.94 ( (zero_zero int), skv_2 ) 15.83/15.94 ( (zero_zero int), skv_8 ) 15.83/15.94 ( (zero_zero int), skv_9 ) 15.83/15.94 ) 15.83/15.94 (instantiation (forall ((X_1 $$unsorted) (A_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) X_1) (hAPP int real (real_1 int) A_1)))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP real int (archimedean_ceiling real) X_1)) A_1))) ) 15.83/15.94 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero int) ) 15.83/15.94 ) 15.83/15.94 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_125881 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (or (not (linord219039673up_add X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_125881)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_125881)) BOUND_VARIABLE_125881)))))) ) 15.83/15.94 ( int, (one_one int) ) 15.83/15.94 ( int, pls ) 15.83/15.94 ( int, min_1 ) 15.83/15.94 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/15.94 ( int, s ) 15.83/15.94 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.83/15.94 ( int, (hAPP int int (number_number_of int) pls) ) 15.83/15.94 ( int, skv_4 ) 15.83/15.94 ( int, skv_10 ) 15.83/15.94 ( real, (one_one real) ) 15.83/15.94 ( real, pi ) 15.83/15.94 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/15.94 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.83/15.94 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/15.94 ( real, skv_3 ) 15.83/15.94 ( real, skv_5 ) 15.83/15.94 ( real, skv_7 ) 15.83/15.94 ( real, skv_12 ) 15.83/15.94 ( complex, (one_one complex) ) 15.83/15.94 ( complex, ii ) 15.83/15.94 ) 15.83/15.94 (instantiation (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (zero_zero int)) B_1))) (= (hBOOL (hAPP rat bool (hAPP rat (fun rat bool) (ord_less_eq rat) (hAPP int rat (hAPP int (fun int rat) fract A_2) B_1)) (one_one rat))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) A_2) B_1))))) ) 15.83/15.94 ( (one_one int), (one_one int) ) 15.83/15.94 ( (one_one int), t ) 15.83/15.94 ( (zero_zero int), (one_one int) ) 15.83/15.94 ( (zero_zero int), min_1 ) 15.83/15.94 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/15.94 ( (zero_zero int), s ) 15.83/15.94 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.83/15.94 ( (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.83/15.94 ( (zero_zero int), skv_4 ) 15.83/15.94 ( (zero_zero int), skv_10 ) 15.83/15.94 ( min_1, pls ) 15.83/15.94 ( min_1, min_1 ) 15.83/15.94 ) 15.83/15.94 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (S $$unsorted) (R_3 $$unsorted)) (let ((_let_0 (fun (product_prod X_a X_b) bool))) (= (= (ti _let_0 R_3) (ti _let_0 S)) (forall ((X $$unsorted) (Xa $$unsorted)) (let ((_let_1 (product_prod X_a X_b))) (let ((_let_2 (hAPP _let_1 (fun _let_0 bool) (member _let_1) (hAPP X_b _let_1 (hAPP X_a (fun X_b _let_1) (product_Pair X_a X_b) X) Xa)))) (= (hBOOL (hAPP _let_0 bool _let_2 S)) (hBOOL (hAPP _let_0 bool _let_2 R_3))))) ))) ) 15.83/15.94 ( nat, nat, pred_nat, pred_nat ) 15.83/15.94 ( int, int, frac_1, frac_1 ) 15.83/15.94 ( (product_prod nat nat), (product_prod nat nat), pair_less, pair_less ) 15.83/15.94 ( (product_prod nat nat), (product_prod nat nat), pair_less, pair_leq ) 15.83/15.94 ( (product_prod nat nat), (product_prod nat nat), pair_leq, pair_less ) 15.83/15.94 ( (product_prod int int), (product_prod int int), ratrel, ratrel ) 15.83/15.94 ) 15.83/15.94 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_125960 $$unsorted)) (or (not (linordered_idom X_a)) (= (ti X_a BOUND_VARIABLE_125960) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) (hAPP X_a X_a (sgn_sgn X_a) BOUND_VARIABLE_125960)) (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_125960)))) ) 15.83/15.94 ( bool, fFalse ) 15.83/15.94 ( bool, fTrue ) 15.83/15.94 ( int, pls ) 15.83/15.94 ( int, min_1 ) 15.83/15.94 ( int, s ) 15.83/15.94 ( int, m ) 15.83/15.94 ( int, s1 ) 15.83/15.94 ( int, t ) 15.83/15.94 ( (fun int bool), nat_neg ) 15.83/15.94 ( (fun int bool), zprime ) 15.83/15.94 ( (fun int bool), zEven ) 15.83/15.94 ( (fun int bool), zOdd ) 15.83/15.94 ( (fun int bool), (even_odd_even int) ) 15.83/15.94 ( (fun int bool), twoSqu1091635170sum2sq ) 15.83/15.94 ( (fun int bool), nat_is_nat ) 15.83/15.94 ( (fun int (fun int bool)), norRRset ) 15.83/15.94 ( (fun int (fun int bool)), quadRes ) 15.83/15.94 ( (fun int (fun int bool)), sRStar ) 15.83/15.94 ( (fun int (fun int bool)), d22set ) 15.83/15.94 ( (fun int (fun int bool)), sr ) 15.83/15.94 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 15.83/15.94 ( (fun int int), zfact ) 15.83/15.94 ( (fun int int), bit0 ) 15.83/15.94 ( (fun int int), bit1 ) 15.83/15.94 ( (fun int int), (fact_fact int) ) 15.83/15.94 ( (fun int int), pred ) 15.83/15.94 ( (fun int int), succ ) 15.83/15.94 ( (fun nat bool), (even_odd_even nat) ) 15.83/15.94 ( (fun nat bool), prime ) 15.83/15.94 ( (fun nat nat), suc ) 15.83/15.94 ( (fun nat nat), (fact_fact nat) ) 15.83/15.94 ( (fun nat nat), fact ) 15.83/15.94 ( (fun nat nat), nat_size ) 15.83/15.94 ( (fun nat nat), (size_size nat) ) 15.83/15.94 ( (fun (product_prod nat nat) bool), pred_nat ) 15.83/15.94 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 15.83/15.94 ( real, (zero_zero real) ) 15.83/15.94 ( real, pi ) 15.83/15.94 ( (fun real real), ln ) 15.83/15.94 ( (fun real real), cos ) 15.83/15.94 ( (fun real real), sqrt ) 15.83/15.94 ( (fun real real), sin ) 15.83/15.94 ( (fun real real), arccos ) 15.83/15.94 ( (fun real real), arcsin ) 15.83/15.94 ( (fun real real), tan ) 15.83/15.94 ( (fun real real), arctan ) 15.83/15.94 ( rat, (zero_zero rat) ) 15.83/15.94 ( (fun nat (fun nat bool)), coprime ) 15.83/15.94 ( complex, ii ) 15.83/15.94 ( (fun nat real), (real_1 nat) ) 15.83/15.94 ( (fun nat real), sin_coeff ) 15.83/15.94 ( (fun nat real), cos_coeff ) 15.83/15.94 ( (filter nat), sequentially ) 15.83/15.94 ( (fun int (fun int int)), (gcd_gcd int) ) 15.83/15.94 ( (fun int (fun int int)), legendre ) 15.83/15.94 ( (fun int (fun int int)), legacy_zgcd ) 15.83/15.94 ( (fun int (fun int int)), standardRes ) 15.83/15.94 ( (fun int (fun int int)), nat_tsub ) 15.83/15.94 ( (fun int (fun int int)), multInv ) 15.83/15.94 ( (fun int (fun int int)), z3mod ) 15.83/15.94 ( (fun int (fun int int)), z3div ) 15.83/15.94 ( (fun int (fun int int)), int_gcd ) 15.83/15.94 ( (fun int (fun int int)), int_lcm ) 15.83/15.94 ( (fun int (fun int int)), inv ) 15.83/15.94 ( (fun complex complex), expi ) 15.83/15.94 ( (fun complex complex), cnj ) 15.83/15.94 ( (fun real complex), cis ) 15.83/15.94 ( (fun int nat), nat_1 ) 15.83/15.94 ( (fun int nat), phi ) 15.83/15.94 ( (fun (fun int bool) bool), nat_nat_set ) 15.83/15.94 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 15.83/15.94 ( (fun nat (fun nat nat)), nat_gcd ) 15.83/15.94 ( (fun nat (fun nat nat)), nat_lcm ) 15.83/15.94 ( (fun (fun int bool) int), (the int) ) 15.83/15.94 ( (fun complex real), re ) 15.83/15.94 ( (fun complex real), im ) 15.83/15.94 ( (fun complex real), arg ) 15.83/15.94 ( (fun bool bool), fNot ) 15.83/15.94 ( (fun nat (fun real real)), root ) 15.83/15.94 ( (fun real (fun real real)), log ) 15.83/15.94 ( (fun real (fun real real)), powr ) 15.83/15.94 ( (fun bool (fun bool bool)), fimplies ) 15.83/15.94 ( (fun bool (fun bool bool)), fconj ) 15.83/15.94 ( (fun bool (fun bool bool)), fdisj ) 15.83/15.94 ( (fun int (fun int (product_prod int int))), negDivAlg ) 15.83/15.94 ( (fun int (fun int (product_prod int int))), posDivAlg ) 15.83/15.94 ( (fun int (fun int (product_prod int int))), divmod_int ) 15.83/15.94 ( (fun int (fun int (product_prod int int))), pdivmod ) 15.83/15.94 ( (fun int (fun int (product_prod int int))), norm_frac ) 15.83/15.94 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 15.83/15.94 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 15.83/15.94 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 15.83/15.94 ( (fun int (fun int (fun int bool))), zcong ) 15.83/15.94 ( (fun int (fun int (fun int bool))), zcongm ) 15.83/15.94 ( (fun int (fun int (fun int bool))), noXRRset ) 15.83/15.94 ( (fun int (fun int (fun int bool))), bnorRset ) 15.83/15.94 ( (fun int (fun int (fun int bool))), wset ) 15.83/15.94 ( (fun (product_prod int int) bool), frac_1 ) 15.83/15.94 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 15.83/15.94 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 15.83/15.94 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 15.83/15.94 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 15.83/15.94 ( (fun (fun nat rat) bool), vanishes ) 15.83/15.94 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 15.83/15.94 ( (fun code_code_numeral nat), code_c271388182l_size ) 15.83/15.94 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 15.83/15.94 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 15.83/15.94 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 15.83/15.94 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 15.83/15.94 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 15.83/15.94 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 15.83/15.94 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 15.83/15.94 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 15.83/15.94 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 15.83/15.94 ( (fun complex nat), complex_size ) 15.83/15.94 ( (fun complex nat), (size_size complex) ) 15.83/15.94 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 15.83/15.94 ( (fun nat (fun nat (product_prod int int))), bezw ) 15.83/15.94 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 15.83/15.94 ( (fun int (fun nat nat)), nat_aux ) 15.83/15.94 ( (fun int (fun (fun int bool) bool)), rsetR ) 15.83/15.94 ( (fun int (fun (fun int bool) bool)), resSet ) 15.83/15.94 ( (fun int (list int)), quickc666637781d_zero ) 15.83/15.94 ( (fun (product_prod int int) rat), frct ) 15.83/15.94 ( (fun int (fun int rat)), fract ) 15.83/15.94 ( (fun real (fun real complex)), complex_1 ) 15.83/15.94 ( (fun real (fun real complex)), rcis ) 15.83/15.94 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 15.83/15.94 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 15.83/15.94 ( (fun int real), (real_1 int) ) 15.83/15.94 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 15.83/15.94 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 15.83/15.94 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 15.83/15.94 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 15.83/15.94 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 15.83/15.94 ( (fun real nat), natfloor ) 15.83/15.94 ( (fun real nat), natceiling ) 15.83/15.94 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 15.83/15.94 ( (fun quickcheck_code_int int), quickcheck_int_of ) 15.83/15.94 ( (fun rat (product_prod int int)), quotient_of ) 15.83/15.94 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 15.83/15.94 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 15.83/15.94 ( (fun rat real), ratreal ) 15.83/15.94 ( (fun code_code_numeral int), code_int_of ) 15.83/15.94 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 15.83/15.94 ( (fun int quickcheck_code_int), quickcheck_of_int ) 15.83/15.94 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 15.83/15.94 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 15.83/15.94 ) 15.83/15.94 (instantiation (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_0 (hAPP real (fun real bool) (ord_less real) (zero_zero real)))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_1))) (not (hBOOL (hAPP real bool _let_0 X_1))) (hBOOL (hAPP real bool _let_0 (hAPP real real (hAPP nat (fun real real) root N_1) X_1))))) ) 15.83/15.94 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/15.94 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/15.94 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/15.94 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/15.94 ) 15.83/15.94 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_126004 $$unsorted) (BOUND_VARIABLE_126005 $$unsorted)) (let ((_let_0 (uminus_uminus X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (times_times X_a))) (or (not (real_normed_algebra X_a)) (= (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a _let_0 BOUND_VARIABLE_126004)) BOUND_VARIABLE_126005) (hAPP X_a X_a _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_126004) BOUND_VARIABLE_126005))))))) ) 15.83/15.94 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 15.83/15.94 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.83/15.94 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13 ) 15.83/15.94 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.83/15.94 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.83/15.94 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.83/15.94 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 15.83/15.94 ( complex, ii, ii ) 15.83/15.94 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 15.83/15.94 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 15.83/15.94 ) 15.83/15.94 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_126064 $$unsorted)) (let ((_let_0 (norm_norm X_a))) (or (not (real_n1866405975lgebra X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_126064)) (= (hAPP real real (inverse_inverse real) (hAPP X_a real _let_0 BOUND_VARIABLE_126064)) (hAPP X_a real _let_0 (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_126064))))) ) 15.83/15.94 ( bool, fFalse ) 15.83/15.94 ( bool, fTrue ) 15.83/15.94 ( int, pls ) 15.83/15.94 ( int, min_1 ) 15.83/15.94 ( int, s ) 15.83/15.94 ( int, m ) 15.83/15.94 ( int, s1 ) 15.83/15.94 ( int, t ) 15.83/15.94 ( (fun int bool), nat_neg ) 15.83/15.94 ( (fun int bool), zprime ) 15.83/15.94 ( (fun int bool), zEven ) 15.83/15.94 ( (fun int bool), zOdd ) 15.83/15.94 ( (fun int bool), (even_odd_even int) ) 15.83/15.94 ( (fun int bool), twoSqu1091635170sum2sq ) 15.83/15.94 ( (fun int bool), nat_is_nat ) 15.83/15.94 ( (fun int (fun int bool)), norRRset ) 15.83/15.94 ( (fun int (fun int bool)), quadRes ) 15.83/15.94 ( (fun int (fun int bool)), sRStar ) 15.83/15.94 ( (fun int (fun int bool)), d22set ) 15.83/15.94 ( (fun int (fun int bool)), sr ) 15.83/15.94 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 15.83/15.94 ( (fun int int), zfact ) 15.83/15.94 ( (fun int int), bit0 ) 15.83/15.94 ( (fun int int), bit1 ) 15.83/15.94 ( (fun int int), (fact_fact int) ) 15.83/15.94 ( (fun int int), pred ) 15.83/15.94 ( (fun int int), succ ) 15.83/15.94 ( (fun nat bool), (even_odd_even nat) ) 15.83/15.94 ( (fun nat bool), prime ) 15.83/15.94 ( (fun nat nat), suc ) 15.83/15.94 ( (fun nat nat), (fact_fact nat) ) 15.83/15.94 ( (fun nat nat), fact ) 15.83/15.94 ( (fun nat nat), nat_size ) 15.83/15.94 ( (fun nat nat), (size_size nat) ) 15.83/15.94 ( (fun (product_prod nat nat) bool), pred_nat ) 15.83/15.94 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 15.83/15.94 ( real, (zero_zero real) ) 15.83/15.94 ( real, pi ) 15.83/15.94 ( (fun real real), ln ) 15.83/15.94 ( (fun real real), cos ) 15.83/15.94 ( (fun real real), sqrt ) 15.83/15.94 ( (fun real real), sin ) 15.83/15.94 ( (fun real real), arccos ) 15.83/15.94 ( (fun real real), arcsin ) 15.83/15.94 ( (fun real real), tan ) 15.83/15.94 ( (fun real real), arctan ) 15.83/15.94 ( (fun nat (fun nat bool)), coprime ) 15.83/15.94 ( complex, ii ) 15.83/15.94 ( (fun nat real), (real_1 nat) ) 15.83/15.94 ( (fun nat real), sin_coeff ) 15.83/15.94 ( (fun nat real), cos_coeff ) 15.83/15.94 ( (filter nat), sequentially ) 15.83/15.94 ( (fun int (fun int int)), (gcd_gcd int) ) 15.83/15.94 ( (fun int (fun int int)), legendre ) 15.83/15.94 ( (fun int (fun int int)), legacy_zgcd ) 15.83/15.94 ( (fun int (fun int int)), standardRes ) 15.83/15.94 ( (fun int (fun int int)), nat_tsub ) 15.83/15.94 ( (fun int (fun int int)), multInv ) 15.83/15.94 ( (fun int (fun int int)), z3mod ) 15.83/15.94 ( (fun int (fun int int)), z3div ) 15.83/15.94 ( (fun int (fun int int)), int_gcd ) 15.83/15.94 ( (fun int (fun int int)), int_lcm ) 15.83/15.94 ( (fun int (fun int int)), inv ) 15.83/15.94 ( (fun complex complex), expi ) 15.83/15.94 ( (fun complex complex), cnj ) 15.83/15.94 ( (fun real complex), cis ) 15.83/15.94 ( (fun int nat), nat_1 ) 15.83/15.94 ( (fun int nat), phi ) 15.83/15.94 ( (fun (fun int bool) bool), nat_nat_set ) 15.83/15.94 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 15.83/15.94 ( (fun nat (fun nat nat)), nat_gcd ) 15.83/15.94 ( (fun nat (fun nat nat)), nat_lcm ) 15.83/15.94 ( (fun (fun int bool) int), (the int) ) 15.83/15.94 ( (fun complex real), re ) 15.83/15.94 ( (fun complex real), im ) 15.83/15.94 ( (fun complex real), arg ) 15.83/15.94 ( (fun bool bool), fNot ) 15.83/15.94 ( (fun nat (fun real real)), root ) 15.83/15.95 ( (fun real (fun real real)), log ) 15.83/15.95 ( (fun real (fun real real)), powr ) 15.83/15.95 ( (fun bool (fun bool bool)), fimplies ) 15.83/15.95 ( (fun bool (fun bool bool)), fconj ) 15.83/15.95 ( (fun bool (fun bool bool)), fdisj ) 15.83/15.95 ( (fun int (fun int (product_prod int int))), negDivAlg ) 15.83/15.95 ( (fun int (fun int (product_prod int int))), posDivAlg ) 15.83/15.95 ( (fun int (fun int (product_prod int int))), divmod_int ) 15.83/15.95 ( (fun int (fun int (product_prod int int))), pdivmod ) 15.83/15.95 ( (fun int (fun int (product_prod int int))), norm_frac ) 15.83/15.95 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 15.83/15.95 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 15.83/15.95 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 15.83/15.95 ( (fun int (fun int (fun int bool))), zcong ) 15.83/15.95 ( (fun int (fun int (fun int bool))), zcongm ) 15.83/15.95 ( (fun int (fun int (fun int bool))), noXRRset ) 15.83/15.95 ( (fun int (fun int (fun int bool))), bnorRset ) 15.83/15.95 ( (fun int (fun int (fun int bool))), wset ) 15.83/15.95 ( (fun (product_prod int int) bool), frac_1 ) 15.83/15.95 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 15.83/15.95 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 15.83/15.95 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 15.83/15.95 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 15.83/15.95 ( (fun (fun nat rat) bool), vanishes ) 15.83/15.95 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 15.83/15.95 ( (fun code_code_numeral nat), code_c271388182l_size ) 15.83/15.95 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 15.83/15.95 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 15.83/15.95 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 15.83/15.95 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 15.83/15.95 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 15.83/15.95 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 15.83/15.95 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 15.83/15.95 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 15.83/15.95 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 15.83/15.95 ( (fun complex nat), complex_size ) 15.83/15.95 ( (fun complex nat), (size_size complex) ) 15.83/15.95 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 15.83/15.95 ( (fun nat (fun nat (product_prod int int))), bezw ) 15.83/15.95 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 15.83/15.95 ( (fun int (fun nat nat)), nat_aux ) 15.83/15.95 ( (fun int (fun (fun int bool) bool)), rsetR ) 15.83/15.95 ( (fun int (fun (fun int bool) bool)), resSet ) 15.83/15.95 ( (fun int (list int)), quickc666637781d_zero ) 15.83/15.95 ( (fun (product_prod int int) rat), frct ) 15.83/15.95 ( (fun int (fun int rat)), fract ) 15.83/15.95 ( (fun real (fun real complex)), complex_1 ) 15.83/15.95 ( (fun real (fun real complex)), rcis ) 15.83/15.95 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 15.83/15.95 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 15.83/15.95 ( (fun int real), (real_1 int) ) 15.83/15.95 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 15.83/15.95 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 15.83/15.95 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 15.83/15.95 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 15.83/15.95 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 15.83/15.95 ( (fun real nat), natfloor ) 15.83/15.95 ( (fun real nat), natceiling ) 15.83/15.95 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 15.83/15.95 ( (fun quickcheck_code_int int), quickcheck_int_of ) 15.83/15.95 ( (fun rat (product_prod int int)), quotient_of ) 15.83/15.95 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 15.83/15.95 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 15.83/15.95 ( (fun rat real), ratreal ) 15.83/15.95 ( (fun code_code_numeral int), code_int_of ) 15.83/15.95 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 15.83/15.95 ( (fun int quickcheck_code_int), quickcheck_of_int ) 15.83/15.95 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 15.83/15.95 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 15.83/15.95 ) 15.83/15.95 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (complex_rec X_a))) (= _let_0 (ti (fun (fun real (fun real X_a)) (fun complex X_a)) _let_0))) ) 15.83/15.95 ( bool ) 15.83/15.95 ( nat ) 15.83/15.95 ( real ) 15.83/15.95 ( complex ) 15.83/15.95 ( (fun nat (product_prod real real)) ) 15.83/15.95 ) 15.83/15.95 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_126189 $$unsorted) (BOUND_VARIABLE_126190 $$unsorted)) (let ((_let_0 (filter X_a))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun X_a X_b))) (let ((_let_3 (fun X_a real))) (let ((_let_4 (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_126190))) (or (not (real_normed_vector X_b)) (not (topological_space X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP real _let_1 (hAPP _let_3 (fun real _let_1) (tendsto X_a real) (hAPP _let_2 _let_3 (hAPP (fun X_b real) (fun _let_2 _let_3) (combb X_b real X_a) (norm_norm X_b)) BOUND_VARIABLE_126189)) (zero_zero real)) _let_4))) (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (hAPP _let_2 (fun X_b _let_1) (tendsto X_a X_b) BOUND_VARIABLE_126189) (zero_zero X_b)) _let_4)))))))) ) 15.83/15.95 ( real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/15.95 ) 15.83/15.95 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (uminus_uminus real) _let_2)) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) _let_2))) (= X_1 (hAPP real real arcsin (hAPP real real sin X_1))))))) ) 15.83/15.95 ( (zero_zero real) ) 15.83/15.95 ( pi ) 15.83/15.95 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/15.95 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/15.95 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.83/15.95 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.83/15.95 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.83/15.95 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/15.95 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.83/15.95 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.83/15.95 ( skv_5 ) 15.83/15.95 ) 15.83/15.95 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (product_prod X_a X_b))) (or (not (hBOOL (hAPP _let_1 bool (hAPP (fun X_a _let_0) (fun _let_1 bool) (product_prod_case X_a X_b bool) F) (hAPP X_b _let_1 (hAPP X_a (fun X_b _let_1) (product_Pair X_a X_b) A_2) B_1)))) (hBOOL (hAPP X_b bool (hAPP X_a _let_0 F A_2) B_1))))) ) 15.83/15.95 ( nat, nat, (ord_less nat), (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/15.95 ( int, int, (ord_less_eq int), (one_one int), t ) 15.83/15.95 ( int, int, (ord_less_eq int), (zero_zero int), (one_one int) ) 15.83/15.95 ( int, int, (ord_less_eq int), (zero_zero int), min_1 ) 15.83/15.95 ( int, int, (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/15.95 ( int, int, (ord_less_eq int), (zero_zero int), s ) 15.83/15.95 ( int, int, (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.83/15.95 ( int, int, (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.83/15.95 ( int, int, (ord_less_eq int), (zero_zero int), skv_4 ) 15.83/15.95 ( int, int, (ord_less_eq int), (zero_zero int), skv_10 ) 15.83/15.95 ( int, int, (ord_less_eq int), min_1, pls ) 15.83/15.95 ( int, int, (ord_less_eq int), min_1, min_1 ) 15.83/15.95 ( int, int, (ord_less int), (one_one int), t ) 15.83/15.95 ( int, int, (ord_less int), pls, (one_one int) ) 15.83/15.95 ( int, int, (ord_less int), pls, pls ) 15.83/15.95 ( int, int, (ord_less int), pls, min_1 ) 15.83/15.95 ( int, int, (ord_less int), pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.83/15.95 ( int, int, (ord_less int), min_1, pls ) 15.83/15.95 ( int, int, (ord_less int), min_1, min_1 ) 15.83/15.95 ( int, int, (ord_less int), s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.83/15.95 ( int, int, (ord_less int), t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.83/15.95 ( int, int, (ord_less int), skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.83/15.95 ( int, int, (ord_less int), skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.83/15.95 ( int, int, (dvd_dvd int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 15.83/15.95 ( int, int, quadRes, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (number_number_of int) min_1) ) 15.83/15.95 ( int, int, (hAPP int (fun int (fun int bool)) zcong s1), s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.83/15.95 ( int, int, (hAPP int (fun int (fun int bool)) zcong s1), skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.83/15.95 ( int, int, (hAPP int (fun int (fun int bool)) zcong s1), skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.83/15.95 ( int, int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.83/15.95 ( int, int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.83/15.95 ( int, int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.83/15.95 ( int, int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.83/15.95 ( int, (fun int bool), (member int), (one_one int), zEven ) 15.83/15.95 ( real, real, (ord_less real), (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/15.95 ( real, real, (ord_less real), (zero_zero real), pi ) 15.83/15.95 ( real, real, (ord_less real), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/15.95 ( real, real, (ord_less real), (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/15.95 ( real, real, (ord_less real), (zero_zero real), skv_2 ) 15.83/15.95 ( real, real, (ord_less real), (zero_zero real), skv_8 ) 15.83/15.95 ( real, real, (ord_less real), (zero_zero real), skv_9 ) 15.83/15.95 ( real, real, (ord_less real), pi, (zero_zero real) ) 15.83/15.95 ( real, real, (ord_less real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/15.95 ( real, real, (ord_less real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/15.95 ( real, real, (ord_less real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 15.83/15.95 ( real, real, (ord_less real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.83/15.95 ( real, real, (ord_less real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 15.83/15.95 ( real, real, (ord_less_eq real), (zero_zero real), pi ) 15.83/15.95 ( real, real, (ord_less_eq real), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/15.95 ( real, real, (ord_less_eq real), (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/15.95 ( real, real, (ord_less_eq real), (zero_zero real), skv_3 ) 15.83/15.95 ( real, real, (ord_less_eq real), (zero_zero real), skv_5 ) 15.83/15.95 ( real, real, (ord_less_eq real), (zero_zero real), skv_7 ) 15.83/15.95 ( real, real, (ord_less_eq real), (zero_zero real), skv_12 ) 15.83/15.95 ( real, real, (ord_less_eq real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.83/15.95 ( real, real, (ord_less_eq real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/15.95 ( real, real, (ord_less_eq real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.83/15.95 ( real, real, (ord_less_eq real), skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/15.95 ( real, (filter nat), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 (fun real (fun (filter nat) bool)) (tendsto nat real) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))))), (zero_zero real), sequentially ) 15.83/15.95 ( real, (filter real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 (fun real (fun (filter real) bool)) (tendsto real real) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin)))), (zero_zero real), (hAPP real (filter real) (at real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.83/15.95 ( (fun nat int), (fun nat bool), (nat_tr1645093318rphism nat int), (semiring_1_of_nat int), (hAPP bool (fun nat bool) (combk bool nat) fTrue) ) 15.83/15.95 ( (fun nat real), real, (sums real), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (hAPP real _let_1 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc))), (one_one real) ) 15.83/15.95 ( (fun int nat), (fun int bool), (nat_tr1645093318rphism int nat), nat_1, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 15.83/15.95 ) 15.83/15.95 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_0 (sgn_sgn int))) (= (hAPP rat rat (sgn_sgn rat) (hAPP int rat (hAPP int (fun int rat) fract A_1) B)) (hAPP int rat (ring_1_of_int rat) (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int _let_0 A_1)) (hAPP int int _let_0 B))))) ) 15.83/15.95 ( (one_one int), (one_one int) ) 15.83/15.95 ( (zero_zero int), (one_one int) ) 15.83/15.95 ) 15.83/15.95 (instantiation (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (times_times real))) (or (= (zero_zero real) C_1) (= (= (hAPP real real (hAPP real _let_0 _let_1 B_1) C_1) (hAPP real real (hAPP real _let_0 _let_1 A_2) C_1)) (= A_2 B_1))))) ) 15.83/15.95 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.83/15.95 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.83/15.95 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.83/15.95 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.83/15.95 ) 15.83/15.95 (instantiation (forall ((A_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (one_one int))) (let ((_let_3 (ord_less int))) (let ((_let_4 (ti int A_1))) (or (not (hBOOL (hAPP int bool zprime P_5))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_3 (zero_zero int)) A_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_3 A_1) P_5))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP int int (hAPP int _let_1 (times_times int) A_1) A_1)) _let_2) P_5))) (= _let_2 _let_4) (= _let_4 (hAPP int int (hAPP int _let_1 (minus_minus int) P_5) _let_2)))))))) ) 15.83/15.95 ( (one_one int), t ) 15.83/15.95 ( pls, (one_one int) ) 15.83/15.95 ( pls, pls ) 15.83/15.95 ( pls, min_1 ) 15.83/15.95 ( pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.83/15.95 ( min_1, pls ) 15.83/15.95 ( min_1, min_1 ) 15.83/15.95 ( s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.83/15.95 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.83/15.95 ( skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.83/15.95 ( skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.83/15.95 ) 15.83/15.95 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_126590 $$unsorted) (BOUND_VARIABLE_126599 $$unsorted)) (let ((_let_0 (number_number_of int))) (let ((_let_1 (number_number_of nat))) (let ((_let_2 (semiring_1_of_nat X_a))) (or (not (number_ring X_a)) (and (or (not (hBOOL (hAPP int bool nat_neg (hAPP int int _let_0 BOUND_VARIABLE_126590)))) (= (zero_zero X_a) (hAPP nat X_a _let_2 (hAPP int nat _let_1 BOUND_VARIABLE_126590)))) (or (hBOOL (hAPP int bool nat_neg (hAPP int int _let_0 BOUND_VARIABLE_126599))) (= (hAPP nat X_a _let_2 (hAPP int nat _let_1 BOUND_VARIABLE_126599)) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_126599)))))))) ) 15.83/15.95 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/15.95 ( real, min_1, min_1 ) 15.83/15.95 ( rat, (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 15.83/15.95 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.83/15.95 ) 15.83/15.95 (instantiation (forall ((N_1 $$unsorted) (D $$unsorted)) (let ((_let_0 (real_1 int))) (or (= (zero_zero int) (ti int D)) (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (dvd_dvd int) D) N_1))) (= (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_0 N_1)) (hAPP int real _let_0 D)) (hAPP int real _let_0 (hAPP int int (hAPP int (fun int int) (div_div int) N_1) D))))) ) 15.83/15.95 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.83/15.95 ) 15.83/15.95 (instantiation (forall ((R_4 $$unsorted) (S_3 $$unsorted)) (let ((_let_0 (number_number_of real))) (let ((_let_1 (number_number_of rat))) (= (hAPP rat real ratreal (hAPP rat rat (hAPP rat (fun rat rat) (inverse_divide rat) (hAPP int rat _let_1 R_4)) (hAPP int rat _let_1 S_3))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_0 R_4)) (hAPP int real _let_0 S_3))))) ) 15.83/15.95 ( (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.83/15.95 ) 15.83/15.95 (instantiation (forall ((W $$unsorted)) (= (hAPP int int (ring_1_of_int int) W) (hAPP int int (number_number_of int) W)) ) 15.83/15.95 ( pls ) 15.83/15.95 ( (hAPP int int bit1 pls) ) 15.83/15.95 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.83/15.95 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.83/15.95 ( min_1 ) 15.83/15.95 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/15.95 ) 15.83/15.95 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (ord_gr676655987ssThan X_a))) (or (not (ordered_ab_group_add X_a)) (= _let_0 (ti (fun X_a (fun X_a (fun X_a bool))) _let_0)))) ) 15.83/15.95 ( bool ) 15.83/15.95 ( nat ) 15.83/15.95 ( int ) 15.83/15.95 ( (fun int bool) ) 15.83/15.95 ( (fun nat bool) ) 15.83/15.95 ( (product_prod nat nat) ) 15.83/15.95 ( real ) 15.83/15.95 ( rat ) 15.83/15.95 ( (filter nat) ) 15.83/15.95 ( (product_prod int int) ) 15.83/15.95 ( (product_prod real real) ) 15.83/15.95 ( (fun nat rat) ) 15.83/15.95 ( (filter real) ) 15.83/15.95 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 15.83/15.95 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 15.83/15.95 ) 15.83/15.95 (instantiation (forall ((F $$unsorted)) (let ((_let_0 (fun nat real))) (or (not (hBOOL (hAPP _let_0 bool (summable real) F))) (not (forall ((N_2 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) (hAPP nat real F N_2))) )) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) (hAPP _let_0 real (suminf real) F))))) ) 15.83/15.95 ( (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat (fun nat nat)))) (let ((_let_3 (fun nat _let_0))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun _let_1 _let_3))) (let ((_let_6 (combb real _let_0 nat))) (let ((_let_7 (combc nat nat nat))) (hAPP _let_1 _let_1 (hAPP _let_3 (fun _let_1 _let_1) (combs nat real real) (hAPP _let_1 _let_3 (hAPP _let_4 _let_5 _let_6 (inverse_divide real)) (hAPP real _let_1 (hAPP _let_3 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_3 (hAPP _let_4 _let_5 _let_6 (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) (one_one real)))) (hAPP (fun nat nat) _let_1 (hAPP _let_1 (fun (fun nat nat) _let_1) (combb nat real nat) (real_1 nat)) (hAPP nat (fun nat nat) (hAPP _let_2 _let_2 _let_7 (hAPP (fun nat nat) _let_2 (hAPP _let_2 (fun (fun nat nat) _let_2) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_2 _let_2 _let_7 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))))))))))) ) 15.83/15.95 ) 15.83/15.95 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_126703 $$unsorted) (BOUND_VARIABLE_126704 $$unsorted)) (or (not (semiri456707255roduct X_a)) (= (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_126703) BOUND_VARIABLE_126704) (ti X_a BOUND_VARIABLE_126703)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_126704)))) ) 15.83/15.95 ( nat, (one_one nat), (one_one nat) ) 15.83/15.95 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 15.83/15.95 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 15.83/15.95 ) 15.83/15.95 (instantiation (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP int bool nat_is_nat X_1))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) (hAPP int int (fact_fact int) X_1)))) ) 15.83/15.95 ( (one_one int) ) 15.83/15.95 ( (zero_zero int) ) 15.83/15.95 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/15.95 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.83/15.95 ) 15.83/15.95 (instantiation (forall ((I $$unsorted) (P_1 $$unsorted) (K $$unsorted)) (or (not (hBOOL (hAPP int bool P_1 K))) (not (forall ((I_2 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) K) I_2))) (not (hBOOL (hAPP int bool P_1 I_2))) (hBOOL (hAPP int bool P_1 (hAPP int int (hAPP int (fun int int) (plus_plus int) I_2) (one_one int))))) )) (not (forall ((I_2 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) I_2) K))) (not (hBOOL (hAPP int bool P_1 I_2))) (hBOOL (hAPP int bool P_1 (hAPP int int (hAPP int (fun int int) (minus_minus int) I_2) (one_one int))))) )) (hBOOL (hAPP int bool P_1 I))) ) 15.83/15.95 ( (one_one int), nat_neg, (one_one int) ) 15.83/15.95 ( (one_one int), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (one_one int) ) 15.83/15.95 ( (one_one int), (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (one_one int) ) 15.83/15.95 ( (one_one int), (even_odd_even int), (one_one int) ) 15.83/15.95 ( (one_one int), nat_is_nat, (one_one int) ) 15.83/15.95 ( (zero_zero int), (even_odd_even int), (zero_zero int) ) 15.83/15.95 ( (zero_zero int), nat_is_nat, (zero_zero int) ) 15.83/15.95 ( pls, (hAPP int (fun int bool) (ord_less int) pls), pls ) 15.83/15.95 ( pls, (hAPP int (fun int bool) (ord_less int) min_1), pls ) 15.83/15.95 ( pls, (hAPP int (fun int bool) (ord_less_eq int) min_1), pls ) 15.83/15.95 ( min_1, (hAPP int (fun int bool) (ord_less int) pls), min_1 ) 15.83/15.95 ( min_1, (hAPP int (fun int bool) (ord_less_eq int) pls), min_1 ) 15.83/15.95 ( min_1, (hAPP int (fun int bool) (ord_less int) min_1), min_1 ) 15.83/15.95 ( min_1, (hAPP int (fun int bool) (ord_less_eq int) min_1), min_1 ) 15.83/15.95 ( (hAPP int int (number_number_of int) min_1), nat_neg, (hAPP int int (number_number_of int) min_1) ) 15.83/15.95 ( (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int (fun int bool) quadRes (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int int (number_number_of int) min_1) ) 15.83/15.95 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/15.95 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), zprime, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/15.95 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/15.95 ( s, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), s ) 15.83/15.95 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.83/15.95 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), zprime, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.83/15.95 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int (fun int bool) (ord_less int) s), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.83/15.95 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) s)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.83/15.95 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (let ((_let_3 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int _let_1 _let_2 s) _let_3)) (hAPP nat int (hAPP int _let_1 _let_2 s1) _let_3)))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.83/15.95 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.83/15.95 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int (fun int bool) (ord_less int) t), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.83/15.95 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.83/15.95 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_4)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.83/15.95 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int (fun int bool) (ord_less int) skv_4), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.83/15.95 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int (fun int bool) (ord_less int) skv_10), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.83/15.95 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_10)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.83/15.95 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.83/15.95 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 15.83/15.95 ( t, (hAPP int (fun int bool) (ord_less_eq int) (one_one int)), t ) 15.83/15.95 ( t, (hAPP int (fun int bool) (ord_less int) (one_one int)), t ) 15.83/15.95 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) t))), twoSqu1091635170sum2sq, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) t))) ) 15.83/15.95 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.83/15.95 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.83/15.95 ( (hAPP int int (number_number_of int) pls), nat_neg, (hAPP int int (number_number_of int) pls) ) 15.83/15.95 ( (hAPP int int (number_number_of int) pls), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) pls) ) 15.83/15.95 ( skv_4, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_4 ) 15.83/15.95 ( skv_10, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_10 ) 15.83/15.95 ) 15.83/15.95 (instantiation (forall ((Ma $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat bool))) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) Ma) N))) (= (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) N) (hAPP nat nat suc Ma))) (= Ma N)))) ) 15.83/15.95 ( (hAPP nat nat suc (zero_zero nat)), (zero_zero nat) ) 15.83/15.95 ) 15.83/15.95 (instantiation (forall ((P_2 $$unsorted) (P_1 $$unsorted) (X_2 $$unsorted)) (let ((_let_0 (hBOOL P_1))) (let ((_let_1 (hBOOL P_2))) (let ((_let_2 (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) X_2))))) (or (and (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) X_2)) (= (not _let_1) _let_0)) (= (or _let_2 _let_0) (or _let_2 _let_1)))))) ) 15.83/15.95 ( (hAPP int bool (hAPP int (fun int bool) (ord_less int) pls) pls), (hAPP int bool (hAPP int (fun int bool) (ord_less int) pls) pls), s ) 15.83/15.95 ( (hAPP int bool (hAPP int (fun int bool) (ord_less int) pls) pls), (let ((_let_0 (fun int int))) (hAPP int bool (hAPP int (fun int bool) (ord_less int) s) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), s ) 15.83/15.95 ( (let ((_let_0 (fun int int))) (hAPP int bool (hAPP int (fun int bool) (ord_less int) s) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int bool (hAPP int (fun int bool) (ord_less int) pls) pls), (one_one int) ) 15.83/15.95 ( (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) s) (hAPP int int (hAPP int _let_1 (plus_plus int) (hAPP int int (hAPP int _let_1 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) s) (hAPP int int (hAPP int _let_1 (plus_plus int) (hAPP int int (hAPP int _let_1 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))))), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.83/15.95 ( (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) s) (hAPP int int (hAPP int _let_1 (plus_plus int) (hAPP int int (hAPP int _let_1 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))))), (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) s), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.83/15.95 ( (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) s), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) s) (hAPP int int (hAPP int _let_1 (plus_plus int) (hAPP int int (hAPP int _let_1 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))))), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/15.95 ( (let ((_let_0 (fun int int))) (let ((_let_1 (one_one int))) (let ((_let_2 (plus_plus int))) (let ((_let_3 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int bool (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 _let_3))) m)) _let_1)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) _let_3))) _let_1)))))), (let ((_let_0 (fun int int))) (let ((_let_1 (one_one int))) (let ((_let_2 (plus_plus int))) (let ((_let_3 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int bool (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 _let_3))) m)) _let_1)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) _let_3))) _let_1)))))), (hAPP int int (number_number_of int) pls) ) 15.83/15.95 ( (let ((_let_0 (fun int int))) (let ((_let_1 (one_one int))) (let ((_let_2 (plus_plus int))) (let ((_let_3 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int bool (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 _let_3))) m)) _let_1)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) _let_3))) _let_1)))))), (hAPP nat bool prime (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) pls) ) 15.83/15.95 ( (hAPP nat bool prime (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (let ((_let_1 (one_one int))) (let ((_let_2 (plus_plus int))) (let ((_let_3 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int bool (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 _let_3))) m)) _let_1)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) _let_3))) _let_1)))))), min_1 ) 15.83/15.95 ( (let ((_let_0 (fun real real))) (let ((_let_1 (inverse_divide real))) (let ((_let_2 (fun real _let_0))) (let ((_let_3 (filter real))) (let ((_let_4 (fun _let_3 bool))) (hAPP _let_3 bool (hAPP real _let_4 (hAPP _let_0 (fun real _let_4) (tendsto real real) (hAPP _let_0 _let_0 (hAPP _let_2 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_2 (hAPP _let_2 (fun _let_0 _let_2) (combb real _let_0 real) _let_1) cos)) sin)) (zero_zero real)) (hAPP real _let_3 (at real) (hAPP real real (hAPP real _let_0 _let_1 pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))))))), (let ((_let_0 (fun real real))) (let ((_let_1 (inverse_divide real))) (let ((_let_2 (fun real _let_0))) (let ((_let_3 (filter real))) (let ((_let_4 (fun _let_3 bool))) (hAPP _let_3 bool (hAPP real _let_4 (hAPP _let_0 (fun real _let_4) (tendsto real real) (hAPP _let_0 _let_0 (hAPP _let_2 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_2 (hAPP _let_2 (fun _let_0 _let_2) (combb real _let_0 real) _let_1) cos)) sin)) (zero_zero real)) (hAPP real _let_3 (at real) (hAPP real real (hAPP real _let_0 _let_1 pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))))))), skv_4 ) 15.83/15.95 ( (let ((_let_0 (fun real real))) (let ((_let_1 (inverse_divide real))) (let ((_let_2 (fun real _let_0))) (let ((_let_3 (filter real))) (let ((_let_4 (fun _let_3 bool))) (hAPP _let_3 bool (hAPP real _let_4 (hAPP _let_0 (fun real _let_4) (tendsto real real) (hAPP _let_0 _let_0 (hAPP _let_2 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_2 (hAPP _let_2 (fun _let_0 _let_2) (combb real _let_0 real) _let_1) cos)) sin)) (zero_zero real)) (hAPP real _let_3 (at real) (hAPP real real (hAPP real _let_0 _let_1 pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))))))), (hAPP nat bool (even_odd_even nat) (zero_zero nat)), skv_4 ) 15.83/15.95 ( (hAPP nat bool (even_odd_even nat) (zero_zero nat)), (let ((_let_0 (fun real real))) (let ((_let_1 (inverse_divide real))) (let ((_let_2 (fun real _let_0))) (let ((_let_3 (filter real))) (let ((_let_4 (fun _let_3 bool))) (hAPP _let_3 bool (hAPP real _let_4 (hAPP _let_0 (fun real _let_4) (tendsto real real) (hAPP _let_0 _let_0 (hAPP _let_2 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_2 (hAPP _let_2 (fun _let_0 _let_2) (combb real _let_0 real) _let_1) cos)) sin)) (zero_zero real)) (hAPP real _let_3 (at real) (hAPP real real (hAPP real _let_0 _let_1 pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))))))), skv_10 ) 15.83/15.95 ) 15.83/15.95 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted) (N $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (hAPP nat (fun real real) root N))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N))) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real _let_2 X_2)) (hAPP real real _let_2 Y_2))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_2) Y_2))))))) ) 15.83/15.95 ( (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/15.95 ( (zero_zero real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/15.95 ) 15.83/15.95 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int int pred K_4) (hAPP int int (hAPP int (fun int int) (plus_plus int) min_1) K_4)) ) 15.83/15.95 ( pls ) 15.83/15.95 ( min_1 ) 15.83/15.95 ) 15.83/15.95 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (the X_a))) (or (not (metric_space X_a)) (= _let_0 (ti (fun (fun X_a bool) X_a) _let_0)))) ) 15.83/15.95 ( bool ) 15.83/15.95 ( nat ) 15.83/15.95 ( int ) 15.83/15.95 ( (fun int bool) ) 15.83/15.95 ( (fun nat bool) ) 15.83/15.95 ( (product_prod nat nat) ) 15.83/15.95 ( real ) 15.83/15.95 ( complex ) 15.83/15.95 ( (filter nat) ) 15.83/15.95 ( (product_prod int int) ) 15.83/15.95 ( (product_prod real real) ) 15.83/15.95 ( (fun nat rat) ) 15.83/15.95 ( (filter real) ) 15.83/15.95 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 15.83/15.95 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 15.83/15.95 ) 15.83/15.99 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted) (X_d $$unsorted) (F $$unsorted) (G $$unsorted)) (let ((_let_0 (fun X_b X_c))) (let ((_let_1 (fun X_a _let_0))) (let ((_let_2 (product_prod X_a X_b))) (let ((_let_3 (fun _let_2 X_c))) (let ((_let_4 (fun X_a X_d))) (let ((_let_5 (fun X_d _let_0))) (let ((_let_6 (fun _let_2 X_b))) (let ((_let_7 (fun _let_2 _let_0))) (let ((_let_8 (fun _let_2 X_d))) (let ((_let_9 (fun _let_2 X_a))) (= (hAPP _let_6 _let_3 (hAPP _let_7 (fun _let_6 _let_3) (combs _let_2 X_b X_c) (hAPP _let_8 _let_7 (hAPP _let_5 (fun _let_8 _let_7) (combb X_d _let_0 _let_2) F) (hAPP _let_9 _let_8 (hAPP _let_4 (fun _let_9 _let_8) (combb X_a X_d _let_2) G) (product_fst X_a X_b)))) (product_snd X_a X_b)) (hAPP _let_1 _let_3 (product_prod_case X_a X_b X_c) (hAPP _let_4 _let_1 (hAPP _let_5 (fun _let_4 _let_1) (combb X_d _let_0 X_a) F) G))))))))))))) ) 15.83/15.99 ( nat, nat, bool, nat, (let ((_let_0 (fun nat (fun nat bool)))) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat))), suc ) 15.83/15.99 ( nat, nat, nat, nat, (plus_plus nat), (let ((_let_0 (fun nat (fun nat nat)))) (hAPP nat (fun nat nat) (hAPP _let_0 _let_0 (combc nat nat nat) (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.83/15.99 ( nat, real, real, real, (inverse_divide real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (hAPP real _let_1 (hAPP _let_2 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 nat) (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) (one_one real))))) ) 15.83/15.99 ( nat, real, real, real, (times_times real), (hAPP real (fun nat real) (power_power real) (hAPP int real (number_number_of real) min_1)) ) 15.83/15.99 ( int, bool, bool, bool, fconj, (hAPP int (fun int bool) (ord_less int) (zero_zero int)) ) 15.83/15.99 ( int, int, bool, (fun int bool), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun int _let_1))) (hAPP _let_2 (fun _let_0 _let_0) (combs int bool bool) (hAPP _let_0 _let_2 (hAPP (fun bool _let_1) (fun _let_0 _let_2) (combb bool _let_1 int) fconj) (hAPP int _let_0 (ord_less int) (zero_zero int))))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int _let_1))) (let ((_let_5 (fun _let_2 _let_1))) (hAPP int _let_1 (hAPP _let_4 _let_4 (combc int int _let_0) (hAPP _let_4 _let_4 (hAPP (fun _let_1 _let_1) (fun _let_4 _let_4) (combb _let_1 _let_1 int) (combc int int bool)) (hAPP _let_3 _let_4 (hAPP _let_5 (fun _let_3 _let_4) (combb _let_2 _let_1 int) (hAPP _let_1 _let_5 (combb int _let_0 int) (fequal int))) int_gcd))) (one_one int)))))))) ) 15.83/15.99 ( int, int, int, int, (plus_plus int), (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/15.99 ( int, int, int, int, (plus_plus int), (let ((_let_0 (fun int int))) (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.83/15.99 ( int, int, (fun int bool), (fun int (fun int bool)), (combc int int bool), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int _let_1))) (let ((_let_5 (fun _let_2 _let_1))) (hAPP _let_3 _let_4 (hAPP _let_5 (fun _let_3 _let_4) (combb _let_2 _let_1 int) (hAPP _let_1 _let_5 (combb int _let_0 int) (fequal int))) int_gcd))))))) ) 15.83/15.99 ( int, int, (fun int bool), (fun int int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (hAPP _let_1 (fun (fun int int) _let_1) (combb int _let_0 int) (fequal int)))), int_gcd ) 15.83/15.99 ( int, (fun int int), (fun int bool), (fun int bool), (combb int bool int), (fequal int) ) 15.83/15.99 ( int, (fun int int), (fun int int), (fun int int), (combb int int int), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)) (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 15.83/15.99 ( int, real, real, real, (inverse_divide real), (real_1 int) ) 15.83/15.99 ( int, (fun nat real), (fun nat real), (fun real real), (combb real real nat), (let ((_let_0 (fun real real))) (let ((_let_1 (fun int real))) (let ((_let_2 (fun int _let_0))) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 int) (inverse_divide real)) (real_1 int))))) ) 15.83/15.99 ( int, (fun int real), (fun int real), (fun real real), (combb real real int), (let ((_let_0 (fun real real))) (let ((_let_1 (fun int real))) (let ((_let_2 (fun int _let_0))) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 int) (inverse_divide real)) (real_1 int))))) ) 15.83/15.99 ( real, bool, bool, bool, fconj, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) ) 15.83/15.99 ( real, bool, bool, bool, fconj, (let ((_let_0 (fun real (fun real bool)))) (hAPP real (fun real bool) (hAPP _let_0 _let_0 (combc real real bool) (ord_less_eq real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.83/15.99 ( real, int, bool, (fun int (fun int bool)), (let ((_let_0 (fun int bool))) (hAPP (fun _let_0 bool) (fun (fun int _let_0) _let_0) (combb _let_0 bool int) (fEx int))), (let ((_let_0 (fun int (fun int bool)))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real real))) (let ((_let_3 (real_1 int))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun int _let_4))) (let ((_let_7 (fun (fun int bool) (fun int bool)))) (let ((_let_8 (fun (fun int bool) _let_6))) (let ((_let_9 (fun int real))) (let ((_let_10 (fun int _let_7))) (let ((_let_11 (fun (fun int bool) _let_0))) (let ((_let_12 (fun int _let_6))) (let ((_let_13 (fun _let_12 _let_10))) (let ((_let_14 (fun _let_0 _let_12))) (let ((_let_15 (fun real _let_0))) (let ((_let_16 (fun real _let_11))) (let ((_let_17 (fun real _let_10))) (let ((_let_18 (fun real _let_12))) (let ((_let_19 (fun int _let_9))) (let ((_let_20 (fun _let_19 _let_0))) (let ((_let_21 (fun real _let_20))) (let ((_let_22 (fun _let_9 (fun int bool)))) (let ((_let_23 (fun real _let_22))) (let ((_let_24 (fun _let_9 _let_9))) (let ((_let_25 (fun int _let_24))) (let ((_let_26 (fun int _let_2))) (hAPP (fun int bool) _let_15 (hAPP _let_16 (fun (fun int bool) _let_15) (combc real (fun int bool) _let_0) (hAPP _let_17 _let_16 (hAPP (fun _let_10 _let_11) (fun _let_17 _let_16) (combb _let_10 _let_11 real) (combc int (fun int bool) (fun int bool))) (hAPP _let_18 _let_17 (hAPP _let_13 (fun _let_18 _let_17) (combb _let_12 _let_10 real) (hAPP (fun _let_6 _let_7) _let_13 (combb _let_6 _let_7 int) (combs int bool bool))) (hAPP _let_15 _let_18 (hAPP _let_14 (fun _let_15 _let_18) (combb _let_0 _let_12 real) (hAPP _let_8 _let_14 (combb (fun int bool) _let_6 int) (hAPP (fun bool _let_4) _let_8 (combb bool _let_4 int) fconj))) (hAPP _let_19 _let_15 (hAPP _let_21 (fun _let_19 _let_15) (combc real _let_19 _let_0) (hAPP _let_23 _let_21 (hAPP (fun _let_22 _let_20) (fun _let_23 _let_21) (combb _let_22 _let_20 real) (combb _let_9 (fun int bool) int)) (hAPP _let_5 _let_23 (hAPP (fun _let_1 _let_22) (fun _let_5 _let_23) (combb _let_1 _let_22 real) (combb real bool int)) (fequal real)))) (hAPP _let_9 _let_19 (hAPP _let_25 (fun _let_9 _let_19) (combc int _let_9 _let_9) (hAPP _let_26 _let_25 (hAPP (fun _let_2 _let_24) (fun _let_26 _let_25) (combb _let_2 _let_24 int) (combb real real int)) (hAPP _let_9 _let_26 (hAPP (fun real _let_2) (fun _let_9 _let_26) (combb real _let_2 int) (inverse_divide real)) _let_3))) _let_3)))))) (hAPP (fun int bool) (fun int bool) (hAPP _let_4 _let_7 (combb bool bool int) fNot) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (fequal int)) (zero_zero int))))))))))))))))))))))))))))))) ) 15.83/15.99 ( real, int, bool, (fun int (fun nat bool)), (let ((_let_0 (fun nat bool))) (hAPP (fun _let_0 bool) (fun (fun int _let_0) (fun int bool)) (combb _let_0 bool int) (fEx nat))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat (fun nat bool)))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun (fun nat real) (fun nat real)))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun (fun nat bool) (fun nat bool)))) (let ((_let_7 (fun int real))) (let ((_let_8 (fun nat _let_3))) (let ((_let_9 (fun (fun nat bool) _let_8))) (let ((_let_10 (fun int _let_1))) (let ((_let_11 (fun real (fun int (fun nat bool))))) (let ((_let_12 (fun (fun nat bool) (fun int (fun nat bool))))) (let ((_let_13 (fun real _let_12))) (let ((_let_14 (fun int _let_6))) (let ((_let_15 (fun real _let_14))) (let ((_let_16 (fun int _let_8))) (let ((_let_17 (fun real _let_16))) (let ((_let_18 (fun _let_16 _let_14))) (let ((_let_19 (fun (fun int (fun nat bool)) _let_16))) (let ((_let_20 (fun int (fun nat real)))) (let ((_let_21 (fun _let_20 (fun int (fun nat bool))))) (let ((_let_22 (fun real _let_21))) (let ((_let_23 (fun (fun nat real) (fun nat bool)))) (let ((_let_24 (fun real _let_23))) (let ((_let_25 (fun int _let_4))) (hAPP (fun nat bool) _let_11 (hAPP _let_13 (fun (fun nat bool) _let_11) (combc real (fun nat bool) (fun int (fun nat bool))) (hAPP _let_15 _let_13 (hAPP (fun _let_14 _let_12) (fun _let_15 _let_13) (combb _let_14 _let_12 real) (combc int (fun nat bool) (fun nat bool))) (hAPP _let_17 _let_15 (hAPP _let_18 (fun _let_17 _let_15) (combb _let_16 _let_14 real) (hAPP (fun _let_8 _let_6) _let_18 (combb _let_8 _let_6 int) (combs nat bool bool))) (hAPP _let_11 _let_17 (hAPP _let_19 (fun _let_11 _let_17) (combb (fun int (fun nat bool)) _let_16 real) (hAPP _let_9 _let_19 (combb (fun nat bool) _let_8 int) (hAPP (fun bool _let_3) _let_9 (combb bool _let_3 nat) fconj))) (hAPP _let_20 _let_11 (hAPP _let_22 (fun _let_20 _let_11) (combc real _let_20 (fun int (fun nat bool))) (hAPP _let_24 _let_22 (hAPP (fun _let_23 _let_21) (fun _let_24 _let_22) (combb _let_23 _let_21 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_5 _let_24 (hAPP (fun _let_0 _let_23) (fun _let_5 _let_24) (combb _let_0 _let_23 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_20 (hAPP _let_25 (fun (fun nat real) _let_20) (combc int (fun nat real) (fun nat real)) (hAPP _let_10 _let_25 (hAPP (fun _let_1 _let_4) (fun _let_10 _let_25) (combb _let_1 _let_4 int) (combb real real nat)) (hAPP _let_7 _let_10 (hAPP (fun real _let_1) (fun _let_7 _let_10) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat))))))) (hAPP (fun nat bool) (fun nat bool) (hAPP _let_3 _let_6 (combb bool bool nat) fNot) (hAPP nat (fun nat bool) (hAPP _let_2 _let_2 (combc nat nat bool) (fequal nat)) (zero_zero nat)))))))))))))))))))))))))))))) ) 15.83/15.99 ( real, int, (fun int (fun bool bool)), (fun int (fun int bool)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (fun _let_0 _let_2))) (hAPP _let_3 (fun (fun int _let_0) (fun int _let_2)) (combb _let_0 _let_2 int) (hAPP (fun bool _let_1) _let_3 (combb bool _let_1 int) fconj)))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun real _let_0))) (let ((_let_4 (fun int real))) (let ((_let_5 (fun real (fun int (fun int bool))))) (let ((_let_6 (fun int _let_4))) (let ((_let_7 (fun _let_6 (fun int (fun int bool))))) (let ((_let_8 (fun real _let_7))) (let ((_let_9 (fun _let_4 (fun int bool)))) (let ((_let_10 (fun real _let_9))) (let ((_let_11 (fun _let_4 _let_4))) (let ((_let_12 (fun int _let_11))) (let ((_let_13 (fun int _let_1))) (hAPP _let_6 _let_5 (hAPP _let_8 (fun _let_6 _let_5) (combc real _let_6 (fun int (fun int bool))) (hAPP _let_10 _let_8 (hAPP (fun _let_9 _let_7) (fun _let_10 _let_8) (combb _let_9 _let_7 real) (combb _let_4 (fun int bool) int)) (hAPP _let_3 _let_10 (hAPP (fun _let_0 _let_9) (fun _let_3 _let_10) (combb _let_0 _let_9 real) (combb real bool int)) (fequal real)))) (hAPP _let_4 _let_6 (hAPP _let_12 (fun _let_4 _let_6) (combc int _let_4 _let_4) (hAPP _let_13 _let_12 (hAPP (fun _let_1 _let_11) (fun _let_13 _let_12) (combb _let_1 _let_11 int) (combb real real int)) (hAPP _let_4 _let_13 (hAPP (fun real _let_1) (fun _let_4 _let_13) (combb real _let_1 int) (inverse_divide real)) _let_2))) _let_2)))))))))))))))) ) 15.83/15.99 ( real, int, (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), (fun int (fun int (fun bool bool))), (let ((_let_0 (fun int (fun bool bool)))) (let ((_let_1 (fun (fun int bool) (fun int bool)))) (hAPP (fun _let_0 _let_1) (fun (fun int _let_0) (fun int _let_1)) (combb _let_0 _let_1 int) (combs int bool bool)))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun int _let_3))) (let ((_let_6 (fun (fun int bool) _let_5))) (let ((_let_7 (fun int real))) (let ((_let_8 (fun int _let_5))) (let ((_let_9 (fun (fun int (fun int bool)) _let_8))) (let ((_let_10 (fun real (fun int (fun int bool))))) (let ((_let_11 (fun real _let_8))) (let ((_let_12 (fun int _let_7))) (let ((_let_13 (fun _let_12 (fun int (fun int bool))))) (let ((_let_14 (fun real _let_13))) (let ((_let_15 (fun _let_7 (fun int bool)))) (let ((_let_16 (fun real _let_15))) (let ((_let_17 (fun _let_7 _let_7))) (let ((_let_18 (fun int _let_17))) (let ((_let_19 (fun int _let_1))) (hAPP _let_10 _let_11 (hAPP _let_9 (fun _let_10 _let_11) (combb (fun int (fun int bool)) _let_8 real) (hAPP _let_6 _let_9 (combb (fun int bool) _let_5 int) (hAPP (fun bool _let_3) _let_6 (combb bool _let_3 int) fconj))) (hAPP _let_12 _let_10 (hAPP _let_14 (fun _let_12 _let_10) (combc real _let_12 (fun int (fun int bool))) (hAPP _let_16 _let_14 (hAPP (fun _let_15 _let_13) (fun _let_16 _let_14) (combb _let_15 _let_13 real) (combb _let_7 (fun int bool) int)) (hAPP _let_4 _let_16 (hAPP (fun _let_0 _let_15) (fun _let_4 _let_16) (combb _let_0 _let_15 real) (combb real bool int)) (fequal real)))) (hAPP _let_7 _let_12 (hAPP _let_18 (fun _let_7 _let_12) (combc int _let_7 _let_7) (hAPP _let_19 _let_18 (hAPP (fun _let_1 _let_17) (fun _let_19 _let_18) (combb _let_1 _let_17 int) (combb real real int)) (hAPP _let_7 _let_19 (hAPP (fun real _let_1) (fun _let_7 _let_19) (combb real _let_1 int) (inverse_divide real)) _let_2))) _let_2))))))))))))))))))))))) ) 15.83/15.99 ( real, int, (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)), (fun int (fun nat (fun bool bool))), (let ((_let_0 (fun (fun nat bool) (fun nat bool)))) (let ((_let_1 (fun nat (fun bool bool)))) (hAPP (fun _let_1 _let_0) (fun (fun int _let_1) (fun int _let_0)) (combb _let_1 _let_0 int) (combs nat bool bool)))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun (fun nat real) (fun nat real)))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun int real))) (let ((_let_6 (fun nat _let_2))) (let ((_let_7 (fun (fun nat bool) _let_6))) (let ((_let_8 (fun int _let_1))) (let ((_let_9 (fun real (fun int (fun nat bool))))) (let ((_let_10 (fun int _let_6))) (let ((_let_11 (fun real _let_10))) (let ((_let_12 (fun (fun int (fun nat bool)) _let_10))) (let ((_let_13 (fun int (fun nat real)))) (let ((_let_14 (fun _let_13 (fun int (fun nat bool))))) (let ((_let_15 (fun real _let_14))) (let ((_let_16 (fun (fun nat real) (fun nat bool)))) (let ((_let_17 (fun real _let_16))) (let ((_let_18 (fun int _let_3))) (hAPP _let_9 _let_11 (hAPP _let_12 (fun _let_9 _let_11) (combb (fun int (fun nat bool)) _let_10 real) (hAPP _let_7 _let_12 (combb (fun nat bool) _let_6 int) (hAPP (fun bool _let_2) _let_7 (combb bool _let_2 nat) fconj))) (hAPP _let_13 _let_9 (hAPP _let_15 (fun _let_13 _let_9) (combc real _let_13 (fun int (fun nat bool))) (hAPP _let_17 _let_15 (hAPP (fun _let_16 _let_14) (fun _let_17 _let_15) (combb _let_16 _let_14 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_4 _let_17 (hAPP (fun _let_0 _let_16) (fun _let_4 _let_17) (combb _let_0 _let_16 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_13 (hAPP _let_18 (fun (fun nat real) _let_13) (combc int (fun nat real) (fun nat real)) (hAPP _let_8 _let_18 (hAPP (fun _let_1 _let_3) (fun _let_8 _let_18) (combb _let_1 _let_3 int) (combb real real nat)) (hAPP _let_5 _let_8 (hAPP (fun real _let_1) (fun _let_5 _let_8) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat))))))))))))))))))))))) ) 15.83/15.99 ( real, int, (fun nat (fun bool bool)), (fun int (fun nat bool)), (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun nat _let_1))) (let ((_let_3 (fun _let_0 _let_2))) (hAPP _let_3 (fun (fun int _let_0) (fun int _let_2)) (combb _let_0 _let_2 int) (hAPP (fun bool _let_1) _let_3 (combb bool _let_1 nat) fconj)))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun (fun nat real) (fun nat real)))) (let ((_let_3 (fun real _let_0))) (let ((_let_4 (fun int real))) (let ((_let_5 (fun int _let_1))) (let ((_let_6 (fun real (fun int (fun nat bool))))) (let ((_let_7 (fun int (fun nat real)))) (let ((_let_8 (fun _let_7 (fun int (fun nat bool))))) (let ((_let_9 (fun real _let_8))) (let ((_let_10 (fun (fun nat real) (fun nat bool)))) (let ((_let_11 (fun real _let_10))) (let ((_let_12 (fun int _let_2))) (hAPP _let_7 _let_6 (hAPP _let_9 (fun _let_7 _let_6) (combc real _let_7 (fun int (fun nat bool))) (hAPP _let_11 _let_9 (hAPP (fun _let_10 _let_8) (fun _let_11 _let_9) (combb _let_10 _let_8 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_3 _let_11 (hAPP (fun _let_0 _let_10) (fun _let_3 _let_11) (combb _let_0 _let_10 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_7 (hAPP _let_12 (fun (fun nat real) _let_7) (combc int (fun nat real) (fun nat real)) (hAPP _let_5 _let_12 (hAPP (fun _let_1 _let_2) (fun _let_5 _let_12) (combb _let_1 _let_2 int) (combb real real nat)) (hAPP _let_4 _let_5 (hAPP (fun real _let_1) (fun _let_4 _let_5) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat)))))))))))))))) ) 15.83/15.99 ( real, (fun int bool), (fun int (fun int bool)), (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun int bool))) (combc int _let_0 _let_0)), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun int _let_3))) (let ((_let_6 (fun (fun int bool) (fun int bool)))) (let ((_let_7 (fun (fun int bool) _let_5))) (let ((_let_8 (fun int real))) (let ((_let_9 (fun int _let_6))) (let ((_let_10 (fun int _let_5))) (let ((_let_11 (fun _let_10 _let_9))) (let ((_let_12 (fun (fun int (fun int bool)) _let_10))) (let ((_let_13 (fun real (fun int (fun int bool))))) (let ((_let_14 (fun real _let_9))) (let ((_let_15 (fun real _let_10))) (let ((_let_16 (fun int _let_8))) (let ((_let_17 (fun _let_16 (fun int (fun int bool))))) (let ((_let_18 (fun real _let_17))) (let ((_let_19 (fun _let_8 (fun int bool)))) (let ((_let_20 (fun real _let_19))) (let ((_let_21 (fun _let_8 _let_8))) (let ((_let_22 (fun int _let_21))) (let ((_let_23 (fun int _let_1))) (hAPP _let_15 _let_14 (hAPP _let_11 (fun _let_15 _let_14) (combb _let_10 _let_9 real) (hAPP (fun _let_5 _let_6) _let_11 (combb _let_5 _let_6 int) (combs int bool bool))) (hAPP _let_13 _let_15 (hAPP _let_12 (fun _let_13 _let_15) (combb (fun int (fun int bool)) _let_10 real) (hAPP _let_7 _let_12 (combb (fun int bool) _let_5 int) (hAPP (fun bool _let_3) _let_7 (combb bool _let_3 int) fconj))) (hAPP _let_16 _let_13 (hAPP _let_18 (fun _let_16 _let_13) (combc real _let_16 (fun int (fun int bool))) (hAPP _let_20 _let_18 (hAPP (fun _let_19 _let_17) (fun _let_20 _let_18) (combb _let_19 _let_17 real) (combb _let_8 (fun int bool) int)) (hAPP _let_4 _let_20 (hAPP (fun _let_0 _let_19) (fun _let_4 _let_20) (combb _let_0 _let_19 real) (combb real bool int)) (fequal real)))) (hAPP _let_8 _let_16 (hAPP _let_22 (fun _let_8 _let_16) (combc int _let_8 _let_8) (hAPP _let_23 _let_22 (hAPP (fun _let_1 _let_21) (fun _let_23 _let_22) (combb _let_1 _let_21 int) (combb real real int)) (hAPP _let_8 _let_23 (hAPP (fun real _let_1) (fun _let_8 _let_23) (combb real _let_1 int) (inverse_divide real)) _let_2))) _let_2)))))))))))))))))))))))))))) ) 15.83/15.99 ( real, (fun nat bool), (fun int (fun nat bool)), (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun nat bool))) (combc int _let_0 _let_0)), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun (fun nat real) (fun nat real)))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun (fun nat bool) (fun nat bool)))) (let ((_let_6 (fun int real))) (let ((_let_7 (fun nat _let_2))) (let ((_let_8 (fun (fun nat bool) _let_7))) (let ((_let_9 (fun int _let_1))) (let ((_let_10 (fun real (fun int (fun nat bool))))) (let ((_let_11 (fun int _let_5))) (let ((_let_12 (fun real _let_11))) (let ((_let_13 (fun int _let_7))) (let ((_let_14 (fun real _let_13))) (let ((_let_15 (fun _let_13 _let_11))) (let ((_let_16 (fun (fun int (fun nat bool)) _let_13))) (let ((_let_17 (fun int (fun nat real)))) (let ((_let_18 (fun _let_17 (fun int (fun nat bool))))) (let ((_let_19 (fun real _let_18))) (let ((_let_20 (fun (fun nat real) (fun nat bool)))) (let ((_let_21 (fun real _let_20))) (let ((_let_22 (fun int _let_3))) (hAPP _let_14 _let_12 (hAPP _let_15 (fun _let_14 _let_12) (combb _let_13 _let_11 real) (hAPP (fun _let_7 _let_5) _let_15 (combb _let_7 _let_5 int) (combs nat bool bool))) (hAPP _let_10 _let_14 (hAPP _let_16 (fun _let_10 _let_14) (combb (fun int (fun nat bool)) _let_13 real) (hAPP _let_8 _let_16 (combb (fun nat bool) _let_7 int) (hAPP (fun bool _let_2) _let_8 (combb bool _let_2 nat) fconj))) (hAPP _let_17 _let_10 (hAPP _let_19 (fun _let_17 _let_10) (combc real _let_17 (fun int (fun nat bool))) (hAPP _let_21 _let_19 (hAPP (fun _let_20 _let_18) (fun _let_21 _let_19) (combb _let_20 _let_18 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_4 _let_21 (hAPP (fun _let_0 _let_20) (fun _let_4 _let_21) (combb _let_0 _let_20 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_17 (hAPP _let_22 (fun (fun nat real) _let_17) (combc int (fun nat real) (fun nat real)) (hAPP _let_9 _let_22 (hAPP (fun _let_1 _let_3) (fun _let_9 _let_22) (combb _let_1 _let_3 int) (combb real real nat)) (hAPP _let_6 _let_9 (hAPP (fun real _let_1) (fun _let_6 _let_9) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat)))))))))))))))))))))))))))) ) 15.83/15.99 ( real, real, bool, real, (fequal real), cos ) 15.83/15.99 ( real, real, real, real, (inverse_divide real), cos ) 15.83/15.99 ( real, (fun nat real), (fun nat bool), (fun real bool), (combb real bool nat), (fequal real) ) 15.83/15.99 ( real, (fun int real), (fun int bool), (fun real bool), (combb real bool int), (fequal real) ) 15.83/15.99 ( real, (fun int (fun int real)), (fun int (fun int bool)), (fun (fun int real) (fun int bool)), (combb (fun int real) (fun int bool) int), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun int real) (fun int bool)))) (let ((_let_3 (fun real _let_2))) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 real) (combb real bool int)) (fequal real)))))) ) 15.83/15.99 ( real, (fun int (fun nat real)), (fun int (fun nat bool)), (fun (fun nat real) (fun nat bool)), (combb (fun nat real) (fun nat bool) int), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun nat real) (fun nat bool)))) (let ((_let_3 (fun real _let_2))) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 real) (combb real bool nat)) (fequal real)))))) ) 15.83/15.99 ( (product_prod int int), bool, bool, bool, fconj, (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun _let_1 _let_0))) (let ((_let_4 (fun _let_1 int))) (hAPP _let_2 _let_2 (hAPP (fun bool bool) (fun _let_2 _let_2) (combb bool bool _let_1) fNot) (hAPP int _let_2 (hAPP _let_3 (fun int _let_2) (combc _let_1 int bool) (hAPP _let_4 _let_3 (hAPP (fun int _let_0) (fun _let_4 _let_3) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int)))))))) ) 15.83/15.99 ( (product_prod int int), int, bool, int, (fequal int), (product_snd int int) ) 15.83/15.99 ( (product_prod int int), int, int, int, (times_times int), (product_fst int int) ) 15.83/15.99 ( (product_prod int int), (product_prod int int), bool, (fun (product_prod int int) bool), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_3 _let_3))) (let ((_let_5 (fun _let_1 _let_2))) (let ((_let_6 (fun _let_1 _let_0))) (let ((_let_7 (fun _let_1 int))) (hAPP _let_5 _let_4 (combs _let_1 bool bool) (hAPP _let_3 _let_5 (hAPP (fun bool _let_2) (fun _let_3 _let_5) (combb bool _let_2 _let_1) fconj) (hAPP _let_3 _let_3 (hAPP _let_2 _let_4 (combb bool bool _let_1) fNot) (hAPP int _let_3 (hAPP _let_6 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_7 _let_6 (hAPP (fun int _let_0) (fun _let_7 _let_6) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))))))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun _let_2 (fun _let_2 bool)))) (let ((_let_4 (fun _let_2 _let_0))) (let ((_let_5 (fun _let_2 int))) (let ((_let_6 (fun _let_5 _let_4))) (let ((_let_7 (product_snd int int))) (let ((_let_8 (fun _let_2 _let_5))) (let ((_let_9 (fun _let_5 (fun _let_2 bool)))) (let ((_let_10 (fun _let_2 _let_9))) (let ((_let_11 (fun _let_2 _let_4))) (let ((_let_12 (fun _let_5 _let_5))) (let ((_let_13 (fun _let_2 _let_12))) (let ((_let_14 (fun _let_5 _let_8))) (let ((_let_15 (fun _let_2 _let_1))) (let ((_let_16 (hAPP _let_5 _let_15 (hAPP (fun int _let_1) (fun _let_5 _let_15) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (let ((_let_17 (fun int _let_5))) (hAPP _let_8 _let_3 (hAPP _let_10 (fun _let_8 _let_3) (combs _let_2 _let_5 (fun _let_2 bool)) (hAPP _let_11 _let_10 (hAPP (fun _let_4 _let_9) (fun _let_11 _let_10) (combb _let_4 _let_9 _let_2) (combs _let_2 int bool)) (hAPP _let_8 _let_11 (hAPP _let_6 (fun _let_8 _let_11) (combb _let_5 _let_4 _let_2) (hAPP (fun int _let_0) _let_6 (combb int _let_0 _let_2) (fequal int))) (hAPP _let_5 _let_8 (hAPP _let_13 _let_14 (combc _let_2 _let_5 _let_5) (hAPP _let_15 _let_13 (hAPP (fun _let_1 _let_12) (fun _let_15 _let_13) (combb _let_1 _let_12 _let_2) (combb int int _let_2)) _let_16)) _let_7)))) (hAPP _let_5 _let_8 (hAPP _let_17 _let_14 (combb int _let_5 _let_2) (hAPP _let_15 _let_17 (combc _let_2 int int) _let_16)) _let_7)))))))))))))))))))) ) 15.83/15.99 ( (product_prod int int), (product_prod int int), int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_0))) (hAPP _let_3 (fun int _let_2) (combc _let_1 int int) (hAPP _let_2 _let_3 (hAPP (fun int _let_0) (fun _let_2 _let_3) (combb int _let_0 _let_1) (times_times int)) (product_fst int int))))))), (product_snd int int) ) 15.83/15.99 ( (product_prod int int), (product_prod int int), (fun int bool), (fun (product_prod int int) int), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (hAPP (fun int _let_0) (fun (fun _let_1 int) (fun _let_1 _let_0)) (combb int _let_0 _let_1) (fequal int)))), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_2))) (let ((_let_4 (fun _let_2 _let_2))) (let ((_let_5 (fun _let_1 _let_4))) (let ((_let_6 (fun _let_1 _let_0))) (hAPP _let_2 _let_3 (hAPP _let_5 (fun _let_2 _let_3) (combc _let_1 _let_2 _let_2) (hAPP _let_6 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_6 _let_5) (combb _let_0 _let_4 _let_1) (combb int int _let_1)) (hAPP _let_2 _let_6 (hAPP (fun int _let_0) (fun _let_2 _let_6) (combb int _let_0 _let_1) (times_times int)) (product_fst int int)))) (product_snd int int))))))))) ) 15.83/15.99 ( (product_prod int int), (fun (product_prod int int) bool), (fun (product_prod int int) bool), (fun bool bool), (combb bool bool (product_prod int int)), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_1 _let_2))) (let ((_let_5 (fun _let_1 _let_0))) (let ((_let_6 (fun _let_1 int))) (hAPP _let_3 _let_4 (hAPP (fun bool _let_2) (fun _let_3 _let_4) (combb bool _let_2 _let_1) fconj) (hAPP _let_3 _let_3 (hAPP _let_2 (fun _let_3 _let_3) (combb bool bool _let_1) fNot) (hAPP int _let_3 (hAPP _let_5 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_6 _let_5 (hAPP (fun int _let_0) (fun _let_6 _let_5) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))))))) ) 15.83/15.99 ( (product_prod int int), (fun (product_prod int int) int), (fun (product_prod int int) bool), (fun (product_prod int int) (fun int bool)), (combs (product_prod int int) int bool), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun _let_2 _let_0))) (let ((_let_4 (fun _let_2 int))) (let ((_let_5 (fun _let_4 _let_3))) (let ((_let_6 (fun _let_2 _let_4))) (let ((_let_7 (fun _let_2 _let_3))) (let ((_let_8 (fun _let_4 _let_4))) (let ((_let_9 (fun _let_2 _let_8))) (let ((_let_10 (fun _let_2 _let_1))) (hAPP _let_6 _let_7 (hAPP _let_5 (fun _let_6 _let_7) (combb _let_4 _let_3 _let_2) (hAPP (fun int _let_0) _let_5 (combb int _let_0 _let_2) (fequal int))) (hAPP _let_4 _let_6 (hAPP _let_9 (fun _let_4 _let_6) (combc _let_2 _let_4 _let_4) (hAPP _let_10 _let_9 (hAPP (fun _let_1 _let_8) (fun _let_10 _let_9) (combb _let_1 _let_8 _let_2) (combb int int _let_2)) (hAPP _let_4 _let_10 (hAPP (fun int _let_1) (fun _let_4 _let_10) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (product_snd int int)))))))))))))) ) 15.83/15.99 ( (product_prod int int), (fun (product_prod int int) int), (fun (product_prod int int) int), (fun int int), (combb int int (product_prod int int)), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_0))) (hAPP _let_2 _let_3 (hAPP (fun int _let_0) (fun _let_2 _let_3) (combb int _let_0 _let_1) (times_times int)) (product_fst int int)))))) ) 15.83/15.99 ) 15.83/15.99 (instantiation (forall ((W_1 $$unsorted) (Z $$unsorted)) (= (not (forall ((N_2 $$unsorted)) (not (= (hAPP int int (hAPP int (fun int int) (plus_plus int) W_1) (hAPP nat int (semiring_1_of_nat int) N_2)) (ti int Z))) )) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) W_1) Z))) ) 15.83/15.99 ( (one_one int), t ) 15.83/15.99 ( (zero_zero int), (one_one int) ) 15.83/15.99 ( (zero_zero int), min_1 ) 15.83/15.99 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/15.99 ( (zero_zero int), s ) 15.83/15.99 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.83/15.99 ( (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.83/15.99 ( (zero_zero int), skv_4 ) 15.83/15.99 ( (zero_zero int), skv_10 ) 15.83/15.99 ( min_1, pls ) 15.83/15.99 ( min_1, min_1 ) 15.83/15.99 ) 15.83/15.99 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_127025 $$unsorted)) (or (not (ordere142940540dd_abs X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_127025) (zero_zero X_a)))) (= (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_127025) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_127025))) ) 15.83/15.99 ( int, (one_one int) ) 15.83/15.99 ( int, (zero_zero int) ) 15.83/15.99 ( int, pls ) 15.83/15.99 ( int, min_1 ) 15.83/15.99 ( real, (one_one real) ) 15.83/15.99 ( real, (zero_zero real) ) 15.83/15.99 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/15.99 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/15.99 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.83/15.99 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/15.99 ( real, skv_5 ) 15.83/15.99 ( complex, (one_one complex) ) 15.83/15.99 ( complex, ii ) 15.83/15.99 ) 15.83/15.99 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (comple44059174attice T_1)) (comple44059174attice (fun T_2 T_1))) ) 15.83/15.99 ( bool, bool ) 15.83/15.99 ( bool, (fun bool bool) ) 15.83/15.99 ( nat, bool ) 15.83/15.99 ( nat, nat ) 15.83/15.99 ( nat, int ) 15.83/15.99 ( nat, (fun int int) ) 15.83/15.99 ( nat, (fun nat bool) ) 15.83/15.99 ( nat, (fun nat nat) ) 15.83/15.99 ( nat, (product_prod nat nat) ) 15.83/15.99 ( nat, (fun (product_prod nat nat) bool) ) 15.83/15.99 ( nat, (fun nat (fun (product_prod nat nat) bool)) ) 15.83/15.99 ( nat, real ) 15.83/15.99 ( nat, (fun real real) ) 15.83/15.99 ( nat, rat ) 15.83/15.99 ( nat, (fun nat (fun nat bool)) ) 15.83/15.99 ( nat, complex ) 15.83/15.99 ( nat, (product_prod int int) ) 15.83/15.99 ( nat, (fun bool bool) ) 15.83/15.99 ( nat, (product_prod real real) ) 15.83/15.99 ( nat, (fun nat (product_prod nat nat)) ) 15.83/15.99 ( nat, (fun nat (product_prod int int)) ) 15.83/15.99 ( int, bool ) 15.83/15.99 ( int, nat ) 15.83/15.99 ( int, int ) 15.83/15.99 ( int, (fun int bool) ) 15.83/15.99 ( int, (fun int (fun int bool)) ) 15.83/15.99 ( int, (fun int int) ) 15.83/15.99 ( int, (fun nat bool) ) 15.83/15.99 ( int, (fun nat nat) ) 15.83/15.99 ( int, real ) 15.83/15.99 ( int, (fun real real) ) 15.83/15.99 ( int, rat ) 15.83/15.99 ( int, (fun int rat) ) 15.83/15.99 ( int, (fun nat int) ) 15.83/15.99 ( int, (fun nat real) ) 15.83/15.99 ( int, (product_prod int int) ) 15.83/15.99 ( int, (fun int (product_prod int int)) ) 15.83/15.99 ( int, (fun (fun int bool) bool) ) 15.83/15.99 ( int, quickcheck_code_int ) 15.83/15.99 ( int, (fun bool bool) ) 15.83/15.99 ( int, (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 15.83/15.99 ( int, (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)) ) 15.83/15.99 ( int, (fun int (fun int (fun int bool))) ) 15.83/15.99 ( int, (fun (product_prod int int) bool) ) 15.83/15.99 ( int, (fun int (fun (product_prod int int) bool)) ) 15.83/15.99 ( int, (fun int (fun bool bool)) ) 15.83/15.99 ( int, (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 15.83/15.99 ( int, (fun (fun int int) (fun int bool)) ) 15.83/15.99 ( int, (fun (product_prod int int) int) ) 15.83/15.99 ( int, (product_prod int (product_prod int int)) ) 15.83/15.99 ( int, (fun int (product_prod int (product_prod int int))) ) 15.83/15.99 ( int, (fun int (fun int (product_prod int (product_prod int int)))) ) 15.83/15.99 ( int, (fun int (fun int (fun int (product_prod int (product_prod int int))))) ) 15.83/15.99 ( int, (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))) ) 15.83/15.99 ( int, (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))) ) 15.83/15.99 ( int, (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))) ) 15.83/15.99 ( int, (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))))) ) 15.83/15.99 ( int, (fun int (fun (fun int bool) bool)) ) 15.83/15.99 ( int, (list int) ) 15.83/15.99 ( int, (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 15.83/15.99 ( int, (fun int real) ) 15.83/15.99 ( int, (fun nat (fun bool bool)) ) 15.83/15.99 ( int, (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 15.83/15.99 ( int, (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 15.83/15.99 ( (fun int bool), bool ) 15.83/15.99 ( (fun int bool), int ) 15.83/15.99 ( (fun int bool), (fun int bool) ) 15.83/15.99 ( (fun int bool), (fun int (fun int bool)) ) 15.83/15.99 ( (fun int bool), (fun int (fun int int)) ) 15.83/15.99 ( (fun int bool), (fun int (fun bool bool)) ) 15.83/15.99 ( (fun int bool), (fun (fun int int) (fun int bool)) ) 15.83/15.99 ( (fun int bool), (fun real (fun int (fun int bool))) ) 15.83/15.99 ( (fun int (fun int bool)), (fun int bool) ) 15.83/15.99 ( (fun int (fun int bool)), (fun int (fun int bool)) ) 15.83/15.99 ( (fun int (fun int bool)), (fun int (fun (fun int int) (fun int bool))) ) 15.83/15.99 ( (fun int (fun int bool)), (fun int (fun int (fun bool bool))) ) 15.83/15.99 ( (fun int int), (fun int bool) ) 15.83/15.99 ( (fun int int), (fun int (fun int bool)) ) 15.83/15.99 ( (fun int int), (fun int int) ) 15.83/15.99 ( (fun int int), (fun int (fun int int)) ) 15.83/15.99 ( (fun int int), (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 15.83/15.99 ( (fun int int), (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 15.83/15.99 ( (fun nat bool), bool ) 15.83/15.99 ( (fun nat bool), (fun nat bool) ) 15.83/15.99 ( (fun nat bool), (fun nat (fun bool bool)) ) 15.83/15.99 ( (fun nat bool), (fun int (fun nat bool)) ) 15.83/15.99 ( (fun nat bool), (fun real (fun int (fun nat bool))) ) 15.83/15.99 ( (fun nat nat), (fun nat (fun nat bool)) ) 15.83/15.99 ( (fun nat nat), (fun nat real) ) 15.83/15.99 ( (fun nat nat), (fun nat (fun nat nat)) ) 15.83/15.99 ( (product_prod nat nat), bool ) 15.83/15.99 ( (product_prod nat nat), (fun (product_prod nat nat) bool) ) 15.83/15.99 ( real, bool ) 15.83/15.99 ( real, nat ) 15.83/15.99 ( real, (fun int bool) ) 15.83/15.99 ( real, (fun int (fun int bool)) ) 15.83/15.99 ( real, real ) 15.83/15.99 ( real, (fun real bool) ) 15.83/15.99 ( real, (fun real real) ) 15.83/15.99 ( real, complex ) 15.83/15.99 ( real, (fun nat real) ) 15.83/15.99 ( real, (fun real complex) ) 15.83/15.99 ( real, (fun bool bool) ) 15.83/15.99 ( real, (fun (filter nat) bool) ) 15.83/15.99 ( real, (fun nat (product_prod real real)) ) 15.83/15.99 ( real, (fun real (fun nat (product_prod real real))) ) 15.83/15.99 ( real, (fun (filter real) bool) ) 15.83/15.99 ( real, (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 15.83/15.99 ( real, (let ((_let_0 (fun int bool))) (fun _let_0 (fun int _let_0))) ) 15.83/15.99 ( real, (fun int (fun int (fun bool bool))) ) 15.83/15.99 ( real, (fun (fun int (fun int real)) (fun int (fun int bool))) ) 15.83/15.99 ( real, (fun (fun int real) (fun int bool)) ) 15.83/15.99 ( real, (fun int (fun nat bool)) ) 15.83/15.99 ( real, (let ((_let_0 (fun nat bool))) (fun _let_0 (fun int _let_0))) ) 15.83/15.99 ( real, (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 15.83/15.99 ( real, (fun int (fun nat (fun bool bool))) ) 15.83/15.99 ( real, (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 15.83/15.99 ( real, (fun (fun nat real) (fun nat bool)) ) 15.83/15.99 ( (fun real bool), real ) 15.83/15.99 ( (fun real bool), (fun real bool) ) 15.83/15.99 ( (fun real bool), (fun real (fun bool bool)) ) 15.83/15.99 ( (fun real bool), (fun (fun int real) (fun int bool)) ) 15.83/15.99 ( (fun real bool), (fun (fun nat real) (fun nat bool)) ) 15.83/15.99 ( (fun real real), (fun real real) ) 15.83/15.99 ( (fun real real), (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 15.83/15.99 ( (fun real real), (fun real (fun real real)) ) 15.83/15.99 ( (fun real real), (fun real (fun real bool)) ) 15.83/15.99 ( (fun real real), (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 15.83/15.99 ( rat, real ) 15.83/15.99 ( rat, (product_prod int int) ) 15.83/15.99 ( complex, nat ) 15.83/15.99 ( complex, real ) 15.83/15.99 ( complex, complex ) 15.83/15.99 ( (fun nat real), (fun nat bool) ) 15.83/15.99 ( (fun nat real), (fun nat real) ) 15.83/15.99 ( (fun nat real), (fun nat (fun real real)) ) 15.83/15.99 ( (fun nat real), (fun int (fun nat real)) ) 15.83/15.99 ( (filter nat), bool ) 15.83/15.99 ( (fun int (fun int int)), (fun int (fun int (fun int bool))) ) 15.83/15.99 ( (fun int (fun int int)), (let ((_let_0 (fun int int))) (fun int (fun _let_0 _let_0))) ) 15.83/15.99 ( (product_prod int int), bool ) 15.83/15.99 ( (product_prod int int), int ) 15.83/15.99 ( (product_prod int int), (fun int bool) ) 15.83/15.99 ( (product_prod int int), (fun int int) ) 15.83/15.99 ( (product_prod int int), rat ) 15.83/15.99 ( (product_prod int int), (product_prod int int) ) 15.83/15.99 ( (product_prod int int), (fun bool bool) ) 15.83/15.99 ( (product_prod int int), (fun (product_prod int int) bool) ) 15.83/15.99 ( (product_prod int int), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 15.83/15.99 ( (product_prod int int), (fun (product_prod int int) (fun int bool)) ) 15.83/15.99 ( (product_prod int int), (fun (product_prod int int) int) ) 15.83/15.99 ( (product_prod int int), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 15.83/15.99 ( (product_prod int int), (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 15.83/15.99 ( quickcheck_code_int, nat ) 15.83/15.99 ( quickcheck_code_int, int ) 15.83/15.99 ( quickcheck_code_int, (product_prod quickcheck_code_int quickcheck_code_int) ) 15.83/15.99 ( quickcheck_code_int, (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int)) ) 15.83/15.99 ( (fun bool bool), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 15.83/15.99 ( code_code_numeral, nat ) 15.83/15.99 ( code_code_numeral, int ) 15.83/15.99 ( code_code_numeral, (fun nat nat) ) 15.83/15.99 ( code_code_numeral, code_code_numeral ) 15.83/15.99 ( code_code_numeral, (product_prod code_code_numeral code_code_numeral) ) 15.83/15.99 ( code_code_numeral, (fun code_code_numeral (product_prod code_code_numeral code_code_numeral)) ) 15.83/15.99 ( (fun int (fun int (fun int bool))), (fun int (fun int (fun int bool))) ) 15.83/15.99 ( (fun real (fun real bool)), (fun real (fun (fun int real) (fun int bool))) ) 15.83/15.99 ( (fun real (fun real bool)), (fun real (fun (fun nat real) (fun nat bool))) ) 15.83/15.99 ( (product_prod real real), bool ) 15.83/15.99 ( (fun (product_prod real real) bool), (fun real (fun real (fun nat (product_prod real real)))) ) 15.83/15.99 ( (fun (product_prod int int) bool), (fun (product_prod int int) bool) ) 15.83/15.99 ( (fun (product_prod int int) bool), (fun (product_prod int int) (fun bool bool)) ) 15.83/15.99 ( (fun int (fun bool bool)), (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 15.83/15.99 ( (fun nat rat), bool ) 15.83/15.99 ( (filter real), bool ) 15.83/15.99 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)), bool ) 15.83/15.99 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 15.83/15.99 ( (fun (product_prod int int) (fun bool bool)), (let ((_let_0 (fun (product_prod int int) bool))) (fun (product_prod int int) (fun _let_0 _let_0))) ) 15.83/15.99 ( (fun (product_prod int int) (fun int bool)), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 15.83/15.99 ( (fun (product_prod int int) int), (fun (product_prod int int) bool) ) 15.83/16.00 ( (fun (product_prod int int) int), (fun (product_prod int int) (fun int bool)) ) 15.83/16.00 ( (fun (product_prod int int) int), (fun (product_prod int int) int) ) 15.83/16.00 ( (fun (product_prod int int) int), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))) ) 15.83/16.00 ( (fun (product_prod int int) int), (fun (product_prod int int) (fun int int)) ) 15.83/16.00 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 15.83/16.00 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 (fun int bool)))) ) 15.83/16.00 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 (fun int bool)))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun (fun _let_0 int) (fun _let_0 bool)))) ) 15.83/16.00 ( (fun (product_prod int int) (fun int int)), (let ((_let_0 (fun (product_prod int int) int))) (fun (product_prod int int) (fun _let_0 _let_0))) ) 15.83/16.00 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), bool ) 15.83/16.00 ( (fun int real), (fun int bool) ) 15.83/16.00 ( (fun int real), (fun int real) ) 15.83/16.00 ( (fun int real), (fun int (fun int real)) ) 15.83/16.00 ( (fun int real), (fun int (fun real real)) ) 15.83/16.00 ( (fun nat (fun bool bool)), (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 15.83/16.00 ( (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun int bool))) (fun _let_0 (fun int _let_0))) ) 15.83/16.00 ( (fun int (fun int (fun bool bool))), (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 15.83/16.00 ( (fun real (fun int bool)), (fun real bool) ) 15.83/16.00 ( (fun real (fun int (fun int bool))), (fun real (fun int bool)) ) 15.83/16.00 ( (fun real (fun int (fun int bool))), (fun real (fun int (fun int (fun bool bool)))) ) 15.83/16.00 ( (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun int bool))) (fun real (fun _let_0 (fun int _let_0)))) ) 15.83/16.00 ( (fun real (fun int (fun int (fun bool bool)))), (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))) ) 15.83/16.00 ( (fun int (fun int real)), (fun int (fun int bool)) ) 15.83/16.00 ( (fun int (fun int real)), (fun real (fun int (fun int bool))) ) 15.83/16.00 ( (fun (fun int real) (fun int bool)), (fun (fun int (fun int real)) (fun int (fun int bool))) ) 15.83/16.00 ( (fun real (fun (fun int real) (fun int bool))), (fun real (fun (fun int (fun int real)) (fun int (fun int bool)))) ) 15.83/16.00 ( (fun int (fun real real)), (let ((_let_0 (fun int real))) (fun int (fun _let_0 _let_0))) ) 15.83/16.00 ( (fun int (fun real real)), (let ((_let_0 (fun nat real))) (fun int (fun _let_0 _let_0))) ) 15.83/16.00 ( (fun int (fun nat bool)), (fun int bool) ) 15.83/16.00 ( (fun int (fun nat bool)), (fun int (fun nat (fun bool bool))) ) 15.83/16.00 ( (fun real (fun int (fun nat bool))), (fun real (fun int bool)) ) 15.83/16.00 ( (fun real (fun int (fun nat bool))), (fun real (fun int (fun nat (fun bool bool)))) ) 15.83/16.00 ( (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun nat bool))) (fun _let_0 (fun int _let_0))) ) 15.83/16.00 ( (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun nat bool))) (fun real (fun _let_0 (fun int _let_0)))) ) 15.83/16.00 ( (fun int (fun nat (fun bool bool))), (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 15.83/16.00 ( (fun real (fun int (fun nat (fun bool bool)))), (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))) ) 15.83/16.00 ( (fun int (fun nat real)), (fun int (fun nat bool)) ) 15.83/16.00 ( (fun int (fun nat real)), (fun real (fun int (fun nat bool))) ) 15.83/16.00 ( (fun (fun nat real) (fun nat bool)), (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 15.83/16.00 ( (fun real (fun (fun nat real) (fun nat bool))), (fun real (fun (fun int (fun nat real)) (fun int (fun nat bool)))) ) 15.83/16.00 ) 15.83/16.00 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (plus_plus X_a))) (or (not (plus X_a)) (not (dvd X_a)) (not (linorder X_a)) (= _let_0 (ti (fun X_a (fun X_a X_a)) _let_0)))) ) 15.83/16.00 ( bool ) 15.83/16.00 ( nat ) 15.83/16.00 ( int ) 15.83/16.00 ( (fun int bool) ) 15.83/16.00 ( (fun int (fun int bool)) ) 15.83/16.00 ( (fun int int) ) 15.83/16.00 ( (fun nat bool) ) 15.83/16.00 ( real ) 15.83/16.00 ( (fun real bool) ) 15.83/16.00 ( (fun real real) ) 15.83/16.00 ( rat ) 15.83/16.00 ( complex ) 15.83/16.00 ( (fun nat real) ) 15.83/16.00 ( (product_prod int int) ) 15.83/16.00 ( quickcheck_code_int ) 15.83/16.00 ( code_code_numeral ) 15.83/16.00 ( (fun int (fun int (fun int bool))) ) 15.83/16.00 ( (fun (product_prod int int) bool) ) 15.83/16.00 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 15.83/16.00 ( (fun (product_prod int int) int) ) 15.83/16.00 ( (fun int real) ) 15.83/16.00 ) 15.83/16.00 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (power_power real))) (let ((_let_3 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_4 (hAPP int nat (number_number_of nat) _let_3))) (let ((_let_5 (number_number_of real))) (let ((_let_6 (times_times real))) (= (hAPP nat real (hAPP real _let_1 _let_2 (hAPP real real (hAPP real _let_0 _let_6 (hAPP int real _let_5 _let_3)) X_1)) _let_4) (hAPP real real (hAPP real _let_0 _let_6 (hAPP int real _let_5 (hAPP int int bit0 _let_3))) (hAPP nat real (hAPP real _let_1 _let_2 X_1) _let_4)))))))))) ) 15.83/16.00 ( pi ) 15.83/16.00 ( (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.83/16.00 ) 15.83/16.00 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_127119 $$unsorted)) (or (not (number_ring X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_127119) (hAPP int X_a (number_number_of X_a) (hAPP int int bit1 pls))) (ti X_a BOUND_VARIABLE_127119))) ) 15.83/16.00 ( bool, fFalse ) 15.83/16.00 ( bool, fTrue ) 15.83/16.00 ( int, pls ) 15.83/16.00 ( int, min_1 ) 15.83/16.00 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.00 ( int, s ) 15.83/16.00 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/16.00 ( int, m ) 15.83/16.00 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.83/16.00 ( int, s1 ) 15.83/16.00 ( int, t ) 15.83/16.00 ( (fun int bool), nat_neg ) 15.83/16.00 ( (fun int bool), zprime ) 15.83/16.00 ( (fun int bool), zEven ) 15.83/16.00 ( (fun int bool), zOdd ) 15.83/16.00 ( (fun int bool), (even_odd_even int) ) 15.83/16.00 ( (fun int bool), twoSqu1091635170sum2sq ) 15.83/16.00 ( (fun int bool), nat_is_nat ) 15.83/16.00 ( (fun int (fun int bool)), norRRset ) 15.83/16.00 ( (fun int (fun int bool)), quadRes ) 15.83/16.00 ( (fun int (fun int bool)), sRStar ) 15.83/16.00 ( (fun int (fun int bool)), d22set ) 15.83/16.00 ( (fun int (fun int bool)), sr ) 15.83/16.00 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 15.83/16.00 ( (fun int int), zfact ) 15.83/16.00 ( (fun int int), bit0 ) 15.83/16.00 ( (fun int int), bit1 ) 15.83/16.00 ( (fun int int), (fact_fact int) ) 15.83/16.00 ( (fun int int), pred ) 15.83/16.00 ( (fun int int), succ ) 15.83/16.00 ( (fun nat bool), (even_odd_even nat) ) 15.83/16.00 ( (fun nat bool), prime ) 15.83/16.00 ( (fun nat nat), suc ) 15.83/16.00 ( (fun nat nat), (fact_fact nat) ) 15.83/16.00 ( (fun nat nat), fact ) 15.83/16.00 ( (fun nat nat), nat_size ) 15.83/16.00 ( (fun nat nat), (size_size nat) ) 15.83/16.00 ( (fun (product_prod nat nat) bool), pred_nat ) 15.83/16.00 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 15.83/16.00 ( real, pi ) 15.83/16.00 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.00 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/16.00 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 15.83/16.00 ( (fun real real), ln ) 15.83/16.00 ( (fun real real), cos ) 15.83/16.00 ( (fun real real), sqrt ) 15.83/16.00 ( (fun real real), sin ) 15.83/16.00 ( (fun real real), arccos ) 15.83/16.00 ( (fun real real), arcsin ) 15.83/16.00 ( (fun real real), tan ) 15.83/16.00 ( (fun real real), arctan ) 15.83/16.00 ( (fun nat (fun nat bool)), coprime ) 15.83/16.00 ( complex, ii ) 15.83/16.00 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.00 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 15.83/16.00 ( (fun nat real), (real_1 nat) ) 15.83/16.00 ( (fun nat real), sin_coeff ) 15.83/16.00 ( (fun nat real), cos_coeff ) 15.83/16.00 ( (filter nat), sequentially ) 15.83/16.00 ( (fun int (fun int int)), (gcd_gcd int) ) 15.83/16.00 ( (fun int (fun int int)), legendre ) 15.83/16.00 ( (fun int (fun int int)), legacy_zgcd ) 15.83/16.00 ( (fun int (fun int int)), standardRes ) 15.83/16.00 ( (fun int (fun int int)), nat_tsub ) 15.83/16.00 ( (fun int (fun int int)), multInv ) 15.83/16.00 ( (fun int (fun int int)), z3mod ) 15.83/16.00 ( (fun int (fun int int)), z3div ) 15.83/16.00 ( (fun int (fun int int)), int_gcd ) 15.83/16.00 ( (fun int (fun int int)), int_lcm ) 15.83/16.00 ( (fun int (fun int int)), inv ) 15.83/16.00 ( (fun complex complex), expi ) 15.83/16.00 ( (fun complex complex), cnj ) 15.83/16.00 ( (fun real complex), cis ) 15.83/16.00 ( (fun int nat), nat_1 ) 15.83/16.00 ( (fun int nat), phi ) 15.83/16.00 ( (fun (fun int bool) bool), nat_nat_set ) 15.83/16.00 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 15.83/16.00 ( (fun nat (fun nat nat)), nat_gcd ) 15.83/16.00 ( (fun nat (fun nat nat)), nat_lcm ) 15.83/16.00 ( (fun (fun int bool) int), (the int) ) 15.83/16.00 ( (fun complex real), re ) 15.83/16.00 ( (fun complex real), im ) 15.83/16.00 ( (fun complex real), arg ) 15.83/16.00 ( (fun bool bool), fNot ) 15.83/16.00 ( (fun nat (fun real real)), root ) 15.83/16.00 ( (fun real (fun real real)), log ) 15.83/16.00 ( (fun real (fun real real)), powr ) 15.83/16.00 ( (fun bool (fun bool bool)), fimplies ) 15.83/16.00 ( (fun bool (fun bool bool)), fconj ) 15.83/16.00 ( (fun bool (fun bool bool)), fdisj ) 15.83/16.00 ( (fun int (fun int (product_prod int int))), negDivAlg ) 15.83/16.00 ( (fun int (fun int (product_prod int int))), posDivAlg ) 15.83/16.00 ( (fun int (fun int (product_prod int int))), divmod_int ) 15.83/16.00 ( (fun int (fun int (product_prod int int))), pdivmod ) 15.83/16.00 ( (fun int (fun int (product_prod int int))), norm_frac ) 15.83/16.00 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 15.83/16.00 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 15.83/16.00 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 15.83/16.00 ( (fun int (fun int (fun int bool))), zcong ) 15.83/16.00 ( (fun int (fun int (fun int bool))), zcongm ) 15.83/16.00 ( (fun int (fun int (fun int bool))), noXRRset ) 15.83/16.00 ( (fun int (fun int (fun int bool))), bnorRset ) 15.83/16.00 ( (fun int (fun int (fun int bool))), wset ) 15.83/16.00 ( (fun (product_prod int int) bool), frac_1 ) 15.83/16.00 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 15.83/16.00 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 15.83/16.00 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 15.83/16.00 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 15.83/16.00 ( (fun (fun nat rat) bool), vanishes ) 15.83/16.00 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 15.83/16.00 ( (fun code_code_numeral nat), code_c271388182l_size ) 15.83/16.00 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 15.83/16.00 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 15.83/16.00 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 15.83/16.00 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 15.83/16.00 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 15.83/16.00 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 15.83/16.00 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 15.83/16.00 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 15.83/16.00 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 15.83/16.00 ( (fun complex nat), complex_size ) 15.83/16.00 ( (fun complex nat), (size_size complex) ) 15.83/16.00 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 15.83/16.00 ( (fun nat (fun nat (product_prod int int))), bezw ) 15.83/16.00 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 15.83/16.00 ( (fun int (fun nat nat)), nat_aux ) 15.83/16.00 ( (fun int (fun (fun int bool) bool)), rsetR ) 15.83/16.00 ( (fun int (fun (fun int bool) bool)), resSet ) 15.83/16.00 ( (fun int (list int)), quickc666637781d_zero ) 15.83/16.00 ( (fun (product_prod int int) rat), frct ) 15.83/16.00 ( (fun int (fun int rat)), fract ) 15.83/16.00 ( (fun real (fun real complex)), complex_1 ) 15.83/16.00 ( (fun real (fun real complex)), rcis ) 15.83/16.00 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 15.83/16.00 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 15.83/16.00 ( (fun int real), (real_1 int) ) 15.83/16.00 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 15.83/16.00 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 15.83/16.00 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 15.83/16.00 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 15.83/16.00 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 15.83/16.00 ( (fun real nat), natfloor ) 15.83/16.00 ( (fun real nat), natceiling ) 15.83/16.00 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 15.83/16.00 ( (fun quickcheck_code_int int), quickcheck_int_of ) 15.83/16.00 ( (fun rat (product_prod int int)), quotient_of ) 15.83/16.00 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 15.83/16.00 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 15.83/16.00 ( (fun rat real), ratreal ) 15.83/16.00 ( (fun code_code_numeral int), code_int_of ) 15.83/16.00 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 15.83/16.00 ( (fun int quickcheck_code_int), quickcheck_of_int ) 15.83/16.00 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 15.83/16.00 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 15.83/16.00 ) 15.83/16.00 (instantiation (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (hAPP nat (fun real real) root N_1))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) Y_1))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real _let_2 X_1)) (hAPP real real _let_2 Y_1))))))) ) 15.83/16.00 ( (zero_zero real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.00 ) 15.83/16.00 (instantiation (forall ((X_a $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (one_one int) (hAPP X_a int (archim2085082626_floor X_a) (one_one X_a)))) ) 15.83/16.00 ( nat ) 15.83/16.00 ( int ) 15.83/16.00 ( real ) 15.83/16.00 ( rat ) 15.83/16.00 ( complex ) 15.83/16.00 ( quickcheck_code_int ) 15.83/16.00 ( code_code_numeral ) 15.83/16.00 ) 15.83/16.00 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_127363 $$unsorted) (BOUND_VARIABLE_127364 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)))) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_127364))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_127363))) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_127364) BOUND_VARIABLE_127363))))) ) 15.83/16.00 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 15.83/16.00 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.83/16.00 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.83/16.00 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.83/16.00 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/16.00 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 15.83/16.00 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), pi ) 15.83/16.00 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (one_one real) ) 15.83/16.00 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))), pi ) 15.83/16.00 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 15.83/16.00 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))), (one_one real) ) 15.83/16.00 ) 15.83/16.00 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))) (or (not (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) X_2) zEven))) (= (ti int X_2) (hAPP int int (hAPP int _let_1 (times_times int) _let_2) (hAPP int int (hAPP int _let_1 (div_div int) X_2) _let_2))))))) ) 15.83/16.00 ( (one_one int) ) 15.83/16.00 ( pls ) 15.83/16.00 ( min_1 ) 15.83/16.00 ( s ) 15.83/16.00 ( m ) 15.83/16.00 ( s1 ) 15.83/16.00 ( t ) 15.83/16.00 ) 15.83/16.00 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_127476 $$unsorted) (BOUND_VARIABLE_127477 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (times_times X_a))) (let ((_let_3 (inverse_inverse X_a))) (let ((_let_4 (minus_minus X_a))) (let ((_let_5 (hAPP X_a X_a _let_3 BOUND_VARIABLE_127477))) (let ((_let_6 (hAPP X_a X_a _let_3 BOUND_VARIABLE_127476))) (or (not (division_ring X_a)) (= _let_0 (ti X_a BOUND_VARIABLE_127477)) (= _let_0 (ti X_a BOUND_VARIABLE_127476)) (= (hAPP X_a X_a (hAPP X_a _let_1 _let_4 _let_5) _let_6) (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 _let_5) (hAPP X_a X_a (hAPP X_a _let_1 _let_4 BOUND_VARIABLE_127476) BOUND_VARIABLE_127477))) _let_6)))))))))) ) 15.83/16.00 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.83/16.00 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 15.83/16.00 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 15.83/16.00 ) 15.83/16.00 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_127514 $$unsorted) (BOUND_VARIABLE_127515 $$unsorted) (BOUND_VARIABLE_127516 $$unsorted)) (let ((_let_0 (filter X_a))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun X_a real))) (let ((_let_3 (fun X_a X_b))) (let ((_let_4 (norm_norm X_b))) (let ((_let_5 (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_127516))) (or (not (real_normed_vector X_b)) (not (topological_space X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (hAPP _let_3 (fun X_b _let_1) (tendsto X_a X_b) BOUND_VARIABLE_127514) BOUND_VARIABLE_127515) _let_5))) (hBOOL (hAPP _let_0 bool (hAPP real _let_1 (hAPP _let_2 (fun real _let_1) (tendsto X_a real) (hAPP _let_3 _let_2 (hAPP (fun X_b real) (fun _let_3 _let_2) (combb X_b real X_a) _let_4) BOUND_VARIABLE_127514)) (hAPP X_b real _let_4 BOUND_VARIABLE_127515)) _let_5))))))))) ) 15.83/16.00 ( real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/16.00 ) 15.83/16.00 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_127543 $$unsorted) (BOUND_VARIABLE_127544 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (or (not (order X_a)) (= (= (ti X_a BOUND_VARIABLE_127543) (ti X_a BOUND_VARIABLE_127544)) (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_127543) BOUND_VARIABLE_127544)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_127544) BOUND_VARIABLE_127543))))))) ) 15.83/16.00 ( int, (one_one int), (zero_zero int) ) 15.83/16.00 ( int, (one_one int), t ) 15.83/16.00 ( int, (zero_zero int), (one_one int) ) 15.83/16.00 ( int, (zero_zero int), min_1 ) 15.83/16.00 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.00 ( int, (zero_zero int), s ) 15.83/16.00 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.83/16.00 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.83/16.00 ( int, (zero_zero int), skv_4 ) 15.83/16.00 ( int, (zero_zero int), skv_10 ) 15.83/16.00 ( int, pls, min_1 ) 15.83/16.00 ( int, min_1, (zero_zero int) ) 15.83/16.00 ( int, min_1, pls ) 15.83/16.00 ( int, min_1, min_1 ) 15.83/16.00 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 15.83/16.00 ( int, s, (zero_zero int) ) 15.83/16.00 ( int, t, (one_one int) ) 15.83/16.00 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 15.83/16.00 ( int, (hAPP int int (number_number_of int) pls), (zero_zero int) ) 15.83/16.00 ( int, skv_4, (zero_zero int) ) 15.83/16.00 ( int, skv_10, (zero_zero int) ) 15.83/16.00 ( real, (zero_zero real), pi ) 15.83/16.00 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/16.00 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/16.00 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/16.00 ( real, (zero_zero real), skv_3 ) 15.83/16.00 ( real, (zero_zero real), skv_5 ) 15.83/16.00 ( real, (zero_zero real), skv_7 ) 15.83/16.00 ( real, (zero_zero real), skv_12 ) 15.83/16.00 ( real, pi, (zero_zero real) ) 15.83/16.00 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.00 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.83/16.00 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/16.00 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_5 ) 15.83/16.00 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.83/16.00 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.00 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.83/16.00 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.83/16.00 ( real, skv_3, (zero_zero real) ) 15.83/16.00 ( real, skv_5, (zero_zero real) ) 15.83/16.00 ( real, skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.00 ( real, skv_7, (zero_zero real) ) 15.83/16.00 ( real, skv_12, (zero_zero real) ) 15.83/16.00 ) 15.83/16.00 (instantiation (forall ((X_a $$unsorted)) (or (not (number_ring X_a)) (= (hAPP int X_a (number_number_of X_a) min_1) (hAPP X_a X_a (uminus_uminus X_a) (one_one X_a)))) ) 15.83/16.00 ( nat ) 15.83/16.00 ( int ) 15.83/16.00 ( real ) 15.83/16.00 ( rat ) 15.83/16.00 ( complex ) 15.83/16.00 ( quickcheck_code_int ) 15.83/16.00 ( code_code_numeral ) 15.83/16.00 ) 15.83/16.00 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_127568 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)))) (or (not (linordered_idom X_a)) (= (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (sgn_sgn X_a) BOUND_VARIABLE_127568))) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_127568))))) ) 15.83/16.00 ( real, (zero_zero real) ) 15.83/16.00 ( rat, (zero_zero rat) ) 15.83/16.00 ) 15.83/16.00 (instantiation (forall ((N_1 $$unsorted)) (not (= (zero_zero real) (hAPP nat real (real_1 nat) (hAPP nat nat (fact_fact nat) N_1)))) ) 15.83/16.00 ( (zero_zero nat) ) 15.83/16.00 ( (hAPP nat nat suc (zero_zero nat)) ) 15.83/16.00 ) 15.83/16.00 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_0 (fun bool bool))) (let ((_let_1 (product_prod X_a X_b))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun X_b bool))) (let ((_let_4 (fun X_a _let_3))) (let ((_let_5 (fun _let_3 _let_3))) (let ((_let_6 (fun X_a _let_5))) (let ((_let_7 (fun X_a _let_0))) (let ((_let_8 (fun X_a bool))) (= (hAPP X_b _let_1 (hAPP X_a (fun X_b _let_1) (product_Pair X_a X_b) X_2) Y_2) (hAPP _let_2 _let_1 (the _let_1) (hAPP _let_4 _let_2 (product_prod_case X_a X_b bool) (hAPP _let_3 _let_4 (hAPP _let_6 (fun _let_3 _let_4) (combc X_a _let_3 _let_3) (hAPP _let_7 _let_6 (hAPP (fun _let_0 _let_5) (fun _let_7 _let_6) (combb _let_0 _let_5 X_a) (combb bool bool X_b)) (hAPP _let_8 _let_7 (hAPP (fun bool _let_0) (fun _let_8 _let_7) (combb bool _let_0 X_a) fconj) (hAPP X_a _let_8 (fequal X_a) X_2)))) (hAPP X_b _let_3 (fequal X_b) Y_2)))))))))))))) ) 15.83/16.00 ( int, int, (one_one int), (one_one int) ) 15.83/16.00 ( int, int, (zero_zero int), (one_one int) ) 15.83/16.00 ( int, int, s, (one_one int) ) 15.83/16.00 ) 15.83/16.00 (instantiation (forall ((Z $$unsorted) (P_1 $$unsorted)) (or (not (forall ((N_2 $$unsorted)) (hBOOL (hAPP int bool P_1 (hAPP nat int (semiring_1_of_nat int) N_2))) )) (not (forall ((N_2 $$unsorted)) (hBOOL (hAPP int bool P_1 (hAPP int int (uminus_uminus int) (hAPP nat int (semiring_1_of_nat int) (hAPP nat nat suc N_2))))) )) (hBOOL (hAPP int bool P_1 Z))) ) 15.83/16.00 ( (one_one int), nat_neg ) 15.83/16.00 ( (one_one int), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 15.83/16.00 ( (one_one int), (hAPP int (fun int bool) (ord_less int) (zero_zero int)) ) 15.83/16.00 ( (one_one int), (even_odd_even int) ) 15.83/16.00 ( (one_one int), nat_is_nat ) 15.83/16.00 ( (zero_zero int), (even_odd_even int) ) 15.83/16.00 ( (zero_zero int), nat_is_nat ) 15.83/16.00 ( pls, (hAPP int (fun int bool) (ord_less int) pls) ) 15.83/16.00 ( pls, (hAPP int (fun int bool) (ord_less int) min_1) ) 15.83/16.00 ( pls, (hAPP int (fun int bool) (ord_less_eq int) min_1) ) 15.83/16.00 ( min_1, (hAPP int (fun int bool) (ord_less int) pls) ) 15.83/16.00 ( min_1, (hAPP int (fun int bool) (ord_less_eq int) pls) ) 15.83/16.00 ( min_1, (hAPP int (fun int bool) (ord_less int) min_1) ) 15.83/16.00 ( min_1, (hAPP int (fun int bool) (ord_less_eq int) min_1) ) 15.83/16.00 ( (hAPP int int (number_number_of int) min_1), nat_neg ) 15.83/16.00 ( (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int (fun int bool) quadRes (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))) ) 15.83/16.00 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 15.83/16.00 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), zprime ) 15.83/16.00 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), nat_is_nat ) 15.83/16.00 ( s, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 15.83/16.00 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int (fun int bool) (ord_less int) (zero_zero int)) ) 15.83/16.00 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), zprime ) 15.83/16.00 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int (fun int bool) (ord_less int) s) ) 15.83/16.00 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) s)) ) 15.83/16.00 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (let ((_let_3 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int _let_1 _let_2 s) _let_3)) (hAPP nat int (hAPP int _let_1 _let_2 s1) _let_3)))))) ) 15.83/16.00 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))) ) 15.83/16.00 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int (fun int bool) (ord_less int) t) ) 15.83/16.00 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))) ) 15.83/16.00 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_4)) ) 15.83/16.00 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int (fun int bool) (ord_less int) skv_4) ) 15.83/16.00 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int (fun int bool) (ord_less int) skv_10) ) 15.83/16.00 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_10)) ) 15.83/16.00 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))) ) 15.83/16.00 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))) ) 15.83/16.00 ( t, (hAPP int (fun int bool) (ord_less_eq int) (one_one int)) ) 15.83/16.00 ( t, (hAPP int (fun int bool) (ord_less int) (one_one int)) ) 15.83/16.00 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) t))), twoSqu1091635170sum2sq ) 15.83/16.00 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 15.83/16.00 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), nat_is_nat ) 15.83/16.00 ( (hAPP int int (number_number_of int) pls), nat_neg ) 15.83/16.00 ( (hAPP int int (number_number_of int) pls), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 15.83/16.00 ( skv_4, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 15.83/16.00 ( skv_10, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 15.83/16.00 ) 15.83/16.00 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_127743 $$unsorted) (BOUND_VARIABLE_127744 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (or (not (linord20386208strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_127744))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_127743) _let_2))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_127744) BOUND_VARIABLE_127743)) _let_2)))))) ) 15.83/16.00 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/16.00 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.83/16.00 ( int, skv_13, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.83/16.00 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.00 ( real, pi, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 15.83/16.00 ( real, (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.00 ( real, (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/16.00 ( complex, ii, ii ) 15.83/16.00 ( complex, ii, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 15.83/16.00 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.00 ) 15.83/16.00 (instantiation (forall ((Ma $$unsorted) (K $$unsorted) (N $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int (fun int bool) (dvd_dvd int) K))) (or (not (= (one_one int) (hAPP int int (hAPP int _let_0 (gcd_gcd int) K) N))) (= (hBOOL (hAPP int bool _let_1 Ma)) (hBOOL (hAPP int bool _let_1 (hAPP int int (hAPP int _let_0 (times_times int) Ma) N))))))) ) 15.83/16.00 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.83/16.00 ) 15.83/16.00 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_127788 $$unsorted) (BOUND_VARIABLE_127789 $$unsorted)) (let ((_let_0 (fun nat X_a))) (let ((_let_1 (power_power X_a))) (or (not (comm_ring_1 X_a)) (not (hBOOL (hAPP nat bool (even_odd_even nat) BOUND_VARIABLE_127789))) (= (hAPP nat X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_127788)) BOUND_VARIABLE_127789) (hAPP nat X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_127788) BOUND_VARIABLE_127789))))) ) 15.83/16.00 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.00 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.00 ( int, skv_14, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.00 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.00 ) 15.83/16.00 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_0 (fun nat nat))) (or (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) M) N_1)) (= M (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) N_1) (hAPP nat nat (hAPP nat _let_0 (minus_minus nat) M) N_1))))) ) 15.83/16.00 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.00 ) 15.83/16.00 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_127818 $$unsorted) (BOUND_VARIABLE_127819 $$unsorted)) (or (not (semiring_div X_a)) (= (= (zero_zero X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (div_mod X_a) BOUND_VARIABLE_127819) BOUND_VARIABLE_127818)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_127818) BOUND_VARIABLE_127819)))) ) 15.83/16.00 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 15.83/16.00 ) 15.83/16.00 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_127866 $$unsorted)) (or (not (linordered_idom X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_127866) (hAPP X_a X_a (sgn_sgn X_a) BOUND_VARIABLE_127866)) (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_127866))) ) 15.83/16.00 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.00 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/16.00 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.83/16.00 ( real, (zero_zero real) ) 15.83/16.00 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.00 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/16.00 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 15.83/16.00 ( rat, (zero_zero rat) ) 15.83/16.00 ( complex, ii ) 15.83/16.00 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.00 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 15.83/16.00 ) 15.83/16.00 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_127945 $$unsorted) (BOUND_VARIABLE_127946 $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (linorder X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_127945) BOUND_VARIABLE_127946))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_127946) BOUND_VARIABLE_127945))))) ) 15.83/16.00 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 15.83/16.00 ( int, (one_one int), pls ) 15.83/16.00 ( int, (one_one int), t ) 15.83/16.00 ( int, (zero_zero int), (one_one int) ) 15.83/16.00 ( int, (zero_zero int), min_1 ) 15.83/16.00 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.00 ( int, (zero_zero int), s ) 15.83/16.00 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.83/16.00 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.83/16.00 ( int, (zero_zero int), skv_4 ) 15.83/16.00 ( int, (zero_zero int), skv_10 ) 15.83/16.00 ( int, pls, pls ) 15.83/16.00 ( int, pls, min_1 ) 15.83/16.00 ( int, min_1, pls ) 15.83/16.00 ( int, min_1, min_1 ) 15.83/16.00 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), pls ) 15.83/16.00 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s ) 15.83/16.00 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.83/16.00 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_4 ) 15.83/16.00 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_10 ) 15.83/16.00 ( int, t, (one_one int) ) 15.83/16.00 ( real, (zero_zero real), pi ) 15.83/16.00 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/16.00 ( real, (zero_zero real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.83/16.00 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/16.00 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/16.00 ( real, (zero_zero real), skv_3 ) 15.83/16.00 ( real, (zero_zero real), skv_5 ) 15.83/16.00 ( real, (zero_zero real), skv_7 ) 15.83/16.00 ( real, (zero_zero real), skv_12 ) 15.83/16.00 ( real, pi, (zero_zero real) ) 15.83/16.00 ( real, pi, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 15.83/16.00 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.83/16.00 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/16.00 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.83/16.00 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.00 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 15.83/16.00 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 15.83/16.00 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.83/16.00 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.83/16.00 ( real, skv_2, (zero_zero real) ) 15.83/16.00 ( real, skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.00 ( real, skv_8, (zero_zero real) ) 15.83/16.00 ( real, skv_9, (zero_zero real) ) 15.83/16.00 ) 15.83/16.00 (instantiation (forall ((X_2 $$unsorted) (N $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP nat _let_1 root N))) (or (hBOOL (hAPP nat bool (even_odd_even nat) N)) (= (zero_zero real) X_2) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP _let_1 (fun real _let_0) (deriv real) _let_2) X_2) (hAPP real real (inverse_inverse real) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP nat real (real_1 nat) N)) (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP real real _let_2 X_2)) (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) N) (hAPP nat nat suc (zero_zero nat)))))))))))) ) 15.83/16.00 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.00 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.00 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.00 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.00 ) 15.83/16.00 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_128003 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hAPP int int (uminus_uminus int) (hAPP X_a int (archim2085082626_floor X_a) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_128003))) (hAPP X_a int (archimedean_ceiling X_a) BOUND_VARIABLE_128003))) ) 15.83/16.00 ( int, (one_one int) ) 15.83/16.00 ( int, pls ) 15.83/16.00 ( int, min_1 ) 15.83/16.00 ( real, (one_one real) ) 15.83/16.00 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/16.00 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.83/16.00 ( complex, (one_one complex) ) 15.83/16.00 ( complex, ii ) 15.83/16.00 ) 15.83/16.00 (instantiation (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (or (not (= (hAPP nat nat suc Y_1) (hAPP nat nat suc X_1))) (= X_1 Y_1)) ) 15.83/16.00 ( (zero_zero nat), (zero_zero nat) ) 15.83/16.00 ( (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 15.83/16.00 ( (zero_zero nat), (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 15.83/16.00 ( (hAPP nat nat suc (zero_zero nat)), (zero_zero nat) ) 15.83/16.00 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))), (hAPP nat nat suc (zero_zero nat)) ) 15.83/16.00 ) 15.83/16.00 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_128055 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (times_times X_a))) (or (not (monoid_mult X_a)) (= (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_128055) (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls)))) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_128055) BOUND_VARIABLE_128055)) BOUND_VARIABLE_128055))))) ) 15.83/16.00 ( int, s ) 15.83/16.00 ( int, s1 ) 15.83/16.00 ( int, skv_14 ) 15.83/16.00 ( real, (hAPP int real (number_number_of real) min_1) ) 15.83/16.00 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/16.00 ( complex, ii ) 15.83/16.00 ) 15.83/16.00 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_128084 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member X_a))) (let ((_let_3 (ring_1_Ints X_a))) (or (not (ring_1 X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_128084) _let_3))) (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_128084)) _let_3))))))) ) 15.83/16.00 ( int, (one_one int) ) 15.83/16.00 ( int, pls ) 15.83/16.00 ( int, min_1 ) 15.83/16.00 ( real, (one_one real) ) 15.83/16.00 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/16.00 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.83/16.00 ( complex, (one_one complex) ) 15.83/16.00 ( complex, ii ) 15.83/16.00 ) 15.83/16.00 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (one_one real))) (let ((_let_2 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 (hAPP int real (number_number_of real) min_1)) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 X_1) _let_1))) (= (hAPP real real sin (hAPP real real arccos X_1)) (hAPP real real sqrt (hAPP real real (hAPP real (fun real real) (minus_minus real) _let_1) (hAPP nat real (hAPP real (fun nat real) (power_power real) X_1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))))))) ) 15.83/16.00 ( (zero_zero real) ) 15.83/16.00 ( (hAPP int real (number_number_of real) min_1) ) 15.83/16.00 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.00 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/16.00 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/16.00 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/16.00 ( skv_5 ) 15.83/16.00 ) 15.83/16.00 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_128176 $$unsorted) (BOUND_VARIABLE_128177 $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (ord X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_128176) BOUND_VARIABLE_128177)) (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) BOUND_VARIABLE_128176) (hAPP X_a _let_0 (ord_atMost X_a) BOUND_VARIABLE_128177)))))) ) 15.83/16.00 ( int, (one_one int), t ) 15.83/16.00 ( int, (zero_zero int), (one_one int) ) 15.83/16.00 ( int, (zero_zero int), min_1 ) 15.83/16.00 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.00 ( int, (zero_zero int), s ) 15.83/16.00 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.83/16.00 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.83/16.00 ( int, (zero_zero int), skv_4 ) 15.83/16.00 ( int, (zero_zero int), skv_10 ) 15.83/16.00 ( int, min_1, pls ) 15.83/16.00 ( int, min_1, min_1 ) 15.83/16.00 ( real, (zero_zero real), pi ) 15.83/16.00 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/16.00 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/16.00 ( real, (zero_zero real), skv_3 ) 15.83/16.00 ( real, (zero_zero real), skv_5 ) 15.83/16.00 ( real, (zero_zero real), skv_7 ) 15.83/16.00 ( real, (zero_zero real), skv_12 ) 15.83/16.00 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.83/16.00 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.00 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.83/16.00 ( real, skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.00 ) 15.83/16.00 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_128310 $$unsorted) (BOUND_VARIABLE_128311 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_128311))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_128311) (one_one X_a)))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_128311) (hAPP nat nat suc BOUND_VARIABLE_128310))) BOUND_VARIABLE_128311))))) ) 15.83/16.00 ( int, (hAPP nat nat suc (zero_zero nat)), s ) 15.83/16.00 ( int, (hAPP nat nat suc (zero_zero nat)), s1 ) 15.83/16.00 ( int, (hAPP nat nat suc (zero_zero nat)), skv_14 ) 15.83/16.00 ( complex, (hAPP nat nat suc (zero_zero nat)), ii ) 15.83/16.00 ) 15.83/16.00 (instantiation (forall ((N $$unsorted)) (let ((_let_0 (fun int (fun int bool)))) (let ((_let_1 (ord_less int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (hAPP int (fun int bool) _let_1 (zero_zero int)))) (let ((_let_4 (fun int _let_2))) (or (not (hBOOL (hAPP int bool _let_3 N))) (= (hAPP (fun int bool) nat (finite_card int) (hAPP (fun int bool) (fun int bool) (collect int) (hAPP (fun int bool) (fun int bool) (hAPP _let_4 (fun (fun int bool) (fun int bool)) (combs int bool bool) (hAPP (fun int bool) _let_4 (hAPP (fun bool _let_2) (fun (fun int bool) _let_4) (combb bool _let_2 int) fconj) _let_3)) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) _let_1) N)))) (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) (hAPP int nat nat_1 N)) (one_one nat))))))))) ) 15.83/16.00 ( (one_one int) ) 15.83/16.00 ( (zero_zero int) ) 15.83/16.00 ( pls ) 15.83/16.00 ( min_1 ) 15.83/16.00 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.00 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.83/16.00 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.83/16.00 ) 15.83/16.01 (instantiation (forall ((X_a $$unsorted)) (or (not (real_normed_vector X_a)) (not (real_algebra_1 X_a)) (not (forall ((K_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) K_2))) (not (forall ((X $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP X_a real (norm_norm X_a) (hAPP real X_a (of_real X_a) X))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP real real (norm_norm real) X)) K_2))) ))) ))) ) 15.83/16.01 ( real ) 15.83/16.01 ( complex ) 15.83/16.01 ) 15.83/16.01 (instantiation (forall ((U_1 $$unsorted)) (let ((_let_0 (fun int bool))) (= (hAPP _let_0 nat (finite_card int) (hAPP int _let_0 (hAPP int (fun int _let_0) (ord_atLeastLessThan int) (zero_zero int)) U_1)) (hAPP int nat nat_1 U_1))) ) 15.83/16.01 ( (one_one int) ) 15.83/16.01 ( (zero_zero int) ) 15.83/16.01 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.01 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.83/16.01 ) 15.83/16.01 (instantiation (forall ((N_1 $$unsorted)) (let ((_let_0 (hAPP nat int (semiring_1_of_nat int) N_1))) (= _let_0 (hAPP int int (ring_1_of_int int) _let_0))) ) 15.83/16.01 ( (zero_zero nat) ) 15.83/16.01 ( (hAPP nat nat suc (zero_zero nat)) ) 15.83/16.01 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.83/16.01 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.01 ) 15.83/16.01 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_128512 $$unsorted)) (let ((_let_0 (exp X_a))) (or (not (banach X_a)) (not (real_normed_field X_a)) (= (hAPP X_a X_a _let_0 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_128512)) (hAPP X_a X_a (inverse_inverse X_a) (hAPP X_a X_a _let_0 BOUND_VARIABLE_128512))))) ) 15.83/16.01 ( int, (one_one int) ) 15.83/16.01 ( int, pls ) 15.83/16.01 ( int, min_1 ) 15.83/16.01 ( real, (one_one real) ) 15.83/16.01 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/16.01 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.83/16.01 ( complex, (one_one complex) ) 15.83/16.01 ( complex, ii ) 15.83/16.01 ) 15.83/16.01 (instantiation (forall ((R_4 $$unsorted) (P_5 $$unsorted) (Q_3 $$unsorted)) (let ((_let_0 (product_prod int int))) (or (not (= (hAPP rat _let_0 quotient_of R_4) (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) P_5) Q_3))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) Q_3)))) ) 15.83/16.01 ( (zero_zero rat), s, (one_one int) ) 15.83/16.01 ( (one_one rat), (zero_zero int), (one_one int) ) 15.83/16.01 ) 15.83/16.01 (instantiation (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_1))) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) X_1))) (= X_1 (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP real real (hAPP nat (fun real real) root N_1) X_1)) N_1))) ) 15.83/16.01 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.01 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.01 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.01 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.01 ) 15.83/16.01 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_128571 $$unsorted) (BOUND_VARIABLE_128572 $$unsorted)) (let ((_let_0 (fun (filter nat) bool))) (let ((_let_1 (fun nat X_a))) (or (not (real_n1866405975lgebra X_a)) (not (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_0 (hAPP _let_1 (fun X_a _let_0) (tendsto nat X_a) BOUND_VARIABLE_128571) BOUND_VARIABLE_128572) sequentially))) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_128572)) (hBOOL (hAPP _let_1 bool (bseq X_a) (hAPP _let_1 _let_1 (hAPP (fun X_a X_a) (fun _let_1 _let_1) (combb X_a X_a nat) (inverse_inverse X_a)) BOUND_VARIABLE_128571)))))) ) 15.83/16.01 ( real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real) ) 15.83/16.01 ) 15.83/16.01 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_128656 $$unsorted) (BOUND_VARIABLE_128657 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (uminus_uminus X_a))) (or (not (boolean_algebra X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_128656)) BOUND_VARIABLE_128657))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_128657)) BOUND_VARIABLE_128656)))))) ) 15.83/16.01 ( int, (one_one int), pls ) 15.83/16.01 ( int, (one_one int), min_1 ) 15.83/16.01 ( int, pls, (one_one int) ) 15.83/16.01 ( int, pls, pls ) 15.83/16.01 ( int, pls, min_1 ) 15.83/16.01 ( int, pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.83/16.01 ( int, min_1, (one_one int) ) 15.83/16.01 ( int, min_1, pls ) 15.83/16.01 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), pls ) 15.83/16.01 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/16.01 ( real, pi, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.83/16.01 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.83/16.01 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi), pi ) 15.83/16.01 ) 15.83/16.01 (instantiation (forall ((F $$unsorted) (L $$unsorted) (C_1 $$unsorted)) (let ((_let_0 (filter real))) (let ((_let_1 (fun _let_0 bool))) (or (not (hBOOL (hAPP _let_0 bool (hAPP real _let_1 (hAPP (fun real real) (fun real _let_1) (tendsto real real) F) L) (hAPP real _let_0 (at real) C_1)))) (= (zero_zero real) L) (not (forall ((R_2 $$unsorted)) (or (not (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP real real (abs_abs real) (hAPP real real (hAPP real (fun real real) (minus_minus real) C_1) X))) R_2))) (= C_1 X) (not (= (zero_zero real) (hAPP real real F X)))) )) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) R_2)))) ))))) ) 15.83/16.01 ( (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/16.01 ) 15.83/16.01 (instantiation (forall ((N_1 $$unsorted)) (= (hAPP nat nat suc (hAPP nat nat suc N_1)) (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) N_1)) ) 15.83/16.01 ( (zero_zero nat) ) 15.83/16.01 ( (hAPP nat nat suc (zero_zero nat)) ) 15.83/16.01 ) 15.83/16.01 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_128719 $$unsorted) (BOUND_VARIABLE_128720 $$unsorted) (BOUND_VARIABLE_128721 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_128720))) (or (not (comm_semiring_1 X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_128721))) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_128719) BOUND_VARIABLE_128721))))) ) 15.83/16.01 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.83/16.01 ) 15.83/16.01 (instantiation (forall ((N_1 $$unsorted)) (or (hBOOL (hAPP nat bool (even_odd_even nat) N_1)) (not (forall ((X $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (number_number_of nat))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (not (= (hAPP nat nat (hAPP nat _let_0 (power_power nat) N_1) (hAPP int nat _let_1 _let_2)) (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) (hAPP nat nat (hAPP nat _let_0 (times_times nat) (hAPP int nat _let_1 (hAPP int int bit0 _let_2))) X)) (one_one nat))))))) ))) ) 15.83/16.01 ( (zero_zero nat) ) 15.83/16.01 ( (one_one nat) ) 15.83/16.01 ) 15.83/16.01 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_128830 $$unsorted) (BOUND_VARIABLE_128831 $$unsorted)) (or (not (dist_norm X_a)) (= (hAPP X_a real (norm_norm X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) BOUND_VARIABLE_128830) BOUND_VARIABLE_128831)) (hAPP X_a real (hAPP X_a (fun X_a real) (dist_dist X_a) BOUND_VARIABLE_128830) BOUND_VARIABLE_128831))) ) 15.83/16.01 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.83/16.01 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 15.83/16.01 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 15.83/16.01 ) 15.83/16.01 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_128868 $$unsorted) (BOUND_VARIABLE_128869 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (no_zero_divisors X_a)) (= _let_0 (ti X_a BOUND_VARIABLE_128869)) (= _let_0 (ti X_a BOUND_VARIABLE_128868)) (not (= _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_128869) BOUND_VARIABLE_128868))))) ) 15.83/16.01 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/16.01 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.83/16.01 ( int, skv_13, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.83/16.01 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.01 ( real, pi, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 15.83/16.01 ( real, (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.01 ( real, (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/16.01 ( complex, ii, ii ) 15.83/16.01 ( complex, ii, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 15.83/16.01 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.01 ) 15.83/16.01 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_128891 $$unsorted)) (or (not (comm_monoid_mult X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_128891) (one_one X_a)) (ti X_a BOUND_VARIABLE_128891))) ) 15.83/16.01 ( bool, fFalse ) 15.83/16.01 ( bool, fTrue ) 15.83/16.01 ( int, pls ) 15.83/16.01 ( int, min_1 ) 15.83/16.01 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.01 ( int, s ) 15.83/16.01 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/16.01 ( int, m ) 15.83/16.01 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.83/16.01 ( int, s1 ) 15.83/16.01 ( int, t ) 15.83/16.01 ( (fun int bool), nat_neg ) 15.83/16.01 ( (fun int bool), zprime ) 15.83/16.01 ( (fun int bool), zEven ) 15.83/16.01 ( (fun int bool), zOdd ) 15.83/16.01 ( (fun int bool), (even_odd_even int) ) 15.83/16.01 ( (fun int bool), twoSqu1091635170sum2sq ) 15.83/16.01 ( (fun int bool), nat_is_nat ) 15.83/16.01 ( (fun int (fun int bool)), norRRset ) 15.83/16.01 ( (fun int (fun int bool)), quadRes ) 15.83/16.01 ( (fun int (fun int bool)), sRStar ) 15.83/16.01 ( (fun int (fun int bool)), d22set ) 15.83/16.01 ( (fun int (fun int bool)), sr ) 15.83/16.01 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 15.83/16.01 ( (fun int int), zfact ) 15.83/16.01 ( (fun int int), bit0 ) 15.83/16.01 ( (fun int int), bit1 ) 15.83/16.01 ( (fun int int), (fact_fact int) ) 15.83/16.01 ( (fun int int), pred ) 15.83/16.01 ( (fun int int), succ ) 15.83/16.01 ( (fun nat bool), (even_odd_even nat) ) 15.83/16.01 ( (fun nat bool), prime ) 15.83/16.01 ( (fun nat nat), suc ) 15.83/16.01 ( (fun nat nat), (fact_fact nat) ) 15.83/16.01 ( (fun nat nat), fact ) 15.83/16.01 ( (fun nat nat), nat_size ) 15.83/16.01 ( (fun nat nat), (size_size nat) ) 15.83/16.01 ( (fun (product_prod nat nat) bool), pred_nat ) 15.83/16.01 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 15.83/16.01 ( real, pi ) 15.83/16.01 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.01 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/16.01 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 15.83/16.01 ( (fun real real), ln ) 15.83/16.01 ( (fun real real), cos ) 15.83/16.01 ( (fun real real), sqrt ) 15.83/16.01 ( (fun real real), sin ) 15.83/16.01 ( (fun real real), arccos ) 15.83/16.01 ( (fun real real), arcsin ) 15.83/16.01 ( (fun real real), tan ) 15.83/16.01 ( (fun real real), arctan ) 15.83/16.01 ( (fun nat (fun nat bool)), coprime ) 15.83/16.01 ( complex, ii ) 15.83/16.01 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.01 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 15.83/16.01 ( (fun nat real), (real_1 nat) ) 15.83/16.01 ( (fun nat real), sin_coeff ) 15.83/16.01 ( (fun nat real), cos_coeff ) 15.83/16.01 ( (filter nat), sequentially ) 15.83/16.01 ( (fun int (fun int int)), (gcd_gcd int) ) 15.83/16.01 ( (fun int (fun int int)), legendre ) 15.83/16.01 ( (fun int (fun int int)), legacy_zgcd ) 15.83/16.01 ( (fun int (fun int int)), standardRes ) 15.83/16.01 ( (fun int (fun int int)), nat_tsub ) 15.83/16.01 ( (fun int (fun int int)), multInv ) 15.83/16.01 ( (fun int (fun int int)), z3mod ) 15.83/16.01 ( (fun int (fun int int)), z3div ) 15.83/16.01 ( (fun int (fun int int)), int_gcd ) 15.83/16.01 ( (fun int (fun int int)), int_lcm ) 15.83/16.01 ( (fun int (fun int int)), inv ) 15.83/16.01 ( (fun complex complex), expi ) 15.83/16.01 ( (fun complex complex), cnj ) 15.83/16.01 ( (fun real complex), cis ) 15.83/16.01 ( (fun int nat), nat_1 ) 15.83/16.01 ( (fun int nat), phi ) 15.83/16.01 ( (fun (fun int bool) bool), nat_nat_set ) 15.83/16.01 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 15.83/16.01 ( (fun nat (fun nat nat)), nat_gcd ) 15.83/16.01 ( (fun nat (fun nat nat)), nat_lcm ) 15.83/16.01 ( (fun (fun int bool) int), (the int) ) 15.83/16.01 ( (fun complex real), re ) 15.83/16.01 ( (fun complex real), im ) 15.83/16.01 ( (fun complex real), arg ) 15.83/16.01 ( (fun bool bool), fNot ) 15.83/16.01 ( (fun nat (fun real real)), root ) 15.83/16.01 ( (fun real (fun real real)), log ) 15.83/16.01 ( (fun real (fun real real)), powr ) 15.83/16.01 ( (fun bool (fun bool bool)), fimplies ) 15.83/16.01 ( (fun bool (fun bool bool)), fconj ) 15.83/16.01 ( (fun bool (fun bool bool)), fdisj ) 15.83/16.01 ( (fun int (fun int (product_prod int int))), negDivAlg ) 15.83/16.01 ( (fun int (fun int (product_prod int int))), posDivAlg ) 15.83/16.01 ( (fun int (fun int (product_prod int int))), divmod_int ) 15.83/16.01 ( (fun int (fun int (product_prod int int))), pdivmod ) 15.83/16.01 ( (fun int (fun int (product_prod int int))), norm_frac ) 15.83/16.01 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 15.83/16.01 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 15.83/16.01 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 15.83/16.01 ( (fun int (fun int (fun int bool))), zcong ) 15.83/16.01 ( (fun int (fun int (fun int bool))), zcongm ) 15.83/16.01 ( (fun int (fun int (fun int bool))), noXRRset ) 15.83/16.01 ( (fun int (fun int (fun int bool))), bnorRset ) 15.83/16.01 ( (fun int (fun int (fun int bool))), wset ) 15.83/16.01 ( (fun (product_prod int int) bool), frac_1 ) 15.83/16.01 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 15.83/16.01 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 15.83/16.01 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 15.83/16.01 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 15.83/16.01 ( (fun (fun nat rat) bool), vanishes ) 15.83/16.01 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 15.83/16.01 ( (fun code_code_numeral nat), code_c271388182l_size ) 15.83/16.01 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 15.83/16.01 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 15.83/16.01 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 15.83/16.01 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 15.83/16.01 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 15.83/16.01 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 15.83/16.01 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 15.83/16.01 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 15.83/16.01 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 15.83/16.01 ( (fun complex nat), complex_size ) 15.83/16.01 ( (fun complex nat), (size_size complex) ) 15.83/16.01 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 15.83/16.01 ( (fun nat (fun nat (product_prod int int))), bezw ) 15.83/16.01 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 15.83/16.01 ( (fun int (fun nat nat)), nat_aux ) 15.83/16.01 ( (fun int (fun (fun int bool) bool)), rsetR ) 15.83/16.01 ( (fun int (fun (fun int bool) bool)), resSet ) 15.83/16.01 ( (fun int (list int)), quickc666637781d_zero ) 15.83/16.01 ( (fun (product_prod int int) rat), frct ) 15.83/16.01 ( (fun int (fun int rat)), fract ) 15.83/16.01 ( (fun real (fun real complex)), complex_1 ) 15.83/16.01 ( (fun real (fun real complex)), rcis ) 15.83/16.01 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 15.83/16.01 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 15.83/16.01 ( (fun int real), (real_1 int) ) 15.83/16.01 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 15.83/16.01 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 15.83/16.01 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 15.83/16.01 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 15.83/16.01 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 15.83/16.01 ( (fun real nat), natfloor ) 15.83/16.01 ( (fun real nat), natceiling ) 15.83/16.01 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 15.83/16.01 ( (fun quickcheck_code_int int), quickcheck_int_of ) 15.83/16.01 ( (fun rat (product_prod int int)), quotient_of ) 15.83/16.01 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 15.83/16.01 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 15.83/16.01 ( (fun rat real), ratreal ) 15.83/16.01 ( (fun code_code_numeral int), code_int_of ) 15.83/16.01 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 15.83/16.01 ( (fun int quickcheck_code_int), quickcheck_of_int ) 15.83/16.01 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 15.83/16.01 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 15.83/16.01 ) 15.83/16.01 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less real))) (let ((_let_3 (one_one real))) (let ((_let_4 (fun real real))) (let ((_let_5 (fun nat real))) (let ((_let_6 (power_power real))) (let ((_let_7 (number_number_of real))) (let ((_let_8 (fun nat _let_0))) (let ((_let_9 (fun nat _let_4))) (let ((_let_10 (fun _let_5 _let_5))) (let ((_let_11 (combs nat real real))) (let ((_let_12 (fun _let_0 _let_5))) (let ((_let_13 (combb nat real nat))) (let ((_let_14 (hAPP (fun real _let_4) (fun _let_5 _let_9) (combb real _let_4 nat) (times_times real)))) (or (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (zero_zero real)) X_2))) (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 X_2) (hAPP int real _let_7 (hAPP int int bit0 (hAPP int int bit1 pls)))))) (= (hAPP _let_5 real (suminf real) (hAPP _let_5 _let_5 (hAPP _let_9 _let_10 _let_11 (hAPP _let_5 _let_9 _let_14 (hAPP _let_5 _let_5 (hAPP _let_9 _let_10 _let_11 (hAPP _let_5 _let_9 _let_14 (hAPP real _let_5 _let_6 (hAPP int real _let_7 min_1)))) (hAPP _let_5 _let_5 (hAPP _let_4 _let_10 (combb real real nat) (hAPP real _let_4 (inverse_divide real) _let_3)) (hAPP _let_0 _let_5 (hAPP _let_5 _let_12 _let_13 (real_1 nat)) (hAPP nat _let_0 (hAPP _let_8 _let_8 (combc nat nat nat) (plus_plus nat)) (one_one nat))))))) (hAPP _let_0 _let_5 (hAPP _let_5 _let_12 _let_13 (hAPP real _let_5 _let_6 (hAPP real real (hAPP real _let_4 (minus_minus real) X_2) _let_3))) suc))) (hAPP real real ln X_2)))))))))))))))))) ) 15.83/16.01 ( (one_one real) ) 15.83/16.01 ( (zero_zero real) ) 15.83/16.01 ( pi ) 15.83/16.01 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/16.01 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.83/16.01 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/16.01 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/16.01 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 15.83/16.01 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))) ) 15.83/16.01 ( skv_2 ) 15.83/16.01 ( skv_8 ) 15.83/16.01 ( skv_9 ) 15.83/16.01 ) 15.83/16.01 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (zero_zero real))) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) _let_0) X_1))) (not (= _let_0 (hAPP real real sin X_1))) (not (forall ((N_2 $$unsorted)) (let ((_let_0 (fun real real))) (or (not (= X_1 (hAPP real real (hAPP real _let_0 (times_times real) (hAPP nat real (real_1 nat) N_2)) (hAPP real real (hAPP real _let_0 (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))) (not (hBOOL (hAPP nat bool (even_odd_even nat) N_2))))) )))) ) 15.83/16.01 ( (zero_zero real) ) 15.83/16.01 ( pi ) 15.83/16.01 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/16.01 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.83/16.01 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.83/16.01 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/16.01 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.83/16.01 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.83/16.01 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.83/16.01 ( skv_3 ) 15.83/16.01 ( skv_5 ) 15.83/16.01 ( skv_7 ) 15.83/16.01 ( skv_12 ) 15.83/16.01 ) 15.83/16.01 (instantiation (forall ((R_4 $$unsorted)) (= (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP real complex (of_real complex) R_4)) ii) (hAPP real complex (hAPP real (fun real complex) complex_1 (zero_zero real)) R_4)) ) 15.83/16.01 ( (one_one real) ) 15.83/16.01 ( (zero_zero real) ) 15.83/16.01 ( pi ) 15.83/16.01 ( (hAPP int real (number_number_of real) min_1) ) 15.83/16.01 ( (hAPP real real (uminus_uminus real) (one_one real)) ) 15.83/16.01 ) 15.83/16.01 (instantiation (forall ((Z_1 $$unsorted)) (= Z_1 (hAPP real complex (hAPP real (fun real complex) complex_1 (hAPP complex real re Z_1)) (hAPP complex real im Z_1))) ) 15.83/16.01 ( (one_one complex) ) 15.83/16.01 ( ii ) 15.83/16.01 ( (zero_zero complex) ) 15.83/16.01 ) 15.83/16.01 (instantiation (forall ((R $$unsorted) (S_5 $$unsorted)) (let ((_let_0 (fun real real))) (= (hAPP real real (hAPP real _let_0 (inverse_divide real) R) S_5) (hAPP real real (hAPP real _let_0 (times_times real) R) (hAPP real real (inverse_inverse real) S_5)))) ) 15.83/16.01 ( (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.01 ( (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.83/16.01 ( (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/16.01 ( (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 15.83/16.01 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.01 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.83/16.01 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.83/16.01 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.83/16.01 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.01 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.01 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.83/16.01 ) 15.83/16.01 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (finite_finite T_2)) (not (finite_finite T_1)) (finite_finite (fun T_2 T_1))) ) 15.83/16.01 ( bool, bool ) 15.83/16.01 ( bool, (fun bool bool) ) 15.83/16.01 ( nat, bool ) 15.83/16.01 ( nat, nat ) 15.83/16.01 ( nat, int ) 15.83/16.01 ( nat, (fun int int) ) 15.83/16.01 ( nat, (fun nat bool) ) 15.83/16.01 ( nat, (fun nat nat) ) 15.83/16.01 ( nat, (product_prod nat nat) ) 15.83/16.01 ( nat, (fun (product_prod nat nat) bool) ) 15.83/16.01 ( nat, (fun nat (fun (product_prod nat nat) bool)) ) 15.83/16.01 ( nat, real ) 15.83/16.01 ( nat, (fun real real) ) 15.83/16.01 ( nat, rat ) 15.83/16.01 ( nat, (fun nat (fun nat bool)) ) 15.83/16.01 ( nat, complex ) 15.83/16.01 ( nat, (product_prod int int) ) 15.83/16.01 ( nat, (fun bool bool) ) 15.83/16.01 ( nat, (product_prod real real) ) 15.83/16.01 ( nat, (fun nat (product_prod nat nat)) ) 15.83/16.01 ( nat, (fun nat (product_prod int int)) ) 15.83/16.01 ( int, bool ) 15.83/16.01 ( int, nat ) 15.83/16.01 ( int, int ) 15.83/16.01 ( int, (fun int bool) ) 15.83/16.01 ( int, (fun int (fun int bool)) ) 15.83/16.01 ( int, (fun int int) ) 15.83/16.01 ( int, (fun nat bool) ) 15.83/16.01 ( int, (fun nat nat) ) 15.83/16.01 ( int, real ) 15.83/16.01 ( int, (fun real real) ) 15.83/16.01 ( int, rat ) 15.83/16.01 ( int, (fun int rat) ) 15.83/16.01 ( int, (fun nat int) ) 15.83/16.01 ( int, (fun nat real) ) 15.83/16.01 ( int, (product_prod int int) ) 15.83/16.01 ( int, (fun int (product_prod int int)) ) 15.83/16.01 ( int, (fun (fun int bool) bool) ) 15.83/16.01 ( int, quickcheck_code_int ) 15.83/16.01 ( int, (fun bool bool) ) 15.83/16.01 ( int, (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 15.83/16.01 ( int, (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)) ) 15.83/16.01 ( int, (fun int (fun int (fun int bool))) ) 15.83/16.01 ( int, (fun (product_prod int int) bool) ) 15.83/16.01 ( int, (fun int (fun (product_prod int int) bool)) ) 15.83/16.01 ( int, (fun int (fun bool bool)) ) 15.83/16.01 ( int, (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 15.83/16.01 ( int, (fun (fun int int) (fun int bool)) ) 15.83/16.01 ( int, (fun (product_prod int int) int) ) 15.83/16.01 ( int, (product_prod int (product_prod int int)) ) 15.83/16.01 ( int, (fun int (product_prod int (product_prod int int))) ) 15.83/16.01 ( int, (fun int (fun int (product_prod int (product_prod int int)))) ) 15.83/16.01 ( int, (fun int (fun int (fun int (product_prod int (product_prod int int))))) ) 15.83/16.01 ( int, (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))) ) 15.83/16.01 ( int, (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))) ) 15.83/16.01 ( int, (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))) ) 15.83/16.01 ( int, (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))))) ) 15.83/16.01 ( int, (fun int (fun (fun int bool) bool)) ) 15.83/16.01 ( int, (list int) ) 15.83/16.01 ( int, (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 15.83/16.01 ( int, (fun int real) ) 15.83/16.01 ( int, (fun nat (fun bool bool)) ) 15.83/16.01 ( int, (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 15.83/16.01 ( int, (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 15.83/16.01 ( (fun int bool), bool ) 15.83/16.01 ( (fun int bool), int ) 15.83/16.01 ( (fun int bool), (fun int bool) ) 15.83/16.01 ( (fun int bool), (fun int (fun int bool)) ) 15.83/16.01 ( (fun int bool), (fun int (fun int int)) ) 15.83/16.01 ( (fun int bool), (fun int (fun bool bool)) ) 15.83/16.01 ( (fun int bool), (fun (fun int int) (fun int bool)) ) 15.83/16.01 ( (fun int bool), (fun real (fun int (fun int bool))) ) 15.83/16.01 ( (fun int (fun int bool)), (fun int bool) ) 15.83/16.01 ( (fun int (fun int bool)), (fun int (fun int bool)) ) 15.83/16.01 ( (fun int (fun int bool)), (fun int (fun (fun int int) (fun int bool))) ) 15.83/16.01 ( (fun int (fun int bool)), (fun int (fun int (fun bool bool))) ) 15.83/16.01 ( (fun int int), (fun int bool) ) 15.83/16.01 ( (fun int int), (fun int (fun int bool)) ) 15.83/16.01 ( (fun int int), (fun int int) ) 15.83/16.01 ( (fun int int), (fun int (fun int int)) ) 15.83/16.01 ( (fun int int), (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 15.83/16.01 ( (fun int int), (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 15.83/16.01 ( (fun nat bool), bool ) 15.83/16.01 ( (fun nat bool), (fun nat bool) ) 15.83/16.01 ( (fun nat bool), (fun nat (fun bool bool)) ) 15.83/16.01 ( (fun nat bool), (fun int (fun nat bool)) ) 15.83/16.01 ( (fun nat bool), (fun real (fun int (fun nat bool))) ) 15.83/16.01 ( (fun nat nat), (fun nat (fun nat bool)) ) 15.83/16.01 ( (fun nat nat), (fun nat real) ) 15.83/16.01 ( (fun nat nat), (fun nat (fun nat nat)) ) 15.83/16.01 ( (product_prod nat nat), bool ) 15.83/16.01 ( (product_prod nat nat), (fun (product_prod nat nat) bool) ) 15.83/16.01 ( real, bool ) 15.83/16.01 ( real, nat ) 15.83/16.01 ( real, (fun int bool) ) 15.83/16.01 ( real, (fun int (fun int bool)) ) 15.83/16.01 ( real, real ) 15.83/16.01 ( real, (fun real bool) ) 15.83/16.01 ( real, (fun real real) ) 15.83/16.01 ( real, complex ) 15.83/16.01 ( real, (fun nat real) ) 15.83/16.01 ( real, (fun real complex) ) 15.83/16.01 ( real, (fun bool bool) ) 15.83/16.01 ( real, (fun (filter nat) bool) ) 15.83/16.01 ( real, (fun nat (product_prod real real)) ) 15.83/16.01 ( real, (fun real (fun nat (product_prod real real))) ) 15.83/16.01 ( real, (fun (filter real) bool) ) 15.83/16.01 ( real, (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 15.83/16.01 ( real, (let ((_let_0 (fun int bool))) (fun _let_0 (fun int _let_0))) ) 15.83/16.01 ( real, (fun int (fun int (fun bool bool))) ) 15.83/16.01 ( real, (fun (fun int (fun int real)) (fun int (fun int bool))) ) 15.83/16.01 ( real, (fun (fun int real) (fun int bool)) ) 15.83/16.01 ( real, (fun int (fun nat bool)) ) 15.83/16.01 ( real, (let ((_let_0 (fun nat bool))) (fun _let_0 (fun int _let_0))) ) 15.83/16.01 ( real, (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 15.83/16.01 ( real, (fun int (fun nat (fun bool bool))) ) 15.83/16.01 ( real, (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 15.83/16.01 ( real, (fun (fun nat real) (fun nat bool)) ) 15.83/16.01 ( (fun real bool), real ) 15.83/16.01 ( (fun real bool), (fun real bool) ) 15.83/16.01 ( (fun real bool), (fun real (fun bool bool)) ) 15.83/16.01 ( (fun real bool), (fun (fun int real) (fun int bool)) ) 15.83/16.01 ( (fun real bool), (fun (fun nat real) (fun nat bool)) ) 15.83/16.01 ( (fun real real), (fun real real) ) 15.83/16.01 ( (fun real real), (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 15.83/16.01 ( (fun real real), (fun real (fun real real)) ) 15.83/16.01 ( (fun real real), (fun real (fun real bool)) ) 15.83/16.01 ( (fun real real), (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 15.83/16.01 ( rat, real ) 15.83/16.01 ( rat, (product_prod int int) ) 15.83/16.01 ( complex, nat ) 15.83/16.01 ( complex, real ) 15.83/16.01 ( complex, complex ) 15.83/16.01 ( (fun nat real), (fun nat bool) ) 15.83/16.01 ( (fun nat real), (fun nat real) ) 15.83/16.01 ( (fun nat real), (fun nat (fun real real)) ) 15.83/16.01 ( (fun nat real), (fun int (fun nat real)) ) 15.83/16.01 ( (filter nat), bool ) 15.83/16.01 ( (fun int (fun int int)), (fun int (fun int (fun int bool))) ) 15.83/16.01 ( (fun int (fun int int)), (let ((_let_0 (fun int int))) (fun int (fun _let_0 _let_0))) ) 15.83/16.01 ( (product_prod int int), bool ) 15.83/16.01 ( (product_prod int int), int ) 15.83/16.01 ( (product_prod int int), (fun int bool) ) 15.83/16.01 ( (product_prod int int), (fun int int) ) 15.83/16.01 ( (product_prod int int), rat ) 15.83/16.01 ( (product_prod int int), (product_prod int int) ) 15.83/16.01 ( (product_prod int int), (fun bool bool) ) 15.83/16.01 ( (product_prod int int), (fun (product_prod int int) bool) ) 15.83/16.01 ( (product_prod int int), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 15.83/16.01 ( (product_prod int int), (fun (product_prod int int) (fun int bool)) ) 15.83/16.01 ( (product_prod int int), (fun (product_prod int int) int) ) 15.83/16.01 ( (product_prod int int), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 15.83/16.01 ( (product_prod int int), (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 15.83/16.01 ( quickcheck_code_int, nat ) 15.83/16.01 ( quickcheck_code_int, int ) 15.83/16.01 ( quickcheck_code_int, (product_prod quickcheck_code_int quickcheck_code_int) ) 15.83/16.01 ( quickcheck_code_int, (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int)) ) 15.83/16.01 ( (fun bool bool), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 15.83/16.01 ( code_code_numeral, nat ) 15.83/16.01 ( code_code_numeral, int ) 15.83/16.01 ( code_code_numeral, (fun nat nat) ) 15.83/16.01 ( code_code_numeral, code_code_numeral ) 15.83/16.01 ( code_code_numeral, (product_prod code_code_numeral code_code_numeral) ) 15.83/16.01 ( code_code_numeral, (fun code_code_numeral (product_prod code_code_numeral code_code_numeral)) ) 15.83/16.01 ( (fun int (fun int (fun int bool))), (fun int (fun int (fun int bool))) ) 15.83/16.01 ( (fun real (fun real bool)), (fun real (fun (fun int real) (fun int bool))) ) 15.83/16.01 ( (fun real (fun real bool)), (fun real (fun (fun nat real) (fun nat bool))) ) 15.83/16.01 ( (product_prod real real), bool ) 15.83/16.01 ( (fun (product_prod real real) bool), (fun real (fun real (fun nat (product_prod real real)))) ) 15.83/16.01 ( (fun (product_prod int int) bool), (fun (product_prod int int) bool) ) 15.83/16.01 ( (fun (product_prod int int) bool), (fun (product_prod int int) (fun bool bool)) ) 15.83/16.01 ( (fun int (fun bool bool)), (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 15.83/16.01 ( (fun nat rat), bool ) 15.83/16.01 ( (filter real), bool ) 15.83/16.01 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)), bool ) 15.83/16.01 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 15.83/16.01 ( (fun (product_prod int int) (fun bool bool)), (let ((_let_0 (fun (product_prod int int) bool))) (fun (product_prod int int) (fun _let_0 _let_0))) ) 15.83/16.01 ( (fun (product_prod int int) (fun int bool)), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 15.83/16.01 ( (fun (product_prod int int) int), (fun (product_prod int int) bool) ) 15.83/16.01 ( (fun (product_prod int int) int), (fun (product_prod int int) (fun int bool)) ) 15.83/16.01 ( (fun (product_prod int int) int), (fun (product_prod int int) int) ) 15.83/16.01 ( (fun (product_prod int int) int), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))) ) 15.83/16.01 ( (fun (product_prod int int) int), (fun (product_prod int int) (fun int int)) ) 15.83/16.01 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 15.83/16.01 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 (fun int bool)))) ) 15.83/16.01 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 (fun int bool)))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun (fun _let_0 int) (fun _let_0 bool)))) ) 15.83/16.01 ( (fun (product_prod int int) (fun int int)), (let ((_let_0 (fun (product_prod int int) int))) (fun (product_prod int int) (fun _let_0 _let_0))) ) 15.83/16.01 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), bool ) 15.83/16.01 ( (fun int real), (fun int bool) ) 15.83/16.01 ( (fun int real), (fun int real) ) 15.83/16.01 ( (fun int real), (fun int (fun int real)) ) 15.83/16.01 ( (fun int real), (fun int (fun real real)) ) 15.83/16.01 ( (fun nat (fun bool bool)), (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 15.83/16.01 ( (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun int bool))) (fun _let_0 (fun int _let_0))) ) 15.83/16.01 ( (fun int (fun int (fun bool bool))), (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 15.83/16.01 ( (fun real (fun int bool)), (fun real bool) ) 15.83/16.01 ( (fun real (fun int (fun int bool))), (fun real (fun int bool)) ) 15.83/16.01 ( (fun real (fun int (fun int bool))), (fun real (fun int (fun int (fun bool bool)))) ) 15.83/16.01 ( (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun int bool))) (fun real (fun _let_0 (fun int _let_0)))) ) 15.83/16.01 ( (fun real (fun int (fun int (fun bool bool)))), (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))) ) 15.83/16.01 ( (fun int (fun int real)), (fun int (fun int bool)) ) 15.83/16.01 ( (fun int (fun int real)), (fun real (fun int (fun int bool))) ) 15.83/16.01 ( (fun (fun int real) (fun int bool)), (fun (fun int (fun int real)) (fun int (fun int bool))) ) 15.83/16.01 ( (fun real (fun (fun int real) (fun int bool))), (fun real (fun (fun int (fun int real)) (fun int (fun int bool)))) ) 15.83/16.01 ( (fun int (fun real real)), (let ((_let_0 (fun int real))) (fun int (fun _let_0 _let_0))) ) 15.83/16.01 ( (fun int (fun real real)), (let ((_let_0 (fun nat real))) (fun int (fun _let_0 _let_0))) ) 15.83/16.01 ( (fun int (fun nat bool)), (fun int bool) ) 15.83/16.01 ( (fun int (fun nat bool)), (fun int (fun nat (fun bool bool))) ) 15.83/16.01 ( (fun real (fun int (fun nat bool))), (fun real (fun int bool)) ) 15.83/16.01 ( (fun real (fun int (fun nat bool))), (fun real (fun int (fun nat (fun bool bool)))) ) 15.91/16.01 ( (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun nat bool))) (fun _let_0 (fun int _let_0))) ) 15.91/16.01 ( (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun nat bool))) (fun real (fun _let_0 (fun int _let_0)))) ) 15.91/16.01 ( (fun int (fun nat (fun bool bool))), (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 15.91/16.01 ( (fun real (fun int (fun nat (fun bool bool)))), (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))) ) 15.91/16.01 ( (fun int (fun nat real)), (fun int (fun nat bool)) ) 15.91/16.01 ( (fun int (fun nat real)), (fun real (fun int (fun nat bool))) ) 15.91/16.01 ( (fun (fun nat real) (fun nat bool)), (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 15.91/16.01 ( (fun real (fun (fun nat real) (fun nat bool))), (fun real (fun (fun int (fun nat real)) (fun int (fun nat bool)))) ) 15.91/16.01 ) 15.91/16.01 (instantiation (forall ((Ma $$unsorted) (Z $$unsorted)) (= (= (hAPP nat int (semiring_1_of_nat int) Ma) (ti int Z)) (and (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) Z)) (= Ma (hAPP int nat nat_1 Z)))) ) 15.91/16.01 ( (zero_zero nat), pls ) 15.91/16.01 ( (hAPP nat nat suc (zero_zero nat)), s1 ) 15.91/16.01 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))), m ) 15.91/16.01 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 15.91/16.01 ) 15.91/16.01 (instantiation (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) A_1) _let_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) B) A_1))) (= _let_1 (hAPP int int (hAPP int (fun int int) (div_div int) A_1) B))))) ) 15.91/16.01 ( (one_one int), t ) 15.91/16.01 ( pls, (one_one int) ) 15.91/16.01 ( pls, pls ) 15.91/16.01 ( pls, min_1 ) 15.91/16.01 ( pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.01 ( min_1, pls ) 15.91/16.01 ( min_1, min_1 ) 15.91/16.01 ( s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.01 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.01 ( skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.01 ( skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.01 ) 15.91/16.01 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_129157 $$unsorted)) (let ((_let_0 (inverse_inverse X_a))) (let ((_let_1 (ti X_a BOUND_VARIABLE_129157))) (or (not (division_ring X_a)) (= (zero_zero X_a) _let_1) (= _let_1 (hAPP X_a X_a _let_0 (hAPP X_a X_a _let_0 BOUND_VARIABLE_129157)))))) ) 15.91/16.01 ( bool, fFalse ) 15.91/16.01 ( bool, fTrue ) 15.91/16.01 ( int, pls ) 15.91/16.01 ( int, min_1 ) 15.91/16.01 ( int, s ) 15.91/16.01 ( int, m ) 15.91/16.01 ( int, s1 ) 15.91/16.01 ( int, t ) 15.91/16.01 ( (fun int bool), nat_neg ) 15.91/16.01 ( (fun int bool), zprime ) 15.91/16.01 ( (fun int bool), zEven ) 15.91/16.01 ( (fun int bool), zOdd ) 15.91/16.01 ( (fun int bool), (even_odd_even int) ) 15.91/16.01 ( (fun int bool), twoSqu1091635170sum2sq ) 15.91/16.01 ( (fun int bool), nat_is_nat ) 15.91/16.01 ( (fun int (fun int bool)), norRRset ) 15.91/16.01 ( (fun int (fun int bool)), quadRes ) 15.91/16.01 ( (fun int (fun int bool)), sRStar ) 15.91/16.01 ( (fun int (fun int bool)), d22set ) 15.91/16.01 ( (fun int (fun int bool)), sr ) 15.91/16.01 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 15.91/16.01 ( (fun int int), zfact ) 15.91/16.01 ( (fun int int), bit0 ) 15.91/16.01 ( (fun int int), bit1 ) 15.91/16.01 ( (fun int int), (fact_fact int) ) 15.91/16.01 ( (fun int int), pred ) 15.91/16.01 ( (fun int int), succ ) 15.91/16.01 ( (fun nat bool), (even_odd_even nat) ) 15.91/16.01 ( (fun nat bool), prime ) 15.91/16.01 ( (fun nat nat), suc ) 15.91/16.01 ( (fun nat nat), (fact_fact nat) ) 15.91/16.01 ( (fun nat nat), fact ) 15.91/16.01 ( (fun nat nat), nat_size ) 15.91/16.01 ( (fun nat nat), (size_size nat) ) 15.91/16.01 ( (fun (product_prod nat nat) bool), pred_nat ) 15.91/16.01 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 15.91/16.01 ( real, (zero_zero real) ) 15.91/16.01 ( real, pi ) 15.91/16.01 ( (fun real real), ln ) 15.91/16.01 ( (fun real real), cos ) 15.91/16.01 ( (fun real real), sqrt ) 15.91/16.01 ( (fun real real), sin ) 15.91/16.01 ( (fun real real), arccos ) 15.91/16.01 ( (fun real real), arcsin ) 15.91/16.01 ( (fun real real), tan ) 15.91/16.01 ( (fun real real), arctan ) 15.91/16.01 ( (fun nat (fun nat bool)), coprime ) 15.91/16.01 ( complex, ii ) 15.91/16.01 ( (fun nat real), (real_1 nat) ) 15.91/16.01 ( (fun nat real), sin_coeff ) 15.91/16.01 ( (fun nat real), cos_coeff ) 15.91/16.01 ( (filter nat), sequentially ) 15.91/16.01 ( (fun int (fun int int)), (gcd_gcd int) ) 15.91/16.01 ( (fun int (fun int int)), legendre ) 15.91/16.01 ( (fun int (fun int int)), legacy_zgcd ) 15.91/16.01 ( (fun int (fun int int)), standardRes ) 15.91/16.01 ( (fun int (fun int int)), nat_tsub ) 15.91/16.01 ( (fun int (fun int int)), multInv ) 15.91/16.01 ( (fun int (fun int int)), z3mod ) 15.91/16.01 ( (fun int (fun int int)), z3div ) 15.91/16.01 ( (fun int (fun int int)), int_gcd ) 15.91/16.01 ( (fun int (fun int int)), int_lcm ) 15.91/16.01 ( (fun int (fun int int)), inv ) 15.91/16.01 ( (fun complex complex), expi ) 15.91/16.01 ( (fun complex complex), cnj ) 15.91/16.01 ( (fun real complex), cis ) 15.91/16.01 ( (fun int nat), nat_1 ) 15.91/16.01 ( (fun int nat), phi ) 15.91/16.01 ( (fun (fun int bool) bool), nat_nat_set ) 15.91/16.01 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 15.91/16.01 ( (fun nat (fun nat nat)), nat_gcd ) 15.91/16.01 ( (fun nat (fun nat nat)), nat_lcm ) 15.91/16.01 ( (fun (fun int bool) int), (the int) ) 15.91/16.01 ( (fun complex real), re ) 15.91/16.01 ( (fun complex real), im ) 15.91/16.01 ( (fun complex real), arg ) 15.91/16.01 ( (fun bool bool), fNot ) 15.91/16.01 ( (fun nat (fun real real)), root ) 15.91/16.01 ( (fun real (fun real real)), log ) 15.91/16.01 ( (fun real (fun real real)), powr ) 15.91/16.01 ( (fun bool (fun bool bool)), fimplies ) 15.91/16.01 ( (fun bool (fun bool bool)), fconj ) 15.91/16.01 ( (fun bool (fun bool bool)), fdisj ) 15.91/16.01 ( (fun int (fun int (product_prod int int))), negDivAlg ) 15.91/16.01 ( (fun int (fun int (product_prod int int))), posDivAlg ) 15.91/16.01 ( (fun int (fun int (product_prod int int))), divmod_int ) 15.91/16.01 ( (fun int (fun int (product_prod int int))), pdivmod ) 15.91/16.01 ( (fun int (fun int (product_prod int int))), norm_frac ) 15.91/16.01 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 15.91/16.01 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 15.91/16.01 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 15.91/16.01 ( (fun int (fun int (fun int bool))), zcong ) 15.91/16.01 ( (fun int (fun int (fun int bool))), zcongm ) 15.91/16.01 ( (fun int (fun int (fun int bool))), noXRRset ) 15.91/16.01 ( (fun int (fun int (fun int bool))), bnorRset ) 15.91/16.01 ( (fun int (fun int (fun int bool))), wset ) 15.91/16.01 ( (fun (product_prod int int) bool), frac_1 ) 15.91/16.01 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 15.91/16.01 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 15.91/16.01 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 15.91/16.01 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 15.91/16.01 ( (fun (fun nat rat) bool), vanishes ) 15.91/16.01 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 15.91/16.01 ( (fun code_code_numeral nat), code_c271388182l_size ) 15.91/16.01 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 15.91/16.01 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 15.91/16.01 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 15.91/16.01 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 15.91/16.01 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 15.91/16.01 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 15.91/16.01 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 15.91/16.01 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 15.91/16.01 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 15.91/16.01 ( (fun complex nat), complex_size ) 15.91/16.01 ( (fun complex nat), (size_size complex) ) 15.91/16.01 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 15.91/16.01 ( (fun nat (fun nat (product_prod int int))), bezw ) 15.91/16.01 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 15.91/16.01 ( (fun int (fun nat nat)), nat_aux ) 15.91/16.01 ( (fun int (fun (fun int bool) bool)), rsetR ) 15.91/16.01 ( (fun int (fun (fun int bool) bool)), resSet ) 15.91/16.01 ( (fun int (list int)), quickc666637781d_zero ) 15.91/16.01 ( (fun (product_prod int int) rat), frct ) 15.91/16.01 ( (fun int (fun int rat)), fract ) 15.91/16.01 ( (fun real (fun real complex)), complex_1 ) 15.91/16.01 ( (fun real (fun real complex)), rcis ) 15.91/16.01 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 15.91/16.01 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 15.91/16.01 ( (fun int real), (real_1 int) ) 15.91/16.01 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 15.91/16.01 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 15.91/16.01 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 15.91/16.01 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 15.91/16.01 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 15.91/16.01 ( (fun real nat), natfloor ) 15.91/16.01 ( (fun real nat), natceiling ) 15.91/16.01 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 15.91/16.01 ( (fun quickcheck_code_int int), quickcheck_int_of ) 15.91/16.01 ( (fun rat (product_prod int int)), quotient_of ) 15.91/16.01 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 15.91/16.01 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 15.91/16.01 ( (fun rat real), ratreal ) 15.91/16.01 ( (fun code_code_numeral int), code_int_of ) 15.91/16.01 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 15.91/16.01 ( (fun int quickcheck_code_int), quickcheck_of_int ) 15.91/16.01 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 15.91/16.01 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 15.91/16.01 ) 15.91/16.01 (instantiation (forall ((X_2 $$unsorted)) (= (not (hBOOL (hAPP int bool (even_odd_even int) X_2))) (not (forall ((Y $$unsorted)) (let ((_let_0 (fun int int))) (not (= (ti int X_2) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) Y)) (one_one int))))) ))) ) 15.91/16.01 ( (one_one int) ) 15.91/16.01 ( (zero_zero int) ) 15.91/16.01 ) 15.91/16.01 (instantiation (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_129257 $$unsorted) (BOUND_VARIABLE_129258 $$unsorted) (BOUND_VARIABLE_129259 $$unsorted) (BOUND_VARIABLE_129260 $$unsorted) (BOUND_VARIABLE_129261 $$unsorted)) (let ((_let_0 (filter X_a))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_129261))) (or (not (metric_space X_b)) (not (metric_space X_c)) (not (topological_space X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (hAPP (fun X_a X_b) (fun X_b _let_1) (tendsto X_a X_b) BOUND_VARIABLE_129259) BOUND_VARIABLE_129260) _let_2))) (not (forall ((X $$unsorted)) (or (= (ti X_a X) (ti X_a BOUND_VARIABLE_129261)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP X_c real (hAPP X_c (fun X_c real) (dist_dist X_c) (hAPP X_a X_c BOUND_VARIABLE_129257 X)) BOUND_VARIABLE_129258)) (hAPP X_b real (hAPP X_b (fun X_b real) (dist_dist X_b) (hAPP X_a X_b BOUND_VARIABLE_129259 X)) BOUND_VARIABLE_129260)))) )) (hBOOL (hAPP _let_0 bool (hAPP X_c _let_1 (hAPP (fun X_a X_c) (fun X_c _let_1) (tendsto X_a X_c) BOUND_VARIABLE_129257) BOUND_VARIABLE_129258) _let_2)))))) ) 15.91/16.01 ( real, real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.01 ) 15.91/16.01 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_129304 $$unsorted) (BOUND_VARIABLE_129305 $$unsorted)) (let ((_let_0 (number_number_of X_a))) (or (not (number_ring X_a)) (= (hAPP int X_a _let_0 (hAPP int int (hAPP int (fun int int) (plus_plus int) BOUND_VARIABLE_129304) BOUND_VARIABLE_129305)) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (hAPP int X_a _let_0 BOUND_VARIABLE_129304)) (hAPP int X_a _let_0 BOUND_VARIABLE_129305))))) ) 15.91/16.01 ( nat, (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 15.91/16.01 ) 15.91/16.01 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_129332 $$unsorted) (BOUND_VARIABLE_129333 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (inverse_inverse X_a))) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_129332)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_129333)))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_129333) (zero_zero X_a)))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_129333) BOUND_VARIABLE_129332)))))) ) 15.91/16.01 ( int, (one_one int), (zero_zero int) ) 15.91/16.01 ( int, pls, min_1 ) 15.91/16.01 ( int, min_1, (zero_zero int) ) 15.91/16.01 ( int, min_1, min_1 ) 15.91/16.01 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 15.91/16.01 ( int, s, (zero_zero int) ) 15.91/16.01 ( int, t, (one_one int) ) 15.91/16.01 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 15.91/16.01 ( int, (hAPP int int (number_number_of int) pls), (zero_zero int) ) 15.91/16.01 ( int, skv_4, (zero_zero int) ) 15.91/16.01 ( int, skv_10, (zero_zero int) ) 15.91/16.01 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.01 ( real, pi, (zero_zero real) ) 15.91/16.01 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.01 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.01 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_5 ) 15.91/16.01 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.91/16.01 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.91/16.01 ( real, skv_3, (zero_zero real) ) 15.91/16.01 ( real, skv_5, (zero_zero real) ) 15.91/16.01 ( real, skv_7, (zero_zero real) ) 15.91/16.01 ( real, skv_12, (zero_zero real) ) 15.91/16.01 ) 15.91/16.01 (instantiation (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (or (not (= (hAPP complex real re X_1) (hAPP complex real re Y_1))) (not (= (hAPP complex real im Y_1) (hAPP complex real im X_1))) (= X_1 Y_1)) ) 15.91/16.01 ( (one_one complex), (zero_zero complex) ) 15.91/16.01 ( ii, (one_one complex) ) 15.91/16.01 ( ii, (zero_zero complex) ) 15.91/16.01 ( (zero_zero complex), ii ) 15.91/16.01 ( (zero_zero complex), (zero_zero complex) ) 15.91/16.01 ) 15.91/16.02 (instantiation (forall ((P_4 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (ord_less int))) (let ((_let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 _let_3) P_4))) (not (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) P_4) zOdd))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 (zero_zero int)) (hAPP int int (hAPP int _let_1 (div_div int) (hAPP int int (hAPP int _let_1 (minus_minus int) P_4) (one_one int))) _let_3)))))))) ) 15.91/16.02 ( (one_one int) ) 15.91/16.02 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.02 ) 15.91/16.02 (instantiation (forall ((X_1 $$unsorted)) (or (not (= (zero_zero real) (hAPP real real sin X_1))) (= (one_one real) (hAPP real real (abs_abs real) (hAPP real real cos X_1)))) ) 15.91/16.02 ( (zero_zero real) ) 15.91/16.02 ( pi ) 15.91/16.02 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.02 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.02 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.91/16.02 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.91/16.02 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.91/16.02 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.91/16.02 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.91/16.02 ( skv_5 ) 15.91/16.02 ) 15.91/16.02 (instantiation (forall ((A_1 $$unsorted) (X_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) X_1))) (= (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP real nat natceiling X_1)) A_1) (hAPP real nat natceiling (hAPP real real (hAPP real (fun real real) (plus_plus real) X_1) (hAPP nat real (real_1 nat) A_1))))) ) 15.91/16.02 ( (one_one nat), (one_one real) ) 15.91/16.02 ) 15.91/16.02 (instantiation (forall ((A_2 $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat nat))) (let ((_let_2 (fun real real))) (let ((_let_3 (fun nat _let_0))) (let ((_let_4 (fun nat real))) (let ((_let_5 (fun _let_0 real))) (let ((_let_6 (fun nat _let_2))) (let ((_let_7 (fun (filter nat) bool))) (let ((_let_8 (fun real _let_7))) (let ((_let_9 (tendsto nat real))) (let ((_let_10 (hAPP _let_4 _let_4 (hAPP _let_6 (fun _let_4 _let_4) (combs nat real real) (hAPP _let_4 _let_6 (hAPP (fun real _let_2) (fun _let_4 _let_6) (combb real _let_2 nat) (times_times real)) (hAPP real _let_4 (power_power real) (hAPP int real (number_number_of real) min_1)))) A_2))) (or (not (hBOOL (hAPP (filter nat) bool (hAPP real _let_7 (hAPP _let_4 _let_8 _let_9 A_2) (zero_zero real)) sequentially))) (not (forall ((N_2 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) (hAPP nat real A_2 N_2))) )) (not (forall ((N_2 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP nat real A_2 (hAPP nat nat suc N_2))) (hAPP nat real A_2 N_2))) )) (hBOOL (hAPP (filter nat) bool (hAPP real _let_7 (hAPP _let_4 _let_8 _let_9 (hAPP _let_3 _let_4 (hAPP _let_5 (fun _let_3 _let_4) (combb _let_0 real nat) (hAPP _let_4 _let_5 (big_co1399186613setsum nat real) _let_10)) (hAPP _let_1 _let_3 (hAPP _let_3 (fun _let_1 _let_3) (combb nat _let_0 nat) (hAPP nat _let_3 (ord_atLeastLessThan nat) (zero_zero nat))) (hAPP nat _let_1 (times_times nat) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) (hAPP _let_4 real (suminf real) _let_10)) sequentially)))))))))))))) ) 15.91/16.02 ( (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))) ) 15.91/16.02 ) 15.91/16.02 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (hAPP real _let_0 _let_1 (zero_zero real)))) (or (not (hBOOL (hAPP real bool _let_2 X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hBOOL (hAPP real bool _let_2 (hAPP real real sin X_1))))))) ) 15.91/16.02 ( (one_one real) ) 15.91/16.02 ( (zero_zero real) ) 15.91/16.02 ( pi ) 15.91/16.02 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.02 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.91/16.02 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.91/16.02 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.91/16.02 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.91/16.02 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.02 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 15.91/16.02 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.91/16.02 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.91/16.02 ) 15.91/16.02 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_0 (fun int rat))) (or (= (zero_zero int) (ti int N_1)) (= (hAPP int rat (hAPP int _let_0 fract (hAPP int int (hAPP int (fun int int) (plus_plus int) M) N_1)) N_1) (hAPP rat rat (hAPP rat (fun rat rat) (plus_plus rat) (hAPP int rat (hAPP int _let_0 fract M) N_1)) (one_one rat))))) ) 15.91/16.02 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 15.91/16.02 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 15.91/16.02 ) 15.91/16.02 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun nat real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) X_2))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_2) (one_one real)))) (hBOOL (hAPP _let_2 bool (monoseq real) (hAPP real _let_2 (power_power real) X_2))))))) ) 15.91/16.02 ( (zero_zero real) ) 15.91/16.02 ( pi ) 15.91/16.02 ( (hAPP int real (number_number_of real) min_1) ) 15.91/16.02 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.02 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.02 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.02 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.02 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.02 ( skv_3 ) 15.91/16.02 ( skv_5 ) 15.91/16.02 ( skv_7 ) 15.91/16.02 ( skv_12 ) 15.91/16.02 ) 15.91/16.02 (instantiation (forall ((Ma $$unsorted) (N $$unsorted)) (let ((_let_0 (zero_zero nat))) (= (= _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) Ma) N)) (and (= _let_0 Ma) (= _let_0 N)))) ) 15.91/16.02 ( (one_one nat), (one_one nat) ) 15.91/16.02 ) 15.91/16.02 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_129634 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (plus_plus X_a))) (or (not (ring_char_0 X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) BOUND_VARIABLE_129634) (ring_1_Ints X_a)))) (not (= (zero_zero X_a) (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (one_one X_a)) BOUND_VARIABLE_129634)) BOUND_VARIABLE_129634))))))) ) 15.91/16.02 ( nat, (one_one nat) ) 15.91/16.02 ( int, (one_one int) ) 15.91/16.02 ) 15.91/16.02 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_129668 $$unsorted) (BOUND_VARIABLE_129669 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (minus_minus X_a))) (or (not (ab_group_add X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_129669) BOUND_VARIABLE_129668) (hAPP X_a X_a (uminus_uminus X_a) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_129668) BOUND_VARIABLE_129669)))))) ) 15.91/16.02 ( int, (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.02 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.91/16.02 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 15.91/16.02 ( real, (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))), (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))) ) 15.91/16.02 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 15.91/16.02 ( code_code_numeral, (one_one code_code_numeral), (zero_zero code_code_numeral) ) 15.91/16.02 ) 15.91/16.02 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_129691 $$unsorted) (BOUND_VARIABLE_129692 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)))) (or (not (ordere453448008miring X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_129692))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_129691))) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_129692) BOUND_VARIABLE_129691))))) ) 15.91/16.02 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.02 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.02 ( int, skv_13, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.02 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.02 ( real, pi, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 15.91/16.02 ( real, (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.02 ( real, (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.02 ( complex, ii, ii ) 15.91/16.02 ( complex, ii, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 15.91/16.02 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.02 ) 15.91/16.02 (instantiation (forall ((Z_1 $$unsorted) (N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP real nat natfloor Z_1)) (one_one nat))) N_1))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) Z_1) (hAPP nat real (real_1 nat) N_1)))) ) 15.91/16.02 ( pi, (zero_zero nat) ) 15.91/16.02 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero nat) ) 15.91/16.02 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero nat) ) 15.91/16.02 ) 15.91/16.02 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (inverse_divide X_a))) (or (not (division_ring X_a)) (= _let_0 (ti (fun X_a (fun X_a X_a)) _let_0)))) ) 15.91/16.02 ( bool ) 15.91/16.02 ( nat ) 15.91/16.02 ( int ) 15.91/16.02 ( (fun int bool) ) 15.91/16.02 ( (fun int (fun int bool)) ) 15.91/16.02 ( (fun int int) ) 15.91/16.02 ( (fun nat bool) ) 15.91/16.02 ( real ) 15.91/16.02 ( (fun real bool) ) 15.91/16.02 ( (fun real real) ) 15.91/16.02 ( rat ) 15.91/16.02 ( complex ) 15.91/16.02 ( (fun nat real) ) 15.91/16.02 ( (product_prod int int) ) 15.91/16.02 ( code_code_numeral ) 15.91/16.02 ( (fun int (fun int (fun int bool))) ) 15.91/16.02 ( (fun (product_prod int int) bool) ) 15.91/16.02 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 15.91/16.02 ( (fun (product_prod int int) int) ) 15.91/16.02 ( (fun int real) ) 15.91/16.02 ) 15.91/16.02 (instantiation (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (abs_abs int))) (let ((_let_2 (div_div int))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (dvd_dvd int) Y_1) X_1))) (= (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int _let_1 X_1)) (hAPP int int _let_1 Y_1)) (hAPP int int _let_1 (hAPP int int (hAPP int _let_0 _let_2 X_1) Y_1))))))) ) 15.91/16.02 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 15.91/16.02 ) 15.91/16.02 (instantiation (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)))) (or (not (hBOOL (hAPP int bool _let_0 X_1))) (not (hBOOL (hAPP int bool _let_0 Y_1))) (hBOOL (hAPP int bool _let_0 (hAPP int int (hAPP int (fun int int) (plus_plus int) X_1) Y_1))))) ) 15.91/16.02 ( (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.91/16.02 ( (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.02 ) 15.91/16.02 (instantiation (forall ((K $$unsorted) (L $$unsorted)) (= (= (ti int K) (ti int L)) (= (hAPP int int bit1 L) (hAPP int int bit1 K))) ) 15.91/16.02 ( pls, s ) 15.91/16.02 ( min_1, m ) 15.91/16.02 ( s, s ) 15.91/16.02 ( s, s1 ) 15.91/16.02 ( m, m ) 15.91/16.02 ( m, t ) 15.91/16.02 ( s1, pls ) 15.91/16.02 ( s1, s ) 15.91/16.02 ( t, min_1 ) 15.91/16.02 ( t, m ) 15.91/16.02 ) 15.91/16.02 (instantiation (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_0 (product_prod X_a X_b))) (let ((_let_1 (product_prod X_a X_c))) (= (hAPP _let_1 _let_0 (hAPP (fun X_c X_b) (fun _let_1 _let_0) (product_apsnd X_c X_b X_a) F) (hAPP X_c _let_1 (hAPP X_a (fun X_c _let_1) (product_Pair X_a X_c) X_2) Y_2)) (hAPP X_b _let_0 (hAPP X_a (fun X_b _let_0) (product_Pair X_a X_b) X_2) (hAPP X_c X_b F Y_2))))) ) 15.91/16.02 ( int, int, int, (fact_fact int), (one_one int), (one_one int) ) 15.91/16.02 ( int, int, int, (fact_fact int), (zero_zero int), (one_one int) ) 15.91/16.02 ( int, int, int, (fact_fact int), s, (one_one int) ) 15.91/16.02 ) 15.91/16.02 (instantiation (forall ((X_2 $$unsorted) (N $$unsorted)) (let ((_let_0 (even_odd_even int))) (= (and (hBOOL (hAPP int bool _let_0 X_2)) (not (= (zero_zero nat) N))) (hBOOL (hAPP int bool _let_0 (hAPP nat int (hAPP int (fun nat int) (power_power int) X_2) N))))) ) 15.91/16.02 ( s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.02 ( s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.02 ( skv_14, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.02 ) 15.91/16.02 (instantiation (forall ((J $$unsorted) (I $$unsorted) (P_1 $$unsorted) (P_4 $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less nat))) (or (not (forall ((I_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 I_2) P_4))) (not (hBOOL (hAPP nat bool P_1 I_2))) (hBOOL (hAPP nat bool P_1 (hAPP nat nat (hAPP nat (fun nat nat) (div_mod nat) (hAPP nat nat suc I_2)) P_4)))) )) (not (hBOOL (hAPP nat bool P_1 I))) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 I) P_4))) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 J) P_4))) (hBOOL (hAPP nat bool P_1 J))))) ) 15.91/16.02 ( (zero_zero nat), (zero_zero nat), (even_odd_even nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.02 ) 15.91/16.02 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) X_2) zEven))) (= (zero_zero int) (hAPP int int (hAPP int (fun int int) (div_mod int) X_2) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 15.91/16.02 ( (one_one int) ) 15.91/16.02 ) 15.91/16.02 (instantiation (forall ((X_1 $$unsorted)) (= (hAPP real real tan X_1) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP real real sin X_1)) (hAPP real real cos X_1))) ) 15.91/16.02 ( (zero_zero real) ) 15.91/16.02 ( pi ) 15.91/16.02 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.02 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.02 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.91/16.02 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.91/16.02 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.91/16.02 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.91/16.02 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.91/16.02 ( skv_5 ) 15.91/16.02 ) 15.91/16.02 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))))))) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) X_1))) (= (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP real real ln (hAPP real real (exp real) (one_one real)))) (hAPP real real ln _let_1))) (hAPP real real ln X_1)) (hAPP real real (hAPP real _let_0 log _let_1) X_1))))) ) 15.91/16.02 ( (one_one real) ) 15.91/16.02 ( pi ) 15.91/16.02 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.02 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.02 ( skv_2 ) 15.91/16.02 ( skv_8 ) 15.91/16.02 ( skv_9 ) 15.91/16.02 ) 15.91/16.02 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_129990 $$unsorted) (BOUND_VARIABLE_129991 $$unsorted)) (or (not (division_ring X_a)) (not (= (one_one X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_129990) BOUND_VARIABLE_129991))) (= (ti X_a BOUND_VARIABLE_129991) (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_129990))) ) 15.91/16.02 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 15.91/16.02 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.91/16.02 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13 ) 15.91/16.02 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.91/16.02 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.91/16.02 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.91/16.02 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 15.91/16.02 ( complex, ii, ii ) 15.91/16.02 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 15.91/16.02 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 15.91/16.02 ) 15.91/16.02 (instantiation (forall ((X_2 $$unsorted)) (= (not (forall ((Y $$unsorted)) (not (= X_2 (hAPP nat nat suc (hAPP nat nat (hAPP nat (fun nat nat) (times_times nat) (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat)))) Y)))) )) (not (hBOOL (hAPP nat bool (even_odd_even nat) X_2)))) ) 15.91/16.02 ( (zero_zero nat) ) 15.91/16.02 ( (one_one nat) ) 15.91/16.02 ) 15.91/16.02 (instantiation (forall ((P_1 $$unsorted) (Ma $$unsorted) (N $$unsorted)) (let ((_let_0 (ord_less nat))) (let ((_let_1 (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) P_1 N) Ma)))) (let ((_let_2 (not _let_1))) (or (and (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) _let_0 Ma) N)) _let_2) (and (= Ma N) _let_2) (and (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) _let_0 N) Ma)) _let_2) _let_1)))) ) 15.91/16.02 ( (ord_less nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 15.91/16.02 ) 15.91/16.02 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_130095 $$unsorted) (BOUND_VARIABLE_130096 $$unsorted)) (let ((_let_0 (semiring_1_of_nat X_a))) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP nat X_a _let_0 BOUND_VARIABLE_130095)) (hAPP nat X_a _let_0 BOUND_VARIABLE_130096)))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) BOUND_VARIABLE_130095) BOUND_VARIABLE_130096)))) ) 15.91/16.02 ( int, (zero_zero nat), (zero_zero nat) ) 15.91/16.02 ( int, (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 15.91/16.02 ) 15.91/16.02 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_130187 $$unsorted) (BOUND_VARIABLE_130188 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (inverse_inverse X_a))) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_130187) BOUND_VARIABLE_130188))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_130188) (zero_zero X_a)))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_130188)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_130187))))))) ) 15.91/16.02 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.02 ( int, (one_one int), t ) 15.91/16.02 ( int, pls, (one_one int) ) 15.91/16.02 ( int, pls, pls ) 15.91/16.02 ( int, pls, min_1 ) 15.91/16.02 ( int, pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.02 ( int, min_1, pls ) 15.91/16.02 ( int, min_1, min_1 ) 15.91/16.02 ( int, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.02 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.02 ( int, skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.02 ( int, skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.02 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.02 ( real, (zero_zero real), pi ) 15.91/16.02 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.02 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.02 ( real, (zero_zero real), skv_2 ) 15.91/16.02 ( real, (zero_zero real), skv_8 ) 15.91/16.02 ( real, (zero_zero real), skv_9 ) 15.91/16.02 ( real, pi, (zero_zero real) ) 15.91/16.02 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.02 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.02 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 15.91/16.02 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.91/16.02 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 15.91/16.02 ) 15.91/16.02 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_130247 $$unsorted)) (or (not (group_add X_a)) (= (zero_zero X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) BOUND_VARIABLE_130247) BOUND_VARIABLE_130247))) ) 15.91/16.02 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.02 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))) ) 15.91/16.02 ( code_code_numeral, (zero_zero code_code_numeral) ) 15.91/16.02 ) 15.91/16.02 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_130257 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (one_one int)) (hAPP X_a int (archim2085082626_floor X_a) BOUND_VARIABLE_130257))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (one_one X_a)) BOUND_VARIABLE_130257)))) ) 15.91/16.02 ( int, t ) 15.91/16.02 ) 15.91/16.02 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_130275 $$unsorted) (BOUND_VARIABLE_130276 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (uminus_uminus X_a))) (or (not (boolean_algebra X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_130275) BOUND_VARIABLE_130276))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_130276)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_130275))))))) ) 15.91/16.02 ( int, (one_one int), (one_one int) ) 15.91/16.02 ( int, (one_one int), pls ) 15.91/16.02 ( int, (one_one int), t ) 15.91/16.02 ( int, (zero_zero int), (one_one int) ) 15.91/16.02 ( int, (zero_zero int), min_1 ) 15.91/16.02 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.02 ( int, (zero_zero int), s ) 15.91/16.02 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.91/16.02 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.91/16.02 ( int, (zero_zero int), skv_4 ) 15.91/16.02 ( int, (zero_zero int), skv_10 ) 15.91/16.02 ( int, pls, (one_one int) ) 15.91/16.02 ( int, pls, pls ) 15.91/16.02 ( int, min_1, pls ) 15.91/16.02 ( int, min_1, min_1 ) 15.91/16.02 ( real, (zero_zero real), pi ) 15.91/16.02 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.02 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.02 ( real, (zero_zero real), skv_3 ) 15.91/16.02 ( real, (zero_zero real), skv_5 ) 15.91/16.02 ( real, (zero_zero real), skv_7 ) 15.91/16.02 ( real, (zero_zero real), skv_12 ) 15.91/16.02 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.91/16.02 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.02 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.91/16.02 ( real, skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.02 ) 15.91/16.02 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_130353 $$unsorted)) (or (not (comm_semiring_1 X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_130353) (zero_zero X_a)))) ) 15.91/16.02 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.02 ) 15.91/16.02 (instantiation (forall ((P_5 $$unsorted)) (or (not (hBOOL (hAPP nat bool prime P_5))) (= (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) P_5) (not (hBOOL (hAPP nat bool (even_odd_even nat) P_5)))) ) 15.91/16.02 ( (zero_zero nat) ) 15.91/16.02 ( (hAPP nat nat suc (zero_zero nat)) ) 15.91/16.02 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.02 ( (one_one nat) ) 15.91/16.02 ) 15.91/16.02 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (BOUND_VARIABLE_130464 $$unsorted) (BOUND_VARIABLE_130465 $$unsorted) (BOUND_VARIABLE_130466 $$unsorted) (BOUND_VARIABLE_130467 $$unsorted)) (let ((_let_0 (fun (filter X_a) bool))) (let ((_let_1 (hAPP (fun X_a X_b) (fun X_b _let_0) (tendsto X_a X_b) BOUND_VARIABLE_130465))) (or (not (t2_space X_b)) (hBOOL (hAPP (filter X_a) bool (trivial_limit X_a) BOUND_VARIABLE_130467)) (not (hBOOL (hAPP (filter X_a) bool (hAPP X_b _let_0 _let_1 BOUND_VARIABLE_130466) BOUND_VARIABLE_130467))) (not (hBOOL (hAPP (filter X_a) bool (hAPP X_b _let_0 _let_1 BOUND_VARIABLE_130464) BOUND_VARIABLE_130467))) (= (ti X_b BOUND_VARIABLE_130466) (ti X_b BOUND_VARIABLE_130464))))) ) 15.91/16.02 ( nat, real, (zero_zero real), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real), sequentially ) 15.91/16.02 ) 15.91/16.02 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_130494 $$unsorted) (BOUND_VARIABLE_130495 $$unsorted)) (let ((_let_0 (filter X_a))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun X_a real))) (let ((_let_3 (fun X_a X_b))) (let ((_let_4 (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_130495))) (or (not (topological_space X_a)) (not (real_normed_vector X_b)) (= (hBOOL (hAPP _let_0 bool (hAPP real _let_1 (hAPP _let_2 (fun real _let_1) (tendsto X_a real) (hAPP _let_3 _let_2 (hAPP (fun X_b real) (fun _let_3 _let_2) (combb X_b real X_a) (norm_norm X_b)) BOUND_VARIABLE_130494)) (zero_zero real)) _let_4)) (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (hAPP _let_3 (fun X_b _let_1) (tendsto X_a X_b) BOUND_VARIABLE_130494) (zero_zero X_b)) _let_4))))))))) ) 15.91/16.02 ( real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.02 ) 15.91/16.02 (instantiation (forall ((X_1 $$unsorted)) (= (hAPP real real cos X_1) (hAPP real real cos (hAPP real real (uminus_uminus real) X_1))) ) 15.91/16.02 ( (one_one real) ) 15.91/16.02 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.02 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.91/16.02 ) 15.91/16.02 (instantiation (forall ((Ta $$unsorted) (A_3 $$unsorted) (D_2 $$unsorted) (BOUND_VARIABLE_130580 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ti int Ta))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (zero_zero int)) D_2))) (not (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) Ta) A_3))) (not (forall ((Xa $$unsorted) (BOUND_VARIABLE_130548 $$unsorted)) (let ((_let_1 (member int))) (let ((_let_2 (fun _let_0 bool))) (or (not (hBOOL (hAPP _let_0 bool (hAPP int _let_2 _let_1 Xa) (hAPP int _let_0 (hAPP int (fun int _let_0) (ord_atLeastAtMost int) (one_one int)) D_2)))) (not (hBOOL (hAPP _let_0 bool (hAPP int _let_2 _let_1 BOUND_VARIABLE_130548) A_3))) (not (= (hAPP int int (hAPP int (fun int int) (minus_minus int) BOUND_VARIABLE_130548) Xa) (ti int BOUND_VARIABLE_130580)))))) )) (= _let_1 (ti int BOUND_VARIABLE_130580)) (not (= _let_1 (hAPP int int (hAPP int (fun int int) (plus_plus int) BOUND_VARIABLE_130580) D_2)))))) ) 15.91/16.02 ( (one_one int), zEven, pls, s ) 15.91/16.02 ) 15.91/16.02 (instantiation (forall ((Y_1 $$unsorted)) (= Y_1 (hAPP real real tan (hAPP real real arctan Y_1))) ) 15.91/16.02 ( (one_one real) ) 15.91/16.02 ( (zero_zero real) ) 15.91/16.02 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.91/16.02 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))))) ) 15.91/16.02 ) 15.91/16.02 (instantiation (forall ((X_a $$unsorted) (P_1 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (collect X_a))) (= (hAPP _let_0 _let_0 _let_1 (hAPP _let_0 _let_0 (hAPP (fun bool bool) (fun _let_0 _let_0) (combb bool bool X_a) fNot) P_1)) (hAPP _let_0 _let_0 (uminus_uminus _let_0) (hAPP _let_0 _let_0 _let_1 P_1))))) ) 15.91/16.02 ( nat, (let ((_let_0 (fun nat (fun nat bool)))) (hAPP nat (fun nat bool) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat)) (zero_zero nat))) ) 15.91/16.02 ( int, (let ((_let_0 (fun int (fun int bool)))) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (fequal int)) (zero_zero int))) ) 15.91/16.02 ( (product_prod int int), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun _let_1 _let_0))) (let ((_let_4 (fun _let_1 int))) (hAPP int _let_2 (hAPP _let_3 (fun int _let_2) (combc _let_1 int bool) (hAPP _let_4 _let_3 (hAPP (fun int _let_0) (fun _let_4 _let_3) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))) ) 15.91/16.02 ) 15.91/16.02 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_130705 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (division_ring X_a)) (not (= _let_0 (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_130705))) (= _let_0 (ti X_a BOUND_VARIABLE_130705)))) ) 15.91/16.02 ( bool, fFalse ) 15.91/16.02 ( bool, fTrue ) 15.91/16.02 ( int, pls ) 15.91/16.02 ( int, min_1 ) 15.91/16.02 ( int, s ) 15.91/16.02 ( int, m ) 15.91/16.02 ( int, s1 ) 15.91/16.02 ( int, t ) 15.91/16.02 ( (fun int bool), nat_neg ) 15.91/16.02 ( (fun int bool), zprime ) 15.91/16.02 ( (fun int bool), zEven ) 15.91/16.02 ( (fun int bool), zOdd ) 15.91/16.02 ( (fun int bool), (even_odd_even int) ) 15.91/16.02 ( (fun int bool), twoSqu1091635170sum2sq ) 15.91/16.02 ( (fun int bool), nat_is_nat ) 15.91/16.02 ( (fun int (fun int bool)), norRRset ) 15.91/16.02 ( (fun int (fun int bool)), quadRes ) 15.91/16.02 ( (fun int (fun int bool)), sRStar ) 15.91/16.02 ( (fun int (fun int bool)), d22set ) 15.91/16.02 ( (fun int (fun int bool)), sr ) 15.91/16.02 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 15.91/16.02 ( (fun int int), zfact ) 15.91/16.02 ( (fun int int), bit0 ) 15.91/16.02 ( (fun int int), bit1 ) 15.91/16.02 ( (fun int int), (fact_fact int) ) 15.91/16.02 ( (fun int int), pred ) 15.91/16.02 ( (fun int int), succ ) 15.91/16.02 ( (fun nat bool), (even_odd_even nat) ) 15.91/16.02 ( (fun nat bool), prime ) 15.91/16.02 ( (fun nat nat), suc ) 15.91/16.02 ( (fun nat nat), (fact_fact nat) ) 15.91/16.02 ( (fun nat nat), fact ) 15.91/16.02 ( (fun nat nat), nat_size ) 15.91/16.02 ( (fun nat nat), (size_size nat) ) 15.91/16.02 ( (fun (product_prod nat nat) bool), pred_nat ) 15.91/16.02 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 15.91/16.02 ( real, (zero_zero real) ) 15.91/16.02 ( real, pi ) 15.91/16.02 ( (fun real real), ln ) 15.91/16.02 ( (fun real real), cos ) 15.91/16.02 ( (fun real real), sqrt ) 15.91/16.02 ( (fun real real), sin ) 15.91/16.02 ( (fun real real), arccos ) 15.91/16.02 ( (fun real real), arcsin ) 15.91/16.02 ( (fun real real), tan ) 15.91/16.02 ( (fun real real), arctan ) 15.91/16.02 ( (fun nat (fun nat bool)), coprime ) 15.91/16.02 ( complex, ii ) 15.91/16.02 ( (fun nat real), (real_1 nat) ) 15.91/16.02 ( (fun nat real), sin_coeff ) 15.91/16.02 ( (fun nat real), cos_coeff ) 15.91/16.02 ( (filter nat), sequentially ) 15.91/16.02 ( (fun int (fun int int)), (gcd_gcd int) ) 15.91/16.02 ( (fun int (fun int int)), legendre ) 15.91/16.02 ( (fun int (fun int int)), legacy_zgcd ) 15.91/16.02 ( (fun int (fun int int)), standardRes ) 15.91/16.02 ( (fun int (fun int int)), nat_tsub ) 15.91/16.02 ( (fun int (fun int int)), multInv ) 15.91/16.02 ( (fun int (fun int int)), z3mod ) 15.91/16.02 ( (fun int (fun int int)), z3div ) 15.91/16.02 ( (fun int (fun int int)), int_gcd ) 15.91/16.02 ( (fun int (fun int int)), int_lcm ) 15.91/16.02 ( (fun int (fun int int)), inv ) 15.91/16.02 ( (fun complex complex), expi ) 15.91/16.02 ( (fun complex complex), cnj ) 15.91/16.02 ( (fun real complex), cis ) 15.91/16.02 ( (fun int nat), nat_1 ) 15.91/16.02 ( (fun int nat), phi ) 15.91/16.02 ( (fun (fun int bool) bool), nat_nat_set ) 15.91/16.02 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 15.91/16.02 ( (fun nat (fun nat nat)), nat_gcd ) 15.91/16.02 ( (fun nat (fun nat nat)), nat_lcm ) 15.91/16.02 ( (fun (fun int bool) int), (the int) ) 15.91/16.02 ( (fun complex real), re ) 15.91/16.02 ( (fun complex real), im ) 15.91/16.02 ( (fun complex real), arg ) 15.91/16.02 ( (fun bool bool), fNot ) 15.91/16.02 ( (fun nat (fun real real)), root ) 15.91/16.02 ( (fun real (fun real real)), log ) 15.91/16.02 ( (fun real (fun real real)), powr ) 15.91/16.02 ( (fun bool (fun bool bool)), fimplies ) 15.91/16.02 ( (fun bool (fun bool bool)), fconj ) 15.91/16.02 ( (fun bool (fun bool bool)), fdisj ) 15.91/16.02 ( (fun int (fun int (product_prod int int))), negDivAlg ) 15.91/16.02 ( (fun int (fun int (product_prod int int))), posDivAlg ) 15.91/16.02 ( (fun int (fun int (product_prod int int))), divmod_int ) 15.91/16.02 ( (fun int (fun int (product_prod int int))), pdivmod ) 15.91/16.02 ( (fun int (fun int (product_prod int int))), norm_frac ) 15.91/16.02 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 15.91/16.02 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 15.91/16.02 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 15.91/16.02 ( (fun int (fun int (fun int bool))), zcong ) 15.91/16.02 ( (fun int (fun int (fun int bool))), zcongm ) 15.91/16.02 ( (fun int (fun int (fun int bool))), noXRRset ) 15.91/16.02 ( (fun int (fun int (fun int bool))), bnorRset ) 15.91/16.02 ( (fun int (fun int (fun int bool))), wset ) 15.91/16.02 ( (fun (product_prod int int) bool), frac_1 ) 15.91/16.02 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 15.91/16.02 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 15.91/16.02 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 15.91/16.02 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 15.91/16.02 ( (fun (fun nat rat) bool), vanishes ) 15.91/16.02 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 15.91/16.02 ( (fun code_code_numeral nat), code_c271388182l_size ) 15.91/16.02 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 15.91/16.02 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 15.91/16.02 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 15.91/16.02 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 15.91/16.02 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 15.91/16.02 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 15.91/16.02 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 15.91/16.02 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 15.91/16.02 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 15.91/16.02 ( (fun complex nat), complex_size ) 15.91/16.02 ( (fun complex nat), (size_size complex) ) 15.91/16.02 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 15.91/16.02 ( (fun nat (fun nat (product_prod int int))), bezw ) 15.91/16.02 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 15.91/16.02 ( (fun int (fun nat nat)), nat_aux ) 15.91/16.02 ( (fun int (fun (fun int bool) bool)), rsetR ) 15.91/16.02 ( (fun int (fun (fun int bool) bool)), resSet ) 15.91/16.02 ( (fun int (list int)), quickc666637781d_zero ) 15.91/16.02 ( (fun (product_prod int int) rat), frct ) 15.91/16.02 ( (fun int (fun int rat)), fract ) 15.91/16.02 ( (fun real (fun real complex)), complex_1 ) 15.91/16.02 ( (fun real (fun real complex)), rcis ) 15.91/16.02 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 15.91/16.02 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 15.91/16.02 ( (fun int real), (real_1 int) ) 15.91/16.02 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 15.91/16.02 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 15.91/16.02 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 15.91/16.02 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 15.91/16.02 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 15.91/16.02 ( (fun real nat), natfloor ) 15.91/16.02 ( (fun real nat), natceiling ) 15.91/16.02 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 15.91/16.02 ( (fun quickcheck_code_int int), quickcheck_int_of ) 15.91/16.02 ( (fun rat (product_prod int int)), quotient_of ) 15.91/16.02 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 15.91/16.02 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 15.91/16.02 ( (fun rat real), ratreal ) 15.91/16.02 ( (fun code_code_numeral int), code_int_of ) 15.91/16.02 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 15.91/16.02 ( (fun int quickcheck_code_int), quickcheck_of_int ) 15.91/16.02 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 15.91/16.02 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 15.91/16.02 ) 15.91/16.02 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_130738 $$unsorted) (BOUND_VARIABLE_130739 $$unsorted) (BOUND_VARIABLE_130740 $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat _let_0))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (dvd_dvd nat))) (let ((_let_4 (fun _let_0 _let_0))) (let ((_let_5 (fun nat _let_4))) (let ((_let_6 (fun _let_1 _let_1))) (let ((_let_7 (fun nat _let_2))) (let ((_let_8 (fun nat _let_7))) (let ((_let_9 (fun _let_0 _let_7))) (let ((_let_10 (fun nat X_a))) (or (not (order X_a)) (not (hBOOL (hAPP _let_10 bool (hAPP _let_1 (fun _let_10 bool) (strict_mono nat X_a) (hAPP _let_1 _let_1 (hAPP _let_5 _let_6 (combs nat _let_0 _let_0) (hAPP _let_8 _let_5 (hAPP (fun _let_7 _let_4) (fun _let_8 _let_5) (combb _let_7 _let_4 nat) (combs nat bool bool)) (hAPP _let_1 _let_8 (hAPP _let_9 (fun _let_1 _let_8) (combb _let_0 _let_7 nat) (hAPP (fun bool _let_2) _let_9 (combb bool _let_2 nat) fconj)) _let_3))) (hAPP _let_1 _let_1 (hAPP _let_4 _let_6 (combb _let_0 _let_0 nat) (hAPP _let_2 _let_4 (combb bool bool nat) fNot)) (hAPP _let_1 _let_1 (combc nat nat bool) _let_3)))) BOUND_VARIABLE_130740))) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_3 BOUND_VARIABLE_130739) BOUND_VARIABLE_130738)) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_3 BOUND_VARIABLE_130738) BOUND_VARIABLE_130739))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP nat X_a BOUND_VARIABLE_130740 BOUND_VARIABLE_130738)) (hAPP nat X_a BOUND_VARIABLE_130740 BOUND_VARIABLE_130739))))))))))))))) ) 15.91/16.02 ( int, (zero_zero nat), (zero_zero nat), (semiring_1_of_nat int) ) 15.91/16.02 ( int, (zero_zero nat), (hAPP nat nat suc (zero_zero nat)), (semiring_1_of_nat int) ) 15.91/16.02 ) 15.91/16.02 (instantiation (forall ((N_1 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) _let_1) N_1))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) _let_1) (hAPP int int (fact_fact int) N_1)))))) ) 15.91/16.02 ( (one_one int) ) 15.91/16.02 ( (zero_zero int) ) 15.91/16.02 ( min_1 ) 15.91/16.02 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.02 ( s ) 15.91/16.02 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.91/16.02 ( (hAPP int int (number_number_of int) pls) ) 15.91/16.02 ( skv_4 ) 15.91/16.02 ( skv_10 ) 15.91/16.02 ) 15.91/16.02 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_130819 $$unsorted) (BOUND_VARIABLE_130820 $$unsorted) (BOUND_VARIABLE_130821 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (plus_plus X_a))) (or (not (cancel_semigroup_add X_a)) (= (= (ti X_a BOUND_VARIABLE_130819) (ti X_a BOUND_VARIABLE_130821)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_130821) BOUND_VARIABLE_130820) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_130819) BOUND_VARIABLE_130820)))))) ) 15.91/16.02 ( int, s, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.91/16.02 ( int, s1, (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.02 ) 15.91/16.02 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_130837 $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (ring_1 X_a)) (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) (hAPP nat X_a (semiring_1_of_nat X_a) BOUND_VARIABLE_130837)) (ring_1_Ints X_a))))) ) 15.91/16.02 ( int, (zero_zero nat) ) 15.91/16.02 ( int, (hAPP nat nat suc (zero_zero nat)) ) 15.91/16.02 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.91/16.02 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.02 ( real, (zero_zero nat) ) 15.91/16.02 ( real, (hAPP nat nat suc (zero_zero nat)) ) 15.91/16.02 ) 15.91/16.02 (instantiation (forall ((A_2 $$unsorted) (Ma $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) A_2) Ma))) (= (one_one int) (hAPP int int (hAPP int _let_1 legacy_zgcd (hAPP _let_0 int (hAPP _let_1 (fun _let_0 int) (big_co302546470etprod int int) (combi int)) (hAPP int _let_0 (hAPP int (fun int _let_0) bnorRset A_2) Ma))) Ma))))) ) 15.91/16.02 ( (one_one int), t ) 15.91/16.02 ( pls, (one_one int) ) 15.91/16.02 ( pls, pls ) 15.91/16.02 ( pls, min_1 ) 15.91/16.02 ( pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.02 ( min_1, pls ) 15.91/16.02 ( min_1, min_1 ) 15.91/16.02 ( s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.02 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.02 ( skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.02 ( skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.02 ) 15.91/16.02 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_130937 $$unsorted) (BOUND_VARIABLE_130938 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP X_a int (archim2085082626_floor X_a) BOUND_VARIABLE_130937)) (hAPP int int (number_number_of int) BOUND_VARIABLE_130938))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_130937) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_130938)) (one_one X_a)))))) ) 15.91/16.02 ( nat, (zero_zero nat), (hAPP int int bit1 pls) ) 15.91/16.02 ) 15.91/16.03 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (F1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (product_prod X_a X_b))) (or (not (hBOOL (hAPP X_b bool (hAPP X_a _let_0 F1 A_2) B_1))) (hBOOL (hAPP _let_1 bool (hAPP (fun X_a _let_0) (fun _let_1 bool) (product_prod_case X_a X_b bool) F1) (hAPP X_b _let_1 (hAPP X_a (fun X_b _let_1) (product_Pair X_a X_b) A_2) B_1)))))) ) 15.91/16.03 ( nat, nat, (ord_less nat), (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.03 ( int, int, (ord_less_eq int), (one_one int), t ) 15.91/16.03 ( int, int, (ord_less_eq int), (zero_zero int), (one_one int) ) 15.91/16.03 ( int, int, (ord_less_eq int), (zero_zero int), min_1 ) 15.91/16.03 ( int, int, (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.03 ( int, int, (ord_less_eq int), (zero_zero int), s ) 15.91/16.03 ( int, int, (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.91/16.03 ( int, int, (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.91/16.03 ( int, int, (ord_less_eq int), (zero_zero int), skv_4 ) 15.91/16.03 ( int, int, (ord_less_eq int), (zero_zero int), skv_10 ) 15.91/16.03 ( int, int, (ord_less_eq int), min_1, pls ) 15.91/16.03 ( int, int, (ord_less_eq int), min_1, min_1 ) 15.91/16.03 ( int, int, (ord_less int), (one_one int), t ) 15.91/16.03 ( int, int, (ord_less int), pls, (one_one int) ) 15.91/16.03 ( int, int, (ord_less int), pls, pls ) 15.91/16.03 ( int, int, (ord_less int), pls, min_1 ) 15.91/16.03 ( int, int, (ord_less int), pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.03 ( int, int, (ord_less int), min_1, pls ) 15.91/16.03 ( int, int, (ord_less int), min_1, min_1 ) 15.91/16.03 ( int, int, (ord_less int), s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.03 ( int, int, (ord_less int), t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.03 ( int, int, (ord_less int), skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.03 ( int, int, (ord_less int), skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.03 ( int, int, (dvd_dvd int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 15.91/16.03 ( int, int, quadRes, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (number_number_of int) min_1) ) 15.91/16.03 ( int, int, (hAPP int (fun int (fun int bool)) zcong s1), s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.03 ( int, int, (hAPP int (fun int (fun int bool)) zcong s1), skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.03 ( int, int, (hAPP int (fun int (fun int bool)) zcong s1), skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.03 ( int, int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.03 ( int, int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.03 ( int, int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.03 ( int, int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.03 ( (fun int bool), int, (member int), (one_one int), zEven ) 15.91/16.03 ( (fun int bool), (fun int nat), (nat_tr1645093318rphism int nat), nat_1, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 15.91/16.03 ( (fun nat bool), (fun nat int), (nat_tr1645093318rphism nat int), (semiring_1_of_nat int), (hAPP bool (fun nat bool) (combk bool nat) fTrue) ) 15.91/16.03 ( real, real, (ord_less real), (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.03 ( real, real, (ord_less real), (zero_zero real), pi ) 15.91/16.03 ( real, real, (ord_less real), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.03 ( real, real, (ord_less real), (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.03 ( real, real, (ord_less real), (zero_zero real), skv_2 ) 15.91/16.03 ( real, real, (ord_less real), (zero_zero real), skv_8 ) 15.91/16.03 ( real, real, (ord_less real), (zero_zero real), skv_9 ) 15.91/16.03 ( real, real, (ord_less real), pi, (zero_zero real) ) 15.91/16.03 ( real, real, (ord_less real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.03 ( real, real, (ord_less real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.03 ( real, real, (ord_less real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 15.91/16.03 ( real, real, (ord_less real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.91/16.03 ( real, real, (ord_less real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 15.91/16.03 ( real, real, (ord_less_eq real), (zero_zero real), pi ) 15.91/16.03 ( real, real, (ord_less_eq real), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.03 ( real, real, (ord_less_eq real), (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.03 ( real, real, (ord_less_eq real), (zero_zero real), skv_3 ) 15.91/16.03 ( real, real, (ord_less_eq real), (zero_zero real), skv_5 ) 15.91/16.03 ( real, real, (ord_less_eq real), (zero_zero real), skv_7 ) 15.91/16.03 ( real, real, (ord_less_eq real), (zero_zero real), skv_12 ) 15.91/16.03 ( real, real, (ord_less_eq real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.91/16.03 ( real, real, (ord_less_eq real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.03 ( real, real, (ord_less_eq real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.91/16.03 ( real, real, (ord_less_eq real), skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.03 ( real, (fun nat real), (sums real), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (hAPP real _let_1 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc))), (one_one real) ) 15.91/16.03 ( (filter nat), real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 (fun real (fun (filter nat) bool)) (tendsto nat real) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))))), (zero_zero real), sequentially ) 15.91/16.03 ( (filter real), real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 (fun real (fun (filter real) bool)) (tendsto real real) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin)))), (zero_zero real), (hAPP real (filter real) (at real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.91/16.03 ) 15.91/16.03 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_130964 $$unsorted)) (or (not (linorder X_a)) (= (ti X_a BOUND_VARIABLE_130964) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (ord_min X_a) BOUND_VARIABLE_130964) BOUND_VARIABLE_130964))) ) 15.91/16.03 ( bool, fFalse ) 15.91/16.03 ( bool, fTrue ) 15.91/16.03 ( int, pls ) 15.91/16.03 ( int, min_1 ) 15.91/16.03 ( int, s ) 15.91/16.03 ( int, m ) 15.91/16.03 ( int, s1 ) 15.91/16.03 ( int, t ) 15.91/16.03 ( (fun int bool), nat_neg ) 15.91/16.03 ( (fun int bool), zprime ) 15.91/16.03 ( (fun int bool), zEven ) 15.91/16.03 ( (fun int bool), zOdd ) 15.91/16.03 ( (fun int bool), (even_odd_even int) ) 15.91/16.03 ( (fun int bool), twoSqu1091635170sum2sq ) 15.91/16.03 ( (fun int bool), nat_is_nat ) 15.91/16.03 ( (fun int (fun int bool)), norRRset ) 15.91/16.03 ( (fun int (fun int bool)), quadRes ) 15.91/16.03 ( (fun int (fun int bool)), sRStar ) 15.91/16.03 ( (fun int (fun int bool)), d22set ) 15.91/16.03 ( (fun int (fun int bool)), sr ) 15.91/16.03 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 15.91/16.03 ( (fun int int), zfact ) 15.91/16.03 ( (fun int int), bit0 ) 15.91/16.03 ( (fun int int), bit1 ) 15.91/16.03 ( (fun int int), (fact_fact int) ) 15.91/16.03 ( (fun int int), pred ) 15.91/16.03 ( (fun int int), succ ) 15.91/16.03 ( (fun nat bool), (even_odd_even nat) ) 15.91/16.03 ( (fun nat bool), prime ) 15.91/16.03 ( (fun nat nat), suc ) 15.91/16.03 ( (fun nat nat), (fact_fact nat) ) 15.91/16.03 ( (fun nat nat), fact ) 15.91/16.03 ( (fun nat nat), nat_size ) 15.91/16.03 ( (fun nat nat), (size_size nat) ) 15.91/16.03 ( (fun (product_prod nat nat) bool), pred_nat ) 15.91/16.03 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 15.91/16.03 ( real, pi ) 15.91/16.03 ( (fun real real), ln ) 15.91/16.03 ( (fun real real), cos ) 15.91/16.03 ( (fun real real), sqrt ) 15.91/16.03 ( (fun real real), sin ) 15.91/16.03 ( (fun real real), arccos ) 15.91/16.03 ( (fun real real), arcsin ) 15.91/16.03 ( (fun real real), tan ) 15.91/16.03 ( (fun real real), arctan ) 15.91/16.03 ( (fun nat (fun nat bool)), coprime ) 15.91/16.03 ( complex, ii ) 15.91/16.03 ( (fun nat real), (real_1 nat) ) 15.91/16.03 ( (fun nat real), sin_coeff ) 15.91/16.03 ( (fun nat real), cos_coeff ) 15.91/16.03 ( (filter nat), sequentially ) 15.91/16.03 ( (fun int (fun int int)), (gcd_gcd int) ) 15.91/16.03 ( (fun int (fun int int)), legendre ) 15.91/16.03 ( (fun int (fun int int)), legacy_zgcd ) 15.91/16.03 ( (fun int (fun int int)), standardRes ) 15.91/16.03 ( (fun int (fun int int)), nat_tsub ) 15.91/16.03 ( (fun int (fun int int)), multInv ) 15.91/16.03 ( (fun int (fun int int)), z3mod ) 15.91/16.03 ( (fun int (fun int int)), z3div ) 15.91/16.03 ( (fun int (fun int int)), int_gcd ) 15.91/16.03 ( (fun int (fun int int)), int_lcm ) 15.91/16.03 ( (fun int (fun int int)), inv ) 15.91/16.03 ( (fun complex complex), expi ) 15.91/16.03 ( (fun complex complex), cnj ) 15.91/16.03 ( (fun real complex), cis ) 15.91/16.03 ( (fun int nat), nat_1 ) 15.91/16.03 ( (fun int nat), phi ) 15.91/16.03 ( (fun (fun int bool) bool), nat_nat_set ) 15.91/16.03 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 15.91/16.03 ( (fun nat (fun nat nat)), nat_gcd ) 15.91/16.03 ( (fun nat (fun nat nat)), nat_lcm ) 15.91/16.03 ( (fun (fun int bool) int), (the int) ) 15.91/16.03 ( (fun complex real), re ) 15.91/16.03 ( (fun complex real), im ) 15.91/16.03 ( (fun complex real), arg ) 15.91/16.03 ( (fun bool bool), fNot ) 15.91/16.03 ( (fun nat (fun real real)), root ) 15.91/16.03 ( (fun real (fun real real)), log ) 15.91/16.03 ( (fun real (fun real real)), powr ) 15.91/16.03 ( (fun bool (fun bool bool)), fimplies ) 15.91/16.03 ( (fun bool (fun bool bool)), fconj ) 15.91/16.03 ( (fun bool (fun bool bool)), fdisj ) 15.91/16.03 ( (fun int (fun int (product_prod int int))), negDivAlg ) 15.91/16.03 ( (fun int (fun int (product_prod int int))), posDivAlg ) 15.91/16.03 ( (fun int (fun int (product_prod int int))), divmod_int ) 15.91/16.03 ( (fun int (fun int (product_prod int int))), pdivmod ) 15.91/16.03 ( (fun int (fun int (product_prod int int))), norm_frac ) 15.91/16.03 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 15.91/16.03 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 15.91/16.03 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 15.91/16.03 ( (fun int (fun int (fun int bool))), zcong ) 15.91/16.03 ( (fun int (fun int (fun int bool))), zcongm ) 15.91/16.03 ( (fun int (fun int (fun int bool))), noXRRset ) 15.91/16.03 ( (fun int (fun int (fun int bool))), bnorRset ) 15.91/16.03 ( (fun int (fun int (fun int bool))), wset ) 15.91/16.03 ( (fun (product_prod int int) bool), frac_1 ) 15.91/16.03 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 15.91/16.03 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 15.91/16.03 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 15.91/16.03 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 15.91/16.03 ( (fun (fun nat rat) bool), vanishes ) 15.91/16.03 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 15.91/16.03 ( (fun code_code_numeral nat), code_c271388182l_size ) 15.91/16.03 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 15.91/16.03 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 15.91/16.03 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 15.91/16.03 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 15.91/16.03 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 15.91/16.03 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 15.91/16.03 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 15.91/16.03 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 15.91/16.03 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 15.91/16.03 ( (fun complex nat), complex_size ) 15.91/16.03 ( (fun complex nat), (size_size complex) ) 15.91/16.03 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 15.91/16.03 ( (fun nat (fun nat (product_prod int int))), bezw ) 15.91/16.03 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 15.91/16.03 ( (fun int (fun nat nat)), nat_aux ) 15.91/16.03 ( (fun int (fun (fun int bool) bool)), rsetR ) 15.91/16.03 ( (fun int (fun (fun int bool) bool)), resSet ) 15.91/16.03 ( (fun int (list int)), quickc666637781d_zero ) 15.91/16.03 ( (fun (product_prod int int) rat), frct ) 15.91/16.03 ( (fun int (fun int rat)), fract ) 15.91/16.03 ( (fun real (fun real complex)), complex_1 ) 15.91/16.03 ( (fun real (fun real complex)), rcis ) 15.91/16.03 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 15.91/16.03 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 15.91/16.03 ( (fun int real), (real_1 int) ) 15.91/16.03 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 15.91/16.03 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 15.91/16.03 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 15.91/16.03 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 15.91/16.03 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 15.91/16.03 ( (fun real nat), natfloor ) 15.91/16.03 ( (fun real nat), natceiling ) 15.91/16.03 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 15.91/16.03 ( (fun quickcheck_code_int int), quickcheck_int_of ) 15.91/16.03 ( (fun rat (product_prod int int)), quotient_of ) 15.91/16.03 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 15.91/16.03 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 15.91/16.03 ( (fun rat real), ratreal ) 15.91/16.03 ( (fun code_code_numeral int), code_int_of ) 15.91/16.03 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 15.91/16.03 ( (fun int quickcheck_code_int), quickcheck_of_int ) 15.91/16.03 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 15.91/16.03 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 15.91/16.03 ) 15.91/16.03 (instantiation (forall ((K_4 $$unsorted)) (not (= pls (hAPP int int bit1 K_4))) ) 15.91/16.03 ( pls ) 15.91/16.03 ( (hAPP int int bit1 pls) ) 15.91/16.03 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.91/16.03 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.91/16.03 ( min_1 ) 15.91/16.03 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.91/16.03 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.91/16.03 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 15.91/16.03 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 15.91/16.03 ) 15.91/16.03 (instantiation (forall ((X_a $$unsorted)) (or (not (real_n2089651433ebra_1 X_a)) (= (one_one real) (hAPP X_a real (norm_norm X_a) (one_one X_a)))) ) 15.91/16.03 ( nat ) 15.91/16.03 ( int ) 15.91/16.03 ( real ) 15.91/16.03 ( rat ) 15.91/16.03 ( complex ) 15.91/16.03 ( quickcheck_code_int ) 15.91/16.03 ( code_code_numeral ) 15.91/16.03 ) 15.91/16.03 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_0 (product_prod X_a X_b))) (= (hAPP _let_0 X_a (product_fst X_a X_b) (hAPP X_b _let_0 (hAPP X_a (fun X_b _let_0) (product_Pair X_a X_b) A_1) B)) (ti X_a A_1))) ) 15.91/16.03 ( int, int, (one_one int), (one_one int) ) 15.91/16.03 ( int, int, (zero_zero int), (one_one int) ) 15.91/16.03 ( int, int, s, (one_one int) ) 15.91/16.03 ) 15.91/16.03 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_131061 $$unsorted) (BOUND_VARIABLE_131062 $$unsorted) (BOUND_VARIABLE_131063 $$unsorted)) (let ((_let_0 (fun (filter nat) bool))) (or (not (real_normed_vector X_a)) (not (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_0 (hAPP (fun nat X_a) (fun X_a _let_0) (tendsto nat X_a) BOUND_VARIABLE_131062) BOUND_VARIABLE_131063) sequentially))) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) BOUND_VARIABLE_131061))) (not (forall ((No $$unsorted)) (not (forall ((N_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) No) N_2))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP X_a real (norm_norm X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) (hAPP nat X_a BOUND_VARIABLE_131062 N_2)) BOUND_VARIABLE_131063))) BOUND_VARIABLE_131061))) )) )))) ) 15.91/16.03 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real) ) 15.91/16.03 ) 15.91/16.03 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_131102 $$unsorted) (BOUND_VARIABLE_131103 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (zero_zero X_a))) (or (not (ordere453448008miring X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_131103))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_131102) _let_2))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_131103) BOUND_VARIABLE_131102)) _let_2)))))) ) 15.91/16.03 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.03 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.03 ( int, skv_13, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.03 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.03 ( real, pi, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 15.91/16.03 ( real, (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.03 ( real, (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.03 ( complex, ii, ii ) 15.91/16.03 ( complex, ii, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 15.91/16.03 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.03 ) 15.91/16.03 (instantiation (forall ((K $$unsorted)) (= (= min_1 (ti int K)) (= min_1 (hAPP int int bit1 K))) ) 15.91/16.03 ( pls ) 15.91/16.03 ( (hAPP int int bit1 pls) ) 15.91/16.03 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.91/16.03 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.91/16.03 ( min_1 ) 15.91/16.03 ( s ) 15.91/16.03 ( m ) 15.91/16.03 ( s1 ) 15.91/16.03 ( t ) 15.91/16.03 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.91/16.03 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.91/16.03 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 15.91/16.03 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 15.91/16.03 ) 15.91/16.03 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_0 (product_prod int int))) (= (hAPP rat _let_0 quotient_of (hAPP int rat (hAPP int (fun int rat) fract A_1) B)) (hAPP _let_0 _let_0 normalize (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) A_1) B)))) ) 15.91/16.03 ( (one_one int), (one_one int) ) 15.91/16.03 ( (zero_zero int), (one_one int) ) 15.91/16.03 ( s, (one_one int) ) 15.91/16.03 ) 15.91/16.03 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_131150 $$unsorted) (BOUND_VARIABLE_131151 $$unsorted) (BOUND_VARIABLE_131152 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (let ((_let_3 (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_131150))) (let ((_let_4 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_131152)))) (let ((_let_5 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_131152) _let_2)))) (let ((_let_6 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_131150) BOUND_VARIABLE_131152))) (or (not (linord1117847801e_zero X_a)) (= (hBOOL (hAPP X_a bool _let_3 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_131151) BOUND_VARIABLE_131152))) (and (or _let_4 (and (or (not _let_5) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_131151) _let_6))) (or _let_5 (hBOOL (hAPP X_a bool _let_3 _let_2))))) (or (not _let_4) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_6) BOUND_VARIABLE_131151))))))))))))) ) 15.91/16.03 ( real, (zero_zero real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.03 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.91/16.03 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.91/16.03 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.91/16.03 ) 15.91/16.03 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) M) N_1))) (= M (hAPP nat nat (hAPP nat (fun nat nat) (div_mod nat) M) N_1))) ) 15.91/16.03 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.03 ) 15.91/16.03 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_131243 $$unsorted) (BOUND_VARIABLE_131244 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (or (not (division_ring X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_131243) (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_131244)) (hAPP X_a X_a (hAPP X_a _let_0 (inverse_divide X_a) BOUND_VARIABLE_131243) BOUND_VARIABLE_131244)))) ) 15.91/16.03 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.03 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.91/16.03 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.03 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 15.91/16.03 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.03 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.03 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.91/16.03 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.91/16.03 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.03 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.03 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.03 ) 15.91/16.03 (instantiation (forall ((Z1 $$unsorted) (Z2 $$unsorted) (Z3 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (times_times real))) (let ((_let_2 (hAPP real _let_0 _let_1 Z1))) (= (hAPP real real _let_2 (hAPP real real (hAPP real _let_0 _let_1 Z2) Z3)) (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real _let_2 Z2)) Z3))))) ) 15.91/16.03 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.91/16.03 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.91/16.03 ) 15.91/16.03 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_0 (fun int rat))) (= (hAPP rat rat (uminus_uminus rat) (hAPP int rat (hAPP int _let_0 fract A_1) B)) (hAPP int rat (hAPP int _let_0 fract (hAPP int int (uminus_uminus int) A_1)) B))) ) 15.91/16.03 ( pls, (one_one int) ) 15.91/16.03 ) 15.91/16.03 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (one_one real))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 (zero_zero real)) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 X_1) _let_1))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 (hAPP real real (exp real) (hAPP real real (hAPP real _let_3 (minus_minus real) X_1) (hAPP nat real (hAPP real (fun nat real) (power_power real) X_1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) (hAPP real real (hAPP real _let_3 (plus_plus real) _let_1) X_1)))))))) ) 15.91/16.03 ( pi ) 15.91/16.03 ( (hAPP int real (number_number_of real) min_1) ) 15.91/16.03 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.03 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.03 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.03 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))) ) 15.91/16.03 ( skv_3 ) 15.91/16.03 ( skv_5 ) 15.91/16.03 ( skv_7 ) 15.91/16.03 ( skv_12 ) 15.91/16.03 ) 15.91/16.03 (instantiation (forall ((N $$unsorted)) (let ((_let_0 (fun int (fun int bool)))) (let ((_let_1 (ord_less_eq int))) (let ((_let_2 (hAPP int (fun int bool) _let_1 (zero_zero int)))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun int _let_3))) (or (not (hBOOL (hAPP int bool _let_2 N))) (= (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP int nat nat_1 N)) (one_one nat)) (hAPP (fun int bool) nat (finite_card int) (hAPP (fun int bool) (fun int bool) (collect int) (hAPP (fun int bool) (fun int bool) (hAPP _let_4 (fun (fun int bool) (fun int bool)) (combs int bool bool) (hAPP (fun int bool) _let_4 (hAPP (fun bool _let_3) (fun (fun int bool) _let_4) (combb bool _let_3 int) fconj) _let_2)) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) _let_1) N))))))))))) ) 15.91/16.03 ( (one_one int) ) 15.91/16.03 ( (zero_zero int) ) 15.91/16.03 ( min_1 ) 15.91/16.03 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.03 ( s ) 15.91/16.03 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.91/16.03 ( (hAPP int int (number_number_of int) pls) ) 15.91/16.03 ( skv_4 ) 15.91/16.03 ( skv_10 ) 15.91/16.03 ) 15.91/16.03 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int int (hAPP int (fun int int) (minus_minus int) K_4) min_1) (hAPP int int succ K_4)) ) 15.91/16.03 ( pls ) 15.91/16.03 ( min_1 ) 15.91/16.03 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.03 ) 15.91/16.03 (instantiation (forall ((F $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 A_2) B_1))) (not (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X) B_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 A_2) X))) (not (forall ((Y $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) Y))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP (fun real real) (fun real _let_0) (deriv real) F) X) Y)))) ))) )) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real F A_2)) (hAPP real real F B_1)))))) ) 15.91/16.03 ( cos, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_5 ) 15.91/16.03 ( sqrt, (zero_zero real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.03 ) 15.91/16.03 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_131388 $$unsorted)) (or (not (ordere142940540dd_abs X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)) BOUND_VARIABLE_131388))) (= (ti X_a BOUND_VARIABLE_131388) (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_131388))) ) 15.91/16.03 ( bool, fFalse ) 15.91/16.03 ( bool, fTrue ) 15.91/16.03 ( int, (one_one int) ) 15.91/16.03 ( int, pls ) 15.91/16.03 ( int, min_1 ) 15.91/16.03 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.03 ( int, s ) 15.91/16.03 ( int, m ) 15.91/16.03 ( int, s1 ) 15.91/16.03 ( int, t ) 15.91/16.03 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.91/16.03 ( int, (hAPP int int (number_number_of int) pls) ) 15.91/16.03 ( int, skv_4 ) 15.91/16.03 ( int, skv_10 ) 15.91/16.03 ( (fun int bool), nat_neg ) 15.91/16.03 ( (fun int bool), zprime ) 15.91/16.03 ( (fun int bool), zEven ) 15.91/16.03 ( (fun int bool), zOdd ) 15.91/16.03 ( (fun int bool), (even_odd_even int) ) 15.91/16.03 ( (fun int bool), twoSqu1091635170sum2sq ) 15.91/16.03 ( (fun int bool), nat_is_nat ) 15.91/16.03 ( (fun int (fun int bool)), norRRset ) 15.91/16.03 ( (fun int (fun int bool)), quadRes ) 15.91/16.03 ( (fun int (fun int bool)), sRStar ) 15.91/16.03 ( (fun int (fun int bool)), d22set ) 15.91/16.03 ( (fun int (fun int bool)), sr ) 15.91/16.03 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 15.91/16.03 ( (fun int int), zfact ) 15.91/16.03 ( (fun int int), bit0 ) 15.91/16.03 ( (fun int int), bit1 ) 15.91/16.03 ( (fun int int), (fact_fact int) ) 15.91/16.03 ( (fun int int), pred ) 15.91/16.03 ( (fun int int), succ ) 15.91/16.03 ( (fun nat bool), (even_odd_even nat) ) 15.91/16.03 ( (fun nat bool), prime ) 15.91/16.03 ( (fun nat nat), suc ) 15.91/16.03 ( (fun nat nat), (fact_fact nat) ) 15.91/16.03 ( (fun nat nat), fact ) 15.91/16.03 ( (fun nat nat), nat_size ) 15.91/16.03 ( (fun nat nat), (size_size nat) ) 15.91/16.03 ( (fun (product_prod nat nat) bool), pred_nat ) 15.91/16.03 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 15.91/16.03 ( real, pi ) 15.91/16.03 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.03 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.03 ( real, skv_3 ) 15.91/16.03 ( real, skv_5 ) 15.91/16.03 ( real, skv_7 ) 15.91/16.03 ( real, skv_12 ) 15.91/16.03 ( (fun real real), ln ) 15.91/16.03 ( (fun real real), cos ) 15.91/16.03 ( (fun real real), sqrt ) 15.91/16.03 ( (fun real real), sin ) 15.91/16.03 ( (fun real real), arccos ) 15.91/16.03 ( (fun real real), arcsin ) 15.91/16.03 ( (fun real real), tan ) 15.91/16.03 ( (fun real real), arctan ) 15.91/16.03 ( (fun nat (fun nat bool)), coprime ) 15.91/16.03 ( complex, ii ) 15.91/16.03 ( (fun nat real), (real_1 nat) ) 15.91/16.03 ( (fun nat real), sin_coeff ) 15.91/16.03 ( (fun nat real), cos_coeff ) 15.91/16.03 ( (filter nat), sequentially ) 15.91/16.03 ( (fun int (fun int int)), (gcd_gcd int) ) 15.91/16.03 ( (fun int (fun int int)), legendre ) 15.91/16.03 ( (fun int (fun int int)), legacy_zgcd ) 15.91/16.03 ( (fun int (fun int int)), standardRes ) 15.91/16.03 ( (fun int (fun int int)), nat_tsub ) 15.91/16.03 ( (fun int (fun int int)), multInv ) 15.91/16.03 ( (fun int (fun int int)), z3mod ) 15.91/16.03 ( (fun int (fun int int)), z3div ) 15.91/16.03 ( (fun int (fun int int)), int_gcd ) 15.91/16.03 ( (fun int (fun int int)), int_lcm ) 15.91/16.03 ( (fun int (fun int int)), inv ) 15.91/16.03 ( (fun complex complex), expi ) 15.91/16.03 ( (fun complex complex), cnj ) 15.91/16.03 ( (fun real complex), cis ) 15.91/16.03 ( (fun int nat), nat_1 ) 15.91/16.03 ( (fun int nat), phi ) 15.91/16.03 ( (fun (fun int bool) bool), nat_nat_set ) 15.91/16.03 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 15.91/16.03 ( (fun nat (fun nat nat)), nat_gcd ) 15.91/16.03 ( (fun nat (fun nat nat)), nat_lcm ) 15.91/16.03 ( (fun (fun int bool) int), (the int) ) 15.91/16.03 ( (fun complex real), re ) 15.91/16.03 ( (fun complex real), im ) 15.91/16.03 ( (fun complex real), arg ) 15.91/16.03 ( (fun bool bool), fNot ) 15.91/16.03 ( (fun nat (fun real real)), root ) 15.91/16.03 ( (fun real (fun real real)), log ) 15.91/16.03 ( (fun real (fun real real)), powr ) 15.91/16.03 ( (fun bool (fun bool bool)), fimplies ) 15.91/16.03 ( (fun bool (fun bool bool)), fconj ) 15.91/16.03 ( (fun bool (fun bool bool)), fdisj ) 15.91/16.03 ( (fun int (fun int (product_prod int int))), negDivAlg ) 15.91/16.03 ( (fun int (fun int (product_prod int int))), posDivAlg ) 15.91/16.03 ( (fun int (fun int (product_prod int int))), divmod_int ) 15.91/16.03 ( (fun int (fun int (product_prod int int))), pdivmod ) 15.91/16.03 ( (fun int (fun int (product_prod int int))), norm_frac ) 15.91/16.03 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 15.91/16.03 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 15.91/16.03 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 15.91/16.03 ( (fun int (fun int (fun int bool))), zcong ) 15.91/16.03 ( (fun int (fun int (fun int bool))), zcongm ) 15.91/16.03 ( (fun int (fun int (fun int bool))), noXRRset ) 15.91/16.03 ( (fun int (fun int (fun int bool))), bnorRset ) 15.91/16.03 ( (fun int (fun int (fun int bool))), wset ) 15.91/16.03 ( (fun (product_prod int int) bool), frac_1 ) 15.91/16.03 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 15.91/16.03 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 15.91/16.03 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 15.91/16.03 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 15.91/16.03 ( (fun (fun nat rat) bool), vanishes ) 15.91/16.03 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 15.91/16.03 ( (fun code_code_numeral nat), code_c271388182l_size ) 15.91/16.03 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 15.91/16.03 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 15.91/16.03 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 15.91/16.03 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 15.91/16.03 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 15.91/16.03 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 15.91/16.03 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 15.91/16.03 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 15.91/16.03 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 15.91/16.03 ( (fun complex nat), complex_size ) 15.91/16.03 ( (fun complex nat), (size_size complex) ) 15.91/16.03 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 15.91/16.03 ( (fun nat (fun nat (product_prod int int))), bezw ) 15.91/16.03 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 15.91/16.03 ( (fun int (fun nat nat)), nat_aux ) 15.91/16.03 ( (fun int (fun (fun int bool) bool)), rsetR ) 15.91/16.03 ( (fun int (fun (fun int bool) bool)), resSet ) 15.91/16.03 ( (fun int (list int)), quickc666637781d_zero ) 15.91/16.03 ( (fun (product_prod int int) rat), frct ) 15.91/16.03 ( (fun int (fun int rat)), fract ) 15.91/16.03 ( (fun real (fun real complex)), complex_1 ) 15.91/16.03 ( (fun real (fun real complex)), rcis ) 15.91/16.03 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 15.91/16.03 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 15.91/16.03 ( (fun int real), (real_1 int) ) 15.91/16.03 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 15.91/16.03 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 15.91/16.03 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 15.91/16.03 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 15.91/16.03 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 15.91/16.03 ( (fun real nat), natfloor ) 15.91/16.03 ( (fun real nat), natceiling ) 15.91/16.03 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 15.91/16.03 ( (fun quickcheck_code_int int), quickcheck_int_of ) 15.91/16.03 ( (fun rat (product_prod int int)), quotient_of ) 15.91/16.03 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 15.91/16.03 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 15.91/16.03 ( (fun rat real), ratreal ) 15.91/16.03 ( (fun code_code_numeral int), code_int_of ) 15.91/16.03 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 15.91/16.03 ( (fun int quickcheck_code_int), quickcheck_of_int ) 15.91/16.03 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 15.91/16.03 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 15.91/16.03 ) 15.91/16.03 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_131411 $$unsorted)) (or (not (ring_char_0 X_a)) (= (= (zero_zero int) (ti int BOUND_VARIABLE_131411)) (= (zero_zero X_a) (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_131411)))) ) 15.91/16.03 ( real, (one_one int) ) 15.91/16.03 ( real, (zero_zero int) ) 15.91/16.03 ) 15.91/16.03 (instantiation (forall ((Z_1 $$unsorted)) (= (zero_zero real) (hAPP complex real im (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) Z_1) (hAPP complex complex cnj Z_1)))) ) 15.91/16.03 ( (one_one complex) ) 15.91/16.03 ( ii ) 15.91/16.03 ( (zero_zero complex) ) 15.91/16.03 ( (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.03 ( (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 15.91/16.03 ) 15.91/16.03 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_131511 $$unsorted)) (or (not (real_vector X_a)) (= (hAPP X_a X_a (hAPP real (fun X_a X_a) (scaleR_scaleR X_a) (one_one real)) BOUND_VARIABLE_131511) (ti X_a BOUND_VARIABLE_131511))) ) 15.91/16.03 ( bool, fFalse ) 15.91/16.03 ( bool, fTrue ) 15.91/16.03 ( int, pls ) 15.91/16.03 ( int, min_1 ) 15.91/16.03 ( int, s ) 15.91/16.03 ( int, m ) 15.91/16.03 ( int, s1 ) 15.91/16.03 ( int, t ) 15.91/16.03 ( (fun int bool), nat_neg ) 15.91/16.03 ( (fun int bool), zprime ) 15.91/16.03 ( (fun int bool), zEven ) 15.91/16.03 ( (fun int bool), zOdd ) 15.91/16.03 ( (fun int bool), (even_odd_even int) ) 15.91/16.03 ( (fun int bool), twoSqu1091635170sum2sq ) 15.91/16.03 ( (fun int bool), nat_is_nat ) 15.91/16.03 ( (fun int (fun int bool)), norRRset ) 15.91/16.03 ( (fun int (fun int bool)), quadRes ) 15.91/16.03 ( (fun int (fun int bool)), sRStar ) 15.91/16.03 ( (fun int (fun int bool)), d22set ) 15.91/16.03 ( (fun int (fun int bool)), sr ) 15.91/16.03 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 15.91/16.03 ( (fun int int), zfact ) 15.91/16.03 ( (fun int int), bit0 ) 15.91/16.03 ( (fun int int), bit1 ) 15.91/16.03 ( (fun int int), (fact_fact int) ) 15.91/16.03 ( (fun int int), pred ) 15.91/16.03 ( (fun int int), succ ) 15.91/16.03 ( (fun nat bool), (even_odd_even nat) ) 15.91/16.03 ( (fun nat bool), prime ) 15.91/16.03 ( (fun nat nat), suc ) 15.91/16.03 ( (fun nat nat), (fact_fact nat) ) 15.91/16.03 ( (fun nat nat), fact ) 15.91/16.03 ( (fun nat nat), nat_size ) 15.91/16.03 ( (fun nat nat), (size_size nat) ) 15.91/16.03 ( (fun (product_prod nat nat) bool), pred_nat ) 15.91/16.03 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 15.91/16.03 ( real, pi ) 15.91/16.03 ( (fun real real), ln ) 15.91/16.03 ( (fun real real), cos ) 15.91/16.03 ( (fun real real), sqrt ) 15.91/16.03 ( (fun real real), sin ) 15.91/16.03 ( (fun real real), arccos ) 15.91/16.03 ( (fun real real), arcsin ) 15.91/16.03 ( (fun real real), tan ) 15.91/16.03 ( (fun real real), arctan ) 15.91/16.03 ( (fun nat (fun nat bool)), coprime ) 15.91/16.03 ( complex, ii ) 15.91/16.03 ( (fun nat real), (real_1 nat) ) 15.91/16.03 ( (fun nat real), sin_coeff ) 15.91/16.03 ( (fun nat real), cos_coeff ) 15.91/16.03 ( (filter nat), sequentially ) 15.91/16.03 ( (fun int (fun int int)), (gcd_gcd int) ) 15.91/16.03 ( (fun int (fun int int)), legendre ) 15.91/16.03 ( (fun int (fun int int)), legacy_zgcd ) 15.91/16.03 ( (fun int (fun int int)), standardRes ) 15.91/16.03 ( (fun int (fun int int)), nat_tsub ) 15.91/16.03 ( (fun int (fun int int)), multInv ) 15.91/16.03 ( (fun int (fun int int)), z3mod ) 15.91/16.03 ( (fun int (fun int int)), z3div ) 15.91/16.03 ( (fun int (fun int int)), int_gcd ) 15.91/16.03 ( (fun int (fun int int)), int_lcm ) 15.91/16.03 ( (fun int (fun int int)), inv ) 15.91/16.03 ( (fun complex complex), expi ) 15.91/16.03 ( (fun complex complex), cnj ) 15.91/16.03 ( (fun real complex), cis ) 15.91/16.03 ( (fun int nat), nat_1 ) 15.91/16.03 ( (fun int nat), phi ) 15.91/16.03 ( (fun (fun int bool) bool), nat_nat_set ) 15.91/16.03 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 15.91/16.03 ( (fun nat (fun nat nat)), nat_gcd ) 15.91/16.03 ( (fun nat (fun nat nat)), nat_lcm ) 15.91/16.03 ( (fun (fun int bool) int), (the int) ) 15.91/16.03 ( (fun complex real), re ) 15.91/16.03 ( (fun complex real), im ) 15.91/16.03 ( (fun complex real), arg ) 15.91/16.03 ( (fun bool bool), fNot ) 15.91/16.03 ( (fun nat (fun real real)), root ) 15.91/16.03 ( (fun real (fun real real)), log ) 15.91/16.03 ( (fun real (fun real real)), powr ) 15.91/16.03 ( (fun bool (fun bool bool)), fimplies ) 15.91/16.03 ( (fun bool (fun bool bool)), fconj ) 15.91/16.03 ( (fun bool (fun bool bool)), fdisj ) 15.91/16.03 ( (fun int (fun int (product_prod int int))), negDivAlg ) 15.91/16.03 ( (fun int (fun int (product_prod int int))), posDivAlg ) 15.91/16.03 ( (fun int (fun int (product_prod int int))), divmod_int ) 15.91/16.03 ( (fun int (fun int (product_prod int int))), pdivmod ) 15.91/16.03 ( (fun int (fun int (product_prod int int))), norm_frac ) 15.91/16.03 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 15.91/16.03 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 15.91/16.03 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 15.91/16.03 ( (fun int (fun int (fun int bool))), zcong ) 15.91/16.03 ( (fun int (fun int (fun int bool))), zcongm ) 15.91/16.03 ( (fun int (fun int (fun int bool))), noXRRset ) 15.91/16.03 ( (fun int (fun int (fun int bool))), bnorRset ) 15.91/16.03 ( (fun int (fun int (fun int bool))), wset ) 15.91/16.03 ( (fun (product_prod int int) bool), frac_1 ) 15.91/16.03 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 15.91/16.03 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 15.91/16.03 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 15.91/16.03 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 15.91/16.03 ( (fun (fun nat rat) bool), vanishes ) 15.91/16.03 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 15.91/16.03 ( (fun code_code_numeral nat), code_c271388182l_size ) 15.91/16.03 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 15.91/16.03 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 15.91/16.03 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 15.91/16.03 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 15.91/16.03 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 15.91/16.03 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 15.91/16.03 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 15.91/16.03 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 15.91/16.03 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 15.91/16.03 ( (fun complex nat), complex_size ) 15.91/16.03 ( (fun complex nat), (size_size complex) ) 15.91/16.03 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 15.91/16.03 ( (fun nat (fun nat (product_prod int int))), bezw ) 15.91/16.03 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 15.91/16.03 ( (fun int (fun nat nat)), nat_aux ) 15.91/16.03 ( (fun int (fun (fun int bool) bool)), rsetR ) 15.91/16.03 ( (fun int (fun (fun int bool) bool)), resSet ) 15.91/16.03 ( (fun int (list int)), quickc666637781d_zero ) 15.91/16.03 ( (fun (product_prod int int) rat), frct ) 15.91/16.03 ( (fun int (fun int rat)), fract ) 15.91/16.03 ( (fun real (fun real complex)), complex_1 ) 15.91/16.03 ( (fun real (fun real complex)), rcis ) 15.91/16.03 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 15.91/16.03 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 15.91/16.03 ( (fun int real), (real_1 int) ) 15.91/16.03 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 15.91/16.03 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 15.91/16.03 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 15.91/16.03 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 15.91/16.03 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 15.91/16.03 ( (fun real nat), natfloor ) 15.91/16.03 ( (fun real nat), natceiling ) 15.91/16.03 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 15.91/16.03 ( (fun quickcheck_code_int int), quickcheck_int_of ) 15.91/16.03 ( (fun rat (product_prod int int)), quotient_of ) 15.91/16.03 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 15.91/16.03 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 15.91/16.03 ( (fun rat real), ratreal ) 15.91/16.03 ( (fun code_code_numeral int), code_int_of ) 15.91/16.03 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 15.91/16.03 ( (fun int quickcheck_code_int), quickcheck_of_int ) 15.91/16.03 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 15.91/16.03 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 15.91/16.03 ) 15.91/16.03 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (abs_abs int))) (let ((_let_2 (dvd_dvd int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 A_1) B))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 B) A_1))) (= (hAPP int int _let_1 A_1) (hAPP int int _let_1 B)))))) ) 15.91/16.03 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 15.91/16.03 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.03 ) 15.91/16.03 (instantiation (forall ((N_1 $$unsorted)) (= (hAPP nat int (semiring_1_of_nat int) N_1) (hAPP real int (archimedean_ceiling real) (hAPP nat real (real_1 nat) N_1))) ) 15.91/16.03 ( (zero_zero nat) ) 15.91/16.03 ( (hAPP nat nat suc (zero_zero nat)) ) 15.91/16.03 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.91/16.03 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.03 ) 15.91/16.03 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_131545 $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat X_a))) (let ((_let_2 (norm_norm X_a))) (let ((_let_3 (hAPP _let_1 _let_0 (hAPP (fun X_a real) (fun _let_1 _let_0) (combb X_a real nat) _let_2) BOUND_VARIABLE_131545))) (or (not (banach X_a)) (not (hBOOL (hAPP _let_0 bool (summable real) _let_3))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP X_a real _let_2 (hAPP _let_1 X_a (suminf X_a) BOUND_VARIABLE_131545))) (hAPP _let_0 real (suminf real) _let_3)))))))) ) 15.91/16.04 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat (fun nat nat)))) (let ((_let_3 (fun nat _let_0))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun _let_1 _let_3))) (let ((_let_6 (combb real _let_0 nat))) (let ((_let_7 (combc nat nat nat))) (hAPP _let_1 _let_1 (hAPP _let_3 (fun _let_1 _let_1) (combs nat real real) (hAPP _let_1 _let_3 (hAPP _let_4 _let_5 _let_6 (inverse_divide real)) (hAPP real _let_1 (hAPP _let_3 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_3 (hAPP _let_4 _let_5 _let_6 (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) (one_one real)))) (hAPP (fun nat nat) _let_1 (hAPP _let_1 (fun (fun nat nat) _let_1) (combb nat real nat) (real_1 nat)) (hAPP nat (fun nat nat) (hAPP _let_2 _let_2 _let_7 (hAPP (fun nat nat) _let_2 (hAPP _let_2 (fun (fun nat nat) _let_2) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_2 _let_2 _let_7 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))))))))))) ) 15.91/16.04 ) 15.91/16.04 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_131595 $$unsorted) (BOUND_VARIABLE_131596 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (dvd_dvd X_a))) (or (not (comm_ring_1 X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_131595) BOUND_VARIABLE_131596)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_131595)) BOUND_VARIABLE_131596)))))) ) 15.91/16.04 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 15.91/16.04 ) 15.91/16.04 (instantiation (forall ((P $$unsorted)) (let ((_let_0 (ti bool P))) (or (= fFalse _let_0) (= fTrue _let_0))) ) 15.91/16.04 ( fTrue ) 15.91/16.04 ) 15.91/16.04 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_131668 $$unsorted) (BOUND_VARIABLE_131669 $$unsorted)) (let ((_let_0 (abs_abs X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (plus_plus X_a))) (or (not (ordere142940540dd_abs X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (hAPP X_a X_a _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_131668) BOUND_VARIABLE_131669))) (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a _let_0 BOUND_VARIABLE_131668)) (hAPP X_a X_a _let_0 BOUND_VARIABLE_131669)))))))) ) 15.91/16.04 ( nat, (one_one nat), (one_one nat) ) 15.91/16.04 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 15.91/16.04 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 15.91/16.04 ) 15.91/16.04 (instantiation (forall ((Z_1 $$unsorted)) (= (hAPP complex complex expi Z_1) (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP real complex (of_real complex) (hAPP real real (exp real) (hAPP complex real re Z_1)))) (hAPP real complex cis (hAPP complex real im Z_1)))) ) 15.91/16.04 ( (one_one complex) ) 15.91/16.04 ( ii ) 15.91/16.04 ( (zero_zero complex) ) 15.91/16.04 ( (let ((_let_0 (fun complex complex))) (let ((_let_1 (times_times complex))) (hAPP complex complex (hAPP complex _let_0 _let_1 (hAPP complex complex (hAPP complex _let_0 _let_1 (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi))) ii))) ) 15.91/16.04 ) 15.91/16.04 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (one_one real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat real))) (let ((_let_3 (power_power real))) (let ((_let_4 (fun nat _let_1))) (let ((_let_5 (fun _let_2 _let_2))) (let ((_let_6 (combs nat real real))) (let ((_let_7 (fun (fun nat nat) _let_2))) (let ((_let_8 (combb nat real nat))) (let ((_let_9 (hAPP (fun real _let_1) (fun _let_2 _let_4) (combb real _let_1 nat) (times_times real)))) (let ((_let_10 (combc nat nat nat))) (let ((_let_11 (hAPP nat (fun nat nat) (hAPP (fun nat (fun nat nat)) (fun nat (fun nat nat)) _let_10 (hAPP (fun nat nat) (fun nat (fun nat nat)) (hAPP (fun nat (fun nat nat)) (fun (fun nat nat) (fun nat (fun nat nat))) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP (fun nat (fun nat nat)) (fun nat (fun nat nat)) _let_10 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (abs_abs real) X_2)) _let_0))) (= (hAPP _let_2 real (suminf real) (hAPP _let_2 _let_2 (hAPP _let_4 _let_5 _let_6 (hAPP _let_2 _let_4 _let_9 (hAPP real _let_2 _let_3 (hAPP int real (number_number_of real) min_1)))) (hAPP _let_2 _let_2 (hAPP _let_4 _let_5 _let_6 (hAPP _let_2 _let_4 _let_9 (hAPP _let_2 _let_2 (hAPP _let_1 _let_5 (combb real real nat) (hAPP real _let_1 (inverse_divide real) _let_0)) (hAPP (fun nat nat) _let_2 (hAPP _let_2 _let_7 _let_8 (real_1 nat)) _let_11)))) (hAPP (fun nat nat) _let_2 (hAPP _let_2 _let_7 _let_8 (hAPP real _let_2 _let_3 X_2)) _let_11)))) (hAPP real real arctan X_2))))))))))))))) ) 15.91/16.04 ( (one_one real) ) 15.91/16.04 ( (zero_zero real) ) 15.91/16.04 ( (hAPP int real (number_number_of real) min_1) ) 15.91/16.04 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.04 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.91/16.04 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))))) ) 15.91/16.04 ) 15.91/16.04 (instantiation (forall ((V_1 $$unsorted)) (or (hBOOL (hAPP int bool nat_neg (hAPP int int (number_number_of int) V_1))) (= (hAPP nat real (real_1 nat) (hAPP int nat (number_number_of nat) V_1)) (hAPP int real (number_number_of real) V_1))) ) 15.91/16.04 ( pls ) 15.91/16.04 ( (hAPP int int bit1 pls) ) 15.91/16.04 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.91/16.04 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.91/16.04 ( min_1 ) 15.91/16.04 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.04 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.91/16.04 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.04 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 15.91/16.04 ) 15.91/16.04 (instantiation (forall ((V_1 $$unsorted)) (or (not (hBOOL (hAPP int bool nat_neg (hAPP int int (number_number_of int) V_1)))) (= (zero_zero real) (hAPP nat real (real_1 nat) (hAPP int nat (number_number_of nat) V_1)))) ) 15.91/16.04 ( pls ) 15.91/16.04 ( (hAPP int int bit1 pls) ) 15.91/16.04 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.91/16.04 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.91/16.04 ( min_1 ) 15.91/16.04 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.04 ) 15.91/16.04 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_131784 $$unsorted)) (or (not (linordered_idom X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_131784) (zero_zero X_a))) (= (hAPP X_a X_a (uminus_uminus X_a) (one_one X_a)) (hAPP X_a X_a (sgn_sgn X_a) BOUND_VARIABLE_131784)))) ) 15.91/16.04 ( nat, (zero_zero nat) ) 15.91/16.04 ( int, (one_one int) ) 15.91/16.04 ( int, pls ) 15.91/16.04 ( int, min_1 ) 15.91/16.04 ( int, s ) 15.91/16.04 ( int, t ) 15.91/16.04 ( int, skv_4 ) 15.91/16.04 ( int, skv_10 ) 15.91/16.04 ( real, (one_one real) ) 15.91/16.04 ( real, (zero_zero real) ) 15.91/16.04 ( real, pi ) 15.91/16.04 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.04 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.91/16.04 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.04 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 15.91/16.04 ( rat, (zero_zero rat) ) 15.91/16.04 ) 15.91/16.04 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_131874 $$unsorted)) (or (not (preorder X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_131874) BOUND_VARIABLE_131874))) ) 15.91/16.04 ( int, (one_one int) ) 15.91/16.04 ( int, (zero_zero int) ) 15.91/16.04 ( int, min_1 ) 15.91/16.04 ( real, (zero_zero real) ) 15.91/16.04 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.04 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.04 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.04 ( real, skv_5 ) 15.91/16.04 ) 15.91/16.04 (instantiation (forall ((X_1 $$unsorted)) (= (hAPP complex real im (hAPP complex complex cnj X_1)) (hAPP real real (uminus_uminus real) (hAPP complex real im X_1))) ) 15.91/16.04 ( (one_one complex) ) 15.91/16.04 ( ii ) 15.91/16.04 ( (zero_zero complex) ) 15.91/16.04 ) 15.91/16.04 (instantiation (forall ((X_a $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (uminus_uminus _let_0))) (= (= (ti _let_0 A_3) (ti _let_0 B_2)) (= (hAPP _let_0 _let_0 _let_1 B_2) (hAPP _let_0 _let_0 _let_1 A_3))))) ) 15.91/16.04 ( bool, fNot, fNot ) 15.91/16.04 ( nat, (even_odd_even nat), (even_odd_even nat) ) 15.91/16.04 ( nat, (even_odd_even nat), prime ) 15.91/16.04 ( nat, prime, (even_odd_even nat) ) 15.91/16.04 ( int, nat_neg, zprime ) 15.91/16.04 ( int, nat_neg, (even_odd_even int) ) 15.91/16.04 ( int, zprime, (even_odd_even int) ) 15.91/16.04 ( int, zEven, twoSqu1091635170sum2sq ) 15.91/16.04 ( int, zEven, nat_is_nat ) 15.91/16.04 ( int, zOdd, zOdd ) 15.91/16.04 ( int, (even_odd_even int), nat_neg ) 15.91/16.04 ( int, (even_odd_even int), (even_odd_even int) ) 15.91/16.04 ( int, twoSqu1091635170sum2sq, zEven ) 15.91/16.04 ( int, twoSqu1091635170sum2sq, twoSqu1091635170sum2sq ) 15.91/16.04 ( int, nat_is_nat, twoSqu1091635170sum2sq ) 15.91/16.04 ( (fun int bool), nat_nat_set, nat_nat_set ) 15.91/16.04 ( (product_prod nat nat), pred_nat, pred_nat ) 15.91/16.04 ( (product_prod int int), frac_1, frac_1 ) 15.91/16.04 ( (fun nat rat), vanishes, vanishes ) 15.91/16.04 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)), ratrel, ratrel ) 15.91/16.04 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), pair_less, pair_less ) 15.91/16.04 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), pair_less, pair_leq ) 15.91/16.04 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), pair_leq, pair_less ) 15.91/16.04 ) 15.91/16.04 (instantiation (forall ((N_1 $$unsorted) (X_1 $$unsorted)) (or (not (hBOOL (hAPP int bool nat_is_nat X_1))) (hBOOL (hAPP int bool nat_is_nat (hAPP nat int (hAPP int (fun nat int) (power_power int) X_1) N_1)))) ) 15.91/16.04 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 15.91/16.04 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 15.91/16.04 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_14 ) 15.91/16.04 ) 15.91/16.04 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_131936 $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (ring_1 X_a)) (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_131936)) (ring_1_Ints X_a))))) ) 15.91/16.04 ( real, (one_one int) ) 15.91/16.04 ( real, (zero_zero int) ) 15.91/16.04 ) 15.91/16.04 (instantiation (forall ((A_2 $$unsorted) (P_4 $$unsorted)) (let ((_let_0 (fun int (fun int bool)))) (let ((_let_1 (fun int int))) (let ((_let_2 (fun (fun int bool) bool))) (let ((_let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))) (or (not (hBOOL (hAPP int bool zprime P_4))) (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) _let_3) P_4))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (hAPP int _let_0 zcong A_2) (zero_zero int)) P_4)) (hBOOL (hAPP int bool (hAPP int (fun int bool) quadRes P_4) A_2)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (hAPP int _let_0 zcong (hAPP (fun int bool) int (hAPP _let_1 (fun (fun int bool) int) (big_co302546470etprod int int) (combi int)) (hAPP _let_2 (fun int bool) (complete_Sup_Sup (fun int bool)) (hAPP int _let_2 (hAPP int (fun int _let_2) setS A_2) P_4)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) A_2) (hAPP int nat nat_1 (hAPP int int (hAPP int _let_1 (div_div int) (hAPP int int (hAPP int _let_1 (minus_minus int) P_4) (one_one int))) _let_3)))) P_4))))))) ) 15.91/16.04 ( (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.04 ) 15.91/16.04 (instantiation (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (times_times real))) (= (hAPP real real (hAPP real _let_0 (minus_minus real) (hAPP real real (hAPP real _let_0 _let_1 (hAPP complex real re X_1)) (hAPP complex real re Y_1))) (hAPP real real (hAPP real _let_0 _let_1 (hAPP complex real im X_1)) (hAPP complex real im Y_1))) (hAPP complex real re (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) X_1) Y_1))))) ) 15.91/16.04 ( ii, ii ) 15.91/16.04 ( (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 15.91/16.04 ( (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 15.91/16.04 ) 15.91/16.04 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_132001 $$unsorted)) (or (not (division_ring X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_132001)) (= (one_one X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_132001) BOUND_VARIABLE_132001))) ) 15.91/16.04 ( bool, fFalse ) 15.91/16.04 ( bool, fTrue ) 15.91/16.04 ( int, pls ) 15.91/16.04 ( int, min_1 ) 15.91/16.04 ( int, s ) 15.91/16.04 ( int, m ) 15.91/16.04 ( int, s1 ) 15.91/16.04 ( int, t ) 15.91/16.04 ( (fun int bool), nat_neg ) 15.91/16.04 ( (fun int bool), zprime ) 15.91/16.04 ( (fun int bool), zEven ) 15.91/16.04 ( (fun int bool), zOdd ) 15.91/16.04 ( (fun int bool), (even_odd_even int) ) 15.91/16.04 ( (fun int bool), twoSqu1091635170sum2sq ) 15.91/16.04 ( (fun int bool), nat_is_nat ) 15.91/16.04 ( (fun int (fun int bool)), norRRset ) 15.91/16.04 ( (fun int (fun int bool)), quadRes ) 15.91/16.04 ( (fun int (fun int bool)), sRStar ) 15.91/16.04 ( (fun int (fun int bool)), d22set ) 15.91/16.04 ( (fun int (fun int bool)), sr ) 15.91/16.04 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 15.91/16.04 ( (fun int int), zfact ) 15.91/16.04 ( (fun int int), bit0 ) 15.91/16.04 ( (fun int int), bit1 ) 15.91/16.04 ( (fun int int), (fact_fact int) ) 15.91/16.04 ( (fun int int), pred ) 15.91/16.04 ( (fun int int), succ ) 15.91/16.04 ( (fun nat bool), (even_odd_even nat) ) 15.91/16.04 ( (fun nat bool), prime ) 15.91/16.04 ( (fun nat nat), suc ) 15.91/16.04 ( (fun nat nat), (fact_fact nat) ) 15.91/16.04 ( (fun nat nat), fact ) 15.91/16.04 ( (fun nat nat), nat_size ) 15.91/16.04 ( (fun nat nat), (size_size nat) ) 15.91/16.04 ( (fun (product_prod nat nat) bool), pred_nat ) 15.91/16.04 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 15.91/16.04 ( real, (one_one real) ) 15.91/16.04 ( real, pi ) 15.91/16.04 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.91/16.04 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.91/16.04 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.04 ( (fun real real), ln ) 15.91/16.04 ( (fun real real), cos ) 15.91/16.04 ( (fun real real), sqrt ) 15.91/16.04 ( (fun real real), sin ) 15.91/16.04 ( (fun real real), arccos ) 15.91/16.04 ( (fun real real), arcsin ) 15.91/16.04 ( (fun real real), tan ) 15.91/16.04 ( (fun real real), arctan ) 15.91/16.04 ( (fun nat (fun nat bool)), coprime ) 15.91/16.04 ( complex, ii ) 15.91/16.04 ( (fun nat real), (real_1 nat) ) 15.91/16.04 ( (fun nat real), sin_coeff ) 15.91/16.04 ( (fun nat real), cos_coeff ) 15.91/16.04 ( (filter nat), sequentially ) 15.91/16.04 ( (fun int (fun int int)), (gcd_gcd int) ) 15.91/16.04 ( (fun int (fun int int)), legendre ) 15.91/16.04 ( (fun int (fun int int)), legacy_zgcd ) 15.91/16.04 ( (fun int (fun int int)), standardRes ) 15.91/16.04 ( (fun int (fun int int)), nat_tsub ) 15.91/16.04 ( (fun int (fun int int)), multInv ) 15.91/16.04 ( (fun int (fun int int)), z3mod ) 15.91/16.04 ( (fun int (fun int int)), z3div ) 15.91/16.04 ( (fun int (fun int int)), int_gcd ) 15.91/16.04 ( (fun int (fun int int)), int_lcm ) 15.91/16.04 ( (fun int (fun int int)), inv ) 15.91/16.04 ( (fun complex complex), expi ) 15.91/16.04 ( (fun complex complex), cnj ) 15.91/16.04 ( (fun real complex), cis ) 15.91/16.04 ( (fun int nat), nat_1 ) 15.91/16.04 ( (fun int nat), phi ) 15.91/16.04 ( (fun (fun int bool) bool), nat_nat_set ) 15.91/16.04 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 15.91/16.04 ( (fun nat (fun nat nat)), nat_gcd ) 15.91/16.04 ( (fun nat (fun nat nat)), nat_lcm ) 15.91/16.04 ( (fun (fun int bool) int), (the int) ) 15.91/16.04 ( (fun complex real), re ) 15.91/16.04 ( (fun complex real), im ) 15.91/16.04 ( (fun complex real), arg ) 15.91/16.04 ( (fun bool bool), fNot ) 15.91/16.04 ( (fun nat (fun real real)), root ) 15.91/16.04 ( (fun real (fun real real)), log ) 15.91/16.04 ( (fun real (fun real real)), powr ) 15.91/16.04 ( (fun bool (fun bool bool)), fimplies ) 15.91/16.04 ( (fun bool (fun bool bool)), fconj ) 15.91/16.04 ( (fun bool (fun bool bool)), fdisj ) 15.91/16.04 ( (fun int (fun int (product_prod int int))), negDivAlg ) 15.91/16.04 ( (fun int (fun int (product_prod int int))), posDivAlg ) 15.91/16.04 ( (fun int (fun int (product_prod int int))), divmod_int ) 15.91/16.04 ( (fun int (fun int (product_prod int int))), pdivmod ) 15.91/16.04 ( (fun int (fun int (product_prod int int))), norm_frac ) 15.91/16.04 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 15.91/16.04 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 15.91/16.04 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 15.91/16.04 ( (fun int (fun int (fun int bool))), zcong ) 15.91/16.04 ( (fun int (fun int (fun int bool))), zcongm ) 15.91/16.04 ( (fun int (fun int (fun int bool))), noXRRset ) 15.91/16.04 ( (fun int (fun int (fun int bool))), bnorRset ) 15.91/16.04 ( (fun int (fun int (fun int bool))), wset ) 15.91/16.04 ( (fun (product_prod int int) bool), frac_1 ) 15.91/16.04 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 15.91/16.04 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 15.91/16.04 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 15.91/16.04 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 15.91/16.04 ( (fun (fun nat rat) bool), vanishes ) 15.91/16.04 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 15.91/16.04 ( (fun code_code_numeral nat), code_c271388182l_size ) 15.91/16.04 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 15.91/16.04 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 15.91/16.04 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 15.91/16.04 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 15.91/16.04 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 15.91/16.04 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 15.91/16.04 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 15.91/16.04 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 15.91/16.04 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 15.91/16.04 ( (fun complex nat), complex_size ) 15.91/16.04 ( (fun complex nat), (size_size complex) ) 15.91/16.04 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 15.91/16.04 ( (fun nat (fun nat (product_prod int int))), bezw ) 15.91/16.04 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 15.91/16.04 ( (fun int (fun nat nat)), nat_aux ) 15.91/16.04 ( (fun int (fun (fun int bool) bool)), rsetR ) 15.91/16.04 ( (fun int (fun (fun int bool) bool)), resSet ) 15.91/16.04 ( (fun int (list int)), quickc666637781d_zero ) 15.91/16.04 ( (fun (product_prod int int) rat), frct ) 15.91/16.04 ( (fun int (fun int rat)), fract ) 15.91/16.04 ( (fun real (fun real complex)), complex_1 ) 15.91/16.04 ( (fun real (fun real complex)), rcis ) 15.91/16.04 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 15.91/16.04 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 15.91/16.04 ( (fun int real), (real_1 int) ) 15.91/16.04 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 15.91/16.04 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 15.91/16.04 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 15.91/16.04 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 15.91/16.04 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 15.91/16.04 ( (fun real nat), natfloor ) 15.91/16.04 ( (fun real nat), natceiling ) 15.91/16.04 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 15.91/16.04 ( (fun quickcheck_code_int int), quickcheck_int_of ) 15.91/16.04 ( (fun rat (product_prod int int)), quotient_of ) 15.91/16.04 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 15.91/16.04 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 15.91/16.04 ( (fun rat real), ratreal ) 15.91/16.04 ( (fun code_code_numeral int), code_int_of ) 15.91/16.04 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 15.91/16.04 ( (fun int quickcheck_code_int), quickcheck_of_int ) 15.91/16.04 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 15.91/16.04 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 15.91/16.04 ) 15.91/16.04 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_132022 $$unsorted)) (or (not (semiring_div X_a)) (= (ti X_a BOUND_VARIABLE_132022) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (div_div X_a) BOUND_VARIABLE_132022) (one_one X_a)))) ) 15.91/16.04 ( bool, fFalse ) 15.91/16.04 ( bool, fTrue ) 15.91/16.04 ( int, pls ) 15.91/16.04 ( int, min_1 ) 15.91/16.04 ( int, s ) 15.91/16.04 ( int, m ) 15.91/16.04 ( int, s1 ) 15.91/16.04 ( int, t ) 15.91/16.04 ( (fun int bool), nat_neg ) 15.91/16.04 ( (fun int bool), zprime ) 15.91/16.04 ( (fun int bool), zEven ) 15.91/16.04 ( (fun int bool), zOdd ) 15.91/16.04 ( (fun int bool), (even_odd_even int) ) 15.91/16.04 ( (fun int bool), twoSqu1091635170sum2sq ) 15.91/16.04 ( (fun int bool), nat_is_nat ) 15.91/16.04 ( (fun int (fun int bool)), norRRset ) 15.91/16.04 ( (fun int (fun int bool)), quadRes ) 15.91/16.04 ( (fun int (fun int bool)), sRStar ) 15.91/16.04 ( (fun int (fun int bool)), d22set ) 15.91/16.04 ( (fun int (fun int bool)), sr ) 15.91/16.04 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 15.91/16.04 ( (fun int int), zfact ) 15.91/16.04 ( (fun int int), bit0 ) 15.91/16.04 ( (fun int int), bit1 ) 15.91/16.04 ( (fun int int), (fact_fact int) ) 15.91/16.04 ( (fun int int), pred ) 15.91/16.04 ( (fun int int), succ ) 15.91/16.04 ( (fun nat bool), (even_odd_even nat) ) 15.91/16.04 ( (fun nat bool), prime ) 15.91/16.04 ( (fun nat nat), suc ) 15.91/16.04 ( (fun nat nat), (fact_fact nat) ) 15.91/16.04 ( (fun nat nat), fact ) 15.91/16.04 ( (fun nat nat), nat_size ) 15.91/16.04 ( (fun nat nat), (size_size nat) ) 15.91/16.04 ( (fun (product_prod nat nat) bool), pred_nat ) 15.91/16.04 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 15.91/16.04 ( real, pi ) 15.91/16.04 ( (fun real real), ln ) 15.91/16.04 ( (fun real real), cos ) 15.91/16.04 ( (fun real real), sqrt ) 15.91/16.04 ( (fun real real), sin ) 15.91/16.04 ( (fun real real), arccos ) 15.91/16.04 ( (fun real real), arcsin ) 15.91/16.04 ( (fun real real), tan ) 15.91/16.04 ( (fun real real), arctan ) 15.91/16.04 ( (fun nat (fun nat bool)), coprime ) 15.91/16.04 ( complex, ii ) 15.91/16.04 ( (fun nat real), (real_1 nat) ) 15.91/16.04 ( (fun nat real), sin_coeff ) 15.91/16.04 ( (fun nat real), cos_coeff ) 15.91/16.04 ( (filter nat), sequentially ) 15.91/16.04 ( (fun int (fun int int)), (gcd_gcd int) ) 15.91/16.04 ( (fun int (fun int int)), legendre ) 15.91/16.04 ( (fun int (fun int int)), legacy_zgcd ) 15.91/16.04 ( (fun int (fun int int)), standardRes ) 15.91/16.04 ( (fun int (fun int int)), nat_tsub ) 15.91/16.04 ( (fun int (fun int int)), multInv ) 15.91/16.04 ( (fun int (fun int int)), z3mod ) 15.91/16.04 ( (fun int (fun int int)), z3div ) 15.91/16.04 ( (fun int (fun int int)), int_gcd ) 15.91/16.04 ( (fun int (fun int int)), int_lcm ) 15.91/16.04 ( (fun int (fun int int)), inv ) 15.91/16.04 ( (fun complex complex), expi ) 15.91/16.04 ( (fun complex complex), cnj ) 15.91/16.04 ( (fun real complex), cis ) 15.91/16.04 ( (fun int nat), nat_1 ) 15.91/16.04 ( (fun int nat), phi ) 15.91/16.04 ( (fun (fun int bool) bool), nat_nat_set ) 15.91/16.04 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 15.91/16.04 ( (fun nat (fun nat nat)), nat_gcd ) 15.91/16.04 ( (fun nat (fun nat nat)), nat_lcm ) 15.91/16.04 ( (fun (fun int bool) int), (the int) ) 15.91/16.04 ( (fun complex real), re ) 15.91/16.04 ( (fun complex real), im ) 15.91/16.04 ( (fun complex real), arg ) 15.91/16.04 ( (fun bool bool), fNot ) 15.91/16.04 ( (fun nat (fun real real)), root ) 15.91/16.04 ( (fun real (fun real real)), log ) 15.91/16.04 ( (fun real (fun real real)), powr ) 15.91/16.04 ( (fun bool (fun bool bool)), fimplies ) 15.91/16.04 ( (fun bool (fun bool bool)), fconj ) 15.91/16.04 ( (fun bool (fun bool bool)), fdisj ) 15.91/16.04 ( (fun int (fun int (product_prod int int))), negDivAlg ) 15.91/16.04 ( (fun int (fun int (product_prod int int))), posDivAlg ) 15.91/16.04 ( (fun int (fun int (product_prod int int))), divmod_int ) 15.91/16.04 ( (fun int (fun int (product_prod int int))), pdivmod ) 15.91/16.04 ( (fun int (fun int (product_prod int int))), norm_frac ) 15.91/16.04 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 15.91/16.04 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 15.91/16.04 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 15.91/16.04 ( (fun int (fun int (fun int bool))), zcong ) 15.91/16.04 ( (fun int (fun int (fun int bool))), zcongm ) 15.91/16.04 ( (fun int (fun int (fun int bool))), noXRRset ) 15.91/16.04 ( (fun int (fun int (fun int bool))), bnorRset ) 15.91/16.04 ( (fun int (fun int (fun int bool))), wset ) 15.91/16.04 ( (fun (product_prod int int) bool), frac_1 ) 15.91/16.04 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 15.91/16.04 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 15.91/16.04 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 15.91/16.04 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 15.91/16.04 ( (fun (fun nat rat) bool), vanishes ) 15.91/16.04 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 15.91/16.04 ( (fun code_code_numeral nat), code_c271388182l_size ) 15.91/16.04 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 15.91/16.04 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 15.91/16.04 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 15.91/16.04 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 15.91/16.04 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 15.91/16.04 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 15.91/16.04 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 15.91/16.04 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 15.91/16.04 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 15.91/16.04 ( (fun complex nat), complex_size ) 15.91/16.04 ( (fun complex nat), (size_size complex) ) 15.91/16.04 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 15.91/16.04 ( (fun nat (fun nat (product_prod int int))), bezw ) 15.91/16.04 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 15.91/16.04 ( (fun int (fun nat nat)), nat_aux ) 15.91/16.04 ( (fun int (fun (fun int bool) bool)), rsetR ) 15.91/16.04 ( (fun int (fun (fun int bool) bool)), resSet ) 15.91/16.04 ( (fun int (list int)), quickc666637781d_zero ) 15.91/16.04 ( (fun (product_prod int int) rat), frct ) 15.91/16.04 ( (fun int (fun int rat)), fract ) 15.91/16.04 ( (fun real (fun real complex)), complex_1 ) 15.91/16.04 ( (fun real (fun real complex)), rcis ) 15.91/16.04 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 15.91/16.04 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 15.91/16.04 ( (fun int real), (real_1 int) ) 15.91/16.04 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 15.91/16.04 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 15.91/16.04 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 15.91/16.04 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 15.91/16.04 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 15.91/16.04 ( (fun real nat), natfloor ) 15.91/16.04 ( (fun real nat), natceiling ) 15.91/16.04 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 15.91/16.04 ( (fun quickcheck_code_int int), quickcheck_int_of ) 15.91/16.04 ( (fun rat (product_prod int int)), quotient_of ) 15.91/16.04 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 15.91/16.04 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 15.91/16.04 ( (fun rat real), ratreal ) 15.91/16.04 ( (fun code_code_numeral int), code_int_of ) 15.91/16.04 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 15.91/16.04 ( (fun int quickcheck_code_int), quickcheck_of_int ) 15.91/16.04 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 15.91/16.04 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 15.91/16.04 ) 15.91/16.04 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_132033 $$unsorted) (BOUND_VARIABLE_132034 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (dvd_dvd X_a))) (or (not (linordered_idom X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_132033) BOUND_VARIABLE_132034)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_132033)) BOUND_VARIABLE_132034)))))) ) 15.91/16.04 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 15.91/16.04 ) 15.91/16.04 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_132060 $$unsorted) (BOUND_VARIABLE_132061 $$unsorted)) (let ((_let_0 (fun nat X_a))) (or (not (comm_monoid_add X_a)) (not (t2_space X_a)) (not (hBOOL (hAPP X_a bool (hAPP _let_0 (fun X_a bool) (sums X_a) BOUND_VARIABLE_132060) BOUND_VARIABLE_132061))) (= (hAPP _let_0 X_a (suminf X_a) BOUND_VARIABLE_132060) (ti X_a BOUND_VARIABLE_132061)))) ) 15.91/16.04 ( real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (hAPP real _let_1 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc))), (one_one real) ) 15.91/16.04 ) 15.91/16.04 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_132112 $$unsorted) (BOUND_VARIABLE_132113 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (times_times X_a))) (let ((_let_3 (inverse_inverse X_a))) (let ((_let_4 (plus_plus X_a))) (let ((_let_5 (hAPP X_a X_a _let_3 BOUND_VARIABLE_132113))) (let ((_let_6 (hAPP X_a X_a _let_3 BOUND_VARIABLE_132112))) (or (not (division_ring X_a)) (= _let_0 (ti X_a BOUND_VARIABLE_132113)) (= _let_0 (ti X_a BOUND_VARIABLE_132112)) (= (hAPP X_a X_a (hAPP X_a _let_1 _let_4 _let_5) _let_6) (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 _let_5) (hAPP X_a X_a (hAPP X_a _let_1 _let_4 BOUND_VARIABLE_132113) BOUND_VARIABLE_132112))) _let_6)))))))))) ) 15.91/16.04 ( nat, (one_one nat), (one_one nat) ) 15.91/16.04 ( int, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.91/16.04 ( int, (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.04 ) 15.91/16.04 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (power_power real))) (let ((_let_3 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_4 (hAPP complex real re X_1))) (= (hAPP real real (hAPP real _let_0 (inverse_divide real) _let_4) (hAPP real real (hAPP real _let_0 (plus_plus real) (hAPP nat real (hAPP real _let_1 _let_2 _let_4) _let_3)) (hAPP nat real (hAPP real _let_1 _let_2 (hAPP complex real im X_1)) _let_3))) (hAPP complex real re (hAPP complex complex (inverse_inverse complex) X_1)))))))) ) 15.91/16.04 ( (one_one complex) ) 15.91/16.04 ( ii ) 15.91/16.04 ( (zero_zero complex) ) 15.91/16.04 ) 15.91/16.04 (instantiation (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted) (F1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun X_c X_a))) (let ((_let_1 (product_prod X_b X_c))) (= (hAPP _let_1 X_a (hAPP (fun X_b _let_0) (fun _let_1 X_a) (product_prod_rec X_b X_c X_a) F1) (hAPP X_c _let_1 (hAPP X_b (fun X_c _let_1) (product_Pair X_b X_c) A_2) B_1)) (hAPP X_c X_a (hAPP X_b _let_0 F1 A_2) B_1)))) ) 15.91/16.04 ( nat, nat, bool, (ord_less nat), (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.04 ( nat, nat, nat, (plus_plus nat), (one_one nat), (one_one nat) ) 15.91/16.04 ( nat, real, real, root, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 15.91/16.04 ( nat, real, real, root, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real) ) 15.91/16.04 ( nat, real, real, root, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.04 ( nat, real, real, root, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.91/16.04 ( int, nat, int, (power_power int), s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.04 ( int, nat, int, (power_power int), s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.04 ( int, nat, int, (power_power int), skv_14, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.04 ( int, int, bool, (ord_less_eq int), (one_one int), t ) 15.91/16.04 ( int, int, bool, (ord_less_eq int), (zero_zero int), (one_one int) ) 15.91/16.04 ( int, int, bool, (ord_less_eq int), (zero_zero int), min_1 ) 15.91/16.04 ( int, int, bool, (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.04 ( int, int, bool, (ord_less_eq int), (zero_zero int), s ) 15.91/16.04 ( int, int, bool, (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.91/16.04 ( int, int, bool, (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.91/16.04 ( int, int, bool, (ord_less_eq int), (zero_zero int), skv_4 ) 15.91/16.04 ( int, int, bool, (ord_less_eq int), (zero_zero int), skv_10 ) 15.91/16.04 ( int, int, bool, (ord_less_eq int), min_1, pls ) 15.91/16.04 ( int, int, bool, (ord_less_eq int), min_1, min_1 ) 15.91/16.04 ( int, int, bool, (ord_less int), (one_one int), t ) 15.91/16.04 ( int, int, bool, (ord_less int), pls, (one_one int) ) 15.91/16.04 ( int, int, bool, (ord_less int), pls, pls ) 15.91/16.04 ( int, int, bool, (ord_less int), pls, min_1 ) 15.91/16.04 ( int, int, bool, (ord_less int), pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.04 ( int, int, bool, (ord_less int), min_1, pls ) 15.91/16.04 ( int, int, bool, (ord_less int), min_1, min_1 ) 15.91/16.04 ( int, int, bool, (ord_less int), s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.04 ( int, int, bool, (ord_less int), t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.04 ( int, int, bool, (ord_less int), skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.04 ( int, int, bool, (ord_less int), skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.04 ( int, int, bool, (dvd_dvd int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 15.91/16.04 ( int, int, bool, quadRes, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (number_number_of int) min_1) ) 15.91/16.04 ( int, int, bool, (hAPP int (fun int (fun int bool)) zcong s1), s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.04 ( int, int, bool, (hAPP int (fun int (fun int bool)) zcong s1), skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.04 ( int, int, bool, (hAPP int (fun int (fun int bool)) zcong s1), skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.04 ( int, int, bool, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.04 ( int, int, bool, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.04 ( int, int, bool, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.04 ( int, int, bool, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.04 ( int, int, int, (times_times int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 15.91/16.04 ( int, int, int, (times_times int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.91/16.04 ( int, int, int, (times_times int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13 ) 15.91/16.04 ( int, int, int, (minus_minus int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.91/16.04 ( int, int, int, (plus_plus int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 15.91/16.04 ( int, int, int, (plus_plus int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 15.91/16.04 ( int, int, int, legendre, (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.91/16.04 ( int, int, (fun int bool), zcong, s1, s ) 15.91/16.04 ( int, int, (fun int bool), zcong, s1, skv_4 ) 15.91/16.04 ( int, int, (fun int bool), zcong, s1, skv_10 ) 15.91/16.04 ( int, int, (fun int bool), zcong, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.91/16.04 ( int, int, (fun int bool), zcong, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.04 ( int, int, (fun int bool), zcong, (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.91/16.04 ( int, int, (fun int bool), zcong, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.91/16.04 ( int, int, rat, fract, (one_one int), (one_one int) ) 15.91/16.04 ( int, int, rat, fract, (zero_zero int), (one_one int) ) 15.91/16.04 ( int, int, (product_prod int int), (product_Pair int int), (one_one int), (one_one int) ) 15.91/16.04 ( int, int, (product_prod int int), (product_Pair int int), (zero_zero int), (one_one int) ) 15.91/16.04 ( int, int, (product_prod int int), (product_Pair int int), s, (one_one int) ) 15.91/16.04 ( int, (fun int bool), bool, (member int), (one_one int), zEven ) 15.91/16.04 ( (fun int (fun int bool)), int, (fun int bool), (combc int int bool), (fequal int), (zero_zero int) ) 15.91/16.04 ( (fun int (fun int bool)), (fun (product_prod int int) int), (fun (product_prod int int) (fun int bool)), (combb int (fun int bool) (product_prod int int)), (fequal int), (product_snd int int) ) 15.91/16.04 ( real, real, bool, (ord_less real), (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.04 ( real, real, bool, (ord_less real), (zero_zero real), pi ) 15.91/16.04 ( real, real, bool, (ord_less real), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.04 ( real, real, bool, (ord_less real), (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.04 ( real, real, bool, (ord_less real), (zero_zero real), skv_2 ) 15.91/16.04 ( real, real, bool, (ord_less real), (zero_zero real), skv_8 ) 15.91/16.04 ( real, real, bool, (ord_less real), (zero_zero real), skv_9 ) 15.91/16.04 ( real, real, bool, (ord_less real), pi, (zero_zero real) ) 15.91/16.04 ( real, real, bool, (ord_less real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.04 ( real, real, bool, (ord_less real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.04 ( real, real, bool, (ord_less real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 15.91/16.04 ( real, real, bool, (ord_less real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.91/16.04 ( real, real, bool, (ord_less real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 15.91/16.04 ( real, real, bool, (ord_less_eq real), (zero_zero real), pi ) 15.91/16.04 ( real, real, bool, (ord_less_eq real), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.04 ( real, real, bool, (ord_less_eq real), (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.04 ( real, real, bool, (ord_less_eq real), (zero_zero real), skv_3 ) 15.91/16.04 ( real, real, bool, (ord_less_eq real), (zero_zero real), skv_5 ) 15.91/16.04 ( real, real, bool, (ord_less_eq real), (zero_zero real), skv_7 ) 15.91/16.04 ( real, real, bool, (ord_less_eq real), (zero_zero real), skv_12 ) 15.91/16.04 ( real, real, bool, (ord_less_eq real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.91/16.04 ( real, real, bool, (ord_less_eq real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.04 ( real, real, bool, (ord_less_eq real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.91/16.04 ( real, real, bool, (ord_less_eq real), skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.04 ( real, real, real, (minus_minus real), (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 15.91/16.04 ( real, real, real, (inverse_divide real), (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.04 ( real, real, real, (inverse_divide real), (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.91/16.04 ( real, real, real, (inverse_divide real), (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.04 ( real, real, real, (inverse_divide real), (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 15.91/16.04 ( real, real, real, (inverse_divide real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.04 ( real, real, real, (inverse_divide real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.04 ( real, real, real, (inverse_divide real), pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.91/16.04 ( real, real, real, (inverse_divide real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.91/16.04 ( real, real, real, (inverse_divide real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.04 ( real, real, real, (inverse_divide real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.04 ( real, real, real, (inverse_divide real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.04 ( real, real, real, (times_times real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.91/16.04 ( real, real, real, (times_times real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.91/16.04 ( real, real, real, (times_times real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.91/16.04 ( real, real, real, (times_times real), (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 15.91/16.04 ( real, real, complex, complex_1, (one_one real), (zero_zero real) ) 15.91/16.04 ( real, real, complex, complex_1, (zero_zero real), (one_one real) ) 15.91/16.04 ( real, real, complex, complex_1, (zero_zero real), (zero_zero real) ) 15.91/16.04 ( real, (filter nat), bool, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 (fun real (fun (filter nat) bool)) (tendsto nat real) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))))), (zero_zero real), sequentially ) 15.91/16.04 ( real, (filter real), bool, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 (fun real (fun (filter real) bool)) (tendsto real real) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin)))), (zero_zero real), (hAPP real (filter real) (at real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.91/16.04 ( (fun real real), real, (fun (filter real) bool), (tendsto real real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real) ) 15.91/16.04 ( (fun real real), (fun nat real), (fun nat real), (combb real real nat), (inverse_inverse real), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))) ) 15.91/16.04 ( (fun nat (fun nat bool)), nat, (fun nat bool), (combc nat nat bool), (fequal nat), (zero_zero nat) ) 15.91/16.04 ( (fun nat (fun nat bool)), (fun nat nat), (fun nat (fun nat bool)), (combb nat (fun nat bool) nat), (let ((_let_0 (fun nat (fun nat bool)))) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat))), suc ) 15.91/16.04 ( (fun nat int), (fun nat bool), bool, (nat_tr1645093318rphism nat int), (semiring_1_of_nat int), (hAPP bool (fun nat bool) (combk bool nat) fTrue) ) 15.91/16.04 ( complex, nat, complex, (power_power complex), ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.04 ( complex, complex, complex, (times_times complex), ii, ii ) 15.91/16.04 ( complex, complex, complex, (times_times complex), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 15.91/16.04 ( complex, complex, complex, (times_times complex), (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 15.91/16.04 ( (fun nat real), (fun nat nat), (fun nat real), (combb nat real nat), (real_1 nat), suc ) 15.91/16.04 ( (fun nat real), (fun nat nat), (fun nat real), (combb nat real nat), (real_1 nat), (let ((_let_0 (fun nat (fun nat nat)))) (let ((_let_1 (combc nat nat nat))) (hAPP nat (fun nat nat) (hAPP _let_0 _let_0 _let_1 (hAPP (fun nat nat) _let_0 (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_0 _let_0 _let_1 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))) ) 15.91/16.04 ( (fun nat real), (fun nat nat), (fun nat real), (combb nat real nat), (hAPP real (fun nat real) (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), suc ) 15.91/16.04 ( (fun nat real), real, bool, (sums real), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (hAPP real _let_1 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc))), (one_one real) ) 15.91/16.04 ( (fun nat real), real, (fun (filter nat) bool), (tendsto nat real), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real) ) 15.91/16.04 ( (fun int (fun int int)), int, (fun int int), (combc int int int), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)) (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))))), (one_one int) ) 15.91/16.04 ( (fun int (fun int int)), (fun int int), (fun int (fun int int)), (combb int (fun int int) int), (plus_plus int), (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.91/16.04 ( (fun int (fun int int)), (fun int int), (fun int (fun int int)), (combb int (fun int int) int), (plus_plus int), (let ((_let_0 (fun int int))) (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.91/16.04 ( (fun int (fun int int)), (product_prod int int), int, (product_prod_case int int int), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun _let_0 _let_1))) (let ((_let_3 (fun _let_0 _let_0))) (let ((_let_4 (fun int _let_3))) (let ((_let_5 (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP _let_0 _let_1 (hAPP _let_4 _let_2 (combc int _let_0 _let_0) (hAPP _let_1 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_1 _let_4) (combb _let_0 _let_3 int) (combb int int int)) (hAPP _let_0 _let_1 (hAPP _let_1 _let_2 (combb int _let_0 int) (plus_plus int)) _let_5))) _let_5))))))), (let ((_let_0 (product_prod int int))) (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) s) (one_one int))) ) 15.91/16.04 ( (fun int (fun int int)), (fun (product_prod int int) int), (fun (product_prod int int) (fun int int)), (combb int (fun int int) (product_prod int int)), (times_times int), (product_fst int int) ) 15.91/16.04 ( (fun int nat), (fun int bool), bool, (nat_tr1645093318rphism int nat), nat_1, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 15.91/16.04 ( (fun (fun int bool) bool), (fun int (fun int bool)), (fun int bool), (combb (fun int bool) bool int), (fEx int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun _let_2 _let_0))) (let ((_let_4 (fun int _let_3))) (hAPP _let_2 _let_1 (hAPP _let_4 (fun _let_2 _let_1) (combc int _let_2 _let_0) (hAPP _let_1 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_1 _let_4) (combb _let_0 _let_3 int) (combb int bool int)) (fequal int))) (hAPP int _let_2 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))))))) ) 15.91/16.04 ( (fun (fun int bool) bool), (fun int (fun int bool)), (fun int bool), (combb (fun int bool) bool int), (fEx int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun _let_2 _let_0))) (let ((_let_5 (fun int _let_4))) (hAPP _let_2 _let_1 (hAPP _let_5 (fun _let_2 _let_1) (combc int _let_2 _let_0) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_1 _let_5) (combb _let_0 _let_4 int) (combb int bool int)) (fequal int))) (hAPP int _let_2 (hAPP _let_3 _let_3 (combc int int int) (hAPP _let_2 _let_3 (hAPP _let_3 (fun _let_2 _let_3) (combb int _let_2 int) (plus_plus int)) (hAPP int _let_2 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one int))))))))) ) 15.91/16.05 ( (fun (fun int bool) bool), (fun real (fun int bool)), (fun real bool), (combb (fun int bool) bool real), (fEx int), (let ((_let_0 (fun int (fun int bool)))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real real))) (let ((_let_3 (real_1 int))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun int _let_4))) (let ((_let_7 (fun (fun int bool) (fun int bool)))) (let ((_let_8 (fun (fun int bool) _let_6))) (let ((_let_9 (fun _let_0 (fun int bool)))) (let ((_let_10 (fun int real))) (let ((_let_11 (fun int _let_7))) (let ((_let_12 (fun (fun int bool) _let_0))) (let ((_let_13 (fun int _let_6))) (let ((_let_14 (fun _let_13 _let_11))) (let ((_let_15 (fun _let_0 _let_13))) (let ((_let_16 (fun real (fun int bool)))) (let ((_let_17 (fun real _let_0))) (let ((_let_18 (fun real _let_12))) (let ((_let_19 (fun real _let_11))) (let ((_let_20 (fun real _let_13))) (let ((_let_21 (fun int _let_10))) (let ((_let_22 (fun _let_21 _let_0))) (let ((_let_23 (fun real _let_22))) (let ((_let_24 (fun _let_10 (fun int bool)))) (let ((_let_25 (fun real _let_24))) (let ((_let_26 (fun _let_10 _let_10))) (let ((_let_27 (fun int _let_26))) (let ((_let_28 (fun int _let_2))) (hAPP _let_17 _let_16 (hAPP _let_9 (fun _let_17 _let_16) (combb _let_0 (fun int bool) real) (hAPP (fun (fun int bool) bool) _let_9 (combb (fun int bool) bool int) (fEx int))) (hAPP (fun int bool) _let_17 (hAPP _let_18 (fun (fun int bool) _let_17) (combc real (fun int bool) _let_0) (hAPP _let_19 _let_18 (hAPP (fun _let_11 _let_12) (fun _let_19 _let_18) (combb _let_11 _let_12 real) (combc int (fun int bool) (fun int bool))) (hAPP _let_20 _let_19 (hAPP _let_14 (fun _let_20 _let_19) (combb _let_13 _let_11 real) (hAPP (fun _let_6 _let_7) _let_14 (combb _let_6 _let_7 int) (combs int bool bool))) (hAPP _let_17 _let_20 (hAPP _let_15 (fun _let_17 _let_20) (combb _let_0 _let_13 real) (hAPP _let_8 _let_15 (combb (fun int bool) _let_6 int) (hAPP (fun bool _let_4) _let_8 (combb bool _let_4 int) fconj))) (hAPP _let_21 _let_17 (hAPP _let_23 (fun _let_21 _let_17) (combc real _let_21 _let_0) (hAPP _let_25 _let_23 (hAPP (fun _let_24 _let_22) (fun _let_25 _let_23) (combb _let_24 _let_22 real) (combb _let_10 (fun int bool) int)) (hAPP _let_5 _let_25 (hAPP (fun _let_1 _let_24) (fun _let_5 _let_25) (combb _let_1 _let_24 real) (combb real bool int)) (fequal real)))) (hAPP _let_10 _let_21 (hAPP _let_27 (fun _let_10 _let_21) (combc int _let_10 _let_10) (hAPP _let_28 _let_27 (hAPP (fun _let_2 _let_26) (fun _let_28 _let_27) (combb _let_2 _let_26 int) (combb real real int)) (hAPP _let_10 _let_28 (hAPP (fun real _let_2) (fun _let_10 _let_28) (combb real _let_2 int) (inverse_divide real)) _let_3))) _let_3)))))) (hAPP (fun int bool) (fun int bool) (hAPP _let_4 _let_7 (combb bool bool int) fNot) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (fequal int)) (zero_zero int)))))))))))))))))))))))))))))))))) ) 15.91/16.05 ( (fun (fun int bool) bool), (fun real (fun int bool)), (fun real bool), (combb (fun int bool) bool real), (fEx int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real real))) (let ((_let_3 (fun nat (fun nat bool)))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun (fun nat real) (fun nat real)))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun (fun nat bool) (fun nat bool)))) (let ((_let_8 (fun int real))) (let ((_let_9 (fun nat _let_4))) (let ((_let_10 (fun (fun nat bool) _let_9))) (let ((_let_11 (fun real _let_0))) (let ((_let_12 (fun int _let_2))) (let ((_let_13 (fun real (fun int (fun nat bool))))) (let ((_let_14 (fun (fun int (fun nat bool)) _let_0))) (let ((_let_15 (fun (fun nat bool) (fun int (fun nat bool))))) (let ((_let_16 (fun real _let_15))) (let ((_let_17 (fun int _let_7))) (let ((_let_18 (fun real _let_17))) (let ((_let_19 (fun int _let_9))) (let ((_let_20 (fun real _let_19))) (let ((_let_21 (fun _let_19 _let_17))) (let ((_let_22 (fun (fun int (fun nat bool)) _let_19))) (let ((_let_23 (fun int (fun nat real)))) (let ((_let_24 (fun _let_23 (fun int (fun nat bool))))) (let ((_let_25 (fun real _let_24))) (let ((_let_26 (fun (fun nat real) (fun nat bool)))) (let ((_let_27 (fun real _let_26))) (let ((_let_28 (fun int _let_5))) (hAPP _let_13 _let_11 (hAPP _let_14 (fun _let_13 _let_11) (combb (fun int (fun nat bool)) _let_0 real) (hAPP (fun (fun nat bool) bool) _let_14 (combb (fun nat bool) bool int) (fEx nat))) (hAPP (fun nat bool) _let_13 (hAPP _let_16 (fun (fun nat bool) _let_13) (combc real (fun nat bool) (fun int (fun nat bool))) (hAPP _let_18 _let_16 (hAPP (fun _let_17 _let_15) (fun _let_18 _let_16) (combb _let_17 _let_15 real) (combc int (fun nat bool) (fun nat bool))) (hAPP _let_20 _let_18 (hAPP _let_21 (fun _let_20 _let_18) (combb _let_19 _let_17 real) (hAPP (fun _let_9 _let_7) _let_21 (combb _let_9 _let_7 int) (combs nat bool bool))) (hAPP _let_13 _let_20 (hAPP _let_22 (fun _let_13 _let_20) (combb (fun int (fun nat bool)) _let_19 real) (hAPP _let_10 _let_22 (combb (fun nat bool) _let_9 int) (hAPP (fun bool _let_4) _let_10 (combb bool _let_4 nat) fconj))) (hAPP _let_23 _let_13 (hAPP _let_25 (fun _let_23 _let_13) (combc real _let_23 (fun int (fun nat bool))) (hAPP _let_27 _let_25 (hAPP (fun _let_26 _let_24) (fun _let_27 _let_25) (combb _let_26 _let_24 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_6 _let_27 (hAPP (fun _let_1 _let_26) (fun _let_6 _let_27) (combb _let_1 _let_26 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_23 (hAPP _let_28 (fun (fun nat real) _let_23) (combc int (fun nat real) (fun nat real)) (hAPP _let_12 _let_28 (hAPP (fun _let_2 _let_5) (fun _let_12 _let_28) (combb _let_2 _let_5 int) (combb real real nat)) (hAPP _let_8 _let_12 (hAPP (fun real _let_2) (fun _let_8 _let_12) (combb real _let_2 int) (inverse_divide real)) (real_1 int)))) (real_1 nat))))))) (hAPP (fun nat bool) (fun nat bool) (hAPP _let_4 _let_7 (combb bool bool nat) fNot) (hAPP nat (fun nat bool) (hAPP _let_3 _let_3 (combc nat nat bool) (fequal nat)) (zero_zero nat)))))))))))))))))))))))))))))))))) ) 15.91/16.05 ( (fun nat (fun nat nat)), nat, (fun nat nat), (combc nat nat nat), (times_times nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.91/16.05 ( (fun nat (fun nat nat)), nat, (fun nat nat), (combc nat nat nat), (let ((_let_0 (fun nat (fun nat nat)))) (hAPP (fun nat nat) _let_0 (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_0 _let_0 (combc nat nat nat) (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))), (one_one nat) ) 15.91/16.05 ( (fun nat (fun nat nat)), (fun nat nat), (fun nat (fun nat nat)), (combb nat (fun nat nat) nat), (plus_plus nat), (let ((_let_0 (fun nat (fun nat nat)))) (hAPP nat (fun nat nat) (hAPP _let_0 _let_0 (combc nat nat nat) (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.91/16.05 ( (fun bool bool), (fun int bool), (fun int bool), (combb bool bool int), fNot, (let ((_let_0 (fun int (fun int bool)))) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (fequal int)) (zero_zero int))) ) 15.91/16.05 ( (fun bool bool), (fun nat bool), (fun nat bool), (combb bool bool nat), fNot, (let ((_let_0 (fun nat (fun nat bool)))) (hAPP nat (fun nat bool) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat)) (zero_zero nat))) ) 15.91/16.05 ( (fun bool bool), (fun (product_prod int int) bool), (fun (product_prod int int) bool), (combb bool bool (product_prod int int)), fNot, (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun _let_1 _let_0))) (let ((_let_4 (fun _let_1 int))) (hAPP int _let_2 (hAPP _let_3 (fun int _let_2) (combc _let_1 int bool) (hAPP _let_4 _let_3 (hAPP (fun int _let_0) (fun _let_4 _let_3) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))) ) 15.91/16.05 ( (fun nat (fun real real)), real, (fun nat real), (combc nat real real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 nat) (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))))), (one_one real) ) 15.91/16.05 ( (fun nat (fun real real)), (fun nat real), (fun nat real), (combs nat real real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (let ((_let_3 (fun real _let_0))) (let ((_let_4 (fun _let_1 _let_2))) (let ((_let_5 (combb real _let_0 nat))) (hAPP _let_1 _let_2 (hAPP _let_3 _let_4 _let_5 (inverse_divide real)) (hAPP real _let_1 (hAPP _let_2 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_2 (hAPP _let_3 _let_4 _let_5 (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) (one_one real))))))))), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat (fun nat nat)))) (let ((_let_2 (combc nat nat nat))) (hAPP (fun nat nat) _let_0 (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat real nat) (real_1 nat)) (hAPP nat (fun nat nat) (hAPP _let_1 _let_1 _let_2 (hAPP (fun nat nat) _let_1 (hAPP _let_1 (fun (fun nat nat) _let_1) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_1 _let_1 _let_2 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))))) ) 15.91/16.05 ( (fun real (fun real real)), (fun real real), (fun real real), (combs real real real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos))), sin ) 15.91/16.05 ( (fun real (fun real real)), (fun real real), (fun real (fun real real)), (combb real (fun real real) real), (inverse_divide real), cos ) 15.91/16.05 ( (fun real (fun real real)), (fun nat real), (fun nat (fun real real)), (combb real (fun real real) nat), (inverse_divide real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (hAPP real _let_1 (hAPP _let_2 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 nat) (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) (one_one real))))) ) 15.91/16.05 ( (fun real (fun real real)), (fun nat real), (fun nat (fun real real)), (combb real (fun real real) nat), (times_times real), (hAPP real (fun nat real) (power_power real) (hAPP int real (number_number_of real) min_1)) ) 15.91/16.05 ( (fun real (fun real real)), (fun int real), (fun int (fun real real)), (combb real (fun real real) int), (inverse_divide real), (real_1 int) ) 15.91/16.05 ( (fun bool (fun bool bool)), (fun int bool), (fun int (fun bool bool)), (combb bool (fun bool bool) int), fconj, (hAPP int (fun int bool) (ord_less int) (zero_zero int)) ) 15.91/16.05 ( (fun bool (fun bool bool)), (fun real bool), (fun real (fun bool bool)), (combb bool (fun bool bool) real), fconj, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) ) 15.91/16.05 ( (fun bool (fun bool bool)), (fun real bool), (fun real (fun bool bool)), (combb bool (fun bool bool) real), fconj, (let ((_let_0 (fun real (fun real bool)))) (hAPP real (fun real bool) (hAPP _let_0 _let_0 (combc real real bool) (ord_less_eq real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.99/16.08 ( (fun bool (fun bool bool)), (fun (product_prod int int) bool), (fun (product_prod int int) (fun bool bool)), (combb bool (fun bool bool) (product_prod int int)), fconj, (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun _let_1 _let_0))) (let ((_let_4 (fun _let_1 int))) (hAPP _let_2 _let_2 (hAPP (fun bool bool) (fun _let_2 _let_2) (combb bool bool _let_1) fNot) (hAPP int _let_2 (hAPP _let_3 (fun int _let_2) (combc _let_1 int bool) (hAPP _let_4 _let_3 (hAPP (fun int _let_0) (fun _let_4 _let_3) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int)))))))) ) 15.99/16.08 ( code_code_numeral, code_code_numeral, code_code_numeral, (minus_minus code_code_numeral), (zero_zero code_code_numeral), (one_one code_code_numeral) ) 15.99/16.08 ( (fun int (fun int (fun int bool))), int, (fun int (fun int bool)), (combc int int (fun int bool)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int _let_1))) (let ((_let_5 (fun _let_2 _let_1))) (hAPP _let_4 _let_4 (hAPP (fun _let_1 _let_1) (fun _let_4 _let_4) (combb _let_1 _let_1 int) (combc int int bool)) (hAPP _let_3 _let_4 (hAPP _let_5 (fun _let_3 _let_4) (combb _let_2 _let_1 int) (hAPP _let_1 _let_5 (combb int _let_0 int) (fequal int))) int_gcd)))))))), (one_one int) ) 15.99/16.08 ( (fun real (fun real bool)), real, (fun real bool), (combc real real bool), (ord_less_eq real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.08 ( (fun real (fun real bool)), real, (fun real bool), (combc real real bool), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun real _let_0))) (hAPP _let_1 _let_2 (hAPP _let_2 (fun _let_1 _let_2) (combb real _let_0 real) (fequal real)) cos)))), (zero_zero real) ) 15.99/16.08 ( (fun real (fun real bool)), (fun real real), (fun real (fun real bool)), (combb real (fun real bool) real), (fequal real), cos ) 15.99/16.08 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), (fun int (fun int bool)), (fun int (fun int bool)), (let ((_let_0 (fun int bool))) (combb _let_0 _let_0 int)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun int _let_1))) (hAPP _let_2 (fun _let_0 _let_0) (combs int bool bool) (hAPP _let_0 _let_2 (hAPP (fun bool _let_1) (fun _let_0 _let_2) (combb bool _let_1 int) fconj) (hAPP int _let_0 (ord_less int) (zero_zero int))))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int _let_1))) (let ((_let_5 (fun _let_2 _let_1))) (hAPP int _let_1 (hAPP _let_4 _let_4 (combc int int _let_0) (hAPP _let_4 _let_4 (hAPP (fun _let_1 _let_1) (fun _let_4 _let_4) (combb _let_1 _let_1 int) (combc int int bool)) (hAPP _let_3 _let_4 (hAPP _let_5 (fun _let_3 _let_4) (combb _let_2 _let_1 int) (hAPP _let_1 _let_5 (combb int _let_0 int) (fequal int))) int_gcd))) (one_one int)))))))) ) 15.99/16.08 ( (let ((_let_0 (fun int bool))) (fun (fun int _let_0) _let_0)), (fun real (fun int (fun int bool))), (fun real (fun int bool)), (let ((_let_0 (fun int bool))) (combb (fun int _let_0) _let_0 real)), (let ((_let_0 (fun int bool))) (hAPP (fun _let_0 bool) (fun (fun int _let_0) _let_0) (combb _let_0 bool int) (fEx int))), (let ((_let_0 (fun int (fun int bool)))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real real))) (let ((_let_3 (real_1 int))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun int _let_4))) (let ((_let_7 (fun (fun int bool) (fun int bool)))) (let ((_let_8 (fun (fun int bool) _let_6))) (let ((_let_9 (fun int real))) (let ((_let_10 (fun int _let_7))) (let ((_let_11 (fun (fun int bool) _let_0))) (let ((_let_12 (fun int _let_6))) (let ((_let_13 (fun _let_12 _let_10))) (let ((_let_14 (fun _let_0 _let_12))) (let ((_let_15 (fun real _let_0))) (let ((_let_16 (fun real _let_11))) (let ((_let_17 (fun real _let_10))) (let ((_let_18 (fun real _let_12))) (let ((_let_19 (fun int _let_9))) (let ((_let_20 (fun _let_19 _let_0))) (let ((_let_21 (fun real _let_20))) (let ((_let_22 (fun _let_9 (fun int bool)))) (let ((_let_23 (fun real _let_22))) (let ((_let_24 (fun _let_9 _let_9))) (let ((_let_25 (fun int _let_24))) (let ((_let_26 (fun int _let_2))) (hAPP (fun int bool) _let_15 (hAPP _let_16 (fun (fun int bool) _let_15) (combc real (fun int bool) _let_0) (hAPP _let_17 _let_16 (hAPP (fun _let_10 _let_11) (fun _let_17 _let_16) (combb _let_10 _let_11 real) (combc int (fun int bool) (fun int bool))) (hAPP _let_18 _let_17 (hAPP _let_13 (fun _let_18 _let_17) (combb _let_12 _let_10 real) (hAPP (fun _let_6 _let_7) _let_13 (combb _let_6 _let_7 int) (combs int bool bool))) (hAPP _let_15 _let_18 (hAPP _let_14 (fun _let_15 _let_18) (combb _let_0 _let_12 real) (hAPP _let_8 _let_14 (combb (fun int bool) _let_6 int) (hAPP (fun bool _let_4) _let_8 (combb bool _let_4 int) fconj))) (hAPP _let_19 _let_15 (hAPP _let_21 (fun _let_19 _let_15) (combc real _let_19 _let_0) (hAPP _let_23 _let_21 (hAPP (fun _let_22 _let_20) (fun _let_23 _let_21) (combb _let_22 _let_20 real) (combb _let_9 (fun int bool) int)) (hAPP _let_5 _let_23 (hAPP (fun _let_1 _let_22) (fun _let_5 _let_23) (combb _let_1 _let_22 real) (combb real bool int)) (fequal real)))) (hAPP _let_9 _let_19 (hAPP _let_25 (fun _let_9 _let_19) (combc int _let_9 _let_9) (hAPP _let_26 _let_25 (hAPP (fun _let_2 _let_24) (fun _let_26 _let_25) (combb _let_2 _let_24 int) (combb real real int)) (hAPP _let_9 _let_26 (hAPP (fun real _let_2) (fun _let_9 _let_26) (combb real _let_2 int) (inverse_divide real)) _let_3))) _let_3)))))) (hAPP (fun int bool) (fun int bool) (hAPP _let_4 _let_7 (combb bool bool int) fNot) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (fequal int)) (zero_zero int))))))))))))))))))))))))))))))) ) 15.99/16.08 ( (fun int (fun (fun int int) (fun int bool))), (fun int int), (fun int (fun int bool)), (combc int (fun int int) (fun int bool)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun (fun int int) _let_0))) (let ((_let_3 (fun int _let_2))) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 int) (combb int bool int)) (fequal int)))))), (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.08 ( (fun int (fun (fun int int) (fun int bool))), (fun int int), (fun int (fun int bool)), (combc int (fun int int) (fun int bool)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun (fun int int) _let_0))) (let ((_let_3 (fun int _let_2))) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 int) (combb int bool int)) (fequal int)))))), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (hAPP int _let_0 (hAPP _let_1 _let_1 (combc int int int) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)) (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one int)))) ) 15.99/16.08 ( (fun (fun int int) (fun int (fun int bool))), (fun int (fun int int)), (fun int (fun int (fun int bool))), (combb (fun int int) (fun int (fun int bool)) int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (hAPP _let_1 (fun (fun int int) _let_1) (combb int _let_0 int) (fequal int)))), int_gcd ) 15.99/16.08 ( (let ((_let_0 (fun int bool))) (fun _let_0 (fun (fun int int) _let_0))), (fun int (fun int bool)), (fun int (fun (fun int int) (fun int bool))), (let ((_let_0 (fun int bool))) (combb _let_0 (fun (fun int int) _let_0) int)), (combb int bool int), (fequal int) ) 15.99/16.08 ( (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 bool))) (combb _let_1 _let_1 _let_0))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_3 _let_3))) (let ((_let_5 (fun _let_1 _let_2))) (let ((_let_6 (fun _let_1 _let_0))) (let ((_let_7 (fun _let_1 int))) (hAPP _let_5 _let_4 (combs _let_1 bool bool) (hAPP _let_3 _let_5 (hAPP (fun bool _let_2) (fun _let_3 _let_5) (combb bool _let_2 _let_1) fconj) (hAPP _let_3 _let_3 (hAPP _let_2 _let_4 (combb bool bool _let_1) fNot) (hAPP int _let_3 (hAPP _let_6 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_7 _let_6 (hAPP (fun int _let_0) (fun _let_7 _let_6) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))))))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun _let_2 (fun _let_2 bool)))) (let ((_let_4 (fun _let_2 _let_0))) (let ((_let_5 (fun _let_2 int))) (let ((_let_6 (fun _let_5 _let_4))) (let ((_let_7 (product_snd int int))) (let ((_let_8 (fun _let_2 _let_5))) (let ((_let_9 (fun _let_5 (fun _let_2 bool)))) (let ((_let_10 (fun _let_2 _let_9))) (let ((_let_11 (fun _let_2 _let_4))) (let ((_let_12 (fun _let_5 _let_5))) (let ((_let_13 (fun _let_2 _let_12))) (let ((_let_14 (fun _let_5 _let_8))) (let ((_let_15 (fun _let_2 _let_1))) (let ((_let_16 (hAPP _let_5 _let_15 (hAPP (fun int _let_1) (fun _let_5 _let_15) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (let ((_let_17 (fun int _let_5))) (hAPP _let_8 _let_3 (hAPP _let_10 (fun _let_8 _let_3) (combs _let_2 _let_5 (fun _let_2 bool)) (hAPP _let_11 _let_10 (hAPP (fun _let_4 _let_9) (fun _let_11 _let_10) (combb _let_4 _let_9 _let_2) (combs _let_2 int bool)) (hAPP _let_8 _let_11 (hAPP _let_6 (fun _let_8 _let_11) (combb _let_5 _let_4 _let_2) (hAPP (fun int _let_0) _let_6 (combb int _let_0 _let_2) (fequal int))) (hAPP _let_5 _let_8 (hAPP _let_13 _let_14 (combc _let_2 _let_5 _let_5) (hAPP _let_15 _let_13 (hAPP (fun _let_1 _let_12) (fun _let_15 _let_13) (combb _let_1 _let_12 _let_2) (combb int int _let_2)) _let_16)) _let_7)))) (hAPP _let_5 _let_8 (hAPP _let_17 _let_14 (combb int _let_5 _let_2) (hAPP _let_15 _let_17 (combc _let_2 int int) _let_16)) _let_7)))))))))))))))))))) ) 15.99/16.08 ( (let ((_let_0 (fun (product_prod int int) bool))) (fun (product_prod int int) (fun _let_0 _let_0))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (fun (product_prod int int) bool))) (combs (product_prod int int) _let_0 _let_0)), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_3 _let_3))) (let ((_let_5 (fun _let_1 _let_4))) (let ((_let_6 (fun _let_1 _let_2))) (let ((_let_7 (combb bool bool _let_1))) (let ((_let_8 (fun _let_1 _let_0))) (let ((_let_9 (fun _let_1 int))) (hAPP _let_6 _let_5 (hAPP (fun _let_2 _let_4) (fun _let_6 _let_5) (combb _let_2 _let_4 _let_1) _let_7) (hAPP _let_3 _let_6 (hAPP (fun bool _let_2) (fun _let_3 _let_6) (combb bool _let_2 _let_1) fconj) (hAPP _let_3 _let_3 (hAPP _let_2 _let_4 _let_7 fNot) (hAPP int _let_3 (hAPP _let_8 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_9 _let_8 (hAPP (fun int _let_0) (fun _let_9 _let_8) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))))))))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun _let_2 (fun _let_2 bool)))) (let ((_let_5 (fun (fun _let_2 bool) (fun _let_2 bool)))) (let ((_let_6 (fun _let_2 _let_3))) (let ((_let_7 (fun _let_2 _let_0))) (let ((_let_8 (fun _let_2 int))) (let ((_let_9 (fun _let_8 _let_7))) (let ((_let_10 (hAPP (fun int _let_0) _let_9 (combb int _let_0 _let_2) (fequal int)))) (let ((_let_11 (product_snd int int))) (let ((_let_12 (fun _let_2 _let_8))) (let ((_let_13 (fun _let_8 (fun _let_2 bool)))) (let ((_let_14 (fun _let_2 _let_13))) (let ((_let_15 (fun _let_2 _let_7))) (let ((_let_16 (fun _let_8 _let_8))) (let ((_let_17 (fun _let_2 _let_16))) (let ((_let_18 (fun _let_8 _let_12))) (let ((_let_19 (fun _let_2 _let_1))) (let ((_let_20 (hAPP _let_8 _let_19 (hAPP (fun int _let_1) (fun _let_8 _let_19) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (let ((_let_21 (fun int _let_8))) (hAPP _let_4 _let_4 (hAPP _let_5 (fun _let_4 _let_4) (combb (fun _let_2 bool) (fun _let_2 bool) _let_2) (hAPP _let_6 _let_5 (combs _let_2 bool bool) (hAPP (fun _let_2 bool) _let_6 (hAPP (fun bool _let_3) (fun (fun _let_2 bool) _let_6) (combb bool _let_3 _let_2) fconj) (hAPP (fun _let_2 bool) (fun _let_2 bool) (hAPP _let_3 _let_5 (combb bool bool _let_2) fNot) (hAPP int (fun _let_2 bool) (hAPP _let_7 (fun int (fun _let_2 bool)) (combc _let_2 int bool) (hAPP _let_8 _let_7 _let_10 _let_11)) (zero_zero int)))))) (hAPP _let_12 _let_4 (hAPP _let_14 (fun _let_12 _let_4) (combs _let_2 _let_8 (fun _let_2 bool)) (hAPP _let_15 _let_14 (hAPP (fun _let_7 _let_13) (fun _let_15 _let_14) (combb _let_7 _let_13 _let_2) (combs _let_2 int bool)) (hAPP _let_12 _let_15 (hAPP _let_9 (fun _let_12 _let_15) (combb _let_8 _let_7 _let_2) _let_10) (hAPP _let_8 _let_12 (hAPP _let_17 _let_18 (combc _let_2 _let_8 _let_8) (hAPP _let_19 _let_17 (hAPP (fun _let_1 _let_16) (fun _let_19 _let_17) (combb _let_1 _let_16 _let_2) (combb int int _let_2)) _let_20)) _let_11)))) (hAPP _let_8 _let_12 (hAPP _let_21 _let_18 (combb int _let_8 _let_2) (hAPP _let_19 _let_21 (combc _let_2 int int) _let_20)) _let_11))))))))))))))))))))))))) ) 15.99/16.08 ( (let ((_let_0 (fun (product_prod int int) bool))) (fun (fun bool bool) (fun _let_0 _let_0))), (fun (product_prod int int) (fun bool bool)), (let ((_let_0 (fun (product_prod int int) bool))) (fun (product_prod int int) (fun _let_0 _let_0))), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 bool))) (combb (fun bool bool) (fun _let_1 _let_1) _let_0))), (combb bool bool (product_prod int int)), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_1 _let_2))) (let ((_let_5 (fun _let_1 _let_0))) (let ((_let_6 (fun _let_1 int))) (hAPP _let_3 _let_4 (hAPP (fun bool _let_2) (fun _let_3 _let_4) (combb bool _let_2 _let_1) fconj) (hAPP _let_3 _let_3 (hAPP _let_2 (fun _let_3 _let_3) (combb bool bool _let_1) fNot) (hAPP int _let_3 (hAPP _let_5 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_6 _let_5 (hAPP (fun int _let_0) (fun _let_6 _let_5) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))))))) ) 15.99/16.08 ( (fun (product_prod int int) (fun int bool)), int, (fun (product_prod int int) bool), (combc (product_prod int int) int bool), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 _let_0))) (let ((_let_3 (fun _let_1 int))) (hAPP _let_3 _let_2 (hAPP (fun int _let_0) (fun _let_3 _let_2) (combb int _let_0 _let_1) (fequal int)) (product_snd int int)))))), (zero_zero int) ) 15.99/16.08 ( (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 (fun int bool)))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 (fun int bool)))), (let ((_let_0 (product_prod int int))) (combb (fun _let_0 int) (fun _let_0 (fun int bool)) _let_0)), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (hAPP (fun int _let_0) (fun (fun _let_1 int) (fun _let_1 _let_0)) (combb int _let_0 _let_1) (fequal int)))), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_2))) (let ((_let_4 (fun _let_2 _let_2))) (let ((_let_5 (fun _let_1 _let_4))) (let ((_let_6 (fun _let_1 _let_0))) (hAPP _let_2 _let_3 (hAPP _let_5 (fun _let_2 _let_3) (combc _let_1 _let_2 _let_2) (hAPP _let_6 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_6 _let_5) (combb _let_0 _let_4 _let_1) (combb int int _let_1)) (hAPP _let_2 _let_6 (hAPP (fun int _let_0) (fun _let_2 _let_6) (combb int _let_0 _let_1) (times_times int)) (product_fst int int)))) (product_snd int int))))))))) ) 15.99/16.08 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun (fun _let_0 int) (fun _let_0 bool)))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (combs _let_0 (fun _let_0 int) (fun _let_0 bool))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun _let_2 _let_0))) (let ((_let_4 (fun _let_2 int))) (let ((_let_5 (fun _let_4 _let_3))) (let ((_let_6 (fun _let_2 _let_4))) (let ((_let_7 (fun _let_4 (fun _let_2 bool)))) (let ((_let_8 (fun _let_2 _let_7))) (let ((_let_9 (fun _let_2 _let_3))) (let ((_let_10 (fun _let_4 _let_4))) (let ((_let_11 (fun _let_2 _let_10))) (let ((_let_12 (fun _let_2 _let_1))) (hAPP _let_9 _let_8 (hAPP (fun _let_3 _let_7) (fun _let_9 _let_8) (combb _let_3 _let_7 _let_2) (combs _let_2 int bool)) (hAPP _let_6 _let_9 (hAPP _let_5 (fun _let_6 _let_9) (combb _let_4 _let_3 _let_2) (hAPP (fun int _let_0) _let_5 (combb int _let_0 _let_2) (fequal int))) (hAPP _let_4 _let_6 (hAPP _let_11 (fun _let_4 _let_6) (combc _let_2 _let_4 _let_4) (hAPP _let_12 _let_11 (hAPP (fun _let_1 _let_10) (fun _let_12 _let_11) (combb _let_1 _let_10 _let_2) (combb int int _let_2)) (hAPP _let_4 _let_12 (hAPP (fun int _let_1) (fun _let_4 _let_12) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (product_snd int int))))))))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_2))) (let ((_let_4 (fun _let_1 _let_0))) (let ((_let_5 (fun int _let_2))) (hAPP _let_2 _let_3 (hAPP _let_5 (fun _let_2 _let_3) (combb int _let_2 _let_1) (hAPP _let_4 _let_5 (combc _let_1 int int) (hAPP _let_2 _let_4 (hAPP (fun int _let_0) (fun _let_2 _let_4) (combb int _let_0 _let_1) (times_times int)) (product_fst int int)))) (product_snd int int)))))))) ) 15.99/16.08 ( (let ((_let_0 (product_prod int int))) (fun (fun _let_0 (fun int bool)) (fun (fun _let_0 int) (fun _let_0 bool)))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 (fun int bool)))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun (fun _let_0 int) (fun _let_0 bool)))), (let ((_let_0 (product_prod int int))) (combb (fun _let_0 (fun int bool)) (fun (fun _let_0 int) (fun _let_0 bool)) _let_0)), (combs (product_prod int int) int bool), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun _let_2 _let_0))) (let ((_let_4 (fun _let_2 int))) (let ((_let_5 (fun _let_4 _let_3))) (let ((_let_6 (fun _let_2 _let_4))) (let ((_let_7 (fun _let_2 _let_3))) (let ((_let_8 (fun _let_4 _let_4))) (let ((_let_9 (fun _let_2 _let_8))) (let ((_let_10 (fun _let_2 _let_1))) (hAPP _let_6 _let_7 (hAPP _let_5 (fun _let_6 _let_7) (combb _let_4 _let_3 _let_2) (hAPP (fun int _let_0) _let_5 (combb int _let_0 _let_2) (fequal int))) (hAPP _let_4 _let_6 (hAPP _let_9 (fun _let_4 _let_6) (combc _let_2 _let_4 _let_4) (hAPP _let_10 _let_9 (hAPP (fun _let_1 _let_8) (fun _let_10 _let_9) (combb _let_1 _let_8 _let_2) (combb int int _let_2)) (hAPP _let_4 _let_10 (hAPP (fun int _let_1) (fun _let_4 _let_10) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (product_snd int int)))))))))))))) ) 15.99/16.08 ( (let ((_let_0 (fun (product_prod int int) int))) (fun (product_prod int int) (fun _let_0 _let_0))), (fun (product_prod int int) int), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (let ((_let_0 (fun (product_prod int int) int))) (combc (product_prod int int) _let_0 _let_0)), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_2 _let_2))) (let ((_let_4 (fun _let_1 _let_3))) (let ((_let_5 (fun _let_1 _let_0))) (hAPP _let_5 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_5 _let_4) (combb _let_0 _let_3 _let_1) (combb int int _let_1)) (hAPP _let_2 _let_5 (hAPP (fun int _let_0) (fun _let_2 _let_5) (combb int _let_0 _let_1) (times_times int)) (product_fst int int))))))))), (product_snd int int) ) 15.99/16.08 ( (let ((_let_0 (fun (product_prod int int) int))) (fun (fun int int) (fun _let_0 _let_0))), (fun (product_prod int int) (fun int int)), (let ((_let_0 (fun (product_prod int int) int))) (fun (product_prod int int) (fun _let_0 _let_0))), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 int))) (combb (fun int int) (fun _let_1 _let_1) _let_0))), (combb int int (product_prod int int)), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_0))) (hAPP _let_2 _let_3 (hAPP (fun int _let_0) (fun _let_2 _let_3) (combb int _let_0 _let_1) (times_times int)) (product_fst int int)))))) ) 15.99/16.08 ( (fun int (fun (product_prod int int) int)), (fun (product_prod int int) int), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (let ((_let_0 (product_prod int int))) (combb int (fun _let_0 int) _let_0)), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_0))) (hAPP _let_3 (fun int _let_2) (combc _let_1 int int) (hAPP _let_2 _let_3 (hAPP (fun int _let_0) (fun _let_2 _let_3) (combb int _let_0 _let_1) (times_times int)) (product_fst int int))))))), (product_snd int int) ) 15.99/16.08 ( (fun real (fun bool bool)), (fun real bool), (fun real bool), (combs real bool bool), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun real _let_1))) (hAPP _let_0 _let_2 (hAPP (fun bool _let_1) (fun _let_0 _let_2) (combb bool _let_1 real) fconj) (hAPP real _let_0 (ord_less_eq real) (zero_zero real)))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun real _let_0))) (let ((_let_4 (fun real _let_2))) (let ((_let_5 (combc real real bool))) (hAPP _let_0 _let_0 (hAPP _let_4 (fun _let_0 _let_0) (combs real bool bool) (hAPP _let_0 _let_4 (hAPP (fun bool _let_2) (fun _let_0 _let_4) (combb bool _let_2 real) fconj) (hAPP real _let_0 (hAPP _let_3 _let_3 _let_5 (ord_less_eq real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_3 _let_3 _let_5 (hAPP _let_1 _let_3 (hAPP _let_3 (fun _let_1 _let_3) (combb real _let_0 real) (fequal real)) cos)) (zero_zero real))))))))) ) 15.99/16.09 ( (fun real (fun bool bool)), (fun real bool), (fun real bool), (combs real bool bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun real (fun real bool)))) (let ((_let_2 (fun real _let_0))) (hAPP (fun real bool) _let_2 (hAPP (fun bool _let_0) (fun (fun real bool) _let_2) (combb bool _let_0 real) fconj) (hAPP real (fun real bool) (hAPP _let_1 _let_1 (combc real real bool) (ord_less_eq real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun real _let_0))) (hAPP real _let_0 (hAPP _let_2 _let_2 (combc real real bool) (hAPP _let_1 _let_2 (hAPP _let_2 (fun _let_1 _let_2) (combb real _let_0 real) (fequal real)) cos)) (zero_zero real))))) ) 15.99/16.09 ( (let ((_let_0 (fun int bool))) (fun (fun int (fun int (fun bool bool))) (fun int (fun _let_0 _let_0)))), (fun real (fun int (fun int (fun bool bool)))), (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun int bool))) (combb (fun int (fun int (fun bool bool))) (fun int (fun _let_0 _let_0)) real)), (let ((_let_0 (fun int (fun bool bool)))) (let ((_let_1 (fun (fun int bool) (fun int bool)))) (hAPP (fun _let_0 _let_1) (fun (fun int _let_0) (fun int _let_1)) (combb _let_0 _let_1 int) (combs int bool bool)))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun int _let_3))) (let ((_let_6 (fun (fun int bool) _let_5))) (let ((_let_7 (fun int real))) (let ((_let_8 (fun int _let_5))) (let ((_let_9 (fun (fun int (fun int bool)) _let_8))) (let ((_let_10 (fun real (fun int (fun int bool))))) (let ((_let_11 (fun real _let_8))) (let ((_let_12 (fun int _let_7))) (let ((_let_13 (fun _let_12 (fun int (fun int bool))))) (let ((_let_14 (fun real _let_13))) (let ((_let_15 (fun _let_7 (fun int bool)))) (let ((_let_16 (fun real _let_15))) (let ((_let_17 (fun _let_7 _let_7))) (let ((_let_18 (fun int _let_17))) (let ((_let_19 (fun int _let_1))) (hAPP _let_10 _let_11 (hAPP _let_9 (fun _let_10 _let_11) (combb (fun int (fun int bool)) _let_8 real) (hAPP _let_6 _let_9 (combb (fun int bool) _let_5 int) (hAPP (fun bool _let_3) _let_6 (combb bool _let_3 int) fconj))) (hAPP _let_12 _let_10 (hAPP _let_14 (fun _let_12 _let_10) (combc real _let_12 (fun int (fun int bool))) (hAPP _let_16 _let_14 (hAPP (fun _let_15 _let_13) (fun _let_16 _let_14) (combb _let_15 _let_13 real) (combb _let_7 (fun int bool) int)) (hAPP _let_4 _let_16 (hAPP (fun _let_0 _let_15) (fun _let_4 _let_16) (combb _let_0 _let_15 real) (combb real bool int)) (fequal real)))) (hAPP _let_7 _let_12 (hAPP _let_18 (fun _let_7 _let_12) (combc int _let_7 _let_7) (hAPP _let_19 _let_18 (hAPP (fun _let_1 _let_17) (fun _let_19 _let_18) (combb _let_1 _let_17 int) (combb real real int)) (hAPP _let_7 _let_19 (hAPP (fun real _let_1) (fun _let_7 _let_19) (combb real _let_1 int) (inverse_divide real)) _let_2))) _let_2))))))))))))))))))))))) ) 15.99/16.09 ( (fun (fun int (fun int bool)) (fun int (fun int (fun bool bool)))), (fun real (fun int (fun int bool))), (fun real (fun int (fun int (fun bool bool)))), (combb (fun int (fun int bool)) (fun int (fun int (fun bool bool))) real), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (fun _let_0 _let_2))) (hAPP _let_3 (fun (fun int _let_0) (fun int _let_2)) (combb _let_0 _let_2 int) (hAPP (fun bool _let_1) _let_3 (combb bool _let_1 int) fconj)))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun real _let_0))) (let ((_let_4 (fun int real))) (let ((_let_5 (fun real (fun int (fun int bool))))) (let ((_let_6 (fun int _let_4))) (let ((_let_7 (fun _let_6 (fun int (fun int bool))))) (let ((_let_8 (fun real _let_7))) (let ((_let_9 (fun _let_4 (fun int bool)))) (let ((_let_10 (fun real _let_9))) (let ((_let_11 (fun _let_4 _let_4))) (let ((_let_12 (fun int _let_11))) (let ((_let_13 (fun int _let_1))) (hAPP _let_6 _let_5 (hAPP _let_8 (fun _let_6 _let_5) (combc real _let_6 (fun int (fun int bool))) (hAPP _let_10 _let_8 (hAPP (fun _let_9 _let_7) (fun _let_10 _let_8) (combb _let_9 _let_7 real) (combb _let_4 (fun int bool) int)) (hAPP _let_3 _let_10 (hAPP (fun _let_0 _let_9) (fun _let_3 _let_10) (combb _let_0 _let_9 real) (combb real bool int)) (fequal real)))) (hAPP _let_4 _let_6 (hAPP _let_12 (fun _let_4 _let_6) (combc int _let_4 _let_4) (hAPP _let_13 _let_12 (hAPP (fun _let_1 _let_11) (fun _let_13 _let_12) (combb _let_1 _let_11 int) (combb real real int)) (hAPP _let_4 _let_13 (hAPP (fun real _let_1) (fun _let_4 _let_13) (combb real _let_1 int) (inverse_divide real)) _let_2))) _let_2)))))))))))))))) ) 15.99/16.09 ( (fun int (fun nat int)), nat, (fun int int), (combc int nat int), (power_power int), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.09 ( (let ((_let_0 (fun int bool))) (fun real (fun _let_0 (fun int _let_0)))), (fun int bool), (fun real (fun int (fun int bool))), (let ((_let_0 (fun int bool))) (combc real _let_0 (fun int _let_0))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun int _let_3))) (let ((_let_6 (fun (fun int bool) (fun int bool)))) (let ((_let_7 (fun (fun int bool) _let_5))) (let ((_let_8 (fun int real))) (let ((_let_9 (fun int _let_6))) (let ((_let_10 (fun (fun int bool) (fun int (fun int bool))))) (let ((_let_11 (fun int _let_5))) (let ((_let_12 (fun _let_11 _let_9))) (let ((_let_13 (fun (fun int (fun int bool)) _let_11))) (let ((_let_14 (fun real (fun int (fun int bool))))) (let ((_let_15 (fun real _let_10))) (let ((_let_16 (fun real _let_9))) (let ((_let_17 (fun real _let_11))) (let ((_let_18 (fun int _let_8))) (let ((_let_19 (fun _let_18 (fun int (fun int bool))))) (let ((_let_20 (fun real _let_19))) (let ((_let_21 (fun _let_8 (fun int bool)))) (let ((_let_22 (fun real _let_21))) (let ((_let_23 (fun _let_8 _let_8))) (let ((_let_24 (fun int _let_23))) (let ((_let_25 (fun int _let_1))) (hAPP _let_16 _let_15 (hAPP (fun _let_9 _let_10) (fun _let_16 _let_15) (combb _let_9 _let_10 real) (combc int (fun int bool) (fun int bool))) (hAPP _let_17 _let_16 (hAPP _let_12 (fun _let_17 _let_16) (combb _let_11 _let_9 real) (hAPP (fun _let_5 _let_6) _let_12 (combb _let_5 _let_6 int) (combs int bool bool))) (hAPP _let_14 _let_17 (hAPP _let_13 (fun _let_14 _let_17) (combb (fun int (fun int bool)) _let_11 real) (hAPP _let_7 _let_13 (combb (fun int bool) _let_5 int) (hAPP (fun bool _let_3) _let_7 (combb bool _let_3 int) fconj))) (hAPP _let_18 _let_14 (hAPP _let_20 (fun _let_18 _let_14) (combc real _let_18 (fun int (fun int bool))) (hAPP _let_22 _let_20 (hAPP (fun _let_21 _let_19) (fun _let_22 _let_20) (combb _let_21 _let_19 real) (combb _let_8 (fun int bool) int)) (hAPP _let_4 _let_22 (hAPP (fun _let_0 _let_21) (fun _let_4 _let_22) (combb _let_0 _let_21 real) (combb real bool int)) (fequal real)))) (hAPP _let_8 _let_18 (hAPP _let_24 (fun _let_8 _let_18) (combc int _let_8 _let_8) (hAPP _let_25 _let_24 (hAPP (fun _let_1 _let_23) (fun _let_25 _let_24) (combb _let_1 _let_23 int) (combb real real int)) (hAPP _let_8 _let_25 (hAPP (fun real _let_1) (fun _let_8 _let_25) (combb real _let_1 int) (inverse_divide real)) _let_2))) _let_2))))))))))))))))))))))))))))))), (let ((_let_0 (fun int (fun int bool)))) (hAPP (fun int bool) (fun int bool) (hAPP (fun bool bool) (fun (fun int bool) (fun int bool)) (combb bool bool int) fNot) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (fequal int)) (zero_zero int)))) ) 15.99/16.09 ( (let ((_let_0 (fun int bool))) (fun (fun int (fun _let_0 _let_0)) (fun _let_0 (fun int _let_0)))), (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun int bool))) (fun real (fun _let_0 (fun int _let_0)))), (let ((_let_0 (fun int bool))) (combb (fun int (fun _let_0 _let_0)) (fun _let_0 (fun int _let_0)) real)), (let ((_let_0 (fun int bool))) (combc int _let_0 _let_0)), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun int _let_3))) (let ((_let_6 (fun (fun int bool) (fun int bool)))) (let ((_let_7 (fun (fun int bool) _let_5))) (let ((_let_8 (fun int real))) (let ((_let_9 (fun int _let_6))) (let ((_let_10 (fun int _let_5))) (let ((_let_11 (fun _let_10 _let_9))) (let ((_let_12 (fun (fun int (fun int bool)) _let_10))) (let ((_let_13 (fun real (fun int (fun int bool))))) (let ((_let_14 (fun real _let_9))) (let ((_let_15 (fun real _let_10))) (let ((_let_16 (fun int _let_8))) (let ((_let_17 (fun _let_16 (fun int (fun int bool))))) (let ((_let_18 (fun real _let_17))) (let ((_let_19 (fun _let_8 (fun int bool)))) (let ((_let_20 (fun real _let_19))) (let ((_let_21 (fun _let_8 _let_8))) (let ((_let_22 (fun int _let_21))) (let ((_let_23 (fun int _let_1))) (hAPP _let_15 _let_14 (hAPP _let_11 (fun _let_15 _let_14) (combb _let_10 _let_9 real) (hAPP (fun _let_5 _let_6) _let_11 (combb _let_5 _let_6 int) (combs int bool bool))) (hAPP _let_13 _let_15 (hAPP _let_12 (fun _let_13 _let_15) (combb (fun int (fun int bool)) _let_10 real) (hAPP _let_7 _let_12 (combb (fun int bool) _let_5 int) (hAPP (fun bool _let_3) _let_7 (combb bool _let_3 int) fconj))) (hAPP _let_16 _let_13 (hAPP _let_18 (fun _let_16 _let_13) (combc real _let_16 (fun int (fun int bool))) (hAPP _let_20 _let_18 (hAPP (fun _let_19 _let_17) (fun _let_20 _let_18) (combb _let_19 _let_17 real) (combb _let_8 (fun int bool) int)) (hAPP _let_4 _let_20 (hAPP (fun _let_0 _let_19) (fun _let_4 _let_20) (combb _let_0 _let_19 real) (combb real bool int)) (fequal real)))) (hAPP _let_8 _let_16 (hAPP _let_22 (fun _let_8 _let_16) (combc int _let_8 _let_8) (hAPP _let_23 _let_22 (hAPP (fun _let_1 _let_21) (fun _let_23 _let_22) (combb _let_1 _let_21 int) (combb real real int)) (hAPP _let_8 _let_23 (hAPP (fun real _let_1) (fun _let_8 _let_23) (combb real _let_1 int) (inverse_divide real)) _let_2))) _let_2)))))))))))))))))))))))))))) ) 15.99/16.09 ( (fun real (fun (fun int (fun int real)) (fun int (fun int bool)))), (fun int (fun int real)), (fun real (fun int (fun int bool))), (combc real (fun int (fun int real)) (fun int (fun int bool))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun int (fun int real)) (fun int (fun int bool))))) (let ((_let_3 (fun real _let_2))) (let ((_let_4 (fun (fun int real) (fun int bool)))) (let ((_let_5 (fun real _let_4))) (hAPP _let_5 _let_3 (hAPP (fun _let_4 _let_2) (fun _let_5 _let_3) (combb _let_4 _let_2 real) (combb (fun int real) (fun int bool) int)) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_1 _let_5) (combb _let_0 _let_4 real) (combb real bool int)) (fequal real))))))))), (let ((_let_0 (fun real real))) (let ((_let_1 (real_1 int))) (let ((_let_2 (fun int real))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun _let_2 _let_2))) (let ((_let_5 (fun int _let_4))) (let ((_let_6 (fun int _let_0))) (hAPP _let_2 _let_3 (hAPP _let_5 (fun _let_2 _let_3) (combc int _let_2 _let_2) (hAPP _let_6 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_6 _let_5) (combb _let_0 _let_4 int) (combb real real int)) (hAPP _let_2 _let_6 (hAPP (fun real _let_0) (fun _let_2 _let_6) (combb real _let_0 int) (inverse_divide real)) _let_1))) _let_1)))))))) ) 15.99/16.09 ( (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int real))) (fun (fun _let_1 _let_0) (fun (fun int _let_1) (fun int _let_0))))), (fun real (fun (fun int real) (fun int bool))), (fun real (fun (fun int (fun int real)) (fun int (fun int bool)))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int real))) (combb (fun _let_1 _let_0) (fun (fun int _let_1) (fun int _let_0)) real))), (combb (fun int real) (fun int bool) int), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun int real) (fun int bool)))) (let ((_let_3 (fun real _let_2))) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 real) (combb real bool int)) (fequal real)))))) ) 15.99/16.09 ( (fun (fun real bool) (fun (fun int real) (fun int bool))), (fun real (fun real bool)), (fun real (fun (fun int real) (fun int bool))), (combb (fun real bool) (fun (fun int real) (fun int bool)) real), (combb real bool int), (fequal real) ) 15.99/16.09 ( (let ((_let_0 (fun int real))) (fun int (fun _let_0 _let_0))), (fun int real), (fun int (fun int real)), (let ((_let_0 (fun int real))) (combc int _let_0 _let_0)), (let ((_let_0 (fun real real))) (let ((_let_1 (fun int real))) (let ((_let_2 (fun _let_1 _let_1))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int _let_0))) (hAPP _let_4 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_4 _let_3) (combb _let_0 _let_2 int) (combb real real int)) (hAPP _let_1 _let_4 (hAPP (fun real _let_0) (fun _let_1 _let_4) (combb real _let_0 int) (inverse_divide real)) (real_1 int)))))))), (real_1 int) ) 15.99/16.09 ( (let ((_let_0 (fun int real))) (fun (fun real real) (fun _let_0 _let_0))), (fun int (fun real real)), (let ((_let_0 (fun int real))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun int real))) (combb (fun real real) (fun _let_0 _let_0) int)), (combb real real int), (let ((_let_0 (fun real real))) (let ((_let_1 (fun int real))) (let ((_let_2 (fun int _let_0))) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 int) (inverse_divide real)) (real_1 int))))) ) 15.99/16.09 ( (let ((_let_0 (fun int (fun int bool)))) (fun _let_0 _let_0)), (fun int (fun int (fun int bool))), (fun int (fun int (fun int bool))), (let ((_let_0 (fun int (fun int bool)))) (combb _let_0 _let_0 int)), (combc int int bool), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int _let_1))) (let ((_let_5 (fun _let_2 _let_1))) (hAPP _let_3 _let_4 (hAPP _let_5 (fun _let_3 _let_4) (combb _let_2 _let_1 int) (hAPP _let_1 _let_5 (combb int _let_0 int) (fequal int))) int_gcd))))))) ) 15.99/16.09 ( (fun (fun int (fun nat bool)) (fun int bool)), (fun real (fun int (fun nat bool))), (fun real (fun int bool)), (combb (fun int (fun nat bool)) (fun int bool) real), (let ((_let_0 (fun nat bool))) (hAPP (fun _let_0 bool) (fun (fun int _let_0) (fun int bool)) (combb _let_0 bool int) (fEx nat))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat (fun nat bool)))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun (fun nat real) (fun nat real)))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun (fun nat bool) (fun nat bool)))) (let ((_let_7 (fun int real))) (let ((_let_8 (fun nat _let_3))) (let ((_let_9 (fun (fun nat bool) _let_8))) (let ((_let_10 (fun int _let_1))) (let ((_let_11 (fun real (fun int (fun nat bool))))) (let ((_let_12 (fun (fun nat bool) (fun int (fun nat bool))))) (let ((_let_13 (fun real _let_12))) (let ((_let_14 (fun int _let_6))) (let ((_let_15 (fun real _let_14))) (let ((_let_16 (fun int _let_8))) (let ((_let_17 (fun real _let_16))) (let ((_let_18 (fun _let_16 _let_14))) (let ((_let_19 (fun (fun int (fun nat bool)) _let_16))) (let ((_let_20 (fun int (fun nat real)))) (let ((_let_21 (fun _let_20 (fun int (fun nat bool))))) (let ((_let_22 (fun real _let_21))) (let ((_let_23 (fun (fun nat real) (fun nat bool)))) (let ((_let_24 (fun real _let_23))) (let ((_let_25 (fun int _let_4))) (hAPP (fun nat bool) _let_11 (hAPP _let_13 (fun (fun nat bool) _let_11) (combc real (fun nat bool) (fun int (fun nat bool))) (hAPP _let_15 _let_13 (hAPP (fun _let_14 _let_12) (fun _let_15 _let_13) (combb _let_14 _let_12 real) (combc int (fun nat bool) (fun nat bool))) (hAPP _let_17 _let_15 (hAPP _let_18 (fun _let_17 _let_15) (combb _let_16 _let_14 real) (hAPP (fun _let_8 _let_6) _let_18 (combb _let_8 _let_6 int) (combs nat bool bool))) (hAPP _let_11 _let_17 (hAPP _let_19 (fun _let_11 _let_17) (combb (fun int (fun nat bool)) _let_16 real) (hAPP _let_9 _let_19 (combb (fun nat bool) _let_8 int) (hAPP (fun bool _let_3) _let_9 (combb bool _let_3 nat) fconj))) (hAPP _let_20 _let_11 (hAPP _let_22 (fun _let_20 _let_11) (combc real _let_20 (fun int (fun nat bool))) (hAPP _let_24 _let_22 (hAPP (fun _let_23 _let_21) (fun _let_24 _let_22) (combb _let_23 _let_21 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_5 _let_24 (hAPP (fun _let_0 _let_23) (fun _let_5 _let_24) (combb _let_0 _let_23 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_20 (hAPP _let_25 (fun (fun nat real) _let_20) (combc int (fun nat real) (fun nat real)) (hAPP _let_10 _let_25 (hAPP (fun _let_1 _let_4) (fun _let_10 _let_25) (combb _let_1 _let_4 int) (combb real real nat)) (hAPP _let_7 _let_10 (hAPP (fun real _let_1) (fun _let_7 _let_10) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat))))))) (hAPP (fun nat bool) (fun nat bool) (hAPP _let_3 _let_6 (combb bool bool nat) fNot) (hAPP nat (fun nat bool) (hAPP _let_2 _let_2 (combc nat nat bool) (fequal nat)) (zero_zero nat)))))))))))))))))))))))))))))) ) 15.99/16.09 ( (let ((_let_0 (fun nat bool))) (fun real (fun _let_0 (fun int _let_0)))), (fun nat bool), (fun real (fun int (fun nat bool))), (let ((_let_0 (fun nat bool))) (combc real _let_0 (fun int _let_0))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun (fun nat real) (fun nat real)))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun (fun nat bool) (fun nat bool)))) (let ((_let_6 (fun int real))) (let ((_let_7 (fun nat _let_2))) (let ((_let_8 (fun (fun nat bool) _let_7))) (let ((_let_9 (fun int _let_1))) (let ((_let_10 (fun real (fun int (fun nat bool))))) (let ((_let_11 (fun (fun nat bool) (fun int (fun nat bool))))) (let ((_let_12 (fun real _let_11))) (let ((_let_13 (fun int _let_5))) (let ((_let_14 (fun real _let_13))) (let ((_let_15 (fun int _let_7))) (let ((_let_16 (fun real _let_15))) (let ((_let_17 (fun _let_15 _let_13))) (let ((_let_18 (fun (fun int (fun nat bool)) _let_15))) (let ((_let_19 (fun int (fun nat real)))) (let ((_let_20 (fun _let_19 (fun int (fun nat bool))))) (let ((_let_21 (fun real _let_20))) (let ((_let_22 (fun (fun nat real) (fun nat bool)))) (let ((_let_23 (fun real _let_22))) (let ((_let_24 (fun int _let_3))) (hAPP _let_14 _let_12 (hAPP (fun _let_13 _let_11) (fun _let_14 _let_12) (combb _let_13 _let_11 real) (combc int (fun nat bool) (fun nat bool))) (hAPP _let_16 _let_14 (hAPP _let_17 (fun _let_16 _let_14) (combb _let_15 _let_13 real) (hAPP (fun _let_7 _let_5) _let_17 (combb _let_7 _let_5 int) (combs nat bool bool))) (hAPP _let_10 _let_16 (hAPP _let_18 (fun _let_10 _let_16) (combb (fun int (fun nat bool)) _let_15 real) (hAPP _let_8 _let_18 (combb (fun nat bool) _let_7 int) (hAPP (fun bool _let_2) _let_8 (combb bool _let_2 nat) fconj))) (hAPP _let_19 _let_10 (hAPP _let_21 (fun _let_19 _let_10) (combc real _let_19 (fun int (fun nat bool))) (hAPP _let_23 _let_21 (hAPP (fun _let_22 _let_20) (fun _let_23 _let_21) (combb _let_22 _let_20 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_4 _let_23 (hAPP (fun _let_0 _let_22) (fun _let_4 _let_23) (combb _let_0 _let_22 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_19 (hAPP _let_24 (fun (fun nat real) _let_19) (combc int (fun nat real) (fun nat real)) (hAPP _let_9 _let_24 (hAPP (fun _let_1 _let_3) (fun _let_9 _let_24) (combb _let_1 _let_3 int) (combb real real nat)) (hAPP _let_6 _let_9 (hAPP (fun real _let_1) (fun _let_6 _let_9) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat))))))))))))))))))))))))))))))), (let ((_let_0 (fun nat (fun nat bool)))) (hAPP (fun nat bool) (fun nat bool) (hAPP (fun bool bool) (fun (fun nat bool) (fun nat bool)) (combb bool bool nat) fNot) (hAPP nat (fun nat bool) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat)) (zero_zero nat)))) ) 15.99/16.09 ( (let ((_let_0 (fun nat bool))) (fun (fun int (fun _let_0 _let_0)) (fun _let_0 (fun int _let_0)))), (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun nat bool))) (fun real (fun _let_0 (fun int _let_0)))), (let ((_let_0 (fun nat bool))) (combb (fun int (fun _let_0 _let_0)) (fun _let_0 (fun int _let_0)) real)), (let ((_let_0 (fun nat bool))) (combc int _let_0 _let_0)), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun (fun nat real) (fun nat real)))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun (fun nat bool) (fun nat bool)))) (let ((_let_6 (fun int real))) (let ((_let_7 (fun nat _let_2))) (let ((_let_8 (fun (fun nat bool) _let_7))) (let ((_let_9 (fun int _let_1))) (let ((_let_10 (fun real (fun int (fun nat bool))))) (let ((_let_11 (fun int _let_5))) (let ((_let_12 (fun real _let_11))) (let ((_let_13 (fun int _let_7))) (let ((_let_14 (fun real _let_13))) (let ((_let_15 (fun _let_13 _let_11))) (let ((_let_16 (fun (fun int (fun nat bool)) _let_13))) (let ((_let_17 (fun int (fun nat real)))) (let ((_let_18 (fun _let_17 (fun int (fun nat bool))))) (let ((_let_19 (fun real _let_18))) (let ((_let_20 (fun (fun nat real) (fun nat bool)))) (let ((_let_21 (fun real _let_20))) (let ((_let_22 (fun int _let_3))) (hAPP _let_14 _let_12 (hAPP _let_15 (fun _let_14 _let_12) (combb _let_13 _let_11 real) (hAPP (fun _let_7 _let_5) _let_15 (combb _let_7 _let_5 int) (combs nat bool bool))) (hAPP _let_10 _let_14 (hAPP _let_16 (fun _let_10 _let_14) (combb (fun int (fun nat bool)) _let_13 real) (hAPP _let_8 _let_16 (combb (fun nat bool) _let_7 int) (hAPP (fun bool _let_2) _let_8 (combb bool _let_2 nat) fconj))) (hAPP _let_17 _let_10 (hAPP _let_19 (fun _let_17 _let_10) (combc real _let_17 (fun int (fun nat bool))) (hAPP _let_21 _let_19 (hAPP (fun _let_20 _let_18) (fun _let_21 _let_19) (combb _let_20 _let_18 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_4 _let_21 (hAPP (fun _let_0 _let_20) (fun _let_4 _let_21) (combb _let_0 _let_20 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_17 (hAPP _let_22 (fun (fun nat real) _let_17) (combc int (fun nat real) (fun nat real)) (hAPP _let_9 _let_22 (hAPP (fun _let_1 _let_3) (fun _let_9 _let_22) (combb _let_1 _let_3 int) (combb real real nat)) (hAPP _let_6 _let_9 (hAPP (fun real _let_1) (fun _let_6 _let_9) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat)))))))))))))))))))))))))))) ) 15.99/16.09 ( (let ((_let_0 (fun nat bool))) (fun (fun int (fun nat (fun bool bool))) (fun int (fun _let_0 _let_0)))), (fun real (fun int (fun nat (fun bool bool)))), (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun nat bool))) (combb (fun int (fun nat (fun bool bool))) (fun int (fun _let_0 _let_0)) real)), (let ((_let_0 (fun (fun nat bool) (fun nat bool)))) (let ((_let_1 (fun nat (fun bool bool)))) (hAPP (fun _let_1 _let_0) (fun (fun int _let_1) (fun int _let_0)) (combb _let_1 _let_0 int) (combs nat bool bool)))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun (fun nat real) (fun nat real)))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun int real))) (let ((_let_6 (fun nat _let_2))) (let ((_let_7 (fun (fun nat bool) _let_6))) (let ((_let_8 (fun int _let_1))) (let ((_let_9 (fun real (fun int (fun nat bool))))) (let ((_let_10 (fun int _let_6))) (let ((_let_11 (fun real _let_10))) (let ((_let_12 (fun (fun int (fun nat bool)) _let_10))) (let ((_let_13 (fun int (fun nat real)))) (let ((_let_14 (fun _let_13 (fun int (fun nat bool))))) (let ((_let_15 (fun real _let_14))) (let ((_let_16 (fun (fun nat real) (fun nat bool)))) (let ((_let_17 (fun real _let_16))) (let ((_let_18 (fun int _let_3))) (hAPP _let_9 _let_11 (hAPP _let_12 (fun _let_9 _let_11) (combb (fun int (fun nat bool)) _let_10 real) (hAPP _let_7 _let_12 (combb (fun nat bool) _let_6 int) (hAPP (fun bool _let_2) _let_7 (combb bool _let_2 nat) fconj))) (hAPP _let_13 _let_9 (hAPP _let_15 (fun _let_13 _let_9) (combc real _let_13 (fun int (fun nat bool))) (hAPP _let_17 _let_15 (hAPP (fun _let_16 _let_14) (fun _let_17 _let_15) (combb _let_16 _let_14 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_4 _let_17 (hAPP (fun _let_0 _let_16) (fun _let_4 _let_17) (combb _let_0 _let_16 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_13 (hAPP _let_18 (fun (fun nat real) _let_13) (combc int (fun nat real) (fun nat real)) (hAPP _let_8 _let_18 (hAPP (fun _let_1 _let_3) (fun _let_8 _let_18) (combb _let_1 _let_3 int) (combb real real nat)) (hAPP _let_5 _let_8 (hAPP (fun real _let_1) (fun _let_5 _let_8) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat))))))))))))))))))))))) ) 15.99/16.09 ( (fun (fun int (fun nat bool)) (fun int (fun nat (fun bool bool)))), (fun real (fun int (fun nat bool))), (fun real (fun int (fun nat (fun bool bool)))), (combb (fun int (fun nat bool)) (fun int (fun nat (fun bool bool))) real), (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun nat _let_1))) (let ((_let_3 (fun _let_0 _let_2))) (hAPP _let_3 (fun (fun int _let_0) (fun int _let_2)) (combb _let_0 _let_2 int) (hAPP (fun bool _let_1) _let_3 (combb bool _let_1 nat) fconj)))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun (fun nat real) (fun nat real)))) (let ((_let_3 (fun real _let_0))) (let ((_let_4 (fun int real))) (let ((_let_5 (fun int _let_1))) (let ((_let_6 (fun real (fun int (fun nat bool))))) (let ((_let_7 (fun int (fun nat real)))) (let ((_let_8 (fun _let_7 (fun int (fun nat bool))))) (let ((_let_9 (fun real _let_8))) (let ((_let_10 (fun (fun nat real) (fun nat bool)))) (let ((_let_11 (fun real _let_10))) (let ((_let_12 (fun int _let_2))) (hAPP _let_7 _let_6 (hAPP _let_9 (fun _let_7 _let_6) (combc real _let_7 (fun int (fun nat bool))) (hAPP _let_11 _let_9 (hAPP (fun _let_10 _let_8) (fun _let_11 _let_9) (combb _let_10 _let_8 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_3 _let_11 (hAPP (fun _let_0 _let_10) (fun _let_3 _let_11) (combb _let_0 _let_10 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_7 (hAPP _let_12 (fun (fun nat real) _let_7) (combc int (fun nat real) (fun nat real)) (hAPP _let_5 _let_12 (hAPP (fun _let_1 _let_2) (fun _let_5 _let_12) (combb _let_1 _let_2 int) (combb real real nat)) (hAPP _let_4 _let_5 (hAPP (fun real _let_1) (fun _let_4 _let_5) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat)))))))))))))))) ) 15.99/16.09 ( (fun real (fun (fun int (fun nat real)) (fun int (fun nat bool)))), (fun int (fun nat real)), (fun real (fun int (fun nat bool))), (combc real (fun int (fun nat real)) (fun int (fun nat bool))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun int (fun nat real)) (fun int (fun nat bool))))) (let ((_let_3 (fun real _let_2))) (let ((_let_4 (fun (fun nat real) (fun nat bool)))) (let ((_let_5 (fun real _let_4))) (hAPP _let_5 _let_3 (hAPP (fun _let_4 _let_2) (fun _let_5 _let_3) (combb _let_4 _let_2 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_1 _let_5) (combb _let_0 _let_4 real) (combb real bool nat)) (fequal real))))))))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun (fun nat real) (fun nat real)))) (let ((_let_2 (fun int real))) (let ((_let_3 (fun int _let_0))) (let ((_let_4 (fun int (fun nat real)))) (let ((_let_5 (fun int _let_1))) (hAPP (fun nat real) _let_4 (hAPP _let_5 (fun (fun nat real) _let_4) (combc int (fun nat real) (fun nat real)) (hAPP _let_3 _let_5 (hAPP (fun _let_0 _let_1) (fun _let_3 _let_5) (combb _let_0 _let_1 int) (combb real real nat)) (hAPP _let_2 _let_3 (hAPP (fun real _let_0) (fun _let_2 _let_3) (combb real _let_0 int) (inverse_divide real)) (real_1 int)))) (real_1 nat)))))))) ) 15.99/16.09 ( (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat real))) (fun (fun _let_1 _let_0) (fun (fun int _let_1) (fun int _let_0))))), (fun real (fun (fun nat real) (fun nat bool))), (fun real (fun (fun int (fun nat real)) (fun int (fun nat bool)))), (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat real))) (combb (fun _let_1 _let_0) (fun (fun int _let_1) (fun int _let_0)) real))), (combb (fun nat real) (fun nat bool) int), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun nat real) (fun nat bool)))) (let ((_let_3 (fun real _let_2))) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 real) (combb real bool nat)) (fequal real)))))) ) 15.99/16.09 ( (fun (fun real bool) (fun (fun nat real) (fun nat bool))), (fun real (fun real bool)), (fun real (fun (fun nat real) (fun nat bool))), (combb (fun real bool) (fun (fun nat real) (fun nat bool)) real), (combb real bool nat), (fequal real) ) 15.99/16.09 ( (let ((_let_0 (fun nat real))) (fun int (fun _let_0 _let_0))), (fun nat real), (fun int (fun nat real)), (let ((_let_0 (fun nat real))) (combc int _let_0 _let_0)), (let ((_let_0 (fun real real))) (let ((_let_1 (fun (fun nat real) (fun nat real)))) (let ((_let_2 (fun int real))) (let ((_let_3 (fun int _let_0))) (let ((_let_4 (fun int _let_1))) (hAPP _let_3 _let_4 (hAPP (fun _let_0 _let_1) (fun _let_3 _let_4) (combb _let_0 _let_1 int) (combb real real nat)) (hAPP _let_2 _let_3 (hAPP (fun real _let_0) (fun _let_2 _let_3) (combb real _let_0 int) (inverse_divide real)) (real_1 int)))))))), (real_1 nat) ) 15.99/16.09 ( (let ((_let_0 (fun nat real))) (fun (fun real real) (fun _let_0 _let_0))), (fun int (fun real real)), (let ((_let_0 (fun nat real))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun nat real))) (combb (fun real real) (fun _let_0 _let_0) int)), (combb real real nat), (let ((_let_0 (fun real real))) (let ((_let_1 (fun int real))) (let ((_let_2 (fun int _let_0))) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 int) (inverse_divide real)) (real_1 int))))) ) 15.99/16.09 ( (let ((_let_0 (fun int int))) (fun int (fun _let_0 _let_0))), (fun int int), (fun int (fun int int)), (let ((_let_0 (fun int int))) (combc int _let_0 _let_0)), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun _let_0 _let_0))) (let ((_let_3 (fun int _let_2))) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 int) (combb int int int)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)) (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))))), (let ((_let_0 (fun int int))) (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.99/16.09 ( (let ((_let_0 (fun int int))) (fun _let_0 (fun _let_0 _let_0))), (fun int (fun int int)), (let ((_let_0 (fun int int))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun int int))) (combb _let_0 (fun _let_0 _let_0) int)), (combb int int int), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)) (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 15.99/16.09 ) 15.99/16.09 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted) (A_6 $$unsorted) (B_5 $$unsorted)) (let ((_let_0 (product_prod X_a X_b))) (let ((_let_1 (fun X_b _let_0))) (let ((_let_2 (product_Pair X_a X_b))) (or (not (= (hAPP X_b _let_0 (hAPP X_a _let_1 _let_2 A_1) B) (hAPP X_b _let_0 (hAPP X_a _let_1 _let_2 A_6) B_5))) (and (= (ti X_a A_6) (ti X_a A_1)) (= (ti X_b B_5) (ti X_b B))))))) ) 15.99/16.09 ( int, int, (one_one int), (one_one int), s, (one_one int) ) 15.99/16.09 ( int, int, (zero_zero int), (one_one int), (one_one int), (one_one int) ) 15.99/16.09 ( int, int, (zero_zero int), (one_one int), s, (one_one int) ) 15.99/16.09 ( int, int, s, (one_one int), (zero_zero int), (one_one int) ) 15.99/16.09 ( int, int, s, (one_one int), s, (one_one int) ) 15.99/16.09 ) 15.99/16.09 (instantiation (forall ((X_c $$unsorted) (X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_132314 $$unsorted) (BOUND_VARIABLE_132315 $$unsorted) (BOUND_VARIABLE_132316 $$unsorted) (BOUND_VARIABLE_132317 $$unsorted) (BOUND_VARIABLE_132318 $$unsorted) (BOUND_VARIABLE_132319 $$unsorted)) (let ((_let_0 (filter X_b))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun X_b X_c))) (let ((_let_3 (filter X_a))) (let ((_let_4 (fun _let_3 bool))) (let ((_let_5 (fun X_a X_c))) (let ((_let_6 (fun X_a X_b))) (let ((_let_7 (hAPP X_a _let_3 (at X_a) BOUND_VARIABLE_132318))) (or (not (metric_space X_a)) (not (topological_space X_c)) (not (topological_space X_b)) (not (hBOOL (hAPP _let_3 bool (hAPP X_b _let_4 (hAPP _let_6 (fun X_b _let_4) (tendsto X_a X_b) BOUND_VARIABLE_132316) BOUND_VARIABLE_132317) _let_7))) (not (hBOOL (hAPP _let_0 bool (hAPP X_c _let_1 (hAPP _let_2 (fun X_c _let_1) (tendsto X_b X_c) BOUND_VARIABLE_132314) BOUND_VARIABLE_132315) (hAPP X_b _let_0 (at X_b) BOUND_VARIABLE_132317)))) (hBOOL (hAPP _let_3 bool (hAPP X_c _let_4 (hAPP _let_5 (fun X_c _let_4) (tendsto X_a X_c) (hAPP _let_6 _let_5 (hAPP _let_2 (fun _let_6 _let_5) (combb X_b X_c X_a) BOUND_VARIABLE_132314) BOUND_VARIABLE_132316)) BOUND_VARIABLE_132315) _let_7)) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) BOUND_VARIABLE_132319))) (not (forall ((X $$unsorted)) (or (= (ti X_a X) (ti X_a BOUND_VARIABLE_132318)) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP X_a real (hAPP X_a (fun X_a real) (dist_dist X_a) X) BOUND_VARIABLE_132318)) BOUND_VARIABLE_132319))) (not (= (ti X_b BOUND_VARIABLE_132317) (hAPP X_a X_b BOUND_VARIABLE_132316 X)))) ))))))))))) ) 15.99/16.09 ( real, real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.09 ) 15.99/16.09 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (abs_abs X_a))) (or (not (abs_if X_a)) (= _let_0 (ti (fun X_a X_a) _let_0)))) ) 15.99/16.09 ( bool ) 15.99/16.09 ( nat ) 15.99/16.09 ( int ) 15.99/16.09 ( (fun int bool) ) 15.99/16.09 ( (fun int (fun int bool)) ) 15.99/16.09 ( (fun int int) ) 15.99/16.09 ( (fun nat bool) ) 15.99/16.09 ( real ) 15.99/16.09 ( (fun real bool) ) 15.99/16.09 ( (fun real real) ) 15.99/16.09 ( rat ) 15.99/16.09 ( complex ) 15.99/16.09 ( (fun nat real) ) 15.99/16.09 ( (product_prod int int) ) 15.99/16.09 ( code_code_numeral ) 15.99/16.09 ( (fun int (fun int (fun int bool))) ) 15.99/16.09 ( (fun (product_prod int int) bool) ) 15.99/16.09 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 15.99/16.09 ( (fun (product_prod int int) int) ) 15.99/16.09 ( (fun int real) ) 15.99/16.09 ) 15.99/16.09 (instantiation (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted)) (let ((_let_0 (product_prod_rec X_b X_c X_a))) (= _let_0 (ti (fun (fun X_b (fun X_c X_a)) (fun (product_prod X_b X_c) X_a)) _let_0))) ) 15.99/16.09 ( nat, nat, bool ) 15.99/16.09 ( nat, nat, (fun (product_prod nat nat) bool) ) 15.99/16.09 ( int, int, bool ) 15.99/16.09 ( int, int, int ) 15.99/16.09 ( int, int, (fun int bool) ) 15.99/16.09 ( int, int, (fun int int) ) 15.99/16.09 ( int, int, rat ) 15.99/16.09 ( int, int, (product_prod int int) ) 15.99/16.09 ( int, int, (fun bool bool) ) 15.99/16.09 ( int, int, (fun (product_prod int int) bool) ) 15.99/16.09 ( int, int, (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 15.99/16.09 ( int, int, (fun (product_prod int int) (fun int bool)) ) 15.99/16.09 ( int, int, (fun (product_prod int int) int) ) 15.99/16.09 ( int, int, (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 15.99/16.09 ( int, int, (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 15.99/16.09 ( (product_prod nat nat), (product_prod nat nat), bool ) 15.99/16.09 ( real, real, bool ) 15.99/16.09 ( (product_prod int int), (product_prod int int), bool ) 15.99/16.09 ) 15.99/16.09 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_132478 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) BOUND_VARIABLE_132478)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) (hAPP X_a int (archimedean_ceiling X_a) BOUND_VARIABLE_132478))))) ) 15.99/16.09 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.09 ( int, (one_one int) ) 15.99/16.09 ( int, pls ) 15.99/16.09 ( int, min_1 ) 15.99/16.09 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.09 ( real, pi ) 15.99/16.09 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.09 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.09 ( real, skv_2 ) 15.99/16.09 ( real, skv_8 ) 15.99/16.09 ( real, skv_9 ) 15.99/16.09 ) 15.99/16.09 (instantiation (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (let ((_let_2 (zero_zero int))) (let ((_let_3 (number_number_of int))) (let ((_let_4 (product_prod int int))) (let ((_let_5 (fun int _let_4))) (let ((_let_6 (product_Pair int int))) (let ((_let_7 (fun _let_4 bool))) (let ((_let_8 (hAPP int int (hAPP int (fun int int) (plus_plus int) A_2) B_1))) (let ((_let_9 (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 _let_2) _let_8)))) (let ((_let_10 (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 B_1) _let_2)))) (let ((_let_11 (hAPP int _let_5 negDivAlg A_2))) (let ((_let_12 (hAPP int _let_4 _let_11 B_1))) (or (not (hBOOL (hAPP _let_4 bool (hAPP (fun _let_4 _let_7) _let_7 (accp _let_4) negDivAlg_rel) (hAPP int _let_4 (hAPP int _let_5 _let_6 A_2) B_1)))) (and (or _let_9 _let_10 (= _let_12 (hAPP _let_4 _let_4 (hAPP int (fun _let_4 _let_4) adjust B_1) (hAPP int _let_4 _let_11 (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int _let_3 (hAPP int int bit0 (hAPP int int bit1 pls)))) B_1))))) (or (and (not _let_10) (not _let_9)) (= _let_12 (hAPP int _let_4 (hAPP int _let_5 _let_6 (hAPP int int _let_3 min_1)) _let_8)))))))))))))))))) ) 15.99/16.09 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 15.99/16.09 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 15.99/16.09 ) 15.99/16.09 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_132585 $$unsorted)) (or (not (power X_a)) (= (one_one X_a) (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_132585) (zero_zero nat)))) ) 15.99/16.09 ( int, s ) 15.99/16.09 ( int, s1 ) 15.99/16.09 ( int, skv_14 ) 15.99/16.09 ( real, (hAPP int real (number_number_of real) min_1) ) 15.99/16.09 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.09 ( complex, ii ) 15.99/16.09 ) 15.99/16.09 (instantiation (forall ((Y_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) Y_1))) (= Y_1 (hAPP real real sqrt (hAPP nat real (hAPP real (fun nat real) (power_power real) Y_1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 15.99/16.09 ( pi ) 15.99/16.09 ( (hAPP int real (number_number_of real) min_1) ) 15.99/16.09 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.09 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.09 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.09 ( skv_3 ) 15.99/16.09 ( skv_5 ) 15.99/16.09 ( skv_7 ) 15.99/16.09 ( skv_12 ) 15.99/16.09 ) 15.99/16.09 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_132618 $$unsorted) (BOUND_VARIABLE_132619 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member X_a))) (let ((_let_3 (ring_1_Ints X_a))) (or (not (ring_1 X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_132619) _let_3))) (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_132619) BOUND_VARIABLE_132618)) _let_3))))))) ) 15.99/16.09 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 15.99/16.09 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 15.99/16.09 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_14 ) 15.99/16.09 ( complex, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), ii ) 15.99/16.09 ) 15.99/16.09 (instantiation (forall ((N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_1))) (= N_1 (hAPP nat nat suc (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) N_1) (one_one nat))))) ) 15.99/16.09 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.09 ) 15.99/16.09 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_132786 $$unsorted) (BOUND_VARIABLE_132787 $$unsorted)) (let ((_let_0 (fun nat X_a))) (let ((_let_1 (suminf X_a))) (let ((_let_2 (fun X_a X_a))) (let ((_let_3 (fun nat _let_2))) (let ((_let_4 (times_times X_a))) (or (not (real_normed_algebra X_a)) (not (hBOOL (hAPP _let_0 bool (summable X_a) BOUND_VARIABLE_132787))) (= (hAPP X_a X_a (hAPP X_a _let_2 _let_4 (hAPP _let_0 X_a _let_1 BOUND_VARIABLE_132787)) BOUND_VARIABLE_132786) (hAPP _let_0 X_a _let_1 (hAPP X_a _let_0 (hAPP _let_3 (fun X_a _let_0) (combc nat X_a X_a) (hAPP _let_0 _let_3 (hAPP (fun X_a _let_2) (fun _let_0 _let_3) (combb X_a _let_2 nat) _let_4) BOUND_VARIABLE_132787)) BOUND_VARIABLE_132786))))))))) ) 15.99/16.09 ( real, (one_one real), (hAPP real (fun nat real) (power_power real) (hAPP int real (number_number_of real) min_1)) ) 15.99/16.09 ) 15.99/16.09 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_132855 $$unsorted)) (let ((_let_0 (number_number_of X_a))) (or (not (number_ring X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) (hAPP int X_a _let_0 BOUND_VARIABLE_132855)) (one_one X_a)) (hAPP int X_a _let_0 (hAPP int int (hAPP int (fun int int) (plus_plus int) BOUND_VARIABLE_132855) (hAPP int int (uminus_uminus int) (hAPP int int bit1 pls))))))) ) 15.99/16.09 ( code_code_numeral, pls ) 15.99/16.09 ) 15.99/16.09 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_132877 $$unsorted)) (or (not (number_ring X_a)) (not (linordered_idom X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_132877))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) pls) BOUND_VARIABLE_132877)))) ) 15.99/16.09 ( nat, pls ) 15.99/16.09 ( nat, (hAPP int int bit1 pls) ) 15.99/16.09 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.99/16.09 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.99/16.09 ( int, pls ) 15.99/16.09 ( int, (hAPP int int bit1 pls) ) 15.99/16.09 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.99/16.09 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.99/16.09 ( int, min_1 ) 15.99/16.09 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.09 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.99/16.09 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.99/16.09 ( real, min_1 ) 15.99/16.09 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.09 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.99/16.09 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.09 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 15.99/16.09 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.99/16.09 ( complex, min_1 ) 15.99/16.09 ( quickcheck_code_int, (one_one int) ) 15.99/16.09 ( quickcheck_code_int, (zero_zero int) ) 15.99/16.09 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 15.99/16.09 ( code_code_numeral, pls ) 15.99/16.09 ( code_code_numeral, (hAPP int int bit1 pls) ) 15.99/16.09 ) 15.99/16.09 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (= (= X_2 Y_2) (= (hAPP complex complex cnj Y_2) (hAPP complex complex cnj X_2))) ) 15.99/16.09 ( (one_one complex), (zero_zero complex) ) 15.99/16.09 ( ii, (one_one complex) ) 15.99/16.09 ( ii, ii ) 15.99/16.09 ( ii, (zero_zero complex) ) 15.99/16.09 ( (zero_zero complex), ii ) 15.99/16.09 ) 15.99/16.09 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_132951 $$unsorted) (BOUND_VARIABLE_132952 $$unsorted)) (let ((_let_0 (uminus_uminus X_a))) (or (not (boolean_algebra X_a)) (= (= (ti X_a BOUND_VARIABLE_132952) (ti X_a BOUND_VARIABLE_132951)) (= (hAPP X_a X_a _let_0 BOUND_VARIABLE_132952) (hAPP X_a X_a _let_0 BOUND_VARIABLE_132951))))) ) 15.99/16.09 ( bool, fFalse, fFalse ) 15.99/16.09 ( bool, fFalse, fTrue ) 15.99/16.09 ( bool, fTrue, fFalse ) 15.99/16.09 ( int, pls, s1 ) 15.99/16.09 ( int, min_1, t ) 15.99/16.09 ( int, s, pls ) 15.99/16.09 ( int, s, s ) 15.99/16.09 ( int, s, s1 ) 15.99/16.09 ( int, m, min_1 ) 15.99/16.09 ( int, m, m ) 15.99/16.09 ( int, m, t ) 15.99/16.09 ( int, s1, s ) 15.99/16.09 ( int, t, m ) 15.99/16.09 ( (fun int bool), nat_neg, (even_odd_even int) ) 15.99/16.09 ( (fun int bool), zprime, nat_neg ) 15.99/16.09 ( (fun int bool), zEven, twoSqu1091635170sum2sq ) 15.99/16.09 ( (fun int bool), zOdd, zOdd ) 15.99/16.09 ( (fun int bool), (even_odd_even int), nat_neg ) 15.99/16.09 ( (fun int bool), (even_odd_even int), zprime ) 15.99/16.09 ( (fun int bool), (even_odd_even int), (even_odd_even int) ) 15.99/16.09 ( (fun int bool), twoSqu1091635170sum2sq, zEven ) 15.99/16.09 ( (fun int bool), twoSqu1091635170sum2sq, twoSqu1091635170sum2sq ) 15.99/16.09 ( (fun int bool), twoSqu1091635170sum2sq, nat_is_nat ) 15.99/16.09 ( (fun int bool), nat_is_nat, zEven ) 15.99/16.09 ( (fun int (fun int bool)), norRRset, norRRset ) 15.99/16.09 ( (fun int (fun int bool)), norRRset, d22set ) 15.99/16.09 ( (fun int (fun int bool)), norRRset, sr ) 15.99/16.09 ( (fun int (fun int bool)), quadRes, quadRes ) 15.99/16.09 ( (fun int (fun int bool)), quadRes, sRStar ) 15.99/16.09 ( (fun int (fun int bool)), quadRes, quickc1265749348ro_rel ) 15.99/16.09 ( (fun int (fun int bool)), sRStar, quadRes ) 15.99/16.09 ( (fun int (fun int bool)), d22set, sr ) 15.99/16.09 ( (fun int (fun int bool)), sr, norRRset ) 15.99/16.09 ( (fun int (fun int bool)), quickc1265749348ro_rel, sRStar ) 15.99/16.09 ( (fun int int), zfact, pred ) 15.99/16.09 ( (fun int int), bit0, (fact_fact int) ) 15.99/16.09 ( (fun int int), bit1, zfact ) 15.99/16.09 ( (fun int int), bit1, bit1 ) 15.99/16.09 ( (fun int int), bit1, pred ) 15.99/16.09 ( (fun int int), (fact_fact int), bit0 ) 15.99/16.09 ( (fun int int), (fact_fact int), (fact_fact int) ) 15.99/16.09 ( (fun int int), (fact_fact int), succ ) 15.99/16.09 ( (fun int int), pred, bit1 ) 15.99/16.09 ( (fun int int), succ, bit0 ) 15.99/16.09 ( (fun nat bool), (even_odd_even nat), (even_odd_even nat) ) 15.99/16.09 ( (fun nat bool), (even_odd_even nat), prime ) 15.99/16.09 ( (fun nat bool), prime, (even_odd_even nat) ) 15.99/16.09 ( (fun nat nat), suc, fact ) 15.99/16.09 ( (fun nat nat), (fact_fact nat), (size_size nat) ) 15.99/16.09 ( (fun nat nat), fact, suc ) 15.99/16.09 ( (fun nat nat), fact, fact ) 15.99/16.09 ( (fun nat nat), nat_size, (fact_fact nat) ) 15.99/16.09 ( (fun nat nat), nat_size, nat_size ) 15.99/16.09 ( (fun nat nat), nat_size, (size_size nat) ) 15.99/16.09 ( (fun nat nat), (size_size nat), nat_size ) 15.99/16.09 ( (fun (product_prod nat nat) bool), pred_nat, pred_nat ) 15.99/16.09 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel, divmod_nat_rel ) 15.99/16.09 ( real, pi, pi ) 15.99/16.09 ( (fun real real), ln, sqrt ) 15.99/16.09 ( (fun real real), cos, cos ) 15.99/16.09 ( (fun real real), cos, tan ) 15.99/16.09 ( (fun real real), sqrt, ln ) 15.99/16.09 ( (fun real real), sqrt, sqrt ) 15.99/16.09 ( (fun real real), sqrt, arccos ) 15.99/16.09 ( (fun real real), sin, arcsin ) 15.99/16.09 ( (fun real real), arccos, ln ) 15.99/16.09 ( (fun real real), arcsin, sin ) 15.99/16.09 ( (fun real real), arcsin, arcsin ) 15.99/16.09 ( (fun real real), arcsin, arctan ) 15.99/16.09 ( (fun real real), tan, cos ) 15.99/16.09 ( (fun real real), arctan, sin ) 15.99/16.09 ( (fun nat (fun nat bool)), coprime, coprime ) 15.99/16.09 ( complex, ii, ii ) 15.99/16.09 ( (fun nat real), (real_1 nat), sin_coeff ) 15.99/16.09 ( (fun nat real), sin_coeff, (real_1 nat) ) 15.99/16.09 ( (fun nat real), sin_coeff, sin_coeff ) 15.99/16.09 ( (fun nat real), sin_coeff, cos_coeff ) 15.99/16.09 ( (fun nat real), cos_coeff, (real_1 nat) ) 15.99/16.09 ( (filter nat), sequentially, sequentially ) 15.99/16.09 ( (fun int (fun int int)), (gcd_gcd int), (gcd_gcd int) ) 15.99/16.09 ( (fun int (fun int int)), (gcd_gcd int), int_gcd ) 15.99/16.09 ( (fun int (fun int int)), legendre, z3div ) 15.99/16.09 ( (fun int (fun int int)), legacy_zgcd, legendre ) 15.99/16.09 ( (fun int (fun int int)), standardRes, multInv ) 15.99/16.09 ( (fun int (fun int int)), nat_tsub, z3mod ) 15.99/16.09 ( (fun int (fun int int)), multInv, standardRes ) 15.99/16.09 ( (fun int (fun int int)), multInv, multInv ) 15.99/16.09 ( (fun int (fun int int)), multInv, inv ) 15.99/16.09 ( (fun int (fun int int)), z3mod, nat_tsub ) 15.99/16.09 ( (fun int (fun int int)), z3mod, z3mod ) 15.99/16.09 ( (fun int (fun int int)), z3mod, int_lcm ) 15.99/16.09 ( (fun int (fun int int)), z3div, legendre ) 15.99/16.09 ( (fun int (fun int int)), z3div, legacy_zgcd ) 15.99/16.09 ( (fun int (fun int int)), z3div, z3div ) 15.99/16.09 ( (fun int (fun int int)), int_gcd, (gcd_gcd int) ) 15.99/16.09 ( (fun int (fun int int)), int_lcm, nat_tsub ) 15.99/16.09 ( (fun int (fun int int)), inv, standardRes ) 15.99/16.09 ( (fun complex complex), expi, expi ) 15.99/16.09 ( (fun complex complex), expi, cnj ) 15.99/16.09 ( (fun complex complex), cnj, expi ) 15.99/16.09 ( (fun real complex), cis, cis ) 15.99/16.10 ( (fun int nat), nat_1, phi ) 15.99/16.10 ( (fun int nat), phi, nat_1 ) 15.99/16.10 ( (fun int nat), phi, phi ) 15.99/16.10 ( (fun (fun int bool) bool), nat_nat_set, nat_nat_set ) 15.99/16.10 ( (fun nat (fun nat nat)), (gcd_gcd nat), (gcd_gcd nat) ) 15.99/16.10 ( (fun nat (fun nat nat)), (gcd_gcd nat), nat_gcd ) 15.99/16.10 ( (fun nat (fun nat nat)), (gcd_gcd nat), nat_lcm ) 15.99/16.10 ( (fun nat (fun nat nat)), nat_gcd, (gcd_gcd nat) ) 15.99/16.10 ( (fun nat (fun nat nat)), nat_lcm, nat_gcd ) 15.99/16.10 ( (fun (fun int bool) int), (the int), (the int) ) 15.99/16.10 ( (fun complex real), re, arg ) 15.99/16.10 ( (fun complex real), im, re ) 15.99/16.10 ( (fun complex real), im, im ) 15.99/16.10 ( (fun complex real), im, arg ) 15.99/16.10 ( (fun complex real), arg, im ) 15.99/16.10 ( (fun bool bool), fNot, fNot ) 15.99/16.10 ( (fun nat (fun real real)), root, root ) 15.99/16.10 ( (fun real (fun real real)), log, log ) 15.99/16.10 ( (fun real (fun real real)), log, powr ) 15.99/16.10 ( (fun real (fun real real)), powr, log ) 15.99/16.10 ( (fun bool (fun bool bool)), fimplies, fimplies ) 15.99/16.10 ( (fun bool (fun bool bool)), fimplies, fconj ) 15.99/16.10 ( (fun bool (fun bool bool)), fimplies, fdisj ) 15.99/16.10 ( (fun bool (fun bool bool)), fconj, fimplies ) 15.99/16.10 ( (fun bool (fun bool bool)), fdisj, fconj ) 15.99/16.10 ( (fun int (fun int (product_prod int int))), negDivAlg, norm_frac ) 15.99/16.10 ( (fun int (fun int (product_prod int int))), posDivAlg, divmod_int ) 15.99/16.10 ( (fun int (fun int (product_prod int int))), divmod_int, posDivAlg ) 15.99/16.10 ( (fun int (fun int (product_prod int int))), divmod_int, divmod_int ) 15.99/16.10 ( (fun int (fun int (product_prod int int))), pdivmod, negDivAlg ) 15.99/16.10 ( (fun int (fun int (product_prod int int))), norm_frac, negDivAlg ) 15.99/16.10 ( (fun int (fun int (product_prod int int))), norm_frac, pdivmod ) 15.99/16.10 ( (fun int (fun int (product_prod int int))), norm_frac, norm_frac ) 15.99/16.10 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd, negateSnd ) 15.99/16.10 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd, normalize ) 15.99/16.10 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize, negateSnd ) 15.99/16.10 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust, adjust ) 15.99/16.10 ( (fun int (fun int (fun int bool))), zcong, noXRRset ) 15.99/16.10 ( (fun int (fun int (fun int bool))), zcongm, zcong ) 15.99/16.10 ( (fun int (fun int (fun int bool))), noXRRset, zcong ) 15.99/16.10 ( (fun int (fun int (fun int bool))), noXRRset, zcongm ) 15.99/16.10 ( (fun int (fun int (fun int bool))), noXRRset, noXRRset ) 15.99/16.10 ( (fun int (fun int (fun int bool))), bnorRset, bnorRset ) 15.99/16.10 ( (fun int (fun int (fun int bool))), bnorRset, wset ) 15.99/16.10 ( (fun int (fun int (fun int bool))), wset, bnorRset ) 15.99/16.10 ( (fun (product_prod int int) bool), frac_1, frac_1 ) 15.99/16.10 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than, int_ge_less_than ) 15.99/16.10 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than, int_ge_less_than2 ) 15.99/16.10 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2, int_ge_less_than ) 15.99/16.10 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral, code_S1047413653umeral ) 15.99/16.10 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset, is_RRset ) 15.99/16.10 ( (fun (fun nat rat) bool), vanishes, vanishes ) 15.99/16.10 ( (fun code_code_numeral nat), (size_size code_code_numeral), (size_size code_code_numeral) ) 15.99/16.10 ( (fun code_code_numeral nat), (size_size code_code_numeral), code_c271388182l_size ) 15.99/16.10 ( (fun code_code_numeral nat), code_c271388182l_size, (size_size code_code_numeral) ) 15.99/16.10 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel, ratrel ) 15.99/16.10 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel, norm_frac_rel ) 15.99/16.10 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel, lazy_small_lazy_rel ) 15.99/16.10 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel, negDivAlg_rel ) 15.99/16.10 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel, posDivAlg_rel ) 15.99/16.10 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel, upto_rel ) 15.99/16.10 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel, norm_frac_rel ) 15.99/16.10 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel, lazy_small_lazy_rel ) 15.99/16.10 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel, posDivAlg_rel ) 15.99/16.10 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq, twoSqu1094008024sum2sq ) 15.99/16.10 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less, pair_less ) 15.99/16.10 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less, pair_leq ) 15.99/16.10 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq, pair_less ) 15.99/16.10 ( (fun complex nat), complex_size, complex_size ) 15.99/16.10 ( (fun complex nat), complex_size, (size_size complex) ) 15.99/16.10 ( (fun complex nat), (size_size complex), complex_size ) 15.99/16.10 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel, nat_gcd_rel ) 15.99/16.10 ( (fun nat (fun nat (product_prod int int))), bezw, bezw ) 15.99/16.10 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd, xzgcd ) 15.99/16.10 ( (fun int (fun nat nat)), nat_aux, nat_aux ) 15.99/16.10 ( (fun int (fun (fun int bool) bool)), rsetR, resSet ) 15.99/16.10 ( (fun int (fun (fun int bool) bool)), resSet, rsetR ) 15.99/16.10 ( (fun int (fun (fun int bool) bool)), resSet, resSet ) 15.99/16.10 ( (fun int (list int)), quickc666637781d_zero, quickc666637781d_zero ) 15.99/16.10 ( (fun (product_prod int int) rat), frct, frct ) 15.99/16.10 ( (fun int (fun int rat)), fract, fract ) 15.99/16.10 ( (fun real (fun real complex)), complex_1, rcis ) 15.99/16.10 ( (fun real (fun real complex)), rcis, complex_1 ) 15.99/16.10 ( (fun real (fun real complex)), rcis, rcis ) 15.99/16.10 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat), (ord_gr676655987ssThan nat) ) 15.99/16.10 ( (fun quickcheck_code_int nat), quickcheck_nat_of, quickcheck_nat_of ) 15.99/16.10 ( (fun int real), (real_1 int), (real_1 int) ) 15.99/16.10 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect, bolzano_bisect ) 15.99/16.10 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR, rRset2norRR ) 15.99/16.10 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int, quickc495462417de_int ) 15.99/16.10 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda, xzgcda ) 15.99/16.10 ( (fun int (fun int (fun int (fun int bool)))), multInvPair, multInvPair ) 15.99/16.10 ( (fun real nat), natfloor, natceiling ) 15.99/16.10 ( (fun real nat), natceiling, natfloor ) 15.99/16.10 ( (fun real nat), natceiling, natceiling ) 15.99/16.10 ( (fun (fun real bool) real), (complete_Sup_Sup real), (complete_Sup_Sup real) ) 15.99/16.10 ( (fun quickcheck_code_int int), quickcheck_int_of, quickcheck_int_of ) 15.99/16.10 ( (fun rat (product_prod int int)), quotient_of, quotient_of ) 15.99/16.10 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral, code_d418564891umeral ) 15.99/16.10 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat, divmod_nat ) 15.99/16.10 ( (fun rat real), ratreal, ratreal ) 15.99/16.10 ( (fun code_code_numeral int), code_int_of, code_int_of ) 15.99/16.10 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel, divmod_int_rel ) 15.99/16.10 ( (fun int quickcheck_code_int), quickcheck_of_int, quickcheck_of_int ) 15.99/16.10 ( (fun int (fun int (fun (fun int bool) bool))), setS, setS ) 15.99/16.10 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux, code_nat_of_aux ) 15.99/16.10 ) 15.99/16.10 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (real_1 int))) (= (hAPP real real (uminus_uminus real) (hAPP int real _let_0 X_1)) (hAPP int real _let_0 (hAPP int int (uminus_uminus int) X_1)))) ) 15.99/16.10 ( (one_one int) ) 15.99/16.10 ( pls ) 15.99/16.10 ( min_1 ) 15.99/16.10 ) 15.99/16.10 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_132995 $$unsorted) (BOUND_VARIABLE_132996 $$unsorted)) (let ((_let_0 (abs_abs X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (times_times X_a))) (let ((_let_3 (fun X_a bool))) (let ((_let_4 (ord_less_eq X_a))) (let ((_let_5 (zero_zero X_a))) (let ((_let_6 (hAPP X_a _let_3 _let_4 _let_5))) (or (not (ordered_ring_abs X_a)) (and (not (hBOOL (hAPP X_a bool (hAPP X_a _let_3 _let_4 BOUND_VARIABLE_132996) _let_5))) (not (hBOOL (hAPP X_a bool _let_6 BOUND_VARIABLE_132996)))) (and (not (hBOOL (hAPP X_a bool (hAPP X_a _let_3 _let_4 BOUND_VARIABLE_132995) _let_5))) (not (hBOOL (hAPP X_a bool _let_6 BOUND_VARIABLE_132995)))) (= (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a _let_0 BOUND_VARIABLE_132996)) (hAPP X_a X_a _let_0 BOUND_VARIABLE_132995)) (hAPP X_a X_a _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_132996) BOUND_VARIABLE_132995))))))))))) ) 15.99/16.10 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.10 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.10 ( int, skv_13, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.10 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.10 ( real, pi, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 15.99/16.10 ( real, (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.10 ( real, (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.10 ( complex, ii, ii ) 15.99/16.10 ( complex, ii, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 15.99/16.10 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.10 ) 15.99/16.10 (instantiation (forall ((V_1 $$unsorted)) (or (not (hBOOL (hAPP int bool nat_neg (hAPP int int (number_number_of int) V_1)))) (= (zero_zero nat) (hAPP int nat (number_number_of nat) V_1))) ) 15.99/16.10 ( pls ) 15.99/16.10 ( (hAPP int int bit1 pls) ) 15.99/16.10 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.99/16.10 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.99/16.10 ( min_1 ) 15.99/16.10 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.10 ) 15.99/16.10 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_133094 $$unsorted) (BOUND_VARIABLE_133095 $$unsorted) (BOUND_VARIABLE_133096 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_133094))) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) BOUND_VARIABLE_133096))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_133095))) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_133096) BOUND_VARIABLE_133095))))) ) 15.99/16.10 ( nat, (zero_zero nat), (one_one nat), (one_one nat) ) 15.99/16.10 ( int, pls, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.99/16.10 ( int, s, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.99/16.10 ( int, t, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.99/16.10 ( int, skv_4, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.99/16.10 ( int, skv_10, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.99/16.10 ) 15.99/16.10 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (hAPP int int (number_number_of int) min_1))) (or (not (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) X_2) zOdd))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (zero_zero int)) X_2))) (= _let_1 (hAPP nat int (hAPP int (fun nat int) (power_power int) _let_1) (hAPP int nat nat_1 X_2)))))) ) 15.99/16.10 ( (one_one int) ) 15.99/16.10 ( (zero_zero int) ) 15.99/16.10 ( min_1 ) 15.99/16.10 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.10 ( s ) 15.99/16.10 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.99/16.10 ( (hAPP int int (number_number_of int) pls) ) 15.99/16.10 ( skv_4 ) 15.99/16.10 ( skv_10 ) 15.99/16.10 ) 15.99/16.10 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_133191 $$unsorted) (BOUND_VARIABLE_133192 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (zero_zero X_a))) (let ((_let_2 (ord_less_eq X_a))) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 _let_1) BOUND_VARIABLE_133192))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_133191) _let_1))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_133192) BOUND_VARIABLE_133191)) _let_1)))))) ) 15.99/16.10 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 15.99/16.10 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.99/16.10 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.99/16.10 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.99/16.10 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.10 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 15.99/16.10 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), pi ) 15.99/16.10 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (one_one real) ) 15.99/16.10 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))), pi ) 15.99/16.10 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 15.99/16.10 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))), (one_one real) ) 15.99/16.10 ) 15.99/16.10 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_133223 $$unsorted) (BOUND_VARIABLE_133224 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (hAPP X_a _let_0 _let_1 (zero_zero X_a)))) (or (not (linordered_idom X_a)) (not (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_133224))) (not (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_133223))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_133223) (one_one X_a)))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_133223) BOUND_VARIABLE_133224)) BOUND_VARIABLE_133224)))))) ) 15.99/16.10 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 15.99/16.10 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.99/16.10 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13 ) 15.99/16.10 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.99/16.10 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.99/16.10 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.99/16.10 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 15.99/16.10 ( complex, ii, ii ) 15.99/16.10 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 15.99/16.10 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 15.99/16.10 ) 15.99/16.10 (instantiation (forall ((X_a $$unsorted)) (or (not (real_normed_vector X_a)) (not (real_algebra_1 X_a)) (not (forall ((K_2 $$unsorted)) (or (not (forall ((X $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP X_a real (norm_norm X_a) (hAPP real X_a (of_real X_a) X))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP real real (norm_norm real) X)) K_2))) )) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) K_2)))) ))) ) 15.99/16.10 ( real ) 15.99/16.10 ( complex ) 15.99/16.10 ) 15.99/16.10 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_133305 $$unsorted) (BOUND_VARIABLE_133306 $$unsorted)) (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun X_a bool))) (let ((_let_2 (ord_less_eq X_a))) (let ((_let_3 (fun nat X_a))) (let ((_let_4 (power_power X_a))) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_1 _let_2 (hAPP nat X_a (hAPP X_a _let_3 _let_4 BOUND_VARIABLE_133305) _let_0)) (hAPP nat X_a (hAPP X_a _let_3 _let_4 BOUND_VARIABLE_133306) _let_0)))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_1 _let_2 (zero_zero X_a)) BOUND_VARIABLE_133306))) (hBOOL (hAPP X_a bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_133305) BOUND_VARIABLE_133306)))))))) ) 15.99/16.10 ( int, (one_one int), t ) 15.99/16.10 ( int, (zero_zero int), (one_one int) ) 15.99/16.10 ( int, (zero_zero int), min_1 ) 15.99/16.10 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.10 ( int, (zero_zero int), s ) 15.99/16.10 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.99/16.10 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.99/16.10 ( int, (zero_zero int), skv_4 ) 15.99/16.10 ( int, (zero_zero int), skv_10 ) 15.99/16.10 ( int, min_1, pls ) 15.99/16.10 ( int, min_1, min_1 ) 15.99/16.10 ( real, (zero_zero real), pi ) 15.99/16.10 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.10 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.10 ( real, (zero_zero real), skv_3 ) 15.99/16.10 ( real, (zero_zero real), skv_5 ) 15.99/16.10 ( real, (zero_zero real), skv_7 ) 15.99/16.10 ( real, (zero_zero real), skv_12 ) 15.99/16.10 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.99/16.10 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.10 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.99/16.10 ( real, skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.10 ) 15.99/16.10 (instantiation (forall ((X_a $$unsorted)) (or (not (real_normed_algebra X_a)) (not (forall ((K_2 $$unsorted)) (or (not (forall ((A_4 $$unsorted) (B_4 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (times_times real))) (let ((_let_2 (norm_norm X_a))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP X_a real _let_2 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) A_4) B_4))) (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real (hAPP real _let_0 _let_1 (hAPP X_a real _let_2 A_4)) (hAPP X_a real _let_2 B_4))) K_2)))))) )) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) K_2)))) ))) ) 15.99/16.10 ( real ) 15.99/16.10 ( complex ) 15.99/16.10 ) 15.99/16.10 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_133346 $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (number_ring X_a)) (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_133346)) (ring_1_Ints X_a))))) ) 15.99/16.10 ( nat, pls ) 15.99/16.10 ( nat, (hAPP int int bit1 pls) ) 15.99/16.10 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.99/16.10 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.99/16.10 ( int, pls ) 15.99/16.10 ( int, (hAPP int int bit1 pls) ) 15.99/16.10 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.99/16.10 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.99/16.10 ( int, min_1 ) 15.99/16.10 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.10 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.99/16.10 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.99/16.10 ( real, min_1 ) 15.99/16.10 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.10 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.99/16.10 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.10 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 15.99/16.10 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.99/16.10 ( complex, min_1 ) 15.99/16.10 ( quickcheck_code_int, (one_one int) ) 15.99/16.10 ( quickcheck_code_int, (zero_zero int) ) 15.99/16.10 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 15.99/16.10 ( code_code_numeral, pls ) 15.99/16.10 ( code_code_numeral, (hAPP int int bit1 pls) ) 15.99/16.10 ) 15.99/16.10 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (plus_plus X_a))) (or (not (ab_semigroup_add X_a)) (= _let_0 (ti (fun X_a (fun X_a X_a)) _let_0)))) ) 15.99/16.10 ( bool ) 15.99/16.10 ( nat ) 15.99/16.10 ( int ) 15.99/16.10 ( (fun int bool) ) 15.99/16.10 ( (fun int (fun int bool)) ) 15.99/16.10 ( (fun int int) ) 15.99/16.10 ( (fun nat bool) ) 15.99/16.10 ( real ) 15.99/16.10 ( (fun real bool) ) 15.99/16.10 ( (fun real real) ) 15.99/16.10 ( rat ) 15.99/16.10 ( complex ) 15.99/16.10 ( (fun nat real) ) 15.99/16.10 ( (product_prod int int) ) 15.99/16.10 ( quickcheck_code_int ) 15.99/16.10 ( code_code_numeral ) 15.99/16.10 ( (fun int (fun int (fun int bool))) ) 15.99/16.10 ( (fun (product_prod int int) bool) ) 15.99/16.10 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 15.99/16.10 ( (fun (product_prod int int) int) ) 15.99/16.10 ( (fun int real) ) 15.99/16.10 ) 15.99/16.10 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (hAPP int (fun _let_0 bool) (member int) X_2))) (or (not (hBOOL (hAPP _let_0 bool _let_1 zEven))) (not (hBOOL (hAPP _let_0 bool _let_1 zOdd)))))) ) 15.99/16.10 ( (one_one int) ) 15.99/16.10 ) 15.99/16.10 (instantiation (forall ((V $$unsorted) (V_2 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (let ((_let_2 (number_number_of nat))) (let ((_let_3 (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 V) V_2)))) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (hAPP int nat _let_2 V)) (hAPP int nat _let_2 V_2))) (and _let_3 (or (not _let_3) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 pls) V_2))))))))) ) 15.99/16.10 ( (one_one int), t ) 15.99/16.10 ( pls, (one_one int) ) 15.99/16.10 ( pls, pls ) 15.99/16.10 ( pls, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.99/16.10 ( pls, min_1 ) 15.99/16.10 ( pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.10 ( min_1, pls ) 15.99/16.10 ( min_1, min_1 ) 15.99/16.10 ( s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.10 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.10 ( skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.10 ( skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.10 ) 15.99/16.10 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_133418 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (zero_zero X_a))) (or (not (ordered_ab_group_add X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_133418))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_133418) _let_2))))))) ) 15.99/16.10 ( int, (one_one int) ) 15.99/16.10 ( int, (zero_zero int) ) 15.99/16.10 ( int, pls ) 15.99/16.10 ( int, min_1 ) 15.99/16.10 ( real, (one_one real) ) 15.99/16.10 ( real, (zero_zero real) ) 15.99/16.10 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.10 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.10 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.99/16.10 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.10 ( real, skv_5 ) 15.99/16.10 ( complex, (one_one complex) ) 15.99/16.10 ( complex, ii ) 15.99/16.10 ) 15.99/16.10 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_133476 $$unsorted) (BOUND_VARIABLE_133477 $$unsorted) (BOUND_VARIABLE_133478 $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (dvd_dvd nat))) (let ((_let_2 (fun nat X_a))) (or (not (order X_a)) (not (hBOOL (hAPP _let_2 bool (hAPP (fun nat _let_0) (fun _let_2 bool) (mono nat X_a) _let_1) BOUND_VARIABLE_133478))) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 BOUND_VARIABLE_133476) BOUND_VARIABLE_133477))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (hAPP nat X_a BOUND_VARIABLE_133478 BOUND_VARIABLE_133476)) (hAPP nat X_a BOUND_VARIABLE_133478 BOUND_VARIABLE_133477))))))) ) 15.99/16.10 ( int, (zero_zero nat), (zero_zero nat), (semiring_1_of_nat int) ) 15.99/16.10 ( int, (zero_zero nat), (hAPP nat nat suc (zero_zero nat)), (semiring_1_of_nat int) ) 15.99/16.10 ( int, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))), (semiring_1_of_nat int) ) 15.99/16.10 ( int, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (semiring_1_of_nat int) ) 15.99/16.10 ) 15.99/16.10 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_133500 $$unsorted) (BOUND_VARIABLE_133501 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)))) (or (not (linord581940658strict X_a)) (= (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_133500) BOUND_VARIABLE_133501))) (or (and (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_133500) (zero_zero X_a))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_133501) (zero_zero X_a)))) (and (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_133501)) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_133500))))))) ) 15.99/16.10 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 15.99/16.10 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.99/16.10 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13 ) 15.99/16.10 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.99/16.10 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.99/16.10 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.99/16.10 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 15.99/16.10 ( complex, ii, ii ) 15.99/16.10 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 15.99/16.10 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 15.99/16.10 ) 15.99/16.10 (instantiation (forall ((B $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (let ((_let_2 (ord_less int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 A_1) C))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 B) C))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 B) A_1)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 A_1) B)))))) ) 15.99/16.10 ( (one_one int), pls, min_1 ) 15.99/16.10 ( pls, pls, pls ) 15.99/16.10 ( min_1, min_1, pls ) 15.99/16.10 ( s, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.10 ( t, min_1, min_1 ) 15.99/16.10 ( skv_4, pls, (one_one int) ) 15.99/16.10 ( skv_10, pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.10 ) 15.99/16.10 (instantiation (forall ((U_1 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun nat bool))) (let ((_let_2 (zero_zero int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) _let_2) U_1))) (= (hAPP _let_1 _let_0 (hAPP (fun nat int) (fun _let_1 _let_0) (image nat int) (semiring_1_of_nat int)) (hAPP nat _let_1 (ord_lessThan nat) (hAPP int nat nat_1 U_1))) (hAPP int _let_0 (hAPP int (fun int _let_0) (ord_atLeastLessThan int) _let_2) U_1)))))) ) 15.99/16.10 ( (one_one int) ) 15.99/16.10 ( (zero_zero int) ) 15.99/16.10 ( min_1 ) 15.99/16.10 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.10 ( s ) 15.99/16.10 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.99/16.10 ( (hAPP int int (number_number_of int) pls) ) 15.99/16.10 ( skv_4 ) 15.99/16.10 ( skv_10 ) 15.99/16.10 ) 15.99/16.10 (instantiation (forall ((X_1 $$unsorted) (N_1 $$unsorted) (M $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)))) (or (not (hBOOL (hAPP nat bool _let_1 M))) (not (hBOOL (hAPP nat bool _let_1 N_1))) (= (hAPP real real (hAPP nat _let_0 root (hAPP nat nat (hAPP nat (fun nat nat) (times_times nat) M) N_1)) X_1) (hAPP real real (hAPP nat _let_0 root M) (hAPP real real (hAPP nat _let_0 root N_1) X_1)))))) ) 15.99/16.10 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.10 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.10 ) 15.99/16.10 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_133691 $$unsorted)) (or (not (linordered_idom X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) BOUND_VARIABLE_133691))) (= (one_one X_a) (hAPP X_a X_a (sgn_sgn X_a) BOUND_VARIABLE_133691))) ) 15.99/16.10 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.10 ( int, (one_one int) ) 15.99/16.10 ( int, pls ) 15.99/16.10 ( int, min_1 ) 15.99/16.10 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.10 ( real, (zero_zero real) ) 15.99/16.10 ( real, pi ) 15.99/16.10 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.10 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.10 ( real, skv_2 ) 15.99/16.10 ( real, skv_8 ) 15.99/16.10 ( real, skv_9 ) 15.99/16.10 ( rat, (zero_zero rat) ) 15.99/16.10 ) 15.99/16.10 (instantiation (forall ((W $$unsorted)) (let ((_let_0 (one_one int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (uminus_uminus int))) (let ((_let_3 (hAPP int int (number_number_of int) W))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) _let_3) (zero_zero int)))) (= (hAPP int int (hAPP int (fun int int) (div_div int) _let_0) _let_3) (hAPP _let_1 int (product_fst int int) (hAPP _let_1 _let_1 negateSnd (hAPP int _let_1 (hAPP int (fun int _let_1) negDivAlg (hAPP int int _let_2 _let_0)) (hAPP int int _let_2 _let_3)))))))))) ) 15.99/16.10 ( pls ) 15.99/16.10 ( (hAPP int int bit1 pls) ) 15.99/16.10 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.99/16.10 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.99/16.10 ( min_1 ) 15.99/16.10 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.10 ) 15.99/16.10 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_133868 $$unsorted) (BOUND_VARIABLE_133869 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) BOUND_VARIABLE_133868) (hAPP X_a int (archim2085082626_floor X_a) BOUND_VARIABLE_133869))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_133868)) BOUND_VARIABLE_133869)))) ) 15.99/16.10 ( real, (zero_zero int), pi ) 15.99/16.10 ( real, (zero_zero int), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.10 ( real, (zero_zero int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.10 ( real, (zero_zero int), skv_3 ) 15.99/16.10 ( real, (zero_zero int), skv_5 ) 15.99/16.10 ( real, (zero_zero int), skv_7 ) 15.99/16.10 ( real, (zero_zero int), skv_12 ) 15.99/16.10 ) 15.99/16.10 (instantiation (forall ((Ma $$unsorted) (N $$unsorted)) (let ((_let_0 (even_odd_even nat))) (= (= (hBOOL (hAPP nat bool _let_0 Ma)) (not (hBOOL (hAPP nat bool _let_0 N)))) (not (hBOOL (hAPP nat bool _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) Ma) N)))))) ) 15.99/16.10 ( (one_one nat), (one_one nat) ) 15.99/16.10 ) 15.99/16.10 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (uminus_uminus X_a))) (or (not (uminus X_a)) (= _let_0 (ti (fun X_a X_a) _let_0)))) ) 15.99/16.10 ( bool ) 15.99/16.10 ( nat ) 15.99/16.10 ( int ) 15.99/16.10 ( (fun int bool) ) 15.99/16.10 ( (fun int (fun int bool)) ) 15.99/16.10 ( (fun int int) ) 15.99/16.10 ( (fun nat bool) ) 15.99/16.10 ( real ) 15.99/16.10 ( (fun real bool) ) 15.99/16.10 ( (fun real real) ) 15.99/16.10 ( rat ) 15.99/16.10 ( complex ) 15.99/16.10 ( (fun nat real) ) 15.99/16.10 ( (product_prod int int) ) 15.99/16.10 ( code_code_numeral ) 15.99/16.10 ( (fun int (fun int (fun int bool))) ) 15.99/16.10 ( (fun (product_prod int int) bool) ) 15.99/16.10 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 15.99/16.10 ( (fun (product_prod int int) int) ) 15.99/16.10 ( (fun int real) ) 15.99/16.10 ) 15.99/16.10 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_0 (fun nat bool))) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) M) N_1))) (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) (hAPP nat nat suc M)) N_1)))) ) 15.99/16.10 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.10 ) 15.99/16.10 (instantiation (forall ((Z_1 $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted) (M $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun nat int))) (let ((_let_3 (power_power int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int _let_1 zcong X_1) Y_1) M))) (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int _let_1 zcong (hAPP nat int (hAPP int _let_2 _let_3 X_1) Z_1)) (hAPP nat int (hAPP int _let_2 _let_3 Y_1) Z_1)) M))))))) ) 15.99/16.10 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s, s1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.10 ) 15.99/16.10 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (combi X_a))) (= _let_0 (ti (fun X_a X_a) _let_0))) ) 15.99/16.10 ( bool ) 15.99/16.10 ( nat ) 15.99/16.10 ( int ) 15.99/16.10 ( (fun int bool) ) 15.99/16.10 ( (fun int (fun int bool)) ) 15.99/16.10 ( (fun int int) ) 15.99/16.10 ( (fun nat bool) ) 15.99/16.10 ( real ) 15.99/16.10 ( (fun real bool) ) 15.99/16.10 ( (fun real real) ) 15.99/16.10 ( complex ) 15.99/16.10 ( (fun nat real) ) 15.99/16.10 ( (product_prod int int) ) 15.99/16.10 ( code_code_numeral ) 15.99/16.10 ( (fun int (fun int (fun int bool))) ) 15.99/16.10 ( (fun (product_prod int int) bool) ) 15.99/16.10 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 15.99/16.10 ( (fun (product_prod int int) int) ) 15.99/16.10 ( (fun int real) ) 15.99/16.10 ) 15.99/16.10 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_0 (fun int rat))) (= (hAPP int rat (hAPP int _let_0 fract B) A_1) (hAPP rat rat (inverse_inverse rat) (hAPP int rat (hAPP int _let_0 fract A_1) B)))) ) 15.99/16.10 ( (one_one int), (one_one int) ) 15.99/16.10 ( (one_one int), (zero_zero int) ) 15.99/16.10 ( (zero_zero int), (one_one int) ) 15.99/16.10 ) 15.99/16.10 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_134080 $$unsorted) (BOUND_VARIABLE_134081 $$unsorted)) (or (not (ab_group_add X_a)) (= (= (zero_zero X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) BOUND_VARIABLE_134080) BOUND_VARIABLE_134081)) (= (ti X_a BOUND_VARIABLE_134081) (ti X_a BOUND_VARIABLE_134080)))) ) 15.99/16.10 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.99/16.10 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 15.99/16.10 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 15.99/16.10 ) 15.99/16.10 (instantiation (forall ((P_5 $$unsorted)) (let ((_let_0 (number_number_of int))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (hAPP int int bit0 _let_1))) (let ((_let_3 (ti int P_5))) (or (not (hBOOL (hAPP int bool zprime P_5))) (= (hAPP int int _let_0 _let_2) _let_3) (= (hAPP int int _let_0 (hAPP int int bit1 _let_1)) _let_3) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP int int _let_0 (hAPP int int bit1 _let_2))) P_5))))))) ) 15.99/16.10 ( pls ) 15.99/16.10 ( min_1 ) 15.99/16.10 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.10 ( s ) 15.99/16.10 ( m ) 15.99/16.10 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.10 ( s1 ) 15.99/16.10 ( t ) 15.99/16.10 ) 15.99/16.10 (instantiation (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) X_1))) (= X_1 (hAPP real real (exp real) (hAPP real real ln X_1)))) ) 15.99/16.10 ( (one_one real) ) 15.99/16.10 ( pi ) 15.99/16.10 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.10 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.10 ( skv_2 ) 15.99/16.10 ( skv_8 ) 15.99/16.10 ( skv_9 ) 15.99/16.10 ) 15.99/16.10 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_134129 $$unsorted)) (or (not (number_ring X_a)) (= (ti X_a BOUND_VARIABLE_134129) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_134129) (hAPP int X_a (number_number_of X_a) pls)))) ) 15.99/16.10 ( bool, fFalse ) 15.99/16.10 ( bool, fTrue ) 15.99/16.10 ( nat, (one_one nat) ) 15.99/16.10 ( int, pls ) 15.99/16.10 ( int, min_1 ) 15.99/16.10 ( int, s ) 15.99/16.10 ( int, m ) 15.99/16.10 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.99/16.10 ( int, s1 ) 15.99/16.10 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.10 ( int, t ) 15.99/16.10 ( (fun int bool), nat_neg ) 15.99/16.10 ( (fun int bool), zprime ) 15.99/16.10 ( (fun int bool), zEven ) 15.99/16.10 ( (fun int bool), zOdd ) 15.99/16.10 ( (fun int bool), (even_odd_even int) ) 15.99/16.10 ( (fun int bool), twoSqu1091635170sum2sq ) 15.99/16.10 ( (fun int bool), nat_is_nat ) 15.99/16.10 ( (fun int (fun int bool)), norRRset ) 15.99/16.10 ( (fun int (fun int bool)), quadRes ) 15.99/16.10 ( (fun int (fun int bool)), sRStar ) 15.99/16.10 ( (fun int (fun int bool)), d22set ) 15.99/16.10 ( (fun int (fun int bool)), sr ) 15.99/16.10 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 15.99/16.10 ( (fun int int), zfact ) 15.99/16.10 ( (fun int int), bit0 ) 15.99/16.10 ( (fun int int), bit1 ) 15.99/16.10 ( (fun int int), (fact_fact int) ) 15.99/16.10 ( (fun int int), pred ) 15.99/16.10 ( (fun int int), succ ) 15.99/16.10 ( (fun nat bool), (even_odd_even nat) ) 15.99/16.10 ( (fun nat bool), prime ) 15.99/16.10 ( (fun nat nat), suc ) 15.99/16.10 ( (fun nat nat), (fact_fact nat) ) 15.99/16.10 ( (fun nat nat), fact ) 15.99/16.10 ( (fun nat nat), nat_size ) 15.99/16.10 ( (fun nat nat), (size_size nat) ) 15.99/16.10 ( (fun (product_prod nat nat) bool), pred_nat ) 15.99/16.10 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 15.99/16.10 ( real, pi ) 15.99/16.10 ( (fun real real), ln ) 15.99/16.10 ( (fun real real), cos ) 15.99/16.10 ( (fun real real), sqrt ) 15.99/16.10 ( (fun real real), sin ) 15.99/16.10 ( (fun real real), arccos ) 15.99/16.10 ( (fun real real), arcsin ) 15.99/16.10 ( (fun real real), tan ) 15.99/16.10 ( (fun real real), arctan ) 15.99/16.10 ( (fun nat (fun nat bool)), coprime ) 15.99/16.10 ( complex, ii ) 15.99/16.10 ( (fun nat real), (real_1 nat) ) 15.99/16.10 ( (fun nat real), sin_coeff ) 15.99/16.10 ( (fun nat real), cos_coeff ) 15.99/16.10 ( (filter nat), sequentially ) 15.99/16.10 ( (fun int (fun int int)), (gcd_gcd int) ) 15.99/16.10 ( (fun int (fun int int)), legendre ) 15.99/16.10 ( (fun int (fun int int)), legacy_zgcd ) 15.99/16.10 ( (fun int (fun int int)), standardRes ) 15.99/16.10 ( (fun int (fun int int)), nat_tsub ) 15.99/16.10 ( (fun int (fun int int)), multInv ) 15.99/16.10 ( (fun int (fun int int)), z3mod ) 15.99/16.10 ( (fun int (fun int int)), z3div ) 15.99/16.10 ( (fun int (fun int int)), int_gcd ) 15.99/16.10 ( (fun int (fun int int)), int_lcm ) 15.99/16.10 ( (fun int (fun int int)), inv ) 15.99/16.10 ( (fun complex complex), expi ) 15.99/16.10 ( (fun complex complex), cnj ) 15.99/16.10 ( (fun real complex), cis ) 15.99/16.10 ( (fun int nat), nat_1 ) 15.99/16.10 ( (fun int nat), phi ) 15.99/16.10 ( (fun (fun int bool) bool), nat_nat_set ) 15.99/16.10 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 15.99/16.10 ( (fun nat (fun nat nat)), nat_gcd ) 15.99/16.10 ( (fun nat (fun nat nat)), nat_lcm ) 15.99/16.10 ( (fun (fun int bool) int), (the int) ) 15.99/16.10 ( (fun complex real), re ) 15.99/16.10 ( (fun complex real), im ) 15.99/16.10 ( (fun complex real), arg ) 15.99/16.10 ( (fun bool bool), fNot ) 15.99/16.10 ( (fun nat (fun real real)), root ) 15.99/16.10 ( (fun real (fun real real)), log ) 15.99/16.10 ( (fun real (fun real real)), powr ) 15.99/16.10 ( (fun bool (fun bool bool)), fimplies ) 15.99/16.10 ( (fun bool (fun bool bool)), fconj ) 15.99/16.10 ( (fun bool (fun bool bool)), fdisj ) 15.99/16.10 ( (fun int (fun int (product_prod int int))), negDivAlg ) 15.99/16.10 ( (fun int (fun int (product_prod int int))), posDivAlg ) 15.99/16.10 ( (fun int (fun int (product_prod int int))), divmod_int ) 15.99/16.10 ( (fun int (fun int (product_prod int int))), pdivmod ) 15.99/16.10 ( (fun int (fun int (product_prod int int))), norm_frac ) 15.99/16.10 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 15.99/16.10 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 15.99/16.10 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 15.99/16.10 ( (fun int (fun int (fun int bool))), zcong ) 15.99/16.10 ( (fun int (fun int (fun int bool))), zcongm ) 15.99/16.10 ( (fun int (fun int (fun int bool))), noXRRset ) 15.99/16.10 ( (fun int (fun int (fun int bool))), bnorRset ) 15.99/16.10 ( (fun int (fun int (fun int bool))), wset ) 15.99/16.10 ( (fun (product_prod int int) bool), frac_1 ) 15.99/16.10 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 15.99/16.10 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 15.99/16.10 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 15.99/16.10 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 15.99/16.10 ( (fun (fun nat rat) bool), vanishes ) 15.99/16.10 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 15.99/16.10 ( (fun code_code_numeral nat), code_c271388182l_size ) 15.99/16.10 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 15.99/16.10 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 15.99/16.10 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 15.99/16.10 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 15.99/16.10 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 15.99/16.10 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 15.99/16.10 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 15.99/16.10 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 15.99/16.10 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 15.99/16.10 ( (fun complex nat), complex_size ) 15.99/16.10 ( (fun complex nat), (size_size complex) ) 15.99/16.10 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 15.99/16.10 ( (fun nat (fun nat (product_prod int int))), bezw ) 15.99/16.10 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 15.99/16.10 ( (fun int (fun nat nat)), nat_aux ) 15.99/16.10 ( (fun int (fun (fun int bool) bool)), rsetR ) 15.99/16.10 ( (fun int (fun (fun int bool) bool)), resSet ) 15.99/16.10 ( (fun int (list int)), quickc666637781d_zero ) 15.99/16.10 ( (fun (product_prod int int) rat), frct ) 15.99/16.10 ( (fun int (fun int rat)), fract ) 15.99/16.10 ( (fun real (fun real complex)), complex_1 ) 15.99/16.10 ( (fun real (fun real complex)), rcis ) 15.99/16.10 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 15.99/16.10 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 15.99/16.10 ( (fun int real), (real_1 int) ) 15.99/16.10 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 15.99/16.10 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 15.99/16.10 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 15.99/16.10 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 15.99/16.10 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 15.99/16.10 ( (fun real nat), natfloor ) 15.99/16.10 ( (fun real nat), natceiling ) 15.99/16.10 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 15.99/16.10 ( (fun quickcheck_code_int int), quickcheck_int_of ) 15.99/16.10 ( (fun rat (product_prod int int)), quotient_of ) 15.99/16.10 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 15.99/16.10 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 15.99/16.10 ( (fun rat real), ratreal ) 15.99/16.10 ( (fun code_code_numeral int), code_int_of ) 15.99/16.10 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 15.99/16.10 ( (fun int quickcheck_code_int), quickcheck_of_int ) 15.99/16.10 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 15.99/16.10 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 15.99/16.10 ) 15.99/16.10 (instantiation (forall ((Y_2 $$unsorted) (X_2 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member int))) (or (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 X_2) zEven))) (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 Y_2) zEven))) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP int int (hAPP int (fun int int) (plus_plus int) X_2) Y_2)) zEven)))))) ) 15.99/16.10 ( (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.99/16.10 ( (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.10 ) 15.99/16.10 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_134154 $$unsorted) (BOUND_VARIABLE_134155 $$unsorted)) (let ((_let_0 (fun (filter nat) bool))) (let ((_let_1 (fun nat X_a))) (or (not (metric_space X_a)) (not (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_0 (hAPP _let_1 (fun X_a _let_0) (tendsto nat X_a) BOUND_VARIABLE_134154) BOUND_VARIABLE_134155) sequentially))) (= (hAPP _let_1 X_a (lim X_a) BOUND_VARIABLE_134154) (ti X_a BOUND_VARIABLE_134155))))) ) 15.99/16.10 ( real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real) ) 15.99/16.10 ) 15.99/16.10 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_134250 $$unsorted) (BOUND_VARIABLE_134251 $$unsorted)) (or (not (group_add X_a)) (= (= (zero_zero X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_134250) BOUND_VARIABLE_134251)) (= (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_134250) (ti X_a BOUND_VARIABLE_134251)))) ) 15.99/16.10 ( nat, (one_one nat), (one_one nat) ) 15.99/16.10 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 15.99/16.10 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 15.99/16.10 ) 15.99/16.10 (instantiation (forall ((Y_2 $$unsorted) (X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) Y_2) X_2))) (= X_2 (hAPP _let_0 real (complete_Sup_Sup real) (hAPP real _let_0 (hAPP real (fun real _let_0) (ord_atLeastLessThan real) Y_2) X_2))))) ) 15.99/16.10 ( (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.10 ( (zero_zero real), pi ) 15.99/16.10 ( (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.10 ( (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.10 ( (zero_zero real), skv_2 ) 15.99/16.10 ( (zero_zero real), skv_8 ) 15.99/16.10 ( (zero_zero real), skv_9 ) 15.99/16.10 ( pi, (zero_zero real) ) 15.99/16.10 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.10 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.10 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 15.99/16.10 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.99/16.10 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 15.99/16.10 ) 15.99/16.10 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_134312 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (one_one X_a)) BOUND_VARIABLE_134312)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (one_one int)) (hAPP X_a int (archimedean_ceiling X_a) BOUND_VARIABLE_134312))))) ) 15.99/16.10 ( int, t ) 15.99/16.10 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.10 ) 15.99/16.10 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_134329 $$unsorted) (BOUND_VARIABLE_134330 $$unsorted)) (let ((_let_0 (norm_norm X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (minus_minus X_a))) (or (not (real_normed_vector X_a)) (= (hAPP X_a real _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_134329) BOUND_VARIABLE_134330)) (hAPP X_a real _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_134330) BOUND_VARIABLE_134329))))))) ) 15.99/16.10 ( int, (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.10 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.99/16.10 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 15.99/16.10 ( real, (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))), (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))) ) 15.99/16.10 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 15.99/16.10 ( code_code_numeral, (one_one code_code_numeral), (zero_zero code_code_numeral) ) 15.99/16.10 ) 15.99/16.10 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_134379 $$unsorted) (BOUND_VARIABLE_134380 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (div_mod X_a))) (or (not (semiring_div X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_0 (plus_plus X_a) BOUND_VARIABLE_134379) BOUND_VARIABLE_134380)) BOUND_VARIABLE_134379) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_134380) BOUND_VARIABLE_134379))))) ) 15.99/16.10 ( nat, (one_one nat), (one_one nat) ) 15.99/16.10 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 15.99/16.10 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 15.99/16.10 ) 15.99/16.11 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_134398 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)))) (or (not (linord219039673up_add X_a)) (= (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_134398)) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_134398) BOUND_VARIABLE_134398)))))) ) 15.99/16.11 ( nat, (one_one nat) ) 15.99/16.11 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.99/16.11 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.11 ) 15.99/16.11 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_134456 $$unsorted) (BOUND_VARIABLE_134457 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (or (not (ordere142940540dd_abs X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_134456) BOUND_VARIABLE_134457))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_134456)) BOUND_VARIABLE_134457))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_134456)) BOUND_VARIABLE_134457))))) ) 15.99/16.11 ( int, (one_one int), pls ) 15.99/16.11 ( int, (one_one int), min_1 ) 15.99/16.11 ( int, (one_one int), t ) 15.99/16.11 ( int, (zero_zero int), (one_one int) ) 15.99/16.11 ( int, (zero_zero int), min_1 ) 15.99/16.11 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.11 ( int, (zero_zero int), s ) 15.99/16.11 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.99/16.11 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.99/16.11 ( int, (zero_zero int), skv_4 ) 15.99/16.11 ( int, (zero_zero int), skv_10 ) 15.99/16.11 ( int, pls, (one_one int) ) 15.99/16.11 ( int, pls, min_1 ) 15.99/16.11 ( int, pls, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.11 ( int, pls, s ) 15.99/16.11 ( int, pls, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.99/16.11 ( int, pls, (hAPP int int (number_number_of int) pls) ) 15.99/16.11 ( int, pls, skv_4 ) 15.99/16.11 ( int, pls, skv_10 ) 15.99/16.11 ( int, min_1, pls ) 15.99/16.11 ( int, min_1, min_1 ) 15.99/16.11 ( real, (zero_zero real), pi ) 15.99/16.11 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.11 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.11 ( real, (zero_zero real), skv_3 ) 15.99/16.11 ( real, (zero_zero real), skv_5 ) 15.99/16.11 ( real, (zero_zero real), skv_7 ) 15.99/16.11 ( real, (zero_zero real), skv_12 ) 15.99/16.11 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.99/16.11 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.11 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.99/16.11 ( real, skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.11 ) 15.99/16.11 (instantiation (forall ((N $$unsorted)) (= (hBOOL (hAPP nat bool (even_odd_even nat) N)) (not (forall ((M_2 $$unsorted)) (not (= N (hAPP nat nat (hAPP nat (fun nat nat) (times_times nat) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) M_2))) ))) ) 15.99/16.11 ( (zero_zero nat) ) 15.99/16.11 ( (one_one nat) ) 15.99/16.11 ) 15.99/16.11 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_134594 $$unsorted) (BOUND_VARIABLE_134595 $$unsorted) (BOUND_VARIABLE_134596 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (or (not (order X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_134595) BOUND_VARIABLE_134596))) (not (= (ti X_a BOUND_VARIABLE_134594) (ti X_a BOUND_VARIABLE_134595))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_134594) BOUND_VARIABLE_134596))))) ) 15.99/16.11 ( int, pls, min_1, pls ) 15.99/16.11 ( int, min_1, pls, (one_one int) ) 15.99/16.11 ( int, s, pls, pls ) 15.99/16.11 ( int, m, min_1, min_1 ) 15.99/16.11 ( int, s1, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.11 ( int, t, pls, min_1 ) 15.99/16.11 ( real, pi, pi, (zero_zero real) ) 15.99/16.11 ) 15.99/16.11 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_134667 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (or (not (number_ring X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_134667) (hAPP int X_a (number_number_of X_a) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP X_a X_a (hAPP X_a _let_0 (plus_plus X_a) BOUND_VARIABLE_134667) BOUND_VARIABLE_134667)))) ) 15.99/16.11 ( nat, (one_one nat) ) 15.99/16.11 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.11 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.11 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.99/16.11 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.11 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.11 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.11 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.11 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 15.99/16.11 ( complex, ii ) 15.99/16.11 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.11 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 15.99/16.11 ) 15.99/16.11 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_134823 $$unsorted)) (or (not (sgn_div_norm X_a)) (= (hAPP X_a X_a (hAPP real (fun X_a X_a) (scaleR_scaleR X_a) (hAPP real real (inverse_inverse real) (hAPP X_a real (norm_norm X_a) BOUND_VARIABLE_134823))) BOUND_VARIABLE_134823) (hAPP X_a X_a (sgn_sgn X_a) BOUND_VARIABLE_134823))) ) 15.99/16.11 ( real, (zero_zero real) ) 15.99/16.11 ( rat, (zero_zero rat) ) 15.99/16.11 ) 15.99/16.11 (instantiation (forall ((Nat_1 $$unsorted)) (= (hAPP nat nat nat_size (hAPP nat nat suc Nat_1)) (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP nat nat nat_size Nat_1)) (hAPP nat nat suc (zero_zero nat)))) ) 15.99/16.11 ( (zero_zero nat) ) 15.99/16.11 ( (hAPP nat nat suc (zero_zero nat)) ) 15.99/16.11 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 15.99/16.11 ) 15.99/16.11 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (preorder T_1)) (preorder (fun T_2 T_1))) ) 15.99/16.11 ( bool, bool ) 15.99/16.11 ( bool, (fun bool bool) ) 15.99/16.11 ( nat, bool ) 15.99/16.11 ( nat, nat ) 15.99/16.11 ( nat, int ) 15.99/16.11 ( nat, (fun int int) ) 15.99/16.11 ( nat, (fun nat bool) ) 15.99/16.11 ( nat, (fun nat nat) ) 15.99/16.11 ( nat, (product_prod nat nat) ) 15.99/16.11 ( nat, (fun (product_prod nat nat) bool) ) 15.99/16.11 ( nat, (fun nat (fun (product_prod nat nat) bool)) ) 15.99/16.11 ( nat, real ) 15.99/16.11 ( nat, (fun real real) ) 15.99/16.11 ( nat, rat ) 15.99/16.11 ( nat, (fun nat (fun nat bool)) ) 15.99/16.11 ( nat, complex ) 15.99/16.11 ( nat, (product_prod int int) ) 15.99/16.11 ( nat, (fun bool bool) ) 15.99/16.11 ( nat, (product_prod real real) ) 15.99/16.11 ( nat, (fun nat (product_prod nat nat)) ) 15.99/16.11 ( nat, (fun nat (product_prod int int)) ) 15.99/16.11 ( int, bool ) 15.99/16.11 ( int, nat ) 15.99/16.11 ( int, int ) 15.99/16.11 ( int, (fun int bool) ) 15.99/16.11 ( int, (fun int (fun int bool)) ) 15.99/16.11 ( int, (fun int int) ) 15.99/16.11 ( int, (fun nat bool) ) 15.99/16.11 ( int, (fun nat nat) ) 15.99/16.11 ( int, real ) 15.99/16.11 ( int, (fun real real) ) 15.99/16.11 ( int, rat ) 15.99/16.11 ( int, (fun int rat) ) 15.99/16.11 ( int, (fun nat int) ) 15.99/16.11 ( int, (fun nat real) ) 15.99/16.11 ( int, (product_prod int int) ) 15.99/16.11 ( int, (fun int (product_prod int int)) ) 15.99/16.11 ( int, (fun (fun int bool) bool) ) 15.99/16.11 ( int, quickcheck_code_int ) 15.99/16.11 ( int, (fun bool bool) ) 15.99/16.11 ( int, (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 15.99/16.11 ( int, (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)) ) 15.99/16.11 ( int, (fun int (fun int (fun int bool))) ) 15.99/16.11 ( int, (fun (product_prod int int) bool) ) 15.99/16.11 ( int, (fun int (fun (product_prod int int) bool)) ) 15.99/16.11 ( int, (fun int (fun bool bool)) ) 15.99/16.11 ( int, (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 15.99/16.11 ( int, (fun (fun int int) (fun int bool)) ) 15.99/16.11 ( int, (fun (product_prod int int) int) ) 15.99/16.11 ( int, (product_prod int (product_prod int int)) ) 15.99/16.11 ( int, (fun int (product_prod int (product_prod int int))) ) 15.99/16.11 ( int, (fun int (fun int (product_prod int (product_prod int int)))) ) 15.99/16.11 ( int, (fun int (fun int (fun int (product_prod int (product_prod int int))))) ) 15.99/16.11 ( int, (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))) ) 15.99/16.11 ( int, (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))) ) 15.99/16.11 ( int, (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))) ) 15.99/16.11 ( int, (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))))) ) 15.99/16.11 ( int, (fun int (fun (fun int bool) bool)) ) 15.99/16.11 ( int, (list int) ) 15.99/16.11 ( int, (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 15.99/16.11 ( int, (fun int real) ) 15.99/16.11 ( int, (fun nat (fun bool bool)) ) 15.99/16.11 ( int, (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 15.99/16.11 ( int, (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 15.99/16.11 ( (fun int bool), bool ) 15.99/16.11 ( (fun int bool), int ) 15.99/16.11 ( (fun int bool), (fun int bool) ) 15.99/16.11 ( (fun int bool), (fun int (fun int bool)) ) 15.99/16.11 ( (fun int bool), (fun int (fun int int)) ) 15.99/16.11 ( (fun int bool), (fun int (fun bool bool)) ) 15.99/16.11 ( (fun int bool), (fun (fun int int) (fun int bool)) ) 15.99/16.11 ( (fun int bool), (fun real (fun int (fun int bool))) ) 15.99/16.11 ( (fun int (fun int bool)), (fun int bool) ) 15.99/16.11 ( (fun int (fun int bool)), (fun int (fun int bool)) ) 15.99/16.11 ( (fun int (fun int bool)), (fun int (fun (fun int int) (fun int bool))) ) 15.99/16.11 ( (fun int (fun int bool)), (fun int (fun int (fun bool bool))) ) 15.99/16.11 ( (fun int int), (fun int bool) ) 15.99/16.11 ( (fun int int), (fun int (fun int bool)) ) 15.99/16.11 ( (fun int int), (fun int int) ) 15.99/16.11 ( (fun int int), (fun int (fun int int)) ) 15.99/16.11 ( (fun int int), (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 15.99/16.11 ( (fun int int), (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 15.99/16.11 ( (fun nat bool), bool ) 15.99/16.11 ( (fun nat bool), (fun nat bool) ) 15.99/16.11 ( (fun nat bool), (fun nat (fun bool bool)) ) 15.99/16.11 ( (fun nat bool), (fun int (fun nat bool)) ) 15.99/16.11 ( (fun nat bool), (fun real (fun int (fun nat bool))) ) 15.99/16.11 ( (fun nat nat), (fun nat (fun nat bool)) ) 15.99/16.11 ( (fun nat nat), (fun nat real) ) 15.99/16.11 ( (fun nat nat), (fun nat (fun nat nat)) ) 15.99/16.11 ( (product_prod nat nat), bool ) 15.99/16.11 ( (product_prod nat nat), (fun (product_prod nat nat) bool) ) 15.99/16.11 ( real, bool ) 15.99/16.11 ( real, nat ) 15.99/16.11 ( real, (fun int bool) ) 15.99/16.11 ( real, (fun int (fun int bool)) ) 15.99/16.11 ( real, real ) 15.99/16.11 ( real, (fun real bool) ) 15.99/16.11 ( real, (fun real real) ) 15.99/16.11 ( real, complex ) 15.99/16.11 ( real, (fun nat real) ) 15.99/16.11 ( real, (fun real complex) ) 15.99/16.11 ( real, (fun bool bool) ) 15.99/16.11 ( real, (fun (filter nat) bool) ) 15.99/16.11 ( real, (fun nat (product_prod real real)) ) 15.99/16.11 ( real, (fun real (fun nat (product_prod real real))) ) 15.99/16.11 ( real, (fun (filter real) bool) ) 15.99/16.11 ( real, (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 15.99/16.11 ( real, (let ((_let_0 (fun int bool))) (fun _let_0 (fun int _let_0))) ) 15.99/16.11 ( real, (fun int (fun int (fun bool bool))) ) 15.99/16.11 ( real, (fun (fun int (fun int real)) (fun int (fun int bool))) ) 15.99/16.11 ( real, (fun (fun int real) (fun int bool)) ) 15.99/16.11 ( real, (fun int (fun nat bool)) ) 15.99/16.11 ( real, (let ((_let_0 (fun nat bool))) (fun _let_0 (fun int _let_0))) ) 15.99/16.11 ( real, (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 15.99/16.11 ( real, (fun int (fun nat (fun bool bool))) ) 15.99/16.11 ( real, (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 15.99/16.11 ( real, (fun (fun nat real) (fun nat bool)) ) 15.99/16.11 ( (fun real bool), real ) 15.99/16.11 ( (fun real bool), (fun real bool) ) 15.99/16.11 ( (fun real bool), (fun real (fun bool bool)) ) 15.99/16.11 ( (fun real bool), (fun (fun int real) (fun int bool)) ) 15.99/16.11 ( (fun real bool), (fun (fun nat real) (fun nat bool)) ) 15.99/16.11 ( (fun real real), (fun real real) ) 15.99/16.11 ( (fun real real), (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 15.99/16.11 ( (fun real real), (fun real (fun real real)) ) 15.99/16.11 ( (fun real real), (fun real (fun real bool)) ) 15.99/16.11 ( (fun real real), (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 15.99/16.11 ( rat, real ) 15.99/16.11 ( rat, (product_prod int int) ) 15.99/16.11 ( complex, nat ) 15.99/16.11 ( complex, real ) 15.99/16.11 ( complex, complex ) 15.99/16.11 ( (fun nat real), (fun nat bool) ) 15.99/16.11 ( (fun nat real), (fun nat real) ) 15.99/16.11 ( (fun nat real), (fun nat (fun real real)) ) 15.99/16.11 ( (fun nat real), (fun int (fun nat real)) ) 15.99/16.11 ( (filter nat), bool ) 15.99/16.11 ( (fun int (fun int int)), (fun int (fun int (fun int bool))) ) 15.99/16.11 ( (fun int (fun int int)), (let ((_let_0 (fun int int))) (fun int (fun _let_0 _let_0))) ) 15.99/16.11 ( (product_prod int int), bool ) 15.99/16.11 ( (product_prod int int), int ) 15.99/16.11 ( (product_prod int int), (fun int bool) ) 15.99/16.11 ( (product_prod int int), (fun int int) ) 15.99/16.11 ( (product_prod int int), rat ) 15.99/16.11 ( (product_prod int int), (product_prod int int) ) 15.99/16.11 ( (product_prod int int), (fun bool bool) ) 15.99/16.11 ( (product_prod int int), (fun (product_prod int int) bool) ) 15.99/16.11 ( (product_prod int int), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 15.99/16.11 ( (product_prod int int), (fun (product_prod int int) (fun int bool)) ) 15.99/16.11 ( (product_prod int int), (fun (product_prod int int) int) ) 15.99/16.11 ( (product_prod int int), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 15.99/16.11 ( (product_prod int int), (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 15.99/16.11 ( quickcheck_code_int, nat ) 15.99/16.11 ( quickcheck_code_int, int ) 15.99/16.11 ( quickcheck_code_int, (product_prod quickcheck_code_int quickcheck_code_int) ) 15.99/16.11 ( quickcheck_code_int, (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int)) ) 15.99/16.11 ( (fun bool bool), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 15.99/16.11 ( code_code_numeral, nat ) 15.99/16.11 ( code_code_numeral, int ) 15.99/16.11 ( code_code_numeral, (fun nat nat) ) 15.99/16.11 ( code_code_numeral, code_code_numeral ) 15.99/16.11 ( code_code_numeral, (product_prod code_code_numeral code_code_numeral) ) 15.99/16.11 ( code_code_numeral, (fun code_code_numeral (product_prod code_code_numeral code_code_numeral)) ) 15.99/16.11 ( (fun int (fun int (fun int bool))), (fun int (fun int (fun int bool))) ) 15.99/16.11 ( (fun real (fun real bool)), (fun real (fun (fun int real) (fun int bool))) ) 15.99/16.11 ( (fun real (fun real bool)), (fun real (fun (fun nat real) (fun nat bool))) ) 15.99/16.11 ( (product_prod real real), bool ) 15.99/16.11 ( (fun (product_prod real real) bool), (fun real (fun real (fun nat (product_prod real real)))) ) 15.99/16.11 ( (fun (product_prod int int) bool), (fun (product_prod int int) bool) ) 15.99/16.11 ( (fun (product_prod int int) bool), (fun (product_prod int int) (fun bool bool)) ) 15.99/16.11 ( (fun int (fun bool bool)), (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 15.99/16.11 ( (fun nat rat), bool ) 15.99/16.11 ( (filter real), bool ) 15.99/16.11 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)), bool ) 15.99/16.11 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 15.99/16.11 ( (fun (product_prod int int) (fun bool bool)), (let ((_let_0 (fun (product_prod int int) bool))) (fun (product_prod int int) (fun _let_0 _let_0))) ) 15.99/16.11 ( (fun (product_prod int int) (fun int bool)), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 15.99/16.11 ( (fun (product_prod int int) int), (fun (product_prod int int) bool) ) 15.99/16.11 ( (fun (product_prod int int) int), (fun (product_prod int int) (fun int bool)) ) 15.99/16.11 ( (fun (product_prod int int) int), (fun (product_prod int int) int) ) 15.99/16.11 ( (fun (product_prod int int) int), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))) ) 15.99/16.11 ( (fun (product_prod int int) int), (fun (product_prod int int) (fun int int)) ) 15.99/16.11 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 15.99/16.11 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 (fun int bool)))) ) 15.99/16.11 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 (fun int bool)))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun (fun _let_0 int) (fun _let_0 bool)))) ) 15.99/16.11 ( (fun (product_prod int int) (fun int int)), (let ((_let_0 (fun (product_prod int int) int))) (fun (product_prod int int) (fun _let_0 _let_0))) ) 15.99/16.11 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), bool ) 15.99/16.11 ( (fun int real), (fun int bool) ) 15.99/16.11 ( (fun int real), (fun int real) ) 15.99/16.11 ( (fun int real), (fun int (fun int real)) ) 15.99/16.11 ( (fun int real), (fun int (fun real real)) ) 15.99/16.11 ( (fun nat (fun bool bool)), (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 15.99/16.11 ( (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun int bool))) (fun _let_0 (fun int _let_0))) ) 15.99/16.11 ( (fun int (fun int (fun bool bool))), (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 15.99/16.11 ( (fun real (fun int bool)), (fun real bool) ) 15.99/16.11 ( (fun real (fun int (fun int bool))), (fun real (fun int bool)) ) 15.99/16.11 ( (fun real (fun int (fun int bool))), (fun real (fun int (fun int (fun bool bool)))) ) 15.99/16.11 ( (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun int bool))) (fun real (fun _let_0 (fun int _let_0)))) ) 15.99/16.11 ( (fun real (fun int (fun int (fun bool bool)))), (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))) ) 15.99/16.11 ( (fun int (fun int real)), (fun int (fun int bool)) ) 15.99/16.11 ( (fun int (fun int real)), (fun real (fun int (fun int bool))) ) 15.99/16.11 ( (fun (fun int real) (fun int bool)), (fun (fun int (fun int real)) (fun int (fun int bool))) ) 15.99/16.11 ( (fun real (fun (fun int real) (fun int bool))), (fun real (fun (fun int (fun int real)) (fun int (fun int bool)))) ) 15.99/16.11 ( (fun int (fun real real)), (let ((_let_0 (fun int real))) (fun int (fun _let_0 _let_0))) ) 15.99/16.11 ( (fun int (fun real real)), (let ((_let_0 (fun nat real))) (fun int (fun _let_0 _let_0))) ) 15.99/16.11 ( (fun int (fun nat bool)), (fun int bool) ) 15.99/16.11 ( (fun int (fun nat bool)), (fun int (fun nat (fun bool bool))) ) 15.99/16.11 ( (fun real (fun int (fun nat bool))), (fun real (fun int bool)) ) 15.99/16.11 ( (fun real (fun int (fun nat bool))), (fun real (fun int (fun nat (fun bool bool)))) ) 15.99/16.11 ( (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun nat bool))) (fun _let_0 (fun int _let_0))) ) 15.99/16.11 ( (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun nat bool))) (fun real (fun _let_0 (fun int _let_0)))) ) 15.99/16.11 ( (fun int (fun nat (fun bool bool))), (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 15.99/16.11 ( (fun real (fun int (fun nat (fun bool bool)))), (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))) ) 15.99/16.11 ( (fun int (fun nat real)), (fun int (fun nat bool)) ) 15.99/16.11 ( (fun int (fun nat real)), (fun real (fun int (fun nat bool))) ) 15.99/16.11 ( (fun (fun nat real) (fun nat bool)), (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 15.99/16.11 ( (fun real (fun (fun nat real) (fun nat bool))), (fun real (fun (fun int (fun nat real)) (fun int (fun nat bool)))) ) 15.99/16.11 ) 15.99/16.11 (instantiation (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) X_1) (zero_zero real)))) (= (zero_zero nat) (hAPP real nat natceiling X_1))) ) 15.99/16.11 ( (one_one real) ) 15.99/16.11 ( (zero_zero real) ) 15.99/16.11 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.11 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.11 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.11 ( skv_5 ) 15.99/16.11 ) 15.99/16.11 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_0 (semiring_1_of_nat int))) (= (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int _let_0 M)) (hAPP nat int _let_0 N_1)) (hAPP nat int _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) M) N_1)))) ) 15.99/16.11 ( (one_one nat), (one_one nat) ) 15.99/16.11 ) 15.99/16.11 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_134889 $$unsorted) (BOUND_VARIABLE_134890 $$unsorted) (BOUND_VARIABLE_134891 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (fun X_a X_a))) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) (zero_zero X_a)) BOUND_VARIABLE_134891))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_134889) (hAPP X_a X_a (hAPP X_a _let_2 (times_times X_a) BOUND_VARIABLE_134890) BOUND_VARIABLE_134891)))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_2 (inverse_divide X_a) BOUND_VARIABLE_134889) BOUND_VARIABLE_134891)) BOUND_VARIABLE_134890)))))) ) 15.99/16.11 ( real, (zero_zero real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.99/16.11 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.11 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.99/16.11 ) 15.99/16.11 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_134924 $$unsorted) (BOUND_VARIABLE_134925 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (inverse_divide X_a))) (let ((_let_2 (abs_abs X_a))) (or (not (linord1117847801e_zero X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) BOUND_VARIABLE_134925))) (= (hAPP X_a X_a _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_134924) BOUND_VARIABLE_134925)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_134924)) BOUND_VARIABLE_134925)))))) ) 15.99/16.11 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.11 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.99/16.11 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.11 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 15.99/16.11 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.11 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.11 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.99/16.11 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.99/16.11 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.11 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.11 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.11 ) 15.99/16.11 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (ring_1_of_int X_a))) (or (not (ring_1 X_a)) (= _let_0 (ti (fun int X_a) _let_0)))) ) 15.99/16.11 ( bool ) 15.99/16.11 ( nat ) 15.99/16.11 ( int ) 15.99/16.11 ( (fun int bool) ) 15.99/16.11 ( (fun int (fun int bool)) ) 15.99/16.11 ( (fun int int) ) 15.99/16.11 ( (fun nat bool) ) 15.99/16.11 ( (fun nat nat) ) 15.99/16.11 ( real ) 15.99/16.11 ( (fun real real) ) 15.99/16.11 ( rat ) 15.99/16.11 ( (fun int rat) ) 15.99/16.11 ( (fun nat int) ) 15.99/16.11 ( complex ) 15.99/16.11 ( (fun nat real) ) 15.99/16.11 ( (product_prod int int) ) 15.99/16.11 ( (fun int (product_prod int int)) ) 15.99/16.11 ( (fun (fun int bool) bool) ) 15.99/16.11 ( quickcheck_code_int ) 15.99/16.11 ( (fun bool bool) ) 15.99/16.11 ( (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 15.99/16.11 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)) ) 15.99/16.11 ( (fun int (fun int (fun int bool))) ) 15.99/16.11 ( (fun (product_prod int int) bool) ) 15.99/16.11 ( (fun int (fun (product_prod int int) bool)) ) 15.99/16.11 ( (fun int (fun bool bool)) ) 15.99/16.11 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 15.99/16.11 ( (fun (fun int int) (fun int bool)) ) 15.99/16.11 ( (fun (product_prod int int) int) ) 15.99/16.11 ( (product_prod int (product_prod int int)) ) 15.99/16.11 ( (fun int (product_prod int (product_prod int int))) ) 15.99/16.11 ( (fun int (fun int (product_prod int (product_prod int int)))) ) 15.99/16.11 ( (fun int (fun int (fun int (product_prod int (product_prod int int))))) ) 15.99/16.11 ( (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))) ) 15.99/16.11 ( (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))) ) 15.99/16.11 ( (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))) ) 15.99/16.11 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))))) ) 15.99/16.11 ( (fun int (fun (fun int bool) bool)) ) 15.99/16.11 ( (list int) ) 15.99/16.11 ( (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 15.99/16.11 ( (fun int real) ) 15.99/16.11 ( (fun nat (fun bool bool)) ) 15.99/16.11 ( (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 15.99/16.11 ( (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 15.99/16.11 ) 15.99/16.11 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_134981 $$unsorted) (BOUND_VARIABLE_134982 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (or (not (order X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_134981) BOUND_VARIABLE_134982))) (= (= (ti X_a BOUND_VARIABLE_134981) (ti X_a BOUND_VARIABLE_134982)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_134982) BOUND_VARIABLE_134981)))))) ) 15.99/16.11 ( int, (one_one int), (zero_zero int) ) 15.99/16.11 ( int, (one_one int), t ) 15.99/16.11 ( int, (zero_zero int), (one_one int) ) 15.99/16.11 ( int, (zero_zero int), min_1 ) 15.99/16.11 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.11 ( int, (zero_zero int), s ) 15.99/16.11 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.99/16.11 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.99/16.11 ( int, (zero_zero int), skv_4 ) 15.99/16.11 ( int, (zero_zero int), skv_10 ) 15.99/16.11 ( int, pls, min_1 ) 15.99/16.11 ( int, min_1, (zero_zero int) ) 15.99/16.11 ( int, min_1, pls ) 15.99/16.11 ( int, min_1, min_1 ) 15.99/16.11 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 15.99/16.11 ( int, s, (zero_zero int) ) 15.99/16.11 ( int, t, (one_one int) ) 15.99/16.11 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 15.99/16.11 ( int, (hAPP int int (number_number_of int) pls), (zero_zero int) ) 15.99/16.11 ( int, skv_4, (zero_zero int) ) 15.99/16.11 ( int, skv_10, (zero_zero int) ) 15.99/16.11 ( real, (zero_zero real), pi ) 15.99/16.11 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.11 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.11 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.11 ( real, (zero_zero real), skv_3 ) 15.99/16.11 ( real, (zero_zero real), skv_5 ) 15.99/16.11 ( real, (zero_zero real), skv_7 ) 15.99/16.11 ( real, (zero_zero real), skv_12 ) 15.99/16.11 ( real, pi, (zero_zero real) ) 15.99/16.11 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.11 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.99/16.11 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.11 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_5 ) 15.99/16.11 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.99/16.11 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.11 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.99/16.11 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.99/16.11 ( real, skv_3, (zero_zero real) ) 15.99/16.11 ( real, skv_5, (zero_zero real) ) 15.99/16.11 ( real, skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.11 ( real, skv_7, (zero_zero real) ) 15.99/16.11 ( real, skv_12, (zero_zero real) ) 15.99/16.11 ) 15.99/16.11 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_135048 $$unsorted)) (or (not (linordered_semidom X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) (hAPP nat X_a (semiring_1_of_nat X_a) BOUND_VARIABLE_135048))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) BOUND_VARIABLE_135048)))) ) 15.99/16.11 ( int, (zero_zero nat) ) 15.99/16.11 ( int, (hAPP nat nat suc (zero_zero nat)) ) 15.99/16.11 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.99/16.11 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.11 ( real, (zero_zero nat) ) 15.99/16.11 ( real, (hAPP nat nat suc (zero_zero nat)) ) 15.99/16.11 ) 15.99/16.11 (instantiation (forall ((N_1 $$unsorted) (M $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (fact_fact nat))) (let ((_let_2 (minus_minus nat))) (let ((_let_3 (hAPP nat nat (hAPP nat _let_0 _let_2 (hAPP nat nat suc M)) N_1))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) N_1) (hAPP nat nat suc M)))) (= (hAPP nat nat (hAPP nat _let_0 (times_times nat) _let_3) (hAPP nat nat _let_1 (hAPP nat nat (hAPP nat _let_0 _let_2 M) N_1))) (hAPP nat nat _let_1 _let_3))))))) ) 15.99/16.11 ( (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 15.99/16.11 ) 15.99/16.11 (instantiation (forall ((Y_1 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (inverse_divide real))) (= (hAPP real real (hAPP real _let_0 _let_1 (one_one real)) (hAPP real real tan Y_1)) (hAPP real real tan (hAPP real real (hAPP real _let_0 (minus_minus real) (hAPP real real (hAPP real _let_0 _let_1 pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) Y_1))))) ) 15.99/16.11 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.99/16.11 ) 15.99/16.11 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_135141 $$unsorted) (BOUND_VARIABLE_135142 $$unsorted) (BOUND_VARIABLE_135143 $$unsorted)) (or (not (order X_a)) (not (forall ((N_2 $$unsorted)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (hAPP nat X_a BOUND_VARIABLE_135143 N_2)) (hAPP nat X_a BOUND_VARIABLE_135143 (hAPP nat nat suc N_2)))) )) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) BOUND_VARIABLE_135141) BOUND_VARIABLE_135142))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (hAPP nat X_a BOUND_VARIABLE_135143 BOUND_VARIABLE_135141)) (hAPP nat X_a BOUND_VARIABLE_135143 BOUND_VARIABLE_135142)))) ) 15.99/16.11 ( int, (zero_zero nat), (zero_zero nat), (semiring_1_of_nat int) ) 15.99/16.11 ( int, (zero_zero nat), (hAPP nat nat suc (zero_zero nat)), (semiring_1_of_nat int) ) 15.99/16.11 ( int, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))), (semiring_1_of_nat int) ) 15.99/16.11 ( int, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (semiring_1_of_nat int) ) 15.99/16.11 ) 15.99/16.11 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_135205 $$unsorted)) (or (not (comm_semiring_1 X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_135205) BOUND_VARIABLE_135205) (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_135205) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.99/16.11 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.11 ( int, s ) 15.99/16.11 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.11 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.11 ( int, s1 ) 15.99/16.11 ( int, skv_14 ) 15.99/16.11 ( real, (hAPP int real (number_number_of real) min_1) ) 15.99/16.11 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.11 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.11 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.11 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 15.99/16.11 ( complex, ii ) 15.99/16.11 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.11 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 15.99/16.11 ) 15.99/16.11 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_135256 $$unsorted) (BOUND_VARIABLE_135257 $$unsorted) (BOUND_VARIABLE_135258 $$unsorted) (BOUND_VARIABLE_135259 $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (order X_a)) (not (ord X_b)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) (hAPP X_b X_a BOUND_VARIABLE_135257 BOUND_VARIABLE_135258)) BOUND_VARIABLE_135259))) (not (hBOOL (hAPP X_b bool (hAPP X_b (fun X_b bool) (ord_less X_b) BOUND_VARIABLE_135256) BOUND_VARIABLE_135258))) (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (hBOOL (hAPP X_b bool (hAPP X_b (fun X_b bool) (ord_less X_b) Y) X))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) (hAPP X_b X_a BOUND_VARIABLE_135257 Y)) (hAPP X_b X_a BOUND_VARIABLE_135257 X)))) )) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) (hAPP X_b X_a BOUND_VARIABLE_135257 BOUND_VARIABLE_135256)) BOUND_VARIABLE_135259)))) ) 15.99/16.11 ( nat, int, (zero_zero nat), (semiring_1_of_nat int), (zero_zero nat), s ) 15.99/16.11 ( int, int, (one_one int), (number_number_of int), pls, (hAPP int int (number_number_of int) pls) ) 15.99/16.11 ( int, int, pls, (number_number_of int), pls, (one_one int) ) 15.99/16.11 ( int, int, min_1, (number_number_of int), pls, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.99/16.11 ( int, int, s, bit1, min_1, pls ) 15.99/16.11 ( int, int, t, (number_number_of int), pls, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.11 ( int, int, skv_4, (number_number_of int), pls, min_1 ) 15.99/16.11 ( int, int, skv_10, (fact_fact int), (one_one int), t ) 15.99/16.11 ( real, real, (one_one real), cos, skv_5, skv_5 ) 15.99/16.11 ( real, real, (zero_zero real), cos, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real) ) 15.99/16.11 ( real, real, pi, cos, skv_5, pi ) 15.99/16.11 ( real, real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), cos, skv_5, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.11 ( real, real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.11 ( real, real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), cos, skv_5, skv_3 ) 15.99/16.11 ( real, real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), cos, skv_5, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.11 ) 15.99/16.11 (instantiation (forall ((I $$unsorted) (K $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (hAPP int _let_0 (ord_less int) (zero_zero int)))) (or (not (hBOOL (hAPP int bool _let_1 K))) (= (hBOOL (hAPP int bool _let_1 (hAPP int int (hAPP int (fun int int) (div_div int) I) K))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) K) I)))))) ) 15.99/16.11 ( (one_one int), (zero_zero int) ) 15.99/16.11 ( pls, min_1 ) 15.99/16.11 ( min_1, (zero_zero int) ) 15.99/16.11 ( min_1, min_1 ) 15.99/16.11 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 15.99/16.11 ( s, (zero_zero int) ) 15.99/16.11 ( t, (one_one int) ) 15.99/16.11 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 15.99/16.11 ( (hAPP int int (number_number_of int) pls), (zero_zero int) ) 15.99/16.11 ( skv_4, (zero_zero int) ) 15.99/16.11 ( skv_10, (zero_zero int) ) 15.99/16.11 ) 15.99/16.11 (instantiation (forall ((K_4 $$unsorted)) (= (ti int K_4) (hAPP int int (hAPP int (fun int int) (minus_minus int) K_4) pls)) ) 15.99/16.11 ( pls ) 15.99/16.11 ( min_1 ) 15.99/16.11 ( s ) 15.99/16.11 ( m ) 15.99/16.11 ( s1 ) 15.99/16.11 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.11 ( t ) 15.99/16.11 ) 15.99/16.11 (instantiation (forall ((X_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (number_number_of int))) (let ((_let_4 (hAPP int int _let_3 (hAPP int int bit0 (hAPP int int bit1 pls))))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) _let_4) P_5))) (not (hBOOL (hAPP int bool zprime P_5))) (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int _let_1 zcong X_1) (zero_zero int)) P_5)) (hBOOL (hAPP int bool (hAPP int _let_0 quadRes P_5) X_1)) (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int _let_1 zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) X_1) (hAPP int nat nat_1 (hAPP int int (hAPP int _let_2 (div_div int) (hAPP int int (hAPP int _let_2 (minus_minus int) P_5) (one_one int))) _let_4)))) (hAPP int int _let_3 min_1)) P_5)))))))) ) 15.99/16.11 ( (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.11 ) 15.99/16.11 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_135369 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (zero_zero X_a))) (or (not (ordered_ab_group_add X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_135369)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_135369)) _let_2))))))) ) 15.99/16.11 ( int, (one_one int) ) 15.99/16.11 ( int, pls ) 15.99/16.11 ( int, min_1 ) 15.99/16.11 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.11 ( int, s ) 15.99/16.11 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.99/16.11 ( int, (hAPP int int (number_number_of int) pls) ) 15.99/16.11 ( int, skv_4 ) 15.99/16.11 ( int, skv_10 ) 15.99/16.11 ( real, (one_one real) ) 15.99/16.11 ( real, pi ) 15.99/16.11 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.11 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.99/16.11 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.11 ( real, skv_3 ) 15.99/16.11 ( real, skv_5 ) 15.99/16.11 ( real, skv_7 ) 15.99/16.11 ( real, skv_12 ) 15.99/16.11 ( complex, (one_one complex) ) 15.99/16.11 ( complex, ii ) 15.99/16.11 ) 15.99/16.11 (instantiation (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) X_1))) (= X_1 (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP real real sqrt X_1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.99/16.11 ( (one_one real) ) 15.99/16.11 ( (zero_zero real) ) 15.99/16.11 ( pi ) 15.99/16.11 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.11 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.11 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.99/16.11 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.11 ( skv_3 ) 15.99/16.11 ( skv_5 ) 15.99/16.11 ( skv_7 ) 15.99/16.11 ( skv_12 ) 15.99/16.11 ) 15.99/16.11 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_135496 $$unsorted)) (or (not (number_ring X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) (hAPP int X_a (number_number_of X_a) min_1)) BOUND_VARIABLE_135496) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_135496))) ) 15.99/16.11 ( int, (one_one int) ) 15.99/16.11 ( int, pls ) 15.99/16.11 ( int, min_1 ) 15.99/16.11 ( real, (one_one real) ) 15.99/16.11 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.11 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.99/16.11 ( complex, (one_one complex) ) 15.99/16.11 ( complex, ii ) 15.99/16.11 ) 15.99/16.11 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) X_1))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real ln (hAPP real real (hAPP real (fun real real) (plus_plus real) (one_one real)) X_1))) X_1))))) ) 15.99/16.11 ( pi ) 15.99/16.11 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.11 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.11 ( skv_3 ) 15.99/16.11 ( skv_5 ) 15.99/16.11 ( skv_7 ) 15.99/16.11 ( skv_12 ) 15.99/16.11 ) 15.99/16.11 (instantiation (forall ((R_4 $$unsorted)) (= (hAPP real complex (hAPP real (fun real complex) complex_1 (zero_zero real)) R_4) (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) ii) (hAPP real complex (of_real complex) R_4))) ) 15.99/16.11 ( (one_one real) ) 15.99/16.11 ( (zero_zero real) ) 15.99/16.11 ( pi ) 15.99/16.11 ( (hAPP int real (number_number_of real) min_1) ) 15.99/16.11 ( (hAPP real real (uminus_uminus real) (one_one real)) ) 15.99/16.11 ) 15.99/16.11 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_135574 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_135574)) _let_2))) (= _let_2 (ti X_a BOUND_VARIABLE_135574)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_135574) _let_2)))))) ) 15.99/16.11 ( bool, fFalse ) 15.99/16.11 ( bool, fTrue ) 15.99/16.11 ( int, pls ) 15.99/16.11 ( int, min_1 ) 15.99/16.11 ( int, s ) 15.99/16.11 ( int, m ) 15.99/16.11 ( int, s1 ) 15.99/16.11 ( int, t ) 15.99/16.11 ( (fun int bool), nat_neg ) 15.99/16.11 ( (fun int bool), zprime ) 15.99/16.11 ( (fun int bool), zEven ) 15.99/16.11 ( (fun int bool), zOdd ) 15.99/16.11 ( (fun int bool), (even_odd_even int) ) 15.99/16.11 ( (fun int bool), twoSqu1091635170sum2sq ) 15.99/16.11 ( (fun int bool), nat_is_nat ) 15.99/16.11 ( (fun int (fun int bool)), norRRset ) 15.99/16.11 ( (fun int (fun int bool)), quadRes ) 15.99/16.11 ( (fun int (fun int bool)), sRStar ) 15.99/16.11 ( (fun int (fun int bool)), d22set ) 15.99/16.11 ( (fun int (fun int bool)), sr ) 15.99/16.11 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 15.99/16.11 ( (fun int int), zfact ) 15.99/16.11 ( (fun int int), bit0 ) 15.99/16.11 ( (fun int int), bit1 ) 15.99/16.11 ( (fun int int), (fact_fact int) ) 15.99/16.11 ( (fun int int), pred ) 15.99/16.11 ( (fun int int), succ ) 15.99/16.11 ( (fun nat bool), (even_odd_even nat) ) 15.99/16.11 ( (fun nat bool), prime ) 15.99/16.11 ( (fun nat nat), suc ) 15.99/16.11 ( (fun nat nat), (fact_fact nat) ) 15.99/16.11 ( (fun nat nat), fact ) 15.99/16.11 ( (fun nat nat), nat_size ) 15.99/16.11 ( (fun nat nat), (size_size nat) ) 15.99/16.11 ( (fun (product_prod nat nat) bool), pred_nat ) 15.99/16.11 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 15.99/16.11 ( real, (zero_zero real) ) 15.99/16.11 ( real, pi ) 15.99/16.11 ( (fun real real), ln ) 15.99/16.11 ( (fun real real), cos ) 15.99/16.11 ( (fun real real), sqrt ) 15.99/16.11 ( (fun real real), sin ) 15.99/16.11 ( (fun real real), arccos ) 15.99/16.11 ( (fun real real), arcsin ) 15.99/16.11 ( (fun real real), tan ) 15.99/16.11 ( (fun real real), arctan ) 15.99/16.11 ( (fun nat (fun nat bool)), coprime ) 15.99/16.11 ( complex, ii ) 15.99/16.11 ( (fun nat real), (real_1 nat) ) 15.99/16.11 ( (fun nat real), sin_coeff ) 15.99/16.11 ( (fun nat real), cos_coeff ) 15.99/16.11 ( (filter nat), sequentially ) 15.99/16.11 ( (fun int (fun int int)), (gcd_gcd int) ) 15.99/16.11 ( (fun int (fun int int)), legendre ) 15.99/16.11 ( (fun int (fun int int)), legacy_zgcd ) 15.99/16.11 ( (fun int (fun int int)), standardRes ) 15.99/16.11 ( (fun int (fun int int)), nat_tsub ) 15.99/16.11 ( (fun int (fun int int)), multInv ) 15.99/16.11 ( (fun int (fun int int)), z3mod ) 15.99/16.11 ( (fun int (fun int int)), z3div ) 15.99/16.11 ( (fun int (fun int int)), int_gcd ) 15.99/16.11 ( (fun int (fun int int)), int_lcm ) 15.99/16.11 ( (fun int (fun int int)), inv ) 15.99/16.11 ( (fun complex complex), expi ) 15.99/16.11 ( (fun complex complex), cnj ) 15.99/16.11 ( (fun real complex), cis ) 15.99/16.11 ( (fun int nat), nat_1 ) 15.99/16.11 ( (fun int nat), phi ) 15.99/16.11 ( (fun (fun int bool) bool), nat_nat_set ) 15.99/16.11 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 15.99/16.11 ( (fun nat (fun nat nat)), nat_gcd ) 15.99/16.11 ( (fun nat (fun nat nat)), nat_lcm ) 15.99/16.11 ( (fun (fun int bool) int), (the int) ) 15.99/16.11 ( (fun complex real), re ) 15.99/16.11 ( (fun complex real), im ) 15.99/16.11 ( (fun complex real), arg ) 15.99/16.11 ( (fun bool bool), fNot ) 15.99/16.11 ( (fun nat (fun real real)), root ) 15.99/16.11 ( (fun real (fun real real)), log ) 15.99/16.11 ( (fun real (fun real real)), powr ) 15.99/16.11 ( (fun bool (fun bool bool)), fimplies ) 15.99/16.11 ( (fun bool (fun bool bool)), fconj ) 15.99/16.11 ( (fun bool (fun bool bool)), fdisj ) 15.99/16.11 ( (fun int (fun int (product_prod int int))), negDivAlg ) 15.99/16.11 ( (fun int (fun int (product_prod int int))), posDivAlg ) 15.99/16.11 ( (fun int (fun int (product_prod int int))), divmod_int ) 15.99/16.11 ( (fun int (fun int (product_prod int int))), pdivmod ) 15.99/16.11 ( (fun int (fun int (product_prod int int))), norm_frac ) 15.99/16.11 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 15.99/16.11 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 15.99/16.11 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 15.99/16.11 ( (fun int (fun int (fun int bool))), zcong ) 15.99/16.11 ( (fun int (fun int (fun int bool))), zcongm ) 15.99/16.11 ( (fun int (fun int (fun int bool))), noXRRset ) 15.99/16.11 ( (fun int (fun int (fun int bool))), bnorRset ) 15.99/16.11 ( (fun int (fun int (fun int bool))), wset ) 15.99/16.11 ( (fun (product_prod int int) bool), frac_1 ) 15.99/16.11 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 15.99/16.11 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 15.99/16.11 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 15.99/16.11 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 15.99/16.11 ( (fun (fun nat rat) bool), vanishes ) 15.99/16.11 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 15.99/16.11 ( (fun code_code_numeral nat), code_c271388182l_size ) 15.99/16.11 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 15.99/16.11 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 15.99/16.11 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 15.99/16.11 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 15.99/16.11 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 15.99/16.11 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 15.99/16.11 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 15.99/16.11 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 15.99/16.11 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 15.99/16.11 ( (fun complex nat), complex_size ) 15.99/16.11 ( (fun complex nat), (size_size complex) ) 15.99/16.11 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 15.99/16.11 ( (fun nat (fun nat (product_prod int int))), bezw ) 15.99/16.11 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 15.99/16.11 ( (fun int (fun nat nat)), nat_aux ) 15.99/16.11 ( (fun int (fun (fun int bool) bool)), rsetR ) 15.99/16.11 ( (fun int (fun (fun int bool) bool)), resSet ) 15.99/16.11 ( (fun int (list int)), quickc666637781d_zero ) 15.99/16.11 ( (fun (product_prod int int) rat), frct ) 15.99/16.11 ( (fun int (fun int rat)), fract ) 15.99/16.11 ( (fun real (fun real complex)), complex_1 ) 15.99/16.11 ( (fun real (fun real complex)), rcis ) 15.99/16.11 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 15.99/16.11 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 15.99/16.11 ( (fun int real), (real_1 int) ) 15.99/16.11 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 15.99/16.11 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 15.99/16.11 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 15.99/16.11 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 15.99/16.11 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 15.99/16.11 ( (fun real nat), natfloor ) 15.99/16.11 ( (fun real nat), natceiling ) 15.99/16.11 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 15.99/16.11 ( (fun quickcheck_code_int int), quickcheck_int_of ) 15.99/16.11 ( (fun rat (product_prod int int)), quotient_of ) 15.99/16.11 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 15.99/16.11 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 15.99/16.11 ( (fun rat real), ratreal ) 15.99/16.11 ( (fun code_code_numeral int), code_int_of ) 15.99/16.11 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 15.99/16.11 ( (fun int quickcheck_code_int), quickcheck_of_int ) 15.99/16.11 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 15.99/16.11 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 15.99/16.11 ) 15.99/16.11 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_135594 $$unsorted)) (or (not (comm_semiring_1 X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_135594) BOUND_VARIABLE_135594))) ) 15.99/16.11 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.11 ) 15.99/16.11 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_135631 $$unsorted) (BOUND_VARIABLE_135632 $$unsorted) (BOUND_VARIABLE_135633 $$unsorted)) (or (not (order X_a)) (not (forall ((N_2 $$unsorted)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP nat X_a BOUND_VARIABLE_135633 N_2)) (hAPP nat X_a BOUND_VARIABLE_135633 (hAPP nat nat suc N_2)))) )) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) BOUND_VARIABLE_135631) BOUND_VARIABLE_135632))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP nat X_a BOUND_VARIABLE_135633 BOUND_VARIABLE_135631)) (hAPP nat X_a BOUND_VARIABLE_135633 BOUND_VARIABLE_135632)))) ) 15.99/16.11 ( int, (zero_zero nat), (zero_zero nat), (semiring_1_of_nat int) ) 15.99/16.11 ( int, (zero_zero nat), (hAPP nat nat suc (zero_zero nat)), (semiring_1_of_nat int) ) 15.99/16.11 ) 15.99/16.11 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (norm_norm X_a))) (or (not (sgn_div_norm X_a)) (= _let_0 (ti (fun X_a real) _let_0)))) ) 15.99/16.11 ( nat ) 15.99/16.11 ( int ) 15.99/16.11 ( real ) 15.99/16.11 ( (fun real bool) ) 15.99/16.11 ( rat ) 15.99/16.11 ( complex ) 15.99/16.11 ) 15.99/16.11 (instantiation (forall ((N $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (zero_zero int)) N))) (= (hAPP int int (fact_fact int) N) (hAPP _let_0 int (hAPP (fun int int) (fun _let_0 int) (big_co302546470etprod int int) (combi int)) (hAPP int _let_0 (hAPP int (fun int _let_0) (ord_atLeastAtMost int) (one_one int)) N))))) ) 15.99/16.11 ( (one_one int) ) 15.99/16.11 ( (zero_zero int) ) 15.99/16.11 ( min_1 ) 15.99/16.11 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.11 ( s ) 15.99/16.11 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.99/16.11 ( (hAPP int int (number_number_of int) pls) ) 15.99/16.11 ( skv_4 ) 15.99/16.11 ( skv_10 ) 15.99/16.11 ) 15.99/16.11 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (mono nat X_a))) (or (not (order X_a)) (= _let_0 (ti (fun (fun nat (fun nat bool)) (fun (fun nat X_a) bool)) _let_0)))) ) 15.99/16.11 ( bool ) 15.99/16.11 ( nat ) 15.99/16.11 ( int ) 15.99/16.11 ( (fun int int) ) 15.99/16.11 ( (fun nat bool) ) 15.99/16.11 ( (fun nat nat) ) 15.99/16.11 ( (product_prod nat nat) ) 15.99/16.11 ( (fun (product_prod nat nat) bool) ) 15.99/16.11 ( (fun nat (fun (product_prod nat nat) bool)) ) 15.99/16.11 ( real ) 15.99/16.11 ( (fun real real) ) 15.99/16.11 ( rat ) 15.99/16.11 ( (fun nat (fun nat bool)) ) 15.99/16.11 ( complex ) 15.99/16.11 ( (product_prod int int) ) 15.99/16.11 ( quickcheck_code_int ) 15.99/16.11 ( (fun bool bool) ) 15.99/16.11 ( code_code_numeral ) 15.99/16.11 ( (product_prod real real) ) 15.99/16.11 ( (fun nat (product_prod nat nat)) ) 15.99/16.11 ( (fun nat (product_prod int int)) ) 15.99/16.11 ) 15.99/16.11 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_135689 $$unsorted) (BOUND_VARIABLE_135690 $$unsorted)) (or (not (order X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_135689) BOUND_VARIABLE_135690))) (not (= (ti X_a BOUND_VARIABLE_135690) (ti X_a BOUND_VARIABLE_135689)))) ) 15.99/16.11 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.11 ( int, (one_one int), t ) 15.99/16.11 ( int, pls, (one_one int) ) 15.99/16.11 ( int, pls, pls ) 15.99/16.11 ( int, pls, min_1 ) 15.99/16.11 ( int, pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.11 ( int, min_1, pls ) 15.99/16.11 ( int, min_1, min_1 ) 15.99/16.11 ( int, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.11 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.11 ( int, skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.11 ( int, skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.11 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.11 ( real, (zero_zero real), pi ) 15.99/16.11 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.11 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.11 ( real, (zero_zero real), skv_2 ) 15.99/16.11 ( real, (zero_zero real), skv_8 ) 15.99/16.11 ( real, (zero_zero real), skv_9 ) 15.99/16.11 ( real, pi, (zero_zero real) ) 15.99/16.11 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.11 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.11 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 15.99/16.11 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.99/16.11 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 15.99/16.11 ) 15.99/16.11 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_135736 $$unsorted) (BOUND_VARIABLE_135737 $$unsorted)) (let ((_let_0 (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_135736))) (or (not (comm_semiring_1 X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) (hAPP nat X_a _let_0 BOUND_VARIABLE_135737)) BOUND_VARIABLE_135736) (hAPP nat X_a _let_0 (hAPP nat nat suc BOUND_VARIABLE_135737))))) ) 15.99/16.11 ( int, s, (hAPP nat nat suc (zero_zero nat)) ) 15.99/16.11 ( int, s1, (hAPP nat nat suc (zero_zero nat)) ) 15.99/16.11 ( int, skv_14, (hAPP nat nat suc (zero_zero nat)) ) 15.99/16.11 ( complex, ii, (hAPP nat nat suc (zero_zero nat)) ) 15.99/16.11 ) 15.99/16.11 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (one_one real))) (let ((_let_3 (fun real real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP int real (number_number_of real) min_1)) X_2))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_2) _let_2))) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP _let_3 (fun real _let_0) (deriv real) arcsin) X_2) (hAPP real real (inverse_inverse real) (hAPP real real sqrt (hAPP real real (hAPP real _let_3 (minus_minus real) _let_2) (hAPP nat real (hAPP real (fun nat real) (power_power real) X_2) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))))))))) ) 15.99/16.11 ( (one_one real) ) 15.99/16.11 ( (zero_zero real) ) 15.99/16.11 ( pi ) 15.99/16.11 ( (hAPP int real (number_number_of real) min_1) ) 15.99/16.11 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.11 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.99/16.11 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.11 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.12 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 15.99/16.12 ) 15.99/16.12 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_135823 $$unsorted) (BOUND_VARIABLE_135824 $$unsorted) (BOUND_VARIABLE_135825 $$unsorted) (BOUND_VARIABLE_135826 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (fun X_a _let_0))) (let ((_let_2 (ord_atLeastLessThan X_a))) (let ((_let_3 (ord_less X_a))) (or (not (linorder X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_3 BOUND_VARIABLE_135825) BOUND_VARIABLE_135826))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_3 BOUND_VARIABLE_135823) BOUND_VARIABLE_135824))) (= (and (= (ti X_a BOUND_VARIABLE_135825) (ti X_a BOUND_VARIABLE_135823)) (= (ti X_a BOUND_VARIABLE_135824) (ti X_a BOUND_VARIABLE_135826))) (= (hAPP X_a _let_0 (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_135823) BOUND_VARIABLE_135824) (hAPP X_a _let_0 (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_135825) BOUND_VARIABLE_135826)))))))) ) 15.99/16.12 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.12 ( int, (one_one int), t, (one_one int), t ) 15.99/16.12 ( int, (one_one int), t, skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.12 ( int, pls, (one_one int), pls, min_1 ) 15.99/16.12 ( int, pls, pls, pls, pls ) 15.99/16.12 ( int, pls, pls, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.12 ( int, pls, min_1, pls, (one_one int) ) 15.99/16.12 ( int, pls, min_1, pls, min_1 ) 15.99/16.12 ( int, pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.12 ( int, pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.12 ( int, min_1, pls, min_1, pls ) 15.99/16.12 ( int, min_1, pls, min_1, min_1 ) 15.99/16.12 ( int, min_1, min_1, min_1, pls ) 15.99/16.12 ( int, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), pls, pls ) 15.99/16.12 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.12 ( int, skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (one_one int), t ) 15.99/16.12 ( int, skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.12 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.12 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.12 ( real, (zero_zero real), pi, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.12 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.99/16.12 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.12 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 15.99/16.12 ( real, (zero_zero real), skv_2, (zero_zero real), skv_2 ) 15.99/16.12 ( real, (zero_zero real), skv_2, (zero_zero real), skv_8 ) 15.99/16.12 ( real, (zero_zero real), skv_8, (zero_zero real), skv_2 ) 15.99/16.12 ( real, (zero_zero real), skv_9, (zero_zero real), skv_9 ) 15.99/16.12 ( real, pi, (zero_zero real), pi, (zero_zero real) ) 15.99/16.12 ( real, pi, (zero_zero real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 15.99/16.12 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.12 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real), pi ) 15.99/16.12 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.12 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real), pi, (zero_zero real) ) 15.99/16.12 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.12 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.99/16.12 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.12 ) 15.99/16.12 (instantiation (forall ((N $$unsorted) (P_1 $$unsorted)) (or (hBOOL (hAPP nat bool P_1 (zero_zero nat))) (not (hBOOL (hAPP nat bool P_1 N))) (not (forall ((K_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) K_1) N))) (not (forall ((I_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) I_2) K_1))) (not (hBOOL (hAPP nat bool P_1 I_2)))) )) (not (hBOOL (hAPP nat bool P_1 K_1)))) ))) ) 15.99/16.12 ( (zero_zero nat), (even_odd_even nat) ) 15.99/16.12 ( (zero_zero nat), prime ) 15.99/16.12 ( (hAPP nat nat suc (zero_zero nat)), prime ) 15.99/16.12 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) ) 15.99/16.12 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), prime ) 15.99/16.12 ( (one_one nat), (even_odd_even nat) ) 15.99/16.12 ) 15.99/16.12 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_135934 $$unsorted)) (or (not (real_normed_vector X_a)) (= (not (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_135934))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) (hAPP X_a real (norm_norm X_a) BOUND_VARIABLE_135934))))) ) 15.99/16.12 ( bool, fFalse ) 15.99/16.12 ( bool, fTrue ) 15.99/16.12 ( int, pls ) 15.99/16.12 ( int, min_1 ) 15.99/16.12 ( int, s ) 15.99/16.12 ( int, m ) 15.99/16.12 ( int, s1 ) 15.99/16.12 ( int, t ) 15.99/16.12 ( (fun int bool), nat_neg ) 15.99/16.12 ( (fun int bool), zprime ) 15.99/16.12 ( (fun int bool), zEven ) 15.99/16.12 ( (fun int bool), zOdd ) 15.99/16.12 ( (fun int bool), (even_odd_even int) ) 15.99/16.12 ( (fun int bool), twoSqu1091635170sum2sq ) 15.99/16.12 ( (fun int bool), nat_is_nat ) 15.99/16.12 ( (fun int (fun int bool)), norRRset ) 15.99/16.12 ( (fun int (fun int bool)), quadRes ) 15.99/16.12 ( (fun int (fun int bool)), sRStar ) 15.99/16.12 ( (fun int (fun int bool)), d22set ) 15.99/16.12 ( (fun int (fun int bool)), sr ) 15.99/16.12 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 15.99/16.12 ( (fun int int), zfact ) 15.99/16.12 ( (fun int int), bit0 ) 15.99/16.12 ( (fun int int), bit1 ) 15.99/16.12 ( (fun int int), (fact_fact int) ) 15.99/16.12 ( (fun int int), pred ) 15.99/16.12 ( (fun int int), succ ) 15.99/16.12 ( (fun nat bool), (even_odd_even nat) ) 15.99/16.12 ( (fun nat bool), prime ) 15.99/16.12 ( (fun nat nat), suc ) 15.99/16.12 ( (fun nat nat), (fact_fact nat) ) 15.99/16.12 ( (fun nat nat), fact ) 15.99/16.12 ( (fun nat nat), nat_size ) 15.99/16.12 ( (fun nat nat), (size_size nat) ) 15.99/16.12 ( (fun (product_prod nat nat) bool), pred_nat ) 15.99/16.12 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 15.99/16.12 ( real, pi ) 15.99/16.12 ( (fun real real), ln ) 15.99/16.12 ( (fun real real), cos ) 15.99/16.12 ( (fun real real), sqrt ) 15.99/16.12 ( (fun real real), sin ) 15.99/16.12 ( (fun real real), arccos ) 15.99/16.12 ( (fun real real), arcsin ) 15.99/16.12 ( (fun real real), tan ) 15.99/16.12 ( (fun real real), arctan ) 15.99/16.12 ( (fun nat (fun nat bool)), coprime ) 15.99/16.12 ( complex, ii ) 15.99/16.12 ( (fun nat real), (real_1 nat) ) 15.99/16.12 ( (fun nat real), sin_coeff ) 15.99/16.12 ( (fun nat real), cos_coeff ) 15.99/16.12 ( (filter nat), sequentially ) 15.99/16.12 ( (fun int (fun int int)), (gcd_gcd int) ) 15.99/16.12 ( (fun int (fun int int)), legendre ) 15.99/16.12 ( (fun int (fun int int)), legacy_zgcd ) 15.99/16.12 ( (fun int (fun int int)), standardRes ) 15.99/16.12 ( (fun int (fun int int)), nat_tsub ) 15.99/16.12 ( (fun int (fun int int)), multInv ) 15.99/16.12 ( (fun int (fun int int)), z3mod ) 15.99/16.12 ( (fun int (fun int int)), z3div ) 15.99/16.12 ( (fun int (fun int int)), int_gcd ) 15.99/16.12 ( (fun int (fun int int)), int_lcm ) 15.99/16.12 ( (fun int (fun int int)), inv ) 15.99/16.12 ( (fun complex complex), expi ) 15.99/16.12 ( (fun complex complex), cnj ) 15.99/16.12 ( (fun real complex), cis ) 15.99/16.12 ( (fun int nat), nat_1 ) 15.99/16.12 ( (fun int nat), phi ) 15.99/16.12 ( (fun (fun int bool) bool), nat_nat_set ) 15.99/16.12 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 15.99/16.12 ( (fun nat (fun nat nat)), nat_gcd ) 15.99/16.12 ( (fun nat (fun nat nat)), nat_lcm ) 15.99/16.12 ( (fun (fun int bool) int), (the int) ) 15.99/16.12 ( (fun complex real), re ) 15.99/16.12 ( (fun complex real), im ) 15.99/16.12 ( (fun complex real), arg ) 15.99/16.12 ( (fun bool bool), fNot ) 15.99/16.12 ( (fun nat (fun real real)), root ) 15.99/16.12 ( (fun real (fun real real)), log ) 15.99/16.12 ( (fun real (fun real real)), powr ) 15.99/16.12 ( (fun bool (fun bool bool)), fimplies ) 15.99/16.12 ( (fun bool (fun bool bool)), fconj ) 15.99/16.12 ( (fun bool (fun bool bool)), fdisj ) 15.99/16.12 ( (fun int (fun int (product_prod int int))), negDivAlg ) 15.99/16.12 ( (fun int (fun int (product_prod int int))), posDivAlg ) 15.99/16.12 ( (fun int (fun int (product_prod int int))), divmod_int ) 15.99/16.12 ( (fun int (fun int (product_prod int int))), pdivmod ) 15.99/16.12 ( (fun int (fun int (product_prod int int))), norm_frac ) 15.99/16.12 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 15.99/16.12 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 15.99/16.12 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 15.99/16.12 ( (fun int (fun int (fun int bool))), zcong ) 15.99/16.12 ( (fun int (fun int (fun int bool))), zcongm ) 15.99/16.12 ( (fun int (fun int (fun int bool))), noXRRset ) 15.99/16.12 ( (fun int (fun int (fun int bool))), bnorRset ) 15.99/16.12 ( (fun int (fun int (fun int bool))), wset ) 15.99/16.12 ( (fun (product_prod int int) bool), frac_1 ) 15.99/16.12 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 15.99/16.12 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 15.99/16.12 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 15.99/16.12 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 15.99/16.12 ( (fun (fun nat rat) bool), vanishes ) 15.99/16.12 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 15.99/16.12 ( (fun code_code_numeral nat), code_c271388182l_size ) 15.99/16.12 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 15.99/16.12 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 15.99/16.12 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 15.99/16.12 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 15.99/16.12 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 15.99/16.12 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 15.99/16.12 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 15.99/16.12 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 15.99/16.12 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 15.99/16.12 ( (fun complex nat), complex_size ) 15.99/16.12 ( (fun complex nat), (size_size complex) ) 15.99/16.12 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 15.99/16.12 ( (fun nat (fun nat (product_prod int int))), bezw ) 15.99/16.12 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 15.99/16.12 ( (fun int (fun nat nat)), nat_aux ) 15.99/16.12 ( (fun int (fun (fun int bool) bool)), rsetR ) 15.99/16.12 ( (fun int (fun (fun int bool) bool)), resSet ) 15.99/16.12 ( (fun int (list int)), quickc666637781d_zero ) 15.99/16.12 ( (fun (product_prod int int) rat), frct ) 15.99/16.12 ( (fun int (fun int rat)), fract ) 15.99/16.12 ( (fun real (fun real complex)), complex_1 ) 15.99/16.12 ( (fun real (fun real complex)), rcis ) 15.99/16.12 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 15.99/16.12 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 15.99/16.12 ( (fun int real), (real_1 int) ) 15.99/16.12 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 15.99/16.12 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 15.99/16.12 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 15.99/16.12 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 15.99/16.12 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 15.99/16.12 ( (fun real nat), natfloor ) 15.99/16.12 ( (fun real nat), natceiling ) 15.99/16.12 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 15.99/16.12 ( (fun quickcheck_code_int int), quickcheck_int_of ) 15.99/16.12 ( (fun rat (product_prod int int)), quotient_of ) 15.99/16.12 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 15.99/16.12 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 15.99/16.12 ( (fun rat real), ratreal ) 15.99/16.12 ( (fun code_code_numeral int), code_int_of ) 15.99/16.12 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 15.99/16.12 ( (fun int quickcheck_code_int), quickcheck_of_int ) 15.99/16.12 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 15.99/16.12 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 15.99/16.12 ) 15.99/16.12 (instantiation (forall ((W $$unsorted)) (let ((_let_0 (one_one int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (hAPP int int (number_number_of int) W))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) _let_2))) (= (hAPP _let_1 int (product_snd int int) (hAPP int _let_1 (hAPP int (fun int _let_1) posDivAlg _let_0) _let_2)) (hAPP int int (hAPP int (fun int int) (div_mod int) _let_0) _let_2)))))) ) 15.99/16.12 ( pls ) 15.99/16.12 ( (hAPP int int bit1 pls) ) 15.99/16.12 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.99/16.12 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.99/16.12 ( min_1 ) 15.99/16.12 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.12 ) 15.99/16.12 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_135999 $$unsorted)) (or (not (linordered_idom X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) BOUND_VARIABLE_135999)) (= (one_one X_a) (hAPP X_a X_a (sgn_sgn X_a) BOUND_VARIABLE_135999)))) ) 15.99/16.12 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.12 ( int, (one_one int) ) 15.99/16.12 ( int, pls ) 15.99/16.12 ( int, min_1 ) 15.99/16.12 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.12 ( real, (zero_zero real) ) 15.99/16.12 ( real, pi ) 15.99/16.12 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.12 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.12 ( real, skv_2 ) 15.99/16.12 ( real, skv_8 ) 15.99/16.12 ( real, skv_9 ) 15.99/16.12 ( rat, (zero_zero rat) ) 15.99/16.12 ) 15.99/16.12 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_0 (product_prod X_b X_a))) (let ((_let_1 (ti X_a A_1))) (or (not (= _let_1 (hAPP _let_0 X_a (product_snd X_b X_a) (hAPP X_a _let_0 (hAPP X_b (fun X_a _let_0) (product_Pair X_b X_a) X_1) Y_1)))) (= _let_1 (ti X_a Y_1))))) ) 15.99/16.12 ( int, int, (one_one int), (one_one int), pls ) 15.99/16.12 ( int, int, (zero_zero int), (one_one int), s1 ) 15.99/16.12 ( int, int, s, (one_one int), s ) 15.99/16.12 ) 15.99/16.12 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_136083 $$unsorted) (BOUND_VARIABLE_136084 $$unsorted) (BOUND_VARIABLE_136085 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (let ((_let_3 (hAPP X_a _let_0 _let_1 (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_136083)))) (let ((_let_4 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_136085)))) (let ((_let_5 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_136085) _let_2)))) (let ((_let_6 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_136083)) BOUND_VARIABLE_136085))) (or (not (linord1117847801e_zero X_a)) (not (number X_a)) (= (hBOOL (hAPP X_a bool _let_3 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_136084) BOUND_VARIABLE_136085))) (and (or _let_4 (and (or _let_5 (hBOOL (hAPP X_a bool _let_3 _let_2))) (or (not _let_5) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_136084) _let_6))))) (or (not _let_4) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_6) BOUND_VARIABLE_136084))))))))))))) ) 15.99/16.12 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)), (zero_zero real), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.99/16.12 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.99/16.12 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.99/16.12 ) 15.99/16.12 (instantiation (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (zero_zero int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) _let_2) A_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (hAPP int int (hAPP int _let_1 (plus_plus int) A_1) B)) _let_2))) (= (hAPP int int (number_number_of int) min_1) (hAPP int int (hAPP int _let_1 (div_div int) A_1) B)))))) ) 15.99/16.12 ( (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.99/16.12 ( (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.12 ) 15.99/16.12 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_136176 $$unsorted) (BOUND_VARIABLE_136177 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)))) (let ((_let_1 (hBOOL (hAPP nat bool (even_odd_even nat) BOUND_VARIABLE_136177)))) (or (not (linordered_idom X_a)) (= (or (and (not _let_1) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_136176))) _let_1) (hBOOL (hAPP X_a bool _let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_136176) BOUND_VARIABLE_136177))))))) ) 15.99/16.12 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.12 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.12 ( int, skv_14, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.12 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.12 ) 15.99/16.12 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_136246 $$unsorted)) (or (not (linordered_idom X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_136246)) (zero_zero X_a))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) BOUND_VARIABLE_136246) (zero_zero int))))) ) 15.99/16.12 ( real, (one_one int) ) 15.99/16.12 ( real, (zero_zero int) ) 15.99/16.12 ) 15.99/16.12 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_136300 $$unsorted) (BOUND_VARIABLE_136301 $$unsorted) (BOUND_VARIABLE_136302 $$unsorted) (BOUND_VARIABLE_136303 $$unsorted) (BOUND_VARIABLE_136304 $$unsorted)) (let ((_let_0 (filter X_a))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun X_a X_b))) (let ((_let_3 (fun X_b _let_1))) (let ((_let_4 (tendsto X_a X_b))) (let ((_let_5 (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_136303))) (or (not (metric_space X_a)) (not (topological_space X_b)) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) BOUND_VARIABLE_136304))) (not (forall ((X $$unsorted)) (or (= (ti X_a X) (ti X_a BOUND_VARIABLE_136303)) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP X_a real (hAPP X_a (fun X_a real) (dist_dist X_a) X) BOUND_VARIABLE_136303)) BOUND_VARIABLE_136304))) (= (hAPP X_a X_b BOUND_VARIABLE_136302 X) (hAPP X_a X_b BOUND_VARIABLE_136301 X))) )) (not (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (hAPP _let_2 _let_3 _let_4 BOUND_VARIABLE_136302) BOUND_VARIABLE_136300) _let_5))) (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (hAPP _let_2 _let_3 _let_4 BOUND_VARIABLE_136301) BOUND_VARIABLE_136300) _let_5))))))))) ) 15.99/16.12 ( real, real, (zero_zero real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.12 ) 15.99/16.12 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_136386 $$unsorted) (BOUND_VARIABLE_136393 $$unsorted)) (let ((_let_0 (fun int (fun int bool)))) (let ((_let_1 (zero_zero int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (ring_1_of_int X_a))) (let ((_let_4 (fun int X_a))) (let ((_let_5 (fun int _let_4))) (let ((_let_6 (fun X_a _let_4))) (let ((_let_7 (fun int _let_6))) (let ((_let_8 (fun X_a X_a))) (let ((_let_9 (fun int _let_8))) (let ((_let_10 (fun int _let_9))) (let ((_let_11 (combc int X_a X_a))) (let ((_let_12 (fun X_a _let_9))) (let ((_let_13 (fun int (fun X_a _let_8)))) (let ((_let_14 (hAPP (fun X_a _let_8) (fun _let_4 _let_9) (combb X_a _let_8 int) (plus_plus X_a)))) (let ((_let_15 (hAPP _let_4 _let_4 (hAPP _let_9 (fun _let_4 _let_4) (combs int X_a X_a) (hAPP _let_4 _let_9 _let_14 _let_3)) _let_3))) (let ((_let_16 (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) BOUND_VARIABLE_136393) _let_1)))) (let ((_let_17 (hAPP int X_a _let_3 BOUND_VARIABLE_136393))) (or (not (ring_1 X_a)) (and (or (not (= _let_1 (ti int BOUND_VARIABLE_136386))) (= (zero_zero X_a) (hAPP int X_a _let_3 BOUND_VARIABLE_136386))) (or (= _let_1 (ti int BOUND_VARIABLE_136393)) (and (or (not _let_16) (= _let_17 (hAPP X_a X_a (uminus_uminus X_a) (hAPP int X_a _let_3 (hAPP int int (uminus_uminus int) BOUND_VARIABLE_136393))))) (or _let_16 (= _let_17 (hAPP _let_2 X_a (hAPP _let_5 (fun _let_2 X_a) (product_prod_case int int X_a) (hAPP _let_4 _let_5 (hAPP _let_7 (fun _let_4 _let_5) (combs int X_a _let_4) (hAPP _let_10 _let_7 (hAPP (fun _let_9 _let_6) (fun _let_10 _let_7) (combb _let_9 _let_6 int) _let_11) (hAPP _let_4 _let_10 (hAPP _let_12 (fun _let_4 _let_10) (combb X_a _let_9 int) (hAPP _let_13 _let_12 (combc int X_a _let_8) (hAPP (fun int bool) _let_13 (hAPP (fun bool (fun X_a _let_8)) (fun (fun int bool) _let_13) (combb bool (fun X_a _let_8) int) (if X_a)) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (fequal int)) _let_1)))) _let_15))) (hAPP X_a _let_4 (hAPP _let_9 _let_6 _let_11 (hAPP _let_4 _let_9 _let_14 _let_15)) (one_one X_a)))) (hAPP int _let_2 (hAPP int (fun int _let_2) divmod_int BOUND_VARIABLE_136393) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))))))))))))))))))))))))))) ) 15.99/16.12 ( int, pls, pls ) 15.99/16.12 ( real, m, m ) 15.99/16.12 ( rat, s, s ) 15.99/16.12 ( complex, s1, s1 ) 15.99/16.12 ) 15.99/16.12 (instantiation (forall ((N_1 $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (fact_fact nat))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_1))) (= (hAPP nat nat (hAPP nat _let_0 (times_times nat) N_1) (hAPP nat nat _let_1 (hAPP nat nat (hAPP nat _let_0 (minus_minus nat) N_1) (one_one nat)))) (hAPP nat nat _let_1 N_1))))) ) 15.99/16.12 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.12 ) 15.99/16.12 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (fun real complex))) (let ((_let_2 (times_times real))) (let ((_let_3 (hAPP real _let_0 _let_2 A_1))) (let ((_let_4 (hAPP real _let_0 _let_2 B))) (= (hAPP real complex (hAPP real _let_1 complex_1 (hAPP real real (hAPP real _let_0 (minus_minus real) (hAPP real real _let_3 C)) (hAPP real real _let_4 D))) (hAPP real real (hAPP real _let_0 (plus_plus real) (hAPP real real _let_3 D)) (hAPP real real _let_4 C))) (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP real complex (hAPP real _let_1 complex_1 A_1) B)) (hAPP real complex (hAPP real _let_1 complex_1 C) D)))))))) ) 15.99/16.12 ( (zero_zero real), (one_one real), (zero_zero real), (one_one real) ) 15.99/16.12 ) 15.99/16.12 (instantiation (forall ((X_2 $$unsorted) (N $$unsorted)) (let ((_let_0 (zero_zero nat))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real real))) (let ((_let_3 (hAPP nat _let_2 root N))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) _let_0) N))) (not (hBOOL (hAPP real bool (hAPP real _let_1 (ord_less real) (zero_zero real)) X_2))) (hBOOL (hAPP real bool (hAPP real _let_1 (hAPP _let_2 (fun real _let_1) (deriv real) _let_3) X_2) (hAPP real real (inverse_inverse real) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP nat real (real_1 nat) N)) (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP real real _let_3 X_2)) (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) N) (hAPP nat nat suc _let_0)))))))))))) ) 15.99/16.12 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.12 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.12 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.12 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.12 ) 15.99/16.12 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (order T_1)) (order (fun T_2 T_1))) ) 15.99/16.12 ( bool, bool ) 15.99/16.12 ( bool, (fun bool bool) ) 15.99/16.12 ( nat, bool ) 15.99/16.12 ( nat, nat ) 15.99/16.12 ( nat, int ) 15.99/16.12 ( nat, (fun int int) ) 15.99/16.12 ( nat, (fun nat bool) ) 15.99/16.12 ( nat, (fun nat nat) ) 15.99/16.12 ( nat, (product_prod nat nat) ) 15.99/16.12 ( nat, (fun (product_prod nat nat) bool) ) 15.99/16.12 ( nat, (fun nat (fun (product_prod nat nat) bool)) ) 15.99/16.12 ( nat, real ) 15.99/16.12 ( nat, (fun real real) ) 15.99/16.12 ( nat, rat ) 15.99/16.12 ( nat, (fun nat (fun nat bool)) ) 15.99/16.12 ( nat, complex ) 15.99/16.12 ( nat, (product_prod int int) ) 15.99/16.12 ( nat, (fun bool bool) ) 15.99/16.12 ( nat, (product_prod real real) ) 15.99/16.12 ( nat, (fun nat (product_prod nat nat)) ) 15.99/16.12 ( nat, (fun nat (product_prod int int)) ) 15.99/16.12 ( int, bool ) 15.99/16.12 ( int, nat ) 15.99/16.12 ( int, int ) 15.99/16.12 ( int, (fun int bool) ) 15.99/16.12 ( int, (fun int (fun int bool)) ) 15.99/16.12 ( int, (fun int int) ) 15.99/16.12 ( int, (fun nat bool) ) 15.99/16.12 ( int, (fun nat nat) ) 15.99/16.12 ( int, real ) 15.99/16.12 ( int, (fun real real) ) 15.99/16.12 ( int, rat ) 15.99/16.12 ( int, (fun int rat) ) 15.99/16.12 ( int, (fun nat int) ) 15.99/16.12 ( int, (fun nat real) ) 15.99/16.12 ( int, (product_prod int int) ) 15.99/16.12 ( int, (fun int (product_prod int int)) ) 15.99/16.12 ( int, (fun (fun int bool) bool) ) 15.99/16.12 ( int, quickcheck_code_int ) 15.99/16.12 ( int, (fun bool bool) ) 15.99/16.12 ( int, (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 15.99/16.12 ( int, (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)) ) 15.99/16.12 ( int, (fun int (fun int (fun int bool))) ) 15.99/16.12 ( int, (fun (product_prod int int) bool) ) 15.99/16.12 ( int, (fun int (fun (product_prod int int) bool)) ) 15.99/16.12 ( int, (fun int (fun bool bool)) ) 15.99/16.12 ( int, (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 15.99/16.12 ( int, (fun (fun int int) (fun int bool)) ) 15.99/16.12 ( int, (fun (product_prod int int) int) ) 15.99/16.12 ( int, (product_prod int (product_prod int int)) ) 15.99/16.12 ( int, (fun int (product_prod int (product_prod int int))) ) 15.99/16.12 ( int, (fun int (fun int (product_prod int (product_prod int int)))) ) 15.99/16.12 ( int, (fun int (fun int (fun int (product_prod int (product_prod int int))))) ) 15.99/16.12 ( int, (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))) ) 15.99/16.12 ( int, (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))) ) 15.99/16.12 ( int, (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))) ) 15.99/16.12 ( int, (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))))) ) 15.99/16.12 ( int, (fun int (fun (fun int bool) bool)) ) 15.99/16.12 ( int, (list int) ) 15.99/16.12 ( int, (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 15.99/16.12 ( int, (fun int real) ) 15.99/16.12 ( int, (fun nat (fun bool bool)) ) 15.99/16.12 ( int, (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 15.99/16.12 ( int, (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 15.99/16.12 ( (fun int bool), bool ) 15.99/16.12 ( (fun int bool), int ) 15.99/16.12 ( (fun int bool), (fun int bool) ) 15.99/16.12 ( (fun int bool), (fun int (fun int bool)) ) 15.99/16.12 ( (fun int bool), (fun int (fun int int)) ) 15.99/16.12 ( (fun int bool), (fun int (fun bool bool)) ) 15.99/16.12 ( (fun int bool), (fun (fun int int) (fun int bool)) ) 15.99/16.12 ( (fun int bool), (fun real (fun int (fun int bool))) ) 15.99/16.12 ( (fun int (fun int bool)), (fun int bool) ) 15.99/16.12 ( (fun int (fun int bool)), (fun int (fun int bool)) ) 15.99/16.12 ( (fun int (fun int bool)), (fun int (fun (fun int int) (fun int bool))) ) 15.99/16.12 ( (fun int (fun int bool)), (fun int (fun int (fun bool bool))) ) 15.99/16.12 ( (fun int int), (fun int bool) ) 15.99/16.12 ( (fun int int), (fun int (fun int bool)) ) 15.99/16.12 ( (fun int int), (fun int int) ) 15.99/16.12 ( (fun int int), (fun int (fun int int)) ) 15.99/16.12 ( (fun int int), (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 15.99/16.12 ( (fun int int), (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 15.99/16.12 ( (fun nat bool), bool ) 15.99/16.12 ( (fun nat bool), (fun nat bool) ) 15.99/16.12 ( (fun nat bool), (fun nat (fun bool bool)) ) 15.99/16.12 ( (fun nat bool), (fun int (fun nat bool)) ) 15.99/16.12 ( (fun nat bool), (fun real (fun int (fun nat bool))) ) 15.99/16.12 ( (fun nat nat), (fun nat (fun nat bool)) ) 15.99/16.12 ( (fun nat nat), (fun nat real) ) 15.99/16.12 ( (fun nat nat), (fun nat (fun nat nat)) ) 15.99/16.12 ( (product_prod nat nat), bool ) 15.99/16.12 ( (product_prod nat nat), (fun (product_prod nat nat) bool) ) 15.99/16.12 ( real, bool ) 15.99/16.12 ( real, nat ) 15.99/16.12 ( real, (fun int bool) ) 15.99/16.12 ( real, (fun int (fun int bool)) ) 15.99/16.12 ( real, real ) 15.99/16.12 ( real, (fun real bool) ) 15.99/16.12 ( real, (fun real real) ) 15.99/16.12 ( real, complex ) 15.99/16.12 ( real, (fun nat real) ) 15.99/16.12 ( real, (fun real complex) ) 15.99/16.12 ( real, (fun bool bool) ) 15.99/16.12 ( real, (fun (filter nat) bool) ) 15.99/16.12 ( real, (fun nat (product_prod real real)) ) 15.99/16.12 ( real, (fun real (fun nat (product_prod real real))) ) 15.99/16.12 ( real, (fun (filter real) bool) ) 15.99/16.12 ( real, (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 15.99/16.12 ( real, (let ((_let_0 (fun int bool))) (fun _let_0 (fun int _let_0))) ) 15.99/16.12 ( real, (fun int (fun int (fun bool bool))) ) 15.99/16.12 ( real, (fun (fun int (fun int real)) (fun int (fun int bool))) ) 15.99/16.12 ( real, (fun (fun int real) (fun int bool)) ) 15.99/16.12 ( real, (fun int (fun nat bool)) ) 15.99/16.12 ( real, (let ((_let_0 (fun nat bool))) (fun _let_0 (fun int _let_0))) ) 15.99/16.12 ( real, (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 15.99/16.12 ( real, (fun int (fun nat (fun bool bool))) ) 15.99/16.12 ( real, (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 15.99/16.12 ( real, (fun (fun nat real) (fun nat bool)) ) 15.99/16.12 ( (fun real bool), real ) 15.99/16.12 ( (fun real bool), (fun real bool) ) 15.99/16.12 ( (fun real bool), (fun real (fun bool bool)) ) 15.99/16.12 ( (fun real bool), (fun (fun int real) (fun int bool)) ) 15.99/16.12 ( (fun real bool), (fun (fun nat real) (fun nat bool)) ) 15.99/16.12 ( (fun real real), (fun real real) ) 15.99/16.12 ( (fun real real), (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 15.99/16.12 ( (fun real real), (fun real (fun real real)) ) 15.99/16.12 ( (fun real real), (fun real (fun real bool)) ) 15.99/16.12 ( (fun real real), (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 15.99/16.12 ( rat, real ) 15.99/16.12 ( rat, (product_prod int int) ) 15.99/16.12 ( complex, nat ) 15.99/16.12 ( complex, real ) 15.99/16.12 ( complex, complex ) 15.99/16.12 ( (fun nat real), (fun nat bool) ) 15.99/16.12 ( (fun nat real), (fun nat real) ) 15.99/16.12 ( (fun nat real), (fun nat (fun real real)) ) 15.99/16.12 ( (fun nat real), (fun int (fun nat real)) ) 15.99/16.12 ( (filter nat), bool ) 15.99/16.12 ( (fun int (fun int int)), (fun int (fun int (fun int bool))) ) 15.99/16.12 ( (fun int (fun int int)), (let ((_let_0 (fun int int))) (fun int (fun _let_0 _let_0))) ) 15.99/16.12 ( (product_prod int int), bool ) 15.99/16.12 ( (product_prod int int), int ) 15.99/16.12 ( (product_prod int int), (fun int bool) ) 15.99/16.12 ( (product_prod int int), (fun int int) ) 15.99/16.12 ( (product_prod int int), rat ) 15.99/16.12 ( (product_prod int int), (product_prod int int) ) 15.99/16.12 ( (product_prod int int), (fun bool bool) ) 15.99/16.12 ( (product_prod int int), (fun (product_prod int int) bool) ) 15.99/16.12 ( (product_prod int int), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 15.99/16.12 ( (product_prod int int), (fun (product_prod int int) (fun int bool)) ) 15.99/16.12 ( (product_prod int int), (fun (product_prod int int) int) ) 15.99/16.12 ( (product_prod int int), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 15.99/16.12 ( (product_prod int int), (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 15.99/16.12 ( quickcheck_code_int, nat ) 15.99/16.12 ( quickcheck_code_int, int ) 15.99/16.12 ( quickcheck_code_int, (product_prod quickcheck_code_int quickcheck_code_int) ) 15.99/16.12 ( quickcheck_code_int, (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int)) ) 15.99/16.12 ( (fun bool bool), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 15.99/16.12 ( code_code_numeral, nat ) 15.99/16.12 ( code_code_numeral, int ) 15.99/16.12 ( code_code_numeral, (fun nat nat) ) 15.99/16.12 ( code_code_numeral, code_code_numeral ) 15.99/16.12 ( code_code_numeral, (product_prod code_code_numeral code_code_numeral) ) 15.99/16.12 ( code_code_numeral, (fun code_code_numeral (product_prod code_code_numeral code_code_numeral)) ) 15.99/16.12 ( (fun int (fun int (fun int bool))), (fun int (fun int (fun int bool))) ) 15.99/16.12 ( (fun real (fun real bool)), (fun real (fun (fun int real) (fun int bool))) ) 15.99/16.12 ( (fun real (fun real bool)), (fun real (fun (fun nat real) (fun nat bool))) ) 15.99/16.12 ( (product_prod real real), bool ) 15.99/16.12 ( (fun (product_prod real real) bool), (fun real (fun real (fun nat (product_prod real real)))) ) 15.99/16.12 ( (fun (product_prod int int) bool), (fun (product_prod int int) bool) ) 15.99/16.12 ( (fun (product_prod int int) bool), (fun (product_prod int int) (fun bool bool)) ) 15.99/16.12 ( (fun int (fun bool bool)), (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 15.99/16.12 ( (fun nat rat), bool ) 15.99/16.12 ( (filter real), bool ) 15.99/16.12 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)), bool ) 15.99/16.12 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 15.99/16.12 ( (fun (product_prod int int) (fun bool bool)), (let ((_let_0 (fun (product_prod int int) bool))) (fun (product_prod int int) (fun _let_0 _let_0))) ) 15.99/16.12 ( (fun (product_prod int int) (fun int bool)), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 15.99/16.12 ( (fun (product_prod int int) int), (fun (product_prod int int) bool) ) 15.99/16.12 ( (fun (product_prod int int) int), (fun (product_prod int int) (fun int bool)) ) 15.99/16.12 ( (fun (product_prod int int) int), (fun (product_prod int int) int) ) 15.99/16.12 ( (fun (product_prod int int) int), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))) ) 15.99/16.12 ( (fun (product_prod int int) int), (fun (product_prod int int) (fun int int)) ) 15.99/16.12 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 15.99/16.12 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 (fun int bool)))) ) 15.99/16.12 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 (fun int bool)))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun (fun _let_0 int) (fun _let_0 bool)))) ) 15.99/16.12 ( (fun (product_prod int int) (fun int int)), (let ((_let_0 (fun (product_prod int int) int))) (fun (product_prod int int) (fun _let_0 _let_0))) ) 15.99/16.12 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), bool ) 15.99/16.12 ( (fun int real), (fun int bool) ) 15.99/16.12 ( (fun int real), (fun int real) ) 15.99/16.12 ( (fun int real), (fun int (fun int real)) ) 15.99/16.12 ( (fun int real), (fun int (fun real real)) ) 15.99/16.12 ( (fun nat (fun bool bool)), (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 15.99/16.12 ( (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun int bool))) (fun _let_0 (fun int _let_0))) ) 15.99/16.12 ( (fun int (fun int (fun bool bool))), (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 15.99/16.12 ( (fun real (fun int bool)), (fun real bool) ) 15.99/16.12 ( (fun real (fun int (fun int bool))), (fun real (fun int bool)) ) 15.99/16.12 ( (fun real (fun int (fun int bool))), (fun real (fun int (fun int (fun bool bool)))) ) 15.99/16.12 ( (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun int bool))) (fun real (fun _let_0 (fun int _let_0)))) ) 15.99/16.12 ( (fun real (fun int (fun int (fun bool bool)))), (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))) ) 15.99/16.12 ( (fun int (fun int real)), (fun int (fun int bool)) ) 15.99/16.12 ( (fun int (fun int real)), (fun real (fun int (fun int bool))) ) 15.99/16.12 ( (fun (fun int real) (fun int bool)), (fun (fun int (fun int real)) (fun int (fun int bool))) ) 15.99/16.12 ( (fun real (fun (fun int real) (fun int bool))), (fun real (fun (fun int (fun int real)) (fun int (fun int bool)))) ) 15.99/16.12 ( (fun int (fun real real)), (let ((_let_0 (fun int real))) (fun int (fun _let_0 _let_0))) ) 15.99/16.12 ( (fun int (fun real real)), (let ((_let_0 (fun nat real))) (fun int (fun _let_0 _let_0))) ) 15.99/16.12 ( (fun int (fun nat bool)), (fun int bool) ) 15.99/16.12 ( (fun int (fun nat bool)), (fun int (fun nat (fun bool bool))) ) 15.99/16.12 ( (fun real (fun int (fun nat bool))), (fun real (fun int bool)) ) 15.99/16.12 ( (fun real (fun int (fun nat bool))), (fun real (fun int (fun nat (fun bool bool)))) ) 15.99/16.12 ( (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun nat bool))) (fun _let_0 (fun int _let_0))) ) 15.99/16.12 ( (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun nat bool))) (fun real (fun _let_0 (fun int _let_0)))) ) 15.99/16.12 ( (fun int (fun nat (fun bool bool))), (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 15.99/16.12 ( (fun real (fun int (fun nat (fun bool bool)))), (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))) ) 15.99/16.12 ( (fun int (fun nat real)), (fun int (fun nat bool)) ) 15.99/16.12 ( (fun int (fun nat real)), (fun real (fun int (fun nat bool))) ) 15.99/16.12 ( (fun (fun nat real) (fun nat bool)), (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 15.99/16.12 ( (fun real (fun (fun nat real) (fun nat bool))), (fun real (fun (fun int (fun nat real)) (fun int (fun nat bool)))) ) 15.99/16.12 ) 15.99/16.12 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (inverse_inverse X_a))) (or (not (division_ring X_a)) (= _let_0 (ti (fun X_a X_a) _let_0)))) ) 15.99/16.12 ( bool ) 15.99/16.12 ( nat ) 15.99/16.12 ( int ) 15.99/16.12 ( (fun int bool) ) 15.99/16.12 ( (fun int (fun int bool)) ) 15.99/16.12 ( (fun int int) ) 15.99/16.12 ( (fun nat bool) ) 15.99/16.12 ( real ) 15.99/16.12 ( (fun real bool) ) 15.99/16.12 ( (fun real real) ) 15.99/16.12 ( rat ) 15.99/16.12 ( complex ) 15.99/16.12 ( (fun nat real) ) 15.99/16.12 ( (product_prod int int) ) 15.99/16.12 ( code_code_numeral ) 15.99/16.12 ( (fun int (fun int (fun int bool))) ) 15.99/16.12 ( (fun (product_prod int int) bool) ) 15.99/16.12 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 15.99/16.12 ( (fun (product_prod int int) int) ) 15.99/16.12 ( (fun int real) ) 15.99/16.12 ) 15.99/16.12 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_0 (one_one int))) (let ((_let_1 (ti int M))) (or (not (= _let_0 (hAPP int int (hAPP int (fun int int) (times_times int) M) N_1))) (= (hAPP int int (number_number_of int) min_1) _let_1) (= _let_0 _let_1)))) ) 15.99/16.12 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 15.99/16.12 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.99/16.12 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13 ) 15.99/16.12 ) 15.99/16.12 (instantiation (forall ((V_1 $$unsorted)) (or (not (hBOOL (hAPP int bool nat_neg (hAPP int int (number_number_of int) V_1)))) (= (one_one nat) (hAPP nat nat suc (hAPP int nat (number_number_of nat) V_1)))) ) 15.99/16.12 ( pls ) 15.99/16.12 ( (hAPP int int bit1 pls) ) 15.99/16.12 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.99/16.12 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.99/16.12 ( min_1 ) 15.99/16.12 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.12 ) 15.99/16.12 (instantiation (forall ((V_1 $$unsorted)) (let ((_let_0 (number_number_of nat))) (or (hBOOL (hAPP int bool nat_neg (hAPP int int (number_number_of int) V_1))) (= (hAPP nat nat suc (hAPP int nat _let_0 V_1)) (hAPP int nat _let_0 (hAPP int int succ V_1))))) ) 15.99/16.12 ( pls ) 15.99/16.12 ( (hAPP int int bit1 pls) ) 15.99/16.12 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.99/16.12 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.99/16.12 ( min_1 ) 15.99/16.12 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.12 ) 15.99/16.12 (instantiation (forall ((U_1 $$unsorted)) (let ((_let_0 (fun nat bool))) (= (hAPP nat nat suc U_1) (hAPP _let_0 nat (finite_card nat) (hAPP nat _let_0 (ord_atMost nat) U_1)))) ) 15.99/16.12 ( (zero_zero nat) ) 15.99/16.12 ( (hAPP nat nat suc (zero_zero nat)) ) 15.99/16.12 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 15.99/16.12 ) 15.99/16.12 (instantiation (forall ((K_4 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) K_4))) (not (forall ((N_2 $$unsorted)) (not (= (hAPP nat int (semiring_1_of_nat int) N_2) (ti int K_4))) ))) ) 15.99/16.12 ( (one_one int) ) 15.99/16.12 ( min_1 ) 15.99/16.12 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.12 ( s ) 15.99/16.12 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.99/16.12 ( (hAPP int int (number_number_of int) pls) ) 15.99/16.12 ( skv_4 ) 15.99/16.12 ( skv_10 ) 15.99/16.12 ) 15.99/16.12 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_136955 $$unsorted) (BOUND_VARIABLE_136956 $$unsorted)) (let ((_let_0 (ti X_a BOUND_VARIABLE_136956))) (or (not (division_ring X_a)) (= (zero_zero X_a) _let_0) (= (= (one_one X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_136955) BOUND_VARIABLE_136956)) (= _let_0 (ti X_a BOUND_VARIABLE_136955))))) ) 15.99/16.12 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.12 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.99/16.12 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.12 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 15.99/16.12 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.12 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.12 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.99/16.12 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.99/16.12 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.12 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.12 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.12 ) 15.99/16.12 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted) (P_5 $$unsorted) (Q_3 $$unsorted)) (let ((_let_0 (fun int rat))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (product_Pair int int))) (or (not (= (hAPP int _let_1 (hAPP int _let_2 _let_3 P_5) Q_3) (hAPP _let_1 _let_1 normalize (hAPP int _let_1 (hAPP int _let_2 _let_3 A_1) B)))) (= (hAPP int rat (hAPP int _let_0 fract A_1) B) (hAPP int rat (hAPP int _let_0 fract P_5) Q_3))))))) ) 15.99/16.12 ( (one_one int), (one_one int), (one_one int), (one_one int) ) 15.99/16.12 ( (zero_zero int), (one_one int), s, (one_one int) ) 15.99/16.12 ( s, (one_one int), (zero_zero int), (one_one int) ) 15.99/16.12 ( s, (one_one int), s, (one_one int) ) 15.99/16.12 ) 15.99/16.12 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_137010 $$unsorted)) (or (not (group_add X_a)) (= (zero_zero X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_137010)) BOUND_VARIABLE_137010))) ) 15.99/16.12 ( int, (one_one int) ) 15.99/16.12 ( int, pls ) 15.99/16.12 ( int, min_1 ) 15.99/16.12 ( real, (one_one real) ) 15.99/16.12 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.12 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.99/16.12 ( complex, (one_one complex) ) 15.99/16.12 ( complex, ii ) 15.99/16.12 ) 15.99/16.12 (instantiation (forall ((Y_2 $$unsorted) (X_2 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member int))) (or (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 X_2) zEven))) (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 Y_2) zOdd))) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP int int (hAPP int (fun int int) (minus_minus int) X_2) Y_2)) zOdd)))))) ) 15.99/16.12 ( (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.12 ) 15.99/16.12 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_137174 $$unsorted) (BOUND_VARIABLE_137175 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (or (not (ordere142940540dd_abs X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_137174)) BOUND_VARIABLE_137175))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_137174)) BOUND_VARIABLE_137175))))) ) 15.99/16.12 ( int, (one_one int), pls ) 15.99/16.12 ( int, (one_one int), min_1 ) 15.99/16.12 ( int, pls, (one_one int) ) 15.99/16.12 ( int, pls, min_1 ) 15.99/16.12 ( int, pls, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.12 ( int, pls, s ) 15.99/16.12 ( int, pls, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.99/16.12 ( int, pls, (hAPP int int (number_number_of int) pls) ) 15.99/16.12 ( int, pls, skv_4 ) 15.99/16.12 ( int, pls, skv_10 ) 15.99/16.12 ) 15.99/16.12 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_137202 $$unsorted) (BOUND_VARIABLE_137203 $$unsorted) (BOUND_VARIABLE_137204 $$unsorted) (BOUND_VARIABLE_137205 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (minus_minus X_a))) (let ((_let_2 (fun X_a bool))) (let ((_let_3 (ord_less X_a))) (or (not (ordered_ab_group_add X_a)) (not (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_137204) BOUND_VARIABLE_137205) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_137202) BOUND_VARIABLE_137203))) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_137204) BOUND_VARIABLE_137205)) (hBOOL (hAPP X_a bool (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_137202) BOUND_VARIABLE_137203)))))))) ) 15.99/16.12 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.99/16.12 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))), (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 15.99/16.12 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral), (zero_zero code_code_numeral), (one_one code_code_numeral) ) 15.99/16.12 ) 15.99/16.12 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun X_a bool))) (let ((_let_2 (product_prod _let_1 _let_1))) (let ((_let_3 (fun _let_2 bool))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun _let_1 _let_4))) (let ((_let_6 (fun _let_4 _let_4))) (let ((_let_7 (fun _let_1 _let_6))) (let ((_let_8 (fun _let_1 _let_0))) (let ((_let_9 (fun _let_1 _let_8))) (let ((_let_10 (fun _let_4 _let_8))) (= (hAPP _let_3 _let_3 (collect _let_2) (hAPP _let_5 _let_3 (product_prod_case _let_1 _let_1 bool) (hAPP _let_4 _let_5 (hAPP _let_7 (fun _let_4 _let_5) (combc _let_1 _let_4 _let_4) (hAPP _let_9 _let_7 (hAPP (fun _let_8 _let_6) (fun _let_9 _let_7) (combb _let_8 _let_6 _let_1) (combs _let_1 bool bool)) (hAPP _let_5 _let_9 (hAPP _let_10 (fun _let_5 _let_9) (combb _let_4 _let_8 _let_1) (hAPP (fun bool _let_0) _let_10 (combb bool _let_0 _let_1) fconj)) (ord_less _let_1)))) (finite_finite_1 X_a)))) (finite_psubset X_a))))))))))))) ) 15.99/16.12 ( nat ) 15.99/16.12 ( int ) 15.99/16.12 ) 15.99/16.13 (instantiation (forall ((D_1 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun (product_prod int int) bool))) (let ((_let_4 (fun int _let_2))) (let ((_let_5 (fun _let_0 _let_0))) (let ((_let_6 (fun int _let_5))) (= (hAPP _let_3 _let_3 (collect (product_prod int int)) (hAPP _let_1 _let_3 (product_prod_case int int bool) (hAPP _let_1 _let_1 (hAPP _let_6 (fun _let_1 _let_1) (combs int _let_0 _let_0) (hAPP _let_4 _let_6 (hAPP (fun _let_2 _let_5) (fun _let_4 _let_6) (combb _let_2 _let_5 int) (combb bool bool int)) (hAPP _let_0 _let_4 (hAPP (fun bool _let_2) (fun _let_0 _let_4) (combb bool _let_2 int) fconj) (hAPP int _let_0 (ord_less_eq int) D_1)))) (ord_less int)))) (hAPP int _let_3 int_ge_less_than D_1))))))))) ) 15.99/16.13 ( (one_one int) ) 15.99/16.13 ( (zero_zero int) ) 15.99/16.13 ( min_1 ) 15.99/16.13 ) 15.99/16.13 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_137267 $$unsorted)) (or (not (ring_1 X_a)) (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) BOUND_VARIABLE_137267))) (= (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_137267) (hAPP nat X_a (semiring_1_of_nat X_a) (hAPP int nat nat_1 BOUND_VARIABLE_137267)))) ) 15.99/16.13 ( int, (one_one int) ) 15.99/16.13 ( int, (zero_zero int) ) 15.99/16.13 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.13 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.99/16.13 ( real, (one_one int) ) 15.99/16.13 ( real, (zero_zero int) ) 15.99/16.13 ) 15.99/16.13 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (hAPP real _let_0 _let_1 (zero_zero real)))) (or (not (hBOOL (hAPP real bool _let_2 X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) pi))) (hBOOL (hAPP real bool _let_2 (hAPP real real sin X_1))))))) ) 15.99/16.13 ( (one_one real) ) 15.99/16.13 ( (zero_zero real) ) 15.99/16.13 ( pi ) 15.99/16.13 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.13 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.99/16.13 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.99/16.13 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.99/16.13 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.99/16.13 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.13 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 15.99/16.13 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.99/16.13 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 15.99/16.13 ) 15.99/16.13 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_137363 $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (field_char_0 X_a)) (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) (hAPP nat X_a (semiring_1_of_nat X_a) BOUND_VARIABLE_137363)) (field_char_0_Rats X_a))))) ) 15.99/16.13 ( int, (zero_zero nat) ) 15.99/16.13 ( int, (hAPP nat nat suc (zero_zero nat)) ) 15.99/16.13 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.99/16.13 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.13 ( real, (zero_zero nat) ) 15.99/16.13 ( real, (hAPP nat nat suc (zero_zero nat)) ) 15.99/16.13 ) 15.99/16.13 (instantiation (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_0 (fun real real))) (= (hAPP real real (hAPP real _let_0 (dist_dist real) X_1) Y_1) (hAPP real real (abs_abs real) (hAPP real real (hAPP real _let_0 (minus_minus real) X_1) Y_1)))) ) 15.99/16.13 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 15.99/16.13 ) 15.99/16.13 (instantiation (forall ((S $$unsorted)) (= (not (forall ((K_1 $$unsorted)) (let ((_let_0 (fun nat bool))) (not (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) S) (hAPP nat _let_0 (ord_atMost nat) K_1))))) )) (hBOOL (hAPP (fun nat bool) bool (finite_finite_1 nat) S))) ) 15.99/16.13 ( (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 15.99/16.13 ) 15.99/16.13 (instantiation (forall ((N_1 $$unsorted) (M $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (dvd_dvd int))) (let ((_let_2 (hAPP int _let_0 (ord_less_eq int) (zero_zero int)))) (or (not (hBOOL (hAPP int bool _let_2 M))) (not (hBOOL (hAPP int bool _let_2 N_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 M) N_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 N_1) M))) (= (ti int N_1) (ti int M)))))) ) 15.99/16.13 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 15.99/16.13 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.13 ) 15.99/16.13 (instantiation (forall ((A_1 $$unsorted) (N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_1))) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) A_1))) (not (forall ((R_2 $$unsorted)) (or (not (= A_1 (hAPP nat real (hAPP real (fun nat real) (power_power real) R_2) N_1))) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) R_2)))) ))) ) 15.99/16.13 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.13 ) 15.99/16.13 (instantiation (forall ((A_2 $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat nat))) (let ((_let_2 (fun real real))) (let ((_let_3 (fun nat _let_0))) (let ((_let_4 (fun nat real))) (let ((_let_5 (fun _let_0 real))) (let ((_let_6 (fun nat _let_2))) (let ((_let_7 (fun (filter nat) bool))) (let ((_let_8 (fun real _let_7))) (let ((_let_9 (tendsto nat real))) (let ((_let_10 (hAPP _let_4 _let_4 (hAPP _let_6 (fun _let_4 _let_4) (combs nat real real) (hAPP _let_4 _let_6 (hAPP (fun real _let_2) (fun _let_4 _let_6) (combb real _let_2 nat) (times_times real)) (hAPP real _let_4 (power_power real) (hAPP int real (number_number_of real) min_1)))) A_2))) (or (not (hBOOL (hAPP (filter nat) bool (hAPP real _let_7 (hAPP _let_4 _let_8 _let_9 A_2) (zero_zero real)) sequentially))) (not (hBOOL (hAPP _let_4 bool (monoseq real) A_2))) (hBOOL (hAPP (filter nat) bool (hAPP real _let_7 (hAPP _let_4 _let_8 _let_9 (hAPP _let_3 _let_4 (hAPP _let_5 (fun _let_3 _let_4) (combb _let_0 real nat) (hAPP _let_4 _let_5 (big_co1399186613setsum nat real) _let_10)) (hAPP _let_1 _let_3 (hAPP _let_3 (fun _let_1 _let_3) (combb nat _let_0 nat) (hAPP nat _let_3 (ord_atLeastLessThan nat) (zero_zero nat))) (hAPP nat _let_1 (times_times nat) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) (hAPP _let_4 real (suminf real) _let_10)) sequentially)))))))))))))) ) 15.99/16.13 ( (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))) ) 15.99/16.13 ) 15.99/16.13 (instantiation (forall ((Z_1 $$unsorted)) (let ((_let_0 (fun nat nat))) (= (hAPP nat nat (hAPP nat _let_0 (times_times nat) Z_1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) Z_1) Z_1))) ) 15.99/16.13 ( (one_one nat) ) 15.99/16.13 ) 15.99/16.13 (instantiation (forall ((N $$unsorted) (Ma $$unsorted)) (let ((_let_0 (zero_zero nat))) (let ((_let_1 (semiring_1_of_nat int))) (= (= (hAPP nat int _let_1 Ma) (hAPP int int (uminus_uminus int) (hAPP nat int _let_1 N))) (and (= _let_0 Ma) (= _let_0 N))))) ) 15.99/16.13 ( (zero_zero nat), (zero_zero nat) ) 15.99/16.13 ( (hAPP nat nat suc (zero_zero nat)), (hAPP nat nat suc (zero_zero nat)) ) 15.99/16.13 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.99/16.13 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.13 ) 15.99/16.13 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_137742 $$unsorted) (BOUND_VARIABLE_137743 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (times_times X_a))) (let ((_let_2 (uminus_uminus X_a))) (or (not (ring X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_137742)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_137743)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_137742) BOUND_VARIABLE_137743)))))) ) 15.99/16.13 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 15.99/16.13 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.99/16.13 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13 ) 15.99/16.13 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.99/16.13 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.99/16.13 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.99/16.13 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 15.99/16.13 ( complex, ii, ii ) 15.99/16.13 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 15.99/16.13 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 15.99/16.13 ) 15.99/16.13 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_137786 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (or (not (linord219039673up_add X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_137786) BOUND_VARIABLE_137786)) _let_2)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_137786) _let_2))))))) ) 15.99/16.13 ( nat, (one_one nat) ) 15.99/16.13 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.99/16.13 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.13 ) 15.99/16.13 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (fun nat X_a))) (or (not (topological_space X_a)) (not (comm_monoid_add X_a)) (hBOOL (hAPP _let_0 bool (summable X_a) (hAPP X_a _let_0 (combk X_a nat) (zero_zero X_a)))))) ) 15.99/16.13 ( bool ) 15.99/16.13 ( nat ) 15.99/16.13 ( int ) 15.99/16.13 ( (fun int int) ) 15.99/16.13 ( (fun nat bool) ) 15.99/16.13 ( (fun nat nat) ) 15.99/16.13 ( (product_prod nat nat) ) 15.99/16.13 ( (fun (product_prod nat nat) bool) ) 15.99/16.13 ( (fun nat (fun (product_prod nat nat) bool)) ) 15.99/16.13 ( real ) 15.99/16.13 ( (fun real real) ) 15.99/16.13 ( rat ) 15.99/16.13 ( (fun nat (fun nat bool)) ) 15.99/16.13 ( complex ) 15.99/16.13 ( (product_prod int int) ) 15.99/16.13 ( quickcheck_code_int ) 15.99/16.13 ( (fun bool bool) ) 15.99/16.13 ( code_code_numeral ) 15.99/16.13 ( (product_prod real real) ) 15.99/16.13 ( (fun nat (product_prod nat nat)) ) 15.99/16.13 ( (fun nat (product_prod int int)) ) 15.99/16.13 ) 15.99/16.13 (instantiation (forall ((Y_2 $$unsorted) (X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) Y_2) X_2))) (= X_2 (hAPP _let_0 real (complete_Sup_Sup real) (hAPP real _let_0 (hAPP real (fun real _let_0) (ord_gr676655987ssThan real) Y_2) X_2))))) ) 15.99/16.13 ( (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.13 ( (zero_zero real), pi ) 15.99/16.13 ( (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.13 ( (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.13 ( (zero_zero real), skv_2 ) 15.99/16.13 ( (zero_zero real), skv_8 ) 15.99/16.13 ( (zero_zero real), skv_9 ) 15.99/16.13 ( pi, (zero_zero real) ) 15.99/16.13 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.13 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.13 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 15.99/16.13 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.99/16.13 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 15.99/16.13 ) 15.99/16.13 (instantiation (forall ((P_1 $$unsorted) (A0 $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP int bool (hAPP (fun int _let_0) _let_0 (accp int) quickc1265749348ro_rel) A0))) (not (forall ((I_2 $$unsorted)) (let ((_let_1 (zero_zero int))) (or (not (hBOOL (hAPP int bool (hAPP (fun int _let_0) _let_0 (accp int) quickc1265749348ro_rel) I_2))) (and (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) I_2) _let_1))) (not (= _let_1 (ti int I_2))) (not (hBOOL (hAPP int bool P_1 (hAPP int int (hAPP int (fun int int) (minus_minus int) I_2) (one_one int)))))) (hBOOL (hAPP int bool P_1 I_2)))) )) (hBOOL (hAPP int bool P_1 A0)))) ) 15.99/16.13 ( (hAPP int (fun int bool) (ord_less int) pls), pls ) 15.99/16.13 ( (hAPP int (fun int bool) (ord_less int) pls), min_1 ) 15.99/16.13 ( (hAPP int (fun int bool) (ord_less_eq int) pls), min_1 ) 15.99/16.13 ( (hAPP int (fun int bool) (ord_less_eq int) (one_one int)), t ) 15.99/16.13 ( nat_neg, (one_one int) ) 15.99/16.13 ( nat_neg, (hAPP int int (number_number_of int) min_1) ) 15.99/16.13 ( nat_neg, (hAPP int int (number_number_of int) pls) ) 15.99/16.13 ( (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (one_one int) ) 15.99/16.13 ( (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.13 ( (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), s ) 15.99/16.13 ( (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.99/16.13 ( (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) pls) ) 15.99/16.13 ( (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_4 ) 15.99/16.13 ( (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_10 ) 15.99/16.13 ( (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (one_one int) ) 15.99/16.13 ( (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.13 ( zprime, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.13 ( zprime, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.13 ( (hAPP int (fun int bool) (ord_less int) s), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.13 ( (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) s)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.13 ( (let ((_let_0 (fun int int))) (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 15.99/16.13 ( (hAPP int (fun int bool) (ord_less int) (one_one int)), t ) 15.99/16.13 ( (even_odd_even int), (one_one int) ) 15.99/16.13 ( (even_odd_even int), (zero_zero int) ) 15.99/16.13 ( twoSqu1091635170sum2sq, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) t))) ) 15.99/16.13 ( nat_is_nat, (one_one int) ) 15.99/16.13 ( nat_is_nat, (zero_zero int) ) 15.99/16.13 ( nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.13 ( nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.99/16.13 ( (hAPP int (fun int bool) (ord_less int) min_1), pls ) 15.99/16.13 ( (hAPP int (fun int bool) (ord_less int) min_1), min_1 ) 15.99/16.13 ( (hAPP int (fun int bool) (ord_less_eq int) min_1), pls ) 15.99/16.13 ( (hAPP int (fun int bool) (ord_less_eq int) min_1), min_1 ) 15.99/16.13 ( (let ((_let_0 (fun int int))) (hAPP int (fun int bool) quadRes (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int int (number_number_of int) min_1) ) 15.99/16.13 ( (let ((_let_0 (fun int bool))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (let ((_let_3 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int _let_1 _let_2 s) _let_3)) (hAPP nat int (hAPP int _let_1 _let_2 s1) _let_3)))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.13 ( (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.13 ( (hAPP int (fun int bool) (ord_less int) t), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.13 ( (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.13 ( (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_4)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.13 ( (hAPP int (fun int bool) (ord_less int) skv_4), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.13 ( (hAPP int (fun int bool) (ord_less int) skv_10), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.13 ( (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_10)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.13 ( (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.13 ) 15.99/16.13 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_137900 $$unsorted) (BOUND_VARIABLE_137901 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member X_a))) (let ((_let_3 (field_char_0_Rats X_a))) (or (not (field_char_0 X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_137901) _let_3))) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_137900) _let_3))) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_137900)) (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_137901) BOUND_VARIABLE_137900)) _let_3))))))) ) 15.99/16.13 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 15.99/16.13 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.99/16.13 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.99/16.13 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.99/16.13 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.13 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 15.99/16.13 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), pi ) 15.99/16.13 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (one_one real) ) 15.99/16.13 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))), pi ) 15.99/16.13 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 15.99/16.13 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))), (one_one real) ) 15.99/16.13 ) 15.99/16.13 (instantiation (forall ((Y_2 $$unsorted) (X_2 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (hAPP int _let_0 (ord_less_eq int) (zero_zero int)))) (or (not (hBOOL (hAPP int bool _let_1 X_2))) (not (hBOOL (hAPP int bool _let_1 Y_2))) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (dvd_dvd nat) (hAPP int nat nat_1 X_2)) (hAPP int nat nat_1 Y_2))) (hBOOL (hAPP int bool (hAPP int _let_0 (dvd_dvd int) X_2) Y_2)))))) ) 15.99/16.13 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.13 ) 15.99/16.13 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (gcd_gcd nat))) (= (hAPP nat nat (hAPP nat _let_0 _let_1 (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) M) N_1)) N_1) (hAPP nat nat (hAPP nat _let_0 _let_1 M) N_1)))) ) 15.99/16.13 ( (one_one nat), (one_one nat) ) 15.99/16.13 ) 15.99/16.13 (instantiation (forall ((Nat $$unsorted) (Nat_5 $$unsorted)) (= (= (hAPP nat nat suc Nat) (hAPP nat nat suc Nat_5)) (= Nat Nat_5)) ) 15.99/16.13 ( (zero_zero nat), (zero_zero nat) ) 15.99/16.13 ( (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 15.99/16.13 ( (hAPP nat nat suc (zero_zero nat)), (zero_zero nat) ) 15.99/16.13 ( (hAPP nat nat suc (zero_zero nat)), (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 15.99/16.13 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))), (zero_zero nat) ) 15.99/16.13 ) 15.99/16.13 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (BOUND_VARIABLE_138020 $$unsorted) (BOUND_VARIABLE_138021 $$unsorted) (BOUND_VARIABLE_138022 $$unsorted) (BOUND_VARIABLE_138023 $$unsorted)) (let ((_let_0 (filter X_a))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (hAPP (fun X_a X_b) (fun X_b _let_1) (tendsto X_a X_b) BOUND_VARIABLE_138021))) (let ((_let_3 (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_138023))) (or (not (real_n2089651433ebra_1 X_a)) (not (metric_space X_b)) (not (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 _let_2 BOUND_VARIABLE_138022) _let_3))) (not (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 _let_2 BOUND_VARIABLE_138020) _let_3))) (= (ti X_b BOUND_VARIABLE_138022) (ti X_b BOUND_VARIABLE_138020))))))) ) 15.99/16.13 ( real, real, (zero_zero real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.13 ) 15.99/16.13 (instantiation (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (product_prod int int))) (= (= A_2 B_1) (= (hAPP rat _let_0 quotient_of A_2) (hAPP rat _let_0 quotient_of B_1)))) ) 15.99/16.13 ( (zero_zero rat), (zero_zero rat) ) 15.99/16.13 ( (zero_zero rat), (one_one rat) ) 15.99/16.13 ( (one_one rat), (zero_zero rat) ) 15.99/16.13 ) 15.99/16.13 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (inverse_divide real))) (or (= (zero_zero real) X_1) (= (hAPP real real arctan (hAPP real real (hAPP real _let_0 _let_1 (one_one real)) X_1)) (hAPP real real (hAPP real _let_0 (minus_minus real) (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (sgn_sgn real) X_1)) pi)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP real real arctan X_1)))))) ) 15.99/16.13 ( (zero_zero real) ) 15.99/16.13 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.13 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.99/16.13 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.13 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 15.99/16.13 ) 15.99/16.13 (instantiation (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (let ((_let_2 (ord_less int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 _let_1) B_1))) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 A_2) _let_1)) (hBOOL (hAPP rat bool (hAPP rat (fun rat bool) (ord_less rat) (hAPP int rat (hAPP int (fun int rat) fract A_2) B_1)) (zero_zero rat)))))))) ) 15.99/16.13 ( (one_one int), (one_one int) ) 15.99/16.13 ( (zero_zero int), (one_one int) ) 15.99/16.13 ) 15.99/16.13 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_138088 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hAPP X_a int (archim2085082626_floor X_a) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_138088)) (hAPP int int (uminus_uminus int) (hAPP X_a int (archimedean_ceiling X_a) BOUND_VARIABLE_138088)))) ) 15.99/16.13 ( int, (one_one int) ) 15.99/16.13 ( int, pls ) 15.99/16.13 ( int, min_1 ) 15.99/16.13 ( real, (one_one real) ) 15.99/16.13 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.13 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.99/16.13 ( complex, (one_one complex) ) 15.99/16.13 ( complex, ii ) 15.99/16.13 ) 15.99/16.13 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member int))) (or (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 X_2) zOdd))) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP int int (hAPP int (fun int int) (minus_minus int) X_2) (one_one int))) zEven)))))) ) 15.99/16.13 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.13 ) 15.99/16.13 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_138194 $$unsorted) (BOUND_VARIABLE_138195 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (minus_minus X_a))) (let ((_let_3 (inverse_inverse X_a))) (let ((_let_4 (times_times X_a))) (let ((_let_5 (hAPP X_a X_a _let_3 BOUND_VARIABLE_138195))) (let ((_let_6 (hAPP X_a X_a _let_3 BOUND_VARIABLE_138194))) (or (not (division_ring X_a)) (= _let_0 (ti X_a BOUND_VARIABLE_138195)) (= _let_0 (ti X_a BOUND_VARIABLE_138194)) (= (hAPP X_a X_a (uminus_uminus X_a) (hAPP X_a X_a (hAPP X_a _let_1 _let_4 (hAPP X_a X_a (hAPP X_a _let_1 _let_4 _let_5) (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_138195) BOUND_VARIABLE_138194))) _let_6)) (hAPP X_a X_a (hAPP X_a _let_1 _let_2 _let_5) _let_6)))))))))) ) 15.99/16.13 ( int, (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.13 ( real, (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))), (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))) ) 15.99/16.13 ( code_code_numeral, (one_one code_code_numeral), (zero_zero code_code_numeral) ) 15.99/16.13 ) 15.99/16.13 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_138232 $$unsorted)) (let ((_let_0 (abs_abs X_a))) (let ((_let_1 (inverse_inverse X_a))) (or (not (linordered_field X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_138232)) (= (hAPP X_a X_a _let_1 (hAPP X_a X_a _let_0 BOUND_VARIABLE_138232)) (hAPP X_a X_a _let_0 (hAPP X_a X_a _let_1 BOUND_VARIABLE_138232)))))) ) 15.99/16.13 ( bool, fFalse ) 15.99/16.13 ( bool, fTrue ) 15.99/16.13 ( int, pls ) 15.99/16.13 ( int, min_1 ) 15.99/16.13 ( int, s ) 15.99/16.13 ( int, m ) 15.99/16.13 ( int, s1 ) 15.99/16.13 ( int, t ) 15.99/16.13 ( (fun int bool), nat_neg ) 15.99/16.13 ( (fun int bool), zprime ) 15.99/16.13 ( (fun int bool), zEven ) 15.99/16.13 ( (fun int bool), zOdd ) 15.99/16.13 ( (fun int bool), (even_odd_even int) ) 15.99/16.13 ( (fun int bool), twoSqu1091635170sum2sq ) 15.99/16.13 ( (fun int bool), nat_is_nat ) 15.99/16.13 ( (fun int (fun int bool)), norRRset ) 15.99/16.13 ( (fun int (fun int bool)), quadRes ) 15.99/16.13 ( (fun int (fun int bool)), sRStar ) 15.99/16.13 ( (fun int (fun int bool)), d22set ) 15.99/16.13 ( (fun int (fun int bool)), sr ) 15.99/16.13 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 15.99/16.13 ( (fun int int), zfact ) 15.99/16.13 ( (fun int int), bit0 ) 15.99/16.13 ( (fun int int), bit1 ) 15.99/16.13 ( (fun int int), (fact_fact int) ) 15.99/16.13 ( (fun int int), pred ) 15.99/16.13 ( (fun int int), succ ) 15.99/16.13 ( (fun nat bool), (even_odd_even nat) ) 15.99/16.13 ( (fun nat bool), prime ) 15.99/16.13 ( (fun nat nat), suc ) 15.99/16.13 ( (fun nat nat), (fact_fact nat) ) 15.99/16.13 ( (fun nat nat), fact ) 15.99/16.13 ( (fun nat nat), nat_size ) 15.99/16.13 ( (fun nat nat), (size_size nat) ) 15.99/16.13 ( (fun (product_prod nat nat) bool), pred_nat ) 15.99/16.13 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 15.99/16.13 ( real, (zero_zero real) ) 15.99/16.13 ( real, pi ) 15.99/16.13 ( (fun real real), ln ) 15.99/16.13 ( (fun real real), cos ) 15.99/16.13 ( (fun real real), sqrt ) 15.99/16.13 ( (fun real real), sin ) 15.99/16.13 ( (fun real real), arccos ) 15.99/16.13 ( (fun real real), arcsin ) 15.99/16.13 ( (fun real real), tan ) 15.99/16.13 ( (fun real real), arctan ) 15.99/16.13 ( (fun nat (fun nat bool)), coprime ) 15.99/16.13 ( complex, ii ) 15.99/16.13 ( (fun nat real), (real_1 nat) ) 15.99/16.13 ( (fun nat real), sin_coeff ) 15.99/16.13 ( (fun nat real), cos_coeff ) 15.99/16.13 ( (filter nat), sequentially ) 15.99/16.13 ( (fun int (fun int int)), (gcd_gcd int) ) 15.99/16.13 ( (fun int (fun int int)), legendre ) 15.99/16.13 ( (fun int (fun int int)), legacy_zgcd ) 15.99/16.13 ( (fun int (fun int int)), standardRes ) 15.99/16.13 ( (fun int (fun int int)), nat_tsub ) 15.99/16.13 ( (fun int (fun int int)), multInv ) 15.99/16.13 ( (fun int (fun int int)), z3mod ) 15.99/16.13 ( (fun int (fun int int)), z3div ) 15.99/16.13 ( (fun int (fun int int)), int_gcd ) 15.99/16.13 ( (fun int (fun int int)), int_lcm ) 15.99/16.13 ( (fun int (fun int int)), inv ) 15.99/16.13 ( (fun complex complex), expi ) 15.99/16.13 ( (fun complex complex), cnj ) 15.99/16.13 ( (fun real complex), cis ) 15.99/16.13 ( (fun int nat), nat_1 ) 15.99/16.13 ( (fun int nat), phi ) 15.99/16.13 ( (fun (fun int bool) bool), nat_nat_set ) 15.99/16.13 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 15.99/16.13 ( (fun nat (fun nat nat)), nat_gcd ) 15.99/16.13 ( (fun nat (fun nat nat)), nat_lcm ) 15.99/16.13 ( (fun (fun int bool) int), (the int) ) 15.99/16.13 ( (fun complex real), re ) 15.99/16.13 ( (fun complex real), im ) 15.99/16.13 ( (fun complex real), arg ) 15.99/16.13 ( (fun bool bool), fNot ) 15.99/16.13 ( (fun nat (fun real real)), root ) 15.99/16.13 ( (fun real (fun real real)), log ) 15.99/16.13 ( (fun real (fun real real)), powr ) 15.99/16.13 ( (fun bool (fun bool bool)), fimplies ) 15.99/16.13 ( (fun bool (fun bool bool)), fconj ) 15.99/16.13 ( (fun bool (fun bool bool)), fdisj ) 15.99/16.13 ( (fun int (fun int (product_prod int int))), negDivAlg ) 15.99/16.13 ( (fun int (fun int (product_prod int int))), posDivAlg ) 15.99/16.13 ( (fun int (fun int (product_prod int int))), divmod_int ) 15.99/16.13 ( (fun int (fun int (product_prod int int))), pdivmod ) 15.99/16.13 ( (fun int (fun int (product_prod int int))), norm_frac ) 15.99/16.13 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 15.99/16.13 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 15.99/16.13 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 15.99/16.13 ( (fun int (fun int (fun int bool))), zcong ) 15.99/16.13 ( (fun int (fun int (fun int bool))), zcongm ) 15.99/16.13 ( (fun int (fun int (fun int bool))), noXRRset ) 15.99/16.13 ( (fun int (fun int (fun int bool))), bnorRset ) 15.99/16.13 ( (fun int (fun int (fun int bool))), wset ) 15.99/16.13 ( (fun (product_prod int int) bool), frac_1 ) 15.99/16.13 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 15.99/16.13 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 15.99/16.13 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 15.99/16.13 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 15.99/16.13 ( (fun (fun nat rat) bool), vanishes ) 15.99/16.13 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 15.99/16.13 ( (fun code_code_numeral nat), code_c271388182l_size ) 15.99/16.13 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 15.99/16.13 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 15.99/16.13 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 15.99/16.13 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 15.99/16.13 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 15.99/16.13 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 15.99/16.13 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 15.99/16.13 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 15.99/16.13 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 15.99/16.13 ( (fun complex nat), complex_size ) 15.99/16.13 ( (fun complex nat), (size_size complex) ) 15.99/16.13 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 15.99/16.13 ( (fun nat (fun nat (product_prod int int))), bezw ) 15.99/16.13 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 15.99/16.13 ( (fun int (fun nat nat)), nat_aux ) 15.99/16.13 ( (fun int (fun (fun int bool) bool)), rsetR ) 15.99/16.13 ( (fun int (fun (fun int bool) bool)), resSet ) 15.99/16.13 ( (fun int (list int)), quickc666637781d_zero ) 15.99/16.13 ( (fun (product_prod int int) rat), frct ) 15.99/16.13 ( (fun int (fun int rat)), fract ) 15.99/16.13 ( (fun real (fun real complex)), complex_1 ) 15.99/16.13 ( (fun real (fun real complex)), rcis ) 15.99/16.13 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 15.99/16.13 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 15.99/16.13 ( (fun int real), (real_1 int) ) 15.99/16.13 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 15.99/16.13 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 15.99/16.13 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 15.99/16.13 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 15.99/16.13 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 15.99/16.13 ( (fun real nat), natfloor ) 15.99/16.13 ( (fun real nat), natceiling ) 15.99/16.13 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 15.99/16.13 ( (fun quickcheck_code_int int), quickcheck_int_of ) 15.99/16.13 ( (fun rat (product_prod int int)), quotient_of ) 15.99/16.13 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 15.99/16.13 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 15.99/16.13 ( (fun rat real), ratreal ) 15.99/16.13 ( (fun code_code_numeral int), code_int_of ) 15.99/16.13 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 15.99/16.13 ( (fun int quickcheck_code_int), quickcheck_of_int ) 15.99/16.13 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 15.99/16.13 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 15.99/16.13 ) 15.99/16.13 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))))) (let ((_let_1 (fun nat nat))) (or (not (hBOOL (hAPP nat bool (even_odd_even nat) X_1))) (= X_1 (hAPP nat nat (hAPP nat _let_1 (times_times nat) _let_0) (hAPP nat nat (hAPP nat _let_1 (div_div nat) X_1) _let_0)))))) ) 15.99/16.13 ( (zero_zero nat) ) 15.99/16.13 ( (one_one nat) ) 15.99/16.13 ) 15.99/16.13 (instantiation (forall ((N_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (hAPP nat real (real_1 nat) N_1))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) _let_1) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) X_1) (hAPP real real (hAPP real (fun real real) (plus_plus real) _let_1) (one_one real))))) (= N_1 (hAPP real nat natfloor X_1))))) ) 15.99/16.13 ( (zero_zero nat), pi ) 15.99/16.13 ( (zero_zero nat), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.13 ( (zero_zero nat), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.13 ( (zero_zero nat), skv_3 ) 15.99/16.13 ( (zero_zero nat), skv_5 ) 15.99/16.13 ( (zero_zero nat), skv_7 ) 15.99/16.13 ( (zero_zero nat), skv_12 ) 15.99/16.13 ) 15.99/16.13 (instantiation (forall ((Ma $$unsorted) (N $$unsorted)) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) Ma) (hAPP nat nat suc N))) (or (= (zero_zero nat) Ma) (not (forall ((J_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) J_1) N))) (not (= Ma (hAPP nat nat suc J_1)))) )))) ) 15.99/16.13 ( (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 15.99/16.13 ) 15.99/16.13 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (plus_plus nat))) (= (hAPP nat nat (hAPP nat _let_0 _let_1 (hAPP nat nat suc M)) N_1) (hAPP nat nat (hAPP nat _let_0 _let_1 M) (hAPP nat nat suc N_1))))) ) 15.99/16.13 ( (zero_zero nat), (one_one nat) ) 15.99/16.13 ( (one_one nat), (zero_zero nat) ) 15.99/16.13 ) 15.99/16.13 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (one_one real))) (let ((_let_2 (fun real real))) (let ((_let_3 (fun nat real))) (let ((_let_4 (power_power real))) (let ((_let_5 (fun nat _let_2))) (let ((_let_6 (fun _let_3 _let_3))) (let ((_let_7 (combs nat real real))) (let ((_let_8 (fun (fun nat nat) _let_3))) (let ((_let_9 (combb nat real nat))) (let ((_let_10 (hAPP (fun real _let_2) (fun _let_3 _let_5) (combb real _let_2 nat) (times_times real)))) (let ((_let_11 (fun real _let_3))) (let ((_let_12 (suminf real))) (let ((_let_13 (hAPP _let_5 _let_6 _let_7 (hAPP _let_3 _let_5 _let_10 (hAPP real _let_3 _let_4 (hAPP int real (number_number_of real) min_1)))))) (let ((_let_14 (fun _let_11 _let_11))) (let ((_let_15 (combb _let_3 _let_3 real))) (let ((_let_16 (fun real _let_8))) (let ((_let_17 (hAPP nat (fun nat nat) (hAPP (fun nat (fun nat nat)) (fun nat (fun nat nat)) (combc nat nat nat) (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (let ((_let_18 (hAPP nat (fun nat nat) (hAPP (fun nat (fun nat nat)) (fun nat (fun nat nat)) (combc nat nat nat) (hAPP (fun nat nat) (fun nat (fun nat nat)) (hAPP (fun nat (fun nat nat)) (fun (fun nat nat) (fun nat (fun nat nat))) (combb nat (fun nat nat) nat) (plus_plus nat)) _let_17)) (one_one nat)))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) (hAPP real real (abs_abs real) X_2)) _let_1))) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP _let_2 (fun real _let_0) (deriv real) (hAPP _let_11 _let_2 (hAPP (fun _let_3 real) (fun _let_11 _let_2) (combb _let_3 real real) _let_12) (hAPP _let_11 _let_11 (hAPP _let_6 _let_14 _let_15 _let_13) (hAPP _let_11 _let_11 (hAPP _let_6 _let_14 _let_15 (hAPP _let_5 _let_6 _let_7 (hAPP _let_3 _let_5 _let_10 (hAPP _let_3 _let_3 (hAPP _let_2 _let_6 (combb real real nat) (hAPP real _let_2 (inverse_divide real) _let_1)) (hAPP (fun nat nat) _let_3 (hAPP _let_3 _let_8 _let_9 (real_1 nat)) _let_18))))) (hAPP (fun nat nat) _let_11 (hAPP _let_16 (fun (fun nat nat) _let_11) (combc real (fun nat nat) _let_3) (hAPP _let_11 _let_16 (hAPP (fun _let_3 _let_8) (fun _let_11 _let_16) (combb _let_3 _let_8 real) _let_9) _let_4)) _let_18))))) X_2) (hAPP _let_3 real _let_12 (hAPP _let_3 _let_3 _let_13 (hAPP (fun nat nat) _let_3 (hAPP _let_3 _let_8 _let_9 (hAPP real _let_3 _let_4 X_2)) _let_17))))))))))))))))))))))))) ) 15.99/16.13 ( (hAPP int real (number_number_of real) min_1) ) 15.99/16.13 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.13 ) 15.99/16.13 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_138330 $$unsorted) (BOUND_VARIABLE_138331 $$unsorted) (BOUND_VARIABLE_138332 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (inverse_divide X_a))) (let ((_let_2 (minus_minus X_a))) (or (not (field X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_138332)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_138330) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_138331) BOUND_VARIABLE_138332)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_0 _let_2 (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_138332) BOUND_VARIABLE_138330)) BOUND_VARIABLE_138331)) BOUND_VARIABLE_138332)))))) ) 15.99/16.13 ( real, (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.13 ) 15.99/16.13 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_138381 $$unsorted) (BOUND_VARIABLE_138382 $$unsorted) (BOUND_VARIABLE_138383 $$unsorted) (BOUND_VARIABLE_138384 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (let ((_let_1 (fun X_a bool))) (let ((_let_2 (dvd_dvd X_a))) (let ((_let_3 (fun X_a X_a))) (let ((_let_4 (times_times X_a))) (let ((_let_5 (div_div X_a))) (or (not (semiring_div X_a)) (= _let_0 (ti X_a BOUND_VARIABLE_138384)) (= _let_0 (ti X_a BOUND_VARIABLE_138383)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_138384) BOUND_VARIABLE_138382))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_138383) BOUND_VARIABLE_138381))) (= (= (hAPP X_a X_a (hAPP X_a _let_3 _let_4 BOUND_VARIABLE_138384) BOUND_VARIABLE_138381) (hAPP X_a X_a (hAPP X_a _let_3 _let_4 BOUND_VARIABLE_138382) BOUND_VARIABLE_138383)) (= (hAPP X_a X_a (hAPP X_a _let_3 _let_5 BOUND_VARIABLE_138382) BOUND_VARIABLE_138384) (hAPP X_a X_a (hAPP X_a _let_3 _let_5 BOUND_VARIABLE_138381) BOUND_VARIABLE_138383)))))))))) ) 15.99/16.13 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.13 ) 15.99/16.13 (instantiation (forall ((N $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun nat bool))) (= (hAPP _let_0 _let_1 (hAPP (fun int nat) (fun _let_0 _let_1) (image int nat) nat_1) (hAPP int _let_0 (hAPP int (fun int _let_0) (ord_atLeastAtMost int) (zero_zero int)) (hAPP nat int (semiring_1_of_nat int) N))) (hAPP nat _let_1 (ord_atMost nat) N)))) ) 15.99/16.13 ( (zero_zero nat) ) 15.99/16.13 ( (hAPP nat nat suc (zero_zero nat)) ) 15.99/16.13 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.99/16.13 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.13 ) 15.99/16.13 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun int (fun int int)))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (ring_1_of_int real))) (let ((_let_5 (fun int _let_3))) (let ((_let_6 (fun int real))) (let ((_let_7 (fun int _let_1))) (= (hAPP _let_0 int (the int) (hAPP _let_0 _let_0 (hAPP _let_5 (fun _let_0 _let_0) (combs int bool bool) (hAPP _let_0 _let_5 (hAPP (fun bool _let_3) (fun _let_0 _let_5) (combb bool _let_3 int) fconj) (hAPP real _let_0 (hAPP _let_7 (fun real _let_0) (combc int real bool) (hAPP _let_6 _let_7 (hAPP (fun real _let_1) (fun _let_6 _let_7) (combb real _let_1 int) (ord_less_eq real)) _let_4)) X_2))) (hAPP _let_6 _let_0 (hAPP _let_1 (fun _let_6 _let_0) (combb real bool int) (hAPP real _let_1 (ord_less real) X_2)) (hAPP (fun int int) _let_6 (hAPP _let_6 (fun (fun int int) _let_6) (combb int real int) _let_4) (hAPP int (fun int int) (hAPP _let_2 _let_2 (combc int int int) (plus_plus int)) (one_one int)))))) (hAPP real int (archim2085082626_floor real) X_2)))))))))) ) 15.99/16.13 ( (one_one real) ) 15.99/16.13 ( (zero_zero real) ) 15.99/16.13 ( pi ) 15.99/16.13 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.13 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.99/16.13 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.13 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 15.99/16.13 ) 15.99/16.13 (instantiation (forall ((F $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 A_2) B_1))) (not (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X) B_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 A_2) X))) (not (forall ((Y $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP (fun real real) (fun real _let_0) (deriv real) F) X) Y))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Y) (zero_zero real))))) ))) )) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real F B_1)) (hAPP real real F A_2)))))) ) 15.99/16.13 ( cos, skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.13 ( sqrt, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real) ) 15.99/16.13 ) 15.99/16.13 (instantiation (forall ((X_2 $$unsorted) (P_1 $$unsorted)) (or (not (forall ((A_4 $$unsorted)) (let ((_let_0 (one_one int))) (or (and (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) _let_0) A_4)) (not (hBOOL (hAPP int bool P_1 (hAPP int int (hAPP int (fun int int) (minus_minus int) A_4) _let_0))))) (hBOOL (hAPP int bool P_1 A_4)))) )) (hBOOL (hAPP int bool P_1 X_2))) ) 15.99/16.13 ( (one_one int), nat_neg ) 15.99/16.13 ( (one_one int), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 15.99/16.13 ( (one_one int), (hAPP int (fun int bool) (ord_less int) (zero_zero int)) ) 15.99/16.13 ( (one_one int), (even_odd_even int) ) 15.99/16.13 ( (one_one int), nat_is_nat ) 15.99/16.13 ( (zero_zero int), (even_odd_even int) ) 15.99/16.13 ( (zero_zero int), nat_is_nat ) 15.99/16.13 ( pls, (hAPP int (fun int bool) (ord_less int) pls) ) 15.99/16.13 ( pls, (hAPP int (fun int bool) (ord_less int) min_1) ) 15.99/16.13 ( pls, (hAPP int (fun int bool) (ord_less_eq int) min_1) ) 15.99/16.13 ( min_1, (hAPP int (fun int bool) (ord_less int) pls) ) 15.99/16.13 ( min_1, (hAPP int (fun int bool) (ord_less_eq int) pls) ) 15.99/16.13 ( min_1, (hAPP int (fun int bool) (ord_less int) min_1) ) 15.99/16.13 ( min_1, (hAPP int (fun int bool) (ord_less_eq int) min_1) ) 15.99/16.13 ( (hAPP int int (number_number_of int) min_1), nat_neg ) 15.99/16.13 ( (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int (fun int bool) quadRes (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))) ) 15.99/16.13 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 15.99/16.13 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), zprime ) 15.99/16.13 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), nat_is_nat ) 15.99/16.13 ( s, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 15.99/16.14 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int (fun int bool) (ord_less int) (zero_zero int)) ) 15.99/16.14 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), zprime ) 15.99/16.14 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int (fun int bool) (ord_less int) s) ) 15.99/16.14 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) s)) ) 15.99/16.14 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (let ((_let_3 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int _let_1 _let_2 s) _let_3)) (hAPP nat int (hAPP int _let_1 _let_2 s1) _let_3)))))) ) 15.99/16.14 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))) ) 15.99/16.14 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int (fun int bool) (ord_less int) t) ) 15.99/16.14 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))) ) 15.99/16.14 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_4)) ) 15.99/16.14 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int (fun int bool) (ord_less int) skv_4) ) 15.99/16.14 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int (fun int bool) (ord_less int) skv_10) ) 15.99/16.14 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_10)) ) 15.99/16.14 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))) ) 15.99/16.14 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))) ) 15.99/16.14 ( t, (hAPP int (fun int bool) (ord_less_eq int) (one_one int)) ) 15.99/16.14 ( t, (hAPP int (fun int bool) (ord_less int) (one_one int)) ) 15.99/16.14 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) t))), twoSqu1091635170sum2sq ) 15.99/16.14 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 15.99/16.14 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), nat_is_nat ) 15.99/16.14 ( (hAPP int int (number_number_of int) pls), nat_neg ) 15.99/16.14 ( (hAPP int int (number_number_of int) pls), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 15.99/16.14 ( skv_4, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 15.99/16.14 ( skv_10, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 15.99/16.14 ) 15.99/16.14 (instantiation (forall ((I_1 $$unsorted)) (= (hAPP int nat nat_1 (hAPP quickcheck_code_int int quickcheck_int_of I_1)) (hAPP quickcheck_code_int nat quickcheck_nat_of I_1)) ) 15.99/16.14 ( (zero_zero quickcheck_code_int) ) 15.99/16.14 ) 15.99/16.14 (instantiation (forall ((A_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (ord_less int))) (or (not (hBOOL (hAPP int bool zprime P_5))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 (zero_zero int)) A_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 A_1) P_5))) (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP int int (hAPP int _let_1 (times_times int) A_1) (hAPP int int (hAPP int _let_1 inv P_5) A_1))) (one_one int)) P_5)))))) ) 15.99/16.14 ( (one_one int), t ) 15.99/16.14 ( pls, (one_one int) ) 15.99/16.14 ( pls, pls ) 15.99/16.14 ( pls, min_1 ) 15.99/16.14 ( pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.14 ( min_1, pls ) 15.99/16.14 ( min_1, min_1 ) 15.99/16.14 ( s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.14 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.14 ( skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.14 ( skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.14 ) 15.99/16.14 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_138597 $$unsorted) (BOUND_VARIABLE_138598 $$unsorted) (BOUND_VARIABLE_138599 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (or (not (ordere216010020id_add X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_138599))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_138597) BOUND_VARIABLE_138598))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_138597) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_138599) BOUND_VARIABLE_138598)))))) ) 15.99/16.14 ( nat, (zero_zero nat), (one_one nat), (one_one nat) ) 15.99/16.14 ( int, pls, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.99/16.14 ( int, s, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.99/16.14 ( int, t, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.99/16.14 ( int, skv_4, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.99/16.14 ( int, skv_10, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 15.99/16.14 ) 15.99/16.14 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_138621 $$unsorted) (BOUND_VARIABLE_138622 $$unsorted)) (let ((_let_0 (abs_abs X_a))) (let ((_let_1 (fun X_a X_a))) (or (not (ordere142940540dd_abs X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (hAPP X_a X_a _let_0 (hAPP X_a X_a (hAPP X_a _let_1 (minus_minus X_a) BOUND_VARIABLE_138621) BOUND_VARIABLE_138622))) (hAPP X_a X_a (hAPP X_a _let_1 (plus_plus X_a) (hAPP X_a X_a _let_0 BOUND_VARIABLE_138621)) (hAPP X_a X_a _let_0 BOUND_VARIABLE_138622))))))) ) 15.99/16.14 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 15.99/16.14 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 15.99/16.14 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 15.99/16.14 ) 15.99/16.14 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_138678 $$unsorted) (BOUND_VARIABLE_138679 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_138679) _let_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_138678))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_138679) BOUND_VARIABLE_138678)) _let_2)))))) ) 15.99/16.14 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 15.99/16.14 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.99/16.14 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.99/16.14 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.99/16.14 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.14 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 15.99/16.14 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), pi ) 15.99/16.14 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (one_one real) ) 15.99/16.14 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))), pi ) 15.99/16.14 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 15.99/16.14 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))), (one_one real) ) 15.99/16.14 ) 15.99/16.14 (instantiation (forall ((Y_1 $$unsorted)) (let ((_let_0 (zero_zero real))) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) Y_1) _let_0))) (= _let_0 (hAPP real real cos (hAPP complex real arg (hAPP real complex (hAPP real (fun real complex) complex_1 _let_0) Y_1)))))) ) 15.99/16.14 ( (one_one real) ) 15.99/16.14 ( (zero_zero real) ) 15.99/16.14 ( pi ) 15.99/16.14 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.14 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.99/16.14 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.14 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 15.99/16.14 ) 15.99/16.14 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_138723 $$unsorted) (BOUND_VARIABLE_138724 $$unsorted) (BOUND_VARIABLE_138725 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_138724))) (or (not (ord X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_138725))) (not (= (ti X_a BOUND_VARIABLE_138725) (ti X_a BOUND_VARIABLE_138723))) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_138723)))) ) 15.99/16.14 ( int, pls, min_1, pls ) 15.99/16.14 ( int, min_1, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 15.99/16.14 ( int, s, (zero_zero int), s ) 15.99/16.14 ( int, m, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 15.99/16.14 ( int, s1, (zero_zero int), (one_one int) ) 15.99/16.14 ( int, t, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.14 ( real, pi, (zero_zero real), pi ) 15.99/16.14 ) 15.99/16.14 (instantiation (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_0 (real_1 int))) (= (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real _let_0 X_1)) (hAPP int real _let_0 Y_1)) (hAPP int real _let_0 (hAPP int int (hAPP int (fun int int) (times_times int) X_1) Y_1)))) ) 15.99/16.14 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 15.99/16.14 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.99/16.14 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13 ) 15.99/16.14 ) 15.99/16.14 (instantiation (forall ((D $$unsorted) (I_1 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (abs_abs int))) (or (= (zero_zero int) (ti int I_1)) (not (hBOOL (hAPP int bool (hAPP int _let_0 (dvd_dvd int) D) I_1))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (hAPP int int _let_1 D)) (hAPP int int _let_1 I_1)))))) ) 15.99/16.14 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 15.99/16.14 ) 15.99/16.14 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (one_one real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat real))) (let ((_let_3 (fun nat _let_1))) (let ((_let_4 (fun _let_2 _let_2))) (let ((_let_5 (fun (fun nat nat) _let_2))) (let ((_let_6 (combb nat real nat))) (let ((_let_7 (combc nat nat nat))) (let ((_let_8 (hAPP nat (fun nat nat) (hAPP (fun nat (fun nat nat)) (fun nat (fun nat nat)) _let_7 (hAPP (fun nat nat) (fun nat (fun nat nat)) (hAPP (fun nat (fun nat nat)) (fun (fun nat nat) (fun nat (fun nat nat))) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP (fun nat (fun nat nat)) (fun nat (fun nat nat)) _let_7 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (abs_abs real) X_2)) _let_0))) (hBOOL (hAPP _let_2 bool (monoseq real) (hAPP _let_2 _let_2 (hAPP _let_3 _let_4 (combs nat real real) (hAPP _let_2 _let_3 (hAPP (fun real _let_1) (fun _let_2 _let_3) (combb real _let_1 nat) (times_times real)) (hAPP _let_2 _let_2 (hAPP _let_1 _let_4 (combb real real nat) (hAPP real _let_1 (inverse_divide real) _let_0)) (hAPP (fun nat nat) _let_2 (hAPP _let_2 _let_5 _let_6 (real_1 nat)) _let_8)))) (hAPP (fun nat nat) _let_2 (hAPP _let_2 _let_5 _let_6 (hAPP real _let_2 (power_power real) X_2)) _let_8)))))))))))))) ) 15.99/16.14 ( (hAPP int real (number_number_of real) min_1) ) 15.99/16.14 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.14 ) 15.99/16.14 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_138825 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (linordered_idom X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) _let_0) (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_138825) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (not (= _let_0 (ti X_a BOUND_VARIABLE_138825)))))) ) 15.99/16.14 ( bool, fFalse ) 15.99/16.14 ( bool, fTrue ) 15.99/16.14 ( int, pls ) 15.99/16.14 ( int, min_1 ) 15.99/16.14 ( int, s ) 15.99/16.14 ( int, m ) 15.99/16.14 ( int, s1 ) 15.99/16.14 ( int, t ) 15.99/16.14 ( int, skv_14 ) 15.99/16.14 ( (fun int bool), nat_neg ) 15.99/16.14 ( (fun int bool), zprime ) 15.99/16.14 ( (fun int bool), zEven ) 15.99/16.14 ( (fun int bool), zOdd ) 15.99/16.14 ( (fun int bool), (even_odd_even int) ) 15.99/16.14 ( (fun int bool), twoSqu1091635170sum2sq ) 15.99/16.14 ( (fun int bool), nat_is_nat ) 15.99/16.14 ( (fun int (fun int bool)), norRRset ) 15.99/16.14 ( (fun int (fun int bool)), quadRes ) 15.99/16.14 ( (fun int (fun int bool)), sRStar ) 15.99/16.14 ( (fun int (fun int bool)), d22set ) 15.99/16.14 ( (fun int (fun int bool)), sr ) 15.99/16.14 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 15.99/16.14 ( (fun int int), zfact ) 15.99/16.14 ( (fun int int), bit0 ) 15.99/16.14 ( (fun int int), bit1 ) 15.99/16.14 ( (fun int int), (fact_fact int) ) 15.99/16.14 ( (fun int int), pred ) 15.99/16.14 ( (fun int int), succ ) 15.99/16.14 ( (fun nat bool), (even_odd_even nat) ) 15.99/16.14 ( (fun nat bool), prime ) 15.99/16.14 ( (fun nat nat), suc ) 15.99/16.14 ( (fun nat nat), (fact_fact nat) ) 15.99/16.14 ( (fun nat nat), fact ) 15.99/16.14 ( (fun nat nat), nat_size ) 15.99/16.14 ( (fun nat nat), (size_size nat) ) 15.99/16.14 ( (fun (product_prod nat nat) bool), pred_nat ) 15.99/16.14 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 15.99/16.14 ( real, pi ) 15.99/16.14 ( real, (hAPP int real (number_number_of real) min_1) ) 15.99/16.14 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.14 ( (fun real real), ln ) 15.99/16.14 ( (fun real real), cos ) 15.99/16.14 ( (fun real real), sqrt ) 15.99/16.14 ( (fun real real), sin ) 15.99/16.14 ( (fun real real), arccos ) 15.99/16.14 ( (fun real real), arcsin ) 15.99/16.14 ( (fun real real), tan ) 15.99/16.14 ( (fun real real), arctan ) 15.99/16.14 ( (fun nat (fun nat bool)), coprime ) 15.99/16.14 ( complex, ii ) 15.99/16.14 ( (fun nat real), (real_1 nat) ) 15.99/16.14 ( (fun nat real), sin_coeff ) 15.99/16.14 ( (fun nat real), cos_coeff ) 15.99/16.14 ( (filter nat), sequentially ) 15.99/16.14 ( (fun int (fun int int)), (gcd_gcd int) ) 15.99/16.14 ( (fun int (fun int int)), legendre ) 15.99/16.14 ( (fun int (fun int int)), legacy_zgcd ) 15.99/16.14 ( (fun int (fun int int)), standardRes ) 15.99/16.14 ( (fun int (fun int int)), nat_tsub ) 15.99/16.14 ( (fun int (fun int int)), multInv ) 15.99/16.14 ( (fun int (fun int int)), z3mod ) 15.99/16.14 ( (fun int (fun int int)), z3div ) 15.99/16.14 ( (fun int (fun int int)), int_gcd ) 15.99/16.14 ( (fun int (fun int int)), int_lcm ) 15.99/16.14 ( (fun int (fun int int)), inv ) 15.99/16.14 ( (fun complex complex), expi ) 15.99/16.14 ( (fun complex complex), cnj ) 15.99/16.14 ( (fun real complex), cis ) 15.99/16.14 ( (fun int nat), nat_1 ) 15.99/16.14 ( (fun int nat), phi ) 15.99/16.14 ( (fun (fun int bool) bool), nat_nat_set ) 15.99/16.14 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 15.99/16.14 ( (fun nat (fun nat nat)), nat_gcd ) 15.99/16.14 ( (fun nat (fun nat nat)), nat_lcm ) 15.99/16.14 ( (fun (fun int bool) int), (the int) ) 15.99/16.14 ( (fun complex real), re ) 15.99/16.14 ( (fun complex real), im ) 15.99/16.14 ( (fun complex real), arg ) 15.99/16.14 ( (fun bool bool), fNot ) 15.99/16.14 ( (fun nat (fun real real)), root ) 15.99/16.14 ( (fun real (fun real real)), log ) 15.99/16.14 ( (fun real (fun real real)), powr ) 15.99/16.14 ( (fun bool (fun bool bool)), fimplies ) 15.99/16.14 ( (fun bool (fun bool bool)), fconj ) 15.99/16.14 ( (fun bool (fun bool bool)), fdisj ) 15.99/16.14 ( (fun int (fun int (product_prod int int))), negDivAlg ) 15.99/16.14 ( (fun int (fun int (product_prod int int))), posDivAlg ) 15.99/16.14 ( (fun int (fun int (product_prod int int))), divmod_int ) 15.99/16.14 ( (fun int (fun int (product_prod int int))), pdivmod ) 15.99/16.14 ( (fun int (fun int (product_prod int int))), norm_frac ) 15.99/16.14 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 15.99/16.14 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 15.99/16.14 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 15.99/16.14 ( (fun int (fun int (fun int bool))), zcong ) 15.99/16.14 ( (fun int (fun int (fun int bool))), zcongm ) 15.99/16.14 ( (fun int (fun int (fun int bool))), noXRRset ) 15.99/16.14 ( (fun int (fun int (fun int bool))), bnorRset ) 15.99/16.14 ( (fun int (fun int (fun int bool))), wset ) 15.99/16.14 ( (fun (product_prod int int) bool), frac_1 ) 15.99/16.14 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 15.99/16.14 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 15.99/16.14 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 15.99/16.14 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 15.99/16.14 ( (fun (fun nat rat) bool), vanishes ) 15.99/16.14 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 15.99/16.14 ( (fun code_code_numeral nat), code_c271388182l_size ) 15.99/16.14 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 15.99/16.14 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 15.99/16.14 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 15.99/16.14 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 15.99/16.14 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 15.99/16.14 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 15.99/16.14 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 15.99/16.14 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 15.99/16.14 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 15.99/16.14 ( (fun complex nat), complex_size ) 15.99/16.14 ( (fun complex nat), (size_size complex) ) 15.99/16.14 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 15.99/16.14 ( (fun nat (fun nat (product_prod int int))), bezw ) 15.99/16.14 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 15.99/16.14 ( (fun int (fun nat nat)), nat_aux ) 15.99/16.14 ( (fun int (fun (fun int bool) bool)), rsetR ) 15.99/16.14 ( (fun int (fun (fun int bool) bool)), resSet ) 15.99/16.14 ( (fun int (list int)), quickc666637781d_zero ) 15.99/16.14 ( (fun (product_prod int int) rat), frct ) 15.99/16.14 ( (fun int (fun int rat)), fract ) 15.99/16.14 ( (fun real (fun real complex)), complex_1 ) 15.99/16.14 ( (fun real (fun real complex)), rcis ) 15.99/16.14 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 15.99/16.14 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 15.99/16.14 ( (fun int real), (real_1 int) ) 15.99/16.14 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 15.99/16.14 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 15.99/16.14 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 15.99/16.14 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 15.99/16.14 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 15.99/16.14 ( (fun real nat), natfloor ) 15.99/16.14 ( (fun real nat), natceiling ) 15.99/16.14 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 15.99/16.14 ( (fun quickcheck_code_int int), quickcheck_int_of ) 15.99/16.14 ( (fun rat (product_prod int int)), quotient_of ) 15.99/16.14 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 15.99/16.14 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 15.99/16.14 ( (fun rat real), ratreal ) 15.99/16.14 ( (fun code_code_numeral int), code_int_of ) 15.99/16.14 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 15.99/16.14 ( (fun int quickcheck_code_int), quickcheck_of_int ) 15.99/16.14 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 15.99/16.14 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 15.99/16.14 ) 15.99/16.14 (instantiation (forall ((X_1 $$unsorted)) (= (hAPP int nat nat_1 (hAPP real int (archim2085082626_floor real) X_1)) (hAPP real nat natfloor X_1)) ) 15.99/16.14 ( (one_one real) ) 15.99/16.14 ( (zero_zero real) ) 15.99/16.14 ) 15.99/16.14 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_138913 $$unsorted) (BOUND_VARIABLE_138914 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (plus_plus X_a))) (let ((_let_2 (one_one X_a))) (let ((_let_3 (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_138913))) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_138914))) (hBOOL (hAPP X_a bool _let_3 (hAPP X_a X_a (hAPP X_a _let_0 (inverse_divide X_a) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_138913) BOUND_VARIABLE_138914)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 _let_2) _let_2))))))))) ) 15.99/16.14 ( nat, (one_one nat), (one_one nat) ) 15.99/16.14 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 15.99/16.14 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 15.99/16.14 ) 15.99/16.14 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_138967 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hAPP int int (uminus_uminus int) (hAPP X_a int (archim2085082626_floor X_a) BOUND_VARIABLE_138967)) (hAPP X_a int (archimedean_ceiling X_a) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_138967)))) ) 15.99/16.14 ( int, (one_one int) ) 15.99/16.14 ( int, pls ) 15.99/16.14 ( int, min_1 ) 15.99/16.14 ( real, (one_one real) ) 15.99/16.14 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.14 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.99/16.14 ( complex, (one_one complex) ) 15.99/16.14 ( complex, ii ) 15.99/16.14 ) 15.99/16.14 (instantiation (forall ((X_2 $$unsorted) (N $$unsorted)) (let ((_let_0 (one_one real))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N))) (= (= _let_0 X_2) (= _let_0 (hAPP real real (hAPP nat (fun real real) root N) X_2))))) ) 15.99/16.14 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.14 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.14 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.14 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.14 ) 15.99/16.14 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int int succ (hAPP int int bit1 K_4)) (hAPP int int bit0 (hAPP int int succ K_4))) ) 15.99/16.14 ( pls ) 15.99/16.14 ( (hAPP int int bit1 pls) ) 15.99/16.14 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 15.99/16.14 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 15.99/16.14 ( min_1 ) 15.99/16.14 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 15.99/16.14 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 15.99/16.14 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 15.99/16.14 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 15.99/16.14 ) 15.99/16.14 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_139100 $$unsorted) (BOUND_VARIABLE_139101 $$unsorted)) (let ((_let_0 (fun nat X_a))) (let ((_let_1 (power_power X_a))) (let ((_let_2 (uminus_uminus X_a))) (or (not (ring_1 X_a)) (= (hAPP nat X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_139100)) BOUND_VARIABLE_139101) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) (hAPP nat X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 (one_one X_a))) BOUND_VARIABLE_139101)) (hAPP nat X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_139100) BOUND_VARIABLE_139101))))))) ) 15.99/16.14 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.14 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.14 ( int, skv_14, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.14 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.14 ) 15.99/16.14 (instantiation (forall ((R_4 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) R_4))) (not (forall ((N_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (real_1 nat))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) (hAPP nat real _let_1 (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) N_2) (one_one nat)))) R_4))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) R_4) (hAPP nat real _let_1 N_2))))))) ))) ) 15.99/16.14 ( pi ) 15.99/16.14 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.14 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.14 ( skv_3 ) 15.99/16.14 ( skv_5 ) 15.99/16.14 ( skv_7 ) 15.99/16.14 ( skv_12 ) 15.99/16.14 ) 15.99/16.14 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_139150 $$unsorted)) (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat X_a))) (let ((_let_2 (power_power X_a))) (or (not (ring_1 X_a)) (= (hAPP nat X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_139150)) _let_0) (hAPP nat X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_139150) _let_0)))))) ) 15.99/16.14 ( int, (one_one int) ) 15.99/16.14 ( int, pls ) 15.99/16.14 ( int, min_1 ) 15.99/16.14 ( int, s ) 15.99/16.14 ( int, s1 ) 15.99/16.14 ( int, skv_14 ) 15.99/16.14 ( real, (one_one real) ) 15.99/16.14 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.14 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 15.99/16.14 ( complex, (one_one complex) ) 15.99/16.14 ( complex, ii ) 15.99/16.14 ) 15.99/16.14 (instantiation (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) X_1))) (= (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP real nat natfloor X_1)) (one_one nat)) (hAPP real nat natfloor (hAPP real real (hAPP real (fun real real) (plus_plus real) X_1) (one_one real))))) ) 15.99/16.14 ( (one_one real) ) 15.99/16.14 ( pi ) 15.99/16.14 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.14 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.14 ( skv_3 ) 15.99/16.14 ( skv_5 ) 15.99/16.14 ( skv_7 ) 15.99/16.14 ( skv_12 ) 15.99/16.14 ) 15.99/16.14 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (semiring_1_of_nat X_a))) (or (not (semiring_1 X_a)) (= _let_0 (ti (fun nat X_a) _let_0)))) ) 15.99/16.14 ( bool ) 15.99/16.14 ( nat ) 15.99/16.14 ( int ) 15.99/16.14 ( (fun int int) ) 15.99/16.14 ( (fun nat bool) ) 15.99/16.14 ( (fun nat nat) ) 15.99/16.14 ( (product_prod nat nat) ) 15.99/16.14 ( (fun (product_prod nat nat) bool) ) 15.99/16.14 ( (fun nat (fun (product_prod nat nat) bool)) ) 15.99/16.14 ( real ) 15.99/16.14 ( (fun real real) ) 15.99/16.14 ( rat ) 15.99/16.14 ( (fun nat (fun nat bool)) ) 15.99/16.14 ( complex ) 15.99/16.14 ( (product_prod int int) ) 15.99/16.14 ( quickcheck_code_int ) 15.99/16.14 ( (fun bool bool) ) 15.99/16.14 ( code_code_numeral ) 15.99/16.14 ( (product_prod real real) ) 15.99/16.14 ( (fun nat (product_prod nat nat)) ) 15.99/16.14 ( (fun nat (product_prod int int)) ) 15.99/16.14 ) 15.99/16.14 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (zero_zero real))) (= (= _let_0 X_2) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) _let_0) (hAPP real real (hAPP real (fun real real) (times_times real) X_2) X_2)))))) ) 15.99/16.14 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.14 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.14 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 15.99/16.14 ) 15.99/16.14 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_139217 $$unsorted) (BOUND_VARIABLE_139218 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)))) (or (not (linord20386208strict X_a)) (not (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_139217) BOUND_VARIABLE_139218)))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_139217))) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_139218)))) ) 15.99/16.14 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 15.99/16.14 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.99/16.14 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13 ) 15.99/16.14 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.99/16.14 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 15.99/16.14 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 15.99/16.14 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 15.99/16.14 ( complex, ii, ii ) 15.99/16.14 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 15.99/16.14 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 15.99/16.14 ) 15.99/16.14 (instantiation (forall ((Z_1 $$unsorted) (W $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Z_1) W))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 W) Z_1))) (= Z_1 W)))) ) 15.99/16.14 ( (zero_zero real), pi ) 15.99/16.14 ( (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.14 ( (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.14 ( (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.14 ( (zero_zero real), skv_3 ) 15.99/16.14 ( (zero_zero real), skv_5 ) 15.99/16.14 ( (zero_zero real), skv_7 ) 15.99/16.14 ( (zero_zero real), skv_12 ) 15.99/16.14 ( pi, (zero_zero real) ) 15.99/16.14 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.14 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 15.99/16.14 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 15.99/16.14 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_5 ) 15.99/16.14 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.99/16.14 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.14 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.99/16.14 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 15.99/16.14 ( skv_3, (zero_zero real) ) 15.99/16.14 ( skv_5, (zero_zero real) ) 15.99/16.14 ( skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 15.99/16.14 ( skv_7, (zero_zero real) ) 15.99/16.14 ( skv_12, (zero_zero real) ) 15.99/16.14 ) 15.99/16.14 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_0 (product_prod int int))) (or (not (= (hAPP rat _let_0 quotient_of A_1) (hAPP rat _let_0 quotient_of B))) (= A_1 B))) ) 15.99/16.14 ( (zero_zero rat), (zero_zero rat) ) 15.99/16.14 ( (zero_zero rat), (one_one rat) ) 15.99/16.14 ( (one_one rat), (zero_zero rat) ) 15.99/16.14 ) 15.99/16.14 (instantiation (forall ((A_1 $$unsorted)) (or (= (zero_zero int) (ti int A_1)) (= (one_one int) (hAPP int int (hAPP int (fun int int) (div_div int) A_1) A_1))) ) 15.99/16.14 ( min_1 ) 15.99/16.14 ( s ) 15.99/16.14 ( m ) 15.99/16.14 ( s1 ) 15.99/16.14 ( t ) 15.99/16.14 ) 15.99/16.14 (instantiation (forall ((X_c $$unsorted) (X_a $$unsorted) (X_b $$unsorted) (R_3 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted)) (let ((_let_0 (fun X_c bool))) (let ((_let_1 (fun X_b _let_0))) (let ((_let_2 (product_prod X_a X_b))) (or (not (hBOOL (hAPP X_c bool (hAPP _let_2 _let_0 (hAPP (fun X_a _let_1) (fun _let_2 _let_0) (product_prod_case X_a X_b _let_0) R_3) (hAPP X_b _let_2 (hAPP X_a (fun X_b _let_2) (product_Pair X_a X_b) A_2) B_1)) C_1))) (hBOOL (hAPP X_c bool (hAPP X_b _let_0 (hAPP X_a _let_1 R_3 A_2) B_1) C_1)))))) ) 15.99/16.14 ( int, int, int, zcong, s1, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.14 ( int, int, int, zcong, s1, skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.14 ( int, int, int, zcong, s1, skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.14 ( int, int, int, zcong, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.14 ( int, int, int, zcong, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.14 ( int, int, int, zcong, (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.14 ( int, int, int, zcong, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 15.99/16.14 ( (filter nat), (fun nat real), real, (tendsto nat real), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real), sequentially ) 15.99/16.14 ( (filter real), (fun real real), real, (tendsto real real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (hAPP real (filter real) (at real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 15.99/16.14 ) 15.99/16.14 (instantiation (forall ((Real1_1 $$unsorted) (Real2_1 $$unsorted)) (= (zero_zero nat) (hAPP complex nat complex_size (hAPP real complex (hAPP real (fun real complex) complex_1 Real1_1) Real2_1))) ) 15.99/16.14 ( (one_one real), (zero_zero real) ) 15.99/16.14 ( (zero_zero real), (one_one real) ) 15.99/16.14 ( (zero_zero real), (zero_zero real) ) 15.99/16.14 ) 15.99/16.14 (instantiation (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (zero_zero int)) B_1))) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 B_1) A_2)) (hBOOL (hAPP rat bool (hAPP rat (fun rat bool) (ord_less rat) (one_one rat)) (hAPP int rat (hAPP int (fun int rat) fract A_2) B_1))))))) ) 15.99/16.14 ( (one_one int), (one_one int) ) 15.99/16.14 ( (one_one int), pls ) 15.99/16.14 ( (zero_zero int), (one_one int) ) 15.99/16.14 ( pls, pls ) 15.99/16.14 ( pls, min_1 ) 15.99/16.14 ( min_1, pls ) 15.99/16.14 ( min_1, min_1 ) 15.99/16.14 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), pls ) 15.99/16.14 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s ) 15.99/16.14 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 15.99/16.14 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_4 ) 15.99/16.14 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_10 ) 15.99/16.14 ( t, (one_one int) ) 15.99/16.14 ) 15.99/16.14 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_139464 $$unsorted) (BOUND_VARIABLE_139465 $$unsorted) (BOUND_VARIABLE_139466 $$unsorted)) (let ((_let_0 (filter X_a))) (let ((_let_1 (fun _let_0 bool))) (or (not (real_normed_vector X_a)) (not (real_normed_vector X_b)) (not (forall ((R_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) R_2))) (not (forall ((S_1 $$unsorted)) (or (not (forall ((X $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP X_a real (norm_norm X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) X) BOUND_VARIABLE_139466))) S_1))) (= (ti X_a X) (ti X_a BOUND_VARIABLE_139466)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP X_b real (norm_norm X_b) (hAPP X_b X_b (hAPP X_b (fun X_b X_b) (minus_minus X_b) (hAPP X_a X_b BOUND_VARIABLE_139464 X)) BOUND_VARIABLE_139465))) R_2))))) )) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) S_1)))) ))) )) (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (hAPP (fun X_a X_b) (fun X_b _let_1) (tendsto X_a X_b) BOUND_VARIABLE_139464) BOUND_VARIABLE_139465) (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_139466)))))) ) 16.09/16.18 ( real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.09/16.18 ) 16.09/16.18 (instantiation (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) A_1) (zero_zero int)))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) B) A_1))) (= (ti int A_1) (hAPP int int (hAPP int (fun int int) (div_mod int) A_1) B)))) ) 16.09/16.18 ( (one_one int), t ) 16.09/16.18 ( pls, (one_one int) ) 16.09/16.18 ( pls, pls ) 16.09/16.18 ( pls, min_1 ) 16.09/16.18 ( pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.09/16.18 ( min_1, pls ) 16.09/16.18 ( min_1, min_1 ) 16.09/16.18 ( s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.09/16.18 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.09/16.18 ( skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.09/16.18 ( skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.09/16.18 ) 16.09/16.18 (instantiation (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_0 (even_odd_even int))) (or (not (hBOOL (hAPP int bool _let_0 X_1))) (hBOOL (hAPP int bool _let_0 Y_1)) (not (hBOOL (hAPP int bool _let_0 (hAPP int int (hAPP int (fun int int) (plus_plus int) X_1) Y_1)))))) ) 16.09/16.18 ( (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 16.09/16.18 ( (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.09/16.18 ) 16.09/16.18 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (ring_1 X_a)) (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) (zero_zero X_a)) (ring_1_Ints X_a))))) ) 16.09/16.18 ( nat ) 16.09/16.18 ( int ) 16.09/16.18 ( real ) 16.09/16.18 ( rat ) 16.09/16.18 ( complex ) 16.09/16.18 ( quickcheck_code_int ) 16.09/16.18 ( code_code_numeral ) 16.09/16.18 ) 16.09/16.18 (instantiation (forall ((Y_1 $$unsorted) (X_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (or (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int _let_1 zcong X_1) (zero_zero int)) P_5)) (not (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int _let_1 zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) Y_1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) X_1) P_5))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (dvd_dvd int) P_5) Y_1)))))) ) 16.09/16.18 ( s, (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.09/16.18 ( s, (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.09/16.18 ( s1, (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.09/16.18 ( skv_14, (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.09/16.18 ) 16.09/16.18 (instantiation (forall ((X_a $$unsorted)) (or (not (real_normed_vector X_a)) (not (forall ((K_2 $$unsorted)) (not (forall ((A_4 $$unsorted) (B_4 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (times_times real))) (let ((_let_2 (norm_norm X_a))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP X_a real _let_2 (hAPP X_a X_a (hAPP real (fun X_a X_a) (scaleR_scaleR X_a) A_4) B_4))) (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real (norm_norm real) A_4)) (hAPP X_a real _let_2 B_4))) K_2)))))) )) ))) ) 16.09/16.18 ( real ) 16.09/16.18 ( complex ) 16.09/16.18 ) 16.09/16.18 (instantiation (forall ((N_1 $$unsorted)) (let ((_let_0 (one_one real))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_1))) (= _let_0 (hAPP real real (hAPP nat (fun real real) root N_1) _let_0)))) ) 16.09/16.18 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.09/16.18 ) 16.09/16.18 (instantiation (forall ((X_1 $$unsorted)) (= (hAPP real real (hAPP real (fun real real) (inverse_divide real) X_1) (hAPP real real (abs_abs real) X_1)) (hAPP real real (sgn_sgn real) X_1)) ) 16.09/16.18 ( (one_one real) ) 16.09/16.18 ( (zero_zero real) ) 16.09/16.18 ( pi ) 16.09/16.18 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.09/16.18 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.09/16.18 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.09/16.18 ) 16.09/16.18 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (number_of_frac X_a))) (= _let_0 (ti (fun int X_a) _let_0))) ) 16.09/16.18 ( bool ) 16.09/16.18 ( nat ) 16.09/16.18 ( int ) 16.09/16.18 ( (fun int bool) ) 16.09/16.18 ( (fun int (fun int bool)) ) 16.09/16.18 ( (fun int int) ) 16.09/16.18 ( (fun nat bool) ) 16.09/16.18 ( (fun nat nat) ) 16.09/16.18 ( real ) 16.09/16.18 ( (fun real real) ) 16.09/16.18 ( rat ) 16.09/16.18 ( (fun int rat) ) 16.09/16.18 ( (fun nat int) ) 16.09/16.18 ( (fun nat real) ) 16.09/16.18 ( (product_prod int int) ) 16.09/16.18 ( (fun int (product_prod int int)) ) 16.09/16.18 ( (fun (fun int bool) bool) ) 16.09/16.18 ( quickcheck_code_int ) 16.09/16.18 ( (fun bool bool) ) 16.09/16.18 ( (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 16.09/16.18 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)) ) 16.09/16.18 ( (fun int (fun int (fun int bool))) ) 16.09/16.18 ( (fun (product_prod int int) bool) ) 16.09/16.18 ( (fun int (fun (product_prod int int) bool)) ) 16.09/16.18 ( (fun int (fun bool bool)) ) 16.09/16.18 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 16.09/16.18 ( (fun (fun int int) (fun int bool)) ) 16.09/16.18 ( (fun (product_prod int int) int) ) 16.09/16.18 ( (product_prod int (product_prod int int)) ) 16.09/16.18 ( (fun int (product_prod int (product_prod int int))) ) 16.09/16.18 ( (fun int (fun int (product_prod int (product_prod int int)))) ) 16.09/16.18 ( (fun int (fun int (fun int (product_prod int (product_prod int int))))) ) 16.09/16.18 ( (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))) ) 16.09/16.18 ( (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))) ) 16.09/16.18 ( (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))) ) 16.09/16.18 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))))) ) 16.09/16.18 ( (fun int (fun (fun int bool) bool)) ) 16.09/16.18 ( (list int) ) 16.09/16.18 ( (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 16.09/16.18 ( (fun int real) ) 16.09/16.18 ( (fun nat (fun bool bool)) ) 16.09/16.18 ( (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 16.09/16.18 ( (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 16.09/16.18 ) 16.09/16.18 (instantiation (forall ((Sa $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (zero_zero real))) (let ((_let_2 (fun nat real))) (let ((_let_3 (fun nat _let_0))) (let ((_let_4 (fun (filter nat) bool))) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) _let_1) Sa))) (hBOOL (hAPP (filter nat) bool (hAPP real _let_4 (hAPP _let_2 (fun real _let_4) (tendsto nat real) (hAPP real _let_2 (hAPP _let_3 (fun real _let_2) (combc nat real real) (hAPP _let_2 _let_3 (hAPP (fun real _let_0) (fun _let_2 _let_3) (combb real _let_0 nat) powr) (real_1 nat))) (hAPP real real (uminus_uminus real) Sa))) _let_1) sequentially)))))))) ) 16.09/16.18 ( (one_one real) ) 16.09/16.18 ( pi ) 16.09/16.18 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.09/16.18 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.09/16.18 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.09/16.18 ( skv_2 ) 16.09/16.18 ( skv_8 ) 16.09/16.18 ( skv_9 ) 16.09/16.18 ) 16.09/16.18 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (zero_zero real))) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) _let_0) X_2))) (= (= (one_one real) X_2) (= _let_0 (hAPP real real ln X_2))))) ) 16.09/16.18 ( (one_one real) ) 16.09/16.18 ( pi ) 16.09/16.18 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.09/16.18 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.09/16.18 ( skv_2 ) 16.09/16.18 ( skv_8 ) 16.09/16.18 ( skv_9 ) 16.09/16.18 ) 16.09/16.18 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_139988 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)))) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_139988))) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_139988))))) ) 16.09/16.18 ( real, (zero_zero real) ) 16.09/16.18 ( complex, ii ) 16.09/16.18 ) 16.09/16.18 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_140014 $$unsorted) (BOUND_VARIABLE_140015 $$unsorted) (BOUND_VARIABLE_140016 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (or (not (ord X_a)) (not (= (ti X_a BOUND_VARIABLE_140016) (ti X_a BOUND_VARIABLE_140015))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_140016) BOUND_VARIABLE_140014))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_140015) BOUND_VARIABLE_140014))))) ) 16.09/16.18 ( int, (one_one int), min_1, pls ) 16.09/16.18 ( int, pls, pls, min_1 ) 16.09/16.18 ( int, pls, s, pls ) 16.09/16.18 ( int, min_1, m, min_1 ) 16.09/16.18 ( int, min_1, t, pls ) 16.09/16.18 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s1, s ) 16.09/16.18 ( real, (zero_zero real), pi, pi ) 16.09/16.18 ) 16.09/16.18 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_140048 $$unsorted)) (or (not (number_ring X_a)) (not (linordered_idom X_a)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) pls) BOUND_VARIABLE_140048)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_140048))))) ) 16.09/16.18 ( nat, pls ) 16.09/16.18 ( nat, (hAPP int int bit1 pls) ) 16.09/16.18 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.11/16.18 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.11/16.18 ( int, pls ) 16.11/16.18 ( int, (hAPP int int bit1 pls) ) 16.11/16.18 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.11/16.18 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.11/16.18 ( int, min_1 ) 16.11/16.18 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.18 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.11/16.18 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.11/16.18 ( real, min_1 ) 16.11/16.18 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.18 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.11/16.18 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.18 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 16.11/16.18 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.11/16.18 ( complex, min_1 ) 16.11/16.18 ( quickcheck_code_int, (one_one int) ) 16.11/16.18 ( quickcheck_code_int, (zero_zero int) ) 16.11/16.18 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 16.11/16.18 ( code_code_numeral, pls ) 16.11/16.18 ( code_code_numeral, (hAPP int int bit1 pls) ) 16.11/16.18 ) 16.11/16.18 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted) (Q_1 $$unsorted) (P_1 $$unsorted) (Z $$unsorted)) (let ((_let_0 (product_prod X_b X_c))) (or (not (hBOOL (hAPP X_a bool Q_1 (hAPP _let_0 X_a (hAPP (fun X_b (fun X_c X_a)) (fun _let_0 X_a) (product_prod_case X_b X_c X_a) P_1) Z)))) (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (hAPP X_c _let_0 (hAPP X_b (fun X_c _let_0) (product_Pair X_b X_c) X) Y) (ti _let_0 Z))) (not (hBOOL (hAPP X_a bool Q_1 (hAPP X_c X_a (hAPP X_b (fun X_c X_a) P_1 X) Y))))) )))) ) 16.11/16.18 ( int, int, int, (let ((_let_0 (fun int int))) (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun _let_0 _let_1))) (let ((_let_3 (fun _let_0 _let_0))) (let ((_let_4 (fun int _let_3))) (let ((_let_5 (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP _let_0 _let_1 (hAPP _let_4 _let_2 (combc int _let_0 _let_0) (hAPP _let_1 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_1 _let_4) (combb _let_0 _let_3 int) (combb int int int)) (hAPP _let_0 _let_1 (hAPP _let_1 _let_2 (combb int _let_0 int) (plus_plus int)) _let_5))) _let_5))))))), (let ((_let_0 (product_prod int int))) (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) s) (one_one int))) ) 16.11/16.18 ( int, int, int, twoSqu1091635170sum2sq, (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun _let_0 _let_1))) (let ((_let_3 (fun _let_0 _let_0))) (let ((_let_4 (fun int _let_3))) (let ((_let_5 (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP _let_0 _let_1 (hAPP _let_4 _let_2 (combc int _let_0 _let_0) (hAPP _let_1 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_1 _let_4) (combb _let_0 _let_3 int) (combb int int int)) (hAPP _let_0 _let_1 (hAPP _let_1 _let_2 (combb int _let_0 int) (plus_plus int)) _let_5))) _let_5))))))), (let ((_let_0 (product_prod int int))) (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) s) (one_one int))) ) 16.11/16.18 ) 16.11/16.18 (instantiation (forall ((L_4 $$unsorted)) (let ((_let_0 (hAPP int (fun int int) (minus_minus int) min_1))) (= (hAPP int int bit1 (hAPP int int _let_0 L_4)) (hAPP int int _let_0 (hAPP int int bit0 L_4)))) ) 16.11/16.18 ( pls ) 16.11/16.18 ( (hAPP int int bit1 pls) ) 16.11/16.18 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.11/16.18 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.11/16.18 ( min_1 ) 16.11/16.18 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.11/16.18 ) 16.11/16.18 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_140114 $$unsorted)) (let ((_let_0 (hAPP int X_b (number_number_of X_b) BOUND_VARIABLE_140114))) (or (not (number X_b)) (not (monoid_mult X_b)) (= (hAPP X_b X_b (hAPP X_b (fun X_b X_b) (times_times X_b) _let_0) _let_0) (hAPP nat X_b (hAPP X_b (fun nat X_b) (power_power X_b) _let_0) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 16.11/16.18 ( nat, pls ) 16.11/16.18 ( nat, (hAPP int int bit1 pls) ) 16.11/16.18 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.11/16.18 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.11/16.18 ( int, pls ) 16.11/16.18 ( int, (hAPP int int bit1 pls) ) 16.11/16.18 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.11/16.18 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.11/16.18 ( int, min_1 ) 16.11/16.18 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.18 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.11/16.18 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.11/16.18 ( real, min_1 ) 16.11/16.18 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.18 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.11/16.18 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.18 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 16.11/16.18 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.11/16.18 ( complex, min_1 ) 16.11/16.18 ( quickcheck_code_int, (one_one int) ) 16.11/16.18 ( quickcheck_code_int, (zero_zero int) ) 16.11/16.18 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 16.11/16.18 ( code_code_numeral, pls ) 16.11/16.18 ( code_code_numeral, (hAPP int int bit1 pls) ) 16.11/16.18 ) 16.11/16.18 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (ord_less X_a))) (or (not (ord X_a)) (= _let_0 (ti (fun X_a (fun X_a bool)) _let_0)))) ) 16.11/16.18 ( bool ) 16.11/16.18 ( nat ) 16.11/16.18 ( int ) 16.11/16.18 ( (fun int bool) ) 16.11/16.18 ( (fun nat bool) ) 16.11/16.18 ( (product_prod nat nat) ) 16.11/16.18 ( real ) 16.11/16.18 ( rat ) 16.11/16.18 ( (filter nat) ) 16.11/16.18 ( (product_prod int int) ) 16.11/16.18 ( quickcheck_code_int ) 16.11/16.18 ( code_code_numeral ) 16.11/16.18 ( (product_prod real real) ) 16.11/16.18 ( (fun nat rat) ) 16.11/16.18 ( (filter real) ) 16.11/16.18 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 16.11/16.18 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 16.11/16.18 ) 16.11/16.18 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_140133 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)))) (or (not (linord219039673up_add X_a)) (= (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_140133) BOUND_VARIABLE_140133))) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_140133))))) ) 16.11/16.18 ( nat, (one_one nat) ) 16.11/16.18 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 16.11/16.18 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.18 ) 16.11/16.18 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (ord_gr676655987ssThan X_a))) (or (not (dense_linorder X_a)) (= _let_0 (ti (fun X_a (fun X_a (fun X_a bool))) _let_0)))) ) 16.11/16.18 ( bool ) 16.11/16.18 ( nat ) 16.11/16.18 ( int ) 16.11/16.18 ( (fun int bool) ) 16.11/16.18 ( (fun nat bool) ) 16.11/16.18 ( (product_prod nat nat) ) 16.11/16.18 ( real ) 16.11/16.18 ( rat ) 16.11/16.18 ( (filter nat) ) 16.11/16.18 ( (product_prod int int) ) 16.11/16.18 ( (product_prod real real) ) 16.11/16.18 ( (fun nat rat) ) 16.11/16.18 ( (filter real) ) 16.11/16.18 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 16.11/16.18 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 16.11/16.18 ) 16.11/16.18 (instantiation (forall ((Z_1 $$unsorted)) (= (hAPP int int (hAPP int (fun int int) (plus_plus int) Z_1) (zero_zero int)) (ti int Z_1)) ) 16.11/16.18 ( pls ) 16.11/16.18 ( min_1 ) 16.11/16.18 ( s ) 16.11/16.18 ( m ) 16.11/16.18 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 16.11/16.18 ( s1 ) 16.11/16.18 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.18 ( t ) 16.11/16.18 ) 16.11/16.18 (instantiation (forall ((N_1 $$unsorted)) (let ((_let_0 (zero_zero int))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) _let_0) N_1))) (not (= _let_0 (hAPP int int (fact_fact int) N_1))))) ) 16.11/16.18 ( (one_one int) ) 16.11/16.18 ( (zero_zero int) ) 16.11/16.18 ( min_1 ) 16.11/16.18 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.18 ( s ) 16.11/16.18 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.11/16.18 ( (hAPP int int (number_number_of int) pls) ) 16.11/16.18 ( skv_4 ) 16.11/16.18 ( skv_10 ) 16.11/16.18 ) 16.11/16.18 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_140347 $$unsorted)) (let ((_let_0 (number_number_of X_a))) (or (not (number_ring X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (hAPP int X_a _let_0 BOUND_VARIABLE_140347)) (one_one X_a)) (hAPP int X_a _let_0 (hAPP int int (hAPP int (fun int int) (plus_plus int) BOUND_VARIABLE_140347) (hAPP int int bit1 pls)))))) ) 16.11/16.18 ( nat, (hAPP int int bit1 pls) ) 16.11/16.18 ) 16.11/16.18 (instantiation (forall ((X_a $$unsorted)) (or (not (real_normed_algebra X_a)) (not (forall ((K_2 $$unsorted)) (not (forall ((A_4 $$unsorted) (B_4 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (times_times real))) (let ((_let_2 (norm_norm X_a))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP X_a real _let_2 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) A_4) B_4))) (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real (hAPP real _let_0 _let_1 (hAPP X_a real _let_2 A_4)) (hAPP X_a real _let_2 B_4))) K_2)))))) )) ))) ) 16.11/16.18 ( real ) 16.11/16.18 ( complex ) 16.11/16.18 ) 16.11/16.18 (instantiation (forall ((X_1 $$unsorted)) (= (hAPP real real (uminus_uminus real) (hAPP rat real ratreal X_1)) (hAPP rat real ratreal (hAPP rat rat (uminus_uminus rat) X_1))) ) 16.11/16.18 ( (one_one rat) ) 16.11/16.18 ) 16.11/16.18 (instantiation (forall ((X_a $$unsorted)) (or (not (real_algebra_1 X_a)) (= (hAPP real X_a (of_real X_a) (one_one real)) (one_one X_a))) ) 16.11/16.18 ( nat ) 16.11/16.18 ( int ) 16.11/16.18 ( real ) 16.11/16.18 ( rat ) 16.11/16.18 ( complex ) 16.11/16.18 ( quickcheck_code_int ) 16.11/16.18 ( code_code_numeral ) 16.11/16.18 ) 16.11/16.18 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) M) N_1))) (not (forall ((K_1 $$unsorted)) (not (= N_1 (hAPP nat nat suc (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) M) K_1)))) ))) ) 16.11/16.18 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.18 ) 16.11/16.18 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (ord T_1)) (ord (fun T_2 T_1))) ) 16.11/16.18 ( bool, bool ) 16.11/16.18 ( bool, (fun bool bool) ) 16.11/16.18 ( nat, bool ) 16.11/16.18 ( nat, nat ) 16.11/16.18 ( nat, int ) 16.11/16.18 ( nat, (fun int int) ) 16.11/16.18 ( nat, (fun nat bool) ) 16.11/16.18 ( nat, (fun nat nat) ) 16.11/16.18 ( nat, (product_prod nat nat) ) 16.11/16.18 ( nat, (fun (product_prod nat nat) bool) ) 16.11/16.18 ( nat, (fun nat (fun (product_prod nat nat) bool)) ) 16.11/16.18 ( nat, real ) 16.11/16.18 ( nat, (fun real real) ) 16.11/16.18 ( nat, rat ) 16.11/16.18 ( nat, (fun nat (fun nat bool)) ) 16.11/16.18 ( nat, complex ) 16.11/16.18 ( nat, (product_prod int int) ) 16.11/16.18 ( nat, (fun bool bool) ) 16.11/16.18 ( nat, (product_prod real real) ) 16.11/16.18 ( nat, (fun nat (product_prod nat nat)) ) 16.11/16.18 ( nat, (fun nat (product_prod int int)) ) 16.11/16.18 ( int, bool ) 16.11/16.18 ( int, nat ) 16.11/16.18 ( int, int ) 16.11/16.18 ( int, (fun int bool) ) 16.11/16.18 ( int, (fun int (fun int bool)) ) 16.11/16.18 ( int, (fun int int) ) 16.11/16.18 ( int, (fun nat bool) ) 16.11/16.18 ( int, (fun nat nat) ) 16.11/16.18 ( int, real ) 16.11/16.18 ( int, (fun real real) ) 16.11/16.18 ( int, rat ) 16.11/16.18 ( int, (fun int rat) ) 16.11/16.18 ( int, (fun nat int) ) 16.11/16.18 ( int, (fun nat real) ) 16.11/16.18 ( int, (product_prod int int) ) 16.11/16.18 ( int, (fun int (product_prod int int)) ) 16.11/16.18 ( int, (fun (fun int bool) bool) ) 16.11/16.18 ( int, quickcheck_code_int ) 16.11/16.18 ( int, (fun bool bool) ) 16.11/16.18 ( int, (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 16.11/16.18 ( int, (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)) ) 16.11/16.18 ( int, (fun int (fun int (fun int bool))) ) 16.11/16.18 ( int, (fun (product_prod int int) bool) ) 16.11/16.18 ( int, (fun int (fun (product_prod int int) bool)) ) 16.11/16.18 ( int, (fun int (fun bool bool)) ) 16.11/16.18 ( int, (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 16.11/16.18 ( int, (fun (fun int int) (fun int bool)) ) 16.11/16.18 ( int, (fun (product_prod int int) int) ) 16.11/16.18 ( int, (product_prod int (product_prod int int)) ) 16.11/16.18 ( int, (fun int (product_prod int (product_prod int int))) ) 16.11/16.18 ( int, (fun int (fun int (product_prod int (product_prod int int)))) ) 16.11/16.18 ( int, (fun int (fun int (fun int (product_prod int (product_prod int int))))) ) 16.11/16.18 ( int, (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))) ) 16.11/16.18 ( int, (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))) ) 16.11/16.18 ( int, (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))) ) 16.11/16.18 ( int, (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))))) ) 16.11/16.18 ( int, (fun int (fun (fun int bool) bool)) ) 16.11/16.18 ( int, (list int) ) 16.11/16.18 ( int, (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 16.11/16.18 ( int, (fun int real) ) 16.11/16.18 ( int, (fun nat (fun bool bool)) ) 16.11/16.18 ( int, (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 16.11/16.18 ( int, (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 16.11/16.18 ( (fun int bool), bool ) 16.11/16.18 ( (fun int bool), int ) 16.11/16.18 ( (fun int bool), (fun int bool) ) 16.11/16.18 ( (fun int bool), (fun int (fun int bool)) ) 16.11/16.18 ( (fun int bool), (fun int (fun int int)) ) 16.11/16.18 ( (fun int bool), (fun int (fun bool bool)) ) 16.11/16.18 ( (fun int bool), (fun (fun int int) (fun int bool)) ) 16.11/16.18 ( (fun int bool), (fun real (fun int (fun int bool))) ) 16.11/16.18 ( (fun int (fun int bool)), (fun int bool) ) 16.11/16.18 ( (fun int (fun int bool)), (fun int (fun int bool)) ) 16.11/16.18 ( (fun int (fun int bool)), (fun int (fun (fun int int) (fun int bool))) ) 16.11/16.18 ( (fun int (fun int bool)), (fun int (fun int (fun bool bool))) ) 16.11/16.18 ( (fun int int), (fun int bool) ) 16.11/16.18 ( (fun int int), (fun int (fun int bool)) ) 16.11/16.18 ( (fun int int), (fun int int) ) 16.11/16.18 ( (fun int int), (fun int (fun int int)) ) 16.11/16.18 ( (fun int int), (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 16.11/16.18 ( (fun int int), (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 16.11/16.18 ( (fun nat bool), bool ) 16.11/16.18 ( (fun nat bool), (fun nat bool) ) 16.11/16.18 ( (fun nat bool), (fun nat (fun bool bool)) ) 16.11/16.18 ( (fun nat bool), (fun int (fun nat bool)) ) 16.11/16.18 ( (fun nat bool), (fun real (fun int (fun nat bool))) ) 16.11/16.18 ( (fun nat nat), (fun nat (fun nat bool)) ) 16.11/16.18 ( (fun nat nat), (fun nat real) ) 16.11/16.18 ( (fun nat nat), (fun nat (fun nat nat)) ) 16.11/16.18 ( (product_prod nat nat), bool ) 16.11/16.18 ( (product_prod nat nat), (fun (product_prod nat nat) bool) ) 16.11/16.18 ( real, bool ) 16.11/16.18 ( real, nat ) 16.11/16.18 ( real, (fun int bool) ) 16.11/16.18 ( real, (fun int (fun int bool)) ) 16.11/16.18 ( real, real ) 16.11/16.18 ( real, (fun real bool) ) 16.11/16.18 ( real, (fun real real) ) 16.11/16.18 ( real, complex ) 16.11/16.18 ( real, (fun nat real) ) 16.11/16.18 ( real, (fun real complex) ) 16.11/16.18 ( real, (fun bool bool) ) 16.11/16.18 ( real, (fun (filter nat) bool) ) 16.11/16.18 ( real, (fun nat (product_prod real real)) ) 16.11/16.18 ( real, (fun real (fun nat (product_prod real real))) ) 16.11/16.18 ( real, (fun (filter real) bool) ) 16.11/16.18 ( real, (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 16.11/16.18 ( real, (let ((_let_0 (fun int bool))) (fun _let_0 (fun int _let_0))) ) 16.11/16.18 ( real, (fun int (fun int (fun bool bool))) ) 16.11/16.18 ( real, (fun (fun int (fun int real)) (fun int (fun int bool))) ) 16.11/16.18 ( real, (fun (fun int real) (fun int bool)) ) 16.11/16.18 ( real, (fun int (fun nat bool)) ) 16.11/16.18 ( real, (let ((_let_0 (fun nat bool))) (fun _let_0 (fun int _let_0))) ) 16.11/16.18 ( real, (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 16.11/16.18 ( real, (fun int (fun nat (fun bool bool))) ) 16.11/16.18 ( real, (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 16.11/16.18 ( real, (fun (fun nat real) (fun nat bool)) ) 16.11/16.18 ( (fun real bool), real ) 16.11/16.18 ( (fun real bool), (fun real bool) ) 16.11/16.18 ( (fun real bool), (fun real (fun bool bool)) ) 16.11/16.18 ( (fun real bool), (fun (fun int real) (fun int bool)) ) 16.11/16.18 ( (fun real bool), (fun (fun nat real) (fun nat bool)) ) 16.11/16.18 ( (fun real real), (fun real real) ) 16.11/16.18 ( (fun real real), (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 16.11/16.18 ( (fun real real), (fun real (fun real real)) ) 16.11/16.18 ( (fun real real), (fun real (fun real bool)) ) 16.11/16.18 ( (fun real real), (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 16.11/16.18 ( rat, real ) 16.11/16.18 ( rat, (product_prod int int) ) 16.11/16.18 ( complex, nat ) 16.11/16.18 ( complex, real ) 16.11/16.18 ( complex, complex ) 16.11/16.18 ( (fun nat real), (fun nat bool) ) 16.11/16.18 ( (fun nat real), (fun nat real) ) 16.11/16.18 ( (fun nat real), (fun nat (fun real real)) ) 16.11/16.18 ( (fun nat real), (fun int (fun nat real)) ) 16.11/16.18 ( (filter nat), bool ) 16.11/16.18 ( (fun int (fun int int)), (fun int (fun int (fun int bool))) ) 16.11/16.18 ( (fun int (fun int int)), (let ((_let_0 (fun int int))) (fun int (fun _let_0 _let_0))) ) 16.11/16.18 ( (product_prod int int), bool ) 16.11/16.18 ( (product_prod int int), int ) 16.11/16.18 ( (product_prod int int), (fun int bool) ) 16.11/16.18 ( (product_prod int int), (fun int int) ) 16.11/16.18 ( (product_prod int int), rat ) 16.11/16.18 ( (product_prod int int), (product_prod int int) ) 16.11/16.18 ( (product_prod int int), (fun bool bool) ) 16.11/16.18 ( (product_prod int int), (fun (product_prod int int) bool) ) 16.11/16.18 ( (product_prod int int), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 16.11/16.18 ( (product_prod int int), (fun (product_prod int int) (fun int bool)) ) 16.11/16.18 ( (product_prod int int), (fun (product_prod int int) int) ) 16.11/16.18 ( (product_prod int int), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 16.11/16.18 ( (product_prod int int), (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 16.11/16.18 ( quickcheck_code_int, nat ) 16.11/16.18 ( quickcheck_code_int, int ) 16.11/16.18 ( quickcheck_code_int, (product_prod quickcheck_code_int quickcheck_code_int) ) 16.11/16.18 ( quickcheck_code_int, (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int)) ) 16.11/16.18 ( (fun bool bool), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 16.11/16.18 ( code_code_numeral, nat ) 16.11/16.18 ( code_code_numeral, int ) 16.11/16.18 ( code_code_numeral, (fun nat nat) ) 16.11/16.18 ( code_code_numeral, code_code_numeral ) 16.11/16.18 ( code_code_numeral, (product_prod code_code_numeral code_code_numeral) ) 16.11/16.18 ( code_code_numeral, (fun code_code_numeral (product_prod code_code_numeral code_code_numeral)) ) 16.11/16.18 ( (fun int (fun int (fun int bool))), (fun int (fun int (fun int bool))) ) 16.11/16.18 ( (fun real (fun real bool)), (fun real (fun (fun int real) (fun int bool))) ) 16.11/16.18 ( (fun real (fun real bool)), (fun real (fun (fun nat real) (fun nat bool))) ) 16.11/16.18 ( (product_prod real real), bool ) 16.11/16.18 ( (fun (product_prod real real) bool), (fun real (fun real (fun nat (product_prod real real)))) ) 16.11/16.18 ( (fun (product_prod int int) bool), (fun (product_prod int int) bool) ) 16.11/16.18 ( (fun (product_prod int int) bool), (fun (product_prod int int) (fun bool bool)) ) 16.11/16.18 ( (fun int (fun bool bool)), (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 16.11/16.18 ( (fun nat rat), bool ) 16.11/16.18 ( (filter real), bool ) 16.11/16.18 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)), bool ) 16.11/16.18 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 16.11/16.18 ( (fun (product_prod int int) (fun bool bool)), (let ((_let_0 (fun (product_prod int int) bool))) (fun (product_prod int int) (fun _let_0 _let_0))) ) 16.11/16.18 ( (fun (product_prod int int) (fun int bool)), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 16.11/16.18 ( (fun (product_prod int int) int), (fun (product_prod int int) bool) ) 16.11/16.18 ( (fun (product_prod int int) int), (fun (product_prod int int) (fun int bool)) ) 16.11/16.18 ( (fun (product_prod int int) int), (fun (product_prod int int) int) ) 16.11/16.18 ( (fun (product_prod int int) int), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))) ) 16.11/16.18 ( (fun (product_prod int int) int), (fun (product_prod int int) (fun int int)) ) 16.11/16.18 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 16.11/16.18 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 (fun int bool)))) ) 16.11/16.18 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 (fun int bool)))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun (fun _let_0 int) (fun _let_0 bool)))) ) 16.11/16.18 ( (fun (product_prod int int) (fun int int)), (let ((_let_0 (fun (product_prod int int) int))) (fun (product_prod int int) (fun _let_0 _let_0))) ) 16.11/16.18 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), bool ) 16.11/16.18 ( (fun int real), (fun int bool) ) 16.11/16.18 ( (fun int real), (fun int real) ) 16.11/16.18 ( (fun int real), (fun int (fun int real)) ) 16.11/16.18 ( (fun int real), (fun int (fun real real)) ) 16.11/16.18 ( (fun nat (fun bool bool)), (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 16.11/16.18 ( (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun int bool))) (fun _let_0 (fun int _let_0))) ) 16.11/16.18 ( (fun int (fun int (fun bool bool))), (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 16.11/16.18 ( (fun real (fun int bool)), (fun real bool) ) 16.11/16.18 ( (fun real (fun int (fun int bool))), (fun real (fun int bool)) ) 16.11/16.18 ( (fun real (fun int (fun int bool))), (fun real (fun int (fun int (fun bool bool)))) ) 16.11/16.18 ( (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun int bool))) (fun real (fun _let_0 (fun int _let_0)))) ) 16.11/16.18 ( (fun real (fun int (fun int (fun bool bool)))), (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))) ) 16.11/16.18 ( (fun int (fun int real)), (fun int (fun int bool)) ) 16.11/16.18 ( (fun int (fun int real)), (fun real (fun int (fun int bool))) ) 16.11/16.18 ( (fun (fun int real) (fun int bool)), (fun (fun int (fun int real)) (fun int (fun int bool))) ) 16.11/16.18 ( (fun real (fun (fun int real) (fun int bool))), (fun real (fun (fun int (fun int real)) (fun int (fun int bool)))) ) 16.11/16.18 ( (fun int (fun real real)), (let ((_let_0 (fun int real))) (fun int (fun _let_0 _let_0))) ) 16.11/16.18 ( (fun int (fun real real)), (let ((_let_0 (fun nat real))) (fun int (fun _let_0 _let_0))) ) 16.11/16.18 ( (fun int (fun nat bool)), (fun int bool) ) 16.11/16.18 ( (fun int (fun nat bool)), (fun int (fun nat (fun bool bool))) ) 16.11/16.18 ( (fun real (fun int (fun nat bool))), (fun real (fun int bool)) ) 16.11/16.18 ( (fun real (fun int (fun nat bool))), (fun real (fun int (fun nat (fun bool bool)))) ) 16.11/16.18 ( (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun nat bool))) (fun _let_0 (fun int _let_0))) ) 16.11/16.18 ( (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun nat bool))) (fun real (fun _let_0 (fun int _let_0)))) ) 16.11/16.18 ( (fun int (fun nat (fun bool bool))), (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 16.11/16.18 ( (fun real (fun int (fun nat (fun bool bool)))), (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))) ) 16.11/16.18 ( (fun int (fun nat real)), (fun int (fun nat bool)) ) 16.11/16.18 ( (fun int (fun nat real)), (fun real (fun int (fun nat bool))) ) 16.11/16.18 ( (fun (fun nat real) (fun nat bool)), (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 16.11/16.18 ( (fun real (fun (fun nat real) (fun nat bool))), (fun real (fun (fun int (fun nat real)) (fun int (fun nat bool)))) ) 16.11/16.18 ) 16.11/16.18 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_140666 $$unsorted) (BOUND_VARIABLE_140667 $$unsorted)) (let ((_let_0 (filter X_a))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun X_a X_b))) (let ((_let_3 (fun X_a real))) (let ((_let_4 (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_140667))) (or (not (real_normed_vector X_b)) (not (topological_space X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (hAPP _let_2 (fun X_b _let_1) (tendsto X_a X_b) BOUND_VARIABLE_140666) (zero_zero X_b)) _let_4))) (hBOOL (hAPP _let_0 bool (hAPP real _let_1 (hAPP _let_3 (fun real _let_1) (tendsto X_a real) (hAPP _let_2 _let_3 (hAPP (fun X_b real) (fun _let_2 _let_3) (combb X_b real X_a) (norm_norm X_b)) BOUND_VARIABLE_140666)) (zero_zero real)) _let_4)))))))) ) 16.11/16.18 ( real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.18 ) 16.11/16.19 (instantiation (forall ((A_2 $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat nat))) (let ((_let_2 (fun real real))) (let ((_let_3 (fun nat _let_0))) (let ((_let_4 (fun nat real))) (let ((_let_5 (fun nat _let_1))) (let ((_let_6 (fun _let_0 real))) (let ((_let_7 (fun nat _let_2))) (let ((_let_8 (fun (filter nat) bool))) (let ((_let_9 (fun real _let_8))) (let ((_let_10 (tendsto nat real))) (let ((_let_11 (hAPP _let_4 _let_4 (hAPP _let_7 (fun _let_4 _let_4) (combs nat real real) (hAPP _let_4 _let_7 (hAPP (fun real _let_2) (fun _let_4 _let_7) (combb real _let_2 nat) (times_times real)) (hAPP real _let_4 (power_power real) (hAPP int real (number_number_of real) min_1)))) A_2))) (or (not (hBOOL (hAPP (filter nat) bool (hAPP real _let_8 (hAPP _let_4 _let_9 _let_10 A_2) (zero_zero real)) sequentially))) (not (forall ((N_2 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) (hAPP nat real A_2 N_2))) )) (not (forall ((N_2 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP nat real A_2 (hAPP nat nat suc N_2))) (hAPP nat real A_2 N_2))) )) (hBOOL (hAPP (filter nat) bool (hAPP real _let_8 (hAPP _let_4 _let_9 _let_10 (hAPP _let_3 _let_4 (hAPP _let_6 (fun _let_3 _let_4) (combb _let_0 real nat) (hAPP _let_4 _let_6 (big_co1399186613setsum nat real) _let_11)) (hAPP _let_1 _let_3 (hAPP _let_3 (fun _let_1 _let_3) (combb nat _let_0 nat) (hAPP nat _let_3 (ord_atLeastLessThan nat) (zero_zero nat))) (hAPP nat _let_1 (hAPP _let_5 _let_5 (combc nat nat nat) (hAPP _let_1 _let_5 (hAPP _let_5 (fun _let_1 _let_5) (combb nat _let_1 nat) (plus_plus nat)) (hAPP nat _let_1 (times_times nat) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat))))) (hAPP _let_4 real (suminf real) _let_11)) sequentially))))))))))))))) ) 16.11/16.19 ( (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))) ) 16.11/16.19 ) 16.11/16.19 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (one_one real))) (let ((_let_1 (hAPP real real (sgn_sgn real) X_1))) (let ((_let_2 (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) X_1)))) (or (= (zero_zero real) X_1) (and (or (not _let_2) (= _let_0 _let_1)) (or _let_2 (= (hAPP real real (uminus_uminus real) _let_0) _let_1))))))) ) 16.11/16.19 ( (zero_zero real) ) 16.11/16.19 ( pi ) 16.11/16.19 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.19 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.19 ( skv_2 ) 16.11/16.19 ( skv_8 ) 16.11/16.19 ( skv_9 ) 16.11/16.19 ) 16.11/16.19 (instantiation (forall ((Z_1 $$unsorted)) (let ((_let_0 (uminus_uminus int))) (= (ti int Z_1) (hAPP int int _let_0 (hAPP int int _let_0 Z_1)))) ) 16.11/16.19 ( (one_one int) ) 16.11/16.19 ( pls ) 16.11/16.19 ( min_1 ) 16.11/16.19 ( s ) 16.11/16.19 ( m ) 16.11/16.19 ( s1 ) 16.11/16.19 ( t ) 16.11/16.19 ) 16.11/16.19 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_140938 $$unsorted)) (or (not (comm_monoid_add X_a)) (= (ti X_a BOUND_VARIABLE_140938) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_140938) (zero_zero X_a)))) ) 16.11/16.19 ( bool, fFalse ) 16.11/16.19 ( bool, fTrue ) 16.11/16.19 ( nat, (one_one nat) ) 16.11/16.19 ( int, pls ) 16.11/16.19 ( int, min_1 ) 16.11/16.19 ( int, s ) 16.11/16.19 ( int, m ) 16.11/16.19 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 16.11/16.19 ( int, s1 ) 16.11/16.19 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.19 ( int, t ) 16.11/16.19 ( (fun int bool), nat_neg ) 16.11/16.19 ( (fun int bool), zprime ) 16.11/16.19 ( (fun int bool), zEven ) 16.11/16.19 ( (fun int bool), zOdd ) 16.11/16.19 ( (fun int bool), (even_odd_even int) ) 16.11/16.19 ( (fun int bool), twoSqu1091635170sum2sq ) 16.11/16.19 ( (fun int bool), nat_is_nat ) 16.11/16.19 ( (fun int (fun int bool)), norRRset ) 16.11/16.19 ( (fun int (fun int bool)), quadRes ) 16.11/16.19 ( (fun int (fun int bool)), sRStar ) 16.11/16.19 ( (fun int (fun int bool)), d22set ) 16.11/16.19 ( (fun int (fun int bool)), sr ) 16.11/16.19 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 16.11/16.19 ( (fun int int), zfact ) 16.11/16.19 ( (fun int int), bit0 ) 16.11/16.19 ( (fun int int), bit1 ) 16.11/16.19 ( (fun int int), (fact_fact int) ) 16.11/16.19 ( (fun int int), pred ) 16.11/16.19 ( (fun int int), succ ) 16.11/16.19 ( (fun nat bool), (even_odd_even nat) ) 16.11/16.19 ( (fun nat bool), prime ) 16.11/16.19 ( (fun nat nat), suc ) 16.11/16.19 ( (fun nat nat), (fact_fact nat) ) 16.11/16.19 ( (fun nat nat), fact ) 16.11/16.19 ( (fun nat nat), nat_size ) 16.11/16.19 ( (fun nat nat), (size_size nat) ) 16.11/16.19 ( (fun (product_prod nat nat) bool), pred_nat ) 16.11/16.19 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 16.11/16.19 ( real, pi ) 16.11/16.19 ( (fun real real), ln ) 16.11/16.19 ( (fun real real), cos ) 16.11/16.19 ( (fun real real), sqrt ) 16.11/16.19 ( (fun real real), sin ) 16.11/16.19 ( (fun real real), arccos ) 16.11/16.19 ( (fun real real), arcsin ) 16.11/16.19 ( (fun real real), tan ) 16.11/16.19 ( (fun real real), arctan ) 16.11/16.19 ( (fun nat (fun nat bool)), coprime ) 16.11/16.19 ( complex, ii ) 16.11/16.19 ( (fun nat real), (real_1 nat) ) 16.11/16.19 ( (fun nat real), sin_coeff ) 16.11/16.19 ( (fun nat real), cos_coeff ) 16.11/16.19 ( (filter nat), sequentially ) 16.11/16.19 ( (fun int (fun int int)), (gcd_gcd int) ) 16.11/16.19 ( (fun int (fun int int)), legendre ) 16.11/16.19 ( (fun int (fun int int)), legacy_zgcd ) 16.11/16.19 ( (fun int (fun int int)), standardRes ) 16.11/16.19 ( (fun int (fun int int)), nat_tsub ) 16.11/16.19 ( (fun int (fun int int)), multInv ) 16.11/16.19 ( (fun int (fun int int)), z3mod ) 16.11/16.19 ( (fun int (fun int int)), z3div ) 16.11/16.19 ( (fun int (fun int int)), int_gcd ) 16.11/16.19 ( (fun int (fun int int)), int_lcm ) 16.11/16.19 ( (fun int (fun int int)), inv ) 16.11/16.19 ( (fun complex complex), expi ) 16.11/16.19 ( (fun complex complex), cnj ) 16.11/16.19 ( (fun real complex), cis ) 16.11/16.19 ( (fun int nat), nat_1 ) 16.11/16.19 ( (fun int nat), phi ) 16.11/16.19 ( (fun (fun int bool) bool), nat_nat_set ) 16.11/16.19 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 16.11/16.19 ( (fun nat (fun nat nat)), nat_gcd ) 16.11/16.19 ( (fun nat (fun nat nat)), nat_lcm ) 16.11/16.19 ( (fun (fun int bool) int), (the int) ) 16.11/16.19 ( (fun complex real), re ) 16.11/16.19 ( (fun complex real), im ) 16.11/16.19 ( (fun complex real), arg ) 16.11/16.19 ( (fun bool bool), fNot ) 16.11/16.19 ( (fun nat (fun real real)), root ) 16.11/16.19 ( (fun real (fun real real)), log ) 16.11/16.19 ( (fun real (fun real real)), powr ) 16.11/16.19 ( (fun bool (fun bool bool)), fimplies ) 16.11/16.19 ( (fun bool (fun bool bool)), fconj ) 16.11/16.19 ( (fun bool (fun bool bool)), fdisj ) 16.11/16.19 ( (fun int (fun int (product_prod int int))), negDivAlg ) 16.11/16.19 ( (fun int (fun int (product_prod int int))), posDivAlg ) 16.11/16.19 ( (fun int (fun int (product_prod int int))), divmod_int ) 16.11/16.19 ( (fun int (fun int (product_prod int int))), pdivmod ) 16.11/16.19 ( (fun int (fun int (product_prod int int))), norm_frac ) 16.11/16.19 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 16.11/16.19 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 16.11/16.19 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 16.11/16.19 ( (fun int (fun int (fun int bool))), zcong ) 16.11/16.19 ( (fun int (fun int (fun int bool))), zcongm ) 16.11/16.19 ( (fun int (fun int (fun int bool))), noXRRset ) 16.11/16.19 ( (fun int (fun int (fun int bool))), bnorRset ) 16.11/16.19 ( (fun int (fun int (fun int bool))), wset ) 16.11/16.19 ( (fun (product_prod int int) bool), frac_1 ) 16.11/16.19 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 16.11/16.19 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 16.11/16.19 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 16.11/16.19 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 16.11/16.19 ( (fun (fun nat rat) bool), vanishes ) 16.11/16.19 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 16.11/16.19 ( (fun code_code_numeral nat), code_c271388182l_size ) 16.11/16.19 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 16.11/16.19 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 16.11/16.19 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 16.11/16.19 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 16.11/16.19 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 16.11/16.19 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 16.11/16.19 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 16.11/16.19 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 16.11/16.19 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 16.11/16.19 ( (fun complex nat), complex_size ) 16.11/16.19 ( (fun complex nat), (size_size complex) ) 16.11/16.19 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 16.11/16.19 ( (fun nat (fun nat (product_prod int int))), bezw ) 16.11/16.19 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 16.11/16.19 ( (fun int (fun nat nat)), nat_aux ) 16.11/16.19 ( (fun int (fun (fun int bool) bool)), rsetR ) 16.11/16.19 ( (fun int (fun (fun int bool) bool)), resSet ) 16.11/16.19 ( (fun int (list int)), quickc666637781d_zero ) 16.11/16.19 ( (fun (product_prod int int) rat), frct ) 16.11/16.19 ( (fun int (fun int rat)), fract ) 16.11/16.19 ( (fun real (fun real complex)), complex_1 ) 16.11/16.19 ( (fun real (fun real complex)), rcis ) 16.11/16.19 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 16.11/16.19 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 16.11/16.19 ( (fun int real), (real_1 int) ) 16.11/16.19 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 16.11/16.19 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 16.11/16.19 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 16.11/16.19 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 16.11/16.19 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 16.11/16.19 ( (fun real nat), natfloor ) 16.11/16.19 ( (fun real nat), natceiling ) 16.11/16.19 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 16.11/16.19 ( (fun quickcheck_code_int int), quickcheck_int_of ) 16.11/16.19 ( (fun rat (product_prod int int)), quotient_of ) 16.11/16.19 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 16.11/16.19 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 16.11/16.19 ( (fun rat real), ratreal ) 16.11/16.19 ( (fun code_code_numeral int), code_int_of ) 16.11/16.19 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 16.11/16.19 ( (fun int quickcheck_code_int), quickcheck_of_int ) 16.11/16.19 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 16.11/16.19 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 16.11/16.19 ) 16.11/16.19 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_140953 $$unsorted) (BOUND_VARIABLE_140954 $$unsorted) (BOUND_VARIABLE_140955 $$unsorted)) (let ((_let_0 (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_140953))) (or (not (monoid_mult X_a)) (= (hAPP nat X_a _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) BOUND_VARIABLE_140954) BOUND_VARIABLE_140955)) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) (hAPP nat X_a _let_0 BOUND_VARIABLE_140954)) (hAPP nat X_a _let_0 BOUND_VARIABLE_140955))))) ) 16.11/16.19 ( int, s, (one_one nat), (one_one nat) ) 16.11/16.19 ( int, s1, (one_one nat), (one_one nat) ) 16.11/16.19 ( int, skv_14, (one_one nat), (one_one nat) ) 16.11/16.19 ( complex, ii, (one_one nat), (one_one nat) ) 16.11/16.19 ) 16.11/16.19 (instantiation (forall ((P_5 $$unsorted) (R_4 $$unsorted) (S_3 $$unsorted) (Q_3 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (zero_zero int))) (let ((_let_3 (product_prod int int))) (let ((_let_4 (fun int _let_3))) (let ((_let_5 (product_Pair int int))) (or (= _let_2 (ti int Q_3)) (= _let_2 (ti int S_3)) (not (= (hAPP _let_3 _let_3 normalize (hAPP int _let_3 (hAPP int _let_4 _let_5 P_5) Q_3)) (hAPP _let_3 _let_3 normalize (hAPP int _let_3 (hAPP int _let_4 _let_5 R_4) S_3)))) (= (hAPP int int (hAPP int _let_0 _let_1 R_4) Q_3) (hAPP int int (hAPP int _let_0 _let_1 P_5) S_3))))))))) ) 16.11/16.19 ( (one_one int), (one_one int), m, m ) 16.11/16.19 ( (one_one int), (one_one int), t, m ) 16.11/16.19 ( (zero_zero int), s, s1, s1 ) 16.11/16.19 ( s, (zero_zero int), s, s ) 16.11/16.19 ( s, s, s, s ) 16.11/16.19 ) 16.11/16.19 (instantiation (forall ((X_2 $$unsorted)) (= (not (forall ((Y $$unsorted)) (not (= X_2 (hAPP nat nat (hAPP nat (fun nat nat) (times_times nat) (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat)))) Y))) )) (hBOOL (hAPP nat bool (even_odd_even nat) X_2))) ) 16.11/16.19 ( (zero_zero nat) ) 16.11/16.19 ( (one_one nat) ) 16.11/16.19 ) 16.11/16.19 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (zero_zero int))) (or (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) _let_0) X_1)) (= _let_0 (hAPP int int (fact_fact int) X_1)))) ) 16.11/16.19 ( (one_one int) ) 16.11/16.19 ( (zero_zero int) ) 16.11/16.19 ( min_1 ) 16.11/16.19 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.19 ( s ) 16.11/16.19 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.11/16.19 ( (hAPP int int (number_number_of int) pls) ) 16.11/16.19 ( skv_4 ) 16.11/16.19 ( skv_10 ) 16.11/16.19 ) 16.11/16.19 (instantiation (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) X_1))) (= (hAPP int int (fact_fact int) X_1) (hAPP nat int (semiring_1_of_nat int) (hAPP nat nat (fact_fact nat) (hAPP int nat nat_1 X_1))))) ) 16.11/16.19 ( (one_one int) ) 16.11/16.19 ( (zero_zero int) ) 16.11/16.19 ( min_1 ) 16.11/16.19 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.19 ( s ) 16.11/16.19 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.11/16.19 ( (hAPP int int (number_number_of int) pls) ) 16.11/16.19 ( skv_4 ) 16.11/16.19 ( skv_10 ) 16.11/16.19 ) 16.11/16.19 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_141012 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)))) (or (not (linord1117847801e_zero X_a)) (= (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_141012))) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_141012))))) ) 16.11/16.19 ( real, (zero_zero real) ) 16.11/16.19 ( complex, ii ) 16.11/16.19 ) 16.11/16.19 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_141029 $$unsorted) (BOUND_VARIABLE_141030 $$unsorted)) (let ((_let_0 (abs_abs X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (inverse_divide X_a))) (or (not (linord1117847801e_zero X_a)) (= (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a _let_0 BOUND_VARIABLE_141029)) (hAPP X_a X_a _let_0 BOUND_VARIABLE_141030)) (hAPP X_a X_a _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_141029) BOUND_VARIABLE_141030))))))) ) 16.11/16.19 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.19 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.11/16.19 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.19 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 16.11/16.19 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.19 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.19 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.11/16.19 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.11/16.19 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.19 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.19 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.19 ) 16.11/16.19 (instantiation (forall ((N_1 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (one_one int))) (= _let_1 (hAPP int int (hAPP int _let_0 (gcd_gcd int) (hAPP int int (hAPP int _let_0 (minus_minus int) N_1) _let_1)) N_1)))) ) 16.11/16.19 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.19 ) 16.11/16.19 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_141098 $$unsorted) (BOUND_VARIABLE_141099 $$unsorted)) (let ((_let_0 (semiring_1_of_nat X_a))) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) BOUND_VARIABLE_141098) BOUND_VARIABLE_141099))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP nat X_a _let_0 BOUND_VARIABLE_141098)) (hAPP nat X_a _let_0 BOUND_VARIABLE_141099))))) ) 16.11/16.19 ( int, (zero_zero nat), (zero_zero nat) ) 16.11/16.19 ( int, (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 16.11/16.19 ) 16.11/16.19 (instantiation (forall ((X_2 $$unsorted) (N $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (one_one real))) (let ((_let_2 (ord_less_eq real))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N))) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 (hAPP real real (hAPP nat (fun real real) root N) X_2)) _let_1)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 X_2) _let_1))))))) ) 16.11/16.19 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.19 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.19 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.19 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.19 ) 16.11/16.19 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (fun real real))) (let ((_let_3 (inverse_divide real))) (let ((_let_4 (hAPP real real (hAPP real _let_2 _let_3 pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (let ((_let_5 (hAPP real real (hAPP real _let_2 (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) X_1))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (uminus_uminus real) _let_4)) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) _let_4))) (= (hAPP real real (hAPP real _let_2 _let_3 (hAPP real real sin _let_5)) (hAPP real real (hAPP real _let_2 (plus_plus real) (hAPP real real cos _let_5)) (one_one real))) (hAPP real real tan X_1))))))))) ) 16.11/16.19 ( (one_one real) ) 16.11/16.19 ( (zero_zero real) ) 16.11/16.19 ( pi ) 16.11/16.19 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.19 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.11/16.19 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.11/16.19 ( (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 16.11/16.19 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.11/16.19 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.19 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 16.11/16.19 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 16.11/16.19 ) 16.11/16.19 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_141318 $$unsorted) (BOUND_VARIABLE_141319 $$unsorted)) (let ((_let_0 (uminus_uminus X_a))) (or (not (group_add X_a)) (= (= (hAPP X_a X_a _let_0 BOUND_VARIABLE_141318) (hAPP X_a X_a _let_0 BOUND_VARIABLE_141319)) (= (ti X_a BOUND_VARIABLE_141319) (ti X_a BOUND_VARIABLE_141318))))) ) 16.11/16.19 ( int, (one_one int), min_1 ) 16.11/16.19 ( int, pls, (one_one int) ) 16.11/16.19 ( int, pls, min_1 ) 16.11/16.19 ( int, min_1, pls ) 16.11/16.19 ( int, min_1, min_1 ) 16.11/16.19 ( real, (one_one real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.19 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.19 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.11/16.19 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi), (one_one real) ) 16.11/16.19 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.19 ( complex, (one_one complex), ii ) 16.11/16.19 ( complex, ii, (one_one complex) ) 16.11/16.19 ( complex, ii, ii ) 16.11/16.19 ) 16.11/16.19 (instantiation (forall ((K_4 $$unsorted)) (= (ti int K_4) (hAPP int int (hAPP int (fun int int) (plus_plus int) K_4) pls)) ) 16.11/16.19 ( pls ) 16.11/16.19 ( min_1 ) 16.11/16.19 ( s ) 16.11/16.19 ( m ) 16.11/16.19 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 16.11/16.19 ( s1 ) 16.11/16.19 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.19 ( t ) 16.11/16.19 ) 16.11/16.19 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (uminus_uminus real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) (zero_zero real)))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real _let_2 pi)) X_1))) (= (hAPP real real _let_2 X_1) (hAPP real real arccos (hAPP real real cos X_1))))))) ) 16.11/16.19 ( (one_one real) ) 16.11/16.19 ( (zero_zero real) ) 16.11/16.19 ( pi ) 16.11/16.19 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.19 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.19 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.11/16.19 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.11/16.19 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.11/16.19 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.19 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 16.11/16.19 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 16.11/16.19 ( skv_5 ) 16.11/16.19 ) 16.11/16.19 (instantiation (forall ((W_1 $$unsorted) (Z $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) W_1) Z)) (not (forall ((N_2 $$unsorted)) (not (= (hAPP int int (hAPP int (fun int int) (plus_plus int) W_1) (hAPP nat int (semiring_1_of_nat int) (hAPP nat nat suc N_2))) (ti int Z))) ))) ) 16.11/16.19 ( (one_one int), t ) 16.11/16.19 ( pls, (one_one int) ) 16.11/16.19 ( pls, pls ) 16.11/16.19 ( pls, min_1 ) 16.11/16.19 ( pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.11/16.19 ( min_1, pls ) 16.11/16.19 ( min_1, min_1 ) 16.11/16.19 ( s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.11/16.19 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.11/16.19 ( skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.11/16.19 ( skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.11/16.19 ) 16.11/16.19 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_141383 $$unsorted) (BOUND_VARIABLE_141384 $$unsorted) (BOUND_VARIABLE_141385 $$unsorted) (BOUND_VARIABLE_141386 $$unsorted)) (let ((_let_0 (filter X_a))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (hAPP (fun X_a X_b) (fun X_b _let_1) (tendsto X_a X_b) BOUND_VARIABLE_141384))) (let ((_let_3 (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_141386))) (or (not (topological_space X_b)) (not (topological_space X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 _let_2 BOUND_VARIABLE_141385) _let_3))) (not (= (ti X_b BOUND_VARIABLE_141383) (ti X_b BOUND_VARIABLE_141385))) (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 _let_2 BOUND_VARIABLE_141383) _let_3))))))) ) 16.11/16.19 ( real, real, pi, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.19 ) 16.11/16.19 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_141418 $$unsorted) (BOUND_VARIABLE_141419 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (div_div X_a))) (let ((_let_2 (plus_plus X_a))) (or (not (semiring_div X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_141419)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_141418) BOUND_VARIABLE_141419)) (one_one X_a)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_141419) BOUND_VARIABLE_141418)) BOUND_VARIABLE_141419)))))) ) 16.11/16.19 ( nat, (one_one nat), (one_one nat) ) 16.11/16.19 ( int, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 16.11/16.19 ( int, (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.19 ) 16.11/16.19 (instantiation (forall ((V_3 $$unsorted) (V_1 $$unsorted)) (let ((_let_0 (number_number_of nat))) (let ((_let_1 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP int nat _let_0 V_1)) (hAPP int nat _let_0 V_3)))) (let ((_let_2 (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) V_3) pls)))) (or (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) V_1) pls)) (and (or (not _let_2) (= (hAPP int nat _let_0 V_1) _let_1)) (or _let_2 (= _let_1 (hAPP int nat _let_0 (hAPP int int (hAPP int (fun int int) (plus_plus int) V_1) V_3))))))))) ) 16.11/16.19 ( (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 16.11/16.19 ( (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.19 ( (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 16.11/16.19 ) 16.11/16.19 (instantiation (forall ((V_3 $$unsorted) (V_1 $$unsorted)) (let ((_let_0 (number_number_of nat))) (let ((_let_1 (hAPP int nat _let_0 V_3))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) V_1) pls))) (= _let_1 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP int nat _let_0 V_1)) _let_1))))) ) 16.11/16.19 ( (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 16.11/16.19 ) 16.11/16.19 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_141458 $$unsorted)) (or (not (comm_semiring_1 X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) (one_one X_a)) BOUND_VARIABLE_141458) (ti X_a BOUND_VARIABLE_141458))) ) 16.11/16.19 ( bool, fFalse ) 16.11/16.19 ( bool, fTrue ) 16.11/16.19 ( int, pls ) 16.11/16.19 ( int, min_1 ) 16.11/16.19 ( int, s ) 16.11/16.19 ( int, m ) 16.11/16.19 ( int, s1 ) 16.11/16.19 ( int, t ) 16.11/16.19 ( (fun int bool), nat_neg ) 16.11/16.19 ( (fun int bool), zprime ) 16.11/16.19 ( (fun int bool), zEven ) 16.11/16.19 ( (fun int bool), zOdd ) 16.11/16.19 ( (fun int bool), (even_odd_even int) ) 16.11/16.19 ( (fun int bool), twoSqu1091635170sum2sq ) 16.11/16.19 ( (fun int bool), nat_is_nat ) 16.11/16.19 ( (fun int (fun int bool)), norRRset ) 16.11/16.19 ( (fun int (fun int bool)), quadRes ) 16.11/16.19 ( (fun int (fun int bool)), sRStar ) 16.11/16.19 ( (fun int (fun int bool)), d22set ) 16.11/16.19 ( (fun int (fun int bool)), sr ) 16.11/16.19 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 16.11/16.19 ( (fun int int), zfact ) 16.11/16.19 ( (fun int int), bit0 ) 16.11/16.19 ( (fun int int), bit1 ) 16.11/16.19 ( (fun int int), (fact_fact int) ) 16.11/16.19 ( (fun int int), pred ) 16.11/16.19 ( (fun int int), succ ) 16.11/16.19 ( (fun nat bool), (even_odd_even nat) ) 16.11/16.19 ( (fun nat bool), prime ) 16.11/16.19 ( (fun nat nat), suc ) 16.11/16.19 ( (fun nat nat), (fact_fact nat) ) 16.11/16.19 ( (fun nat nat), fact ) 16.11/16.19 ( (fun nat nat), nat_size ) 16.11/16.19 ( (fun nat nat), (size_size nat) ) 16.11/16.19 ( (fun (product_prod nat nat) bool), pred_nat ) 16.11/16.19 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 16.11/16.19 ( real, pi ) 16.11/16.19 ( (fun real real), ln ) 16.11/16.19 ( (fun real real), cos ) 16.11/16.19 ( (fun real real), sqrt ) 16.11/16.19 ( (fun real real), sin ) 16.11/16.19 ( (fun real real), arccos ) 16.11/16.19 ( (fun real real), arcsin ) 16.11/16.19 ( (fun real real), tan ) 16.11/16.19 ( (fun real real), arctan ) 16.11/16.19 ( (fun nat (fun nat bool)), coprime ) 16.11/16.19 ( complex, ii ) 16.11/16.19 ( (fun nat real), (real_1 nat) ) 16.11/16.19 ( (fun nat real), sin_coeff ) 16.11/16.19 ( (fun nat real), cos_coeff ) 16.11/16.19 ( (filter nat), sequentially ) 16.11/16.19 ( (fun int (fun int int)), (gcd_gcd int) ) 16.11/16.19 ( (fun int (fun int int)), legendre ) 16.11/16.19 ( (fun int (fun int int)), legacy_zgcd ) 16.11/16.19 ( (fun int (fun int int)), standardRes ) 16.11/16.19 ( (fun int (fun int int)), nat_tsub ) 16.11/16.19 ( (fun int (fun int int)), multInv ) 16.11/16.19 ( (fun int (fun int int)), z3mod ) 16.11/16.19 ( (fun int (fun int int)), z3div ) 16.11/16.19 ( (fun int (fun int int)), int_gcd ) 16.11/16.19 ( (fun int (fun int int)), int_lcm ) 16.11/16.19 ( (fun int (fun int int)), inv ) 16.11/16.19 ( (fun complex complex), expi ) 16.11/16.19 ( (fun complex complex), cnj ) 16.11/16.19 ( (fun real complex), cis ) 16.11/16.19 ( (fun int nat), nat_1 ) 16.11/16.19 ( (fun int nat), phi ) 16.11/16.19 ( (fun (fun int bool) bool), nat_nat_set ) 16.11/16.19 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 16.11/16.19 ( (fun nat (fun nat nat)), nat_gcd ) 16.11/16.19 ( (fun nat (fun nat nat)), nat_lcm ) 16.11/16.19 ( (fun (fun int bool) int), (the int) ) 16.11/16.19 ( (fun complex real), re ) 16.11/16.19 ( (fun complex real), im ) 16.11/16.19 ( (fun complex real), arg ) 16.11/16.19 ( (fun bool bool), fNot ) 16.11/16.19 ( (fun nat (fun real real)), root ) 16.11/16.19 ( (fun real (fun real real)), log ) 16.11/16.19 ( (fun real (fun real real)), powr ) 16.11/16.19 ( (fun bool (fun bool bool)), fimplies ) 16.11/16.19 ( (fun bool (fun bool bool)), fconj ) 16.11/16.19 ( (fun bool (fun bool bool)), fdisj ) 16.11/16.19 ( (fun int (fun int (product_prod int int))), negDivAlg ) 16.11/16.19 ( (fun int (fun int (product_prod int int))), posDivAlg ) 16.11/16.19 ( (fun int (fun int (product_prod int int))), divmod_int ) 16.11/16.19 ( (fun int (fun int (product_prod int int))), pdivmod ) 16.11/16.19 ( (fun int (fun int (product_prod int int))), norm_frac ) 16.11/16.19 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 16.11/16.19 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 16.11/16.19 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 16.11/16.19 ( (fun int (fun int (fun int bool))), zcong ) 16.11/16.19 ( (fun int (fun int (fun int bool))), zcongm ) 16.11/16.19 ( (fun int (fun int (fun int bool))), noXRRset ) 16.11/16.19 ( (fun int (fun int (fun int bool))), bnorRset ) 16.11/16.19 ( (fun int (fun int (fun int bool))), wset ) 16.11/16.19 ( (fun (product_prod int int) bool), frac_1 ) 16.11/16.19 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 16.11/16.19 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 16.11/16.19 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 16.11/16.19 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 16.11/16.19 ( (fun (fun nat rat) bool), vanishes ) 16.11/16.19 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 16.11/16.19 ( (fun code_code_numeral nat), code_c271388182l_size ) 16.11/16.19 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 16.11/16.19 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 16.11/16.19 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 16.11/16.19 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 16.11/16.19 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 16.11/16.19 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 16.11/16.19 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 16.11/16.19 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 16.11/16.19 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 16.11/16.19 ( (fun complex nat), complex_size ) 16.11/16.19 ( (fun complex nat), (size_size complex) ) 16.11/16.19 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 16.11/16.19 ( (fun nat (fun nat (product_prod int int))), bezw ) 16.11/16.19 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 16.11/16.19 ( (fun int (fun nat nat)), nat_aux ) 16.11/16.19 ( (fun int (fun (fun int bool) bool)), rsetR ) 16.11/16.19 ( (fun int (fun (fun int bool) bool)), resSet ) 16.11/16.19 ( (fun int (list int)), quickc666637781d_zero ) 16.11/16.19 ( (fun (product_prod int int) rat), frct ) 16.11/16.19 ( (fun int (fun int rat)), fract ) 16.11/16.19 ( (fun real (fun real complex)), complex_1 ) 16.11/16.19 ( (fun real (fun real complex)), rcis ) 16.11/16.19 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 16.11/16.19 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 16.11/16.19 ( (fun int real), (real_1 int) ) 16.11/16.19 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 16.11/16.19 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 16.11/16.19 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 16.11/16.19 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 16.11/16.19 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 16.11/16.19 ( (fun real nat), natfloor ) 16.11/16.19 ( (fun real nat), natceiling ) 16.11/16.19 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 16.11/16.19 ( (fun quickcheck_code_int int), quickcheck_int_of ) 16.11/16.19 ( (fun rat (product_prod int int)), quotient_of ) 16.11/16.19 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 16.11/16.19 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 16.11/16.19 ( (fun rat real), ratreal ) 16.11/16.19 ( (fun code_code_numeral int), code_int_of ) 16.11/16.19 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 16.11/16.19 ( (fun int quickcheck_code_int), quickcheck_of_int ) 16.11/16.19 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 16.11/16.19 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 16.11/16.19 ) 16.11/16.19 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_141468 $$unsorted) (BOUND_VARIABLE_141469 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (minus_minus X_a))) (let ((_let_2 (abs_abs X_a))) (or (not (ordere142940540dd_abs X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_141468)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_141469))) (hAPP X_a X_a _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_141468) BOUND_VARIABLE_141469)))))))) ) 16.11/16.19 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 16.11/16.19 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 16.11/16.19 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 16.11/16.19 ) 16.11/16.19 (instantiation (forall ((A_2 $$unsorted) (B_1 $$unsorted) (W_1 $$unsorted)) (= (and (= (zero_zero real) B_1) (= A_2 (hAPP int real (number_number_of real) W_1))) (= (hAPP real complex (hAPP real (fun real complex) complex_1 A_2) B_1) (hAPP int complex (number_number_of complex) W_1))) ) 16.11/16.19 ( (one_one real), (zero_zero real), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.11/16.19 ( (zero_zero real), (one_one real), min_1 ) 16.11/16.19 ( (zero_zero real), (zero_zero real), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.11/16.19 ) 16.11/16.19 (instantiation (forall ((P_4 $$unsorted)) (= (and (forall ((M_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (dvd_dvd nat) M_2) P_4))) (= (one_one nat) M_2) (= P_4 M_2)) ) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (one_one nat)) P_4))) (hBOOL (hAPP nat bool prime P_4))) ) 16.11/16.19 ( (zero_zero nat) ) 16.11/16.19 ( (hAPP nat nat suc (zero_zero nat)) ) 16.11/16.19 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.19 ) 16.11/16.19 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_141525 $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (times_times X_a))) (let ((_let_3 (plus_plus X_a))) (let ((_let_4 (one_one X_a))) (let ((_let_5 (hAPP nat X_a (semiring_1_of_nat X_a) BOUND_VARIABLE_141525))) (or (not (comm_semiring_1 X_a)) (= (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a (hAPP X_a _let_1 _let_3 _let_4) _let_4)) (hAPP _let_0 X_a (hAPP (fun nat X_a) (fun _let_0 X_a) (big_co1399186613setsum nat X_a) (semiring_1_of_nat X_a)) (hAPP nat _let_0 (hAPP nat (fun nat _let_0) (ord_atLeastAtMost nat) (one_one nat)) BOUND_VARIABLE_141525))) (hAPP X_a X_a (hAPP X_a _let_1 _let_2 _let_5) (hAPP X_a X_a (hAPP X_a _let_1 _let_3 _let_5) _let_4)))))))))) ) 16.11/16.19 ( int, (zero_zero nat) ) 16.11/16.19 ( int, (hAPP nat nat suc (zero_zero nat)) ) 16.11/16.19 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.11/16.19 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.19 ( real, (zero_zero nat) ) 16.11/16.19 ( real, (hAPP nat nat suc (zero_zero nat)) ) 16.11/16.19 ) 16.11/16.19 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (cauchy X_a))) (or (not (metric_space X_a)) (= _let_0 (ti (fun (fun nat X_a) bool) _let_0)))) ) 16.11/16.19 ( bool ) 16.11/16.19 ( nat ) 16.11/16.19 ( int ) 16.11/16.19 ( (fun int int) ) 16.11/16.19 ( (fun nat bool) ) 16.11/16.19 ( (fun nat nat) ) 16.11/16.19 ( (product_prod nat nat) ) 16.11/16.19 ( (fun (product_prod nat nat) bool) ) 16.11/16.19 ( (fun nat (fun (product_prod nat nat) bool)) ) 16.11/16.19 ( real ) 16.11/16.19 ( (fun real real) ) 16.11/16.19 ( rat ) 16.11/16.19 ( (fun nat (fun nat bool)) ) 16.11/16.19 ( complex ) 16.11/16.19 ( (product_prod int int) ) 16.11/16.19 ( (fun bool bool) ) 16.11/16.19 ( (product_prod real real) ) 16.11/16.19 ( (fun nat (product_prod nat nat)) ) 16.11/16.19 ( (fun nat (product_prod int int)) ) 16.11/16.19 ) 16.11/16.19 (instantiation (forall ((Z_1 $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_0 (hAPP nat (fun nat bool) (ord_less nat) X_1))) (or (not (hBOOL (hAPP nat bool _let_0 Y_1))) (hBOOL (hAPP nat bool _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) Y_1) Z_1))))) ) 16.11/16.19 ( (one_one nat), (zero_zero nat), (one_one nat) ) 16.11/16.19 ) 16.11/16.19 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_141595 $$unsorted) (BOUND_VARIABLE_141596 $$unsorted) (BOUND_VARIABLE_141597 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (let ((_let_3 (hAPP X_a _let_0 _let_1 _let_2))) (let ((_let_4 (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_141597))) (let ((_let_5 (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_141596)))) (let ((_let_6 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) _let_4) BOUND_VARIABLE_141596))) (let ((_let_7 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_141596) _let_2)))) (or (not (number X_a)) (not (linord1117847801e_zero X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_141595) BOUND_VARIABLE_141596)) _let_4)) (and (or (not _let_5) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_141595) _let_6))) (or _let_5 (and (or (not _let_7) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_6) BOUND_VARIABLE_141595))) (or _let_7 (hBOOL (hAPP X_a bool _let_3 _let_4)))))))))))))))) ) 16.11/16.19 ( real, (zero_zero real), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.11/16.19 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.11/16.19 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.11/16.19 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.11/16.19 ) 16.11/16.19 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_141673 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (one_one X_a))) (or (not (linord1117847801e_zero X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_141673)) _let_2)) (or (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_141673)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_141673) (zero_zero X_a))))))))) ) 16.11/16.19 ( int, (zero_zero int) ) 16.11/16.19 ( int, min_1 ) 16.11/16.19 ( real, (zero_zero real) ) 16.11/16.19 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.19 ( complex, ii ) 16.11/16.19 ) 16.11/16.19 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (fun nat X_a))) (let ((_let_1 (zero_zero X_a))) (or (not (comm_monoid_add X_a)) (not (t2_space X_a)) (= _let_1 (hAPP _let_0 X_a (suminf X_a) (hAPP X_a _let_0 (combk X_a nat) _let_1)))))) ) 16.11/16.19 ( bool ) 16.11/16.19 ( nat ) 16.11/16.19 ( int ) 16.11/16.19 ( (fun int int) ) 16.11/16.19 ( (fun nat bool) ) 16.11/16.19 ( (fun nat nat) ) 16.11/16.19 ( (product_prod nat nat) ) 16.11/16.19 ( (fun (product_prod nat nat) bool) ) 16.11/16.19 ( (fun nat (fun (product_prod nat nat) bool)) ) 16.11/16.19 ( real ) 16.11/16.19 ( (fun real real) ) 16.11/16.19 ( rat ) 16.11/16.19 ( (fun nat (fun nat bool)) ) 16.11/16.19 ( complex ) 16.11/16.19 ( (product_prod int int) ) 16.11/16.19 ( quickcheck_code_int ) 16.11/16.19 ( (fun bool bool) ) 16.11/16.19 ( code_code_numeral ) 16.11/16.19 ( (product_prod real real) ) 16.11/16.19 ( (fun nat (product_prod nat nat)) ) 16.11/16.19 ( (fun nat (product_prod int int)) ) 16.11/16.19 ) 16.11/16.19 (instantiation (forall ((N_1 $$unsorted)) (= N_1 (hAPP nat nat (size_size nat) N_1)) ) 16.11/16.19 ( (zero_zero nat) ) 16.11/16.19 ) 16.11/16.19 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_141726 $$unsorted) (BOUND_VARIABLE_141727 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (or (not (linorder X_a)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_141726) BOUND_VARIABLE_141727)) (= (ti X_a BOUND_VARIABLE_141727) (ti X_a BOUND_VARIABLE_141726)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_141727) BOUND_VARIABLE_141726))))) ) 16.11/16.19 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.19 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 16.11/16.19 ( int, (one_one int), pls ) 16.11/16.19 ( int, (one_one int), t ) 16.11/16.19 ( int, pls, (one_one int) ) 16.11/16.19 ( int, pls, pls ) 16.11/16.19 ( int, pls, min_1 ) 16.11/16.19 ( int, pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.11/16.19 ( int, min_1, pls ) 16.11/16.19 ( int, min_1, min_1 ) 16.11/16.19 ( int, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.11/16.19 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), pls ) 16.11/16.19 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s ) 16.11/16.19 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 16.11/16.19 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_4 ) 16.11/16.19 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_10 ) 16.11/16.19 ( int, t, (one_one int) ) 16.11/16.19 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.11/16.19 ( int, skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.11/16.19 ( int, skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.11/16.19 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.19 ( real, (zero_zero real), pi ) 16.11/16.19 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.19 ( real, (zero_zero real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.11/16.19 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.19 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.19 ( real, (zero_zero real), skv_2 ) 16.11/16.19 ( real, (zero_zero real), skv_8 ) 16.11/16.19 ( real, (zero_zero real), skv_9 ) 16.11/16.19 ( real, pi, (zero_zero real) ) 16.11/16.19 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.19 ( real, pi, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 16.11/16.19 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.19 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.11/16.19 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.19 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 16.11/16.19 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 16.11/16.19 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 16.11/16.19 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.11/16.19 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.11/16.19 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 16.11/16.19 ( real, skv_2, (zero_zero real) ) 16.11/16.19 ( real, skv_8, (zero_zero real) ) 16.11/16.19 ( real, skv_9, (zero_zero real) ) 16.11/16.19 ) 16.11/16.19 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)))) (or (not (hBOOL (hAPP int bool _let_0 X_1))) (hBOOL (hAPP int bool _let_0 (hAPP int int (fact_fact int) X_1))))) ) 16.11/16.19 ( (one_one int) ) 16.11/16.19 ( (zero_zero int) ) 16.11/16.19 ) 16.11/16.19 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_141830 $$unsorted) (BOUND_VARIABLE_141831 $$unsorted) (BOUND_VARIABLE_141832 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (fun X_a X_a))) (let ((_let_3 (ord_less X_a))) (let ((_let_4 (zero_zero X_a))) (let ((_let_5 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_3 _let_4) BOUND_VARIABLE_141831)))) (let ((_let_6 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_3 BOUND_VARIABLE_141831) _let_4)))) (let ((_let_7 (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_141832))) (let ((_let_8 (hAPP X_a X_a (hAPP X_a _let_2 (times_times X_a) _let_7) BOUND_VARIABLE_141831))) (or (not (number X_a)) (not (linord1117847801e_zero X_a)) (= (and (or _let_5 (and (or (not _let_6) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_8) BOUND_VARIABLE_141830))) (or _let_6 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_4) _let_7))))) (or (not _let_5) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_141830) _let_8)))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_2 (inverse_divide X_a) BOUND_VARIABLE_141830) BOUND_VARIABLE_141831)) _let_7))))))))))))) ) 16.11/16.19 ( real, (zero_zero real), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.11/16.19 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.11/16.19 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.11/16.20 ) 16.11/16.20 (instantiation (forall ((M $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) M))) (= (hAPP int int (hAPP int (fun int int) legacy_zgcd M) M) (ti int M))) ) 16.11/16.20 ( (one_one int) ) 16.11/16.20 ( pls ) 16.11/16.20 ( min_1 ) 16.11/16.20 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.20 ( s ) 16.11/16.20 ( m ) 16.11/16.20 ( s1 ) 16.11/16.20 ( t ) 16.11/16.20 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.11/16.20 ( (hAPP int int (number_number_of int) pls) ) 16.11/16.20 ( skv_4 ) 16.11/16.20 ( skv_10 ) 16.11/16.20 ) 16.11/16.20 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (power_power real))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (= (hAPP nat real (hAPP real _let_0 _let_1 (hAPP real real cos X_1)) _let_2) (hAPP real real (hAPP real (fun real real) (minus_minus real) (one_one real)) (hAPP nat real (hAPP real _let_0 _let_1 (hAPP real real sin X_1)) _let_2)))))) ) 16.11/16.20 ( (zero_zero real) ) 16.11/16.20 ( pi ) 16.11/16.20 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.20 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.20 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.11/16.20 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.11/16.20 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.11/16.20 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 16.11/16.20 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 16.11/16.20 ( skv_5 ) 16.11/16.20 ) 16.11/16.20 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_141927 $$unsorted) (BOUND_VARIABLE_141928 $$unsorted)) (let ((_let_0 (archimedean_ceiling X_a))) (or (not (archim1727834104eiling X_a)) (= (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP X_a int _let_0 BOUND_VARIABLE_141927)) (hAPP int int (number_number_of int) BOUND_VARIABLE_141928)) (hAPP X_a int _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_141927) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_141928)))))) ) 16.11/16.20 ( nat, (one_one nat), (hAPP int int bit1 pls) ) 16.11/16.20 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (hAPP int int bit1 pls) ) 16.11/16.20 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int bit1 pls) ) 16.11/16.20 ) 16.11/16.20 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (fun nat X_a))) (let ((_let_1 (diffs X_a))) (or (not (ring_1 X_a)) (= _let_1 (ti (fun _let_0 _let_0) _let_1))))) ) 16.11/16.20 ( bool ) 16.11/16.20 ( nat ) 16.11/16.20 ( int ) 16.11/16.20 ( (fun int int) ) 16.11/16.20 ( (fun nat bool) ) 16.11/16.20 ( (fun nat nat) ) 16.11/16.20 ( (product_prod nat nat) ) 16.11/16.20 ( (fun (product_prod nat nat) bool) ) 16.11/16.20 ( (fun nat (fun (product_prod nat nat) bool)) ) 16.11/16.20 ( real ) 16.11/16.20 ( (fun real real) ) 16.11/16.20 ( rat ) 16.11/16.20 ( (fun nat (fun nat bool)) ) 16.11/16.20 ( complex ) 16.11/16.20 ( (product_prod int int) ) 16.11/16.20 ( (fun bool bool) ) 16.11/16.20 ( (product_prod real real) ) 16.11/16.20 ( (fun nat (product_prod nat nat)) ) 16.11/16.20 ( (fun nat (product_prod int int)) ) 16.11/16.20 ) 16.11/16.20 (instantiation (forall ((B $$unsorted) (M $$unsorted) (A_1 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (let ((_let_2 (hAPP int _let_0 _let_1 (zero_zero int)))) (or (not (hBOOL (hAPP int bool _let_2 A_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 A_1) M))) (not (hBOOL (hAPP int bool _let_2 B))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 B) A_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong A_1) B) M))))))) ) 16.11/16.20 ( (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.20 ( (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.20 ( (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.20 ( s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s1 ) 16.11/16.20 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.20 ( skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s1 ) 16.11/16.20 ( skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s1 ) 16.11/16.20 ) 16.11/16.20 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (let ((_let_2 (ti int X_1))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) _let_1) X_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) X_1) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (= (one_one int) _let_2) (= _let_1 _let_2))))) ) 16.11/16.20 ( (one_one int) ) 16.11/16.20 ( pls ) 16.11/16.20 ( min_1 ) 16.11/16.20 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.20 ( s ) 16.11/16.20 ( m ) 16.11/16.20 ( s1 ) 16.11/16.20 ( t ) 16.11/16.20 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.11/16.20 ( (hAPP int int (number_number_of int) pls) ) 16.11/16.20 ( skv_4 ) 16.11/16.20 ( skv_10 ) 16.11/16.20 ) 16.11/16.20 (instantiation (forall ((Y_1 $$unsorted)) (let ((_let_0 (one_one real))) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (abs_abs real) Y_1)) _let_0))) (= (hAPP real real sqrt (hAPP real real (hAPP real (fun real real) (minus_minus real) _let_0) (hAPP nat real (hAPP real (fun nat real) (power_power real) Y_1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real real sin (hAPP real real arccos Y_1))))) ) 16.11/16.20 ( (hAPP int real (number_number_of real) min_1) ) 16.11/16.20 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.20 ) 16.11/16.20 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_142116 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_142116))) (or (not (linordered_idom X_a)) (= (hBOOL (hAPP X_a bool _let_0 (zero_zero X_a))) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_142116)))))) ) 16.11/16.20 ( nat, (zero_zero nat) ) 16.11/16.20 ( int, (one_one int) ) 16.11/16.20 ( int, pls ) 16.11/16.20 ( int, min_1 ) 16.11/16.20 ( int, s ) 16.11/16.20 ( int, t ) 16.11/16.20 ( int, skv_4 ) 16.11/16.20 ( int, skv_10 ) 16.11/16.20 ( real, (one_one real) ) 16.11/16.20 ( real, (zero_zero real) ) 16.11/16.20 ( real, pi ) 16.11/16.20 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.20 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.11/16.20 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.11/16.20 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.20 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 16.11/16.20 ( complex, (one_one complex) ) 16.11/16.20 ( complex, ii ) 16.11/16.20 ) 16.11/16.20 (instantiation (forall ((K $$unsorted) (F $$unsorted) (N $$unsorted) (Ma $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (or (not (forall ((I_2 $$unsorted)) (let ((_let_2 (fun nat bool))) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_2 (ord_less_eq nat) Ma) I_2))) (not (hBOOL (hAPP nat bool (hAPP nat _let_2 (ord_less nat) I_2) N))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int (abs_abs int) (hAPP int int (hAPP int (fun int int) (minus_minus int) (hAPP nat int F (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) I_2) (one_one nat)))) (hAPP nat int F I_2)))) (one_one int))))) )) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) Ma) N))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP nat int F Ma)) K))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) (hAPP nat int F N)))) (not (forall ((I_2 $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less_eq nat))) (or (not (= (ti int K) (hAPP nat int F I_2))) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 I_2) N))) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 Ma) I_2)))))) ))))) ) 16.11/16.20 ( s, (semiring_1_of_nat int), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 16.11/16.20 ) 16.11/16.20 (instantiation (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) X_1) Y_1))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP real nat natfloor X_1)) (hAPP real nat natfloor Y_1)))) ) 16.11/16.20 ( (zero_zero real), pi ) 16.11/16.20 ( (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.20 ( (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.20 ( (zero_zero real), skv_3 ) 16.11/16.20 ( (zero_zero real), skv_5 ) 16.11/16.20 ( (zero_zero real), skv_7 ) 16.11/16.20 ( (zero_zero real), skv_12 ) 16.11/16.20 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.11/16.20 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.20 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.11/16.20 ( skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.20 ) 16.11/16.20 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_142170 $$unsorted) (BOUND_VARIABLE_142171 $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat X_a))) (let ((_let_2 (fun X_a bool))) (let ((_let_3 (sums X_a))) (or (not (real_normed_vector X_a)) (not (hBOOL (hAPP X_a bool (hAPP _let_1 _let_2 _let_3 (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat X_a nat) BOUND_VARIABLE_142170) suc)) BOUND_VARIABLE_142171))) (hBOOL (hAPP X_a bool (hAPP _let_1 _let_2 _let_3 BOUND_VARIABLE_142170) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_142171) (hAPP nat X_a BOUND_VARIABLE_142170 (zero_zero nat)))))))))) ) 16.11/16.20 ( nat, fact, (one_one nat) ) 16.11/16.20 ( real, (hAPP real (fun nat real) (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (one_one real) ) 16.11/16.20 ) 16.11/16.20 (instantiation (forall ((Y_2 $$unsorted) (X_2 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (hAPP int _let_0 (ord_less_eq int) (zero_zero int)))) (let ((_let_3 (member int))) (let ((_let_4 (hAPP int (fun nat int) (power_power int) (hAPP int int (number_number_of int) min_1)))) (or (not (hBOOL (hAPP int bool _let_2 X_2))) (not (hBOOL (hAPP int bool _let_2 Y_2))) (= (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_3 X_2) zEven))) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_3 Y_2) zEven))) (= (hAPP nat int _let_4 (hAPP int nat nat_1 X_2)) (hAPP nat int _let_4 (hAPP int nat nat_1 Y_2))))))))) ) 16.11/16.20 ( (one_one int), s ) 16.11/16.20 ( min_1, (hAPP int int (number_number_of int) pls) ) 16.11/16.20 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.11/16.20 ( s, (one_one int) ) 16.11/16.20 ( s, s ) 16.11/16.20 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.20 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.11/16.20 ( (hAPP int int (number_number_of int) pls), min_1 ) 16.11/16.20 ( (hAPP int int (number_number_of int) pls), (hAPP int int (number_number_of int) pls) ) 16.11/16.20 ( skv_4, skv_4 ) 16.11/16.20 ( skv_4, skv_10 ) 16.11/16.20 ( skv_10, skv_4 ) 16.11/16.20 ) 16.11/16.20 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (one_one real))) (= (= _let_0 (hAPP real real sqrt X_2)) (= _let_0 X_2))) ) 16.11/16.20 ( (one_one real) ) 16.11/16.20 ( (zero_zero real) ) 16.11/16.20 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.20 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.11/16.20 ) 16.11/16.20 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (sums X_a))) (or (not (comm_monoid_add X_a)) (not (topological_space X_a)) (= _let_0 (ti (fun (fun nat X_a) (fun X_a bool)) _let_0)))) ) 16.11/16.20 ( bool ) 16.11/16.20 ( nat ) 16.11/16.20 ( int ) 16.11/16.20 ( (fun int bool) ) 16.11/16.20 ( (fun int int) ) 16.11/16.20 ( (fun nat bool) ) 16.11/16.20 ( (fun nat nat) ) 16.11/16.20 ( (product_prod nat nat) ) 16.11/16.20 ( (fun (product_prod nat nat) bool) ) 16.11/16.20 ( (fun nat (fun (product_prod nat nat) bool)) ) 16.11/16.20 ( real ) 16.11/16.20 ( (fun real real) ) 16.11/16.20 ( rat ) 16.11/16.20 ( (fun nat (fun nat bool)) ) 16.11/16.20 ( complex ) 16.11/16.20 ( (filter nat) ) 16.11/16.20 ( (product_prod int int) ) 16.11/16.20 ( quickcheck_code_int ) 16.11/16.20 ( (fun bool bool) ) 16.11/16.20 ( code_code_numeral ) 16.11/16.20 ( (product_prod real real) ) 16.11/16.20 ( (fun nat (product_prod nat nat)) ) 16.11/16.20 ( (fun nat rat) ) 16.11/16.20 ( (filter real) ) 16.11/16.20 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 16.11/16.20 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 16.11/16.20 ( (fun nat (product_prod int int)) ) 16.11/16.20 ) 16.11/16.20 (instantiation (forall ((X_a $$unsorted) (A_3 $$unsorted)) (= (hBOOL (hAPP (fun X_a bool) bool (finite_finite_1 X_a) A_3)) (not (forall ((N_2 $$unsorted) (F_3 $$unsorted)) (let ((_let_0 (fun nat (fun nat bool)))) (let ((_let_1 (fun X_a bool))) (not (= (ti _let_1 A_3) (hAPP (fun nat bool) _let_1 (hAPP (fun nat X_a) (fun (fun nat bool) _let_1) (image nat X_a) F_3) (hAPP (fun nat bool) (fun nat bool) (collect nat) (hAPP nat (fun nat bool) (hAPP _let_0 _let_0 (combc nat nat bool) (ord_less nat)) N_2))))))) ))) ) 16.11/16.20 ( nat, (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 16.11/16.20 ) 16.11/16.20 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_142403 $$unsorted) (BOUND_VARIABLE_142404 $$unsorted)) (let ((_let_0 (inverse_inverse X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (times_times X_a))) (let ((_let_3 (zero_zero X_a))) (or (not (division_ring X_a)) (= _let_3 (ti X_a BOUND_VARIABLE_142404)) (= _let_3 (ti X_a BOUND_VARIABLE_142403)) (= (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a _let_0 BOUND_VARIABLE_142403)) (hAPP X_a X_a _let_0 BOUND_VARIABLE_142404)) (hAPP X_a X_a _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_142404) BOUND_VARIABLE_142403)))))))) ) 16.11/16.20 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.20 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.11/16.20 ( int, skv_13, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.11/16.20 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.20 ( real, pi, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 16.11/16.20 ( real, (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.20 ( real, (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.20 ( complex, ii, ii ) 16.11/16.20 ( complex, ii, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 16.11/16.20 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.20 ) 16.11/16.20 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_142435 $$unsorted) (BOUND_VARIABLE_142436 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (or (not (preorder X_a)) (= (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_142435) BOUND_VARIABLE_142436)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_142436) BOUND_VARIABLE_142435)))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_142435) BOUND_VARIABLE_142436)))))) ) 16.11/16.20 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.20 ( int, (one_one int), (zero_zero int) ) 16.11/16.20 ( int, (one_one int), t ) 16.11/16.20 ( int, (zero_zero int), (one_one int) ) 16.11/16.20 ( int, (zero_zero int), min_1 ) 16.11/16.20 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.20 ( int, (zero_zero int), s ) 16.11/16.20 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.11/16.20 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 16.11/16.20 ( int, (zero_zero int), skv_4 ) 16.11/16.20 ( int, (zero_zero int), skv_10 ) 16.11/16.20 ( int, pls, (one_one int) ) 16.11/16.20 ( int, pls, pls ) 16.11/16.20 ( int, pls, min_1 ) 16.11/16.20 ( int, pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.11/16.20 ( int, min_1, (zero_zero int) ) 16.11/16.20 ( int, min_1, pls ) 16.11/16.20 ( int, min_1, min_1 ) 16.11/16.20 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 16.11/16.20 ( int, s, (zero_zero int) ) 16.11/16.20 ( int, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.11/16.20 ( int, t, (one_one int) ) 16.11/16.20 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.11/16.20 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 16.11/16.20 ( int, (hAPP int int (number_number_of int) pls), (zero_zero int) ) 16.11/16.20 ( int, skv_4, (zero_zero int) ) 16.11/16.20 ( int, skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.11/16.20 ( int, skv_10, (zero_zero int) ) 16.11/16.20 ( int, skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.11/16.20 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.20 ( real, (zero_zero real), pi ) 16.11/16.20 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.20 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.20 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.20 ( real, (zero_zero real), skv_2 ) 16.11/16.20 ( real, (zero_zero real), skv_3 ) 16.11/16.20 ( real, (zero_zero real), skv_5 ) 16.11/16.20 ( real, (zero_zero real), skv_7 ) 16.11/16.20 ( real, (zero_zero real), skv_8 ) 16.11/16.20 ( real, (zero_zero real), skv_9 ) 16.11/16.20 ( real, (zero_zero real), skv_12 ) 16.11/16.20 ( real, pi, (zero_zero real) ) 16.11/16.20 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.20 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.20 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.11/16.20 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.20 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_5 ) 16.11/16.20 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.11/16.20 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.20 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 16.11/16.20 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.11/16.20 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.11/16.20 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 16.11/16.20 ( real, skv_3, (zero_zero real) ) 16.11/16.20 ( real, skv_5, (zero_zero real) ) 16.11/16.20 ( real, skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.20 ( real, skv_7, (zero_zero real) ) 16.11/16.20 ( real, skv_12, (zero_zero real) ) 16.11/16.20 ) 16.11/16.20 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_142455 $$unsorted)) (or (not (linordered_idom X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_142455)) (zero_zero X_a))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) BOUND_VARIABLE_142455) (zero_zero int))))) ) 16.11/16.20 ( real, (one_one int) ) 16.11/16.20 ( real, (zero_zero int) ) 16.11/16.20 ) 16.11/16.20 (instantiation (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z_1 $$unsorted)) (let ((_let_0 (hAPP int (fun nat int) (power_power int) X_1))) (= (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP nat int _let_0 Y_1)) (hAPP nat int _let_0 Z_1)) (hAPP nat int _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) Y_1) Z_1)))) ) 16.11/16.20 ( s, (one_one nat), (one_one nat) ) 16.11/16.20 ( s1, (one_one nat), (one_one nat) ) 16.11/16.20 ( skv_14, (one_one nat), (one_one nat) ) 16.11/16.20 ) 16.11/16.20 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_142586 $$unsorted) (BOUND_VARIABLE_142587 $$unsorted) (BOUND_VARIABLE_142588 $$unsorted) (BOUND_VARIABLE_142589 $$unsorted) (BOUND_VARIABLE_142590 $$unsorted)) (let ((_let_0 (filter X_a))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun X_a X_b))) (let ((_let_3 (fun X_b _let_1))) (let ((_let_4 (tendsto X_a X_b))) (let ((_let_5 (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_142589))) (or (not (real_normed_vector X_a)) (not (topological_space X_b)) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) BOUND_VARIABLE_142590))) (not (forall ((X $$unsorted)) (or (= (ti X_a X) (ti X_a BOUND_VARIABLE_142589)) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP X_a real (norm_norm X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) X) BOUND_VARIABLE_142589))) BOUND_VARIABLE_142590))) (= (hAPP X_a X_b BOUND_VARIABLE_142587 X) (hAPP X_a X_b BOUND_VARIABLE_142588 X))) )) (not (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (hAPP _let_2 _let_3 _let_4 BOUND_VARIABLE_142588) BOUND_VARIABLE_142586) _let_5))) (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (hAPP _let_2 _let_3 _let_4 BOUND_VARIABLE_142587) BOUND_VARIABLE_142586) _let_5))))))))) ) 16.11/16.20 ( real, real, (zero_zero real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.20 ) 16.11/16.20 (instantiation (forall ((X_2 $$unsorted) (N $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (zero_zero real))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N))) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (hAPP nat (fun real real) root N) X_2)) _let_2)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_2) _let_2))))))) ) 16.11/16.20 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.20 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.20 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.20 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.20 ) 16.11/16.20 (instantiation (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) _let_1) B_1))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) A_2) _let_1)) (hBOOL (hAPP rat bool (hAPP rat (fun rat bool) (ord_less_eq rat) (hAPP int rat (hAPP int (fun int rat) fract A_2) B_1)) (zero_zero rat))))))) ) 16.11/16.20 ( (one_one int), (one_one int) ) 16.11/16.20 ( (zero_zero int), (one_one int) ) 16.11/16.20 ) 16.11/16.20 (instantiation (forall ((M $$unsorted) (Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (let ((_let_2 (hAPP int _let_0 _let_1 (zero_zero int)))) (or (not (hBOOL (hAPP int bool _let_2 X_1))) (not (hBOOL (hAPP int bool _let_2 Y_1))) (not (hBOOL (hAPP int bool _let_2 M))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong X_1) Y_1) M))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 X_1) M))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 Y_1) M))) (= (ti int X_1) (ti int Y_1)))))) ) 16.11/16.20 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.20 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.20 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.20 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s, s1 ) 16.11/16.20 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.20 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_4, s1 ) 16.11/16.20 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_10, s1 ) 16.11/16.20 ) 16.11/16.20 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_142825 $$unsorted)) (or (not (ab_sem1668676832m_mult X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_142825) BOUND_VARIABLE_142825) (ti X_a BOUND_VARIABLE_142825))) ) 16.11/16.20 ( bool, fFalse ) 16.11/16.20 ( bool, fTrue ) 16.11/16.20 ( int, pls ) 16.11/16.20 ( int, min_1 ) 16.11/16.20 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.20 ( int, s ) 16.11/16.20 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.20 ( int, m ) 16.11/16.20 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.11/16.20 ( int, s1 ) 16.11/16.20 ( int, t ) 16.11/16.20 ( (fun int bool), nat_neg ) 16.11/16.20 ( (fun int bool), zprime ) 16.11/16.20 ( (fun int bool), zEven ) 16.11/16.20 ( (fun int bool), zOdd ) 16.11/16.20 ( (fun int bool), (even_odd_even int) ) 16.11/16.20 ( (fun int bool), twoSqu1091635170sum2sq ) 16.11/16.20 ( (fun int bool), nat_is_nat ) 16.11/16.20 ( (fun int (fun int bool)), norRRset ) 16.11/16.20 ( (fun int (fun int bool)), quadRes ) 16.11/16.20 ( (fun int (fun int bool)), sRStar ) 16.11/16.20 ( (fun int (fun int bool)), d22set ) 16.11/16.20 ( (fun int (fun int bool)), sr ) 16.11/16.20 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 16.11/16.20 ( (fun int int), zfact ) 16.11/16.20 ( (fun int int), bit0 ) 16.11/16.20 ( (fun int int), bit1 ) 16.11/16.20 ( (fun int int), (fact_fact int) ) 16.11/16.20 ( (fun int int), pred ) 16.11/16.20 ( (fun int int), succ ) 16.11/16.20 ( (fun nat bool), (even_odd_even nat) ) 16.11/16.20 ( (fun nat bool), prime ) 16.11/16.20 ( (fun nat nat), suc ) 16.11/16.20 ( (fun nat nat), (fact_fact nat) ) 16.11/16.20 ( (fun nat nat), fact ) 16.11/16.20 ( (fun nat nat), nat_size ) 16.11/16.20 ( (fun nat nat), (size_size nat) ) 16.11/16.20 ( (fun (product_prod nat nat) bool), pred_nat ) 16.11/16.20 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 16.11/16.20 ( real, pi ) 16.11/16.20 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.20 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.20 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 16.11/16.20 ( (fun real real), ln ) 16.11/16.20 ( (fun real real), cos ) 16.11/16.20 ( (fun real real), sqrt ) 16.11/16.20 ( (fun real real), sin ) 16.11/16.20 ( (fun real real), arccos ) 16.11/16.20 ( (fun real real), arcsin ) 16.11/16.20 ( (fun real real), tan ) 16.11/16.20 ( (fun real real), arctan ) 16.11/16.20 ( (fun nat (fun nat bool)), coprime ) 16.11/16.20 ( complex, ii ) 16.11/16.20 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.20 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 16.11/16.20 ( (fun nat real), (real_1 nat) ) 16.11/16.20 ( (fun nat real), sin_coeff ) 16.11/16.20 ( (fun nat real), cos_coeff ) 16.11/16.20 ( (filter nat), sequentially ) 16.11/16.20 ( (fun int (fun int int)), (gcd_gcd int) ) 16.11/16.20 ( (fun int (fun int int)), legendre ) 16.11/16.20 ( (fun int (fun int int)), legacy_zgcd ) 16.11/16.20 ( (fun int (fun int int)), standardRes ) 16.11/16.20 ( (fun int (fun int int)), nat_tsub ) 16.11/16.20 ( (fun int (fun int int)), multInv ) 16.11/16.20 ( (fun int (fun int int)), z3mod ) 16.11/16.20 ( (fun int (fun int int)), z3div ) 16.11/16.20 ( (fun int (fun int int)), int_gcd ) 16.11/16.20 ( (fun int (fun int int)), int_lcm ) 16.11/16.20 ( (fun int (fun int int)), inv ) 16.11/16.20 ( (fun complex complex), expi ) 16.11/16.20 ( (fun complex complex), cnj ) 16.11/16.20 ( (fun real complex), cis ) 16.11/16.20 ( (fun int nat), nat_1 ) 16.11/16.20 ( (fun int nat), phi ) 16.11/16.20 ( (fun (fun int bool) bool), nat_nat_set ) 16.11/16.20 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 16.11/16.20 ( (fun nat (fun nat nat)), nat_gcd ) 16.11/16.20 ( (fun nat (fun nat nat)), nat_lcm ) 16.11/16.20 ( (fun (fun int bool) int), (the int) ) 16.11/16.20 ( (fun complex real), re ) 16.11/16.20 ( (fun complex real), im ) 16.11/16.20 ( (fun complex real), arg ) 16.11/16.20 ( (fun bool bool), fNot ) 16.11/16.20 ( (fun nat (fun real real)), root ) 16.11/16.20 ( (fun real (fun real real)), log ) 16.11/16.20 ( (fun real (fun real real)), powr ) 16.11/16.20 ( (fun bool (fun bool bool)), fimplies ) 16.11/16.20 ( (fun bool (fun bool bool)), fconj ) 16.11/16.20 ( (fun bool (fun bool bool)), fdisj ) 16.11/16.20 ( (fun int (fun int (product_prod int int))), negDivAlg ) 16.11/16.20 ( (fun int (fun int (product_prod int int))), posDivAlg ) 16.11/16.20 ( (fun int (fun int (product_prod int int))), divmod_int ) 16.11/16.20 ( (fun int (fun int (product_prod int int))), pdivmod ) 16.11/16.20 ( (fun int (fun int (product_prod int int))), norm_frac ) 16.11/16.20 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 16.11/16.20 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 16.11/16.20 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 16.11/16.20 ( (fun int (fun int (fun int bool))), zcong ) 16.11/16.20 ( (fun int (fun int (fun int bool))), zcongm ) 16.11/16.20 ( (fun int (fun int (fun int bool))), noXRRset ) 16.11/16.20 ( (fun int (fun int (fun int bool))), bnorRset ) 16.11/16.20 ( (fun int (fun int (fun int bool))), wset ) 16.11/16.20 ( (fun (product_prod int int) bool), frac_1 ) 16.11/16.20 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 16.11/16.20 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 16.11/16.20 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 16.11/16.20 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 16.11/16.20 ( (fun (fun nat rat) bool), vanishes ) 16.11/16.20 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 16.11/16.20 ( (fun code_code_numeral nat), code_c271388182l_size ) 16.11/16.20 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 16.11/16.20 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 16.11/16.20 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 16.11/16.20 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 16.11/16.20 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 16.11/16.20 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 16.11/16.20 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 16.11/16.20 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 16.11/16.20 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 16.11/16.20 ( (fun complex nat), complex_size ) 16.11/16.20 ( (fun complex nat), (size_size complex) ) 16.11/16.20 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 16.11/16.20 ( (fun nat (fun nat (product_prod int int))), bezw ) 16.11/16.20 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 16.11/16.20 ( (fun int (fun nat nat)), nat_aux ) 16.11/16.20 ( (fun int (fun (fun int bool) bool)), rsetR ) 16.11/16.20 ( (fun int (fun (fun int bool) bool)), resSet ) 16.11/16.20 ( (fun int (list int)), quickc666637781d_zero ) 16.11/16.20 ( (fun (product_prod int int) rat), frct ) 16.11/16.20 ( (fun int (fun int rat)), fract ) 16.11/16.20 ( (fun real (fun real complex)), complex_1 ) 16.11/16.20 ( (fun real (fun real complex)), rcis ) 16.11/16.20 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 16.11/16.20 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 16.11/16.20 ( (fun int real), (real_1 int) ) 16.11/16.20 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 16.11/16.20 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 16.11/16.20 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 16.11/16.20 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 16.11/16.20 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 16.11/16.20 ( (fun real nat), natfloor ) 16.11/16.20 ( (fun real nat), natceiling ) 16.11/16.20 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 16.11/16.20 ( (fun quickcheck_code_int int), quickcheck_int_of ) 16.11/16.20 ( (fun rat (product_prod int int)), quotient_of ) 16.11/16.20 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 16.11/16.20 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 16.11/16.20 ( (fun rat real), ratreal ) 16.11/16.20 ( (fun code_code_numeral int), code_int_of ) 16.11/16.20 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 16.11/16.20 ( (fun int quickcheck_code_int), quickcheck_of_int ) 16.11/16.20 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 16.11/16.20 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 16.11/16.20 ) 16.11/16.20 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (uminus_uminus real))) (= (hAPP real real _let_0 (hAPP real real sin X_1)) (hAPP real real sin (hAPP real real _let_0 X_1)))) ) 16.11/16.20 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.20 ) 16.11/16.20 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (trivial_limit X_a))) (= _let_0 (ti (fun (filter X_a) bool) _let_0))) ) 16.11/16.20 ( nat ) 16.11/16.20 ( real ) 16.11/16.20 ) 16.11/16.20 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_142888 $$unsorted)) (or (not (real_vector X_a)) (= (hAPP X_a X_a (hAPP real (fun X_a X_a) (scaleR_scaleR X_a) (hAPP int real (number_number_of real) min_1)) BOUND_VARIABLE_142888) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_142888))) ) 16.11/16.20 ( int, (one_one int) ) 16.11/16.20 ( int, pls ) 16.11/16.20 ( int, min_1 ) 16.11/16.20 ( real, (one_one real) ) 16.11/16.20 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.20 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.11/16.20 ( complex, (one_one complex) ) 16.11/16.20 ( complex, ii ) 16.11/16.20 ) 16.11/16.20 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_142916 $$unsorted) (BOUND_VARIABLE_142917 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (uminus_uminus X_a))) (or (not (boolean_algebra X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_142916)) BOUND_VARIABLE_142917))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_142917)) BOUND_VARIABLE_142916)))))) ) 16.11/16.20 ( int, (one_one int), pls ) 16.11/16.20 ( int, (one_one int), min_1 ) 16.11/16.20 ( int, pls, (one_one int) ) 16.11/16.20 ( int, pls, min_1 ) 16.11/16.20 ( int, pls, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.20 ( int, pls, s ) 16.11/16.20 ( int, pls, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.11/16.20 ( int, pls, (hAPP int int (number_number_of int) pls) ) 16.11/16.20 ( int, pls, skv_4 ) 16.11/16.20 ( int, pls, skv_10 ) 16.11/16.20 ( int, min_1, (one_one int) ) 16.11/16.20 ( int, min_1, pls ) 16.11/16.20 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), pls ) 16.11/16.20 ( int, s, pls ) 16.11/16.20 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), pls ) 16.11/16.20 ( int, (hAPP int int (number_number_of int) pls), pls ) 16.11/16.20 ( int, skv_4, pls ) 16.11/16.20 ( int, skv_10, pls ) 16.11/16.20 ) 16.11/16.20 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_143011 $$unsorted) (BOUND_VARIABLE_143012 $$unsorted) (BOUND_VARIABLE_143013 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_143012))) (or (not (comm_semiring_1 X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_143013))) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_143013) BOUND_VARIABLE_143011))))) ) 16.11/16.20 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.11/16.20 ) 16.11/16.20 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))) (or (not (hBOOL (hAPP int bool (even_odd_even int) X_1))) (= (hAPP int int (hAPP int _let_0 (times_times int) _let_1) (hAPP int int (hAPP int _let_0 (div_div int) X_1) _let_1)) (ti int X_1))))) ) 16.11/16.20 ( (one_one int) ) 16.11/16.20 ( (zero_zero int) ) 16.11/16.20 ( pls ) 16.11/16.20 ( min_1 ) 16.11/16.20 ( s ) 16.11/16.20 ( m ) 16.11/16.20 ( s1 ) 16.11/16.20 ( t ) 16.11/16.20 ) 16.11/16.20 (instantiation (forall ((W $$unsorted)) (= (hAPP int complex (number_number_of complex) W) (hAPP int complex (ring_1_of_int complex) W)) ) 16.11/16.20 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.11/16.20 ( min_1 ) 16.11/16.20 ) 16.11/16.20 (instantiation (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 (hAPP real real (uminus_uminus real) pi)) Y_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Y_1) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 X_1) (zero_zero real)))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real cos Y_1)) (hAPP real real cos X_1))))))) ) 16.11/16.20 ( skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.20 ) 16.11/16.20 (instantiation (forall ((X_2 $$unsorted) (N $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member int))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N))) (= (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 X_2) zOdd)) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP nat int (hAPP int (fun nat int) (power_power int) X_2) N)) zOdd))))))) ) 16.11/16.20 ( s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.20 ( s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.20 ( skv_14, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.20 ) 16.11/16.20 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_1 (hAPP real (fun real real) (plus_plus real) (one_one real)))) (= (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) _let_0)) (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) X_1) (hAPP real real _let_1 (hAPP real real sqrt (hAPP real real _let_1 (hAPP nat real (hAPP real (fun nat real) (power_power real) X_1) (hAPP int nat (number_number_of nat) _let_0)))))))) (hAPP real real arctan X_1)))) ) 16.11/16.20 ( (one_one real) ) 16.11/16.20 ( pi ) 16.11/16.20 ( (hAPP int real (number_number_of real) min_1) ) 16.11/16.20 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.20 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.11/16.20 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.11/16.20 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.20 ) 16.11/16.20 (instantiation (forall ((X_a $$unsorted)) (or (not (linordered_idom X_a)) (not (number_ring X_a)) (= (hAPP X_a X_a (abs_abs X_a) (hAPP int X_a (number_number_of X_a) min_1)) (one_one X_a))) ) 16.11/16.20 ( nat ) 16.11/16.20 ( int ) 16.11/16.20 ( real ) 16.11/16.20 ( rat ) 16.11/16.20 ( complex ) 16.11/16.20 ( quickcheck_code_int ) 16.11/16.20 ( code_code_numeral ) 16.11/16.20 ) 16.11/16.20 (instantiation (forall ((Z_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (dvd_dvd int) Z_1) N_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (zero_zero int)) N_1))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) Z_1) N_1)))) ) 16.11/16.20 ( (one_one int), t ) 16.11/16.20 ( (zero_zero int), (one_one int) ) 16.11/16.20 ( (zero_zero int), min_1 ) 16.11/16.20 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.20 ( (zero_zero int), s ) 16.11/16.20 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.11/16.20 ( (zero_zero int), (hAPP int int (number_number_of int) pls) ) 16.11/16.20 ( (zero_zero int), skv_4 ) 16.11/16.20 ( (zero_zero int), skv_10 ) 16.11/16.20 ( min_1, pls ) 16.11/16.20 ( min_1, min_1 ) 16.11/16.20 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 16.11/16.20 ) 16.11/16.20 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_143296 $$unsorted)) (let ((_let_0 (norm_norm X_a))) (or (not (real_normed_vector X_a)) (= (hAPP X_a real _let_0 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_143296)) (hAPP X_a real _let_0 BOUND_VARIABLE_143296)))) ) 16.11/16.20 ( int, (one_one int) ) 16.11/16.20 ( int, pls ) 16.11/16.20 ( int, min_1 ) 16.11/16.20 ( real, (one_one real) ) 16.11/16.20 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.20 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.11/16.20 ( complex, (one_one complex) ) 16.11/16.20 ( complex, ii ) 16.11/16.20 ) 16.11/16.20 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_143332 $$unsorted) (BOUND_VARIABLE_143333 $$unsorted)) (let ((_let_0 (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_143332))) (or (not (monoid_mult X_a)) (= (hAPP nat X_a _let_0 (hAPP nat nat suc BOUND_VARIABLE_143333)) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) (hAPP nat X_a _let_0 BOUND_VARIABLE_143333)) BOUND_VARIABLE_143332)))) ) 16.11/16.20 ( int, s, (hAPP nat nat suc (zero_zero nat)) ) 16.11/16.20 ( int, s1, (hAPP nat nat suc (zero_zero nat)) ) 16.11/16.20 ( int, skv_14, (hAPP nat nat suc (zero_zero nat)) ) 16.11/16.20 ( complex, ii, (hAPP nat nat suc (zero_zero nat)) ) 16.11/16.20 ) 16.11/16.20 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_143351 $$unsorted)) (let ((_let_0 (uminus_uminus X_a))) (or (not (comm_ring_1 X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) (hAPP X_a X_a _let_0 (one_one X_a))) BOUND_VARIABLE_143351) (hAPP X_a X_a _let_0 BOUND_VARIABLE_143351)))) ) 16.11/16.20 ( int, (one_one int) ) 16.11/16.20 ( int, pls ) 16.11/16.20 ( int, min_1 ) 16.11/16.20 ( real, (one_one real) ) 16.11/16.20 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.20 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.11/16.20 ( complex, (one_one complex) ) 16.11/16.20 ( complex, ii ) 16.11/16.20 ) 16.11/16.20 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_143371 $$unsorted) (BOUND_VARIABLE_143372 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (ring_11004092258visors X_a)) (= _let_0 (ti X_a BOUND_VARIABLE_143372)) (not (= _let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_143372) BOUND_VARIABLE_143371))))) ) 16.11/16.20 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 16.11/16.20 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 16.11/16.20 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_14 ) 16.11/16.20 ( complex, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), ii ) 16.11/16.20 ) 16.11/16.20 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))))) (let ((_let_1 (fun nat nat))) (or (hBOOL (hAPP nat bool (even_odd_even nat) X_1)) (= X_1 (hAPP nat nat suc (hAPP nat nat (hAPP nat _let_1 (times_times nat) _let_0) (hAPP nat nat (hAPP nat _let_1 (div_div nat) X_1) _let_0))))))) ) 16.11/16.20 ( (zero_zero nat) ) 16.11/16.20 ( (one_one nat) ) 16.11/16.20 ) 16.11/16.20 (instantiation (forall ((N_1 $$unsorted)) (= (hAPP int real (real_1 int) (hAPP nat int (semiring_1_of_nat int) N_1)) (hAPP nat real (real_1 nat) N_1)) ) 16.11/16.20 ( (zero_zero nat) ) 16.11/16.20 ( (hAPP nat nat suc (zero_zero nat)) ) 16.11/16.20 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.11/16.20 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.20 ) 16.11/16.20 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_143401 $$unsorted) (BOUND_VARIABLE_143402 $$unsorted) (BOUND_VARIABLE_143403 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_143401))) (or (not (cancel_semigroup_add X_a)) (not (= (hAPP X_a X_a _let_0 BOUND_VARIABLE_143403) (hAPP X_a X_a _let_0 BOUND_VARIABLE_143402))) (= (ti X_a BOUND_VARIABLE_143402) (ti X_a BOUND_VARIABLE_143403)))) ) 16.11/16.20 ( nat, (one_one nat), (one_one nat), (one_one nat) ) 16.11/16.20 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int), (one_one int) ) 16.11/16.20 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int), (one_one int) ) 16.11/16.20 ) 16.11/16.20 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fact_fact nat))) (let ((_let_1 (hAPP nat nat suc X_1))) (= (hAPP nat nat (hAPP nat (fun nat nat) (times_times nat) _let_1) (hAPP nat nat _let_0 X_1)) (hAPP nat nat _let_0 _let_1)))) ) 16.11/16.20 ( (zero_zero nat) ) 16.11/16.20 ( (hAPP nat nat suc (zero_zero nat)) ) 16.11/16.20 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 16.11/16.20 ) 16.11/16.20 (instantiation (forall ((X_a $$unsorted) (A_2 $$unsorted) (P_1 $$unsorted) (BOUND_VARIABLE_143474 $$unsorted)) (or (not (hBOOL (hAPP X_a bool P_1 A_2))) (= (hAPP (fun X_a bool) X_a (hilbert_Eps X_a) P_1) (ti X_a A_2)) (not (hBOOL (hAPP X_a bool P_1 BOUND_VARIABLE_143474))) (not (forall ((Y $$unsorted)) (or (not (hBOOL (hAPP X_a bool P_1 Y))) (= (ti X_a Y) (ti X_a BOUND_VARIABLE_143474))) ))) ) 16.11/16.20 ( nat, (zero_zero nat), (even_odd_even nat), (zero_zero nat) ) 16.11/16.20 ( nat, (zero_zero nat), prime, (zero_zero nat) ) 16.11/16.20 ( nat, (hAPP nat nat suc (zero_zero nat)), prime, (hAPP nat nat suc (zero_zero nat)) ) 16.11/16.20 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.20 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), prime, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.20 ( nat, (one_one nat), (even_odd_even nat), (one_one nat) ) 16.11/16.20 ( int, (one_one int), nat_neg, (one_one int) ) 16.11/16.20 ( int, (one_one int), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (one_one int) ) 16.11/16.20 ( int, (one_one int), (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (one_one int) ) 16.11/16.20 ( int, (one_one int), (even_odd_even int), (one_one int) ) 16.11/16.20 ( int, (one_one int), nat_is_nat, (one_one int) ) 16.11/16.20 ( int, (zero_zero int), (even_odd_even int), (zero_zero int) ) 16.11/16.20 ( int, (zero_zero int), nat_is_nat, (zero_zero int) ) 16.11/16.20 ( int, pls, (hAPP int (fun int bool) (ord_less int) pls), pls ) 16.11/16.20 ( int, pls, (hAPP int (fun int bool) (ord_less int) min_1), pls ) 16.11/16.20 ( int, pls, (hAPP int (fun int bool) (ord_less_eq int) min_1), pls ) 16.11/16.20 ( int, min_1, (hAPP int (fun int bool) (ord_less int) pls), min_1 ) 16.11/16.20 ( int, min_1, (hAPP int (fun int bool) (ord_less_eq int) pls), min_1 ) 16.11/16.20 ( int, min_1, (hAPP int (fun int bool) (ord_less int) min_1), min_1 ) 16.11/16.20 ( int, min_1, (hAPP int (fun int bool) (ord_less_eq int) min_1), min_1 ) 16.11/16.20 ( int, (hAPP int int (number_number_of int) min_1), nat_neg, (hAPP int int (number_number_of int) min_1) ) 16.11/16.20 ( int, (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int (fun int bool) quadRes (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int int (number_number_of int) min_1) ) 16.11/16.20 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.20 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), zprime, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.20 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.21 ( int, s, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), s ) 16.11/16.21 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.11/16.21 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), zprime, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.11/16.21 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int (fun int bool) (ord_less int) s), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.11/16.21 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) s)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.11/16.21 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (let ((_let_3 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int _let_1 _let_2 s) _let_3)) (hAPP nat int (hAPP int _let_1 _let_2 s1) _let_3)))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.11/16.21 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.11/16.21 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int (fun int bool) (ord_less int) t), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.11/16.21 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.11/16.21 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_4)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.11/16.21 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int (fun int bool) (ord_less int) skv_4), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.11/16.21 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int (fun int bool) (ord_less int) skv_10), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.11/16.21 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_10)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.11/16.21 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.11/16.21 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 16.11/16.21 ( int, t, (hAPP int (fun int bool) (ord_less_eq int) (one_one int)), t ) 16.11/16.21 ( int, t, (hAPP int (fun int bool) (ord_less int) (one_one int)), t ) 16.11/16.21 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) t))), twoSqu1091635170sum2sq, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) t))) ) 16.11/16.21 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.11/16.21 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.11/16.21 ( int, (hAPP int int (number_number_of int) pls), nat_neg, (hAPP int int (number_number_of int) pls) ) 16.11/16.21 ( int, (hAPP int int (number_number_of int) pls), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) pls) ) 16.11/16.21 ( int, skv_4, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_4 ) 16.11/16.21 ( int, skv_10, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_10 ) 16.11/16.21 ( (fun int bool), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP (fun int nat) (fun (fun int bool) bool) (nat_tr1645093318rphism int nat) nat_1), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 16.11/16.21 ( (fun int bool), zEven, (hAPP int (fun (fun int bool) bool) (member int) (one_one int)), zEven ) 16.11/16.21 ( (fun nat bool), (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)), (finite_finite_1 nat), (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 16.11/16.21 ( (fun nat bool), (hAPP bool (fun nat bool) (combk bool nat) fTrue), (hAPP (fun nat int) (fun (fun nat bool) bool) (nat_tr1645093318rphism nat int) (semiring_1_of_nat int)), (hAPP bool (fun nat bool) (combk bool nat) fTrue) ) 16.11/16.21 ( real, (one_one real), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 (fun real bool) (sums real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (hAPP real _let_1 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc)))), (one_one real) ) 16.11/16.21 ( real, (zero_zero real), (hAPP real (fun real bool) (ord_less real) (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))), (zero_zero real) ) 16.11/16.21 ( real, (zero_zero real), (hAPP real (fun real bool) (ord_less real) pi), (zero_zero real) ) 16.11/16.21 ( real, (zero_zero real), (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 16.11/16.21 ( real, (zero_zero real), (hAPP real (fun real bool) (ord_less real) (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 16.11/16.21 ( real, pi, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), pi ) 16.11/16.21 ( real, pi, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), pi ) 16.11/16.21 ( real, pi, (hAPP real (fun real bool) (ord_less real) (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi))), pi ) 16.11/16.21 ( real, pi, (hAPP real (fun real bool) (ord_less_eq real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 16.11/16.21 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.21 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real (fun real bool) (ord_less real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.21 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real (fun real bool) (ord_less_eq real) skv_5), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.21 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.21 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real (fun real bool) (ord_less real) (zero_zero real)), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.21 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real (fun real bool) (ord_less real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.21 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.21 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real (fun real bool) (ord_less real) (zero_zero real)), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.21 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real (fun real bool) (ord_less real) (one_one real)), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.21 ( real, skv_2, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_2 ) 16.11/16.21 ( real, skv_3, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_3 ) 16.11/16.21 ( real, skv_5, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_5 ) 16.11/16.21 ( real, skv_7, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_7 ) 16.11/16.21 ( real, skv_8, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_8 ) 16.11/16.21 ( real, skv_9, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_9 ) 16.11/16.21 ( real, skv_12, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_12 ) 16.11/16.21 ( (filter nat), sequentially, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun (filter nat) bool))) (hAPP real _let_2 (hAPP _let_1 (fun real _let_2) (tendsto nat real) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))) (zero_zero real))))), sequentially ) 16.11/16.21 ( (filter nat), sequentially, (trivial_limit nat), sequentially ) 16.11/16.21 ( (filter real), (hAPP real (filter real) (at real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (filter real) bool))) (hAPP real _let_2 (hAPP _let_0 (fun real _let_2) (tendsto real real) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin)) (zero_zero real))))), (hAPP real (filter real) (at real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.11/16.21 ) 16.11/16.21 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_143496 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (plus_plus X_a))) (let ((_let_2 (one_one X_a))) (or (not (comm_semiring_1 X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_143496) BOUND_VARIABLE_143496) (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 _let_2) _let_2)) BOUND_VARIABLE_143496)))))) ) 16.11/16.21 ( nat, (one_one nat) ) 16.11/16.21 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 16.11/16.21 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.21 ) 16.11/16.21 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_143539 $$unsorted) (BOUND_VARIABLE_143540 $$unsorted) (BOUND_VARIABLE_143541 $$unsorted)) (let ((_let_0 (filter X_a))) (let ((_let_1 (fun _let_0 bool))) (or (not (real_normed_vector X_a)) (not (real_normed_vector X_b)) (= (forall ((R_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) R_2))) (not (forall ((S_1 $$unsorted)) (or (not (forall ((X $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP X_a real (norm_norm X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) X) BOUND_VARIABLE_143541))) S_1))) (= (ti X_a X) (ti X_a BOUND_VARIABLE_143541)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP X_b real (norm_norm X_b) (hAPP X_b X_b (hAPP X_b (fun X_b X_b) (minus_minus X_b) (hAPP X_a X_b BOUND_VARIABLE_143539 X)) BOUND_VARIABLE_143540))) R_2))))) )) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) S_1)))) ))) ) (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (hAPP (fun X_a X_b) (fun X_b _let_1) (tendsto X_a X_b) BOUND_VARIABLE_143539) BOUND_VARIABLE_143540) (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_143541))))))) ) 16.11/16.21 ( real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.21 ) 16.11/16.21 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_143582 $$unsorted)) (or (not (semiring_1 X_a)) (= (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_143582)) (hBOOL (hAPP X_a bool (iszero X_a) BOUND_VARIABLE_143582)))) ) 16.11/16.21 ( bool, fFalse ) 16.11/16.21 ( bool, fTrue ) 16.11/16.21 ( int, pls ) 16.11/16.21 ( int, min_1 ) 16.11/16.21 ( int, s ) 16.11/16.21 ( int, m ) 16.11/16.21 ( int, s1 ) 16.11/16.21 ( int, t ) 16.11/16.21 ( (fun int bool), nat_neg ) 16.11/16.21 ( (fun int bool), zprime ) 16.11/16.21 ( (fun int bool), zEven ) 16.11/16.21 ( (fun int bool), zOdd ) 16.11/16.21 ( (fun int bool), (even_odd_even int) ) 16.11/16.21 ( (fun int bool), twoSqu1091635170sum2sq ) 16.11/16.21 ( (fun int bool), nat_is_nat ) 16.11/16.21 ( (fun int (fun int bool)), norRRset ) 16.11/16.21 ( (fun int (fun int bool)), quadRes ) 16.11/16.21 ( (fun int (fun int bool)), sRStar ) 16.11/16.21 ( (fun int (fun int bool)), d22set ) 16.11/16.21 ( (fun int (fun int bool)), sr ) 16.11/16.21 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 16.11/16.21 ( (fun int int), zfact ) 16.11/16.21 ( (fun int int), bit0 ) 16.11/16.21 ( (fun int int), bit1 ) 16.11/16.21 ( (fun int int), (fact_fact int) ) 16.11/16.21 ( (fun int int), pred ) 16.11/16.21 ( (fun int int), succ ) 16.11/16.21 ( (fun nat bool), (even_odd_even nat) ) 16.11/16.21 ( (fun nat bool), prime ) 16.11/16.21 ( (fun nat nat), suc ) 16.11/16.21 ( (fun nat nat), (fact_fact nat) ) 16.11/16.21 ( (fun nat nat), fact ) 16.11/16.21 ( (fun nat nat), nat_size ) 16.11/16.21 ( (fun nat nat), (size_size nat) ) 16.11/16.21 ( (fun (product_prod nat nat) bool), pred_nat ) 16.11/16.21 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 16.11/16.21 ( real, pi ) 16.11/16.21 ( (fun real real), ln ) 16.11/16.21 ( (fun real real), cos ) 16.11/16.21 ( (fun real real), sqrt ) 16.11/16.21 ( (fun real real), sin ) 16.11/16.21 ( (fun real real), arccos ) 16.11/16.21 ( (fun real real), arcsin ) 16.11/16.21 ( (fun real real), tan ) 16.11/16.21 ( (fun real real), arctan ) 16.11/16.21 ( (fun nat (fun nat bool)), coprime ) 16.11/16.21 ( complex, ii ) 16.11/16.21 ( (fun nat real), (real_1 nat) ) 16.11/16.21 ( (fun nat real), sin_coeff ) 16.11/16.21 ( (fun nat real), cos_coeff ) 16.11/16.21 ( (filter nat), sequentially ) 16.11/16.21 ( (fun int (fun int int)), (gcd_gcd int) ) 16.11/16.21 ( (fun int (fun int int)), legendre ) 16.11/16.21 ( (fun int (fun int int)), legacy_zgcd ) 16.11/16.21 ( (fun int (fun int int)), standardRes ) 16.11/16.21 ( (fun int (fun int int)), nat_tsub ) 16.11/16.21 ( (fun int (fun int int)), multInv ) 16.11/16.21 ( (fun int (fun int int)), z3mod ) 16.11/16.21 ( (fun int (fun int int)), z3div ) 16.11/16.21 ( (fun int (fun int int)), int_gcd ) 16.11/16.21 ( (fun int (fun int int)), int_lcm ) 16.11/16.21 ( (fun int (fun int int)), inv ) 16.11/16.21 ( (fun complex complex), expi ) 16.11/16.21 ( (fun complex complex), cnj ) 16.11/16.21 ( (fun real complex), cis ) 16.11/16.21 ( (fun int nat), nat_1 ) 16.11/16.21 ( (fun int nat), phi ) 16.11/16.21 ( (fun (fun int bool) bool), nat_nat_set ) 16.11/16.21 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 16.11/16.21 ( (fun nat (fun nat nat)), nat_gcd ) 16.11/16.21 ( (fun nat (fun nat nat)), nat_lcm ) 16.11/16.21 ( (fun (fun int bool) int), (the int) ) 16.11/16.21 ( (fun complex real), re ) 16.11/16.21 ( (fun complex real), im ) 16.11/16.21 ( (fun complex real), arg ) 16.11/16.21 ( (fun bool bool), fNot ) 16.11/16.21 ( (fun nat (fun real real)), root ) 16.11/16.21 ( (fun real (fun real real)), log ) 16.11/16.21 ( (fun real (fun real real)), powr ) 16.11/16.21 ( (fun bool (fun bool bool)), fimplies ) 16.11/16.21 ( (fun bool (fun bool bool)), fconj ) 16.11/16.21 ( (fun bool (fun bool bool)), fdisj ) 16.11/16.21 ( (fun int (fun int (product_prod int int))), negDivAlg ) 16.11/16.21 ( (fun int (fun int (product_prod int int))), posDivAlg ) 16.11/16.21 ( (fun int (fun int (product_prod int int))), divmod_int ) 16.11/16.21 ( (fun int (fun int (product_prod int int))), pdivmod ) 16.11/16.21 ( (fun int (fun int (product_prod int int))), norm_frac ) 16.11/16.21 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 16.11/16.21 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 16.11/16.21 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 16.11/16.21 ( (fun int (fun int (fun int bool))), zcong ) 16.11/16.21 ( (fun int (fun int (fun int bool))), zcongm ) 16.11/16.21 ( (fun int (fun int (fun int bool))), noXRRset ) 16.11/16.21 ( (fun int (fun int (fun int bool))), bnorRset ) 16.11/16.21 ( (fun int (fun int (fun int bool))), wset ) 16.11/16.21 ( (fun (product_prod int int) bool), frac_1 ) 16.11/16.21 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 16.11/16.21 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 16.11/16.21 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 16.11/16.21 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 16.11/16.21 ( (fun (fun nat rat) bool), vanishes ) 16.11/16.21 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 16.11/16.21 ( (fun code_code_numeral nat), code_c271388182l_size ) 16.11/16.21 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 16.11/16.21 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 16.11/16.21 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 16.11/16.21 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 16.11/16.21 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 16.11/16.21 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 16.11/16.21 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 16.11/16.21 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 16.11/16.21 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 16.11/16.21 ( (fun complex nat), complex_size ) 16.11/16.21 ( (fun complex nat), (size_size complex) ) 16.11/16.21 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 16.11/16.21 ( (fun nat (fun nat (product_prod int int))), bezw ) 16.11/16.21 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 16.11/16.21 ( (fun int (fun nat nat)), nat_aux ) 16.11/16.21 ( (fun int (fun (fun int bool) bool)), rsetR ) 16.11/16.21 ( (fun int (fun (fun int bool) bool)), resSet ) 16.11/16.21 ( (fun int (list int)), quickc666637781d_zero ) 16.11/16.21 ( (fun (product_prod int int) rat), frct ) 16.11/16.21 ( (fun int (fun int rat)), fract ) 16.11/16.21 ( (fun real (fun real complex)), complex_1 ) 16.11/16.21 ( (fun real (fun real complex)), rcis ) 16.11/16.21 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 16.11/16.21 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 16.11/16.21 ( (fun int real), (real_1 int) ) 16.11/16.21 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 16.11/16.21 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 16.11/16.21 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 16.11/16.21 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 16.11/16.21 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 16.11/16.21 ( (fun real nat), natfloor ) 16.11/16.21 ( (fun real nat), natceiling ) 16.11/16.21 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 16.11/16.21 ( (fun quickcheck_code_int int), quickcheck_int_of ) 16.11/16.21 ( (fun rat (product_prod int int)), quotient_of ) 16.11/16.21 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 16.11/16.21 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 16.11/16.21 ( (fun rat real), ratreal ) 16.11/16.21 ( (fun code_code_numeral int), code_int_of ) 16.11/16.21 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 16.11/16.21 ( (fun int quickcheck_code_int), quickcheck_of_int ) 16.11/16.21 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 16.11/16.21 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 16.11/16.21 ) 16.11/16.21 (instantiation (forall ((X_a $$unsorted)) (or (not (semiring_1 X_a)) (not (hBOOL (hAPP X_a bool (iszero X_a) (one_one X_a))))) ) 16.11/16.21 ( nat ) 16.11/16.21 ( int ) 16.11/16.21 ( real ) 16.11/16.21 ( rat ) 16.11/16.21 ( complex ) 16.11/16.21 ( quickcheck_code_int ) 16.11/16.21 ( code_code_numeral ) 16.11/16.21 ) 16.11/16.21 (instantiation (forall ((N $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat nat))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun nat real))) (let ((_let_5 (power_power real))) (let ((_let_6 (fun nat _let_1))) (let ((_let_7 (fun nat _let_2))) (let ((_let_8 (fun _let_4 _let_4))) (let ((_let_9 (combs nat real real))) (let ((_let_10 (fun real _let_2))) (let ((_let_11 (fun _let_4 _let_7))) (let ((_let_12 (combb real _let_2 nat))) (let ((_let_13 (fun _let_1 _let_4))) (let ((_let_14 (combb nat real nat))) (let ((_let_15 (fun nat _let_10))) (= (one_one real) (hAPP _let_0 real (hAPP _let_4 (fun _let_0 real) (big_co1399186613setsum nat real) (hAPP _let_4 _let_4 (hAPP _let_7 _let_8 _let_9 (hAPP _let_4 _let_7 (hAPP _let_10 _let_11 _let_12 (times_times real)) (hAPP real _let_4 (hAPP _let_7 (fun real _let_4) (combc nat real real) (hAPP _let_4 _let_7 (hAPP _let_15 _let_11 (combs nat real _let_2) (hAPP _let_0 _let_15 (hAPP (fun bool _let_10) (fun _let_0 _let_15) (combb bool _let_10 nat) (if real)) (even_odd_even nat))) (hAPP _let_4 _let_4 (hAPP _let_7 _let_8 _let_9 (hAPP _let_4 _let_7 (hAPP _let_10 _let_11 _let_12 (inverse_divide real)) (hAPP _let_1 _let_4 (hAPP _let_4 _let_13 _let_14 (hAPP real _let_4 _let_5 (hAPP int real (number_number_of real) min_1))) (hAPP nat _let_1 (hAPP _let_6 _let_6 (combc nat nat nat) (div_div nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) (hAPP _let_1 _let_4 (hAPP _let_4 _let_13 _let_14 (real_1 nat)) (fact_fact nat))))) _let_3))) (hAPP real _let_4 _let_5 _let_3))) (hAPP nat _let_0 (hAPP nat (fun nat _let_0) (ord_atLeastLessThan nat) (zero_zero nat)) (hAPP nat nat suc N)))))))))))))))))))) ) 16.11/16.21 ( (zero_zero nat) ) 16.11/16.21 ( (hAPP nat nat suc (zero_zero nat)) ) 16.11/16.21 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 16.11/16.21 ) 16.11/16.21 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_143657 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_143657) (hAPP int X_a (number_number_of X_a) min_1))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP X_a int (archimedean_ceiling X_a) BOUND_VARIABLE_143657)) (zero_zero int))))) ) 16.11/16.21 ( int, (one_one int) ) 16.11/16.21 ( int, (zero_zero int) ) 16.11/16.21 ( int, min_1 ) 16.11/16.21 ( real, (zero_zero real) ) 16.11/16.21 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.21 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.21 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.21 ( real, skv_5 ) 16.11/16.21 ) 16.11/16.21 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_0 (semiring_1_of_nat int))) (= (= (hAPP nat int _let_0 Y_2) (hAPP nat int _let_0 X_2)) (= X_2 Y_2))) ) 16.11/16.21 ( (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 16.11/16.21 ( (hAPP nat nat suc (zero_zero nat)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.21 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.11/16.21 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 16.11/16.21 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP nat nat suc (zero_zero nat)) ) 16.11/16.21 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.21 ) 16.11/16.21 (instantiation (forall ((N_1 $$unsorted)) (= (hAPP complex real re (hAPP nat complex (semiring_1_of_nat complex) N_1)) (hAPP nat real (semiring_1_of_nat real) N_1)) ) 16.11/16.21 ( (zero_zero nat) ) 16.11/16.21 ( (hAPP nat nat suc (zero_zero nat)) ) 16.11/16.21 ) 16.11/16.21 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (BOUND_VARIABLE_143809 $$unsorted) (BOUND_VARIABLE_143810 $$unsorted) (BOUND_VARIABLE_143811 $$unsorted) (BOUND_VARIABLE_143812 $$unsorted)) (let ((_let_0 (fun X_b bool))) (or (not (order X_b)) (not (order X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_143811) BOUND_VARIABLE_143812))) (not (hBOOL (hAPP X_b bool (hAPP X_b _let_0 (ord_less_eq X_b) (hAPP X_a X_b BOUND_VARIABLE_143809 BOUND_VARIABLE_143812)) BOUND_VARIABLE_143810))) (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) X) Y))) (hBOOL (hAPP X_b bool (hAPP X_b _let_0 (ord_less X_b) (hAPP X_a X_b BOUND_VARIABLE_143809 X)) (hAPP X_a X_b BOUND_VARIABLE_143809 Y)))) )) (hBOOL (hAPP X_b bool (hAPP X_b _let_0 (ord_less X_b) (hAPP X_a X_b BOUND_VARIABLE_143809 BOUND_VARIABLE_143811)) BOUND_VARIABLE_143810)))) ) 16.11/16.21 ( int, int, bit1, pls, pls, min_1 ) 16.11/16.21 ( int, int, (number_number_of int), s, pls, pls ) 16.11/16.21 ( int, int, (uminus_uminus int), min_1, pls, (one_one int) ) 16.11/16.21 ( int, int, succ, (one_one int), min_1, min_1 ) 16.11/16.21 ( int, int, (hAPP int (fun int int) legendre (hAPP int int (number_number_of int) min_1)), t, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.11/16.21 ( int, real, (real_1 int), pi, min_1, pls ) 16.11/16.21 ( real, real, cos, skv_12, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.21 ( real, real, (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.21 ( real, real, tan, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 16.11/16.21 ( real, real, tan, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi, (zero_zero real) ) 16.11/16.21 ( real, real, tan, skv_3, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 16.11/16.21 ( real, real, tan, skv_5, (zero_zero real), pi ) 16.11/16.21 ( real, real, tan, skv_7, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.11/16.21 ) 16.11/16.21 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_143860 $$unsorted) (BOUND_VARIABLE_143861 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (inverse_inverse X_a))) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_143860)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_143861)))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_143860))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_143861) BOUND_VARIABLE_143860)))))) ) 16.11/16.21 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 16.11/16.21 ( int, (one_one int), pls ) 16.11/16.21 ( int, pls, pls ) 16.11/16.21 ( int, pls, min_1 ) 16.11/16.21 ( int, min_1, pls ) 16.11/16.21 ( int, min_1, min_1 ) 16.11/16.21 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), pls ) 16.11/16.21 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s ) 16.11/16.21 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 16.11/16.21 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_4 ) 16.11/16.21 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_10 ) 16.11/16.21 ( int, t, (one_one int) ) 16.11/16.21 ( real, (zero_zero real), pi ) 16.11/16.21 ( real, (zero_zero real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.11/16.21 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.21 ( real, pi, (zero_zero real) ) 16.11/16.21 ( real, pi, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 16.11/16.21 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.21 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.11/16.21 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 16.11/16.21 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 16.11/16.21 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.11/16.21 ( real, skv_2, (zero_zero real) ) 16.11/16.21 ( real, skv_8, (zero_zero real) ) 16.11/16.21 ( real, skv_9, (zero_zero real) ) 16.11/16.21 ) 16.11/16.21 (instantiation (forall ((Y_2 $$unsorted) (X_2 $$unsorted)) (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)))) (or (not (hBOOL (hAPP int bool _let_0 X_2))) (not (hBOOL (hAPP int bool _let_0 Y_2))) (= (= (hAPP int nat nat_1 X_2) (hAPP int nat nat_1 Y_2)) (= (ti int X_2) (ti int Y_2))))) ) 16.11/16.21 ( (one_one int), s ) 16.11/16.21 ( min_1, (hAPP int int (number_number_of int) pls) ) 16.11/16.21 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.11/16.21 ( s, (one_one int) ) 16.11/16.21 ( s, s ) 16.11/16.21 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.21 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.11/16.21 ( (hAPP int int (number_number_of int) pls), min_1 ) 16.11/16.21 ( (hAPP int int (number_number_of int) pls), (hAPP int int (number_number_of int) pls) ) 16.11/16.21 ( skv_4, skv_4 ) 16.11/16.21 ( skv_4, skv_10 ) 16.11/16.21 ( skv_10, skv_4 ) 16.11/16.21 ) 16.11/16.21 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_143904 $$unsorted) (BOUND_VARIABLE_143905 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (uminus_uminus X_a))) (or (not (boolean_algebra X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_143904) (hAPP X_a X_a _let_2 BOUND_VARIABLE_143905)))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_143905) (hAPP X_a X_a _let_2 BOUND_VARIABLE_143904))))))) ) 16.11/16.21 ( int, (one_one int), pls ) 16.11/16.21 ( int, (one_one int), min_1 ) 16.11/16.21 ( int, pls, (one_one int) ) 16.11/16.21 ( int, pls, pls ) 16.11/16.21 ( int, pls, min_1 ) 16.11/16.21 ( int, min_1, (one_one int) ) 16.11/16.21 ( int, min_1, pls ) 16.11/16.21 ) 16.11/16.21 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (hAPP int X_a (number_number_of X_a) (hAPP int int bit1 pls)))) (or (not (number_ring X_a)) (not (field X_a)) (= _let_0 (hAPP X_a X_a (inverse_inverse X_a) _let_0)))) ) 16.11/16.21 ( nat ) 16.11/16.21 ( int ) 16.11/16.21 ( real ) 16.11/16.21 ( rat ) 16.11/16.21 ( complex ) 16.11/16.21 ( quickcheck_code_int ) 16.11/16.21 ( code_code_numeral ) 16.11/16.21 ) 16.11/16.21 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) (zero_zero real)) X_2))) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP (fun real real) (fun real _let_0) (deriv real) ln) X_2) (hAPP real real (inverse_inverse real) X_2))))) ) 16.11/16.21 ( (zero_zero real) ) 16.11/16.21 ( pi ) 16.11/16.21 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.21 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.21 ( skv_2 ) 16.11/16.21 ( skv_8 ) 16.11/16.21 ( skv_9 ) 16.11/16.21 ) 16.11/16.21 (instantiation (forall ((X_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (one_one int))) (or (not (hBOOL (hAPP int bool zprime P_5))) (hBOOL (hAPP int bool (hAPP int _let_0 (dvd_dvd int) P_5) X_1)) (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) X_1) (hAPP int nat nat_1 (hAPP int int (hAPP int (fun int int) (minus_minus int) P_5) _let_1)))) _let_1) P_5))))) ) 16.11/16.21 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.11/16.21 ) 16.11/16.21 (instantiation (forall ((X_a $$unsorted)) (or (not (ord X_a)) (= (hAPP (fun X_a (fun X_a bool)) (fun X_a (fun X_a X_a)) (min X_a) (ord_less_eq X_a)) (ord_min X_a))) ) 16.11/16.21 ( bool ) 16.11/16.21 ( nat ) 16.11/16.21 ( int ) 16.11/16.21 ( (fun int bool) ) 16.11/16.21 ( (fun int (fun int bool)) ) 16.11/16.21 ( (fun int int) ) 16.11/16.21 ( (fun nat bool) ) 16.11/16.21 ( (product_prod nat nat) ) 16.11/16.21 ( real ) 16.11/16.21 ( (fun real bool) ) 16.11/16.21 ( (fun real real) ) 16.11/16.21 ( rat ) 16.11/16.21 ( complex ) 16.11/16.21 ( (fun nat real) ) 16.11/16.21 ( (filter nat) ) 16.11/16.21 ( (product_prod int int) ) 16.11/16.21 ( quickcheck_code_int ) 16.11/16.21 ( code_code_numeral ) 16.11/16.21 ( (fun int (fun int (fun int bool))) ) 16.11/16.21 ( (product_prod real real) ) 16.11/16.21 ( (fun (product_prod int int) bool) ) 16.11/16.21 ( (fun nat rat) ) 16.11/16.21 ( (filter real) ) 16.11/16.21 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 16.11/16.21 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 16.11/16.21 ( (fun (product_prod int int) int) ) 16.11/16.21 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 16.11/16.21 ( (fun int real) ) 16.11/16.21 ) 16.11/16.21 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted) (K_4 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int (fun int bool) (dvd_dvd int) K_4))) (or (not (= (one_one int) (hAPP int int (hAPP int _let_0 legacy_zgcd N_1) K_4))) (not (hBOOL (hAPP int bool _let_1 (hAPP int int (hAPP int _let_0 (times_times int) M) N_1)))) (hBOOL (hAPP int bool _let_1 M))))) ) 16.11/16.21 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.11/16.21 ) 16.11/16.21 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_144024 $$unsorted) (BOUND_VARIABLE_144025 $$unsorted)) (or (not (comm_semiring_1 X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_144024) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_144024) BOUND_VARIABLE_144025)))) ) 16.11/16.21 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 16.11/16.21 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 16.11/16.21 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13 ) 16.11/16.21 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.11/16.21 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 16.11/16.21 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 16.11/16.21 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 16.11/16.21 ( complex, ii, ii ) 16.11/16.21 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 16.11/16.21 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 16.11/16.21 ) 16.11/16.21 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_144045 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (comm_semiring_1 X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (dvd_dvd X_a) _let_0) BOUND_VARIABLE_144045))) (= _let_0 (ti X_a BOUND_VARIABLE_144045)))) ) 16.11/16.21 ( bool, fFalse ) 16.11/16.21 ( bool, fTrue ) 16.11/16.21 ( int, pls ) 16.11/16.21 ( int, min_1 ) 16.11/16.21 ( int, s ) 16.11/16.21 ( int, m ) 16.11/16.21 ( int, s1 ) 16.11/16.21 ( int, t ) 16.11/16.21 ( (fun int bool), nat_neg ) 16.11/16.21 ( (fun int bool), zprime ) 16.11/16.21 ( (fun int bool), zEven ) 16.11/16.21 ( (fun int bool), zOdd ) 16.11/16.21 ( (fun int bool), (even_odd_even int) ) 16.11/16.21 ( (fun int bool), twoSqu1091635170sum2sq ) 16.11/16.21 ( (fun int bool), nat_is_nat ) 16.11/16.21 ( (fun int (fun int bool)), norRRset ) 16.11/16.21 ( (fun int (fun int bool)), quadRes ) 16.11/16.21 ( (fun int (fun int bool)), sRStar ) 16.11/16.21 ( (fun int (fun int bool)), d22set ) 16.11/16.21 ( (fun int (fun int bool)), sr ) 16.11/16.21 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 16.11/16.21 ( (fun int int), zfact ) 16.11/16.21 ( (fun int int), bit0 ) 16.11/16.21 ( (fun int int), bit1 ) 16.11/16.21 ( (fun int int), (fact_fact int) ) 16.11/16.21 ( (fun int int), pred ) 16.11/16.21 ( (fun int int), succ ) 16.11/16.21 ( (fun nat bool), (even_odd_even nat) ) 16.11/16.21 ( (fun nat bool), prime ) 16.11/16.21 ( (fun nat nat), suc ) 16.11/16.21 ( (fun nat nat), (fact_fact nat) ) 16.11/16.21 ( (fun nat nat), fact ) 16.11/16.21 ( (fun nat nat), nat_size ) 16.11/16.21 ( (fun nat nat), (size_size nat) ) 16.11/16.21 ( (fun (product_prod nat nat) bool), pred_nat ) 16.11/16.21 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 16.11/16.21 ( real, pi ) 16.11/16.21 ( (fun real real), ln ) 16.11/16.21 ( (fun real real), cos ) 16.11/16.21 ( (fun real real), sqrt ) 16.11/16.21 ( (fun real real), sin ) 16.11/16.21 ( (fun real real), arccos ) 16.11/16.21 ( (fun real real), arcsin ) 16.11/16.21 ( (fun real real), tan ) 16.11/16.21 ( (fun real real), arctan ) 16.11/16.21 ( (fun nat (fun nat bool)), coprime ) 16.11/16.21 ( complex, ii ) 16.11/16.21 ( (fun nat real), (real_1 nat) ) 16.11/16.21 ( (fun nat real), sin_coeff ) 16.11/16.21 ( (fun nat real), cos_coeff ) 16.11/16.21 ( (filter nat), sequentially ) 16.11/16.21 ( (fun int (fun int int)), (gcd_gcd int) ) 16.11/16.21 ( (fun int (fun int int)), legendre ) 16.11/16.21 ( (fun int (fun int int)), legacy_zgcd ) 16.11/16.21 ( (fun int (fun int int)), standardRes ) 16.11/16.21 ( (fun int (fun int int)), nat_tsub ) 16.11/16.21 ( (fun int (fun int int)), multInv ) 16.11/16.21 ( (fun int (fun int int)), z3mod ) 16.11/16.21 ( (fun int (fun int int)), z3div ) 16.11/16.21 ( (fun int (fun int int)), int_gcd ) 16.11/16.21 ( (fun int (fun int int)), int_lcm ) 16.11/16.21 ( (fun int (fun int int)), inv ) 16.11/16.21 ( (fun complex complex), expi ) 16.11/16.21 ( (fun complex complex), cnj ) 16.11/16.21 ( (fun real complex), cis ) 16.11/16.21 ( (fun int nat), nat_1 ) 16.11/16.21 ( (fun int nat), phi ) 16.11/16.21 ( (fun (fun int bool) bool), nat_nat_set ) 16.11/16.21 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 16.11/16.21 ( (fun nat (fun nat nat)), nat_gcd ) 16.11/16.21 ( (fun nat (fun nat nat)), nat_lcm ) 16.11/16.21 ( (fun (fun int bool) int), (the int) ) 16.11/16.21 ( (fun complex real), re ) 16.11/16.21 ( (fun complex real), im ) 16.11/16.21 ( (fun complex real), arg ) 16.11/16.21 ( (fun bool bool), fNot ) 16.11/16.21 ( (fun nat (fun real real)), root ) 16.11/16.21 ( (fun real (fun real real)), log ) 16.11/16.21 ( (fun real (fun real real)), powr ) 16.11/16.21 ( (fun bool (fun bool bool)), fimplies ) 16.11/16.21 ( (fun bool (fun bool bool)), fconj ) 16.11/16.21 ( (fun bool (fun bool bool)), fdisj ) 16.11/16.21 ( (fun int (fun int (product_prod int int))), negDivAlg ) 16.11/16.21 ( (fun int (fun int (product_prod int int))), posDivAlg ) 16.11/16.21 ( (fun int (fun int (product_prod int int))), divmod_int ) 16.11/16.21 ( (fun int (fun int (product_prod int int))), pdivmod ) 16.11/16.21 ( (fun int (fun int (product_prod int int))), norm_frac ) 16.11/16.21 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 16.11/16.21 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 16.11/16.21 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 16.11/16.21 ( (fun int (fun int (fun int bool))), zcong ) 16.11/16.21 ( (fun int (fun int (fun int bool))), zcongm ) 16.11/16.21 ( (fun int (fun int (fun int bool))), noXRRset ) 16.11/16.21 ( (fun int (fun int (fun int bool))), bnorRset ) 16.11/16.21 ( (fun int (fun int (fun int bool))), wset ) 16.11/16.21 ( (fun (product_prod int int) bool), frac_1 ) 16.11/16.21 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 16.11/16.21 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 16.11/16.21 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 16.11/16.21 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 16.11/16.21 ( (fun (fun nat rat) bool), vanishes ) 16.11/16.21 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 16.11/16.21 ( (fun code_code_numeral nat), code_c271388182l_size ) 16.11/16.21 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 16.11/16.21 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 16.11/16.21 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 16.11/16.21 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 16.11/16.21 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 16.11/16.21 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 16.11/16.21 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 16.11/16.21 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 16.11/16.21 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 16.11/16.21 ( (fun complex nat), complex_size ) 16.11/16.21 ( (fun complex nat), (size_size complex) ) 16.11/16.21 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 16.11/16.21 ( (fun nat (fun nat (product_prod int int))), bezw ) 16.11/16.21 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 16.11/16.21 ( (fun int (fun nat nat)), nat_aux ) 16.11/16.21 ( (fun int (fun (fun int bool) bool)), rsetR ) 16.11/16.21 ( (fun int (fun (fun int bool) bool)), resSet ) 16.11/16.21 ( (fun int (list int)), quickc666637781d_zero ) 16.11/16.21 ( (fun (product_prod int int) rat), frct ) 16.11/16.21 ( (fun int (fun int rat)), fract ) 16.11/16.21 ( (fun real (fun real complex)), complex_1 ) 16.11/16.21 ( (fun real (fun real complex)), rcis ) 16.11/16.21 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 16.11/16.21 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 16.11/16.21 ( (fun int real), (real_1 int) ) 16.11/16.21 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 16.11/16.21 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 16.11/16.21 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 16.11/16.21 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 16.11/16.21 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 16.11/16.21 ( (fun real nat), natfloor ) 16.11/16.21 ( (fun real nat), natceiling ) 16.11/16.21 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 16.11/16.21 ( (fun quickcheck_code_int int), quickcheck_int_of ) 16.11/16.21 ( (fun rat (product_prod int int)), quotient_of ) 16.11/16.21 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 16.11/16.21 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 16.11/16.21 ( (fun rat real), ratreal ) 16.11/16.21 ( (fun code_code_numeral int), code_int_of ) 16.11/16.21 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 16.11/16.21 ( (fun int quickcheck_code_int), quickcheck_of_int ) 16.11/16.21 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 16.11/16.21 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 16.11/16.21 ) 16.11/16.21 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_144064 $$unsorted) (BOUND_VARIABLE_144065 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (or (not (group_add X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 (plus_plus X_a) BOUND_VARIABLE_144064) BOUND_VARIABLE_144065) (hAPP X_a X_a (hAPP X_a _let_0 (minus_minus X_a) BOUND_VARIABLE_144064) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_144065))))) ) 16.11/16.21 ( nat, (one_one nat), (one_one nat) ) 16.11/16.21 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 16.11/16.21 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 16.11/16.21 ) 16.11/16.21 (instantiation (forall ((A_9 $$unsorted) (B_8 $$unsorted) (Q_6 $$unsorted) (Y_1 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (ord_less_eq int))) (let ((_let_3 (zero_zero int))) (let ((_let_4 (ord_less int))) (let ((_let_5 (hBOOL (hAPP int bool (hAPP int _let_0 _let_4 _let_3) B_8)))) (or (not (= (hAPP int int (hAPP int _let_1 (plus_plus int) (hAPP int int (hAPP int _let_1 (times_times int) B_8) Q_6)) Y_1) (ti int A_9))) (and (not _let_5) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_4 B_8) Y_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 Y_1) _let_3))))) (and _let_5 (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 _let_3) Y_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_4 Y_1) B_8))))) (= _let_3 (ti int B_8)) (= (hAPP int int (hAPP int _let_1 (div_mod int) A_9) B_8) (ti int Y_1))))))))) ) 16.11/16.21 ( s, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m, (one_one int) ) 16.11/16.21 ) 16.11/16.21 (instantiation (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_0 (zero_zero int))) (or (and (= _let_0 (ti int A_1)) (= _let_0 (ti int B))) (not (forall ((C_4 $$unsorted) (D_3 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int _let_0 (times_times int) (hAPP int int (hAPP int _let_0 legacy_zgcd A_1) B)))) (or (not (= (hAPP int int _let_1 C_4) (ti int A_1))) (not (= (ti int B) (hAPP int int _let_1 D_3))) (not (= (one_one int) (hAPP int int (hAPP int _let_0 legacy_zgcd C_4) D_3)))))) )))) ) 16.11/16.21 ( pls, pls ) 16.11/16.21 ( min_1, min_1 ) 16.11/16.21 ( s, s ) 16.11/16.21 ( m, m ) 16.11/16.21 ( s1, s1 ) 16.11/16.21 ( t, t ) 16.11/16.21 ) 16.11/16.21 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted) (Xa_2 $$unsorted)) (= (and (= (zero_zero real) Y_2) (= X_2 Xa_2)) (= (hAPP real complex (of_real complex) Xa_2) (hAPP real complex (hAPP real (fun real complex) complex_1 X_2) Y_2))) ) 16.11/16.21 ( (one_one real), (zero_zero real), (hAPP real real (uminus_uminus real) (one_one real)) ) 16.11/16.21 ( (zero_zero real), (one_one real), (hAPP int real (number_number_of real) min_1) ) 16.11/16.21 ( (zero_zero real), (zero_zero real), pi ) 16.11/16.21 ) 16.11/16.21 (instantiation (forall ((X_a $$unsorted)) (or (not (number_ring X_a)) (= (hAPP int X_a (ring_1_of_int X_a) (hAPP int int (number_number_of int) min_1)) (hAPP int X_a (number_number_of X_a) min_1))) ) 16.11/16.21 ( nat ) 16.11/16.21 ( int ) 16.11/16.21 ( real ) 16.11/16.21 ( rat ) 16.11/16.21 ( complex ) 16.11/16.21 ( quickcheck_code_int ) 16.11/16.21 ( code_code_numeral ) 16.11/16.21 ) 16.11/16.21 (instantiation (forall ((Z_1 $$unsorted)) (= (zero_zero real) (hAPP complex real im (hAPP real complex (of_real complex) Z_1))) ) 16.11/16.21 ( pi ) 16.11/16.21 ( (hAPP int real (number_number_of real) min_1) ) 16.11/16.21 ( (hAPP real real (uminus_uminus real) (one_one real)) ) 16.11/16.21 ) 16.11/16.21 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_144168 $$unsorted)) (let ((_let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_144168) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (or (not (linordered_idom X_a)) (= _let_0 (hAPP X_a X_a (abs_abs X_a) _let_0)))) ) 16.11/16.21 ( int, s ) 16.11/16.21 ( int, s1 ) 16.11/16.21 ( int, skv_14 ) 16.11/16.21 ( real, (hAPP int real (number_number_of real) min_1) ) 16.11/16.21 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.21 ( complex, ii ) 16.11/16.21 ) 16.11/16.22 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_144186 $$unsorted) (BOUND_VARIABLE_144187 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member X_a))) (let ((_let_3 (field_char_0_Rats X_a))) (or (not (field_char_0 X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_144187) _let_3))) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_144186) _let_3))) (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_144187) BOUND_VARIABLE_144186)) _let_3))))))) ) 16.11/16.22 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.22 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.11/16.22 ( int, skv_13, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.11/16.22 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.22 ( real, pi, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 16.11/16.22 ( real, (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.22 ( real, (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.22 ( complex, ii, ii ) 16.11/16.22 ( complex, ii, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 16.11/16.22 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.22 ) 16.11/16.22 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) pi))) (= X_1 (hAPP real real arccos (hAPP real real cos X_1)))))) ) 16.11/16.22 ( (zero_zero real) ) 16.11/16.22 ( pi ) 16.11/16.22 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.22 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.22 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.11/16.22 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.11/16.22 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.22 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.11/16.22 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.22 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 16.11/16.22 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 16.11/16.22 ( skv_3 ) 16.11/16.22 ( skv_5 ) 16.11/16.22 ( skv_7 ) 16.11/16.22 ( skv_12 ) 16.11/16.22 ) 16.11/16.22 (instantiation (forall ((Z $$unsorted)) (let ((_let_0 (zero_zero complex))) (= (= _let_0 (hAPP complex complex cnj Z)) (= _let_0 Z))) ) 16.11/16.22 ( (one_one complex) ) 16.11/16.22 ( ii ) 16.11/16.22 ( (zero_zero complex) ) 16.11/16.22 ) 16.11/16.22 (instantiation (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_0 (inverse_inverse real))) (let ((_let_1 (hAPP nat (fun real real) root N_1))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_1))) (= (hAPP real real _let_0 (hAPP real real _let_1 X_1)) (hAPP real real _let_1 (hAPP real real _let_0 X_1)))))) ) 16.11/16.22 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.22 ) 16.11/16.22 (instantiation (forall ((X_a $$unsorted)) (or (not (real_normed_field X_a)) (not (banach X_a)) (= (hAPP X_a X_a (exp X_a) (zero_zero X_a)) (one_one X_a))) ) 16.11/16.22 ( nat ) 16.11/16.22 ( int ) 16.11/16.22 ( real ) 16.11/16.22 ( rat ) 16.11/16.22 ( complex ) 16.11/16.22 ( quickcheck_code_int ) 16.11/16.22 ( code_code_numeral ) 16.11/16.22 ) 16.11/16.22 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_144521 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP X_a int (archimedean_ceiling X_a) BOUND_VARIABLE_144521)) (one_one int))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_144521) (one_one X_a))))) ) 16.11/16.22 ( int, (one_one int) ) 16.11/16.22 ( int, (zero_zero int) ) 16.11/16.22 ( int, min_1 ) 16.11/16.22 ( real, (zero_zero real) ) 16.11/16.22 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.11/16.22 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.22 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.11/16.22 ( real, skv_5 ) 16.11/16.22 ) 16.15/16.22 (instantiation (forall ((B $$unsorted) (A_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 A_1) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) B))) (not (forall ((D_3 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) D_3))) (not (forall ((Y $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (abs_abs real) (hAPP real real (hAPP real (fun real real) (minus_minus real) X_1) Y))) D_3))) (and (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 A_1) Y)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Y) B)))) ))) ))))) ) 16.15/16.22 ( (zero_zero real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 16.15/16.22 ( pi, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 16.15/16.22 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.15/16.22 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.15/16.22 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real), pi ) 16.15/16.22 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi, (zero_zero real) ) 16.15/16.22 ) 16.15/16.22 (instantiation (forall ((N_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (real_1 nat))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) (hAPP nat real _let_1 N_1)) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) X_1) (hAPP nat real _let_1 (hAPP nat nat suc N_1))))) (= N_1 (hAPP int nat nat_1 (hAPP real int (archim2085082626_floor real) X_1)))))) ) 16.15/16.22 ( (zero_zero nat), pi ) 16.15/16.22 ( (zero_zero nat), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.15/16.22 ( (zero_zero nat), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.15/16.22 ( (zero_zero nat), skv_3 ) 16.15/16.22 ( (zero_zero nat), skv_5 ) 16.15/16.22 ( (zero_zero nat), skv_7 ) 16.15/16.22 ( (zero_zero nat), skv_12 ) 16.15/16.22 ) 16.15/16.22 (instantiation (forall ((V_1 $$unsorted)) (let ((_let_0 (one_one nat))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) V_1) pls))) (= _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP int nat (number_number_of nat) V_1)) _let_0)))) ) 16.15/16.22 ( (one_one int) ) 16.15/16.22 ( pls ) 16.15/16.22 ( (hAPP int int bit1 pls) ) 16.15/16.22 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.15/16.22 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.15/16.22 ( min_1 ) 16.15/16.22 ( s ) 16.15/16.22 ( t ) 16.15/16.22 ( skv_4 ) 16.15/16.22 ( skv_10 ) 16.15/16.22 ) 16.15/16.22 (instantiation (forall ((V_1 $$unsorted)) (let ((_let_0 (number_number_of nat))) (or (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) V_1) pls)) (= (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP int nat _let_0 V_1)) (one_one nat)) (hAPP int nat _let_0 (hAPP int int succ V_1))))) ) 16.15/16.22 ( (one_one int) ) 16.15/16.22 ( pls ) 16.15/16.22 ( (hAPP int int bit1 pls) ) 16.15/16.22 ( min_1 ) 16.15/16.22 ( s ) 16.15/16.22 ( t ) 16.15/16.22 ( skv_4 ) 16.15/16.22 ( skv_10 ) 16.15/16.22 ) 16.15/16.22 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_144714 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (or (not (linord219039673up_add X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_144714)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_144714)) BOUND_VARIABLE_144714)))))) ) 16.15/16.22 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.15/16.22 ( int, (one_one int) ) 16.15/16.22 ( int, pls ) 16.15/16.22 ( int, min_1 ) 16.15/16.22 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.15/16.22 ( real, (one_one real) ) 16.15/16.22 ( real, pi ) 16.15/16.22 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.15/16.22 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.15/16.22 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.15/16.22 ( real, skv_2 ) 16.15/16.22 ( real, skv_8 ) 16.15/16.22 ( real, skv_9 ) 16.15/16.22 ( complex, (one_one complex) ) 16.15/16.22 ( complex, ii ) 16.15/16.22 ) 16.15/16.22 (instantiation (forall ((P_5 $$unsorted)) (let ((_let_0 (product_prod int int))) (= (hAPP rat _let_0 quotient_of (hAPP rat rat (sgn_sgn rat) P_5)) (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) (hAPP int int (sgn_sgn int) (hAPP _let_0 int (product_fst int int) (hAPP rat _let_0 quotient_of P_5)))) (one_one int)))) ) 16.15/16.22 ( (zero_zero rat) ) 16.15/16.22 ) 16.15/16.22 (instantiation (forall ((M $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (div_div nat))) (= (hAPP nat nat (hAPP nat _let_0 _let_2 (hAPP nat nat suc (hAPP nat nat suc M))) _let_1) (hAPP nat nat suc (hAPP nat nat (hAPP nat _let_0 _let_2 M) _let_1)))))) ) 16.15/16.22 ( (zero_zero nat) ) 16.15/16.22 ( (hAPP nat nat suc (zero_zero nat)) ) 16.15/16.22 ) 16.15/16.22 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_144738 $$unsorted) (BOUND_VARIABLE_144739 $$unsorted) (BOUND_VARIABLE_144740 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_144738))) (or (not (cancel_semigroup_add X_a)) (= (= (ti X_a BOUND_VARIABLE_144739) (ti X_a BOUND_VARIABLE_144740)) (= (hAPP X_a X_a _let_0 BOUND_VARIABLE_144739) (hAPP X_a X_a _let_0 BOUND_VARIABLE_144740))))) ) 16.15/16.22 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), s, s ) 16.15/16.22 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), s, s1 ) 16.15/16.22 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), s, s ) 16.15/16.22 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), s1, s ) 16.15/16.22 ) 16.15/16.22 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_0 (product_prod nat nat))) (let ((_let_1 (fun nat _let_0))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) M) N_1))) (= (hAPP nat _let_0 (hAPP nat _let_1 divmod_nat M) N_1) (hAPP nat _let_0 (hAPP nat _let_1 (product_Pair nat nat) (zero_zero nat)) M))))) ) 16.15/16.22 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.15/16.22 ) 16.15/16.22 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (semiring_1_of_nat int))) (= (hAPP nat int _let_0 (hAPP nat nat (fact_fact nat) X_1)) (hAPP int int (fact_fact int) (hAPP nat int _let_0 X_1)))) ) 16.15/16.22 ( (zero_zero nat) ) 16.15/16.22 ( (hAPP nat nat suc (zero_zero nat)) ) 16.15/16.22 ) 16.15/16.22 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_144802 $$unsorted) (BOUND_VARIABLE_144803 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (or (not (comm_ring_1 X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 (minus_minus X_a) BOUND_VARIABLE_144802) BOUND_VARIABLE_144803) (hAPP X_a X_a (hAPP X_a _let_0 (plus_plus X_a) BOUND_VARIABLE_144802) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_144803))))) ) 16.15/16.22 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 16.15/16.22 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 16.15/16.22 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 16.15/16.22 ) 16.15/16.22 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_144821 $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (fun (filter nat) bool))) (let ((_let_2 (fun nat X_a))) (or (not (real_normed_vector X_a)) (= (hBOOL (hAPP (filter nat) bool (hAPP real _let_1 (hAPP _let_0 (fun real _let_1) (tendsto nat real) (hAPP _let_2 _let_0 (hAPP (fun X_a real) (fun _let_2 _let_0) (combb X_a real nat) (norm_norm X_a)) BOUND_VARIABLE_144821)) (zero_zero real)) sequentially)) (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_1 (hAPP _let_2 (fun X_a _let_1) (tendsto nat X_a) BOUND_VARIABLE_144821) (zero_zero X_a)) sequentially))))))) ) 16.15/16.22 ( real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))) ) 16.15/16.22 ) 16.15/16.22 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_144904 $$unsorted)) (or (not (field_inverse_zero X_a)) (not (number_ring X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_144904) (hAPP int X_a (number_number_of X_a) min_1)) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_144904))) ) 16.15/16.22 ( int, (one_one int) ) 16.15/16.22 ( int, pls ) 16.15/16.22 ( int, min_1 ) 16.15/16.22 ( real, (one_one real) ) 16.15/16.22 ( real, pi ) 16.15/16.22 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.15/16.22 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.15/16.22 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.15/16.22 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.15/16.22 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.15/16.22 ( complex, (one_one complex) ) 16.15/16.22 ( complex, ii ) 16.15/16.22 ) 16.15/16.22 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_144920 $$unsorted) (BOUND_VARIABLE_144921 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (uminus_uminus X_a))) (or (not (ordered_ab_group_add X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_144920) BOUND_VARIABLE_144921))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_144921)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_144920))))))) ) 16.15/16.22 ( int, (one_one int), (one_one int) ) 16.15/16.22 ( int, (one_one int), pls ) 16.15/16.22 ( int, (one_one int), t ) 16.15/16.22 ( int, (zero_zero int), (one_one int) ) 16.15/16.22 ( int, (zero_zero int), min_1 ) 16.15/16.22 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.15/16.22 ( int, (zero_zero int), s ) 16.15/16.22 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.15/16.22 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 16.15/16.22 ( int, (zero_zero int), skv_4 ) 16.15/16.22 ( int, (zero_zero int), skv_10 ) 16.15/16.22 ( int, pls, (one_one int) ) 16.15/16.22 ( int, pls, pls ) 16.15/16.22 ( int, min_1, pls ) 16.15/16.22 ( int, min_1, min_1 ) 16.15/16.22 ( real, (zero_zero real), pi ) 16.15/16.22 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.15/16.22 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.15/16.22 ( real, (zero_zero real), skv_3 ) 16.15/16.22 ( real, (zero_zero real), skv_5 ) 16.15/16.22 ( real, (zero_zero real), skv_7 ) 16.15/16.22 ( real, (zero_zero real), skv_12 ) 16.15/16.22 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.15/16.22 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.15/16.22 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.15/16.22 ( real, skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.15/16.22 ) 16.15/16.22 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_144957 $$unsorted) (BOUND_VARIABLE_144958 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (let ((_let_1 (hAPP int nat (number_number_of nat) BOUND_VARIABLE_144958))) (or (not (mult_zero X_a)) (not (no_zero_divisors X_a)) (not (zero_neq_one X_a)) (not (power X_a)) (= (and (= _let_0 (ti X_a BOUND_VARIABLE_144957)) (not (= (zero_zero nat) _let_1))) (= _let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_144957) _let_1)))))) ) 16.15/16.22 ( int, s, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.15/16.22 ( int, s1, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.15/16.22 ( int, skv_14, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.15/16.22 ( complex, ii, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.15/16.22 ) 16.15/16.22 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_144999 $$unsorted)) (or (not (linordered_idom X_a)) (not (number_ring X_a)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) BOUND_VARIABLE_144999) (hAPP int int bit1 pls))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_144999)) (one_one X_a))))) ) 16.15/16.22 ( nat, pls ) 16.15/16.22 ( nat, (hAPP int int bit1 pls) ) 16.15/16.22 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.15/16.22 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.15/16.22 ( int, pls ) 16.15/16.22 ( int, (hAPP int int bit1 pls) ) 16.15/16.22 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.15/16.22 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.15/16.22 ( int, min_1 ) 16.15/16.22 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.15/16.22 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.15/16.22 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.15/16.22 ( real, min_1 ) 16.15/16.22 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.15/16.22 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.15/16.22 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.15/16.22 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 16.15/16.22 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.15/16.22 ( complex, min_1 ) 16.15/16.22 ( quickcheck_code_int, (one_one int) ) 16.15/16.22 ( quickcheck_code_int, (zero_zero int) ) 16.15/16.22 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 16.15/16.22 ( code_code_numeral, pls ) 16.15/16.22 ( code_code_numeral, (hAPP int int bit1 pls) ) 16.15/16.22 ) 16.15/16.22 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_145021 $$unsorted) (BOUND_VARIABLE_145022 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)))) (or (not (ordere216010020id_add X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_145022))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_145021))) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_145022) BOUND_VARIABLE_145021))))) ) 16.15/16.22 ( nat, (one_one nat), (one_one nat) ) 16.15/16.22 ( int, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 16.15/16.22 ( int, (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.15/16.22 ) 16.15/16.22 (instantiation (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) _let_1) B_1))) (= (hBOOL (hAPP rat bool (hAPP rat (fun rat bool) (ord_less_eq rat) (zero_zero rat)) (hAPP int rat (hAPP int (fun int rat) fract A_2) B_1))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) _let_1) A_2)))))) ) 16.15/16.22 ( (one_one int), (one_one int) ) 16.15/16.22 ( (zero_zero int), (one_one int) ) 16.15/16.22 ) 16.15/16.22 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_145074 $$unsorted)) (let ((_let_0 (inverse_inverse X_a))) (or (not (divisi14063676e_zero X_a)) (= (hAPP X_a X_a _let_0 (hAPP X_a X_a _let_0 BOUND_VARIABLE_145074)) (ti X_a BOUND_VARIABLE_145074)))) ) 16.15/16.22 ( bool, fFalse ) 16.15/16.22 ( bool, fTrue ) 16.15/16.22 ( int, pls ) 16.15/16.22 ( int, min_1 ) 16.15/16.22 ( int, s ) 16.15/16.22 ( int, m ) 16.15/16.22 ( int, s1 ) 16.15/16.22 ( int, t ) 16.15/16.22 ( (fun int bool), nat_neg ) 16.15/16.22 ( (fun int bool), zprime ) 16.15/16.22 ( (fun int bool), zEven ) 16.15/16.22 ( (fun int bool), zOdd ) 16.15/16.22 ( (fun int bool), (even_odd_even int) ) 16.15/16.22 ( (fun int bool), twoSqu1091635170sum2sq ) 16.15/16.22 ( (fun int bool), nat_is_nat ) 16.15/16.22 ( (fun int (fun int bool)), norRRset ) 16.15/16.22 ( (fun int (fun int bool)), quadRes ) 16.15/16.22 ( (fun int (fun int bool)), sRStar ) 16.15/16.22 ( (fun int (fun int bool)), d22set ) 16.15/16.22 ( (fun int (fun int bool)), sr ) 16.15/16.22 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 16.15/16.22 ( (fun int int), zfact ) 16.15/16.22 ( (fun int int), bit0 ) 16.15/16.22 ( (fun int int), bit1 ) 16.15/16.22 ( (fun int int), (fact_fact int) ) 16.15/16.22 ( (fun int int), pred ) 16.15/16.22 ( (fun int int), succ ) 16.15/16.22 ( (fun nat bool), (even_odd_even nat) ) 16.15/16.22 ( (fun nat bool), prime ) 16.15/16.22 ( (fun nat nat), suc ) 16.15/16.22 ( (fun nat nat), (fact_fact nat) ) 16.15/16.22 ( (fun nat nat), fact ) 16.15/16.22 ( (fun nat nat), nat_size ) 16.15/16.22 ( (fun nat nat), (size_size nat) ) 16.15/16.22 ( (fun (product_prod nat nat) bool), pred_nat ) 16.15/16.22 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 16.15/16.22 ( real, (zero_zero real) ) 16.15/16.22 ( real, pi ) 16.15/16.22 ( (fun real real), ln ) 16.15/16.22 ( (fun real real), cos ) 16.15/16.22 ( (fun real real), sqrt ) 16.15/16.22 ( (fun real real), sin ) 16.15/16.22 ( (fun real real), arccos ) 16.15/16.22 ( (fun real real), arcsin ) 16.15/16.22 ( (fun real real), tan ) 16.15/16.22 ( (fun real real), arctan ) 16.15/16.22 ( (fun nat (fun nat bool)), coprime ) 16.15/16.22 ( complex, ii ) 16.15/16.22 ( (fun nat real), (real_1 nat) ) 16.15/16.22 ( (fun nat real), sin_coeff ) 16.15/16.22 ( (fun nat real), cos_coeff ) 16.15/16.22 ( (filter nat), sequentially ) 16.15/16.22 ( (fun int (fun int int)), (gcd_gcd int) ) 16.15/16.22 ( (fun int (fun int int)), legendre ) 16.15/16.22 ( (fun int (fun int int)), legacy_zgcd ) 16.15/16.22 ( (fun int (fun int int)), standardRes ) 16.15/16.22 ( (fun int (fun int int)), nat_tsub ) 16.15/16.22 ( (fun int (fun int int)), multInv ) 16.15/16.22 ( (fun int (fun int int)), z3mod ) 16.15/16.22 ( (fun int (fun int int)), z3div ) 16.15/16.22 ( (fun int (fun int int)), int_gcd ) 16.15/16.22 ( (fun int (fun int int)), int_lcm ) 16.15/16.22 ( (fun int (fun int int)), inv ) 16.15/16.22 ( (fun complex complex), expi ) 16.15/16.22 ( (fun complex complex), cnj ) 16.15/16.22 ( (fun real complex), cis ) 16.15/16.22 ( (fun int nat), nat_1 ) 16.15/16.22 ( (fun int nat), phi ) 16.15/16.22 ( (fun (fun int bool) bool), nat_nat_set ) 16.15/16.22 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 16.15/16.22 ( (fun nat (fun nat nat)), nat_gcd ) 16.15/16.22 ( (fun nat (fun nat nat)), nat_lcm ) 16.15/16.22 ( (fun (fun int bool) int), (the int) ) 16.15/16.22 ( (fun complex real), re ) 16.15/16.22 ( (fun complex real), im ) 16.15/16.22 ( (fun complex real), arg ) 16.15/16.22 ( (fun bool bool), fNot ) 16.15/16.22 ( (fun nat (fun real real)), root ) 16.15/16.22 ( (fun real (fun real real)), log ) 16.15/16.22 ( (fun real (fun real real)), powr ) 16.15/16.22 ( (fun bool (fun bool bool)), fimplies ) 16.15/16.22 ( (fun bool (fun bool bool)), fconj ) 16.15/16.22 ( (fun bool (fun bool bool)), fdisj ) 16.15/16.22 ( (fun int (fun int (product_prod int int))), negDivAlg ) 16.15/16.22 ( (fun int (fun int (product_prod int int))), posDivAlg ) 16.15/16.22 ( (fun int (fun int (product_prod int int))), divmod_int ) 16.15/16.22 ( (fun int (fun int (product_prod int int))), pdivmod ) 16.15/16.22 ( (fun int (fun int (product_prod int int))), norm_frac ) 16.15/16.22 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 16.15/16.22 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 16.15/16.22 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 16.15/16.22 ( (fun int (fun int (fun int bool))), zcong ) 16.15/16.22 ( (fun int (fun int (fun int bool))), zcongm ) 16.15/16.22 ( (fun int (fun int (fun int bool))), noXRRset ) 16.15/16.22 ( (fun int (fun int (fun int bool))), bnorRset ) 16.15/16.22 ( (fun int (fun int (fun int bool))), wset ) 16.15/16.22 ( (fun (product_prod int int) bool), frac_1 ) 16.15/16.22 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 16.15/16.22 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 16.15/16.22 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 16.15/16.22 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 16.15/16.22 ( (fun (fun nat rat) bool), vanishes ) 16.15/16.22 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 16.15/16.22 ( (fun code_code_numeral nat), code_c271388182l_size ) 16.15/16.22 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 16.15/16.22 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 16.15/16.22 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 16.15/16.22 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 16.15/16.22 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 16.15/16.22 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 16.15/16.22 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 16.15/16.22 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 16.15/16.22 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 16.15/16.22 ( (fun complex nat), complex_size ) 16.15/16.22 ( (fun complex nat), (size_size complex) ) 16.15/16.22 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 16.15/16.22 ( (fun nat (fun nat (product_prod int int))), bezw ) 16.15/16.22 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 16.15/16.22 ( (fun int (fun nat nat)), nat_aux ) 16.15/16.22 ( (fun int (fun (fun int bool) bool)), rsetR ) 16.15/16.22 ( (fun int (fun (fun int bool) bool)), resSet ) 16.15/16.22 ( (fun int (list int)), quickc666637781d_zero ) 16.15/16.22 ( (fun (product_prod int int) rat), frct ) 16.15/16.22 ( (fun int (fun int rat)), fract ) 16.15/16.22 ( (fun real (fun real complex)), complex_1 ) 16.15/16.22 ( (fun real (fun real complex)), rcis ) 16.15/16.22 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 16.15/16.22 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 16.15/16.22 ( (fun int real), (real_1 int) ) 16.15/16.22 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 16.15/16.22 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 16.15/16.22 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 16.15/16.22 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 16.15/16.22 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 16.15/16.22 ( (fun real nat), natfloor ) 16.15/16.22 ( (fun real nat), natceiling ) 16.15/16.22 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 16.15/16.22 ( (fun quickcheck_code_int int), quickcheck_int_of ) 16.15/16.22 ( (fun rat (product_prod int int)), quotient_of ) 16.15/16.22 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 16.15/16.22 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 16.15/16.22 ( (fun rat real), ratreal ) 16.15/16.22 ( (fun code_code_numeral int), code_int_of ) 16.15/16.22 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 16.15/16.22 ( (fun int quickcheck_code_int), quickcheck_of_int ) 16.15/16.22 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 16.15/16.22 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 16.15/16.22 ) 16.15/16.22 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (divisi14063676e_zero X_a)) (= _let_0 (hAPP X_a X_a (inverse_inverse X_a) _let_0)))) ) 16.15/16.22 ( nat ) 16.15/16.22 ( int ) 16.15/16.22 ( real ) 16.15/16.22 ( rat ) 16.15/16.22 ( complex ) 16.15/16.22 ( quickcheck_code_int ) 16.15/16.22 ( code_code_numeral ) 16.15/16.22 ) 16.15/16.22 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_145088 $$unsorted) (BOUND_VARIABLE_145089 $$unsorted)) (let ((_let_0 (norm_norm X_a))) (or (not (real_normed_vector X_a)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (abs_abs real) (hAPP real real (hAPP real (fun real real) (minus_minus real) (hAPP X_a real _let_0 BOUND_VARIABLE_145088)) (hAPP X_a real _let_0 BOUND_VARIABLE_145089)))) (hAPP X_a real _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) BOUND_VARIABLE_145088) BOUND_VARIABLE_145089)))))) ) 16.15/16.22 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 16.15/16.22 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 16.15/16.22 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 16.15/16.22 ) 16.15/16.22 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_145114 $$unsorted) (BOUND_VARIABLE_145115 $$unsorted)) (let ((_let_0 (abs_abs X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (minus_minus X_a))) (or (not (ordere142940540dd_abs X_a)) (= (hAPP X_a X_a _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_145114) BOUND_VARIABLE_145115)) (hAPP X_a X_a _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_145115) BOUND_VARIABLE_145114))))))) ) 16.15/16.22 ( int, (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.15/16.22 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 16.15/16.22 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 16.15/16.22 ( real, (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))), (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))) ) 16.15/16.22 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 16.15/16.22 ( code_code_numeral, (one_one code_code_numeral), (zero_zero code_code_numeral) ) 16.15/16.22 ) 16.15/16.22 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_145148 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_145148) _let_2))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_145148)) _let_2)))))) ) 16.15/16.22 ( int, pls ) 16.15/16.22 ( int, min_1 ) 16.15/16.22 ( real, (zero_zero real) ) 16.15/16.22 ( real, pi ) 16.15/16.22 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.15/16.22 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.15/16.22 ( complex, ii ) 16.15/16.22 ) 16.15/16.22 (instantiation (forall ((Ma $$unsorted) (X_2 $$unsorted)) (= (not (forall ((Y $$unsorted)) (let ((_let_0 (fun int bool))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) Y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) X_2) Ma)))) )) (hBOOL (hAPP int bool (hAPP int (fun int bool) quadRes Ma) X_2))) ) 16.15/16.22 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (number_number_of int) min_1) ) 16.15/16.22 ) 16.15/16.22 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_145189 $$unsorted) (BOUND_VARIABLE_145190 $$unsorted) (BOUND_VARIABLE_145191 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (= _let_0 (ti X_a BOUND_VARIABLE_145190)))) (let ((_let_3 (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_145191))) (or (not (field_inverse_zero X_a)) (not (number X_a)) (= (and (or (not _let_2) (= _let_0 _let_3)) (or _let_2 (= (hAPP X_a X_a (hAPP X_a _let_1 (times_times X_a) _let_3) BOUND_VARIABLE_145190) (ti X_a BOUND_VARIABLE_145189)))) (= _let_3 (hAPP X_a X_a (hAPP X_a _let_1 (inverse_divide X_a) BOUND_VARIABLE_145189) BOUND_VARIABLE_145190)))))))) ) 16.15/16.22 ( int, pls, pls, (hAPP int int bit1 pls) ) 16.15/16.22 ( int, min_1, min_1, pls ) 16.15/16.22 ( int, s, s, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.15/16.22 ( int, m, m, min_1 ) 16.15/16.22 ( int, s1, s1, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.15/16.22 ( int, t, t, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.15/16.22 ( real, pi, pi, min_1 ) 16.15/16.22 ( complex, ii, ii, min_1 ) 16.15/16.22 ) 16.15/16.22 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_145352 $$unsorted) (BOUND_VARIABLE_145353 $$unsorted)) (let ((_let_0 (sgn_sgn X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (times_times X_a))) (or (not (real_n1866405975lgebra X_a)) (= (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a _let_0 BOUND_VARIABLE_145352)) (hAPP X_a X_a _let_0 BOUND_VARIABLE_145353)) (hAPP X_a X_a _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_145352) BOUND_VARIABLE_145353))))))) ) 16.15/16.22 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 16.15/16.22 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 16.15/16.22 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13 ) 16.15/16.22 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.15/16.22 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 16.15/16.22 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 16.15/16.22 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 16.15/16.22 ( complex, ii, ii ) 16.15/16.22 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 16.15/16.22 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 16.15/16.22 ) 16.15/16.22 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_145379 $$unsorted) (BOUND_VARIABLE_145380 $$unsorted) (BOUND_VARIABLE_145381 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_145379))) (or (not (order X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_145380) BOUND_VARIABLE_145381))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_145380))) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_145381)))) ) 16.15/16.22 ( nat, (zero_zero nat), (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.15/16.22 ( int, (one_one int), pls, min_1 ) 16.15/16.22 ( int, pls, pls, pls ) 16.15/16.22 ( int, min_1, min_1, pls ) 16.15/16.22 ( int, s, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.15/16.22 ( int, t, min_1, min_1 ) 16.15/16.22 ( int, skv_4, pls, (one_one int) ) 16.15/16.22 ( int, skv_10, pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.15/16.22 ( real, (one_one real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.15/16.22 ( real, (zero_zero real), (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.15/16.22 ( real, pi, pi, (zero_zero real) ) 16.15/16.22 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.15/16.22 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 16.15/16.22 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real), pi ) 16.15/16.22 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 16.15/16.22 ) 16.15/16.22 (instantiation (forall ((P_5 $$unsorted)) (or (not (hBOOL (hAPP nat bool prime P_5))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) P_5))) ) 16.15/16.22 ( (zero_zero nat) ) 16.15/16.22 ( (hAPP nat nat suc (zero_zero nat)) ) 16.15/16.22 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.15/16.22 ) 16.15/16.22 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_0 (real_1 int))) (= (= (ti int X_2) (ti int Y_2)) (= (hAPP int real _let_0 Y_2) (hAPP int real _let_0 X_2)))) ) 16.15/16.22 ( pls, s ) 16.15/16.22 ( min_1, m ) 16.15/16.22 ( s, s ) 16.15/16.22 ( s, s1 ) 16.15/16.22 ( m, m ) 16.15/16.22 ( m, t ) 16.15/16.22 ( s1, pls ) 16.15/16.22 ( s1, s ) 16.15/16.22 ( t, min_1 ) 16.15/16.22 ( t, m ) 16.15/16.22 ) 16.15/16.22 (instantiation (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_0 (even_odd_even int))) (or (hBOOL (hAPP int bool _let_0 X_1)) (hBOOL (hAPP int bool _let_0 Y_1)) (hBOOL (hAPP int bool _let_0 (hAPP int int (hAPP int (fun int int) (plus_plus int) X_1) Y_1))))) ) 16.15/16.22 ( (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 16.15/16.22 ( (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.15/16.22 ) 16.15/16.22 (instantiation (forall ((X_2 $$unsorted) (N $$unsorted)) (let ((_let_0 (zero_zero nat))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real real))) (let ((_let_3 (hAPP nat _let_2 root N))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) _let_0) N))) (not (hBOOL (hAPP nat bool (even_odd_even nat) N))) (not (hBOOL (hAPP real bool (hAPP real _let_1 (ord_less real) X_2) (zero_zero real)))) (hBOOL (hAPP real bool (hAPP real _let_1 (hAPP _let_2 (fun real _let_1) (deriv real) _let_3) X_2) (hAPP real real (inverse_inverse real) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (uminus_uminus real) (hAPP nat real (real_1 nat) N))) (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP real real _let_3 X_2)) (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) N) (hAPP nat nat suc _let_0)))))))))))) ) 16.15/16.22 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.15/16.22 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.15/16.22 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.15/16.22 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.15/16.22 ) 16.15/16.22 (instantiation (forall ((K_4 $$unsorted) (L_4 $$unsorted)) (let ((_let_0 (number_number_of int))) (let ((_let_1 (number_number_of rat))) (= (hAPP rat rat (hAPP rat (fun rat rat) (inverse_divide rat) (hAPP int rat _let_1 K_4)) (hAPP int rat _let_1 L_4)) (hAPP int rat (hAPP int (fun int rat) fract (hAPP int int _let_0 K_4)) (hAPP int int _let_0 L_4))))) ) 16.15/16.22 ( pls, (hAPP int int bit1 pls) ) 16.15/16.22 ( (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 16.15/16.22 ) 16.15/16.22 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_145525 $$unsorted) (BOUND_VARIABLE_145526 $$unsorted)) (let ((_let_0 (norm_norm X_a))) (or (not (real_normed_vector X_a)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP X_a real _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_145525) BOUND_VARIABLE_145526))) (hAPP real real (hAPP real (fun real real) (plus_plus real) (hAPP X_a real _let_0 BOUND_VARIABLE_145525)) (hAPP X_a real _let_0 BOUND_VARIABLE_145526)))))) ) 16.15/16.22 ( nat, (one_one nat), (one_one nat) ) 16.15/16.22 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 16.15/16.22 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 16.15/16.22 ) 16.15/16.22 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_145593 $$unsorted) (BOUND_VARIABLE_145594 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (uminus_uminus X_a))) (or (not (ordered_ab_group_add X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_145594)) BOUND_VARIABLE_145593)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_145593)) BOUND_VARIABLE_145594))))))) ) 16.15/16.22 ( int, (one_one int), pls ) 16.15/16.22 ( int, (one_one int), min_1 ) 16.15/16.22 ( int, pls, (one_one int) ) 16.15/16.22 ( int, pls, min_1 ) 16.15/16.22 ( int, pls, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.15/16.22 ( int, pls, s ) 16.15/16.22 ( int, pls, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.15/16.22 ( int, pls, (hAPP int int (number_number_of int) pls) ) 16.15/16.22 ( int, pls, skv_4 ) 16.15/16.22 ( int, pls, skv_10 ) 16.15/16.22 ( int, min_1, (one_one int) ) 16.15/16.22 ( int, min_1, pls ) 16.15/16.22 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), pls ) 16.15/16.22 ( int, s, pls ) 16.15/16.22 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), pls ) 16.15/16.22 ( int, (hAPP int int (number_number_of int) pls), pls ) 16.15/16.22 ( int, skv_4, pls ) 16.15/16.22 ( int, skv_10, pls ) 16.15/16.22 ) 16.15/16.22 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (one_one real))) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) X_1))) (not (= (hAPP real real ln X_1) (hAPP real real (hAPP real (fun real real) (minus_minus real) X_1) _let_0))) (= _let_0 X_1))) ) 16.15/16.22 ( (one_one real) ) 16.15/16.22 ( pi ) 16.15/16.22 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.15/16.22 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.15/16.22 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))) ) 16.15/16.22 ( skv_2 ) 16.15/16.22 ( skv_8 ) 16.15/16.22 ( skv_9 ) 16.15/16.22 ) 16.15/16.22 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_145635 $$unsorted)) (let ((_let_0 (number_number_of X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (plus_plus X_a))) (let ((_let_3 (hAPP int X_a _let_0 BOUND_VARIABLE_145635))) (or (not (number_ring X_a)) (= (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (zero_zero X_a)) _let_3)) _let_3) (hAPP int X_a _let_0 (hAPP int int bit0 BOUND_VARIABLE_145635)))))))) ) 16.15/16.22 ( nat, pls ) 16.15/16.22 ( nat, (hAPP int int bit1 pls) ) 16.15/16.22 ( int, pls ) 16.15/16.22 ( int, (hAPP int int bit1 pls) ) 16.15/16.22 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.15/16.22 ( real, (hAPP int int bit1 pls) ) 16.15/16.22 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.15/16.22 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.15/16.22 ( complex, (hAPP int int bit1 pls) ) 16.15/16.22 ( quickcheck_code_int, pls ) 16.15/16.22 ( code_code_numeral, pls ) 16.15/16.22 ) 16.15/16.22 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_145659 $$unsorted) (BOUND_VARIABLE_145660 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (let ((_let_1 (fun X_a bool))) (let ((_let_2 (ord_less_eq X_a))) (let ((_let_3 (hBOOL (hAPP nat bool (even_odd_even nat) BOUND_VARIABLE_145660)))) (or (not (linordered_idom X_a)) (= (and (or (and (= _let_0 (ti X_a BOUND_VARIABLE_145659)) _let_3) (and (not _let_3) (hBOOL (hAPP X_a bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_145659) _let_0)))) (not (= (zero_zero nat) BOUND_VARIABLE_145660))) (hBOOL (hAPP X_a bool (hAPP X_a _let_1 _let_2 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_145659) BOUND_VARIABLE_145660)) _let_0)))))))) ) 16.15/16.22 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.15/16.22 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.15/16.22 ( int, skv_14, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.15/16.22 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.15/16.22 ) 16.15/16.22 (instantiation (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) X_1))) (= (one_one real) (hAPP real real (sgn_sgn real) X_1))) ) 16.15/16.22 ( (zero_zero real) ) 16.15/16.22 ( pi ) 16.15/16.22 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.15/16.22 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.15/16.22 ( skv_2 ) 16.15/16.22 ( skv_8 ) 16.15/16.22 ( skv_9 ) 16.15/16.22 ) 16.15/16.22 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_145790 $$unsorted)) (or (not (monoid_add X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_145790) (zero_zero X_a)) (ti X_a BOUND_VARIABLE_145790))) ) 16.15/16.22 ( bool, fFalse ) 16.15/16.22 ( bool, fTrue ) 16.15/16.22 ( nat, (one_one nat) ) 16.15/16.22 ( int, pls ) 16.15/16.22 ( int, min_1 ) 16.15/16.22 ( int, s ) 16.15/16.22 ( int, m ) 16.15/16.22 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 16.15/16.22 ( int, s1 ) 16.15/16.22 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.15/16.22 ( int, t ) 16.15/16.22 ( (fun int bool), nat_neg ) 16.15/16.22 ( (fun int bool), zprime ) 16.15/16.22 ( (fun int bool), zEven ) 16.15/16.22 ( (fun int bool), zOdd ) 16.15/16.22 ( (fun int bool), (even_odd_even int) ) 16.15/16.22 ( (fun int bool), twoSqu1091635170sum2sq ) 16.15/16.22 ( (fun int bool), nat_is_nat ) 16.15/16.22 ( (fun int (fun int bool)), norRRset ) 16.15/16.22 ( (fun int (fun int bool)), quadRes ) 16.15/16.22 ( (fun int (fun int bool)), sRStar ) 16.15/16.22 ( (fun int (fun int bool)), d22set ) 16.15/16.22 ( (fun int (fun int bool)), sr ) 16.15/16.22 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 16.15/16.22 ( (fun int int), zfact ) 16.15/16.22 ( (fun int int), bit0 ) 16.15/16.22 ( (fun int int), bit1 ) 16.15/16.22 ( (fun int int), (fact_fact int) ) 16.15/16.22 ( (fun int int), pred ) 16.15/16.22 ( (fun int int), succ ) 16.15/16.22 ( (fun nat bool), (even_odd_even nat) ) 16.15/16.22 ( (fun nat bool), prime ) 16.15/16.22 ( (fun nat nat), suc ) 16.15/16.22 ( (fun nat nat), (fact_fact nat) ) 16.15/16.22 ( (fun nat nat), fact ) 16.15/16.22 ( (fun nat nat), nat_size ) 16.15/16.22 ( (fun nat nat), (size_size nat) ) 16.15/16.22 ( (fun (product_prod nat nat) bool), pred_nat ) 16.15/16.22 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 16.15/16.22 ( real, pi ) 16.15/16.22 ( (fun real real), ln ) 16.15/16.22 ( (fun real real), cos ) 16.15/16.22 ( (fun real real), sqrt ) 16.15/16.22 ( (fun real real), sin ) 16.15/16.22 ( (fun real real), arccos ) 16.15/16.22 ( (fun real real), arcsin ) 16.15/16.22 ( (fun real real), tan ) 16.15/16.22 ( (fun real real), arctan ) 16.15/16.22 ( (fun nat (fun nat bool)), coprime ) 16.15/16.22 ( complex, ii ) 16.15/16.22 ( (fun nat real), (real_1 nat) ) 16.15/16.22 ( (fun nat real), sin_coeff ) 16.15/16.22 ( (fun nat real), cos_coeff ) 16.15/16.22 ( (filter nat), sequentially ) 16.15/16.22 ( (fun int (fun int int)), (gcd_gcd int) ) 16.15/16.22 ( (fun int (fun int int)), legendre ) 16.15/16.22 ( (fun int (fun int int)), legacy_zgcd ) 16.15/16.22 ( (fun int (fun int int)), standardRes ) 16.15/16.22 ( (fun int (fun int int)), nat_tsub ) 16.15/16.22 ( (fun int (fun int int)), multInv ) 16.15/16.22 ( (fun int (fun int int)), z3mod ) 16.15/16.22 ( (fun int (fun int int)), z3div ) 16.15/16.22 ( (fun int (fun int int)), int_gcd ) 16.15/16.22 ( (fun int (fun int int)), int_lcm ) 16.15/16.22 ( (fun int (fun int int)), inv ) 16.15/16.22 ( (fun complex complex), expi ) 16.15/16.22 ( (fun complex complex), cnj ) 16.15/16.22 ( (fun real complex), cis ) 16.15/16.22 ( (fun int nat), nat_1 ) 16.15/16.22 ( (fun int nat), phi ) 16.15/16.22 ( (fun (fun int bool) bool), nat_nat_set ) 16.15/16.22 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 16.15/16.22 ( (fun nat (fun nat nat)), nat_gcd ) 16.15/16.22 ( (fun nat (fun nat nat)), nat_lcm ) 16.15/16.22 ( (fun (fun int bool) int), (the int) ) 16.15/16.22 ( (fun complex real), re ) 16.15/16.22 ( (fun complex real), im ) 16.15/16.22 ( (fun complex real), arg ) 16.15/16.22 ( (fun bool bool), fNot ) 16.15/16.22 ( (fun nat (fun real real)), root ) 16.15/16.22 ( (fun real (fun real real)), log ) 16.15/16.22 ( (fun real (fun real real)), powr ) 16.15/16.22 ( (fun bool (fun bool bool)), fimplies ) 16.15/16.22 ( (fun bool (fun bool bool)), fconj ) 16.15/16.22 ( (fun bool (fun bool bool)), fdisj ) 16.15/16.22 ( (fun int (fun int (product_prod int int))), negDivAlg ) 16.15/16.22 ( (fun int (fun int (product_prod int int))), posDivAlg ) 16.15/16.22 ( (fun int (fun int (product_prod int int))), divmod_int ) 16.15/16.22 ( (fun int (fun int (product_prod int int))), pdivmod ) 16.15/16.22 ( (fun int (fun int (product_prod int int))), norm_frac ) 16.15/16.22 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 16.15/16.22 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 16.15/16.22 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 16.15/16.22 ( (fun int (fun int (fun int bool))), zcong ) 16.15/16.22 ( (fun int (fun int (fun int bool))), zcongm ) 16.15/16.22 ( (fun int (fun int (fun int bool))), noXRRset ) 16.15/16.22 ( (fun int (fun int (fun int bool))), bnorRset ) 16.15/16.22 ( (fun int (fun int (fun int bool))), wset ) 16.15/16.22 ( (fun (product_prod int int) bool), frac_1 ) 16.15/16.22 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 16.15/16.22 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 16.15/16.22 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 16.15/16.22 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 16.15/16.22 ( (fun (fun nat rat) bool), vanishes ) 16.15/16.22 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 16.15/16.22 ( (fun code_code_numeral nat), code_c271388182l_size ) 16.15/16.22 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 16.15/16.22 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 16.15/16.22 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 16.15/16.22 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 16.15/16.22 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 16.15/16.23 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 16.15/16.23 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 16.15/16.23 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 16.15/16.23 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 16.15/16.23 ( (fun complex nat), complex_size ) 16.15/16.23 ( (fun complex nat), (size_size complex) ) 16.15/16.23 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 16.15/16.23 ( (fun nat (fun nat (product_prod int int))), bezw ) 16.15/16.23 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 16.15/16.23 ( (fun int (fun nat nat)), nat_aux ) 16.15/16.23 ( (fun int (fun (fun int bool) bool)), rsetR ) 16.15/16.23 ( (fun int (fun (fun int bool) bool)), resSet ) 16.15/16.23 ( (fun int (list int)), quickc666637781d_zero ) 16.15/16.23 ( (fun (product_prod int int) rat), frct ) 16.15/16.23 ( (fun int (fun int rat)), fract ) 16.15/16.23 ( (fun real (fun real complex)), complex_1 ) 16.15/16.23 ( (fun real (fun real complex)), rcis ) 16.15/16.23 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 16.15/16.23 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 16.15/16.23 ( (fun int real), (real_1 int) ) 16.15/16.23 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 16.15/16.23 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 16.15/16.23 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 16.15/16.23 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 16.15/16.23 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 16.15/16.23 ( (fun real nat), natfloor ) 16.15/16.23 ( (fun real nat), natceiling ) 16.15/16.23 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 16.15/16.23 ( (fun quickcheck_code_int int), quickcheck_int_of ) 16.15/16.23 ( (fun rat (product_prod int int)), quotient_of ) 16.15/16.23 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 16.15/16.23 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 16.15/16.23 ( (fun rat real), ratreal ) 16.15/16.23 ( (fun code_code_numeral int), code_int_of ) 16.15/16.23 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 16.15/16.23 ( (fun int quickcheck_code_int), quickcheck_of_int ) 16.15/16.23 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 16.15/16.23 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 16.15/16.23 ) 16.15/16.23 (instantiation (forall ((X_2 $$unsorted)) (= (not (forall ((Y $$unsorted)) (not (= (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) Y) (ti int X_2))) )) (hBOOL (hAPP int bool (even_odd_even int) X_2))) ) 16.15/16.23 ( (one_one int) ) 16.15/16.23 ( (zero_zero int) ) 16.15/16.23 ) 16.15/16.23 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (zero_zero real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP real real (uminus_uminus real) pi)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) _let_2))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real tan X_1)) _let_2)))))) ) 16.15/16.23 ( (zero_zero real) ) 16.15/16.23 ( pi ) 16.15/16.23 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.15/16.23 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.15/16.23 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 16.15/16.23 ) 16.15/16.23 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (complete_Sup_Sup X_a))) (or (not (comple44059174attice X_a)) (= _let_0 (ti (fun (fun X_a bool) X_a) _let_0)))) ) 16.15/16.23 ( bool ) 16.15/16.23 ( nat ) 16.15/16.23 ( int ) 16.15/16.23 ( (fun int bool) ) 16.15/16.23 ( (fun nat bool) ) 16.15/16.23 ( (product_prod nat nat) ) 16.15/16.23 ( real ) 16.15/16.23 ( (filter nat) ) 16.15/16.23 ( (product_prod int int) ) 16.15/16.23 ( (product_prod real real) ) 16.15/16.23 ( (fun nat rat) ) 16.15/16.23 ( (filter real) ) 16.15/16.23 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 16.15/16.23 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 16.15/16.23 ) 16.15/16.23 (instantiation (forall ((N $$unsorted)) (let ((_let_0 (fun nat (fun nat bool)))) (= (hAPP (fun nat bool) nat (finite_card nat) (hAPP (fun nat bool) (fun nat bool) (collect nat) (hAPP nat (fun nat bool) (hAPP _let_0 _let_0 (combc nat nat bool) (ord_less_eq nat)) N))) (hAPP nat nat suc N))) ) 16.15/16.23 ( (zero_zero nat) ) 16.15/16.23 ( (hAPP nat nat suc (zero_zero nat)) ) 16.15/16.23 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 16.15/16.23 ) 16.15/16.23 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_145876 $$unsorted)) (let ((_let_0 (fun nat X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (fun nat _let_1))) (or (not (real_n2089651433ebra_1 X_a)) (= (hAPP nat X_a BOUND_VARIABLE_145876 (zero_zero nat)) (hAPP _let_0 X_a (suminf X_a) (hAPP _let_0 _let_0 (hAPP _let_2 (fun _let_0 _let_0) (combs nat X_a X_a) (hAPP _let_0 _let_2 (hAPP (fun X_a _let_1) (fun _let_0 _let_2) (combb X_a _let_1 nat) (times_times X_a)) BOUND_VARIABLE_145876)) (hAPP X_a _let_0 (power_power X_a) (zero_zero X_a))))))))) ) 16.15/16.23 ( bool, (even_odd_even nat) ) 16.15/16.23 ( bool, prime ) 16.15/16.23 ( nat, suc ) 16.15/16.23 ( nat, (fact_fact nat) ) 16.15/16.23 ( nat, fact ) 16.15/16.23 ( nat, nat_size ) 16.15/16.23 ( nat, (size_size nat) ) 16.15/16.23 ( int, (semiring_1_of_nat int) ) 16.15/16.23 ( (fun nat bool), (ord_less nat) ) 16.15/16.23 ( (fun nat bool), (let ((_let_0 (fun nat (fun nat bool)))) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat))) ) 16.15/16.23 ( real, (real_1 nat) ) 16.15/16.23 ( real, (hAPP real (fun nat real) (power_power real) (hAPP int real (number_number_of real) min_1)) ) 16.15/16.23 ) 16.15/16.23 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_145894 $$unsorted) (BOUND_VARIABLE_145895 $$unsorted)) (let ((_let_0 (archimedean_ceiling X_a))) (or (not (archim1727834104eiling X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_145894) BOUND_VARIABLE_145895))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP X_a int _let_0 BOUND_VARIABLE_145894)) (hAPP X_a int _let_0 BOUND_VARIABLE_145895))))) ) 16.15/16.23 ( int, (one_one int), t ) 16.15/16.23 ( int, (zero_zero int), (one_one int) ) 16.15/16.23 ( int, (zero_zero int), min_1 ) 16.15/16.23 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.15/16.23 ( int, (zero_zero int), s ) 16.15/16.23 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.15/16.23 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 16.15/16.23 ( int, (zero_zero int), skv_4 ) 16.15/16.23 ( int, (zero_zero int), skv_10 ) 16.15/16.23 ( int, min_1, pls ) 16.15/16.23 ( int, min_1, min_1 ) 16.15/16.23 ( real, (zero_zero real), pi ) 16.15/16.23 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.15/16.23 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.15/16.23 ( real, (zero_zero real), skv_3 ) 16.15/16.23 ( real, (zero_zero real), skv_5 ) 16.15/16.23 ( real, (zero_zero real), skv_7 ) 16.15/16.23 ( real, (zero_zero real), skv_12 ) 16.15/16.23 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.15/16.23 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.15/16.23 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.15/16.23 ( real, skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.15/16.23 ) 16.15/16.23 (instantiation (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_0 (even_odd_even int))) (or (not (hBOOL (hAPP int bool _let_0 X_1))) (hBOOL (hAPP int bool _let_0 (hAPP int int (hAPP int (fun int int) (times_times int) X_1) Y_1))))) ) 16.15/16.23 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.15/16.23 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.15/16.23 ( skv_13, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.15/16.23 ) 16.15/16.23 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_0 (big_co302546470etprod X_a X_b))) (or (not (comm_monoid_mult X_b)) (= _let_0 (ti (fun (fun X_a X_b) (fun (fun X_a bool) X_b)) _let_0)))) ) 16.15/16.23 ( bool, (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 16.15/16.23 ( nat, bool ) 16.15/16.23 ( nat, (fun nat bool) ) 16.15/16.23 ( nat, (fun nat (fun bool bool)) ) 16.15/16.23 ( nat, (fun int (fun nat bool)) ) 16.15/16.23 ( nat, (fun real (fun int (fun nat bool))) ) 16.15/16.23 ( int, bool ) 16.15/16.23 ( int, int ) 16.15/16.23 ( int, (fun int bool) ) 16.15/16.23 ( int, (fun int (fun int bool)) ) 16.15/16.23 ( int, (fun int (fun int int)) ) 16.15/16.23 ( int, (fun int (fun bool bool)) ) 16.15/16.23 ( int, (fun (fun int int) (fun int bool)) ) 16.15/16.23 ( int, (fun real (fun int (fun int bool))) ) 16.15/16.23 ( real, real ) 16.15/16.23 ( real, (fun real bool) ) 16.15/16.23 ( real, (fun real (fun bool bool)) ) 16.15/16.23 ( real, (fun (fun int real) (fun int bool)) ) 16.15/16.23 ( real, (fun (fun nat real) (fun nat bool)) ) 16.15/16.23 ( (product_prod int int), (fun (product_prod int int) bool) ) 16.15/16.23 ( (product_prod int int), (fun (product_prod int int) (fun bool bool)) ) 16.15/16.23 ( (product_prod real real), (fun real (fun real (fun nat (product_prod real real)))) ) 16.15/16.23 ) 16.15/16.23 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member int))) (or (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP int int (hAPP int (fun int int) (times_times int) X_2) Y_2)) zEven))) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 Y_2) zEven)) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 X_2) zEven)))))) ) 16.15/16.23 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 16.15/16.23 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 16.15/16.23 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13 ) 16.15/16.23 ) 16.15/16.23 (instantiation (forall ((X_a $$unsorted) (C_1 $$unsorted) (P_1 $$unsorted) (BOUND_VARIABLE_145948 $$unsorted)) (or (not (hBOOL (hAPP X_a bool P_1 BOUND_VARIABLE_145948))) (not (= (ti X_a C_1) (hAPP (fun X_a bool) X_a (hilbert_Eps X_a) P_1))) (hBOOL (hAPP X_a bool P_1 C_1))) ) 16.15/16.23 ( int, pls, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) s)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.15/16.23 ( int, min_1, nat_is_nat, (one_one int) ) 16.15/16.23 ( int, s, (hAPP int (fun int bool) (ord_less int) pls), pls ) 16.15/16.23 ( int, m, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), s ) 16.15/16.23 ( int, s1, (hAPP int (fun int bool) (ord_less int) s), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.15/16.23 ( int, t, (let ((_let_0 (fun int int))) (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 16.15/16.23 ( (fun int bool), zEven, (hAPP int (fun (fun int bool) bool) (member int) (one_one int)), zEven ) 16.15/16.23 ( (fun int bool), twoSqu1091635170sum2sq, (hAPP (fun int nat) (fun (fun int bool) bool) (nat_tr1645093318rphism int nat) nat_1), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 16.15/16.23 ( (fun nat bool), (even_odd_even nat), (finite_finite_1 nat), (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 16.15/16.23 ( (fun nat bool), prime, (hAPP (fun nat int) (fun (fun nat bool) bool) (nat_tr1645093318rphism nat int) (semiring_1_of_nat int)), (hAPP bool (fun nat bool) (combk bool nat) fTrue) ) 16.15/16.23 ( real, pi, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), pi ) 16.15/16.23 ( (filter nat), sequentially, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun (filter nat) bool))) (hAPP real _let_2 (hAPP _let_1 (fun real _let_2) (tendsto nat real) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))) (zero_zero real))))), sequentially ) 16.15/16.23 ) 16.15/16.23 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_145973 $$unsorted) (BOUND_VARIABLE_145974 $$unsorted) (BOUND_VARIABLE_145975 $$unsorted) (BOUND_VARIABLE_145986 $$unsorted) (BOUND_VARIABLE_145987 $$unsorted) (BOUND_VARIABLE_145988 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (div_div X_a))) (let ((_let_3 (hAPP X_a _let_1 (times_times X_a) BOUND_VARIABLE_145975))) (let ((_let_4 (hAPP X_a _let_1 (times_times X_a) BOUND_VARIABLE_145988))) (or (not (semiring_div X_a)) (and (or (not (= _let_0 (ti X_a BOUND_VARIABLE_145975))) (= _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a _let_3 BOUND_VARIABLE_145973)) (hAPP X_a X_a _let_3 BOUND_VARIABLE_145974)))) (or (= _let_0 (ti X_a BOUND_VARIABLE_145988)) (= (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a _let_4 BOUND_VARIABLE_145986)) (hAPP X_a X_a _let_4 BOUND_VARIABLE_145987)) (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_145986) BOUND_VARIABLE_145987)))))))))) ) 16.15/16.23 ( int, m, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.15/16.23 ( int, t, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.15/16.23 ( int, skv_13, skv_13, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13, skv_13, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.15/16.23 ( real, pi, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.15/16.23 ( real, pi, pi, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi, pi, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 16.15/16.23 ( real, (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.15/16.23 ( real, (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.15/16.23 ( complex, ii, ii, ii, ii, ii, ii ) 16.15/16.23 ( complex, ii, ii, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii, ii, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 16.15/16.23 ( complex, (hAPP real complex (of_real complex) pi), (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi), (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.15/16.23 ) 16.15/16.23 (instantiation (forall ((I $$unsorted)) (let ((_let_0 (fun int (fun int bool)))) (or (= (zero_zero int) (ti int I)) (hBOOL (hAPP (fun int bool) bool (finite_finite_1 int) (hAPP (fun int bool) (fun int bool) (collect int) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (dvd_dvd int)) I)))))) ) 16.15/16.23 ( min_1 ) 16.15/16.23 ( s ) 16.15/16.23 ( m ) 16.15/16.23 ( s1 ) 16.15/16.23 ( t ) 16.15/16.23 ) 16.15/16.23 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_146028 $$unsorted) (BOUND_VARIABLE_146029 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (inverse_inverse X_a))) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_146028) BOUND_VARIABLE_146029))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_146028))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_146029)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_146028))))))) ) 16.15/16.23 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.15/16.23 ( int, (one_one int), t ) 16.15/16.23 ( int, pls, (one_one int) ) 16.15/16.23 ( int, pls, pls ) 16.15/16.23 ( int, pls, min_1 ) 16.15/16.23 ( int, pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.15/16.23 ( int, min_1, pls ) 16.15/16.23 ( int, min_1, min_1 ) 16.15/16.23 ( int, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.15/16.23 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.15/16.23 ( int, skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.15/16.23 ( int, skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.15/16.23 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.15/16.23 ( real, (zero_zero real), pi ) 16.15/16.23 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.15/16.23 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.15/16.23 ( real, (zero_zero real), skv_2 ) 16.15/16.23 ( real, (zero_zero real), skv_8 ) 16.15/16.23 ( real, (zero_zero real), skv_9 ) 16.15/16.23 ( real, pi, (zero_zero real) ) 16.15/16.23 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.15/16.23 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.15/16.23 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 16.15/16.23 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.15/16.23 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 16.15/16.23 ) 16.15/16.23 (instantiation (forall ((N_1 $$unsorted)) (= (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP int real (number_number_of real) min_1)) N_1) (hAPP real real cos (hAPP real real (hAPP real (fun real real) (times_times real) pi) (hAPP nat real (real_1 nat) N_1)))) ) 16.15/16.23 ( (zero_zero nat) ) 16.15/16.23 ( (hAPP nat nat suc (zero_zero nat)) ) 16.15/16.23 ) 16.15/16.23 (instantiation (forall ((Y_2 $$unsorted) (X_2 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member int))) (or (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 X_2) zOdd))) (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 Y_2) zOdd))) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP int int (hAPP int (fun int int) (times_times int) X_2) Y_2)) zOdd)))))) ) 16.15/16.23 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.15/16.23 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.15/16.23 ( skv_13, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.15/16.23 ) 16.15/16.23 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted) (A_8 $$unsorted) (B_7 $$unsorted)) (let ((_let_0 (product_prod X_a X_b))) (let ((_let_1 (fun X_b _let_0))) (let ((_let_2 (product_Pair X_a X_b))) (= (= (hAPP X_b _let_0 (hAPP X_a _let_1 _let_2 A_2) B_1) (hAPP X_b _let_0 (hAPP X_a _let_1 _let_2 A_8) B_7)) (and (= (ti X_a A_2) (ti X_a A_8)) (= (ti X_b B_7) (ti X_b B_1))))))) ) 16.15/16.23 ( int, int, (one_one int), (one_one int), s, (one_one int) ) 16.15/16.23 ( int, int, (zero_zero int), (one_one int), (one_one int), (one_one int) ) 16.15/16.23 ( int, int, (zero_zero int), (one_one int), s, (one_one int) ) 16.15/16.23 ( int, int, s, (one_one int), (zero_zero int), (one_one int) ) 16.15/16.23 ( int, int, s, (one_one int), s, (one_one int) ) 16.15/16.23 ) 16.15/16.23 (instantiation (forall ((Z_1 $$unsorted) (Z_4 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (zero_zero int)) Z_4))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 Z_4) Z_1))) (= (hAPP int nat nat_1 (hAPP int int (hAPP int (fun int int) (minus_minus int) Z_1) Z_4)) (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) (hAPP int nat nat_1 Z_1)) (hAPP int nat nat_1 Z_4)))))) ) 16.15/16.23 ( (one_one int), (zero_zero int) ) 16.15/16.23 ( pls, min_1 ) 16.15/16.23 ( min_1, (zero_zero int) ) 16.15/16.23 ( min_1, min_1 ) 16.15/16.23 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 16.15/16.23 ( s, (zero_zero int) ) 16.15/16.23 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 16.15/16.23 ( t, (one_one int) ) 16.15/16.23 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 16.15/16.23 ( (hAPP int int (number_number_of int) pls), (zero_zero int) ) 16.15/16.23 ( skv_4, (zero_zero int) ) 16.15/16.23 ( skv_10, (zero_zero int) ) 16.15/16.23 ) 16.15/16.23 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_146134 $$unsorted) (BOUND_VARIABLE_146135 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (or (not (group_add X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 (minus_minus X_a) (hAPP X_a X_a (hAPP X_a _let_0 (plus_plus X_a) BOUND_VARIABLE_146134) BOUND_VARIABLE_146135)) BOUND_VARIABLE_146135) (ti X_a BOUND_VARIABLE_146134)))) ) 16.15/16.23 ( nat, (one_one nat), (one_one nat) ) 16.15/16.23 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 16.15/16.23 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 16.15/16.23 ) 16.15/16.23 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_146158 $$unsorted) (BOUND_VARIABLE_146159 $$unsorted) (BOUND_VARIABLE_146160 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (or (not (ord X_a)) (not (= (ti X_a BOUND_VARIABLE_146159) (ti X_a BOUND_VARIABLE_146160))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_146160) BOUND_VARIABLE_146158))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_146159) BOUND_VARIABLE_146158))))) ) 16.15/16.23 ( int, (one_one int), s1, (zero_zero int) ) 16.15/16.23 ( int, pls, pls, min_1 ) 16.15/16.23 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), t, (zero_zero int) ) 16.15/16.23 ( int, s, s, (zero_zero int) ) 16.15/16.23 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), m, (zero_zero int) ) 16.15/16.23 ( int, (hAPP int int (number_number_of int) pls), min_1, (zero_zero int) ) 16.15/16.23 ( real, pi, pi, (zero_zero real) ) 16.15/16.23 ) 16.15/16.23 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_146189 $$unsorted) (BOUND_VARIABLE_146190 $$unsorted) (BOUND_VARIABLE_146191 $$unsorted) (BOUND_VARIABLE_146192 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (minus_minus X_a))) (let ((_let_2 (fun X_a bool))) (let ((_let_3 (ord_less_eq X_a))) (or (not (ordered_ab_group_add X_a)) (not (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_146191) BOUND_VARIABLE_146192) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_146189) BOUND_VARIABLE_146190))) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_146189) BOUND_VARIABLE_146190)) (hBOOL (hAPP X_a bool (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_146191) BOUND_VARIABLE_146192)))))))) ) 16.15/16.23 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 16.15/16.23 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))), (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 16.15/16.23 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral), (zero_zero code_code_numeral), (one_one code_code_numeral) ) 16.15/16.23 ) 16.15/16.23 (instantiation (forall ((X_1 $$unsorted) (A_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) X_1) (hAPP nat real (real_1 nat) A_1)))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP real nat natceiling X_1)) A_1))) ) 16.15/16.23 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero nat) ) 16.15/16.23 ) 16.15/16.23 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_146274 $$unsorted) (BOUND_VARIABLE_146275 $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (ring_1 X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) BOUND_VARIABLE_146275) (ring_1_Ints X_a)))) (not (forall ((Z_2 $$unsorted)) (hBOOL (hAPP X_a bool BOUND_VARIABLE_146274 (hAPP int X_a (ring_1_of_int X_a) Z_2))) )) (hBOOL (hAPP X_a bool BOUND_VARIABLE_146274 BOUND_VARIABLE_146275)))) ) 16.15/16.23 ( nat, (even_odd_even nat), (zero_zero nat) ) 16.15/16.23 ( nat, (even_odd_even nat), (one_one nat) ) 16.15/16.23 ( nat, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.15/16.23 ( nat, prime, (zero_zero nat) ) 16.15/16.23 ( nat, prime, (hAPP nat nat suc (zero_zero nat)) ) 16.15/16.23 ( nat, prime, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.15/16.23 ( int, (hAPP int (fun int bool) (ord_less int) pls), pls ) 16.15/16.23 ( int, (hAPP int (fun int bool) (ord_less int) pls), min_1 ) 16.15/16.23 ( int, (hAPP int (fun int bool) (ord_less_eq int) pls), min_1 ) 16.15/16.23 ( int, (hAPP int (fun int bool) (ord_less_eq int) (one_one int)), t ) 16.15/16.23 ( int, nat_neg, (one_one int) ) 16.15/16.23 ( int, nat_neg, (hAPP int int (number_number_of int) min_1) ) 16.15/16.23 ( int, nat_neg, (hAPP int int (number_number_of int) pls) ) 16.15/16.23 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (one_one int) ) 16.15/16.23 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.15/16.23 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), s ) 16.15/16.23 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.15/16.23 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) pls) ) 16.15/16.23 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_4 ) 16.15/16.23 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_10 ) 16.15/16.23 ( int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (one_one int) ) 16.15/16.23 ( int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.15/16.23 ( int, zprime, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.15/16.23 ( int, zprime, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.15/16.23 ( int, (hAPP int (fun int bool) (ord_less int) s), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.15/16.23 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) s)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.15/16.23 ( int, (let ((_let_0 (fun int int))) (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 16.15/16.23 ( int, (hAPP int (fun int bool) (ord_less int) (one_one int)), t ) 16.15/16.23 ( int, (even_odd_even int), (one_one int) ) 16.15/16.23 ( int, (even_odd_even int), (zero_zero int) ) 16.15/16.23 ( int, twoSqu1091635170sum2sq, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) t))) ) 16.15/16.23 ( int, nat_is_nat, (one_one int) ) 16.15/16.23 ( int, nat_is_nat, (zero_zero int) ) 16.15/16.23 ( int, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.15/16.23 ( int, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.15/16.23 ( int, (hAPP int (fun int bool) (ord_less int) min_1), pls ) 16.15/16.23 ( int, (hAPP int (fun int bool) (ord_less int) min_1), min_1 ) 16.15/16.23 ( int, (hAPP int (fun int bool) (ord_less_eq int) min_1), pls ) 16.15/16.23 ( int, (hAPP int (fun int bool) (ord_less_eq int) min_1), min_1 ) 16.18/16.23 ( int, (let ((_let_0 (fun int int))) (hAPP int (fun int bool) quadRes (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int int (number_number_of int) min_1) ) 16.18/16.23 ( int, (let ((_let_0 (fun int bool))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (let ((_let_3 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int _let_1 _let_2 s) _let_3)) (hAPP nat int (hAPP int _let_1 _let_2 s1) _let_3)))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.18/16.23 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.18/16.23 ( int, (hAPP int (fun int bool) (ord_less int) t), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.18/16.23 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.18/16.23 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_4)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.18/16.23 ( int, (hAPP int (fun int bool) (ord_less int) skv_4), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.18/16.23 ( int, (hAPP int (fun int bool) (ord_less int) skv_10), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.18/16.23 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_10)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.18/16.23 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.18/16.23 ( (fun int bool), (hAPP (fun int nat) (fun (fun int bool) bool) (nat_tr1645093318rphism int nat) nat_1), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 16.18/16.23 ( (fun int bool), (hAPP int (fun (fun int bool) bool) (member int) (one_one int)), zEven ) 16.18/16.23 ( (fun nat bool), (finite_finite_1 nat), (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 16.18/16.23 ( (fun nat bool), (hAPP (fun nat int) (fun (fun nat bool) bool) (nat_tr1645093318rphism nat int) (semiring_1_of_nat int)), (hAPP bool (fun nat bool) (combk bool nat) fTrue) ) 16.18/16.23 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), pi ) 16.18/16.23 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.18/16.23 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.18/16.23 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_3 ) 16.18/16.23 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_5 ) 16.18/16.23 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_7 ) 16.18/16.23 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_12 ) 16.18/16.23 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), pi ) 16.18/16.23 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.18/16.23 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.18/16.23 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_2 ) 16.18/16.23 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_8 ) 16.18/16.23 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_9 ) 16.18/16.23 ( real, (hAPP real (fun real bool) (ord_less real) (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))), (zero_zero real) ) 16.18/16.23 ( real, (hAPP real (fun real bool) (ord_less real) (one_one real)), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.18/16.23 ( real, (hAPP real (fun real bool) (ord_less real) pi), (zero_zero real) ) 16.18/16.23 ( real, (hAPP real (fun real bool) (ord_less real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.18/16.23 ( real, (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.18/16.23 ( real, (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 16.18/16.23 ( real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 (fun real bool) (sums real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (hAPP real _let_1 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc)))), (one_one real) ) 16.18/16.23 ( real, (hAPP real (fun real bool) (ord_less real) (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi))), pi ) 16.18/16.23 ( real, (hAPP real (fun real bool) (ord_less real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.18/16.23 ( real, (hAPP real (fun real bool) (ord_less real) (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 16.18/16.23 ( real, (hAPP real (fun real bool) (ord_less_eq real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 16.18/16.23 ( real, (hAPP real (fun real bool) (ord_less_eq real) skv_5), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.18/16.23 ( (filter nat), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun (filter nat) bool))) (hAPP real _let_2 (hAPP _let_1 (fun real _let_2) (tendsto nat real) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))) (zero_zero real))))), sequentially ) 16.18/16.23 ( (filter nat), (trivial_limit nat), sequentially ) 16.18/16.23 ( (filter real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (filter real) bool))) (hAPP real _let_2 (hAPP _let_0 (fun real _let_2) (tendsto real real) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin)) (zero_zero real))))), (hAPP real (filter real) (at real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.18/16.23 ) 16.18/16.23 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (let ((_let_2 (real_1 nat))) (let ((_let_3 (fact_fact nat))) (let ((_let_4 (inverse_inverse real))) (= (hAPP real real _let_4 (hAPP nat real _let_2 (hAPP nat nat _let_3 X))) (hAPP nat real (hAPP _let_1 _let_1 (diffs real) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) _let_4) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) _let_2) _let_3))) X))))))) ) 16.18/16.23 ( (zero_zero nat) ) 16.18/16.23 ( (hAPP nat nat suc (zero_zero nat)) ) 16.18/16.23 ) 16.18/16.23 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (one_one real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat real))) (let ((_let_3 (power_power real))) (let ((_let_4 (fun nat _let_1))) (let ((_let_5 (fun _let_2 _let_2))) (let ((_let_6 (combs nat real real))) (let ((_let_7 (fun (fun nat nat) _let_2))) (let ((_let_8 (combb nat real nat))) (let ((_let_9 (hAPP (fun real _let_1) (fun _let_2 _let_4) (combb real _let_1 nat) (times_times real)))) (let ((_let_10 (combc nat nat nat))) (let ((_let_11 (hAPP nat (fun nat nat) (hAPP (fun nat (fun nat nat)) (fun nat (fun nat nat)) _let_10 (hAPP (fun nat nat) (fun nat (fun nat nat)) (hAPP (fun nat (fun nat nat)) (fun (fun nat nat) (fun nat (fun nat nat))) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP (fun nat (fun nat nat)) (fun nat (fun nat nat)) _let_10 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (abs_abs real) X_2)) _let_0))) (hBOOL (hAPP _let_2 bool (summable real) (hAPP _let_2 _let_2 (hAPP _let_4 _let_5 _let_6 (hAPP _let_2 _let_4 _let_9 (hAPP real _let_2 _let_3 (hAPP int real (number_number_of real) min_1)))) (hAPP _let_2 _let_2 (hAPP _let_4 _let_5 _let_6 (hAPP _let_2 _let_4 _let_9 (hAPP _let_2 _let_2 (hAPP _let_1 _let_5 (combb real real nat) (hAPP real _let_1 (inverse_divide real) _let_0)) (hAPP (fun nat nat) _let_2 (hAPP _let_2 _let_7 _let_8 (real_1 nat)) _let_11)))) (hAPP (fun nat nat) _let_2 (hAPP _let_2 _let_7 _let_8 (hAPP real _let_2 _let_3 X_2)) _let_11)))))))))))))))))) ) 16.18/16.23 ( (hAPP int real (number_number_of real) min_1) ) 16.18/16.23 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.18/16.23 ) 16.18/16.23 (instantiation (forall ((N $$unsorted)) (let ((_let_0 (zero_zero nat))) (= (not (= _let_0 N)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) _let_0) N)))) ) 16.18/16.23 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.18/16.23 ) 16.18/16.23 (instantiation (forall ((Ta $$unsorted) (A_3 $$unsorted) (D_2 $$unsorted) (BOUND_VARIABLE_146440 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (zero_zero int)) D_2))) (not (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) Ta) A_3))) (not (forall ((Xa $$unsorted) (BOUND_VARIABLE_146410 $$unsorted)) (let ((_let_1 (member int))) (let ((_let_2 (fun _let_0 bool))) (or (not (hBOOL (hAPP _let_0 bool (hAPP int _let_2 _let_1 Xa) (hAPP int _let_0 (hAPP int (fun int _let_0) (ord_atLeastAtMost int) (one_one int)) D_2)))) (not (hBOOL (hAPP _let_0 bool (hAPP int _let_2 _let_1 BOUND_VARIABLE_146410) A_3))) (not (= (hAPP int int (hAPP int (fun int int) (minus_minus int) BOUND_VARIABLE_146410) Xa) (ti int BOUND_VARIABLE_146440)))))) )) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 BOUND_VARIABLE_146440) Ta))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int (hAPP int (fun int int) (plus_plus int) BOUND_VARIABLE_146440) D_2)) Ta))))) ) 16.18/16.23 ( (one_one int), zEven, pls, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 16.18/16.23 ) 16.18/16.23 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_146483 $$unsorted) (BOUND_VARIABLE_146484 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_atMost X_a))) (or (not (linorder X_a)) (= (= (ti X_a BOUND_VARIABLE_146484) (ti X_a BOUND_VARIABLE_146483)) (= (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_146483) (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_146484)))))) ) 16.18/16.23 ( bool, fFalse, fFalse ) 16.18/16.23 ( bool, fFalse, fTrue ) 16.18/16.23 ( bool, fTrue, fFalse ) 16.18/16.23 ( int, pls, s1 ) 16.18/16.23 ( int, min_1, t ) 16.18/16.23 ( int, s, pls ) 16.18/16.23 ( int, s, s ) 16.18/16.23 ( int, s, s1 ) 16.18/16.23 ( int, m, min_1 ) 16.18/16.23 ( int, m, m ) 16.18/16.23 ( int, m, t ) 16.18/16.23 ( int, s1, s ) 16.18/16.23 ( int, t, m ) 16.18/16.23 ( (fun int bool), nat_neg, (even_odd_even int) ) 16.18/16.23 ( (fun int bool), zprime, nat_neg ) 16.18/16.23 ( (fun int bool), zEven, twoSqu1091635170sum2sq ) 16.18/16.23 ( (fun int bool), zOdd, zOdd ) 16.18/16.23 ( (fun int bool), (even_odd_even int), nat_neg ) 16.18/16.23 ( (fun int bool), (even_odd_even int), zprime ) 16.18/16.23 ( (fun int bool), (even_odd_even int), (even_odd_even int) ) 16.18/16.23 ( (fun int bool), twoSqu1091635170sum2sq, zEven ) 16.18/16.23 ( (fun int bool), twoSqu1091635170sum2sq, twoSqu1091635170sum2sq ) 16.18/16.23 ( (fun int bool), twoSqu1091635170sum2sq, nat_is_nat ) 16.18/16.23 ( (fun int bool), nat_is_nat, zEven ) 16.18/16.23 ( (fun int (fun int bool)), norRRset, norRRset ) 16.18/16.23 ( (fun int (fun int bool)), norRRset, d22set ) 16.18/16.23 ( (fun int (fun int bool)), norRRset, sr ) 16.18/16.23 ( (fun int (fun int bool)), quadRes, quadRes ) 16.18/16.23 ( (fun int (fun int bool)), quadRes, sRStar ) 16.18/16.23 ( (fun int (fun int bool)), quadRes, quickc1265749348ro_rel ) 16.18/16.23 ( (fun int (fun int bool)), sRStar, quadRes ) 16.18/16.23 ( (fun int (fun int bool)), d22set, sr ) 16.18/16.23 ( (fun int (fun int bool)), sr, norRRset ) 16.18/16.23 ( (fun int (fun int bool)), quickc1265749348ro_rel, sRStar ) 16.18/16.23 ( (fun int int), zfact, pred ) 16.18/16.23 ( (fun int int), bit0, (fact_fact int) ) 16.18/16.23 ( (fun int int), bit1, zfact ) 16.18/16.23 ( (fun int int), bit1, bit1 ) 16.18/16.23 ( (fun int int), bit1, pred ) 16.18/16.23 ( (fun int int), (fact_fact int), bit0 ) 16.18/16.23 ( (fun int int), (fact_fact int), (fact_fact int) ) 16.18/16.23 ( (fun int int), (fact_fact int), succ ) 16.18/16.23 ( (fun int int), pred, bit1 ) 16.18/16.23 ( (fun int int), succ, bit0 ) 16.18/16.23 ( (fun nat bool), (even_odd_even nat), (even_odd_even nat) ) 16.18/16.23 ( (fun nat bool), (even_odd_even nat), prime ) 16.18/16.23 ( (fun nat bool), prime, (even_odd_even nat) ) 16.18/16.23 ( (fun nat nat), suc, fact ) 16.18/16.23 ( (fun nat nat), (fact_fact nat), (size_size nat) ) 16.18/16.23 ( (fun nat nat), fact, suc ) 16.18/16.23 ( (fun nat nat), fact, fact ) 16.18/16.23 ( (fun nat nat), nat_size, (fact_fact nat) ) 16.18/16.23 ( (fun nat nat), nat_size, nat_size ) 16.18/16.23 ( (fun nat nat), nat_size, (size_size nat) ) 16.18/16.23 ( (fun nat nat), (size_size nat), nat_size ) 16.18/16.23 ( (fun (product_prod nat nat) bool), pred_nat, pred_nat ) 16.18/16.24 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel, divmod_nat_rel ) 16.18/16.24 ( real, pi, pi ) 16.18/16.24 ( (fun real real), ln, sqrt ) 16.18/16.24 ( (fun real real), cos, cos ) 16.18/16.24 ( (fun real real), cos, tan ) 16.18/16.24 ( (fun real real), sqrt, ln ) 16.18/16.24 ( (fun real real), sqrt, sqrt ) 16.18/16.24 ( (fun real real), sqrt, arccos ) 16.18/16.24 ( (fun real real), sin, arcsin ) 16.18/16.24 ( (fun real real), arccos, ln ) 16.18/16.24 ( (fun real real), arcsin, sin ) 16.18/16.24 ( (fun real real), arcsin, arcsin ) 16.18/16.24 ( (fun real real), arcsin, arctan ) 16.18/16.24 ( (fun real real), tan, cos ) 16.18/16.24 ( (fun real real), arctan, sin ) 16.18/16.24 ( (fun nat (fun nat bool)), coprime, coprime ) 16.18/16.24 ( complex, ii, ii ) 16.18/16.24 ( (fun nat real), (real_1 nat), sin_coeff ) 16.18/16.24 ( (fun nat real), sin_coeff, (real_1 nat) ) 16.18/16.24 ( (fun nat real), sin_coeff, sin_coeff ) 16.18/16.24 ( (fun nat real), sin_coeff, cos_coeff ) 16.18/16.24 ( (fun nat real), cos_coeff, (real_1 nat) ) 16.18/16.24 ( (filter nat), sequentially, sequentially ) 16.18/16.24 ( (fun int (fun int int)), (gcd_gcd int), (gcd_gcd int) ) 16.18/16.24 ( (fun int (fun int int)), (gcd_gcd int), int_gcd ) 16.18/16.24 ( (fun int (fun int int)), legendre, z3div ) 16.18/16.24 ( (fun int (fun int int)), legacy_zgcd, legendre ) 16.18/16.24 ( (fun int (fun int int)), standardRes, multInv ) 16.18/16.24 ( (fun int (fun int int)), nat_tsub, z3mod ) 16.18/16.24 ( (fun int (fun int int)), multInv, standardRes ) 16.18/16.24 ( (fun int (fun int int)), multInv, multInv ) 16.18/16.24 ( (fun int (fun int int)), multInv, inv ) 16.18/16.24 ( (fun int (fun int int)), z3mod, nat_tsub ) 16.18/16.24 ( (fun int (fun int int)), z3mod, z3mod ) 16.18/16.24 ( (fun int (fun int int)), z3mod, int_lcm ) 16.18/16.24 ( (fun int (fun int int)), z3div, legendre ) 16.18/16.24 ( (fun int (fun int int)), z3div, legacy_zgcd ) 16.18/16.24 ( (fun int (fun int int)), z3div, z3div ) 16.18/16.24 ( (fun int (fun int int)), int_gcd, (gcd_gcd int) ) 16.18/16.24 ( (fun int (fun int int)), int_lcm, nat_tsub ) 16.18/16.24 ( (fun int (fun int int)), inv, standardRes ) 16.18/16.24 ( (fun complex complex), expi, expi ) 16.18/16.24 ( (fun complex complex), expi, cnj ) 16.18/16.24 ( (fun complex complex), cnj, expi ) 16.18/16.24 ( (fun real complex), cis, cis ) 16.18/16.24 ( (fun int nat), nat_1, phi ) 16.18/16.24 ( (fun int nat), phi, nat_1 ) 16.18/16.24 ( (fun int nat), phi, phi ) 16.18/16.24 ( (fun (fun int bool) bool), nat_nat_set, nat_nat_set ) 16.18/16.24 ( (fun nat (fun nat nat)), (gcd_gcd nat), (gcd_gcd nat) ) 16.18/16.24 ( (fun nat (fun nat nat)), (gcd_gcd nat), nat_gcd ) 16.18/16.24 ( (fun nat (fun nat nat)), (gcd_gcd nat), nat_lcm ) 16.18/16.24 ( (fun nat (fun nat nat)), nat_gcd, (gcd_gcd nat) ) 16.18/16.24 ( (fun nat (fun nat nat)), nat_lcm, nat_gcd ) 16.18/16.24 ( (fun (fun int bool) int), (the int), (the int) ) 16.18/16.24 ( (fun complex real), re, arg ) 16.18/16.24 ( (fun complex real), im, re ) 16.18/16.24 ( (fun complex real), im, im ) 16.18/16.24 ( (fun complex real), im, arg ) 16.18/16.24 ( (fun complex real), arg, im ) 16.18/16.24 ( (fun bool bool), fNot, fNot ) 16.18/16.24 ( (fun nat (fun real real)), root, root ) 16.18/16.24 ( (fun real (fun real real)), log, log ) 16.18/16.24 ( (fun real (fun real real)), log, powr ) 16.18/16.24 ( (fun real (fun real real)), powr, log ) 16.18/16.24 ( (fun bool (fun bool bool)), fimplies, fimplies ) 16.18/16.24 ( (fun bool (fun bool bool)), fimplies, fconj ) 16.18/16.24 ( (fun bool (fun bool bool)), fimplies, fdisj ) 16.18/16.24 ( (fun bool (fun bool bool)), fconj, fimplies ) 16.18/16.24 ( (fun bool (fun bool bool)), fdisj, fconj ) 16.18/16.24 ( (fun int (fun int (product_prod int int))), negDivAlg, norm_frac ) 16.18/16.24 ( (fun int (fun int (product_prod int int))), posDivAlg, divmod_int ) 16.18/16.24 ( (fun int (fun int (product_prod int int))), divmod_int, posDivAlg ) 16.18/16.24 ( (fun int (fun int (product_prod int int))), divmod_int, divmod_int ) 16.18/16.24 ( (fun int (fun int (product_prod int int))), pdivmod, negDivAlg ) 16.18/16.24 ( (fun int (fun int (product_prod int int))), norm_frac, negDivAlg ) 16.18/16.24 ( (fun int (fun int (product_prod int int))), norm_frac, pdivmod ) 16.18/16.24 ( (fun int (fun int (product_prod int int))), norm_frac, norm_frac ) 16.18/16.24 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd, negateSnd ) 16.18/16.24 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd, normalize ) 16.18/16.24 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize, negateSnd ) 16.18/16.24 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust, adjust ) 16.18/16.24 ( (fun int (fun int (fun int bool))), zcong, noXRRset ) 16.18/16.24 ( (fun int (fun int (fun int bool))), zcongm, zcong ) 16.18/16.24 ( (fun int (fun int (fun int bool))), noXRRset, zcong ) 16.18/16.24 ( (fun int (fun int (fun int bool))), noXRRset, zcongm ) 16.18/16.24 ( (fun int (fun int (fun int bool))), noXRRset, noXRRset ) 16.18/16.24 ( (fun int (fun int (fun int bool))), bnorRset, bnorRset ) 16.18/16.24 ( (fun int (fun int (fun int bool))), bnorRset, wset ) 16.18/16.24 ( (fun int (fun int (fun int bool))), wset, bnorRset ) 16.18/16.24 ( (fun (product_prod int int) bool), frac_1, frac_1 ) 16.18/16.24 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than, int_ge_less_than ) 16.18/16.24 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than, int_ge_less_than2 ) 16.18/16.24 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2, int_ge_less_than ) 16.18/16.24 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral, code_S1047413653umeral ) 16.18/16.24 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset, is_RRset ) 16.18/16.24 ( (fun (fun nat rat) bool), vanishes, vanishes ) 16.18/16.24 ( (fun code_code_numeral nat), (size_size code_code_numeral), (size_size code_code_numeral) ) 16.18/16.24 ( (fun code_code_numeral nat), (size_size code_code_numeral), code_c271388182l_size ) 16.18/16.24 ( (fun code_code_numeral nat), code_c271388182l_size, (size_size code_code_numeral) ) 16.18/16.24 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel, ratrel ) 16.18/16.24 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel, norm_frac_rel ) 16.18/16.24 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel, lazy_small_lazy_rel ) 16.18/16.24 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel, negDivAlg_rel ) 16.18/16.24 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel, posDivAlg_rel ) 16.18/16.24 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel, upto_rel ) 16.18/16.24 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel, norm_frac_rel ) 16.18/16.24 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel, lazy_small_lazy_rel ) 16.18/16.24 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel, posDivAlg_rel ) 16.18/16.24 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq, twoSqu1094008024sum2sq ) 16.18/16.24 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less, pair_less ) 16.18/16.24 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less, pair_leq ) 16.18/16.24 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq, pair_less ) 16.18/16.24 ( (fun complex nat), complex_size, complex_size ) 16.18/16.24 ( (fun complex nat), complex_size, (size_size complex) ) 16.18/16.24 ( (fun complex nat), (size_size complex), complex_size ) 16.18/16.24 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel, nat_gcd_rel ) 16.18/16.24 ( (fun nat (fun nat (product_prod int int))), bezw, bezw ) 16.18/16.24 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd, xzgcd ) 16.18/16.24 ( (fun int (fun nat nat)), nat_aux, nat_aux ) 16.18/16.24 ( (fun int (fun (fun int bool) bool)), rsetR, resSet ) 16.18/16.24 ( (fun int (fun (fun int bool) bool)), resSet, rsetR ) 16.18/16.24 ( (fun int (fun (fun int bool) bool)), resSet, resSet ) 16.18/16.24 ( (fun int (list int)), quickc666637781d_zero, quickc666637781d_zero ) 16.18/16.24 ( (fun (product_prod int int) rat), frct, frct ) 16.18/16.24 ( (fun int (fun int rat)), fract, fract ) 16.18/16.24 ( (fun real (fun real complex)), complex_1, rcis ) 16.18/16.24 ( (fun real (fun real complex)), rcis, complex_1 ) 16.18/16.24 ( (fun real (fun real complex)), rcis, rcis ) 16.18/16.24 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat), (ord_gr676655987ssThan nat) ) 16.18/16.24 ( (fun quickcheck_code_int nat), quickcheck_nat_of, quickcheck_nat_of ) 16.18/16.24 ( (fun int real), (real_1 int), (real_1 int) ) 16.18/16.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect, bolzano_bisect ) 16.18/16.24 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR, rRset2norRR ) 16.18/16.24 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int, quickc495462417de_int ) 16.18/16.24 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda, xzgcda ) 16.18/16.24 ( (fun int (fun int (fun int (fun int bool)))), multInvPair, multInvPair ) 16.18/16.24 ( (fun real nat), natfloor, natceiling ) 16.18/16.24 ( (fun real nat), natceiling, natfloor ) 16.18/16.24 ( (fun real nat), natceiling, natceiling ) 16.18/16.24 ( (fun (fun real bool) real), (complete_Sup_Sup real), (complete_Sup_Sup real) ) 16.18/16.24 ( (fun quickcheck_code_int int), quickcheck_int_of, quickcheck_int_of ) 16.18/16.24 ( (fun rat (product_prod int int)), quotient_of, quotient_of ) 16.18/16.24 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral, code_d418564891umeral ) 16.18/16.24 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat, divmod_nat ) 16.18/16.24 ( (fun rat real), ratreal, ratreal ) 16.18/16.24 ( (fun code_code_numeral int), code_int_of, code_int_of ) 16.18/16.24 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel, divmod_int_rel ) 16.18/16.24 ( (fun int quickcheck_code_int), quickcheck_of_int, quickcheck_of_int ) 16.18/16.24 ( (fun int (fun int (fun (fun int bool) bool))), setS, setS ) 16.18/16.24 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux, code_nat_of_aux ) 16.18/16.24 ) 16.18/16.24 (instantiation (forall ((N_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (real_1 nat))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP nat real _let_2 N_1)) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) (hAPP nat real _let_2 (hAPP nat nat suc N_1))))) (= N_1 (hAPP int nat nat_1 (hAPP real int (archim2085082626_floor real) X_1))))))) ) 16.18/16.24 ( (zero_zero nat), pi ) 16.18/16.24 ( (zero_zero nat), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.18/16.24 ( (zero_zero nat), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.18/16.24 ( (zero_zero nat), skv_2 ) 16.18/16.24 ( (zero_zero nat), skv_8 ) 16.18/16.24 ( (zero_zero nat), skv_9 ) 16.18/16.24 ( (hAPP nat nat suc (zero_zero nat)), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.18/16.24 ) 16.18/16.24 (instantiation (forall ((W_1 $$unsorted) (Z $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (zero_zero int)) Z))) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (hAPP int nat nat_1 W_1)) (hAPP int nat nat_1 Z))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 W_1) Z)))))) ) 16.18/16.24 ( (one_one int), t ) 16.18/16.24 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.18/16.24 ( pls, (one_one int) ) 16.18/16.24 ( pls, pls ) 16.18/16.24 ( pls, min_1 ) 16.18/16.24 ( pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.18/16.24 ( min_1, pls ) 16.18/16.24 ( min_1, min_1 ) 16.18/16.24 ( s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.18/16.24 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.18/16.24 ( skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.18/16.24 ( skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.18/16.24 ) 16.18/16.24 (instantiation (forall ((Ta $$unsorted) (B_2 $$unsorted) (D_2 $$unsorted) (BOUND_VARIABLE_146578 $$unsorted)) (let ((_let_0 (hAPP int (fun int bool) (ord_less int) Ta))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) D_2))) (not (hBOOL (hAPP (fun int bool) bool (hAPP int (fun (fun int bool) bool) (member int) Ta) B_2))) (not (forall ((Xa $$unsorted) (BOUND_VARIABLE_146548 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member int))) (or (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 Xa) (hAPP int _let_0 (hAPP int (fun int _let_0) (ord_atLeastAtMost int) (one_one int)) D_2)))) (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 BOUND_VARIABLE_146548) B_2))) (not (= (hAPP int int (hAPP int (fun int int) (plus_plus int) BOUND_VARIABLE_146548) Xa) (ti int BOUND_VARIABLE_146578))))))) )) (not (hBOOL (hAPP int bool _let_0 BOUND_VARIABLE_146578))) (hBOOL (hAPP int bool _let_0 (hAPP int int (hAPP int (fun int int) (minus_minus int) BOUND_VARIABLE_146578) D_2))))) ) 16.18/16.24 ( (one_one int), zEven, pls, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.18/16.24 ) 16.18/16.24 (instantiation (forall ((Ma $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (product_prod nat nat))) (let ((_let_2 (fun nat _let_1))) (let ((_let_3 (fun nat _let_2))) (or (= (zero_zero nat) N) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) Ma) N)) (= (hAPP nat _let_1 (hAPP nat _let_2 divmod_nat Ma) N) (hAPP _let_1 _let_1 (hAPP _let_3 (fun _let_1 _let_1) (product_prod_case nat nat _let_1) (hAPP _let_0 _let_3 (hAPP _let_3 (fun _let_0 _let_3) (combb nat _let_2 nat) (product_Pair nat nat)) suc)) (hAPP nat _let_1 (hAPP nat _let_2 divmod_nat (hAPP nat nat (hAPP nat _let_0 (minus_minus nat) Ma) N)) N)))))))) ) 16.18/16.24 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.18/16.24 ) 16.18/16.24 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun real _let_0))) (= (hAPP _let_0 real (the real) (hAPP real _let_0 (hAPP _let_2 _let_2 (combc real real bool) (hAPP _let_1 _let_2 (hAPP _let_2 (fun _let_1 _let_2) (combb real _let_0 real) (fequal real)) (exp real))) X_2)) (hAPP real real ln X_2))))) ) 16.18/16.24 ( (one_one real) ) 16.18/16.24 ) 16.18/16.24 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_146725 $$unsorted)) (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat X_a))) (let ((_let_2 (power_power X_a))) (or (not (linordered_idom X_a)) (= (hAPP nat X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_146725) _let_0) (hAPP nat X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_146725)) _let_0)))))) ) 16.18/16.24 ( int, s ) 16.18/16.24 ( int, s1 ) 16.18/16.24 ( int, skv_14 ) 16.18/16.24 ( complex, ii ) 16.18/16.24 ) 16.18/16.24 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_146800 $$unsorted) (BOUND_VARIABLE_146801 $$unsorted)) (let ((_let_0 (fun X_a X_b))) (let ((_let_1 (fun X_a bool))) (let ((_let_2 (isCont X_a X_b))) (or (not (topological_space X_a)) (not (real_n1866405975lgebra X_b)) (not (hBOOL (hAPP X_a bool (hAPP _let_0 _let_1 _let_2 BOUND_VARIABLE_146800) BOUND_VARIABLE_146801))) (= (zero_zero X_b) (hAPP X_a X_b BOUND_VARIABLE_146800 BOUND_VARIABLE_146801)) (hBOOL (hAPP X_a bool (hAPP _let_0 _let_1 _let_2 (hAPP _let_0 _let_0 (hAPP (fun X_b X_b) (fun _let_0 _let_0) (combb X_b X_b X_a) (inverse_inverse X_b)) BOUND_VARIABLE_146800)) BOUND_VARIABLE_146801)))))) ) 16.18/16.24 ( bool, nat, (even_odd_even nat), (zero_zero nat) ) 16.18/16.24 ( bool, nat, (even_odd_even nat), (one_one nat) ) 16.18/16.24 ( bool, nat, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.18/16.24 ( bool, nat, prime, (zero_zero nat) ) 16.18/16.24 ( bool, nat, prime, (hAPP nat nat suc (zero_zero nat)) ) 16.18/16.24 ( bool, nat, prime, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.18/16.24 ( bool, int, (hAPP int (fun int bool) (ord_less int) pls), pls ) 16.18/16.24 ( bool, int, (hAPP int (fun int bool) (ord_less int) pls), min_1 ) 16.18/16.24 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) pls), min_1 ) 16.18/16.24 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (one_one int)), t ) 16.18/16.24 ( bool, int, nat_neg, (one_one int) ) 16.18/16.24 ( bool, int, nat_neg, (hAPP int int (number_number_of int) min_1) ) 16.18/16.24 ( bool, int, nat_neg, (hAPP int int (number_number_of int) pls) ) 16.18/16.24 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (one_one int) ) 16.18/16.24 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.18/16.24 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), s ) 16.18/16.24 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.18/16.24 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) pls) ) 16.18/16.24 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_4 ) 16.18/16.24 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_10 ) 16.18/16.24 ( bool, int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (one_one int) ) 16.18/16.24 ( bool, int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.18/16.24 ( bool, int, zprime, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.18/16.24 ( bool, int, zprime, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.18/16.24 ( bool, int, (hAPP int (fun int bool) (ord_less int) s), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.18/16.24 ( bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) s)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.18/16.24 ( bool, int, (let ((_let_0 (fun int int))) (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 16.18/16.24 ( bool, int, (hAPP int (fun int bool) (ord_less int) (one_one int)), t ) 16.18/16.24 ( bool, int, (even_odd_even int), (one_one int) ) 16.18/16.24 ( bool, int, (even_odd_even int), (zero_zero int) ) 16.18/16.24 ( bool, int, twoSqu1091635170sum2sq, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) t))) ) 16.18/16.24 ( bool, int, nat_is_nat, (one_one int) ) 16.18/16.24 ( bool, int, nat_is_nat, (zero_zero int) ) 16.18/16.24 ( bool, int, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.18/16.24 ( bool, int, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.18/16.24 ( bool, int, (hAPP int (fun int bool) (ord_less int) min_1), pls ) 16.18/16.24 ( bool, int, (hAPP int (fun int bool) (ord_less int) min_1), min_1 ) 16.18/16.24 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) min_1), pls ) 16.18/16.24 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) min_1), min_1 ) 16.18/16.24 ( bool, int, (let ((_let_0 (fun int int))) (hAPP int (fun int bool) quadRes (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int int (number_number_of int) min_1) ) 16.18/16.24 ( bool, int, (let ((_let_0 (fun int bool))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (let ((_let_3 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int _let_1 _let_2 s) _let_3)) (hAPP nat int (hAPP int _let_1 _let_2 s1) _let_3)))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.18/16.24 ( bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.18/16.24 ( bool, int, (hAPP int (fun int bool) (ord_less int) t), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.18/16.24 ( bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.18/16.24 ( bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_4)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.18/16.24 ( bool, int, (hAPP int (fun int bool) (ord_less int) skv_4), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.18/16.24 ( bool, int, (hAPP int (fun int bool) (ord_less int) skv_10), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.18/16.24 ( bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_10)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.18/16.24 ( bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.18/16.24 ( bool, (fun int bool), (hAPP (fun int nat) (fun (fun int bool) bool) (nat_tr1645093318rphism int nat) nat_1), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 16.18/16.24 ( bool, (fun int bool), (hAPP int (fun (fun int bool) bool) (member int) (one_one int)), zEven ) 16.18/16.24 ( bool, (fun nat bool), (finite_finite_1 nat), (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 16.18/16.24 ( bool, (fun nat bool), (hAPP (fun nat int) (fun (fun nat bool) bool) (nat_tr1645093318rphism nat int) (semiring_1_of_nat int)), (hAPP bool (fun nat bool) (combk bool nat) fTrue) ) 16.18/16.24 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), pi ) 16.18/16.24 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.18/16.24 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.18/16.24 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_3 ) 16.18/16.24 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_5 ) 16.18/16.24 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_7 ) 16.18/16.24 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_12 ) 16.18/16.24 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), pi ) 16.18/16.24 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.18/16.24 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.18/16.24 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_2 ) 16.18/16.24 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_8 ) 16.18/16.24 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_9 ) 16.18/16.24 ( bool, real, (hAPP real (fun real bool) (ord_less real) (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))), (zero_zero real) ) 16.18/16.24 ( bool, real, (hAPP real (fun real bool) (ord_less real) (one_one real)), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.18/16.24 ( bool, real, (hAPP real (fun real bool) (ord_less real) pi), (zero_zero real) ) 16.18/16.24 ( bool, real, (hAPP real (fun real bool) (ord_less real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.18/16.24 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.18/16.24 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 16.18/16.24 ( bool, real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 (fun real bool) (sums real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (hAPP real _let_1 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc)))), (one_one real) ) 16.18/16.24 ( bool, real, (hAPP real (fun real bool) (ord_less real) (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi))), pi ) 16.18/16.24 ( bool, real, (hAPP real (fun real bool) (ord_less real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.18/16.24 ( bool, real, (hAPP real (fun real bool) (ord_less real) (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 16.18/16.24 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 16.18/16.24 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) skv_5), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.18/16.24 ( bool, (filter nat), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun (filter nat) bool))) (hAPP real _let_2 (hAPP _let_1 (fun real _let_2) (tendsto nat real) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))) (zero_zero real))))), sequentially ) 16.18/16.24 ( bool, (filter nat), (trivial_limit nat), sequentially ) 16.18/16.24 ( bool, (filter real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (filter real) bool))) (hAPP real _let_2 (hAPP _let_0 (fun real _let_2) (tendsto real real) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin)) (zero_zero real))))), (hAPP real (filter real) (at real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.18/16.24 ( nat, nat, suc, (zero_zero nat) ) 16.18/16.24 ( nat, nat, suc, (hAPP nat nat suc (zero_zero nat)) ) 16.18/16.24 ( nat, nat, suc, (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 16.18/16.24 ( nat, nat, (fact_fact nat), (zero_zero nat) ) 16.18/16.24 ( nat, nat, (fact_fact nat), (hAPP nat nat suc (zero_zero nat)) ) 16.18/16.24 ( nat, nat, fact, (zero_zero nat) ) 16.18/16.24 ( nat, nat, (hAPP nat (fun nat nat) (plus_plus nat) (one_one nat)), (one_one nat) ) 16.18/16.24 ( nat, nat, nat_size, (zero_zero nat) ) 16.18/16.24 ( nat, nat, (size_size nat), (zero_zero nat) ) 16.18/16.24 ( nat, int, (number_number_of nat), pls ) 16.18/16.24 ( nat, int, (number_number_of nat), (hAPP int int bit1 pls) ) 16.18/16.24 ( nat, int, (number_number_of nat), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.18/16.24 ( nat, int, (number_number_of nat), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.18/16.24 ( nat, int, nat_1, (one_one int) ) 16.18/16.24 ( nat, int, nat_1, (zero_zero int) ) 16.18/16.24 ( nat, int, nat_1, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.18/16.24 ( nat, int, nat_1, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.18/16.24 ( nat, real, natfloor, (one_one real) ) 16.18/16.24 ( nat, real, natfloor, (zero_zero real) ) 16.18/16.24 ( nat, real, natceiling, (one_one real) ) 16.18/16.24 ( nat, real, natceiling, (zero_zero real) ) 16.18/16.24 ( nat, code_code_numeral, (size_size code_code_numeral), (zero_zero code_code_numeral) ) 16.18/16.24 ( nat, code_code_numeral, code_c271388182l_size, (zero_zero code_code_numeral) ) 16.18/16.24 ( int, nat, (semiring_1_of_nat int), (zero_zero nat) ) 16.18/16.24 ( int, nat, (semiring_1_of_nat int), (hAPP nat nat suc (zero_zero nat)) ) 16.18/16.24 ( int, nat, (semiring_1_of_nat int), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.18/16.24 ( int, nat, (semiring_1_of_nat int), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.18/16.24 ( int, nat, (hAPP int (fun nat int) (power_power int) s), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.18/16.24 ( int, nat, (hAPP int (fun nat int) (power_power int) s1), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.18/16.24 ( int, nat, (hAPP int (fun nat int) (power_power int) skv_14), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.18/16.24 ( int, int, bit0, pls ) 16.18/16.24 ( int, int, bit0, (hAPP int int bit1 pls) ) 16.18/16.24 ( int, int, bit0, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.18/16.24 ( int, int, bit0, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.18/16.24 ( int, int, bit0, min_1 ) 16.18/16.24 ( int, int, bit0, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.18/16.24 ( int, int, bit1, pls ) 16.18/16.24 ( int, int, bit1, (hAPP int int bit1 pls) ) 16.18/16.24 ( int, int, bit1, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.18/16.24 ( int, int, bit1, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.18/16.24 ( int, int, bit1, min_1 ) 16.18/16.24 ( int, int, bit1, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.18/16.24 ( int, int, bit1, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 16.18/16.24 ( int, int, bit1, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 16.18/16.24 ( int, int, bit1, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 16.18/16.24 ( int, int, (number_number_of int), pls ) 16.18/16.24 ( int, int, (number_number_of int), (hAPP int int bit1 pls) ) 16.18/16.24 ( int, int, (number_number_of int), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.18/16.24 ( int, int, (number_number_of int), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.18/16.24 ( int, int, (number_number_of int), min_1 ) 16.18/16.24 ( int, int, (number_number_of int), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.18/16.24 ( int, int, (fact_fact int), (one_one int) ) 16.18/16.24 ( int, int, (fact_fact int), (zero_zero int) ) 16.18/16.24 ( int, int, (uminus_uminus int), (one_one int) ) 16.18/16.24 ( int, int, (uminus_uminus int), pls ) 16.18/16.24 ( int, int, (uminus_uminus int), min_1 ) 16.18/16.24 ( int, int, pred, pls ) 16.18/16.24 ( int, int, pred, min_1 ) 16.18/16.24 ( int, int, (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))), m ) 16.18/16.24 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m))), (one_one int) ) 16.18/16.24 ( int, int, (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (one_one int) ) 16.18/16.24 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))))), t ) 16.18/16.24 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))))), skv_13 ) 16.18/16.24 ( int, int, succ, pls ) 16.18/16.24 ( int, int, succ, min_1 ) 16.18/16.24 ( int, int, (hAPP int (fun int int) legendre (hAPP int int (number_number_of int) min_1)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.18/16.24 ( int, int, (hAPP int (fun int int) (minus_minus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1) ) 16.18/16.24 ( int, (product_prod int int), twoSqu1094008024sum2sq, (let ((_let_0 (product_prod int int))) (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) s) (one_one int))) ) 16.18/16.24 ( int, quickcheck_code_int, quickcheck_int_of, (zero_zero quickcheck_code_int) ) 16.18/16.24 ( int, code_code_numeral, code_int_of, (zero_zero code_code_numeral) ) 16.18/16.24 ( (fun int bool), int, (ord_less_eq int), (one_one int) ) 16.18/16.24 ( (fun int bool), int, (ord_less_eq int), (zero_zero int) ) 16.18/16.24 ( (fun int bool), int, (ord_less_eq int), min_1 ) 16.18/16.24 ( (fun int bool), int, (ord_less int), (one_one int) ) 16.18/16.24 ( (fun int bool), int, (ord_less int), pls ) 16.18/16.24 ( (fun int bool), int, (ord_less int), min_1 ) 16.18/16.24 ( (fun int bool), int, (ord_less int), s ) 16.18/16.24 ( (fun int bool), int, (ord_less int), t ) 16.18/16.24 ( (fun int bool), int, (ord_less int), skv_4 ) 16.18/16.24 ( (fun int bool), int, (ord_less int), skv_10 ) 16.18/16.24 ( (fun int bool), int, (dvd_dvd int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.18/16.24 ( (fun int bool), int, quadRes, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.18/16.24 ( (fun int bool), int, (let ((_let_0 (fun int (fun int bool)))) (hAPP _let_0 _let_0 (combc int int bool) (fequal int))), (zero_zero int) ) 16.18/16.24 ( (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong s1), s ) 16.18/16.24 ( (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong s1), skv_4 ) 16.18/16.24 ( (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong s1), skv_10 ) 16.18/16.24 ( (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1) ) 16.18/16.24 ( (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.18/16.24 ( (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1) ) 16.18/16.24 ( (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1) ) 16.18/16.24 ( (fun int bool), (fun int bool), (collect int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun _let_2 _let_0))) (let ((_let_4 (fun int _let_3))) (hAPP _let_1 _let_0 (hAPP (fun _let_0 bool) (fun _let_1 _let_0) (combb _let_0 bool int) (fEx int)) (hAPP _let_2 _let_1 (hAPP _let_4 (fun _let_2 _let_1) (combc int _let_2 _let_0) (hAPP _let_1 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_1 _let_4) (combb _let_0 _let_3 int) (combb int bool int)) (fequal int))) (hAPP int _let_2 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))))))))) ) 16.18/16.24 ( (fun int bool), (fun int bool), (collect int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun _let_2 _let_0))) (let ((_let_5 (fun int _let_4))) (hAPP _let_1 _let_0 (hAPP (fun _let_0 bool) (fun _let_1 _let_0) (combb _let_0 bool int) (fEx int)) (hAPP _let_2 _let_1 (hAPP _let_5 (fun _let_2 _let_1) (combc int _let_2 _let_0) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_1 _let_5) (combb _let_0 _let_4 int) (combb int bool int)) (fequal int))) (hAPP int _let_2 (hAPP _let_3 _let_3 (combc int int int) (hAPP _let_2 _let_3 (hAPP _let_3 (fun _let_2 _let_3) (combb int _let_2 int) (plus_plus int)) (hAPP int _let_2 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one int)))))))))) ) 16.18/16.24 ( (fun int bool), (fun int bool), (let ((_let_0 (fun int bool))) (hAPP (fun bool bool) (fun _let_0 _let_0) (combb bool bool int) fNot)), (let ((_let_0 (fun int (fun int bool)))) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (fequal int)) (zero_zero int))) ) 16.18/16.24 ( (fun int bool), (fun int (fun int bool)), (let ((_let_0 (fun int bool))) (hAPP (fun _let_0 bool) (fun (fun int _let_0) _let_0) (combb _let_0 bool int) (fEx int))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun _let_2 _let_0))) (let ((_let_4 (fun int _let_3))) (hAPP _let_2 _let_1 (hAPP _let_4 (fun _let_2 _let_1) (combc int _let_2 _let_0) (hAPP _let_1 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_1 _let_4) (combb _let_0 _let_3 int) (combb int bool int)) (fequal int))) (hAPP int _let_2 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))))))) ) 16.18/16.24 ( (fun int bool), (fun int (fun int bool)), (let ((_let_0 (fun int bool))) (hAPP (fun _let_0 bool) (fun (fun int _let_0) _let_0) (combb _let_0 bool int) (fEx int))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun _let_2 _let_0))) (let ((_let_5 (fun int _let_4))) (hAPP _let_2 _let_1 (hAPP _let_5 (fun _let_2 _let_1) (combc int _let_2 _let_0) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_1 _let_5) (combb _let_0 _let_4 int) (combb int bool int)) (fequal int))) (hAPP int _let_2 (hAPP _let_3 _let_3 (combc int int int) (hAPP _let_2 _let_3 (hAPP _let_3 (fun _let_2 _let_3) (combb int _let_2 int) (plus_plus int)) (hAPP int _let_2 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one int))))))))) ) 16.18/16.24 ( (fun int (fun int bool)), int, zcong, s1 ) 16.18/16.24 ( (fun int (fun int bool)), int, zcong, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.18/16.24 ( (fun int (fun int bool)), int, zcong, (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.18/16.24 ( (fun int (fun int bool)), int, zcong, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.18/16.24 ( (fun int (fun int bool)), int, (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int _let_1))) (let ((_let_5 (fun _let_2 _let_1))) (hAPP _let_4 _let_4 (combc int int _let_0) (hAPP _let_4 _let_4 (hAPP (fun _let_1 _let_1) (fun _let_4 _let_4) (combb _let_1 _let_1 int) (combc int int bool)) (hAPP _let_3 _let_4 (hAPP _let_5 (fun _let_3 _let_4) (combb _let_2 _let_1 int) (hAPP _let_1 _let_5 (combb int _let_0 int) (fequal int))) int_gcd))))))))), (one_one int) ) 16.18/16.24 ( (fun int (fun int bool)), (fun int (fun int bool)), (combc int int bool), (fequal int) ) 16.18/16.24 ( (fun int (fun int bool)), (fun int (fun int bool)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun _let_0 _let_0))) (hAPP _let_4 (fun _let_1 _let_1) (combb _let_0 _let_0 int) (hAPP _let_3 _let_4 (combs int bool bool) (hAPP _let_0 _let_3 (hAPP (fun bool _let_2) (fun _let_0 _let_3) (combb bool _let_2 int) fconj) (hAPP int _let_0 (ord_less int) (zero_zero int)))))))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int _let_1))) (let ((_let_5 (fun _let_2 _let_1))) (hAPP int _let_1 (hAPP _let_4 _let_4 (combc int int _let_0) (hAPP _let_4 _let_4 (hAPP (fun _let_1 _let_1) (fun _let_4 _let_4) (combb _let_1 _let_1 int) (combc int int bool)) (hAPP _let_3 _let_4 (hAPP _let_5 (fun _let_3 _let_4) (combb _let_2 _let_1 int) (hAPP _let_1 _let_5 (combb int _let_0 int) (fequal int))) int_gcd))) (one_one int)))))))) ) 16.18/16.27 ( (fun int (fun int bool)), (fun int int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun (fun int int) _let_0))) (let ((_let_3 (fun int _let_2))) (hAPP _let_3 (fun (fun int int) _let_1) (combc int (fun int int) _let_0) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 int) (combb int bool int)) (fequal int))))))), (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.18/16.27 ( (fun int (fun int bool)), (fun int int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun (fun int int) _let_0))) (let ((_let_3 (fun int _let_2))) (hAPP _let_3 (fun (fun int int) _let_1) (combc int (fun int int) _let_0) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 int) (combb int bool int)) (fequal int))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (hAPP int _let_0 (hAPP _let_1 _let_1 (combc int int int) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)) (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one int)))) ) 16.18/16.27 ( (fun int int), nat, (hAPP (fun int (fun nat int)) (fun nat (fun int int)) (combc int nat int) (power_power int)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.18/16.27 ( (fun int int), int, (times_times int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.18/16.27 ( (fun int int), int, (times_times int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.18/16.27 ( (fun int int), int, (times_times int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.18/16.27 ( (fun int int), int, (minus_minus int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.18/16.28 ( (fun int int), int, (plus_plus int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 16.18/16.28 ( (fun int int), int, (plus_plus int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.18/16.28 ( (fun int int), int, legendre, (hAPP int int (number_number_of int) min_1) ) 16.18/16.28 ( (fun int int), int, (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (hAPP _let_1 _let_1 (combc int int int) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)) (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))))), (one_one int) ) 16.18/16.28 ( (fun nat bool), bool, (combk bool nat), fTrue ) 16.18/16.28 ( (fun nat bool), nat, (ord_less nat), (zero_zero nat) ) 16.18/16.28 ( (fun nat bool), nat, (let ((_let_0 (fun nat (fun nat bool)))) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat))), (zero_zero nat) ) 16.18/16.28 ( (fun nat bool), (fun nat bool), (collect nat), prime ) 16.18/16.28 ( (fun nat bool), (fun nat bool), (let ((_let_0 (fun nat bool))) (hAPP (fun bool bool) (fun _let_0 _let_0) (combb bool bool nat) fNot)), (let ((_let_0 (fun nat (fun nat bool)))) (hAPP nat (fun nat bool) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat)) (zero_zero nat))) ) 16.18/16.28 ( (fun nat nat), nat, (plus_plus nat), (one_one nat) ) 16.18/16.28 ( (fun nat nat), nat, (let ((_let_0 (fun nat (fun nat nat)))) (hAPP _let_0 _let_0 (combc nat nat nat) (times_times nat))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.18/16.28 ( (fun nat nat), nat, (let ((_let_0 (fun nat (fun nat nat)))) (let ((_let_1 (combc nat nat nat))) (hAPP _let_0 _let_0 _let_1 (hAPP (fun nat nat) _let_0 (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_0 _let_0 _let_1 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))), (one_one nat) ) 16.18/16.28 ( (fun (product_prod nat nat) bool), (fun (product_prod nat nat) bool), (collect (product_prod nat nat)), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat (fun nat bool)))) (hAPP _let_1 (fun (product_prod nat nat) bool) (product_prod_case nat nat bool) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat (fun nat bool) nat) (hAPP _let_1 _let_1 (combc nat nat bool) (fequal nat))) suc)))) ) 16.18/16.28 ( (fun (product_prod nat nat) bool), (fun nat (fun nat bool)), (product_prod_case nat nat bool), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat (fun nat bool)))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat (fun nat bool) nat) (hAPP _let_1 _let_1 (combc nat nat bool) (fequal nat))) suc))) ) 16.18/16.28 ( real, nat, (real_1 nat), (zero_zero nat) ) 16.18/16.28 ( real, nat, (real_1 nat), (hAPP nat nat suc (zero_zero nat)) ) 16.18/16.28 ( real, int, (real_1 int), (one_one int) ) 16.18/16.28 ( real, int, (real_1 int), (zero_zero int) ) 16.18/16.28 ( real, int, (number_number_of real), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.18/16.28 ( real, int, (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.18/16.28 ( real, int, (number_number_of real), min_1 ) 16.18/16.28 ( real, int, (number_number_of real), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.18/16.28 ( real, int, (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.18/16.28 ( real, int, (number_number_of real), (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.18/16.28 ( real, int, (number_number_of real), (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 16.18/16.28 ( real, real, ln, (one_one real) ) 16.18/16.28 ( real, real, (uminus_uminus real), (one_one real) ) 16.18/16.28 ( real, real, (uminus_uminus real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.18/16.28 ( real, real, (uminus_uminus real), (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.18/16.28 ( real, real, cos, (zero_zero real) ) 16.18/16.28 ( real, real, cos, pi ) 16.18/16.28 ( real, real, cos, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.18/16.28 ( real, real, cos, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.18/16.28 ( real, real, cos, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.18/16.28 ( real, real, cos, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.18/16.28 ( real, real, cos, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.18/16.28 ( real, real, cos, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 16.18/16.28 ( real, real, cos, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 16.18/16.28 ( real, real, cos, skv_5 ) 16.18/16.28 ( real, real, sqrt, (one_one real) ) 16.18/16.28 ( real, real, sqrt, (zero_zero real) ) 16.18/16.28 ( real, real, sqrt, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.18/16.28 ( real, real, sqrt, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.18/16.28 ( real, real, sin, (zero_zero real) ) 16.18/16.28 ( real, real, sin, pi ) 16.18/16.28 ( real, real, sin, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.18/16.28 ( real, real, sin, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.18/16.28 ( real, real, sin, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.18/16.28 ( real, real, sin, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.18/16.28 ( real, real, sin, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 16.18/16.28 ( real, real, sin, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 16.18/16.28 ( real, real, (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.18/16.28 ( real, real, (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.18/16.28 ( real, real, (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.18/16.28 ( real, real, (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.18/16.28 ( real, real, tan, (zero_zero real) ) 16.18/16.28 ( real, real, tan, pi ) 16.18/16.28 ( real, real, tan, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.18/16.28 ( real, real, tan, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.18/16.28 ( real, real, tan, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 16.18/16.28 ( real, real, (hAPP real (fun real real) (inverse_divide real) (one_one real)), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.18/16.28 ( real, real, (hAPP real (fun real real) (inverse_divide real) (one_one real)), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.18/16.28 ( real, real, (hAPP real (fun real real) (inverse_divide real) (one_one real)), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.18/16.28 ( real, real, (hAPP real (fun real real) (inverse_divide real) (one_one real)), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 16.18/16.28 ( real, real, (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 16.18/16.28 ( real, real, (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 16.18/16.28 ( real, real, (inverse_inverse real), (zero_zero real) ) 16.18/16.28 ( real, real, arctan, (one_one real) ) 16.18/16.28 ( real, real, arctan, (zero_zero real) ) 16.18/16.28 ( real, real, arctan, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.18/16.28 ( real, real, arctan, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))))) ) 16.18/16.28 ( real, real, (hAPP real (fun real real) (inverse_divide real) (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.18/16.28 ( real, real, (sgn_sgn real), (zero_zero real) ) 16.18/16.28 ( real, real, (hAPP real (fun real real) (inverse_divide real) (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.18/16.28 ( real, real, (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 16.18/16.28 ( real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real _let_0 (minus_minus real) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1))))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 16.18/16.28 ( real, real, (hAPP real (fun real real) (inverse_divide real) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.18/16.28 ( real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1))))))), pi ) 16.18/16.28 ( real, (fun real bool), (the real), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3)))))))))))))) ) 16.18/16.28 ( real, rat, ratreal, (zero_zero rat) ) 16.18/16.28 ( real, rat, ratreal, (one_one rat) ) 16.18/16.28 ( real, complex, re, (one_one complex) ) 16.18/16.28 ( real, complex, re, ii ) 16.18/16.28 ( real, complex, re, (zero_zero complex) ) 16.18/16.28 ( real, complex, im, (one_one complex) ) 16.18/16.28 ( real, complex, im, ii ) 16.18/16.28 ( real, complex, im, (zero_zero complex) ) 16.18/16.28 ( real, (fun nat real), (suminf real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat (fun nat nat)))) (let ((_let_3 (fun nat _let_0))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun _let_1 _let_3))) (let ((_let_6 (combb real _let_0 nat))) (let ((_let_7 (combc nat nat nat))) (hAPP _let_1 _let_1 (hAPP _let_3 (fun _let_1 _let_1) (combs nat real real) (hAPP _let_1 _let_3 (hAPP _let_4 _let_5 _let_6 (inverse_divide real)) (hAPP real _let_1 (hAPP _let_3 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_3 (hAPP _let_4 _let_5 _let_6 (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) (one_one real)))) (hAPP (fun nat nat) _let_1 (hAPP _let_1 (fun (fun nat nat) _let_1) (combb nat real nat) (real_1 nat)) (hAPP nat (fun nat nat) (hAPP _let_2 _let_2 _let_7 (hAPP (fun nat nat) _let_2 (hAPP _let_2 (fun (fun nat nat) _let_2) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_2 _let_2 _let_7 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))))))))))) ) 16.18/16.28 ( (fun real bool), real, (ord_less real), (one_one real) ) 16.18/16.28 ( (fun real bool), real, (ord_less real), (zero_zero real) ) 16.18/16.28 ( (fun real bool), real, (ord_less real), pi ) 16.18/16.28 ( (fun real bool), real, (ord_less real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.18/16.28 ( (fun real bool), real, (ord_less real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.18/16.28 ( (fun real bool), real, (ord_less real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.18/16.28 ( (fun real bool), real, (ord_less real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 16.18/16.28 ( (fun real bool), real, (ord_less_eq real), (zero_zero real) ) 16.18/16.28 ( (fun real bool), real, (ord_less_eq real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.18/16.28 ( (fun real bool), real, (ord_less_eq real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.18/16.28 ( (fun real bool), real, (ord_less_eq real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.18/16.28 ( (fun real bool), real, (ord_less_eq real), skv_5 ) 16.18/16.28 ( (fun real bool), real, (let ((_let_0 (fun real (fun real bool)))) (hAPP _let_0 _let_0 (combc real real bool) (ord_less_eq real))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.18/16.28 ( (fun real bool), real, (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun real _let_0))) (hAPP _let_2 _let_2 (combc real real bool) (hAPP _let_1 _let_2 (hAPP _let_2 (fun _let_1 _let_2) (combb real _let_0 real) (fequal real)) cos))))), (zero_zero real) ) 16.18/16.28 ( (fun real bool), (fun real bool), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun real _let_1))) (hAPP _let_2 (fun _let_0 _let_0) (combs real bool bool) (hAPP _let_0 _let_2 (hAPP (fun bool _let_1) (fun _let_0 _let_2) (combb bool _let_1 real) fconj) (hAPP real _let_0 (ord_less_eq real) (zero_zero real))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun real _let_0))) (let ((_let_4 (fun real _let_2))) (let ((_let_5 (combc real real bool))) (hAPP _let_0 _let_0 (hAPP _let_4 (fun _let_0 _let_0) (combs real bool bool) (hAPP _let_0 _let_4 (hAPP (fun bool _let_2) (fun _let_0 _let_4) (combb bool _let_2 real) fconj) (hAPP real _let_0 (hAPP _let_3 _let_3 _let_5 (ord_less_eq real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_3 _let_3 _let_5 (hAPP _let_1 _let_3 (hAPP _let_3 (fun _let_1 _let_3) (combb real _let_0 real) (fequal real)) cos)) (zero_zero real))))))))) ) 16.18/16.28 ( (fun real bool), (fun real bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun real (fun real bool)))) (let ((_let_2 (fun real _let_0))) (hAPP _let_2 (fun (fun real bool) (fun real bool)) (combs real bool bool) (hAPP (fun real bool) _let_2 (hAPP (fun bool _let_0) (fun (fun real bool) _let_2) (combb bool _let_0 real) fconj) (hAPP real (fun real bool) (hAPP _let_1 _let_1 (combc real real bool) (ord_less_eq real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun real _let_0))) (hAPP real _let_0 (hAPP _let_2 _let_2 (combc real real bool) (hAPP _let_1 _let_2 (hAPP _let_2 (fun _let_1 _let_2) (combb real _let_0 real) (fequal real)) cos)) (zero_zero real))))) ) 16.18/16.28 ( (fun real bool), (fun real bool), (collect real), (let ((_let_0 (fun int (fun int bool)))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real real))) (let ((_let_3 (real_1 int))) (let ((_let_4 (fun (fun int bool) bool))) (let ((_let_5 (fun bool bool))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun int _let_5))) (let ((_let_8 (fun (fun int bool) (fun int bool)))) (let ((_let_9 (fun (fun int bool) _let_7))) (let ((_let_10 (fun _let_0 (fun int bool)))) (let ((_let_11 (fEx int))) (let ((_let_12 (fun int real))) (let ((_let_13 (fun int _let_8))) (let ((_let_14 (fun (fun int bool) _let_0))) (let ((_let_15 (fun int _let_7))) (let ((_let_16 (fun _let_15 _let_13))) (let ((_let_17 (fun _let_0 _let_15))) (let ((_let_18 (fun real (fun int bool)))) (let ((_let_19 (fun real _let_0))) (let ((_let_20 (fun real _let_14))) (let ((_let_21 (fun real _let_13))) (let ((_let_22 (fun real _let_15))) (let ((_let_23 (fun int _let_12))) (let ((_let_24 (fun _let_23 _let_0))) (let ((_let_25 (fun real _let_24))) (let ((_let_26 (fun _let_12 (fun int bool)))) (let ((_let_27 (fun real _let_26))) (let ((_let_28 (fun _let_12 _let_12))) (let ((_let_29 (fun int _let_28))) (let ((_let_30 (fun int _let_2))) (hAPP _let_18 _let_1 (hAPP _let_4 (fun _let_18 _let_1) (combb (fun int bool) bool real) _let_11) (hAPP _let_19 _let_18 (hAPP _let_10 (fun _let_19 _let_18) (combb _let_0 (fun int bool) real) (hAPP _let_4 _let_10 (combb (fun int bool) bool int) _let_11)) (hAPP (fun int bool) _let_19 (hAPP _let_20 (fun (fun int bool) _let_19) (combc real (fun int bool) _let_0) (hAPP _let_21 _let_20 (hAPP (fun _let_13 _let_14) (fun _let_21 _let_20) (combb _let_13 _let_14 real) (combc int (fun int bool) (fun int bool))) (hAPP _let_22 _let_21 (hAPP _let_16 (fun _let_22 _let_21) (combb _let_15 _let_13 real) (hAPP (fun _let_7 _let_8) _let_16 (combb _let_7 _let_8 int) (combs int bool bool))) (hAPP _let_19 _let_22 (hAPP _let_17 (fun _let_19 _let_22) (combb _let_0 _let_15 real) (hAPP _let_9 _let_17 (combb (fun int bool) _let_7 int) (hAPP (fun bool _let_5) _let_9 (combb bool _let_5 int) fconj))) (hAPP _let_23 _let_19 (hAPP _let_25 (fun _let_23 _let_19) (combc real _let_23 _let_0) (hAPP _let_27 _let_25 (hAPP (fun _let_26 _let_24) (fun _let_27 _let_25) (combb _let_26 _let_24 real) (combb _let_12 (fun int bool) int)) (hAPP _let_6 _let_27 (hAPP (fun _let_1 _let_26) (fun _let_6 _let_27) (combb _let_1 _let_26 real) (combb real bool int)) (fequal real)))) (hAPP _let_12 _let_23 (hAPP _let_29 (fun _let_12 _let_23) (combc int _let_12 _let_12) (hAPP _let_30 _let_29 (hAPP (fun _let_2 _let_28) (fun _let_30 _let_29) (combb _let_2 _let_28 int) (combb real real int)) (hAPP _let_12 _let_30 (hAPP (fun real _let_2) (fun _let_12 _let_30) (combb real _let_2 int) (inverse_divide real)) _let_3))) _let_3)))))) (hAPP (fun int bool) (fun int bool) (hAPP _let_5 _let_8 (combb bool bool int) fNot) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (fequal int)) (zero_zero int))))))))))))))))))))))))))))))))))))) ) 16.18/16.28 ( (fun real bool), (fun real bool), (collect real), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real real))) (let ((_let_3 (fun nat (fun nat bool)))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun (fun nat real) (fun nat real)))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun (fun nat bool) (fun nat bool)))) (let ((_let_8 (fun int real))) (let ((_let_9 (fun nat _let_4))) (let ((_let_10 (fun (fun nat bool) _let_9))) (let ((_let_11 (fun real _let_0))) (let ((_let_12 (fun int _let_2))) (let ((_let_13 (fun real (fun int (fun nat bool))))) (let ((_let_14 (fun (fun int (fun nat bool)) _let_0))) (let ((_let_15 (fun (fun nat bool) (fun int (fun nat bool))))) (let ((_let_16 (fun real _let_15))) (let ((_let_17 (fun int _let_7))) (let ((_let_18 (fun real _let_17))) (let ((_let_19 (fun int _let_9))) (let ((_let_20 (fun real _let_19))) (let ((_let_21 (fun _let_19 _let_17))) (let ((_let_22 (fun (fun int (fun nat bool)) _let_19))) (let ((_let_23 (fun int (fun nat real)))) (let ((_let_24 (fun _let_23 (fun int (fun nat bool))))) (let ((_let_25 (fun real _let_24))) (let ((_let_26 (fun (fun nat real) (fun nat bool)))) (let ((_let_27 (fun real _let_26))) (let ((_let_28 (fun int _let_5))) (hAPP _let_11 _let_1 (hAPP (fun _let_0 bool) (fun _let_11 _let_1) (combb _let_0 bool real) (fEx int)) (hAPP _let_13 _let_11 (hAPP _let_14 (fun _let_13 _let_11) (combb (fun int (fun nat bool)) _let_0 real) (hAPP (fun (fun nat bool) bool) _let_14 (combb (fun nat bool) bool int) (fEx nat))) (hAPP (fun nat bool) _let_13 (hAPP _let_16 (fun (fun nat bool) _let_13) (combc real (fun nat bool) (fun int (fun nat bool))) (hAPP _let_18 _let_16 (hAPP (fun _let_17 _let_15) (fun _let_18 _let_16) (combb _let_17 _let_15 real) (combc int (fun nat bool) (fun nat bool))) (hAPP _let_20 _let_18 (hAPP _let_21 (fun _let_20 _let_18) (combb _let_19 _let_17 real) (hAPP (fun _let_9 _let_7) _let_21 (combb _let_9 _let_7 int) (combs nat bool bool))) (hAPP _let_13 _let_20 (hAPP _let_22 (fun _let_13 _let_20) (combb (fun int (fun nat bool)) _let_19 real) (hAPP _let_10 _let_22 (combb (fun nat bool) _let_9 int) (hAPP (fun bool _let_4) _let_10 (combb bool _let_4 nat) fconj))) (hAPP _let_23 _let_13 (hAPP _let_25 (fun _let_23 _let_13) (combc real _let_23 (fun int (fun nat bool))) (hAPP _let_27 _let_25 (hAPP (fun _let_26 _let_24) (fun _let_27 _let_25) (combb _let_26 _let_24 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_6 _let_27 (hAPP (fun _let_1 _let_26) (fun _let_6 _let_27) (combb _let_1 _let_26 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_23 (hAPP _let_28 (fun (fun nat real) _let_23) (combc int (fun nat real) (fun nat real)) (hAPP _let_12 _let_28 (hAPP (fun _let_2 _let_5) (fun _let_12 _let_28) (combb _let_2 _let_5 int) (combb real real nat)) (hAPP _let_8 _let_12 (hAPP (fun real _let_2) (fun _let_8 _let_12) (combb real _let_2 int) (inverse_divide real)) (real_1 int)))) (real_1 nat))))))) (hAPP (fun nat bool) (fun nat bool) (hAPP _let_4 _let_7 (combb bool bool nat) fNot) (hAPP nat (fun nat bool) (hAPP _let_3 _let_3 (combc nat nat bool) (fequal nat)) (zero_zero nat))))))))))))))))))))))))))))))))))) ) 16.18/16.28 ( (fun real bool), (fun nat real), (sums real), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (hAPP real _let_1 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc))) ) 16.18/16.28 ( (fun real bool), (fun real (fun int bool)), (let ((_let_0 (fun int bool))) (hAPP (fun _let_0 bool) (fun (fun real _let_0) (fun real bool)) (combb _let_0 bool real) (fEx int))), (let ((_let_0 (fun int (fun int bool)))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real real))) (let ((_let_3 (real_1 int))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun int _let_4))) (let ((_let_7 (fun (fun int bool) (fun int bool)))) (let ((_let_8 (fun (fun int bool) _let_6))) (let ((_let_9 (fun _let_0 (fun int bool)))) (let ((_let_10 (fun int real))) (let ((_let_11 (fun int _let_7))) (let ((_let_12 (fun (fun int bool) _let_0))) (let ((_let_13 (fun int _let_6))) (let ((_let_14 (fun _let_13 _let_11))) (let ((_let_15 (fun _let_0 _let_13))) (let ((_let_16 (fun real (fun int bool)))) (let ((_let_17 (fun real _let_0))) (let ((_let_18 (fun real _let_12))) (let ((_let_19 (fun real _let_11))) (let ((_let_20 (fun real _let_13))) (let ((_let_21 (fun int _let_10))) (let ((_let_22 (fun _let_21 _let_0))) (let ((_let_23 (fun real _let_22))) (let ((_let_24 (fun _let_10 (fun int bool)))) (let ((_let_25 (fun real _let_24))) (let ((_let_26 (fun _let_10 _let_10))) (let ((_let_27 (fun int _let_26))) (let ((_let_28 (fun int _let_2))) (hAPP _let_17 _let_16 (hAPP _let_9 (fun _let_17 _let_16) (combb _let_0 (fun int bool) real) (hAPP (fun (fun int bool) bool) _let_9 (combb (fun int bool) bool int) (fEx int))) (hAPP (fun int bool) _let_17 (hAPP _let_18 (fun (fun int bool) _let_17) (combc real (fun int bool) _let_0) (hAPP _let_19 _let_18 (hAPP (fun _let_11 _let_12) (fun _let_19 _let_18) (combb _let_11 _let_12 real) (combc int (fun int bool) (fun int bool))) (hAPP _let_20 _let_19 (hAPP _let_14 (fun _let_20 _let_19) (combb _let_13 _let_11 real) (hAPP (fun _let_6 _let_7) _let_14 (combb _let_6 _let_7 int) (combs int bool bool))) (hAPP _let_17 _let_20 (hAPP _let_15 (fun _let_17 _let_20) (combb _let_0 _let_13 real) (hAPP _let_8 _let_15 (combb (fun int bool) _let_6 int) (hAPP (fun bool _let_4) _let_8 (combb bool _let_4 int) fconj))) (hAPP _let_21 _let_17 (hAPP _let_23 (fun _let_21 _let_17) (combc real _let_21 _let_0) (hAPP _let_25 _let_23 (hAPP (fun _let_24 _let_22) (fun _let_25 _let_23) (combb _let_24 _let_22 real) (combb _let_10 (fun int bool) int)) (hAPP _let_5 _let_25 (hAPP (fun _let_1 _let_24) (fun _let_5 _let_25) (combb _let_1 _let_24 real) (combb real bool int)) (fequal real)))) (hAPP _let_10 _let_21 (hAPP _let_27 (fun _let_10 _let_21) (combc int _let_10 _let_10) (hAPP _let_28 _let_27 (hAPP (fun _let_2 _let_26) (fun _let_28 _let_27) (combb _let_2 _let_26 int) (combb real real int)) (hAPP _let_10 _let_28 (hAPP (fun real _let_2) (fun _let_10 _let_28) (combb real _let_2 int) (inverse_divide real)) _let_3))) _let_3)))))) (hAPP (fun int bool) (fun int bool) (hAPP _let_4 _let_7 (combb bool bool int) fNot) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (fequal int)) (zero_zero int)))))))))))))))))))))))))))))))))) ) 16.18/16.28 ( (fun real bool), (fun real (fun int bool)), (let ((_let_0 (fun int bool))) (hAPP (fun _let_0 bool) (fun (fun real _let_0) (fun real bool)) (combb _let_0 bool real) (fEx int))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real real))) (let ((_let_3 (fun nat (fun nat bool)))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun (fun nat real) (fun nat real)))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun (fun nat bool) (fun nat bool)))) (let ((_let_8 (fun int real))) (let ((_let_9 (fun nat _let_4))) (let ((_let_10 (fun (fun nat bool) _let_9))) (let ((_let_11 (fun real _let_0))) (let ((_let_12 (fun int _let_2))) (let ((_let_13 (fun real (fun int (fun nat bool))))) (let ((_let_14 (fun (fun int (fun nat bool)) _let_0))) (let ((_let_15 (fun (fun nat bool) (fun int (fun nat bool))))) (let ((_let_16 (fun real _let_15))) (let ((_let_17 (fun int _let_7))) (let ((_let_18 (fun real _let_17))) (let ((_let_19 (fun int _let_9))) (let ((_let_20 (fun real _let_19))) (let ((_let_21 (fun _let_19 _let_17))) (let ((_let_22 (fun (fun int (fun nat bool)) _let_19))) (let ((_let_23 (fun int (fun nat real)))) (let ((_let_24 (fun _let_23 (fun int (fun nat bool))))) (let ((_let_25 (fun real _let_24))) (let ((_let_26 (fun (fun nat real) (fun nat bool)))) (let ((_let_27 (fun real _let_26))) (let ((_let_28 (fun int _let_5))) (hAPP _let_13 _let_11 (hAPP _let_14 (fun _let_13 _let_11) (combb (fun int (fun nat bool)) _let_0 real) (hAPP (fun (fun nat bool) bool) _let_14 (combb (fun nat bool) bool int) (fEx nat))) (hAPP (fun nat bool) _let_13 (hAPP _let_16 (fun (fun nat bool) _let_13) (combc real (fun nat bool) (fun int (fun nat bool))) (hAPP _let_18 _let_16 (hAPP (fun _let_17 _let_15) (fun _let_18 _let_16) (combb _let_17 _let_15 real) (combc int (fun nat bool) (fun nat bool))) (hAPP _let_20 _let_18 (hAPP _let_21 (fun _let_20 _let_18) (combb _let_19 _let_17 real) (hAPP (fun _let_9 _let_7) _let_21 (combb _let_9 _let_7 int) (combs nat bool bool))) (hAPP _let_13 _let_20 (hAPP _let_22 (fun _let_13 _let_20) (combb (fun int (fun nat bool)) _let_19 real) (hAPP _let_10 _let_22 (combb (fun nat bool) _let_9 int) (hAPP (fun bool _let_4) _let_10 (combb bool _let_4 nat) fconj))) (hAPP _let_23 _let_13 (hAPP _let_25 (fun _let_23 _let_13) (combc real _let_23 (fun int (fun nat bool))) (hAPP _let_27 _let_25 (hAPP (fun _let_26 _let_24) (fun _let_27 _let_25) (combb _let_26 _let_24 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_6 _let_27 (hAPP (fun _let_1 _let_26) (fun _let_6 _let_27) (combb _let_1 _let_26 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_23 (hAPP _let_28 (fun (fun nat real) _let_23) (combc int (fun nat real) (fun nat real)) (hAPP _let_12 _let_28 (hAPP (fun _let_2 _let_5) (fun _let_12 _let_28) (combb _let_2 _let_5 int) (combb real real nat)) (hAPP _let_8 _let_12 (hAPP (fun real _let_2) (fun _let_8 _let_12) (combb real _let_2 int) (inverse_divide real)) (real_1 int)))) (real_1 nat))))))) (hAPP (fun nat bool) (fun nat bool) (hAPP _let_4 _let_7 (combb bool bool nat) fNot) (hAPP nat (fun nat bool) (hAPP _let_3 _let_3 (combc nat nat bool) (fequal nat)) (zero_zero nat)))))))))))))))))))))))))))))))))) ) 16.18/16.28 ( (fun real real), nat, root, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.18/16.28 ( (fun real real), real, (minus_minus real), (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))) ) 16.18/16.28 ( (fun real real), real, (inverse_divide real), (one_one real) ) 16.18/16.28 ( (fun real real), real, (inverse_divide real), pi ) 16.18/16.28 ( (fun real real), real, (inverse_divide real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.18/16.28 ( (fun real real), real, (inverse_divide real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.18/16.28 ( (fun real real), real, (inverse_divide real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.18/16.28 ( (fun real real), real, (times_times real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.18/16.28 ( (fun real real), real, (times_times real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.18/16.28 ( (fun real real), real, (times_times real), (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 16.18/16.28 ( (fun real real), (fun real real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)))), sin ) 16.18/16.28 ( rat, int, (hAPP int (fun int rat) fract (zero_zero int)), (one_one int) ) 16.18/16.28 ( rat, int, (hAPP int (fun int rat) fract (one_one int)), (one_one int) ) 16.18/16.28 ( rat, rat, (sgn_sgn rat), (zero_zero rat) ) 16.18/16.28 ( rat, (product_prod int int), frct, (let ((_let_0 (one_one int))) (let ((_let_1 (product_prod int int))) (hAPP int _let_1 (hAPP int (fun int _let_1) (product_Pair int int) _let_0) _let_0))) ) 16.18/16.28 ( (fun int rat), int, fract, (one_one int) ) 16.18/16.28 ( (fun int rat), int, fract, (zero_zero int) ) 16.18/16.28 ( (fun nat (fun nat bool)), (fun nat nat), (let ((_let_0 (fun nat (fun nat bool)))) (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat (fun nat bool) nat) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat)))), suc ) 16.18/16.28 ( (fun nat (fun nat bool)), (fun nat (fun nat bool)), (combc nat nat bool), (fequal nat) ) 16.18/16.28 ( (fun nat int), int, (power_power int), s ) 16.18/16.28 ( (fun nat int), int, (power_power int), s1 ) 16.18/16.28 ( (fun nat int), int, (power_power int), skv_14 ) 16.18/16.28 ( complex, nat, (hAPP complex (fun nat complex) (power_power complex) ii), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.18/16.28 ( complex, int, (number_number_of complex), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.18/16.28 ( complex, int, (number_number_of complex), min_1 ) 16.18/16.28 ( complex, real, cis, (zero_zero real) ) 16.18/16.28 ( complex, real, (hAPP real (fun real complex) complex_1 (zero_zero real)), (one_one real) ) 16.18/16.28 ( complex, real, (hAPP real (fun real complex) complex_1 (zero_zero real)), (zero_zero real) ) 16.18/16.28 ( complex, real, (of_real complex), pi ) 16.18/16.28 ( complex, real, (of_real complex), (hAPP int real (number_number_of real) min_1) ) 16.18/16.28 ( complex, real, (of_real complex), (hAPP real real (uminus_uminus real) (one_one real)) ) 16.18/16.28 ( complex, real, (hAPP real (fun real complex) complex_1 (one_one real)), (zero_zero real) ) 16.18/16.28 ( complex, complex, (inverse_inverse complex), ii ) 16.18/16.28 ( complex, complex, expi, (zero_zero complex) ) 16.18/16.28 ( complex, complex, expi, (let ((_let_0 (fun complex complex))) (let ((_let_1 (times_times complex))) (hAPP complex complex (hAPP complex _let_0 _let_1 (hAPP complex complex (hAPP complex _let_0 _let_1 (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi))) ii))) ) 16.18/16.28 ( complex, complex, (uminus_uminus complex), (one_one complex) ) 16.18/16.28 ( complex, complex, (uminus_uminus complex), ii ) 16.18/16.28 ( complex, complex, cnj, (one_one complex) ) 16.18/16.28 ( complex, complex, cnj, ii ) 16.18/16.28 ( complex, complex, cnj, (zero_zero complex) ) 16.18/16.28 ( complex, complex, (hAPP complex (fun complex complex) (times_times complex) ii), ii ) 16.18/16.28 ( complex, complex, (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real complex (of_real complex) pi) ) 16.18/16.28 ( complex, complex, (let ((_let_0 (fun complex complex))) (let ((_let_1 (times_times complex))) (hAPP complex _let_0 _let_1 (hAPP complex complex (hAPP complex _let_0 _let_1 (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi))))), ii ) 16.18/16.28 ( (fun nat real), (fun nat nat), (let ((_let_0 (fun nat real))) (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat real nat) (real_1 nat))), suc ) 16.18/16.28 ( (fun nat real), (fun nat nat), (let ((_let_0 (fun nat real))) (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat real nat) (real_1 nat))), (let ((_let_0 (fun nat (fun nat nat)))) (let ((_let_1 (combc nat nat nat))) (hAPP nat (fun nat nat) (hAPP _let_0 _let_0 _let_1 (hAPP (fun nat nat) _let_0 (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_0 _let_0 _let_1 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))) ) 16.18/16.28 ( (fun nat real), (fun nat nat), (let ((_let_0 (fun nat real))) (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat real nat) (hAPP real _let_0 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))), suc ) 16.18/16.28 ( (fun nat real), real, (power_power real), (hAPP int real (number_number_of real) min_1) ) 16.18/16.28 ( (fun nat real), real, (power_power real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.18/16.28 ( (fun nat real), real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (hAPP _let_2 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 nat) (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1))))))), (one_one real) ) 16.18/16.28 ( (fun nat real), (fun nat real), (diffs real), sin_coeff ) 16.18/16.28 ( (fun nat real), (fun nat real), (let ((_let_0 (fun nat real))) (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real))), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))) ) 16.18/16.28 ( (fun nat real), (fun nat real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (let ((_let_3 (fun real _let_0))) (let ((_let_4 (fun _let_1 _let_2))) (let ((_let_5 (combb real _let_0 nat))) (hAPP _let_2 (fun _let_1 _let_1) (combs nat real real) (hAPP _let_1 _let_2 (hAPP _let_3 _let_4 _let_5 (inverse_divide real)) (hAPP real _let_1 (hAPP _let_2 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_2 (hAPP _let_3 _let_4 _let_5 (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) (one_one real)))))))))), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat (fun nat nat)))) (let ((_let_2 (combc nat nat nat))) (hAPP (fun nat nat) _let_0 (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat real nat) (real_1 nat)) (hAPP nat (fun nat nat) (hAPP _let_1 _let_1 _let_2 (hAPP (fun nat nat) _let_1 (hAPP _let_1 (fun (fun nat nat) _let_1) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_1 _let_1 _let_2 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))))) ) 16.18/16.28 ( (fun int (fun int int)), (fun int int), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)))), (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.18/16.28 ( (fun int (fun int int)), (fun int int), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)))), (let ((_let_0 (fun int int))) (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.18/16.28 ( (fun int (fun int int)), (fun int int), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun _let_0 _let_1))) (let ((_let_3 (fun _let_0 _let_0))) (let ((_let_4 (fun int _let_3))) (hAPP _let_4 _let_2 (combc int _let_0 _let_0) (hAPP _let_1 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_1 _let_4) (combb _let_0 _let_3 int) (combb int int int)) (hAPP _let_0 _let_1 (hAPP _let_1 _let_2 (combb int _let_0 int) (plus_plus int)) (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))))))), (let ((_let_0 (fun int int))) (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.18/16.28 ( (fun int (fun int int)), (fun int (fun int int)), (combc int int int), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)) (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 16.18/16.28 ( (fun complex complex), complex, (times_times complex), ii ) 16.18/16.28 ( (fun complex complex), complex, (times_times complex), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.18/16.28 ( (fun complex complex), complex, (times_times complex), (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 16.18/16.28 ( (fun real complex), real, complex_1, (one_one real) ) 16.18/16.28 ( (fun real complex), real, complex_1, (zero_zero real) ) 16.18/16.28 ( (product_prod int int), int, (hAPP int (fun int (product_prod int int)) (product_Pair int int) (zero_zero int)), (one_one int) ) 16.18/16.28 ( (product_prod int int), int, (hAPP int (fun int (product_prod int int)) (product_Pair int int) s), (one_one int) ) 16.18/16.28 ( (product_prod int int), int, (hAPP int (fun int (product_prod int int)) (product_Pair int int) (one_one int)), (one_one int) ) 16.18/16.28 ( (product_prod int int), rat, quotient_of, (zero_zero rat) ) 16.18/16.28 ( (product_prod int int), rat, quotient_of, (one_one rat) ) 16.18/16.28 ( (fun int (product_prod int int)), int, (product_Pair int int), (one_one int) ) 16.18/16.28 ( (fun int (product_prod int int)), int, (product_Pair int int), (zero_zero int) ) 16.18/16.28 ( (fun int (product_prod int int)), int, (product_Pair int int), s ) 16.18/16.28 ( (fun (fun nat bool) bool), (fun nat int), (nat_tr1645093318rphism nat int), (semiring_1_of_nat int) ) 16.18/16.28 ( (fun (fun int bool) bool), int, (member int), (one_one int) ) 16.18/16.28 ( (fun (fun int bool) bool), (fun int nat), (nat_tr1645093318rphism int nat), nat_1 ) 16.18/16.28 ( quickcheck_code_int, int, (number_number_of quickcheck_code_int), (hAPP int int bit1 pls) ) 16.18/16.28 ( quickcheck_code_int, int, quickcheck_of_int, (one_one int) ) 16.18/16.28 ( quickcheck_code_int, int, quickcheck_of_int, (zero_zero int) ) 16.18/16.28 ( (fun nat (fun nat nat)), (fun nat nat), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat _let_0))) (hAPP _let_1 (fun _let_0 _let_1) (combb nat _let_0 nat) (plus_plus nat)))), (let ((_let_0 (fun nat (fun nat nat)))) (hAPP nat (fun nat nat) (hAPP _let_0 _let_0 (combc nat nat nat) (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.18/16.28 ( (fun nat (fun nat nat)), (fun nat (fun nat nat)), (combc nat nat nat), (times_times nat) ) 16.18/16.28 ( (fun nat (fun nat nat)), (fun nat (fun nat nat)), (combc nat nat nat), (let ((_let_0 (fun nat (fun nat nat)))) (hAPP (fun nat nat) _let_0 (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_0 _let_0 (combc nat nat nat) (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 16.18/16.28 ( (fun nat complex), complex, (power_power complex), ii ) 16.18/16.28 ( (fun nat (fun real real)), (fun nat real), (let ((_let_0 (fun real real))) (hAPP (fun real _let_0) (fun (fun nat real) (fun nat _let_0)) (combb real _let_0 nat) (inverse_divide real))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (hAPP real _let_1 (hAPP _let_2 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 nat) (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) (one_one real))))) ) 16.18/16.28 ( (fun nat (fun real real)), (fun nat real), (let ((_let_0 (fun real real))) (hAPP (fun real _let_0) (fun (fun nat real) (fun nat _let_0)) (combb real _let_0 nat) (times_times real))), (hAPP real (fun nat real) (power_power real) (hAPP int real (number_number_of real) min_1)) ) 16.18/16.28 ( (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)), (fun real real), (combb real real nat), (inverse_inverse real) ) 16.18/16.28 ( (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)), (fun nat (fun real real)), (combs nat real real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (let ((_let_3 (fun real _let_0))) (let ((_let_4 (fun _let_1 _let_2))) (let ((_let_5 (combb real _let_0 nat))) (hAPP _let_1 _let_2 (hAPP _let_3 _let_4 _let_5 (inverse_divide real)) (hAPP real _let_1 (hAPP _let_2 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_2 (hAPP _let_3 _let_4 _let_5 (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) (one_one real))))))))) ) 16.18/16.28 ( (fun real (fun real real)), (fun real real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)))), cos ) 16.18/16.28 ( (fun (fun nat real) (fun nat (fun real real))), (fun real (fun real real)), (combb real (fun real real) nat), (inverse_divide real) ) 16.18/16.28 ( (fun (fun nat real) (fun nat (fun real real))), (fun real (fun real real)), (combb real (fun real real) nat), (times_times real) ) 16.18/16.28 ( (fun (fun nat nat) (fun nat real)), (fun nat real), (combb nat real nat), (real_1 nat) ) 16.18/16.28 ( (fun (fun nat nat) (fun nat real)), (fun nat real), (combb nat real nat), (hAPP real (fun nat real) (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.18/16.28 ( (fun (filter nat) bool), real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 (fun real (fun (filter nat) bool)) (tendsto nat real) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))))), (zero_zero real) ) 16.18/16.28 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), (fun int int), (product_apsnd int int int), (uminus_uminus int) ) 16.18/16.28 ( (let ((_let_0 (fun int int))) (fun _let_0 (fun int _let_0))), (fun int (fun int int)), (combb int (fun int int) int), (plus_plus int) ) 16.18/16.28 ( (let ((_let_0 (fun int int))) (fun _let_0 (fun int _let_0))), (let ((_let_0 (fun int int))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun int int))) (combc int _let_0 _let_0)), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun _let_0 _let_0))) (let ((_let_3 (fun int _let_2))) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 int) (combb int int int)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)) (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))))) ) 16.18/16.28 ( code_code_numeral, int, (number_number_of code_code_numeral), pls ) 16.18/16.28 ( code_code_numeral, int, (number_number_of code_code_numeral), (hAPP int int bit1 pls) ) 16.18/16.28 ( code_code_numeral, code_code_numeral, (hAPP code_code_numeral (fun code_code_numeral code_code_numeral) (minus_minus code_code_numeral) (zero_zero code_code_numeral)), (one_one code_code_numeral) ) 16.18/16.28 ( (fun int (fun int (fun int bool))), (fun int (fun int int)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun _let_2 _let_1))) (hAPP _let_3 (fun (fun int _let_2) (fun int _let_1)) (combb _let_2 _let_1 int) (hAPP _let_1 _let_3 (combb int _let_0 int) (fequal int))))))), int_gcd ) 16.18/16.28 ( (fun int (fun int (fun int bool))), (fun int (fun int (fun int bool))), (combc int int (fun int bool)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int _let_1))) (let ((_let_5 (fun _let_2 _let_1))) (hAPP _let_4 _let_4 (hAPP (fun _let_1 _let_1) (fun _let_4 _let_4) (combb _let_1 _let_1 int) (combc int int bool)) (hAPP _let_3 _let_4 (hAPP _let_5 (fun _let_3 _let_4) (combb _let_2 _let_1 int) (hAPP _let_1 _let_5 (combb int _let_0 int) (fequal int))) int_gcd)))))))) ) 16.18/16.28 ( (fun int (fun int (fun int bool))), (fun int (fun int (fun int bool))), (let ((_let_0 (fun int (fun int bool)))) (let ((_let_1 (fun int _let_0))) (hAPP (fun _let_0 _let_0) (fun _let_1 _let_1) (combb _let_0 _let_0 int) (combc int int bool)))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int _let_1))) (let ((_let_5 (fun _let_2 _let_1))) (hAPP _let_3 _let_4 (hAPP _let_5 (fun _let_3 _let_4) (combb _let_2 _let_1 int) (hAPP _let_1 _let_5 (combb int _let_0 int) (fequal int))) int_gcd))))))) ) 16.18/16.28 ( (fun real (fun real bool)), (fun real real), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (hAPP _let_1 (fun (fun real real) _let_1) (combb real _let_0 real) (fequal real)))), cos ) 16.18/16.28 ( (fun real (fun real bool)), (fun real (fun real bool)), (combc real real bool), (ord_less_eq real) ) 16.18/16.28 ( (fun real (fun real bool)), (fun real (fun real bool)), (combc real real bool), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun real _let_0))) (hAPP _let_1 _let_2 (hAPP _let_2 (fun _let_1 _let_2) (combb real _let_0 real) (fequal real)) cos)))) ) 16.18/16.28 ( (fun real (fun nat real)), (fun nat (fun real real)), (combc nat real real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 nat) (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))))) ) 16.18/16.28 ( (let ((_let_0 (fun real real))) (fun _let_0 _let_0)), (fun real (fun real real)), (combs real real real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos))) ) 16.18/16.28 ( (let ((_let_0 (fun real real))) (fun _let_0 (fun real _let_0))), (fun real (fun real real)), (combb real (fun real real) real), (inverse_divide real) ) 16.18/16.28 ( (fun (product_prod int int) bool), int, (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 _let_0))) (let ((_let_3 (fun _let_1 int))) (hAPP _let_2 (fun int (fun _let_1 bool)) (combc _let_1 int bool) (hAPP _let_3 _let_2 (hAPP (fun int _let_0) (fun _let_3 _let_2) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))))))), (zero_zero int) ) 16.18/16.28 ( (fun (product_prod int int) bool), (fun int (fun int bool)), (product_prod_case int int bool), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun int _let_1))) (let ((_let_6 (fun int _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (fun _let_2 _let_1))) (let ((_let_9 (fun _let_1 _let_1))) (hAPP _let_1 _let_1 (hAPP _let_7 _let_9 (combb _let_0 _let_0 int) (hAPP _let_6 _let_7 (combs int bool bool) (hAPP _let_0 _let_6 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 int) fconj) (hAPP int _let_0 (ord_less int) (zero_zero int))))) (hAPP int _let_1 (hAPP _let_5 _let_5 (combc int int _let_0) (hAPP _let_5 _let_5 (hAPP _let_9 (fun _let_5 _let_5) (combb _let_1 _let_1 int) (combc int int bool)) (hAPP _let_3 _let_5 (hAPP _let_8 (fun _let_3 _let_5) (combb _let_2 _let_1 int) (hAPP _let_1 _let_8 (combb int _let_0 int) (fequal int))) int_gcd))) (one_one int))))))))))))) ) 16.18/16.28 ( (fun (product_prod int int) bool), (fun (product_prod int int) bool), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 bool))) (hAPP (fun bool bool) (fun _let_1 _let_1) (combb bool bool _let_0) fNot))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun _let_1 _let_0))) (let ((_let_4 (fun _let_1 int))) (hAPP int _let_2 (hAPP _let_3 (fun int _let_2) (combc _let_1 int bool) (hAPP _let_4 _let_3 (hAPP (fun int _let_0) (fun _let_4 _let_3) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))) ) 16.18/16.28 ( (fun int (fun (product_prod int int) bool)), (fun (product_prod int int) (fun int bool)), (combc (product_prod int int) int bool), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 _let_0))) (let ((_let_3 (fun _let_1 int))) (hAPP _let_3 _let_2 (hAPP (fun int _let_0) (fun _let_3 _let_2) (combb int _let_0 _let_1) (fequal int)) (product_snd int int)))))) ) 16.18/16.29 ( (fun real (fun (filter nat) bool)), (fun nat real), (tendsto nat real), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))) ) 16.18/16.29 ( (fun code_code_numeral code_code_numeral), code_code_numeral, (minus_minus code_code_numeral), (zero_zero code_code_numeral) ) 16.18/16.29 ( (fun int (fun bool bool)), (fun int bool), (let ((_let_0 (fun bool bool))) (hAPP (fun bool _let_0) (fun (fun int bool) (fun int _let_0)) (combb bool _let_0 int) fconj)), (hAPP int (fun int bool) (ord_less int) (zero_zero int)) ) 16.18/16.29 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), (fun bool bool), (combb bool bool int), fNot ) 16.18/16.29 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), (fun int (fun bool bool)), (combs int bool bool), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun int _let_1))) (hAPP _let_0 _let_2 (hAPP (fun bool _let_1) (fun _let_0 _let_2) (combb bool _let_1 int) fconj) (hAPP int _let_0 (ord_less int) (zero_zero int)))))) ) 16.18/16.29 ( (fun (fun int bool) (fun int (fun bool bool))), (fun bool (fun bool bool)), (combb bool (fun bool bool) int), fconj ) 16.18/16.29 ( (let ((_let_0 (fun int bool))) (fun (fun int _let_0) _let_0)), (fun (fun int bool) bool), (combb (fun int bool) bool int), (fEx int) ) 16.18/16.29 ( (fun int (fun (fun int int) (fun int bool))), (fun int (fun int bool)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun (fun int int) _let_0))) (hAPP (fun _let_0 _let_1) (fun (fun int _let_0) (fun int _let_1)) (combb _let_0 _let_1 int) (combb int bool int)))), (fequal int) ) 16.18/16.29 ( (fun (fun int int) (fun int (fun int bool))), (fun int (fun int bool)), (combb int (fun int bool) int), (fequal int) ) 16.18/16.29 ( (fun (fun int int) (fun int (fun int bool))), (fun int (fun (fun int int) (fun int bool))), (combc int (fun int int) (fun int bool)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun (fun int int) _let_0))) (let ((_let_3 (fun int _let_2))) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 int) (combb int bool int)) (fequal int)))))) ) 16.18/16.29 ( (let ((_let_0 (fun int bool))) (fun (fun int _let_0) (fun int (fun (fun int int) _let_0)))), (let ((_let_0 (fun int bool))) (fun _let_0 (fun (fun int int) _let_0))), (let ((_let_0 (fun int bool))) (combb _let_0 (fun (fun int int) _let_0) int)), (combb int bool int) ) 16.18/16.29 ( (filter real), real, (at real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.18/16.29 ( (fun (filter real) bool), real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 (fun real (fun (filter real) bool)) (tendsto real real) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin)))), (zero_zero real) ) 16.18/16.29 ( (fun real (fun (filter real) bool)), (fun real real), (tendsto real real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))) ) 16.18/16.29 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), (let ((_let_0 (product_prod int int))) (collect (product_prod _let_0 _let_0))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun _let_2 (fun _let_2 bool)))) (let ((_let_5 (fun (fun _let_2 bool) (fun _let_2 bool)))) (let ((_let_6 (fun _let_2 _let_5))) (let ((_let_7 (fun _let_4 _let_4))) (let ((_let_8 (fun _let_2 _let_3))) (let ((_let_9 (fun _let_2 _let_0))) (let ((_let_10 (fun _let_2 int))) (let ((_let_11 (fun _let_10 _let_9))) (let ((_let_12 (hAPP (fun int _let_0) _let_11 (combb int _let_0 _let_2) (fequal int)))) (let ((_let_13 (product_snd int int))) (let ((_let_14 (hAPP (fun _let_2 bool) _let_8 (hAPP (fun bool _let_3) (fun (fun _let_2 bool) _let_8) (combb bool _let_3 _let_2) fconj) (hAPP (fun _let_2 bool) (fun _let_2 bool) (hAPP _let_3 _let_5 (combb bool bool _let_2) fNot) (hAPP int (fun _let_2 bool) (hAPP _let_9 (fun int (fun _let_2 bool)) (combc _let_2 int bool) (hAPP _let_10 _let_9 _let_12 _let_13)) (zero_zero int)))))) (let ((_let_15 (fun _let_2 _let_10))) (let ((_let_16 (fun _let_10 (fun _let_2 bool)))) (let ((_let_17 (fun _let_2 _let_16))) (let ((_let_18 (fun _let_2 _let_9))) (let ((_let_19 (fun _let_10 _let_10))) (let ((_let_20 (fun _let_2 _let_19))) (let ((_let_21 (fun _let_10 _let_15))) (let ((_let_22 (fun _let_2 _let_1))) (let ((_let_23 (hAPP _let_10 _let_22 (hAPP (fun int _let_1) (fun _let_10 _let_22) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (let ((_let_24 (fun int _let_10))) (hAPP _let_4 (fun (product_prod _let_2 _let_2) bool) (product_prod_case _let_2 _let_2 bool) (hAPP _let_4 _let_4 (hAPP _let_6 _let_7 (combs _let_2 (fun _let_2 bool) (fun _let_2 bool)) (hAPP _let_8 _let_6 (hAPP (fun _let_3 _let_5) (fun _let_8 _let_6) (combb _let_3 _let_5 _let_2) (combb bool bool _let_2)) _let_14)) (hAPP _let_4 _let_4 (hAPP _let_5 _let_7 (combb (fun _let_2 bool) (fun _let_2 bool) _let_2) (hAPP _let_8 _let_5 (combs _let_2 bool bool) _let_14)) (hAPP _let_15 _let_4 (hAPP _let_17 (fun _let_15 _let_4) (combs _let_2 _let_10 (fun _let_2 bool)) (hAPP _let_18 _let_17 (hAPP (fun _let_9 _let_16) (fun _let_18 _let_17) (combb _let_9 _let_16 _let_2) (combs _let_2 int bool)) (hAPP _let_15 _let_18 (hAPP _let_11 (fun _let_15 _let_18) (combb _let_10 _let_9 _let_2) _let_12) (hAPP _let_10 _let_15 (hAPP _let_20 _let_21 (combc _let_2 _let_10 _let_10) (hAPP _let_22 _let_20 (hAPP (fun _let_1 _let_19) (fun _let_22 _let_20) (combb _let_1 _let_19 _let_2) (combb int int _let_2)) _let_23)) _let_13)))) (hAPP _let_10 _let_15 (hAPP _let_24 _let_21 (combb int _let_10 _let_2) (hAPP _let_22 _let_24 (combc _let_2 int int) _let_23)) _let_13)))))))))))))))))))))))))))))) ) 16.18/16.29 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (product_prod_case _let_0 _let_0 bool)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun _let_2 (fun _let_2 bool)))) (let ((_let_5 (fun (fun _let_2 bool) (fun _let_2 bool)))) (let ((_let_6 (fun _let_2 _let_5))) (let ((_let_7 (fun _let_4 _let_4))) (let ((_let_8 (fun _let_2 _let_3))) (let ((_let_9 (fun _let_2 _let_0))) (let ((_let_10 (fun _let_2 int))) (let ((_let_11 (fun _let_10 _let_9))) (let ((_let_12 (hAPP (fun int _let_0) _let_11 (combb int _let_0 _let_2) (fequal int)))) (let ((_let_13 (product_snd int int))) (let ((_let_14 (hAPP (fun _let_2 bool) _let_8 (hAPP (fun bool _let_3) (fun (fun _let_2 bool) _let_8) (combb bool _let_3 _let_2) fconj) (hAPP (fun _let_2 bool) (fun _let_2 bool) (hAPP _let_3 _let_5 (combb bool bool _let_2) fNot) (hAPP int (fun _let_2 bool) (hAPP _let_9 (fun int (fun _let_2 bool)) (combc _let_2 int bool) (hAPP _let_10 _let_9 _let_12 _let_13)) (zero_zero int)))))) (let ((_let_15 (fun _let_2 _let_10))) (let ((_let_16 (fun _let_10 (fun _let_2 bool)))) (let ((_let_17 (fun _let_2 _let_16))) (let ((_let_18 (fun _let_2 _let_9))) (let ((_let_19 (fun _let_10 _let_10))) (let ((_let_20 (fun _let_2 _let_19))) (let ((_let_21 (fun _let_10 _let_15))) (let ((_let_22 (fun _let_2 _let_1))) (let ((_let_23 (hAPP _let_10 _let_22 (hAPP (fun int _let_1) (fun _let_10 _let_22) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (let ((_let_24 (fun int _let_10))) (hAPP _let_4 _let_4 (hAPP _let_6 _let_7 (combs _let_2 (fun _let_2 bool) (fun _let_2 bool)) (hAPP _let_8 _let_6 (hAPP (fun _let_3 _let_5) (fun _let_8 _let_6) (combb _let_3 _let_5 _let_2) (combb bool bool _let_2)) _let_14)) (hAPP _let_4 _let_4 (hAPP _let_5 _let_7 (combb (fun _let_2 bool) (fun _let_2 bool) _let_2) (hAPP _let_8 _let_5 (combs _let_2 bool bool) _let_14)) (hAPP _let_15 _let_4 (hAPP _let_17 (fun _let_15 _let_4) (combs _let_2 _let_10 (fun _let_2 bool)) (hAPP _let_18 _let_17 (hAPP (fun _let_9 _let_16) (fun _let_18 _let_17) (combb _let_9 _let_16 _let_2) (combs _let_2 int bool)) (hAPP _let_15 _let_18 (hAPP _let_11 (fun _let_15 _let_18) (combb _let_10 _let_9 _let_2) _let_12) (hAPP _let_10 _let_15 (hAPP _let_20 _let_21 (combc _let_2 _let_10 _let_10) (hAPP _let_22 _let_20 (hAPP (fun _let_1 _let_19) (fun _let_22 _let_20) (combb _let_1 _let_19 _let_2) (combb int int _let_2)) _let_23)) _let_13)))) (hAPP _let_10 _let_15 (hAPP _let_24 _let_21 (combb int _let_10 _let_2) (hAPP _let_22 _let_24 (combc _let_2 int int) _let_23)) _let_13))))))))))))))))))))))))))))) ) 16.18/16.29 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_1 _let_3))) (let ((_let_5 (fun _let_3 _let_3))) (let ((_let_6 (fun _let_1 _let_5))) (let ((_let_7 (fun _let_1 _let_2))) (let ((_let_8 (combb bool bool _let_1))) (let ((_let_9 (fun _let_1 _let_0))) (let ((_let_10 (fun _let_1 int))) (hAPP _let_6 (fun _let_4 _let_4) (combs _let_1 _let_3 _let_3) (hAPP _let_7 _let_6 (hAPP (fun _let_2 _let_5) (fun _let_7 _let_6) (combb _let_2 _let_5 _let_1) _let_8) (hAPP _let_3 _let_7 (hAPP (fun bool _let_2) (fun _let_3 _let_7) (combb bool _let_2 _let_1) fconj) (hAPP _let_3 _let_3 (hAPP _let_2 _let_5 _let_8 fNot) (hAPP int _let_3 (hAPP _let_9 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_10 _let_9 (hAPP (fun int _let_0) (fun _let_10 _let_9) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))))))))))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun _let_2 (fun _let_2 bool)))) (let ((_let_5 (fun (fun _let_2 bool) (fun _let_2 bool)))) (let ((_let_6 (fun _let_2 _let_3))) (let ((_let_7 (fun _let_2 _let_0))) (let ((_let_8 (fun _let_2 int))) (let ((_let_9 (fun _let_8 _let_7))) (let ((_let_10 (hAPP (fun int _let_0) _let_9 (combb int _let_0 _let_2) (fequal int)))) (let ((_let_11 (product_snd int int))) (let ((_let_12 (fun _let_2 _let_8))) (let ((_let_13 (fun _let_8 (fun _let_2 bool)))) (let ((_let_14 (fun _let_2 _let_13))) (let ((_let_15 (fun _let_2 _let_7))) (let ((_let_16 (fun _let_8 _let_8))) (let ((_let_17 (fun _let_2 _let_16))) (let ((_let_18 (fun _let_8 _let_12))) (let ((_let_19 (fun _let_2 _let_1))) (let ((_let_20 (hAPP _let_8 _let_19 (hAPP (fun int _let_1) (fun _let_8 _let_19) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (let ((_let_21 (fun int _let_8))) (hAPP _let_4 _let_4 (hAPP _let_5 (fun _let_4 _let_4) (combb (fun _let_2 bool) (fun _let_2 bool) _let_2) (hAPP _let_6 _let_5 (combs _let_2 bool bool) (hAPP (fun _let_2 bool) _let_6 (hAPP (fun bool _let_3) (fun (fun _let_2 bool) _let_6) (combb bool _let_3 _let_2) fconj) (hAPP (fun _let_2 bool) (fun _let_2 bool) (hAPP _let_3 _let_5 (combb bool bool _let_2) fNot) (hAPP int (fun _let_2 bool) (hAPP _let_7 (fun int (fun _let_2 bool)) (combc _let_2 int bool) (hAPP _let_8 _let_7 _let_10 _let_11)) (zero_zero int)))))) (hAPP _let_12 _let_4 (hAPP _let_14 (fun _let_12 _let_4) (combs _let_2 _let_8 (fun _let_2 bool)) (hAPP _let_15 _let_14 (hAPP (fun _let_7 _let_13) (fun _let_15 _let_14) (combb _let_7 _let_13 _let_2) (combs _let_2 int bool)) (hAPP _let_12 _let_15 (hAPP _let_9 (fun _let_12 _let_15) (combb _let_8 _let_7 _let_2) _let_10) (hAPP _let_8 _let_12 (hAPP _let_17 _let_18 (combc _let_2 _let_8 _let_8) (hAPP _let_19 _let_17 (hAPP (fun _let_1 _let_16) (fun _let_19 _let_17) (combb _let_1 _let_16 _let_2) (combb int int _let_2)) _let_20)) _let_11)))) (hAPP _let_8 _let_12 (hAPP _let_21 _let_18 (combb int _let_8 _let_2) (hAPP _let_19 _let_21 (combc _let_2 int int) _let_20)) _let_11))))))))))))))))))))))))) ) 16.18/16.29 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_1 _let_3))) (let ((_let_5 (fun _let_3 _let_3))) (let ((_let_6 (fun _let_1 _let_2))) (let ((_let_7 (fun _let_1 _let_0))) (let ((_let_8 (fun _let_1 int))) (hAPP _let_5 (fun _let_4 _let_4) (combb _let_3 _let_3 _let_1) (hAPP _let_6 _let_5 (combs _let_1 bool bool) (hAPP _let_3 _let_6 (hAPP (fun bool _let_2) (fun _let_3 _let_6) (combb bool _let_2 _let_1) fconj) (hAPP _let_3 _let_3 (hAPP _let_2 _let_5 (combb bool bool _let_1) fNot) (hAPP int _let_3 (hAPP _let_7 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_8 _let_7 (hAPP (fun int _let_0) (fun _let_8 _let_7) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))))))))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun _let_2 (fun _let_2 bool)))) (let ((_let_4 (fun _let_2 _let_0))) (let ((_let_5 (fun _let_2 int))) (let ((_let_6 (fun _let_5 _let_4))) (let ((_let_7 (product_snd int int))) (let ((_let_8 (fun _let_2 _let_5))) (let ((_let_9 (fun _let_5 (fun _let_2 bool)))) (let ((_let_10 (fun _let_2 _let_9))) (let ((_let_11 (fun _let_2 _let_4))) (let ((_let_12 (fun _let_5 _let_5))) (let ((_let_13 (fun _let_2 _let_12))) (let ((_let_14 (fun _let_5 _let_8))) (let ((_let_15 (fun _let_2 _let_1))) (let ((_let_16 (hAPP _let_5 _let_15 (hAPP (fun int _let_1) (fun _let_5 _let_15) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (let ((_let_17 (fun int _let_5))) (hAPP _let_8 _let_3 (hAPP _let_10 (fun _let_8 _let_3) (combs _let_2 _let_5 (fun _let_2 bool)) (hAPP _let_11 _let_10 (hAPP (fun _let_4 _let_9) (fun _let_11 _let_10) (combb _let_4 _let_9 _let_2) (combs _let_2 int bool)) (hAPP _let_8 _let_11 (hAPP _let_6 (fun _let_8 _let_11) (combb _let_5 _let_4 _let_2) (hAPP (fun int _let_0) _let_6 (combb int _let_0 _let_2) (fequal int))) (hAPP _let_5 _let_8 (hAPP _let_13 _let_14 (combc _let_2 _let_5 _let_5) (hAPP _let_15 _let_13 (hAPP (fun _let_1 _let_12) (fun _let_15 _let_13) (combb _let_1 _let_12 _let_2) (combb int int _let_2)) _let_16)) _let_7)))) (hAPP _let_5 _let_8 (hAPP _let_17 _let_14 (combb int _let_5 _let_2) (hAPP _let_15 _let_17 (combc _let_2 int int) _let_16)) _let_7)))))))))))))))))))) ) 16.18/16.29 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun _let_2 _let_0))) (let ((_let_4 (fun _let_2 int))) (let ((_let_5 (fun _let_4 _let_3))) (let ((_let_6 (fun _let_2 _let_4))) (let ((_let_7 (fun _let_4 (fun _let_2 bool)))) (let ((_let_8 (fun _let_2 _let_7))) (let ((_let_9 (fun _let_2 _let_3))) (let ((_let_10 (fun _let_4 _let_4))) (let ((_let_11 (fun _let_2 _let_10))) (let ((_let_12 (fun _let_2 _let_1))) (hAPP _let_8 (fun _let_6 (fun _let_2 (fun _let_2 bool))) (combs _let_2 _let_4 (fun _let_2 bool)) (hAPP _let_9 _let_8 (hAPP (fun _let_3 _let_7) (fun _let_9 _let_8) (combb _let_3 _let_7 _let_2) (combs _let_2 int bool)) (hAPP _let_6 _let_9 (hAPP _let_5 (fun _let_6 _let_9) (combb _let_4 _let_3 _let_2) (hAPP (fun int _let_0) _let_5 (combb int _let_0 _let_2) (fequal int))) (hAPP _let_4 _let_6 (hAPP _let_11 (fun _let_4 _let_6) (combc _let_2 _let_4 _let_4) (hAPP _let_12 _let_11 (hAPP (fun _let_1 _let_10) (fun _let_12 _let_11) (combb _let_1 _let_10 _let_2) (combb int int _let_2)) (hAPP _let_4 _let_12 (hAPP (fun int _let_1) (fun _let_4 _let_12) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (product_snd int int)))))))))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_2))) (let ((_let_4 (fun _let_1 _let_0))) (let ((_let_5 (fun int _let_2))) (hAPP _let_2 _let_3 (hAPP _let_5 (fun _let_2 _let_3) (combb int _let_2 _let_1) (hAPP _let_4 _let_5 (combc _let_1 int int) (hAPP _let_2 _let_4 (hAPP (fun int _let_0) (fun _let_2 _let_4) (combb int _let_0 _let_1) (times_times int)) (product_fst int int)))) (product_snd int int)))))))) ) 16.18/16.29 ( (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)), (fun bool bool), (combb bool bool (product_prod int int)), fNot ) 16.18/16.29 ( (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)), (fun (product_prod int int) (fun bool bool)), (combs (product_prod int int) bool bool), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_1 _let_2))) (let ((_let_5 (fun _let_1 _let_0))) (let ((_let_6 (fun _let_1 int))) (hAPP _let_3 _let_4 (hAPP (fun bool _let_2) (fun _let_3 _let_4) (combb bool _let_2 _let_1) fconj) (hAPP _let_3 _let_3 (hAPP _let_2 (fun _let_3 _let_3) (combb bool bool _let_1) fNot) (hAPP int _let_3 (hAPP _let_5 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_6 _let_5 (hAPP (fun int _let_0) (fun _let_6 _let_5) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))))))) ) 16.18/16.29 ( (let ((_let_0 (fun (product_prod int int) bool))) (fun (product_prod int int) (fun _let_0 _let_0))), (fun (product_prod int int) (fun bool bool)), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun (fun _let_0 bool) (fun _let_0 bool)))) (hAPP (fun _let_1 _let_2) (fun (fun _let_0 _let_1) (fun _let_0 _let_2)) (combb _let_1 _let_2 _let_0) (combb bool bool _let_0))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_1 _let_2))) (let ((_let_5 (fun _let_1 _let_0))) (let ((_let_6 (fun _let_1 int))) (hAPP _let_3 _let_4 (hAPP (fun bool _let_2) (fun _let_3 _let_4) (combb bool _let_2 _let_1) fconj) (hAPP _let_3 _let_3 (hAPP _let_2 (fun _let_3 _let_3) (combb bool bool _let_1) fNot) (hAPP int _let_3 (hAPP _let_5 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_6 _let_5 (hAPP (fun int _let_0) (fun _let_6 _let_5) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))))))) ) 16.18/16.29 ( (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (fun _let_1 _let_1))), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 bool))) (combb _let_1 _let_1 _let_0))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_3 _let_3))) (let ((_let_5 (fun _let_1 _let_2))) (let ((_let_6 (fun _let_1 _let_0))) (let ((_let_7 (fun _let_1 int))) (hAPP _let_5 _let_4 (combs _let_1 bool bool) (hAPP _let_3 _let_5 (hAPP (fun bool _let_2) (fun _let_3 _let_5) (combb bool _let_2 _let_1) fconj) (hAPP _let_3 _let_3 (hAPP _let_2 _let_4 (combb bool bool _let_1) fNot) (hAPP int _let_3 (hAPP _let_6 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_7 _let_6 (hAPP (fun int _let_0) (fun _let_7 _let_6) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))))))))) ) 16.18/16.29 ( (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (fun _let_1 _let_1))), (let ((_let_0 (fun (product_prod int int) bool))) (fun (product_prod int int) (fun _let_0 _let_0))), (let ((_let_0 (fun (product_prod int int) bool))) (combs (product_prod int int) _let_0 _let_0)), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_3 _let_3))) (let ((_let_5 (fun _let_1 _let_4))) (let ((_let_6 (fun _let_1 _let_2))) (let ((_let_7 (combb bool bool _let_1))) (let ((_let_8 (fun _let_1 _let_0))) (let ((_let_9 (fun _let_1 int))) (hAPP _let_6 _let_5 (hAPP (fun _let_2 _let_4) (fun _let_6 _let_5) (combb _let_2 _let_4 _let_1) _let_7) (hAPP _let_3 _let_6 (hAPP (fun bool _let_2) (fun _let_3 _let_6) (combb bool _let_2 _let_1) fconj) (hAPP _let_3 _let_3 (hAPP _let_2 _let_4 _let_7 fNot) (hAPP int _let_3 (hAPP _let_8 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_9 _let_8 (hAPP (fun int _let_0) (fun _let_9 _let_8) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))))))))))) ) 16.18/16.29 ( (fun (product_prod int int) (fun bool bool)), (fun (product_prod int int) bool), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun bool bool))) (hAPP (fun bool _let_1) (fun (fun _let_0 bool) (fun _let_0 _let_1)) (combb bool _let_1 _let_0) fconj))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun _let_1 _let_0))) (let ((_let_4 (fun _let_1 int))) (hAPP _let_2 _let_2 (hAPP (fun bool bool) (fun _let_2 _let_2) (combb bool bool _let_1) fNot) (hAPP int _let_2 (hAPP _let_3 (fun int _let_2) (combc _let_1 int bool) (hAPP _let_4 _let_3 (hAPP (fun int _let_0) (fun _let_4 _let_3) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int)))))))) ) 16.18/16.29 ( (let ((_let_0 (fun (product_prod int int) bool))) (fun (fun (product_prod int int) (fun bool bool)) (fun (product_prod int int) (fun _let_0 _let_0)))), (let ((_let_0 (fun (product_prod int int) bool))) (fun (fun bool bool) (fun _let_0 _let_0))), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 bool))) (combb (fun bool bool) (fun _let_1 _let_1) _let_0))), (combb bool bool (product_prod int int)) ) 16.18/16.29 ( (let ((_let_0 (product_prod int int))) (fun (fun _let_0 bool) (fun _let_0 (fun bool bool)))), (fun bool (fun bool bool)), (combb bool (fun bool bool) (product_prod int int)), fconj ) 16.18/16.29 ( (fun (product_prod int int) (fun int bool)), (fun (product_prod int int) int), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (hAPP (fun int _let_0) (fun (fun _let_1 int) (fun _let_1 _let_0)) (combb int _let_0 _let_1) (fequal int)))), (product_snd int int) ) 16.18/16.29 ( (fun (product_prod int int) int), (fun int (fun int int)), (product_prod_case int int int), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun _let_0 _let_1))) (let ((_let_3 (fun _let_0 _let_0))) (let ((_let_4 (fun int _let_3))) (let ((_let_5 (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP _let_0 _let_1 (hAPP _let_4 _let_2 (combc int _let_0 _let_0) (hAPP _let_1 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_1 _let_4) (combb _let_0 _let_3 int) (combb int int int)) (hAPP _let_0 _let_1 (hAPP _let_1 _let_2 (combb int _let_0 int) (plus_plus int)) _let_5))) _let_5))))))) ) 16.18/16.29 ( (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 (fun int bool)))), (fun int (fun int bool)), (combb int (fun int bool) (product_prod int int)), (fequal int) ) 16.18/16.29 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (fun (product_prod int int) int), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_2 _let_2))) (let ((_let_4 (fun _let_1 _let_3))) (let ((_let_5 (fun _let_1 _let_0))) (hAPP _let_4 (fun _let_2 (fun _let_1 _let_2)) (combc _let_1 _let_2 _let_2) (hAPP _let_5 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_5 _let_4) (combb _let_0 _let_3 _let_1) (combb int int _let_1)) (hAPP _let_2 _let_5 (hAPP (fun int _let_0) (fun _let_2 _let_5) (combb int _let_0 _let_1) (times_times int)) (product_fst int int)))))))))), (product_snd int int) ) 16.18/16.29 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (fun (product_prod int int) int), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_0))) (let ((_let_4 (fun int _let_2))) (hAPP _let_4 (fun _let_2 (fun _let_1 _let_2)) (combb int _let_2 _let_1) (hAPP _let_3 _let_4 (combc _let_1 int int) (hAPP _let_2 _let_3 (hAPP (fun int _let_0) (fun _let_2 _let_3) (combb int _let_0 _let_1) (times_times int)) (product_fst int int))))))))), (product_snd int int) ) 16.18/16.29 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun (fun _let_0 int) (fun _let_0 bool)))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 (fun int bool)))), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 (fun int bool)))) (let ((_let_2 (fun (fun _let_0 int) (fun _let_0 bool)))) (hAPP (fun _let_1 _let_2) (fun (fun _let_0 _let_1) (fun _let_0 _let_2)) (combb _let_1 _let_2 _let_0) (combs _let_0 int bool))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun _let_2 _let_0))) (let ((_let_4 (fun _let_2 int))) (let ((_let_5 (fun _let_4 _let_3))) (let ((_let_6 (fun _let_2 _let_4))) (let ((_let_7 (fun _let_2 _let_3))) (let ((_let_8 (fun _let_4 _let_4))) (let ((_let_9 (fun _let_2 _let_8))) (let ((_let_10 (fun _let_2 _let_1))) (hAPP _let_6 _let_7 (hAPP _let_5 (fun _let_6 _let_7) (combb _let_4 _let_3 _let_2) (hAPP (fun int _let_0) _let_5 (combb int _let_0 _let_2) (fequal int))) (hAPP _let_4 _let_6 (hAPP _let_9 (fun _let_4 _let_6) (combc _let_2 _let_4 _let_4) (hAPP _let_10 _let_9 (hAPP (fun _let_1 _let_8) (fun _let_10 _let_9) (combb _let_1 _let_8 _let_2) (combb int int _let_2)) (hAPP _let_4 _let_10 (hAPP (fun int _let_1) (fun _let_4 _let_10) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (product_snd int int)))))))))))))) ) 16.18/16.29 ( (let ((_let_0 (product_prod int int))) (fun (fun _let_0 (fun _let_0 int)) (fun _let_0 (fun _let_0 bool)))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun (fun _let_0 int) (fun _let_0 bool)))), (let ((_let_0 (product_prod int int))) (combs _let_0 (fun _let_0 int) (fun _let_0 bool))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun _let_2 _let_0))) (let ((_let_4 (fun _let_2 int))) (let ((_let_5 (fun _let_4 _let_3))) (let ((_let_6 (fun _let_2 _let_4))) (let ((_let_7 (fun _let_4 (fun _let_2 bool)))) (let ((_let_8 (fun _let_2 _let_7))) (let ((_let_9 (fun _let_2 _let_3))) (let ((_let_10 (fun _let_4 _let_4))) (let ((_let_11 (fun _let_2 _let_10))) (let ((_let_12 (fun _let_2 _let_1))) (hAPP _let_9 _let_8 (hAPP (fun _let_3 _let_7) (fun _let_9 _let_8) (combb _let_3 _let_7 _let_2) (combs _let_2 int bool)) (hAPP _let_6 _let_9 (hAPP _let_5 (fun _let_6 _let_9) (combb _let_4 _let_3 _let_2) (hAPP (fun int _let_0) _let_5 (combb int _let_0 _let_2) (fequal int))) (hAPP _let_4 _let_6 (hAPP _let_11 (fun _let_4 _let_6) (combc _let_2 _let_4 _let_4) (hAPP _let_12 _let_11 (hAPP (fun _let_1 _let_10) (fun _let_12 _let_11) (combb _let_1 _let_10 _let_2) (combb int int _let_2)) (hAPP _let_4 _let_12 (hAPP (fun int _let_1) (fun _let_4 _let_12) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (product_snd int int))))))))))))))))) ) 16.18/16.29 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 (fun int bool)))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 _let_0))) (let ((_let_3 (fun _let_1 int))) (let ((_let_4 (fun _let_3 _let_2))) (hAPP _let_4 (fun (fun _let_1 _let_3) (fun _let_1 _let_2)) (combb _let_3 _let_2 _let_1) (hAPP (fun int _let_0) _let_4 (combb int _let_0 _let_1) (fequal int)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_2))) (let ((_let_4 (fun _let_2 _let_2))) (let ((_let_5 (fun _let_1 _let_4))) (let ((_let_6 (fun _let_1 _let_0))) (hAPP _let_2 _let_3 (hAPP _let_5 (fun _let_2 _let_3) (combc _let_1 _let_2 _let_2) (hAPP _let_6 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_6 _let_5) (combb _let_0 _let_4 _let_1) (combb int int _let_1)) (hAPP _let_2 _let_6 (hAPP (fun int _let_0) (fun _let_2 _let_6) (combb int _let_0 _let_1) (times_times int)) (product_fst int int)))) (product_snd int int))))))))) ) 16.18/16.29 ( (let ((_let_0 (product_prod int int))) (fun (fun _let_0 (fun _let_0 (fun int bool))) (fun _let_0 (fun (fun _let_0 int) (fun _let_0 bool))))), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 (fun int bool)) (fun (fun _let_0 int) (fun _let_0 bool)))), (let ((_let_0 (product_prod int int))) (combb (fun _let_0 (fun int bool)) (fun (fun _let_0 int) (fun _let_0 bool)) _let_0)), (combs (product_prod int int) int bool) ) 16.18/16.29 ( (let ((_let_0 (product_prod int int))) (fun (fun _let_0 (fun _let_0 int)) (fun _let_0 (fun _let_0 (fun int bool))))), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 (fun int bool)))), (let ((_let_0 (product_prod int int))) (combb (fun _let_0 int) (fun _let_0 (fun int bool)) _let_0)), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (hAPP (fun int _let_0) (fun (fun _let_1 int) (fun _let_1 _let_0)) (combb int _let_0 _let_1) (fequal int)))) ) 16.18/16.29 ( (let ((_let_0 (fun (product_prod int int) int))) (fun (product_prod int int) (fun _let_0 _let_0))), (fun (product_prod int int) (fun int int)), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun (fun _let_1 int) (fun _let_1 int)))) (hAPP (fun _let_0 _let_2) (fun (fun _let_1 _let_0) (fun _let_1 _let_2)) (combb _let_0 _let_2 _let_1) (combb int int _let_1))))), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_0))) (hAPP _let_2 _let_3 (hAPP (fun int _let_0) (fun _let_2 _let_3) (combb int _let_0 _let_1) (times_times int)) (product_fst int int)))))) ) 16.18/16.29 ( (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 int))) (fun _let_1 (fun _let_0 _let_1)))), (let ((_let_0 (fun (product_prod int int) int))) (fun (product_prod int int) (fun _let_0 _let_0))), (let ((_let_0 (fun (product_prod int int) int))) (combc (product_prod int int) _let_0 _let_0)), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_2 _let_2))) (let ((_let_4 (fun _let_1 _let_3))) (let ((_let_5 (fun _let_1 _let_0))) (hAPP _let_5 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_5 _let_4) (combb _let_0 _let_3 _let_1) (combb int int _let_1)) (hAPP _let_2 _let_5 (hAPP (fun int _let_0) (fun _let_2 _let_5) (combb int _let_0 _let_1) (times_times int)) (product_fst int int))))))))) ) 16.18/16.29 ( (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 int))) (fun _let_1 (fun _let_0 _let_1)))), (fun int (fun (product_prod int int) int)), (let ((_let_0 (product_prod int int))) (combb int (fun _let_0 int) _let_0)), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_0))) (hAPP _let_3 (fun int _let_2) (combc _let_1 int int) (hAPP _let_2 _let_3 (hAPP (fun int _let_0) (fun _let_2 _let_3) (combb int _let_0 _let_1) (times_times int)) (product_fst int int))))))) ) 16.18/16.29 ( (fun (product_prod int int) (fun int int)), (fun (product_prod int int) int), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (hAPP (fun int _let_0) (fun (fun _let_1 int) (fun _let_1 _let_0)) (combb int _let_0 _let_1) (times_times int)))), (product_fst int int) ) 16.18/16.29 ( (let ((_let_0 (fun (product_prod int int) int))) (fun (fun (product_prod int int) (fun int int)) (fun (product_prod int int) (fun _let_0 _let_0)))), (let ((_let_0 (fun (product_prod int int) int))) (fun (fun int int) (fun _let_0 _let_0))), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 int))) (combb (fun int int) (fun _let_1 _let_1) _let_0))), (combb int int (product_prod int int)) ) 16.18/16.29 ( (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 (fun int int)))), (fun int (fun int int)), (combb int (fun int int) (product_prod int int)), (times_times int) ) 16.18/16.29 ( (fun int (fun (product_prod int int) int)), (fun (product_prod int int) (fun int int)), (combc (product_prod int int) int int), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_0))) (hAPP _let_2 _let_3 (hAPP (fun int _let_0) (fun _let_2 _let_3) (combb int _let_0 _let_1) (times_times int)) (product_fst int int)))))) ) 16.18/16.29 ( (fun (fun nat nat) (fun nat (fun nat bool))), (fun nat (fun nat bool)), (combb nat (fun nat bool) nat), (let ((_let_0 (fun nat (fun nat bool)))) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat))) ) 16.18/16.29 ( (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)), (fun bool bool), (combb bool bool nat), fNot ) 16.18/16.29 ( (let ((_let_0 (fun nat nat))) (fun _let_0 (fun nat _let_0))), (fun nat (fun nat nat)), (combb nat (fun nat nat) nat), (plus_plus nat) ) 16.18/16.29 ( (fun real (fun bool bool)), (fun real bool), (let ((_let_0 (fun bool bool))) (hAPP (fun bool _let_0) (fun (fun real bool) (fun real _let_0)) (combb bool _let_0 real) fconj)), (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) ) 16.18/16.29 ( (fun real (fun bool bool)), (fun real bool), (let ((_let_0 (fun bool bool))) (hAPP (fun bool _let_0) (fun (fun real bool) (fun real _let_0)) (combb bool _let_0 real) fconj)), (let ((_let_0 (fun real (fun real bool)))) (hAPP real (fun real bool) (hAPP _let_0 _let_0 (combc real real bool) (ord_less_eq real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.18/16.29 ( (let ((_let_0 (fun real bool))) (fun _let_0 _let_0)), (fun real (fun bool bool)), (combs real bool bool), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun real _let_1))) (hAPP _let_0 _let_2 (hAPP (fun bool _let_1) (fun _let_0 _let_2) (combb bool _let_1 real) fconj) (hAPP real _let_0 (ord_less_eq real) (zero_zero real)))))) ) 16.18/16.29 ( (let ((_let_0 (fun real bool))) (fun _let_0 _let_0)), (fun real (fun bool bool)), (combs real bool bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun real (fun real bool)))) (let ((_let_2 (fun real _let_0))) (hAPP (fun real bool) _let_2 (hAPP (fun bool _let_0) (fun (fun real bool) _let_2) (combb bool _let_0 real) fconj) (hAPP real (fun real bool) (hAPP _let_1 _let_1 (combc real real bool) (ord_less_eq real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 16.18/16.29 ( (fun (fun real bool) (fun real (fun bool bool))), (fun bool (fun bool bool)), (combb bool (fun bool bool) real), fconj ) 16.18/16.29 ( (fun (fun real real) (fun real (fun real bool))), (fun real (fun real bool)), (combb real (fun real bool) real), (fequal real) ) 16.18/16.29 ( (fun (fun nat bool) (fun nat (fun bool bool))), (fun bool (fun bool bool)), (combb bool (fun bool bool) nat), fconj ) 16.18/16.29 ( (let ((_let_0 (fun int bool))) (fun (fun int (fun int (fun bool bool))) (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun int bool))) (fun (fun int (fun bool bool)) (fun _let_0 _let_0))), (let ((_let_0 (fun int bool))) (combb (fun int (fun bool bool)) (fun _let_0 _let_0) int)), (combs int bool bool) ) 16.18/16.29 ( (fun (fun int (fun int bool)) (fun int (fun int (fun bool bool)))), (fun (fun int bool) (fun int (fun bool bool))), (combb (fun int bool) (fun int (fun bool bool)) int), (let ((_let_0 (fun bool bool))) (hAPP (fun bool _let_0) (fun (fun int bool) (fun int _let_0)) (combb bool _let_0 int) fconj)) ) 16.18/16.29 ( (fun nat (fun int int)), (fun int (fun nat int)), (combc int nat int), (power_power int) ) 16.18/16.29 ( (fun real (fun int bool)), (fun real (fun int (fun int bool))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun _let_1 _let_0))) (hAPP _let_2 (fun (fun real _let_1) (fun real _let_0)) (combb _let_1 _let_0 real) (hAPP (fun _let_0 bool) _let_2 (combb _let_0 bool int) (fEx int)))))), (let ((_let_0 (fun int (fun int bool)))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real real))) (let ((_let_3 (real_1 int))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun int _let_4))) (let ((_let_7 (fun (fun int bool) (fun int bool)))) (let ((_let_8 (fun (fun int bool) _let_6))) (let ((_let_9 (fun int real))) (let ((_let_10 (fun int _let_7))) (let ((_let_11 (fun (fun int bool) _let_0))) (let ((_let_12 (fun int _let_6))) (let ((_let_13 (fun _let_12 _let_10))) (let ((_let_14 (fun _let_0 _let_12))) (let ((_let_15 (fun real _let_0))) (let ((_let_16 (fun real _let_11))) (let ((_let_17 (fun real _let_10))) (let ((_let_18 (fun real _let_12))) (let ((_let_19 (fun int _let_9))) (let ((_let_20 (fun _let_19 _let_0))) (let ((_let_21 (fun real _let_20))) (let ((_let_22 (fun _let_9 (fun int bool)))) (let ((_let_23 (fun real _let_22))) (let ((_let_24 (fun _let_9 _let_9))) (let ((_let_25 (fun int _let_24))) (let ((_let_26 (fun int _let_2))) (hAPP (fun int bool) _let_15 (hAPP _let_16 (fun (fun int bool) _let_15) (combc real (fun int bool) _let_0) (hAPP _let_17 _let_16 (hAPP (fun _let_10 _let_11) (fun _let_17 _let_16) (combb _let_10 _let_11 real) (combc int (fun int bool) (fun int bool))) (hAPP _let_18 _let_17 (hAPP _let_13 (fun _let_18 _let_17) (combb _let_12 _let_10 real) (hAPP (fun _let_6 _let_7) _let_13 (combb _let_6 _let_7 int) (combs int bool bool))) (hAPP _let_15 _let_18 (hAPP _let_14 (fun _let_15 _let_18) (combb _let_0 _let_12 real) (hAPP _let_8 _let_14 (combb (fun int bool) _let_6 int) (hAPP (fun bool _let_4) _let_8 (combb bool _let_4 int) fconj))) (hAPP _let_19 _let_15 (hAPP _let_21 (fun _let_19 _let_15) (combc real _let_19 _let_0) (hAPP _let_23 _let_21 (hAPP (fun _let_22 _let_20) (fun _let_23 _let_21) (combb _let_22 _let_20 real) (combb _let_9 (fun int bool) int)) (hAPP _let_5 _let_23 (hAPP (fun _let_1 _let_22) (fun _let_5 _let_23) (combb _let_1 _let_22 real) (combb real bool int)) (fequal real)))) (hAPP _let_9 _let_19 (hAPP _let_25 (fun _let_9 _let_19) (combc int _let_9 _let_9) (hAPP _let_26 _let_25 (hAPP (fun _let_2 _let_24) (fun _let_26 _let_25) (combb _let_2 _let_24 int) (combb real real int)) (hAPP _let_9 _let_26 (hAPP (fun real _let_2) (fun _let_9 _let_26) (combb real _let_2 int) (inverse_divide real)) _let_3))) _let_3)))))) (hAPP (fun int bool) (fun int bool) (hAPP _let_4 _let_7 (combb bool bool int) fNot) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (fequal int)) (zero_zero int))))))))))))))))))))))))))))))) ) 16.18/16.29 ( (fun real (fun int bool)), (fun real (fun int (fun nat bool))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun nat bool))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (fun _let_2 _let_0))) (hAPP _let_3 (fun (fun real _let_2) (fun real _let_0)) (combb _let_2 _let_0 real) (hAPP (fun _let_1 bool) _let_3 (combb _let_1 bool int) (fEx nat))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat (fun nat bool)))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun (fun nat real) (fun nat real)))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun (fun nat bool) (fun nat bool)))) (let ((_let_7 (fun int real))) (let ((_let_8 (fun nat _let_3))) (let ((_let_9 (fun (fun nat bool) _let_8))) (let ((_let_10 (fun int _let_1))) (let ((_let_11 (fun real (fun int (fun nat bool))))) (let ((_let_12 (fun (fun nat bool) (fun int (fun nat bool))))) (let ((_let_13 (fun real _let_12))) (let ((_let_14 (fun int _let_6))) (let ((_let_15 (fun real _let_14))) (let ((_let_16 (fun int _let_8))) (let ((_let_17 (fun real _let_16))) (let ((_let_18 (fun _let_16 _let_14))) (let ((_let_19 (fun (fun int (fun nat bool)) _let_16))) (let ((_let_20 (fun int (fun nat real)))) (let ((_let_21 (fun _let_20 (fun int (fun nat bool))))) (let ((_let_22 (fun real _let_21))) (let ((_let_23 (fun (fun nat real) (fun nat bool)))) (let ((_let_24 (fun real _let_23))) (let ((_let_25 (fun int _let_4))) (hAPP (fun nat bool) _let_11 (hAPP _let_13 (fun (fun nat bool) _let_11) (combc real (fun nat bool) (fun int (fun nat bool))) (hAPP _let_15 _let_13 (hAPP (fun _let_14 _let_12) (fun _let_15 _let_13) (combb _let_14 _let_12 real) (combc int (fun nat bool) (fun nat bool))) (hAPP _let_17 _let_15 (hAPP _let_18 (fun _let_17 _let_15) (combb _let_16 _let_14 real) (hAPP (fun _let_8 _let_6) _let_18 (combb _let_8 _let_6 int) (combs nat bool bool))) (hAPP _let_11 _let_17 (hAPP _let_19 (fun _let_11 _let_17) (combb (fun int (fun nat bool)) _let_16 real) (hAPP _let_9 _let_19 (combb (fun nat bool) _let_8 int) (hAPP (fun bool _let_3) _let_9 (combb bool _let_3 nat) fconj))) (hAPP _let_20 _let_11 (hAPP _let_22 (fun _let_20 _let_11) (combc real _let_20 (fun int (fun nat bool))) (hAPP _let_24 _let_22 (hAPP (fun _let_23 _let_21) (fun _let_24 _let_22) (combb _let_23 _let_21 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_5 _let_24 (hAPP (fun _let_0 _let_23) (fun _let_5 _let_24) (combb _let_0 _let_23 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_20 (hAPP _let_25 (fun (fun nat real) _let_20) (combc int (fun nat real) (fun nat real)) (hAPP _let_10 _let_25 (hAPP (fun _let_1 _let_4) (fun _let_10 _let_25) (combb _let_1 _let_4 int) (combb real real nat)) (hAPP _let_7 _let_10 (hAPP (fun real _let_1) (fun _let_7 _let_10) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat))))))) (hAPP (fun nat bool) (fun nat bool) (hAPP _let_3 _let_6 (combb bool bool nat) fNot) (hAPP nat (fun nat bool) (hAPP _let_2 _let_2 (combc nat nat bool) (fequal nat)) (zero_zero nat)))))))))))))))))))))))))))))) ) 16.18/16.29 ( (fun (fun real (fun int bool)) (fun real bool)), (fun (fun int bool) bool), (combb (fun int bool) bool real), (fEx int) ) 16.18/16.29 ( (fun real (fun int (fun int bool))), (fun int bool), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun int _let_3))) (let ((_let_6 (fun (fun int bool) (fun int bool)))) (let ((_let_7 (fun (fun int bool) _let_5))) (let ((_let_8 (fun int real))) (let ((_let_9 (fun int _let_6))) (let ((_let_10 (fun (fun int bool) (fun int (fun int bool))))) (let ((_let_11 (fun int _let_5))) (let ((_let_12 (fun _let_11 _let_9))) (let ((_let_13 (fun (fun int (fun int bool)) _let_11))) (let ((_let_14 (fun real (fun int (fun int bool))))) (let ((_let_15 (fun real _let_10))) (let ((_let_16 (fun real _let_9))) (let ((_let_17 (fun real _let_11))) (let ((_let_18 (fun int _let_8))) (let ((_let_19 (fun _let_18 (fun int (fun int bool))))) (let ((_let_20 (fun real _let_19))) (let ((_let_21 (fun _let_8 (fun int bool)))) (let ((_let_22 (fun real _let_21))) (let ((_let_23 (fun _let_8 _let_8))) (let ((_let_24 (fun int _let_23))) (let ((_let_25 (fun int _let_1))) (hAPP _let_15 (fun (fun int bool) _let_14) (combc real (fun int bool) (fun int (fun int bool))) (hAPP _let_16 _let_15 (hAPP (fun _let_9 _let_10) (fun _let_16 _let_15) (combb _let_9 _let_10 real) (combc int (fun int bool) (fun int bool))) (hAPP _let_17 _let_16 (hAPP _let_12 (fun _let_17 _let_16) (combb _let_11 _let_9 real) (hAPP (fun _let_5 _let_6) _let_12 (combb _let_5 _let_6 int) (combs int bool bool))) (hAPP _let_14 _let_17 (hAPP _let_13 (fun _let_14 _let_17) (combb (fun int (fun int bool)) _let_11 real) (hAPP _let_7 _let_13 (combb (fun int bool) _let_5 int) (hAPP (fun bool _let_3) _let_7 (combb bool _let_3 int) fconj))) (hAPP _let_18 _let_14 (hAPP _let_20 (fun _let_18 _let_14) (combc real _let_18 (fun int (fun int bool))) (hAPP _let_22 _let_20 (hAPP (fun _let_21 _let_19) (fun _let_22 _let_20) (combb _let_21 _let_19 real) (combb _let_8 (fun int bool) int)) (hAPP _let_4 _let_22 (hAPP (fun _let_0 _let_21) (fun _let_4 _let_22) (combb _let_0 _let_21 real) (combb real bool int)) (fequal real)))) (hAPP _let_8 _let_18 (hAPP _let_24 (fun _let_8 _let_18) (combc int _let_8 _let_8) (hAPP _let_25 _let_24 (hAPP (fun _let_1 _let_23) (fun _let_25 _let_24) (combb _let_1 _let_23 int) (combb real real int)) (hAPP _let_8 _let_25 (hAPP (fun real _let_1) (fun _let_8 _let_25) (combb real _let_1 int) (inverse_divide real)) _let_2))) _let_2)))))))))))))))))))))))))))))))), (let ((_let_0 (fun int (fun int bool)))) (hAPP (fun int bool) (fun int bool) (hAPP (fun bool bool) (fun (fun int bool) (fun int bool)) (combb bool bool int) fNot) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (fequal int)) (zero_zero int)))) ) 16.18/16.29 ( (fun real (fun int (fun int bool))), (fun int (fun int real)), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun int (fun int real)) (fun int (fun int bool))))) (let ((_let_3 (fun real _let_2))) (let ((_let_4 (fun (fun int real) (fun int bool)))) (let ((_let_5 (fun real _let_4))) (hAPP _let_3 (fun (fun int (fun int real)) (fun real (fun int (fun int bool)))) (combc real (fun int (fun int real)) (fun int (fun int bool))) (hAPP _let_5 _let_3 (hAPP (fun _let_4 _let_2) (fun _let_5 _let_3) (combb _let_4 _let_2 real) (combb (fun int real) (fun int bool) int)) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_1 _let_5) (combb _let_0 _let_4 real) (combb real bool int)) (fequal real)))))))))), (let ((_let_0 (fun real real))) (let ((_let_1 (real_1 int))) (let ((_let_2 (fun int real))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun _let_2 _let_2))) (let ((_let_5 (fun int _let_4))) (let ((_let_6 (fun int _let_0))) (hAPP _let_2 _let_3 (hAPP _let_5 (fun _let_2 _let_3) (combc int _let_2 _let_2) (hAPP _let_6 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_6 _let_5) (combb _let_0 _let_4 int) (combb real real int)) (hAPP _let_2 _let_6 (hAPP (fun real _let_0) (fun _let_2 _let_6) (combb real _let_0 int) (inverse_divide real)) _let_1))) _let_1)))))))) ) 16.18/16.29 ( (let ((_let_0 (fun int bool))) (fun (fun real (fun int _let_0)) (fun real _let_0))), (let ((_let_0 (fun int bool))) (fun (fun int _let_0) _let_0)), (let ((_let_0 (fun int bool))) (combb (fun int _let_0) _let_0 real)), (let ((_let_0 (fun int bool))) (hAPP (fun _let_0 bool) (fun (fun int _let_0) _let_0) (combb _let_0 bool int) (fEx int))) ) 16.18/16.30 ( (let ((_let_0 (fun int bool))) (fun real (fun _let_0 (fun int _let_0)))), (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int (fun _let_0 _let_0)))) (let ((_let_2 (fun _let_0 (fun int _let_0)))) (hAPP (fun _let_1 _let_2) (fun (fun real _let_1) (fun real _let_2)) (combb _let_1 _let_2 real) (combc int _let_0 _let_0))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun int _let_3))) (let ((_let_6 (fun (fun int bool) (fun int bool)))) (let ((_let_7 (fun (fun int bool) _let_5))) (let ((_let_8 (fun int real))) (let ((_let_9 (fun int _let_6))) (let ((_let_10 (fun int _let_5))) (let ((_let_11 (fun _let_10 _let_9))) (let ((_let_12 (fun (fun int (fun int bool)) _let_10))) (let ((_let_13 (fun real (fun int (fun int bool))))) (let ((_let_14 (fun real _let_9))) (let ((_let_15 (fun real _let_10))) (let ((_let_16 (fun int _let_8))) (let ((_let_17 (fun _let_16 (fun int (fun int bool))))) (let ((_let_18 (fun real _let_17))) (let ((_let_19 (fun _let_8 (fun int bool)))) (let ((_let_20 (fun real _let_19))) (let ((_let_21 (fun _let_8 _let_8))) (let ((_let_22 (fun int _let_21))) (let ((_let_23 (fun int _let_1))) (hAPP _let_15 _let_14 (hAPP _let_11 (fun _let_15 _let_14) (combb _let_10 _let_9 real) (hAPP (fun _let_5 _let_6) _let_11 (combb _let_5 _let_6 int) (combs int bool bool))) (hAPP _let_13 _let_15 (hAPP _let_12 (fun _let_13 _let_15) (combb (fun int (fun int bool)) _let_10 real) (hAPP _let_7 _let_12 (combb (fun int bool) _let_5 int) (hAPP (fun bool _let_3) _let_7 (combb bool _let_3 int) fconj))) (hAPP _let_16 _let_13 (hAPP _let_18 (fun _let_16 _let_13) (combc real _let_16 (fun int (fun int bool))) (hAPP _let_20 _let_18 (hAPP (fun _let_19 _let_17) (fun _let_20 _let_18) (combb _let_19 _let_17 real) (combb _let_8 (fun int bool) int)) (hAPP _let_4 _let_20 (hAPP (fun _let_0 _let_19) (fun _let_4 _let_20) (combb _let_0 _let_19 real) (combb real bool int)) (fequal real)))) (hAPP _let_8 _let_16 (hAPP _let_22 (fun _let_8 _let_16) (combc int _let_8 _let_8) (hAPP _let_23 _let_22 (hAPP (fun _let_1 _let_21) (fun _let_23 _let_22) (combb _let_1 _let_21 int) (combb real real int)) (hAPP _let_8 _let_23 (hAPP (fun real _let_1) (fun _let_8 _let_23) (combb real _let_1 int) (inverse_divide real)) _let_2))) _let_2)))))))))))))))))))))))))))) ) 16.18/16.30 ( (let ((_let_0 (fun int bool))) (fun _let_0 (fun real (fun int _let_0)))), (let ((_let_0 (fun int bool))) (fun real (fun _let_0 (fun int _let_0)))), (let ((_let_0 (fun int bool))) (combc real _let_0 (fun int _let_0))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun int _let_3))) (let ((_let_6 (fun (fun int bool) (fun int bool)))) (let ((_let_7 (fun (fun int bool) _let_5))) (let ((_let_8 (fun int real))) (let ((_let_9 (fun int _let_6))) (let ((_let_10 (fun (fun int bool) (fun int (fun int bool))))) (let ((_let_11 (fun int _let_5))) (let ((_let_12 (fun _let_11 _let_9))) (let ((_let_13 (fun (fun int (fun int bool)) _let_11))) (let ((_let_14 (fun real (fun int (fun int bool))))) (let ((_let_15 (fun real _let_10))) (let ((_let_16 (fun real _let_9))) (let ((_let_17 (fun real _let_11))) (let ((_let_18 (fun int _let_8))) (let ((_let_19 (fun _let_18 (fun int (fun int bool))))) (let ((_let_20 (fun real _let_19))) (let ((_let_21 (fun _let_8 (fun int bool)))) (let ((_let_22 (fun real _let_21))) (let ((_let_23 (fun _let_8 _let_8))) (let ((_let_24 (fun int _let_23))) (let ((_let_25 (fun int _let_1))) (hAPP _let_16 _let_15 (hAPP (fun _let_9 _let_10) (fun _let_16 _let_15) (combb _let_9 _let_10 real) (combc int (fun int bool) (fun int bool))) (hAPP _let_17 _let_16 (hAPP _let_12 (fun _let_17 _let_16) (combb _let_11 _let_9 real) (hAPP (fun _let_5 _let_6) _let_12 (combb _let_5 _let_6 int) (combs int bool bool))) (hAPP _let_14 _let_17 (hAPP _let_13 (fun _let_14 _let_17) (combb (fun int (fun int bool)) _let_11 real) (hAPP _let_7 _let_13 (combb (fun int bool) _let_5 int) (hAPP (fun bool _let_3) _let_7 (combb bool _let_3 int) fconj))) (hAPP _let_18 _let_14 (hAPP _let_20 (fun _let_18 _let_14) (combc real _let_18 (fun int (fun int bool))) (hAPP _let_22 _let_20 (hAPP (fun _let_21 _let_19) (fun _let_22 _let_20) (combb _let_21 _let_19 real) (combb _let_8 (fun int bool) int)) (hAPP _let_4 _let_22 (hAPP (fun _let_0 _let_21) (fun _let_4 _let_22) (combb _let_0 _let_21 real) (combb real bool int)) (fequal real)))) (hAPP _let_8 _let_18 (hAPP _let_24 (fun _let_8 _let_18) (combc int _let_8 _let_8) (hAPP _let_25 _let_24 (hAPP (fun _let_1 _let_23) (fun _let_25 _let_24) (combb _let_1 _let_23 int) (combb real real int)) (hAPP _let_8 _let_25 (hAPP (fun real _let_1) (fun _let_8 _let_25) (combb real _let_1 int) (inverse_divide real)) _let_2))) _let_2))))))))))))))))))))))))))))))) ) 16.18/16.30 ( (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))), (fun real (fun int (fun int (fun bool bool)))), (let ((_let_0 (fun int (fun bool bool)))) (let ((_let_1 (fun (fun int bool) (fun int bool)))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (fun int _let_0))) (let ((_let_4 (fun _let_3 _let_2))) (hAPP _let_4 (fun (fun real _let_3) (fun real _let_2)) (combb _let_3 _let_2 real) (hAPP (fun _let_0 _let_1) _let_4 (combb _let_0 _let_1 int) (combs int bool bool)))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun int _let_3))) (let ((_let_6 (fun (fun int bool) _let_5))) (let ((_let_7 (fun int real))) (let ((_let_8 (fun int _let_5))) (let ((_let_9 (fun (fun int (fun int bool)) _let_8))) (let ((_let_10 (fun real (fun int (fun int bool))))) (let ((_let_11 (fun real _let_8))) (let ((_let_12 (fun int _let_7))) (let ((_let_13 (fun _let_12 (fun int (fun int bool))))) (let ((_let_14 (fun real _let_13))) (let ((_let_15 (fun _let_7 (fun int bool)))) (let ((_let_16 (fun real _let_15))) (let ((_let_17 (fun _let_7 _let_7))) (let ((_let_18 (fun int _let_17))) (let ((_let_19 (fun int _let_1))) (hAPP _let_10 _let_11 (hAPP _let_9 (fun _let_10 _let_11) (combb (fun int (fun int bool)) _let_8 real) (hAPP _let_6 _let_9 (combb (fun int bool) _let_5 int) (hAPP (fun bool _let_3) _let_6 (combb bool _let_3 int) fconj))) (hAPP _let_12 _let_10 (hAPP _let_14 (fun _let_12 _let_10) (combc real _let_12 (fun int (fun int bool))) (hAPP _let_16 _let_14 (hAPP (fun _let_15 _let_13) (fun _let_16 _let_14) (combb _let_15 _let_13 real) (combb _let_7 (fun int bool) int)) (hAPP _let_4 _let_16 (hAPP (fun _let_0 _let_15) (fun _let_4 _let_16) (combb _let_0 _let_15 real) (combb real bool int)) (fequal real)))) (hAPP _let_7 _let_12 (hAPP _let_18 (fun _let_7 _let_12) (combc int _let_7 _let_7) (hAPP _let_19 _let_18 (hAPP (fun _let_1 _let_17) (fun _let_19 _let_18) (combb _let_1 _let_17 int) (combb real real int)) (hAPP _let_7 _let_19 (hAPP (fun real _let_1) (fun _let_7 _let_19) (combb real _let_1 int) (inverse_divide real)) _let_2))) _let_2))))))))))))))))))))))) ) 16.18/16.30 ( (let ((_let_0 (fun int bool))) (fun (fun real (fun int (fun _let_0 _let_0))) (fun real (fun _let_0 (fun int _let_0))))), (let ((_let_0 (fun int bool))) (fun (fun int (fun _let_0 _let_0)) (fun _let_0 (fun int _let_0)))), (let ((_let_0 (fun int bool))) (combb (fun int (fun _let_0 _let_0)) (fun _let_0 (fun int _let_0)) real)), (let ((_let_0 (fun int bool))) (combc int _let_0 _let_0)) ) 16.18/16.30 ( (fun real (fun int (fun int (fun bool bool)))), (fun real (fun int (fun int bool))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun _let_0 _let_3))) (let ((_let_5 (fun int _let_3))) (let ((_let_6 (fun _let_1 _let_5))) (hAPP _let_6 (fun (fun real _let_1) (fun real _let_5)) (combb _let_1 _let_5 real) (hAPP _let_4 _let_6 (combb _let_0 _let_3 int) (hAPP (fun bool _let_2) _let_4 (combb bool _let_2 int) fconj)))))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun real _let_0))) (let ((_let_4 (fun int real))) (let ((_let_5 (fun real (fun int (fun int bool))))) (let ((_let_6 (fun int _let_4))) (let ((_let_7 (fun _let_6 (fun int (fun int bool))))) (let ((_let_8 (fun real _let_7))) (let ((_let_9 (fun _let_4 (fun int bool)))) (let ((_let_10 (fun real _let_9))) (let ((_let_11 (fun _let_4 _let_4))) (let ((_let_12 (fun int _let_11))) (let ((_let_13 (fun int _let_1))) (hAPP _let_6 _let_5 (hAPP _let_8 (fun _let_6 _let_5) (combc real _let_6 (fun int (fun int bool))) (hAPP _let_10 _let_8 (hAPP (fun _let_9 _let_7) (fun _let_10 _let_8) (combb _let_9 _let_7 real) (combb _let_4 (fun int bool) int)) (hAPP _let_3 _let_10 (hAPP (fun _let_0 _let_9) (fun _let_3 _let_10) (combb _let_0 _let_9 real) (combb real bool int)) (fequal real)))) (hAPP _let_4 _let_6 (hAPP _let_12 (fun _let_4 _let_6) (combc int _let_4 _let_4) (hAPP _let_13 _let_12 (hAPP (fun _let_1 _let_11) (fun _let_13 _let_12) (combb _let_1 _let_11 int) (combb real real int)) (hAPP _let_4 _let_13 (hAPP (fun real _let_1) (fun _let_4 _let_13) (combb real _let_1 int) (inverse_divide real)) _let_2))) _let_2)))))))))))))))) ) 16.18/16.30 ( (let ((_let_0 (fun int bool))) (fun (fun real (fun int (fun int (fun bool bool)))) (fun real (fun int (fun _let_0 _let_0))))), (let ((_let_0 (fun int bool))) (fun (fun int (fun int (fun bool bool))) (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun int bool))) (combb (fun int (fun int (fun bool bool))) (fun int (fun _let_0 _let_0)) real)), (let ((_let_0 (fun int (fun bool bool)))) (let ((_let_1 (fun (fun int bool) (fun int bool)))) (hAPP (fun _let_0 _let_1) (fun (fun int _let_0) (fun int _let_1)) (combb _let_0 _let_1 int) (combs int bool bool)))) ) 16.18/16.30 ( (fun (fun real (fun int (fun int bool))) (fun real (fun int (fun int (fun bool bool))))), (fun (fun int (fun int bool)) (fun int (fun int (fun bool bool)))), (combb (fun int (fun int bool)) (fun int (fun int (fun bool bool))) real), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (fun _let_0 _let_2))) (hAPP _let_3 (fun (fun int _let_0) (fun int _let_2)) (combb _let_0 _let_2 int) (hAPP (fun bool _let_1) _let_3 (combb bool _let_1 int) fconj)))))) ) 16.26/16.33 ( (fun int (fun int real)), (fun int real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun int real))) (let ((_let_2 (fun _let_1 _let_1))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int _let_0))) (hAPP _let_3 (fun _let_1 (fun int _let_1)) (combc int _let_1 _let_1) (hAPP _let_4 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_4 _let_3) (combb _let_0 _let_2 int) (combb real real int)) (hAPP _let_1 _let_4 (hAPP (fun real _let_0) (fun _let_1 _let_4) (combb real _let_0 int) (inverse_divide real)) (real_1 int))))))))), (real_1 int) ) 16.26/16.33 ( (fun real (fun (fun int (fun int real)) (fun int (fun int bool)))), (fun real (fun (fun int real) (fun int bool))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int real))) (let ((_let_2 (fun (fun int _let_1) (fun int _let_0)))) (let ((_let_3 (fun _let_1 _let_0))) (hAPP (fun _let_3 _let_2) (fun (fun real _let_3) (fun real _let_2)) (combb _let_3 _let_2 real) (combb _let_1 _let_0 int)))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun int real) (fun int bool)))) (let ((_let_3 (fun real _let_2))) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 real) (combb real bool int)) (fequal real)))))) ) 16.26/16.33 ( (fun (fun int (fun int real)) (fun real (fun int (fun int bool)))), (fun real (fun (fun int (fun int real)) (fun int (fun int bool)))), (combc real (fun int (fun int real)) (fun int (fun int bool))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun int (fun int real)) (fun int (fun int bool))))) (let ((_let_3 (fun real _let_2))) (let ((_let_4 (fun (fun int real) (fun int bool)))) (let ((_let_5 (fun real _let_4))) (hAPP _let_5 _let_3 (hAPP (fun _let_4 _let_2) (fun _let_5 _let_3) (combb _let_4 _let_2 real) (combb (fun int real) (fun int bool) int)) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_1 _let_5) (combb _let_0 _let_4 real) (combb real bool int)) (fequal real))))))))) ) 16.26/16.33 ( (fun real (fun (fun int real) (fun int bool))), (fun real (fun real bool)), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun (fun int real) (fun int bool)))) (hAPP (fun _let_0 _let_1) (fun (fun real _let_0) (fun real _let_1)) (combb _let_0 _let_1 real) (combb real bool int)))), (fequal real) ) 16.26/16.33 ( (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int real))) (fun (fun real (fun _let_1 _let_0)) (fun real (fun (fun int _let_1) (fun int _let_0)))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int real))) (fun (fun _let_1 _let_0) (fun (fun int _let_1) (fun int _let_0))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int real))) (combb (fun _let_1 _let_0) (fun (fun int _let_1) (fun int _let_0)) real))), (combb (fun int real) (fun int bool) int) ) 16.26/16.33 ( (fun (fun real (fun real bool)) (fun real (fun (fun int real) (fun int bool)))), (fun (fun real bool) (fun (fun int real) (fun int bool))), (combb (fun real bool) (fun (fun int real) (fun int bool)) real), (combb real bool int) ) 16.26/16.33 ( (let ((_let_0 (fun int real))) (fun int (fun _let_0 _let_0))), (fun int (fun real real)), (let ((_let_0 (fun real real))) (let ((_let_1 (fun (fun int real) (fun int real)))) (hAPP (fun _let_0 _let_1) (fun (fun int _let_0) (fun int _let_1)) (combb _let_0 _let_1 int) (combb real real int)))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun int real))) (let ((_let_2 (fun int _let_0))) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 int) (inverse_divide real)) (real_1 int))))) ) 16.26/16.33 ( (let ((_let_0 (fun int real))) (fun _let_0 (fun int _let_0))), (let ((_let_0 (fun int real))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun int real))) (combc int _let_0 _let_0)), (let ((_let_0 (fun real real))) (let ((_let_1 (fun int real))) (let ((_let_2 (fun _let_1 _let_1))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int _let_0))) (hAPP _let_4 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_4 _let_3) (combb _let_0 _let_2 int) (combb real real int)) (hAPP _let_1 _let_4 (hAPP (fun real _let_0) (fun _let_1 _let_4) (combb real _let_0 int) (inverse_divide real)) (real_1 int)))))))) ) 16.26/16.33 ( (fun int (fun real real)), (fun int real), (let ((_let_0 (fun real real))) (hAPP (fun real _let_0) (fun (fun int real) (fun int _let_0)) (combb real _let_0 int) (inverse_divide real))), (real_1 int) ) 16.26/16.33 ( (let ((_let_0 (fun int real))) (fun (fun int (fun real real)) (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun int real))) (fun (fun real real) (fun _let_0 _let_0))), (let ((_let_0 (fun int real))) (combb (fun real real) (fun _let_0 _let_0) int)), (combb real real int) ) 16.26/16.33 ( (fun (fun int real) (fun int (fun real real))), (fun real (fun real real)), (combb real (fun real real) int), (inverse_divide real) ) 16.26/16.33 ( (let ((_let_0 (fun int (fun int bool)))) (fun _let_0 _let_0)), (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), (let ((_let_0 (fun int bool))) (combb _let_0 _let_0 int)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun int _let_1))) (hAPP _let_2 (fun _let_0 _let_0) (combs int bool bool) (hAPP _let_0 _let_2 (hAPP (fun bool _let_1) (fun _let_0 _let_2) (combb bool _let_1 int) fconj) (hAPP int _let_0 (ord_less int) (zero_zero int))))))) ) 16.26/16.33 ( (fun real (fun int (fun nat bool))), (fun nat bool), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun (fun nat real) (fun nat real)))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun (fun nat bool) (fun nat bool)))) (let ((_let_6 (fun int real))) (let ((_let_7 (fun nat _let_2))) (let ((_let_8 (fun (fun nat bool) _let_7))) (let ((_let_9 (fun int _let_1))) (let ((_let_10 (fun real (fun int (fun nat bool))))) (let ((_let_11 (fun (fun nat bool) (fun int (fun nat bool))))) (let ((_let_12 (fun real _let_11))) (let ((_let_13 (fun int _let_5))) (let ((_let_14 (fun real _let_13))) (let ((_let_15 (fun int _let_7))) (let ((_let_16 (fun real _let_15))) (let ((_let_17 (fun _let_15 _let_13))) (let ((_let_18 (fun (fun int (fun nat bool)) _let_15))) (let ((_let_19 (fun int (fun nat real)))) (let ((_let_20 (fun _let_19 (fun int (fun nat bool))))) (let ((_let_21 (fun real _let_20))) (let ((_let_22 (fun (fun nat real) (fun nat bool)))) (let ((_let_23 (fun real _let_22))) (let ((_let_24 (fun int _let_3))) (hAPP _let_12 (fun (fun nat bool) _let_10) (combc real (fun nat bool) (fun int (fun nat bool))) (hAPP _let_14 _let_12 (hAPP (fun _let_13 _let_11) (fun _let_14 _let_12) (combb _let_13 _let_11 real) (combc int (fun nat bool) (fun nat bool))) (hAPP _let_16 _let_14 (hAPP _let_17 (fun _let_16 _let_14) (combb _let_15 _let_13 real) (hAPP (fun _let_7 _let_5) _let_17 (combb _let_7 _let_5 int) (combs nat bool bool))) (hAPP _let_10 _let_16 (hAPP _let_18 (fun _let_10 _let_16) (combb (fun int (fun nat bool)) _let_15 real) (hAPP _let_8 _let_18 (combb (fun nat bool) _let_7 int) (hAPP (fun bool _let_2) _let_8 (combb bool _let_2 nat) fconj))) (hAPP _let_19 _let_10 (hAPP _let_21 (fun _let_19 _let_10) (combc real _let_19 (fun int (fun nat bool))) (hAPP _let_23 _let_21 (hAPP (fun _let_22 _let_20) (fun _let_23 _let_21) (combb _let_22 _let_20 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_4 _let_23 (hAPP (fun _let_0 _let_22) (fun _let_4 _let_23) (combb _let_0 _let_22 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_19 (hAPP _let_24 (fun (fun nat real) _let_19) (combc int (fun nat real) (fun nat real)) (hAPP _let_9 _let_24 (hAPP (fun _let_1 _let_3) (fun _let_9 _let_24) (combb _let_1 _let_3 int) (combb real real nat)) (hAPP _let_6 _let_9 (hAPP (fun real _let_1) (fun _let_6 _let_9) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat)))))))))))))))))))))))))))))))), (let ((_let_0 (fun nat (fun nat bool)))) (hAPP (fun nat bool) (fun nat bool) (hAPP (fun bool bool) (fun (fun nat bool) (fun nat bool)) (combb bool bool nat) fNot) (hAPP nat (fun nat bool) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat)) (zero_zero nat)))) ) 16.26/16.33 ( (fun real (fun int (fun nat bool))), (fun int (fun nat real)), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun int (fun nat real)) (fun int (fun nat bool))))) (let ((_let_3 (fun real _let_2))) (let ((_let_4 (fun (fun nat real) (fun nat bool)))) (let ((_let_5 (fun real _let_4))) (hAPP _let_3 (fun (fun int (fun nat real)) (fun real (fun int (fun nat bool)))) (combc real (fun int (fun nat real)) (fun int (fun nat bool))) (hAPP _let_5 _let_3 (hAPP (fun _let_4 _let_2) (fun _let_5 _let_3) (combb _let_4 _let_2 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_1 _let_5) (combb _let_0 _let_4 real) (combb real bool nat)) (fequal real)))))))))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun (fun nat real) (fun nat real)))) (let ((_let_2 (fun int real))) (let ((_let_3 (fun int _let_0))) (let ((_let_4 (fun int (fun nat real)))) (let ((_let_5 (fun int _let_1))) (hAPP (fun nat real) _let_4 (hAPP _let_5 (fun (fun nat real) _let_4) (combc int (fun nat real) (fun nat real)) (hAPP _let_3 _let_5 (hAPP (fun _let_0 _let_1) (fun _let_3 _let_5) (combb _let_0 _let_1 int) (combb real real nat)) (hAPP _let_2 _let_3 (hAPP (fun real _let_0) (fun _let_2 _let_3) (combb real _let_0 int) (inverse_divide real)) (real_1 int)))) (real_1 nat)))))))) ) 16.26/16.33 ( (fun (fun int (fun nat bool)) (fun int bool)), (fun (fun nat bool) bool), (combb (fun nat bool) bool int), (fEx nat) ) 16.26/16.33 ( (fun (fun real (fun int (fun nat bool))) (fun real (fun int bool))), (fun (fun int (fun nat bool)) (fun int bool)), (combb (fun int (fun nat bool)) (fun int bool) real), (let ((_let_0 (fun nat bool))) (hAPP (fun _let_0 bool) (fun (fun int _let_0) (fun int bool)) (combb _let_0 bool int) (fEx nat))) ) 16.26/16.33 ( (let ((_let_0 (fun nat bool))) (fun real (fun _let_0 (fun int _let_0)))), (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun _let_0 (fun int _let_0)))) (let ((_let_2 (fun int (fun _let_0 _let_0)))) (hAPP (fun _let_2 _let_1) (fun (fun real _let_2) (fun real _let_1)) (combb _let_2 _let_1 real) (combc int _let_0 _let_0))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun (fun nat real) (fun nat real)))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun (fun nat bool) (fun nat bool)))) (let ((_let_6 (fun int real))) (let ((_let_7 (fun nat _let_2))) (let ((_let_8 (fun (fun nat bool) _let_7))) (let ((_let_9 (fun int _let_1))) (let ((_let_10 (fun real (fun int (fun nat bool))))) (let ((_let_11 (fun int _let_5))) (let ((_let_12 (fun real _let_11))) (let ((_let_13 (fun int _let_7))) (let ((_let_14 (fun real _let_13))) (let ((_let_15 (fun _let_13 _let_11))) (let ((_let_16 (fun (fun int (fun nat bool)) _let_13))) (let ((_let_17 (fun int (fun nat real)))) (let ((_let_18 (fun _let_17 (fun int (fun nat bool))))) (let ((_let_19 (fun real _let_18))) (let ((_let_20 (fun (fun nat real) (fun nat bool)))) (let ((_let_21 (fun real _let_20))) (let ((_let_22 (fun int _let_3))) (hAPP _let_14 _let_12 (hAPP _let_15 (fun _let_14 _let_12) (combb _let_13 _let_11 real) (hAPP (fun _let_7 _let_5) _let_15 (combb _let_7 _let_5 int) (combs nat bool bool))) (hAPP _let_10 _let_14 (hAPP _let_16 (fun _let_10 _let_14) (combb (fun int (fun nat bool)) _let_13 real) (hAPP _let_8 _let_16 (combb (fun nat bool) _let_7 int) (hAPP (fun bool _let_2) _let_8 (combb bool _let_2 nat) fconj))) (hAPP _let_17 _let_10 (hAPP _let_19 (fun _let_17 _let_10) (combc real _let_17 (fun int (fun nat bool))) (hAPP _let_21 _let_19 (hAPP (fun _let_20 _let_18) (fun _let_21 _let_19) (combb _let_20 _let_18 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_4 _let_21 (hAPP (fun _let_0 _let_20) (fun _let_4 _let_21) (combb _let_0 _let_20 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_17 (hAPP _let_22 (fun (fun nat real) _let_17) (combc int (fun nat real) (fun nat real)) (hAPP _let_9 _let_22 (hAPP (fun _let_1 _let_3) (fun _let_9 _let_22) (combb _let_1 _let_3 int) (combb real real nat)) (hAPP _let_6 _let_9 (hAPP (fun real _let_1) (fun _let_6 _let_9) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat)))))))))))))))))))))))))))) ) 16.26/16.33 ( (let ((_let_0 (fun nat bool))) (fun _let_0 (fun real (fun int _let_0)))), (let ((_let_0 (fun nat bool))) (fun real (fun _let_0 (fun int _let_0)))), (let ((_let_0 (fun nat bool))) (combc real _let_0 (fun int _let_0))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun (fun nat real) (fun nat real)))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun (fun nat bool) (fun nat bool)))) (let ((_let_6 (fun int real))) (let ((_let_7 (fun nat _let_2))) (let ((_let_8 (fun (fun nat bool) _let_7))) (let ((_let_9 (fun int _let_1))) (let ((_let_10 (fun real (fun int (fun nat bool))))) (let ((_let_11 (fun (fun nat bool) (fun int (fun nat bool))))) (let ((_let_12 (fun real _let_11))) (let ((_let_13 (fun int _let_5))) (let ((_let_14 (fun real _let_13))) (let ((_let_15 (fun int _let_7))) (let ((_let_16 (fun real _let_15))) (let ((_let_17 (fun _let_15 _let_13))) (let ((_let_18 (fun (fun int (fun nat bool)) _let_15))) (let ((_let_19 (fun int (fun nat real)))) (let ((_let_20 (fun _let_19 (fun int (fun nat bool))))) (let ((_let_21 (fun real _let_20))) (let ((_let_22 (fun (fun nat real) (fun nat bool)))) (let ((_let_23 (fun real _let_22))) (let ((_let_24 (fun int _let_3))) (hAPP _let_14 _let_12 (hAPP (fun _let_13 _let_11) (fun _let_14 _let_12) (combb _let_13 _let_11 real) (combc int (fun nat bool) (fun nat bool))) (hAPP _let_16 _let_14 (hAPP _let_17 (fun _let_16 _let_14) (combb _let_15 _let_13 real) (hAPP (fun _let_7 _let_5) _let_17 (combb _let_7 _let_5 int) (combs nat bool bool))) (hAPP _let_10 _let_16 (hAPP _let_18 (fun _let_10 _let_16) (combb (fun int (fun nat bool)) _let_15 real) (hAPP _let_8 _let_18 (combb (fun nat bool) _let_7 int) (hAPP (fun bool _let_2) _let_8 (combb bool _let_2 nat) fconj))) (hAPP _let_19 _let_10 (hAPP _let_21 (fun _let_19 _let_10) (combc real _let_19 (fun int (fun nat bool))) (hAPP _let_23 _let_21 (hAPP (fun _let_22 _let_20) (fun _let_23 _let_21) (combb _let_22 _let_20 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_4 _let_23 (hAPP (fun _let_0 _let_22) (fun _let_4 _let_23) (combb _let_0 _let_22 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_19 (hAPP _let_24 (fun (fun nat real) _let_19) (combc int (fun nat real) (fun nat real)) (hAPP _let_9 _let_24 (hAPP (fun _let_1 _let_3) (fun _let_9 _let_24) (combb _let_1 _let_3 int) (combb real real nat)) (hAPP _let_6 _let_9 (hAPP (fun real _let_1) (fun _let_6 _let_9) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat))))))))))))))))))))))))))))))) ) 16.26/16.33 ( (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))), (fun real (fun int (fun nat (fun bool bool)))), (let ((_let_0 (fun (fun nat bool) (fun nat bool)))) (let ((_let_1 (fun nat (fun bool bool)))) (let ((_let_2 (fun int _let_0))) (let ((_let_3 (fun int _let_1))) (let ((_let_4 (fun _let_3 _let_2))) (hAPP _let_4 (fun (fun real _let_3) (fun real _let_2)) (combb _let_3 _let_2 real) (hAPP (fun _let_1 _let_0) _let_4 (combb _let_1 _let_0 int) (combs nat bool bool)))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun (fun nat real) (fun nat real)))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun int real))) (let ((_let_6 (fun nat _let_2))) (let ((_let_7 (fun (fun nat bool) _let_6))) (let ((_let_8 (fun int _let_1))) (let ((_let_9 (fun real (fun int (fun nat bool))))) (let ((_let_10 (fun int _let_6))) (let ((_let_11 (fun real _let_10))) (let ((_let_12 (fun (fun int (fun nat bool)) _let_10))) (let ((_let_13 (fun int (fun nat real)))) (let ((_let_14 (fun _let_13 (fun int (fun nat bool))))) (let ((_let_15 (fun real _let_14))) (let ((_let_16 (fun (fun nat real) (fun nat bool)))) (let ((_let_17 (fun real _let_16))) (let ((_let_18 (fun int _let_3))) (hAPP _let_9 _let_11 (hAPP _let_12 (fun _let_9 _let_11) (combb (fun int (fun nat bool)) _let_10 real) (hAPP _let_7 _let_12 (combb (fun nat bool) _let_6 int) (hAPP (fun bool _let_2) _let_7 (combb bool _let_2 nat) fconj))) (hAPP _let_13 _let_9 (hAPP _let_15 (fun _let_13 _let_9) (combc real _let_13 (fun int (fun nat bool))) (hAPP _let_17 _let_15 (hAPP (fun _let_16 _let_14) (fun _let_17 _let_15) (combb _let_16 _let_14 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_4 _let_17 (hAPP (fun _let_0 _let_16) (fun _let_4 _let_17) (combb _let_0 _let_16 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_13 (hAPP _let_18 (fun (fun nat real) _let_13) (combc int (fun nat real) (fun nat real)) (hAPP _let_8 _let_18 (hAPP (fun _let_1 _let_3) (fun _let_8 _let_18) (combb _let_1 _let_3 int) (combb real real nat)) (hAPP _let_5 _let_8 (hAPP (fun real _let_1) (fun _let_5 _let_8) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat))))))))))))))))))))))) ) 16.26/16.33 ( (let ((_let_0 (fun nat bool))) (fun (fun real (fun int (fun _let_0 _let_0))) (fun real (fun _let_0 (fun int _let_0))))), (let ((_let_0 (fun nat bool))) (fun (fun int (fun _let_0 _let_0)) (fun _let_0 (fun int _let_0)))), (let ((_let_0 (fun nat bool))) (combb (fun int (fun _let_0 _let_0)) (fun _let_0 (fun int _let_0)) real)), (let ((_let_0 (fun nat bool))) (combc int _let_0 _let_0)) ) 16.26/16.33 ( (fun real (fun int (fun nat (fun bool bool)))), (fun real (fun int (fun nat bool))), (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun nat _let_1))) (let ((_let_3 (fun _let_0 _let_2))) (let ((_let_4 (fun int _let_0))) (let ((_let_5 (fun int _let_2))) (let ((_let_6 (fun _let_4 _let_5))) (hAPP _let_6 (fun (fun real _let_4) (fun real _let_5)) (combb _let_4 _let_5 real) (hAPP _let_3 _let_6 (combb _let_0 _let_2 int) (hAPP (fun bool _let_1) _let_3 (combb bool _let_1 nat) fconj)))))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun (fun nat real) (fun nat real)))) (let ((_let_3 (fun real _let_0))) (let ((_let_4 (fun int real))) (let ((_let_5 (fun int _let_1))) (let ((_let_6 (fun real (fun int (fun nat bool))))) (let ((_let_7 (fun int (fun nat real)))) (let ((_let_8 (fun _let_7 (fun int (fun nat bool))))) (let ((_let_9 (fun real _let_8))) (let ((_let_10 (fun (fun nat real) (fun nat bool)))) (let ((_let_11 (fun real _let_10))) (let ((_let_12 (fun int _let_2))) (hAPP _let_7 _let_6 (hAPP _let_9 (fun _let_7 _let_6) (combc real _let_7 (fun int (fun nat bool))) (hAPP _let_11 _let_9 (hAPP (fun _let_10 _let_8) (fun _let_11 _let_9) (combb _let_10 _let_8 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_3 _let_11 (hAPP (fun _let_0 _let_10) (fun _let_3 _let_11) (combb _let_0 _let_10 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_7 (hAPP _let_12 (fun (fun nat real) _let_7) (combc int (fun nat real) (fun nat real)) (hAPP _let_5 _let_12 (hAPP (fun _let_1 _let_2) (fun _let_5 _let_12) (combb _let_1 _let_2 int) (combb real real nat)) (hAPP _let_4 _let_5 (hAPP (fun real _let_1) (fun _let_4 _let_5) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat)))))))))))))))) ) 16.26/16.33 ( (let ((_let_0 (fun nat bool))) (fun (fun int (fun nat (fun bool bool))) (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun nat bool))) (fun (fun nat (fun bool bool)) (fun _let_0 _let_0))), (let ((_let_0 (fun nat bool))) (combb (fun nat (fun bool bool)) (fun _let_0 _let_0) int)), (combs nat bool bool) ) 16.26/16.33 ( (let ((_let_0 (fun nat bool))) (fun (fun real (fun int (fun nat (fun bool bool)))) (fun real (fun int (fun _let_0 _let_0))))), (let ((_let_0 (fun nat bool))) (fun (fun int (fun nat (fun bool bool))) (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun nat bool))) (combb (fun int (fun nat (fun bool bool))) (fun int (fun _let_0 _let_0)) real)), (let ((_let_0 (fun (fun nat bool) (fun nat bool)))) (let ((_let_1 (fun nat (fun bool bool)))) (hAPP (fun _let_1 _let_0) (fun (fun int _let_1) (fun int _let_0)) (combb _let_1 _let_0 int) (combs nat bool bool)))) ) 16.26/16.33 ( (fun (fun int (fun nat bool)) (fun int (fun nat (fun bool bool)))), (fun (fun nat bool) (fun nat (fun bool bool))), (combb (fun nat bool) (fun nat (fun bool bool)) int), (let ((_let_0 (fun bool bool))) (hAPP (fun bool _let_0) (fun (fun nat bool) (fun nat _let_0)) (combb bool _let_0 nat) fconj)) ) 16.26/16.33 ( (fun (fun real (fun int (fun nat bool))) (fun real (fun int (fun nat (fun bool bool))))), (fun (fun int (fun nat bool)) (fun int (fun nat (fun bool bool)))), (combb (fun int (fun nat bool)) (fun int (fun nat (fun bool bool))) real), (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun nat _let_1))) (let ((_let_3 (fun _let_0 _let_2))) (hAPP _let_3 (fun (fun int _let_0) (fun int _let_2)) (combb _let_0 _let_2 int) (hAPP (fun bool _let_1) _let_3 (combb bool _let_1 nat) fconj)))))) ) 16.26/16.33 ( (fun int (fun nat real)), (fun nat real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun (fun nat real) (fun nat real)))) (let ((_let_2 (fun int real))) (let ((_let_3 (fun int _let_0))) (let ((_let_4 (fun int _let_1))) (hAPP _let_4 (fun (fun nat real) (fun int (fun nat real))) (combc int (fun nat real) (fun nat real)) (hAPP _let_3 _let_4 (hAPP (fun _let_0 _let_1) (fun _let_3 _let_4) (combb _let_0 _let_1 int) (combb real real nat)) (hAPP _let_2 _let_3 (hAPP (fun real _let_0) (fun _let_2 _let_3) (combb real _let_0 int) (inverse_divide real)) (real_1 int))))))))), (real_1 nat) ) 16.26/16.33 ( (fun real (fun (fun int (fun nat real)) (fun int (fun nat bool)))), (fun real (fun (fun nat real) (fun nat bool))), (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun (fun int _let_1) (fun int _let_0)))) (let ((_let_3 (fun _let_1 _let_0))) (hAPP (fun _let_3 _let_2) (fun (fun real _let_3) (fun real _let_2)) (combb _let_3 _let_2 real) (combb _let_1 _let_0 int)))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun nat real) (fun nat bool)))) (let ((_let_3 (fun real _let_2))) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 real) (combb real bool nat)) (fequal real)))))) ) 16.26/16.33 ( (fun (fun int (fun nat real)) (fun real (fun int (fun nat bool)))), (fun real (fun (fun int (fun nat real)) (fun int (fun nat bool)))), (combc real (fun int (fun nat real)) (fun int (fun nat bool))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun int (fun nat real)) (fun int (fun nat bool))))) (let ((_let_3 (fun real _let_2))) (let ((_let_4 (fun (fun nat real) (fun nat bool)))) (let ((_let_5 (fun real _let_4))) (hAPP _let_5 _let_3 (hAPP (fun _let_4 _let_2) (fun _let_5 _let_3) (combb _let_4 _let_2 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_1 _let_5) (combb _let_0 _let_4 real) (combb real bool nat)) (fequal real))))))))) ) 16.26/16.33 ( (fun real (fun (fun nat real) (fun nat bool))), (fun real (fun real bool)), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun (fun nat real) (fun nat bool)))) (hAPP (fun _let_0 _let_1) (fun (fun real _let_0) (fun real _let_1)) (combb _let_0 _let_1 real) (combb real bool nat)))), (fequal real) ) 16.26/16.33 ( (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat real))) (fun (fun real (fun _let_1 _let_0)) (fun real (fun (fun int _let_1) (fun int _let_0)))))), (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat real))) (fun (fun _let_1 _let_0) (fun (fun int _let_1) (fun int _let_0))))), (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat real))) (combb (fun _let_1 _let_0) (fun (fun int _let_1) (fun int _let_0)) real))), (combb (fun nat real) (fun nat bool) int) ) 16.26/16.33 ( (fun (fun real (fun real bool)) (fun real (fun (fun nat real) (fun nat bool)))), (fun (fun real bool) (fun (fun nat real) (fun nat bool))), (combb (fun real bool) (fun (fun nat real) (fun nat bool)) real), (combb real bool nat) ) 16.26/16.33 ( (let ((_let_0 (fun nat real))) (fun int (fun _let_0 _let_0))), (fun int (fun real real)), (let ((_let_0 (fun real real))) (let ((_let_1 (fun (fun nat real) (fun nat real)))) (hAPP (fun _let_0 _let_1) (fun (fun int _let_0) (fun int _let_1)) (combb _let_0 _let_1 int) (combb real real nat)))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun int real))) (let ((_let_2 (fun int _let_0))) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 int) (inverse_divide real)) (real_1 int))))) ) 16.26/16.33 ( (let ((_let_0 (fun nat real))) (fun _let_0 (fun int _let_0))), (let ((_let_0 (fun nat real))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun nat real))) (combc int _let_0 _let_0)), (let ((_let_0 (fun real real))) (let ((_let_1 (fun (fun nat real) (fun nat real)))) (let ((_let_2 (fun int real))) (let ((_let_3 (fun int _let_0))) (let ((_let_4 (fun int _let_1))) (hAPP _let_3 _let_4 (hAPP (fun _let_0 _let_1) (fun _let_3 _let_4) (combb _let_0 _let_1 int) (combb real real nat)) (hAPP _let_2 _let_3 (hAPP (fun real _let_0) (fun _let_2 _let_3) (combb real _let_0 int) (inverse_divide real)) (real_1 int)))))))) ) 16.26/16.33 ( (let ((_let_0 (fun nat real))) (fun (fun int (fun real real)) (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun nat real))) (fun (fun real real) (fun _let_0 _let_0))), (let ((_let_0 (fun nat real))) (combb (fun real real) (fun _let_0 _let_0) int)), (combb real real nat) ) 16.26/16.33 ( (let ((_let_0 (fun int int))) (fun int (fun _let_0 _let_0))), (fun int (fun int int)), (let ((_let_0 (fun (fun int int) (fun int int)))) (hAPP (fun (fun int int) _let_0) (fun (fun int (fun int int)) (fun int _let_0)) (combb (fun int int) _let_0 int) (combb int int int))), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)) (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 16.26/16.33 ( (let ((_let_0 (fun int int))) (fun (fun int _let_0) (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun int int))) (fun _let_0 (fun _let_0 _let_0))), (let ((_let_0 (fun int int))) (combb _let_0 (fun _let_0 _let_0) int)), (combb int int int) ) 16.26/16.33 ( (let ((_let_0 (fun int (fun int (fun int bool))))) (fun _let_0 _let_0)), (let ((_let_0 (fun int (fun int bool)))) (fun _let_0 _let_0)), (let ((_let_0 (fun int (fun int bool)))) (combb _let_0 _let_0 int)), (combc int int bool) ) 16.26/16.33 ( (fun (fun int (fun int int)) (fun int (fun int (fun int bool)))), (fun (fun int int) (fun int (fun int bool))), (combb (fun int int) (fun int (fun int bool)) int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (hAPP _let_1 (fun (fun int int) _let_1) (combb int _let_0 int) (fequal int)))) ) 16.26/16.33 ) 16.26/16.33 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_146833 $$unsorted)) (let ((_let_0 (one_one X_a))) (let ((_let_1 (ti X_a BOUND_VARIABLE_146833))) (or (not (ring_11004092258visors X_a)) (= (or (= (hAPP X_a X_a (uminus_uminus X_a) _let_0) _let_1) (= _let_0 _let_1)) (= _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_146833) BOUND_VARIABLE_146833)))))) ) 16.26/16.33 ( bool, fFalse ) 16.26/16.33 ( bool, fTrue ) 16.26/16.33 ( int, pls ) 16.26/16.33 ( int, min_1 ) 16.26/16.33 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.33 ( int, s ) 16.26/16.33 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.33 ( int, m ) 16.26/16.33 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.33 ( int, s1 ) 16.26/16.33 ( int, t ) 16.26/16.33 ( (fun int bool), nat_neg ) 16.26/16.33 ( (fun int bool), zprime ) 16.26/16.33 ( (fun int bool), zEven ) 16.26/16.33 ( (fun int bool), zOdd ) 16.26/16.33 ( (fun int bool), (even_odd_even int) ) 16.26/16.33 ( (fun int bool), twoSqu1091635170sum2sq ) 16.26/16.33 ( (fun int bool), nat_is_nat ) 16.26/16.33 ( (fun int (fun int bool)), norRRset ) 16.26/16.33 ( (fun int (fun int bool)), quadRes ) 16.26/16.33 ( (fun int (fun int bool)), sRStar ) 16.26/16.33 ( (fun int (fun int bool)), d22set ) 16.26/16.33 ( (fun int (fun int bool)), sr ) 16.26/16.33 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 16.26/16.33 ( (fun int int), zfact ) 16.26/16.33 ( (fun int int), bit0 ) 16.26/16.33 ( (fun int int), bit1 ) 16.26/16.33 ( (fun int int), (fact_fact int) ) 16.26/16.33 ( (fun int int), pred ) 16.26/16.33 ( (fun int int), succ ) 16.26/16.33 ( (fun nat bool), (even_odd_even nat) ) 16.26/16.33 ( (fun nat bool), prime ) 16.26/16.33 ( (fun nat nat), suc ) 16.26/16.33 ( (fun nat nat), (fact_fact nat) ) 16.26/16.33 ( (fun nat nat), fact ) 16.26/16.33 ( (fun nat nat), nat_size ) 16.26/16.33 ( (fun nat nat), (size_size nat) ) 16.26/16.33 ( (fun (product_prod nat nat) bool), pred_nat ) 16.26/16.33 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 16.26/16.33 ( real, pi ) 16.26/16.33 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.33 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.33 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 16.26/16.33 ( (fun real real), ln ) 16.26/16.33 ( (fun real real), cos ) 16.26/16.33 ( (fun real real), sqrt ) 16.26/16.33 ( (fun real real), sin ) 16.26/16.33 ( (fun real real), arccos ) 16.26/16.33 ( (fun real real), arcsin ) 16.26/16.33 ( (fun real real), tan ) 16.26/16.33 ( (fun real real), arctan ) 16.26/16.33 ( (fun nat (fun nat bool)), coprime ) 16.26/16.33 ( complex, ii ) 16.26/16.33 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.33 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 16.26/16.33 ( (fun nat real), (real_1 nat) ) 16.26/16.33 ( (fun nat real), sin_coeff ) 16.26/16.33 ( (fun nat real), cos_coeff ) 16.26/16.33 ( (filter nat), sequentially ) 16.26/16.33 ( (fun int (fun int int)), (gcd_gcd int) ) 16.26/16.33 ( (fun int (fun int int)), legendre ) 16.26/16.33 ( (fun int (fun int int)), legacy_zgcd ) 16.26/16.33 ( (fun int (fun int int)), standardRes ) 16.26/16.33 ( (fun int (fun int int)), nat_tsub ) 16.26/16.33 ( (fun int (fun int int)), multInv ) 16.26/16.33 ( (fun int (fun int int)), z3mod ) 16.26/16.33 ( (fun int (fun int int)), z3div ) 16.26/16.33 ( (fun int (fun int int)), int_gcd ) 16.26/16.33 ( (fun int (fun int int)), int_lcm ) 16.26/16.33 ( (fun int (fun int int)), inv ) 16.26/16.33 ( (fun complex complex), expi ) 16.26/16.33 ( (fun complex complex), cnj ) 16.26/16.33 ( (fun real complex), cis ) 16.26/16.33 ( (fun int nat), nat_1 ) 16.26/16.33 ( (fun int nat), phi ) 16.26/16.33 ( (fun (fun int bool) bool), nat_nat_set ) 16.26/16.33 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 16.26/16.33 ( (fun nat (fun nat nat)), nat_gcd ) 16.26/16.34 ( (fun nat (fun nat nat)), nat_lcm ) 16.26/16.34 ( (fun (fun int bool) int), (the int) ) 16.26/16.34 ( (fun complex real), re ) 16.26/16.34 ( (fun complex real), im ) 16.26/16.34 ( (fun complex real), arg ) 16.26/16.34 ( (fun bool bool), fNot ) 16.26/16.34 ( (fun nat (fun real real)), root ) 16.26/16.34 ( (fun real (fun real real)), log ) 16.26/16.34 ( (fun real (fun real real)), powr ) 16.26/16.34 ( (fun bool (fun bool bool)), fimplies ) 16.26/16.34 ( (fun bool (fun bool bool)), fconj ) 16.26/16.34 ( (fun bool (fun bool bool)), fdisj ) 16.26/16.34 ( (fun int (fun int (product_prod int int))), negDivAlg ) 16.26/16.34 ( (fun int (fun int (product_prod int int))), posDivAlg ) 16.26/16.34 ( (fun int (fun int (product_prod int int))), divmod_int ) 16.26/16.34 ( (fun int (fun int (product_prod int int))), pdivmod ) 16.26/16.34 ( (fun int (fun int (product_prod int int))), norm_frac ) 16.26/16.34 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 16.26/16.34 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 16.26/16.34 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 16.26/16.34 ( (fun int (fun int (fun int bool))), zcong ) 16.26/16.34 ( (fun int (fun int (fun int bool))), zcongm ) 16.26/16.34 ( (fun int (fun int (fun int bool))), noXRRset ) 16.26/16.34 ( (fun int (fun int (fun int bool))), bnorRset ) 16.26/16.34 ( (fun int (fun int (fun int bool))), wset ) 16.26/16.34 ( (fun (product_prod int int) bool), frac_1 ) 16.26/16.34 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 16.26/16.34 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 16.26/16.34 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 16.26/16.34 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 16.26/16.34 ( (fun (fun nat rat) bool), vanishes ) 16.26/16.34 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 16.26/16.34 ( (fun code_code_numeral nat), code_c271388182l_size ) 16.26/16.34 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 16.26/16.34 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 16.26/16.34 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 16.26/16.34 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 16.26/16.34 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 16.26/16.34 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 16.26/16.34 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 16.26/16.34 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 16.26/16.34 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 16.26/16.34 ( (fun complex nat), complex_size ) 16.26/16.34 ( (fun complex nat), (size_size complex) ) 16.26/16.34 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 16.26/16.34 ( (fun nat (fun nat (product_prod int int))), bezw ) 16.26/16.34 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 16.26/16.34 ( (fun int (fun nat nat)), nat_aux ) 16.26/16.34 ( (fun int (fun (fun int bool) bool)), rsetR ) 16.26/16.34 ( (fun int (fun (fun int bool) bool)), resSet ) 16.26/16.34 ( (fun int (list int)), quickc666637781d_zero ) 16.26/16.34 ( (fun (product_prod int int) rat), frct ) 16.26/16.34 ( (fun int (fun int rat)), fract ) 16.26/16.34 ( (fun real (fun real complex)), complex_1 ) 16.26/16.34 ( (fun real (fun real complex)), rcis ) 16.26/16.34 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 16.26/16.34 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 16.26/16.34 ( (fun int real), (real_1 int) ) 16.26/16.34 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 16.26/16.34 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 16.26/16.34 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 16.26/16.34 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 16.26/16.34 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 16.26/16.34 ( (fun real nat), natfloor ) 16.26/16.34 ( (fun real nat), natceiling ) 16.26/16.34 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 16.26/16.34 ( (fun quickcheck_code_int int), quickcheck_int_of ) 16.26/16.34 ( (fun rat (product_prod int int)), quotient_of ) 16.26/16.34 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 16.26/16.34 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 16.26/16.34 ( (fun rat real), ratreal ) 16.26/16.34 ( (fun code_code_numeral int), code_int_of ) 16.26/16.34 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 16.26/16.34 ( (fun int quickcheck_code_int), quickcheck_of_int ) 16.26/16.34 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 16.26/16.34 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 16.26/16.34 ) 16.26/16.34 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_0 (fun int int))) (or (not (= (ti int C) (hAPP int int (hAPP int _let_0 (minus_minus int) A_1) B))) (= (ti int A_1) (hAPP int int (hAPP int _let_0 (plus_plus int) C) B)))) ) 16.26/16.34 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), s ) 16.26/16.34 ) 16.26/16.34 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_146955 $$unsorted) (BOUND_VARIABLE_146956 $$unsorted) (BOUND_VARIABLE_146966 $$unsorted) (BOUND_VARIABLE_146967 $$unsorted)) (let ((_let_0 (fun X_b X_b))) (let ((_let_1 (ord_min X_b))) (let ((_let_2 (number_number_of X_b))) (let ((_let_3 (fun X_b bool))) (let ((_let_4 (ord_less_eq X_b))) (let ((_let_5 (hAPP int X_b _let_2 BOUND_VARIABLE_146955))) (let ((_let_6 (hAPP int X_b _let_2 BOUND_VARIABLE_146956))) (let ((_let_7 (hAPP int X_b _let_2 BOUND_VARIABLE_146966))) (let ((_let_8 (hAPP int X_b _let_2 BOUND_VARIABLE_146967))) (or (not (number X_b)) (not (ord X_b)) (and (or (hBOOL (hAPP X_b bool (hAPP X_b _let_3 _let_4 _let_5) _let_6)) (= _let_6 (hAPP X_b X_b (hAPP X_b _let_0 _let_1 _let_5) _let_6))) (or (not (hBOOL (hAPP X_b bool (hAPP X_b _let_3 _let_4 _let_7) _let_8))) (= _let_7 (hAPP X_b X_b (hAPP X_b _let_0 _let_1 _let_7) _let_8)))))))))))))) ) 16.26/16.34 ( nat, pls, pls, pls, pls ) 16.26/16.34 ( nat, (hAPP int int bit1 pls), (hAPP int int bit1 pls), (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 16.26/16.34 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.26/16.34 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.26/16.34 ( int, pls, pls, pls, pls ) 16.26/16.34 ( int, (hAPP int int bit1 pls), (hAPP int int bit1 pls), (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 16.26/16.34 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.26/16.34 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.26/16.34 ( int, min_1, min_1, min_1, min_1 ) 16.26/16.34 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.34 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.26/16.34 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.26/16.34 ( real, min_1, min_1, min_1, min_1 ) 16.26/16.34 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.34 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.26/16.34 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.34 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))), (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))), (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))), (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 16.26/16.34 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.26/16.34 ( complex, min_1, min_1, min_1, min_1 ) 16.26/16.34 ( quickcheck_code_int, (one_one int), (one_one int), (one_one int), (one_one int) ) 16.26/16.34 ( quickcheck_code_int, (zero_zero int), (zero_zero int), (zero_zero int), (zero_zero int) ) 16.26/16.34 ( quickcheck_code_int, (hAPP int int bit1 pls), (hAPP int int bit1 pls), (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 16.26/16.34 ( code_code_numeral, pls, pls, pls, pls ) 16.26/16.34 ( code_code_numeral, (hAPP int int bit1 pls), (hAPP int int bit1 pls), (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 16.26/16.34 ) 16.26/16.34 (instantiation (forall ((A_2 $$unsorted) (B_1 $$unsorted) (Ma $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (div_mod int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (zero_zero int)) Ma))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong A_2) B_1) Ma)) (= (hAPP int int (hAPP int _let_1 _let_2 B_1) Ma) (hAPP int int (hAPP int _let_1 _let_2 A_2) Ma))))))) ) 16.26/16.34 ( s1, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.34 ( s1, skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.34 ( s1, skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.34 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.34 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.34 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.34 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.34 ) 16.26/16.34 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_147084 $$unsorted)) (or (not (monoid_add X_a)) (= (ti X_a BOUND_VARIABLE_147084) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (zero_zero X_a)) BOUND_VARIABLE_147084))) ) 16.26/16.34 ( bool, fFalse ) 16.26/16.34 ( bool, fTrue ) 16.26/16.34 ( int, pls ) 16.26/16.34 ( int, min_1 ) 16.26/16.34 ( int, s ) 16.26/16.34 ( int, m ) 16.26/16.34 ( int, s1 ) 16.26/16.34 ( int, t ) 16.26/16.34 ( (fun int bool), nat_neg ) 16.26/16.34 ( (fun int bool), zprime ) 16.26/16.34 ( (fun int bool), zEven ) 16.26/16.34 ( (fun int bool), zOdd ) 16.26/16.34 ( (fun int bool), (even_odd_even int) ) 16.26/16.34 ( (fun int bool), twoSqu1091635170sum2sq ) 16.26/16.34 ( (fun int bool), nat_is_nat ) 16.26/16.34 ( (fun int (fun int bool)), norRRset ) 16.26/16.34 ( (fun int (fun int bool)), quadRes ) 16.26/16.34 ( (fun int (fun int bool)), sRStar ) 16.26/16.34 ( (fun int (fun int bool)), d22set ) 16.26/16.34 ( (fun int (fun int bool)), sr ) 16.26/16.34 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 16.26/16.34 ( (fun int int), zfact ) 16.26/16.34 ( (fun int int), bit0 ) 16.26/16.34 ( (fun int int), bit1 ) 16.26/16.34 ( (fun int int), (fact_fact int) ) 16.26/16.34 ( (fun int int), pred ) 16.26/16.34 ( (fun int int), succ ) 16.26/16.34 ( (fun nat bool), (even_odd_even nat) ) 16.26/16.34 ( (fun nat bool), prime ) 16.26/16.34 ( (fun nat nat), suc ) 16.26/16.34 ( (fun nat nat), (fact_fact nat) ) 16.26/16.34 ( (fun nat nat), fact ) 16.26/16.34 ( (fun nat nat), nat_size ) 16.26/16.34 ( (fun nat nat), (size_size nat) ) 16.26/16.34 ( (fun (product_prod nat nat) bool), pred_nat ) 16.26/16.34 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 16.26/16.34 ( real, pi ) 16.26/16.34 ( (fun real real), ln ) 16.26/16.34 ( (fun real real), cos ) 16.26/16.34 ( (fun real real), sqrt ) 16.26/16.34 ( (fun real real), sin ) 16.26/16.34 ( (fun real real), arccos ) 16.26/16.34 ( (fun real real), arcsin ) 16.26/16.34 ( (fun real real), tan ) 16.26/16.34 ( (fun real real), arctan ) 16.26/16.34 ( (fun nat (fun nat bool)), coprime ) 16.26/16.34 ( complex, ii ) 16.26/16.34 ( (fun nat real), (real_1 nat) ) 16.26/16.34 ( (fun nat real), sin_coeff ) 16.26/16.34 ( (fun nat real), cos_coeff ) 16.26/16.34 ( (filter nat), sequentially ) 16.26/16.34 ( (fun int (fun int int)), (gcd_gcd int) ) 16.26/16.34 ( (fun int (fun int int)), legendre ) 16.26/16.34 ( (fun int (fun int int)), legacy_zgcd ) 16.26/16.34 ( (fun int (fun int int)), standardRes ) 16.26/16.34 ( (fun int (fun int int)), nat_tsub ) 16.26/16.34 ( (fun int (fun int int)), multInv ) 16.26/16.34 ( (fun int (fun int int)), z3mod ) 16.26/16.34 ( (fun int (fun int int)), z3div ) 16.26/16.34 ( (fun int (fun int int)), int_gcd ) 16.26/16.34 ( (fun int (fun int int)), int_lcm ) 16.26/16.34 ( (fun int (fun int int)), inv ) 16.26/16.34 ( (fun complex complex), expi ) 16.26/16.34 ( (fun complex complex), cnj ) 16.26/16.34 ( (fun real complex), cis ) 16.26/16.34 ( (fun int nat), nat_1 ) 16.26/16.34 ( (fun int nat), phi ) 16.26/16.34 ( (fun (fun int bool) bool), nat_nat_set ) 16.26/16.34 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 16.26/16.34 ( (fun nat (fun nat nat)), nat_gcd ) 16.26/16.34 ( (fun nat (fun nat nat)), nat_lcm ) 16.26/16.34 ( (fun (fun int bool) int), (the int) ) 16.26/16.34 ( (fun complex real), re ) 16.26/16.34 ( (fun complex real), im ) 16.26/16.34 ( (fun complex real), arg ) 16.26/16.34 ( (fun bool bool), fNot ) 16.26/16.34 ( (fun nat (fun real real)), root ) 16.26/16.34 ( (fun real (fun real real)), log ) 16.26/16.34 ( (fun real (fun real real)), powr ) 16.26/16.34 ( (fun bool (fun bool bool)), fimplies ) 16.26/16.34 ( (fun bool (fun bool bool)), fconj ) 16.26/16.34 ( (fun bool (fun bool bool)), fdisj ) 16.26/16.34 ( (fun int (fun int (product_prod int int))), negDivAlg ) 16.26/16.34 ( (fun int (fun int (product_prod int int))), posDivAlg ) 16.26/16.34 ( (fun int (fun int (product_prod int int))), divmod_int ) 16.26/16.34 ( (fun int (fun int (product_prod int int))), pdivmod ) 16.26/16.34 ( (fun int (fun int (product_prod int int))), norm_frac ) 16.26/16.34 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 16.26/16.34 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 16.26/16.34 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 16.26/16.34 ( (fun int (fun int (fun int bool))), zcong ) 16.26/16.34 ( (fun int (fun int (fun int bool))), zcongm ) 16.26/16.34 ( (fun int (fun int (fun int bool))), noXRRset ) 16.26/16.34 ( (fun int (fun int (fun int bool))), bnorRset ) 16.26/16.34 ( (fun int (fun int (fun int bool))), wset ) 16.26/16.34 ( (fun (product_prod int int) bool), frac_1 ) 16.26/16.34 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 16.26/16.34 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 16.26/16.34 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 16.26/16.34 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 16.26/16.34 ( (fun (fun nat rat) bool), vanishes ) 16.26/16.34 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 16.26/16.34 ( (fun code_code_numeral nat), code_c271388182l_size ) 16.26/16.34 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 16.26/16.34 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 16.26/16.34 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 16.26/16.34 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 16.26/16.34 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 16.26/16.34 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 16.26/16.34 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 16.26/16.34 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 16.26/16.34 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 16.26/16.34 ( (fun complex nat), complex_size ) 16.26/16.34 ( (fun complex nat), (size_size complex) ) 16.26/16.34 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 16.26/16.34 ( (fun nat (fun nat (product_prod int int))), bezw ) 16.26/16.34 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 16.26/16.34 ( (fun int (fun nat nat)), nat_aux ) 16.26/16.34 ( (fun int (fun (fun int bool) bool)), rsetR ) 16.26/16.34 ( (fun int (fun (fun int bool) bool)), resSet ) 16.26/16.34 ( (fun int (list int)), quickc666637781d_zero ) 16.26/16.34 ( (fun (product_prod int int) rat), frct ) 16.26/16.34 ( (fun int (fun int rat)), fract ) 16.26/16.34 ( (fun real (fun real complex)), complex_1 ) 16.26/16.34 ( (fun real (fun real complex)), rcis ) 16.26/16.34 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 16.26/16.34 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 16.26/16.34 ( (fun int real), (real_1 int) ) 16.26/16.34 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 16.26/16.34 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 16.26/16.34 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 16.26/16.34 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 16.26/16.34 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 16.26/16.34 ( (fun real nat), natfloor ) 16.26/16.34 ( (fun real nat), natceiling ) 16.26/16.34 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 16.26/16.34 ( (fun quickcheck_code_int int), quickcheck_int_of ) 16.26/16.34 ( (fun rat (product_prod int int)), quotient_of ) 16.26/16.34 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 16.26/16.34 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 16.26/16.34 ( (fun rat real), ratreal ) 16.26/16.34 ( (fun code_code_numeral int), code_int_of ) 16.26/16.34 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 16.26/16.34 ( (fun int quickcheck_code_int), quickcheck_of_int ) 16.26/16.34 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 16.26/16.34 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 16.26/16.34 ) 16.26/16.34 (instantiation (forall ((N_1 $$unsorted)) (= (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) N_1) (one_one nat)) (hAPP nat nat suc N_1)) ) 16.26/16.34 ( (zero_zero nat) ) 16.26/16.34 ( (hAPP nat nat suc (zero_zero nat)) ) 16.26/16.34 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 16.26/16.34 ( (one_one nat) ) 16.26/16.34 ) 16.26/16.34 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_147133 $$unsorted) (BOUND_VARIABLE_147134 $$unsorted)) (let ((_let_0 (norm_norm X_a))) (or (not (real_normed_field X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_147134)) (= (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP X_a real _let_0 BOUND_VARIABLE_147133)) (hAPP X_a real _let_0 BOUND_VARIABLE_147134)) (hAPP X_a real _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_147133) BOUND_VARIABLE_147134))))) ) 16.26/16.34 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.34 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.26/16.34 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.34 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 16.26/16.34 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.34 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.34 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.26/16.34 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.26/16.34 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.34 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.34 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.34 ) 16.26/16.34 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_147158 $$unsorted) (BOUND_VARIABLE_147159 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (or (not (group_add X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 (minus_minus X_a) BOUND_VARIABLE_147158) BOUND_VARIABLE_147159) (hAPP X_a X_a (hAPP X_a _let_0 (plus_plus X_a) BOUND_VARIABLE_147158) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_147159))))) ) 16.26/16.34 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 16.26/16.34 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 16.26/16.34 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 16.26/16.34 ) 16.26/16.34 (instantiation (forall ((R_4 $$unsorted) (A_1 $$unsorted)) (let ((_let_0 (inverse_divide real))) (let ((_let_1 (hAPP real (fun real real) (times_times real) R_4))) (= (hAPP real real (hAPP real (fun real real) _let_0 A_1) R_4) (hAPP real real (hAPP real (fun real real) _let_0 (hAPP real real _let_1 A_1)) (hAPP real real _let_1 R_4))))) ) 16.26/16.34 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.26/16.34 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 16.26/16.34 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 16.26/16.34 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 16.26/16.34 ) 16.26/16.34 (instantiation (forall ((A_2 $$unsorted) (B_1 $$unsorted) (Ma $$unsorted)) (let ((_let_0 (fun int bool))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong A_2) B_1) Ma)) (not (forall ((K_1 $$unsorted)) (let ((_let_0 (fun int int))) (not (= (hAPP int int (hAPP int _let_0 (plus_plus int) A_2) (hAPP int int (hAPP int _let_0 (times_times int) Ma) K_1)) (ti int B_1)))) )))) ) 16.26/16.34 ( s1, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.34 ( s1, skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.34 ( s1, skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.34 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.34 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.34 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.34 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.34 ) 16.26/16.34 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (ordere142940540dd_abs X_a)) (= _let_0 (hAPP X_a X_a (abs_abs X_a) _let_0)))) ) 16.26/16.34 ( nat ) 16.26/16.34 ( int ) 16.26/16.34 ( real ) 16.26/16.34 ( rat ) 16.26/16.34 ( complex ) 16.26/16.34 ( quickcheck_code_int ) 16.26/16.34 ( code_code_numeral ) 16.26/16.34 ) 16.26/16.34 (instantiation (forall ((K_4 $$unsorted) (I_1 $$unsorted) (J_2 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (let ((_let_2 (hAPP int _let_0 _let_1 I_1))) (or (not (hBOOL (hAPP int bool _let_2 J_2))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 J_2) K_4))) (hBOOL (hAPP int bool _let_2 K_4)))))) ) 16.26/16.34 ( (one_one int), (zero_zero int), (hAPP int int (number_number_of int) pls) ) 16.26/16.34 ( pls, (zero_zero int), min_1 ) 16.26/16.34 ( min_1, min_1, min_1 ) 16.26/16.34 ( s, min_1, pls ) 16.26/16.34 ( t, (zero_zero int), (one_one int) ) 16.26/16.34 ) 16.26/16.34 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_147293 $$unsorted) (BOUND_VARIABLE_147294 $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (linorder X_a)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_147293) BOUND_VARIABLE_147294)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_147293) BOUND_VARIABLE_147294)) (= (ti X_a BOUND_VARIABLE_147294) (ti X_a BOUND_VARIABLE_147293))))) ) 16.26/16.34 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.34 ( int, (one_one int), t ) 16.26/16.34 ( int, (zero_zero int), (one_one int) ) 16.26/16.34 ( int, (zero_zero int), min_1 ) 16.26/16.34 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.34 ( int, (zero_zero int), s ) 16.26/16.34 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.26/16.34 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 16.26/16.34 ( int, (zero_zero int), skv_4 ) 16.26/16.34 ( int, (zero_zero int), skv_10 ) 16.26/16.34 ( int, pls, (one_one int) ) 16.26/16.34 ( int, pls, pls ) 16.26/16.34 ( int, pls, min_1 ) 16.26/16.34 ( int, pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.34 ( int, min_1, pls ) 16.26/16.34 ( int, min_1, min_1 ) 16.26/16.34 ( int, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.34 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.34 ( int, skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.34 ( int, skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.34 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.34 ( real, (zero_zero real), pi ) 16.26/16.34 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.34 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.34 ( real, (zero_zero real), skv_2 ) 16.26/16.34 ( real, (zero_zero real), skv_3 ) 16.26/16.34 ( real, (zero_zero real), skv_5 ) 16.26/16.34 ( real, (zero_zero real), skv_7 ) 16.26/16.34 ( real, (zero_zero real), skv_8 ) 16.26/16.34 ( real, (zero_zero real), skv_9 ) 16.26/16.34 ( real, (zero_zero real), skv_12 ) 16.26/16.34 ( real, pi, (zero_zero real) ) 16.26/16.34 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.34 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.26/16.34 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.34 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 16.26/16.34 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.26/16.34 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 16.26/16.34 ( real, skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.34 ) 16.26/16.34 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_147321 $$unsorted) (BOUND_VARIABLE_147322 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member X_a))) (let ((_let_3 (ring_1_Ints X_a))) (or (not (ring_1 X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_147322) _let_3))) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_147321) _let_3))) (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_147322) BOUND_VARIABLE_147321)) _let_3))))))) ) 16.26/16.34 ( nat, (one_one nat), (one_one nat) ) 16.26/16.34 ( int, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 16.26/16.34 ( int, (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.34 ) 16.26/16.34 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (plus_plus nat))) (= (hAPP nat nat (hAPP nat _let_0 _let_1 N_1) M) (hAPP nat nat (hAPP nat _let_0 _let_1 M) N_1)))) ) 16.26/16.34 ( (one_one nat), (one_one nat) ) 16.26/16.34 ) 16.26/16.34 (instantiation (forall ((Z_1 $$unsorted)) (= (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP complex real re Z_1)) (hAPP complex real (norm_norm complex) Z_1)) (hAPP complex real re (hAPP complex complex (sgn_sgn complex) Z_1))) ) 16.26/16.34 ( (one_one complex) ) 16.26/16.34 ) 16.26/16.34 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_147407 $$unsorted) (BOUND_VARIABLE_147408 $$unsorted)) (let ((_let_0 (abs_abs X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (inverse_divide X_a))) (or (not (linordered_field X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_147408)) (= (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a _let_0 BOUND_VARIABLE_147407)) (hAPP X_a X_a _let_0 BOUND_VARIABLE_147408)) (hAPP X_a X_a _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_147407) BOUND_VARIABLE_147408))))))) ) 16.26/16.34 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.34 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.26/16.34 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.34 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 16.26/16.34 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.34 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.34 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.26/16.34 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.26/16.34 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.34 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.34 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.34 ) 16.26/16.34 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_147515 $$unsorted) (BOUND_VARIABLE_147516 $$unsorted)) (let ((_let_0 (fun (filter nat) bool))) (or (not (metric_space X_a)) (= (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_0 (hAPP (fun nat X_a) (fun X_a _let_0) (tendsto nat X_a) BOUND_VARIABLE_147515) BOUND_VARIABLE_147516) sequentially)) (forall ((R_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) R_2))) (not (forall ((No $$unsorted)) (not (forall ((N_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) No) N_2))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP X_a real (hAPP X_a (fun X_a real) (dist_dist X_a) (hAPP nat X_a BOUND_VARIABLE_147515 N_2)) BOUND_VARIABLE_147516)) R_2))) )) ))) )))) ) 16.26/16.34 ( real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real) ) 16.26/16.34 ) 16.26/16.34 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (one_one real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat real))) (let ((_let_3 (fun nat _let_1))) (let ((_let_4 (fun _let_2 _let_2))) (let ((_let_5 (fun (fun nat nat) _let_2))) (let ((_let_6 (combb nat real nat))) (let ((_let_7 (fun (filter nat) bool))) (let ((_let_8 (combc nat nat nat))) (let ((_let_9 (hAPP nat (fun nat nat) (hAPP (fun nat (fun nat nat)) (fun nat (fun nat nat)) _let_8 (hAPP (fun nat nat) (fun nat (fun nat nat)) (hAPP (fun nat (fun nat nat)) (fun (fun nat nat) (fun nat (fun nat nat))) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP (fun nat (fun nat nat)) (fun nat (fun nat nat)) _let_8 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (abs_abs real) X_2)) _let_0))) (hBOOL (hAPP (filter nat) bool (hAPP real _let_7 (hAPP _let_2 (fun real _let_7) (tendsto nat real) (hAPP _let_2 _let_2 (hAPP _let_3 _let_4 (combs nat real real) (hAPP _let_2 _let_3 (hAPP (fun real _let_1) (fun _let_2 _let_3) (combb real _let_1 nat) (times_times real)) (hAPP _let_2 _let_2 (hAPP _let_1 _let_4 (combb real real nat) (hAPP real _let_1 (inverse_divide real) _let_0)) (hAPP (fun nat nat) _let_2 (hAPP _let_2 _let_5 _let_6 (real_1 nat)) _let_9)))) (hAPP (fun nat nat) _let_2 (hAPP _let_2 _let_5 _let_6 (hAPP real _let_2 (power_power real) X_2)) _let_9))) (zero_zero real)) sequentially))))))))))))) ) 16.26/16.34 ( (hAPP int real (number_number_of real) min_1) ) 16.26/16.34 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.34 ) 16.26/16.34 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (times_times real))) (let ((_let_2 (hAPP real _let_0 _let_1 (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (= (hAPP real real sin (hAPP real real _let_2 X_1)) (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real _let_2 (hAPP real real sin X_1))) (hAPP real real cos X_1)))))) ) 16.26/16.34 ( (zero_zero real) ) 16.26/16.34 ( pi ) 16.26/16.34 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.34 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.34 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.26/16.34 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.26/16.34 ( (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 16.26/16.34 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.26/16.34 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 16.26/16.34 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 16.26/16.34 ( skv_5 ) 16.26/16.34 ) 16.26/16.34 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_147552 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (ordere142940540dd_abs X_a)) (= (= _let_0 (ti X_a BOUND_VARIABLE_147552)) (= _let_0 (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_147552))))) ) 16.26/16.34 ( bool, fFalse ) 16.26/16.34 ( bool, fTrue ) 16.26/16.34 ( int, pls ) 16.26/16.34 ( int, min_1 ) 16.26/16.34 ( int, s ) 16.26/16.34 ( int, m ) 16.26/16.34 ( int, s1 ) 16.26/16.34 ( int, t ) 16.26/16.34 ( (fun int bool), nat_neg ) 16.26/16.34 ( (fun int bool), zprime ) 16.26/16.34 ( (fun int bool), zEven ) 16.26/16.34 ( (fun int bool), zOdd ) 16.26/16.34 ( (fun int bool), (even_odd_even int) ) 16.26/16.34 ( (fun int bool), twoSqu1091635170sum2sq ) 16.26/16.34 ( (fun int bool), nat_is_nat ) 16.26/16.34 ( (fun int (fun int bool)), norRRset ) 16.26/16.34 ( (fun int (fun int bool)), quadRes ) 16.26/16.34 ( (fun int (fun int bool)), sRStar ) 16.26/16.34 ( (fun int (fun int bool)), d22set ) 16.26/16.34 ( (fun int (fun int bool)), sr ) 16.26/16.34 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 16.26/16.34 ( (fun int int), zfact ) 16.26/16.34 ( (fun int int), bit0 ) 16.26/16.34 ( (fun int int), bit1 ) 16.26/16.34 ( (fun int int), (fact_fact int) ) 16.26/16.34 ( (fun int int), pred ) 16.26/16.34 ( (fun int int), succ ) 16.26/16.34 ( (fun nat bool), (even_odd_even nat) ) 16.26/16.34 ( (fun nat bool), prime ) 16.26/16.34 ( (fun nat nat), suc ) 16.26/16.34 ( (fun nat nat), (fact_fact nat) ) 16.26/16.34 ( (fun nat nat), fact ) 16.26/16.34 ( (fun nat nat), nat_size ) 16.26/16.34 ( (fun nat nat), (size_size nat) ) 16.26/16.34 ( (fun (product_prod nat nat) bool), pred_nat ) 16.26/16.34 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 16.26/16.34 ( real, pi ) 16.26/16.34 ( (fun real real), ln ) 16.26/16.34 ( (fun real real), cos ) 16.26/16.34 ( (fun real real), sqrt ) 16.26/16.34 ( (fun real real), sin ) 16.26/16.34 ( (fun real real), arccos ) 16.26/16.34 ( (fun real real), arcsin ) 16.26/16.34 ( (fun real real), tan ) 16.26/16.34 ( (fun real real), arctan ) 16.26/16.34 ( (fun nat (fun nat bool)), coprime ) 16.26/16.34 ( complex, ii ) 16.26/16.34 ( (fun nat real), (real_1 nat) ) 16.26/16.34 ( (fun nat real), sin_coeff ) 16.26/16.34 ( (fun nat real), cos_coeff ) 16.26/16.34 ( (filter nat), sequentially ) 16.26/16.34 ( (fun int (fun int int)), (gcd_gcd int) ) 16.26/16.34 ( (fun int (fun int int)), legendre ) 16.26/16.34 ( (fun int (fun int int)), legacy_zgcd ) 16.26/16.34 ( (fun int (fun int int)), standardRes ) 16.26/16.34 ( (fun int (fun int int)), nat_tsub ) 16.26/16.34 ( (fun int (fun int int)), multInv ) 16.26/16.34 ( (fun int (fun int int)), z3mod ) 16.26/16.34 ( (fun int (fun int int)), z3div ) 16.26/16.34 ( (fun int (fun int int)), int_gcd ) 16.26/16.34 ( (fun int (fun int int)), int_lcm ) 16.26/16.34 ( (fun int (fun int int)), inv ) 16.26/16.34 ( (fun complex complex), expi ) 16.26/16.34 ( (fun complex complex), cnj ) 16.26/16.34 ( (fun real complex), cis ) 16.26/16.34 ( (fun int nat), nat_1 ) 16.26/16.34 ( (fun int nat), phi ) 16.26/16.34 ( (fun (fun int bool) bool), nat_nat_set ) 16.26/16.34 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 16.26/16.34 ( (fun nat (fun nat nat)), nat_gcd ) 16.26/16.34 ( (fun nat (fun nat nat)), nat_lcm ) 16.26/16.34 ( (fun (fun int bool) int), (the int) ) 16.26/16.34 ( (fun complex real), re ) 16.26/16.34 ( (fun complex real), im ) 16.26/16.34 ( (fun complex real), arg ) 16.26/16.34 ( (fun bool bool), fNot ) 16.26/16.34 ( (fun nat (fun real real)), root ) 16.26/16.34 ( (fun real (fun real real)), log ) 16.26/16.34 ( (fun real (fun real real)), powr ) 16.26/16.34 ( (fun bool (fun bool bool)), fimplies ) 16.26/16.34 ( (fun bool (fun bool bool)), fconj ) 16.26/16.34 ( (fun bool (fun bool bool)), fdisj ) 16.26/16.34 ( (fun int (fun int (product_prod int int))), negDivAlg ) 16.26/16.34 ( (fun int (fun int (product_prod int int))), posDivAlg ) 16.26/16.34 ( (fun int (fun int (product_prod int int))), divmod_int ) 16.26/16.34 ( (fun int (fun int (product_prod int int))), pdivmod ) 16.26/16.34 ( (fun int (fun int (product_prod int int))), norm_frac ) 16.26/16.34 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 16.26/16.34 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 16.26/16.34 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 16.26/16.34 ( (fun int (fun int (fun int bool))), zcong ) 16.26/16.34 ( (fun int (fun int (fun int bool))), zcongm ) 16.26/16.34 ( (fun int (fun int (fun int bool))), noXRRset ) 16.26/16.34 ( (fun int (fun int (fun int bool))), bnorRset ) 16.26/16.34 ( (fun int (fun int (fun int bool))), wset ) 16.26/16.34 ( (fun (product_prod int int) bool), frac_1 ) 16.26/16.34 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 16.26/16.34 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 16.26/16.34 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 16.26/16.34 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 16.26/16.34 ( (fun (fun nat rat) bool), vanishes ) 16.26/16.34 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 16.26/16.34 ( (fun code_code_numeral nat), code_c271388182l_size ) 16.26/16.34 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 16.26/16.34 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 16.26/16.34 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 16.26/16.34 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 16.26/16.34 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 16.26/16.34 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 16.26/16.34 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 16.26/16.34 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 16.26/16.34 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 16.26/16.34 ( (fun complex nat), complex_size ) 16.26/16.34 ( (fun complex nat), (size_size complex) ) 16.26/16.34 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 16.26/16.34 ( (fun nat (fun nat (product_prod int int))), bezw ) 16.26/16.34 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 16.26/16.34 ( (fun int (fun nat nat)), nat_aux ) 16.26/16.34 ( (fun int (fun (fun int bool) bool)), rsetR ) 16.26/16.34 ( (fun int (fun (fun int bool) bool)), resSet ) 16.26/16.34 ( (fun int (list int)), quickc666637781d_zero ) 16.26/16.34 ( (fun (product_prod int int) rat), frct ) 16.26/16.34 ( (fun int (fun int rat)), fract ) 16.26/16.34 ( (fun real (fun real complex)), complex_1 ) 16.26/16.34 ( (fun real (fun real complex)), rcis ) 16.26/16.34 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 16.26/16.34 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 16.26/16.34 ( (fun int real), (real_1 int) ) 16.26/16.34 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 16.26/16.34 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 16.26/16.34 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 16.26/16.34 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 16.26/16.34 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 16.26/16.34 ( (fun real nat), natfloor ) 16.26/16.34 ( (fun real nat), natceiling ) 16.26/16.34 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 16.26/16.34 ( (fun quickcheck_code_int int), quickcheck_int_of ) 16.26/16.34 ( (fun rat (product_prod int int)), quotient_of ) 16.26/16.34 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 16.26/16.34 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 16.26/16.34 ( (fun rat real), ratreal ) 16.26/16.34 ( (fun code_code_numeral int), code_int_of ) 16.26/16.34 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 16.26/16.34 ( (fun int quickcheck_code_int), quickcheck_of_int ) 16.26/16.34 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 16.26/16.34 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 16.26/16.34 ) 16.26/16.34 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (power_power real))) (let ((_let_3 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (= (hAPP real real cos (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) X_1)) (hAPP real real (hAPP real _let_0 (minus_minus real) (hAPP nat real (hAPP real _let_1 _let_2 (hAPP real real cos X_1)) _let_3)) (hAPP nat real (hAPP real _let_1 _let_2 (hAPP real real sin X_1)) _let_3))))))) ) 16.26/16.34 ( (zero_zero real) ) 16.26/16.34 ( pi ) 16.26/16.34 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.34 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.26/16.34 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.26/16.34 ( (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 16.26/16.34 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.26/16.34 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 16.26/16.34 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 16.26/16.34 ) 16.26/16.34 (instantiation (forall ((P_5 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (hAPP int int (hAPP int _let_0 (div_div int) (hAPP int int (hAPP int _let_0 (minus_minus int) P_5) (one_one int))) (hAPP int int (number_number_of int) _let_1)))) (= (hAPP int nat nat_1 (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) _let_1)) _let_2)) (hAPP nat nat (hAPP nat (fun nat nat) (times_times nat) (hAPP int nat (number_number_of nat) _let_1)) (hAPP int nat nat_1 _let_2)))))) ) 16.26/16.34 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.34 ) 16.26/16.34 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_147689 $$unsorted) (BOUND_VARIABLE_147690 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (or (not (linord581940658strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_147690) _let_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_147689) _let_2))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_147690) BOUND_VARIABLE_147689))))))) ) 16.26/16.34 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.34 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.34 ( int, skv_13, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.34 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.34 ( real, pi, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 16.26/16.34 ( real, (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.34 ( real, (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.34 ( complex, ii, ii ) 16.26/16.34 ( complex, ii, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 16.26/16.34 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.34 ) 16.26/16.35 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int rat (hAPP int (fun int rat) fract (one_one int)) (hAPP int int (number_number_of int) K_4)) (hAPP rat rat (hAPP rat (fun rat rat) (inverse_divide rat) (one_one rat)) (hAPP int rat (number_number_of rat) K_4))) ) 16.26/16.35 ( pls ) 16.26/16.35 ( (hAPP int int bit1 pls) ) 16.26/16.35 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.26/16.35 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.26/16.35 ( min_1 ) 16.26/16.35 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.35 ) 16.26/16.35 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_147762 $$unsorted) (BOUND_VARIABLE_147763 $$unsorted)) (let ((_let_0 (archim2085082626_floor X_a))) (or (not (archim1727834104eiling X_a)) (= (hAPP X_a int _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_147762) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_147763))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP X_a int _let_0 BOUND_VARIABLE_147762)) (hAPP int int (number_number_of int) BOUND_VARIABLE_147763))))) ) 16.26/16.35 ( nat, (one_one nat), (hAPP int int bit1 pls) ) 16.26/16.35 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (hAPP int int bit1 pls) ) 16.26/16.35 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int bit1 pls) ) 16.26/16.35 ) 16.26/16.35 (instantiation (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (zero_zero int))) (let ((_let_3 (hAPP int int (hAPP int _let_1 (plus_plus int) A_1) B))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) _let_2) A_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) _let_3) _let_2))) (= _let_3 (hAPP int int (hAPP int _let_1 (div_mod int) A_1) B))))))) ) 16.26/16.35 ( (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 16.26/16.35 ( (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.35 ) 16.26/16.35 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_147820 $$unsorted)) (or (not (group_add X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) BOUND_VARIABLE_147820) (zero_zero X_a)) (ti X_a BOUND_VARIABLE_147820))) ) 16.26/16.35 ( bool, fFalse ) 16.26/16.35 ( bool, fTrue ) 16.26/16.35 ( int, pls ) 16.26/16.35 ( int, min_1 ) 16.26/16.35 ( int, s ) 16.26/16.35 ( int, m ) 16.26/16.35 ( int, s1 ) 16.26/16.35 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.35 ( int, t ) 16.26/16.35 ( (fun int bool), nat_neg ) 16.26/16.35 ( (fun int bool), zprime ) 16.26/16.35 ( (fun int bool), zEven ) 16.26/16.35 ( (fun int bool), zOdd ) 16.26/16.35 ( (fun int bool), (even_odd_even int) ) 16.26/16.35 ( (fun int bool), twoSqu1091635170sum2sq ) 16.26/16.35 ( (fun int bool), nat_is_nat ) 16.26/16.35 ( (fun int (fun int bool)), norRRset ) 16.26/16.35 ( (fun int (fun int bool)), quadRes ) 16.26/16.35 ( (fun int (fun int bool)), sRStar ) 16.26/16.35 ( (fun int (fun int bool)), d22set ) 16.26/16.35 ( (fun int (fun int bool)), sr ) 16.26/16.35 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 16.26/16.35 ( (fun int int), zfact ) 16.26/16.35 ( (fun int int), bit0 ) 16.26/16.35 ( (fun int int), bit1 ) 16.26/16.35 ( (fun int int), (fact_fact int) ) 16.26/16.35 ( (fun int int), pred ) 16.26/16.35 ( (fun int int), succ ) 16.26/16.35 ( (fun nat bool), (even_odd_even nat) ) 16.26/16.35 ( (fun nat bool), prime ) 16.26/16.35 ( (fun nat nat), suc ) 16.26/16.35 ( (fun nat nat), (fact_fact nat) ) 16.26/16.35 ( (fun nat nat), fact ) 16.26/16.35 ( (fun nat nat), nat_size ) 16.26/16.35 ( (fun nat nat), (size_size nat) ) 16.26/16.35 ( (fun (product_prod nat nat) bool), pred_nat ) 16.26/16.35 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 16.26/16.35 ( real, pi ) 16.26/16.35 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))) ) 16.26/16.35 ( (fun real real), ln ) 16.26/16.35 ( (fun real real), cos ) 16.26/16.35 ( (fun real real), sqrt ) 16.26/16.35 ( (fun real real), sin ) 16.26/16.35 ( (fun real real), arccos ) 16.26/16.35 ( (fun real real), arcsin ) 16.26/16.35 ( (fun real real), tan ) 16.26/16.35 ( (fun real real), arctan ) 16.26/16.35 ( (fun nat (fun nat bool)), coprime ) 16.26/16.35 ( complex, ii ) 16.26/16.35 ( (fun nat real), (real_1 nat) ) 16.26/16.35 ( (fun nat real), sin_coeff ) 16.26/16.35 ( (fun nat real), cos_coeff ) 16.26/16.35 ( (filter nat), sequentially ) 16.26/16.35 ( (fun int (fun int int)), (gcd_gcd int) ) 16.26/16.35 ( (fun int (fun int int)), legendre ) 16.26/16.35 ( (fun int (fun int int)), legacy_zgcd ) 16.26/16.35 ( (fun int (fun int int)), standardRes ) 16.26/16.35 ( (fun int (fun int int)), nat_tsub ) 16.26/16.35 ( (fun int (fun int int)), multInv ) 16.26/16.35 ( (fun int (fun int int)), z3mod ) 16.26/16.35 ( (fun int (fun int int)), z3div ) 16.26/16.35 ( (fun int (fun int int)), int_gcd ) 16.26/16.35 ( (fun int (fun int int)), int_lcm ) 16.26/16.35 ( (fun int (fun int int)), inv ) 16.26/16.35 ( (fun complex complex), expi ) 16.26/16.35 ( (fun complex complex), cnj ) 16.26/16.35 ( (fun real complex), cis ) 16.26/16.35 ( (fun int nat), nat_1 ) 16.26/16.35 ( (fun int nat), phi ) 16.26/16.35 ( (fun (fun int bool) bool), nat_nat_set ) 16.26/16.35 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 16.26/16.35 ( (fun nat (fun nat nat)), nat_gcd ) 16.26/16.35 ( (fun nat (fun nat nat)), nat_lcm ) 16.26/16.35 ( (fun (fun int bool) int), (the int) ) 16.26/16.35 ( (fun complex real), re ) 16.26/16.35 ( (fun complex real), im ) 16.26/16.35 ( (fun complex real), arg ) 16.26/16.35 ( (fun bool bool), fNot ) 16.26/16.35 ( (fun nat (fun real real)), root ) 16.26/16.35 ( (fun real (fun real real)), log ) 16.26/16.35 ( (fun real (fun real real)), powr ) 16.26/16.35 ( (fun bool (fun bool bool)), fimplies ) 16.26/16.35 ( (fun bool (fun bool bool)), fconj ) 16.26/16.35 ( (fun bool (fun bool bool)), fdisj ) 16.26/16.35 ( (fun int (fun int (product_prod int int))), negDivAlg ) 16.26/16.35 ( (fun int (fun int (product_prod int int))), posDivAlg ) 16.26/16.35 ( (fun int (fun int (product_prod int int))), divmod_int ) 16.26/16.35 ( (fun int (fun int (product_prod int int))), pdivmod ) 16.26/16.35 ( (fun int (fun int (product_prod int int))), norm_frac ) 16.26/16.35 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 16.26/16.35 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 16.26/16.35 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 16.26/16.35 ( code_code_numeral, (zero_zero code_code_numeral) ) 16.26/16.35 ( (fun int (fun int (fun int bool))), zcong ) 16.26/16.35 ( (fun int (fun int (fun int bool))), zcongm ) 16.26/16.35 ( (fun int (fun int (fun int bool))), noXRRset ) 16.26/16.35 ( (fun int (fun int (fun int bool))), bnorRset ) 16.26/16.35 ( (fun int (fun int (fun int bool))), wset ) 16.26/16.35 ( (fun (product_prod int int) bool), frac_1 ) 16.26/16.35 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 16.26/16.35 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 16.26/16.35 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 16.26/16.35 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 16.26/16.35 ( (fun (fun nat rat) bool), vanishes ) 16.26/16.35 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 16.26/16.35 ( (fun code_code_numeral nat), code_c271388182l_size ) 16.26/16.35 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 16.26/16.35 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 16.26/16.35 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 16.26/16.35 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 16.26/16.35 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 16.26/16.35 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 16.26/16.35 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 16.26/16.35 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 16.26/16.35 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 16.26/16.35 ( (fun complex nat), complex_size ) 16.26/16.35 ( (fun complex nat), (size_size complex) ) 16.26/16.35 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 16.26/16.35 ( (fun nat (fun nat (product_prod int int))), bezw ) 16.26/16.35 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 16.26/16.35 ( (fun int (fun nat nat)), nat_aux ) 16.26/16.35 ( (fun int (fun (fun int bool) bool)), rsetR ) 16.26/16.35 ( (fun int (fun (fun int bool) bool)), resSet ) 16.26/16.35 ( (fun int (list int)), quickc666637781d_zero ) 16.26/16.35 ( (fun (product_prod int int) rat), frct ) 16.26/16.35 ( (fun int (fun int rat)), fract ) 16.26/16.35 ( (fun real (fun real complex)), complex_1 ) 16.26/16.35 ( (fun real (fun real complex)), rcis ) 16.26/16.35 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 16.26/16.35 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 16.26/16.35 ( (fun int real), (real_1 int) ) 16.26/16.35 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 16.26/16.35 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 16.26/16.35 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 16.26/16.35 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 16.26/16.35 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 16.26/16.35 ( (fun real nat), natfloor ) 16.26/16.35 ( (fun real nat), natceiling ) 16.26/16.35 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 16.26/16.35 ( (fun quickcheck_code_int int), quickcheck_int_of ) 16.26/16.35 ( (fun rat (product_prod int int)), quotient_of ) 16.26/16.35 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 16.26/16.35 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 16.26/16.35 ( (fun rat real), ratreal ) 16.26/16.35 ( (fun code_code_numeral int), code_int_of ) 16.26/16.35 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 16.26/16.35 ( (fun int quickcheck_code_int), quickcheck_of_int ) 16.26/16.35 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 16.26/16.35 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 16.26/16.35 ) 16.26/16.35 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_147831 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)))) (or (not (linord1117847801e_zero X_a)) (= (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_147831))) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_147831))))) ) 16.26/16.35 ( real, (zero_zero real) ) 16.26/16.35 ( complex, ii ) 16.26/16.35 ) 16.26/16.35 (instantiation (forall ((N_1 $$unsorted)) (not (= (zero_zero nat) (hAPP nat nat (fact_fact nat) N_1))) ) 16.26/16.35 ( (zero_zero nat) ) 16.26/16.35 ( (hAPP nat nat suc (zero_zero nat)) ) 16.26/16.35 ) 16.26/16.35 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_147888 $$unsorted)) (or (not (semiring_div X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_147888)) (= (one_one X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (div_div X_a) BOUND_VARIABLE_147888) BOUND_VARIABLE_147888))) ) 16.26/16.35 ( bool, fFalse ) 16.26/16.35 ( bool, fTrue ) 16.26/16.35 ( int, pls ) 16.26/16.35 ( int, min_1 ) 16.26/16.35 ( int, s ) 16.26/16.35 ( int, m ) 16.26/16.35 ( int, s1 ) 16.26/16.35 ( int, t ) 16.26/16.35 ( (fun int bool), nat_neg ) 16.26/16.35 ( (fun int bool), zprime ) 16.26/16.35 ( (fun int bool), zEven ) 16.26/16.35 ( (fun int bool), zOdd ) 16.26/16.35 ( (fun int bool), (even_odd_even int) ) 16.26/16.35 ( (fun int bool), twoSqu1091635170sum2sq ) 16.26/16.35 ( (fun int bool), nat_is_nat ) 16.26/16.35 ( (fun int (fun int bool)), norRRset ) 16.26/16.35 ( (fun int (fun int bool)), quadRes ) 16.26/16.35 ( (fun int (fun int bool)), sRStar ) 16.26/16.35 ( (fun int (fun int bool)), d22set ) 16.26/16.35 ( (fun int (fun int bool)), sr ) 16.26/16.35 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 16.26/16.35 ( (fun int int), zfact ) 16.26/16.35 ( (fun int int), bit0 ) 16.26/16.35 ( (fun int int), bit1 ) 16.26/16.35 ( (fun int int), (fact_fact int) ) 16.26/16.35 ( (fun int int), pred ) 16.26/16.35 ( (fun int int), succ ) 16.26/16.35 ( (fun nat bool), (even_odd_even nat) ) 16.26/16.35 ( (fun nat bool), prime ) 16.26/16.35 ( (fun nat nat), suc ) 16.26/16.35 ( (fun nat nat), (fact_fact nat) ) 16.26/16.35 ( (fun nat nat), fact ) 16.26/16.35 ( (fun nat nat), nat_size ) 16.26/16.35 ( (fun nat nat), (size_size nat) ) 16.26/16.35 ( (fun (product_prod nat nat) bool), pred_nat ) 16.26/16.35 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 16.26/16.35 ( real, pi ) 16.26/16.35 ( (fun real real), ln ) 16.26/16.35 ( (fun real real), cos ) 16.26/16.35 ( (fun real real), sqrt ) 16.26/16.35 ( (fun real real), sin ) 16.26/16.35 ( (fun real real), arccos ) 16.26/16.35 ( (fun real real), arcsin ) 16.26/16.35 ( (fun real real), tan ) 16.26/16.35 ( (fun real real), arctan ) 16.26/16.35 ( (fun nat (fun nat bool)), coprime ) 16.26/16.35 ( complex, ii ) 16.26/16.35 ( (fun nat real), (real_1 nat) ) 16.26/16.35 ( (fun nat real), sin_coeff ) 16.26/16.35 ( (fun nat real), cos_coeff ) 16.26/16.35 ( (filter nat), sequentially ) 16.26/16.35 ( (fun int (fun int int)), (gcd_gcd int) ) 16.26/16.35 ( (fun int (fun int int)), legendre ) 16.26/16.35 ( (fun int (fun int int)), legacy_zgcd ) 16.26/16.35 ( (fun int (fun int int)), standardRes ) 16.26/16.35 ( (fun int (fun int int)), nat_tsub ) 16.26/16.35 ( (fun int (fun int int)), multInv ) 16.26/16.35 ( (fun int (fun int int)), z3mod ) 16.26/16.35 ( (fun int (fun int int)), z3div ) 16.26/16.35 ( (fun int (fun int int)), int_gcd ) 16.26/16.35 ( (fun int (fun int int)), int_lcm ) 16.26/16.35 ( (fun int (fun int int)), inv ) 16.26/16.35 ( (fun complex complex), expi ) 16.26/16.35 ( (fun complex complex), cnj ) 16.26/16.35 ( (fun real complex), cis ) 16.26/16.35 ( (fun int nat), nat_1 ) 16.26/16.35 ( (fun int nat), phi ) 16.26/16.35 ( (fun (fun int bool) bool), nat_nat_set ) 16.26/16.35 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 16.26/16.35 ( (fun nat (fun nat nat)), nat_gcd ) 16.26/16.35 ( (fun nat (fun nat nat)), nat_lcm ) 16.26/16.35 ( (fun (fun int bool) int), (the int) ) 16.26/16.35 ( (fun complex real), re ) 16.26/16.35 ( (fun complex real), im ) 16.26/16.35 ( (fun complex real), arg ) 16.26/16.35 ( (fun bool bool), fNot ) 16.26/16.35 ( (fun nat (fun real real)), root ) 16.26/16.35 ( (fun real (fun real real)), log ) 16.26/16.35 ( (fun real (fun real real)), powr ) 16.26/16.35 ( (fun bool (fun bool bool)), fimplies ) 16.26/16.35 ( (fun bool (fun bool bool)), fconj ) 16.26/16.35 ( (fun bool (fun bool bool)), fdisj ) 16.26/16.35 ( (fun int (fun int (product_prod int int))), negDivAlg ) 16.26/16.35 ( (fun int (fun int (product_prod int int))), posDivAlg ) 16.26/16.35 ( (fun int (fun int (product_prod int int))), divmod_int ) 16.26/16.35 ( (fun int (fun int (product_prod int int))), pdivmod ) 16.26/16.35 ( (fun int (fun int (product_prod int int))), norm_frac ) 16.26/16.35 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 16.26/16.35 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 16.26/16.35 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 16.26/16.35 ( (fun int (fun int (fun int bool))), zcong ) 16.26/16.35 ( (fun int (fun int (fun int bool))), zcongm ) 16.26/16.35 ( (fun int (fun int (fun int bool))), noXRRset ) 16.26/16.35 ( (fun int (fun int (fun int bool))), bnorRset ) 16.26/16.35 ( (fun int (fun int (fun int bool))), wset ) 16.26/16.35 ( (fun (product_prod int int) bool), frac_1 ) 16.26/16.35 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 16.26/16.35 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 16.26/16.35 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 16.26/16.35 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 16.26/16.35 ( (fun (fun nat rat) bool), vanishes ) 16.26/16.35 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 16.26/16.35 ( (fun code_code_numeral nat), code_c271388182l_size ) 16.26/16.35 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 16.26/16.35 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 16.26/16.35 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 16.26/16.35 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 16.26/16.35 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 16.26/16.35 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 16.26/16.35 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 16.26/16.35 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 16.26/16.35 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 16.26/16.35 ( (fun complex nat), complex_size ) 16.26/16.35 ( (fun complex nat), (size_size complex) ) 16.26/16.35 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 16.26/16.35 ( (fun nat (fun nat (product_prod int int))), bezw ) 16.26/16.35 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 16.26/16.35 ( (fun int (fun nat nat)), nat_aux ) 16.26/16.35 ( (fun int (fun (fun int bool) bool)), rsetR ) 16.26/16.35 ( (fun int (fun (fun int bool) bool)), resSet ) 16.26/16.35 ( (fun int (list int)), quickc666637781d_zero ) 16.26/16.35 ( (fun (product_prod int int) rat), frct ) 16.26/16.35 ( (fun int (fun int rat)), fract ) 16.26/16.35 ( (fun real (fun real complex)), complex_1 ) 16.26/16.35 ( (fun real (fun real complex)), rcis ) 16.26/16.35 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 16.26/16.35 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 16.26/16.35 ( (fun int real), (real_1 int) ) 16.26/16.35 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 16.26/16.35 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 16.26/16.35 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 16.26/16.35 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 16.26/16.35 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 16.26/16.35 ( (fun real nat), natfloor ) 16.26/16.35 ( (fun real nat), natceiling ) 16.26/16.35 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 16.26/16.35 ( (fun quickcheck_code_int int), quickcheck_int_of ) 16.26/16.35 ( (fun rat (product_prod int int)), quotient_of ) 16.26/16.35 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 16.26/16.35 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 16.26/16.35 ( (fun rat real), ratreal ) 16.26/16.35 ( (fun code_code_numeral int), code_int_of ) 16.26/16.35 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 16.26/16.35 ( (fun int quickcheck_code_int), quickcheck_of_int ) 16.26/16.35 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 16.26/16.35 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 16.26/16.35 ) 16.26/16.35 (instantiation (forall ((W $$unsorted) (Z_1 $$unsorted)) (let ((_let_0 (abs_abs int))) (= (hAPP int nat nat_1 (hAPP int int _let_0 (hAPP int int (hAPP int (fun int int) (times_times int) W) Z_1))) (hAPP nat nat (hAPP nat (fun nat nat) (times_times nat) (hAPP int nat nat_1 (hAPP int int _let_0 W))) (hAPP int nat nat_1 (hAPP int int _let_0 Z_1))))) ) 16.26/16.35 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 16.26/16.35 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 16.26/16.35 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13 ) 16.26/16.35 ) 16.26/16.35 (instantiation (forall ((Z_1 $$unsorted)) (let ((_let_0 (norm_norm complex))) (= (hAPP complex real _let_0 (hAPP complex complex cnj Z_1)) (hAPP complex real _let_0 Z_1))) ) 16.26/16.35 ( (one_one complex) ) 16.26/16.35 ( ii ) 16.26/16.35 ( (zero_zero complex) ) 16.26/16.35 ) 16.26/16.35 (instantiation (forall ((N_1 $$unsorted)) (= (zero_zero nat) (hAPP int nat nat_1 (hAPP int int (uminus_uminus int) (hAPP nat int (semiring_1_of_nat int) N_1)))) ) 16.26/16.35 ( (zero_zero nat) ) 16.26/16.35 ( (hAPP nat nat suc (zero_zero nat)) ) 16.26/16.35 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.26/16.35 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.35 ) 16.26/16.35 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_147934 $$unsorted) (BOUND_VARIABLE_147935 $$unsorted) (BOUND_VARIABLE_147936 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (fun X_a X_a))) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) (zero_zero X_a)) BOUND_VARIABLE_147936))) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_2 (times_times X_a) BOUND_VARIABLE_147934) BOUND_VARIABLE_147936)) BOUND_VARIABLE_147935)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_147934) (hAPP X_a X_a (hAPP X_a _let_2 (inverse_divide X_a) BOUND_VARIABLE_147935) BOUND_VARIABLE_147936)))))))) ) 16.26/16.35 ( real, (zero_zero real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.35 ) 16.26/16.35 (instantiation (forall ((P_5 $$unsorted)) (let ((_let_0 (product_prod int int))) (= (hAPP int rat (hAPP int (fun int rat) fract (hAPP _let_0 int (product_fst int int) P_5)) (hAPP _let_0 int (product_snd int int) P_5)) (hAPP _let_0 rat frct P_5))) ) 16.26/16.35 ( (let ((_let_0 (one_one int))) (let ((_let_1 (product_prod int int))) (hAPP int _let_1 (hAPP int (fun int _let_1) (product_Pair int int) _let_0) _let_0))) ) 16.26/16.35 ) 16.26/16.35 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (zero_zero nat))) (or (not (hBOOL (hAPP nat bool (even_odd_even nat) X_1))) (= _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (div_mod nat) X_1) (hAPP nat nat suc (hAPP nat nat suc _let_0)))))) ) 16.26/16.35 ( (zero_zero nat) ) 16.26/16.35 ( (one_one nat) ) 16.26/16.35 ) 16.26/16.35 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_148010 $$unsorted) (BOUND_VARIABLE_148011 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (zero_zero X_a))) (or (not (ordere216010020id_add X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_148011) _let_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_148010) _let_2))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_148011) BOUND_VARIABLE_148010)) _let_2)))))) ) 16.26/16.35 ( nat, (one_one nat), (one_one nat) ) 16.26/16.35 ( int, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 16.26/16.35 ( int, (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.35 ) 16.26/16.35 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_148034 $$unsorted) (BOUND_VARIABLE_148035 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (or (not (ordere142940540dd_abs X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_148034)) BOUND_VARIABLE_148035)) (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_148034) BOUND_VARIABLE_148035)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_148034)) BOUND_VARIABLE_148035))))))) ) 16.26/16.35 ( int, (one_one int), pls ) 16.26/16.35 ( int, (one_one int), min_1 ) 16.26/16.35 ( int, (one_one int), t ) 16.26/16.35 ( int, (zero_zero int), (one_one int) ) 16.26/16.35 ( int, (zero_zero int), min_1 ) 16.26/16.35 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.35 ( int, (zero_zero int), s ) 16.26/16.35 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.26/16.35 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 16.26/16.35 ( int, (zero_zero int), skv_4 ) 16.26/16.35 ( int, (zero_zero int), skv_10 ) 16.26/16.35 ( int, pls, (one_one int) ) 16.26/16.35 ( int, pls, min_1 ) 16.26/16.35 ( int, pls, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.35 ( int, pls, s ) 16.26/16.35 ( int, pls, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.26/16.35 ( int, pls, (hAPP int int (number_number_of int) pls) ) 16.26/16.35 ( int, pls, skv_4 ) 16.26/16.35 ( int, pls, skv_10 ) 16.26/16.35 ( int, min_1, pls ) 16.26/16.35 ( int, min_1, min_1 ) 16.26/16.35 ( real, (zero_zero real), pi ) 16.26/16.35 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.35 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.35 ( real, (zero_zero real), skv_3 ) 16.26/16.35 ( real, (zero_zero real), skv_5 ) 16.26/16.35 ( real, (zero_zero real), skv_7 ) 16.26/16.35 ( real, (zero_zero real), skv_12 ) 16.26/16.35 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.26/16.35 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.35 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.26/16.35 ( real, skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.35 ) 16.26/16.35 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_148075 $$unsorted) (BOUND_VARIABLE_148076 $$unsorted) (BOUND_VARIABLE_148077 $$unsorted)) (let ((_let_0 (fun nat X_a))) (let ((_let_1 (power_power X_a))) (let ((_let_2 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)))) (or (not (linordered_semidom X_a)) (not (= (hAPP nat X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_148077) BOUND_VARIABLE_148076) (hAPP nat X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_148075) BOUND_VARIABLE_148076))) (not (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_148075))) (not (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_148077))) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) BOUND_VARIABLE_148076))) (= (ti X_a BOUND_VARIABLE_148075) (ti X_a BOUND_VARIABLE_148077)))))) ) 16.26/16.35 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 16.26/16.35 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 16.26/16.35 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 16.26/16.35 ( int, skv_14, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_14 ) 16.26/16.35 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), ii ) 16.26/16.35 ) 16.26/16.35 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_148112 $$unsorted)) (or (not (real_n2089651433ebra_1 X_a)) (not (number_ring X_a)) (= (hAPP real real (abs_abs real) (hAPP int real (number_number_of real) BOUND_VARIABLE_148112)) (hAPP X_a real (norm_norm X_a) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_148112)))) ) 16.26/16.35 ( nat, pls ) 16.26/16.35 ( nat, (hAPP int int bit1 pls) ) 16.26/16.35 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.26/16.35 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.26/16.35 ( int, pls ) 16.26/16.35 ( int, (hAPP int int bit1 pls) ) 16.26/16.35 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.26/16.35 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.26/16.35 ( int, min_1 ) 16.26/16.35 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.35 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.26/16.35 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.26/16.35 ( real, min_1 ) 16.26/16.35 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.35 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.26/16.35 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.35 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 16.26/16.35 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.26/16.35 ( complex, min_1 ) 16.26/16.35 ( quickcheck_code_int, (one_one int) ) 16.26/16.35 ( quickcheck_code_int, (zero_zero int) ) 16.26/16.35 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 16.26/16.35 ( code_code_numeral, pls ) 16.26/16.35 ( code_code_numeral, (hAPP int int bit1 pls) ) 16.26/16.35 ) 16.26/16.35 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_148173 $$unsorted) (BOUND_VARIABLE_148174 $$unsorted)) (let ((_let_0 (number_number_of X_a))) (or (not (ring_char_0 X_a)) (not (number_ring X_a)) (= (= (hAPP int X_a _let_0 BOUND_VARIABLE_148173) (hAPP int X_a _let_0 BOUND_VARIABLE_148174)) (= (ti int BOUND_VARIABLE_148174) (ti int BOUND_VARIABLE_148173))))) ) 16.26/16.35 ( nat, pls, pls ) 16.26/16.35 ( nat, (hAPP int int bit1 pls), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.26/16.35 ( nat, (hAPP int int bit1 pls), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.26/16.35 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.26/16.35 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit1 pls) ) 16.26/16.35 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.26/16.35 ( int, pls, min_1 ) 16.26/16.35 ( int, (hAPP int int bit1 pls), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.35 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)), pls ) 16.26/16.35 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)), min_1 ) 16.26/16.35 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit1 pls) ) 16.26/16.35 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.35 ( int, min_1, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.26/16.35 ( int, min_1, min_1 ) 16.26/16.35 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.26/16.35 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.35 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)), min_1 ) 16.26/16.35 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.26/16.35 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)), min_1 ) 16.26/16.35 ( real, min_1, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.26/16.35 ( real, min_1, min_1 ) 16.26/16.35 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.35 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.26/16.35 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.35 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 16.26/16.35 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.35 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.35 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)), min_1 ) 16.26/16.35 ( complex, min_1, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.26/16.35 ( complex, min_1, min_1 ) 16.26/16.35 ( quickcheck_code_int, (one_one int), (zero_zero int) ) 16.26/16.35 ( quickcheck_code_int, (one_one int), (hAPP int int bit1 pls) ) 16.26/16.35 ( quickcheck_code_int, (zero_zero int), (hAPP int int bit1 pls) ) 16.26/16.35 ( quickcheck_code_int, (hAPP int int bit1 pls), (one_one int) ) 16.26/16.35 ( quickcheck_code_int, (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 16.26/16.35 ( code_code_numeral, pls, pls ) 16.26/16.35 ( code_code_numeral, pls, (hAPP int int bit1 pls) ) 16.26/16.35 ( code_code_numeral, (hAPP int int bit1 pls), pls ) 16.26/16.35 ) 16.26/16.35 (instantiation (forall ((X_3 $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (fun (filter nat) bool))) (or (not (forall ((R_2 $$unsorted)) (not (forall ((N_3 $$unsorted)) (not (forall ((N_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) N_3) N_2))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) R_2) (hAPP nat real X_3 N_2)))) )) )) )) (hBOOL (hAPP (filter nat) bool (hAPP real _let_1 (hAPP _let_0 (fun real _let_1) (tendsto nat real) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)) X_3)) (zero_zero real)) sequentially))))) ) 16.26/16.35 ( (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))) ) 16.26/16.35 ) 16.26/16.35 (instantiation (forall ((A_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_0 (fun real real))) (= (hAPP real real (hAPP real _let_0 (times_times real) A_1) X_1) (hAPP real real (hAPP real _let_0 (scaleR_scaleR real) A_1) X_1))) ) 16.26/16.35 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.26/16.35 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 16.26/16.35 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 16.26/16.35 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 16.26/16.35 ) 16.26/16.35 (instantiation (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_0 (even_odd_even int))) (or (hBOOL (hAPP int bool _let_0 X_1)) (not (hBOOL (hAPP int bool _let_0 Y_1))) (not (hBOOL (hAPP int bool _let_0 (hAPP int int (hAPP int (fun int int) (plus_plus int) X_1) Y_1)))))) ) 16.26/16.35 ( (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 16.26/16.35 ( (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.35 ) 16.26/16.35 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_148387 $$unsorted) (BOUND_VARIABLE_148388 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (or (not (ordere216010020id_add X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_148388) _let_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_148387) _let_2))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_148388) BOUND_VARIABLE_148387)) _let_2)))))) ) 16.26/16.35 ( nat, (one_one nat), (one_one nat) ) 16.26/16.35 ( int, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 16.26/16.35 ( int, (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.35 ) 16.26/16.35 (instantiation (forall ((X_1 $$unsorted)) (= (hAPP real real ln X_1) (hAPP real real (hAPP real (fun real real) log (hAPP real real (exp real) (one_one real))) X_1)) ) 16.26/16.35 ( (one_one real) ) 16.26/16.35 ) 16.26/16.35 (instantiation (forall ((Ma $$unsorted) (K $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (plus_plus nat))) (= (= Ma N) (= (hAPP nat nat (hAPP nat _let_0 _let_1 N) K) (hAPP nat nat (hAPP nat _let_0 _let_1 Ma) K))))) ) 16.26/16.35 ( (one_one nat), (one_one nat), (one_one nat) ) 16.26/16.35 ) 16.26/16.35 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_0 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) M) N_1))) (or (not (= (zero_zero nat) _let_0)) (= (one_one nat) (hAPP nat nat (fact_fact nat) _let_0)))) ) 16.26/16.35 ( (one_one nat), (one_one nat) ) 16.26/16.35 ) 16.26/16.35 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (fact_fact nat))) (let ((_let_2 (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) M) N_1))) (or (= (zero_zero nat) _let_2) (= (hAPP nat nat _let_1 _let_2) (hAPP nat nat (hAPP nat _let_0 (times_times nat) _let_2) (hAPP nat nat _let_1 (hAPP nat nat (hAPP nat _let_0 (minus_minus nat) _let_2) (one_one nat))))))))) ) 16.26/16.35 ( (one_one nat), (one_one nat) ) 16.26/16.35 ) 16.26/16.35 (instantiation (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_0 (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)))) (or (not (hBOOL (hAPP real bool _let_0 A_1))) (not (hBOOL (hAPP real bool _let_0 B))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP nat nat (hAPP nat (fun nat nat) (times_times nat) (hAPP real nat natfloor A_1)) (hAPP real nat natfloor B))) (hAPP real nat natfloor (hAPP real real (hAPP real (fun real real) (times_times real) A_1) B)))))) ) 16.26/16.35 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.35 ( pi, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 16.26/16.35 ( (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.35 ( (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.35 ) 16.26/16.35 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (abs_Frac X_a))) (= _let_0 (ti (fun (product_prod int int) X_a) _let_0))) ) 16.26/16.35 ( bool ) 16.26/16.35 ( int ) 16.26/16.35 ( (fun int bool) ) 16.26/16.35 ( (fun int int) ) 16.26/16.35 ( rat ) 16.26/16.35 ( (product_prod int int) ) 16.26/16.35 ( (fun bool bool) ) 16.26/16.35 ( (fun (product_prod int int) bool) ) 16.26/16.35 ( (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 16.26/16.35 ( (fun (product_prod int int) (fun int bool)) ) 16.26/16.35 ( (fun (product_prod int int) int) ) 16.26/16.35 ( (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 16.26/16.35 ( (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 16.26/16.35 ) 16.26/16.35 (instantiation (forall ((N_1 $$unsorted)) (let ((_let_0 (zero_zero nat))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) N_1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (= (hAPP nat nat suc _let_0) N_1) (= _let_0 N_1))) ) 16.26/16.35 ( (zero_zero nat) ) 16.26/16.35 ) 16.26/16.35 (instantiation (forall ((X_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (number_number_of int))) (let ((_let_2 (hAPP int (fun int _let_0) zcong X_1))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (hAPP int int _let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) P_5))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 (hAPP int int _let_1 min_1)) P_5))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 (one_one int)) P_5))))))) ) 16.26/16.35 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.35 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.35 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.35 ) 16.26/16.35 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_148608 $$unsorted)) (or (not (comm_semiring_1 X_a)) (= (one_one X_a) (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_148608) (zero_zero nat)))) ) 16.26/16.35 ( int, s ) 16.26/16.35 ( int, s1 ) 16.26/16.35 ( int, skv_14 ) 16.26/16.35 ( real, (hAPP int real (number_number_of real) min_1) ) 16.26/16.35 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.35 ( complex, ii ) 16.26/16.35 ) 16.26/16.35 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_148631 $$unsorted) (BOUND_VARIABLE_148632 $$unsorted)) (let ((_let_0 (uminus_uminus X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (div_div X_a))) (or (not (ring_div X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_148631) BOUND_VARIABLE_148632))) (= (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a _let_0 BOUND_VARIABLE_148632)) BOUND_VARIABLE_148631) (hAPP X_a X_a _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_148632) BOUND_VARIABLE_148631))))))) ) 16.26/16.35 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 16.26/16.35 ) 16.26/16.35 (instantiation (forall ((N_1 $$unsorted)) (= (hAPP real int (archimedean_ceiling real) (hAPP int real (real_1 int) N_1)) (ti int N_1)) ) 16.26/16.35 ( (one_one int) ) 16.26/16.35 ( (zero_zero int) ) 16.26/16.35 ( pls ) 16.26/16.35 ( min_1 ) 16.26/16.35 ( s ) 16.26/16.35 ( m ) 16.26/16.35 ( s1 ) 16.26/16.35 ( t ) 16.26/16.35 ) 16.26/16.35 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_148677 $$unsorted) (BOUND_VARIABLE_148678 $$unsorted)) (or (not (linorder X_a)) (= (= (ti X_a BOUND_VARIABLE_148677) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (ord_min X_a) BOUND_VARIABLE_148677) BOUND_VARIABLE_148678)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_148677) BOUND_VARIABLE_148678)))) ) 16.26/16.35 ( int, (one_one int), t ) 16.26/16.35 ( int, (zero_zero int), (one_one int) ) 16.26/16.35 ( int, (zero_zero int), min_1 ) 16.26/16.35 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.35 ( int, (zero_zero int), s ) 16.26/16.35 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.26/16.35 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 16.26/16.35 ( int, (zero_zero int), skv_4 ) 16.26/16.35 ( int, (zero_zero int), skv_10 ) 16.26/16.35 ( int, min_1, pls ) 16.26/16.35 ( int, min_1, min_1 ) 16.26/16.35 ( real, (zero_zero real), pi ) 16.26/16.35 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.35 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.35 ( real, (zero_zero real), skv_3 ) 16.26/16.35 ( real, (zero_zero real), skv_5 ) 16.26/16.35 ( real, (zero_zero real), skv_7 ) 16.26/16.35 ( real, (zero_zero real), skv_12 ) 16.26/16.35 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.26/16.35 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.35 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.26/16.35 ( real, skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.35 ) 16.26/16.35 (instantiation (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (product_Pair int int))) (let ((_let_4 (fun _let_2 bool))) (let ((_let_5 (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) B_1) _let_1)))) (let ((_let_6 (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) A_2) B_1)))) (let ((_let_7 (hAPP int (fun int _let_2) posDivAlg A_2))) (let ((_let_8 (hAPP int _let_2 _let_7 B_1))) (or (not (hBOOL (hAPP _let_2 bool (hAPP (fun _let_2 _let_4) _let_4 (accp _let_2) posDivAlg_rel) (hAPP int _let_2 (hAPP int (fun int _let_2) _let_3 A_2) B_1)))) (and (or (and (not _let_5) (not _let_6)) (= _let_8 (hAPP int _let_2 (hAPP int (fun int _let_2) _let_3 _let_1) A_2))) (or _let_5 _let_6 (= _let_8 (hAPP _let_2 _let_2 (hAPP int (fun _let_2 _let_2) adjust B_1) (hAPP int _let_2 _let_7 (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) B_1)))))))))))))))) ) 16.26/16.35 ( (one_one int), (one_one int) ) 16.26/16.35 ( (one_one int), t ) 16.26/16.35 ( (zero_zero int), (one_one int) ) 16.26/16.35 ( pls, (one_one int) ) 16.26/16.35 ( pls, pls ) 16.26/16.35 ( pls, min_1 ) 16.26/16.35 ( pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.35 ( min_1, pls ) 16.26/16.35 ( min_1, min_1 ) 16.26/16.35 ( s, (one_one int) ) 16.26/16.35 ( s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.35 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.35 ( skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.35 ( skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.35 ) 16.26/16.35 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_148740 $$unsorted)) (let ((_let_0 (fun nat X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (one_one X_a))) (or (not (real_normed_field X_a)) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP X_a real (norm_norm X_a) BOUND_VARIABLE_148740)) (one_one real)))) (hBOOL (hAPP X_a bool (hAPP _let_0 (fun X_a bool) (sums X_a) (hAPP X_a _let_0 (power_power X_a) BOUND_VARIABLE_148740)) (hAPP X_a X_a (hAPP X_a _let_1 (inverse_divide X_a) _let_2) (hAPP X_a X_a (hAPP X_a _let_1 (minus_minus X_a) _let_2) BOUND_VARIABLE_148740)))))))) ) 16.26/16.35 ( int, s ) 16.26/16.35 ( int, s1 ) 16.26/16.35 ( int, skv_14 ) 16.26/16.35 ( real, (hAPP int real (number_number_of real) min_1) ) 16.26/16.35 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.35 ( complex, ii ) 16.26/16.35 ) 16.26/16.35 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_148800 $$unsorted) (BOUND_VARIABLE_148801 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)))) (let ((_let_1 (hBOOL (hAPP nat bool (even_odd_even nat) (hAPP int nat (number_number_of nat) BOUND_VARIABLE_148801))))) (or (not (linordered_idom X_a)) (= (hBOOL (hAPP X_a bool _let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_148800) (hAPP int nat (number_number_of nat) BOUND_VARIABLE_148801)))) (or (and (not _let_1) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_148800))) _let_1))))) ) 16.26/16.35 ( int, s, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.26/16.35 ( int, s1, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.26/16.35 ( int, skv_14, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.26/16.35 ( complex, ii, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.26/16.35 ) 16.26/16.35 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (power_power real))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (hAPP real real cos X_1))) (or (= (zero_zero real) _let_3) (= (hAPP nat real (hAPP real _let_0 _let_1 (hAPP real real (inverse_inverse real) _let_3)) _let_2) (hAPP real real (hAPP real (fun real real) (plus_plus real) (one_one real)) (hAPP nat real (hAPP real _let_0 _let_1 (hAPP real real tan X_1)) _let_2)))))))) ) 16.26/16.35 ( (zero_zero real) ) 16.26/16.35 ( pi ) 16.26/16.35 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.35 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.26/16.35 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.26/16.35 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.26/16.35 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 16.26/16.35 ) 16.26/16.35 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_148916 $$unsorted) (BOUND_VARIABLE_148917 $$unsorted)) (let ((_let_0 (uminus_uminus X_a))) (let ((_let_1 (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_148916))) (or (not (real_normed_algebra X_a)) (= (hAPP X_a X_a _let_0 (hAPP X_a X_a _let_1 BOUND_VARIABLE_148917)) (hAPP X_a X_a _let_1 (hAPP X_a X_a _let_0 BOUND_VARIABLE_148917)))))) ) 16.26/16.35 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 16.26/16.35 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 16.26/16.35 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13 ) 16.26/16.35 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.26/16.35 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 16.26/16.35 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 16.26/16.35 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 16.26/16.35 ( complex, ii, ii ) 16.26/16.35 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 16.26/16.35 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 16.26/16.35 ) 16.26/16.35 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (zero_zero real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 _let_2) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) (one_one real)))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real ln X_1)) _let_2)))))) ) 16.26/16.35 ( (one_one real) ) 16.26/16.35 ( pi ) 16.26/16.35 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.35 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.35 ( skv_2 ) 16.26/16.35 ( skv_8 ) 16.26/16.35 ( skv_9 ) 16.26/16.35 ) 16.26/16.35 (instantiation (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less nat))) (or (= X_1 Y_1) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 X_1) Y_1)) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 Y_1) X_1))))) ) 16.26/16.35 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.35 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 16.26/16.35 ) 16.26/16.35 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (Q_1 $$unsorted) (P_1 $$unsorted)) (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun X_a bool))) (let ((_let_2 (fun X_b bool))) (let ((_let_3 (fun X_b _let_1))) (let ((_let_4 (fun _let_1 _let_1))) (let ((_let_5 (fun X_a _let_0))) (or (not (hBOOL (hAPP _let_1 bool (finite_finite_1 X_a) (hAPP _let_1 _let_1 (collect X_a) P_1)))) (= (hBOOL (hAPP _let_2 bool (finite_finite_1 X_b) (hAPP _let_2 _let_2 (collect X_b) (hAPP _let_3 _let_2 (hAPP (fun _let_1 bool) (fun _let_3 _let_2) (combb _let_1 bool X_b) (fEx X_a)) (hAPP _let_3 _let_3 (hAPP _let_4 (fun _let_3 _let_3) (combb _let_1 _let_1 X_b) (hAPP _let_5 _let_4 (combs X_a bool bool) (hAPP _let_1 _let_5 (hAPP (fun bool _let_0) (fun _let_1 _let_5) (combb bool _let_0 X_a) fconj) P_1))) Q_1))))) (forall ((Y $$unsorted)) (or (not (hBOOL (hAPP X_a bool P_1 Y))) (hBOOL (hAPP _let_2 bool (finite_finite_1 X_b) (hAPP _let_2 _let_2 (collect X_b) (hAPP X_a _let_2 (hAPP _let_3 (fun X_a _let_2) (combc X_b X_a bool) Q_1) Y))))) ))))))))) ) 16.26/16.35 ( int, int, (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int _let_1))) (let ((_let_5 (fun _let_2 _let_1))) (hAPP int _let_1 (hAPP _let_4 _let_4 (combc int int _let_0) (hAPP _let_4 _let_4 (hAPP (fun _let_1 _let_1) (fun _let_4 _let_4) (combb _let_1 _let_1 int) (combc int int bool)) (hAPP _let_3 _let_4 (hAPP _let_5 (fun _let_3 _let_4) (combb _let_2 _let_1 int) (hAPP _let_1 _let_5 (combb int _let_0 int) (fequal int))) int_gcd))) (one_one int)))))))), (hAPP int (fun int bool) (ord_less int) (zero_zero int)) ) 16.26/16.36 ( (product_prod int int), (product_prod int int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun _let_2 (fun _let_2 bool)))) (let ((_let_4 (fun _let_2 _let_0))) (let ((_let_5 (fun _let_2 int))) (let ((_let_6 (fun _let_5 _let_4))) (let ((_let_7 (product_snd int int))) (let ((_let_8 (fun _let_2 _let_5))) (let ((_let_9 (fun _let_5 (fun _let_2 bool)))) (let ((_let_10 (fun _let_2 _let_9))) (let ((_let_11 (fun _let_2 _let_4))) (let ((_let_12 (fun _let_5 _let_5))) (let ((_let_13 (fun _let_2 _let_12))) (let ((_let_14 (fun _let_5 _let_8))) (let ((_let_15 (fun _let_2 _let_1))) (let ((_let_16 (hAPP _let_5 _let_15 (hAPP (fun int _let_1) (fun _let_5 _let_15) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (let ((_let_17 (fun int _let_5))) (hAPP _let_8 _let_3 (hAPP _let_10 (fun _let_8 _let_3) (combs _let_2 _let_5 (fun _let_2 bool)) (hAPP _let_11 _let_10 (hAPP (fun _let_4 _let_9) (fun _let_11 _let_10) (combb _let_4 _let_9 _let_2) (combs _let_2 int bool)) (hAPP _let_8 _let_11 (hAPP _let_6 (fun _let_8 _let_11) (combb _let_5 _let_4 _let_2) (hAPP (fun int _let_0) _let_6 (combb int _let_0 _let_2) (fequal int))) (hAPP _let_5 _let_8 (hAPP _let_13 _let_14 (combc _let_2 _let_5 _let_5) (hAPP _let_15 _let_13 (hAPP (fun _let_1 _let_12) (fun _let_15 _let_13) (combb _let_1 _let_12 _let_2) (combb int int _let_2)) _let_16)) _let_7)))) (hAPP _let_5 _let_8 (hAPP _let_17 _let_14 (combb int _let_5 _let_2) (hAPP _let_15 _let_17 (combc _let_2 int int) _let_16)) _let_7)))))))))))))))))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun _let_1 _let_0))) (let ((_let_4 (fun _let_1 int))) (hAPP _let_2 _let_2 (hAPP (fun bool bool) (fun _let_2 _let_2) (combb bool bool _let_1) fNot) (hAPP int _let_2 (hAPP _let_3 (fun int _let_2) (combc _let_1 int bool) (hAPP _let_4 _let_3 (hAPP (fun int _let_0) (fun _let_4 _let_3) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int)))))))) ) 16.26/16.36 ) 16.26/16.36 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (plus_plus X_a))) (or (not (cancel_semigroup_add X_a)) (= _let_0 (ti (fun X_a (fun X_a X_a)) _let_0)))) ) 16.26/16.36 ( bool ) 16.26/16.36 ( nat ) 16.26/16.36 ( int ) 16.26/16.36 ( (fun int bool) ) 16.26/16.36 ( (fun int (fun int bool)) ) 16.26/16.36 ( (fun int int) ) 16.26/16.36 ( (fun nat bool) ) 16.26/16.36 ( real ) 16.26/16.36 ( (fun real bool) ) 16.26/16.36 ( (fun real real) ) 16.26/16.36 ( rat ) 16.26/16.36 ( complex ) 16.26/16.36 ( (fun nat real) ) 16.26/16.36 ( (product_prod int int) ) 16.26/16.36 ( quickcheck_code_int ) 16.26/16.36 ( code_code_numeral ) 16.26/16.36 ( (fun int (fun int (fun int bool))) ) 16.26/16.36 ( (fun (product_prod int int) bool) ) 16.26/16.36 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 16.26/16.36 ( (fun (product_prod int int) int) ) 16.26/16.36 ( (fun int real) ) 16.26/16.36 ) 16.26/16.36 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_148964 $$unsorted) (BOUND_VARIABLE_148965 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member X_a))) (let ((_let_3 (ring_1_Ints X_a))) (or (not (ring_1 X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_148965) _let_3))) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_148964) _let_3))) (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) BOUND_VARIABLE_148965) BOUND_VARIABLE_148964)) _let_3))))))) ) 16.26/16.36 ( int, (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.36 ( real, (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))), (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))) ) 16.26/16.36 ( code_code_numeral, (one_one code_code_numeral), (zero_zero code_code_numeral) ) 16.26/16.36 ) 16.26/16.36 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_149046 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (ordere142940540dd_abs X_a)) (= (not (= _let_0 (ti X_a BOUND_VARIABLE_149046))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) _let_0) (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_149046)))))) ) 16.26/16.36 ( bool, fFalse ) 16.26/16.36 ( bool, fTrue ) 16.26/16.36 ( int, pls ) 16.26/16.36 ( int, min_1 ) 16.26/16.36 ( int, s ) 16.26/16.36 ( int, m ) 16.26/16.36 ( int, s1 ) 16.26/16.36 ( int, t ) 16.26/16.36 ( (fun int bool), nat_neg ) 16.26/16.36 ( (fun int bool), zprime ) 16.26/16.36 ( (fun int bool), zEven ) 16.26/16.36 ( (fun int bool), zOdd ) 16.26/16.36 ( (fun int bool), (even_odd_even int) ) 16.26/16.36 ( (fun int bool), twoSqu1091635170sum2sq ) 16.26/16.36 ( (fun int bool), nat_is_nat ) 16.26/16.36 ( (fun int (fun int bool)), norRRset ) 16.26/16.36 ( (fun int (fun int bool)), quadRes ) 16.26/16.36 ( (fun int (fun int bool)), sRStar ) 16.26/16.36 ( (fun int (fun int bool)), d22set ) 16.26/16.36 ( (fun int (fun int bool)), sr ) 16.26/16.36 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 16.26/16.36 ( (fun int int), zfact ) 16.26/16.36 ( (fun int int), bit0 ) 16.26/16.36 ( (fun int int), bit1 ) 16.26/16.36 ( (fun int int), (fact_fact int) ) 16.26/16.36 ( (fun int int), pred ) 16.26/16.36 ( (fun int int), succ ) 16.26/16.36 ( (fun nat bool), (even_odd_even nat) ) 16.26/16.36 ( (fun nat bool), prime ) 16.26/16.36 ( (fun nat nat), suc ) 16.26/16.36 ( (fun nat nat), (fact_fact nat) ) 16.26/16.36 ( (fun nat nat), fact ) 16.26/16.36 ( (fun nat nat), nat_size ) 16.26/16.36 ( (fun nat nat), (size_size nat) ) 16.26/16.36 ( (fun (product_prod nat nat) bool), pred_nat ) 16.26/16.36 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 16.26/16.36 ( real, pi ) 16.26/16.36 ( (fun real real), ln ) 16.26/16.36 ( (fun real real), cos ) 16.26/16.36 ( (fun real real), sqrt ) 16.26/16.36 ( (fun real real), sin ) 16.26/16.36 ( (fun real real), arccos ) 16.26/16.36 ( (fun real real), arcsin ) 16.26/16.36 ( (fun real real), tan ) 16.26/16.36 ( (fun real real), arctan ) 16.26/16.36 ( (fun nat (fun nat bool)), coprime ) 16.26/16.36 ( complex, ii ) 16.26/16.36 ( (fun nat real), (real_1 nat) ) 16.26/16.36 ( (fun nat real), sin_coeff ) 16.26/16.36 ( (fun nat real), cos_coeff ) 16.26/16.36 ( (filter nat), sequentially ) 16.26/16.36 ( (fun int (fun int int)), (gcd_gcd int) ) 16.26/16.36 ( (fun int (fun int int)), legendre ) 16.26/16.36 ( (fun int (fun int int)), legacy_zgcd ) 16.26/16.36 ( (fun int (fun int int)), standardRes ) 16.26/16.36 ( (fun int (fun int int)), nat_tsub ) 16.26/16.36 ( (fun int (fun int int)), multInv ) 16.26/16.36 ( (fun int (fun int int)), z3mod ) 16.26/16.36 ( (fun int (fun int int)), z3div ) 16.26/16.36 ( (fun int (fun int int)), int_gcd ) 16.26/16.36 ( (fun int (fun int int)), int_lcm ) 16.26/16.36 ( (fun int (fun int int)), inv ) 16.26/16.36 ( (fun complex complex), expi ) 16.26/16.36 ( (fun complex complex), cnj ) 16.26/16.36 ( (fun real complex), cis ) 16.26/16.36 ( (fun int nat), nat_1 ) 16.26/16.36 ( (fun int nat), phi ) 16.26/16.36 ( (fun (fun int bool) bool), nat_nat_set ) 16.26/16.36 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 16.26/16.36 ( (fun nat (fun nat nat)), nat_gcd ) 16.26/16.36 ( (fun nat (fun nat nat)), nat_lcm ) 16.26/16.36 ( (fun (fun int bool) int), (the int) ) 16.26/16.36 ( (fun complex real), re ) 16.26/16.36 ( (fun complex real), im ) 16.26/16.36 ( (fun complex real), arg ) 16.26/16.36 ( (fun bool bool), fNot ) 16.26/16.36 ( (fun nat (fun real real)), root ) 16.26/16.36 ( (fun real (fun real real)), log ) 16.26/16.36 ( (fun real (fun real real)), powr ) 16.26/16.36 ( (fun bool (fun bool bool)), fimplies ) 16.26/16.36 ( (fun bool (fun bool bool)), fconj ) 16.26/16.36 ( (fun bool (fun bool bool)), fdisj ) 16.26/16.36 ( (fun int (fun int (product_prod int int))), negDivAlg ) 16.26/16.36 ( (fun int (fun int (product_prod int int))), posDivAlg ) 16.26/16.36 ( (fun int (fun int (product_prod int int))), divmod_int ) 16.26/16.36 ( (fun int (fun int (product_prod int int))), pdivmod ) 16.26/16.36 ( (fun int (fun int (product_prod int int))), norm_frac ) 16.26/16.36 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 16.26/16.36 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 16.26/16.36 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 16.26/16.36 ( (fun int (fun int (fun int bool))), zcong ) 16.26/16.36 ( (fun int (fun int (fun int bool))), zcongm ) 16.26/16.36 ( (fun int (fun int (fun int bool))), noXRRset ) 16.26/16.36 ( (fun int (fun int (fun int bool))), bnorRset ) 16.26/16.36 ( (fun int (fun int (fun int bool))), wset ) 16.26/16.36 ( (fun (product_prod int int) bool), frac_1 ) 16.26/16.36 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 16.26/16.36 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 16.26/16.36 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 16.26/16.36 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 16.26/16.36 ( (fun (fun nat rat) bool), vanishes ) 16.26/16.36 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 16.26/16.36 ( (fun code_code_numeral nat), code_c271388182l_size ) 16.26/16.36 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 16.26/16.36 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 16.26/16.36 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 16.26/16.36 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 16.26/16.36 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 16.26/16.36 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 16.26/16.36 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 16.26/16.36 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 16.26/16.36 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 16.26/16.36 ( (fun complex nat), complex_size ) 16.26/16.36 ( (fun complex nat), (size_size complex) ) 16.26/16.36 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 16.26/16.36 ( (fun nat (fun nat (product_prod int int))), bezw ) 16.26/16.36 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 16.26/16.36 ( (fun int (fun nat nat)), nat_aux ) 16.26/16.36 ( (fun int (fun (fun int bool) bool)), rsetR ) 16.26/16.36 ( (fun int (fun (fun int bool) bool)), resSet ) 16.26/16.36 ( (fun int (list int)), quickc666637781d_zero ) 16.26/16.36 ( (fun (product_prod int int) rat), frct ) 16.26/16.36 ( (fun int (fun int rat)), fract ) 16.26/16.36 ( (fun real (fun real complex)), complex_1 ) 16.26/16.36 ( (fun real (fun real complex)), rcis ) 16.26/16.36 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 16.26/16.36 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 16.26/16.36 ( (fun int real), (real_1 int) ) 16.26/16.36 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 16.26/16.36 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 16.26/16.36 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 16.26/16.36 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 16.26/16.36 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 16.26/16.36 ( (fun real nat), natfloor ) 16.26/16.36 ( (fun real nat), natceiling ) 16.26/16.36 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 16.26/16.36 ( (fun quickcheck_code_int int), quickcheck_int_of ) 16.26/16.36 ( (fun rat (product_prod int int)), quotient_of ) 16.26/16.36 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 16.26/16.36 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 16.26/16.36 ( (fun rat real), ratreal ) 16.26/16.36 ( (fun code_code_numeral int), code_int_of ) 16.26/16.36 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 16.26/16.36 ( (fun int quickcheck_code_int), quickcheck_of_int ) 16.26/16.36 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 16.26/16.36 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 16.26/16.36 ) 16.26/16.36 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (power_1 X_a))) (= _let_0 (ti (fun X_a (fun (fun X_a (fun X_a X_a)) (fun X_a (fun nat X_a)))) _let_0))) ) 16.26/16.36 ( bool ) 16.26/16.36 ( nat ) 16.26/16.36 ( int ) 16.26/16.36 ( (fun int bool) ) 16.26/16.36 ( (fun int (fun int bool)) ) 16.26/16.36 ( (fun int int) ) 16.26/16.36 ( (fun nat bool) ) 16.26/16.36 ( (fun nat nat) ) 16.26/16.36 ( (product_prod nat nat) ) 16.26/16.36 ( (fun (product_prod nat nat) bool) ) 16.26/16.36 ( (fun nat (fun (product_prod nat nat) bool)) ) 16.26/16.36 ( real ) 16.26/16.36 ( (fun real bool) ) 16.26/16.36 ( (fun real real) ) 16.26/16.36 ( rat ) 16.26/16.36 ( (fun nat (fun nat bool)) ) 16.26/16.36 ( complex ) 16.26/16.36 ( (fun nat real) ) 16.26/16.36 ( (product_prod int int) ) 16.26/16.36 ( (fun bool bool) ) 16.26/16.36 ( code_code_numeral ) 16.26/16.36 ( (fun int (fun int (fun int bool))) ) 16.26/16.36 ( (product_prod real real) ) 16.26/16.36 ( (fun (product_prod int int) bool) ) 16.26/16.36 ( (fun nat (product_prod nat nat)) ) 16.26/16.36 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 16.26/16.36 ( (fun (product_prod int int) int) ) 16.26/16.36 ( (fun nat (product_prod int int)) ) 16.26/16.36 ( (fun int real) ) 16.26/16.36 ) 16.26/16.36 (instantiation (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_0 (hAPP int (fun int bool) (ord_less int) (zero_zero int)))) (or (not (hBOOL (hAPP int bool _let_0 A_1))) (not (hBOOL (hAPP int bool _let_0 (hAPP int int (hAPP int (fun int int) (times_times int) A_1) B)))) (hBOOL (hAPP int bool _let_0 B)))) ) 16.26/16.36 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.36 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.36 ( skv_13, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.36 ) 16.26/16.36 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (hAPP nat _let_0 (gcd_gcd nat) M))) (= (hAPP nat nat _let_1 (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) M) N_1)) (hAPP nat nat _let_1 N_1)))) ) 16.26/16.36 ( (one_one nat), (one_one nat) ) 16.26/16.36 ) 16.26/16.36 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted) (Z $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP real _let_0 (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (let ((_let_2 (hAPP real _let_0 (inverse_divide real) Y_2))) (= (= (hAPP real real _let_2 Z) (hAPP real real _let_1 X_2)) (= X_2 (hAPP real real _let_2 (hAPP real real _let_1 Z))))))) ) 16.26/16.36 ( pi, pi, pi ) 16.26/16.36 ( (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 16.26/16.36 ) 16.26/16.36 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_149187 $$unsorted) (BOUND_VARIABLE_149195 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (inverse_divide X_a))) (let ((_let_2 (zero_zero X_a))) (or (not (divisi14063676e_zero X_a)) (and (or (not (= _let_2 (ti X_a BOUND_VARIABLE_149187))) (= _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_149187) BOUND_VARIABLE_149187))) (or (= _let_2 (ti X_a BOUND_VARIABLE_149195)) (= (one_one X_a) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_149195) BOUND_VARIABLE_149195)))))))) ) 16.26/16.36 ( bool, fFalse, fFalse ) 16.26/16.36 ( bool, fTrue, fTrue ) 16.26/16.36 ( int, pls, pls ) 16.26/16.36 ( int, min_1, min_1 ) 16.26/16.36 ( int, s, s ) 16.26/16.36 ( int, m, m ) 16.26/16.36 ( int, s1, s1 ) 16.26/16.36 ( int, t, t ) 16.26/16.36 ( (fun int bool), nat_neg, nat_neg ) 16.26/16.36 ( (fun int bool), zprime, zprime ) 16.26/16.36 ( (fun int bool), zEven, zEven ) 16.26/16.36 ( (fun int bool), zOdd, zOdd ) 16.26/16.36 ( (fun int bool), (even_odd_even int), (even_odd_even int) ) 16.26/16.36 ( (fun int bool), twoSqu1091635170sum2sq, twoSqu1091635170sum2sq ) 16.26/16.36 ( (fun int bool), nat_is_nat, nat_is_nat ) 16.26/16.36 ( (fun int (fun int bool)), norRRset, norRRset ) 16.26/16.36 ( (fun int (fun int bool)), quadRes, quadRes ) 16.26/16.36 ( (fun int (fun int bool)), sRStar, sRStar ) 16.26/16.36 ( (fun int (fun int bool)), d22set, d22set ) 16.26/16.36 ( (fun int (fun int bool)), sr, sr ) 16.26/16.36 ( (fun int (fun int bool)), quickc1265749348ro_rel, quickc1265749348ro_rel ) 16.26/16.36 ( (fun int int), zfact, zfact ) 16.26/16.36 ( (fun int int), bit0, bit0 ) 16.26/16.36 ( (fun int int), bit1, bit1 ) 16.26/16.36 ( (fun int int), (fact_fact int), (fact_fact int) ) 16.26/16.36 ( (fun int int), pred, pred ) 16.26/16.36 ( (fun int int), succ, succ ) 16.26/16.36 ( (fun nat bool), (even_odd_even nat), (even_odd_even nat) ) 16.26/16.36 ( (fun nat bool), prime, prime ) 16.26/16.36 ( (fun nat nat), suc, suc ) 16.26/16.36 ( (fun nat nat), (fact_fact nat), (fact_fact nat) ) 16.26/16.36 ( (fun nat nat), fact, fact ) 16.26/16.36 ( (fun nat nat), nat_size, nat_size ) 16.26/16.36 ( (fun nat nat), (size_size nat), (size_size nat) ) 16.26/16.36 ( (fun (product_prod nat nat) bool), pred_nat, pred_nat ) 16.26/16.36 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel, divmod_nat_rel ) 16.26/16.36 ( real, pi, pi ) 16.26/16.36 ( (fun real real), ln, ln ) 16.26/16.36 ( (fun real real), cos, cos ) 16.26/16.36 ( (fun real real), sqrt, sqrt ) 16.26/16.36 ( (fun real real), sin, sin ) 16.26/16.36 ( (fun real real), arccos, arccos ) 16.26/16.36 ( (fun real real), arcsin, arcsin ) 16.26/16.36 ( (fun real real), tan, tan ) 16.26/16.36 ( (fun real real), arctan, arctan ) 16.26/16.36 ( (fun nat (fun nat bool)), coprime, coprime ) 16.26/16.36 ( complex, ii, ii ) 16.26/16.36 ( (fun nat real), (real_1 nat), (real_1 nat) ) 16.26/16.36 ( (fun nat real), sin_coeff, sin_coeff ) 16.26/16.36 ( (fun nat real), cos_coeff, cos_coeff ) 16.26/16.36 ( (filter nat), sequentially, sequentially ) 16.26/16.36 ( (fun int (fun int int)), (gcd_gcd int), (gcd_gcd int) ) 16.26/16.36 ( (fun int (fun int int)), legendre, legendre ) 16.26/16.36 ( (fun int (fun int int)), legacy_zgcd, legacy_zgcd ) 16.26/16.36 ( (fun int (fun int int)), standardRes, standardRes ) 16.26/16.36 ( (fun int (fun int int)), nat_tsub, nat_tsub ) 16.26/16.36 ( (fun int (fun int int)), multInv, multInv ) 16.26/16.36 ( (fun int (fun int int)), z3mod, z3mod ) 16.26/16.36 ( (fun int (fun int int)), z3div, z3div ) 16.26/16.36 ( (fun int (fun int int)), int_gcd, int_gcd ) 16.26/16.36 ( (fun int (fun int int)), int_lcm, int_lcm ) 16.26/16.36 ( (fun int (fun int int)), inv, inv ) 16.26/16.36 ( (fun complex complex), expi, expi ) 16.26/16.36 ( (fun complex complex), cnj, cnj ) 16.26/16.36 ( (fun real complex), cis, cis ) 16.26/16.36 ( (fun int nat), nat_1, nat_1 ) 16.26/16.36 ( (fun int nat), phi, phi ) 16.26/16.36 ( (fun (fun int bool) bool), nat_nat_set, nat_nat_set ) 16.26/16.36 ( (fun nat (fun nat nat)), (gcd_gcd nat), (gcd_gcd nat) ) 16.26/16.36 ( (fun nat (fun nat nat)), nat_gcd, nat_gcd ) 16.26/16.36 ( (fun nat (fun nat nat)), nat_lcm, nat_lcm ) 16.26/16.36 ( (fun (fun int bool) int), (the int), (the int) ) 16.26/16.36 ( (fun complex real), re, re ) 16.26/16.36 ( (fun complex real), im, im ) 16.26/16.36 ( (fun complex real), arg, arg ) 16.26/16.36 ( (fun bool bool), fNot, fNot ) 16.26/16.36 ( (fun nat (fun real real)), root, root ) 16.26/16.36 ( (fun real (fun real real)), log, log ) 16.26/16.36 ( (fun real (fun real real)), powr, powr ) 16.26/16.36 ( (fun bool (fun bool bool)), fimplies, fimplies ) 16.26/16.36 ( (fun bool (fun bool bool)), fconj, fconj ) 16.26/16.36 ( (fun bool (fun bool bool)), fdisj, fdisj ) 16.26/16.36 ( (fun int (fun int (product_prod int int))), negDivAlg, negDivAlg ) 16.26/16.36 ( (fun int (fun int (product_prod int int))), posDivAlg, posDivAlg ) 16.26/16.36 ( (fun int (fun int (product_prod int int))), divmod_int, divmod_int ) 16.26/16.36 ( (fun int (fun int (product_prod int int))), pdivmod, pdivmod ) 16.26/16.36 ( (fun int (fun int (product_prod int int))), norm_frac, norm_frac ) 16.26/16.36 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd, negateSnd ) 16.26/16.36 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize, normalize ) 16.26/16.36 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust, adjust ) 16.26/16.36 ( (fun int (fun int (fun int bool))), zcong, zcong ) 16.26/16.36 ( (fun int (fun int (fun int bool))), zcongm, zcongm ) 16.26/16.36 ( (fun int (fun int (fun int bool))), noXRRset, noXRRset ) 16.26/16.36 ( (fun int (fun int (fun int bool))), bnorRset, bnorRset ) 16.26/16.36 ( (fun int (fun int (fun int bool))), wset, wset ) 16.26/16.36 ( (fun (product_prod int int) bool), frac_1, frac_1 ) 16.26/16.36 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than, int_ge_less_than ) 16.26/16.36 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2, int_ge_less_than2 ) 16.26/16.36 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral, code_S1047413653umeral ) 16.26/16.36 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset, is_RRset ) 16.26/16.36 ( (fun (fun nat rat) bool), vanishes, vanishes ) 16.26/16.36 ( (fun code_code_numeral nat), (size_size code_code_numeral), (size_size code_code_numeral) ) 16.26/16.36 ( (fun code_code_numeral nat), code_c271388182l_size, code_c271388182l_size ) 16.26/16.36 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel, ratrel ) 16.26/16.36 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel, norm_frac_rel ) 16.26/16.36 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel, posDivAlg_rel ) 16.26/16.36 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel, lazy_small_lazy_rel ) 16.26/16.36 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel, negDivAlg_rel ) 16.26/16.36 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel, upto_rel ) 16.26/16.36 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq, twoSqu1094008024sum2sq ) 16.26/16.36 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less, pair_less ) 16.26/16.36 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq, pair_leq ) 16.26/16.36 ( (fun complex nat), complex_size, complex_size ) 16.26/16.36 ( (fun complex nat), (size_size complex), (size_size complex) ) 16.26/16.36 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel, nat_gcd_rel ) 16.26/16.36 ( (fun nat (fun nat (product_prod int int))), bezw, bezw ) 16.26/16.36 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd, xzgcd ) 16.26/16.36 ( (fun int (fun nat nat)), nat_aux, nat_aux ) 16.26/16.36 ( (fun int (fun (fun int bool) bool)), rsetR, rsetR ) 16.26/16.36 ( (fun int (fun (fun int bool) bool)), resSet, resSet ) 16.26/16.36 ( (fun int (list int)), quickc666637781d_zero, quickc666637781d_zero ) 16.26/16.36 ( (fun (product_prod int int) rat), frct, frct ) 16.26/16.36 ( (fun int (fun int rat)), fract, fract ) 16.26/16.36 ( (fun real (fun real complex)), complex_1, complex_1 ) 16.26/16.36 ( (fun real (fun real complex)), rcis, rcis ) 16.26/16.36 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat), (ord_gr676655987ssThan nat) ) 16.26/16.36 ( (fun quickcheck_code_int nat), quickcheck_nat_of, quickcheck_nat_of ) 16.26/16.36 ( (fun int real), (real_1 int), (real_1 int) ) 16.26/16.36 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect, bolzano_bisect ) 16.26/16.36 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR, rRset2norRR ) 16.26/16.36 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int, quickc495462417de_int ) 16.26/16.36 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda, xzgcda ) 16.26/16.36 ( (fun int (fun int (fun int (fun int bool)))), multInvPair, multInvPair ) 16.26/16.36 ( (fun real nat), natfloor, natfloor ) 16.26/16.36 ( (fun real nat), natceiling, natceiling ) 16.26/16.36 ( (fun (fun real bool) real), (complete_Sup_Sup real), (complete_Sup_Sup real) ) 16.26/16.36 ( (fun quickcheck_code_int int), quickcheck_int_of, quickcheck_int_of ) 16.26/16.36 ( (fun rat (product_prod int int)), quotient_of, quotient_of ) 16.26/16.36 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral, code_d418564891umeral ) 16.26/16.36 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat, divmod_nat ) 16.26/16.36 ( (fun rat real), ratreal, ratreal ) 16.26/16.36 ( (fun code_code_numeral int), code_int_of, code_int_of ) 16.26/16.36 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel, divmod_int_rel ) 16.26/16.36 ( (fun int quickcheck_code_int), quickcheck_of_int, quickcheck_of_int ) 16.26/16.36 ( (fun int (fun int (fun (fun int bool) bool))), setS, setS ) 16.26/16.36 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux, code_nat_of_aux ) 16.26/16.36 ) 16.26/16.36 (instantiation (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)))) (or (not (hBOOL (hAPP int bool _let_0 X_1))) (not (hBOOL (hAPP int bool _let_0 Y_1))) (hBOOL (hAPP int bool _let_0 (hAPP int int (hAPP int (fun int int) (times_times int) X_1) Y_1))))) ) 16.26/16.36 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.36 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.36 ( skv_13, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.36 ) 16.26/16.36 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (zero_zero real))) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) _let_0) X_1))) (not (= _let_0 (hAPP real real cos X_1))) (not (forall ((N_2 $$unsorted)) (let ((_let_0 (fun real real))) (or (hBOOL (hAPP nat bool (even_odd_even nat) N_2)) (not (= X_1 (hAPP real real (hAPP real _let_0 (times_times real) (hAPP nat real (real_1 nat) N_2)) (hAPP real real (hAPP real _let_0 (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))))) )))) ) 16.26/16.36 ( (zero_zero real) ) 16.26/16.36 ( pi ) 16.26/16.36 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.36 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.36 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.26/16.36 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.26/16.36 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.36 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.26/16.36 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 16.26/16.36 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 16.26/16.36 ( skv_3 ) 16.26/16.36 ( skv_5 ) 16.26/16.36 ( skv_7 ) 16.26/16.36 ( skv_12 ) 16.26/16.36 ) 16.26/16.36 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (uminus T_1)) (uminus (fun T_2 T_1))) ) 16.26/16.36 ( bool, bool ) 16.26/16.36 ( bool, (fun bool bool) ) 16.26/16.36 ( nat, bool ) 16.26/16.36 ( nat, nat ) 16.26/16.36 ( nat, int ) 16.26/16.36 ( nat, (fun int int) ) 16.26/16.36 ( nat, (fun nat bool) ) 16.26/16.36 ( nat, (fun nat nat) ) 16.26/16.36 ( nat, (product_prod nat nat) ) 16.26/16.36 ( nat, (fun (product_prod nat nat) bool) ) 16.26/16.36 ( nat, (fun nat (fun (product_prod nat nat) bool)) ) 16.26/16.36 ( nat, real ) 16.26/16.36 ( nat, (fun real real) ) 16.26/16.36 ( nat, rat ) 16.26/16.36 ( nat, (fun nat (fun nat bool)) ) 16.26/16.36 ( nat, complex ) 16.26/16.36 ( nat, (product_prod int int) ) 16.26/16.36 ( nat, (fun bool bool) ) 16.26/16.36 ( nat, (product_prod real real) ) 16.26/16.36 ( nat, (fun nat (product_prod nat nat)) ) 16.26/16.36 ( nat, (fun nat (product_prod int int)) ) 16.26/16.36 ( int, bool ) 16.26/16.36 ( int, nat ) 16.26/16.36 ( int, int ) 16.26/16.36 ( int, (fun int bool) ) 16.26/16.36 ( int, (fun int (fun int bool)) ) 16.26/16.36 ( int, (fun int int) ) 16.26/16.36 ( int, (fun nat bool) ) 16.26/16.36 ( int, (fun nat nat) ) 16.26/16.36 ( int, real ) 16.26/16.36 ( int, (fun real real) ) 16.26/16.36 ( int, rat ) 16.26/16.36 ( int, (fun int rat) ) 16.26/16.36 ( int, (fun nat int) ) 16.26/16.36 ( int, (fun nat real) ) 16.26/16.36 ( int, (product_prod int int) ) 16.26/16.36 ( int, (fun int (product_prod int int)) ) 16.26/16.36 ( int, (fun (fun int bool) bool) ) 16.26/16.36 ( int, quickcheck_code_int ) 16.26/16.36 ( int, (fun bool bool) ) 16.26/16.36 ( int, (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 16.26/16.36 ( int, (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)) ) 16.26/16.36 ( int, (fun int (fun int (fun int bool))) ) 16.26/16.36 ( int, (fun (product_prod int int) bool) ) 16.26/16.36 ( int, (fun int (fun (product_prod int int) bool)) ) 16.26/16.36 ( int, (fun int (fun bool bool)) ) 16.26/16.36 ( int, (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 16.26/16.36 ( int, (fun (fun int int) (fun int bool)) ) 16.26/16.36 ( int, (fun (product_prod int int) int) ) 16.26/16.36 ( int, (product_prod int (product_prod int int)) ) 16.26/16.36 ( int, (fun int (product_prod int (product_prod int int))) ) 16.26/16.36 ( int, (fun int (fun int (product_prod int (product_prod int int)))) ) 16.26/16.36 ( int, (fun int (fun int (fun int (product_prod int (product_prod int int))))) ) 16.26/16.36 ( int, (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))) ) 16.26/16.36 ( int, (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))) ) 16.26/16.36 ( int, (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))) ) 16.26/16.36 ( int, (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))))) ) 16.26/16.36 ( int, (fun int (fun (fun int bool) bool)) ) 16.26/16.36 ( int, (list int) ) 16.26/16.36 ( int, (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 16.26/16.36 ( int, (fun int real) ) 16.26/16.36 ( int, (fun nat (fun bool bool)) ) 16.26/16.36 ( int, (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 16.26/16.36 ( int, (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 16.26/16.36 ( (fun int bool), bool ) 16.26/16.36 ( (fun int bool), int ) 16.26/16.36 ( (fun int bool), (fun int bool) ) 16.26/16.36 ( (fun int bool), (fun int (fun int bool)) ) 16.26/16.36 ( (fun int bool), (fun int (fun int int)) ) 16.26/16.36 ( (fun int bool), (fun int (fun bool bool)) ) 16.26/16.36 ( (fun int bool), (fun (fun int int) (fun int bool)) ) 16.26/16.36 ( (fun int bool), (fun real (fun int (fun int bool))) ) 16.26/16.36 ( (fun int (fun int bool)), (fun int bool) ) 16.26/16.36 ( (fun int (fun int bool)), (fun int (fun int bool)) ) 16.26/16.36 ( (fun int (fun int bool)), (fun int (fun (fun int int) (fun int bool))) ) 16.26/16.36 ( (fun int (fun int bool)), (fun int (fun int (fun bool bool))) ) 16.26/16.36 ( (fun int int), (fun int bool) ) 16.26/16.36 ( (fun int int), (fun int (fun int bool)) ) 16.26/16.36 ( (fun int int), (fun int int) ) 16.26/16.36 ( (fun int int), (fun int (fun int int)) ) 16.26/16.36 ( (fun int int), (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 16.26/16.36 ( (fun int int), (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 16.26/16.36 ( (fun nat bool), bool ) 16.26/16.36 ( (fun nat bool), (fun nat bool) ) 16.26/16.36 ( (fun nat bool), (fun nat (fun bool bool)) ) 16.26/16.36 ( (fun nat bool), (fun int (fun nat bool)) ) 16.26/16.36 ( (fun nat bool), (fun real (fun int (fun nat bool))) ) 16.26/16.36 ( (fun nat nat), (fun nat (fun nat bool)) ) 16.26/16.36 ( (fun nat nat), (fun nat real) ) 16.26/16.36 ( (fun nat nat), (fun nat (fun nat nat)) ) 16.26/16.36 ( (product_prod nat nat), bool ) 16.26/16.36 ( (product_prod nat nat), (fun (product_prod nat nat) bool) ) 16.26/16.36 ( real, bool ) 16.26/16.36 ( real, nat ) 16.26/16.36 ( real, (fun int bool) ) 16.26/16.36 ( real, (fun int (fun int bool)) ) 16.26/16.36 ( real, real ) 16.26/16.36 ( real, (fun real bool) ) 16.26/16.36 ( real, (fun real real) ) 16.26/16.36 ( real, complex ) 16.26/16.36 ( real, (fun nat real) ) 16.26/16.36 ( real, (fun real complex) ) 16.26/16.36 ( real, (fun bool bool) ) 16.26/16.36 ( real, (fun (filter nat) bool) ) 16.26/16.36 ( real, (fun nat (product_prod real real)) ) 16.26/16.36 ( real, (fun real (fun nat (product_prod real real))) ) 16.26/16.36 ( real, (fun (filter real) bool) ) 16.26/16.36 ( real, (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 16.26/16.36 ( real, (let ((_let_0 (fun int bool))) (fun _let_0 (fun int _let_0))) ) 16.26/16.36 ( real, (fun int (fun int (fun bool bool))) ) 16.26/16.36 ( real, (fun (fun int (fun int real)) (fun int (fun int bool))) ) 16.26/16.36 ( real, (fun (fun int real) (fun int bool)) ) 16.26/16.36 ( real, (fun int (fun nat bool)) ) 16.26/16.36 ( real, (let ((_let_0 (fun nat bool))) (fun _let_0 (fun int _let_0))) ) 16.26/16.36 ( real, (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 16.26/16.36 ( real, (fun int (fun nat (fun bool bool))) ) 16.26/16.36 ( real, (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 16.26/16.36 ( real, (fun (fun nat real) (fun nat bool)) ) 16.26/16.36 ( (fun real bool), real ) 16.26/16.36 ( (fun real bool), (fun real bool) ) 16.26/16.36 ( (fun real bool), (fun real (fun bool bool)) ) 16.26/16.36 ( (fun real bool), (fun (fun int real) (fun int bool)) ) 16.26/16.36 ( (fun real bool), (fun (fun nat real) (fun nat bool)) ) 16.26/16.36 ( (fun real real), (fun real real) ) 16.26/16.36 ( (fun real real), (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 16.26/16.36 ( (fun real real), (fun real (fun real real)) ) 16.26/16.36 ( (fun real real), (fun real (fun real bool)) ) 16.26/16.36 ( (fun real real), (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 16.26/16.36 ( rat, real ) 16.26/16.36 ( rat, (product_prod int int) ) 16.26/16.36 ( complex, nat ) 16.26/16.36 ( complex, real ) 16.26/16.36 ( complex, complex ) 16.26/16.36 ( (fun nat real), (fun nat bool) ) 16.26/16.36 ( (fun nat real), (fun nat real) ) 16.26/16.36 ( (fun nat real), (fun nat (fun real real)) ) 16.26/16.36 ( (fun nat real), (fun int (fun nat real)) ) 16.26/16.36 ( (filter nat), bool ) 16.26/16.36 ( (fun int (fun int int)), (fun int (fun int (fun int bool))) ) 16.26/16.36 ( (fun int (fun int int)), (let ((_let_0 (fun int int))) (fun int (fun _let_0 _let_0))) ) 16.26/16.36 ( (product_prod int int), bool ) 16.26/16.36 ( (product_prod int int), int ) 16.26/16.36 ( (product_prod int int), (fun int bool) ) 16.26/16.36 ( (product_prod int int), (fun int int) ) 16.26/16.36 ( (product_prod int int), rat ) 16.26/16.36 ( (product_prod int int), (product_prod int int) ) 16.26/16.36 ( (product_prod int int), (fun bool bool) ) 16.26/16.36 ( (product_prod int int), (fun (product_prod int int) bool) ) 16.26/16.36 ( (product_prod int int), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 16.26/16.36 ( (product_prod int int), (fun (product_prod int int) (fun int bool)) ) 16.26/16.36 ( (product_prod int int), (fun (product_prod int int) int) ) 16.26/16.36 ( (product_prod int int), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 16.26/16.36 ( (product_prod int int), (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 16.26/16.36 ( quickcheck_code_int, nat ) 16.26/16.36 ( quickcheck_code_int, int ) 16.26/16.36 ( quickcheck_code_int, (product_prod quickcheck_code_int quickcheck_code_int) ) 16.26/16.36 ( quickcheck_code_int, (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int)) ) 16.26/16.36 ( (fun bool bool), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 16.26/16.36 ( code_code_numeral, nat ) 16.26/16.36 ( code_code_numeral, int ) 16.26/16.36 ( code_code_numeral, (fun nat nat) ) 16.26/16.36 ( code_code_numeral, code_code_numeral ) 16.26/16.36 ( code_code_numeral, (product_prod code_code_numeral code_code_numeral) ) 16.26/16.36 ( code_code_numeral, (fun code_code_numeral (product_prod code_code_numeral code_code_numeral)) ) 16.26/16.36 ( (fun int (fun int (fun int bool))), (fun int (fun int (fun int bool))) ) 16.26/16.36 ( (fun real (fun real bool)), (fun real (fun (fun int real) (fun int bool))) ) 16.26/16.36 ( (fun real (fun real bool)), (fun real (fun (fun nat real) (fun nat bool))) ) 16.26/16.36 ( (product_prod real real), bool ) 16.26/16.36 ( (fun (product_prod real real) bool), (fun real (fun real (fun nat (product_prod real real)))) ) 16.26/16.36 ( (fun (product_prod int int) bool), (fun (product_prod int int) bool) ) 16.26/16.36 ( (fun (product_prod int int) bool), (fun (product_prod int int) (fun bool bool)) ) 16.26/16.36 ( (fun int (fun bool bool)), (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 16.26/16.36 ( (fun nat rat), bool ) 16.26/16.36 ( (filter real), bool ) 16.26/16.36 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)), bool ) 16.26/16.36 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 16.26/16.36 ( (fun (product_prod int int) (fun bool bool)), (let ((_let_0 (fun (product_prod int int) bool))) (fun (product_prod int int) (fun _let_0 _let_0))) ) 16.26/16.36 ( (fun (product_prod int int) (fun int bool)), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 16.26/16.36 ( (fun (product_prod int int) int), (fun (product_prod int int) bool) ) 16.26/16.36 ( (fun (product_prod int int) int), (fun (product_prod int int) (fun int bool)) ) 16.26/16.36 ( (fun (product_prod int int) int), (fun (product_prod int int) int) ) 16.26/16.36 ( (fun (product_prod int int) int), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))) ) 16.26/16.36 ( (fun (product_prod int int) int), (fun (product_prod int int) (fun int int)) ) 16.26/16.36 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 16.26/16.36 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 (fun int bool)))) ) 16.26/16.36 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 (fun int bool)))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun (fun _let_0 int) (fun _let_0 bool)))) ) 16.26/16.36 ( (fun (product_prod int int) (fun int int)), (let ((_let_0 (fun (product_prod int int) int))) (fun (product_prod int int) (fun _let_0 _let_0))) ) 16.26/16.36 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), bool ) 16.26/16.36 ( (fun int real), (fun int bool) ) 16.26/16.36 ( (fun int real), (fun int real) ) 16.26/16.36 ( (fun int real), (fun int (fun int real)) ) 16.26/16.36 ( (fun int real), (fun int (fun real real)) ) 16.26/16.36 ( (fun nat (fun bool bool)), (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 16.26/16.36 ( (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun int bool))) (fun _let_0 (fun int _let_0))) ) 16.26/16.36 ( (fun int (fun int (fun bool bool))), (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 16.26/16.36 ( (fun real (fun int bool)), (fun real bool) ) 16.26/16.36 ( (fun real (fun int (fun int bool))), (fun real (fun int bool)) ) 16.26/16.36 ( (fun real (fun int (fun int bool))), (fun real (fun int (fun int (fun bool bool)))) ) 16.26/16.36 ( (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun int bool))) (fun real (fun _let_0 (fun int _let_0)))) ) 16.26/16.36 ( (fun real (fun int (fun int (fun bool bool)))), (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))) ) 16.26/16.36 ( (fun int (fun int real)), (fun int (fun int bool)) ) 16.26/16.36 ( (fun int (fun int real)), (fun real (fun int (fun int bool))) ) 16.26/16.36 ( (fun (fun int real) (fun int bool)), (fun (fun int (fun int real)) (fun int (fun int bool))) ) 16.26/16.36 ( (fun real (fun (fun int real) (fun int bool))), (fun real (fun (fun int (fun int real)) (fun int (fun int bool)))) ) 16.26/16.36 ( (fun int (fun real real)), (let ((_let_0 (fun int real))) (fun int (fun _let_0 _let_0))) ) 16.26/16.36 ( (fun int (fun real real)), (let ((_let_0 (fun nat real))) (fun int (fun _let_0 _let_0))) ) 16.26/16.36 ( (fun int (fun nat bool)), (fun int bool) ) 16.26/16.36 ( (fun int (fun nat bool)), (fun int (fun nat (fun bool bool))) ) 16.26/16.36 ( (fun real (fun int (fun nat bool))), (fun real (fun int bool)) ) 16.26/16.36 ( (fun real (fun int (fun nat bool))), (fun real (fun int (fun nat (fun bool bool)))) ) 16.26/16.36 ( (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun nat bool))) (fun _let_0 (fun int _let_0))) ) 16.26/16.36 ( (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun nat bool))) (fun real (fun _let_0 (fun int _let_0)))) ) 16.26/16.36 ( (fun int (fun nat (fun bool bool))), (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 16.26/16.36 ( (fun real (fun int (fun nat (fun bool bool)))), (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))) ) 16.26/16.36 ( (fun int (fun nat real)), (fun int (fun nat bool)) ) 16.26/16.36 ( (fun int (fun nat real)), (fun real (fun int (fun nat bool))) ) 16.26/16.36 ( (fun (fun nat real) (fun nat bool)), (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 16.26/16.36 ( (fun real (fun (fun nat real) (fun nat bool))), (fun real (fun (fun int (fun nat real)) (fun int (fun nat bool)))) ) 16.26/16.36 ) 16.26/16.36 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (archim2085082626_floor X_a))) (or (not (archim1727834104eiling X_a)) (= _let_0 (ti (fun X_a int) _let_0)))) ) 16.26/16.36 ( nat ) 16.26/16.36 ( int ) 16.26/16.36 ( (fun int bool) ) 16.26/16.36 ( real ) 16.26/16.36 ( rat ) 16.26/16.36 ( (product_prod int int) ) 16.26/16.36 ( quickcheck_code_int ) 16.26/16.36 ( code_code_numeral ) 16.26/16.36 ) 16.26/16.36 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_149342 $$unsorted) (BOUND_VARIABLE_149343 $$unsorted)) (or (not (order X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_149342) BOUND_VARIABLE_149343))) (not (= (ti X_a BOUND_VARIABLE_149342) (ti X_a BOUND_VARIABLE_149343)))) ) 16.26/16.36 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.36 ( int, (one_one int), t ) 16.26/16.36 ( int, pls, (one_one int) ) 16.26/16.36 ( int, pls, pls ) 16.26/16.36 ( int, pls, min_1 ) 16.26/16.36 ( int, pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.36 ( int, min_1, pls ) 16.26/16.36 ( int, min_1, min_1 ) 16.26/16.36 ( int, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.36 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.36 ( int, skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.36 ( int, skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.36 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.36 ( real, (zero_zero real), pi ) 16.26/16.36 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.36 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.36 ( real, (zero_zero real), skv_2 ) 16.26/16.36 ( real, (zero_zero real), skv_8 ) 16.26/16.36 ( real, (zero_zero real), skv_9 ) 16.26/16.36 ( real, pi, (zero_zero real) ) 16.26/16.36 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.36 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.36 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 16.26/16.36 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.26/16.36 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 16.26/16.36 ) 16.26/16.36 (instantiation (forall ((Z_1 $$unsorted)) (let ((_let_0 (norm_norm complex))) (= (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP complex real _let_0 Z_1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP complex real _let_0 (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) Z_1) (hAPP complex complex cnj Z_1))))) ) 16.26/16.36 ( (one_one complex) ) 16.26/16.36 ( ii ) 16.26/16.36 ( (zero_zero complex) ) 16.26/16.36 ( (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.36 ( (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 16.26/16.36 ) 16.26/16.36 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_149462 $$unsorted) (BOUND_VARIABLE_149463 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (times_times X_a))) (or (not (comm_semiring_1 X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_149463) BOUND_VARIABLE_149462) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_149462) BOUND_VARIABLE_149463))))) ) 16.26/16.36 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 16.26/16.36 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.36 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 16.26/16.36 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13 ) 16.26/16.36 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.36 ( int, skv_13, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.36 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.36 ( real, pi, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 16.26/16.36 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.26/16.36 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 16.26/16.36 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 16.26/16.36 ( real, (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.36 ( real, (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.36 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 16.26/16.36 ( complex, ii, ii ) 16.26/16.36 ( complex, ii, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 16.26/16.36 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 16.26/16.36 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.36 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 16.26/16.36 ) 16.26/16.36 (instantiation (forall ((P_4 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (hAPP int int (hAPP int (fun int int) (minus_minus int) P_4) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (or (not (hBOOL (hAPP int bool zprime P_4))) (= (hAPP int _let_0 (hAPP int (fun int _let_0) wset _let_1) P_4) (hAPP int _let_0 d22set _let_1))))) ) 16.26/16.36 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.36 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.36 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.36 ) 16.26/16.36 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_149530 $$unsorted) (BOUND_VARIABLE_149531 $$unsorted) (BOUND_VARIABLE_149532 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (fun X_a X_a))) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_149532) (zero_zero X_a)))) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_2 (times_times X_a) BOUND_VARIABLE_149531) BOUND_VARIABLE_149532)) BOUND_VARIABLE_149530)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_2 (inverse_divide X_a) BOUND_VARIABLE_149530) BOUND_VARIABLE_149532)) BOUND_VARIABLE_149531))))))) ) 16.26/16.36 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.36 ) 16.26/16.36 (instantiation (forall ((L_4 $$unsorted)) (let ((_let_0 (hAPP int (fun int int) (minus_minus int) min_1))) (= (hAPP int int bit0 (hAPP int int _let_0 L_4)) (hAPP int int _let_0 (hAPP int int bit1 L_4)))) ) 16.26/16.36 ( pls ) 16.26/16.36 ( (hAPP int int bit1 pls) ) 16.26/16.36 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.26/16.36 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.26/16.36 ( min_1 ) 16.26/16.36 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.26/16.36 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 16.26/16.36 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 16.26/16.36 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 16.26/16.36 ) 16.26/16.36 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_149598 $$unsorted) (BOUND_VARIABLE_149599 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (let ((_let_1 (inverse_inverse X_a))) (let ((_let_2 (ti X_a BOUND_VARIABLE_149598))) (let ((_let_3 (ti X_a BOUND_VARIABLE_149599))) (or (not (division_ring X_a)) (not (= (hAPP X_a X_a _let_1 BOUND_VARIABLE_149598) (hAPP X_a X_a _let_1 BOUND_VARIABLE_149599))) (= _let_0 _let_2) (= _let_0 _let_3) (= _let_2 _let_3)))))) ) 16.26/16.36 ( real, (zero_zero real), (zero_zero real) ) 16.26/16.36 ( complex, ii, ii ) 16.26/16.36 ) 16.26/16.36 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_149721 $$unsorted)) (let ((_let_0 (fun X_a (fun X_a X_a)))) (or (not (semiring_1 X_a)) (= (hAPP nat X_a (semiring_1_of_nat X_a) BOUND_VARIABLE_149721) (hAPP X_a X_a (hAPP nat (fun X_a X_a) (hAPP (fun X_a X_a) (fun nat (fun X_a X_a)) (semiri532925092at_aux X_a) (hAPP X_a (fun X_a X_a) (hAPP _let_0 _let_0 (combc X_a X_a X_a) (plus_plus X_a)) (one_one X_a))) BOUND_VARIABLE_149721) (zero_zero X_a))))) ) 16.26/16.36 ( int, (zero_zero nat) ) 16.26/16.36 ( int, (hAPP nat nat suc (zero_zero nat)) ) 16.26/16.36 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.26/16.36 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.36 ( real, (zero_zero nat) ) 16.26/16.36 ( real, (hAPP nat nat suc (zero_zero nat)) ) 16.26/16.36 ) 16.26/16.36 (instantiation (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (or (hBOOL (hAPP int bool nat_neg (hAPP int int (number_number_of int) N_1))) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) X_1))) (= (hAPP real nat natfloor (hAPP real real (hAPP real (fun real real) (plus_plus real) X_1) (hAPP int real (number_number_of real) N_1))) (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP real nat natfloor X_1)) (hAPP int nat (number_number_of nat) N_1)))) ) 16.26/16.36 ( (one_one real), (hAPP int int bit1 pls) ) 16.26/16.36 ) 16.26/16.36 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) X_1))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real ln X_1)) X_1))))) ) 16.26/16.36 ( (one_one real) ) 16.26/16.36 ( pi ) 16.26/16.36 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.36 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.36 ( skv_2 ) 16.26/16.36 ( skv_8 ) 16.26/16.36 ( skv_9 ) 16.26/16.36 ) 16.26/16.36 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_149871 $$unsorted)) (let ((_let_0 (inverse_inverse X_a))) (let ((_let_1 (uminus_uminus X_a))) (or (not (division_ring X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_149871)) (= (hAPP X_a X_a _let_1 (hAPP X_a X_a _let_0 BOUND_VARIABLE_149871)) (hAPP X_a X_a _let_0 (hAPP X_a X_a _let_1 BOUND_VARIABLE_149871)))))) ) 16.26/16.36 ( bool, fFalse ) 16.26/16.36 ( bool, fTrue ) 16.26/16.36 ( int, (one_one int) ) 16.26/16.36 ( int, pls ) 16.26/16.36 ( int, min_1 ) 16.26/16.36 ( int, s ) 16.26/16.36 ( int, m ) 16.26/16.36 ( int, s1 ) 16.26/16.36 ( int, t ) 16.26/16.36 ( (fun int bool), nat_neg ) 16.26/16.36 ( (fun int bool), zprime ) 16.26/16.36 ( (fun int bool), zEven ) 16.26/16.36 ( (fun int bool), zOdd ) 16.26/16.36 ( (fun int bool), (even_odd_even int) ) 16.26/16.36 ( (fun int bool), twoSqu1091635170sum2sq ) 16.26/16.36 ( (fun int bool), nat_is_nat ) 16.26/16.36 ( (fun int (fun int bool)), norRRset ) 16.26/16.36 ( (fun int (fun int bool)), quadRes ) 16.26/16.36 ( (fun int (fun int bool)), sRStar ) 16.26/16.36 ( (fun int (fun int bool)), d22set ) 16.26/16.36 ( (fun int (fun int bool)), sr ) 16.26/16.36 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 16.26/16.36 ( (fun int int), zfact ) 16.26/16.36 ( (fun int int), bit0 ) 16.26/16.36 ( (fun int int), bit1 ) 16.26/16.36 ( (fun int int), (fact_fact int) ) 16.26/16.36 ( (fun int int), pred ) 16.26/16.36 ( (fun int int), succ ) 16.26/16.36 ( (fun nat bool), (even_odd_even nat) ) 16.26/16.36 ( (fun nat bool), prime ) 16.26/16.36 ( (fun nat nat), suc ) 16.26/16.36 ( (fun nat nat), (fact_fact nat) ) 16.26/16.36 ( (fun nat nat), fact ) 16.26/16.36 ( (fun nat nat), nat_size ) 16.26/16.36 ( (fun nat nat), (size_size nat) ) 16.26/16.36 ( (fun (product_prod nat nat) bool), pred_nat ) 16.26/16.36 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 16.26/16.36 ( real, (one_one real) ) 16.26/16.36 ( real, (zero_zero real) ) 16.26/16.36 ( real, pi ) 16.26/16.36 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.36 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.26/16.36 ( (fun real real), ln ) 16.26/16.36 ( (fun real real), cos ) 16.26/16.36 ( (fun real real), sqrt ) 16.26/16.36 ( (fun real real), sin ) 16.26/16.36 ( (fun real real), arccos ) 16.26/16.36 ( (fun real real), arcsin ) 16.26/16.36 ( (fun real real), tan ) 16.26/16.36 ( (fun real real), arctan ) 16.26/16.36 ( (fun nat (fun nat bool)), coprime ) 16.26/16.36 ( complex, (one_one complex) ) 16.26/16.36 ( complex, ii ) 16.26/16.36 ( (fun nat real), (real_1 nat) ) 16.26/16.36 ( (fun nat real), sin_coeff ) 16.26/16.36 ( (fun nat real), cos_coeff ) 16.26/16.36 ( (filter nat), sequentially ) 16.26/16.36 ( (fun int (fun int int)), (gcd_gcd int) ) 16.26/16.36 ( (fun int (fun int int)), legendre ) 16.26/16.36 ( (fun int (fun int int)), legacy_zgcd ) 16.26/16.36 ( (fun int (fun int int)), standardRes ) 16.26/16.36 ( (fun int (fun int int)), nat_tsub ) 16.26/16.36 ( (fun int (fun int int)), multInv ) 16.26/16.36 ( (fun int (fun int int)), z3mod ) 16.26/16.36 ( (fun int (fun int int)), z3div ) 16.26/16.36 ( (fun int (fun int int)), int_gcd ) 16.26/16.36 ( (fun int (fun int int)), int_lcm ) 16.26/16.36 ( (fun int (fun int int)), inv ) 16.26/16.36 ( (fun complex complex), expi ) 16.26/16.36 ( (fun complex complex), cnj ) 16.26/16.36 ( (fun real complex), cis ) 16.26/16.36 ( (fun int nat), nat_1 ) 16.26/16.36 ( (fun int nat), phi ) 16.26/16.36 ( (fun (fun int bool) bool), nat_nat_set ) 16.26/16.36 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 16.26/16.36 ( (fun nat (fun nat nat)), nat_gcd ) 16.26/16.36 ( (fun nat (fun nat nat)), nat_lcm ) 16.26/16.36 ( (fun (fun int bool) int), (the int) ) 16.26/16.36 ( (fun complex real), re ) 16.26/16.36 ( (fun complex real), im ) 16.26/16.36 ( (fun complex real), arg ) 16.26/16.36 ( (fun bool bool), fNot ) 16.26/16.36 ( (fun nat (fun real real)), root ) 16.26/16.36 ( (fun real (fun real real)), log ) 16.26/16.36 ( (fun real (fun real real)), powr ) 16.26/16.36 ( (fun bool (fun bool bool)), fimplies ) 16.26/16.36 ( (fun bool (fun bool bool)), fconj ) 16.26/16.36 ( (fun bool (fun bool bool)), fdisj ) 16.26/16.36 ( (fun int (fun int (product_prod int int))), negDivAlg ) 16.26/16.36 ( (fun int (fun int (product_prod int int))), posDivAlg ) 16.26/16.36 ( (fun int (fun int (product_prod int int))), divmod_int ) 16.26/16.36 ( (fun int (fun int (product_prod int int))), pdivmod ) 16.26/16.36 ( (fun int (fun int (product_prod int int))), norm_frac ) 16.26/16.36 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 16.26/16.36 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 16.26/16.36 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 16.26/16.36 ( (fun int (fun int (fun int bool))), zcong ) 16.26/16.36 ( (fun int (fun int (fun int bool))), zcongm ) 16.26/16.36 ( (fun int (fun int (fun int bool))), noXRRset ) 16.26/16.36 ( (fun int (fun int (fun int bool))), bnorRset ) 16.26/16.36 ( (fun int (fun int (fun int bool))), wset ) 16.26/16.36 ( (fun (product_prod int int) bool), frac_1 ) 16.26/16.36 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 16.26/16.36 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 16.26/16.36 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 16.26/16.36 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 16.26/16.36 ( (fun (fun nat rat) bool), vanishes ) 16.26/16.36 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 16.26/16.36 ( (fun code_code_numeral nat), code_c271388182l_size ) 16.26/16.36 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 16.26/16.36 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 16.26/16.36 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 16.26/16.36 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 16.26/16.36 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 16.26/16.36 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 16.26/16.36 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 16.26/16.36 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 16.26/16.36 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 16.26/16.36 ( (fun complex nat), complex_size ) 16.26/16.36 ( (fun complex nat), (size_size complex) ) 16.26/16.36 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 16.26/16.36 ( (fun nat (fun nat (product_prod int int))), bezw ) 16.26/16.36 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 16.26/16.36 ( (fun int (fun nat nat)), nat_aux ) 16.26/16.36 ( (fun int (fun (fun int bool) bool)), rsetR ) 16.26/16.36 ( (fun int (fun (fun int bool) bool)), resSet ) 16.26/16.36 ( (fun int (list int)), quickc666637781d_zero ) 16.26/16.36 ( (fun (product_prod int int) rat), frct ) 16.26/16.36 ( (fun int (fun int rat)), fract ) 16.26/16.36 ( (fun real (fun real complex)), complex_1 ) 16.26/16.36 ( (fun real (fun real complex)), rcis ) 16.26/16.36 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 16.26/16.36 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 16.26/16.36 ( (fun int real), (real_1 int) ) 16.26/16.36 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 16.26/16.36 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 16.26/16.37 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 16.26/16.37 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 16.26/16.37 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 16.26/16.37 ( (fun real nat), natfloor ) 16.26/16.37 ( (fun real nat), natceiling ) 16.26/16.37 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 16.26/16.37 ( (fun quickcheck_code_int int), quickcheck_int_of ) 16.26/16.37 ( (fun rat (product_prod int int)), quotient_of ) 16.26/16.37 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 16.26/16.37 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 16.26/16.37 ( (fun rat real), ratreal ) 16.26/16.37 ( (fun code_code_numeral int), code_int_of ) 16.26/16.37 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 16.26/16.37 ( (fun int quickcheck_code_int), quickcheck_of_int ) 16.26/16.37 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 16.26/16.37 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((P_5 $$unsorted)) (let ((_let_0 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_1 (hAPP int int (number_number_of int) _let_0))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) _let_1) P_5))) (= (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) (hAPP int nat nat_1 P_5)) (hAPP int nat (number_number_of nat) _let_0)) (hAPP int nat nat_1 (hAPP int int (hAPP int (fun int int) (minus_minus int) P_5) _let_1)))))) ) 16.26/16.37 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((A_2 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (let ((_let_3 (fun (filter nat) bool))) (or (not (hBOOL (hAPP (filter nat) bool (hAPP real _let_3 (hAPP _let_1 (fun real _let_3) (tendsto nat real) A_2) (zero_zero real)) sequentially))) (not (hBOOL (hAPP _let_1 bool (monoseq real) A_2))) (hBOOL (hAPP _let_1 bool (summable real) (hAPP _let_1 _let_1 (hAPP _let_2 (fun _let_1 _let_1) (combs nat real real) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 nat) (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) A_2)))))))) ) 16.26/16.37 ( (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))) ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((Z_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) Z_1) (zero_zero int)))) (= (zero_zero nat) (hAPP int nat nat_1 Z_1))) ) 16.26/16.37 ( (one_one int) ) 16.26/16.37 ( (zero_zero int) ) 16.26/16.37 ( min_1 ) 16.26/16.37 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.37 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (hAPP complex (fun complex complex) (times_times complex) ii))) (= (hAPP complex complex _let_0 (hAPP complex complex _let_0 X_1)) (hAPP complex complex (uminus_uminus complex) X_1))) ) 16.26/16.37 ( (one_one complex) ) 16.26/16.37 ( ii ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_149935 $$unsorted) (BOUND_VARIABLE_149936 $$unsorted)) (let ((_let_0 (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_149935))) (or (not (comm_semiring_1 X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_149935) (hAPP nat X_a _let_0 BOUND_VARIABLE_149936)) (hAPP nat X_a _let_0 (hAPP nat nat suc BOUND_VARIABLE_149936))))) ) 16.26/16.37 ( int, s, (hAPP nat nat suc (zero_zero nat)) ) 16.26/16.37 ( int, s1, (hAPP nat nat suc (zero_zero nat)) ) 16.26/16.37 ( int, skv_14, (hAPP nat nat suc (zero_zero nat)) ) 16.26/16.37 ( complex, ii, (hAPP nat nat suc (zero_zero nat)) ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((W $$unsorted)) (= (hAPP int rat (number_number_of rat) W) (hAPP int rat (hAPP int (fun int rat) fract W) (one_one int))) ) 16.26/16.37 ( (one_one int) ) 16.26/16.37 ( (zero_zero int) ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_149955 $$unsorted)) (let ((_let_0 (filter real))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (of_real X_a))) (or (not (real_normed_vector X_a)) (not (real_algebra_1 X_a)) (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 (hAPP (fun real X_a) (fun X_a _let_1) (tendsto real X_a) _let_2) (hAPP real X_a _let_2 BOUND_VARIABLE_149955)) (hAPP real _let_0 (at real) BOUND_VARIABLE_149955))))))) ) 16.26/16.37 ( complex, pi ) 16.26/16.37 ( complex, (hAPP int real (number_number_of real) min_1) ) 16.26/16.37 ( complex, (hAPP real real (uminus_uminus real) (one_one real)) ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (dvd_dvd X_a))) (or (not (dvd X_a)) (= _let_0 (ti (fun X_a (fun X_a bool)) _let_0)))) ) 16.26/16.37 ( bool ) 16.26/16.37 ( nat ) 16.26/16.37 ( int ) 16.26/16.37 ( (fun int bool) ) 16.26/16.37 ( (fun nat bool) ) 16.26/16.37 ( (product_prod nat nat) ) 16.26/16.37 ( real ) 16.26/16.37 ( rat ) 16.26/16.37 ( complex ) 16.26/16.37 ( (filter nat) ) 16.26/16.37 ( (product_prod int int) ) 16.26/16.37 ( quickcheck_code_int ) 16.26/16.37 ( code_code_numeral ) 16.26/16.37 ( (product_prod real real) ) 16.26/16.37 ( (fun nat rat) ) 16.26/16.37 ( (filter real) ) 16.26/16.37 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 16.26/16.37 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((X_a $$unsorted)) (or (not (number_ring X_a)) (not (linord1117847801e_zero X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) (one_one X_a)) (hAPP int X_a (number_number_of X_a) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 16.26/16.37 ( bool ) 16.26/16.37 ( nat ) 16.26/16.37 ( int ) 16.26/16.37 ( (fun int bool) ) 16.26/16.37 ( (fun int (fun int bool)) ) 16.26/16.37 ( (fun int int) ) 16.26/16.37 ( (fun nat bool) ) 16.26/16.37 ( (product_prod nat nat) ) 16.26/16.37 ( real ) 16.26/16.37 ( (fun real bool) ) 16.26/16.37 ( (fun real real) ) 16.26/16.37 ( rat ) 16.26/16.37 ( complex ) 16.26/16.37 ( (fun nat real) ) 16.26/16.37 ( (filter nat) ) 16.26/16.37 ( (product_prod int int) ) 16.26/16.37 ( quickcheck_code_int ) 16.26/16.37 ( code_code_numeral ) 16.26/16.37 ( (fun int (fun int (fun int bool))) ) 16.26/16.37 ( (product_prod real real) ) 16.26/16.37 ( (fun (product_prod int int) bool) ) 16.26/16.37 ( (fun nat rat) ) 16.26/16.37 ( (filter real) ) 16.26/16.37 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 16.26/16.37 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 16.26/16.37 ( (fun (product_prod int int) int) ) 16.26/16.37 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 16.26/16.37 ( (fun int real) ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_150053 $$unsorted)) (let ((_let_0 (number_number_of X_a))) (or (not (number_semiring X_a)) (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) pls) BOUND_VARIABLE_150053))) (= (hAPP int X_a _let_0 (hAPP int int succ BOUND_VARIABLE_150053)) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (hAPP int X_a _let_0 BOUND_VARIABLE_150053)) (one_one X_a))))) ) 16.26/16.37 ( nat, pls ) 16.26/16.37 ( nat, (hAPP int int bit1 pls) ) 16.26/16.37 ( nat, min_1 ) 16.26/16.37 ( int, pls ) 16.26/16.37 ( int, min_1 ) 16.26/16.37 ( quickcheck_code_int, pls ) 16.26/16.37 ( quickcheck_code_int, min_1 ) 16.26/16.37 ( code_code_numeral, pls ) 16.26/16.37 ( code_code_numeral, min_1 ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_150124 $$unsorted) (BOUND_VARIABLE_150125 $$unsorted) (BOUND_VARIABLE_150126 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_150124))) (or (not (order X_a)) (not (= (ti X_a BOUND_VARIABLE_150126) (ti X_a BOUND_VARIABLE_150125))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_150126))) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_150125)))) ) 16.26/16.37 ( int, (one_one int), t, t ) 16.26/16.37 ( int, pls, s, s ) 16.26/16.37 ( int, min_1, pls, pls ) 16.26/16.37 ( int, s, s1, s1 ) 16.26/16.37 ( int, t, m, m ) 16.26/16.37 ( int, skv_4, min_1, min_1 ) 16.26/16.37 ( real, pi, pi, pi ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (or (hBOOL (hAPP int bool nat_neg (hAPP int int (number_number_of int) N_1))) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) X_1))) (= (hAPP real nat natceiling (hAPP real real (hAPP real (fun real real) (plus_plus real) X_1) (hAPP int real (number_number_of real) N_1))) (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP real nat natceiling X_1)) (hAPP int nat (number_number_of nat) N_1)))) ) 16.26/16.37 ( (one_one real), (hAPP int int bit1 pls) ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_150239 $$unsorted) (BOUND_VARIABLE_150240 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (minus_minus X_a))) (let ((_let_2 (abs_abs X_a))) (or (not (ordere142940540dd_abs X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_150239)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_150240))) (hAPP X_a X_a _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_150240) BOUND_VARIABLE_150239)))))))) ) 16.26/16.37 ( int, (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.37 ( real, (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))), (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))) ) 16.26/16.37 ( code_code_numeral, (one_one code_code_numeral), (zero_zero code_code_numeral) ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (times_times X_a))) (or (not (dvd X_a)) (= _let_0 (ti (fun X_a (fun X_a X_a)) _let_0)))) ) 16.26/16.37 ( bool ) 16.26/16.37 ( nat ) 16.26/16.37 ( int ) 16.26/16.37 ( (fun int bool) ) 16.26/16.37 ( (fun int (fun int bool)) ) 16.26/16.37 ( (fun int int) ) 16.26/16.37 ( (fun nat bool) ) 16.26/16.37 ( real ) 16.26/16.37 ( (fun real bool) ) 16.26/16.37 ( (fun real real) ) 16.26/16.37 ( rat ) 16.26/16.37 ( complex ) 16.26/16.37 ( (fun nat real) ) 16.26/16.37 ( (product_prod int int) ) 16.26/16.37 ( quickcheck_code_int ) 16.26/16.37 ( code_code_numeral ) 16.26/16.37 ( (fun int (fun int (fun int bool))) ) 16.26/16.37 ( (fun (product_prod int int) bool) ) 16.26/16.37 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 16.26/16.37 ( (fun (product_prod int int) int) ) 16.26/16.37 ( (fun int real) ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_150275 $$unsorted) (BOUND_VARIABLE_150276 $$unsorted)) (let ((_let_0 (semiring_1_of_nat X_a))) (or (not (linordered_semidom X_a)) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) BOUND_VARIABLE_150275) BOUND_VARIABLE_150276)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (hAPP nat X_a _let_0 BOUND_VARIABLE_150275)) (hAPP nat X_a _let_0 BOUND_VARIABLE_150276)))))) ) 16.26/16.37 ( int, (zero_zero nat), (zero_zero nat) ) 16.26/16.37 ( int, (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 16.26/16.37 ( int, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.26/16.37 ( int, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_0 (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)))) (let ((_let_1 (archim2085082626_floor real))) (or (not (hBOOL (hAPP real bool _let_0 A_1))) (not (hBOOL (hAPP real bool _let_0 B))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP real int _let_1 A_1)) (hAPP real int _let_1 B))) (hAPP real int _let_1 (hAPP real real (hAPP real (fun real real) (times_times real) A_1) B))))))) ) 16.26/16.37 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.37 ( pi, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 16.26/16.37 ( (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.37 ( (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((K_4 $$unsorted)) (not (= min_1 (hAPP int int bit0 K_4))) ) 16.26/16.37 ( pls ) 16.26/16.37 ( (hAPP int int bit1 pls) ) 16.26/16.37 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.26/16.37 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.26/16.37 ( min_1 ) 16.26/16.37 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((X1_2 $$unsorted) (X2_2 $$unsorted) (Ma $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (hAPP int (fun int int) standardRes Ma))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (zero_zero int)) Ma))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong X1_2) X2_2) Ma)) (= (hAPP int int _let_1 X1_2) (hAPP int int _let_1 X2_2)))))) ) 16.26/16.37 ( s1, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.37 ( s1, skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.37 ( s1, skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.37 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.37 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.37 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.37 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_150378 $$unsorted) (BOUND_VARIABLE_150379 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (times_times X_a))) (let ((_let_2 (inverse_inverse X_a))) (or (not (field_inverse_zero X_a)) (= (hAPP X_a X_a _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_150378) BOUND_VARIABLE_150379)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_150378)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_150379))))))) ) 16.26/16.37 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 16.26/16.37 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 16.26/16.37 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13 ) 16.26/16.37 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.26/16.37 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 16.26/16.37 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 16.26/16.37 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 16.26/16.37 ( complex, ii, ii ) 16.26/16.37 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 16.26/16.37 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (= (= X_2 Y_2) (= (hAPP quickcheck_code_int int quickcheck_int_of Y_2) (hAPP quickcheck_code_int int quickcheck_int_of X_2))) ) 16.26/16.37 ( (zero_zero quickcheck_code_int), (zero_zero quickcheck_code_int) ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (one_one real))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 (zero_zero real)) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 X_1) _let_1))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 (hAPP real real (abs_abs real) (hAPP real real (hAPP real _let_3 (minus_minus real) (hAPP real real ln (hAPP real real (hAPP real _let_3 (plus_plus real) _let_1) X_1))) X_1))) (hAPP nat real (hAPP real (fun nat real) (power_power real) X_1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))))))) ) 16.26/16.37 ( pi ) 16.26/16.37 ( (hAPP int real (number_number_of real) min_1) ) 16.26/16.37 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.37 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.37 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.37 ( skv_3 ) 16.26/16.37 ( skv_5 ) 16.26/16.37 ( skv_7 ) 16.26/16.37 ( skv_12 ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_150593 $$unsorted)) (let ((_let_0 (abs_abs X_a))) (let ((_let_1 (inverse_inverse X_a))) (or (not (linord1117847801e_zero X_a)) (= (hAPP X_a X_a _let_1 (hAPP X_a X_a _let_0 BOUND_VARIABLE_150593)) (hAPP X_a X_a _let_0 (hAPP X_a X_a _let_1 BOUND_VARIABLE_150593)))))) ) 16.26/16.37 ( real, (zero_zero real) ) 16.26/16.37 ( complex, ii ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_150720 $$unsorted) (BOUND_VARIABLE_150721 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (or (not (group_add X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 (plus_plus X_a) (hAPP X_a X_a (hAPP X_a _let_0 (minus_minus X_a) BOUND_VARIABLE_150720) BOUND_VARIABLE_150721)) BOUND_VARIABLE_150721) (ti X_a BOUND_VARIABLE_150720)))) ) 16.26/16.37 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 16.26/16.37 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 16.26/16.37 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) X_2) zOdd))) (not (forall ((K_1 $$unsorted)) (let ((_let_0 (fun int int))) (not (= (ti int X_2) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) K_1)) (one_one int))))) )))) ) 16.26/16.37 ( (one_one int) ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) A_2) B_1))) (not (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) B_1) (hAPP int _let_0 d22set A_2)))))) ) 16.26/16.37 ( (one_one int), t ) 16.26/16.37 ( pls, (one_one int) ) 16.26/16.37 ( pls, pls ) 16.26/16.37 ( pls, min_1 ) 16.26/16.37 ( pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.37 ( min_1, pls ) 16.26/16.37 ( min_1, min_1 ) 16.26/16.37 ( s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.37 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.37 ( skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.37 ( skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((I_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) I_1) (zero_zero int)))) (= (hAPP int int (abs_abs int) I_1) (hAPP int int (uminus_uminus int) I_1))) ) 16.26/16.37 ( (one_one int) ) 16.26/16.37 ( pls ) 16.26/16.37 ( min_1 ) 16.26/16.37 ( s ) 16.26/16.37 ( t ) 16.26/16.37 ( skv_4 ) 16.26/16.37 ( skv_10 ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((I_1 $$unsorted)) (or (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) I_1) (zero_zero int))) (= (hAPP int int (abs_abs int) I_1) (ti int I_1))) ) 16.26/16.37 ( (one_one int) ) 16.26/16.37 ( pls ) 16.26/16.37 ( min_1 ) 16.26/16.37 ( s ) 16.26/16.37 ( m ) 16.26/16.37 ( s1 ) 16.26/16.37 ( t ) 16.26/16.37 ( skv_4 ) 16.26/16.37 ( skv_10 ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((X_1 $$unsorted)) (= (hAPP real real (uminus_uminus real) (hAPP complex real re X_1)) (hAPP complex real re (hAPP complex complex (uminus_uminus complex) X_1))) ) 16.26/16.37 ( (one_one complex) ) 16.26/16.37 ( ii ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (one_one X_a))) (or (not (number_ring X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) _let_0) _let_0) (hAPP int X_a (number_number_of X_a) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 16.26/16.37 ( bool ) 16.26/16.37 ( nat ) 16.26/16.37 ( int ) 16.26/16.37 ( (fun int bool) ) 16.26/16.37 ( (fun int (fun int bool)) ) 16.26/16.37 ( (fun int int) ) 16.26/16.37 ( (fun nat bool) ) 16.26/16.37 ( real ) 16.26/16.37 ( (fun real bool) ) 16.26/16.37 ( (fun real real) ) 16.26/16.37 ( rat ) 16.26/16.37 ( complex ) 16.26/16.37 ( (fun nat real) ) 16.26/16.37 ( (product_prod int int) ) 16.26/16.37 ( quickcheck_code_int ) 16.26/16.37 ( code_code_numeral ) 16.26/16.37 ( (fun int (fun int (fun int bool))) ) 16.26/16.37 ( (fun (product_prod int int) bool) ) 16.26/16.37 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 16.26/16.37 ( (fun (product_prod int int) int) ) 16.26/16.37 ( (fun int real) ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_150872 $$unsorted)) (or (not (number_ring X_a)) (not (field X_a)) (= (ti X_a BOUND_VARIABLE_150872) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_150872) (hAPP int X_a (number_number_of X_a) (hAPP int int bit1 pls))))) ) 16.26/16.37 ( bool, fFalse ) 16.26/16.37 ( bool, fTrue ) 16.26/16.37 ( int, pls ) 16.26/16.37 ( int, min_1 ) 16.26/16.37 ( int, s ) 16.26/16.37 ( int, m ) 16.26/16.37 ( int, s1 ) 16.26/16.37 ( int, t ) 16.26/16.37 ( (fun int bool), nat_neg ) 16.26/16.37 ( (fun int bool), zprime ) 16.26/16.37 ( (fun int bool), zEven ) 16.26/16.37 ( (fun int bool), zOdd ) 16.26/16.37 ( (fun int bool), (even_odd_even int) ) 16.26/16.37 ( (fun int bool), twoSqu1091635170sum2sq ) 16.26/16.37 ( (fun int bool), nat_is_nat ) 16.26/16.37 ( (fun int (fun int bool)), norRRset ) 16.26/16.37 ( (fun int (fun int bool)), quadRes ) 16.26/16.37 ( (fun int (fun int bool)), sRStar ) 16.26/16.37 ( (fun int (fun int bool)), d22set ) 16.26/16.37 ( (fun int (fun int bool)), sr ) 16.26/16.37 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 16.26/16.37 ( (fun int int), zfact ) 16.26/16.37 ( (fun int int), bit0 ) 16.26/16.37 ( (fun int int), bit1 ) 16.26/16.37 ( (fun int int), (fact_fact int) ) 16.26/16.37 ( (fun int int), pred ) 16.26/16.37 ( (fun int int), succ ) 16.26/16.37 ( (fun nat bool), (even_odd_even nat) ) 16.26/16.37 ( (fun nat bool), prime ) 16.26/16.37 ( (fun nat nat), suc ) 16.26/16.37 ( (fun nat nat), (fact_fact nat) ) 16.26/16.37 ( (fun nat nat), fact ) 16.26/16.37 ( (fun nat nat), nat_size ) 16.26/16.37 ( (fun nat nat), (size_size nat) ) 16.26/16.37 ( (fun (product_prod nat nat) bool), pred_nat ) 16.26/16.37 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 16.26/16.37 ( real, (one_one real) ) 16.26/16.37 ( real, pi ) 16.26/16.37 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.26/16.37 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.26/16.37 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.37 ( (fun real real), ln ) 16.26/16.37 ( (fun real real), cos ) 16.26/16.37 ( (fun real real), sqrt ) 16.26/16.37 ( (fun real real), sin ) 16.26/16.37 ( (fun real real), arccos ) 16.26/16.37 ( (fun real real), arcsin ) 16.26/16.37 ( (fun real real), tan ) 16.26/16.37 ( (fun real real), arctan ) 16.26/16.37 ( (fun nat (fun nat bool)), coprime ) 16.26/16.37 ( complex, ii ) 16.26/16.37 ( (fun nat real), (real_1 nat) ) 16.26/16.37 ( (fun nat real), sin_coeff ) 16.26/16.37 ( (fun nat real), cos_coeff ) 16.26/16.37 ( (filter nat), sequentially ) 16.26/16.37 ( (fun int (fun int int)), (gcd_gcd int) ) 16.26/16.37 ( (fun int (fun int int)), legendre ) 16.26/16.37 ( (fun int (fun int int)), legacy_zgcd ) 16.26/16.37 ( (fun int (fun int int)), standardRes ) 16.26/16.37 ( (fun int (fun int int)), nat_tsub ) 16.26/16.37 ( (fun int (fun int int)), multInv ) 16.26/16.37 ( (fun int (fun int int)), z3mod ) 16.26/16.37 ( (fun int (fun int int)), z3div ) 16.26/16.37 ( (fun int (fun int int)), int_gcd ) 16.26/16.37 ( (fun int (fun int int)), int_lcm ) 16.26/16.37 ( (fun int (fun int int)), inv ) 16.26/16.37 ( (fun complex complex), expi ) 16.26/16.37 ( (fun complex complex), cnj ) 16.26/16.37 ( (fun real complex), cis ) 16.26/16.37 ( (fun int nat), nat_1 ) 16.26/16.37 ( (fun int nat), phi ) 16.26/16.37 ( (fun (fun int bool) bool), nat_nat_set ) 16.26/16.37 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 16.26/16.37 ( (fun nat (fun nat nat)), nat_gcd ) 16.26/16.37 ( (fun nat (fun nat nat)), nat_lcm ) 16.26/16.37 ( (fun (fun int bool) int), (the int) ) 16.26/16.37 ( (fun complex real), re ) 16.26/16.37 ( (fun complex real), im ) 16.26/16.37 ( (fun complex real), arg ) 16.26/16.37 ( (fun bool bool), fNot ) 16.26/16.37 ( (fun nat (fun real real)), root ) 16.26/16.37 ( (fun real (fun real real)), log ) 16.26/16.37 ( (fun real (fun real real)), powr ) 16.26/16.37 ( (fun bool (fun bool bool)), fimplies ) 16.26/16.37 ( (fun bool (fun bool bool)), fconj ) 16.26/16.37 ( (fun bool (fun bool bool)), fdisj ) 16.26/16.37 ( (fun int (fun int (product_prod int int))), negDivAlg ) 16.26/16.37 ( (fun int (fun int (product_prod int int))), posDivAlg ) 16.26/16.37 ( (fun int (fun int (product_prod int int))), divmod_int ) 16.26/16.37 ( (fun int (fun int (product_prod int int))), pdivmod ) 16.26/16.37 ( (fun int (fun int (product_prod int int))), norm_frac ) 16.26/16.37 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 16.26/16.37 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 16.26/16.37 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 16.26/16.37 ( (fun int (fun int (fun int bool))), zcong ) 16.26/16.37 ( (fun int (fun int (fun int bool))), zcongm ) 16.26/16.37 ( (fun int (fun int (fun int bool))), noXRRset ) 16.26/16.37 ( (fun int (fun int (fun int bool))), bnorRset ) 16.26/16.37 ( (fun int (fun int (fun int bool))), wset ) 16.26/16.37 ( (fun (product_prod int int) bool), frac_1 ) 16.26/16.37 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 16.26/16.37 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 16.26/16.37 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 16.26/16.37 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 16.26/16.37 ( (fun (fun nat rat) bool), vanishes ) 16.26/16.37 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 16.26/16.37 ( (fun code_code_numeral nat), code_c271388182l_size ) 16.26/16.37 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 16.26/16.37 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 16.26/16.37 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 16.26/16.37 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 16.26/16.37 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 16.26/16.37 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 16.26/16.37 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 16.26/16.37 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 16.26/16.37 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 16.26/16.37 ( (fun complex nat), complex_size ) 16.26/16.37 ( (fun complex nat), (size_size complex) ) 16.26/16.37 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 16.26/16.37 ( (fun nat (fun nat (product_prod int int))), bezw ) 16.26/16.37 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 16.26/16.37 ( (fun int (fun nat nat)), nat_aux ) 16.26/16.37 ( (fun int (fun (fun int bool) bool)), rsetR ) 16.26/16.37 ( (fun int (fun (fun int bool) bool)), resSet ) 16.26/16.37 ( (fun int (list int)), quickc666637781d_zero ) 16.26/16.37 ( (fun (product_prod int int) rat), frct ) 16.26/16.37 ( (fun int (fun int rat)), fract ) 16.26/16.37 ( (fun real (fun real complex)), complex_1 ) 16.26/16.37 ( (fun real (fun real complex)), rcis ) 16.26/16.37 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 16.26/16.37 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 16.26/16.37 ( (fun int real), (real_1 int) ) 16.26/16.37 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 16.26/16.37 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 16.26/16.37 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 16.26/16.37 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 16.26/16.37 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 16.26/16.37 ( (fun real nat), natfloor ) 16.26/16.37 ( (fun real nat), natceiling ) 16.26/16.37 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 16.26/16.37 ( (fun quickcheck_code_int int), quickcheck_int_of ) 16.26/16.37 ( (fun rat (product_prod int int)), quotient_of ) 16.26/16.37 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 16.26/16.37 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 16.26/16.37 ( (fun rat real), ratreal ) 16.26/16.37 ( (fun code_code_numeral int), code_int_of ) 16.26/16.37 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 16.26/16.37 ( (fun int quickcheck_code_int), quickcheck_of_int ) 16.26/16.37 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 16.26/16.37 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_150896 $$unsorted) (BOUND_VARIABLE_150897 $$unsorted) (BOUND_VARIABLE_150898 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (let ((_let_3 (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_150896))) (let ((_let_4 (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_150898))) (let ((_let_5 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) _let_4)))) (let ((_let_6 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_4) _let_2)))) (let ((_let_7 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_150896) _let_4))) (or (not (number X_a)) (not (linord1117847801e_zero X_a)) (= (hBOOL (hAPP X_a bool _let_3 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_150897) _let_4))) (and (or _let_5 (and (or _let_6 (hBOOL (hAPP X_a bool _let_3 _let_2))) (or (not _let_6) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_150897) _let_7))))) (or (not _let_5) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_7) BOUND_VARIABLE_150897)))))))))))))) ) 16.26/16.37 ( real, (zero_zero real), pi, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_150943 $$unsorted) (BOUND_VARIABLE_150944 $$unsorted)) (let ((_let_0 (abs_abs X_a))) (or (not (linordered_idom X_a)) (not (= (hAPP X_a X_a _let_0 BOUND_VARIABLE_150944) (hAPP X_a X_a _let_0 BOUND_VARIABLE_150943))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_150943) BOUND_VARIABLE_150944)))) ) 16.26/16.37 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_150964 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (or (not (linordered_idom X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_150964) _let_2)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (sgn_sgn X_a) BOUND_VARIABLE_150964)) _let_2))))))) ) 16.26/16.37 ( int, pls ) 16.26/16.37 ( int, min_1 ) 16.26/16.37 ( real, (zero_zero real) ) 16.26/16.37 ( real, pi ) 16.26/16.37 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.26/16.37 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.37 ( rat, (zero_zero rat) ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((X_a $$unsorted) (X_2 $$unsorted)) (let ((_let_0 (fun X_a (fun X_a bool)))) (= (hAPP (fun X_a bool) X_a (hilbert_Eps X_a) (hAPP X_a (fun X_a bool) (hAPP _let_0 _let_0 (combc X_a X_a bool) (fequal X_a)) X_2)) (ti X_a X_2))) ) 16.26/16.37 ( bool, fFalse ) 16.26/16.37 ( bool, fTrue ) 16.26/16.37 ( nat, (zero_zero nat) ) 16.26/16.37 ( int, (zero_zero int) ) 16.26/16.37 ( int, pls ) 16.26/16.37 ( int, min_1 ) 16.26/16.37 ( int, s ) 16.26/16.37 ( int, m ) 16.26/16.37 ( int, s1 ) 16.26/16.37 ( int, t ) 16.26/16.37 ( (fun int bool), nat_neg ) 16.26/16.37 ( (fun int bool), zprime ) 16.26/16.37 ( (fun int bool), zEven ) 16.26/16.37 ( (fun int bool), zOdd ) 16.26/16.37 ( (fun int bool), (even_odd_even int) ) 16.26/16.37 ( (fun int bool), twoSqu1091635170sum2sq ) 16.26/16.37 ( (fun int bool), nat_is_nat ) 16.26/16.37 ( (fun int (fun int bool)), norRRset ) 16.26/16.37 ( (fun int (fun int bool)), quadRes ) 16.26/16.37 ( (fun int (fun int bool)), sRStar ) 16.26/16.37 ( (fun int (fun int bool)), d22set ) 16.26/16.37 ( (fun int (fun int bool)), sr ) 16.26/16.37 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 16.26/16.37 ( (fun int int), zfact ) 16.26/16.37 ( (fun int int), bit0 ) 16.26/16.37 ( (fun int int), bit1 ) 16.26/16.37 ( (fun int int), (fact_fact int) ) 16.26/16.37 ( (fun int int), pred ) 16.26/16.37 ( (fun int int), succ ) 16.26/16.37 ( (fun nat bool), (even_odd_even nat) ) 16.26/16.37 ( (fun nat bool), prime ) 16.26/16.37 ( (fun nat nat), suc ) 16.26/16.37 ( (fun nat nat), (fact_fact nat) ) 16.26/16.37 ( (fun nat nat), fact ) 16.26/16.37 ( (fun nat nat), nat_size ) 16.26/16.37 ( (fun nat nat), (size_size nat) ) 16.26/16.37 ( (fun (product_prod nat nat) bool), pred_nat ) 16.26/16.37 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 16.26/16.37 ( real, pi ) 16.26/16.37 ( (fun real real), ln ) 16.26/16.37 ( (fun real real), cos ) 16.26/16.37 ( (fun real real), sqrt ) 16.26/16.37 ( (fun real real), sin ) 16.26/16.37 ( (fun real real), arccos ) 16.26/16.37 ( (fun real real), arcsin ) 16.26/16.37 ( (fun real real), tan ) 16.26/16.37 ( (fun real real), arctan ) 16.26/16.37 ( (fun nat (fun nat bool)), coprime ) 16.26/16.37 ( complex, ii ) 16.26/16.37 ( (fun nat real), (real_1 nat) ) 16.26/16.37 ( (fun nat real), sin_coeff ) 16.26/16.37 ( (fun nat real), cos_coeff ) 16.26/16.37 ( (filter nat), sequentially ) 16.26/16.37 ( (fun int (fun int int)), (gcd_gcd int) ) 16.26/16.37 ( (fun int (fun int int)), legendre ) 16.26/16.37 ( (fun int (fun int int)), legacy_zgcd ) 16.26/16.37 ( (fun int (fun int int)), standardRes ) 16.26/16.37 ( (fun int (fun int int)), nat_tsub ) 16.26/16.37 ( (fun int (fun int int)), multInv ) 16.26/16.37 ( (fun int (fun int int)), z3mod ) 16.26/16.37 ( (fun int (fun int int)), z3div ) 16.26/16.37 ( (fun int (fun int int)), int_gcd ) 16.26/16.37 ( (fun int (fun int int)), int_lcm ) 16.26/16.37 ( (fun int (fun int int)), inv ) 16.26/16.37 ( (fun complex complex), expi ) 16.26/16.37 ( (fun complex complex), cnj ) 16.26/16.37 ( (fun real complex), cis ) 16.26/16.37 ( (fun int nat), nat_1 ) 16.26/16.37 ( (fun int nat), phi ) 16.26/16.37 ( (fun (fun int bool) bool), nat_nat_set ) 16.26/16.37 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 16.26/16.37 ( (fun nat (fun nat nat)), nat_gcd ) 16.26/16.37 ( (fun nat (fun nat nat)), nat_lcm ) 16.26/16.37 ( (fun (fun int bool) int), (the int) ) 16.26/16.37 ( (fun complex real), re ) 16.26/16.37 ( (fun complex real), im ) 16.26/16.37 ( (fun complex real), arg ) 16.26/16.37 ( (fun bool bool), fNot ) 16.26/16.37 ( (fun nat (fun real real)), root ) 16.26/16.37 ( (fun real (fun real real)), log ) 16.26/16.37 ( (fun real (fun real real)), powr ) 16.26/16.37 ( (fun bool (fun bool bool)), fimplies ) 16.26/16.37 ( (fun bool (fun bool bool)), fconj ) 16.26/16.37 ( (fun bool (fun bool bool)), fdisj ) 16.26/16.37 ( (fun int (fun int (product_prod int int))), negDivAlg ) 16.26/16.37 ( (fun int (fun int (product_prod int int))), posDivAlg ) 16.26/16.37 ( (fun int (fun int (product_prod int int))), divmod_int ) 16.26/16.37 ( (fun int (fun int (product_prod int int))), pdivmod ) 16.26/16.37 ( (fun int (fun int (product_prod int int))), norm_frac ) 16.26/16.37 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 16.26/16.37 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 16.26/16.37 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 16.26/16.37 ( (fun int (fun int (fun int bool))), zcong ) 16.26/16.37 ( (fun int (fun int (fun int bool))), zcongm ) 16.26/16.37 ( (fun int (fun int (fun int bool))), noXRRset ) 16.26/16.37 ( (fun int (fun int (fun int bool))), bnorRset ) 16.26/16.37 ( (fun int (fun int (fun int bool))), wset ) 16.26/16.37 ( (fun (product_prod int int) bool), frac_1 ) 16.26/16.37 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 16.26/16.37 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 16.26/16.37 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 16.26/16.37 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 16.26/16.37 ( (fun (fun nat rat) bool), vanishes ) 16.26/16.37 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 16.26/16.37 ( (fun code_code_numeral nat), code_c271388182l_size ) 16.26/16.37 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 16.26/16.37 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 16.26/16.37 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 16.26/16.37 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 16.26/16.37 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 16.26/16.37 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 16.26/16.37 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 16.26/16.37 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 16.26/16.37 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 16.26/16.37 ( (fun complex nat), complex_size ) 16.26/16.37 ( (fun complex nat), (size_size complex) ) 16.26/16.37 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 16.26/16.37 ( (fun nat (fun nat (product_prod int int))), bezw ) 16.26/16.37 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 16.26/16.37 ( (fun int (fun nat nat)), nat_aux ) 16.26/16.37 ( (fun int (fun (fun int bool) bool)), rsetR ) 16.26/16.37 ( (fun int (fun (fun int bool) bool)), resSet ) 16.26/16.37 ( (fun int (list int)), quickc666637781d_zero ) 16.26/16.37 ( (fun (product_prod int int) rat), frct ) 16.26/16.37 ( (fun int (fun int rat)), fract ) 16.26/16.37 ( (fun real (fun real complex)), complex_1 ) 16.26/16.37 ( (fun real (fun real complex)), rcis ) 16.26/16.37 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 16.26/16.37 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 16.26/16.37 ( (fun int real), (real_1 int) ) 16.26/16.37 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 16.26/16.37 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 16.26/16.37 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 16.26/16.37 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 16.26/16.37 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 16.26/16.37 ( (fun real nat), natfloor ) 16.26/16.37 ( (fun real nat), natceiling ) 16.26/16.37 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 16.26/16.37 ( (fun quickcheck_code_int int), quickcheck_int_of ) 16.26/16.37 ( (fun rat (product_prod int int)), quotient_of ) 16.26/16.37 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 16.26/16.37 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 16.26/16.37 ( (fun rat real), ratreal ) 16.26/16.37 ( (fun code_code_numeral int), code_int_of ) 16.26/16.37 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 16.26/16.37 ( (fun int quickcheck_code_int), quickcheck_of_int ) 16.26/16.37 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 16.26/16.37 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (scaleR_scaleR X_a))) (or (not (sgn_div_norm X_a)) (= _let_0 (ti (fun real (fun X_a X_a)) _let_0)))) ) 16.26/16.37 ( bool ) 16.26/16.37 ( nat ) 16.26/16.37 ( int ) 16.26/16.37 ( (fun int bool) ) 16.26/16.37 ( (fun int (fun int bool)) ) 16.26/16.37 ( (fun int int) ) 16.26/16.37 ( (fun nat bool) ) 16.26/16.37 ( real ) 16.26/16.37 ( (fun real bool) ) 16.26/16.37 ( (fun real real) ) 16.26/16.37 ( complex ) 16.26/16.37 ( (fun nat real) ) 16.26/16.37 ( (product_prod int int) ) 16.26/16.37 ( code_code_numeral ) 16.26/16.37 ( (fun int (fun int (fun int bool))) ) 16.26/16.37 ( (fun (product_prod int int) bool) ) 16.26/16.37 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 16.26/16.37 ( (fun (product_prod int int) int) ) 16.26/16.37 ( (fun int real) ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_151007 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (one_one X_a))) (or (not (linord1117847801e_zero X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_151007))) (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_151007) _let_2)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_151007)))))))) ) 16.26/16.37 ( nat, (zero_zero nat) ) 16.26/16.37 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.37 ( int, (one_one int) ) 16.26/16.37 ( int, pls ) 16.26/16.37 ( int, min_1 ) 16.26/16.37 ( int, s ) 16.26/16.37 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.37 ( int, t ) 16.26/16.37 ( int, skv_4 ) 16.26/16.37 ( int, skv_10 ) 16.26/16.37 ( real, (one_one real) ) 16.26/16.37 ( real, (zero_zero real) ) 16.26/16.37 ( real, pi ) 16.26/16.37 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.37 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.26/16.37 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.37 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.37 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 16.26/16.37 ( real, skv_2 ) 16.26/16.37 ( real, skv_8 ) 16.26/16.37 ( real, skv_9 ) 16.26/16.37 ( complex, ii ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((X_1 $$unsorted)) (= (hAPP int int succ (hAPP int int pred X_1)) (ti int X_1)) ) 16.26/16.37 ( pls ) 16.26/16.37 ( min_1 ) 16.26/16.37 ( s ) 16.26/16.37 ( m ) 16.26/16.37 ( s1 ) 16.26/16.37 ( t ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_151074 $$unsorted) (BOUND_VARIABLE_151075 $$unsorted) (BOUND_VARIABLE_151076 $$unsorted)) (let ((_let_0 (fun (filter nat) bool))) (let ((_let_1 (hAPP (fun nat X_a) (fun X_a _let_0) (tendsto nat X_a) BOUND_VARIABLE_151075))) (or (not (metric_space X_a)) (not (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_151076) sequentially))) (not (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_151074) sequentially))) (= (ti X_a BOUND_VARIABLE_151076) (ti X_a BOUND_VARIABLE_151074))))) ) 16.26/16.37 ( real, (zero_zero real), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real) ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((W $$unsorted) (V_1 $$unsorted)) (let ((_let_0 (zero_zero int))) (let ((_let_1 (number_number_of int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (hAPP int int _let_1 V_1))) (let ((_let_5 (hAPP int int _let_1 W))) (let ((_let_6 (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) _let_5) _let_4)))) (let ((_let_7 (hAPP int _let_3 posDivAlg _let_5))) (let ((_let_8 (hAPP int _let_2 _let_7 _let_4))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) _let_0) _let_4))) (and (or _let_6 (= _let_8 (hAPP _let_2 _let_2 (hAPP int (fun _let_2 _let_2) adjust _let_4) (hAPP int _let_2 _let_7 (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int _let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) _let_4))))) (or (not _let_6) (= _let_8 (hAPP int _let_2 (hAPP int _let_3 (product_Pair int int) _let_0) _let_5)))))))))))))) ) 16.26/16.37 ( pls, pls ) 16.26/16.37 ( pls, (hAPP int int bit1 pls) ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_151261 $$unsorted) (BOUND_VARIABLE_151262 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_151261))) (or (not (archim1727834104eiling X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) _let_1) (one_one X_a))) BOUND_VARIABLE_151262))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_151262) _let_1))) (= (ti int BOUND_VARIABLE_151261) (hAPP X_a int (archimedean_ceiling X_a) BOUND_VARIABLE_151262))))) ) 16.26/16.37 ( real, (zero_zero int), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_151310 $$unsorted) (BOUND_VARIABLE_151311 $$unsorted)) (or (not (linorder X_a)) (= (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (ord_max X_a) BOUND_VARIABLE_151310) BOUND_VARIABLE_151311) (ti X_a BOUND_VARIABLE_151311)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_151310) BOUND_VARIABLE_151311)))) ) 16.26/16.37 ( int, (one_one int), t ) 16.26/16.37 ( int, (zero_zero int), (one_one int) ) 16.26/16.37 ( int, (zero_zero int), min_1 ) 16.26/16.37 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.37 ( int, (zero_zero int), s ) 16.26/16.37 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.26/16.37 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 16.26/16.37 ( int, (zero_zero int), skv_4 ) 16.26/16.37 ( int, (zero_zero int), skv_10 ) 16.26/16.37 ( int, min_1, pls ) 16.26/16.37 ( int, min_1, min_1 ) 16.26/16.37 ( real, (zero_zero real), pi ) 16.26/16.37 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.37 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.37 ( real, (zero_zero real), skv_3 ) 16.26/16.37 ( real, (zero_zero real), skv_5 ) 16.26/16.37 ( real, (zero_zero real), skv_7 ) 16.26/16.37 ( real, (zero_zero real), skv_12 ) 16.26/16.37 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.26/16.37 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.37 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.26/16.37 ( real, skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (zero_zero int)) B_1))) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 A_2) B_1)) (hBOOL (hAPP rat bool (hAPP rat (fun rat bool) (ord_less rat) (hAPP int rat (hAPP int (fun int rat) fract A_2) B_1)) (one_one rat))))))) ) 16.26/16.37 ( (one_one int), (one_one int) ) 16.26/16.37 ( (one_one int), t ) 16.26/16.37 ( (zero_zero int), (one_one int) ) 16.26/16.37 ( pls, (one_one int) ) 16.26/16.37 ( pls, pls ) 16.26/16.37 ( pls, min_1 ) 16.26/16.37 ( pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.37 ( min_1, pls ) 16.26/16.37 ( min_1, min_1 ) 16.26/16.37 ( s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.37 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.37 ( skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.37 ( skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_151337 $$unsorted)) (or (not (linordered_idom X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_151337) (zero_zero X_a)))) (= (hAPP X_a X_a (uminus_uminus X_a) (one_one X_a)) (hAPP X_a X_a (sgn_sgn X_a) BOUND_VARIABLE_151337))) ) 16.26/16.37 ( nat, (zero_zero nat) ) 16.26/16.37 ( int, (one_one int) ) 16.26/16.37 ( int, pls ) 16.26/16.37 ( int, min_1 ) 16.26/16.37 ( int, s ) 16.26/16.37 ( int, t ) 16.26/16.37 ( int, skv_4 ) 16.26/16.37 ( int, skv_10 ) 16.26/16.37 ( real, (one_one real) ) 16.26/16.37 ( real, (zero_zero real) ) 16.26/16.37 ( real, pi ) 16.26/16.37 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.37 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.26/16.37 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.37 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 16.26/16.37 ( rat, (zero_zero rat) ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))))) (let ((_let_1 (fun nat nat))) (let ((_let_2 (div_div nat))) (or (not (hBOOL (hAPP nat bool (even_odd_even nat) X_1))) (= (hAPP nat nat (hAPP nat _let_1 _let_2 X_1) _let_0) (hAPP nat nat (hAPP nat _let_1 _let_2 (hAPP nat nat suc X_1)) _let_0)))))) ) 16.26/16.37 ( (zero_zero nat) ) 16.26/16.37 ( (hAPP nat nat suc (zero_zero nat)) ) 16.26/16.37 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 16.26/16.37 ( (one_one nat) ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (B_1 $$unsorted) (F $$unsorted) (X_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (fun X_b bool))) (or (not (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) X_2) A_3))) (not (= (ti X_b B_1) (hAPP X_a X_b F X_2))) (hBOOL (hAPP _let_1 bool (hAPP X_b (fun _let_1 bool) (member X_b) B_1) (hAPP _let_0 _let_1 (hAPP (fun X_a X_b) (fun _let_0 _let_1) (image X_a X_b) F) A_3)))))) ) 16.26/16.37 ( int, int, s, (let ((_let_0 (fun int int))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m))), (one_one int), zEven ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (ring_1_Ints X_a))) (or (not (ring_1 X_a)) (= _let_0 (ti (fun X_a bool) _let_0)))) ) 16.26/16.37 ( bool ) 16.26/16.37 ( nat ) 16.26/16.37 ( int ) 16.26/16.37 ( (fun int bool) ) 16.26/16.37 ( (fun nat bool) ) 16.26/16.37 ( (product_prod nat nat) ) 16.26/16.37 ( real ) 16.26/16.37 ( rat ) 16.26/16.37 ( complex ) 16.26/16.37 ( (filter nat) ) 16.26/16.37 ( (product_prod int int) ) 16.26/16.37 ( (product_prod real real) ) 16.26/16.37 ( (fun nat rat) ) 16.26/16.37 ( (filter real) ) 16.26/16.37 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 16.26/16.37 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 16.26/16.37 ) 16.26/16.37 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_151511 $$unsorted) (BOUND_VARIABLE_151512 $$unsorted)) (let ((_let_0 (ring_1_of_int X_a))) (or (not (ring_char_0 X_a)) (= (= (ti int BOUND_VARIABLE_151512) (ti int BOUND_VARIABLE_151511)) (= (hAPP int X_a _let_0 BOUND_VARIABLE_151512) (hAPP int X_a _let_0 BOUND_VARIABLE_151511))))) ) 16.26/16.37 ( int, s, s ) 16.26/16.37 ( int, s1, s ) 16.26/16.37 ( real, s, s1 ) 16.26/16.37 ( rat, pls, m ) 16.26/16.37 ( complex, pls, pls ) 16.26/16.37 ( complex, m, pls ) 16.26/16.37 ) 16.26/16.38 (instantiation (forall ((N_4 $$unsorted)) (= (hBOOL (hAPP (fun nat bool) bool (finite_finite_1 nat) N_4)) (not (forall ((M_2 $$unsorted)) (not (forall ((X $$unsorted)) (let ((_let_0 (fun nat bool))) (or (not (hBOOL (hAPP _let_0 bool (hAPP nat (fun _let_0 bool) (member nat) X) N_4))) (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) X) M_2)))) )) ))) ) 16.26/16.38 ( (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 16.26/16.38 ) 16.26/16.38 (instantiation (forall ((Z_1 $$unsorted) (W $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 Z_1) W))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 W) Z_1))) (= (ti int W) (ti int Z_1))))) ) 16.26/16.38 ( (one_one int), (zero_zero int) ) 16.26/16.38 ( (one_one int), t ) 16.26/16.38 ( (zero_zero int), (one_one int) ) 16.26/16.38 ( (zero_zero int), min_1 ) 16.26/16.38 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.38 ( (zero_zero int), s ) 16.26/16.38 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.26/16.38 ( (zero_zero int), (hAPP int int (number_number_of int) pls) ) 16.26/16.38 ( (zero_zero int), skv_4 ) 16.26/16.38 ( (zero_zero int), skv_10 ) 16.26/16.38 ( pls, min_1 ) 16.26/16.38 ( min_1, (zero_zero int) ) 16.26/16.38 ( min_1, pls ) 16.26/16.38 ( min_1, min_1 ) 16.26/16.38 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 16.26/16.38 ( s, (zero_zero int) ) 16.26/16.38 ( t, (one_one int) ) 16.26/16.38 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 16.26/16.38 ( (hAPP int int (number_number_of int) pls), (zero_zero int) ) 16.26/16.38 ( skv_4, (zero_zero int) ) 16.26/16.38 ( skv_10, (zero_zero int) ) 16.26/16.38 ) 16.26/16.38 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_151615 $$unsorted) (BOUND_VARIABLE_151616 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (or (not (ordered_ab_group_add X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) BOUND_VARIABLE_151615) BOUND_VARIABLE_151616)) (zero_zero X_a))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_151615) BOUND_VARIABLE_151616)))))) ) 16.26/16.38 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.38 ( int, (one_one int), t ) 16.26/16.38 ( int, pls, (one_one int) ) 16.26/16.38 ( int, pls, pls ) 16.26/16.38 ( int, pls, min_1 ) 16.26/16.38 ( int, pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.38 ( int, min_1, pls ) 16.26/16.38 ( int, min_1, min_1 ) 16.26/16.38 ( int, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.38 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 16.26/16.38 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.38 ( int, skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.38 ( int, skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.38 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.38 ( real, (zero_zero real), pi ) 16.26/16.38 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.38 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.38 ( real, (zero_zero real), skv_2 ) 16.26/16.38 ( real, (zero_zero real), skv_8 ) 16.26/16.38 ( real, (zero_zero real), skv_9 ) 16.26/16.38 ( real, pi, (zero_zero real) ) 16.26/16.38 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.38 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.38 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 16.26/16.38 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.26/16.38 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 16.26/16.38 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 16.26/16.38 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 16.26/16.38 ) 16.26/16.38 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_151683 $$unsorted) (BOUND_VARIABLE_151684 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_151683)) BOUND_VARIABLE_151684)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) BOUND_VARIABLE_151683) (hAPP X_a int (archimedean_ceiling X_a) BOUND_VARIABLE_151684))))) ) 16.26/16.38 ( real, (one_one int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.38 ( real, (zero_zero int), pi ) 16.26/16.38 ( real, (zero_zero int), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.38 ( real, (zero_zero int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.38 ( real, (zero_zero int), skv_2 ) 16.26/16.38 ( real, (zero_zero int), skv_8 ) 16.26/16.38 ( real, (zero_zero int), skv_9 ) 16.26/16.38 ) 16.26/16.38 (instantiation (forall ((X_a $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (uminus_uminus _let_0))) (= (hAPP _let_0 _let_0 _let_1 (hAPP _let_0 _let_0 _let_1 A_3)) (ti _let_0 A_3)))) ) 16.26/16.38 ( bool, fNot ) 16.26/16.38 ( nat, (even_odd_even nat) ) 16.26/16.38 ( nat, prime ) 16.26/16.38 ( int, nat_neg ) 16.26/16.38 ( int, zprime ) 16.26/16.38 ( int, zEven ) 16.26/16.38 ( int, zOdd ) 16.26/16.38 ( int, (even_odd_even int) ) 16.26/16.38 ( int, twoSqu1091635170sum2sq ) 16.26/16.38 ( int, nat_is_nat ) 16.26/16.38 ( (fun int bool), nat_nat_set ) 16.26/16.38 ( (product_prod nat nat), pred_nat ) 16.26/16.38 ( (product_prod int int), frac_1 ) 16.26/16.38 ( (fun nat rat), vanishes ) 16.26/16.38 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)), ratrel ) 16.26/16.38 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), pair_less ) 16.26/16.38 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), pair_leq ) 16.26/16.38 ) 16.26/16.38 (instantiation (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) X_1) Y_1))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP real nat natceiling X_1)) (hAPP real nat natceiling Y_1)))) ) 16.26/16.38 ( (zero_zero real), pi ) 16.26/16.38 ( (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.38 ( (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.38 ( (zero_zero real), skv_3 ) 16.26/16.38 ( (zero_zero real), skv_5 ) 16.26/16.38 ( (zero_zero real), skv_7 ) 16.26/16.38 ( (zero_zero real), skv_12 ) 16.26/16.38 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.26/16.38 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.38 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.26/16.38 ( skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.38 ) 16.26/16.38 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_151765 $$unsorted) (BOUND_VARIABLE_151766 $$unsorted)) (or (not (linordered_field X_a)) (not (forall ((E $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) (zero_zero X_a)) E))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_151765) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_151766) E))))) )) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_151765) BOUND_VARIABLE_151766))) ) 16.26/16.38 ( int, (one_one int), t ) 16.26/16.38 ( int, (zero_zero int), (one_one int) ) 16.26/16.38 ( int, (zero_zero int), min_1 ) 16.26/16.38 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.38 ( int, (zero_zero int), s ) 16.26/16.38 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.26/16.38 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 16.26/16.38 ( int, (zero_zero int), skv_4 ) 16.26/16.38 ( int, (zero_zero int), skv_10 ) 16.26/16.38 ( int, min_1, pls ) 16.26/16.38 ( int, min_1, min_1 ) 16.26/16.38 ( real, (zero_zero real), pi ) 16.26/16.38 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.38 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.38 ( real, (zero_zero real), skv_3 ) 16.26/16.38 ( real, (zero_zero real), skv_5 ) 16.26/16.38 ( real, (zero_zero real), skv_7 ) 16.26/16.38 ( real, (zero_zero real), skv_12 ) 16.26/16.38 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.26/16.38 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.38 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.26/16.38 ( real, skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.38 ) 16.26/16.38 (instantiation (forall ((N_1 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (fact_fact int))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) N_1))) (= (hAPP int int _let_1 N_1) (hAPP int int (hAPP int _let_0 (times_times int) N_1) (hAPP int int _let_1 (hAPP int int (hAPP int _let_0 (minus_minus int) N_1) (one_one int)))))))) ) 16.26/16.38 ( (one_one int) ) 16.26/16.38 ( pls ) 16.26/16.38 ( min_1 ) 16.26/16.38 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.38 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.38 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.38 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.38 ) 16.26/16.38 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_151836 $$unsorted) (BOUND_VARIABLE_151837 $$unsorted) (BOUND_VARIABLE_151838 $$unsorted) (BOUND_VARIABLE_151839 $$unsorted)) (let ((_let_0 (fun (filter nat) bool))) (let ((_let_1 (filter X_a))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun X_a X_b))) (let ((_let_4 (fun nat X_b))) (let ((_let_5 (fun nat X_a))) (or (not (metric_space X_b)) (not (metric_space X_a)) (not (hBOOL (hAPP _let_1 bool (hAPP X_b _let_2 (hAPP _let_3 (fun X_b _let_2) (tendsto X_a X_b) BOUND_VARIABLE_151836) BOUND_VARIABLE_151837) (hAPP X_a _let_1 (at X_a) BOUND_VARIABLE_151838)))) (not (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_0 (hAPP _let_5 (fun X_a _let_0) (tendsto nat X_a) BOUND_VARIABLE_151839) BOUND_VARIABLE_151838) sequentially))) (not (forall ((N_2 $$unsorted)) (not (= (ti X_a BOUND_VARIABLE_151838) (hAPP nat X_a BOUND_VARIABLE_151839 N_2))) )) (hBOOL (hAPP (filter nat) bool (hAPP X_b _let_0 (hAPP _let_4 (fun X_b _let_0) (tendsto nat X_b) (hAPP _let_5 _let_4 (hAPP _let_3 (fun _let_5 _let_4) (combb X_a X_b nat) BOUND_VARIABLE_151836) BOUND_VARIABLE_151839)) BOUND_VARIABLE_151837) sequentially))))))))) ) 16.26/16.38 ( real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))) ) 16.26/16.38 ) 16.26/16.38 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_151915 $$unsorted) (BOUND_VARIABLE_151916 $$unsorted) (BOUND_VARIABLE_151917 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (times_times X_a))) (let ((_let_2 (plus_plus X_a))) (or (not (real_normed_algebra X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_151915) BOUND_VARIABLE_151917)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_151916) BOUND_VARIABLE_151917)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_151915) BOUND_VARIABLE_151916)) BOUND_VARIABLE_151917)))))) ) 16.26/16.38 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int), t ) 16.26/16.38 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int), skv_13 ) 16.26/16.38 ) 16.26/16.38 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_151962 $$unsorted) (BOUND_VARIABLE_151963 $$unsorted)) (let ((_let_0 (fun (filter nat) bool))) (or (not (real_normed_vector X_a)) (not (forall ((R_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) R_2))) (not (forall ((No $$unsorted)) (not (forall ((N_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) No) N_2))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP X_a real (norm_norm X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) (hAPP nat X_a BOUND_VARIABLE_151962 N_2)) BOUND_VARIABLE_151963))) R_2))) )) ))) )) (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_0 (hAPP (fun nat X_a) (fun X_a _let_0) (tendsto nat X_a) BOUND_VARIABLE_151962) BOUND_VARIABLE_151963) sequentially)))) ) 16.26/16.38 ( real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real) ) 16.26/16.38 ) 16.26/16.38 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_152001 $$unsorted)) (or (not (number_semiring X_a)) (= (hAPP int X_a (number_number_of X_a) (hAPP nat int (semiring_1_of_nat int) BOUND_VARIABLE_152001)) (hAPP nat X_a (semiring_1_of_nat X_a) BOUND_VARIABLE_152001))) ) 16.26/16.38 ( nat, (zero_zero nat) ) 16.26/16.38 ( int, (zero_zero nat) ) 16.26/16.38 ( int, (hAPP nat nat suc (zero_zero nat)) ) 16.26/16.38 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.26/16.38 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.38 ( real, (zero_zero nat) ) 16.26/16.38 ( real, (hAPP nat nat suc (zero_zero nat)) ) 16.26/16.38 ( quickcheck_code_int, (zero_zero nat) ) 16.26/16.38 ( quickcheck_code_int, (hAPP nat nat suc (zero_zero nat)) ) 16.26/16.38 ( code_code_numeral, (zero_zero nat) ) 16.26/16.38 ) 16.26/16.38 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_152031 $$unsorted) (BOUND_VARIABLE_152032 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (or (not (semiring_div X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_152031) BOUND_VARIABLE_152032))) (= (ti X_a BOUND_VARIABLE_152032) (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) (hAPP X_a X_a (hAPP X_a _let_0 (div_div X_a) BOUND_VARIABLE_152032) BOUND_VARIABLE_152031)) BOUND_VARIABLE_152031)))) ) 16.26/16.38 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 16.26/16.38 ) 16.26/16.38 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member int))) (or (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP int int (hAPP int (fun int int) (times_times int) X_2) Y_2)) zOdd))) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 X_2) zOdd)))))) ) 16.26/16.38 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 16.26/16.38 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 16.26/16.38 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13 ) 16.26/16.38 ) 16.26/16.38 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_152059 $$unsorted) (BOUND_VARIABLE_152060 $$unsorted) (BOUND_VARIABLE_152061 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (times_times X_a))) (let ((_let_2 (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_152059))) (or (not (ab_semigroup_mult X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_152060)) BOUND_VARIABLE_152061) (hAPP X_a X_a _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_152060) BOUND_VARIABLE_152061))))))) ) 16.26/16.38 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 16.26/16.38 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 16.26/16.38 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi), ii ) 16.26/16.38 ) 16.26/16.38 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_152091 $$unsorted) (BOUND_VARIABLE_152092 $$unsorted)) (let ((_let_0 (fun nat X_a))) (let ((_let_1 (hAPP nat nat suc BOUND_VARIABLE_152092))) (or (not (ring_1 X_a)) (= (hAPP nat X_a (hAPP _let_0 _let_0 (diffs X_a) BOUND_VARIABLE_152091) BOUND_VARIABLE_152092) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) (hAPP nat X_a (semiring_1_of_nat X_a) _let_1)) (hAPP nat X_a BOUND_VARIABLE_152091 _let_1)))))) ) 16.26/16.38 ( bool, (even_odd_even nat), (zero_zero nat) ) 16.26/16.38 ( bool, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), (hAPP nat nat suc (zero_zero nat)) ) 16.26/16.38 ( bool, prime, (zero_zero nat) ) 16.26/16.38 ( bool, prime, (hAPP nat nat suc (zero_zero nat)) ) 16.26/16.38 ( nat, suc, (zero_zero nat) ) 16.26/16.38 ( nat, suc, (hAPP nat nat suc (zero_zero nat)) ) 16.26/16.38 ( nat, (fact_fact nat), (zero_zero nat) ) 16.26/16.38 ( nat, (hAPP nat (fun nat nat) (plus_plus nat) (one_one nat)), (zero_zero nat) ) 16.26/16.38 ( int, (semiring_1_of_nat int), (zero_zero nat) ) 16.26/16.38 ( int, (semiring_1_of_nat int), (hAPP nat nat suc (zero_zero nat)) ) 16.26/16.38 ( int, (semiring_1_of_nat int), (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 16.26/16.38 ( int, (hAPP int (fun nat int) (power_power int) s), (hAPP nat nat suc (zero_zero nat)) ) 16.26/16.38 ( int, (hAPP int (fun nat int) (power_power int) s1), (hAPP nat nat suc (zero_zero nat)) ) 16.26/16.38 ( int, (hAPP int (fun nat int) (power_power int) skv_14), (hAPP nat nat suc (zero_zero nat)) ) 16.26/16.38 ( (fun int int), (hAPP (fun int (fun nat int)) (fun nat (fun int int)) (combc int nat int) (power_power int)), (hAPP nat nat suc (zero_zero nat)) ) 16.26/16.38 ( (fun nat nat), (plus_plus nat), (zero_zero nat) ) 16.26/16.38 ( (fun nat nat), (let ((_let_0 (fun nat (fun nat nat)))) (hAPP _let_0 _let_0 (combc nat nat nat) (times_times nat))), (hAPP nat nat suc (zero_zero nat)) ) 16.26/16.38 ( (fun nat nat), (let ((_let_0 (fun nat (fun nat nat)))) (let ((_let_1 (combc nat nat nat))) (hAPP _let_0 _let_0 _let_1 (hAPP (fun nat nat) _let_0 (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_0 _let_0 _let_1 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))), (zero_zero nat) ) 16.26/16.38 ( real, (real_1 nat), (zero_zero nat) ) 16.26/16.38 ( (fun real real), root, (hAPP nat nat suc (zero_zero nat)) ) 16.26/16.38 ( complex, (hAPP complex (fun nat complex) (power_power complex) ii), (hAPP nat nat suc (zero_zero nat)) ) 16.26/16.38 ) 16.26/16.38 (instantiation (forall ((X_1 $$unsorted) (A_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP nat real (real_1 nat) X_1)) A_1))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) X_1) (hAPP real nat natfloor A_1)))) ) 16.26/16.38 ( (zero_zero nat), pi ) 16.26/16.38 ( (zero_zero nat), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.38 ( (zero_zero nat), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.38 ( (zero_zero nat), skv_3 ) 16.26/16.38 ( (zero_zero nat), skv_5 ) 16.26/16.38 ( (zero_zero nat), skv_7 ) 16.26/16.38 ( (zero_zero nat), skv_12 ) 16.26/16.38 ) 16.26/16.38 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_152262 $$unsorted)) (or (not (real_algebra_1 X_a)) (= (hAPP nat X_a (semiring_1_of_nat X_a) BOUND_VARIABLE_152262) (hAPP real X_a (of_real X_a) (hAPP nat real (semiring_1_of_nat real) BOUND_VARIABLE_152262)))) ) 16.26/16.38 ( int, (zero_zero nat) ) 16.26/16.38 ( int, (hAPP nat nat suc (zero_zero nat)) ) 16.26/16.38 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.26/16.38 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.38 ( real, (zero_zero nat) ) 16.26/16.38 ( real, (hAPP nat nat suc (zero_zero nat)) ) 16.26/16.38 ) 16.26/16.38 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_152301 $$unsorted) (BOUND_VARIABLE_152302 $$unsorted)) (let ((_let_0 (exp X_a))) (let ((_let_1 (fun X_a X_a))) (or (not (real_normed_field X_a)) (not (banach X_a)) (= (hAPP X_a X_a (hAPP X_a _let_1 (times_times X_a) (hAPP X_a X_a _let_0 BOUND_VARIABLE_152301)) (hAPP X_a X_a _let_0 BOUND_VARIABLE_152302)) (hAPP X_a X_a _let_0 (hAPP X_a X_a (hAPP X_a _let_1 (plus_plus X_a) BOUND_VARIABLE_152301) BOUND_VARIABLE_152302)))))) ) 16.26/16.38 ( nat, (one_one nat), (one_one nat) ) 16.26/16.38 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 16.26/16.38 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 16.26/16.38 ) 16.26/16.38 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun real _let_1))) (let ((_let_3 (hAPP real real cos X_2))) (or (= (zero_zero real) _let_3) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP _let_1 (fun real _let_0) (deriv real) (hAPP _let_1 _let_1 (hAPP _let_2 (fun _let_1 _let_1) (combs real real real) (hAPP _let_1 _let_2 (hAPP _let_2 (fun _let_1 _let_2) (combb real _let_1 real) (inverse_divide real)) sin)) cos)) X_2) (hAPP real real (inverse_inverse real) (hAPP nat real (hAPP real (fun nat real) (power_power real) _let_3) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))))))) ) 16.26/16.38 ( (zero_zero real) ) 16.26/16.38 ( pi ) 16.26/16.38 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.38 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.26/16.38 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.26/16.38 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.26/16.38 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 16.26/16.38 ) 16.26/16.38 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_152334 $$unsorted) (BOUND_VARIABLE_152335 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (inverse_inverse X_a))) (let ((_let_3 (zero_zero X_a))) (let ((_let_4 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_152334) BOUND_VARIABLE_152335))) (or (not (linord1117847801e_zero X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_152334)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_152335))) (and (or (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_3) _let_4))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_152335) BOUND_VARIABLE_152334))) (or (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) _let_4) _let_3))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_152334) BOUND_VARIABLE_152335))))))))))) ) 16.26/16.38 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.38 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 16.26/16.38 ( int, (one_one int), pls ) 16.26/16.38 ( int, (one_one int), t ) 16.26/16.38 ( int, pls, (one_one int) ) 16.26/16.38 ( int, pls, pls ) 16.26/16.38 ( int, pls, min_1 ) 16.26/16.38 ( int, pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.38 ( int, min_1, pls ) 16.26/16.38 ( int, min_1, min_1 ) 16.26/16.38 ( int, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.38 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 16.26/16.38 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), pls ) 16.26/16.38 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s ) 16.26/16.38 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 16.26/16.38 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_4 ) 16.26/16.38 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_10 ) 16.26/16.38 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13 ) 16.26/16.38 ( int, t, (one_one int) ) 16.26/16.38 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.38 ( int, skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.38 ( int, skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.38 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.38 ( real, (zero_zero real), pi ) 16.26/16.38 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.38 ( real, (zero_zero real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.26/16.38 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.38 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.38 ( real, (zero_zero real), skv_2 ) 16.26/16.38 ( real, (zero_zero real), skv_8 ) 16.26/16.38 ( real, (zero_zero real), skv_9 ) 16.26/16.38 ( real, pi, (zero_zero real) ) 16.26/16.38 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.38 ( real, pi, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 16.26/16.38 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.26/16.38 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.38 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 16.26/16.38 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.26/16.38 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.38 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 16.26/16.38 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 16.26/16.38 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 16.26/16.38 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 16.26/16.38 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.26/16.38 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.26/16.38 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 16.26/16.38 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 16.26/16.38 ( real, skv_2, (zero_zero real) ) 16.26/16.38 ( real, skv_8, (zero_zero real) ) 16.26/16.38 ( real, skv_9, (zero_zero real) ) 16.26/16.38 ( complex, ii, ii ) 16.26/16.38 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 16.26/16.38 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 16.26/16.38 ) 16.26/16.38 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_152376 $$unsorted)) (or (not (archim1804426504_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) BOUND_VARIABLE_152376))) (not (forall ((N_2 $$unsorted)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP X_a X_a (inverse_inverse X_a) (hAPP nat X_a (semiring_1_of_nat X_a) (hAPP nat nat suc N_2)))) BOUND_VARIABLE_152376))) ))) ) 16.26/16.38 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.38 ( int, (one_one int) ) 16.26/16.38 ( int, pls ) 16.26/16.38 ( int, min_1 ) 16.26/16.38 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.38 ( real, pi ) 16.26/16.38 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.38 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.38 ( real, skv_2 ) 16.26/16.38 ( real, skv_8 ) 16.26/16.38 ( real, skv_9 ) 16.26/16.38 ) 16.26/16.38 (instantiation (forall ((S $$unsorted)) (= (hBOOL (hAPP (fun nat bool) bool (finite_finite_1 nat) S)) (not (forall ((K_1 $$unsorted)) (let ((_let_0 (fun nat bool))) (not (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) S) (hAPP nat _let_0 (ord_lessThan nat) K_1))))) ))) ) 16.26/16.38 ( (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 16.26/16.38 ) 16.26/16.38 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (fun nat X_a))) (let ((_let_1 (zero_zero X_a))) (or (not (topological_space X_a)) (not (comm_monoid_add X_a)) (hBOOL (hAPP X_a bool (hAPP _let_0 (fun X_a bool) (sums X_a) (hAPP X_a _let_0 (combk X_a nat) _let_1)) _let_1))))) ) 16.26/16.38 ( bool ) 16.26/16.38 ( nat ) 16.26/16.38 ( int ) 16.26/16.38 ( (fun int bool) ) 16.26/16.38 ( (fun int int) ) 16.26/16.38 ( (fun nat bool) ) 16.26/16.38 ( (fun nat nat) ) 16.26/16.38 ( (product_prod nat nat) ) 16.26/16.38 ( (fun (product_prod nat nat) bool) ) 16.26/16.38 ( (fun nat (fun (product_prod nat nat) bool)) ) 16.26/16.38 ( real ) 16.26/16.38 ( (fun real real) ) 16.26/16.38 ( rat ) 16.26/16.38 ( (fun nat (fun nat bool)) ) 16.26/16.38 ( complex ) 16.26/16.38 ( (filter nat) ) 16.26/16.38 ( (product_prod int int) ) 16.26/16.38 ( quickcheck_code_int ) 16.26/16.38 ( (fun bool bool) ) 16.26/16.38 ( code_code_numeral ) 16.26/16.38 ( (product_prod real real) ) 16.26/16.38 ( (fun nat (product_prod nat nat)) ) 16.26/16.38 ( (fun nat rat) ) 16.26/16.38 ( (filter real) ) 16.26/16.38 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 16.26/16.38 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 16.26/16.38 ( (fun nat (product_prod int int)) ) 16.26/16.38 ) 16.26/16.38 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_152490 $$unsorted)) (or (not (real_n2089651433ebra_1 X_a)) (= (hAPP nat real (semiring_1_of_nat real) BOUND_VARIABLE_152490) (hAPP X_a real (norm_norm X_a) (hAPP nat X_a (semiring_1_of_nat X_a) BOUND_VARIABLE_152490)))) ) 16.26/16.38 ( int, (zero_zero nat) ) 16.26/16.38 ( int, (hAPP nat nat suc (zero_zero nat)) ) 16.26/16.38 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.26/16.38 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.38 ( real, (zero_zero nat) ) 16.26/16.38 ( real, (hAPP nat nat suc (zero_zero nat)) ) 16.26/16.38 ) 16.26/16.38 (instantiation (forall ((A_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_0 (hAPP nat real (real_1 nat) A_1))) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) _let_0) X_1))) (= (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) (hAPP real nat natfloor X_1)) A_1) (hAPP real nat natfloor (hAPP real real (hAPP real (fun real real) (minus_minus real) X_1) _let_0))))) ) 16.26/16.38 ( (zero_zero nat), pi ) 16.26/16.38 ( (zero_zero nat), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.38 ( (zero_zero nat), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.38 ( (zero_zero nat), skv_3 ) 16.26/16.38 ( (zero_zero nat), skv_5 ) 16.26/16.38 ( (zero_zero nat), skv_7 ) 16.26/16.38 ( (zero_zero nat), skv_12 ) 16.26/16.38 ) 16.26/16.38 (instantiation (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted) (F $$unsorted) (G $$unsorted)) (let ((_let_0 (fun (product_prod X_a X_b) X_c))) (or (not (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_0 (product_prod X_a X_b))) (= (hAPP _let_0 X_c G (hAPP X_b _let_0 (hAPP X_a (fun X_b _let_0) (product_Pair X_a X_b) X) Y)) (hAPP X_b X_c (hAPP X_a (fun X_b X_c) F X) Y))) )) (= (ti _let_0 G) (hAPP (fun X_a (fun X_b X_c)) _let_0 (product_prod_case X_a X_b X_c) F)))) ) 16.26/16.38 ( nat, bool, nat, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat (fun nat bool)))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat (fun nat bool) nat) (hAPP _let_1 _let_1 (combc nat nat bool) (fequal nat))) suc))), pred_nat ) 16.26/16.38 ( int, bool, int, (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun int _let_1))) (let ((_let_6 (fun int _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (fun _let_2 _let_1))) (let ((_let_9 (fun _let_1 _let_1))) (hAPP _let_1 _let_1 (hAPP _let_7 _let_9 (combb _let_0 _let_0 int) (hAPP _let_6 _let_7 (combs int bool bool) (hAPP _let_0 _let_6 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 int) fconj) (hAPP int _let_0 (ord_less int) (zero_zero int))))) (hAPP int _let_1 (hAPP _let_5 _let_5 (combc int int _let_0) (hAPP _let_5 _let_5 (hAPP _let_9 (fun _let_5 _let_5) (combb _let_1 _let_1 int) (combc int int bool)) (hAPP _let_3 _let_5 (hAPP _let_8 (fun _let_3 _let_5) (combb _let_2 _let_1 int) (hAPP _let_1 _let_8 (combb int _let_0 int) (fequal int))) int_gcd))) (one_one int))))))))))))), frac_1 ) 16.26/16.38 ( int, int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun _let_0 _let_1))) (let ((_let_3 (fun _let_0 _let_0))) (let ((_let_4 (fun int _let_3))) (let ((_let_5 (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP _let_0 _let_1 (hAPP _let_4 _let_2 (combc int _let_0 _let_0) (hAPP _let_1 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_1 _let_4) (combb _let_0 _let_3 int) (combb int int int)) (hAPP _let_0 _let_1 (hAPP _let_1 _let_2 (combb int _let_0 int) (plus_plus int)) _let_5))) _let_5))))))), twoSqu1094008024sum2sq ) 16.26/16.38 ( (product_prod int int), bool, (product_prod int int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun _let_2 (fun _let_2 bool)))) (let ((_let_5 (fun (fun _let_2 bool) (fun _let_2 bool)))) (let ((_let_6 (fun _let_2 _let_5))) (let ((_let_7 (fun _let_4 _let_4))) (let ((_let_8 (fun _let_2 _let_3))) (let ((_let_9 (fun _let_2 _let_0))) (let ((_let_10 (fun _let_2 int))) (let ((_let_11 (fun _let_10 _let_9))) (let ((_let_12 (hAPP (fun int _let_0) _let_11 (combb int _let_0 _let_2) (fequal int)))) (let ((_let_13 (product_snd int int))) (let ((_let_14 (hAPP (fun _let_2 bool) _let_8 (hAPP (fun bool _let_3) (fun (fun _let_2 bool) _let_8) (combb bool _let_3 _let_2) fconj) (hAPP (fun _let_2 bool) (fun _let_2 bool) (hAPP _let_3 _let_5 (combb bool bool _let_2) fNot) (hAPP int (fun _let_2 bool) (hAPP _let_9 (fun int (fun _let_2 bool)) (combc _let_2 int bool) (hAPP _let_10 _let_9 _let_12 _let_13)) (zero_zero int)))))) (let ((_let_15 (fun _let_2 _let_10))) (let ((_let_16 (fun _let_10 (fun _let_2 bool)))) (let ((_let_17 (fun _let_2 _let_16))) (let ((_let_18 (fun _let_2 _let_9))) (let ((_let_19 (fun _let_10 _let_10))) (let ((_let_20 (fun _let_2 _let_19))) (let ((_let_21 (fun _let_10 _let_15))) (let ((_let_22 (fun _let_2 _let_1))) (let ((_let_23 (hAPP _let_10 _let_22 (hAPP (fun int _let_1) (fun _let_10 _let_22) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (let ((_let_24 (fun int _let_10))) (hAPP _let_4 _let_4 (hAPP _let_6 _let_7 (combs _let_2 (fun _let_2 bool) (fun _let_2 bool)) (hAPP _let_8 _let_6 (hAPP (fun _let_3 _let_5) (fun _let_8 _let_6) (combb _let_3 _let_5 _let_2) (combb bool bool _let_2)) _let_14)) (hAPP _let_4 _let_4 (hAPP _let_5 _let_7 (combb (fun _let_2 bool) (fun _let_2 bool) _let_2) (hAPP _let_8 _let_5 (combs _let_2 bool bool) _let_14)) (hAPP _let_15 _let_4 (hAPP _let_17 (fun _let_15 _let_4) (combs _let_2 _let_10 (fun _let_2 bool)) (hAPP _let_18 _let_17 (hAPP (fun _let_9 _let_16) (fun _let_18 _let_17) (combb _let_9 _let_16 _let_2) (combs _let_2 int bool)) (hAPP _let_15 _let_18 (hAPP _let_11 (fun _let_15 _let_18) (combb _let_10 _let_9 _let_2) _let_12) (hAPP _let_10 _let_15 (hAPP _let_20 _let_21 (combc _let_2 _let_10 _let_10) (hAPP _let_22 _let_20 (hAPP (fun _let_1 _let_19) (fun _let_22 _let_20) (combb _let_1 _let_19 _let_2) (combb int int _let_2)) _let_23)) _let_13)))) (hAPP _let_10 _let_15 (hAPP _let_24 _let_21 (combb int _let_10 _let_2) (hAPP _let_22 _let_24 (combc _let_2 int int) _let_23)) _let_13))))))))))))))))))))))))))))), ratrel ) 16.26/16.38 ) 16.26/16.38 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_152609 $$unsorted) (BOUND_VARIABLE_152610 $$unsorted)) (let ((_let_0 (archim2085082626_floor X_a))) (or (not (archim1727834104eiling X_a)) (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP X_a int _let_0 BOUND_VARIABLE_152609)) (hAPP X_a int _let_0 BOUND_VARIABLE_152610)))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_152609) BOUND_VARIABLE_152610)))) ) 16.26/16.38 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.38 ( int, (one_one int), t ) 16.26/16.38 ( int, pls, (one_one int) ) 16.26/16.38 ( int, pls, pls ) 16.26/16.38 ( int, pls, min_1 ) 16.26/16.38 ( int, pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.38 ( int, min_1, pls ) 16.26/16.38 ( int, min_1, min_1 ) 16.26/16.38 ( int, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.38 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.38 ( int, skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.38 ( int, skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.38 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.38 ( real, (zero_zero real), pi ) 16.26/16.38 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.38 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.38 ( real, (zero_zero real), skv_2 ) 16.26/16.38 ( real, (zero_zero real), skv_8 ) 16.26/16.38 ( real, (zero_zero real), skv_9 ) 16.26/16.38 ( real, pi, (zero_zero real) ) 16.26/16.38 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.38 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.38 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 16.26/16.38 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.26/16.38 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 16.26/16.38 ) 16.26/16.38 (instantiation (forall ((X_a $$unsorted)) (or (not (number_ring X_a)) (not (hBOOL (hAPP X_a bool (iszero X_a) (hAPP int X_a (number_number_of X_a) (hAPP int int bit1 pls)))))) ) 16.26/16.38 ( nat ) 16.26/16.38 ( int ) 16.26/16.38 ( real ) 16.26/16.38 ( rat ) 16.26/16.38 ( complex ) 16.26/16.38 ( quickcheck_code_int ) 16.26/16.38 ( code_code_numeral ) 16.26/16.38 ) 16.26/16.38 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_152698 $$unsorted)) (let ((_let_0 (filter X_a))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (inverse_inverse X_a))) (or (not (real_n1866405975lgebra X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_152698)) (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 (hAPP (fun X_a X_a) (fun X_a _let_1) (tendsto X_a X_a) _let_2) (hAPP X_a X_a _let_2 BOUND_VARIABLE_152698)) (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_152698))))))) ) 16.26/16.38 ( bool, fFalse ) 16.26/16.38 ( bool, fTrue ) 16.26/16.38 ( int, pls ) 16.26/16.38 ( int, min_1 ) 16.26/16.38 ( int, s ) 16.26/16.38 ( int, m ) 16.26/16.38 ( int, s1 ) 16.26/16.38 ( int, t ) 16.26/16.38 ( (fun int bool), nat_neg ) 16.26/16.38 ( (fun int bool), zprime ) 16.26/16.38 ( (fun int bool), zEven ) 16.26/16.38 ( (fun int bool), zOdd ) 16.26/16.38 ( (fun int bool), (even_odd_even int) ) 16.26/16.38 ( (fun int bool), twoSqu1091635170sum2sq ) 16.26/16.38 ( (fun int bool), nat_is_nat ) 16.26/16.38 ( (fun int (fun int bool)), norRRset ) 16.26/16.38 ( (fun int (fun int bool)), quadRes ) 16.26/16.38 ( (fun int (fun int bool)), sRStar ) 16.26/16.38 ( (fun int (fun int bool)), d22set ) 16.26/16.38 ( (fun int (fun int bool)), sr ) 16.26/16.38 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 16.26/16.38 ( (fun int int), zfact ) 16.26/16.38 ( (fun int int), bit0 ) 16.26/16.38 ( (fun int int), bit1 ) 16.26/16.38 ( (fun int int), (fact_fact int) ) 16.26/16.38 ( (fun int int), pred ) 16.26/16.38 ( (fun int int), succ ) 16.26/16.38 ( (fun nat bool), (even_odd_even nat) ) 16.26/16.38 ( (fun nat bool), prime ) 16.26/16.38 ( (fun nat nat), suc ) 16.26/16.38 ( (fun nat nat), (fact_fact nat) ) 16.26/16.38 ( (fun nat nat), fact ) 16.26/16.38 ( (fun nat nat), nat_size ) 16.26/16.38 ( (fun nat nat), (size_size nat) ) 16.26/16.38 ( (fun (product_prod nat nat) bool), pred_nat ) 16.26/16.38 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 16.26/16.38 ( real, (zero_zero real) ) 16.26/16.38 ( real, pi ) 16.26/16.38 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.38 ( (fun real real), ln ) 16.26/16.38 ( (fun real real), cos ) 16.26/16.38 ( (fun real real), sqrt ) 16.26/16.38 ( (fun real real), sin ) 16.26/16.38 ( (fun real real), arccos ) 16.26/16.38 ( (fun real real), arcsin ) 16.26/16.38 ( (fun real real), tan ) 16.26/16.38 ( (fun real real), arctan ) 16.26/16.38 ( (fun nat (fun nat bool)), coprime ) 16.26/16.38 ( complex, ii ) 16.26/16.38 ( (fun nat real), (real_1 nat) ) 16.26/16.38 ( (fun nat real), sin_coeff ) 16.26/16.38 ( (fun nat real), cos_coeff ) 16.26/16.38 ( (filter nat), sequentially ) 16.26/16.38 ( (fun int (fun int int)), (gcd_gcd int) ) 16.26/16.38 ( (fun int (fun int int)), legendre ) 16.26/16.38 ( (fun int (fun int int)), legacy_zgcd ) 16.26/16.38 ( (fun int (fun int int)), standardRes ) 16.26/16.38 ( (fun int (fun int int)), nat_tsub ) 16.26/16.38 ( (fun int (fun int int)), multInv ) 16.26/16.38 ( (fun int (fun int int)), z3mod ) 16.26/16.38 ( (fun int (fun int int)), z3div ) 16.26/16.38 ( (fun int (fun int int)), int_gcd ) 16.26/16.38 ( (fun int (fun int int)), int_lcm ) 16.26/16.38 ( (fun int (fun int int)), inv ) 16.26/16.38 ( (fun complex complex), expi ) 16.26/16.38 ( (fun complex complex), cnj ) 16.26/16.38 ( (fun real complex), cis ) 16.26/16.38 ( (fun int nat), nat_1 ) 16.26/16.38 ( (fun int nat), phi ) 16.26/16.38 ( (fun (fun int bool) bool), nat_nat_set ) 16.26/16.38 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 16.26/16.38 ( (fun nat (fun nat nat)), nat_gcd ) 16.26/16.38 ( (fun nat (fun nat nat)), nat_lcm ) 16.26/16.38 ( (fun (fun int bool) int), (the int) ) 16.26/16.38 ( (fun complex real), re ) 16.26/16.38 ( (fun complex real), im ) 16.26/16.38 ( (fun complex real), arg ) 16.26/16.38 ( (fun bool bool), fNot ) 16.26/16.38 ( (fun nat (fun real real)), root ) 16.26/16.38 ( (fun real (fun real real)), log ) 16.26/16.38 ( (fun real (fun real real)), powr ) 16.26/16.38 ( (fun bool (fun bool bool)), fimplies ) 16.26/16.38 ( (fun bool (fun bool bool)), fconj ) 16.26/16.38 ( (fun bool (fun bool bool)), fdisj ) 16.26/16.38 ( (fun int (fun int (product_prod int int))), negDivAlg ) 16.26/16.38 ( (fun int (fun int (product_prod int int))), posDivAlg ) 16.26/16.38 ( (fun int (fun int (product_prod int int))), divmod_int ) 16.26/16.38 ( (fun int (fun int (product_prod int int))), pdivmod ) 16.26/16.38 ( (fun int (fun int (product_prod int int))), norm_frac ) 16.26/16.38 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 16.26/16.38 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 16.26/16.38 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 16.26/16.38 ( (fun int (fun int (fun int bool))), zcong ) 16.26/16.38 ( (fun int (fun int (fun int bool))), zcongm ) 16.26/16.38 ( (fun int (fun int (fun int bool))), noXRRset ) 16.26/16.38 ( (fun int (fun int (fun int bool))), bnorRset ) 16.26/16.38 ( (fun int (fun int (fun int bool))), wset ) 16.26/16.38 ( (fun (product_prod int int) bool), frac_1 ) 16.26/16.38 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 16.26/16.38 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 16.26/16.38 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 16.26/16.38 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 16.26/16.38 ( (fun (fun nat rat) bool), vanishes ) 16.26/16.38 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 16.26/16.38 ( (fun code_code_numeral nat), code_c271388182l_size ) 16.26/16.38 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 16.26/16.38 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 16.26/16.38 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 16.26/16.38 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 16.26/16.38 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 16.26/16.38 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 16.26/16.38 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 16.26/16.38 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 16.26/16.38 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 16.26/16.38 ( (fun complex nat), complex_size ) 16.26/16.38 ( (fun complex nat), (size_size complex) ) 16.26/16.39 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 16.26/16.39 ( (fun nat (fun nat (product_prod int int))), bezw ) 16.26/16.39 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 16.26/16.39 ( (fun int (fun nat nat)), nat_aux ) 16.26/16.39 ( (fun int (fun (fun int bool) bool)), rsetR ) 16.26/16.39 ( (fun int (fun (fun int bool) bool)), resSet ) 16.26/16.39 ( (fun int (list int)), quickc666637781d_zero ) 16.26/16.39 ( (fun (product_prod int int) rat), frct ) 16.26/16.39 ( (fun int (fun int rat)), fract ) 16.26/16.39 ( (fun real (fun real complex)), complex_1 ) 16.26/16.39 ( (fun real (fun real complex)), rcis ) 16.26/16.39 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 16.26/16.39 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 16.26/16.39 ( (fun int real), (real_1 int) ) 16.26/16.39 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 16.26/16.39 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 16.26/16.39 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 16.26/16.39 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 16.26/16.39 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 16.26/16.39 ( (fun real nat), natfloor ) 16.26/16.39 ( (fun real nat), natceiling ) 16.26/16.39 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 16.26/16.39 ( (fun quickcheck_code_int int), quickcheck_int_of ) 16.26/16.39 ( (fun rat (product_prod int int)), quotient_of ) 16.26/16.39 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 16.26/16.39 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 16.26/16.39 ( (fun rat real), ratreal ) 16.26/16.39 ( (fun code_code_numeral int), code_int_of ) 16.26/16.39 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 16.26/16.39 ( (fun int quickcheck_code_int), quickcheck_of_int ) 16.26/16.39 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 16.26/16.39 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 16.26/16.39 ) 16.26/16.39 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_152789 $$unsorted)) (or (not (monoid_mult X_a)) (= (ti X_a BOUND_VARIABLE_152789) (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_152789) (one_one nat)))) ) 16.26/16.39 ( bool, fFalse ) 16.26/16.39 ( bool, fTrue ) 16.26/16.39 ( int, pls ) 16.26/16.39 ( int, min_1 ) 16.26/16.39 ( int, s ) 16.26/16.39 ( int, m ) 16.26/16.39 ( int, s1 ) 16.26/16.39 ( int, t ) 16.26/16.39 ( int, skv_14 ) 16.26/16.39 ( (fun int bool), nat_neg ) 16.26/16.39 ( (fun int bool), zprime ) 16.26/16.39 ( (fun int bool), zEven ) 16.26/16.39 ( (fun int bool), zOdd ) 16.26/16.39 ( (fun int bool), (even_odd_even int) ) 16.26/16.39 ( (fun int bool), twoSqu1091635170sum2sq ) 16.26/16.39 ( (fun int bool), nat_is_nat ) 16.26/16.39 ( (fun int (fun int bool)), norRRset ) 16.26/16.39 ( (fun int (fun int bool)), quadRes ) 16.26/16.39 ( (fun int (fun int bool)), sRStar ) 16.26/16.39 ( (fun int (fun int bool)), d22set ) 16.26/16.39 ( (fun int (fun int bool)), sr ) 16.26/16.39 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 16.26/16.39 ( (fun int int), zfact ) 16.26/16.39 ( (fun int int), bit0 ) 16.26/16.39 ( (fun int int), bit1 ) 16.26/16.39 ( (fun int int), (fact_fact int) ) 16.26/16.39 ( (fun int int), pred ) 16.26/16.39 ( (fun int int), succ ) 16.26/16.39 ( (fun nat bool), (even_odd_even nat) ) 16.26/16.39 ( (fun nat bool), prime ) 16.26/16.39 ( (fun nat nat), suc ) 16.26/16.39 ( (fun nat nat), (fact_fact nat) ) 16.26/16.39 ( (fun nat nat), fact ) 16.26/16.39 ( (fun nat nat), nat_size ) 16.26/16.39 ( (fun nat nat), (size_size nat) ) 16.26/16.39 ( (fun (product_prod nat nat) bool), pred_nat ) 16.26/16.39 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 16.26/16.39 ( real, pi ) 16.26/16.39 ( real, (hAPP int real (number_number_of real) min_1) ) 16.26/16.39 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.39 ( (fun real real), ln ) 16.26/16.39 ( (fun real real), cos ) 16.26/16.39 ( (fun real real), sqrt ) 16.26/16.39 ( (fun real real), sin ) 16.26/16.39 ( (fun real real), arccos ) 16.26/16.39 ( (fun real real), arcsin ) 16.26/16.39 ( (fun real real), tan ) 16.26/16.39 ( (fun real real), arctan ) 16.26/16.39 ( (fun nat (fun nat bool)), coprime ) 16.26/16.39 ( complex, ii ) 16.26/16.39 ( (fun nat real), (real_1 nat) ) 16.26/16.39 ( (fun nat real), sin_coeff ) 16.26/16.39 ( (fun nat real), cos_coeff ) 16.26/16.39 ( (filter nat), sequentially ) 16.26/16.39 ( (fun int (fun int int)), (gcd_gcd int) ) 16.26/16.39 ( (fun int (fun int int)), legendre ) 16.26/16.39 ( (fun int (fun int int)), legacy_zgcd ) 16.26/16.39 ( (fun int (fun int int)), standardRes ) 16.26/16.39 ( (fun int (fun int int)), nat_tsub ) 16.26/16.39 ( (fun int (fun int int)), multInv ) 16.26/16.39 ( (fun int (fun int int)), z3mod ) 16.26/16.39 ( (fun int (fun int int)), z3div ) 16.26/16.39 ( (fun int (fun int int)), int_gcd ) 16.26/16.39 ( (fun int (fun int int)), int_lcm ) 16.26/16.39 ( (fun int (fun int int)), inv ) 16.26/16.39 ( (fun complex complex), expi ) 16.26/16.39 ( (fun complex complex), cnj ) 16.26/16.39 ( (fun real complex), cis ) 16.26/16.39 ( (fun int nat), nat_1 ) 16.26/16.39 ( (fun int nat), phi ) 16.26/16.39 ( (fun (fun int bool) bool), nat_nat_set ) 16.26/16.39 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 16.26/16.39 ( (fun nat (fun nat nat)), nat_gcd ) 16.26/16.39 ( (fun nat (fun nat nat)), nat_lcm ) 16.26/16.39 ( (fun (fun int bool) int), (the int) ) 16.26/16.39 ( (fun complex real), re ) 16.26/16.39 ( (fun complex real), im ) 16.26/16.39 ( (fun complex real), arg ) 16.26/16.39 ( (fun bool bool), fNot ) 16.26/16.39 ( (fun nat (fun real real)), root ) 16.26/16.39 ( (fun real (fun real real)), log ) 16.26/16.39 ( (fun real (fun real real)), powr ) 16.26/16.39 ( (fun bool (fun bool bool)), fimplies ) 16.26/16.39 ( (fun bool (fun bool bool)), fconj ) 16.26/16.39 ( (fun bool (fun bool bool)), fdisj ) 16.26/16.39 ( (fun int (fun int (product_prod int int))), negDivAlg ) 16.26/16.39 ( (fun int (fun int (product_prod int int))), posDivAlg ) 16.26/16.39 ( (fun int (fun int (product_prod int int))), divmod_int ) 16.26/16.39 ( (fun int (fun int (product_prod int int))), pdivmod ) 16.26/16.39 ( (fun int (fun int (product_prod int int))), norm_frac ) 16.26/16.39 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 16.26/16.39 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 16.26/16.39 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 16.26/16.39 ( (fun int (fun int (fun int bool))), zcong ) 16.26/16.39 ( (fun int (fun int (fun int bool))), zcongm ) 16.26/16.39 ( (fun int (fun int (fun int bool))), noXRRset ) 16.26/16.39 ( (fun int (fun int (fun int bool))), bnorRset ) 16.26/16.39 ( (fun int (fun int (fun int bool))), wset ) 16.26/16.39 ( (fun (product_prod int int) bool), frac_1 ) 16.26/16.39 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 16.26/16.39 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 16.26/16.39 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 16.26/16.39 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 16.26/16.39 ( (fun (fun nat rat) bool), vanishes ) 16.26/16.39 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 16.26/16.39 ( (fun code_code_numeral nat), code_c271388182l_size ) 16.26/16.39 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 16.26/16.39 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 16.26/16.39 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 16.26/16.39 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 16.26/16.39 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 16.26/16.39 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 16.26/16.39 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 16.26/16.39 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 16.26/16.39 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 16.26/16.39 ( (fun complex nat), complex_size ) 16.26/16.39 ( (fun complex nat), (size_size complex) ) 16.26/16.39 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 16.26/16.39 ( (fun nat (fun nat (product_prod int int))), bezw ) 16.26/16.39 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 16.26/16.39 ( (fun int (fun nat nat)), nat_aux ) 16.26/16.39 ( (fun int (fun (fun int bool) bool)), rsetR ) 16.26/16.39 ( (fun int (fun (fun int bool) bool)), resSet ) 16.26/16.39 ( (fun int (list int)), quickc666637781d_zero ) 16.26/16.39 ( (fun (product_prod int int) rat), frct ) 16.26/16.39 ( (fun int (fun int rat)), fract ) 16.26/16.39 ( (fun real (fun real complex)), complex_1 ) 16.26/16.39 ( (fun real (fun real complex)), rcis ) 16.26/16.39 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 16.26/16.39 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 16.26/16.39 ( (fun int real), (real_1 int) ) 16.26/16.39 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 16.26/16.39 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 16.26/16.39 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 16.26/16.39 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 16.26/16.39 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 16.26/16.39 ( (fun real nat), natfloor ) 16.26/16.39 ( (fun real nat), natceiling ) 16.26/16.39 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 16.26/16.39 ( (fun quickcheck_code_int int), quickcheck_int_of ) 16.26/16.39 ( (fun rat (product_prod int int)), quotient_of ) 16.26/16.39 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 16.26/16.39 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 16.26/16.39 ( (fun rat real), ratreal ) 16.26/16.39 ( (fun code_code_numeral int), code_int_of ) 16.26/16.39 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 16.26/16.39 ( (fun int quickcheck_code_int), quickcheck_of_int ) 16.26/16.39 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 16.26/16.39 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 16.26/16.39 ) 16.26/16.39 (instantiation (forall ((R_4 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) R_4))) (not (forall ((N_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (real_1 int))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) R_4) (hAPP int real _let_1 (hAPP int int (hAPP int (fun int int) (plus_plus int) N_2) (one_one int)))))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) (hAPP int real _let_1 N_2)) R_4)))))) ))) ) 16.26/16.39 ( pi ) 16.26/16.39 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.39 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.39 ( skv_3 ) 16.26/16.39 ( skv_5 ) 16.26/16.39 ( skv_7 ) 16.26/16.39 ( skv_12 ) 16.26/16.39 ) 16.26/16.39 (instantiation (forall ((S $$unsorted)) (= (forall ((M_2 $$unsorted)) (not (forall ((N_2 $$unsorted)) (let ((_let_0 (fun nat bool))) (or (not (hBOOL (hAPP _let_0 bool (hAPP nat (fun _let_0 bool) (member nat) N_2) S))) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) M_2) N_2))))) )) ) (not (hBOOL (hAPP (fun nat bool) bool (finite_finite_1 nat) S)))) ) 16.26/16.39 ( (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 16.26/16.39 ) 16.26/16.39 (instantiation (forall ((X_a $$unsorted) (P_1 $$unsorted) (A_2 $$unsorted)) (or (not (hBOOL (hAPP X_a bool P_1 A_2))) (not (forall ((X $$unsorted)) (or (not (hBOOL (hAPP X_a bool P_1 X))) (= (ti X_a A_2) (ti X_a X))) )) (= (hAPP (fun X_a bool) X_a (hilbert_Eps X_a) P_1) (ti X_a A_2))) ) 16.26/16.39 ( nat, (even_odd_even nat), (zero_zero nat) ) 16.26/16.39 ( nat, (even_odd_even nat), (one_one nat) ) 16.26/16.39 ( nat, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.39 ( nat, prime, (zero_zero nat) ) 16.26/16.39 ( nat, prime, (hAPP nat nat suc (zero_zero nat)) ) 16.26/16.39 ( nat, prime, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.39 ( int, (hAPP int (fun int bool) (ord_less int) pls), pls ) 16.26/16.39 ( int, (hAPP int (fun int bool) (ord_less int) pls), min_1 ) 16.26/16.39 ( int, (hAPP int (fun int bool) (ord_less_eq int) pls), min_1 ) 16.26/16.39 ( int, (hAPP int (fun int bool) (ord_less_eq int) (one_one int)), t ) 16.26/16.39 ( int, nat_neg, (one_one int) ) 16.26/16.39 ( int, nat_neg, (hAPP int int (number_number_of int) min_1) ) 16.26/16.39 ( int, nat_neg, (hAPP int int (number_number_of int) pls) ) 16.26/16.39 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (one_one int) ) 16.26/16.39 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.39 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), s ) 16.26/16.39 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.26/16.39 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) pls) ) 16.26/16.39 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_4 ) 16.26/16.39 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_10 ) 16.26/16.39 ( int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (one_one int) ) 16.26/16.39 ( int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.39 ( int, zprime, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.39 ( int, zprime, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.39 ( int, (hAPP int (fun int bool) (ord_less int) s), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.39 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) s)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.39 ( int, (let ((_let_0 (fun int int))) (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 16.26/16.39 ( int, (hAPP int (fun int bool) (ord_less int) (one_one int)), t ) 16.26/16.39 ( int, (even_odd_even int), (one_one int) ) 16.26/16.39 ( int, (even_odd_even int), (zero_zero int) ) 16.26/16.39 ( int, twoSqu1091635170sum2sq, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) t))) ) 16.26/16.39 ( int, nat_is_nat, (one_one int) ) 16.26/16.39 ( int, nat_is_nat, (zero_zero int) ) 16.26/16.39 ( int, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.39 ( int, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.26/16.39 ( int, (hAPP int (fun int bool) (ord_less int) min_1), pls ) 16.26/16.39 ( int, (hAPP int (fun int bool) (ord_less int) min_1), min_1 ) 16.26/16.39 ( int, (hAPP int (fun int bool) (ord_less_eq int) min_1), pls ) 16.26/16.39 ( int, (hAPP int (fun int bool) (ord_less_eq int) min_1), min_1 ) 16.26/16.39 ( int, (let ((_let_0 (fun int int))) (hAPP int (fun int bool) quadRes (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int int (number_number_of int) min_1) ) 16.26/16.39 ( int, (let ((_let_0 (fun int bool))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (let ((_let_3 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int _let_1 _let_2 s) _let_3)) (hAPP nat int (hAPP int _let_1 _let_2 s1) _let_3)))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.39 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.39 ( int, (hAPP int (fun int bool) (ord_less int) t), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.39 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.39 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_4)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.39 ( int, (hAPP int (fun int bool) (ord_less int) skv_4), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.39 ( int, (hAPP int (fun int bool) (ord_less int) skv_10), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.39 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_10)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.39 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.39 ( (fun int bool), (hAPP (fun int nat) (fun (fun int bool) bool) (nat_tr1645093318rphism int nat) nat_1), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 16.26/16.39 ( (fun int bool), (hAPP int (fun (fun int bool) bool) (member int) (one_one int)), zEven ) 16.26/16.39 ( (fun nat bool), (finite_finite_1 nat), (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 16.26/16.39 ( (fun nat bool), (hAPP (fun nat int) (fun (fun nat bool) bool) (nat_tr1645093318rphism nat int) (semiring_1_of_nat int)), (hAPP bool (fun nat bool) (combk bool nat) fTrue) ) 16.26/16.39 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), pi ) 16.26/16.39 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.39 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.39 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_3 ) 16.26/16.39 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_5 ) 16.26/16.39 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_7 ) 16.26/16.39 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_12 ) 16.26/16.39 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), pi ) 16.26/16.39 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.39 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.39 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_2 ) 16.26/16.39 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_8 ) 16.26/16.39 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_9 ) 16.26/16.39 ( real, (hAPP real (fun real bool) (ord_less real) (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))), (zero_zero real) ) 16.26/16.39 ( real, (hAPP real (fun real bool) (ord_less real) (one_one real)), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.39 ( real, (hAPP real (fun real bool) (ord_less real) pi), (zero_zero real) ) 16.26/16.39 ( real, (hAPP real (fun real bool) (ord_less real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.39 ( real, (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.39 ( real, (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 16.26/16.39 ( real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 (fun real bool) (sums real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (hAPP real _let_1 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc)))), (one_one real) ) 16.26/16.39 ( real, (hAPP real (fun real bool) (ord_less real) (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi))), pi ) 16.26/16.39 ( real, (hAPP real (fun real bool) (ord_less real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.39 ( real, (hAPP real (fun real bool) (ord_less real) (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 16.26/16.39 ( real, (hAPP real (fun real bool) (ord_less_eq real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 16.26/16.39 ( real, (hAPP real (fun real bool) (ord_less_eq real) skv_5), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.39 ( (filter nat), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun (filter nat) bool))) (hAPP real _let_2 (hAPP _let_1 (fun real _let_2) (tendsto nat real) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))) (zero_zero real))))), sequentially ) 16.26/16.39 ( (filter nat), (trivial_limit nat), sequentially ) 16.26/16.39 ( (filter real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (filter real) bool))) (hAPP real _let_2 (hAPP _let_0 (fun real _let_2) (tendsto real real) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin)) (zero_zero real))))), (hAPP real (filter real) (at real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.26/16.39 ) 16.26/16.39 (instantiation (forall ((N_1 $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (div_div nat))) (or (hBOOL (hAPP nat bool (even_odd_even nat) N_1)) (= (hAPP nat nat suc (hAPP nat nat (hAPP nat _let_0 _let_2 N_1) _let_1)) (hAPP nat nat (hAPP nat _let_0 _let_2 (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) N_1) (one_one nat))) _let_1)))))) ) 16.26/16.39 ( (zero_zero nat) ) 16.26/16.39 ( (one_one nat) ) 16.26/16.39 ) 16.26/16.39 (instantiation (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (power_power real))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (= (hAPP complex real (norm_norm complex) (hAPP real complex (hAPP real (fun real complex) complex_1 X_1) Y_1)) (hAPP real real sqrt (hAPP real real (hAPP real (fun real real) (plus_plus real) (hAPP nat real (hAPP real _let_0 _let_1 X_1) _let_2)) (hAPP nat real (hAPP real _let_0 _let_1 Y_1) _let_2))))))) ) 16.26/16.39 ( (one_one real), (zero_zero real) ) 16.26/16.39 ( (zero_zero real), (one_one real) ) 16.26/16.39 ( (zero_zero real), (zero_zero real) ) 16.26/16.39 ) 16.26/16.39 (instantiation (forall ((N_1 $$unsorted) (M $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (dvd_dvd int) N_1) M))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 M) (zero_zero int))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 N_1) M))))) ) 16.26/16.39 ( (one_one int), t ) 16.26/16.39 ( (zero_zero int), (one_one int) ) 16.26/16.39 ( (zero_zero int), min_1 ) 16.26/16.39 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.39 ( (zero_zero int), s ) 16.26/16.39 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.26/16.39 ( (zero_zero int), (hAPP int int (number_number_of int) pls) ) 16.26/16.39 ( (zero_zero int), skv_4 ) 16.26/16.39 ( (zero_zero int), skv_10 ) 16.26/16.39 ( min_1, pls ) 16.26/16.39 ( min_1, min_1 ) 16.26/16.39 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 16.26/16.39 ) 16.26/16.39 (instantiation (forall ((F $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 A_2) B_1))) (not (forall ((X $$unsorted)) (let ((_let_2 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 X) B_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 A_2) X))) (not (forall ((Y $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP (fun real real) (fun real _let_0) (deriv real) F) X) Y))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Y) (zero_zero real))))) )))) )) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real F B_1)) (hAPP real real F A_2)))))) ) 16.26/16.39 ( cos, skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.39 ( sqrt, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 16.26/16.39 ( sqrt, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real) ) 16.26/16.39 ) 16.26/16.39 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_153110 $$unsorted) (BOUND_VARIABLE_153111 $$unsorted)) (or (not (linorder X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_153110) BOUND_VARIABLE_153111))) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (ord_min X_a) BOUND_VARIABLE_153110) BOUND_VARIABLE_153111) (ti X_a BOUND_VARIABLE_153110))) ) 16.26/16.39 ( int, (one_one int), t ) 16.26/16.39 ( int, (zero_zero int), (one_one int) ) 16.26/16.39 ( int, (zero_zero int), min_1 ) 16.26/16.39 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.39 ( int, (zero_zero int), s ) 16.26/16.39 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.26/16.39 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 16.26/16.39 ( int, (zero_zero int), skv_4 ) 16.26/16.39 ( int, (zero_zero int), skv_10 ) 16.26/16.39 ( int, min_1, pls ) 16.26/16.39 ( int, min_1, min_1 ) 16.26/16.39 ( real, (zero_zero real), pi ) 16.26/16.39 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.39 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.39 ( real, (zero_zero real), skv_3 ) 16.26/16.39 ( real, (zero_zero real), skv_5 ) 16.26/16.39 ( real, (zero_zero real), skv_7 ) 16.26/16.39 ( real, (zero_zero real), skv_12 ) 16.26/16.39 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.26/16.39 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.39 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.26/16.39 ( real, skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.39 ) 16.26/16.39 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_153167 $$unsorted) (BOUND_VARIABLE_153168 $$unsorted)) (let ((_let_0 (archimedean_ceiling X_a))) (or (not (archim1727834104eiling X_a)) (= (hAPP X_a int _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) BOUND_VARIABLE_153167) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_153168))) (hAPP int int (hAPP int (fun int int) (minus_minus int) (hAPP X_a int _let_0 BOUND_VARIABLE_153167)) (hAPP int int (number_number_of int) BOUND_VARIABLE_153168))))) ) 16.26/16.39 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), min_1 ) 16.26/16.39 ( code_code_numeral, (zero_zero code_code_numeral), (hAPP int int bit1 pls) ) 16.26/16.39 ) 16.26/16.39 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (ring_1 X_a)) (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) (one_one X_a)) (ring_1_Ints X_a))))) ) 16.26/16.39 ( nat ) 16.26/16.39 ( int ) 16.26/16.39 ( real ) 16.26/16.39 ( rat ) 16.26/16.39 ( complex ) 16.26/16.39 ( quickcheck_code_int ) 16.26/16.39 ( code_code_numeral ) 16.26/16.39 ) 16.26/16.39 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (BOUND_VARIABLE_153254 $$unsorted) (BOUND_VARIABLE_153255 $$unsorted) (BOUND_VARIABLE_153256 $$unsorted) (BOUND_VARIABLE_153257 $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (order X_b)) (not (order X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_153255) (hAPP X_b X_a BOUND_VARIABLE_153256 BOUND_VARIABLE_153257)))) (not (hBOOL (hAPP X_b bool (hAPP X_b (fun X_b bool) (ord_less X_b) BOUND_VARIABLE_153257) BOUND_VARIABLE_153254))) (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (hBOOL (hAPP X_b bool (hAPP X_b (fun X_b bool) (ord_less X_b) X) Y))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) (hAPP X_b X_a BOUND_VARIABLE_153256 X)) (hAPP X_b X_a BOUND_VARIABLE_153256 Y)))) )) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_153255) (hAPP X_b X_a BOUND_VARIABLE_153256 BOUND_VARIABLE_153254))))) ) 16.26/16.39 ( int, int, pls, min_1, bit1, pls ) 16.26/16.39 ( int, int, min_1, (zero_zero int), (uminus_uminus int), min_1 ) 16.26/16.39 ( int, int, t, (one_one int), (let ((_let_0 (fun int int))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m))), (one_one int) ) 16.26/16.39 ( real, int, pls, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (number_number_of real), min_1 ) 16.26/16.39 ( real, real, (zero_zero real), (zero_zero real), cos, pi ) 16.26/16.39 ( real, real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), cos, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.39 ( real, real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), sin, pi ) 16.26/16.39 ( real, real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), skv_5, sqrt, (zero_zero real) ) 16.26/16.39 ) 16.26/16.39 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_153359 $$unsorted) (BOUND_VARIABLE_153360 $$unsorted) (BOUND_VARIABLE_153361 $$unsorted) (BOUND_VARIABLE_153362 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (or (not (order X_b)) (not (order X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_b X_a BOUND_VARIABLE_153360 BOUND_VARIABLE_153361)) BOUND_VARIABLE_153362))) (not (hBOOL (hAPP X_b bool (hAPP X_b (fun X_b bool) (ord_less_eq X_b) BOUND_VARIABLE_153359) BOUND_VARIABLE_153361))) (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (hBOOL (hAPP X_b bool (hAPP X_b (fun X_b bool) (ord_less_eq X_b) Y) X))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) (hAPP X_b X_a BOUND_VARIABLE_153360 Y)) (hAPP X_b X_a BOUND_VARIABLE_153360 X)))) )) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_b X_a BOUND_VARIABLE_153360 BOUND_VARIABLE_153359)) BOUND_VARIABLE_153362))))) ) 16.26/16.39 ( int, int, (one_one int), bit1, min_1, min_1 ) 16.26/16.39 ( int, int, (zero_zero int), (number_number_of int), pls, pls ) 16.26/16.39 ( int, int, min_1, bit1, min_1, pls ) 16.26/16.39 ( real, real, (zero_zero real), (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (zero_zero real) ) 16.26/16.39 ( real, real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (uminus_uminus real), (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi), pi ) 16.26/16.39 ( real, real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (uminus_uminus real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.26/16.39 ( real, real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), cos, skv_5, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.39 ( real, real, skv_5, (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.39 ) 16.26/16.39 (instantiation (forall ((X_1 $$unsorted)) (= (hAPP int nat nat_1 (hAPP real int (archimedean_ceiling real) X_1)) (hAPP real nat natceiling X_1)) ) 16.26/16.39 ( (one_one real) ) 16.26/16.39 ( (zero_zero real) ) 16.26/16.39 ) 16.26/16.39 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_153431 $$unsorted) (BOUND_VARIABLE_153432 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (uminus_uminus X_a))) (or (not (ordered_ab_group_add X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_153432) (hAPP X_a X_a _let_2 BOUND_VARIABLE_153431))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_153431) (hAPP X_a X_a _let_2 BOUND_VARIABLE_153432)))))))) ) 16.26/16.39 ( int, (one_one int), (zero_zero int) ) 16.26/16.39 ( int, (one_one int), min_1 ) 16.26/16.39 ( int, (zero_zero int), (one_one int) ) 16.26/16.39 ( int, (zero_zero int), pls ) 16.26/16.39 ( int, pls, (zero_zero int) ) 16.26/16.39 ( int, pls, min_1 ) 16.26/16.39 ( int, min_1, (one_one int) ) 16.26/16.39 ( int, min_1, pls ) 16.26/16.39 ) 16.26/16.39 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (hAPP nat nat suc (zero_zero nat)))) (or (hBOOL (hAPP nat bool (even_odd_even nat) X_1)) (= _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (div_mod nat) X_1) (hAPP nat nat suc _let_0))))) ) 16.26/16.39 ( (zero_zero nat) ) 16.26/16.39 ( (one_one nat) ) 16.26/16.39 ) 16.26/16.39 (instantiation (forall ((V_1 $$unsorted)) (= (hAPP int real (number_number_of real) V_1) (hAPP complex real re (hAPP int complex (number_number_of complex) V_1))) ) 16.26/16.39 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.26/16.39 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.26/16.39 ( min_1 ) 16.26/16.39 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.39 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.26/16.39 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.39 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 16.26/16.39 ) 16.26/16.39 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (field_char_0 X_a)) (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) (zero_zero X_a)) (field_char_0_Rats X_a))))) ) 16.26/16.39 ( nat ) 16.26/16.39 ( int ) 16.26/16.39 ( real ) 16.26/16.39 ( rat ) 16.26/16.39 ( complex ) 16.26/16.39 ( quickcheck_code_int ) 16.26/16.39 ( code_code_numeral ) 16.26/16.39 ) 16.26/16.39 (instantiation (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted) (M $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (hAPP int _let_1 zcong A_1))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 B) M))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int _let_1 zcong B) C) M))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 C) M)))))) ) 16.26/16.39 ( (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.26/16.39 ) 16.26/16.39 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_153518 $$unsorted) (BOUND_VARIABLE_153519 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)))) (or (not (linord1117847801e_zero X_a)) (= (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_153518) BOUND_VARIABLE_153519))) (or (and (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_153519) (zero_zero X_a))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_153518) (zero_zero X_a)))) (and (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_153519)) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_153518))))))) ) 16.26/16.39 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.39 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.26/16.39 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.39 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 16.26/16.39 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.39 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.39 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.26/16.39 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.26/16.39 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.39 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.39 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.39 ) 16.26/16.39 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (= (and (= (hAPP complex real im Y_2) (hAPP complex real im X_2)) (= (hAPP complex real re Y_2) (hAPP complex real re X_2))) (= X_2 Y_2)) ) 16.26/16.39 ( (one_one complex), (one_one complex) ) 16.26/16.39 ( (one_one complex), ii ) 16.26/16.39 ( (one_one complex), (zero_zero complex) ) 16.26/16.39 ( ii, (one_one complex) ) 16.26/16.39 ( (zero_zero complex), ii ) 16.26/16.39 ) 16.26/16.39 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_0 (fun real bool))) (= (and (not (= X_2 Y_2)) (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) X_2) Y_2))) (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) X_2) Y_2)))) ) 16.26/16.39 ( (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.39 ( (zero_zero real), pi ) 16.26/16.39 ( (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.39 ( (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.39 ( (zero_zero real), skv_2 ) 16.26/16.39 ( (zero_zero real), skv_3 ) 16.26/16.39 ( (zero_zero real), skv_5 ) 16.26/16.39 ( (zero_zero real), skv_7 ) 16.26/16.39 ( (zero_zero real), skv_8 ) 16.26/16.39 ( (zero_zero real), skv_9 ) 16.26/16.39 ( (zero_zero real), skv_12 ) 16.26/16.39 ( pi, (zero_zero real) ) 16.26/16.39 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.26/16.39 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.26/16.39 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.39 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 16.26/16.39 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.26/16.39 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 16.26/16.39 ( skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.26/16.39 ) 16.26/16.39 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_153612 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (ordere142940540dd_abs X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_153612)) _let_0)) (= _let_0 (ti X_a BOUND_VARIABLE_153612))))) ) 16.26/16.39 ( bool, fFalse ) 16.26/16.39 ( bool, fTrue ) 16.26/16.39 ( int, pls ) 16.26/16.39 ( int, min_1 ) 16.26/16.39 ( int, s ) 16.26/16.39 ( int, m ) 16.26/16.39 ( int, s1 ) 16.26/16.39 ( int, t ) 16.26/16.39 ( (fun int bool), nat_neg ) 16.26/16.39 ( (fun int bool), zprime ) 16.26/16.39 ( (fun int bool), zEven ) 16.26/16.39 ( (fun int bool), zOdd ) 16.26/16.39 ( (fun int bool), (even_odd_even int) ) 16.26/16.39 ( (fun int bool), twoSqu1091635170sum2sq ) 16.26/16.39 ( (fun int bool), nat_is_nat ) 16.26/16.39 ( (fun int (fun int bool)), norRRset ) 16.26/16.39 ( (fun int (fun int bool)), quadRes ) 16.26/16.39 ( (fun int (fun int bool)), sRStar ) 16.26/16.39 ( (fun int (fun int bool)), d22set ) 16.26/16.39 ( (fun int (fun int bool)), sr ) 16.26/16.39 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 16.26/16.39 ( (fun int int), zfact ) 16.26/16.39 ( (fun int int), bit0 ) 16.26/16.39 ( (fun int int), bit1 ) 16.26/16.39 ( (fun int int), (fact_fact int) ) 16.26/16.39 ( (fun int int), pred ) 16.26/16.39 ( (fun int int), succ ) 16.26/16.39 ( (fun nat bool), (even_odd_even nat) ) 16.26/16.39 ( (fun nat bool), prime ) 16.26/16.39 ( (fun nat nat), suc ) 16.26/16.39 ( (fun nat nat), (fact_fact nat) ) 16.26/16.39 ( (fun nat nat), fact ) 16.26/16.39 ( (fun nat nat), nat_size ) 16.26/16.39 ( (fun nat nat), (size_size nat) ) 16.26/16.39 ( (fun (product_prod nat nat) bool), pred_nat ) 16.26/16.39 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 16.26/16.39 ( real, pi ) 16.26/16.39 ( (fun real real), ln ) 16.26/16.39 ( (fun real real), cos ) 16.26/16.39 ( (fun real real), sqrt ) 16.26/16.39 ( (fun real real), sin ) 16.26/16.39 ( (fun real real), arccos ) 16.26/16.39 ( (fun real real), arcsin ) 16.26/16.39 ( (fun real real), tan ) 16.26/16.39 ( (fun real real), arctan ) 16.26/16.39 ( (fun nat (fun nat bool)), coprime ) 16.26/16.39 ( complex, ii ) 16.26/16.39 ( (fun nat real), (real_1 nat) ) 16.26/16.39 ( (fun nat real), sin_coeff ) 16.26/16.39 ( (fun nat real), cos_coeff ) 16.26/16.39 ( (filter nat), sequentially ) 16.26/16.39 ( (fun int (fun int int)), (gcd_gcd int) ) 16.26/16.39 ( (fun int (fun int int)), legendre ) 16.26/16.39 ( (fun int (fun int int)), legacy_zgcd ) 16.26/16.39 ( (fun int (fun int int)), standardRes ) 16.26/16.39 ( (fun int (fun int int)), nat_tsub ) 16.26/16.39 ( (fun int (fun int int)), multInv ) 16.26/16.39 ( (fun int (fun int int)), z3mod ) 16.26/16.39 ( (fun int (fun int int)), z3div ) 16.26/16.39 ( (fun int (fun int int)), int_gcd ) 16.26/16.39 ( (fun int (fun int int)), int_lcm ) 16.26/16.39 ( (fun int (fun int int)), inv ) 16.26/16.39 ( (fun complex complex), expi ) 16.26/16.39 ( (fun complex complex), cnj ) 16.26/16.39 ( (fun real complex), cis ) 16.26/16.39 ( (fun int nat), nat_1 ) 16.26/16.39 ( (fun int nat), phi ) 16.26/16.39 ( (fun (fun int bool) bool), nat_nat_set ) 16.26/16.39 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 16.26/16.39 ( (fun nat (fun nat nat)), nat_gcd ) 16.26/16.39 ( (fun nat (fun nat nat)), nat_lcm ) 16.26/16.39 ( (fun (fun int bool) int), (the int) ) 16.26/16.39 ( (fun complex real), re ) 16.26/16.39 ( (fun complex real), im ) 16.26/16.39 ( (fun complex real), arg ) 16.26/16.39 ( (fun bool bool), fNot ) 16.26/16.39 ( (fun nat (fun real real)), root ) 16.26/16.39 ( (fun real (fun real real)), log ) 16.26/16.39 ( (fun real (fun real real)), powr ) 16.26/16.39 ( (fun bool (fun bool bool)), fimplies ) 16.26/16.39 ( (fun bool (fun bool bool)), fconj ) 16.26/16.39 ( (fun bool (fun bool bool)), fdisj ) 16.26/16.39 ( (fun int (fun int (product_prod int int))), negDivAlg ) 16.26/16.39 ( (fun int (fun int (product_prod int int))), posDivAlg ) 16.26/16.39 ( (fun int (fun int (product_prod int int))), divmod_int ) 16.26/16.39 ( (fun int (fun int (product_prod int int))), pdivmod ) 16.26/16.39 ( (fun int (fun int (product_prod int int))), norm_frac ) 16.26/16.39 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 16.26/16.39 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 16.26/16.39 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 16.26/16.39 ( (fun int (fun int (fun int bool))), zcong ) 16.26/16.39 ( (fun int (fun int (fun int bool))), zcongm ) 16.26/16.39 ( (fun int (fun int (fun int bool))), noXRRset ) 16.26/16.39 ( (fun int (fun int (fun int bool))), bnorRset ) 16.26/16.39 ( (fun int (fun int (fun int bool))), wset ) 16.26/16.39 ( (fun (product_prod int int) bool), frac_1 ) 16.26/16.39 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 16.26/16.39 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 16.26/16.39 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 16.26/16.39 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 16.26/16.39 ( (fun (fun nat rat) bool), vanishes ) 16.26/16.39 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 16.26/16.39 ( (fun code_code_numeral nat), code_c271388182l_size ) 16.26/16.39 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 16.26/16.39 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 16.26/16.39 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 16.26/16.39 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 16.26/16.39 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 16.26/16.39 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 16.26/16.39 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 16.26/16.39 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 16.26/16.39 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 16.26/16.39 ( (fun complex nat), complex_size ) 16.26/16.39 ( (fun complex nat), (size_size complex) ) 16.26/16.39 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 16.26/16.39 ( (fun nat (fun nat (product_prod int int))), bezw ) 16.26/16.39 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 16.26/16.39 ( (fun int (fun nat nat)), nat_aux ) 16.26/16.39 ( (fun int (fun (fun int bool) bool)), rsetR ) 16.26/16.39 ( (fun int (fun (fun int bool) bool)), resSet ) 16.26/16.39 ( (fun int (list int)), quickc666637781d_zero ) 16.35/16.39 ( (fun (product_prod int int) rat), frct ) 16.35/16.39 ( (fun int (fun int rat)), fract ) 16.35/16.39 ( (fun real (fun real complex)), complex_1 ) 16.35/16.39 ( (fun real (fun real complex)), rcis ) 16.35/16.39 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 16.35/16.39 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 16.35/16.39 ( (fun int real), (real_1 int) ) 16.35/16.39 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 16.35/16.39 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 16.35/16.39 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 16.35/16.39 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 16.35/16.39 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 16.35/16.39 ( (fun real nat), natfloor ) 16.35/16.39 ( (fun real nat), natceiling ) 16.35/16.39 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 16.35/16.39 ( (fun quickcheck_code_int int), quickcheck_int_of ) 16.35/16.39 ( (fun rat (product_prod int int)), quotient_of ) 16.35/16.39 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 16.35/16.39 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 16.35/16.39 ( (fun rat real), ratreal ) 16.35/16.39 ( (fun code_code_numeral int), code_int_of ) 16.35/16.39 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 16.35/16.39 ( (fun int quickcheck_code_int), quickcheck_of_int ) 16.35/16.39 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 16.35/16.39 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 16.35/16.39 ) 16.35/16.39 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_153630 $$unsorted)) (or (not (ring_1 X_a)) (= (hAPP int X_a (ring_1_of_int X_a) (hAPP nat int (semiring_1_of_nat int) BOUND_VARIABLE_153630)) (hAPP nat X_a (semiring_1_of_nat X_a) BOUND_VARIABLE_153630))) ) 16.35/16.39 ( int, (zero_zero nat) ) 16.35/16.39 ( int, (hAPP nat nat suc (zero_zero nat)) ) 16.35/16.39 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.35/16.39 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.39 ( real, (zero_zero nat) ) 16.35/16.39 ( real, (hAPP nat nat suc (zero_zero nat)) ) 16.35/16.39 ) 16.35/16.39 (instantiation (forall ((M $$unsorted) (K_4 $$unsorted) (N_1 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int _let_0 (gcd_gcd int) M))) (= (hAPP int int _let_1 N_1) (hAPP int int _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) K_4) M)) N_1))))) ) 16.35/16.39 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 16.35/16.39 ) 16.35/16.39 (instantiation (forall ((Ma $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat bool))) (= (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) Ma) N)) (and (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) Ma) N)) (not (= Ma N))))) ) 16.35/16.39 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.39 ) 16.35/16.39 (instantiation (forall ((Y_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP int real (number_number_of real) min_1)) Y_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Y_1) (one_one real)))) (= Y_1 (hAPP real real sin (hAPP real real arcsin Y_1)))))) ) 16.35/16.39 ( (zero_zero real) ) 16.35/16.39 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.39 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.39 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.39 ( skv_5 ) 16.35/16.39 ) 16.35/16.39 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (times_times X_a))) (or (not (ab_semigroup_mult X_a)) (= _let_0 (ti (fun X_a (fun X_a X_a)) _let_0)))) ) 16.35/16.39 ( bool ) 16.35/16.39 ( nat ) 16.35/16.39 ( int ) 16.35/16.39 ( (fun int bool) ) 16.35/16.39 ( (fun int (fun int bool)) ) 16.35/16.39 ( (fun int int) ) 16.35/16.39 ( (fun nat bool) ) 16.35/16.39 ( real ) 16.35/16.39 ( (fun real bool) ) 16.35/16.39 ( (fun real real) ) 16.35/16.39 ( rat ) 16.35/16.39 ( complex ) 16.35/16.39 ( (fun nat real) ) 16.35/16.39 ( (product_prod int int) ) 16.35/16.39 ( quickcheck_code_int ) 16.35/16.39 ( code_code_numeral ) 16.35/16.39 ( (fun int (fun int (fun int bool))) ) 16.35/16.39 ( (fun (product_prod int int) bool) ) 16.35/16.39 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 16.35/16.39 ( (fun (product_prod int int) int) ) 16.35/16.39 ( (fun int real) ) 16.35/16.39 ) 16.35/16.39 (instantiation (forall ((V_3 $$unsorted) (V_1 $$unsorted)) (let ((_let_0 (number_number_of nat))) (or (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) V_1) pls)) (= (hAPP int nat _let_0 (hAPP int int (hAPP int (fun int int) (times_times int) V_1) V_3)) (hAPP nat nat (hAPP nat (fun nat nat) (times_times nat) (hAPP int nat _let_0 V_1)) (hAPP int nat _let_0 V_3))))) ) 16.35/16.39 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.39 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.39 ( skv_13, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.39 ) 16.35/16.39 (instantiation (forall ((X_2 $$unsorted) (N $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (one_one real))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N))) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_2) _let_2)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (hAPP nat (fun real real) root N) X_2)) _let_2))))))) ) 16.35/16.39 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.39 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.39 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.39 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.39 ) 16.35/16.39 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real real))) (= (hAPP real real cos (hAPP real real (hAPP real _let_0 (minus_minus real) (hAPP real real (hAPP real _let_0 (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) X_1)) (hAPP real real sin X_1))) ) 16.35/16.39 ( (zero_zero real) ) 16.35/16.39 ( pi ) 16.35/16.39 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.39 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.35/16.39 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.35/16.39 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.35/16.39 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 16.35/16.40 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 16.35/16.40 ) 16.35/16.40 (instantiation (forall ((A_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_0 (hAPP nat real (real_1 nat) A_1))) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) _let_0) X_1))) (= (hAPP real nat natceiling (hAPP real real (hAPP real (fun real real) (minus_minus real) X_1) _let_0)) (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) (hAPP real nat natceiling X_1)) A_1)))) ) 16.35/16.40 ( (zero_zero nat), pi ) 16.35/16.40 ( (zero_zero nat), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.40 ( (zero_zero nat), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.40 ( (zero_zero nat), skv_3 ) 16.35/16.40 ( (zero_zero nat), skv_5 ) 16.35/16.40 ( (zero_zero nat), skv_7 ) 16.35/16.40 ( (zero_zero nat), skv_12 ) 16.35/16.40 ) 16.35/16.40 (instantiation (forall ((A_1 $$unsorted) (C $$unsorted)) (let ((_let_0 (hAPP int (fun int rat) fract (zero_zero int)))) (= (hAPP int rat _let_0 A_1) (hAPP int rat _let_0 C))) ) 16.35/16.40 ( (one_one int), (one_one int) ) 16.35/16.40 ) 16.35/16.40 (instantiation (forall ((B $$unsorted)) (let ((_let_0 (zero_zero int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 bool))) (or (= _let_0 (ti int B)) (hBOOL (hAPP _let_1 bool (hAPP int _let_2 (hAPP int (fun int _let_2) divmod_int_rel _let_0) B) (hAPP int _let_1 (hAPP int (fun int _let_1) (product_Pair int int) _let_0) _let_0))))))) ) 16.35/16.40 ( min_1 ) 16.35/16.40 ( s ) 16.35/16.40 ( m ) 16.35/16.40 ( s1 ) 16.35/16.40 ( t ) 16.35/16.40 ) 16.35/16.40 (instantiation (forall ((X_a $$unsorted)) (or (not (number_semiring X_a)) (= (one_one X_a) (hAPP int X_a (number_number_of X_a) (hAPP int int bit1 pls)))) ) 16.35/16.40 ( nat ) 16.35/16.40 ( int ) 16.35/16.40 ( real ) 16.35/16.40 ( rat ) 16.35/16.40 ( complex ) 16.35/16.40 ( quickcheck_code_int ) 16.35/16.40 ( code_code_numeral ) 16.35/16.40 ) 16.35/16.40 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_153894 $$unsorted)) (let ((_let_0 (norm_norm X_a))) (or (not (divisi14063676e_zero X_a)) (not (real_n1866405975lgebra X_a)) (= (hAPP real real (inverse_inverse real) (hAPP X_a real _let_0 BOUND_VARIABLE_153894)) (hAPP X_a real _let_0 (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_153894))))) ) 16.35/16.40 ( real, (zero_zero real) ) 16.35/16.40 ( complex, ii ) 16.35/16.40 ) 16.35/16.40 (instantiation (forall ((N_1 $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (div_div nat))) (or (not (hBOOL (hAPP nat bool (even_odd_even nat) N_1))) (= (hAPP nat nat (hAPP nat _let_0 _let_2 (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) N_1) (one_one nat))) _let_1) (hAPP nat nat (hAPP nat _let_0 _let_2 N_1) _let_1)))))) ) 16.35/16.40 ( (zero_zero nat) ) 16.35/16.40 ( (one_one nat) ) 16.35/16.40 ) 16.35/16.40 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (zero_zero real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (hAPP real _let_0 (times_times real) (hAPP int real (number_number_of real) _let_2)))) (let ((_let_4 (hAPP real real _let_3 X_1))) (let ((_let_5 (hAPP real real tan X_1))) (or (= _let_1 (hAPP real real cos X_1)) (= _let_1 (hAPP real real cos _let_4)) (= (hAPP real real tan _let_4) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP real real _let_3 _let_5)) (hAPP real real (hAPP real _let_0 (minus_minus real) (one_one real)) (hAPP nat real (hAPP real (fun nat real) (power_power real) _let_5) (hAPP int nat (number_number_of nat) _let_2)))))))))))) ) 16.35/16.40 ( (zero_zero real) ) 16.35/16.40 ( pi ) 16.35/16.40 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.40 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.35/16.40 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.35/16.40 ( (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 16.35/16.40 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.35/16.40 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 16.35/16.40 ) 16.35/16.40 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_153976 $$unsorted) (BOUND_VARIABLE_153977 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (one_one X_a)))) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_153977))) (hBOOL (hAPP X_a bool _let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_153977) (hAPP nat nat suc BOUND_VARIABLE_153976)))))) ) 16.35/16.40 ( int, (hAPP nat nat suc (zero_zero nat)), s ) 16.35/16.40 ( int, (hAPP nat nat suc (zero_zero nat)), s1 ) 16.35/16.40 ( int, (hAPP nat nat suc (zero_zero nat)), skv_14 ) 16.35/16.40 ( complex, (hAPP nat nat suc (zero_zero nat)), ii ) 16.35/16.40 ) 16.35/16.40 (instantiation (forall ((Y_2 $$unsorted) (N $$unsorted)) (let ((_let_0 (hAPP real (fun real bool) (ord_less real) (one_one real)))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N))) (= (hBOOL (hAPP real bool _let_0 (hAPP real real (hAPP nat (fun real real) root N) Y_2))) (hBOOL (hAPP real bool _let_0 Y_2))))) ) 16.35/16.40 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.40 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.40 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.40 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.40 ) 16.35/16.40 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (abs_abs X_a))) (or (not (ordere142940540dd_abs X_a)) (= _let_0 (ti (fun X_a X_a) _let_0)))) ) 16.35/16.40 ( bool ) 16.35/16.40 ( nat ) 16.35/16.40 ( int ) 16.35/16.40 ( (fun int bool) ) 16.35/16.40 ( (fun int (fun int bool)) ) 16.35/16.40 ( (fun int int) ) 16.35/16.40 ( (fun nat bool) ) 16.35/16.40 ( real ) 16.35/16.40 ( (fun real bool) ) 16.35/16.40 ( (fun real real) ) 16.35/16.40 ( rat ) 16.35/16.40 ( complex ) 16.35/16.40 ( (fun nat real) ) 16.35/16.40 ( (product_prod int int) ) 16.35/16.40 ( code_code_numeral ) 16.35/16.40 ( (fun int (fun int (fun int bool))) ) 16.35/16.40 ( (fun (product_prod int int) bool) ) 16.35/16.40 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 16.35/16.40 ( (fun (product_prod int int) int) ) 16.35/16.40 ( (fun int real) ) 16.35/16.40 ) 16.35/16.40 (instantiation (forall ((A_1 $$unsorted)) (= (hAPP real real cos A_1) (hAPP complex real re (hAPP real complex cis A_1))) ) 16.35/16.40 ( (zero_zero real) ) 16.35/16.40 ( pi ) 16.35/16.40 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.40 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.40 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.35/16.40 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.35/16.40 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.35/16.40 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 16.35/16.40 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 16.35/16.40 ( skv_5 ) 16.35/16.40 ) 16.35/16.40 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_154042 $$unsorted) (BOUND_VARIABLE_154043 $$unsorted) (BOUND_VARIABLE_154044 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (times_times X_a))) (let ((_let_2 (number_number_of X_a))) (or (not (number_ring X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP int X_a _let_2 BOUND_VARIABLE_154042)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP int X_a _let_2 BOUND_VARIABLE_154043)) BOUND_VARIABLE_154044)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP int X_a _let_2 (hAPP int int (hAPP int (fun int int) (times_times int) BOUND_VARIABLE_154042) BOUND_VARIABLE_154043))) BOUND_VARIABLE_154044)))))) ) 16.35/16.40 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 16.35/16.40 ) 16.35/16.40 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_154072 $$unsorted) (BOUND_VARIABLE_154073 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (one_one X_a)))) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_154073))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_154072))) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_154073) BOUND_VARIABLE_154072))))) ) 16.35/16.40 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.40 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.40 ( int, skv_13, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.40 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.40 ( real, pi, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 16.35/16.40 ( real, (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.40 ( real, (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.40 ( complex, ii, ii ) 16.35/16.40 ( complex, ii, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 16.35/16.40 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.40 ) 16.35/16.40 (instantiation (forall ((Z_4 $$unsorted) (Z_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) Z_1))) (= (hAPP nat nat (hAPP nat (fun nat nat) (times_times nat) (hAPP int nat nat_1 Z_1)) (hAPP int nat nat_1 Z_4)) (hAPP int nat nat_1 (hAPP int int (hAPP int (fun int int) (times_times int) Z_1) Z_4)))) ) 16.35/16.40 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.40 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.40 ( skv_13, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.40 ) 16.35/16.40 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_154103 $$unsorted)) (let ((_let_0 (uminus_uminus X_a))) (let ((_let_1 (sgn_sgn X_a))) (or (not (real_normed_vector X_a)) (= (hAPP X_a X_a _let_1 (hAPP X_a X_a _let_0 BOUND_VARIABLE_154103)) (hAPP X_a X_a _let_0 (hAPP X_a X_a _let_1 BOUND_VARIABLE_154103)))))) ) 16.35/16.40 ( int, (one_one int) ) 16.35/16.40 ( int, pls ) 16.35/16.40 ( int, min_1 ) 16.35/16.40 ( real, (one_one real) ) 16.35/16.40 ( real, (zero_zero real) ) 16.35/16.40 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.40 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.35/16.40 ( rat, (zero_zero rat) ) 16.35/16.40 ( complex, (one_one complex) ) 16.35/16.40 ( complex, ii ) 16.35/16.40 ) 16.35/16.40 (instantiation (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_0 (even_odd_even int))) (or (not (hBOOL (hAPP int bool _let_0 Y_1))) (hBOOL (hAPP int bool _let_0 (hAPP int int (hAPP int (fun int int) (times_times int) X_1) Y_1))))) ) 16.35/16.40 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 16.35/16.40 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 16.35/16.40 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13 ) 16.35/16.40 ) 16.35/16.40 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (monoseq X_a))) (or (not (order X_a)) (= _let_0 (ti (fun (fun nat X_a) bool) _let_0)))) ) 16.35/16.40 ( bool ) 16.35/16.40 ( nat ) 16.35/16.40 ( int ) 16.35/16.40 ( (fun int int) ) 16.35/16.40 ( (fun nat bool) ) 16.35/16.40 ( (fun nat nat) ) 16.35/16.40 ( (product_prod nat nat) ) 16.35/16.40 ( (fun (product_prod nat nat) bool) ) 16.35/16.40 ( (fun nat (fun (product_prod nat nat) bool)) ) 16.35/16.40 ( real ) 16.35/16.40 ( (fun real real) ) 16.35/16.40 ( rat ) 16.35/16.40 ( (fun nat (fun nat bool)) ) 16.35/16.40 ( complex ) 16.35/16.40 ( (product_prod int int) ) 16.35/16.40 ( quickcheck_code_int ) 16.35/16.40 ( (fun bool bool) ) 16.35/16.40 ( code_code_numeral ) 16.35/16.40 ( (product_prod real real) ) 16.35/16.40 ( (fun nat (product_prod nat nat)) ) 16.35/16.40 ( (fun nat (product_prod int int)) ) 16.35/16.40 ) 16.35/16.40 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_154185 $$unsorted) (BOUND_VARIABLE_154186 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (or (not (linorder X_a)) (= (not (= (ti X_a BOUND_VARIABLE_154185) (ti X_a BOUND_VARIABLE_154186))) (or (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_154185) BOUND_VARIABLE_154186)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_154186) BOUND_VARIABLE_154185))))))) ) 16.35/16.40 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.40 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 16.35/16.40 ( int, (one_one int), pls ) 16.35/16.40 ( int, (one_one int), t ) 16.35/16.40 ( int, pls, (one_one int) ) 16.35/16.40 ( int, pls, pls ) 16.35/16.40 ( int, pls, min_1 ) 16.35/16.40 ( int, pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.40 ( int, min_1, pls ) 16.35/16.40 ( int, min_1, min_1 ) 16.35/16.40 ( int, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.40 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), pls ) 16.35/16.40 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s ) 16.35/16.40 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 16.35/16.40 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_4 ) 16.35/16.40 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_10 ) 16.35/16.40 ( int, t, (one_one int) ) 16.35/16.40 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.40 ( int, skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.40 ( int, skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.40 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.40 ( real, (zero_zero real), pi ) 16.35/16.40 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.40 ( real, (zero_zero real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.35/16.40 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.40 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.40 ( real, (zero_zero real), skv_2 ) 16.35/16.40 ( real, (zero_zero real), skv_8 ) 16.35/16.40 ( real, (zero_zero real), skv_9 ) 16.35/16.40 ( real, pi, (zero_zero real) ) 16.35/16.40 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.40 ( real, pi, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 16.35/16.40 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.40 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.35/16.40 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.40 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 16.35/16.40 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 16.35/16.40 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 16.35/16.40 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.35/16.40 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.35/16.40 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 16.35/16.40 ( real, skv_2, (zero_zero real) ) 16.35/16.40 ( real, skv_8, (zero_zero real) ) 16.35/16.40 ( real, skv_9, (zero_zero real) ) 16.35/16.40 ) 16.35/16.40 (instantiation (forall ((N_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (hAPP int real (real_1 int) N_1))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 _let_2) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) (hAPP real real (hAPP real (fun real real) (plus_plus real) _let_2) (one_one real))))) (= (hAPP real int (archimedean_ceiling real) X_1) (hAPP int int (hAPP int (fun int int) (plus_plus int) N_1) (one_one int))))))) ) 16.35/16.40 ( (one_one int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.40 ( (zero_zero int), pi ) 16.35/16.40 ( (zero_zero int), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.40 ( (zero_zero int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.40 ( (zero_zero int), skv_2 ) 16.35/16.40 ( (zero_zero int), skv_8 ) 16.35/16.40 ( (zero_zero int), skv_9 ) 16.35/16.40 ) 16.35/16.40 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) (zero_zero real)) X_2))) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP _let_1 (fun real _let_0) (deriv real) sqrt) X_2) (hAPP real real (hAPP real _let_1 (inverse_divide real) (hAPP real real (inverse_inverse real) (hAPP real real sqrt X_2))) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))))) ) 16.35/16.40 ( (one_one real) ) 16.35/16.40 ( (zero_zero real) ) 16.35/16.40 ( pi ) 16.35/16.40 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.40 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.40 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.35/16.40 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.40 ( skv_2 ) 16.35/16.40 ( skv_8 ) 16.35/16.40 ( skv_9 ) 16.35/16.40 ) 16.35/16.40 (instantiation (forall ((N_1 $$unsorted)) (= (hAPP quickcheck_code_int int quickcheck_int_of (hAPP int quickcheck_code_int quickcheck_of_int N_1)) (ti int N_1)) ) 16.35/16.40 ( (one_one int) ) 16.35/16.40 ( (zero_zero int) ) 16.35/16.40 ( pls ) 16.35/16.40 ( (hAPP int int bit1 pls) ) 16.35/16.40 ( min_1 ) 16.35/16.40 ( s ) 16.35/16.40 ( m ) 16.35/16.40 ( s1 ) 16.35/16.40 ( t ) 16.35/16.40 ) 16.35/16.40 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_154300 $$unsorted) (BOUND_VARIABLE_154301 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (or (not (ordered_ab_group_add X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) BOUND_VARIABLE_154300) BOUND_VARIABLE_154301)) (zero_zero X_a))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_154300) BOUND_VARIABLE_154301)))))) ) 16.35/16.40 ( int, (one_one int), t ) 16.35/16.40 ( int, (zero_zero int), (one_one int) ) 16.35/16.40 ( int, (zero_zero int), min_1 ) 16.35/16.40 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.40 ( int, (zero_zero int), s ) 16.35/16.40 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.35/16.40 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 16.35/16.40 ( int, (zero_zero int), skv_4 ) 16.35/16.40 ( int, (zero_zero int), skv_10 ) 16.35/16.40 ( int, min_1, pls ) 16.35/16.40 ( int, min_1, min_1 ) 16.35/16.40 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 16.35/16.40 ( real, (zero_zero real), pi ) 16.35/16.40 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.40 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.40 ( real, (zero_zero real), skv_3 ) 16.35/16.40 ( real, (zero_zero real), skv_5 ) 16.35/16.40 ( real, (zero_zero real), skv_7 ) 16.35/16.40 ( real, (zero_zero real), skv_12 ) 16.35/16.40 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.35/16.40 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.40 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.35/16.40 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 16.35/16.40 ( real, skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.40 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 16.35/16.40 ) 16.35/16.40 (instantiation (forall ((A_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_0 (hAPP int (fun nat int) (power_power int) A_1))) (let ((_let_1 (hAPP int nat nat_1 P_5))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) P_5))) (= (hAPP nat int _let_0 _let_1) (hAPP int int (hAPP int (fun int int) (times_times int) A_1) (hAPP nat int _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) _let_1) (one_one nat)))))))) ) 16.35/16.40 ( s, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.40 ( s1, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.40 ( skv_14, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.40 ) 16.35/16.40 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_154367 $$unsorted) (BOUND_VARIABLE_154368 $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_lessThan nat))) (let ((_let_2 (hAPP (fun nat X_a) (fun _let_0 X_a) (big_co1399186613setsum nat X_a) BOUND_VARIABLE_154367))) (or (not (comm_monoid_add X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (hAPP _let_0 X_a _let_2 (hAPP nat _let_0 _let_1 BOUND_VARIABLE_154368))) (hAPP nat X_a BOUND_VARIABLE_154367 BOUND_VARIABLE_154368)) (hAPP _let_0 X_a _let_2 (hAPP nat _let_0 _let_1 (hAPP nat nat suc BOUND_VARIABLE_154368)))))))) ) 16.35/16.40 ( bool, (even_odd_even nat), (zero_zero nat) ) 16.35/16.40 ( bool, (even_odd_even nat), (one_one nat) ) 16.35/16.40 ( bool, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.40 ( bool, prime, (zero_zero nat) ) 16.35/16.40 ( bool, prime, (hAPP nat nat suc (zero_zero nat)) ) 16.35/16.40 ( bool, prime, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.40 ( nat, suc, (zero_zero nat) ) 16.35/16.40 ( nat, suc, (hAPP nat nat suc (zero_zero nat)) ) 16.35/16.40 ( nat, suc, (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 16.35/16.40 ( nat, (fact_fact nat), (zero_zero nat) ) 16.35/16.40 ( nat, (fact_fact nat), (hAPP nat nat suc (zero_zero nat)) ) 16.35/16.40 ( nat, fact, (zero_zero nat) ) 16.35/16.40 ( nat, (hAPP nat (fun nat nat) (plus_plus nat) (one_one nat)), (one_one nat) ) 16.35/16.40 ( nat, nat_size, (zero_zero nat) ) 16.35/16.40 ( nat, (size_size nat), (zero_zero nat) ) 16.35/16.40 ( int, (semiring_1_of_nat int), (zero_zero nat) ) 16.35/16.40 ( int, (semiring_1_of_nat int), (hAPP nat nat suc (zero_zero nat)) ) 16.35/16.40 ( int, (semiring_1_of_nat int), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.35/16.40 ( int, (semiring_1_of_nat int), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.40 ( int, (hAPP int (fun nat int) (power_power int) s), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.40 ( int, (hAPP int (fun nat int) (power_power int) s1), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.40 ( int, (hAPP int (fun nat int) (power_power int) skv_14), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.40 ( (fun int int), (hAPP (fun int (fun nat int)) (fun nat (fun int int)) (combc int nat int) (power_power int)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.40 ( (fun nat bool), (ord_less nat), (zero_zero nat) ) 16.35/16.40 ( (fun nat bool), (let ((_let_0 (fun nat (fun nat bool)))) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat))), (zero_zero nat) ) 16.35/16.40 ( (fun nat nat), (plus_plus nat), (one_one nat) ) 16.35/16.40 ( (fun nat nat), (let ((_let_0 (fun nat (fun nat nat)))) (hAPP _let_0 _let_0 (combc nat nat nat) (times_times nat))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.40 ( (fun nat nat), (let ((_let_0 (fun nat (fun nat nat)))) (let ((_let_1 (combc nat nat nat))) (hAPP _let_0 _let_0 _let_1 (hAPP (fun nat nat) _let_0 (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_0 _let_0 _let_1 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))), (one_one nat) ) 16.35/16.40 ( real, (real_1 nat), (zero_zero nat) ) 16.35/16.40 ( real, (real_1 nat), (hAPP nat nat suc (zero_zero nat)) ) 16.35/16.40 ( (fun real real), root, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.40 ( complex, (hAPP complex (fun nat complex) (power_power complex) ii), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.40 ) 16.35/16.40 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_154397 $$unsorted) (BOUND_VARIABLE_154398 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_154397) (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_154398))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP X_a int (archim2085082626_floor X_a) BOUND_VARIABLE_154397)) BOUND_VARIABLE_154398)))) ) 16.35/16.40 ( real, pi, (zero_zero int) ) 16.35/16.40 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero int) ) 16.35/16.40 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero int) ) 16.35/16.40 ) 16.35/16.40 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (one_one X_a))) (or (not (one X_a)) (= _let_0 (ti X_a _let_0)))) ) 16.35/16.40 ( nat ) 16.35/16.40 ( int ) 16.35/16.40 ( real ) 16.35/16.40 ( rat ) 16.35/16.40 ( complex ) 16.35/16.40 ( quickcheck_code_int ) 16.35/16.40 ( code_code_numeral ) 16.35/16.40 ) 16.35/16.40 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int int (hAPP int (fun int int) (minus_minus int) K_4) (one_one int)) (hAPP int int pred K_4)) ) 16.35/16.40 ( pls ) 16.35/16.40 ( min_1 ) 16.35/16.40 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.40 ) 16.35/16.40 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_154514 $$unsorted)) (let ((_let_0 (inverse_inverse X_a))) (let ((_let_1 (uminus_uminus X_a))) (or (not (divisi14063676e_zero X_a)) (= (hAPP X_a X_a _let_1 (hAPP X_a X_a _let_0 BOUND_VARIABLE_154514)) (hAPP X_a X_a _let_0 (hAPP X_a X_a _let_1 BOUND_VARIABLE_154514)))))) ) 16.35/16.40 ( int, (one_one int) ) 16.35/16.40 ( int, pls ) 16.35/16.40 ( int, min_1 ) 16.35/16.40 ( real, (one_one real) ) 16.35/16.40 ( real, (zero_zero real) ) 16.35/16.40 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.40 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.35/16.40 ( complex, (one_one complex) ) 16.35/16.40 ( complex, ii ) 16.35/16.40 ) 16.35/16.40 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_154572 $$unsorted) (BOUND_VARIABLE_154573 $$unsorted) (BOUND_VARIABLE_154574 $$unsorted) (BOUND_VARIABLE_154575 $$unsorted)) (let ((_let_0 (filter X_a))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun X_a X_b))) (let ((_let_3 (fun X_b _let_1))) (let ((_let_4 (tendsto X_a X_b))) (let ((_let_5 (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_154575))) (or (not (topological_space X_a)) (not (topological_space X_b)) (not (forall ((X $$unsorted)) (or (= (ti X_a X) (ti X_a BOUND_VARIABLE_154575)) (= (hAPP X_a X_b BOUND_VARIABLE_154574 X) (hAPP X_a X_b BOUND_VARIABLE_154573 X))) )) (= (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (hAPP _let_2 _let_3 _let_4 BOUND_VARIABLE_154573) BOUND_VARIABLE_154572) _let_5)) (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (hAPP _let_2 _let_3 _let_4 BOUND_VARIABLE_154574) BOUND_VARIABLE_154572) _let_5)))))))))) ) 16.35/16.40 ( real, real, (zero_zero real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.40 ) 16.35/16.40 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_154613 $$unsorted) (BOUND_VARIABLE_154614 $$unsorted) (BOUND_VARIABLE_154615 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (fun X_a X_a))) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_154615))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_2 (times_times X_a) BOUND_VARIABLE_154613) BOUND_VARIABLE_154615)) BOUND_VARIABLE_154614))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_154613) (hAPP X_a X_a (hAPP X_a _let_2 (inverse_divide X_a) BOUND_VARIABLE_154614) BOUND_VARIABLE_154615))))))) ) 16.35/16.40 ( real, (zero_zero real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.40 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 16.35/16.40 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 16.35/16.40 ) 16.35/16.40 (instantiation (forall ((A_2 $$unsorted) (X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) X_2))) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP real nat natceiling X_2)) A_2)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_2) (hAPP nat real (real_1 nat) A_2))))))) ) 16.35/16.40 ( (zero_zero nat), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.40 ) 16.35/16.40 (instantiation (forall ((K_4 $$unsorted)) (let ((_let_0 (product_prod int int))) (= (hAPP _let_0 rat frct (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) (one_one int)) (hAPP int int (number_number_of int) K_4))) (hAPP rat rat (hAPP rat (fun rat rat) (inverse_divide rat) (one_one rat)) (hAPP int rat (number_number_of rat) K_4)))) ) 16.35/16.40 ( pls ) 16.35/16.40 ( (hAPP int int bit1 pls) ) 16.35/16.40 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.35/16.40 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.35/16.40 ( min_1 ) 16.35/16.40 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.40 ) 16.35/16.40 (instantiation (forall ((R_4 $$unsorted) (S_3 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (inverse_divide real))) (let ((_let_2 (number_number_of real))) (let ((_let_3 (number_number_of rat))) (= (hAPP real real (hAPP real _let_0 _let_1 (hAPP int real _let_2 R_4)) (hAPP int real _let_2 S_3)) (hAPP real real (hAPP real _let_0 _let_1 (hAPP rat real ratreal (hAPP int rat _let_3 R_4))) (hAPP rat real ratreal (hAPP int rat _let_3 S_3)))))))) ) 16.35/16.40 ( (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.35/16.40 ) 16.35/16.40 (instantiation (forall ((R_4 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) R_4) (zero_zero real)))) (not (forall ((N_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (real_1 int))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) (hAPP int real _let_1 N_2)) R_4))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) R_4) (hAPP int real _let_1 (hAPP int int (hAPP int (fun int int) (plus_plus int) N_2) (one_one int))))))))) ))) ) 16.35/16.40 ( (one_one real) ) 16.35/16.40 ( (zero_zero real) ) 16.35/16.40 ( pi ) 16.35/16.40 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.40 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.35/16.40 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.40 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 16.35/16.40 ) 16.35/16.40 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_154779 $$unsorted) (BOUND_VARIABLE_154780 $$unsorted) (BOUND_VARIABLE_154781 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_154779))) (or (not (order X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_154780) BOUND_VARIABLE_154781))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_154780))) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_154781)))) ) 16.35/16.40 ( int, (one_one int), min_1, pls ) 16.35/16.40 ( int, (zero_zero int), (zero_zero int), s ) 16.35/16.40 ( int, min_1, (zero_zero int), (one_one int) ) 16.35/16.40 ( real, (zero_zero real), (zero_zero real), pi ) 16.35/16.40 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.40 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.40 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.35/16.40 ( real, skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.35/16.40 ) 16.35/16.40 (instantiation (forall ((Ma $$unsorted) (N $$unsorted)) (let ((_let_0 (zero_zero nat))) (let ((_let_1 (hAPP nat nat suc _let_0))) (= (= _let_1 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) Ma) N)) (or (and (= _let_1 Ma) (= _let_0 N)) (and (= _let_1 N) (= _let_0 Ma)))))) ) 16.35/16.40 ( (one_one nat), (one_one nat) ) 16.35/16.40 ) 16.35/16.40 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_154829 $$unsorted) (BOUND_VARIABLE_154830 $$unsorted) (BOUND_VARIABLE_154831 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (zero_zero X_a))) (let ((_let_2 (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_154830))) (let ((_let_3 (ti X_a BOUND_VARIABLE_154831))) (let ((_let_4 (= _let_1 _let_2))) (or (not (number X_a)) (not (field_inverse_zero X_a)) (= (and (or _let_4 (= (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_154831) _let_2) (ti X_a BOUND_VARIABLE_154829))) (or (not _let_4) (= _let_1 _let_3))) (= _let_3 (hAPP X_a X_a (hAPP X_a _let_0 (inverse_divide X_a) BOUND_VARIABLE_154829) _let_2))))))))) ) 16.35/16.40 ( int, pls, (hAPP int int bit1 pls), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.40 ( int, s, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.40 ( int, s1, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.40 ( real, pi, min_1, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.40 ( complex, ii, min_1, ii ) 16.35/16.40 ) 16.35/16.40 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_154875 $$unsorted) (BOUND_VARIABLE_154876 $$unsorted)) (let ((_let_0 (norm_norm X_a))) (or (not (real_normed_vector X_a)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP X_a real _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) BOUND_VARIABLE_154875) BOUND_VARIABLE_154876))) (hAPP real real (hAPP real (fun real real) (plus_plus real) (hAPP X_a real _let_0 BOUND_VARIABLE_154875)) (hAPP X_a real _let_0 BOUND_VARIABLE_154876)))))) ) 16.35/16.40 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 16.35/16.40 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 16.35/16.40 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 16.35/16.40 ) 16.35/16.40 (instantiation (forall ((Ma $$unsorted) (K $$unsorted) (F $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (plus_plus nat))) (or (not (forall ((M_2 $$unsorted) (N_2 $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less nat))) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 M_2) N_2))) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 (hAPP nat nat F M_2)) (hAPP nat nat F N_2)))))) )) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP nat nat (hAPP nat _let_0 _let_1 (hAPP nat nat F Ma)) K)) (hAPP nat nat F (hAPP nat nat (hAPP nat _let_0 _let_1 Ma) K))))))) ) 16.35/16.40 ( (zero_zero nat), (one_one nat), fact ) 16.35/16.40 ( (one_one nat), (one_one nat), suc ) 16.35/16.40 ) 16.35/16.40 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_154941 $$unsorted) (BOUND_VARIABLE_154942 $$unsorted)) (let ((_let_0 (uminus_uminus X_a))) (let ((_let_1 (fun nat X_a))) (let ((_let_2 (power_power X_a))) (or (not (comm_ring_1 X_a)) (hBOOL (hAPP nat bool (even_odd_even nat) BOUND_VARIABLE_154942)) (= (hAPP nat X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a _let_0 BOUND_VARIABLE_154941)) BOUND_VARIABLE_154942) (hAPP X_a X_a _let_0 (hAPP nat X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_154941) BOUND_VARIABLE_154942))))))) ) 16.35/16.40 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.40 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.40 ( int, skv_14, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.40 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.40 ) 16.35/16.40 (instantiation (forall ((Ma $$unsorted) (N $$unsorted) (P_1 $$unsorted)) (or (not (forall ((M_2 $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) P_1 M_2) (zero_zero nat))) )) (not (forall ((M_2 $$unsorted) (N_2 $$unsorted)) (let ((_let_0 (fun nat bool))) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) (zero_zero nat)) N_2))) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 P_1 N_2) (hAPP nat nat (hAPP nat (fun nat nat) (div_mod nat) M_2) N_2)))) (hBOOL (hAPP nat bool (hAPP nat _let_0 P_1 M_2) N_2)))) )) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) P_1 Ma) N))) ) 16.35/16.40 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (ord_less nat) ) 16.35/16.40 ) 16.35/16.40 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (sgn_if X_a)) (= _let_0 (hAPP X_a X_a (sgn_sgn X_a) _let_0)))) ) 16.35/16.40 ( nat ) 16.35/16.40 ( int ) 16.35/16.40 ( real ) 16.35/16.40 ( rat ) 16.35/16.40 ( complex ) 16.35/16.40 ( quickcheck_code_int ) 16.35/16.40 ( code_code_numeral ) 16.35/16.40 ) 16.35/16.40 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_155077 $$unsorted) (BOUND_VARIABLE_155078 $$unsorted)) (or (not (dense_linorder X_a)) (not (forall ((X $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) X) BOUND_VARIABLE_155078))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) X) BOUND_VARIABLE_155077)))) )) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_155078) BOUND_VARIABLE_155077))) ) 16.35/16.40 ( int, (one_one int), (zero_zero int) ) 16.35/16.40 ( int, pls, min_1 ) 16.35/16.40 ( int, min_1, (zero_zero int) ) 16.35/16.40 ( int, min_1, min_1 ) 16.35/16.40 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 16.35/16.40 ( int, s, (zero_zero int) ) 16.35/16.40 ( int, t, (one_one int) ) 16.35/16.40 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 16.35/16.40 ( int, (hAPP int int (number_number_of int) pls), (zero_zero int) ) 16.35/16.40 ( int, skv_4, (zero_zero int) ) 16.35/16.40 ( int, skv_10, (zero_zero int) ) 16.35/16.40 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.40 ( real, pi, (zero_zero real) ) 16.35/16.40 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.40 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.40 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_5 ) 16.35/16.40 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.35/16.40 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.35/16.40 ( real, skv_3, (zero_zero real) ) 16.35/16.40 ( real, skv_5, (zero_zero real) ) 16.35/16.40 ( real, skv_7, (zero_zero real) ) 16.35/16.40 ( real, skv_12, (zero_zero real) ) 16.35/16.40 ) 16.35/16.40 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_155147 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) BOUND_VARIABLE_155147)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (one_one int)) (hAPP X_a int (archimedean_ceiling X_a) BOUND_VARIABLE_155147))))) ) 16.35/16.40 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.40 ( int, (one_one int) ) 16.35/16.40 ( int, pls ) 16.35/16.40 ( int, min_1 ) 16.35/16.40 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.40 ( real, pi ) 16.35/16.40 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.40 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.40 ( real, skv_2 ) 16.35/16.40 ( real, skv_8 ) 16.35/16.40 ( real, skv_9 ) 16.35/16.40 ) 16.35/16.40 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (BOUND_VARIABLE_155165 $$unsorted) (BOUND_VARIABLE_155166 $$unsorted)) (let ((_let_0 (fun (filter X_a) bool))) (let ((_let_1 (fun X_a X_b))) (let ((_let_2 (fun X_a real))) (or (not (real_normed_vector X_b)) (not (hBOOL (hAPP (filter X_a) bool (hAPP real _let_0 (hAPP _let_2 (fun real _let_0) (tendsto X_a real) (hAPP _let_1 _let_2 (hAPP (fun X_b real) (fun _let_1 _let_2) (combb X_b real X_a) (norm_norm X_b)) BOUND_VARIABLE_155165)) (zero_zero real)) BOUND_VARIABLE_155166))) (hBOOL (hAPP (filter X_a) bool (hAPP X_b _let_0 (hAPP _let_1 (fun X_b _let_0) (tendsto X_a X_b) BOUND_VARIABLE_155165) (zero_zero X_b)) BOUND_VARIABLE_155166)))))) ) 16.35/16.40 ( nat, real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))), sequentially ) 16.35/16.40 ( real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (hAPP real (filter real) (at real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.35/16.40 ) 16.35/16.40 (instantiation (forall ((A_1 $$unsorted)) (let ((_let_0 (number_number_of nat))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (hAPP int (fun nat int) (power_power int) A_1))) (= (hAPP nat int _let_2 (hAPP int nat _let_0 (hAPP int int bit1 _let_1))) (hAPP int int (hAPP int (fun int int) (times_times int) A_1) (hAPP nat int _let_2 (hAPP int nat _let_0 (hAPP int int bit0 _let_1)))))))) ) 16.35/16.40 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.40 ( s ) 16.35/16.40 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.40 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.40 ( s1 ) 16.35/16.40 ( skv_14 ) 16.35/16.40 ) 16.35/16.41 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_155278 $$unsorted) (BOUND_VARIABLE_155279 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (zero_zero X_a))) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_155279) _let_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) _let_2) BOUND_VARIABLE_155278))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_155279) BOUND_VARIABLE_155278)) _let_2)))))) ) 16.35/16.41 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 16.35/16.41 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.35/16.41 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.35/16.41 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.35/16.41 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.41 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 16.35/16.41 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), pi ) 16.35/16.41 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (one_one real) ) 16.35/16.41 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))), pi ) 16.35/16.41 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 16.35/16.41 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))), (one_one real) ) 16.35/16.41 ) 16.35/16.41 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_155301 $$unsorted) (BOUND_VARIABLE_155302 $$unsorted) (BOUND_VARIABLE_155303 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (fun X_a X_a))) (let ((_let_3 (minus_minus X_a))) (or (not (linordered_idom X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (abs_abs X_a) (hAPP X_a X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_155301) BOUND_VARIABLE_155302))) BOUND_VARIABLE_155303)) (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_155301) (hAPP X_a X_a (hAPP X_a _let_2 (plus_plus X_a) BOUND_VARIABLE_155302) BOUND_VARIABLE_155303))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_155302) BOUND_VARIABLE_155303)) BOUND_VARIABLE_155301))))))))) ) 16.35/16.41 ( nat, (zero_zero nat), (one_one nat), (one_one nat) ) 16.35/16.41 ( int, pls, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 16.35/16.41 ( int, s, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 16.35/16.41 ( int, t, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 16.35/16.41 ( int, skv_4, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 16.35/16.41 ( int, skv_10, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 16.35/16.41 ) 16.35/16.41 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_155364 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (inverse_divide X_a))) (or (not (number_ring X_a)) (not (field_inverse_zero X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP int X_a (number_number_of X_a) min_1)) BOUND_VARIABLE_155364) (hAPP X_a X_a (uminus_uminus X_a) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (one_one X_a)) BOUND_VARIABLE_155364)))))) ) 16.35/16.41 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.41 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.35/16.41 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.41 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 16.35/16.41 ) 16.35/16.41 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_155418 $$unsorted) (BOUND_VARIABLE_155419 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (or (not (semiring_div X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_155418) BOUND_VARIABLE_155419))) (= (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_155418) (hAPP X_a X_a (hAPP X_a _let_0 (div_div X_a) BOUND_VARIABLE_155419) BOUND_VARIABLE_155418)) (ti X_a BOUND_VARIABLE_155419)))) ) 16.35/16.41 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 16.35/16.41 ) 16.35/16.41 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (one_one X_a))) (or (not (linordered_idom X_a)) (= _let_0 (hAPP X_a X_a (abs_abs X_a) _let_0)))) ) 16.35/16.41 ( nat ) 16.35/16.41 ( int ) 16.35/16.41 ( real ) 16.35/16.41 ( rat ) 16.35/16.41 ( complex ) 16.35/16.41 ( quickcheck_code_int ) 16.35/16.41 ( code_code_numeral ) 16.35/16.41 ) 16.35/16.41 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_155452 $$unsorted)) (let ((_let_0 (fun nat X_a))) (let ((_let_1 (fun X_a bool))) (or (not (topological_space X_a)) (not (comm_monoid_add X_a)) (= (hAPP _let_1 X_a (the X_a) (hAPP _let_0 _let_1 (sums X_a) BOUND_VARIABLE_155452)) (hAPP _let_0 X_a (suminf X_a) BOUND_VARIABLE_155452))))) ) 16.35/16.41 ( real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (hAPP real _let_1 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc))) ) 16.35/16.41 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat (fun nat nat)))) (let ((_let_3 (fun nat _let_0))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun _let_1 _let_3))) (let ((_let_6 (combb real _let_0 nat))) (let ((_let_7 (combc nat nat nat))) (hAPP _let_1 _let_1 (hAPP _let_3 (fun _let_1 _let_1) (combs nat real real) (hAPP _let_1 _let_3 (hAPP _let_4 _let_5 _let_6 (inverse_divide real)) (hAPP real _let_1 (hAPP _let_3 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_3 (hAPP _let_4 _let_5 _let_6 (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) (one_one real)))) (hAPP (fun nat nat) _let_1 (hAPP _let_1 (fun (fun nat nat) _let_1) (combb nat real nat) (real_1 nat)) (hAPP nat (fun nat nat) (hAPP _let_2 _let_2 _let_7 (hAPP (fun nat nat) _let_2 (hAPP _let_2 (fun (fun nat nat) _let_2) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_2 _let_2 _let_7 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))))))))))) ) 16.35/16.41 ) 16.35/16.41 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted)) (= (hAPP real complex cis (hAPP real real (hAPP real (fun real real) (minus_minus real) A_1) B)) (hAPP complex complex (hAPP complex (fun complex complex) (inverse_divide complex) (hAPP real complex cis A_1)) (hAPP real complex cis B))) ) 16.35/16.41 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 16.35/16.41 ) 16.35/16.41 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_155499 $$unsorted) (BOUND_VARIABLE_155500 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (or (not (linordered_idom X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_155499) BOUND_VARIABLE_155500)) _let_2)) (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_155499) _let_2)) (not (hBOOL (hAPP nat bool (even_odd_even nat) BOUND_VARIABLE_155500))))))))) ) 16.35/16.41 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.41 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.41 ( int, skv_14, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.41 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.41 ) 16.35/16.41 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (power_power real))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (= (hAPP nat real (hAPP real _let_0 _let_1 (hAPP real real sin X_1)) _let_2) (hAPP real real (hAPP real (fun real real) (minus_minus real) (one_one real)) (hAPP nat real (hAPP real _let_0 _let_1 (hAPP real real cos X_1)) _let_2)))))) ) 16.35/16.41 ( (zero_zero real) ) 16.35/16.41 ( pi ) 16.35/16.41 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.41 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.41 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.35/16.41 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.35/16.41 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.35/16.41 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 16.35/16.41 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 16.35/16.41 ( skv_5 ) 16.35/16.41 ) 16.35/16.41 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_155546 $$unsorted) (BOUND_VARIABLE_155547 $$unsorted) (BOUND_VARIABLE_155548 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_155548))) (let ((_let_3 (= _let_0 _let_2))) (let ((_let_4 (ti X_a BOUND_VARIABLE_155546))) (or (not (field_inverse_zero X_a)) (not (number X_a)) (= (and (or (not _let_3) (= _let_0 _let_4)) (or _let_3 (= (ti X_a BOUND_VARIABLE_155547) (hAPP X_a X_a (hAPP X_a _let_1 (times_times X_a) BOUND_VARIABLE_155546) _let_2)))) (= _let_4 (hAPP X_a X_a (hAPP X_a _let_1 (inverse_divide X_a) BOUND_VARIABLE_155547) _let_2))))))))) ) 16.35/16.41 ( int, pls, pls, (hAPP int int bit1 pls) ) 16.35/16.41 ( int, min_1, min_1, pls ) 16.35/16.41 ( int, s, s, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.41 ( int, m, m, min_1 ) 16.35/16.41 ( int, s1, s1, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.35/16.41 ( int, t, t, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.35/16.41 ( real, pi, pi, min_1 ) 16.35/16.41 ( complex, ii, ii, min_1 ) 16.35/16.41 ) 16.35/16.41 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_155609 $$unsorted) (BOUND_VARIABLE_155615 $$unsorted)) (let ((_let_0 (even_odd_even nat))) (let ((_let_1 (hAPP X_a (fun nat X_a) (power_power X_a) (hAPP int X_a (number_number_of X_a) min_1)))) (or (not (number_ring X_a)) (and (or (hBOOL (hAPP nat bool _let_0 BOUND_VARIABLE_155609)) (= (hAPP int X_a (number_number_of X_a) min_1) (hAPP nat X_a _let_1 BOUND_VARIABLE_155609))) (or (not (hBOOL (hAPP nat bool _let_0 BOUND_VARIABLE_155615))) (= (one_one X_a) (hAPP nat X_a _let_1 BOUND_VARIABLE_155615))))))) ) 16.35/16.41 ( int, (zero_zero nat), (zero_zero nat) ) 16.35/16.41 ( complex, (one_one nat), (one_one nat) ) 16.35/16.41 ) 16.35/16.41 (instantiation (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_0 (uminus_uminus real))) (let ((_let_1 (hAPP nat (fun real real) root N_1))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_1))) (= (hAPP real real _let_1 (hAPP real real _let_0 X_1)) (hAPP real real _let_0 (hAPP real real _let_1 X_1)))))) ) 16.35/16.41 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.41 ) 16.35/16.41 (instantiation (forall ((P_1 $$unsorted) (A0 $$unsorted) (A1 $$unsorted)) (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 bool))) (or (not (hBOOL (hAPP _let_0 bool (hAPP (fun _let_0 _let_1) _let_1 (accp _let_0) upto_rel) (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) A0) A1)))) (not (forall ((I_2 $$unsorted) (J_1 $$unsorted)) (let ((_let_2 (fun int bool))) (or (not (hBOOL (hAPP _let_0 bool (hAPP (fun _let_0 _let_1) _let_1 (accp _let_0) upto_rel) (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) I_2) J_1)))) (and (hBOOL (hAPP int bool (hAPP int _let_2 (ord_less_eq int) I_2) J_1)) (not (hBOOL (hAPP int bool (hAPP int _let_2 P_1 (hAPP int int (hAPP int (fun int int) (plus_plus int) I_2) (one_one int))) J_1)))) (hBOOL (hAPP int bool (hAPP int _let_2 P_1 I_2) J_1)))) )) (hBOOL (hAPP int bool (hAPP int (fun int bool) P_1 A0) A1))))) ) 16.35/16.41 ( (ord_less_eq int), (one_one int), t ) 16.35/16.41 ( (ord_less_eq int), (zero_zero int), (one_one int) ) 16.35/16.41 ( (ord_less_eq int), (zero_zero int), min_1 ) 16.35/16.41 ( (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.41 ( (ord_less_eq int), (zero_zero int), s ) 16.35/16.41 ( (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.35/16.41 ( (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) pls) ) 16.35/16.41 ( (ord_less_eq int), (zero_zero int), skv_4 ) 16.35/16.41 ( (ord_less_eq int), (zero_zero int), skv_10 ) 16.35/16.41 ( (ord_less_eq int), min_1, pls ) 16.35/16.41 ( (ord_less_eq int), min_1, min_1 ) 16.35/16.41 ( (ord_less int), (one_one int), t ) 16.35/16.41 ( (ord_less int), pls, (one_one int) ) 16.35/16.41 ( (ord_less int), pls, pls ) 16.35/16.41 ( (ord_less int), pls, min_1 ) 16.35/16.41 ( (ord_less int), pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.41 ( (ord_less int), min_1, pls ) 16.35/16.41 ( (ord_less int), min_1, min_1 ) 16.35/16.41 ( (ord_less int), s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.41 ( (ord_less int), t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.41 ( (ord_less int), skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.41 ( (ord_less int), skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.41 ( (dvd_dvd int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 16.35/16.41 ( quadRes, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (number_number_of int) min_1) ) 16.35/16.41 ( (hAPP int (fun int (fun int bool)) zcong s1), s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.41 ( (hAPP int (fun int (fun int bool)) zcong s1), skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.41 ( (hAPP int (fun int (fun int bool)) zcong s1), skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.44 ( (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.44 ( (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.44 ( (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.44 ( (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.44 ) 16.35/16.44 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_155714 $$unsorted)) (let ((_let_0 (semiring_1_of_nat X_a))) (or (not (semiring_1 X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (one_one X_a)) (hAPP nat X_a _let_0 BOUND_VARIABLE_155714)) (hAPP nat X_a _let_0 (hAPP nat nat suc BOUND_VARIABLE_155714))))) ) 16.35/16.44 ( int, (zero_zero nat) ) 16.35/16.44 ( int, (hAPP nat nat suc (zero_zero nat)) ) 16.35/16.44 ( int, (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 16.35/16.44 ( real, (zero_zero nat) ) 16.35/16.44 ) 16.35/16.44 (instantiation (forall ((B $$unsorted) (Q_3 $$unsorted) (R_4 $$unsorted) (B_5 $$unsorted) (Q_5 $$unsorted) (R_5 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (times_times int))) (let ((_let_3 (ord_less_eq int))) (let ((_let_4 (zero_zero int))) (let ((_let_5 (ord_less int))) (let ((_let_6 (plus_plus int))) (let ((_let_7 (hAPP int _let_0 _let_3 _let_4))) (let ((_let_8 (hAPP int int (hAPP int _let_1 _let_6 (hAPP int int (hAPP int _let_1 _let_2 B_5) Q_5)) R_5))) (or (not (= _let_8 (hAPP int int (hAPP int _let_1 _let_6 (hAPP int int (hAPP int _let_1 _let_2 B) Q_3)) R_4))) (not (hBOOL (hAPP int bool _let_7 _let_8))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_5 R_5) B_5))) (not (hBOOL (hAPP int bool _let_7 R_4))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_5 _let_4) B_5))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_3 B_5) B))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_3 Q_3) Q_5)))))))))))) ) 16.35/16.44 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m, (one_one int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m, (one_one int) ) 16.35/16.44 ) 16.35/16.44 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (one_one real))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_5 (hAPP int real (number_number_of real) _let_4))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real _let_3 (inverse_divide real) _let_1) _let_5))) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 X_1) (zero_zero real)))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 (hAPP real real (abs_abs real) (hAPP real real (hAPP real _let_3 (minus_minus real) (hAPP real real ln (hAPP real real (hAPP real _let_3 (plus_plus real) _let_1) X_1))) X_1))) (hAPP real real (hAPP real _let_3 (times_times real) _let_5) (hAPP nat real (hAPP real (fun nat real) (power_power real) X_1) (hAPP int nat (number_number_of nat) _let_4)))))))))))) ) 16.35/16.44 ( (hAPP int real (number_number_of real) min_1) ) 16.35/16.44 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.44 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.44 ) 16.35/16.44 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less nat))) (let ((_let_2 (fun nat nat))) (let ((_let_3 (div_div nat))) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 (zero_zero nat)) N_1))) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 M) N_1)) (= (hAPP nat nat suc (hAPP nat nat (hAPP nat _let_2 _let_3 (hAPP nat nat (hAPP nat _let_2 (minus_minus nat) M) N_1)) N_1)) (hAPP nat nat (hAPP nat _let_2 _let_3 M) N_1))))))) ) 16.35/16.44 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.44 ) 16.35/16.44 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_0 (fun nat bool))) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) M) N_1))) (= M N_1) (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) M) N_1)))) ) 16.35/16.44 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.44 ) 16.35/16.44 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_155897 $$unsorted)) (let ((_let_0 (iszero X_a))) (let ((_let_1 (number_number_of X_a))) (or (not (number_ring X_a)) (not (ring_char_0 X_a)) (= (hBOOL (hAPP X_a bool _let_0 (hAPP int X_a _let_1 (hAPP int int bit0 BOUND_VARIABLE_155897)))) (hBOOL (hAPP X_a bool _let_0 (hAPP int X_a _let_1 BOUND_VARIABLE_155897))))))) ) 16.35/16.44 ( nat, pls ) 16.35/16.44 ( nat, (hAPP int int bit1 pls) ) 16.35/16.44 ( int, pls ) 16.35/16.44 ( int, (hAPP int int bit1 pls) ) 16.35/16.44 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.35/16.44 ( real, (hAPP int int bit1 pls) ) 16.35/16.44 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.35/16.44 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.35/16.44 ( complex, (hAPP int int bit1 pls) ) 16.35/16.44 ( quickcheck_code_int, pls ) 16.35/16.44 ( code_code_numeral, pls ) 16.35/16.44 ) 16.35/16.44 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted) (N $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (hAPP nat (fun real real) root N))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N))) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real _let_2 X_2)) (hAPP real real _let_2 Y_2))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_2) Y_2))))))) ) 16.35/16.44 ( (zero_zero real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.44 ) 16.35/16.44 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_155973 $$unsorted) (BOUND_VARIABLE_155974 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (times_times X_a))) (let ((_let_2 (plus_plus X_a))) (or (not (comm_semiring_1 X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_155973) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_155974) BOUND_VARIABLE_155973)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_155974) (one_one X_a))) BOUND_VARIABLE_155973)))))) ) 16.35/16.44 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.44 ( int, t, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 16.35/16.44 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.44 ( int, skv_13, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 16.35/16.44 ( int, skv_13, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.44 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.44 ( real, pi, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 16.35/16.44 ( real, (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.44 ( real, (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.44 ( complex, ii, ii ) 16.35/16.44 ( complex, ii, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 16.35/16.44 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.44 ) 16.35/16.44 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_155997 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (one_one X_a))) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_155997))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_155997) _let_2))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_155997))))))) ) 16.35/16.44 ( nat, (zero_zero nat) ) 16.35/16.44 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.44 ( int, (one_one int) ) 16.35/16.44 ( int, pls ) 16.35/16.44 ( int, min_1 ) 16.35/16.44 ( int, s ) 16.35/16.44 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.44 ( int, t ) 16.35/16.44 ( int, skv_4 ) 16.35/16.44 ( int, skv_10 ) 16.35/16.44 ( real, (one_one real) ) 16.35/16.44 ( real, (zero_zero real) ) 16.35/16.44 ( real, pi ) 16.35/16.44 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.44 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.35/16.44 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.44 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.44 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 16.35/16.44 ( real, skv_2 ) 16.35/16.44 ( real, skv_8 ) 16.35/16.44 ( real, skv_9 ) 16.35/16.44 ( complex, ii ) 16.35/16.44 ) 16.35/16.44 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_156025 $$unsorted) (BOUND_VARIABLE_156026 $$unsorted)) (let ((_let_0 (archimedean_ceiling X_a))) (or (not (archim1727834104eiling X_a)) (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP X_a int _let_0 BOUND_VARIABLE_156025)) (hAPP X_a int _let_0 BOUND_VARIABLE_156026)))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_156025) BOUND_VARIABLE_156026)))) ) 16.35/16.44 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.44 ( int, (one_one int), t ) 16.35/16.44 ( int, pls, (one_one int) ) 16.35/16.44 ( int, pls, pls ) 16.35/16.44 ( int, pls, min_1 ) 16.35/16.44 ( int, pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.44 ( int, min_1, pls ) 16.35/16.44 ( int, min_1, min_1 ) 16.35/16.44 ( int, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.44 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.44 ( int, skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.44 ( int, skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.44 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.44 ( real, (zero_zero real), pi ) 16.35/16.44 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.44 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.44 ( real, (zero_zero real), skv_2 ) 16.35/16.44 ( real, (zero_zero real), skv_8 ) 16.35/16.44 ( real, (zero_zero real), skv_9 ) 16.35/16.44 ( real, pi, (zero_zero real) ) 16.35/16.44 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.44 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.44 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 16.35/16.44 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.35/16.45 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 16.35/16.45 ) 16.35/16.45 (instantiation (forall ((W $$unsorted)) (let ((_let_0 (one_one int))) (let ((_let_1 (zero_zero int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (hAPP int int (number_number_of int) W))) (let ((_let_5 (hAPP int _let_2 (hAPP int _let_3 posDivAlg _let_0) _let_4))) (let ((_let_6 (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) _let_0) _let_4)))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) _let_1) _let_4))) (and (or _let_6 (= (hAPP _let_2 _let_2 (hAPP int (fun _let_2 _let_2) adjust _let_4) (hAPP int _let_2 (hAPP int _let_3 posDivAlg _let_0) (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) _let_4))) _let_5)) (or (not _let_6) (= (hAPP int _let_2 (hAPP int _let_3 (product_Pair int int) _let_1) _let_0) _let_5))))))))))) ) 16.35/16.45 ( pls ) 16.35/16.45 ( (hAPP int int bit1 pls) ) 16.35/16.45 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.35/16.45 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.35/16.45 ( min_1 ) 16.35/16.45 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.45 ) 16.35/16.45 (instantiation (forall ((X_2 $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) X_2)) (= X_2 (hAPP real real (exp real) (hAPP real real ln X_2)))) ) 16.35/16.45 ( (one_one real) ) 16.35/16.45 ( pi ) 16.35/16.45 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.45 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.45 ( skv_2 ) 16.35/16.45 ( skv_8 ) 16.35/16.45 ( skv_9 ) 16.35/16.45 ) 16.35/16.45 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (number_number_of int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 (plus_plus int) A_1) B))) (let ((_let_4 (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) _let_3)))) (let ((_let_5 (hAPP int (fun int _let_2) negDivAlg A_1))) (let ((_let_6 (hAPP int _let_2 _let_5 B))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) B))) (and (or (not _let_4) (= (hAPP int _let_2 (hAPP int (fun int _let_2) (product_Pair int int) (hAPP int int _let_1 min_1)) _let_3) _let_6)) (or _let_4 (= _let_6 (hAPP _let_2 _let_2 (hAPP int (fun _let_2 _let_2) adjust B) (hAPP int _let_2 _let_5 (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int _let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) B)))))))))))))) ) 16.35/16.45 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 16.35/16.45 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 16.35/16.45 ) 16.35/16.45 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_156158 $$unsorted) (BOUND_VARIABLE_156159 $$unsorted)) (let ((_let_0 (archim2085082626_floor X_a))) (or (not (archim1727834104eiling X_a)) (= (hAPP int int (hAPP int (fun int int) (minus_minus int) (hAPP X_a int _let_0 BOUND_VARIABLE_156158)) (hAPP int int (number_number_of int) BOUND_VARIABLE_156159)) (hAPP X_a int _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) BOUND_VARIABLE_156158) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_156159)))))) ) 16.35/16.45 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), min_1 ) 16.35/16.45 ( code_code_numeral, (zero_zero code_code_numeral), (hAPP int int bit1 pls) ) 16.35/16.45 ) 16.35/16.45 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_156182 $$unsorted) (BOUND_VARIABLE_156183 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)))) (or (not (linord20386208strict X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_156183))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_156182))) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_156183) BOUND_VARIABLE_156182))))) ) 16.35/16.45 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.45 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.45 ( int, skv_13, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.45 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.45 ( real, pi, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 16.35/16.45 ( real, (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.45 ( real, (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.45 ( complex, ii, ii ) 16.35/16.45 ( complex, ii, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 16.35/16.45 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.45 ) 16.35/16.45 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_156256 $$unsorted) (BOUND_VARIABLE_156257 $$unsorted) (BOUND_VARIABLE_156258 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_156257))) (or (not (comm_ring_1 X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_156258))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_156256))) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) BOUND_VARIABLE_156258) BOUND_VARIABLE_156256))))) ) 16.35/16.45 ( int, (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.45 ) 16.35/16.45 (instantiation (forall ((X_a $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (zero_zero int) (hAPP X_a int (archimedean_ceiling X_a) (zero_zero X_a)))) ) 16.35/16.45 ( nat ) 16.35/16.45 ( int ) 16.35/16.45 ( real ) 16.35/16.45 ( rat ) 16.35/16.45 ( complex ) 16.35/16.45 ( quickcheck_code_int ) 16.35/16.45 ( code_code_numeral ) 16.35/16.45 ) 16.35/16.45 (instantiation (forall ((N_1 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (zero_zero int)) N_1))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (one_one int)) (hAPP int int (fact_fact int) N_1)))))) ) 16.35/16.45 ( (one_one int) ) 16.35/16.45 ( (zero_zero int) ) 16.35/16.45 ( min_1 ) 16.35/16.45 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.45 ( s ) 16.35/16.45 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.35/16.45 ( (hAPP int int (number_number_of int) pls) ) 16.35/16.45 ( skv_4 ) 16.35/16.45 ( skv_10 ) 16.35/16.45 ) 16.35/16.45 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_156370 $$unsorted)) (or (not (linordered_idom X_a)) (not (number_ring X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_156370)) (zero_zero X_a))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) BOUND_VARIABLE_156370) pls)))) ) 16.35/16.45 ( nat, pls ) 16.35/16.45 ( nat, (hAPP int int bit1 pls) ) 16.35/16.45 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.35/16.45 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.35/16.45 ( int, pls ) 16.35/16.45 ( int, (hAPP int int bit1 pls) ) 16.35/16.45 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.35/16.45 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.35/16.45 ( int, min_1 ) 16.35/16.45 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.45 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.35/16.45 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.35/16.45 ( real, min_1 ) 16.35/16.45 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.45 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.35/16.45 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.45 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 16.35/16.45 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.35/16.45 ( complex, min_1 ) 16.35/16.45 ( quickcheck_code_int, (one_one int) ) 16.35/16.45 ( quickcheck_code_int, (zero_zero int) ) 16.35/16.45 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 16.35/16.45 ( code_code_numeral, pls ) 16.35/16.45 ( code_code_numeral, (hAPP int int bit1 pls) ) 16.35/16.45 ) 16.35/16.45 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_156394 $$unsorted) (BOUND_VARIABLE_156395 $$unsorted)) (let ((_let_0 (inverse_inverse X_a))) (let ((_let_1 (fun nat X_a))) (let ((_let_2 (power_power X_a))) (or (not (division_ring X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_156395)) (= (hAPP nat X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a _let_0 BOUND_VARIABLE_156395)) BOUND_VARIABLE_156394) (hAPP X_a X_a _let_0 (hAPP nat X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_156395) BOUND_VARIABLE_156394))))))) ) 16.35/16.45 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 16.35/16.45 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 16.35/16.45 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_14 ) 16.35/16.45 ( complex, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), ii ) 16.35/16.45 ) 16.35/16.45 (instantiation (forall ((N $$unsorted)) (let ((_let_0 (even_odd_even nat))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N))) (= (not (hBOOL (hAPP nat bool _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) N) (one_one nat))))) (hBOOL (hAPP nat bool _let_0 N))))) ) 16.35/16.45 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.45 ) 16.35/16.45 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_156472 $$unsorted) (BOUND_VARIABLE_156473 $$unsorted) (BOUND_VARIABLE_156474 $$unsorted) (BOUND_VARIABLE_156475 $$unsorted) (BOUND_VARIABLE_156476 $$unsorted) (BOUND_VARIABLE_156477 $$unsorted)) (let ((_let_0 (filter X_a))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun X_a X_b))) (let ((_let_3 (fun X_b _let_1))) (let ((_let_4 (tendsto X_a X_b))) (let ((_let_5 (at X_a))) (or (not (topological_space X_b)) (not (topological_space X_a)) (not (= (ti X_a BOUND_VARIABLE_156477) (ti X_a BOUND_VARIABLE_156476))) (not (forall ((X $$unsorted)) (or (= (ti X_a X) (ti X_a BOUND_VARIABLE_156477)) (= (hAPP X_a X_b BOUND_VARIABLE_156475 X) (hAPP X_a X_b BOUND_VARIABLE_156474 X))) )) (not (= (ti X_b BOUND_VARIABLE_156472) (ti X_b BOUND_VARIABLE_156473))) (= (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (hAPP _let_2 _let_3 _let_4 BOUND_VARIABLE_156475) BOUND_VARIABLE_156473) (hAPP X_a _let_0 _let_5 BOUND_VARIABLE_156477))) (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (hAPP _let_2 _let_3 _let_4 BOUND_VARIABLE_156474) BOUND_VARIABLE_156472) (hAPP X_a _let_0 _let_5 BOUND_VARIABLE_156476))))))))))) ) 16.35/16.45 ( real, real, pi, pi, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), pi, pi ) 16.35/16.45 ) 16.35/16.45 (instantiation (forall ((X $$unsorted)) (or (not (hBOOL (hAPP nat bool (even_odd_even nat) X))) (= (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP int real (number_number_of real) min_1)) (hAPP nat nat (hAPP nat (fun nat nat) (div_div nat) X) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP nat real (real_1 nat) (hAPP nat nat (fact_fact nat) X))) (hAPP nat real cos_coeff X))) ) 16.35/16.45 ( (zero_zero nat) ) 16.35/16.45 ( (hAPP nat nat suc (zero_zero nat)) ) 16.35/16.45 ( (one_one nat) ) 16.35/16.45 ) 16.35/16.45 (instantiation (forall ((X $$unsorted)) (or (hBOOL (hAPP nat bool (even_odd_even nat) X)) (= (zero_zero real) (hAPP nat real cos_coeff X))) ) 16.35/16.45 ( (zero_zero nat) ) 16.35/16.45 ( (one_one nat) ) 16.35/16.45 ) 16.35/16.45 (instantiation (forall ((P_1 $$unsorted) (A0 $$unsorted) (A1 $$unsorted)) (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 bool))) (or (not (hBOOL (hAPP _let_0 bool (hAPP (fun _let_0 _let_1) _let_1 (accp _let_0) norm_frac_rel) (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) A0) A1)))) (not (forall ((A_4 $$unsorted) (B_4 $$unsorted)) (let ((_let_2 (fun int bool))) (let ((_let_3 (uminus_uminus int))) (or (not (hBOOL (hAPP _let_0 bool (hAPP (fun _let_0 _let_1) _let_1 (accp _let_0) norm_frac_rel) (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) A_4) B_4)))) (and (hBOOL (hAPP int bool (hAPP int _let_2 (ord_less int) B_4) (zero_zero int))) (not (hBOOL (hAPP int bool (hAPP int _let_2 P_1 (hAPP int int _let_3 A_4)) (hAPP int int _let_3 B_4))))) (hBOOL (hAPP int bool (hAPP int _let_2 P_1 A_4) B_4))))) )) (hBOOL (hAPP int bool (hAPP int (fun int bool) P_1 A0) A1))))) ) 16.35/16.45 ( (ord_less_eq int), (one_one int), t ) 16.35/16.45 ( (ord_less_eq int), (zero_zero int), (one_one int) ) 16.35/16.45 ( (ord_less_eq int), (zero_zero int), min_1 ) 16.35/16.45 ( (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.45 ( (ord_less_eq int), (zero_zero int), s ) 16.35/16.45 ( (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.35/16.45 ( (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) pls) ) 16.35/16.45 ( (ord_less_eq int), (zero_zero int), skv_4 ) 16.35/16.45 ( (ord_less_eq int), (zero_zero int), skv_10 ) 16.35/16.45 ( (ord_less_eq int), min_1, pls ) 16.35/16.45 ( (ord_less_eq int), min_1, min_1 ) 16.35/16.45 ( (ord_less int), (one_one int), t ) 16.35/16.45 ( (ord_less int), pls, (one_one int) ) 16.35/16.45 ( (ord_less int), pls, pls ) 16.35/16.45 ( (ord_less int), pls, min_1 ) 16.35/16.45 ( (ord_less int), pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.45 ( (ord_less int), min_1, pls ) 16.35/16.45 ( (ord_less int), min_1, min_1 ) 16.35/16.45 ( (ord_less int), s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.45 ( (ord_less int), t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.45 ( (ord_less int), skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.45 ( (ord_less int), skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.45 ( (dvd_dvd int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 16.35/16.45 ( quadRes, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (number_number_of int) min_1) ) 16.35/16.45 ( (hAPP int (fun int (fun int bool)) zcong s1), s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.45 ( (hAPP int (fun int (fun int bool)) zcong s1), skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.45 ( (hAPP int (fun int (fun int bool)) zcong s1), skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.45 ( (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.45 ( (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.45 ( (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.45 ( (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.45 ) 16.35/16.45 (instantiation (forall ((Real1 $$unsorted) (Real2 $$unsorted) (Real1_2 $$unsorted) (Real2_2 $$unsorted)) (let ((_let_0 (fun real complex))) (= (= (hAPP real complex (hAPP real _let_0 complex_1 Real1) Real2) (hAPP real complex (hAPP real _let_0 complex_1 Real1_2) Real2_2)) (and (= Real2 Real2_2) (= Real1 Real1_2)))) ) 16.35/16.45 ( (one_one real), (zero_zero real), (zero_zero real), (one_one real) ) 16.35/16.45 ( (one_one real), (zero_zero real), (zero_zero real), (zero_zero real) ) 16.35/16.45 ( (zero_zero real), (one_one real), (one_one real), (zero_zero real) ) 16.35/16.45 ( (zero_zero real), (one_one real), (zero_zero real), (one_one real) ) 16.35/16.45 ( (zero_zero real), (zero_zero real), (zero_zero real), (one_one real) ) 16.35/16.45 ) 16.35/16.45 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_0 (fun real complex))) (= (hAPP real complex (hAPP real _let_0 complex_1 (hAPP real real (uminus_uminus real) B)) A_1) (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) ii) (hAPP real complex (hAPP real _let_0 complex_1 A_1) B)))) ) 16.35/16.45 ( (one_one real), (zero_zero real) ) 16.35/16.45 ( (zero_zero real), (one_one real) ) 16.35/16.45 ( (zero_zero real), (zero_zero real) ) 16.35/16.45 ) 16.35/16.45 (instantiation (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (times_times real))) (= (hAPP real real (hAPP real _let_0 (plus_plus real) (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real cos Y_1)) (hAPP real real cos X_1))) (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real sin Y_1)) (hAPP real real sin X_1))) (hAPP real real cos (hAPP real real (hAPP real _let_0 (minus_minus real) X_1) Y_1))))) ) 16.35/16.45 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 16.35/16.45 ) 16.35/16.45 (instantiation (forall ((X_1 $$unsorted)) (= (hAPP complex real re X_1) (hAPP complex real re (hAPP complex complex cnj X_1))) ) 16.35/16.45 ( (one_one complex) ) 16.35/16.45 ( ii ) 16.35/16.45 ( (zero_zero complex) ) 16.35/16.45 ) 16.35/16.45 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_156736 $$unsorted) (BOUND_VARIABLE_156737 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (uminus_uminus X_a))) (or (not (ordered_ab_group_add X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_156736)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_156737))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_156737) BOUND_VARIABLE_156736))))))) ) 16.35/16.45 ( int, (one_one int), (one_one int) ) 16.35/16.45 ( int, (one_one int), (zero_zero int) ) 16.35/16.45 ( int, (one_one int), pls ) 16.35/16.45 ( int, pls, (one_one int) ) 16.35/16.45 ( int, pls, pls ) 16.35/16.45 ( int, pls, min_1 ) 16.35/16.45 ( int, min_1, (zero_zero int) ) 16.35/16.45 ( int, min_1, min_1 ) 16.35/16.45 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 16.35/16.45 ( int, s, (zero_zero int) ) 16.35/16.45 ( int, t, (one_one int) ) 16.35/16.45 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 16.35/16.45 ( int, (hAPP int int (number_number_of int) pls), (zero_zero int) ) 16.35/16.45 ( int, skv_4, (zero_zero int) ) 16.35/16.45 ( int, skv_10, (zero_zero int) ) 16.35/16.45 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.45 ( real, pi, (zero_zero real) ) 16.35/16.45 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.45 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.45 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_5 ) 16.35/16.45 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.35/16.45 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.35/16.45 ( real, skv_3, (zero_zero real) ) 16.35/16.45 ( real, skv_5, (zero_zero real) ) 16.35/16.45 ( real, skv_7, (zero_zero real) ) 16.35/16.45 ( real, skv_12, (zero_zero real) ) 16.35/16.45 ) 16.35/16.45 (instantiation (forall ((Y_2 $$unsorted) (X_2 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member int))) (or (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 X_2) zEven))) (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 Y_2) zEven))) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP int int (hAPP int (fun int int) (minus_minus int) X_2) Y_2)) zEven)))))) ) 16.35/16.45 ( (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.45 ) 16.35/16.45 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_156878 $$unsorted) (BOUND_VARIABLE_156879 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (inverse_inverse X_a))) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_156878)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_156879)))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) (zero_zero X_a)) BOUND_VARIABLE_156878))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_156879) BOUND_VARIABLE_156878)))))) ) 16.35/16.45 ( int, (one_one int), (zero_zero int) ) 16.35/16.45 ( int, pls, min_1 ) 16.35/16.45 ( int, min_1, (zero_zero int) ) 16.35/16.45 ( int, min_1, min_1 ) 16.35/16.45 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 16.35/16.45 ( int, s, (zero_zero int) ) 16.35/16.45 ( int, t, (one_one int) ) 16.35/16.45 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 16.35/16.45 ( int, (hAPP int int (number_number_of int) pls), (zero_zero int) ) 16.35/16.45 ( int, skv_4, (zero_zero int) ) 16.35/16.45 ( int, skv_10, (zero_zero int) ) 16.35/16.45 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.45 ( real, pi, (zero_zero real) ) 16.35/16.45 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.45 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.45 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_5 ) 16.35/16.45 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.35/16.45 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.35/16.45 ( real, skv_3, (zero_zero real) ) 16.35/16.45 ( real, skv_5, (zero_zero real) ) 16.35/16.45 ( real, skv_7, (zero_zero real) ) 16.35/16.45 ( real, skv_12, (zero_zero real) ) 16.35/16.45 ) 16.35/16.45 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (iszero X_a))) (or (not (semiring_1 X_a)) (= _let_0 (ti (fun X_a bool) _let_0)))) ) 16.35/16.45 ( bool ) 16.35/16.45 ( nat ) 16.35/16.45 ( int ) 16.35/16.45 ( (fun int bool) ) 16.35/16.45 ( (fun nat bool) ) 16.35/16.45 ( (product_prod nat nat) ) 16.35/16.45 ( real ) 16.35/16.45 ( rat ) 16.35/16.45 ( complex ) 16.35/16.45 ( (filter nat) ) 16.35/16.45 ( (product_prod int int) ) 16.35/16.45 ( quickcheck_code_int ) 16.35/16.45 ( code_code_numeral ) 16.35/16.45 ( (product_prod real real) ) 16.35/16.45 ( (fun nat rat) ) 16.35/16.45 ( (filter real) ) 16.35/16.45 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 16.35/16.45 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 16.35/16.45 ) 16.35/16.45 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_156943 $$unsorted) (BOUND_VARIABLE_156944 $$unsorted)) (let ((_let_0 (fun (filter nat) bool))) (let ((_let_1 (fun nat X_a))) (let ((_let_2 (fun X_a _let_0))) (let ((_let_3 (tendsto nat X_a))) (let ((_let_4 (inverse_inverse X_a))) (or (not (real_n1866405975lgebra X_a)) (not (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_0 (hAPP _let_1 _let_2 _let_3 BOUND_VARIABLE_156943) BOUND_VARIABLE_156944) sequentially))) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_156944)) (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_0 (hAPP _let_1 _let_2 _let_3 (hAPP _let_1 _let_1 (hAPP (fun X_a X_a) (fun _let_1 _let_1) (combb X_a X_a nat) _let_4) BOUND_VARIABLE_156943)) (hAPP X_a X_a _let_4 BOUND_VARIABLE_156944)) sequentially)))))))) ) 16.35/16.45 ( real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))), (zero_zero real) ) 16.35/16.45 ) 16.35/16.45 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_156978 $$unsorted) (BOUND_VARIABLE_156979 $$unsorted) (BOUND_VARIABLE_156980 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (inverse_divide X_a))) (let ((_let_2 (plus_plus X_a))) (or (not (field X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_156980)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_156978) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_156979) BOUND_VARIABLE_156980)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_0 _let_2 (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_156980) BOUND_VARIABLE_156978)) BOUND_VARIABLE_156979)) BOUND_VARIABLE_156980)))))) ) 16.35/16.45 ( int, m, (one_one int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.45 ) 16.35/16.45 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_157010 $$unsorted)) (or (not (real_algebra_1 X_a)) (= (= (zero_zero real) BOUND_VARIABLE_157010) (= (zero_zero X_a) (hAPP real X_a (of_real X_a) BOUND_VARIABLE_157010)))) ) 16.35/16.45 ( complex, pi ) 16.35/16.45 ( complex, (hAPP int real (number_number_of real) min_1) ) 16.35/16.45 ( complex, (hAPP real real (uminus_uminus real) (one_one real)) ) 16.35/16.45 ) 16.35/16.45 (instantiation (forall ((A_3 $$unsorted) (X_2 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun nat bool))) (or (not (hBOOL (hAPP int bool nat_is_nat X_2))) (not (hBOOL (hAPP _let_0 bool nat_nat_set A_3))) (= (hBOOL (hAPP _let_1 bool (hAPP nat (fun _let_1 bool) (member nat) (hAPP int nat nat_1 X_2)) (hAPP _let_0 _let_1 (hAPP (fun int nat) (fun _let_0 _let_1) (image int nat) nat_1) A_3))) (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) X_2) A_3)))))) ) 16.35/16.45 ( zEven, (one_one int) ) 16.35/16.45 ) 16.35/16.45 (instantiation (forall ((Y_2 $$unsorted) (N $$unsorted)) (let ((_let_0 (hAPP real (fun real bool) (ord_less_eq real) (one_one real)))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N))) (= (hBOOL (hAPP real bool _let_0 (hAPP real real (hAPP nat (fun real real) root N) Y_2))) (hBOOL (hAPP real bool _let_0 Y_2))))) ) 16.35/16.45 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.45 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.45 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.45 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.45 ) 16.35/16.45 (instantiation (forall ((X_2 $$unsorted)) (= (= (zero_zero real) (hAPP real real cos X_2)) (or (not (forall ((N_2 $$unsorted)) (let ((_let_0 (fun real real))) (or (not (= X_2 (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP nat real (real_1 nat) N_2)) (hAPP real real (hAPP real _let_0 (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) (hBOOL (hAPP nat bool (even_odd_even nat) N_2)))) )) (not (forall ((N_2 $$unsorted)) (let ((_let_0 (fun real real))) (or (hBOOL (hAPP nat bool (even_odd_even nat) N_2)) (not (= X_2 (hAPP real real (hAPP real _let_0 (times_times real) (hAPP nat real (real_1 nat) N_2)) (hAPP real real (hAPP real _let_0 (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))))) )))) ) 16.35/16.45 ( (zero_zero real) ) 16.35/16.45 ( pi ) 16.35/16.45 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.45 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.45 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.35/16.45 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.35/16.45 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.35/16.45 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 16.35/16.45 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 16.35/16.45 ( skv_5 ) 16.35/16.45 ) 16.35/16.45 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (field_char_0 X_a)) (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) (one_one X_a)) (field_char_0_Rats X_a))))) ) 16.35/16.45 ( nat ) 16.35/16.45 ( int ) 16.35/16.45 ( real ) 16.35/16.45 ( rat ) 16.35/16.45 ( complex ) 16.35/16.45 ( quickcheck_code_int ) 16.35/16.45 ( code_code_numeral ) 16.35/16.45 ) 16.35/16.45 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_157235 $$unsorted) (BOUND_VARIABLE_157236 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a X_a) (inverse_divide X_a) (one_one X_a)))) (let ((_let_1 (fun nat X_a))) (let ((_let_2 (power_power X_a))) (or (not (field_inverse_zero X_a)) (= (hAPP nat X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a _let_0 BOUND_VARIABLE_157235)) BOUND_VARIABLE_157236) (hAPP X_a X_a _let_0 (hAPP nat X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_157235) BOUND_VARIABLE_157236))))))) ) 16.35/16.45 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.45 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.45 ( int, skv_14, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.45 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.45 ) 16.35/16.45 (instantiation (forall ((R_4 $$unsorted) (P_5 $$unsorted) (Q_3 $$unsorted)) (let ((_let_0 (product_prod int int))) (or (not (= (hAPP rat _let_0 quotient_of R_4) (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) P_5) Q_3))) (= (one_one int) (hAPP int int (hAPP int (fun int int) (gcd_gcd int) P_5) Q_3)))) ) 16.35/16.45 ( (zero_zero rat), s, (one_one int) ) 16.35/16.45 ( (one_one rat), (zero_zero int), (one_one int) ) 16.35/16.45 ) 16.35/16.45 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_157311 $$unsorted) (BOUND_VARIABLE_157312 $$unsorted)) (let ((_let_0 (inverse_inverse X_a))) (or (not (divisi14063676e_zero X_a)) (= (= (ti X_a BOUND_VARIABLE_157312) (ti X_a BOUND_VARIABLE_157311)) (= (hAPP X_a X_a _let_0 BOUND_VARIABLE_157311) (hAPP X_a X_a _let_0 BOUND_VARIABLE_157312))))) ) 16.35/16.45 ( bool, fFalse, fFalse ) 16.35/16.45 ( bool, fFalse, fTrue ) 16.35/16.45 ( bool, fTrue, fFalse ) 16.35/16.45 ( int, pls, s1 ) 16.35/16.45 ( int, min_1, t ) 16.35/16.45 ( int, s, pls ) 16.35/16.45 ( int, s, s ) 16.35/16.45 ( int, s, s1 ) 16.35/16.45 ( int, m, min_1 ) 16.35/16.45 ( int, m, m ) 16.35/16.45 ( int, m, t ) 16.35/16.45 ( int, s1, s ) 16.35/16.45 ( int, t, m ) 16.35/16.45 ( (fun int bool), nat_neg, (even_odd_even int) ) 16.35/16.45 ( (fun int bool), zprime, nat_neg ) 16.35/16.45 ( (fun int bool), zEven, twoSqu1091635170sum2sq ) 16.35/16.45 ( (fun int bool), zOdd, zOdd ) 16.35/16.45 ( (fun int bool), (even_odd_even int), nat_neg ) 16.35/16.45 ( (fun int bool), (even_odd_even int), zprime ) 16.35/16.45 ( (fun int bool), (even_odd_even int), (even_odd_even int) ) 16.35/16.45 ( (fun int bool), twoSqu1091635170sum2sq, zEven ) 16.35/16.45 ( (fun int bool), twoSqu1091635170sum2sq, twoSqu1091635170sum2sq ) 16.35/16.45 ( (fun int bool), twoSqu1091635170sum2sq, nat_is_nat ) 16.35/16.45 ( (fun int bool), nat_is_nat, zEven ) 16.35/16.45 ( (fun int (fun int bool)), norRRset, norRRset ) 16.35/16.45 ( (fun int (fun int bool)), norRRset, d22set ) 16.35/16.45 ( (fun int (fun int bool)), norRRset, sr ) 16.35/16.45 ( (fun int (fun int bool)), quadRes, quadRes ) 16.35/16.45 ( (fun int (fun int bool)), quadRes, sRStar ) 16.35/16.45 ( (fun int (fun int bool)), quadRes, quickc1265749348ro_rel ) 16.35/16.45 ( (fun int (fun int bool)), sRStar, quadRes ) 16.35/16.45 ( (fun int (fun int bool)), d22set, sr ) 16.35/16.45 ( (fun int (fun int bool)), sr, norRRset ) 16.35/16.45 ( (fun int (fun int bool)), quickc1265749348ro_rel, sRStar ) 16.35/16.45 ( (fun int int), zfact, pred ) 16.35/16.45 ( (fun int int), bit0, (fact_fact int) ) 16.35/16.45 ( (fun int int), bit1, zfact ) 16.35/16.45 ( (fun int int), bit1, bit1 ) 16.35/16.45 ( (fun int int), bit1, pred ) 16.35/16.45 ( (fun int int), (fact_fact int), bit0 ) 16.35/16.45 ( (fun int int), (fact_fact int), (fact_fact int) ) 16.35/16.45 ( (fun int int), (fact_fact int), succ ) 16.35/16.45 ( (fun int int), pred, bit1 ) 16.35/16.45 ( (fun int int), succ, bit0 ) 16.35/16.45 ( (fun nat bool), (even_odd_even nat), (even_odd_even nat) ) 16.35/16.45 ( (fun nat bool), (even_odd_even nat), prime ) 16.35/16.45 ( (fun nat bool), prime, (even_odd_even nat) ) 16.35/16.45 ( (fun nat nat), suc, fact ) 16.35/16.45 ( (fun nat nat), (fact_fact nat), (size_size nat) ) 16.35/16.45 ( (fun nat nat), fact, suc ) 16.35/16.45 ( (fun nat nat), fact, fact ) 16.35/16.45 ( (fun nat nat), nat_size, (fact_fact nat) ) 16.35/16.45 ( (fun nat nat), nat_size, nat_size ) 16.35/16.45 ( (fun nat nat), nat_size, (size_size nat) ) 16.35/16.45 ( (fun nat nat), (size_size nat), nat_size ) 16.35/16.45 ( (fun (product_prod nat nat) bool), pred_nat, pred_nat ) 16.35/16.45 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel, divmod_nat_rel ) 16.35/16.45 ( real, pi, pi ) 16.35/16.45 ( (fun real real), ln, sqrt ) 16.35/16.45 ( (fun real real), cos, cos ) 16.35/16.45 ( (fun real real), cos, tan ) 16.35/16.45 ( (fun real real), sqrt, ln ) 16.35/16.45 ( (fun real real), sqrt, sqrt ) 16.35/16.45 ( (fun real real), sqrt, arccos ) 16.35/16.45 ( (fun real real), sin, arcsin ) 16.35/16.45 ( (fun real real), arccos, ln ) 16.35/16.45 ( (fun real real), arcsin, sin ) 16.35/16.45 ( (fun real real), arcsin, arcsin ) 16.35/16.45 ( (fun real real), arcsin, arctan ) 16.35/16.45 ( (fun real real), tan, cos ) 16.35/16.45 ( (fun real real), arctan, sin ) 16.35/16.45 ( (fun nat (fun nat bool)), coprime, coprime ) 16.35/16.45 ( complex, ii, ii ) 16.35/16.45 ( (fun nat real), (real_1 nat), sin_coeff ) 16.35/16.45 ( (fun nat real), sin_coeff, (real_1 nat) ) 16.35/16.45 ( (fun nat real), sin_coeff, sin_coeff ) 16.35/16.45 ( (fun nat real), sin_coeff, cos_coeff ) 16.35/16.45 ( (fun nat real), cos_coeff, (real_1 nat) ) 16.35/16.45 ( (filter nat), sequentially, sequentially ) 16.35/16.45 ( (fun int (fun int int)), (gcd_gcd int), (gcd_gcd int) ) 16.35/16.45 ( (fun int (fun int int)), (gcd_gcd int), int_gcd ) 16.35/16.45 ( (fun int (fun int int)), legendre, z3div ) 16.35/16.45 ( (fun int (fun int int)), legacy_zgcd, legendre ) 16.35/16.45 ( (fun int (fun int int)), standardRes, multInv ) 16.35/16.45 ( (fun int (fun int int)), nat_tsub, z3mod ) 16.35/16.45 ( (fun int (fun int int)), multInv, standardRes ) 16.35/16.45 ( (fun int (fun int int)), multInv, multInv ) 16.35/16.45 ( (fun int (fun int int)), multInv, inv ) 16.35/16.45 ( (fun int (fun int int)), z3mod, nat_tsub ) 16.35/16.45 ( (fun int (fun int int)), z3mod, z3mod ) 16.35/16.45 ( (fun int (fun int int)), z3mod, int_lcm ) 16.35/16.45 ( (fun int (fun int int)), z3div, legendre ) 16.35/16.45 ( (fun int (fun int int)), z3div, legacy_zgcd ) 16.35/16.45 ( (fun int (fun int int)), z3div, z3div ) 16.35/16.45 ( (fun int (fun int int)), int_gcd, (gcd_gcd int) ) 16.35/16.45 ( (fun int (fun int int)), int_lcm, nat_tsub ) 16.35/16.45 ( (fun int (fun int int)), inv, standardRes ) 16.35/16.45 ( (fun complex complex), expi, expi ) 16.35/16.45 ( (fun complex complex), expi, cnj ) 16.35/16.45 ( (fun complex complex), cnj, expi ) 16.35/16.45 ( (fun real complex), cis, cis ) 16.35/16.45 ( (fun int nat), nat_1, phi ) 16.35/16.45 ( (fun int nat), phi, nat_1 ) 16.35/16.45 ( (fun int nat), phi, phi ) 16.35/16.45 ( (fun (fun int bool) bool), nat_nat_set, nat_nat_set ) 16.35/16.45 ( (fun nat (fun nat nat)), (gcd_gcd nat), (gcd_gcd nat) ) 16.35/16.45 ( (fun nat (fun nat nat)), (gcd_gcd nat), nat_gcd ) 16.35/16.45 ( (fun nat (fun nat nat)), (gcd_gcd nat), nat_lcm ) 16.35/16.45 ( (fun nat (fun nat nat)), nat_gcd, (gcd_gcd nat) ) 16.35/16.45 ( (fun nat (fun nat nat)), nat_lcm, nat_gcd ) 16.35/16.45 ( (fun (fun int bool) int), (the int), (the int) ) 16.35/16.45 ( (fun complex real), re, arg ) 16.35/16.45 ( (fun complex real), im, re ) 16.35/16.45 ( (fun complex real), im, im ) 16.35/16.45 ( (fun complex real), im, arg ) 16.35/16.45 ( (fun complex real), arg, im ) 16.35/16.45 ( (fun bool bool), fNot, fNot ) 16.35/16.45 ( (fun nat (fun real real)), root, root ) 16.35/16.45 ( (fun real (fun real real)), log, log ) 16.35/16.45 ( (fun real (fun real real)), log, powr ) 16.35/16.45 ( (fun real (fun real real)), powr, log ) 16.35/16.45 ( (fun bool (fun bool bool)), fimplies, fimplies ) 16.35/16.45 ( (fun bool (fun bool bool)), fimplies, fconj ) 16.35/16.45 ( (fun bool (fun bool bool)), fimplies, fdisj ) 16.35/16.45 ( (fun bool (fun bool bool)), fconj, fimplies ) 16.35/16.45 ( (fun bool (fun bool bool)), fdisj, fconj ) 16.35/16.45 ( (fun int (fun int (product_prod int int))), negDivAlg, norm_frac ) 16.35/16.45 ( (fun int (fun int (product_prod int int))), posDivAlg, divmod_int ) 16.35/16.45 ( (fun int (fun int (product_prod int int))), divmod_int, posDivAlg ) 16.35/16.45 ( (fun int (fun int (product_prod int int))), divmod_int, divmod_int ) 16.35/16.45 ( (fun int (fun int (product_prod int int))), pdivmod, negDivAlg ) 16.35/16.45 ( (fun int (fun int (product_prod int int))), norm_frac, negDivAlg ) 16.35/16.45 ( (fun int (fun int (product_prod int int))), norm_frac, pdivmod ) 16.35/16.45 ( (fun int (fun int (product_prod int int))), norm_frac, norm_frac ) 16.35/16.45 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd, negateSnd ) 16.35/16.45 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd, normalize ) 16.35/16.45 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize, negateSnd ) 16.35/16.45 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust, adjust ) 16.35/16.45 ( (fun int (fun int (fun int bool))), zcong, noXRRset ) 16.35/16.45 ( (fun int (fun int (fun int bool))), zcongm, zcong ) 16.35/16.45 ( (fun int (fun int (fun int bool))), noXRRset, zcong ) 16.35/16.45 ( (fun int (fun int (fun int bool))), noXRRset, zcongm ) 16.35/16.45 ( (fun int (fun int (fun int bool))), noXRRset, noXRRset ) 16.35/16.45 ( (fun int (fun int (fun int bool))), bnorRset, bnorRset ) 16.35/16.45 ( (fun int (fun int (fun int bool))), bnorRset, wset ) 16.35/16.45 ( (fun int (fun int (fun int bool))), wset, bnorRset ) 16.35/16.45 ( (fun (product_prod int int) bool), frac_1, frac_1 ) 16.35/16.45 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than, int_ge_less_than ) 16.35/16.45 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than, int_ge_less_than2 ) 16.35/16.45 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2, int_ge_less_than ) 16.35/16.45 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral, code_S1047413653umeral ) 16.35/16.45 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset, is_RRset ) 16.35/16.45 ( (fun (fun nat rat) bool), vanishes, vanishes ) 16.35/16.45 ( (fun code_code_numeral nat), (size_size code_code_numeral), (size_size code_code_numeral) ) 16.35/16.45 ( (fun code_code_numeral nat), (size_size code_code_numeral), code_c271388182l_size ) 16.35/16.45 ( (fun code_code_numeral nat), code_c271388182l_size, (size_size code_code_numeral) ) 16.35/16.45 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel, ratrel ) 16.35/16.45 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel, norm_frac_rel ) 16.35/16.45 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel, lazy_small_lazy_rel ) 16.35/16.45 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel, negDivAlg_rel ) 16.35/16.45 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel, posDivAlg_rel ) 16.35/16.45 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel, upto_rel ) 16.35/16.45 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel, norm_frac_rel ) 16.35/16.45 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel, lazy_small_lazy_rel ) 16.35/16.45 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel, posDivAlg_rel ) 16.35/16.45 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq, twoSqu1094008024sum2sq ) 16.35/16.45 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less, pair_less ) 16.35/16.45 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less, pair_leq ) 16.35/16.45 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq, pair_less ) 16.35/16.45 ( (fun complex nat), complex_size, complex_size ) 16.35/16.45 ( (fun complex nat), complex_size, (size_size complex) ) 16.35/16.45 ( (fun complex nat), (size_size complex), complex_size ) 16.35/16.45 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel, nat_gcd_rel ) 16.35/16.45 ( (fun nat (fun nat (product_prod int int))), bezw, bezw ) 16.35/16.45 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd, xzgcd ) 16.35/16.45 ( (fun int (fun nat nat)), nat_aux, nat_aux ) 16.35/16.45 ( (fun int (fun (fun int bool) bool)), rsetR, resSet ) 16.35/16.45 ( (fun int (fun (fun int bool) bool)), resSet, rsetR ) 16.35/16.45 ( (fun int (fun (fun int bool) bool)), resSet, resSet ) 16.35/16.45 ( (fun int (list int)), quickc666637781d_zero, quickc666637781d_zero ) 16.35/16.45 ( (fun (product_prod int int) rat), frct, frct ) 16.35/16.45 ( (fun int (fun int rat)), fract, fract ) 16.35/16.45 ( (fun real (fun real complex)), complex_1, rcis ) 16.35/16.45 ( (fun real (fun real complex)), rcis, complex_1 ) 16.35/16.45 ( (fun real (fun real complex)), rcis, rcis ) 16.35/16.45 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat), (ord_gr676655987ssThan nat) ) 16.35/16.45 ( (fun quickcheck_code_int nat), quickcheck_nat_of, quickcheck_nat_of ) 16.35/16.45 ( (fun int real), (real_1 int), (real_1 int) ) 16.35/16.45 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect, bolzano_bisect ) 16.35/16.45 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR, rRset2norRR ) 16.35/16.45 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int, quickc495462417de_int ) 16.35/16.45 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda, xzgcda ) 16.35/16.45 ( (fun int (fun int (fun int (fun int bool)))), multInvPair, multInvPair ) 16.35/16.45 ( (fun real nat), natfloor, natceiling ) 16.35/16.45 ( (fun real nat), natceiling, natfloor ) 16.35/16.45 ( (fun real nat), natceiling, natceiling ) 16.35/16.45 ( (fun (fun real bool) real), (complete_Sup_Sup real), (complete_Sup_Sup real) ) 16.35/16.45 ( (fun quickcheck_code_int int), quickcheck_int_of, quickcheck_int_of ) 16.35/16.45 ( (fun rat (product_prod int int)), quotient_of, quotient_of ) 16.35/16.45 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral, code_d418564891umeral ) 16.35/16.45 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat, divmod_nat ) 16.35/16.45 ( (fun rat real), ratreal, ratreal ) 16.35/16.45 ( (fun code_code_numeral int), code_int_of, code_int_of ) 16.35/16.45 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel, divmod_int_rel ) 16.35/16.45 ( (fun int quickcheck_code_int), quickcheck_of_int, quickcheck_of_int ) 16.35/16.45 ( (fun int (fun int (fun (fun int bool) bool))), setS, setS ) 16.35/16.45 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux, code_nat_of_aux ) 16.35/16.45 ) 16.35/16.45 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_0 (nat_tr1645093318rphism X_a X_b))) (= _let_0 (ti (fun (fun X_a X_b) (fun (fun X_a bool) bool)) _let_0))) ) 16.35/16.45 ( nat, int ) 16.35/16.45 ( int, nat ) 16.35/16.45 ) 16.35/16.45 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (fequal X_a))) (= _let_0 (ti (fun X_a (fun X_a bool)) _let_0))) ) 16.35/16.45 ( bool ) 16.35/16.45 ( nat ) 16.35/16.45 ( int ) 16.35/16.45 ( (fun int bool) ) 16.35/16.45 ( (fun nat bool) ) 16.35/16.45 ( (product_prod nat nat) ) 16.35/16.45 ( real ) 16.35/16.45 ( (filter nat) ) 16.35/16.45 ( (product_prod int int) ) 16.35/16.45 ( (product_prod real real) ) 16.35/16.45 ( (fun nat rat) ) 16.35/16.45 ( (filter real) ) 16.35/16.45 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 16.35/16.45 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 16.35/16.45 ) 16.35/16.45 (instantiation (forall ((P_5 $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP int bool zprime P_5))) (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP int int zfact (hAPP int int (hAPP int (fun int int) (minus_minus int) P_5) (one_one int)))) (hAPP int int (number_number_of int) min_1)) P_5)))) ) 16.35/16.45 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.45 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.45 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.45 ) 16.35/16.45 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (times_times X_a))) (or (not (power X_a)) (= _let_0 (ti (fun X_a (fun X_a X_a)) _let_0)))) ) 16.35/16.45 ( bool ) 16.35/16.45 ( nat ) 16.35/16.45 ( int ) 16.35/16.45 ( (fun int bool) ) 16.35/16.45 ( (fun int (fun int bool)) ) 16.35/16.45 ( (fun int int) ) 16.35/16.45 ( (fun nat bool) ) 16.35/16.45 ( real ) 16.35/16.45 ( (fun real bool) ) 16.35/16.45 ( (fun real real) ) 16.35/16.45 ( rat ) 16.35/16.45 ( complex ) 16.35/16.45 ( (fun nat real) ) 16.35/16.45 ( (product_prod int int) ) 16.35/16.45 ( quickcheck_code_int ) 16.35/16.45 ( code_code_numeral ) 16.35/16.45 ( (fun int (fun int (fun int bool))) ) 16.35/16.45 ( (fun (product_prod int int) bool) ) 16.35/16.45 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 16.35/16.45 ( (fun (product_prod int int) int) ) 16.35/16.45 ( (fun int real) ) 16.35/16.45 ) 16.35/16.45 (instantiation (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (one_one real))) (let ((_let_2 (fun real real))) (let ((_let_3 (plus_plus real))) (let ((_let_4 (abs_abs real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) (hAPP real real _let_4 X_1)) _let_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) (hAPP real real _let_4 Y_1)) _let_1))) (= (hAPP real real arctan (hAPP real real (hAPP real _let_2 (inverse_divide real) (hAPP real real (hAPP real _let_2 _let_3 X_1) Y_1)) (hAPP real real (hAPP real _let_2 (minus_minus real) _let_1) (hAPP real real (hAPP real _let_2 (times_times real) X_1) Y_1)))) (hAPP real real (hAPP real _let_2 _let_3 (hAPP real real arctan X_1)) (hAPP real real arctan Y_1))))))))) ) 16.35/16.45 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.45 ( pi, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 16.35/16.45 ( (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.45 ( (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.45 ) 16.35/16.45 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_157558 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hAPP X_a int (archimedean_ceiling X_a) (hAPP nat X_a (semiring_1_of_nat X_a) BOUND_VARIABLE_157558)) (hAPP nat int (semiring_1_of_nat int) BOUND_VARIABLE_157558))) ) 16.35/16.45 ( int, (zero_zero nat) ) 16.35/16.45 ( int, (hAPP nat nat suc (zero_zero nat)) ) 16.35/16.45 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.35/16.45 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.45 ( real, (zero_zero nat) ) 16.35/16.45 ( real, (hAPP nat nat suc (zero_zero nat)) ) 16.35/16.45 ) 16.35/16.45 (instantiation (forall ((X_a $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (fun _let_0 bool))) (= (hAPP _let_1 _let_0 (complete_Sup_Sup _let_0) (hAPP _let_0 _let_1 (pow X_a) A_3)) (ti _let_0 A_3)))) ) 16.35/16.45 ( bool, fNot ) 16.35/16.45 ( nat, (even_odd_even nat) ) 16.35/16.45 ( nat, prime ) 16.35/16.45 ( int, nat_neg ) 16.35/16.45 ( int, zprime ) 16.35/16.45 ( int, zEven ) 16.35/16.45 ( int, zOdd ) 16.35/16.45 ( int, (even_odd_even int) ) 16.35/16.45 ( int, twoSqu1091635170sum2sq ) 16.35/16.45 ( int, nat_is_nat ) 16.35/16.45 ( (fun int bool), nat_nat_set ) 16.35/16.45 ( (product_prod nat nat), pred_nat ) 16.35/16.45 ( (product_prod int int), frac_1 ) 16.35/16.45 ( (fun nat rat), vanishes ) 16.35/16.45 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)), ratrel ) 16.35/16.45 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), pair_less ) 16.35/16.45 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), pair_leq ) 16.35/16.45 ) 16.35/16.45 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_157601 $$unsorted) (BOUND_VARIABLE_157602 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (or (not (linordered_idom X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_157601)) BOUND_VARIABLE_157602)) (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_157601) BOUND_VARIABLE_157602)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_157601)) BOUND_VARIABLE_157602))))))) ) 16.35/16.45 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.45 ( int, (one_one int), pls ) 16.35/16.45 ( int, (one_one int), min_1 ) 16.35/16.45 ( int, (one_one int), t ) 16.35/16.45 ( int, pls, (one_one int) ) 16.35/16.45 ( int, pls, pls ) 16.35/16.45 ( int, pls, min_1 ) 16.35/16.46 ( int, pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.46 ( int, min_1, pls ) 16.35/16.46 ( int, min_1, min_1 ) 16.35/16.46 ( int, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.46 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.46 ( int, skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.46 ( int, skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.46 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.46 ( real, (zero_zero real), pi ) 16.35/16.46 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.46 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.46 ( real, (zero_zero real), skv_2 ) 16.35/16.46 ( real, (zero_zero real), skv_8 ) 16.35/16.46 ( real, (zero_zero real), skv_9 ) 16.35/16.46 ( real, pi, (zero_zero real) ) 16.35/16.46 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.46 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.35/16.46 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.46 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 16.35/16.46 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi), pi ) 16.35/16.46 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.35/16.46 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 16.35/16.46 ) 16.35/16.46 (instantiation (forall ((M $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (div_mod nat))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (= (hAPP nat nat (hAPP nat _let_0 _let_1 M) _let_2) (hAPP nat nat (hAPP nat _let_0 _let_1 (hAPP nat nat suc (hAPP nat nat suc M))) _let_2))))) ) 16.35/16.46 ( (zero_zero nat) ) 16.35/16.46 ( (hAPP nat nat suc (zero_zero nat)) ) 16.35/16.46 ) 16.35/16.46 (instantiation (forall ((I_1 $$unsorted) (K_4 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) I_1) K_4))) (= K_4 (hAPP nat nat suc I_1)) (not (forall ((J_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) I_1) J_1))) (not (= K_4 (hAPP nat nat suc J_1)))) ))) ) 16.35/16.46 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.46 ) 16.35/16.46 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_157796 $$unsorted) (BOUND_VARIABLE_157805 $$unsorted)) (let ((_let_0 (abs_abs X_a))) (let ((_let_1 (fun X_a bool))) (let ((_let_2 (ord_less X_a))) (let ((_let_3 (zero_zero X_a))) (or (not (abs_if X_a)) (and (or (not (hBOOL (hAPP X_a bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_157796) _let_3))) (= (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_157796) (hAPP X_a X_a _let_0 BOUND_VARIABLE_157796))) (or (hBOOL (hAPP X_a bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_157805) _let_3)) (= (hAPP X_a X_a _let_0 BOUND_VARIABLE_157805) (ti X_a BOUND_VARIABLE_157805))))))))) ) 16.35/16.46 ( nat, (zero_zero nat), (zero_zero nat) ) 16.35/16.46 ( int, (one_one int), (one_one int) ) 16.35/16.46 ( int, pls, pls ) 16.35/16.46 ( int, min_1, min_1 ) 16.35/16.46 ( int, s, s ) 16.35/16.46 ( int, t, t ) 16.35/16.46 ( int, skv_4, skv_4 ) 16.35/16.46 ( int, skv_10, skv_10 ) 16.35/16.46 ( real, (one_one real), (one_one real) ) 16.35/16.46 ( real, (zero_zero real), (zero_zero real) ) 16.35/16.46 ( real, pi, pi ) 16.35/16.46 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.46 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.35/16.46 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.46 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 16.35/16.46 ) 16.35/16.46 (instantiation (forall ((X_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP _let_0 bool nat_nat_set A_3))) (not (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) X_2) A_3))) (hBOOL (hAPP int bool nat_is_nat X_2)))) ) 16.35/16.46 ( (one_one int), zEven ) 16.35/16.46 ) 16.35/16.46 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (hAPP real _let_0 _let_1 (zero_zero real)))) (or (not (hBOOL (hAPP real bool _let_2 X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) pi))) (hBOOL (hAPP real bool _let_2 (hAPP real real sin X_1))))))) ) 16.35/16.46 ( (zero_zero real) ) 16.35/16.46 ( pi ) 16.35/16.46 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.46 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.46 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.35/16.46 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.35/16.46 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.35/16.46 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.46 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 16.35/16.46 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 16.35/16.46 ( skv_5 ) 16.35/16.46 ) 16.35/16.46 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (inverse_divide real))) (let ((_let_2 (fun nat real))) (let ((_let_3 (power_power real))) (let ((_let_4 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_5 (fun real complex))) (let ((_let_6 (hAPP real real (hAPP real _let_0 (plus_plus real) (hAPP nat real (hAPP real _let_2 _let_3 A_1) _let_4)) (hAPP nat real (hAPP real _let_2 _let_3 B) _let_4)))) (= (hAPP complex complex (inverse_inverse complex) (hAPP real complex (hAPP real _let_5 complex_1 A_1) B)) (hAPP real complex (hAPP real _let_5 complex_1 (hAPP real real (hAPP real _let_0 _let_1 A_1) _let_6)) (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real (uminus_uminus real) B)) _let_6)))))))))) ) 16.35/16.46 ( (zero_zero real), (one_one real) ) 16.35/16.46 ) 16.35/16.46 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_157981 $$unsorted) (BOUND_VARIABLE_157982 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (or (not (semiring_div X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_157982)) (= (hAPP X_a X_a (hAPP X_a _let_0 (div_div X_a) (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_157981) BOUND_VARIABLE_157982)) BOUND_VARIABLE_157982) (ti X_a BOUND_VARIABLE_157981)))) ) 16.35/16.46 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 16.35/16.46 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 16.35/16.46 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13 ) 16.35/16.46 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.35/16.46 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 16.35/16.46 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 16.35/16.46 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 16.35/16.46 ( complex, ii, ii ) 16.35/16.46 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 16.35/16.46 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 16.35/16.46 ) 16.35/16.46 (instantiation (forall ((N_1 $$unsorted) (P_5 $$unsorted)) (or (not (hBOOL (hAPP int bool zprime P_5))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (dvd_dvd int) P_5) N_1)) (= (one_one int) (hAPP int int (hAPP int (fun int int) legacy_zgcd N_1) P_5))) ) 16.35/16.46 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.46 ) 16.35/16.46 (instantiation (forall ((N $$unsorted)) (= (= (zero_zero nat) N) (= (zero_zero int) (hAPP nat int (semiring_1_of_nat int) N))) ) 16.35/16.46 ( (zero_zero nat) ) 16.35/16.46 ( (hAPP nat nat suc (zero_zero nat)) ) 16.35/16.46 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.35/16.46 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.46 ) 16.35/16.46 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted)) (or (not (= M (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) M) N_1))) (= (zero_zero nat) N_1)) ) 16.35/16.46 ( (one_one nat), (one_one nat) ) 16.35/16.46 ) 16.35/16.46 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_158098 $$unsorted)) (or (not (semiring_div X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (div_mod X_a) BOUND_VARIABLE_158098) (zero_zero X_a)) (ti X_a BOUND_VARIABLE_158098))) ) 16.35/16.46 ( bool, fFalse ) 16.35/16.46 ( bool, fTrue ) 16.35/16.46 ( int, pls ) 16.35/16.46 ( int, min_1 ) 16.35/16.46 ( int, s ) 16.35/16.46 ( int, m ) 16.35/16.46 ( int, s1 ) 16.35/16.46 ( int, t ) 16.35/16.46 ( (fun int bool), nat_neg ) 16.35/16.46 ( (fun int bool), zprime ) 16.35/16.46 ( (fun int bool), zEven ) 16.35/16.46 ( (fun int bool), zOdd ) 16.35/16.46 ( (fun int bool), (even_odd_even int) ) 16.35/16.46 ( (fun int bool), twoSqu1091635170sum2sq ) 16.35/16.46 ( (fun int bool), nat_is_nat ) 16.35/16.46 ( (fun int (fun int bool)), norRRset ) 16.35/16.46 ( (fun int (fun int bool)), quadRes ) 16.35/16.46 ( (fun int (fun int bool)), sRStar ) 16.35/16.46 ( (fun int (fun int bool)), d22set ) 16.35/16.46 ( (fun int (fun int bool)), sr ) 16.35/16.46 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 16.35/16.46 ( (fun int int), zfact ) 16.35/16.46 ( (fun int int), bit0 ) 16.35/16.46 ( (fun int int), bit1 ) 16.35/16.46 ( (fun int int), (fact_fact int) ) 16.35/16.46 ( (fun int int), pred ) 16.35/16.46 ( (fun int int), succ ) 16.35/16.46 ( (fun nat bool), (even_odd_even nat) ) 16.35/16.46 ( (fun nat bool), prime ) 16.35/16.46 ( (fun nat nat), suc ) 16.35/16.46 ( (fun nat nat), (fact_fact nat) ) 16.35/16.46 ( (fun nat nat), fact ) 16.35/16.46 ( (fun nat nat), nat_size ) 16.35/16.46 ( (fun nat nat), (size_size nat) ) 16.35/16.46 ( (fun (product_prod nat nat) bool), pred_nat ) 16.35/16.46 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 16.35/16.46 ( real, pi ) 16.35/16.46 ( (fun real real), ln ) 16.35/16.46 ( (fun real real), cos ) 16.35/16.46 ( (fun real real), sqrt ) 16.35/16.46 ( (fun real real), sin ) 16.35/16.46 ( (fun real real), arccos ) 16.35/16.46 ( (fun real real), arcsin ) 16.35/16.46 ( (fun real real), tan ) 16.35/16.46 ( (fun real real), arctan ) 16.35/16.46 ( (fun nat (fun nat bool)), coprime ) 16.35/16.46 ( complex, ii ) 16.35/16.46 ( (fun nat real), (real_1 nat) ) 16.35/16.46 ( (fun nat real), sin_coeff ) 16.35/16.46 ( (fun nat real), cos_coeff ) 16.35/16.46 ( (filter nat), sequentially ) 16.35/16.46 ( (fun int (fun int int)), (gcd_gcd int) ) 16.35/16.46 ( (fun int (fun int int)), legendre ) 16.35/16.46 ( (fun int (fun int int)), legacy_zgcd ) 16.35/16.46 ( (fun int (fun int int)), standardRes ) 16.35/16.46 ( (fun int (fun int int)), nat_tsub ) 16.35/16.46 ( (fun int (fun int int)), multInv ) 16.35/16.46 ( (fun int (fun int int)), z3mod ) 16.35/16.46 ( (fun int (fun int int)), z3div ) 16.35/16.46 ( (fun int (fun int int)), int_gcd ) 16.35/16.46 ( (fun int (fun int int)), int_lcm ) 16.35/16.46 ( (fun int (fun int int)), inv ) 16.35/16.46 ( (fun complex complex), expi ) 16.35/16.46 ( (fun complex complex), cnj ) 16.35/16.46 ( (fun real complex), cis ) 16.35/16.46 ( (fun int nat), nat_1 ) 16.35/16.46 ( (fun int nat), phi ) 16.35/16.46 ( (fun (fun int bool) bool), nat_nat_set ) 16.35/16.46 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 16.35/16.46 ( (fun nat (fun nat nat)), nat_gcd ) 16.35/16.46 ( (fun nat (fun nat nat)), nat_lcm ) 16.35/16.46 ( (fun (fun int bool) int), (the int) ) 16.35/16.46 ( (fun complex real), re ) 16.35/16.46 ( (fun complex real), im ) 16.35/16.46 ( (fun complex real), arg ) 16.35/16.46 ( (fun bool bool), fNot ) 16.35/16.46 ( (fun nat (fun real real)), root ) 16.35/16.46 ( (fun real (fun real real)), log ) 16.35/16.46 ( (fun real (fun real real)), powr ) 16.35/16.46 ( (fun bool (fun bool bool)), fimplies ) 16.35/16.46 ( (fun bool (fun bool bool)), fconj ) 16.35/16.46 ( (fun bool (fun bool bool)), fdisj ) 16.35/16.46 ( (fun int (fun int (product_prod int int))), negDivAlg ) 16.35/16.46 ( (fun int (fun int (product_prod int int))), posDivAlg ) 16.35/16.46 ( (fun int (fun int (product_prod int int))), divmod_int ) 16.35/16.46 ( (fun int (fun int (product_prod int int))), pdivmod ) 16.35/16.46 ( (fun int (fun int (product_prod int int))), norm_frac ) 16.35/16.46 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 16.35/16.46 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 16.35/16.46 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 16.35/16.46 ( (fun int (fun int (fun int bool))), zcong ) 16.35/16.46 ( (fun int (fun int (fun int bool))), zcongm ) 16.35/16.46 ( (fun int (fun int (fun int bool))), noXRRset ) 16.35/16.46 ( (fun int (fun int (fun int bool))), bnorRset ) 16.35/16.46 ( (fun int (fun int (fun int bool))), wset ) 16.35/16.46 ( (fun (product_prod int int) bool), frac_1 ) 16.35/16.46 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 16.35/16.46 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 16.35/16.46 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 16.35/16.46 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 16.35/16.46 ( (fun (fun nat rat) bool), vanishes ) 16.35/16.46 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 16.35/16.46 ( (fun code_code_numeral nat), code_c271388182l_size ) 16.35/16.46 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 16.35/16.46 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 16.35/16.46 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 16.35/16.46 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 16.35/16.46 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 16.35/16.46 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 16.35/16.46 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 16.35/16.46 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 16.35/16.46 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 16.35/16.46 ( (fun complex nat), complex_size ) 16.35/16.46 ( (fun complex nat), (size_size complex) ) 16.35/16.46 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 16.35/16.46 ( (fun nat (fun nat (product_prod int int))), bezw ) 16.35/16.46 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 16.35/16.46 ( (fun int (fun nat nat)), nat_aux ) 16.35/16.46 ( (fun int (fun (fun int bool) bool)), rsetR ) 16.35/16.46 ( (fun int (fun (fun int bool) bool)), resSet ) 16.35/16.46 ( (fun int (list int)), quickc666637781d_zero ) 16.35/16.46 ( (fun (product_prod int int) rat), frct ) 16.35/16.46 ( (fun int (fun int rat)), fract ) 16.35/16.46 ( (fun real (fun real complex)), complex_1 ) 16.35/16.46 ( (fun real (fun real complex)), rcis ) 16.35/16.46 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 16.35/16.46 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 16.35/16.46 ( (fun int real), (real_1 int) ) 16.35/16.46 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 16.35/16.46 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 16.35/16.46 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 16.35/16.46 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 16.35/16.46 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 16.35/16.46 ( (fun real nat), natfloor ) 16.35/16.46 ( (fun real nat), natceiling ) 16.35/16.46 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 16.35/16.46 ( (fun quickcheck_code_int int), quickcheck_int_of ) 16.35/16.46 ( (fun rat (product_prod int int)), quotient_of ) 16.35/16.46 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 16.35/16.46 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 16.35/16.46 ( (fun rat real), ratreal ) 16.35/16.46 ( (fun code_code_numeral int), code_int_of ) 16.35/16.46 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 16.35/16.46 ( (fun int quickcheck_code_int), quickcheck_of_int ) 16.35/16.46 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 16.35/16.46 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 16.35/16.46 ) 16.35/16.46 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (hAPP real _let_0 _let_1 (zero_zero real)))) (or (not (hBOOL (hAPP real bool _let_2 X_2))) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (one_one real)) X_2)) (hBOOL (hAPP real bool _let_2 (hAPP real real ln X_2)))))))) ) 16.35/16.46 ( (one_one real) ) 16.35/16.46 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.46 ) 16.35/16.46 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_158149 $$unsorted) (BOUND_VARIABLE_158150 $$unsorted)) (let ((_let_0 (of_real X_a))) (or (not (real_algebra_1 X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) (hAPP real X_a _let_0 BOUND_VARIABLE_158149)) (hAPP real X_a _let_0 BOUND_VARIABLE_158150)) (hAPP real X_a _let_0 (hAPP real real (hAPP real (fun real real) (times_times real) BOUND_VARIABLE_158149) BOUND_VARIABLE_158150))))) ) 16.35/16.46 ( complex, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 16.35/16.46 ) 16.35/16.46 (instantiation (forall ((P_4 $$unsorted)) (= (and (forall ((M_2 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ti int M_2))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (zero_zero int)) M_2))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (dvd_dvd int) M_2) P_4))) (= (one_one int) _let_1) (= _let_1 (ti int P_4))))) ) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (one_one int)) P_4))) (hBOOL (hAPP int bool zprime P_4))) ) 16.35/16.46 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.46 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.46 ( t ) 16.35/16.46 ) 16.35/16.46 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_158218 $$unsorted) (BOUND_VARIABLE_158219 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (zero_zero X_a))) (let ((_let_3 (hAPP X_a _let_0 _let_1 _let_2))) (or (not (ordered_ring X_a)) (and (or (not (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_158218))) (not (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_158219)))) (or (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_158219) _let_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_158218) _let_2))))) (hBOOL (hAPP X_a bool _let_3 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_158219) BOUND_VARIABLE_158218)))))))) ) 16.35/16.46 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.46 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.46 ( int, skv_13, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.46 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.46 ( real, pi, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 16.35/16.46 ( real, (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.46 ( real, (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.46 ( complex, ii, ii ) 16.35/16.46 ( complex, ii, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 16.35/16.46 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.46 ) 16.35/16.46 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_158279 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member X_a))) (let ((_let_3 (field_char_0_Rats X_a))) (or (not (field_inverse_zero X_a)) (not (field_char_0 X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_158279) _let_3))) (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_158279)) _let_3))))))) ) 16.35/16.46 ( real, (zero_zero real) ) 16.35/16.46 ( complex, ii ) 16.35/16.46 ) 16.35/16.46 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_158297 $$unsorted)) (or (not (linordered_idom X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_158297) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (zero_zero X_a))))) ) 16.35/16.46 ( int, s ) 16.35/16.46 ( int, s1 ) 16.35/16.46 ( int, skv_14 ) 16.35/16.46 ( real, (hAPP int real (number_number_of real) min_1) ) 16.35/16.46 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.46 ( complex, ii ) 16.35/16.46 ) 16.35/16.46 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (one_one real)) X_1))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) (hAPP real real ln X_1)))))) ) 16.35/16.46 ( (one_one real) ) 16.35/16.46 ) 16.35/16.46 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_158335 $$unsorted)) (or (not (number_ring X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_158335) (hAPP int X_a (number_number_of X_a) min_1)) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_158335))) ) 16.35/16.46 ( int, (one_one int) ) 16.35/16.46 ( int, pls ) 16.35/16.46 ( int, min_1 ) 16.35/16.46 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.46 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.46 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.46 ( real, (one_one real) ) 16.35/16.46 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.46 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.46 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.46 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.35/16.46 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 16.35/16.46 ( complex, (one_one complex) ) 16.35/16.46 ( complex, ii ) 16.35/16.46 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.46 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 16.35/16.46 ) 16.35/16.46 (instantiation (forall ((L $$unsorted) (F $$unsorted)) (let ((_let_0 (fun (filter nat) bool))) (or (not (forall ((N_2 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP nat real F N_2)) (hAPP nat real F (hAPP nat nat suc N_2)))) )) (not (forall ((N_2 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP nat real F N_2)) L)) )) (not (forall ((E $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) E))) (not (forall ((N_2 $$unsorted)) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) L) (hAPP real real (hAPP real (fun real real) (plus_plus real) (hAPP nat real F N_2)) E)))) ))) )) (hBOOL (hAPP (filter nat) bool (hAPP real _let_0 (hAPP (fun nat real) (fun real _let_0) (tendsto nat real) F) L) sequentially)))) ) 16.35/16.46 ( (zero_zero real), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))) ) 16.35/16.46 ) 16.35/16.46 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (one_one X_a))) (or (not (division_ring X_a)) (= _let_0 (hAPP X_a X_a (inverse_inverse X_a) _let_0)))) ) 16.35/16.46 ( nat ) 16.35/16.46 ( int ) 16.35/16.46 ( real ) 16.35/16.46 ( rat ) 16.35/16.46 ( complex ) 16.35/16.46 ( quickcheck_code_int ) 16.35/16.46 ( code_code_numeral ) 16.35/16.46 ) 16.35/16.46 (instantiation (forall ((Z_1 $$unsorted)) (= (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP complex real im Z_1)) (hAPP complex real (norm_norm complex) Z_1)) (hAPP complex real im (hAPP complex complex (sgn_sgn complex) Z_1))) ) 16.35/16.46 ( ii ) 16.35/16.46 ) 16.35/16.46 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_158471 $$unsorted) (BOUND_VARIABLE_158472 $$unsorted) (BOUND_VARIABLE_158473 $$unsorted) (BOUND_VARIABLE_158474 $$unsorted)) (let ((_let_0 (filter X_a))) (let ((_let_1 (fun _let_0 bool))) (or (not (real_normed_vector X_a)) (not (real_normed_vector X_b)) (not (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (hAPP (fun X_a X_b) (fun X_b _let_1) (tendsto X_a X_b) BOUND_VARIABLE_158472) BOUND_VARIABLE_158473) (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_158474)))) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) BOUND_VARIABLE_158471))) (not (forall ((S_1 $$unsorted)) (or (not (forall ((X $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP X_a real (norm_norm X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) X) BOUND_VARIABLE_158474))) S_1))) (= (ti X_a X) (ti X_a BOUND_VARIABLE_158474)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP X_b real (norm_norm X_b) (hAPP X_b X_b (hAPP X_b (fun X_b X_b) (minus_minus X_b) (hAPP X_a X_b BOUND_VARIABLE_158472 X)) BOUND_VARIABLE_158473))) BOUND_VARIABLE_158471))))) )) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) S_1)))) ))))) ) 16.35/16.46 ( real, real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.46 ) 16.35/16.46 (instantiation (forall ((X_a $$unsorted)) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (one_one X_a)) (zero_zero X_a))))) ) 16.35/16.46 ( bool ) 16.35/16.46 ( nat ) 16.35/16.46 ( int ) 16.35/16.46 ( (fun int bool) ) 16.35/16.46 ( (fun nat bool) ) 16.35/16.46 ( (product_prod nat nat) ) 16.35/16.46 ( real ) 16.35/16.46 ( rat ) 16.35/16.46 ( complex ) 16.35/16.46 ( (filter nat) ) 16.35/16.46 ( (product_prod int int) ) 16.35/16.46 ( quickcheck_code_int ) 16.35/16.46 ( code_code_numeral ) 16.35/16.46 ( (product_prod real real) ) 16.35/16.46 ( (fun nat rat) ) 16.35/16.46 ( (filter real) ) 16.35/16.46 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 16.35/16.46 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 16.35/16.46 ) 16.35/16.46 (instantiation (forall ((A_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (let ((_let_2 (hAPP int (fun int int) inv P_5))) (or (not (hBOOL (hAPP int bool zprime P_5))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))))) P_5))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (zero_zero int)) A_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 A_1) P_5))) (= (ti int A_1) (hAPP int int _let_2 (hAPP int int _let_2 A_1))))))) ) 16.35/16.46 ( (one_one int), t ) 16.35/16.46 ( pls, (one_one int) ) 16.35/16.46 ( pls, pls ) 16.35/16.46 ( pls, min_1 ) 16.35/16.46 ( pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.46 ( min_1, pls ) 16.35/16.46 ( min_1, min_1 ) 16.35/16.46 ( s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.46 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.46 ( skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.46 ( skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.46 ) 16.35/16.46 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (semiring_1 X_a)) (= _let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) _let_0) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 16.35/16.46 ( bool ) 16.35/16.46 ( nat ) 16.35/16.46 ( int ) 16.35/16.46 ( (fun int int) ) 16.35/16.46 ( (fun nat bool) ) 16.35/16.46 ( (fun nat nat) ) 16.35/16.46 ( (product_prod nat nat) ) 16.35/16.46 ( (fun (product_prod nat nat) bool) ) 16.35/16.46 ( (fun nat (fun (product_prod nat nat) bool)) ) 16.35/16.46 ( real ) 16.35/16.46 ( (fun real real) ) 16.35/16.46 ( rat ) 16.35/16.46 ( (fun nat (fun nat bool)) ) 16.35/16.46 ( complex ) 16.35/16.46 ( (product_prod int int) ) 16.35/16.46 ( quickcheck_code_int ) 16.35/16.46 ( (fun bool bool) ) 16.35/16.46 ( code_code_numeral ) 16.35/16.46 ( (product_prod real real) ) 16.35/16.46 ( (fun nat (product_prod nat nat)) ) 16.35/16.46 ( (fun nat (product_prod int int)) ) 16.35/16.46 ) 16.35/16.46 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_158585 $$unsorted) (BOUND_VARIABLE_158586 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (uminus_uminus X_a))) (or (not (boolean_algebra X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_158585) (hAPP X_a X_a _let_2 BOUND_VARIABLE_158586)))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_158586) (hAPP X_a X_a _let_2 BOUND_VARIABLE_158585))))))) ) 16.35/16.46 ( int, (one_one int), (zero_zero int) ) 16.35/16.46 ( int, (one_one int), min_1 ) 16.35/16.46 ( int, (zero_zero int), (one_one int) ) 16.35/16.46 ( int, (zero_zero int), pls ) 16.35/16.46 ( int, pls, (zero_zero int) ) 16.35/16.46 ( int, pls, min_1 ) 16.35/16.46 ( int, min_1, (one_one int) ) 16.35/16.46 ( int, min_1, pls ) 16.35/16.46 ) 16.35/16.46 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_158629 $$unsorted) (BOUND_VARIABLE_158630 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP int int (number_number_of int) BOUND_VARIABLE_158629)) (hAPP X_a int (archim2085082626_floor X_a) BOUND_VARIABLE_158630))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_158629)) BOUND_VARIABLE_158630)))) ) 16.35/16.46 ( int, pls, (one_one int) ) 16.35/16.46 ( int, pls, min_1 ) 16.35/16.46 ( int, pls, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.46 ( int, pls, s ) 16.35/16.46 ( int, pls, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.35/16.46 ( int, pls, (hAPP int int (number_number_of int) pls) ) 16.35/16.46 ( int, pls, skv_4 ) 16.35/16.46 ( int, pls, skv_10 ) 16.35/16.46 ( int, (hAPP int int bit1 pls), t ) 16.35/16.46 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)), pi ) 16.35/16.46 ) 16.35/16.46 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (ord_lessThan X_a))) (or (not (ord X_a)) (= _let_0 (ti (fun X_a (fun X_a bool)) _let_0)))) ) 16.35/16.46 ( bool ) 16.35/16.46 ( nat ) 16.35/16.46 ( int ) 16.35/16.46 ( (fun int bool) ) 16.35/16.46 ( (fun nat bool) ) 16.35/16.46 ( (product_prod nat nat) ) 16.35/16.46 ( real ) 16.35/16.46 ( rat ) 16.35/16.46 ( (filter nat) ) 16.35/16.46 ( (product_prod int int) ) 16.35/16.46 ( quickcheck_code_int ) 16.35/16.46 ( code_code_numeral ) 16.35/16.46 ( (product_prod real real) ) 16.35/16.46 ( (fun nat rat) ) 16.35/16.46 ( (filter real) ) 16.35/16.46 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 16.35/16.46 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 16.35/16.46 ) 16.35/16.46 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) X_2) Y_2))) (not (forall ((X $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (or (not (hBOOL (hAPP _let_0 bool (hAPP real (fun _let_0 bool) (member real) X) (field_char_0_Rats real)))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_2) X))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X) Y_2)))))) ))) ) 16.35/16.46 ( (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.46 ( (zero_zero real), pi ) 16.35/16.46 ( (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.46 ( (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.46 ( (zero_zero real), skv_2 ) 16.35/16.46 ( (zero_zero real), skv_8 ) 16.35/16.46 ( (zero_zero real), skv_9 ) 16.35/16.46 ( pi, (zero_zero real) ) 16.35/16.46 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.46 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.46 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 16.35/16.46 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.35/16.46 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 16.35/16.46 ) 16.35/16.46 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_158671 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (ti int BOUND_VARIABLE_158671) (hAPP X_a int (archimedean_ceiling X_a) (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_158671)))) ) 16.35/16.46 ( real, (one_one int) ) 16.35/16.46 ( real, (zero_zero int) ) 16.35/16.46 ) 16.35/16.46 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_158707 $$unsorted)) (let ((_let_0 (fun (filter nat) bool))) (let ((_let_1 (fun nat X_a))) (or (not (topological_space X_a)) (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_0 (hAPP _let_1 (fun X_a _let_0) (tendsto nat X_a) (hAPP X_a _let_1 (combk X_a nat) BOUND_VARIABLE_158707)) BOUND_VARIABLE_158707) sequentially))))) ) 16.35/16.46 ( bool, fTrue ) 16.35/16.46 ) 16.35/16.46 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_158754 $$unsorted) (BOUND_VARIABLE_158755 $$unsorted) (BOUND_VARIABLE_158756 $$unsorted)) (let ((_let_0 (filter X_a))) (let ((_let_1 (fun _let_0 bool))) (or (not (metric_space X_a)) (not (metric_space X_b)) (not (forall ((R_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) R_2))) (not (forall ((S_1 $$unsorted)) (or (not (forall ((X $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP X_a real (hAPP X_a (fun X_a real) (dist_dist X_a) X) BOUND_VARIABLE_158756)) S_1))) (= (ti X_a X) (ti X_a BOUND_VARIABLE_158756)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP X_b real (hAPP X_b (fun X_b real) (dist_dist X_b) (hAPP X_a X_b BOUND_VARIABLE_158754 X)) BOUND_VARIABLE_158755)) R_2))))) )) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) S_1)))) ))) )) (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (hAPP (fun X_a X_b) (fun X_b _let_1) (tendsto X_a X_b) BOUND_VARIABLE_158754) BOUND_VARIABLE_158755) (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_158756)))))) ) 16.35/16.46 ( real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.46 ) 16.35/16.46 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_158808 $$unsorted) (BOUND_VARIABLE_158809 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)))) (or (not (linordered_idom X_a)) (hBOOL (hAPP nat bool (even_odd_even nat) BOUND_VARIABLE_158809)) (= (hBOOL (hAPP X_a bool _let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_158808) BOUND_VARIABLE_158809))) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_158808))))) ) 16.35/16.46 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.46 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.46 ( int, skv_14, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.46 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.46 ) 16.35/16.46 (instantiation (forall ((B $$unsorted)) (let ((_let_0 (fun int int))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) B))) (= (hAPP int int (hAPP int _let_0 (div_mod int) (hAPP int int (number_number_of int) min_1)) B) (hAPP int int (hAPP int _let_0 (minus_minus int) B) (one_one int))))) ) 16.35/16.46 ( (one_one int) ) 16.35/16.46 ( pls ) 16.35/16.46 ( min_1 ) 16.35/16.46 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.46 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.46 ) 16.35/16.46 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_158915 $$unsorted)) (or (not (linordered_semidom X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_158915) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_158915) (one_one X_a))))) ) 16.35/16.46 ( nat, (zero_zero nat) ) 16.35/16.46 ( nat, (one_one nat) ) 16.35/16.46 ( int, (one_one int) ) 16.35/16.46 ( int, pls ) 16.35/16.46 ( int, min_1 ) 16.35/16.46 ( int, s ) 16.35/16.46 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 16.35/16.46 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.46 ( int, t ) 16.35/16.46 ( int, skv_4 ) 16.35/16.46 ( int, skv_10 ) 16.35/16.46 ( real, (one_one real) ) 16.35/16.46 ( real, (zero_zero real) ) 16.35/16.46 ( real, pi ) 16.35/16.46 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.46 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.35/16.46 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.46 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 16.35/16.46 ) 16.35/16.46 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_158931 $$unsorted)) (or (not (monoid_mult X_a)) (= (ti X_a BOUND_VARIABLE_158931) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_158931) (one_one X_a)))) ) 16.35/16.46 ( bool, fFalse ) 16.35/16.46 ( bool, fTrue ) 16.35/16.46 ( int, pls ) 16.35/16.46 ( int, min_1 ) 16.35/16.46 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.46 ( int, s ) 16.35/16.46 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.46 ( int, m ) 16.35/16.46 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.46 ( int, s1 ) 16.35/16.46 ( int, t ) 16.35/16.46 ( (fun int bool), nat_neg ) 16.35/16.46 ( (fun int bool), zprime ) 16.35/16.46 ( (fun int bool), zEven ) 16.35/16.46 ( (fun int bool), zOdd ) 16.35/16.46 ( (fun int bool), (even_odd_even int) ) 16.35/16.46 ( (fun int bool), twoSqu1091635170sum2sq ) 16.35/16.46 ( (fun int bool), nat_is_nat ) 16.35/16.46 ( (fun int (fun int bool)), norRRset ) 16.35/16.46 ( (fun int (fun int bool)), quadRes ) 16.35/16.46 ( (fun int (fun int bool)), sRStar ) 16.35/16.46 ( (fun int (fun int bool)), d22set ) 16.35/16.46 ( (fun int (fun int bool)), sr ) 16.35/16.46 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 16.35/16.46 ( (fun int int), zfact ) 16.35/16.46 ( (fun int int), bit0 ) 16.35/16.46 ( (fun int int), bit1 ) 16.35/16.46 ( (fun int int), (fact_fact int) ) 16.35/16.46 ( (fun int int), pred ) 16.35/16.46 ( (fun int int), succ ) 16.35/16.46 ( (fun nat bool), (even_odd_even nat) ) 16.35/16.46 ( (fun nat bool), prime ) 16.35/16.46 ( (fun nat nat), suc ) 16.35/16.46 ( (fun nat nat), (fact_fact nat) ) 16.35/16.46 ( (fun nat nat), fact ) 16.35/16.46 ( (fun nat nat), nat_size ) 16.35/16.46 ( (fun nat nat), (size_size nat) ) 16.35/16.46 ( (fun (product_prod nat nat) bool), pred_nat ) 16.35/16.46 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 16.35/16.46 ( real, pi ) 16.35/16.46 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.46 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.46 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 16.35/16.46 ( (fun real real), ln ) 16.35/16.46 ( (fun real real), cos ) 16.35/16.46 ( (fun real real), sqrt ) 16.35/16.46 ( (fun real real), sin ) 16.35/16.46 ( (fun real real), arccos ) 16.35/16.46 ( (fun real real), arcsin ) 16.35/16.46 ( (fun real real), tan ) 16.35/16.46 ( (fun real real), arctan ) 16.35/16.46 ( (fun nat (fun nat bool)), coprime ) 16.35/16.46 ( complex, ii ) 16.35/16.46 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.46 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 16.35/16.46 ( (fun nat real), (real_1 nat) ) 16.35/16.46 ( (fun nat real), sin_coeff ) 16.35/16.46 ( (fun nat real), cos_coeff ) 16.35/16.46 ( (filter nat), sequentially ) 16.35/16.46 ( (fun int (fun int int)), (gcd_gcd int) ) 16.35/16.46 ( (fun int (fun int int)), legendre ) 16.35/16.46 ( (fun int (fun int int)), legacy_zgcd ) 16.35/16.46 ( (fun int (fun int int)), standardRes ) 16.35/16.46 ( (fun int (fun int int)), nat_tsub ) 16.35/16.46 ( (fun int (fun int int)), multInv ) 16.35/16.46 ( (fun int (fun int int)), z3mod ) 16.35/16.46 ( (fun int (fun int int)), z3div ) 16.35/16.46 ( (fun int (fun int int)), int_gcd ) 16.35/16.46 ( (fun int (fun int int)), int_lcm ) 16.35/16.46 ( (fun int (fun int int)), inv ) 16.35/16.46 ( (fun complex complex), expi ) 16.35/16.46 ( (fun complex complex), cnj ) 16.35/16.46 ( (fun real complex), cis ) 16.35/16.46 ( (fun int nat), nat_1 ) 16.35/16.46 ( (fun int nat), phi ) 16.35/16.46 ( (fun (fun int bool) bool), nat_nat_set ) 16.35/16.46 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 16.35/16.46 ( (fun nat (fun nat nat)), nat_gcd ) 16.35/16.46 ( (fun nat (fun nat nat)), nat_lcm ) 16.35/16.46 ( (fun (fun int bool) int), (the int) ) 16.35/16.46 ( (fun complex real), re ) 16.35/16.46 ( (fun complex real), im ) 16.35/16.46 ( (fun complex real), arg ) 16.35/16.46 ( (fun bool bool), fNot ) 16.35/16.46 ( (fun nat (fun real real)), root ) 16.35/16.46 ( (fun real (fun real real)), log ) 16.35/16.46 ( (fun real (fun real real)), powr ) 16.35/16.46 ( (fun bool (fun bool bool)), fimplies ) 16.35/16.46 ( (fun bool (fun bool bool)), fconj ) 16.35/16.46 ( (fun bool (fun bool bool)), fdisj ) 16.35/16.46 ( (fun int (fun int (product_prod int int))), negDivAlg ) 16.35/16.46 ( (fun int (fun int (product_prod int int))), posDivAlg ) 16.35/16.46 ( (fun int (fun int (product_prod int int))), divmod_int ) 16.35/16.46 ( (fun int (fun int (product_prod int int))), pdivmod ) 16.35/16.46 ( (fun int (fun int (product_prod int int))), norm_frac ) 16.35/16.46 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 16.35/16.46 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 16.35/16.46 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 16.35/16.46 ( (fun int (fun int (fun int bool))), zcong ) 16.35/16.46 ( (fun int (fun int (fun int bool))), zcongm ) 16.35/16.46 ( (fun int (fun int (fun int bool))), noXRRset ) 16.35/16.46 ( (fun int (fun int (fun int bool))), bnorRset ) 16.35/16.46 ( (fun int (fun int (fun int bool))), wset ) 16.35/16.46 ( (fun (product_prod int int) bool), frac_1 ) 16.35/16.46 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 16.35/16.46 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 16.35/16.46 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 16.35/16.46 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 16.35/16.46 ( (fun (fun nat rat) bool), vanishes ) 16.35/16.46 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 16.35/16.46 ( (fun code_code_numeral nat), code_c271388182l_size ) 16.35/16.46 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 16.35/16.46 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 16.35/16.46 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 16.35/16.46 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 16.35/16.46 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 16.35/16.46 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 16.35/16.46 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 16.35/16.46 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 16.35/16.46 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 16.35/16.46 ( (fun complex nat), complex_size ) 16.35/16.46 ( (fun complex nat), (size_size complex) ) 16.35/16.46 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 16.35/16.46 ( (fun nat (fun nat (product_prod int int))), bezw ) 16.35/16.46 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 16.35/16.46 ( (fun int (fun nat nat)), nat_aux ) 16.35/16.46 ( (fun int (fun (fun int bool) bool)), rsetR ) 16.35/16.46 ( (fun int (fun (fun int bool) bool)), resSet ) 16.35/16.46 ( (fun int (list int)), quickc666637781d_zero ) 16.35/16.46 ( (fun (product_prod int int) rat), frct ) 16.35/16.46 ( (fun int (fun int rat)), fract ) 16.35/16.46 ( (fun real (fun real complex)), complex_1 ) 16.35/16.46 ( (fun real (fun real complex)), rcis ) 16.35/16.46 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 16.35/16.46 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 16.35/16.46 ( (fun int real), (real_1 int) ) 16.35/16.46 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 16.35/16.46 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 16.35/16.46 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 16.35/16.46 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 16.35/16.46 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 16.35/16.46 ( (fun real nat), natfloor ) 16.35/16.46 ( (fun real nat), natceiling ) 16.35/16.46 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 16.35/16.46 ( (fun quickcheck_code_int int), quickcheck_int_of ) 16.35/16.46 ( (fun rat (product_prod int int)), quotient_of ) 16.35/16.46 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 16.35/16.46 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 16.35/16.46 ( (fun rat real), ratreal ) 16.35/16.46 ( (fun code_code_numeral int), code_int_of ) 16.35/16.46 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 16.35/16.46 ( (fun int quickcheck_code_int), quickcheck_of_int ) 16.35/16.46 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 16.35/16.46 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 16.35/16.46 ) 16.35/16.46 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (uminus_uminus real))) (= (hAPP real real tan (hAPP real real _let_0 X_1)) (hAPP real real _let_0 (hAPP real real tan X_1)))) ) 16.35/16.46 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.35/16.46 ) 16.35/16.46 (instantiation (forall ((Z_1 $$unsorted)) (or (hBOOL (hAPP int bool nat_neg Z_1)) (= (ti int Z_1) (hAPP nat int (semiring_1_of_nat int) (hAPP int nat nat_1 Z_1)))) ) 16.35/16.46 ( (one_one int) ) 16.35/16.46 ( (zero_zero int) ) 16.35/16.46 ( pls ) 16.35/16.46 ( min_1 ) 16.35/16.46 ( (hAPP int int (number_number_of int) min_1) ) 16.35/16.46 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.46 ( s ) 16.35/16.46 ( m ) 16.35/16.46 ( s1 ) 16.35/16.46 ( t ) 16.35/16.46 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.35/16.46 ( (hAPP int int (number_number_of int) pls) ) 16.35/16.46 ) 16.35/16.46 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (one_one X_a))) (or (not (linordered_semidom X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) _let_0) _let_0))))) ) 16.35/16.46 ( bool ) 16.35/16.46 ( nat ) 16.35/16.46 ( int ) 16.35/16.46 ( (fun int bool) ) 16.35/16.46 ( (fun int (fun int bool)) ) 16.35/16.46 ( (fun int int) ) 16.35/16.46 ( (fun nat bool) ) 16.35/16.46 ( (product_prod nat nat) ) 16.35/16.46 ( real ) 16.35/16.46 ( (fun real bool) ) 16.35/16.46 ( (fun real real) ) 16.35/16.46 ( rat ) 16.35/16.46 ( complex ) 16.35/16.46 ( (fun nat real) ) 16.35/16.46 ( (filter nat) ) 16.35/16.46 ( (product_prod int int) ) 16.35/16.46 ( quickcheck_code_int ) 16.35/16.46 ( code_code_numeral ) 16.35/16.46 ( (fun int (fun int (fun int bool))) ) 16.35/16.46 ( (product_prod real real) ) 16.35/16.46 ( (fun (product_prod int int) bool) ) 16.35/16.46 ( (fun nat rat) ) 16.35/16.46 ( (filter real) ) 16.35/16.47 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 16.35/16.47 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 16.35/16.47 ( (fun (product_prod int int) int) ) 16.35/16.47 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 16.35/16.47 ( (fun int real) ) 16.35/16.47 ) 16.35/16.47 (instantiation (forall ((X_a $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (zero_zero nat))) (let ((_let_1 (fun X_a bool))) (or (not (hBOOL (hAPP _let_1 bool (finite_finite_1 X_a) A_3))) (and (not (forall ((X $$unsorted)) (not (hBOOL (hAPP _let_1 bool (hAPP X_a (fun _let_1 bool) (member X_a) X) A_3))) )) (not (= _let_0 (one_one nat)))) (= _let_0 (hAPP _let_1 nat (finite_card X_a) A_3))))) ) 16.35/16.47 ( nat, (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 16.35/16.47 ) 16.35/16.47 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_159208 $$unsorted) (BOUND_VARIABLE_159209 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (zero_zero X_a))) (let ((_let_3 (hAPP X_a _let_0 _let_1 _let_2))) (or (not (linord581940658strict X_a)) (= (or (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_159208) _let_2)) (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_159209))) (and (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_159208)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_159209) _let_2)))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_159208) BOUND_VARIABLE_159209)) _let_2)))))))) ) 16.35/16.47 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 16.35/16.47 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 16.35/16.47 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13 ) 16.35/16.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.35/16.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 16.35/16.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 16.35/16.47 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 16.35/16.47 ( complex, ii, ii ) 16.35/16.47 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 16.35/16.47 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 16.35/16.47 ) 16.35/16.47 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) M) N_1))) (= (zero_zero nat) (hAPP nat nat (hAPP nat (fun nat nat) (div_div nat) M) N_1))) ) 16.35/16.47 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.47 ) 16.35/16.47 (instantiation (forall ((N $$unsorted)) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N)) (not (forall ((M_2 $$unsorted)) (not (= N (hAPP nat nat suc M_2))) ))) ) 16.35/16.47 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.47 ) 16.35/16.47 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_159277 $$unsorted)) (or (not (linordered_field X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) (hAPP X_a X_a (inverse_inverse X_a) (hAPP nat X_a (semiring_1_of_nat X_a) (hAPP nat nat (fact_fact nat) BOUND_VARIABLE_159277)))))) ) 16.35/16.47 ( int, (hAPP nat nat suc (zero_zero nat)) ) 16.35/16.47 ( real, (hAPP nat nat suc (zero_zero nat)) ) 16.35/16.47 ) 16.35/16.47 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_159331 $$unsorted) (BOUND_VARIABLE_159332 $$unsorted)) (let ((_let_0 (fun nat X_a))) (let ((_let_1 (power_power X_a))) (let ((_let_2 (hAPP int nat (number_number_of nat) BOUND_VARIABLE_159332))) (or (not (linordered_idom X_a)) (not (hBOOL (hAPP nat bool (even_odd_even nat) _let_2))) (= (hAPP nat X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_159331) _let_2) (hAPP nat X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_159331)) _let_2)))))) ) 16.35/16.47 ( int, s, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.35/16.47 ( int, s1, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.35/16.47 ( int, skv_14, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.35/16.47 ( complex, ii, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.35/16.47 ) 16.35/16.47 (instantiation (forall ((W $$unsorted)) (let ((_let_0 (number_number_of nat))) (let ((_let_1 (hAPP int nat _let_0 W))) (= (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) _let_1) _let_1) (hAPP int nat _let_0 (hAPP int int bit0 W))))) ) 16.35/16.47 ( pls ) 16.35/16.47 ( (hAPP int int bit1 pls) ) 16.35/16.47 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.35/16.47 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.35/16.47 ( min_1 ) 16.35/16.47 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.35/16.47 ) 16.35/16.47 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_159451 $$unsorted)) (or (not (linordered_idom X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_159451))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) BOUND_VARIABLE_159451)))) ) 16.35/16.47 ( real, (one_one int) ) 16.35/16.47 ( real, (zero_zero int) ) 16.35/16.47 ) 16.35/16.47 (instantiation (forall ((A_1 $$unsorted)) (= (hAPP real complex cis A_1) (hAPP real complex (hAPP real (fun real complex) complex_1 (hAPP real real cos A_1)) (hAPP real real sin A_1))) ) 16.35/16.47 ( (zero_zero real) ) 16.35/16.47 ( pi ) 16.35/16.47 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.47 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.47 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.35/16.47 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.35/16.47 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.35/16.47 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 16.35/16.47 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 16.35/16.47 ( skv_5 ) 16.35/16.47 ) 16.35/16.47 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_159486 $$unsorted) (BOUND_VARIABLE_159487 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (hAPP X_a _let_0 _let_1 (zero_zero X_a)))) (or (not (linordered_idom X_a)) (not (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_159487))) (not (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_159486))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_159486) (one_one X_a)))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_159487) BOUND_VARIABLE_159486)) BOUND_VARIABLE_159487)))))) ) 16.35/16.47 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.47 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.47 ( int, skv_13, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.47 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.47 ( real, pi, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 16.35/16.47 ( real, (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.47 ( real, (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.47 ( complex, ii, ii ) 16.35/16.47 ( complex, ii, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 16.35/16.47 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.47 ) 16.35/16.47 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (one_one real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP real real (hAPP real _let_1 (minus_minus real) _let_0) X_1))) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) X_1) _let_0))) (= (hAPP real real ln _let_2) (hAPP real real (uminus_uminus real) (hAPP real real ln (hAPP real real (hAPP real _let_1 (plus_plus real) _let_0) (hAPP real real (hAPP real _let_1 (inverse_divide real) X_1) _let_2))))))))) ) 16.35/16.47 ( (one_one real) ) 16.35/16.47 ( (zero_zero real) ) 16.35/16.47 ( pi ) 16.35/16.47 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.47 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.35/16.47 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.35/16.47 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.35/16.47 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.47 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.47 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 16.35/16.47 ) 16.35/16.47 (instantiation (forall ((X_a $$unsorted) (F1 $$unsorted) (Real1 $$unsorted) (Real2 $$unsorted)) (let ((_let_0 (fun real X_a))) (= (hAPP real X_a (hAPP real _let_0 F1 Real1) Real2) (hAPP complex X_a (hAPP (fun real _let_0) (fun complex X_a) (complex_case X_a) F1) (hAPP real complex (hAPP real (fun real complex) complex_1 Real1) Real2)))) ) 16.35/16.47 ( bool, (ord_less real), (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.47 ( bool, (ord_less real), (zero_zero real), pi ) 16.35/16.47 ( bool, (ord_less real), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.47 ( bool, (ord_less real), (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.47 ( bool, (ord_less real), (zero_zero real), skv_2 ) 16.35/16.47 ( bool, (ord_less real), (zero_zero real), skv_8 ) 16.35/16.47 ( bool, (ord_less real), (zero_zero real), skv_9 ) 16.35/16.47 ( bool, (ord_less real), pi, (zero_zero real) ) 16.35/16.47 ( bool, (ord_less real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.47 ( bool, (ord_less real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.47 ( bool, (ord_less real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 16.35/16.47 ( bool, (ord_less real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.35/16.47 ( bool, (ord_less real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 16.35/16.47 ( bool, (ord_less_eq real), (zero_zero real), pi ) 16.35/16.47 ( bool, (ord_less_eq real), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.47 ( bool, (ord_less_eq real), (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.47 ( bool, (ord_less_eq real), (zero_zero real), skv_3 ) 16.35/16.47 ( bool, (ord_less_eq real), (zero_zero real), skv_5 ) 16.35/16.47 ( bool, (ord_less_eq real), (zero_zero real), skv_7 ) 16.35/16.47 ( bool, (ord_less_eq real), (zero_zero real), skv_12 ) 16.35/16.47 ( bool, (ord_less_eq real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.35/16.47 ( bool, (ord_less_eq real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.47 ( bool, (ord_less_eq real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.35/16.47 ( bool, (ord_less_eq real), skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.47 ( real, (minus_minus real), (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 16.35/16.47 ( real, (inverse_divide real), (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.47 ( real, (inverse_divide real), (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.35/16.47 ( real, (inverse_divide real), (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.47 ( real, (inverse_divide real), (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 16.35/16.47 ( real, (inverse_divide real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.47 ( real, (inverse_divide real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.47 ( real, (inverse_divide real), pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.35/16.47 ( real, (inverse_divide real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.35/16.47 ( real, (inverse_divide real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.47 ( real, (inverse_divide real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.47 ( real, (inverse_divide real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.47 ( real, (times_times real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.35/16.47 ( real, (times_times real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 16.35/16.47 ( real, (times_times real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 16.35/16.47 ( real, (times_times real), (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 16.35/16.47 ( complex, complex_1, (one_one real), (zero_zero real) ) 16.35/16.47 ( complex, complex_1, (zero_zero real), (one_one real) ) 16.35/16.47 ( complex, complex_1, (zero_zero real), (zero_zero real) ) 16.35/16.47 ) 16.35/16.47 (instantiation (forall ((N_1 $$unsorted)) (let ((_let_0 (zero_zero nat))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) _let_0) N_1))) (= N_1 (hAPP nat nat suc (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) N_1) (hAPP nat nat suc _let_0)))))) ) 16.35/16.47 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.47 ) 16.35/16.47 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_159567 $$unsorted) (BOUND_VARIABLE_159568 $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (fun (filter nat) bool))) (let ((_let_2 (fun nat X_a))) (let ((_let_3 (norm_norm X_a))) (or (not (real_normed_vector X_a)) (not (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_1 (hAPP _let_2 (fun X_a _let_1) (tendsto nat X_a) BOUND_VARIABLE_159567) BOUND_VARIABLE_159568) sequentially))) (hBOOL (hAPP (filter nat) bool (hAPP real _let_1 (hAPP _let_0 (fun real _let_1) (tendsto nat real) (hAPP _let_2 _let_0 (hAPP (fun X_a real) (fun _let_2 _let_0) (combb X_a real nat) _let_3) BOUND_VARIABLE_159567)) (hAPP X_a real _let_3 BOUND_VARIABLE_159568)) sequentially))))))) ) 16.35/16.47 ( real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real) ) 16.35/16.47 ) 16.35/16.47 (instantiation (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) Y_1))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real sqrt X_1)) (hAPP real real sqrt Y_1)))))) ) 16.35/16.47 ( (zero_zero real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.47 ) 16.35/16.47 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted)) (let ((_let_0 (isCont X_a X_b))) (or (not (topological_space X_a)) (not (topological_space X_b)) (= _let_0 (ti (fun (fun X_a X_b) (fun X_a bool)) _let_0)))) ) 16.35/16.47 ( bool, nat ) 16.35/16.47 ( bool, int ) 16.35/16.47 ( bool, real ) 16.35/16.47 ( bool, (product_prod int int) ) 16.35/16.47 ( int, int ) 16.35/16.47 ( int, (product_prod int int) ) 16.35/16.47 ( (fun int bool), int ) 16.35/16.47 ( (fun int bool), real ) 16.35/16.47 ( (fun nat bool), int ) 16.35/16.47 ( real, nat ) 16.35/16.47 ( real, int ) 16.35/16.47 ) 16.35/16.47 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (dist_dist X_a))) (or (not (dist_norm X_a)) (= _let_0 (ti (fun X_a (fun X_a real)) _let_0)))) ) 16.35/16.47 ( nat ) 16.35/16.47 ( int ) 16.35/16.47 ( real ) 16.35/16.47 ( (fun real bool) ) 16.35/16.47 ( rat ) 16.35/16.47 ( complex ) 16.35/16.47 ) 16.35/16.47 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_159694 $$unsorted) (BOUND_VARIABLE_159695 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (uminus_uminus X_a))) (or (not (ordered_ab_group_add X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_159694)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_159695))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_159695) BOUND_VARIABLE_159694))))))) ) 16.35/16.47 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 16.35/16.47 ( int, (one_one int), (one_one int) ) 16.35/16.47 ( int, (one_one int), pls ) 16.35/16.47 ( int, pls, (one_one int) ) 16.35/16.47 ( int, pls, pls ) 16.35/16.47 ( int, pls, min_1 ) 16.35/16.47 ( int, min_1, pls ) 16.35/16.47 ( int, min_1, min_1 ) 16.35/16.47 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), pls ) 16.35/16.47 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s ) 16.35/16.47 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 16.35/16.47 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_4 ) 16.35/16.47 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_10 ) 16.35/16.47 ( int, t, (one_one int) ) 16.35/16.47 ( real, (zero_zero real), pi ) 16.35/16.47 ( real, (zero_zero real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.35/16.47 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.47 ( real, pi, (zero_zero real) ) 16.35/16.47 ( real, pi, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 16.35/16.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.47 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.35/16.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 16.35/16.47 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 16.35/16.47 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.35/16.47 ( real, skv_2, (zero_zero real) ) 16.35/16.47 ( real, skv_8, (zero_zero real) ) 16.35/16.47 ( real, skv_9, (zero_zero real) ) 16.35/16.47 ) 16.35/16.47 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_159731 $$unsorted) (BOUND_VARIABLE_159732 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (inverse_divide X_a))) (or (not (field_inverse_zero X_a)) (= (hAPP X_a X_a (inverse_inverse X_a) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_159731) BOUND_VARIABLE_159732)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_159732) BOUND_VARIABLE_159731))))) ) 16.35/16.47 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.47 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.35/16.47 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.47 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 16.35/16.47 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.47 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.47 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.35/16.47 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.35/16.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 16.35/16.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.35/16.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.35/16.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.35/16.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 16.35/16.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), pi ) 16.35/16.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.47 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (one_one real) ) 16.35/16.47 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.47 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))), pi ) 16.35/16.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 16.35/16.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))), (one_one real) ) 16.35/16.47 ) 16.35/16.47 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_159845 $$unsorted) (BOUND_VARIABLE_159846 $$unsorted) (BOUND_VARIABLE_159847 $$unsorted) (BOUND_VARIABLE_159848 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (times_times X_a))) (let ((_let_2 (inverse_divide X_a))) (let ((_let_3 (zero_zero X_a))) (or (not (field X_a)) (= _let_3 (ti X_a BOUND_VARIABLE_159848)) (= _let_3 (ti X_a BOUND_VARIABLE_159847)) (= (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_159846) BOUND_VARIABLE_159848) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_159845) BOUND_VARIABLE_159847)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_159846) BOUND_VARIABLE_159847) (hAPP X_a X_a (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_159845) BOUND_VARIABLE_159848)))))))) ) 16.35/16.47 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), s, s ) 16.35/16.47 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), s1, s1 ) 16.35/16.47 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), s, s ) 16.35/16.47 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), pls, pls ) 16.35/16.47 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), m, pls ) 16.35/16.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi, pi ) 16.35/16.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi, pi ) 16.35/16.47 ( complex, ii, ii, ii, ii ) 16.35/16.47 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), ii, ii, ii ) 16.35/16.47 ) 16.35/16.47 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (one_one real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (abs_abs real) X_1)) _let_2))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP nat real (hAPP real (fun nat real) (power_power real) X_1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) _let_2)))))) ) 16.35/16.47 ( (hAPP int real (number_number_of real) min_1) ) 16.35/16.47 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.47 ) 16.35/16.47 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (ord_min X_a))) (or (not (ord X_a)) (= _let_0 (ti (fun X_a (fun X_a X_a)) _let_0)))) ) 16.35/16.47 ( bool ) 16.35/16.47 ( nat ) 16.35/16.47 ( int ) 16.35/16.47 ( (fun int bool) ) 16.35/16.47 ( (fun int (fun int bool)) ) 16.35/16.47 ( (fun int int) ) 16.35/16.47 ( (fun nat bool) ) 16.35/16.47 ( real ) 16.35/16.47 ( (fun real bool) ) 16.35/16.47 ( (fun real real) ) 16.35/16.47 ( rat ) 16.35/16.47 ( complex ) 16.35/16.47 ( (fun nat real) ) 16.35/16.47 ( (product_prod int int) ) 16.35/16.47 ( quickcheck_code_int ) 16.35/16.47 ( code_code_numeral ) 16.35/16.47 ( (fun int (fun int (fun int bool))) ) 16.35/16.47 ( (fun (product_prod int int) bool) ) 16.35/16.47 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 16.35/16.47 ( (fun (product_prod int int) int) ) 16.35/16.47 ( (fun int real) ) 16.35/16.47 ) 16.35/16.47 (instantiation (forall ((N $$unsorted) (Ma $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (zero_zero int)) Ma))) (= (= (ti int Ma) (hAPP int int (hAPP int (fun int int) legacy_zgcd N) Ma)) (hBOOL (hAPP int bool (hAPP int _let_0 (dvd_dvd int) Ma) N))))) ) 16.35/16.47 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.47 ) 16.35/16.47 (instantiation (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (zero_zero real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) _let_1) Y_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) _let_1) X_1))) (not (forall ((N_2 $$unsorted)) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 nat))) (let ((_let_3 (times_times real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) X_1) (hAPP real real (hAPP real _let_1 _let_3 (hAPP nat real _let_2 (hAPP nat nat suc N_2))) Y_1)))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) (hAPP real real (hAPP real _let_1 _let_3 (hAPP nat real _let_2 N_2)) Y_1)) X_1))))))) ))))) ) 16.35/16.47 ( pi, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.47 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.47 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 16.35/16.47 ( skv_3, skv_2 ) 16.35/16.47 ( skv_5, skv_8 ) 16.35/16.47 ( skv_7, skv_9 ) 16.35/16.47 ) 16.35/16.47 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_160124 $$unsorted) (BOUND_VARIABLE_160125 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (zero_zero X_a))) (let ((_let_2 (hAPP X_a _let_0 (ord_less_eq X_a) _let_1))) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_160125))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) _let_1) BOUND_VARIABLE_160124))) (hBOOL (hAPP X_a bool _let_2 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_160125) BOUND_VARIABLE_160124))))))) ) 16.35/16.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 16.35/16.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.35/16.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.35/16.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.35/16.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 16.35/16.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), pi ) 16.35/16.47 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (one_one real) ) 16.35/16.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))), pi ) 16.35/16.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 16.35/16.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))), (one_one real) ) 16.35/16.47 ) 16.35/16.47 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (finite_finite T_2)) (not (finite_finite T_1)) (finite_finite (product_prod T_2 T_1))) ) 16.35/16.47 ( nat, nat ) 16.35/16.47 ( int, int ) 16.35/16.47 ( int, (product_prod int int) ) 16.35/16.47 ( (product_prod nat nat), (product_prod nat nat) ) 16.35/16.47 ( real, real ) 16.35/16.47 ( (product_prod int int), (product_prod int int) ) 16.35/16.47 ( quickcheck_code_int, quickcheck_code_int ) 16.35/16.47 ( code_code_numeral, code_code_numeral ) 16.35/16.47 ) 16.35/16.47 (instantiation (forall ((D2 $$unsorted) (D1 $$unsorted)) (let ((_let_0 (hAPP real (fun real bool) (ord_less real) (zero_zero real)))) (or (not (hBOOL (hAPP real bool _let_0 D1))) (not (hBOOL (hAPP real bool _let_0 D2))) (not (forall ((E $$unsorted)) (let ((_let_1 (hAPP real (fun real bool) (ord_less real) E))) (or (not (hBOOL (hAPP real bool _let_1 D1))) (not (hBOOL (hAPP real bool _let_1 D2))) (not (hBOOL (hAPP real bool _let_0 E))))) )))) ) 16.35/16.47 ( pi, pi ) 16.35/16.47 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.47 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.47 ( skv_2, skv_2 ) 16.35/16.47 ( skv_8, skv_8 ) 16.35/16.47 ( skv_9, skv_9 ) 16.35/16.47 ) 16.35/16.47 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_160221 $$unsorted) (BOUND_VARIABLE_160222 $$unsorted) (BOUND_VARIABLE_160223 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (fun X_a X_a))) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) (zero_zero X_a)) BOUND_VARIABLE_160223))) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_160221) (hAPP X_a X_a (hAPP X_a _let_2 (times_times X_a) BOUND_VARIABLE_160222) BOUND_VARIABLE_160223))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_2 (inverse_divide X_a) BOUND_VARIABLE_160221) BOUND_VARIABLE_160223)) BOUND_VARIABLE_160222))))))) ) 16.35/16.47 ( real, (zero_zero real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 16.35/16.47 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 16.35/16.47 ) 16.35/16.47 (instantiation (forall ((X_1 $$unsorted)) (= (hAPP real real cos (hAPP real real (hAPP real (fun real real) (plus_plus real) X_1) pi)) (hAPP real real (uminus_uminus real) (hAPP real real cos X_1))) ) 16.35/16.47 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.35/16.47 ) 16.35/16.47 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_0 (hAPP int (fun int bool) (dvd_dvd int) P_5))) (or (not (hBOOL (hAPP int bool zprime P_5))) (not (hBOOL (hAPP int bool _let_0 (hAPP int int (hAPP int (fun int int) (times_times int) M) N_1)))) (hBOOL (hAPP int bool _let_0 N_1)) (hBOOL (hAPP int bool _let_0 M)))) ) 16.35/16.47 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.47 ) 16.35/16.47 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_160291 $$unsorted)) (let ((_let_0 (filter nat))) (let ((_let_1 (fun X_a bool))) (let ((_let_2 (fun X_a (fun _let_0 bool)))) (let ((_let_3 (fun nat X_a))) (or (not (metric_space X_a)) (= (hAPP _let_3 X_a (lim X_a) BOUND_VARIABLE_160291) (hAPP _let_1 X_a (the X_a) (hAPP _let_0 _let_1 (hAPP _let_2 (fun _let_0 _let_1) (combc X_a _let_0 bool) (hAPP _let_3 _let_2 (tendsto nat X_a) BOUND_VARIABLE_160291)) sequentially)))))))) ) 16.35/16.47 ( real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))) ) 16.35/16.47 ) 16.35/16.47 (instantiation (forall ((N_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (hAPP int real (real_1 int) N_1))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) _let_1) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) X_1) (hAPP real real (hAPP real (fun real real) (plus_plus real) _let_1) (one_one real))))) (= (hAPP real int (archim2085082626_floor real) X_1) (ti int N_1))))) ) 16.35/16.47 ( (zero_zero int), pi ) 16.35/16.47 ( (zero_zero int), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.47 ( (zero_zero int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.47 ( (zero_zero int), skv_3 ) 16.35/16.47 ( (zero_zero int), skv_5 ) 16.35/16.47 ( (zero_zero int), skv_7 ) 16.35/16.47 ( (zero_zero int), skv_12 ) 16.35/16.47 ) 16.35/16.47 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_160328 $$unsorted) (BOUND_VARIABLE_160329 $$unsorted) (BOUND_VARIABLE_160330 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_160329))) (or (not (comm_semiring_1 X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_160330))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_160328))) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_160330) BOUND_VARIABLE_160328))))) ) 16.35/16.47 ( int, (one_one int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.47 ) 16.35/16.47 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_160433 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (or (not (linord1117847801e_zero X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_160433)) _let_2)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_160433) _let_2))))))) ) 16.35/16.47 ( real, (zero_zero real) ) 16.35/16.47 ( complex, ii ) 16.35/16.47 ) 16.35/16.47 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (power_power X_a))) (or (not (power X_a)) (= _let_0 (ti (fun X_a (fun nat X_a)) _let_0)))) ) 16.35/16.47 ( bool ) 16.35/16.47 ( nat ) 16.35/16.47 ( int ) 16.35/16.47 ( (fun int int) ) 16.35/16.47 ( (fun nat bool) ) 16.35/16.47 ( (fun nat nat) ) 16.35/16.47 ( (product_prod nat nat) ) 16.35/16.47 ( (fun (product_prod nat nat) bool) ) 16.35/16.47 ( (fun nat (fun (product_prod nat nat) bool)) ) 16.35/16.47 ( real ) 16.35/16.47 ( (fun real real) ) 16.35/16.47 ( rat ) 16.35/16.47 ( (fun nat (fun nat bool)) ) 16.35/16.47 ( complex ) 16.35/16.47 ( (product_prod int int) ) 16.35/16.47 ( quickcheck_code_int ) 16.35/16.47 ( (fun bool bool) ) 16.35/16.47 ( code_code_numeral ) 16.35/16.47 ( (product_prod real real) ) 16.35/16.47 ( (fun nat (product_prod nat nat)) ) 16.35/16.47 ( (fun nat (product_prod int int)) ) 16.35/16.47 ) 16.35/16.47 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_0 (hAPP nat (fun nat nat) (plus_plus nat) M))) (= (hAPP nat nat _let_0 (hAPP nat nat suc N_1)) (hAPP nat nat suc (hAPP nat nat _let_0 N_1)))) ) 16.35/16.47 ( (one_one nat), (zero_zero nat) ) 16.35/16.47 ( (one_one nat), (one_one nat) ) 16.35/16.47 ) 16.35/16.47 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_160458 $$unsorted) (BOUND_VARIABLE_160459 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (times_times X_a))) (let ((_let_2 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_160458) BOUND_VARIABLE_160459))) (or (not (monoid_mult X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_160458) _let_2) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_160458)))))) ) 16.35/16.47 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.47 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.47 ( int, skv_14, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.47 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.47 ) 16.35/16.47 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (hAPP real (fun real bool) (ord_less real) (zero_zero real)))) (or (not (hBOOL (hAPP real bool _let_0 X_1))) (hBOOL (hAPP real bool _let_0 (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP real real sqrt X_1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 16.35/16.47 ( (one_one real) ) 16.35/16.47 ( (zero_zero real) ) 16.35/16.47 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.47 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.35/16.47 ) 16.35/16.47 (instantiation (forall ((X_2 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) X_2))) (= (hBOOL (hAPP nat bool (even_odd_even nat) (hAPP int nat nat_1 X_2))) (hBOOL (hAPP int bool (even_odd_even int) X_2)))) ) 16.35/16.47 ( (one_one int) ) 16.35/16.47 ( (zero_zero int) ) 16.35/16.47 ( min_1 ) 16.35/16.47 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.47 ( s ) 16.35/16.47 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.35/16.47 ( (hAPP int int (number_number_of int) pls) ) 16.35/16.47 ( skv_4 ) 16.35/16.47 ( skv_10 ) 16.35/16.47 ) 16.35/16.47 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_160486 $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat _let_0))) (let ((_let_2 (fun nat X_a))) (let ((_let_3 (fun _let_0 X_a))) (or (not (metric_space X_a)) (not (comm_monoid_add X_a)) (= (hAPP _let_2 X_a (lim X_a) (hAPP _let_1 _let_2 (hAPP _let_3 (fun _let_1 _let_2) (combb _let_0 X_a nat) (hAPP _let_2 _let_3 (big_co1399186613setsum nat X_a) BOUND_VARIABLE_160486)) (hAPP nat _let_1 (ord_atLeastLessThan nat) (zero_zero nat)))) (hAPP _let_2 X_a (suminf X_a) BOUND_VARIABLE_160486))))))) ) 16.35/16.47 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat (fun nat nat)))) (let ((_let_3 (fun nat _let_0))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun _let_1 _let_3))) (let ((_let_6 (combb real _let_0 nat))) (let ((_let_7 (combc nat nat nat))) (hAPP _let_1 _let_1 (hAPP _let_3 (fun _let_1 _let_1) (combs nat real real) (hAPP _let_1 _let_3 (hAPP _let_4 _let_5 _let_6 (inverse_divide real)) (hAPP real _let_1 (hAPP _let_3 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_3 (hAPP _let_4 _let_5 _let_6 (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) (one_one real)))) (hAPP (fun nat nat) _let_1 (hAPP _let_1 (fun (fun nat nat) _let_1) (combb nat real nat) (real_1 nat)) (hAPP nat (fun nat nat) (hAPP _let_2 _let_2 _let_7 (hAPP (fun nat nat) _let_2 (hAPP _let_2 (fun (fun nat nat) _let_2) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_2 _let_2 _let_7 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))))))))))) ) 16.35/16.47 ) 16.35/16.47 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (strict_mono nat X_a))) (or (not (order X_a)) (= _let_0 (ti (fun (fun nat (fun nat bool)) (fun (fun nat X_a) bool)) _let_0)))) ) 16.35/16.47 ( bool ) 16.35/16.47 ( nat ) 16.35/16.47 ( int ) 16.35/16.47 ( (fun int int) ) 16.35/16.47 ( (fun nat bool) ) 16.35/16.47 ( (fun nat nat) ) 16.35/16.47 ( (product_prod nat nat) ) 16.35/16.47 ( (fun (product_prod nat nat) bool) ) 16.35/16.47 ( (fun nat (fun (product_prod nat nat) bool)) ) 16.35/16.47 ( real ) 16.35/16.47 ( (fun real real) ) 16.35/16.47 ( rat ) 16.35/16.47 ( (fun nat (fun nat bool)) ) 16.35/16.47 ( complex ) 16.35/16.47 ( (product_prod int int) ) 16.35/16.47 ( quickcheck_code_int ) 16.35/16.47 ( (fun bool bool) ) 16.35/16.47 ( code_code_numeral ) 16.35/16.47 ( (product_prod real real) ) 16.35/16.47 ( (fun nat (product_prod nat nat)) ) 16.35/16.47 ( (fun nat (product_prod int int)) ) 16.35/16.47 ) 16.35/16.47 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (fun code_code_numeral X_a))) (let ((_let_1 (code_c600343653l_case X_a))) (= _let_1 (ti (fun X_a (fun _let_0 _let_0)) _let_1)))) ) 16.35/16.47 ( nat ) 16.35/16.47 ( int ) 16.35/16.47 ( (fun nat nat) ) 16.35/16.47 ( code_code_numeral ) 16.35/16.47 ( (product_prod code_code_numeral code_code_numeral) ) 16.35/16.47 ( (fun code_code_numeral (product_prod code_code_numeral code_code_numeral)) ) 16.35/16.47 ) 16.35/16.47 (instantiation (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_0 (hAPP real (fun real bool) (ord_less real) (zero_zero real)))) (or (not (hBOOL (hAPP real bool _let_0 X_1))) (not (hBOOL (hAPP real bool _let_0 Y_1))) (hBOOL (hAPP real bool _let_0 (hAPP real real (hAPP real (fun real real) (times_times real) X_1) Y_1))))) ) 16.35/16.47 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.47 ( pi, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 16.35/16.47 ( (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.47 ( (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.47 ) 16.35/16.47 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_160574 $$unsorted) (BOUND_VARIABLE_160575 $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (comple44059174attice X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) BOUND_VARIABLE_160574) BOUND_VARIABLE_160575))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_160574) (hAPP _let_0 X_a (complete_Sup_Sup X_a) BOUND_VARIABLE_160575))))) ) 16.35/16.47 ( int, (one_one int), zEven ) 16.35/16.47 ) 16.35/16.47 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_160604 $$unsorted) (BOUND_VARIABLE_160605 $$unsorted) (BOUND_VARIABLE_160606 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (let ((_let_3 (hAPP X_a _let_0 _let_1 _let_2))) (let ((_let_4 (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_160605)))) (let ((_let_5 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_160606) BOUND_VARIABLE_160605))) (let ((_let_6 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_160605) _let_2)))) (or (not (linord1117847801e_zero X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_160604) BOUND_VARIABLE_160605)) BOUND_VARIABLE_160606)) (and (or (not _let_4) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_160604) _let_5))) (or _let_4 (and (or _let_6 (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_160606))) (or (not _let_6) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_5) BOUND_VARIABLE_160604))))))))))))))) ) 16.35/16.48 ( real, (zero_zero real), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.48 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.48 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.48 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.48 ) 16.35/16.48 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (one_one X_a))) (or (not (number_semiring X_a)) (= (hAPP int X_a (number_number_of X_a) (hAPP int int bit0 (hAPP int int bit1 pls))) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) _let_0) _let_0)))) ) 16.35/16.48 ( bool ) 16.35/16.48 ( nat ) 16.35/16.48 ( int ) 16.35/16.48 ( (fun int bool) ) 16.35/16.48 ( (fun int (fun int bool)) ) 16.35/16.48 ( (fun int int) ) 16.35/16.48 ( (fun nat bool) ) 16.35/16.48 ( real ) 16.35/16.48 ( (fun real bool) ) 16.35/16.48 ( (fun real real) ) 16.35/16.48 ( rat ) 16.35/16.48 ( complex ) 16.35/16.48 ( (fun nat real) ) 16.35/16.48 ( (product_prod int int) ) 16.35/16.48 ( quickcheck_code_int ) 16.35/16.48 ( code_code_numeral ) 16.35/16.48 ( (fun int (fun int (fun int bool))) ) 16.35/16.48 ( (fun (product_prod int int) bool) ) 16.35/16.48 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 16.35/16.48 ( (fun (product_prod int int) int) ) 16.35/16.48 ( (fun int real) ) 16.35/16.48 ) 16.35/16.48 (instantiation (forall ((K_4 $$unsorted) (I_1 $$unsorted) (J_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (hAPP real _let_0 _let_1 I_1))) (or (not (hBOOL (hAPP real bool _let_2 J_2))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 J_2) K_4))) (hBOOL (hAPP real bool _let_2 K_4)))))) ) 16.35/16.48 ( pi, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.48 ( pi, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.35/16.48 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.48 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real), skv_5 ) 16.35/16.48 ) 16.35/16.48 (instantiation (forall ((L $$unsorted) (U_1 $$unsorted)) (let ((_let_0 (fun int bool))) (= (hAPP _let_0 nat (finite_card int) (hAPP int _let_0 (hAPP int (fun int _let_0) (ord_atLeastLessThan int) L) U_1)) (hAPP int nat nat_1 (hAPP int int (hAPP int (fun int int) (minus_minus int) U_1) L)))) ) 16.35/16.48 ( (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.48 ) 16.35/16.48 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_160691 $$unsorted) (BOUND_VARIABLE_160692 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (power X_a)) (not (mult_zero X_a)) (not (zero_neq_one X_a)) (not (no_zero_divisors X_a)) (= (and (= _let_0 (ti X_a BOUND_VARIABLE_160691)) (not (= (zero_zero nat) BOUND_VARIABLE_160692))) (= _let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_160691) BOUND_VARIABLE_160692))))) ) 16.35/16.48 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.48 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.48 ( int, skv_14, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.48 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.48 ) 16.35/16.48 (instantiation (forall ((Z $$unsorted)) (let ((_let_0 (one_one int))) (let ((_let_1 (ti int Z))) (= (or (= _let_0 _let_1) (= (hAPP int int (number_number_of int) min_1) _let_1)) (= _let_0 (hAPP int int (abs_abs int) Z))))) ) 16.35/16.48 ( pls ) 16.35/16.48 ( min_1 ) 16.35/16.48 ( s ) 16.35/16.48 ( m ) 16.35/16.48 ( s1 ) 16.35/16.48 ( t ) 16.35/16.48 ) 16.35/16.48 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (number_number_of X_a))) (or (not (number X_a)) (= _let_0 (ti (fun int X_a) _let_0)))) ) 16.35/16.48 ( bool ) 16.35/16.48 ( nat ) 16.35/16.48 ( int ) 16.35/16.48 ( (fun int bool) ) 16.35/16.48 ( (fun int (fun int bool)) ) 16.35/16.48 ( (fun int int) ) 16.35/16.48 ( (fun nat bool) ) 16.35/16.48 ( (fun nat nat) ) 16.35/16.48 ( real ) 16.35/16.48 ( (fun real real) ) 16.35/16.48 ( rat ) 16.35/16.48 ( (fun int rat) ) 16.35/16.48 ( (fun nat int) ) 16.35/16.48 ( complex ) 16.35/16.48 ( (fun nat real) ) 16.35/16.48 ( (product_prod int int) ) 16.35/16.48 ( (fun int (product_prod int int)) ) 16.35/16.48 ( (fun (fun int bool) bool) ) 16.35/16.48 ( quickcheck_code_int ) 16.35/16.48 ( (fun bool bool) ) 16.35/16.48 ( (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 16.35/16.48 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)) ) 16.35/16.48 ( code_code_numeral ) 16.35/16.48 ( (fun int (fun int (fun int bool))) ) 16.35/16.48 ( (fun (product_prod int int) bool) ) 16.35/16.48 ( (fun int (fun (product_prod int int) bool)) ) 16.35/16.48 ( (fun int (fun bool bool)) ) 16.35/16.48 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 16.35/16.48 ( (fun (fun int int) (fun int bool)) ) 16.35/16.48 ( (fun (product_prod int int) int) ) 16.35/16.48 ( (product_prod int (product_prod int int)) ) 16.35/16.48 ( (fun int (product_prod int (product_prod int int))) ) 16.35/16.48 ( (fun int (fun int (product_prod int (product_prod int int)))) ) 16.35/16.48 ( (fun int (fun int (fun int (product_prod int (product_prod int int))))) ) 16.35/16.48 ( (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))) ) 16.35/16.48 ( (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))) ) 16.35/16.48 ( (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))) ) 16.35/16.48 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))))) ) 16.35/16.48 ( (fun int (fun (fun int bool) bool)) ) 16.35/16.48 ( (list int) ) 16.35/16.48 ( (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 16.35/16.48 ( (fun int real) ) 16.35/16.48 ( (fun nat (fun bool bool)) ) 16.35/16.48 ( (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 16.35/16.48 ( (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 16.35/16.48 ) 16.35/16.48 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_160834 $$unsorted) (BOUND_VARIABLE_160835 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)))) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_160835))) (hBOOL (hAPP X_a bool _let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_160835) BOUND_VARIABLE_160834))))) ) 16.35/16.48 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 16.35/16.48 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 16.35/16.48 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_14 ) 16.35/16.48 ( complex, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), ii ) 16.35/16.48 ) 16.35/16.48 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_160920 $$unsorted) (BOUND_VARIABLE_160921 $$unsorted) (BOUND_VARIABLE_160938 $$unsorted) (BOUND_VARIABLE_160939 $$unsorted)) (let ((_let_0 (number_number_of int))) (let ((_let_1 (number_number_of nat))) (let ((_let_2 (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)))) (let ((_let_3 (fun X_a X_a))) (let ((_let_4 (times_times X_a))) (let ((_let_5 (fun nat X_a))) (let ((_let_6 (power_power X_a))) (let ((_let_7 (hAPP nat X_a (hAPP X_a _let_5 _let_6 BOUND_VARIABLE_160920) (hAPP int nat _let_1 BOUND_VARIABLE_160921)))) (or (not (monoid_mult X_a)) (and (or (not (hBOOL (hAPP int bool _let_2 (hAPP int int _let_0 BOUND_VARIABLE_160921)))) (= (hAPP nat X_a (hAPP X_a _let_5 _let_6 BOUND_VARIABLE_160920) (hAPP int nat _let_1 (hAPP int int bit1 BOUND_VARIABLE_160921))) (hAPP X_a X_a (hAPP X_a _let_3 _let_4 (hAPP X_a X_a (hAPP X_a _let_3 _let_4 BOUND_VARIABLE_160920) _let_7)) _let_7))) (or (hBOOL (hAPP int bool _let_2 (hAPP int int _let_0 BOUND_VARIABLE_160939))) (= (one_one X_a) (hAPP nat X_a (hAPP X_a _let_5 _let_6 BOUND_VARIABLE_160938) (hAPP int nat _let_1 (hAPP int int bit1 BOUND_VARIABLE_160939))))))))))))))) ) 16.35/16.48 ( int, s, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))), s, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.35/16.48 ( int, s1, (hAPP int int bit0 (hAPP int int bit1 pls)), s1, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.35/16.48 ( int, skv_14, pls, skv_14, pls ) 16.35/16.48 ( real, (hAPP int real (number_number_of real) min_1), min_1, (hAPP int real (number_number_of real) min_1), min_1 ) 16.35/16.48 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int bit1 pls), (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int bit1 pls) ) 16.35/16.48 ( complex, ii, (hAPP int int bit1 (hAPP int int bit1 pls)), ii, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.35/16.48 ) 16.35/16.48 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_160965 $$unsorted) (BOUND_VARIABLE_160966 $$unsorted) (BOUND_VARIABLE_160967 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (plus_plus X_a))) (let ((_let_2 (times_times X_a))) (or (not (comm_semiring X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_160965) BOUND_VARIABLE_160966)) BOUND_VARIABLE_160967) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_160965) BOUND_VARIABLE_160967)) (hAPP X_a X_a (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_160966) BOUND_VARIABLE_160967))))))) ) 16.35/16.48 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int), t ) 16.35/16.48 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int), skv_13 ) 16.35/16.48 ) 16.35/16.48 (instantiation (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (times_times real))) (= (hAPP real real cos (hAPP real real (hAPP real _let_0 (minus_minus real) X_1) Y_1)) (hAPP real real (hAPP real _let_0 (plus_plus real) (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real cos X_1)) (hAPP real real cos Y_1))) (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real sin X_1)) (hAPP real real sin Y_1)))))) ) 16.35/16.48 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 16.35/16.48 ) 16.35/16.48 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_161016 $$unsorted)) (or (not (preorder X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_161016) BOUND_VARIABLE_161016)))) ) 16.35/16.48 ( nat, (zero_zero nat) ) 16.35/16.48 ( int, (one_one int) ) 16.35/16.48 ( int, pls ) 16.35/16.48 ( int, min_1 ) 16.35/16.48 ( int, s ) 16.35/16.48 ( int, t ) 16.35/16.48 ( int, skv_4 ) 16.35/16.48 ( int, skv_10 ) 16.35/16.48 ( real, (one_one real) ) 16.35/16.48 ( real, (zero_zero real) ) 16.35/16.48 ( real, pi ) 16.35/16.48 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.48 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.35/16.48 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.35/16.48 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 16.35/16.48 ) 16.35/16.48 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (real_normed_vector X_a)) (= _let_0 (hAPP X_a X_a (sgn_sgn X_a) _let_0)))) ) 16.35/16.48 ( nat ) 16.35/16.48 ( int ) 16.35/16.48 ( real ) 16.35/16.48 ( rat ) 16.35/16.48 ( complex ) 16.35/16.48 ( quickcheck_code_int ) 16.35/16.48 ( code_code_numeral ) 16.35/16.48 ) 16.35/16.48 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_0 (zero_zero int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) A_1) B)))) (let ((_let_4 (hAPP int _let_1 (hAPP int _let_2 posDivAlg A_1) B))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) _let_0) B))) (and (or _let_3 (= (hAPP _let_1 _let_1 (hAPP int (fun _let_1 _let_1) adjust B) (hAPP int _let_1 (hAPP int _let_2 posDivAlg A_1) (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) B))) _let_4)) (or (not _let_3) (= _let_4 (hAPP int _let_1 (hAPP int _let_2 (product_Pair int int) _let_0) A_1)))))))))) ) 16.35/16.48 ( (one_one int), t ) 16.35/16.48 ( pls, (one_one int) ) 16.35/16.48 ( pls, pls ) 16.35/16.48 ( pls, min_1 ) 16.35/16.48 ( pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.48 ( min_1, pls ) 16.35/16.48 ( min_1, min_1 ) 16.35/16.48 ( s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.35/16.48 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.44/16.48 ( skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.44/16.48 ( skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.44/16.48 ) 16.44/16.48 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (hAPP real _let_0 _let_1 (zero_zero real)))) (or (not (hBOOL (hAPP real bool _let_2 (hAPP real real ln X_1)))) (not (hBOOL (hAPP real bool _let_2 X_1))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (one_one real)) X_1)))))) ) 16.44/16.48 ( (one_one real) ) 16.44/16.48 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.44/16.48 ) 16.44/16.48 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_161168 $$unsorted) (BOUND_VARIABLE_161180 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (let ((_let_2 (ord_less int))) (let ((_let_3 (ring_1_of_int X_a))) (let ((_let_4 (semiring_1_of_nat X_a))) (or (not (ring_1 X_a)) (and (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 BOUND_VARIABLE_161168) _let_1))) (= (hAPP X_a X_a (uminus_uminus X_a) (hAPP nat X_a _let_4 (hAPP int nat nat_1 (hAPP int int (uminus_uminus int) BOUND_VARIABLE_161168)))) (hAPP int X_a _let_3 BOUND_VARIABLE_161168))) (or (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 BOUND_VARIABLE_161180) _let_1)) (= (hAPP int X_a _let_3 BOUND_VARIABLE_161180) (hAPP nat X_a _let_4 (hAPP int nat nat_1 BOUND_VARIABLE_161180))))))))))) ) 16.44/16.48 ( int, min_1, min_1 ) 16.44/16.48 ( real, t, t ) 16.44/16.48 ( rat, pls, pls ) 16.44/16.48 ( complex, s, s ) 16.44/16.48 ) 16.44/16.48 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (hAPP nat nat suc (zero_zero nat)))) (= (= _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (div_mod nat) X_2) (hAPP nat nat suc _let_0))) (not (hBOOL (hAPP nat bool (even_odd_even nat) X_2))))) ) 16.44/16.48 ( (zero_zero nat) ) 16.44/16.48 ( (one_one nat) ) 16.44/16.48 ) 16.44/16.48 (instantiation (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (or (= (ti int X_1) (ti int Y_1)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 Y_1) X_1)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 X_1) Y_1))))) ) 16.44/16.48 ( (one_one int), pls ) 16.44/16.48 ( (one_one int), t ) 16.44/16.48 ( pls, (one_one int) ) 16.44/16.48 ( pls, pls ) 16.44/16.48 ( pls, min_1 ) 16.44/16.48 ( pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.44/16.48 ( min_1, pls ) 16.44/16.48 ( min_1, min_1 ) 16.44/16.48 ( s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.44/16.48 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), pls ) 16.44/16.48 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s ) 16.44/16.48 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 16.44/16.48 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_4 ) 16.44/16.48 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_10 ) 16.44/16.48 ( t, (one_one int) ) 16.44/16.48 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.44/16.48 ( skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.44/16.48 ( skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.44/16.48 ) 16.44/16.48 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (max X_a))) (or (not (ord X_a)) (= _let_0 (ti (fun (fun X_a (fun X_a bool)) (fun X_a (fun X_a X_a))) _let_0)))) ) 16.44/16.48 ( bool ) 16.44/16.48 ( nat ) 16.44/16.48 ( int ) 16.44/16.48 ( (fun int bool) ) 16.44/16.48 ( (fun int (fun int bool)) ) 16.44/16.48 ( (fun int int) ) 16.44/16.48 ( (fun nat bool) ) 16.44/16.48 ( (product_prod nat nat) ) 16.44/16.48 ( real ) 16.44/16.48 ( (fun real bool) ) 16.44/16.48 ( (fun real real) ) 16.44/16.48 ( rat ) 16.44/16.48 ( complex ) 16.44/16.48 ( (fun nat real) ) 16.44/16.48 ( (filter nat) ) 16.44/16.48 ( (product_prod int int) ) 16.44/16.48 ( quickcheck_code_int ) 16.44/16.48 ( code_code_numeral ) 16.44/16.48 ( (fun int (fun int (fun int bool))) ) 16.44/16.48 ( (product_prod real real) ) 16.44/16.48 ( (fun (product_prod int int) bool) ) 16.44/16.48 ( (fun nat rat) ) 16.44/16.48 ( (filter real) ) 16.44/16.48 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 16.44/16.48 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 16.44/16.48 ( (fun (product_prod int int) int) ) 16.44/16.48 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 16.44/16.48 ( (fun int real) ) 16.44/16.48 ) 16.44/16.48 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_161249 $$unsorted)) (or (not (number_ring X_a)) (= (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_161249) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_161249))) ) 16.44/16.48 ( nat, pls ) 16.44/16.48 ( nat, (hAPP int int bit1 pls) ) 16.44/16.48 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.44/16.48 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.44/16.48 ( int, pls ) 16.44/16.48 ( int, (hAPP int int bit1 pls) ) 16.44/16.48 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.44/16.48 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.44/16.48 ( int, min_1 ) 16.44/16.48 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.44/16.48 ( real, (one_one int) ) 16.44/16.48 ( real, (zero_zero int) ) 16.44/16.48 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.44/16.48 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.44/16.48 ( real, min_1 ) 16.44/16.48 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.44/16.48 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.44/16.48 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.44/16.48 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 16.44/16.48 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.44/16.48 ( complex, min_1 ) 16.44/16.48 ( quickcheck_code_int, (one_one int) ) 16.44/16.48 ( quickcheck_code_int, (zero_zero int) ) 16.44/16.48 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 16.44/16.48 ( code_code_numeral, pls ) 16.44/16.48 ( code_code_numeral, (hAPP int int bit1 pls) ) 16.44/16.48 ) 16.44/16.48 (instantiation (forall ((N $$unsorted) (Ma $$unsorted)) (= (= (ti int Ma) (ti int N)) (= (hAPP int quickcheck_code_int quickcheck_of_int Ma) (hAPP int quickcheck_code_int quickcheck_of_int N))) ) 16.44/16.48 ( pls, s1 ) 16.44/16.48 ( min_1, t ) 16.44/16.48 ( s, pls ) 16.44/16.48 ( s, s ) 16.44/16.48 ( s, s1 ) 16.44/16.48 ( m, min_1 ) 16.44/16.48 ( m, m ) 16.44/16.48 ( m, t ) 16.44/16.48 ( s1, s ) 16.44/16.48 ( t, m ) 16.44/16.48 ) 16.44/16.48 (instantiation (forall ((B $$unsorted) (M $$unsorted) (A_1 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (let ((_let_2 (hAPP int _let_0 (ord_less_eq int) (zero_zero int)))) (or (not (hBOOL (hAPP int bool _let_2 A_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 A_1) M))) (not (hBOOL (hAPP int bool _let_2 B))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 B) M))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong A_1) B) M))) (= (ti int A_1) (ti int B)))))) ) 16.44/16.48 ( (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.44/16.48 ( (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.44/16.48 ( (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.44/16.48 ( s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s1 ) 16.44/16.48 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.44/16.48 ( skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s1 ) 16.44/16.48 ( skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s1 ) 16.44/16.48 ) 16.44/16.48 (instantiation (forall ((P_1 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun nat bool))) (let ((_let_2 (fun int nat))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun int _let_3))) (= (hAPP _let_0 _let_1 (hAPP _let_2 (fun _let_0 _let_1) (image int nat) nat_1) (hAPP _let_0 _let_0 (collect int) (hAPP _let_0 _let_0 (hAPP _let_4 (fun _let_0 _let_0) (combs int bool bool) (hAPP _let_0 _let_4 (hAPP (fun bool _let_3) (fun _let_0 _let_4) (combb bool _let_3 int) fconj) (hAPP int _let_0 (ord_less_eq int) (zero_zero int)))) (hAPP _let_2 _let_0 (hAPP _let_1 (fun _let_2 _let_0) (combb nat bool int) P_1) nat_1)))) (hAPP _let_1 _let_1 (collect nat) P_1))))))) ) 16.44/16.48 ( prime ) 16.44/16.48 ) 16.44/16.48 (instantiation (forall ((A_1 $$unsorted) (X_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) A_1) (hAPP real int (archim2085082626_floor real) X_1)))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP int real (real_1 int) A_1)) X_1))) ) 16.44/16.48 ( (zero_zero int), pi ) 16.44/16.48 ( (zero_zero int), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.44/16.48 ( (zero_zero int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.44/16.48 ( (zero_zero int), skv_3 ) 16.44/16.48 ( (zero_zero int), skv_5 ) 16.44/16.48 ( (zero_zero int), skv_7 ) 16.44/16.48 ( (zero_zero int), skv_12 ) 16.44/16.48 ) 16.44/16.48 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_161487 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_161487) (one_one X_a))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP X_a int (archim2085082626_floor X_a) BOUND_VARIABLE_161487)) (zero_zero int))))) ) 16.44/16.48 ( nat, (zero_zero nat) ) 16.44/16.48 ( int, (one_one int) ) 16.44/16.48 ( int, pls ) 16.44/16.48 ( int, min_1 ) 16.44/16.48 ( int, s ) 16.44/16.48 ( int, t ) 16.44/16.48 ( int, skv_4 ) 16.44/16.48 ( int, skv_10 ) 16.44/16.48 ( real, (one_one real) ) 16.44/16.48 ( real, (zero_zero real) ) 16.44/16.48 ( real, pi ) 16.44/16.48 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.44/16.48 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.44/16.48 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.44/16.48 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 16.44/16.48 ) 16.44/16.48 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_161526 $$unsorted) (BOUND_VARIABLE_161527 $$unsorted)) (let ((_let_0 (fun X_a X_b))) (let ((_let_1 (fun X_a bool))) (let ((_let_2 (isCont X_a X_b))) (or (not (real_normed_vector X_b)) (not (topological_space X_a)) (not (hBOOL (hAPP X_a bool (hAPP _let_0 _let_1 _let_2 BOUND_VARIABLE_161526) BOUND_VARIABLE_161527))) (= (zero_zero X_b) (hAPP X_a X_b BOUND_VARIABLE_161526 BOUND_VARIABLE_161527)) (hBOOL (hAPP X_a bool (hAPP _let_0 _let_1 _let_2 (hAPP _let_0 _let_0 (hAPP (fun X_b X_b) (fun _let_0 _let_0) (combb X_b X_b X_a) (sgn_sgn X_b)) BOUND_VARIABLE_161526)) BOUND_VARIABLE_161527)))))) ) 16.44/16.48 ( bool, nat, (even_odd_even nat), (zero_zero nat) ) 16.44/16.48 ( bool, nat, (even_odd_even nat), (one_one nat) ) 16.44/16.48 ( bool, nat, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.44/16.48 ( bool, nat, prime, (zero_zero nat) ) 16.44/16.48 ( bool, nat, prime, (hAPP nat nat suc (zero_zero nat)) ) 16.44/16.48 ( bool, nat, prime, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.44/16.48 ( bool, int, (hAPP int (fun int bool) (ord_less int) pls), pls ) 16.44/16.48 ( bool, int, (hAPP int (fun int bool) (ord_less int) pls), min_1 ) 16.44/16.48 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) pls), min_1 ) 16.44/16.48 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (one_one int)), t ) 16.44/16.48 ( bool, int, nat_neg, (one_one int) ) 16.44/16.48 ( bool, int, nat_neg, (hAPP int int (number_number_of int) min_1) ) 16.44/16.48 ( bool, int, nat_neg, (hAPP int int (number_number_of int) pls) ) 16.44/16.48 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (one_one int) ) 16.44/16.48 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.44/16.48 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), s ) 16.44/16.48 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.44/16.48 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (hAPP int int (number_number_of int) pls) ) 16.44/16.48 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_4 ) 16.44/16.48 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_10 ) 16.44/16.48 ( bool, int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (one_one int) ) 16.44/16.48 ( bool, int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.44/16.48 ( bool, int, zprime, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.44/16.48 ( bool, int, zprime, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.44/16.48 ( bool, int, (hAPP int (fun int bool) (ord_less int) s), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.44/16.48 ( bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) s)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.44/16.48 ( bool, int, (let ((_let_0 (fun int int))) (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 16.44/16.48 ( bool, int, (hAPP int (fun int bool) (ord_less int) (one_one int)), t ) 16.44/16.48 ( bool, int, (even_odd_even int), (one_one int) ) 16.44/16.48 ( bool, int, (even_odd_even int), (zero_zero int) ) 16.44/16.48 ( bool, int, twoSqu1091635170sum2sq, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) t))) ) 16.44/16.48 ( bool, int, nat_is_nat, (one_one int) ) 16.44/16.48 ( bool, int, nat_is_nat, (zero_zero int) ) 16.44/16.48 ( bool, int, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.44/16.48 ( bool, int, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.44/16.48 ( bool, int, (hAPP int (fun int bool) (ord_less int) min_1), pls ) 16.44/16.48 ( bool, int, (hAPP int (fun int bool) (ord_less int) min_1), min_1 ) 16.44/16.48 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) min_1), pls ) 16.44/16.48 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) min_1), min_1 ) 16.44/16.48 ( bool, int, (let ((_let_0 (fun int int))) (hAPP int (fun int bool) quadRes (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), (hAPP int int (number_number_of int) min_1) ) 16.44/16.48 ( bool, int, (let ((_let_0 (fun int bool))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (let ((_let_3 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int _let_1 _let_2 s) _let_3)) (hAPP nat int (hAPP int _let_1 _let_2 s1) _let_3)))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.44/16.48 ( bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.44/16.48 ( bool, int, (hAPP int (fun int bool) (ord_less int) t), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.44/16.48 ( bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.44/16.48 ( bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_4)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.44/16.48 ( bool, int, (hAPP int (fun int bool) (ord_less int) skv_4), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.44/16.48 ( bool, int, (hAPP int (fun int bool) (ord_less int) skv_10), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.44/16.48 ( bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_10)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.44/16.48 ( bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min_1))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.44/16.48 ( bool, (fun int bool), (hAPP (fun int nat) (fun (fun int bool) bool) (nat_tr1645093318rphism int nat) nat_1), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 16.44/16.48 ( bool, (fun int bool), (hAPP int (fun (fun int bool) bool) (member int) (one_one int)), zEven ) 16.44/16.48 ( bool, (fun nat bool), (finite_finite_1 nat), (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 16.44/16.48 ( bool, (fun nat bool), (hAPP (fun nat int) (fun (fun nat bool) bool) (nat_tr1645093318rphism nat int) (semiring_1_of_nat int)), (hAPP bool (fun nat bool) (combk bool nat) fTrue) ) 16.44/16.48 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), pi ) 16.44/16.48 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.44/16.48 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.44/16.48 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_3 ) 16.44/16.48 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_5 ) 16.44/16.48 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_7 ) 16.44/16.48 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_12 ) 16.44/16.48 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), pi ) 16.44/16.48 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.44/16.48 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.44/16.48 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_2 ) 16.44/16.48 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_8 ) 16.44/16.48 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_9 ) 16.44/16.48 ( bool, real, (hAPP real (fun real bool) (ord_less real) (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))), (zero_zero real) ) 16.44/16.48 ( bool, real, (hAPP real (fun real bool) (ord_less real) (one_one real)), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.44/16.48 ( bool, real, (hAPP real (fun real bool) (ord_less real) pi), (zero_zero real) ) 16.44/16.48 ( bool, real, (hAPP real (fun real bool) (ord_less real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.44/16.48 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.44/16.48 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 16.44/16.48 ( bool, real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 (fun real bool) (sums real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (hAPP real _let_1 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc)))), (one_one real) ) 16.44/16.48 ( bool, real, (hAPP real (fun real bool) (ord_less real) (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi))), pi ) 16.44/16.48 ( bool, real, (hAPP real (fun real bool) (ord_less real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.44/16.48 ( bool, real, (hAPP real (fun real bool) (ord_less real) (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 16.44/16.48 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 16.44/16.48 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) skv_5), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.44/16.48 ( bool, (filter nat), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun (filter nat) bool))) (hAPP real _let_2 (hAPP _let_1 (fun real _let_2) (tendsto nat real) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))) (zero_zero real))))), sequentially ) 16.44/16.48 ( bool, (filter nat), (trivial_limit nat), sequentially ) 16.44/16.48 ( bool, (filter real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (filter real) bool))) (hAPP real _let_2 (hAPP _let_0 (fun real _let_2) (tendsto real real) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin)) (zero_zero real))))), (hAPP real (filter real) (at real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.44/16.48 ( nat, nat, suc, (zero_zero nat) ) 16.44/16.48 ( nat, nat, suc, (hAPP nat nat suc (zero_zero nat)) ) 16.44/16.48 ( nat, nat, suc, (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 16.44/16.48 ( nat, nat, (fact_fact nat), (zero_zero nat) ) 16.44/16.48 ( nat, nat, (fact_fact nat), (hAPP nat nat suc (zero_zero nat)) ) 16.44/16.48 ( nat, nat, fact, (zero_zero nat) ) 16.44/16.48 ( nat, nat, (hAPP nat (fun nat nat) (plus_plus nat) (one_one nat)), (one_one nat) ) 16.44/16.48 ( nat, nat, nat_size, (zero_zero nat) ) 16.44/16.48 ( nat, nat, (size_size nat), (zero_zero nat) ) 16.44/16.48 ( nat, int, (number_number_of nat), pls ) 16.44/16.48 ( nat, int, (number_number_of nat), (hAPP int int bit1 pls) ) 16.44/16.48 ( nat, int, (number_number_of nat), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.44/16.48 ( nat, int, (number_number_of nat), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.44/16.48 ( nat, int, nat_1, (one_one int) ) 16.44/16.48 ( nat, int, nat_1, (zero_zero int) ) 16.44/16.48 ( nat, int, nat_1, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.44/16.48 ( nat, int, nat_1, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.44/16.48 ( nat, real, natfloor, (one_one real) ) 16.44/16.48 ( nat, real, natfloor, (zero_zero real) ) 16.44/16.48 ( nat, real, natceiling, (one_one real) ) 16.44/16.48 ( nat, real, natceiling, (zero_zero real) ) 16.44/16.48 ( nat, code_code_numeral, (size_size code_code_numeral), (zero_zero code_code_numeral) ) 16.44/16.48 ( nat, code_code_numeral, code_c271388182l_size, (zero_zero code_code_numeral) ) 16.44/16.48 ( int, nat, (semiring_1_of_nat int), (zero_zero nat) ) 16.44/16.48 ( int, nat, (semiring_1_of_nat int), (hAPP nat nat suc (zero_zero nat)) ) 16.44/16.48 ( int, nat, (semiring_1_of_nat int), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.44/16.48 ( int, nat, (semiring_1_of_nat int), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.44/16.48 ( int, nat, (hAPP int (fun nat int) (power_power int) s), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.44/16.48 ( int, nat, (hAPP int (fun nat int) (power_power int) s1), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.44/16.48 ( int, nat, (hAPP int (fun nat int) (power_power int) skv_14), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.44/16.48 ( int, int, bit0, pls ) 16.44/16.48 ( int, int, bit0, (hAPP int int bit1 pls) ) 16.44/16.48 ( int, int, bit0, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.44/16.48 ( int, int, bit0, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.44/16.48 ( int, int, bit0, min_1 ) 16.44/16.48 ( int, int, bit0, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.44/16.48 ( int, int, bit1, pls ) 16.44/16.48 ( int, int, bit1, (hAPP int int bit1 pls) ) 16.44/16.48 ( int, int, bit1, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.44/16.48 ( int, int, bit1, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.44/16.48 ( int, int, bit1, min_1 ) 16.44/16.48 ( int, int, bit1, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.44/16.48 ( int, int, bit1, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 16.44/16.48 ( int, int, bit1, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 16.44/16.48 ( int, int, bit1, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 16.44/16.48 ( int, int, (number_number_of int), pls ) 16.44/16.48 ( int, int, (number_number_of int), (hAPP int int bit1 pls) ) 16.44/16.48 ( int, int, (number_number_of int), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.44/16.48 ( int, int, (number_number_of int), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.44/16.48 ( int, int, (number_number_of int), min_1 ) 16.44/16.48 ( int, int, (number_number_of int), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.44/16.48 ( int, int, (fact_fact int), (one_one int) ) 16.44/16.48 ( int, int, (fact_fact int), (zero_zero int) ) 16.44/16.48 ( int, int, (uminus_uminus int), (one_one int) ) 16.44/16.48 ( int, int, (uminus_uminus int), pls ) 16.44/16.48 ( int, int, (uminus_uminus int), min_1 ) 16.44/16.48 ( int, int, pred, pls ) 16.44/16.48 ( int, int, pred, min_1 ) 16.44/16.48 ( int, int, (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))), m ) 16.44/16.48 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m))), (one_one int) ) 16.44/16.48 ( int, int, (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (one_one int) ) 16.44/16.48 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))))), t ) 16.44/16.48 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))))), skv_13 ) 16.44/16.48 ( int, int, succ, pls ) 16.44/16.48 ( int, int, succ, min_1 ) 16.44/16.48 ( int, int, (hAPP int (fun int int) legendre (hAPP int int (number_number_of int) min_1)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.44/16.48 ( int, int, (hAPP int (fun int int) (minus_minus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1) ) 16.44/16.48 ( int, (product_prod int int), twoSqu1094008024sum2sq, (let ((_let_0 (product_prod int int))) (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) s) (one_one int))) ) 16.44/16.48 ( int, quickcheck_code_int, quickcheck_int_of, (zero_zero quickcheck_code_int) ) 16.44/16.48 ( int, code_code_numeral, code_int_of, (zero_zero code_code_numeral) ) 16.44/16.48 ( (fun int bool), int, (ord_less_eq int), (one_one int) ) 16.44/16.48 ( (fun int bool), int, (ord_less_eq int), (zero_zero int) ) 16.44/16.48 ( (fun int bool), int, (ord_less_eq int), min_1 ) 16.44/16.48 ( (fun int bool), int, (ord_less int), (one_one int) ) 16.44/16.48 ( (fun int bool), int, (ord_less int), pls ) 16.44/16.48 ( (fun int bool), int, (ord_less int), min_1 ) 16.44/16.48 ( (fun int bool), int, (ord_less int), s ) 16.44/16.48 ( (fun int bool), int, (ord_less int), t ) 16.44/16.48 ( (fun int bool), int, (ord_less int), skv_4 ) 16.44/16.48 ( (fun int bool), int, (ord_less int), skv_10 ) 16.44/16.48 ( (fun int bool), int, (dvd_dvd int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.44/16.48 ( (fun int bool), int, quadRes, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.44/16.48 ( (fun int bool), int, (let ((_let_0 (fun int (fun int bool)))) (hAPP _let_0 _let_0 (combc int int bool) (fequal int))), (zero_zero int) ) 16.44/16.48 ( (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong s1), s ) 16.44/16.48 ( (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong s1), skv_4 ) 16.44/16.48 ( (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong s1), skv_10 ) 16.44/16.48 ( (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1) ) 16.44/16.48 ( (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.44/16.48 ( (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1) ) 16.44/16.48 ( (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1) ) 16.44/16.48 ( (fun int bool), (fun int bool), (collect int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun _let_2 _let_0))) (let ((_let_4 (fun int _let_3))) (hAPP _let_1 _let_0 (hAPP (fun _let_0 bool) (fun _let_1 _let_0) (combb _let_0 bool int) (fEx int)) (hAPP _let_2 _let_1 (hAPP _let_4 (fun _let_2 _let_1) (combc int _let_2 _let_0) (hAPP _let_1 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_1 _let_4) (combb _let_0 _let_3 int) (combb int bool int)) (fequal int))) (hAPP int _let_2 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))))))))) ) 16.44/16.49 ( (fun int bool), (fun int bool), (collect int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun _let_2 _let_0))) (let ((_let_5 (fun int _let_4))) (hAPP _let_1 _let_0 (hAPP (fun _let_0 bool) (fun _let_1 _let_0) (combb _let_0 bool int) (fEx int)) (hAPP _let_2 _let_1 (hAPP _let_5 (fun _let_2 _let_1) (combc int _let_2 _let_0) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_1 _let_5) (combb _let_0 _let_4 int) (combb int bool int)) (fequal int))) (hAPP int _let_2 (hAPP _let_3 _let_3 (combc int int int) (hAPP _let_2 _let_3 (hAPP _let_3 (fun _let_2 _let_3) (combb int _let_2 int) (plus_plus int)) (hAPP int _let_2 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one int)))))))))) ) 16.44/16.49 ( (fun int bool), (fun int bool), (let ((_let_0 (fun int bool))) (hAPP (fun bool bool) (fun _let_0 _let_0) (combb bool bool int) fNot)), (let ((_let_0 (fun int (fun int bool)))) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (fequal int)) (zero_zero int))) ) 16.44/16.49 ( (fun int bool), (fun int (fun int bool)), (let ((_let_0 (fun int bool))) (hAPP (fun _let_0 bool) (fun (fun int _let_0) _let_0) (combb _let_0 bool int) (fEx int))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun _let_2 _let_0))) (let ((_let_4 (fun int _let_3))) (hAPP _let_2 _let_1 (hAPP _let_4 (fun _let_2 _let_1) (combc int _let_2 _let_0) (hAPP _let_1 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_1 _let_4) (combb _let_0 _let_3 int) (combb int bool int)) (fequal int))) (hAPP int _let_2 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))))))) ) 16.44/16.49 ( (fun int bool), (fun int (fun int bool)), (let ((_let_0 (fun int bool))) (hAPP (fun _let_0 bool) (fun (fun int _let_0) _let_0) (combb _let_0 bool int) (fEx int))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun _let_2 _let_0))) (let ((_let_5 (fun int _let_4))) (hAPP _let_2 _let_1 (hAPP _let_5 (fun _let_2 _let_1) (combc int _let_2 _let_0) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_1 _let_5) (combb _let_0 _let_4 int) (combb int bool int)) (fequal int))) (hAPP int _let_2 (hAPP _let_3 _let_3 (combc int int int) (hAPP _let_2 _let_3 (hAPP _let_3 (fun _let_2 _let_3) (combb int _let_2 int) (plus_plus int)) (hAPP int _let_2 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one int))))))))) ) 16.44/16.49 ( (fun int (fun int bool)), int, zcong, s1 ) 16.44/16.49 ( (fun int (fun int bool)), int, zcong, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.44/16.49 ( (fun int (fun int bool)), int, zcong, (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.44/16.49 ( (fun int (fun int bool)), int, zcong, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.44/16.49 ( (fun int (fun int bool)), int, (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int _let_1))) (let ((_let_5 (fun _let_2 _let_1))) (hAPP _let_4 _let_4 (combc int int _let_0) (hAPP _let_4 _let_4 (hAPP (fun _let_1 _let_1) (fun _let_4 _let_4) (combb _let_1 _let_1 int) (combc int int bool)) (hAPP _let_3 _let_4 (hAPP _let_5 (fun _let_3 _let_4) (combb _let_2 _let_1 int) (hAPP _let_1 _let_5 (combb int _let_0 int) (fequal int))) int_gcd))))))))), (one_one int) ) 16.44/16.49 ( (fun int (fun int bool)), (fun int (fun int bool)), (combc int int bool), (fequal int) ) 16.44/16.49 ( (fun int (fun int bool)), (fun int (fun int bool)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun _let_0 _let_0))) (hAPP _let_4 (fun _let_1 _let_1) (combb _let_0 _let_0 int) (hAPP _let_3 _let_4 (combs int bool bool) (hAPP _let_0 _let_3 (hAPP (fun bool _let_2) (fun _let_0 _let_3) (combb bool _let_2 int) fconj) (hAPP int _let_0 (ord_less int) (zero_zero int)))))))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int _let_1))) (let ((_let_5 (fun _let_2 _let_1))) (hAPP int _let_1 (hAPP _let_4 _let_4 (combc int int _let_0) (hAPP _let_4 _let_4 (hAPP (fun _let_1 _let_1) (fun _let_4 _let_4) (combb _let_1 _let_1 int) (combc int int bool)) (hAPP _let_3 _let_4 (hAPP _let_5 (fun _let_3 _let_4) (combb _let_2 _let_1 int) (hAPP _let_1 _let_5 (combb int _let_0 int) (fequal int))) int_gcd))) (one_one int)))))))) ) 16.44/16.49 ( (fun int (fun int bool)), (fun int int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun (fun int int) _let_0))) (let ((_let_3 (fun int _let_2))) (hAPP _let_3 (fun (fun int int) _let_1) (combc int (fun int int) _let_0) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 int) (combb int bool int)) (fequal int))))))), (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.44/16.49 ( (fun int (fun int bool)), (fun int int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun (fun int int) _let_0))) (let ((_let_3 (fun int _let_2))) (hAPP _let_3 (fun (fun int int) _let_1) (combc int (fun int int) _let_0) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 int) (combb int bool int)) (fequal int))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (hAPP int _let_0 (hAPP _let_1 _let_1 (combc int int int) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)) (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one int)))) ) 16.44/16.49 ( (fun int int), nat, (hAPP (fun int (fun nat int)) (fun nat (fun int int)) (combc int nat int) (power_power int)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.44/16.49 ( (fun int int), int, (times_times int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.44/16.49 ( (fun int int), int, (times_times int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.44/16.49 ( (fun int int), int, (times_times int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.44/16.49 ( (fun int int), int, (minus_minus int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.44/16.49 ( (fun int int), int, (plus_plus int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 16.44/16.49 ( (fun int int), int, (plus_plus int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.44/16.49 ( (fun int int), int, legendre, (hAPP int int (number_number_of int) min_1) ) 16.44/16.49 ( (fun int int), int, (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (hAPP _let_1 _let_1 (combc int int int) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)) (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))))), (one_one int) ) 16.44/16.49 ( (fun nat bool), bool, (combk bool nat), fTrue ) 16.44/16.49 ( (fun nat bool), nat, (ord_less nat), (zero_zero nat) ) 16.44/16.49 ( (fun nat bool), nat, (let ((_let_0 (fun nat (fun nat bool)))) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat))), (zero_zero nat) ) 16.44/16.49 ( (fun nat bool), (fun nat bool), (collect nat), prime ) 16.44/16.49 ( (fun nat bool), (fun nat bool), (let ((_let_0 (fun nat bool))) (hAPP (fun bool bool) (fun _let_0 _let_0) (combb bool bool nat) fNot)), (let ((_let_0 (fun nat (fun nat bool)))) (hAPP nat (fun nat bool) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat)) (zero_zero nat))) ) 16.44/16.49 ( (fun nat nat), nat, (plus_plus nat), (one_one nat) ) 16.44/16.49 ( (fun nat nat), nat, (let ((_let_0 (fun nat (fun nat nat)))) (hAPP _let_0 _let_0 (combc nat nat nat) (times_times nat))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.44/16.49 ( (fun nat nat), nat, (let ((_let_0 (fun nat (fun nat nat)))) (let ((_let_1 (combc nat nat nat))) (hAPP _let_0 _let_0 _let_1 (hAPP (fun nat nat) _let_0 (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_0 _let_0 _let_1 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))), (one_one nat) ) 16.44/16.49 ( (fun (product_prod nat nat) bool), (fun (product_prod nat nat) bool), (collect (product_prod nat nat)), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat (fun nat bool)))) (hAPP _let_1 (fun (product_prod nat nat) bool) (product_prod_case nat nat bool) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat (fun nat bool) nat) (hAPP _let_1 _let_1 (combc nat nat bool) (fequal nat))) suc)))) ) 16.44/16.49 ( (fun (product_prod nat nat) bool), (fun nat (fun nat bool)), (product_prod_case nat nat bool), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat (fun nat bool)))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat (fun nat bool) nat) (hAPP _let_1 _let_1 (combc nat nat bool) (fequal nat))) suc))) ) 16.44/16.49 ( real, nat, (real_1 nat), (zero_zero nat) ) 16.44/16.49 ( real, nat, (real_1 nat), (hAPP nat nat suc (zero_zero nat)) ) 16.44/16.49 ( real, int, (real_1 int), (one_one int) ) 16.44/16.49 ( real, int, (real_1 int), (zero_zero int) ) 16.44/16.49 ( real, int, (number_number_of real), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.44/16.49 ( real, int, (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.44/16.49 ( real, int, (number_number_of real), min_1 ) 16.44/16.49 ( real, int, (number_number_of real), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.44/16.49 ( real, int, (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.44/16.49 ( real, int, (number_number_of real), (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.44/16.49 ( real, int, (number_number_of real), (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 16.44/16.49 ( real, real, ln, (one_one real) ) 16.44/16.49 ( real, real, (uminus_uminus real), (one_one real) ) 16.44/16.49 ( real, real, (uminus_uminus real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.44/16.49 ( real, real, (uminus_uminus real), (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.44/16.49 ( real, real, cos, (zero_zero real) ) 16.44/16.49 ( real, real, cos, pi ) 16.44/16.49 ( real, real, cos, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.44/16.49 ( real, real, cos, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.44/16.49 ( real, real, cos, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.44/16.49 ( real, real, cos, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.44/16.49 ( real, real, cos, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.44/16.49 ( real, real, cos, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 16.44/16.49 ( real, real, cos, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 16.44/16.49 ( real, real, cos, skv_5 ) 16.44/16.49 ( real, real, sqrt, (one_one real) ) 16.44/16.49 ( real, real, sqrt, (zero_zero real) ) 16.44/16.49 ( real, real, sqrt, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.44/16.49 ( real, real, sqrt, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.44/16.49 ( real, real, sin, (zero_zero real) ) 16.44/16.49 ( real, real, sin, pi ) 16.44/16.49 ( real, real, sin, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.44/16.49 ( real, real, sin, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.44/16.49 ( real, real, sin, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.44/16.49 ( real, real, sin, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.44/16.49 ( real, real, sin, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 16.44/16.49 ( real, real, sin, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 16.44/16.49 ( real, real, (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.44/16.49 ( real, real, (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.44/16.49 ( real, real, (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.44/16.49 ( real, real, (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.44/16.49 ( real, real, tan, (zero_zero real) ) 16.44/16.49 ( real, real, tan, pi ) 16.44/16.49 ( real, real, tan, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.44/16.49 ( real, real, tan, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.44/16.49 ( real, real, tan, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 16.44/16.49 ( real, real, (hAPP real (fun real real) (inverse_divide real) (one_one real)), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.44/16.49 ( real, real, (hAPP real (fun real real) (inverse_divide real) (one_one real)), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.44/16.49 ( real, real, (hAPP real (fun real real) (inverse_divide real) (one_one real)), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.44/16.49 ( real, real, (hAPP real (fun real real) (inverse_divide real) (one_one real)), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 16.44/16.49 ( real, real, (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 16.44/16.49 ( real, real, (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 16.44/16.49 ( real, real, (inverse_inverse real), (zero_zero real) ) 16.44/16.49 ( real, real, arctan, (one_one real) ) 16.44/16.49 ( real, real, arctan, (zero_zero real) ) 16.44/16.49 ( real, real, arctan, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.44/16.49 ( real, real, arctan, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))))) ) 16.44/16.49 ( real, real, (hAPP real (fun real real) (inverse_divide real) (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.44/16.49 ( real, real, (sgn_sgn real), (zero_zero real) ) 16.44/16.49 ( real, real, (hAPP real (fun real real) (inverse_divide real) (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.44/16.49 ( real, real, (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 16.44/16.49 ( real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real _let_0 (minus_minus real) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1))))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 16.44/16.49 ( real, real, (hAPP real (fun real real) (inverse_divide real) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.44/16.49 ( real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1))))))), pi ) 16.44/16.49 ( real, (fun real bool), (the real), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3)))))))))))))) ) 16.44/16.49 ( real, rat, ratreal, (zero_zero rat) ) 16.44/16.49 ( real, rat, ratreal, (one_one rat) ) 16.44/16.49 ( real, complex, re, (one_one complex) ) 16.44/16.49 ( real, complex, re, ii ) 16.44/16.49 ( real, complex, re, (zero_zero complex) ) 16.44/16.49 ( real, complex, im, (one_one complex) ) 16.44/16.49 ( real, complex, im, ii ) 16.44/16.49 ( real, complex, im, (zero_zero complex) ) 16.44/16.49 ( real, (fun nat real), (suminf real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat (fun nat nat)))) (let ((_let_3 (fun nat _let_0))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun _let_1 _let_3))) (let ((_let_6 (combb real _let_0 nat))) (let ((_let_7 (combc nat nat nat))) (hAPP _let_1 _let_1 (hAPP _let_3 (fun _let_1 _let_1) (combs nat real real) (hAPP _let_1 _let_3 (hAPP _let_4 _let_5 _let_6 (inverse_divide real)) (hAPP real _let_1 (hAPP _let_3 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_3 (hAPP _let_4 _let_5 _let_6 (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) (one_one real)))) (hAPP (fun nat nat) _let_1 (hAPP _let_1 (fun (fun nat nat) _let_1) (combb nat real nat) (real_1 nat)) (hAPP nat (fun nat nat) (hAPP _let_2 _let_2 _let_7 (hAPP (fun nat nat) _let_2 (hAPP _let_2 (fun (fun nat nat) _let_2) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_2 _let_2 _let_7 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))))))))))) ) 16.44/16.49 ( (fun real bool), real, (ord_less real), (one_one real) ) 16.44/16.49 ( (fun real bool), real, (ord_less real), (zero_zero real) ) 16.44/16.49 ( (fun real bool), real, (ord_less real), pi ) 16.44/16.49 ( (fun real bool), real, (ord_less real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.44/16.49 ( (fun real bool), real, (ord_less real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.44/16.49 ( (fun real bool), real, (ord_less real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.44/16.49 ( (fun real bool), real, (ord_less real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 16.44/16.49 ( (fun real bool), real, (ord_less_eq real), (zero_zero real) ) 16.44/16.49 ( (fun real bool), real, (ord_less_eq real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.44/16.49 ( (fun real bool), real, (ord_less_eq real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.44/16.49 ( (fun real bool), real, (ord_less_eq real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.44/16.49 ( (fun real bool), real, (ord_less_eq real), skv_5 ) 16.44/16.49 ( (fun real bool), real, (let ((_let_0 (fun real (fun real bool)))) (hAPP _let_0 _let_0 (combc real real bool) (ord_less_eq real))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.44/16.49 ( (fun real bool), real, (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun real _let_0))) (hAPP _let_2 _let_2 (combc real real bool) (hAPP _let_1 _let_2 (hAPP _let_2 (fun _let_1 _let_2) (combb real _let_0 real) (fequal real)) cos))))), (zero_zero real) ) 16.44/16.49 ( (fun real bool), (fun real bool), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun real _let_1))) (hAPP _let_2 (fun _let_0 _let_0) (combs real bool bool) (hAPP _let_0 _let_2 (hAPP (fun bool _let_1) (fun _let_0 _let_2) (combb bool _let_1 real) fconj) (hAPP real _let_0 (ord_less_eq real) (zero_zero real))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun real _let_0))) (let ((_let_4 (fun real _let_2))) (let ((_let_5 (combc real real bool))) (hAPP _let_0 _let_0 (hAPP _let_4 (fun _let_0 _let_0) (combs real bool bool) (hAPP _let_0 _let_4 (hAPP (fun bool _let_2) (fun _let_0 _let_4) (combb bool _let_2 real) fconj) (hAPP real _let_0 (hAPP _let_3 _let_3 _let_5 (ord_less_eq real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_3 _let_3 _let_5 (hAPP _let_1 _let_3 (hAPP _let_3 (fun _let_1 _let_3) (combb real _let_0 real) (fequal real)) cos)) (zero_zero real))))))))) ) 16.44/16.49 ( (fun real bool), (fun real bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun real (fun real bool)))) (let ((_let_2 (fun real _let_0))) (hAPP _let_2 (fun (fun real bool) (fun real bool)) (combs real bool bool) (hAPP (fun real bool) _let_2 (hAPP (fun bool _let_0) (fun (fun real bool) _let_2) (combb bool _let_0 real) fconj) (hAPP real (fun real bool) (hAPP _let_1 _let_1 (combc real real bool) (ord_less_eq real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun real _let_0))) (hAPP real _let_0 (hAPP _let_2 _let_2 (combc real real bool) (hAPP _let_1 _let_2 (hAPP _let_2 (fun _let_1 _let_2) (combb real _let_0 real) (fequal real)) cos)) (zero_zero real))))) ) 16.44/16.49 ( (fun real bool), (fun real bool), (collect real), (let ((_let_0 (fun int (fun int bool)))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real real))) (let ((_let_3 (real_1 int))) (let ((_let_4 (fun (fun int bool) bool))) (let ((_let_5 (fun bool bool))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun int _let_5))) (let ((_let_8 (fun (fun int bool) (fun int bool)))) (let ((_let_9 (fun (fun int bool) _let_7))) (let ((_let_10 (fun _let_0 (fun int bool)))) (let ((_let_11 (fEx int))) (let ((_let_12 (fun int real))) (let ((_let_13 (fun int _let_8))) (let ((_let_14 (fun (fun int bool) _let_0))) (let ((_let_15 (fun int _let_7))) (let ((_let_16 (fun _let_15 _let_13))) (let ((_let_17 (fun _let_0 _let_15))) (let ((_let_18 (fun real (fun int bool)))) (let ((_let_19 (fun real _let_0))) (let ((_let_20 (fun real _let_14))) (let ((_let_21 (fun real _let_13))) (let ((_let_22 (fun real _let_15))) (let ((_let_23 (fun int _let_12))) (let ((_let_24 (fun _let_23 _let_0))) (let ((_let_25 (fun real _let_24))) (let ((_let_26 (fun _let_12 (fun int bool)))) (let ((_let_27 (fun real _let_26))) (let ((_let_28 (fun _let_12 _let_12))) (let ((_let_29 (fun int _let_28))) (let ((_let_30 (fun int _let_2))) (hAPP _let_18 _let_1 (hAPP _let_4 (fun _let_18 _let_1) (combb (fun int bool) bool real) _let_11) (hAPP _let_19 _let_18 (hAPP _let_10 (fun _let_19 _let_18) (combb _let_0 (fun int bool) real) (hAPP _let_4 _let_10 (combb (fun int bool) bool int) _let_11)) (hAPP (fun int bool) _let_19 (hAPP _let_20 (fun (fun int bool) _let_19) (combc real (fun int bool) _let_0) (hAPP _let_21 _let_20 (hAPP (fun _let_13 _let_14) (fun _let_21 _let_20) (combb _let_13 _let_14 real) (combc int (fun int bool) (fun int bool))) (hAPP _let_22 _let_21 (hAPP _let_16 (fun _let_22 _let_21) (combb _let_15 _let_13 real) (hAPP (fun _let_7 _let_8) _let_16 (combb _let_7 _let_8 int) (combs int bool bool))) (hAPP _let_19 _let_22 (hAPP _let_17 (fun _let_19 _let_22) (combb _let_0 _let_15 real) (hAPP _let_9 _let_17 (combb (fun int bool) _let_7 int) (hAPP (fun bool _let_5) _let_9 (combb bool _let_5 int) fconj))) (hAPP _let_23 _let_19 (hAPP _let_25 (fun _let_23 _let_19) (combc real _let_23 _let_0) (hAPP _let_27 _let_25 (hAPP (fun _let_26 _let_24) (fun _let_27 _let_25) (combb _let_26 _let_24 real) (combb _let_12 (fun int bool) int)) (hAPP _let_6 _let_27 (hAPP (fun _let_1 _let_26) (fun _let_6 _let_27) (combb _let_1 _let_26 real) (combb real bool int)) (fequal real)))) (hAPP _let_12 _let_23 (hAPP _let_29 (fun _let_12 _let_23) (combc int _let_12 _let_12) (hAPP _let_30 _let_29 (hAPP (fun _let_2 _let_28) (fun _let_30 _let_29) (combb _let_2 _let_28 int) (combb real real int)) (hAPP _let_12 _let_30 (hAPP (fun real _let_2) (fun _let_12 _let_30) (combb real _let_2 int) (inverse_divide real)) _let_3))) _let_3)))))) (hAPP (fun int bool) (fun int bool) (hAPP _let_5 _let_8 (combb bool bool int) fNot) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (fequal int)) (zero_zero int))))))))))))))))))))))))))))))))))))) ) 16.44/16.49 ( (fun real bool), (fun real bool), (collect real), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real real))) (let ((_let_3 (fun nat (fun nat bool)))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun (fun nat real) (fun nat real)))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun (fun nat bool) (fun nat bool)))) (let ((_let_8 (fun int real))) (let ((_let_9 (fun nat _let_4))) (let ((_let_10 (fun (fun nat bool) _let_9))) (let ((_let_11 (fun real _let_0))) (let ((_let_12 (fun int _let_2))) (let ((_let_13 (fun real (fun int (fun nat bool))))) (let ((_let_14 (fun (fun int (fun nat bool)) _let_0))) (let ((_let_15 (fun (fun nat bool) (fun int (fun nat bool))))) (let ((_let_16 (fun real _let_15))) (let ((_let_17 (fun int _let_7))) (let ((_let_18 (fun real _let_17))) (let ((_let_19 (fun int _let_9))) (let ((_let_20 (fun real _let_19))) (let ((_let_21 (fun _let_19 _let_17))) (let ((_let_22 (fun (fun int (fun nat bool)) _let_19))) (let ((_let_23 (fun int (fun nat real)))) (let ((_let_24 (fun _let_23 (fun int (fun nat bool))))) (let ((_let_25 (fun real _let_24))) (let ((_let_26 (fun (fun nat real) (fun nat bool)))) (let ((_let_27 (fun real _let_26))) (let ((_let_28 (fun int _let_5))) (hAPP _let_11 _let_1 (hAPP (fun _let_0 bool) (fun _let_11 _let_1) (combb _let_0 bool real) (fEx int)) (hAPP _let_13 _let_11 (hAPP _let_14 (fun _let_13 _let_11) (combb (fun int (fun nat bool)) _let_0 real) (hAPP (fun (fun nat bool) bool) _let_14 (combb (fun nat bool) bool int) (fEx nat))) (hAPP (fun nat bool) _let_13 (hAPP _let_16 (fun (fun nat bool) _let_13) (combc real (fun nat bool) (fun int (fun nat bool))) (hAPP _let_18 _let_16 (hAPP (fun _let_17 _let_15) (fun _let_18 _let_16) (combb _let_17 _let_15 real) (combc int (fun nat bool) (fun nat bool))) (hAPP _let_20 _let_18 (hAPP _let_21 (fun _let_20 _let_18) (combb _let_19 _let_17 real) (hAPP (fun _let_9 _let_7) _let_21 (combb _let_9 _let_7 int) (combs nat bool bool))) (hAPP _let_13 _let_20 (hAPP _let_22 (fun _let_13 _let_20) (combb (fun int (fun nat bool)) _let_19 real) (hAPP _let_10 _let_22 (combb (fun nat bool) _let_9 int) (hAPP (fun bool _let_4) _let_10 (combb bool _let_4 nat) fconj))) (hAPP _let_23 _let_13 (hAPP _let_25 (fun _let_23 _let_13) (combc real _let_23 (fun int (fun nat bool))) (hAPP _let_27 _let_25 (hAPP (fun _let_26 _let_24) (fun _let_27 _let_25) (combb _let_26 _let_24 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_6 _let_27 (hAPP (fun _let_1 _let_26) (fun _let_6 _let_27) (combb _let_1 _let_26 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_23 (hAPP _let_28 (fun (fun nat real) _let_23) (combc int (fun nat real) (fun nat real)) (hAPP _let_12 _let_28 (hAPP (fun _let_2 _let_5) (fun _let_12 _let_28) (combb _let_2 _let_5 int) (combb real real nat)) (hAPP _let_8 _let_12 (hAPP (fun real _let_2) (fun _let_8 _let_12) (combb real _let_2 int) (inverse_divide real)) (real_1 int)))) (real_1 nat))))))) (hAPP (fun nat bool) (fun nat bool) (hAPP _let_4 _let_7 (combb bool bool nat) fNot) (hAPP nat (fun nat bool) (hAPP _let_3 _let_3 (combc nat nat bool) (fequal nat)) (zero_zero nat))))))))))))))))))))))))))))))))))) ) 16.44/16.49 ( (fun real bool), (fun nat real), (sums real), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (hAPP real _let_1 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc))) ) 16.44/16.49 ( (fun real bool), (fun real (fun int bool)), (let ((_let_0 (fun int bool))) (hAPP (fun _let_0 bool) (fun (fun real _let_0) (fun real bool)) (combb _let_0 bool real) (fEx int))), (let ((_let_0 (fun int (fun int bool)))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real real))) (let ((_let_3 (real_1 int))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun int _let_4))) (let ((_let_7 (fun (fun int bool) (fun int bool)))) (let ((_let_8 (fun (fun int bool) _let_6))) (let ((_let_9 (fun _let_0 (fun int bool)))) (let ((_let_10 (fun int real))) (let ((_let_11 (fun int _let_7))) (let ((_let_12 (fun (fun int bool) _let_0))) (let ((_let_13 (fun int _let_6))) (let ((_let_14 (fun _let_13 _let_11))) (let ((_let_15 (fun _let_0 _let_13))) (let ((_let_16 (fun real (fun int bool)))) (let ((_let_17 (fun real _let_0))) (let ((_let_18 (fun real _let_12))) (let ((_let_19 (fun real _let_11))) (let ((_let_20 (fun real _let_13))) (let ((_let_21 (fun int _let_10))) (let ((_let_22 (fun _let_21 _let_0))) (let ((_let_23 (fun real _let_22))) (let ((_let_24 (fun _let_10 (fun int bool)))) (let ((_let_25 (fun real _let_24))) (let ((_let_26 (fun _let_10 _let_10))) (let ((_let_27 (fun int _let_26))) (let ((_let_28 (fun int _let_2))) (hAPP _let_17 _let_16 (hAPP _let_9 (fun _let_17 _let_16) (combb _let_0 (fun int bool) real) (hAPP (fun (fun int bool) bool) _let_9 (combb (fun int bool) bool int) (fEx int))) (hAPP (fun int bool) _let_17 (hAPP _let_18 (fun (fun int bool) _let_17) (combc real (fun int bool) _let_0) (hAPP _let_19 _let_18 (hAPP (fun _let_11 _let_12) (fun _let_19 _let_18) (combb _let_11 _let_12 real) (combc int (fun int bool) (fun int bool))) (hAPP _let_20 _let_19 (hAPP _let_14 (fun _let_20 _let_19) (combb _let_13 _let_11 real) (hAPP (fun _let_6 _let_7) _let_14 (combb _let_6 _let_7 int) (combs int bool bool))) (hAPP _let_17 _let_20 (hAPP _let_15 (fun _let_17 _let_20) (combb _let_0 _let_13 real) (hAPP _let_8 _let_15 (combb (fun int bool) _let_6 int) (hAPP (fun bool _let_4) _let_8 (combb bool _let_4 int) fconj))) (hAPP _let_21 _let_17 (hAPP _let_23 (fun _let_21 _let_17) (combc real _let_21 _let_0) (hAPP _let_25 _let_23 (hAPP (fun _let_24 _let_22) (fun _let_25 _let_23) (combb _let_24 _let_22 real) (combb _let_10 (fun int bool) int)) (hAPP _let_5 _let_25 (hAPP (fun _let_1 _let_24) (fun _let_5 _let_25) (combb _let_1 _let_24 real) (combb real bool int)) (fequal real)))) (hAPP _let_10 _let_21 (hAPP _let_27 (fun _let_10 _let_21) (combc int _let_10 _let_10) (hAPP _let_28 _let_27 (hAPP (fun _let_2 _let_26) (fun _let_28 _let_27) (combb _let_2 _let_26 int) (combb real real int)) (hAPP _let_10 _let_28 (hAPP (fun real _let_2) (fun _let_10 _let_28) (combb real _let_2 int) (inverse_divide real)) _let_3))) _let_3)))))) (hAPP (fun int bool) (fun int bool) (hAPP _let_4 _let_7 (combb bool bool int) fNot) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (fequal int)) (zero_zero int)))))))))))))))))))))))))))))))))) ) 16.44/16.49 ( (fun real bool), (fun real (fun int bool)), (let ((_let_0 (fun int bool))) (hAPP (fun _let_0 bool) (fun (fun real _let_0) (fun real bool)) (combb _let_0 bool real) (fEx int))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real real))) (let ((_let_3 (fun nat (fun nat bool)))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun (fun nat real) (fun nat real)))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun (fun nat bool) (fun nat bool)))) (let ((_let_8 (fun int real))) (let ((_let_9 (fun nat _let_4))) (let ((_let_10 (fun (fun nat bool) _let_9))) (let ((_let_11 (fun real _let_0))) (let ((_let_12 (fun int _let_2))) (let ((_let_13 (fun real (fun int (fun nat bool))))) (let ((_let_14 (fun (fun int (fun nat bool)) _let_0))) (let ((_let_15 (fun (fun nat bool) (fun int (fun nat bool))))) (let ((_let_16 (fun real _let_15))) (let ((_let_17 (fun int _let_7))) (let ((_let_18 (fun real _let_17))) (let ((_let_19 (fun int _let_9))) (let ((_let_20 (fun real _let_19))) (let ((_let_21 (fun _let_19 _let_17))) (let ((_let_22 (fun (fun int (fun nat bool)) _let_19))) (let ((_let_23 (fun int (fun nat real)))) (let ((_let_24 (fun _let_23 (fun int (fun nat bool))))) (let ((_let_25 (fun real _let_24))) (let ((_let_26 (fun (fun nat real) (fun nat bool)))) (let ((_let_27 (fun real _let_26))) (let ((_let_28 (fun int _let_5))) (hAPP _let_13 _let_11 (hAPP _let_14 (fun _let_13 _let_11) (combb (fun int (fun nat bool)) _let_0 real) (hAPP (fun (fun nat bool) bool) _let_14 (combb (fun nat bool) bool int) (fEx nat))) (hAPP (fun nat bool) _let_13 (hAPP _let_16 (fun (fun nat bool) _let_13) (combc real (fun nat bool) (fun int (fun nat bool))) (hAPP _let_18 _let_16 (hAPP (fun _let_17 _let_15) (fun _let_18 _let_16) (combb _let_17 _let_15 real) (combc int (fun nat bool) (fun nat bool))) (hAPP _let_20 _let_18 (hAPP _let_21 (fun _let_20 _let_18) (combb _let_19 _let_17 real) (hAPP (fun _let_9 _let_7) _let_21 (combb _let_9 _let_7 int) (combs nat bool bool))) (hAPP _let_13 _let_20 (hAPP _let_22 (fun _let_13 _let_20) (combb (fun int (fun nat bool)) _let_19 real) (hAPP _let_10 _let_22 (combb (fun nat bool) _let_9 int) (hAPP (fun bool _let_4) _let_10 (combb bool _let_4 nat) fconj))) (hAPP _let_23 _let_13 (hAPP _let_25 (fun _let_23 _let_13) (combc real _let_23 (fun int (fun nat bool))) (hAPP _let_27 _let_25 (hAPP (fun _let_26 _let_24) (fun _let_27 _let_25) (combb _let_26 _let_24 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_6 _let_27 (hAPP (fun _let_1 _let_26) (fun _let_6 _let_27) (combb _let_1 _let_26 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_23 (hAPP _let_28 (fun (fun nat real) _let_23) (combc int (fun nat real) (fun nat real)) (hAPP _let_12 _let_28 (hAPP (fun _let_2 _let_5) (fun _let_12 _let_28) (combb _let_2 _let_5 int) (combb real real nat)) (hAPP _let_8 _let_12 (hAPP (fun real _let_2) (fun _let_8 _let_12) (combb real _let_2 int) (inverse_divide real)) (real_1 int)))) (real_1 nat))))))) (hAPP (fun nat bool) (fun nat bool) (hAPP _let_4 _let_7 (combb bool bool nat) fNot) (hAPP nat (fun nat bool) (hAPP _let_3 _let_3 (combc nat nat bool) (fequal nat)) (zero_zero nat)))))))))))))))))))))))))))))))))) ) 16.44/16.49 ( (fun real real), nat, root, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.44/16.49 ( (fun real real), real, (minus_minus real), (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))) ) 16.44/16.49 ( (fun real real), real, (inverse_divide real), (one_one real) ) 16.44/16.49 ( (fun real real), real, (inverse_divide real), pi ) 16.44/16.49 ( (fun real real), real, (inverse_divide real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.44/16.49 ( (fun real real), real, (inverse_divide real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.44/16.49 ( (fun real real), real, (inverse_divide real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.44/16.49 ( (fun real real), real, (times_times real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.44/16.49 ( (fun real real), real, (times_times real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.44/16.49 ( (fun real real), real, (times_times real), (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 16.44/16.49 ( (fun real real), (fun real real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)))), sin ) 16.44/16.49 ( rat, int, (hAPP int (fun int rat) fract (zero_zero int)), (one_one int) ) 16.44/16.49 ( rat, int, (hAPP int (fun int rat) fract (one_one int)), (one_one int) ) 16.44/16.49 ( rat, rat, (sgn_sgn rat), (zero_zero rat) ) 16.44/16.49 ( rat, (product_prod int int), frct, (let ((_let_0 (one_one int))) (let ((_let_1 (product_prod int int))) (hAPP int _let_1 (hAPP int (fun int _let_1) (product_Pair int int) _let_0) _let_0))) ) 16.44/16.49 ( (fun int rat), int, fract, (one_one int) ) 16.44/16.49 ( (fun int rat), int, fract, (zero_zero int) ) 16.44/16.49 ( (fun nat (fun nat bool)), (fun nat nat), (let ((_let_0 (fun nat (fun nat bool)))) (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat (fun nat bool) nat) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat)))), suc ) 16.44/16.49 ( (fun nat (fun nat bool)), (fun nat (fun nat bool)), (combc nat nat bool), (fequal nat) ) 16.44/16.49 ( (fun nat int), int, (power_power int), s ) 16.44/16.49 ( (fun nat int), int, (power_power int), s1 ) 16.44/16.49 ( (fun nat int), int, (power_power int), skv_14 ) 16.44/16.49 ( complex, nat, (hAPP complex (fun nat complex) (power_power complex) ii), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.44/16.49 ( complex, int, (number_number_of complex), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.44/16.49 ( complex, int, (number_number_of complex), min_1 ) 16.44/16.49 ( complex, real, cis, (zero_zero real) ) 16.44/16.49 ( complex, real, (hAPP real (fun real complex) complex_1 (zero_zero real)), (one_one real) ) 16.44/16.49 ( complex, real, (hAPP real (fun real complex) complex_1 (zero_zero real)), (zero_zero real) ) 16.44/16.49 ( complex, real, (of_real complex), pi ) 16.44/16.49 ( complex, real, (of_real complex), (hAPP int real (number_number_of real) min_1) ) 16.44/16.49 ( complex, real, (of_real complex), (hAPP real real (uminus_uminus real) (one_one real)) ) 16.44/16.49 ( complex, real, (hAPP real (fun real complex) complex_1 (one_one real)), (zero_zero real) ) 16.44/16.49 ( complex, complex, (inverse_inverse complex), ii ) 16.44/16.49 ( complex, complex, expi, (zero_zero complex) ) 16.44/16.49 ( complex, complex, expi, (let ((_let_0 (fun complex complex))) (let ((_let_1 (times_times complex))) (hAPP complex complex (hAPP complex _let_0 _let_1 (hAPP complex complex (hAPP complex _let_0 _let_1 (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi))) ii))) ) 16.44/16.49 ( complex, complex, (uminus_uminus complex), (one_one complex) ) 16.44/16.49 ( complex, complex, (uminus_uminus complex), ii ) 16.44/16.49 ( complex, complex, cnj, (one_one complex) ) 16.44/16.49 ( complex, complex, cnj, ii ) 16.44/16.49 ( complex, complex, cnj, (zero_zero complex) ) 16.44/16.49 ( complex, complex, (hAPP complex (fun complex complex) (times_times complex) ii), ii ) 16.44/16.49 ( complex, complex, (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real complex (of_real complex) pi) ) 16.44/16.49 ( complex, complex, (let ((_let_0 (fun complex complex))) (let ((_let_1 (times_times complex))) (hAPP complex _let_0 _let_1 (hAPP complex complex (hAPP complex _let_0 _let_1 (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi))))), ii ) 16.44/16.49 ( (fun nat real), (fun nat nat), (let ((_let_0 (fun nat real))) (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat real nat) (real_1 nat))), suc ) 16.44/16.49 ( (fun nat real), (fun nat nat), (let ((_let_0 (fun nat real))) (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat real nat) (real_1 nat))), (let ((_let_0 (fun nat (fun nat nat)))) (let ((_let_1 (combc nat nat nat))) (hAPP nat (fun nat nat) (hAPP _let_0 _let_0 _let_1 (hAPP (fun nat nat) _let_0 (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_0 _let_0 _let_1 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))) ) 16.44/16.49 ( (fun nat real), (fun nat nat), (let ((_let_0 (fun nat real))) (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat real nat) (hAPP real _let_0 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))), suc ) 16.44/16.49 ( (fun nat real), real, (power_power real), (hAPP int real (number_number_of real) min_1) ) 16.44/16.49 ( (fun nat real), real, (power_power real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.44/16.49 ( (fun nat real), real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (hAPP _let_2 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 nat) (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1))))))), (one_one real) ) 16.44/16.49 ( (fun nat real), (fun nat real), (diffs real), sin_coeff ) 16.44/16.49 ( (fun nat real), (fun nat real), (let ((_let_0 (fun nat real))) (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real))), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))) ) 16.44/16.49 ( (fun nat real), (fun nat real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (let ((_let_3 (fun real _let_0))) (let ((_let_4 (fun _let_1 _let_2))) (let ((_let_5 (combb real _let_0 nat))) (hAPP _let_2 (fun _let_1 _let_1) (combs nat real real) (hAPP _let_1 _let_2 (hAPP _let_3 _let_4 _let_5 (inverse_divide real)) (hAPP real _let_1 (hAPP _let_2 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_2 (hAPP _let_3 _let_4 _let_5 (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) (one_one real)))))))))), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat (fun nat nat)))) (let ((_let_2 (combc nat nat nat))) (hAPP (fun nat nat) _let_0 (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat real nat) (real_1 nat)) (hAPP nat (fun nat nat) (hAPP _let_1 _let_1 _let_2 (hAPP (fun nat nat) _let_1 (hAPP _let_1 (fun (fun nat nat) _let_1) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_1 _let_1 _let_2 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))))) ) 16.44/16.49 ( (fun int (fun int int)), (fun int int), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)))), (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.44/16.49 ( (fun int (fun int int)), (fun int int), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)))), (let ((_let_0 (fun int int))) (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.44/16.49 ( (fun int (fun int int)), (fun int int), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun _let_0 _let_1))) (let ((_let_3 (fun _let_0 _let_0))) (let ((_let_4 (fun int _let_3))) (hAPP _let_4 _let_2 (combc int _let_0 _let_0) (hAPP _let_1 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_1 _let_4) (combb _let_0 _let_3 int) (combb int int int)) (hAPP _let_0 _let_1 (hAPP _let_1 _let_2 (combb int _let_0 int) (plus_plus int)) (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))))))), (let ((_let_0 (fun int int))) (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.44/16.49 ( (fun int (fun int int)), (fun int (fun int int)), (combc int int int), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)) (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 16.44/16.49 ( (fun complex complex), complex, (times_times complex), ii ) 16.44/16.49 ( (fun complex complex), complex, (times_times complex), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.44/16.49 ( (fun complex complex), complex, (times_times complex), (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 16.44/16.49 ( (fun real complex), real, complex_1, (one_one real) ) 16.44/16.49 ( (fun real complex), real, complex_1, (zero_zero real) ) 16.44/16.49 ( (product_prod int int), int, (hAPP int (fun int (product_prod int int)) (product_Pair int int) (zero_zero int)), (one_one int) ) 16.44/16.49 ( (product_prod int int), int, (hAPP int (fun int (product_prod int int)) (product_Pair int int) s), (one_one int) ) 16.44/16.49 ( (product_prod int int), int, (hAPP int (fun int (product_prod int int)) (product_Pair int int) (one_one int)), (one_one int) ) 16.44/16.49 ( (product_prod int int), rat, quotient_of, (zero_zero rat) ) 16.44/16.49 ( (product_prod int int), rat, quotient_of, (one_one rat) ) 16.44/16.49 ( (fun int (product_prod int int)), int, (product_Pair int int), (one_one int) ) 16.44/16.49 ( (fun int (product_prod int int)), int, (product_Pair int int), (zero_zero int) ) 16.44/16.49 ( (fun int (product_prod int int)), int, (product_Pair int int), s ) 16.44/16.49 ( (fun (fun nat bool) bool), (fun nat int), (nat_tr1645093318rphism nat int), (semiring_1_of_nat int) ) 16.44/16.49 ( (fun (fun int bool) bool), int, (member int), (one_one int) ) 16.44/16.49 ( (fun (fun int bool) bool), (fun int nat), (nat_tr1645093318rphism int nat), nat_1 ) 16.44/16.49 ( quickcheck_code_int, int, (number_number_of quickcheck_code_int), (hAPP int int bit1 pls) ) 16.44/16.49 ( quickcheck_code_int, int, quickcheck_of_int, (one_one int) ) 16.44/16.49 ( quickcheck_code_int, int, quickcheck_of_int, (zero_zero int) ) 16.44/16.49 ( (fun nat (fun nat nat)), (fun nat nat), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat _let_0))) (hAPP _let_1 (fun _let_0 _let_1) (combb nat _let_0 nat) (plus_plus nat)))), (let ((_let_0 (fun nat (fun nat nat)))) (hAPP nat (fun nat nat) (hAPP _let_0 _let_0 (combc nat nat nat) (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.44/16.49 ( (fun nat (fun nat nat)), (fun nat (fun nat nat)), (combc nat nat nat), (times_times nat) ) 16.44/16.49 ( (fun nat (fun nat nat)), (fun nat (fun nat nat)), (combc nat nat nat), (let ((_let_0 (fun nat (fun nat nat)))) (hAPP (fun nat nat) _let_0 (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_0 _let_0 (combc nat nat nat) (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 16.44/16.49 ( (fun nat complex), complex, (power_power complex), ii ) 16.44/16.49 ( (fun nat (fun real real)), (fun nat real), (let ((_let_0 (fun real real))) (hAPP (fun real _let_0) (fun (fun nat real) (fun nat _let_0)) (combb real _let_0 nat) (inverse_divide real))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (hAPP real _let_1 (hAPP _let_2 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 nat) (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) (one_one real))))) ) 16.44/16.49 ( (fun nat (fun real real)), (fun nat real), (let ((_let_0 (fun real real))) (hAPP (fun real _let_0) (fun (fun nat real) (fun nat _let_0)) (combb real _let_0 nat) (times_times real))), (hAPP real (fun nat real) (power_power real) (hAPP int real (number_number_of real) min_1)) ) 16.44/16.49 ( (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)), (fun real real), (combb real real nat), (inverse_inverse real) ) 16.44/16.49 ( (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)), (fun nat (fun real real)), (combs nat real real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (let ((_let_3 (fun real _let_0))) (let ((_let_4 (fun _let_1 _let_2))) (let ((_let_5 (combb real _let_0 nat))) (hAPP _let_1 _let_2 (hAPP _let_3 _let_4 _let_5 (inverse_divide real)) (hAPP real _let_1 (hAPP _let_2 (fun real _let_1) (combc nat real real) (hAPP _let_1 _let_2 (hAPP _let_3 _let_4 _let_5 (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))) (one_one real))))))))) ) 16.44/16.49 ( (fun real (fun real real)), (fun real real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)))), cos ) 16.44/16.49 ( (fun (fun nat real) (fun nat (fun real real))), (fun real (fun real real)), (combb real (fun real real) nat), (inverse_divide real) ) 16.44/16.49 ( (fun (fun nat real) (fun nat (fun real real))), (fun real (fun real real)), (combb real (fun real real) nat), (times_times real) ) 16.44/16.49 ( (fun (fun nat nat) (fun nat real)), (fun nat real), (combb nat real nat), (real_1 nat) ) 16.44/16.49 ( (fun (fun nat nat) (fun nat real)), (fun nat real), (combb nat real nat), (hAPP real (fun nat real) (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.44/16.50 ( (fun (filter nat) bool), real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 (fun real (fun (filter nat) bool)) (tendsto nat real) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc))))), (zero_zero real) ) 16.44/16.50 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), (fun int int), (product_apsnd int int int), (uminus_uminus int) ) 16.44/16.50 ( (let ((_let_0 (fun int int))) (fun _let_0 (fun int _let_0))), (fun int (fun int int)), (combb int (fun int int) int), (plus_plus int) ) 16.44/16.50 ( (let ((_let_0 (fun int int))) (fun _let_0 (fun int _let_0))), (let ((_let_0 (fun int int))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun int int))) (combc int _let_0 _let_0)), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun _let_0 _let_0))) (let ((_let_3 (fun int _let_2))) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 int) (combb int int int)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)) (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))))) ) 16.44/16.50 ( code_code_numeral, int, (number_number_of code_code_numeral), pls ) 16.44/16.50 ( code_code_numeral, int, (number_number_of code_code_numeral), (hAPP int int bit1 pls) ) 16.44/16.50 ( code_code_numeral, code_code_numeral, (hAPP code_code_numeral (fun code_code_numeral code_code_numeral) (minus_minus code_code_numeral) (zero_zero code_code_numeral)), (one_one code_code_numeral) ) 16.44/16.50 ( (fun int (fun int (fun int bool))), (fun int (fun int int)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun _let_2 _let_1))) (hAPP _let_3 (fun (fun int _let_2) (fun int _let_1)) (combb _let_2 _let_1 int) (hAPP _let_1 _let_3 (combb int _let_0 int) (fequal int))))))), int_gcd ) 16.44/16.50 ( (fun int (fun int (fun int bool))), (fun int (fun int (fun int bool))), (combc int int (fun int bool)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int _let_1))) (let ((_let_5 (fun _let_2 _let_1))) (hAPP _let_4 _let_4 (hAPP (fun _let_1 _let_1) (fun _let_4 _let_4) (combb _let_1 _let_1 int) (combc int int bool)) (hAPP _let_3 _let_4 (hAPP _let_5 (fun _let_3 _let_4) (combb _let_2 _let_1 int) (hAPP _let_1 _let_5 (combb int _let_0 int) (fequal int))) int_gcd)))))))) ) 16.44/16.50 ( (fun int (fun int (fun int bool))), (fun int (fun int (fun int bool))), (let ((_let_0 (fun int (fun int bool)))) (let ((_let_1 (fun int _let_0))) (hAPP (fun _let_0 _let_0) (fun _let_1 _let_1) (combb _let_0 _let_0 int) (combc int int bool)))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int _let_1))) (let ((_let_5 (fun _let_2 _let_1))) (hAPP _let_3 _let_4 (hAPP _let_5 (fun _let_3 _let_4) (combb _let_2 _let_1 int) (hAPP _let_1 _let_5 (combb int _let_0 int) (fequal int))) int_gcd))))))) ) 16.44/16.50 ( (fun real (fun real bool)), (fun real real), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (hAPP _let_1 (fun (fun real real) _let_1) (combb real _let_0 real) (fequal real)))), cos ) 16.44/16.50 ( (fun real (fun real bool)), (fun real (fun real bool)), (combc real real bool), (ord_less_eq real) ) 16.44/16.50 ( (fun real (fun real bool)), (fun real (fun real bool)), (combc real real bool), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun real _let_0))) (hAPP _let_1 _let_2 (hAPP _let_2 (fun _let_1 _let_2) (combb real _let_0 real) (fequal real)) cos)))) ) 16.44/16.50 ( (fun real (fun nat real)), (fun nat (fun real real)), (combc nat real real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun nat _let_0))) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 nat) (times_times real)) (hAPP real _let_1 (power_power real) (hAPP int real (number_number_of real) min_1)))))) ) 16.44/16.50 ( (let ((_let_0 (fun real real))) (fun _let_0 _let_0)), (fun real (fun real real)), (combs real real real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos))) ) 16.44/16.50 ( (let ((_let_0 (fun real real))) (fun _let_0 (fun real _let_0))), (fun real (fun real real)), (combb real (fun real real) real), (inverse_divide real) ) 16.44/16.50 ( (fun (product_prod int int) bool), int, (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 _let_0))) (let ((_let_3 (fun _let_1 int))) (hAPP _let_2 (fun int (fun _let_1 bool)) (combc _let_1 int bool) (hAPP _let_3 _let_2 (hAPP (fun int _let_0) (fun _let_3 _let_2) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))))))), (zero_zero int) ) 16.44/16.50 ( (fun (product_prod int int) bool), (fun int (fun int bool)), (product_prod_case int int bool), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun int _let_1))) (let ((_let_6 (fun int _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (fun _let_2 _let_1))) (let ((_let_9 (fun _let_1 _let_1))) (hAPP _let_1 _let_1 (hAPP _let_7 _let_9 (combb _let_0 _let_0 int) (hAPP _let_6 _let_7 (combs int bool bool) (hAPP _let_0 _let_6 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 int) fconj) (hAPP int _let_0 (ord_less int) (zero_zero int))))) (hAPP int _let_1 (hAPP _let_5 _let_5 (combc int int _let_0) (hAPP _let_5 _let_5 (hAPP _let_9 (fun _let_5 _let_5) (combb _let_1 _let_1 int) (combc int int bool)) (hAPP _let_3 _let_5 (hAPP _let_8 (fun _let_3 _let_5) (combb _let_2 _let_1 int) (hAPP _let_1 _let_8 (combb int _let_0 int) (fequal int))) int_gcd))) (one_one int))))))))))))) ) 16.44/16.50 ( (fun (product_prod int int) bool), (fun (product_prod int int) bool), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 bool))) (hAPP (fun bool bool) (fun _let_1 _let_1) (combb bool bool _let_0) fNot))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun _let_1 _let_0))) (let ((_let_4 (fun _let_1 int))) (hAPP int _let_2 (hAPP _let_3 (fun int _let_2) (combc _let_1 int bool) (hAPP _let_4 _let_3 (hAPP (fun int _let_0) (fun _let_4 _let_3) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))) ) 16.44/16.50 ( (fun int (fun (product_prod int int) bool)), (fun (product_prod int int) (fun int bool)), (combc (product_prod int int) int bool), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 _let_0))) (let ((_let_3 (fun _let_1 int))) (hAPP _let_3 _let_2 (hAPP (fun int _let_0) (fun _let_3 _let_2) (combb int _let_0 _let_1) (fequal int)) (product_snd int int)))))) ) 16.44/16.50 ( (fun real (fun (filter nat) bool)), (fun nat real), (tendsto nat real), (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))) ) 16.44/16.50 ( (fun code_code_numeral code_code_numeral), code_code_numeral, (minus_minus code_code_numeral), (zero_zero code_code_numeral) ) 16.44/16.50 ( (fun int (fun bool bool)), (fun int bool), (let ((_let_0 (fun bool bool))) (hAPP (fun bool _let_0) (fun (fun int bool) (fun int _let_0)) (combb bool _let_0 int) fconj)), (hAPP int (fun int bool) (ord_less int) (zero_zero int)) ) 16.44/16.50 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), (fun bool bool), (combb bool bool int), fNot ) 16.44/16.50 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), (fun int (fun bool bool)), (combs int bool bool), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun int _let_1))) (hAPP _let_0 _let_2 (hAPP (fun bool _let_1) (fun _let_0 _let_2) (combb bool _let_1 int) fconj) (hAPP int _let_0 (ord_less int) (zero_zero int)))))) ) 16.44/16.50 ( (fun (fun int bool) (fun int (fun bool bool))), (fun bool (fun bool bool)), (combb bool (fun bool bool) int), fconj ) 16.44/16.50 ( (let ((_let_0 (fun int bool))) (fun (fun int _let_0) _let_0)), (fun (fun int bool) bool), (combb (fun int bool) bool int), (fEx int) ) 16.44/16.50 ( (fun int (fun (fun int int) (fun int bool))), (fun int (fun int bool)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun (fun int int) _let_0))) (hAPP (fun _let_0 _let_1) (fun (fun int _let_0) (fun int _let_1)) (combb _let_0 _let_1 int) (combb int bool int)))), (fequal int) ) 16.44/16.50 ( (fun (fun int int) (fun int (fun int bool))), (fun int (fun int bool)), (combb int (fun int bool) int), (fequal int) ) 16.50/16.53 ( (fun (fun int int) (fun int (fun int bool))), (fun int (fun (fun int int) (fun int bool))), (combc int (fun int int) (fun int bool)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun (fun int int) _let_0))) (let ((_let_3 (fun int _let_2))) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 int) (combb int bool int)) (fequal int)))))) ) 16.50/16.53 ( (let ((_let_0 (fun int bool))) (fun (fun int _let_0) (fun int (fun (fun int int) _let_0)))), (let ((_let_0 (fun int bool))) (fun _let_0 (fun (fun int int) _let_0))), (let ((_let_0 (fun int bool))) (combb _let_0 (fun (fun int int) _let_0) int)), (combb int bool int) ) 16.50/16.53 ( (filter real), real, (at real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.53 ( (fun (filter real) bool), real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 (fun real (fun (filter real) bool)) (tendsto real real) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin)))), (zero_zero real) ) 16.50/16.53 ( (fun real (fun (filter real) bool)), (fun real real), (tendsto real real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))) ) 16.50/16.53 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), (let ((_let_0 (product_prod int int))) (collect (product_prod _let_0 _let_0))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun _let_2 (fun _let_2 bool)))) (let ((_let_5 (fun (fun _let_2 bool) (fun _let_2 bool)))) (let ((_let_6 (fun _let_2 _let_5))) (let ((_let_7 (fun _let_4 _let_4))) (let ((_let_8 (fun _let_2 _let_3))) (let ((_let_9 (fun _let_2 _let_0))) (let ((_let_10 (fun _let_2 int))) (let ((_let_11 (fun _let_10 _let_9))) (let ((_let_12 (hAPP (fun int _let_0) _let_11 (combb int _let_0 _let_2) (fequal int)))) (let ((_let_13 (product_snd int int))) (let ((_let_14 (hAPP (fun _let_2 bool) _let_8 (hAPP (fun bool _let_3) (fun (fun _let_2 bool) _let_8) (combb bool _let_3 _let_2) fconj) (hAPP (fun _let_2 bool) (fun _let_2 bool) (hAPP _let_3 _let_5 (combb bool bool _let_2) fNot) (hAPP int (fun _let_2 bool) (hAPP _let_9 (fun int (fun _let_2 bool)) (combc _let_2 int bool) (hAPP _let_10 _let_9 _let_12 _let_13)) (zero_zero int)))))) (let ((_let_15 (fun _let_2 _let_10))) (let ((_let_16 (fun _let_10 (fun _let_2 bool)))) (let ((_let_17 (fun _let_2 _let_16))) (let ((_let_18 (fun _let_2 _let_9))) (let ((_let_19 (fun _let_10 _let_10))) (let ((_let_20 (fun _let_2 _let_19))) (let ((_let_21 (fun _let_10 _let_15))) (let ((_let_22 (fun _let_2 _let_1))) (let ((_let_23 (hAPP _let_10 _let_22 (hAPP (fun int _let_1) (fun _let_10 _let_22) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (let ((_let_24 (fun int _let_10))) (hAPP _let_4 (fun (product_prod _let_2 _let_2) bool) (product_prod_case _let_2 _let_2 bool) (hAPP _let_4 _let_4 (hAPP _let_6 _let_7 (combs _let_2 (fun _let_2 bool) (fun _let_2 bool)) (hAPP _let_8 _let_6 (hAPP (fun _let_3 _let_5) (fun _let_8 _let_6) (combb _let_3 _let_5 _let_2) (combb bool bool _let_2)) _let_14)) (hAPP _let_4 _let_4 (hAPP _let_5 _let_7 (combb (fun _let_2 bool) (fun _let_2 bool) _let_2) (hAPP _let_8 _let_5 (combs _let_2 bool bool) _let_14)) (hAPP _let_15 _let_4 (hAPP _let_17 (fun _let_15 _let_4) (combs _let_2 _let_10 (fun _let_2 bool)) (hAPP _let_18 _let_17 (hAPP (fun _let_9 _let_16) (fun _let_18 _let_17) (combb _let_9 _let_16 _let_2) (combs _let_2 int bool)) (hAPP _let_15 _let_18 (hAPP _let_11 (fun _let_15 _let_18) (combb _let_10 _let_9 _let_2) _let_12) (hAPP _let_10 _let_15 (hAPP _let_20 _let_21 (combc _let_2 _let_10 _let_10) (hAPP _let_22 _let_20 (hAPP (fun _let_1 _let_19) (fun _let_22 _let_20) (combb _let_1 _let_19 _let_2) (combb int int _let_2)) _let_23)) _let_13)))) (hAPP _let_10 _let_15 (hAPP _let_24 _let_21 (combb int _let_10 _let_2) (hAPP _let_22 _let_24 (combc _let_2 int int) _let_23)) _let_13)))))))))))))))))))))))))))))) ) 16.50/16.53 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (product_prod_case _let_0 _let_0 bool)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun _let_2 (fun _let_2 bool)))) (let ((_let_5 (fun (fun _let_2 bool) (fun _let_2 bool)))) (let ((_let_6 (fun _let_2 _let_5))) (let ((_let_7 (fun _let_4 _let_4))) (let ((_let_8 (fun _let_2 _let_3))) (let ((_let_9 (fun _let_2 _let_0))) (let ((_let_10 (fun _let_2 int))) (let ((_let_11 (fun _let_10 _let_9))) (let ((_let_12 (hAPP (fun int _let_0) _let_11 (combb int _let_0 _let_2) (fequal int)))) (let ((_let_13 (product_snd int int))) (let ((_let_14 (hAPP (fun _let_2 bool) _let_8 (hAPP (fun bool _let_3) (fun (fun _let_2 bool) _let_8) (combb bool _let_3 _let_2) fconj) (hAPP (fun _let_2 bool) (fun _let_2 bool) (hAPP _let_3 _let_5 (combb bool bool _let_2) fNot) (hAPP int (fun _let_2 bool) (hAPP _let_9 (fun int (fun _let_2 bool)) (combc _let_2 int bool) (hAPP _let_10 _let_9 _let_12 _let_13)) (zero_zero int)))))) (let ((_let_15 (fun _let_2 _let_10))) (let ((_let_16 (fun _let_10 (fun _let_2 bool)))) (let ((_let_17 (fun _let_2 _let_16))) (let ((_let_18 (fun _let_2 _let_9))) (let ((_let_19 (fun _let_10 _let_10))) (let ((_let_20 (fun _let_2 _let_19))) (let ((_let_21 (fun _let_10 _let_15))) (let ((_let_22 (fun _let_2 _let_1))) (let ((_let_23 (hAPP _let_10 _let_22 (hAPP (fun int _let_1) (fun _let_10 _let_22) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (let ((_let_24 (fun int _let_10))) (hAPP _let_4 _let_4 (hAPP _let_6 _let_7 (combs _let_2 (fun _let_2 bool) (fun _let_2 bool)) (hAPP _let_8 _let_6 (hAPP (fun _let_3 _let_5) (fun _let_8 _let_6) (combb _let_3 _let_5 _let_2) (combb bool bool _let_2)) _let_14)) (hAPP _let_4 _let_4 (hAPP _let_5 _let_7 (combb (fun _let_2 bool) (fun _let_2 bool) _let_2) (hAPP _let_8 _let_5 (combs _let_2 bool bool) _let_14)) (hAPP _let_15 _let_4 (hAPP _let_17 (fun _let_15 _let_4) (combs _let_2 _let_10 (fun _let_2 bool)) (hAPP _let_18 _let_17 (hAPP (fun _let_9 _let_16) (fun _let_18 _let_17) (combb _let_9 _let_16 _let_2) (combs _let_2 int bool)) (hAPP _let_15 _let_18 (hAPP _let_11 (fun _let_15 _let_18) (combb _let_10 _let_9 _let_2) _let_12) (hAPP _let_10 _let_15 (hAPP _let_20 _let_21 (combc _let_2 _let_10 _let_10) (hAPP _let_22 _let_20 (hAPP (fun _let_1 _let_19) (fun _let_22 _let_20) (combb _let_1 _let_19 _let_2) (combb int int _let_2)) _let_23)) _let_13)))) (hAPP _let_10 _let_15 (hAPP _let_24 _let_21 (combb int _let_10 _let_2) (hAPP _let_22 _let_24 (combc _let_2 int int) _let_23)) _let_13))))))))))))))))))))))))))))) ) 16.50/16.53 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_1 _let_3))) (let ((_let_5 (fun _let_3 _let_3))) (let ((_let_6 (fun _let_1 _let_5))) (let ((_let_7 (fun _let_1 _let_2))) (let ((_let_8 (combb bool bool _let_1))) (let ((_let_9 (fun _let_1 _let_0))) (let ((_let_10 (fun _let_1 int))) (hAPP _let_6 (fun _let_4 _let_4) (combs _let_1 _let_3 _let_3) (hAPP _let_7 _let_6 (hAPP (fun _let_2 _let_5) (fun _let_7 _let_6) (combb _let_2 _let_5 _let_1) _let_8) (hAPP _let_3 _let_7 (hAPP (fun bool _let_2) (fun _let_3 _let_7) (combb bool _let_2 _let_1) fconj) (hAPP _let_3 _let_3 (hAPP _let_2 _let_5 _let_8 fNot) (hAPP int _let_3 (hAPP _let_9 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_10 _let_9 (hAPP (fun int _let_0) (fun _let_10 _let_9) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))))))))))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun _let_2 (fun _let_2 bool)))) (let ((_let_5 (fun (fun _let_2 bool) (fun _let_2 bool)))) (let ((_let_6 (fun _let_2 _let_3))) (let ((_let_7 (fun _let_2 _let_0))) (let ((_let_8 (fun _let_2 int))) (let ((_let_9 (fun _let_8 _let_7))) (let ((_let_10 (hAPP (fun int _let_0) _let_9 (combb int _let_0 _let_2) (fequal int)))) (let ((_let_11 (product_snd int int))) (let ((_let_12 (fun _let_2 _let_8))) (let ((_let_13 (fun _let_8 (fun _let_2 bool)))) (let ((_let_14 (fun _let_2 _let_13))) (let ((_let_15 (fun _let_2 _let_7))) (let ((_let_16 (fun _let_8 _let_8))) (let ((_let_17 (fun _let_2 _let_16))) (let ((_let_18 (fun _let_8 _let_12))) (let ((_let_19 (fun _let_2 _let_1))) (let ((_let_20 (hAPP _let_8 _let_19 (hAPP (fun int _let_1) (fun _let_8 _let_19) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (let ((_let_21 (fun int _let_8))) (hAPP _let_4 _let_4 (hAPP _let_5 (fun _let_4 _let_4) (combb (fun _let_2 bool) (fun _let_2 bool) _let_2) (hAPP _let_6 _let_5 (combs _let_2 bool bool) (hAPP (fun _let_2 bool) _let_6 (hAPP (fun bool _let_3) (fun (fun _let_2 bool) _let_6) (combb bool _let_3 _let_2) fconj) (hAPP (fun _let_2 bool) (fun _let_2 bool) (hAPP _let_3 _let_5 (combb bool bool _let_2) fNot) (hAPP int (fun _let_2 bool) (hAPP _let_7 (fun int (fun _let_2 bool)) (combc _let_2 int bool) (hAPP _let_8 _let_7 _let_10 _let_11)) (zero_zero int)))))) (hAPP _let_12 _let_4 (hAPP _let_14 (fun _let_12 _let_4) (combs _let_2 _let_8 (fun _let_2 bool)) (hAPP _let_15 _let_14 (hAPP (fun _let_7 _let_13) (fun _let_15 _let_14) (combb _let_7 _let_13 _let_2) (combs _let_2 int bool)) (hAPP _let_12 _let_15 (hAPP _let_9 (fun _let_12 _let_15) (combb _let_8 _let_7 _let_2) _let_10) (hAPP _let_8 _let_12 (hAPP _let_17 _let_18 (combc _let_2 _let_8 _let_8) (hAPP _let_19 _let_17 (hAPP (fun _let_1 _let_16) (fun _let_19 _let_17) (combb _let_1 _let_16 _let_2) (combb int int _let_2)) _let_20)) _let_11)))) (hAPP _let_8 _let_12 (hAPP _let_21 _let_18 (combb int _let_8 _let_2) (hAPP _let_19 _let_21 (combc _let_2 int int) _let_20)) _let_11))))))))))))))))))))))))) ) 16.50/16.53 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_1 _let_3))) (let ((_let_5 (fun _let_3 _let_3))) (let ((_let_6 (fun _let_1 _let_2))) (let ((_let_7 (fun _let_1 _let_0))) (let ((_let_8 (fun _let_1 int))) (hAPP _let_5 (fun _let_4 _let_4) (combb _let_3 _let_3 _let_1) (hAPP _let_6 _let_5 (combs _let_1 bool bool) (hAPP _let_3 _let_6 (hAPP (fun bool _let_2) (fun _let_3 _let_6) (combb bool _let_2 _let_1) fconj) (hAPP _let_3 _let_3 (hAPP _let_2 _let_5 (combb bool bool _let_1) fNot) (hAPP int _let_3 (hAPP _let_7 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_8 _let_7 (hAPP (fun int _let_0) (fun _let_8 _let_7) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))))))))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun _let_2 (fun _let_2 bool)))) (let ((_let_4 (fun _let_2 _let_0))) (let ((_let_5 (fun _let_2 int))) (let ((_let_6 (fun _let_5 _let_4))) (let ((_let_7 (product_snd int int))) (let ((_let_8 (fun _let_2 _let_5))) (let ((_let_9 (fun _let_5 (fun _let_2 bool)))) (let ((_let_10 (fun _let_2 _let_9))) (let ((_let_11 (fun _let_2 _let_4))) (let ((_let_12 (fun _let_5 _let_5))) (let ((_let_13 (fun _let_2 _let_12))) (let ((_let_14 (fun _let_5 _let_8))) (let ((_let_15 (fun _let_2 _let_1))) (let ((_let_16 (hAPP _let_5 _let_15 (hAPP (fun int _let_1) (fun _let_5 _let_15) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (let ((_let_17 (fun int _let_5))) (hAPP _let_8 _let_3 (hAPP _let_10 (fun _let_8 _let_3) (combs _let_2 _let_5 (fun _let_2 bool)) (hAPP _let_11 _let_10 (hAPP (fun _let_4 _let_9) (fun _let_11 _let_10) (combb _let_4 _let_9 _let_2) (combs _let_2 int bool)) (hAPP _let_8 _let_11 (hAPP _let_6 (fun _let_8 _let_11) (combb _let_5 _let_4 _let_2) (hAPP (fun int _let_0) _let_6 (combb int _let_0 _let_2) (fequal int))) (hAPP _let_5 _let_8 (hAPP _let_13 _let_14 (combc _let_2 _let_5 _let_5) (hAPP _let_15 _let_13 (hAPP (fun _let_1 _let_12) (fun _let_15 _let_13) (combb _let_1 _let_12 _let_2) (combb int int _let_2)) _let_16)) _let_7)))) (hAPP _let_5 _let_8 (hAPP _let_17 _let_14 (combb int _let_5 _let_2) (hAPP _let_15 _let_17 (combc _let_2 int int) _let_16)) _let_7)))))))))))))))))))) ) 16.50/16.53 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun _let_2 _let_0))) (let ((_let_4 (fun _let_2 int))) (let ((_let_5 (fun _let_4 _let_3))) (let ((_let_6 (fun _let_2 _let_4))) (let ((_let_7 (fun _let_4 (fun _let_2 bool)))) (let ((_let_8 (fun _let_2 _let_7))) (let ((_let_9 (fun _let_2 _let_3))) (let ((_let_10 (fun _let_4 _let_4))) (let ((_let_11 (fun _let_2 _let_10))) (let ((_let_12 (fun _let_2 _let_1))) (hAPP _let_8 (fun _let_6 (fun _let_2 (fun _let_2 bool))) (combs _let_2 _let_4 (fun _let_2 bool)) (hAPP _let_9 _let_8 (hAPP (fun _let_3 _let_7) (fun _let_9 _let_8) (combb _let_3 _let_7 _let_2) (combs _let_2 int bool)) (hAPP _let_6 _let_9 (hAPP _let_5 (fun _let_6 _let_9) (combb _let_4 _let_3 _let_2) (hAPP (fun int _let_0) _let_5 (combb int _let_0 _let_2) (fequal int))) (hAPP _let_4 _let_6 (hAPP _let_11 (fun _let_4 _let_6) (combc _let_2 _let_4 _let_4) (hAPP _let_12 _let_11 (hAPP (fun _let_1 _let_10) (fun _let_12 _let_11) (combb _let_1 _let_10 _let_2) (combb int int _let_2)) (hAPP _let_4 _let_12 (hAPP (fun int _let_1) (fun _let_4 _let_12) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (product_snd int int)))))))))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_2))) (let ((_let_4 (fun _let_1 _let_0))) (let ((_let_5 (fun int _let_2))) (hAPP _let_2 _let_3 (hAPP _let_5 (fun _let_2 _let_3) (combb int _let_2 _let_1) (hAPP _let_4 _let_5 (combc _let_1 int int) (hAPP _let_2 _let_4 (hAPP (fun int _let_0) (fun _let_2 _let_4) (combb int _let_0 _let_1) (times_times int)) (product_fst int int)))) (product_snd int int)))))))) ) 16.50/16.53 ( (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)), (fun bool bool), (combb bool bool (product_prod int int)), fNot ) 16.50/16.53 ( (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)), (fun (product_prod int int) (fun bool bool)), (combs (product_prod int int) bool bool), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_1 _let_2))) (let ((_let_5 (fun _let_1 _let_0))) (let ((_let_6 (fun _let_1 int))) (hAPP _let_3 _let_4 (hAPP (fun bool _let_2) (fun _let_3 _let_4) (combb bool _let_2 _let_1) fconj) (hAPP _let_3 _let_3 (hAPP _let_2 (fun _let_3 _let_3) (combb bool bool _let_1) fNot) (hAPP int _let_3 (hAPP _let_5 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_6 _let_5 (hAPP (fun int _let_0) (fun _let_6 _let_5) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))))))) ) 16.50/16.53 ( (let ((_let_0 (fun (product_prod int int) bool))) (fun (product_prod int int) (fun _let_0 _let_0))), (fun (product_prod int int) (fun bool bool)), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun (fun _let_0 bool) (fun _let_0 bool)))) (hAPP (fun _let_1 _let_2) (fun (fun _let_0 _let_1) (fun _let_0 _let_2)) (combb _let_1 _let_2 _let_0) (combb bool bool _let_0))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_1 _let_2))) (let ((_let_5 (fun _let_1 _let_0))) (let ((_let_6 (fun _let_1 int))) (hAPP _let_3 _let_4 (hAPP (fun bool _let_2) (fun _let_3 _let_4) (combb bool _let_2 _let_1) fconj) (hAPP _let_3 _let_3 (hAPP _let_2 (fun _let_3 _let_3) (combb bool bool _let_1) fNot) (hAPP int _let_3 (hAPP _let_5 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_6 _let_5 (hAPP (fun int _let_0) (fun _let_6 _let_5) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))))))) ) 16.50/16.53 ( (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (fun _let_1 _let_1))), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 bool))) (combb _let_1 _let_1 _let_0))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_3 _let_3))) (let ((_let_5 (fun _let_1 _let_2))) (let ((_let_6 (fun _let_1 _let_0))) (let ((_let_7 (fun _let_1 int))) (hAPP _let_5 _let_4 (combs _let_1 bool bool) (hAPP _let_3 _let_5 (hAPP (fun bool _let_2) (fun _let_3 _let_5) (combb bool _let_2 _let_1) fconj) (hAPP _let_3 _let_3 (hAPP _let_2 _let_4 (combb bool bool _let_1) fNot) (hAPP int _let_3 (hAPP _let_6 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_7 _let_6 (hAPP (fun int _let_0) (fun _let_7 _let_6) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))))))))) ) 16.50/16.53 ( (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (fun _let_1 _let_1))), (let ((_let_0 (fun (product_prod int int) bool))) (fun (product_prod int int) (fun _let_0 _let_0))), (let ((_let_0 (fun (product_prod int int) bool))) (combs (product_prod int int) _let_0 _let_0)), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_3 _let_3))) (let ((_let_5 (fun _let_1 _let_4))) (let ((_let_6 (fun _let_1 _let_2))) (let ((_let_7 (combb bool bool _let_1))) (let ((_let_8 (fun _let_1 _let_0))) (let ((_let_9 (fun _let_1 int))) (hAPP _let_6 _let_5 (hAPP (fun _let_2 _let_4) (fun _let_6 _let_5) (combb _let_2 _let_4 _let_1) _let_7) (hAPP _let_3 _let_6 (hAPP (fun bool _let_2) (fun _let_3 _let_6) (combb bool _let_2 _let_1) fconj) (hAPP _let_3 _let_3 (hAPP _let_2 _let_4 _let_7 fNot) (hAPP int _let_3 (hAPP _let_8 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_9 _let_8 (hAPP (fun int _let_0) (fun _let_9 _let_8) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))))))))))) ) 16.50/16.53 ( (fun (product_prod int int) (fun bool bool)), (fun (product_prod int int) bool), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun bool bool))) (hAPP (fun bool _let_1) (fun (fun _let_0 bool) (fun _let_0 _let_1)) (combb bool _let_1 _let_0) fconj))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun _let_1 _let_0))) (let ((_let_4 (fun _let_1 int))) (hAPP _let_2 _let_2 (hAPP (fun bool bool) (fun _let_2 _let_2) (combb bool bool _let_1) fNot) (hAPP int _let_2 (hAPP _let_3 (fun int _let_2) (combc _let_1 int bool) (hAPP _let_4 _let_3 (hAPP (fun int _let_0) (fun _let_4 _let_3) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int)))))))) ) 16.50/16.53 ( (let ((_let_0 (fun (product_prod int int) bool))) (fun (fun (product_prod int int) (fun bool bool)) (fun (product_prod int int) (fun _let_0 _let_0)))), (let ((_let_0 (fun (product_prod int int) bool))) (fun (fun bool bool) (fun _let_0 _let_0))), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 bool))) (combb (fun bool bool) (fun _let_1 _let_1) _let_0))), (combb bool bool (product_prod int int)) ) 16.50/16.53 ( (let ((_let_0 (product_prod int int))) (fun (fun _let_0 bool) (fun _let_0 (fun bool bool)))), (fun bool (fun bool bool)), (combb bool (fun bool bool) (product_prod int int)), fconj ) 16.50/16.53 ( (fun (product_prod int int) (fun int bool)), (fun (product_prod int int) int), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (hAPP (fun int _let_0) (fun (fun _let_1 int) (fun _let_1 _let_0)) (combb int _let_0 _let_1) (fequal int)))), (product_snd int int) ) 16.50/16.53 ( (fun (product_prod int int) int), (fun int (fun int int)), (product_prod_case int int int), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun _let_0 _let_1))) (let ((_let_3 (fun _let_0 _let_0))) (let ((_let_4 (fun int _let_3))) (let ((_let_5 (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP _let_0 _let_1 (hAPP _let_4 _let_2 (combc int _let_0 _let_0) (hAPP _let_1 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_1 _let_4) (combb _let_0 _let_3 int) (combb int int int)) (hAPP _let_0 _let_1 (hAPP _let_1 _let_2 (combb int _let_0 int) (plus_plus int)) _let_5))) _let_5))))))) ) 16.50/16.53 ( (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 (fun int bool)))), (fun int (fun int bool)), (combb int (fun int bool) (product_prod int int)), (fequal int) ) 16.50/16.53 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (fun (product_prod int int) int), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_2 _let_2))) (let ((_let_4 (fun _let_1 _let_3))) (let ((_let_5 (fun _let_1 _let_0))) (hAPP _let_4 (fun _let_2 (fun _let_1 _let_2)) (combc _let_1 _let_2 _let_2) (hAPP _let_5 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_5 _let_4) (combb _let_0 _let_3 _let_1) (combb int int _let_1)) (hAPP _let_2 _let_5 (hAPP (fun int _let_0) (fun _let_2 _let_5) (combb int _let_0 _let_1) (times_times int)) (product_fst int int)))))))))), (product_snd int int) ) 16.50/16.53 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (fun (product_prod int int) int), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_0))) (let ((_let_4 (fun int _let_2))) (hAPP _let_4 (fun _let_2 (fun _let_1 _let_2)) (combb int _let_2 _let_1) (hAPP _let_3 _let_4 (combc _let_1 int int) (hAPP _let_2 _let_3 (hAPP (fun int _let_0) (fun _let_2 _let_3) (combb int _let_0 _let_1) (times_times int)) (product_fst int int))))))))), (product_snd int int) ) 16.50/16.53 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun (fun _let_0 int) (fun _let_0 bool)))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 (fun int bool)))), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 (fun int bool)))) (let ((_let_2 (fun (fun _let_0 int) (fun _let_0 bool)))) (hAPP (fun _let_1 _let_2) (fun (fun _let_0 _let_1) (fun _let_0 _let_2)) (combb _let_1 _let_2 _let_0) (combs _let_0 int bool))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun _let_2 _let_0))) (let ((_let_4 (fun _let_2 int))) (let ((_let_5 (fun _let_4 _let_3))) (let ((_let_6 (fun _let_2 _let_4))) (let ((_let_7 (fun _let_2 _let_3))) (let ((_let_8 (fun _let_4 _let_4))) (let ((_let_9 (fun _let_2 _let_8))) (let ((_let_10 (fun _let_2 _let_1))) (hAPP _let_6 _let_7 (hAPP _let_5 (fun _let_6 _let_7) (combb _let_4 _let_3 _let_2) (hAPP (fun int _let_0) _let_5 (combb int _let_0 _let_2) (fequal int))) (hAPP _let_4 _let_6 (hAPP _let_9 (fun _let_4 _let_6) (combc _let_2 _let_4 _let_4) (hAPP _let_10 _let_9 (hAPP (fun _let_1 _let_8) (fun _let_10 _let_9) (combb _let_1 _let_8 _let_2) (combb int int _let_2)) (hAPP _let_4 _let_10 (hAPP (fun int _let_1) (fun _let_4 _let_10) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (product_snd int int)))))))))))))) ) 16.50/16.53 ( (let ((_let_0 (product_prod int int))) (fun (fun _let_0 (fun _let_0 int)) (fun _let_0 (fun _let_0 bool)))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun (fun _let_0 int) (fun _let_0 bool)))), (let ((_let_0 (product_prod int int))) (combs _let_0 (fun _let_0 int) (fun _let_0 bool))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun _let_2 _let_0))) (let ((_let_4 (fun _let_2 int))) (let ((_let_5 (fun _let_4 _let_3))) (let ((_let_6 (fun _let_2 _let_4))) (let ((_let_7 (fun _let_4 (fun _let_2 bool)))) (let ((_let_8 (fun _let_2 _let_7))) (let ((_let_9 (fun _let_2 _let_3))) (let ((_let_10 (fun _let_4 _let_4))) (let ((_let_11 (fun _let_2 _let_10))) (let ((_let_12 (fun _let_2 _let_1))) (hAPP _let_9 _let_8 (hAPP (fun _let_3 _let_7) (fun _let_9 _let_8) (combb _let_3 _let_7 _let_2) (combs _let_2 int bool)) (hAPP _let_6 _let_9 (hAPP _let_5 (fun _let_6 _let_9) (combb _let_4 _let_3 _let_2) (hAPP (fun int _let_0) _let_5 (combb int _let_0 _let_2) (fequal int))) (hAPP _let_4 _let_6 (hAPP _let_11 (fun _let_4 _let_6) (combc _let_2 _let_4 _let_4) (hAPP _let_12 _let_11 (hAPP (fun _let_1 _let_10) (fun _let_12 _let_11) (combb _let_1 _let_10 _let_2) (combb int int _let_2)) (hAPP _let_4 _let_12 (hAPP (fun int _let_1) (fun _let_4 _let_12) (combb int _let_1 _let_2) (times_times int)) (product_fst int int)))) (product_snd int int))))))))))))))))) ) 16.50/16.53 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 (fun int bool)))), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 _let_0))) (let ((_let_3 (fun _let_1 int))) (let ((_let_4 (fun _let_3 _let_2))) (hAPP _let_4 (fun (fun _let_1 _let_3) (fun _let_1 _let_2)) (combb _let_3 _let_2 _let_1) (hAPP (fun int _let_0) _let_4 (combb int _let_0 _let_1) (fequal int)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_2))) (let ((_let_4 (fun _let_2 _let_2))) (let ((_let_5 (fun _let_1 _let_4))) (let ((_let_6 (fun _let_1 _let_0))) (hAPP _let_2 _let_3 (hAPP _let_5 (fun _let_2 _let_3) (combc _let_1 _let_2 _let_2) (hAPP _let_6 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_6 _let_5) (combb _let_0 _let_4 _let_1) (combb int int _let_1)) (hAPP _let_2 _let_6 (hAPP (fun int _let_0) (fun _let_2 _let_6) (combb int _let_0 _let_1) (times_times int)) (product_fst int int)))) (product_snd int int))))))))) ) 16.50/16.53 ( (let ((_let_0 (product_prod int int))) (fun (fun _let_0 (fun _let_0 (fun int bool))) (fun _let_0 (fun (fun _let_0 int) (fun _let_0 bool))))), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 (fun int bool)) (fun (fun _let_0 int) (fun _let_0 bool)))), (let ((_let_0 (product_prod int int))) (combb (fun _let_0 (fun int bool)) (fun (fun _let_0 int) (fun _let_0 bool)) _let_0)), (combs (product_prod int int) int bool) ) 16.50/16.53 ( (let ((_let_0 (product_prod int int))) (fun (fun _let_0 (fun _let_0 int)) (fun _let_0 (fun _let_0 (fun int bool))))), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 (fun int bool)))), (let ((_let_0 (product_prod int int))) (combb (fun _let_0 int) (fun _let_0 (fun int bool)) _let_0)), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (hAPP (fun int _let_0) (fun (fun _let_1 int) (fun _let_1 _let_0)) (combb int _let_0 _let_1) (fequal int)))) ) 16.50/16.54 ( (let ((_let_0 (fun (product_prod int int) int))) (fun (product_prod int int) (fun _let_0 _let_0))), (fun (product_prod int int) (fun int int)), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun (fun _let_1 int) (fun _let_1 int)))) (hAPP (fun _let_0 _let_2) (fun (fun _let_1 _let_0) (fun _let_1 _let_2)) (combb _let_0 _let_2 _let_1) (combb int int _let_1))))), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_0))) (hAPP _let_2 _let_3 (hAPP (fun int _let_0) (fun _let_2 _let_3) (combb int _let_0 _let_1) (times_times int)) (product_fst int int)))))) ) 16.50/16.54 ( (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 int))) (fun _let_1 (fun _let_0 _let_1)))), (let ((_let_0 (fun (product_prod int int) int))) (fun (product_prod int int) (fun _let_0 _let_0))), (let ((_let_0 (fun (product_prod int int) int))) (combc (product_prod int int) _let_0 _let_0)), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_2 _let_2))) (let ((_let_4 (fun _let_1 _let_3))) (let ((_let_5 (fun _let_1 _let_0))) (hAPP _let_5 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_5 _let_4) (combb _let_0 _let_3 _let_1) (combb int int _let_1)) (hAPP _let_2 _let_5 (hAPP (fun int _let_0) (fun _let_2 _let_5) (combb int _let_0 _let_1) (times_times int)) (product_fst int int))))))))) ) 16.50/16.54 ( (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 int))) (fun _let_1 (fun _let_0 _let_1)))), (fun int (fun (product_prod int int) int)), (let ((_let_0 (product_prod int int))) (combb int (fun _let_0 int) _let_0)), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_0))) (hAPP _let_3 (fun int _let_2) (combc _let_1 int int) (hAPP _let_2 _let_3 (hAPP (fun int _let_0) (fun _let_2 _let_3) (combb int _let_0 _let_1) (times_times int)) (product_fst int int))))))) ) 16.50/16.54 ( (fun (product_prod int int) (fun int int)), (fun (product_prod int int) int), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (hAPP (fun int _let_0) (fun (fun _let_1 int) (fun _let_1 _let_0)) (combb int _let_0 _let_1) (times_times int)))), (product_fst int int) ) 16.50/16.54 ( (let ((_let_0 (fun (product_prod int int) int))) (fun (fun (product_prod int int) (fun int int)) (fun (product_prod int int) (fun _let_0 _let_0)))), (let ((_let_0 (fun (product_prod int int) int))) (fun (fun int int) (fun _let_0 _let_0))), (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 int))) (combb (fun int int) (fun _let_1 _let_1) _let_0))), (combb int int (product_prod int int)) ) 16.50/16.54 ( (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 (fun int int)))), (fun int (fun int int)), (combb int (fun int int) (product_prod int int)), (times_times int) ) 16.50/16.54 ( (fun int (fun (product_prod int int) int)), (fun (product_prod int int) (fun int int)), (combc (product_prod int int) int int), (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 _let_0))) (hAPP _let_2 _let_3 (hAPP (fun int _let_0) (fun _let_2 _let_3) (combb int _let_0 _let_1) (times_times int)) (product_fst int int)))))) ) 16.50/16.54 ( (fun (fun nat nat) (fun nat (fun nat bool))), (fun nat (fun nat bool)), (combb nat (fun nat bool) nat), (let ((_let_0 (fun nat (fun nat bool)))) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat))) ) 16.50/16.54 ( (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)), (fun bool bool), (combb bool bool nat), fNot ) 16.50/16.54 ( (let ((_let_0 (fun nat nat))) (fun _let_0 (fun nat _let_0))), (fun nat (fun nat nat)), (combb nat (fun nat nat) nat), (plus_plus nat) ) 16.50/16.54 ( (fun real (fun bool bool)), (fun real bool), (let ((_let_0 (fun bool bool))) (hAPP (fun bool _let_0) (fun (fun real bool) (fun real _let_0)) (combb bool _let_0 real) fconj)), (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) ) 16.50/16.54 ( (fun real (fun bool bool)), (fun real bool), (let ((_let_0 (fun bool bool))) (hAPP (fun bool _let_0) (fun (fun real bool) (fun real _let_0)) (combb bool _let_0 real) fconj)), (let ((_let_0 (fun real (fun real bool)))) (hAPP real (fun real bool) (hAPP _let_0 _let_0 (combc real real bool) (ord_less_eq real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.50/16.54 ( (let ((_let_0 (fun real bool))) (fun _let_0 _let_0)), (fun real (fun bool bool)), (combs real bool bool), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun real _let_1))) (hAPP _let_0 _let_2 (hAPP (fun bool _let_1) (fun _let_0 _let_2) (combb bool _let_1 real) fconj) (hAPP real _let_0 (ord_less_eq real) (zero_zero real)))))) ) 16.50/16.54 ( (let ((_let_0 (fun real bool))) (fun _let_0 _let_0)), (fun real (fun bool bool)), (combs real bool bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun real (fun real bool)))) (let ((_let_2 (fun real _let_0))) (hAPP (fun real bool) _let_2 (hAPP (fun bool _let_0) (fun (fun real bool) _let_2) (combb bool _let_0 real) fconj) (hAPP real (fun real bool) (hAPP _let_1 _let_1 (combc real real bool) (ord_less_eq real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 16.50/16.54 ( (fun (fun real bool) (fun real (fun bool bool))), (fun bool (fun bool bool)), (combb bool (fun bool bool) real), fconj ) 16.50/16.54 ( (fun (fun real real) (fun real (fun real bool))), (fun real (fun real bool)), (combb real (fun real bool) real), (fequal real) ) 16.50/16.54 ( (fun (fun nat bool) (fun nat (fun bool bool))), (fun bool (fun bool bool)), (combb bool (fun bool bool) nat), fconj ) 16.50/16.54 ( (let ((_let_0 (fun int bool))) (fun (fun int (fun int (fun bool bool))) (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun int bool))) (fun (fun int (fun bool bool)) (fun _let_0 _let_0))), (let ((_let_0 (fun int bool))) (combb (fun int (fun bool bool)) (fun _let_0 _let_0) int)), (combs int bool bool) ) 16.50/16.54 ( (fun (fun int (fun int bool)) (fun int (fun int (fun bool bool)))), (fun (fun int bool) (fun int (fun bool bool))), (combb (fun int bool) (fun int (fun bool bool)) int), (let ((_let_0 (fun bool bool))) (hAPP (fun bool _let_0) (fun (fun int bool) (fun int _let_0)) (combb bool _let_0 int) fconj)) ) 16.50/16.54 ( (fun nat (fun int int)), (fun int (fun nat int)), (combc int nat int), (power_power int) ) 16.50/16.54 ( (fun real (fun int bool)), (fun real (fun int (fun int bool))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun _let_1 _let_0))) (hAPP _let_2 (fun (fun real _let_1) (fun real _let_0)) (combb _let_1 _let_0 real) (hAPP (fun _let_0 bool) _let_2 (combb _let_0 bool int) (fEx int)))))), (let ((_let_0 (fun int (fun int bool)))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real real))) (let ((_let_3 (real_1 int))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun int _let_4))) (let ((_let_7 (fun (fun int bool) (fun int bool)))) (let ((_let_8 (fun (fun int bool) _let_6))) (let ((_let_9 (fun int real))) (let ((_let_10 (fun int _let_7))) (let ((_let_11 (fun (fun int bool) _let_0))) (let ((_let_12 (fun int _let_6))) (let ((_let_13 (fun _let_12 _let_10))) (let ((_let_14 (fun _let_0 _let_12))) (let ((_let_15 (fun real _let_0))) (let ((_let_16 (fun real _let_11))) (let ((_let_17 (fun real _let_10))) (let ((_let_18 (fun real _let_12))) (let ((_let_19 (fun int _let_9))) (let ((_let_20 (fun _let_19 _let_0))) (let ((_let_21 (fun real _let_20))) (let ((_let_22 (fun _let_9 (fun int bool)))) (let ((_let_23 (fun real _let_22))) (let ((_let_24 (fun _let_9 _let_9))) (let ((_let_25 (fun int _let_24))) (let ((_let_26 (fun int _let_2))) (hAPP (fun int bool) _let_15 (hAPP _let_16 (fun (fun int bool) _let_15) (combc real (fun int bool) _let_0) (hAPP _let_17 _let_16 (hAPP (fun _let_10 _let_11) (fun _let_17 _let_16) (combb _let_10 _let_11 real) (combc int (fun int bool) (fun int bool))) (hAPP _let_18 _let_17 (hAPP _let_13 (fun _let_18 _let_17) (combb _let_12 _let_10 real) (hAPP (fun _let_6 _let_7) _let_13 (combb _let_6 _let_7 int) (combs int bool bool))) (hAPP _let_15 _let_18 (hAPP _let_14 (fun _let_15 _let_18) (combb _let_0 _let_12 real) (hAPP _let_8 _let_14 (combb (fun int bool) _let_6 int) (hAPP (fun bool _let_4) _let_8 (combb bool _let_4 int) fconj))) (hAPP _let_19 _let_15 (hAPP _let_21 (fun _let_19 _let_15) (combc real _let_19 _let_0) (hAPP _let_23 _let_21 (hAPP (fun _let_22 _let_20) (fun _let_23 _let_21) (combb _let_22 _let_20 real) (combb _let_9 (fun int bool) int)) (hAPP _let_5 _let_23 (hAPP (fun _let_1 _let_22) (fun _let_5 _let_23) (combb _let_1 _let_22 real) (combb real bool int)) (fequal real)))) (hAPP _let_9 _let_19 (hAPP _let_25 (fun _let_9 _let_19) (combc int _let_9 _let_9) (hAPP _let_26 _let_25 (hAPP (fun _let_2 _let_24) (fun _let_26 _let_25) (combb _let_2 _let_24 int) (combb real real int)) (hAPP _let_9 _let_26 (hAPP (fun real _let_2) (fun _let_9 _let_26) (combb real _let_2 int) (inverse_divide real)) _let_3))) _let_3)))))) (hAPP (fun int bool) (fun int bool) (hAPP _let_4 _let_7 (combb bool bool int) fNot) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (fequal int)) (zero_zero int))))))))))))))))))))))))))))))) ) 16.50/16.54 ( (fun real (fun int bool)), (fun real (fun int (fun nat bool))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun nat bool))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (fun _let_2 _let_0))) (hAPP _let_3 (fun (fun real _let_2) (fun real _let_0)) (combb _let_2 _let_0 real) (hAPP (fun _let_1 bool) _let_3 (combb _let_1 bool int) (fEx nat))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat (fun nat bool)))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun (fun nat real) (fun nat real)))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun (fun nat bool) (fun nat bool)))) (let ((_let_7 (fun int real))) (let ((_let_8 (fun nat _let_3))) (let ((_let_9 (fun (fun nat bool) _let_8))) (let ((_let_10 (fun int _let_1))) (let ((_let_11 (fun real (fun int (fun nat bool))))) (let ((_let_12 (fun (fun nat bool) (fun int (fun nat bool))))) (let ((_let_13 (fun real _let_12))) (let ((_let_14 (fun int _let_6))) (let ((_let_15 (fun real _let_14))) (let ((_let_16 (fun int _let_8))) (let ((_let_17 (fun real _let_16))) (let ((_let_18 (fun _let_16 _let_14))) (let ((_let_19 (fun (fun int (fun nat bool)) _let_16))) (let ((_let_20 (fun int (fun nat real)))) (let ((_let_21 (fun _let_20 (fun int (fun nat bool))))) (let ((_let_22 (fun real _let_21))) (let ((_let_23 (fun (fun nat real) (fun nat bool)))) (let ((_let_24 (fun real _let_23))) (let ((_let_25 (fun int _let_4))) (hAPP (fun nat bool) _let_11 (hAPP _let_13 (fun (fun nat bool) _let_11) (combc real (fun nat bool) (fun int (fun nat bool))) (hAPP _let_15 _let_13 (hAPP (fun _let_14 _let_12) (fun _let_15 _let_13) (combb _let_14 _let_12 real) (combc int (fun nat bool) (fun nat bool))) (hAPP _let_17 _let_15 (hAPP _let_18 (fun _let_17 _let_15) (combb _let_16 _let_14 real) (hAPP (fun _let_8 _let_6) _let_18 (combb _let_8 _let_6 int) (combs nat bool bool))) (hAPP _let_11 _let_17 (hAPP _let_19 (fun _let_11 _let_17) (combb (fun int (fun nat bool)) _let_16 real) (hAPP _let_9 _let_19 (combb (fun nat bool) _let_8 int) (hAPP (fun bool _let_3) _let_9 (combb bool _let_3 nat) fconj))) (hAPP _let_20 _let_11 (hAPP _let_22 (fun _let_20 _let_11) (combc real _let_20 (fun int (fun nat bool))) (hAPP _let_24 _let_22 (hAPP (fun _let_23 _let_21) (fun _let_24 _let_22) (combb _let_23 _let_21 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_5 _let_24 (hAPP (fun _let_0 _let_23) (fun _let_5 _let_24) (combb _let_0 _let_23 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_20 (hAPP _let_25 (fun (fun nat real) _let_20) (combc int (fun nat real) (fun nat real)) (hAPP _let_10 _let_25 (hAPP (fun _let_1 _let_4) (fun _let_10 _let_25) (combb _let_1 _let_4 int) (combb real real nat)) (hAPP _let_7 _let_10 (hAPP (fun real _let_1) (fun _let_7 _let_10) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat))))))) (hAPP (fun nat bool) (fun nat bool) (hAPP _let_3 _let_6 (combb bool bool nat) fNot) (hAPP nat (fun nat bool) (hAPP _let_2 _let_2 (combc nat nat bool) (fequal nat)) (zero_zero nat)))))))))))))))))))))))))))))) ) 16.50/16.54 ( (fun (fun real (fun int bool)) (fun real bool)), (fun (fun int bool) bool), (combb (fun int bool) bool real), (fEx int) ) 16.50/16.54 ( (fun real (fun int (fun int bool))), (fun int bool), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun int _let_3))) (let ((_let_6 (fun (fun int bool) (fun int bool)))) (let ((_let_7 (fun (fun int bool) _let_5))) (let ((_let_8 (fun int real))) (let ((_let_9 (fun int _let_6))) (let ((_let_10 (fun (fun int bool) (fun int (fun int bool))))) (let ((_let_11 (fun int _let_5))) (let ((_let_12 (fun _let_11 _let_9))) (let ((_let_13 (fun (fun int (fun int bool)) _let_11))) (let ((_let_14 (fun real (fun int (fun int bool))))) (let ((_let_15 (fun real _let_10))) (let ((_let_16 (fun real _let_9))) (let ((_let_17 (fun real _let_11))) (let ((_let_18 (fun int _let_8))) (let ((_let_19 (fun _let_18 (fun int (fun int bool))))) (let ((_let_20 (fun real _let_19))) (let ((_let_21 (fun _let_8 (fun int bool)))) (let ((_let_22 (fun real _let_21))) (let ((_let_23 (fun _let_8 _let_8))) (let ((_let_24 (fun int _let_23))) (let ((_let_25 (fun int _let_1))) (hAPP _let_15 (fun (fun int bool) _let_14) (combc real (fun int bool) (fun int (fun int bool))) (hAPP _let_16 _let_15 (hAPP (fun _let_9 _let_10) (fun _let_16 _let_15) (combb _let_9 _let_10 real) (combc int (fun int bool) (fun int bool))) (hAPP _let_17 _let_16 (hAPP _let_12 (fun _let_17 _let_16) (combb _let_11 _let_9 real) (hAPP (fun _let_5 _let_6) _let_12 (combb _let_5 _let_6 int) (combs int bool bool))) (hAPP _let_14 _let_17 (hAPP _let_13 (fun _let_14 _let_17) (combb (fun int (fun int bool)) _let_11 real) (hAPP _let_7 _let_13 (combb (fun int bool) _let_5 int) (hAPP (fun bool _let_3) _let_7 (combb bool _let_3 int) fconj))) (hAPP _let_18 _let_14 (hAPP _let_20 (fun _let_18 _let_14) (combc real _let_18 (fun int (fun int bool))) (hAPP _let_22 _let_20 (hAPP (fun _let_21 _let_19) (fun _let_22 _let_20) (combb _let_21 _let_19 real) (combb _let_8 (fun int bool) int)) (hAPP _let_4 _let_22 (hAPP (fun _let_0 _let_21) (fun _let_4 _let_22) (combb _let_0 _let_21 real) (combb real bool int)) (fequal real)))) (hAPP _let_8 _let_18 (hAPP _let_24 (fun _let_8 _let_18) (combc int _let_8 _let_8) (hAPP _let_25 _let_24 (hAPP (fun _let_1 _let_23) (fun _let_25 _let_24) (combb _let_1 _let_23 int) (combb real real int)) (hAPP _let_8 _let_25 (hAPP (fun real _let_1) (fun _let_8 _let_25) (combb real _let_1 int) (inverse_divide real)) _let_2))) _let_2)))))))))))))))))))))))))))))))), (let ((_let_0 (fun int (fun int bool)))) (hAPP (fun int bool) (fun int bool) (hAPP (fun bool bool) (fun (fun int bool) (fun int bool)) (combb bool bool int) fNot) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (fequal int)) (zero_zero int)))) ) 16.50/16.54 ( (fun real (fun int (fun int bool))), (fun int (fun int real)), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun int (fun int real)) (fun int (fun int bool))))) (let ((_let_3 (fun real _let_2))) (let ((_let_4 (fun (fun int real) (fun int bool)))) (let ((_let_5 (fun real _let_4))) (hAPP _let_3 (fun (fun int (fun int real)) (fun real (fun int (fun int bool)))) (combc real (fun int (fun int real)) (fun int (fun int bool))) (hAPP _let_5 _let_3 (hAPP (fun _let_4 _let_2) (fun _let_5 _let_3) (combb _let_4 _let_2 real) (combb (fun int real) (fun int bool) int)) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_1 _let_5) (combb _let_0 _let_4 real) (combb real bool int)) (fequal real)))))))))), (let ((_let_0 (fun real real))) (let ((_let_1 (real_1 int))) (let ((_let_2 (fun int real))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun _let_2 _let_2))) (let ((_let_5 (fun int _let_4))) (let ((_let_6 (fun int _let_0))) (hAPP _let_2 _let_3 (hAPP _let_5 (fun _let_2 _let_3) (combc int _let_2 _let_2) (hAPP _let_6 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_6 _let_5) (combb _let_0 _let_4 int) (combb real real int)) (hAPP _let_2 _let_6 (hAPP (fun real _let_0) (fun _let_2 _let_6) (combb real _let_0 int) (inverse_divide real)) _let_1))) _let_1)))))))) ) 16.50/16.54 ( (let ((_let_0 (fun int bool))) (fun (fun real (fun int _let_0)) (fun real _let_0))), (let ((_let_0 (fun int bool))) (fun (fun int _let_0) _let_0)), (let ((_let_0 (fun int bool))) (combb (fun int _let_0) _let_0 real)), (let ((_let_0 (fun int bool))) (hAPP (fun _let_0 bool) (fun (fun int _let_0) _let_0) (combb _let_0 bool int) (fEx int))) ) 16.50/16.54 ( (let ((_let_0 (fun int bool))) (fun real (fun _let_0 (fun int _let_0)))), (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int (fun _let_0 _let_0)))) (let ((_let_2 (fun _let_0 (fun int _let_0)))) (hAPP (fun _let_1 _let_2) (fun (fun real _let_1) (fun real _let_2)) (combb _let_1 _let_2 real) (combc int _let_0 _let_0))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun int _let_3))) (let ((_let_6 (fun (fun int bool) (fun int bool)))) (let ((_let_7 (fun (fun int bool) _let_5))) (let ((_let_8 (fun int real))) (let ((_let_9 (fun int _let_6))) (let ((_let_10 (fun int _let_5))) (let ((_let_11 (fun _let_10 _let_9))) (let ((_let_12 (fun (fun int (fun int bool)) _let_10))) (let ((_let_13 (fun real (fun int (fun int bool))))) (let ((_let_14 (fun real _let_9))) (let ((_let_15 (fun real _let_10))) (let ((_let_16 (fun int _let_8))) (let ((_let_17 (fun _let_16 (fun int (fun int bool))))) (let ((_let_18 (fun real _let_17))) (let ((_let_19 (fun _let_8 (fun int bool)))) (let ((_let_20 (fun real _let_19))) (let ((_let_21 (fun _let_8 _let_8))) (let ((_let_22 (fun int _let_21))) (let ((_let_23 (fun int _let_1))) (hAPP _let_15 _let_14 (hAPP _let_11 (fun _let_15 _let_14) (combb _let_10 _let_9 real) (hAPP (fun _let_5 _let_6) _let_11 (combb _let_5 _let_6 int) (combs int bool bool))) (hAPP _let_13 _let_15 (hAPP _let_12 (fun _let_13 _let_15) (combb (fun int (fun int bool)) _let_10 real) (hAPP _let_7 _let_12 (combb (fun int bool) _let_5 int) (hAPP (fun bool _let_3) _let_7 (combb bool _let_3 int) fconj))) (hAPP _let_16 _let_13 (hAPP _let_18 (fun _let_16 _let_13) (combc real _let_16 (fun int (fun int bool))) (hAPP _let_20 _let_18 (hAPP (fun _let_19 _let_17) (fun _let_20 _let_18) (combb _let_19 _let_17 real) (combb _let_8 (fun int bool) int)) (hAPP _let_4 _let_20 (hAPP (fun _let_0 _let_19) (fun _let_4 _let_20) (combb _let_0 _let_19 real) (combb real bool int)) (fequal real)))) (hAPP _let_8 _let_16 (hAPP _let_22 (fun _let_8 _let_16) (combc int _let_8 _let_8) (hAPP _let_23 _let_22 (hAPP (fun _let_1 _let_21) (fun _let_23 _let_22) (combb _let_1 _let_21 int) (combb real real int)) (hAPP _let_8 _let_23 (hAPP (fun real _let_1) (fun _let_8 _let_23) (combb real _let_1 int) (inverse_divide real)) _let_2))) _let_2)))))))))))))))))))))))))))) ) 16.50/16.54 ( (let ((_let_0 (fun int bool))) (fun _let_0 (fun real (fun int _let_0)))), (let ((_let_0 (fun int bool))) (fun real (fun _let_0 (fun int _let_0)))), (let ((_let_0 (fun int bool))) (combc real _let_0 (fun int _let_0))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun int _let_3))) (let ((_let_6 (fun (fun int bool) (fun int bool)))) (let ((_let_7 (fun (fun int bool) _let_5))) (let ((_let_8 (fun int real))) (let ((_let_9 (fun int _let_6))) (let ((_let_10 (fun (fun int bool) (fun int (fun int bool))))) (let ((_let_11 (fun int _let_5))) (let ((_let_12 (fun _let_11 _let_9))) (let ((_let_13 (fun (fun int (fun int bool)) _let_11))) (let ((_let_14 (fun real (fun int (fun int bool))))) (let ((_let_15 (fun real _let_10))) (let ((_let_16 (fun real _let_9))) (let ((_let_17 (fun real _let_11))) (let ((_let_18 (fun int _let_8))) (let ((_let_19 (fun _let_18 (fun int (fun int bool))))) (let ((_let_20 (fun real _let_19))) (let ((_let_21 (fun _let_8 (fun int bool)))) (let ((_let_22 (fun real _let_21))) (let ((_let_23 (fun _let_8 _let_8))) (let ((_let_24 (fun int _let_23))) (let ((_let_25 (fun int _let_1))) (hAPP _let_16 _let_15 (hAPP (fun _let_9 _let_10) (fun _let_16 _let_15) (combb _let_9 _let_10 real) (combc int (fun int bool) (fun int bool))) (hAPP _let_17 _let_16 (hAPP _let_12 (fun _let_17 _let_16) (combb _let_11 _let_9 real) (hAPP (fun _let_5 _let_6) _let_12 (combb _let_5 _let_6 int) (combs int bool bool))) (hAPP _let_14 _let_17 (hAPP _let_13 (fun _let_14 _let_17) (combb (fun int (fun int bool)) _let_11 real) (hAPP _let_7 _let_13 (combb (fun int bool) _let_5 int) (hAPP (fun bool _let_3) _let_7 (combb bool _let_3 int) fconj))) (hAPP _let_18 _let_14 (hAPP _let_20 (fun _let_18 _let_14) (combc real _let_18 (fun int (fun int bool))) (hAPP _let_22 _let_20 (hAPP (fun _let_21 _let_19) (fun _let_22 _let_20) (combb _let_21 _let_19 real) (combb _let_8 (fun int bool) int)) (hAPP _let_4 _let_22 (hAPP (fun _let_0 _let_21) (fun _let_4 _let_22) (combb _let_0 _let_21 real) (combb real bool int)) (fequal real)))) (hAPP _let_8 _let_18 (hAPP _let_24 (fun _let_8 _let_18) (combc int _let_8 _let_8) (hAPP _let_25 _let_24 (hAPP (fun _let_1 _let_23) (fun _let_25 _let_24) (combb _let_1 _let_23 int) (combb real real int)) (hAPP _let_8 _let_25 (hAPP (fun real _let_1) (fun _let_8 _let_25) (combb real _let_1 int) (inverse_divide real)) _let_2))) _let_2))))))))))))))))))))))))))))))) ) 16.50/16.54 ( (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))), (fun real (fun int (fun int (fun bool bool)))), (let ((_let_0 (fun int (fun bool bool)))) (let ((_let_1 (fun (fun int bool) (fun int bool)))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (fun int _let_0))) (let ((_let_4 (fun _let_3 _let_2))) (hAPP _let_4 (fun (fun real _let_3) (fun real _let_2)) (combb _let_3 _let_2 real) (hAPP (fun _let_0 _let_1) _let_4 (combb _let_0 _let_1 int) (combs int bool bool)))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun int _let_3))) (let ((_let_6 (fun (fun int bool) _let_5))) (let ((_let_7 (fun int real))) (let ((_let_8 (fun int _let_5))) (let ((_let_9 (fun (fun int (fun int bool)) _let_8))) (let ((_let_10 (fun real (fun int (fun int bool))))) (let ((_let_11 (fun real _let_8))) (let ((_let_12 (fun int _let_7))) (let ((_let_13 (fun _let_12 (fun int (fun int bool))))) (let ((_let_14 (fun real _let_13))) (let ((_let_15 (fun _let_7 (fun int bool)))) (let ((_let_16 (fun real _let_15))) (let ((_let_17 (fun _let_7 _let_7))) (let ((_let_18 (fun int _let_17))) (let ((_let_19 (fun int _let_1))) (hAPP _let_10 _let_11 (hAPP _let_9 (fun _let_10 _let_11) (combb (fun int (fun int bool)) _let_8 real) (hAPP _let_6 _let_9 (combb (fun int bool) _let_5 int) (hAPP (fun bool _let_3) _let_6 (combb bool _let_3 int) fconj))) (hAPP _let_12 _let_10 (hAPP _let_14 (fun _let_12 _let_10) (combc real _let_12 (fun int (fun int bool))) (hAPP _let_16 _let_14 (hAPP (fun _let_15 _let_13) (fun _let_16 _let_14) (combb _let_15 _let_13 real) (combb _let_7 (fun int bool) int)) (hAPP _let_4 _let_16 (hAPP (fun _let_0 _let_15) (fun _let_4 _let_16) (combb _let_0 _let_15 real) (combb real bool int)) (fequal real)))) (hAPP _let_7 _let_12 (hAPP _let_18 (fun _let_7 _let_12) (combc int _let_7 _let_7) (hAPP _let_19 _let_18 (hAPP (fun _let_1 _let_17) (fun _let_19 _let_18) (combb _let_1 _let_17 int) (combb real real int)) (hAPP _let_7 _let_19 (hAPP (fun real _let_1) (fun _let_7 _let_19) (combb real _let_1 int) (inverse_divide real)) _let_2))) _let_2))))))))))))))))))))))) ) 16.50/16.54 ( (let ((_let_0 (fun int bool))) (fun (fun real (fun int (fun _let_0 _let_0))) (fun real (fun _let_0 (fun int _let_0))))), (let ((_let_0 (fun int bool))) (fun (fun int (fun _let_0 _let_0)) (fun _let_0 (fun int _let_0)))), (let ((_let_0 (fun int bool))) (combb (fun int (fun _let_0 _let_0)) (fun _let_0 (fun int _let_0)) real)), (let ((_let_0 (fun int bool))) (combc int _let_0 _let_0)) ) 16.50/16.54 ( (fun real (fun int (fun int (fun bool bool)))), (fun real (fun int (fun int bool))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun _let_0 _let_3))) (let ((_let_5 (fun int _let_3))) (let ((_let_6 (fun _let_1 _let_5))) (hAPP _let_6 (fun (fun real _let_1) (fun real _let_5)) (combb _let_1 _let_5 real) (hAPP _let_4 _let_6 (combb _let_0 _let_3 int) (hAPP (fun bool _let_2) _let_4 (combb bool _let_2 int) fconj)))))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (real_1 int))) (let ((_let_3 (fun real _let_0))) (let ((_let_4 (fun int real))) (let ((_let_5 (fun real (fun int (fun int bool))))) (let ((_let_6 (fun int _let_4))) (let ((_let_7 (fun _let_6 (fun int (fun int bool))))) (let ((_let_8 (fun real _let_7))) (let ((_let_9 (fun _let_4 (fun int bool)))) (let ((_let_10 (fun real _let_9))) (let ((_let_11 (fun _let_4 _let_4))) (let ((_let_12 (fun int _let_11))) (let ((_let_13 (fun int _let_1))) (hAPP _let_6 _let_5 (hAPP _let_8 (fun _let_6 _let_5) (combc real _let_6 (fun int (fun int bool))) (hAPP _let_10 _let_8 (hAPP (fun _let_9 _let_7) (fun _let_10 _let_8) (combb _let_9 _let_7 real) (combb _let_4 (fun int bool) int)) (hAPP _let_3 _let_10 (hAPP (fun _let_0 _let_9) (fun _let_3 _let_10) (combb _let_0 _let_9 real) (combb real bool int)) (fequal real)))) (hAPP _let_4 _let_6 (hAPP _let_12 (fun _let_4 _let_6) (combc int _let_4 _let_4) (hAPP _let_13 _let_12 (hAPP (fun _let_1 _let_11) (fun _let_13 _let_12) (combb _let_1 _let_11 int) (combb real real int)) (hAPP _let_4 _let_13 (hAPP (fun real _let_1) (fun _let_4 _let_13) (combb real _let_1 int) (inverse_divide real)) _let_2))) _let_2)))))))))))))))) ) 16.50/16.54 ( (let ((_let_0 (fun int bool))) (fun (fun real (fun int (fun int (fun bool bool)))) (fun real (fun int (fun _let_0 _let_0))))), (let ((_let_0 (fun int bool))) (fun (fun int (fun int (fun bool bool))) (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun int bool))) (combb (fun int (fun int (fun bool bool))) (fun int (fun _let_0 _let_0)) real)), (let ((_let_0 (fun int (fun bool bool)))) (let ((_let_1 (fun (fun int bool) (fun int bool)))) (hAPP (fun _let_0 _let_1) (fun (fun int _let_0) (fun int _let_1)) (combb _let_0 _let_1 int) (combs int bool bool)))) ) 16.50/16.54 ( (fun (fun real (fun int (fun int bool))) (fun real (fun int (fun int (fun bool bool))))), (fun (fun int (fun int bool)) (fun int (fun int (fun bool bool)))), (combb (fun int (fun int bool)) (fun int (fun int (fun bool bool))) real), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (fun _let_0 _let_2))) (hAPP _let_3 (fun (fun int _let_0) (fun int _let_2)) (combb _let_0 _let_2 int) (hAPP (fun bool _let_1) _let_3 (combb bool _let_1 int) fconj)))))) ) 16.50/16.54 ( (fun int (fun int real)), (fun int real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun int real))) (let ((_let_2 (fun _let_1 _let_1))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int _let_0))) (hAPP _let_3 (fun _let_1 (fun int _let_1)) (combc int _let_1 _let_1) (hAPP _let_4 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_4 _let_3) (combb _let_0 _let_2 int) (combb real real int)) (hAPP _let_1 _let_4 (hAPP (fun real _let_0) (fun _let_1 _let_4) (combb real _let_0 int) (inverse_divide real)) (real_1 int))))))))), (real_1 int) ) 16.50/16.54 ( (fun real (fun (fun int (fun int real)) (fun int (fun int bool)))), (fun real (fun (fun int real) (fun int bool))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int real))) (let ((_let_2 (fun (fun int _let_1) (fun int _let_0)))) (let ((_let_3 (fun _let_1 _let_0))) (hAPP (fun _let_3 _let_2) (fun (fun real _let_3) (fun real _let_2)) (combb _let_3 _let_2 real) (combb _let_1 _let_0 int)))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun int real) (fun int bool)))) (let ((_let_3 (fun real _let_2))) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 real) (combb real bool int)) (fequal real)))))) ) 16.50/16.54 ( (fun (fun int (fun int real)) (fun real (fun int (fun int bool)))), (fun real (fun (fun int (fun int real)) (fun int (fun int bool)))), (combc real (fun int (fun int real)) (fun int (fun int bool))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun int (fun int real)) (fun int (fun int bool))))) (let ((_let_3 (fun real _let_2))) (let ((_let_4 (fun (fun int real) (fun int bool)))) (let ((_let_5 (fun real _let_4))) (hAPP _let_5 _let_3 (hAPP (fun _let_4 _let_2) (fun _let_5 _let_3) (combb _let_4 _let_2 real) (combb (fun int real) (fun int bool) int)) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_1 _let_5) (combb _let_0 _let_4 real) (combb real bool int)) (fequal real))))))))) ) 16.50/16.54 ( (fun real (fun (fun int real) (fun int bool))), (fun real (fun real bool)), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun (fun int real) (fun int bool)))) (hAPP (fun _let_0 _let_1) (fun (fun real _let_0) (fun real _let_1)) (combb _let_0 _let_1 real) (combb real bool int)))), (fequal real) ) 16.50/16.54 ( (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int real))) (fun (fun real (fun _let_1 _let_0)) (fun real (fun (fun int _let_1) (fun int _let_0)))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int real))) (fun (fun _let_1 _let_0) (fun (fun int _let_1) (fun int _let_0))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int real))) (combb (fun _let_1 _let_0) (fun (fun int _let_1) (fun int _let_0)) real))), (combb (fun int real) (fun int bool) int) ) 16.50/16.54 ( (fun (fun real (fun real bool)) (fun real (fun (fun int real) (fun int bool)))), (fun (fun real bool) (fun (fun int real) (fun int bool))), (combb (fun real bool) (fun (fun int real) (fun int bool)) real), (combb real bool int) ) 16.50/16.54 ( (let ((_let_0 (fun int real))) (fun int (fun _let_0 _let_0))), (fun int (fun real real)), (let ((_let_0 (fun real real))) (let ((_let_1 (fun (fun int real) (fun int real)))) (hAPP (fun _let_0 _let_1) (fun (fun int _let_0) (fun int _let_1)) (combb _let_0 _let_1 int) (combb real real int)))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun int real))) (let ((_let_2 (fun int _let_0))) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 int) (inverse_divide real)) (real_1 int))))) ) 16.50/16.54 ( (let ((_let_0 (fun int real))) (fun _let_0 (fun int _let_0))), (let ((_let_0 (fun int real))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun int real))) (combc int _let_0 _let_0)), (let ((_let_0 (fun real real))) (let ((_let_1 (fun int real))) (let ((_let_2 (fun _let_1 _let_1))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int _let_0))) (hAPP _let_4 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_4 _let_3) (combb _let_0 _let_2 int) (combb real real int)) (hAPP _let_1 _let_4 (hAPP (fun real _let_0) (fun _let_1 _let_4) (combb real _let_0 int) (inverse_divide real)) (real_1 int)))))))) ) 16.50/16.54 ( (fun int (fun real real)), (fun int real), (let ((_let_0 (fun real real))) (hAPP (fun real _let_0) (fun (fun int real) (fun int _let_0)) (combb real _let_0 int) (inverse_divide real))), (real_1 int) ) 16.50/16.54 ( (let ((_let_0 (fun int real))) (fun (fun int (fun real real)) (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun int real))) (fun (fun real real) (fun _let_0 _let_0))), (let ((_let_0 (fun int real))) (combb (fun real real) (fun _let_0 _let_0) int)), (combb real real int) ) 16.50/16.54 ( (fun (fun int real) (fun int (fun real real))), (fun real (fun real real)), (combb real (fun real real) int), (inverse_divide real) ) 16.50/16.54 ( (let ((_let_0 (fun int (fun int bool)))) (fun _let_0 _let_0)), (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), (let ((_let_0 (fun int bool))) (combb _let_0 _let_0 int)), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun int _let_1))) (hAPP _let_2 (fun _let_0 _let_0) (combs int bool bool) (hAPP _let_0 _let_2 (hAPP (fun bool _let_1) (fun _let_0 _let_2) (combb bool _let_1 int) fconj) (hAPP int _let_0 (ord_less int) (zero_zero int))))))) ) 16.50/16.54 ( (fun real (fun int (fun nat bool))), (fun nat bool), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun (fun nat real) (fun nat real)))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun (fun nat bool) (fun nat bool)))) (let ((_let_6 (fun int real))) (let ((_let_7 (fun nat _let_2))) (let ((_let_8 (fun (fun nat bool) _let_7))) (let ((_let_9 (fun int _let_1))) (let ((_let_10 (fun real (fun int (fun nat bool))))) (let ((_let_11 (fun (fun nat bool) (fun int (fun nat bool))))) (let ((_let_12 (fun real _let_11))) (let ((_let_13 (fun int _let_5))) (let ((_let_14 (fun real _let_13))) (let ((_let_15 (fun int _let_7))) (let ((_let_16 (fun real _let_15))) (let ((_let_17 (fun _let_15 _let_13))) (let ((_let_18 (fun (fun int (fun nat bool)) _let_15))) (let ((_let_19 (fun int (fun nat real)))) (let ((_let_20 (fun _let_19 (fun int (fun nat bool))))) (let ((_let_21 (fun real _let_20))) (let ((_let_22 (fun (fun nat real) (fun nat bool)))) (let ((_let_23 (fun real _let_22))) (let ((_let_24 (fun int _let_3))) (hAPP _let_12 (fun (fun nat bool) _let_10) (combc real (fun nat bool) (fun int (fun nat bool))) (hAPP _let_14 _let_12 (hAPP (fun _let_13 _let_11) (fun _let_14 _let_12) (combb _let_13 _let_11 real) (combc int (fun nat bool) (fun nat bool))) (hAPP _let_16 _let_14 (hAPP _let_17 (fun _let_16 _let_14) (combb _let_15 _let_13 real) (hAPP (fun _let_7 _let_5) _let_17 (combb _let_7 _let_5 int) (combs nat bool bool))) (hAPP _let_10 _let_16 (hAPP _let_18 (fun _let_10 _let_16) (combb (fun int (fun nat bool)) _let_15 real) (hAPP _let_8 _let_18 (combb (fun nat bool) _let_7 int) (hAPP (fun bool _let_2) _let_8 (combb bool _let_2 nat) fconj))) (hAPP _let_19 _let_10 (hAPP _let_21 (fun _let_19 _let_10) (combc real _let_19 (fun int (fun nat bool))) (hAPP _let_23 _let_21 (hAPP (fun _let_22 _let_20) (fun _let_23 _let_21) (combb _let_22 _let_20 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_4 _let_23 (hAPP (fun _let_0 _let_22) (fun _let_4 _let_23) (combb _let_0 _let_22 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_19 (hAPP _let_24 (fun (fun nat real) _let_19) (combc int (fun nat real) (fun nat real)) (hAPP _let_9 _let_24 (hAPP (fun _let_1 _let_3) (fun _let_9 _let_24) (combb _let_1 _let_3 int) (combb real real nat)) (hAPP _let_6 _let_9 (hAPP (fun real _let_1) (fun _let_6 _let_9) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat)))))))))))))))))))))))))))))))), (let ((_let_0 (fun nat (fun nat bool)))) (hAPP (fun nat bool) (fun nat bool) (hAPP (fun bool bool) (fun (fun nat bool) (fun nat bool)) (combb bool bool nat) fNot) (hAPP nat (fun nat bool) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat)) (zero_zero nat)))) ) 16.50/16.54 ( (fun real (fun int (fun nat bool))), (fun int (fun nat real)), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun int (fun nat real)) (fun int (fun nat bool))))) (let ((_let_3 (fun real _let_2))) (let ((_let_4 (fun (fun nat real) (fun nat bool)))) (let ((_let_5 (fun real _let_4))) (hAPP _let_3 (fun (fun int (fun nat real)) (fun real (fun int (fun nat bool)))) (combc real (fun int (fun nat real)) (fun int (fun nat bool))) (hAPP _let_5 _let_3 (hAPP (fun _let_4 _let_2) (fun _let_5 _let_3) (combb _let_4 _let_2 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_1 _let_5) (combb _let_0 _let_4 real) (combb real bool nat)) (fequal real)))))))))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun (fun nat real) (fun nat real)))) (let ((_let_2 (fun int real))) (let ((_let_3 (fun int _let_0))) (let ((_let_4 (fun int (fun nat real)))) (let ((_let_5 (fun int _let_1))) (hAPP (fun nat real) _let_4 (hAPP _let_5 (fun (fun nat real) _let_4) (combc int (fun nat real) (fun nat real)) (hAPP _let_3 _let_5 (hAPP (fun _let_0 _let_1) (fun _let_3 _let_5) (combb _let_0 _let_1 int) (combb real real nat)) (hAPP _let_2 _let_3 (hAPP (fun real _let_0) (fun _let_2 _let_3) (combb real _let_0 int) (inverse_divide real)) (real_1 int)))) (real_1 nat)))))))) ) 16.50/16.54 ( (fun (fun int (fun nat bool)) (fun int bool)), (fun (fun nat bool) bool), (combb (fun nat bool) bool int), (fEx nat) ) 16.50/16.54 ( (fun (fun real (fun int (fun nat bool))) (fun real (fun int bool))), (fun (fun int (fun nat bool)) (fun int bool)), (combb (fun int (fun nat bool)) (fun int bool) real), (let ((_let_0 (fun nat bool))) (hAPP (fun _let_0 bool) (fun (fun int _let_0) (fun int bool)) (combb _let_0 bool int) (fEx nat))) ) 16.50/16.54 ( (let ((_let_0 (fun nat bool))) (fun real (fun _let_0 (fun int _let_0)))), (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun _let_0 (fun int _let_0)))) (let ((_let_2 (fun int (fun _let_0 _let_0)))) (hAPP (fun _let_2 _let_1) (fun (fun real _let_2) (fun real _let_1)) (combb _let_2 _let_1 real) (combc int _let_0 _let_0))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun (fun nat real) (fun nat real)))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun (fun nat bool) (fun nat bool)))) (let ((_let_6 (fun int real))) (let ((_let_7 (fun nat _let_2))) (let ((_let_8 (fun (fun nat bool) _let_7))) (let ((_let_9 (fun int _let_1))) (let ((_let_10 (fun real (fun int (fun nat bool))))) (let ((_let_11 (fun int _let_5))) (let ((_let_12 (fun real _let_11))) (let ((_let_13 (fun int _let_7))) (let ((_let_14 (fun real _let_13))) (let ((_let_15 (fun _let_13 _let_11))) (let ((_let_16 (fun (fun int (fun nat bool)) _let_13))) (let ((_let_17 (fun int (fun nat real)))) (let ((_let_18 (fun _let_17 (fun int (fun nat bool))))) (let ((_let_19 (fun real _let_18))) (let ((_let_20 (fun (fun nat real) (fun nat bool)))) (let ((_let_21 (fun real _let_20))) (let ((_let_22 (fun int _let_3))) (hAPP _let_14 _let_12 (hAPP _let_15 (fun _let_14 _let_12) (combb _let_13 _let_11 real) (hAPP (fun _let_7 _let_5) _let_15 (combb _let_7 _let_5 int) (combs nat bool bool))) (hAPP _let_10 _let_14 (hAPP _let_16 (fun _let_10 _let_14) (combb (fun int (fun nat bool)) _let_13 real) (hAPP _let_8 _let_16 (combb (fun nat bool) _let_7 int) (hAPP (fun bool _let_2) _let_8 (combb bool _let_2 nat) fconj))) (hAPP _let_17 _let_10 (hAPP _let_19 (fun _let_17 _let_10) (combc real _let_17 (fun int (fun nat bool))) (hAPP _let_21 _let_19 (hAPP (fun _let_20 _let_18) (fun _let_21 _let_19) (combb _let_20 _let_18 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_4 _let_21 (hAPP (fun _let_0 _let_20) (fun _let_4 _let_21) (combb _let_0 _let_20 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_17 (hAPP _let_22 (fun (fun nat real) _let_17) (combc int (fun nat real) (fun nat real)) (hAPP _let_9 _let_22 (hAPP (fun _let_1 _let_3) (fun _let_9 _let_22) (combb _let_1 _let_3 int) (combb real real nat)) (hAPP _let_6 _let_9 (hAPP (fun real _let_1) (fun _let_6 _let_9) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat)))))))))))))))))))))))))))) ) 16.50/16.54 ( (let ((_let_0 (fun nat bool))) (fun _let_0 (fun real (fun int _let_0)))), (let ((_let_0 (fun nat bool))) (fun real (fun _let_0 (fun int _let_0)))), (let ((_let_0 (fun nat bool))) (combc real _let_0 (fun int _let_0))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun (fun nat real) (fun nat real)))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun (fun nat bool) (fun nat bool)))) (let ((_let_6 (fun int real))) (let ((_let_7 (fun nat _let_2))) (let ((_let_8 (fun (fun nat bool) _let_7))) (let ((_let_9 (fun int _let_1))) (let ((_let_10 (fun real (fun int (fun nat bool))))) (let ((_let_11 (fun (fun nat bool) (fun int (fun nat bool))))) (let ((_let_12 (fun real _let_11))) (let ((_let_13 (fun int _let_5))) (let ((_let_14 (fun real _let_13))) (let ((_let_15 (fun int _let_7))) (let ((_let_16 (fun real _let_15))) (let ((_let_17 (fun _let_15 _let_13))) (let ((_let_18 (fun (fun int (fun nat bool)) _let_15))) (let ((_let_19 (fun int (fun nat real)))) (let ((_let_20 (fun _let_19 (fun int (fun nat bool))))) (let ((_let_21 (fun real _let_20))) (let ((_let_22 (fun (fun nat real) (fun nat bool)))) (let ((_let_23 (fun real _let_22))) (let ((_let_24 (fun int _let_3))) (hAPP _let_14 _let_12 (hAPP (fun _let_13 _let_11) (fun _let_14 _let_12) (combb _let_13 _let_11 real) (combc int (fun nat bool) (fun nat bool))) (hAPP _let_16 _let_14 (hAPP _let_17 (fun _let_16 _let_14) (combb _let_15 _let_13 real) (hAPP (fun _let_7 _let_5) _let_17 (combb _let_7 _let_5 int) (combs nat bool bool))) (hAPP _let_10 _let_16 (hAPP _let_18 (fun _let_10 _let_16) (combb (fun int (fun nat bool)) _let_15 real) (hAPP _let_8 _let_18 (combb (fun nat bool) _let_7 int) (hAPP (fun bool _let_2) _let_8 (combb bool _let_2 nat) fconj))) (hAPP _let_19 _let_10 (hAPP _let_21 (fun _let_19 _let_10) (combc real _let_19 (fun int (fun nat bool))) (hAPP _let_23 _let_21 (hAPP (fun _let_22 _let_20) (fun _let_23 _let_21) (combb _let_22 _let_20 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_4 _let_23 (hAPP (fun _let_0 _let_22) (fun _let_4 _let_23) (combb _let_0 _let_22 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_19 (hAPP _let_24 (fun (fun nat real) _let_19) (combc int (fun nat real) (fun nat real)) (hAPP _let_9 _let_24 (hAPP (fun _let_1 _let_3) (fun _let_9 _let_24) (combb _let_1 _let_3 int) (combb real real nat)) (hAPP _let_6 _let_9 (hAPP (fun real _let_1) (fun _let_6 _let_9) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat))))))))))))))))))))))))))))))) ) 16.50/16.54 ( (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))), (fun real (fun int (fun nat (fun bool bool)))), (let ((_let_0 (fun (fun nat bool) (fun nat bool)))) (let ((_let_1 (fun nat (fun bool bool)))) (let ((_let_2 (fun int _let_0))) (let ((_let_3 (fun int _let_1))) (let ((_let_4 (fun _let_3 _let_2))) (hAPP _let_4 (fun (fun real _let_3) (fun real _let_2)) (combb _let_3 _let_2 real) (hAPP (fun _let_1 _let_0) _let_4 (combb _let_1 _let_0 int) (combs nat bool bool)))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun (fun nat real) (fun nat real)))) (let ((_let_4 (fun real _let_0))) (let ((_let_5 (fun int real))) (let ((_let_6 (fun nat _let_2))) (let ((_let_7 (fun (fun nat bool) _let_6))) (let ((_let_8 (fun int _let_1))) (let ((_let_9 (fun real (fun int (fun nat bool))))) (let ((_let_10 (fun int _let_6))) (let ((_let_11 (fun real _let_10))) (let ((_let_12 (fun (fun int (fun nat bool)) _let_10))) (let ((_let_13 (fun int (fun nat real)))) (let ((_let_14 (fun _let_13 (fun int (fun nat bool))))) (let ((_let_15 (fun real _let_14))) (let ((_let_16 (fun (fun nat real) (fun nat bool)))) (let ((_let_17 (fun real _let_16))) (let ((_let_18 (fun int _let_3))) (hAPP _let_9 _let_11 (hAPP _let_12 (fun _let_9 _let_11) (combb (fun int (fun nat bool)) _let_10 real) (hAPP _let_7 _let_12 (combb (fun nat bool) _let_6 int) (hAPP (fun bool _let_2) _let_7 (combb bool _let_2 nat) fconj))) (hAPP _let_13 _let_9 (hAPP _let_15 (fun _let_13 _let_9) (combc real _let_13 (fun int (fun nat bool))) (hAPP _let_17 _let_15 (hAPP (fun _let_16 _let_14) (fun _let_17 _let_15) (combb _let_16 _let_14 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_4 _let_17 (hAPP (fun _let_0 _let_16) (fun _let_4 _let_17) (combb _let_0 _let_16 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_13 (hAPP _let_18 (fun (fun nat real) _let_13) (combc int (fun nat real) (fun nat real)) (hAPP _let_8 _let_18 (hAPP (fun _let_1 _let_3) (fun _let_8 _let_18) (combb _let_1 _let_3 int) (combb real real nat)) (hAPP _let_5 _let_8 (hAPP (fun real _let_1) (fun _let_5 _let_8) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat))))))))))))))))))))))) ) 16.50/16.55 ( (let ((_let_0 (fun nat bool))) (fun (fun real (fun int (fun _let_0 _let_0))) (fun real (fun _let_0 (fun int _let_0))))), (let ((_let_0 (fun nat bool))) (fun (fun int (fun _let_0 _let_0)) (fun _let_0 (fun int _let_0)))), (let ((_let_0 (fun nat bool))) (combb (fun int (fun _let_0 _let_0)) (fun _let_0 (fun int _let_0)) real)), (let ((_let_0 (fun nat bool))) (combc int _let_0 _let_0)) ) 16.50/16.55 ( (fun real (fun int (fun nat (fun bool bool)))), (fun real (fun int (fun nat bool))), (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun nat _let_1))) (let ((_let_3 (fun _let_0 _let_2))) (let ((_let_4 (fun int _let_0))) (let ((_let_5 (fun int _let_2))) (let ((_let_6 (fun _let_4 _let_5))) (hAPP _let_6 (fun (fun real _let_4) (fun real _let_5)) (combb _let_4 _let_5 real) (hAPP _let_3 _let_6 (combb _let_0 _let_2 int) (hAPP (fun bool _let_1) _let_3 (combb bool _let_1 nat) fconj)))))))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun (fun nat real) (fun nat real)))) (let ((_let_3 (fun real _let_0))) (let ((_let_4 (fun int real))) (let ((_let_5 (fun int _let_1))) (let ((_let_6 (fun real (fun int (fun nat bool))))) (let ((_let_7 (fun int (fun nat real)))) (let ((_let_8 (fun _let_7 (fun int (fun nat bool))))) (let ((_let_9 (fun real _let_8))) (let ((_let_10 (fun (fun nat real) (fun nat bool)))) (let ((_let_11 (fun real _let_10))) (let ((_let_12 (fun int _let_2))) (hAPP _let_7 _let_6 (hAPP _let_9 (fun _let_7 _let_6) (combc real _let_7 (fun int (fun nat bool))) (hAPP _let_11 _let_9 (hAPP (fun _let_10 _let_8) (fun _let_11 _let_9) (combb _let_10 _let_8 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_3 _let_11 (hAPP (fun _let_0 _let_10) (fun _let_3 _let_11) (combb _let_0 _let_10 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_7 (hAPP _let_12 (fun (fun nat real) _let_7) (combc int (fun nat real) (fun nat real)) (hAPP _let_5 _let_12 (hAPP (fun _let_1 _let_2) (fun _let_5 _let_12) (combb _let_1 _let_2 int) (combb real real nat)) (hAPP _let_4 _let_5 (hAPP (fun real _let_1) (fun _let_4 _let_5) (combb real _let_1 int) (inverse_divide real)) (real_1 int)))) (real_1 nat)))))))))))))))) ) 16.50/16.55 ( (let ((_let_0 (fun nat bool))) (fun (fun int (fun nat (fun bool bool))) (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun nat bool))) (fun (fun nat (fun bool bool)) (fun _let_0 _let_0))), (let ((_let_0 (fun nat bool))) (combb (fun nat (fun bool bool)) (fun _let_0 _let_0) int)), (combs nat bool bool) ) 16.50/16.55 ( (let ((_let_0 (fun nat bool))) (fun (fun real (fun int (fun nat (fun bool bool)))) (fun real (fun int (fun _let_0 _let_0))))), (let ((_let_0 (fun nat bool))) (fun (fun int (fun nat (fun bool bool))) (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun nat bool))) (combb (fun int (fun nat (fun bool bool))) (fun int (fun _let_0 _let_0)) real)), (let ((_let_0 (fun (fun nat bool) (fun nat bool)))) (let ((_let_1 (fun nat (fun bool bool)))) (hAPP (fun _let_1 _let_0) (fun (fun int _let_1) (fun int _let_0)) (combb _let_1 _let_0 int) (combs nat bool bool)))) ) 16.50/16.55 ( (fun (fun int (fun nat bool)) (fun int (fun nat (fun bool bool)))), (fun (fun nat bool) (fun nat (fun bool bool))), (combb (fun nat bool) (fun nat (fun bool bool)) int), (let ((_let_0 (fun bool bool))) (hAPP (fun bool _let_0) (fun (fun nat bool) (fun nat _let_0)) (combb bool _let_0 nat) fconj)) ) 16.50/16.55 ( (fun (fun real (fun int (fun nat bool))) (fun real (fun int (fun nat (fun bool bool))))), (fun (fun int (fun nat bool)) (fun int (fun nat (fun bool bool)))), (combb (fun int (fun nat bool)) (fun int (fun nat (fun bool bool))) real), (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun nat _let_1))) (let ((_let_3 (fun _let_0 _let_2))) (hAPP _let_3 (fun (fun int _let_0) (fun int _let_2)) (combb _let_0 _let_2 int) (hAPP (fun bool _let_1) _let_3 (combb bool _let_1 nat) fconj)))))) ) 16.50/16.55 ( (fun int (fun nat real)), (fun nat real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun (fun nat real) (fun nat real)))) (let ((_let_2 (fun int real))) (let ((_let_3 (fun int _let_0))) (let ((_let_4 (fun int _let_1))) (hAPP _let_4 (fun (fun nat real) (fun int (fun nat real))) (combc int (fun nat real) (fun nat real)) (hAPP _let_3 _let_4 (hAPP (fun _let_0 _let_1) (fun _let_3 _let_4) (combb _let_0 _let_1 int) (combb real real nat)) (hAPP _let_2 _let_3 (hAPP (fun real _let_0) (fun _let_2 _let_3) (combb real _let_0 int) (inverse_divide real)) (real_1 int))))))))), (real_1 nat) ) 16.50/16.55 ( (fun real (fun (fun int (fun nat real)) (fun int (fun nat bool)))), (fun real (fun (fun nat real) (fun nat bool))), (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun (fun int _let_1) (fun int _let_0)))) (let ((_let_3 (fun _let_1 _let_0))) (hAPP (fun _let_3 _let_2) (fun (fun real _let_3) (fun real _let_2)) (combb _let_3 _let_2 real) (combb _let_1 _let_0 int)))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun nat real) (fun nat bool)))) (let ((_let_3 (fun real _let_2))) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 real) (combb real bool nat)) (fequal real)))))) ) 16.50/16.55 ( (fun (fun int (fun nat real)) (fun real (fun int (fun nat bool)))), (fun real (fun (fun int (fun nat real)) (fun int (fun nat bool)))), (combc real (fun int (fun nat real)) (fun int (fun nat bool))), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real _let_0))) (let ((_let_2 (fun (fun int (fun nat real)) (fun int (fun nat bool))))) (let ((_let_3 (fun real _let_2))) (let ((_let_4 (fun (fun nat real) (fun nat bool)))) (let ((_let_5 (fun real _let_4))) (hAPP _let_5 _let_3 (hAPP (fun _let_4 _let_2) (fun _let_5 _let_3) (combb _let_4 _let_2 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_4) (fun _let_1 _let_5) (combb _let_0 _let_4 real) (combb real bool nat)) (fequal real))))))))) ) 16.50/16.55 ( (fun real (fun (fun nat real) (fun nat bool))), (fun real (fun real bool)), (let ((_let_0 (fun real bool))) (let ((_let_1 (fun (fun nat real) (fun nat bool)))) (hAPP (fun _let_0 _let_1) (fun (fun real _let_0) (fun real _let_1)) (combb _let_0 _let_1 real) (combb real bool nat)))), (fequal real) ) 16.50/16.55 ( (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat real))) (fun (fun real (fun _let_1 _let_0)) (fun real (fun (fun int _let_1) (fun int _let_0)))))), (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat real))) (fun (fun _let_1 _let_0) (fun (fun int _let_1) (fun int _let_0))))), (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat real))) (combb (fun _let_1 _let_0) (fun (fun int _let_1) (fun int _let_0)) real))), (combb (fun nat real) (fun nat bool) int) ) 16.50/16.55 ( (fun (fun real (fun real bool)) (fun real (fun (fun nat real) (fun nat bool)))), (fun (fun real bool) (fun (fun nat real) (fun nat bool))), (combb (fun real bool) (fun (fun nat real) (fun nat bool)) real), (combb real bool nat) ) 16.50/16.55 ( (let ((_let_0 (fun nat real))) (fun int (fun _let_0 _let_0))), (fun int (fun real real)), (let ((_let_0 (fun real real))) (let ((_let_1 (fun (fun nat real) (fun nat real)))) (hAPP (fun _let_0 _let_1) (fun (fun int _let_0) (fun int _let_1)) (combb _let_0 _let_1 int) (combb real real nat)))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun int real))) (let ((_let_2 (fun int _let_0))) (hAPP _let_1 _let_2 (hAPP (fun real _let_0) (fun _let_1 _let_2) (combb real _let_0 int) (inverse_divide real)) (real_1 int))))) ) 16.50/16.55 ( (let ((_let_0 (fun nat real))) (fun _let_0 (fun int _let_0))), (let ((_let_0 (fun nat real))) (fun int (fun _let_0 _let_0))), (let ((_let_0 (fun nat real))) (combc int _let_0 _let_0)), (let ((_let_0 (fun real real))) (let ((_let_1 (fun (fun nat real) (fun nat real)))) (let ((_let_2 (fun int real))) (let ((_let_3 (fun int _let_0))) (let ((_let_4 (fun int _let_1))) (hAPP _let_3 _let_4 (hAPP (fun _let_0 _let_1) (fun _let_3 _let_4) (combb _let_0 _let_1 int) (combb real real nat)) (hAPP _let_2 _let_3 (hAPP (fun real _let_0) (fun _let_2 _let_3) (combb real _let_0 int) (inverse_divide real)) (real_1 int)))))))) ) 16.50/16.55 ( (let ((_let_0 (fun nat real))) (fun (fun int (fun real real)) (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun nat real))) (fun (fun real real) (fun _let_0 _let_0))), (let ((_let_0 (fun nat real))) (combb (fun real real) (fun _let_0 _let_0) int)), (combb real real nat) ) 16.50/16.55 ( (let ((_let_0 (fun int int))) (fun int (fun _let_0 _let_0))), (fun int (fun int int)), (let ((_let_0 (fun (fun int int) (fun int int)))) (hAPP (fun (fun int int) _let_0) (fun (fun int (fun int int)) (fun int _let_0)) (combb (fun int int) _let_0 int) (combb int int int))), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb int _let_0 int) (plus_plus int)) (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 16.50/16.55 ( (let ((_let_0 (fun int int))) (fun (fun int _let_0) (fun int (fun _let_0 _let_0)))), (let ((_let_0 (fun int int))) (fun _let_0 (fun _let_0 _let_0))), (let ((_let_0 (fun int int))) (combb _let_0 (fun _let_0 _let_0) int)), (combb int int int) ) 16.50/16.55 ( (let ((_let_0 (fun int (fun int (fun int bool))))) (fun _let_0 _let_0)), (let ((_let_0 (fun int (fun int bool)))) (fun _let_0 _let_0)), (let ((_let_0 (fun int (fun int bool)))) (combb _let_0 _let_0 int)), (combc int int bool) ) 16.50/16.55 ( (fun (fun int (fun int int)) (fun int (fun int (fun int bool)))), (fun (fun int int) (fun int (fun int bool))), (combb (fun int int) (fun int (fun int bool)) int), (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (hAPP _let_1 (fun (fun int int) _let_1) (combb int _let_0 int) (fequal int)))) ) 16.50/16.55 ) 16.50/16.55 (instantiation (forall ((W $$unsorted)) (or (not (hBOOL (hAPP int bool nat_neg (hAPP int int (number_number_of int) W)))) (= (zero_zero nat) (hAPP int nat (number_number_of nat) (hAPP int int bit1 W)))) ) 16.50/16.55 ( pls ) 16.50/16.55 ( (hAPP int int bit1 pls) ) 16.50/16.55 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.50/16.55 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.50/16.55 ( min_1 ) 16.50/16.55 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.55 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.50/16.55 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 16.50/16.55 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 16.50/16.55 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 16.50/16.55 ) 16.50/16.55 (instantiation (forall ((W $$unsorted)) (let ((_let_0 (hAPP int nat (number_number_of nat) W))) (or (hBOOL (hAPP int bool nat_neg (hAPP int int (number_number_of int) W))) (= (hAPP int nat (number_number_of nat) (hAPP int int bit1 W)) (hAPP nat nat suc (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) _let_0) _let_0))))) ) 16.50/16.55 ( pls ) 16.50/16.55 ( (hAPP int int bit1 pls) ) 16.50/16.55 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.50/16.55 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.50/16.55 ( min_1 ) 16.50/16.55 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.55 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.50/16.55 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 16.50/16.55 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 16.50/16.55 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 16.50/16.55 ) 16.50/16.55 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun nat real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) X_2))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_2) (one_one real)))) (hBOOL (hAPP _let_2 bool (bseq real) (hAPP real _let_2 (power_power real) X_2))))))) ) 16.50/16.55 ( (zero_zero real) ) 16.50/16.55 ( pi ) 16.50/16.55 ( (hAPP int real (number_number_of real) min_1) ) 16.50/16.55 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.55 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.55 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.55 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.55 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.55 ( skv_3 ) 16.50/16.55 ( skv_5 ) 16.50/16.55 ( skv_7 ) 16.50/16.55 ( skv_12 ) 16.50/16.55 ) 16.50/16.55 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_161567 $$unsorted) (BOUND_VARIABLE_161568 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_161567) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_161568))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP X_a int (archim2085082626_floor X_a) BOUND_VARIABLE_161567)) (hAPP int int (number_number_of int) BOUND_VARIABLE_161568))))) ) 16.50/16.55 ( nat, (zero_zero nat), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.50/16.55 ( int, pls, pls ) 16.50/16.55 ( int, pls, (hAPP int int bit1 pls) ) 16.50/16.55 ( int, min_1, pls ) 16.50/16.55 ( real, pi, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.55 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.50/16.55 ) 16.50/16.55 (instantiation (forall ((Z_1 $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (power_power real))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (= (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) Z_1) (hAPP complex complex cnj Z_1)) (hAPP real complex (of_real complex) (hAPP real real (hAPP real (fun real real) (plus_plus real) (hAPP nat real (hAPP real _let_0 _let_1 (hAPP complex real re Z_1)) _let_2)) (hAPP nat real (hAPP real _let_0 _let_1 (hAPP complex real im Z_1)) _let_2))))))) ) 16.50/16.55 ( (one_one complex) ) 16.50/16.55 ( ii ) 16.50/16.55 ( (zero_zero complex) ) 16.50/16.55 ( (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.55 ( (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 16.50/16.55 ) 16.50/16.55 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (archimedean_ceiling X_a))) (or (not (archim1727834104eiling X_a)) (= _let_0 (ti (fun X_a int) _let_0)))) ) 16.50/16.55 ( nat ) 16.50/16.55 ( int ) 16.50/16.55 ( (fun int bool) ) 16.50/16.55 ( real ) 16.50/16.55 ( rat ) 16.50/16.55 ( (product_prod int int) ) 16.50/16.55 ( quickcheck_code_int ) 16.50/16.55 ( code_code_numeral ) 16.50/16.55 ) 16.50/16.55 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (fun X_a (fun X_a X_a)))) (let ((_let_1 (fun X_a (fun nat X_a)))) (or (not (power X_a)) (= (hAPP _let_0 _let_1 (hAPP X_a (fun _let_0 _let_1) (power_1 X_a) (one_one X_a)) (times_times X_a)) (power_power X_a))))) ) 16.50/16.55 ( bool ) 16.50/16.55 ( nat ) 16.50/16.55 ( int ) 16.50/16.55 ( (fun int bool) ) 16.50/16.55 ( (fun int (fun int bool)) ) 16.50/16.55 ( (fun int int) ) 16.50/16.55 ( (fun nat bool) ) 16.50/16.55 ( (fun nat nat) ) 16.50/16.55 ( (product_prod nat nat) ) 16.50/16.55 ( (fun (product_prod nat nat) bool) ) 16.50/16.55 ( (fun nat (fun (product_prod nat nat) bool)) ) 16.50/16.55 ( real ) 16.50/16.55 ( (fun real bool) ) 16.50/16.55 ( (fun real real) ) 16.50/16.55 ( rat ) 16.50/16.55 ( (fun nat (fun nat bool)) ) 16.50/16.55 ( complex ) 16.50/16.55 ( (fun nat real) ) 16.50/16.55 ( (product_prod int int) ) 16.50/16.55 ( quickcheck_code_int ) 16.50/16.55 ( (fun bool bool) ) 16.50/16.55 ( code_code_numeral ) 16.50/16.55 ( (fun int (fun int (fun int bool))) ) 16.50/16.55 ( (product_prod real real) ) 16.50/16.55 ( (fun (product_prod int int) bool) ) 16.50/16.55 ( (fun nat (product_prod nat nat)) ) 16.50/16.55 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 16.50/16.55 ( (fun (product_prod int int) int) ) 16.50/16.55 ( (fun nat (product_prod int int)) ) 16.50/16.55 ( (fun int real) ) 16.50/16.55 ) 16.50/16.55 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (dist_dist X_a))) (or (not (metric_space X_a)) (= _let_0 (ti (fun X_a (fun X_a real)) _let_0)))) ) 16.50/16.55 ( nat ) 16.50/16.55 ( int ) 16.50/16.55 ( real ) 16.50/16.55 ( (fun real bool) ) 16.50/16.55 ( rat ) 16.50/16.55 ( complex ) 16.50/16.55 ) 16.50/16.55 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int int (hAPP int (fun int int) (times_times int) min_1) K_4) (hAPP int int (uminus_uminus int) K_4)) ) 16.50/16.55 ( (one_one int) ) 16.50/16.55 ( pls ) 16.50/16.55 ( min_1 ) 16.50/16.55 ) 16.50/16.55 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (one_one real)) X_1))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real ln X_1)) X_1))))) ) 16.50/16.55 ( (one_one real) ) 16.50/16.55 ) 16.50/16.55 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (hAPP real (fun real real) log (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))))) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) X_1))) (= (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP real real _let_0 (hAPP real real (exp real) (one_one real)))) (hAPP real real ln X_1)) (hAPP real real _let_0 X_1)))) ) 16.50/16.55 ( (one_one real) ) 16.50/16.55 ( pi ) 16.50/16.55 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.55 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.55 ( skv_2 ) 16.50/16.55 ( skv_8 ) 16.50/16.55 ( skv_9 ) 16.50/16.55 ) 16.50/16.55 (instantiation (forall ((N_1 $$unsorted)) (let ((_let_0 (hAPP nat nat suc N_1))) (= (hAPP nat nat (hAPP nat (fun nat nat) (times_times nat) _let_0) (hAPP nat nat fact N_1)) (hAPP nat nat fact _let_0))) ) 16.50/16.55 ( (zero_zero nat) ) 16.50/16.55 ( (hAPP nat nat suc (zero_zero nat)) ) 16.50/16.55 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 16.50/16.55 ) 16.50/16.55 (instantiation (forall ((X_1 $$unsorted) (N_1 $$unsorted) (M $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)))) (let ((_let_2 (hAPP nat _let_0 root N_1))) (let ((_let_3 (hAPP nat _let_0 root M))) (or (not (hBOOL (hAPP nat bool _let_1 M))) (not (hBOOL (hAPP nat bool _let_1 N_1))) (= (hAPP real real _let_3 (hAPP real real _let_2 X_1)) (hAPP real real _let_2 (hAPP real real _let_3 X_1)))))))) ) 16.50/16.55 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.55 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.55 ) 16.50/16.55 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (summable X_a))) (or (not (comm_monoid_add X_a)) (not (topological_space X_a)) (= _let_0 (ti (fun (fun nat X_a) bool) _let_0)))) ) 16.50/16.55 ( bool ) 16.50/16.55 ( nat ) 16.50/16.55 ( int ) 16.50/16.55 ( (fun int int) ) 16.50/16.55 ( (fun nat bool) ) 16.50/16.55 ( (fun nat nat) ) 16.50/16.55 ( (product_prod nat nat) ) 16.50/16.55 ( (fun (product_prod nat nat) bool) ) 16.50/16.55 ( (fun nat (fun (product_prod nat nat) bool)) ) 16.50/16.55 ( real ) 16.50/16.55 ( (fun real real) ) 16.50/16.55 ( rat ) 16.50/16.55 ( (fun nat (fun nat bool)) ) 16.50/16.55 ( complex ) 16.50/16.55 ( (product_prod int int) ) 16.50/16.55 ( quickcheck_code_int ) 16.50/16.55 ( (fun bool bool) ) 16.50/16.55 ( code_code_numeral ) 16.50/16.55 ( (product_prod real real) ) 16.50/16.55 ( (fun nat (product_prod nat nat)) ) 16.50/16.55 ( (fun nat (product_prod int int)) ) 16.50/16.55 ) 16.50/16.55 (instantiation (forall ((K_4 $$unsorted) (M $$unsorted) (N_1 $$unsorted)) (let ((_let_0 (hAPP int (fun int bool) (dvd_dvd int) K_4))) (or (not (hBOOL (hAPP int bool _let_0 (hAPP int int (hAPP int (fun int int) (minus_minus int) M) N_1)))) (not (hBOOL (hAPP int bool _let_0 N_1))) (hBOOL (hAPP int bool _let_0 M)))) ) 16.50/16.55 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 16.50/16.55 ) 16.50/16.55 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) (zero_zero real)) X_2))) (hBOOL (hAPP real bool (hAPP (fun real real) _let_0 (isCont real real) ln) X_2)))) ) 16.50/16.55 ( pi ) 16.50/16.55 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.55 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.55 ( skv_2 ) 16.50/16.55 ( skv_8 ) 16.50/16.55 ( skv_9 ) 16.50/16.55 ) 16.50/16.55 (instantiation (forall ((N_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (hAPP nat real (real_1 nat) N_1))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) _let_1) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) X_1) (hAPP real real (hAPP real (fun real real) (plus_plus real) _let_1) (one_one real))))) (= (hAPP real nat natceiling X_1) (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) N_1) (one_one nat)))))) ) 16.50/16.55 ( (zero_zero nat), pi ) 16.50/16.55 ( (zero_zero nat), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.55 ( (zero_zero nat), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.55 ( (zero_zero nat), skv_2 ) 16.50/16.55 ( (zero_zero nat), skv_8 ) 16.50/16.55 ( (zero_zero nat), skv_9 ) 16.50/16.55 ( (hAPP nat nat suc (zero_zero nat)), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.55 ) 16.50/16.55 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (sgn_sgn X_a))) (or (not (sgn_div_norm X_a)) (= _let_0 (ti (fun X_a X_a) _let_0)))) ) 16.50/16.55 ( bool ) 16.50/16.55 ( nat ) 16.50/16.55 ( int ) 16.50/16.55 ( (fun int bool) ) 16.50/16.55 ( (fun int (fun int bool)) ) 16.50/16.55 ( (fun int int) ) 16.50/16.55 ( (fun nat bool) ) 16.50/16.55 ( real ) 16.50/16.55 ( (fun real bool) ) 16.50/16.55 ( (fun real real) ) 16.50/16.55 ( rat ) 16.50/16.55 ( complex ) 16.50/16.55 ( (fun nat real) ) 16.50/16.55 ( (product_prod int int) ) 16.50/16.55 ( code_code_numeral ) 16.50/16.55 ( (fun int (fun int (fun int bool))) ) 16.50/16.55 ( (fun (product_prod int int) bool) ) 16.50/16.55 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 16.50/16.55 ( (fun (product_prod int int) int) ) 16.50/16.55 ( (fun int real) ) 16.50/16.55 ) 16.50/16.55 (instantiation (forall ((N $$unsorted) (Ma $$unsorted)) (or (= (zero_zero int) (ti int Ma)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int (fun int int) (times_times int) Ma) N)) Ma)) (= (one_one int) (hAPP int int (abs_abs int) N)))) ) 16.50/16.55 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.55 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.50/16.55 ( skv_13, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.50/16.55 ) 16.50/16.55 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_161912 $$unsorted)) (or (not (comm_semiring_1 X_a)) (= (ti X_a BOUND_VARIABLE_161912) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (zero_zero X_a)) BOUND_VARIABLE_161912))) ) 16.50/16.55 ( bool, fFalse ) 16.50/16.55 ( bool, fTrue ) 16.50/16.55 ( int, pls ) 16.50/16.55 ( int, min_1 ) 16.50/16.55 ( int, s ) 16.50/16.55 ( int, m ) 16.50/16.55 ( int, s1 ) 16.50/16.55 ( int, t ) 16.50/16.55 ( (fun int bool), nat_neg ) 16.50/16.55 ( (fun int bool), zprime ) 16.50/16.55 ( (fun int bool), zEven ) 16.50/16.55 ( (fun int bool), zOdd ) 16.50/16.55 ( (fun int bool), (even_odd_even int) ) 16.50/16.55 ( (fun int bool), twoSqu1091635170sum2sq ) 16.50/16.55 ( (fun int bool), nat_is_nat ) 16.50/16.55 ( (fun int (fun int bool)), norRRset ) 16.50/16.55 ( (fun int (fun int bool)), quadRes ) 16.50/16.55 ( (fun int (fun int bool)), sRStar ) 16.50/16.55 ( (fun int (fun int bool)), d22set ) 16.50/16.55 ( (fun int (fun int bool)), sr ) 16.50/16.55 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 16.50/16.55 ( (fun int int), zfact ) 16.50/16.55 ( (fun int int), bit0 ) 16.50/16.55 ( (fun int int), bit1 ) 16.50/16.55 ( (fun int int), (fact_fact int) ) 16.50/16.55 ( (fun int int), pred ) 16.50/16.55 ( (fun int int), succ ) 16.50/16.55 ( (fun nat bool), (even_odd_even nat) ) 16.50/16.55 ( (fun nat bool), prime ) 16.50/16.55 ( (fun nat nat), suc ) 16.50/16.55 ( (fun nat nat), (fact_fact nat) ) 16.50/16.55 ( (fun nat nat), fact ) 16.50/16.55 ( (fun nat nat), nat_size ) 16.50/16.55 ( (fun nat nat), (size_size nat) ) 16.50/16.55 ( (fun (product_prod nat nat) bool), pred_nat ) 16.50/16.55 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 16.50/16.55 ( real, pi ) 16.50/16.55 ( (fun real real), ln ) 16.50/16.55 ( (fun real real), cos ) 16.50/16.55 ( (fun real real), sqrt ) 16.50/16.55 ( (fun real real), sin ) 16.50/16.55 ( (fun real real), arccos ) 16.50/16.55 ( (fun real real), arcsin ) 16.50/16.55 ( (fun real real), tan ) 16.50/16.55 ( (fun real real), arctan ) 16.50/16.55 ( (fun nat (fun nat bool)), coprime ) 16.50/16.55 ( complex, ii ) 16.50/16.55 ( (fun nat real), (real_1 nat) ) 16.50/16.55 ( (fun nat real), sin_coeff ) 16.50/16.55 ( (fun nat real), cos_coeff ) 16.50/16.55 ( (filter nat), sequentially ) 16.50/16.55 ( (fun int (fun int int)), (gcd_gcd int) ) 16.50/16.55 ( (fun int (fun int int)), legendre ) 16.50/16.55 ( (fun int (fun int int)), legacy_zgcd ) 16.50/16.55 ( (fun int (fun int int)), standardRes ) 16.50/16.55 ( (fun int (fun int int)), nat_tsub ) 16.50/16.55 ( (fun int (fun int int)), multInv ) 16.50/16.55 ( (fun int (fun int int)), z3mod ) 16.50/16.55 ( (fun int (fun int int)), z3div ) 16.50/16.55 ( (fun int (fun int int)), int_gcd ) 16.50/16.55 ( (fun int (fun int int)), int_lcm ) 16.50/16.55 ( (fun int (fun int int)), inv ) 16.50/16.55 ( (fun complex complex), expi ) 16.50/16.55 ( (fun complex complex), cnj ) 16.50/16.55 ( (fun real complex), cis ) 16.50/16.55 ( (fun int nat), nat_1 ) 16.50/16.55 ( (fun int nat), phi ) 16.50/16.55 ( (fun (fun int bool) bool), nat_nat_set ) 16.50/16.55 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 16.50/16.55 ( (fun nat (fun nat nat)), nat_gcd ) 16.50/16.55 ( (fun nat (fun nat nat)), nat_lcm ) 16.50/16.55 ( (fun (fun int bool) int), (the int) ) 16.50/16.55 ( (fun complex real), re ) 16.50/16.55 ( (fun complex real), im ) 16.50/16.55 ( (fun complex real), arg ) 16.50/16.55 ( (fun bool bool), fNot ) 16.50/16.55 ( (fun nat (fun real real)), root ) 16.50/16.55 ( (fun real (fun real real)), log ) 16.50/16.55 ( (fun real (fun real real)), powr ) 16.50/16.55 ( (fun bool (fun bool bool)), fimplies ) 16.50/16.55 ( (fun bool (fun bool bool)), fconj ) 16.50/16.55 ( (fun bool (fun bool bool)), fdisj ) 16.50/16.55 ( (fun int (fun int (product_prod int int))), negDivAlg ) 16.50/16.55 ( (fun int (fun int (product_prod int int))), posDivAlg ) 16.50/16.55 ( (fun int (fun int (product_prod int int))), divmod_int ) 16.50/16.55 ( (fun int (fun int (product_prod int int))), pdivmod ) 16.50/16.55 ( (fun int (fun int (product_prod int int))), norm_frac ) 16.50/16.55 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 16.50/16.55 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 16.50/16.55 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 16.50/16.55 ( (fun int (fun int (fun int bool))), zcong ) 16.50/16.55 ( (fun int (fun int (fun int bool))), zcongm ) 16.50/16.55 ( (fun int (fun int (fun int bool))), noXRRset ) 16.50/16.55 ( (fun int (fun int (fun int bool))), bnorRset ) 16.50/16.55 ( (fun int (fun int (fun int bool))), wset ) 16.50/16.55 ( (fun (product_prod int int) bool), frac_1 ) 16.50/16.55 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 16.50/16.55 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 16.50/16.55 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 16.50/16.55 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 16.50/16.55 ( (fun (fun nat rat) bool), vanishes ) 16.50/16.55 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 16.50/16.55 ( (fun code_code_numeral nat), code_c271388182l_size ) 16.50/16.55 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 16.50/16.55 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 16.50/16.55 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 16.50/16.55 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 16.50/16.55 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 16.50/16.55 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 16.50/16.55 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 16.50/16.55 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 16.50/16.55 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 16.50/16.55 ( (fun complex nat), complex_size ) 16.50/16.55 ( (fun complex nat), (size_size complex) ) 16.50/16.55 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 16.50/16.55 ( (fun nat (fun nat (product_prod int int))), bezw ) 16.50/16.55 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 16.50/16.55 ( (fun int (fun nat nat)), nat_aux ) 16.50/16.55 ( (fun int (fun (fun int bool) bool)), rsetR ) 16.50/16.55 ( (fun int (fun (fun int bool) bool)), resSet ) 16.50/16.55 ( (fun int (list int)), quickc666637781d_zero ) 16.50/16.55 ( (fun (product_prod int int) rat), frct ) 16.50/16.55 ( (fun int (fun int rat)), fract ) 16.50/16.55 ( (fun real (fun real complex)), complex_1 ) 16.50/16.55 ( (fun real (fun real complex)), rcis ) 16.50/16.55 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 16.50/16.55 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 16.50/16.55 ( (fun int real), (real_1 int) ) 16.50/16.55 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 16.50/16.55 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 16.50/16.55 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 16.50/16.55 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 16.50/16.55 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 16.50/16.55 ( (fun real nat), natfloor ) 16.50/16.55 ( (fun real nat), natceiling ) 16.50/16.55 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 16.50/16.55 ( (fun quickcheck_code_int int), quickcheck_int_of ) 16.50/16.55 ( (fun rat (product_prod int int)), quotient_of ) 16.50/16.55 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 16.50/16.55 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 16.50/16.55 ( (fun rat real), ratreal ) 16.50/16.55 ( (fun code_code_numeral int), code_int_of ) 16.50/16.55 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 16.50/16.55 ( (fun int quickcheck_code_int), quickcheck_of_int ) 16.50/16.55 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 16.50/16.55 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 16.50/16.55 ) 16.50/16.55 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_161926 $$unsorted)) (let ((_let_0 (sgn_sgn X_a))) (let ((_let_1 (hAPP X_a X_a _let_0 BOUND_VARIABLE_161926))) (or (not (linordered_idom X_a)) (= _let_1 (hAPP X_a X_a _let_0 _let_1))))) ) 16.50/16.55 ( real, (zero_zero real) ) 16.50/16.55 ( rat, (zero_zero rat) ) 16.50/16.55 ) 16.50/16.55 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (one_one real))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (minus_minus real))) (let ((_let_5 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_6 (hAPP int real (number_number_of real) _let_5))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 (zero_zero real)) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 X_1) (hAPP real real (hAPP real _let_3 (inverse_divide real) _let_1) _let_6)))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 (hAPP real real (hAPP real _let_3 _let_4 (hAPP real real (uminus_uminus real) X_1)) (hAPP real real (hAPP real _let_3 (times_times real) _let_6) (hAPP nat real (hAPP real (fun nat real) (power_power real) X_1) (hAPP int nat (number_number_of nat) _let_5))))) (hAPP real real ln (hAPP real real (hAPP real _let_3 _let_4 _let_1) X_1)))))))))))) ) 16.50/16.55 ( (one_one real) ) 16.50/16.55 ( pi ) 16.50/16.55 ( (hAPP int real (number_number_of real) min_1) ) 16.50/16.55 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.55 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.55 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.50/16.55 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.55 ( skv_3 ) 16.50/16.55 ( skv_5 ) 16.50/16.55 ( skv_7 ) 16.50/16.55 ( skv_12 ) 16.50/16.55 ) 16.50/16.55 (instantiation (forall ((X_2 $$unsorted) (N $$unsorted) (Y_2 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (div_mod int))) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (dvd_dvd int) N) (hAPP int int (hAPP int _let_0 (minus_minus int) X_2) Y_2))) (= (hAPP int int (hAPP int _let_0 _let_1 X_2) N) (hAPP int int (hAPP int _let_0 _let_1 Y_2) N))))) ) 16.50/16.55 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (number_number_of int) min_1) ) 16.50/16.55 ) 16.50/16.55 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_161972 $$unsorted) (BOUND_VARIABLE_161973 $$unsorted) (BOUND_VARIABLE_161974 $$unsorted)) (or (not (dvd X_a)) (not (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_161973) BOUND_VARIABLE_161974) (ti X_a BOUND_VARIABLE_161972))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_161973) BOUND_VARIABLE_161972))) ) 16.50/16.55 ( int, pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13 ) 16.50/16.55 ( int, s, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 16.50/16.55 ( int, s1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 16.50/16.55 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.50/16.55 ( complex, ii, ii, ii ) 16.50/16.55 ) 16.50/16.55 (instantiation (forall ((N_1 $$unsorted)) (= (one_one nat) (hAPP nat nat (hAPP nat (fun nat nat) (gcd_gcd nat) (hAPP nat nat suc N_1)) N_1)) ) 16.50/16.55 ( (zero_zero nat) ) 16.50/16.55 ( (hAPP nat nat suc (zero_zero nat)) ) 16.50/16.55 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 16.50/16.55 ) 16.50/16.55 (instantiation (forall ((N $$unsorted)) (let ((_let_0 (fun int (fun int bool)))) (let ((_let_1 (ord_less_eq int))) (let ((_let_2 (zero_zero int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun int _let_3))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) _let_1 _let_2) N))) (= (hAPP int nat nat_1 N) (hAPP (fun int bool) nat (finite_card int) (hAPP (fun int bool) (fun int bool) (collect int) (hAPP (fun int bool) (fun int bool) (hAPP _let_4 (fun (fun int bool) (fun int bool)) (combs int bool bool) (hAPP (fun int bool) _let_4 (hAPP (fun bool _let_3) (fun (fun int bool) _let_4) (combb bool _let_3 int) fconj) (hAPP int (fun int bool) (ord_less int) _let_2))) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) _let_1) N))))))))))) ) 16.50/16.55 ( (one_one int) ) 16.50/16.55 ( (zero_zero int) ) 16.50/16.55 ( min_1 ) 16.50/16.55 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.55 ( s ) 16.50/16.55 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.50/16.55 ( (hAPP int int (number_number_of int) pls) ) 16.50/16.55 ( skv_4 ) 16.50/16.55 ( skv_10 ) 16.50/16.55 ) 16.50/16.55 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_162087 $$unsorted) (BOUND_VARIABLE_162088 $$unsorted)) (let ((_let_0 (number_number_of X_a))) (or (not (number_ring X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) (hAPP int X_a _let_0 BOUND_VARIABLE_162087)) (hAPP int X_a _let_0 BOUND_VARIABLE_162088)) (hAPP int X_a _let_0 (hAPP int int (hAPP int (fun int int) (minus_minus int) BOUND_VARIABLE_162087) BOUND_VARIABLE_162088))))) ) 16.50/16.55 ( code_code_numeral, pls, (hAPP int int bit1 pls) ) 16.50/16.55 ) 16.50/16.55 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_162128 $$unsorted) (BOUND_VARIABLE_162129 $$unsorted)) (let ((_let_0 (zero_zero nat))) (let ((_let_1 (fun nat bool))) (let ((_let_2 (fun nat nat))) (let ((_let_3 (fun real real))) (let ((_let_4 (inverse_divide real))) (let ((_let_5 (fun nat real))) (let ((_let_6 (real_1 nat))) (let ((_let_7 (fact_fact nat))) (let ((_let_8 (times_times real))) (let ((_let_9 (fun nat _let_3))) (let ((_let_10 (fun _let_5 _let_5))) (let ((_let_11 (combs nat real real))) (let ((_let_12 (fun real _let_3))) (let ((_let_13 (fun _let_5 _let_9))) (let ((_let_14 (combb real _let_3 nat))) (let ((_let_15 (hAPP real _let_5 (power_power real) (zero_zero real)))) (let ((_let_16 (fun X_a real))) (let ((_let_17 (zero_zero X_a))) (or (not (zero X_a)) (not (hBOOL (hAPP nat bool (hAPP nat _let_1 (ord_less nat) _let_0) BOUND_VARIABLE_162129))) (= (hAPP real real (hAPP real _let_3 (plus_plus real) (hAPP _let_1 real (hAPP _let_5 (fun _let_1 real) (big_co1399186613setsum nat real) (hAPP _let_5 _let_5 (hAPP _let_9 _let_10 _let_11 (hAPP _let_5 _let_9 (hAPP _let_12 _let_13 _let_14 _let_4) (hAPP _let_5 _let_5 (hAPP _let_9 _let_10 _let_11 (hAPP _let_5 _let_9 (hAPP _let_12 _let_13 _let_14 _let_8) (hAPP X_a _let_5 (hAPP (fun nat _let_16) (fun X_a _let_5) (combc nat X_a real) BOUND_VARIABLE_162128) _let_17))) _let_15))) (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb nat real nat) _let_6) _let_7))) (hAPP nat _let_1 (hAPP nat (fun nat _let_1) (ord_atLeastLessThan nat) _let_0) BOUND_VARIABLE_162129))) (hAPP real real (hAPP real _let_3 _let_4 (hAPP real real (hAPP real _let_3 _let_8 (hAPP X_a real (hAPP nat _let_16 BOUND_VARIABLE_162128 BOUND_VARIABLE_162129) _let_17)) (hAPP nat real _let_15 BOUND_VARIABLE_162129))) (hAPP nat real _let_6 (hAPP nat nat _let_7 BOUND_VARIABLE_162129)))) (hAPP X_a real (hAPP nat _let_16 BOUND_VARIABLE_162128 _let_0) _let_17))))))))))))))))))))) ) 16.50/16.55 ( real, root, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.55 ) 16.50/16.55 (instantiation (forall ((M $$unsorted) (N_1 $$unsorted)) (let ((_let_0 (fun nat bool))) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) M) N_1))) (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) M) (hAPP nat nat suc N_1))))) ) 16.50/16.55 ( (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 16.50/16.55 ) 16.50/16.58 (instantiation (forall ((D_1 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun _let_2 bool))) (let ((_let_5 (fun int _let_3))) (let ((_let_6 (fun _let_0 _let_0))) (= (hAPP int _let_4 int_ge_less_than2 D_1) (hAPP _let_4 _let_4 (collect _let_2) (hAPP _let_1 _let_4 (product_prod_case int int bool) (hAPP _let_1 _let_1 (hAPP _let_6 (fun _let_1 _let_1) (combb _let_0 _let_0 int) (hAPP _let_5 _let_6 (combs int bool bool) (hAPP _let_0 _let_5 (hAPP (fun bool _let_3) (fun _let_0 _let_5) (combb bool _let_3 int) fconj) (hAPP int _let_0 (ord_less_eq int) D_1)))) (ord_less int)))))))))))) ) 16.50/16.58 ( (one_one int) ) 16.50/16.58 ( (zero_zero int) ) 16.50/16.58 ( min_1 ) 16.50/16.58 ) 16.50/16.58 (instantiation (forall ((P_1 $$unsorted) (A0 $$unsorted) (A1 $$unsorted)) (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun _let_0 bool))) (or (not (hBOOL (hAPP _let_0 bool (hAPP (fun _let_0 _let_1) _let_1 (accp _let_0) lazy_small_lazy_rel) (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) A0) A1)))) (not (forall ((D_3 $$unsorted) (I_2 $$unsorted)) (let ((_let_2 (hAPP int (fun int bool) P_1 D_3))) (or (not (hBOOL (hAPP _let_0 bool (hAPP (fun _let_0 _let_1) _let_1 (accp _let_0) lazy_small_lazy_rel) (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) D_3) I_2)))) (and (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) D_3) I_2))) (not (hBOOL (hAPP int bool _let_2 (hAPP int int (hAPP int (fun int int) (plus_plus int) I_2) (one_one int)))))) (hBOOL (hAPP int bool _let_2 I_2)))) )) (hBOOL (hAPP int bool (hAPP int (fun int bool) P_1 A0) A1))))) ) 16.50/16.58 ( (ord_less_eq int), (one_one int), t ) 16.50/16.58 ( (ord_less_eq int), (zero_zero int), (one_one int) ) 16.50/16.58 ( (ord_less_eq int), (zero_zero int), min_1 ) 16.50/16.58 ( (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.58 ( (ord_less_eq int), (zero_zero int), s ) 16.50/16.58 ( (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.50/16.58 ( (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) pls) ) 16.50/16.58 ( (ord_less_eq int), (zero_zero int), skv_4 ) 16.50/16.58 ( (ord_less_eq int), (zero_zero int), skv_10 ) 16.50/16.58 ( (ord_less_eq int), min_1, pls ) 16.50/16.58 ( (ord_less_eq int), min_1, min_1 ) 16.50/16.58 ( (ord_less int), (one_one int), t ) 16.50/16.58 ( (ord_less int), pls, (one_one int) ) 16.50/16.58 ( (ord_less int), pls, pls ) 16.50/16.58 ( (ord_less int), pls, min_1 ) 16.50/16.58 ( (ord_less int), pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.50/16.58 ( (ord_less int), min_1, pls ) 16.50/16.58 ( (ord_less int), min_1, min_1 ) 16.50/16.58 ( (ord_less int), s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.50/16.58 ( (ord_less int), t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.50/16.58 ( (ord_less int), skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.50/16.58 ( (ord_less int), skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.50/16.58 ( (dvd_dvd int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 16.50/16.58 ( quadRes, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (number_number_of int) min_1) ) 16.50/16.58 ( (hAPP int (fun int (fun int bool)) zcong s1), s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.50/16.58 ( (hAPP int (fun int (fun int bool)) zcong s1), skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.50/16.58 ( (hAPP int (fun int (fun int bool)) zcong s1), skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.50/16.58 ( (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.50/16.58 ( (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.50/16.58 ( (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.50/16.58 ( (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_14) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.50/16.58 ) 16.50/16.58 (instantiation (forall ((N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (hAPP nat nat suc (zero_zero nat))) N_1))) (hBOOL (hAPP nat bool prime N_1)) (not (forall ((M_2 $$unsorted) (K_1 $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less nat))) (let ((_let_2 (hAPP nat _let_0 _let_1 (hAPP nat nat suc (zero_zero nat))))) (or (not (hBOOL (hAPP nat bool _let_2 K_1))) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 M_2) N_1))) (not (= N_1 (hAPP nat nat (hAPP nat (fun nat nat) (times_times nat) M_2) K_1))) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 K_1) N_1))) (not (hBOOL (hAPP nat bool _let_2 M_2))))))) ))) ) 16.50/16.58 ( (zero_zero nat) ) 16.50/16.58 ( (hAPP nat nat suc (zero_zero nat)) ) 16.50/16.58 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.58 ) 16.50/16.58 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_162246 $$unsorted)) (or (not (division_ring X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_162246)) (= (one_one X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_162246)) BOUND_VARIABLE_162246))) ) 16.50/16.58 ( bool, fFalse ) 16.50/16.58 ( bool, fTrue ) 16.50/16.58 ( int, pls ) 16.50/16.58 ( int, min_1 ) 16.50/16.58 ( int, s ) 16.50/16.58 ( int, m ) 16.50/16.58 ( int, s1 ) 16.50/16.58 ( int, t ) 16.50/16.58 ( (fun int bool), nat_neg ) 16.50/16.58 ( (fun int bool), zprime ) 16.50/16.58 ( (fun int bool), zEven ) 16.50/16.58 ( (fun int bool), zOdd ) 16.50/16.58 ( (fun int bool), (even_odd_even int) ) 16.50/16.58 ( (fun int bool), twoSqu1091635170sum2sq ) 16.50/16.58 ( (fun int bool), nat_is_nat ) 16.50/16.58 ( (fun int (fun int bool)), norRRset ) 16.50/16.58 ( (fun int (fun int bool)), quadRes ) 16.50/16.58 ( (fun int (fun int bool)), sRStar ) 16.50/16.58 ( (fun int (fun int bool)), d22set ) 16.50/16.58 ( (fun int (fun int bool)), sr ) 16.50/16.58 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 16.50/16.58 ( (fun int int), zfact ) 16.50/16.58 ( (fun int int), bit0 ) 16.50/16.58 ( (fun int int), bit1 ) 16.50/16.58 ( (fun int int), (fact_fact int) ) 16.50/16.58 ( (fun int int), pred ) 16.50/16.58 ( (fun int int), succ ) 16.50/16.58 ( (fun nat bool), (even_odd_even nat) ) 16.50/16.58 ( (fun nat bool), prime ) 16.50/16.58 ( (fun nat nat), suc ) 16.50/16.58 ( (fun nat nat), (fact_fact nat) ) 16.50/16.58 ( (fun nat nat), fact ) 16.50/16.58 ( (fun nat nat), nat_size ) 16.50/16.58 ( (fun nat nat), (size_size nat) ) 16.50/16.58 ( (fun (product_prod nat nat) bool), pred_nat ) 16.50/16.58 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 16.50/16.58 ( real, (zero_zero real) ) 16.50/16.58 ( real, pi ) 16.50/16.58 ( (fun real real), ln ) 16.50/16.58 ( (fun real real), cos ) 16.50/16.58 ( (fun real real), sqrt ) 16.50/16.58 ( (fun real real), sin ) 16.50/16.58 ( (fun real real), arccos ) 16.50/16.58 ( (fun real real), arcsin ) 16.50/16.58 ( (fun real real), tan ) 16.50/16.58 ( (fun real real), arctan ) 16.50/16.58 ( (fun nat (fun nat bool)), coprime ) 16.50/16.58 ( complex, ii ) 16.50/16.58 ( (fun nat real), (real_1 nat) ) 16.50/16.58 ( (fun nat real), sin_coeff ) 16.50/16.58 ( (fun nat real), cos_coeff ) 16.50/16.58 ( (filter nat), sequentially ) 16.50/16.58 ( (fun int (fun int int)), (gcd_gcd int) ) 16.50/16.58 ( (fun int (fun int int)), legendre ) 16.50/16.58 ( (fun int (fun int int)), legacy_zgcd ) 16.50/16.58 ( (fun int (fun int int)), standardRes ) 16.50/16.58 ( (fun int (fun int int)), nat_tsub ) 16.50/16.58 ( (fun int (fun int int)), multInv ) 16.50/16.58 ( (fun int (fun int int)), z3mod ) 16.50/16.58 ( (fun int (fun int int)), z3div ) 16.50/16.58 ( (fun int (fun int int)), int_gcd ) 16.50/16.58 ( (fun int (fun int int)), int_lcm ) 16.50/16.58 ( (fun int (fun int int)), inv ) 16.50/16.58 ( (fun complex complex), expi ) 16.50/16.58 ( (fun complex complex), cnj ) 16.50/16.58 ( (fun real complex), cis ) 16.50/16.58 ( (fun int nat), nat_1 ) 16.50/16.58 ( (fun int nat), phi ) 16.50/16.58 ( (fun (fun int bool) bool), nat_nat_set ) 16.50/16.58 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 16.50/16.58 ( (fun nat (fun nat nat)), nat_gcd ) 16.50/16.58 ( (fun nat (fun nat nat)), nat_lcm ) 16.50/16.58 ( (fun (fun int bool) int), (the int) ) 16.50/16.58 ( (fun complex real), re ) 16.50/16.58 ( (fun complex real), im ) 16.50/16.58 ( (fun complex real), arg ) 16.50/16.58 ( (fun bool bool), fNot ) 16.50/16.58 ( (fun nat (fun real real)), root ) 16.50/16.58 ( (fun real (fun real real)), log ) 16.50/16.58 ( (fun real (fun real real)), powr ) 16.50/16.58 ( (fun bool (fun bool bool)), fimplies ) 16.50/16.58 ( (fun bool (fun bool bool)), fconj ) 16.50/16.58 ( (fun bool (fun bool bool)), fdisj ) 16.50/16.59 ( (fun int (fun int (product_prod int int))), negDivAlg ) 16.50/16.59 ( (fun int (fun int (product_prod int int))), posDivAlg ) 16.50/16.59 ( (fun int (fun int (product_prod int int))), divmod_int ) 16.50/16.59 ( (fun int (fun int (product_prod int int))), pdivmod ) 16.50/16.59 ( (fun int (fun int (product_prod int int))), norm_frac ) 16.50/16.59 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 16.50/16.59 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 16.50/16.59 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 16.50/16.59 ( (fun int (fun int (fun int bool))), zcong ) 16.50/16.59 ( (fun int (fun int (fun int bool))), zcongm ) 16.50/16.59 ( (fun int (fun int (fun int bool))), noXRRset ) 16.50/16.59 ( (fun int (fun int (fun int bool))), bnorRset ) 16.50/16.59 ( (fun int (fun int (fun int bool))), wset ) 16.50/16.59 ( (fun (product_prod int int) bool), frac_1 ) 16.50/16.59 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 16.50/16.59 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 16.50/16.59 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 16.50/16.59 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 16.50/16.59 ( (fun (fun nat rat) bool), vanishes ) 16.50/16.59 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 16.50/16.59 ( (fun code_code_numeral nat), code_c271388182l_size ) 16.50/16.59 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 16.50/16.59 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 16.50/16.59 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 16.50/16.59 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 16.50/16.59 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 16.50/16.59 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 16.50/16.59 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 16.50/16.59 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 16.50/16.59 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 16.50/16.59 ( (fun complex nat), complex_size ) 16.50/16.59 ( (fun complex nat), (size_size complex) ) 16.50/16.59 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 16.50/16.59 ( (fun nat (fun nat (product_prod int int))), bezw ) 16.50/16.59 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 16.50/16.59 ( (fun int (fun nat nat)), nat_aux ) 16.50/16.59 ( (fun int (fun (fun int bool) bool)), rsetR ) 16.50/16.59 ( (fun int (fun (fun int bool) bool)), resSet ) 16.50/16.59 ( (fun int (list int)), quickc666637781d_zero ) 16.50/16.59 ( (fun (product_prod int int) rat), frct ) 16.50/16.59 ( (fun int (fun int rat)), fract ) 16.50/16.59 ( (fun real (fun real complex)), complex_1 ) 16.50/16.59 ( (fun real (fun real complex)), rcis ) 16.50/16.59 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 16.50/16.59 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 16.50/16.59 ( (fun int real), (real_1 int) ) 16.50/16.59 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 16.50/16.59 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 16.50/16.59 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 16.50/16.59 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 16.50/16.59 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 16.50/16.59 ( (fun real nat), natfloor ) 16.50/16.59 ( (fun real nat), natceiling ) 16.50/16.59 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 16.50/16.59 ( (fun quickcheck_code_int int), quickcheck_int_of ) 16.50/16.59 ( (fun rat (product_prod int int)), quotient_of ) 16.50/16.59 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 16.50/16.59 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 16.50/16.59 ( (fun rat real), ratreal ) 16.50/16.59 ( (fun code_code_numeral int), code_int_of ) 16.50/16.59 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 16.50/16.59 ( (fun int quickcheck_code_int), quickcheck_of_int ) 16.50/16.59 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 16.50/16.59 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (deriv X_a))) (or (not (real_normed_field X_a)) (= _let_0 (ti (fun (fun X_a X_a) (fun X_a (fun X_a bool))) _let_0)))) ) 16.50/16.59 ( bool ) 16.50/16.59 ( nat ) 16.50/16.59 ( int ) 16.50/16.59 ( (fun int bool) ) 16.50/16.59 ( (fun int (fun int bool)) ) 16.50/16.59 ( (fun int int) ) 16.50/16.59 ( (fun nat bool) ) 16.50/16.59 ( (product_prod nat nat) ) 16.50/16.59 ( real ) 16.50/16.59 ( (fun real bool) ) 16.50/16.59 ( (fun real real) ) 16.50/16.59 ( complex ) 16.50/16.59 ( (fun nat real) ) 16.50/16.59 ( (filter nat) ) 16.50/16.59 ( (product_prod int int) ) 16.50/16.59 ( code_code_numeral ) 16.50/16.59 ( (fun int (fun int (fun int bool))) ) 16.50/16.59 ( (product_prod real real) ) 16.50/16.59 ( (fun (product_prod int int) bool) ) 16.50/16.59 ( (fun nat rat) ) 16.50/16.59 ( (filter real) ) 16.50/16.59 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 16.50/16.59 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 16.50/16.59 ( (fun (product_prod int int) int) ) 16.50/16.59 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 16.50/16.59 ( (fun int real) ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_162432 $$unsorted)) (or (not (real_algebra_1 X_a)) (not (number_ring X_a)) (= (hAPP real X_a (of_real X_a) (hAPP int real (number_number_of real) BOUND_VARIABLE_162432)) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_162432))) ) 16.50/16.59 ( nat, pls ) 16.50/16.59 ( nat, (hAPP int int bit1 pls) ) 16.50/16.59 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.50/16.59 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.50/16.59 ( int, pls ) 16.50/16.59 ( int, (hAPP int int bit1 pls) ) 16.50/16.59 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.50/16.59 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.50/16.59 ( int, min_1 ) 16.50/16.59 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.59 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.50/16.59 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.50/16.59 ( real, min_1 ) 16.50/16.59 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.59 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.50/16.59 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.59 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 16.50/16.59 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.50/16.59 ( complex, min_1 ) 16.50/16.59 ( quickcheck_code_int, (one_one int) ) 16.50/16.59 ( quickcheck_code_int, (zero_zero int) ) 16.50/16.59 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 16.50/16.59 ( code_code_numeral, pls ) 16.50/16.59 ( code_code_numeral, (hAPP int int bit1 pls) ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_162450 $$unsorted) (BOUND_VARIABLE_162451 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member X_a))) (let ((_let_3 (field_char_0_Rats X_a))) (or (not (field_char_0 X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_162451) _let_3))) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_162450) _let_3))) (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_162451) BOUND_VARIABLE_162450)) _let_3))))))) ) 16.50/16.59 ( nat, (one_one nat), (one_one nat) ) 16.50/16.59 ( int, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 16.50/16.59 ( int, (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((A_1 $$unsorted) (N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_1))) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) A_1))) (not (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) X))) (not (= A_1 (hAPP nat real (hAPP real (fun nat real) (power_power real) X) N_1))) (not (forall ((Y $$unsorted)) (or (not (= A_1 (hAPP nat real (hAPP real (fun nat real) (power_power real) Y) N_1))) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) Y))) (= X Y)) ))) ))) ) 16.50/16.59 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((K $$unsorted) (Ma $$unsorted) (N $$unsorted)) (let ((_let_0 (hAPP nat (fun nat nat) (plus_plus nat) K))) (= (= (hAPP nat nat _let_0 Ma) (hAPP nat nat _let_0 N)) (= Ma N))) ) 16.50/16.59 ( (one_one nat), (one_one nat), (one_one nat) ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_162519 $$unsorted) (BOUND_VARIABLE_162527 $$unsorted)) (let ((_let_0 (number_number_of int))) (let ((_let_1 (number_number_of nat))) (let ((_let_2 (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)))) (let ((_let_3 (semiring_1_of_nat X_a))) (or (not (number_ring X_a)) (and (or (hBOOL (hAPP int bool _let_2 (hAPP int int _let_0 BOUND_VARIABLE_162519))) (= (zero_zero X_a) (hAPP nat X_a _let_3 (hAPP int nat _let_1 BOUND_VARIABLE_162519)))) (or (not (hBOOL (hAPP int bool _let_2 (hAPP int int _let_0 BOUND_VARIABLE_162527)))) (= (hAPP nat X_a _let_3 (hAPP int nat _let_1 BOUND_VARIABLE_162527)) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_162527))))))))) ) 16.50/16.59 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.59 ( real, min_1, min_1 ) 16.50/16.59 ( rat, (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 16.50/16.59 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_162556 $$unsorted) (BOUND_VARIABLE_162557 $$unsorted)) (or (not (linord1117847801e_zero X_a)) (not (forall ((Z_2 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (or (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) Z_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 Z_2) (one_one X_a)))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) Z_2) BOUND_VARIABLE_162556)) BOUND_VARIABLE_162557))))) )) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_162556) BOUND_VARIABLE_162557))) ) 16.50/16.59 ( int, (one_one int), t ) 16.50/16.59 ( int, (zero_zero int), (one_one int) ) 16.50/16.59 ( int, (zero_zero int), min_1 ) 16.50/16.59 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.59 ( int, (zero_zero int), s ) 16.50/16.59 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.50/16.59 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 16.50/16.59 ( int, (zero_zero int), skv_4 ) 16.50/16.59 ( int, (zero_zero int), skv_10 ) 16.50/16.59 ( int, min_1, pls ) 16.50/16.59 ( int, min_1, min_1 ) 16.50/16.59 ( real, (zero_zero real), pi ) 16.50/16.59 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.59 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.59 ( real, (zero_zero real), skv_3 ) 16.50/16.59 ( real, (zero_zero real), skv_5 ) 16.50/16.59 ( real, (zero_zero real), skv_7 ) 16.50/16.59 ( real, (zero_zero real), skv_12 ) 16.50/16.59 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.50/16.59 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.59 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.50/16.59 ( real, skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_162672 $$unsorted) (BOUND_VARIABLE_162673 $$unsorted) (BOUND_VARIABLE_162674 $$unsorted)) (let ((_let_0 (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_162674))) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (one_one X_a)) BOUND_VARIABLE_162674))) (= (= BOUND_VARIABLE_162672 BOUND_VARIABLE_162673) (= (hAPP nat X_a _let_0 BOUND_VARIABLE_162673) (hAPP nat X_a _let_0 BOUND_VARIABLE_162672))))) ) 16.50/16.59 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 16.50/16.59 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 16.50/16.59 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_14 ) 16.50/16.59 ( complex, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), ii ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((Y_2 $$unsorted) (N $$unsorted)) (let ((_let_0 (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N))) (= (hBOOL (hAPP real bool _let_0 Y_2)) (hBOOL (hAPP real bool _let_0 (hAPP real real (hAPP nat (fun real real) root N) Y_2)))))) ) 16.50/16.59 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.59 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.59 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.59 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_162703 $$unsorted) (BOUND_VARIABLE_162704 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (one_one X_a))) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_162704))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_162704) _let_2))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_162704) (hAPP nat nat suc BOUND_VARIABLE_162703))) _let_2)))))) ) 16.50/16.59 ( int, (hAPP nat nat suc (zero_zero nat)), s ) 16.50/16.59 ( int, (hAPP nat nat suc (zero_zero nat)), s1 ) 16.50/16.59 ( int, (hAPP nat nat suc (zero_zero nat)), skv_14 ) 16.50/16.59 ( complex, (hAPP nat nat suc (zero_zero nat)), ii ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((Y_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) Y_1))) (not (forall ((X $$unsorted)) (not (= Y_1 (hAPP real real (exp real) X))) ))) ) 16.50/16.59 ( pi ) 16.50/16.59 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.59 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.59 ( skv_2 ) 16.50/16.59 ( skv_8 ) 16.50/16.59 ( skv_9 ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((A_1 $$unsorted)) (let ((_let_0 (one_one int))) (or (not (= _let_0 (hAPP nat int (hAPP int (fun nat int) (power_power int) A_1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (= _let_0 (hAPP int int (abs_abs int) A_1)))) ) 16.50/16.59 ( s ) 16.50/16.59 ( s1 ) 16.50/16.59 ( skv_14 ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((R_4 $$unsorted)) (= (hAPP real complex (hAPP real (fun real complex) rcis R_4) (zero_zero real)) (hAPP real complex (of_real complex) R_4)) ) 16.50/16.59 ( pi ) 16.50/16.59 ( (hAPP int real (number_number_of real) min_1) ) 16.50/16.59 ( (hAPP real real (uminus_uminus real) (one_one real)) ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_162778 $$unsorted) (BOUND_VARIABLE_162779 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (plus_plus X_a))) (or (not (comm_semiring_1 X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_162779) BOUND_VARIABLE_162778) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_162778) BOUND_VARIABLE_162779))))) ) 16.50/16.59 ( nat, (one_one nat), (one_one nat) ) 16.50/16.59 ( int, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 16.50/16.59 ( int, (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.59 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 16.50/16.59 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_162791 $$unsorted) (BOUND_VARIABLE_162792 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP X_a int (archimedean_ceiling X_a) BOUND_VARIABLE_162791)) BOUND_VARIABLE_162792)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_162791) (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_162792))))) ) 16.50/16.59 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero int) ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((F $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) A_2) B_1))) (not (forall ((X $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 A_2) X))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X) B_1))) (hBOOL (hAPP real bool (hAPP (fun real real) _let_0 (isCont real real) F) X))))) )) (not (forall ((X $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 A_2) X))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X) B_1))) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP (fun real real) (fun real _let_0) (deriv real) F) X) (zero_zero real)))))) )) (= (hAPP real real F A_2) (hAPP real real F B_1))) ) 16.50/16.59 ( cos, (zero_zero real), skv_2 ) 16.50/16.59 ( cos, pi, (zero_zero real) ) 16.50/16.59 ( cos, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.59 ( sqrt, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.59 ( sqrt, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.59 ( sin, (zero_zero real), skv_9 ) 16.50/16.59 ( sin, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.59 ( (inverse_inverse real), (zero_zero real), pi ) 16.50/16.59 ( arctan, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.59 ( (sgn_sgn real), (zero_zero real), skv_8 ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((X_1 $$unsorted)) (not (= (zero_zero real) (hAPP real real cos (hAPP real real arctan X_1)))) ) 16.50/16.59 ( (one_one real) ) 16.50/16.59 ( (zero_zero real) ) 16.50/16.59 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.50/16.59 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))))) ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (minus_minus int))) (let ((_let_2 (fun nat int))) (let ((_let_3 (power_power int))) (let ((_let_4 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (= (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (hAPP int _let_0 (plus_plus int) A_1) B)) (hAPP int int (hAPP int _let_0 _let_1 A_1) B)) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_2 _let_3 A_1) _let_4)) (hAPP nat int (hAPP int _let_2 _let_3 B) _let_4)))))))) ) 16.50/16.59 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 16.50/16.59 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((N $$unsorted)) (let ((_let_0 (fun int (fun int bool)))) (let ((_let_1 (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun int _let_2))) (or (not (hBOOL (hAPP int bool _let_1 N))) (= (hAPP (fun int bool) nat (finite_card int) (hAPP (fun int bool) (fun int bool) (collect int) (hAPP (fun int bool) (fun int bool) (hAPP _let_3 (fun (fun int bool) (fun int bool)) (combs int bool bool) (hAPP (fun int bool) _let_3 (hAPP (fun bool _let_2) (fun (fun int bool) _let_3) (combb bool _let_2 int) fconj) _let_1)) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (ord_less int)) N)))) (hAPP int nat nat_1 N))))))) ) 16.50/16.59 ( (one_one int) ) 16.50/16.59 ( (zero_zero int) ) 16.50/16.59 ( min_1 ) 16.50/16.59 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.59 ( s ) 16.50/16.59 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.50/16.59 ( (hAPP int int (number_number_of int) pls) ) 16.50/16.59 ( skv_4 ) 16.50/16.59 ( skv_10 ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_0 (hAPP real (fun real complex) complex_1 A_1))) (= (hAPP complex complex cnj (hAPP real complex _let_0 B)) (hAPP real complex _let_0 (hAPP real real (uminus_uminus real) B)))) ) 16.50/16.59 ( (one_one real), (zero_zero real) ) 16.50/16.59 ( (zero_zero real), (one_one real) ) 16.50/16.59 ( (zero_zero real), (zero_zero real) ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((Y_2 $$unsorted) (X_2 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member int))) (or (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 X_2) zOdd))) (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 Y_2) zEven))) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP int int (hAPP int (fun int int) (minus_minus int) X_2) Y_2)) zOdd)))))) ) 16.50/16.59 ( (hAPP int int (number_number_of int) min_1), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((X_2 $$unsorted) (N $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (zero_zero real))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N))) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (hAPP nat (fun real real) root N) X_2)) _let_2)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_2) _let_2))))))) ) 16.50/16.59 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.59 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.59 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.59 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_162954 $$unsorted) (BOUND_VARIABLE_162955 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)))) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_162955))) (hBOOL (hAPP X_a bool _let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_162955) BOUND_VARIABLE_162954))))) ) 16.50/16.59 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 16.50/16.59 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 16.50/16.59 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_14 ) 16.50/16.59 ( complex, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), ii ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_163010 $$unsorted) (BOUND_VARIABLE_163011 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (plus_plus X_a))) (let ((_let_3 (inverse_inverse X_a))) (let ((_let_4 (times_times X_a))) (let ((_let_5 (hAPP X_a X_a _let_3 BOUND_VARIABLE_163011))) (let ((_let_6 (hAPP X_a X_a _let_3 BOUND_VARIABLE_163010))) (or (not (field X_a)) (= _let_0 (ti X_a BOUND_VARIABLE_163011)) (= _let_0 (ti X_a BOUND_VARIABLE_163010)) (= (hAPP X_a X_a (hAPP X_a _let_1 _let_4 (hAPP X_a X_a (hAPP X_a _let_1 _let_4 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_163011) BOUND_VARIABLE_163010)) _let_5)) _let_6) (hAPP X_a X_a (hAPP X_a _let_1 _let_2 _let_5) _let_6)))))))))) ) 16.50/16.59 ( nat, (one_one nat), (one_one nat) ) 16.50/16.59 ( int, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 16.50/16.59 ( int, (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_163059 $$unsorted) (BOUND_VARIABLE_163060 $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (ord X_a)) (= (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) BOUND_VARIABLE_163059) (hAPP X_a _let_0 (ord_lessThan X_a) BOUND_VARIABLE_163060))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_163059) BOUND_VARIABLE_163060))))) ) 16.50/16.59 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.59 ( int, (one_one int), t ) 16.50/16.59 ( int, pls, (one_one int) ) 16.50/16.59 ( int, pls, pls ) 16.50/16.59 ( int, pls, min_1 ) 16.50/16.59 ( int, pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.50/16.59 ( int, min_1, pls ) 16.50/16.59 ( int, min_1, min_1 ) 16.50/16.59 ( int, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.50/16.59 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.50/16.59 ( int, skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.50/16.59 ( int, skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.50/16.59 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.59 ( real, (zero_zero real), pi ) 16.50/16.59 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.59 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.59 ( real, (zero_zero real), skv_2 ) 16.50/16.59 ( real, (zero_zero real), skv_8 ) 16.50/16.59 ( real, (zero_zero real), skv_9 ) 16.50/16.59 ( real, pi, (zero_zero real) ) 16.50/16.59 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.59 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.59 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 16.50/16.59 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.50/16.59 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_163080 $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (number_ring X_a)) (not (field_char_0 X_a)) (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_163080)) (field_char_0_Rats X_a))))) ) 16.50/16.59 ( nat, pls ) 16.50/16.59 ( nat, (hAPP int int bit1 pls) ) 16.50/16.59 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.50/16.59 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.50/16.59 ( int, pls ) 16.50/16.59 ( int, (hAPP int int bit1 pls) ) 16.50/16.59 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.50/16.59 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.50/16.59 ( int, min_1 ) 16.50/16.59 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.59 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.50/16.59 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.50/16.59 ( real, min_1 ) 16.50/16.59 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.59 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.50/16.59 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.59 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 16.50/16.59 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.50/16.59 ( complex, min_1 ) 16.50/16.59 ( quickcheck_code_int, (one_one int) ) 16.50/16.59 ( quickcheck_code_int, (zero_zero int) ) 16.50/16.59 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 16.50/16.59 ( code_code_numeral, pls ) 16.50/16.59 ( code_code_numeral, (hAPP int int bit1 pls) ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_163095 $$unsorted) (BOUND_VARIABLE_163096 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (plus_plus X_a))) (let ((_let_2 (uminus_uminus X_a))) (or (not (group_add X_a)) (= (hAPP X_a X_a _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_163095) BOUND_VARIABLE_163096)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_163096)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_163095))))))) ) 16.50/16.59 ( nat, (one_one nat), (one_one nat) ) 16.50/16.59 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 16.50/16.59 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((N_1 $$unsorted)) (= N_1 (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) (hAPP nat nat suc N_1)) (one_one nat))) ) 16.50/16.59 ( (zero_zero nat) ) 16.50/16.59 ( (hAPP nat nat suc (zero_zero nat)) ) 16.50/16.59 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((X_a $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) (hAPP _let_0 nat (finite_card X_a) A_3)))) (hBOOL (hAPP _let_0 bool (finite_finite_1 X_a) A_3)))) ) 16.50/16.59 ( nat, (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((X_a $$unsorted)) (or (not (semiring_1 X_a)) (= (hAPP nat X_a (semiring_1_of_nat X_a) (one_one nat)) (one_one X_a))) ) 16.50/16.59 ( nat ) 16.50/16.59 ( int ) 16.50/16.59 ( real ) 16.50/16.59 ( rat ) 16.50/16.59 ( complex ) 16.50/16.59 ( quickcheck_code_int ) 16.50/16.59 ( code_code_numeral ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((A_1 $$unsorted)) (= (hAPP real complex (hAPP real (fun real complex) rcis (one_one real)) A_1) (hAPP real complex cis A_1)) ) 16.50/16.59 ( (zero_zero real) ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_163160 $$unsorted)) (let ((_let_0 (number_number_of X_a))) (or (not (number_ring X_a)) (= (hAPP int X_a _let_0 (hAPP int int pred BOUND_VARIABLE_163160)) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (hAPP X_a X_a (uminus_uminus X_a) (one_one X_a))) (hAPP int X_a _let_0 BOUND_VARIABLE_163160))))) ) 16.50/16.59 ( int, pls ) 16.50/16.59 ( real, pls ) 16.50/16.59 ( complex, pls ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (one_one int))) (let ((_let_2 (plus_plus int))) (let ((_let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_4 (div_div int))) (or (hBOOL (hAPP int bool (even_odd_even int) X_1)) (= (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_4 X_1) _let_3)) _let_1) (hAPP int int (hAPP int _let_0 _let_4 (hAPP int int (hAPP int _let_0 _let_2 X_1) _let_1)) _let_3)))))))) ) 16.50/16.59 ( (one_one int) ) 16.50/16.59 ( (zero_zero int) ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (or (not (hBOOL (hAPP int bool nat_is_nat X_1))) (not (hBOOL (hAPP int bool nat_is_nat Y_1))) (hBOOL (hAPP int bool nat_is_nat (hAPP int int (hAPP int (fun int int) (plus_plus int) X_1) Y_1)))) ) 16.50/16.59 ( (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 16.50/16.59 ( (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_163332 $$unsorted) (BOUND_VARIABLE_163333 $$unsorted)) (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun X_a bool))) (let ((_let_2 (ord_less X_a))) (let ((_let_3 (fun nat X_a))) (let ((_let_4 (power_power X_a))) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_1 _let_2 (hAPP nat X_a (hAPP X_a _let_3 _let_4 BOUND_VARIABLE_163332) _let_0)) (hAPP nat X_a (hAPP X_a _let_3 _let_4 BOUND_VARIABLE_163333) _let_0)))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_1 (ord_less_eq X_a) (zero_zero X_a)) BOUND_VARIABLE_163333))) (hBOOL (hAPP X_a bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_163332) BOUND_VARIABLE_163333)))))))) ) 16.50/16.59 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.59 ( int, (one_one int), t ) 16.50/16.59 ( int, pls, (one_one int) ) 16.50/16.59 ( int, pls, pls ) 16.50/16.59 ( int, pls, min_1 ) 16.50/16.59 ( int, pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.50/16.59 ( int, min_1, pls ) 16.50/16.59 ( int, min_1, min_1 ) 16.50/16.59 ( int, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.50/16.59 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.50/16.59 ( int, skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.50/16.59 ( int, skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.50/16.59 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.59 ( real, (zero_zero real), pi ) 16.50/16.59 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.59 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.59 ( real, (zero_zero real), skv_2 ) 16.50/16.59 ( real, (zero_zero real), skv_8 ) 16.50/16.59 ( real, (zero_zero real), skv_9 ) 16.50/16.59 ( real, pi, (zero_zero real) ) 16.50/16.59 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.59 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.59 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 16.50/16.59 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.50/16.59 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_163373 $$unsorted) (BOUND_VARIABLE_163374 $$unsorted) (BOUND_VARIABLE_163375 $$unsorted)) (let ((_let_0 (filter real))) (let ((_let_1 (fun _let_0 bool))) (or (not (metric_space X_a)) (not (forall ((S_2 $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (fun (filter nat) bool))) (let ((_let_2 (fun nat X_a))) (or (not (forall ((N_2 $$unsorted)) (not (= (hAPP nat real S_2 N_2) BOUND_VARIABLE_163375)) )) (not (hBOOL (hAPP (filter nat) bool (hAPP real _let_1 (hAPP _let_0 (fun real _let_1) (tendsto nat real) S_2) BOUND_VARIABLE_163375) sequentially))) (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_1 (hAPP _let_2 (fun X_a _let_1) (tendsto nat X_a) (hAPP _let_0 _let_2 (hAPP (fun real X_a) (fun _let_0 _let_2) (combb real X_a nat) BOUND_VARIABLE_163373) S_2)) BOUND_VARIABLE_163374) sequentially)))))) )) (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 (hAPP (fun real X_a) (fun X_a _let_1) (tendsto real X_a) BOUND_VARIABLE_163373) BOUND_VARIABLE_163374) (hAPP real _let_0 (at real) BOUND_VARIABLE_163375)))))) ) 16.50/16.59 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((X_2 $$unsorted) (Y_2 $$unsorted) (N $$unsorted)) (let ((_let_0 (hAPP nat (fun real real) root N))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N))) (= (= (hAPP real real _let_0 Y_2) (hAPP real real _let_0 X_2)) (= X_2 Y_2)))) ) 16.50/16.59 ( (one_one real), (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.59 ( (zero_zero real), (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.59 ( (zero_zero real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.59 ( (zero_zero real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.59 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.59 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted) (P_5 $$unsorted) (Q_3 $$unsorted)) (let ((_let_0 (fun int rat))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (hAPP int rat (hAPP int _let_0 fract A_1) B))) (or (not (= (hAPP rat _let_1 quotient_of _let_2) (hAPP int _let_1 (hAPP int (fun int _let_1) (product_Pair int int) P_5) Q_3))) (= (hAPP int rat (hAPP int _let_0 fract P_5) Q_3) _let_2))))) ) 16.50/16.59 ( (one_one int), (one_one int), (zero_zero int), (one_one int) ) 16.50/16.59 ( (zero_zero int), (one_one int), s, (one_one int) ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((N_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_0 (real_1 int))) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP int real _let_0 N_1)) (hAPP real real (hAPP real (fun real real) (plus_plus real) (hAPP int real _let_0 X_1)) (one_one real))))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) N_1) X_1)))) ) 16.50/16.59 ( (one_one int), t ) 16.50/16.59 ( (zero_zero int), (one_one int) ) 16.50/16.59 ( (zero_zero int), min_1 ) 16.50/16.59 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.59 ( (zero_zero int), s ) 16.50/16.59 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.50/16.59 ( (zero_zero int), (hAPP int int (number_number_of int) pls) ) 16.50/16.59 ( (zero_zero int), skv_4 ) 16.50/16.59 ( (zero_zero int), skv_10 ) 16.50/16.59 ( min_1, pls ) 16.50/16.59 ( min_1, min_1 ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_163519 $$unsorted) (BOUND_VARIABLE_163520 $$unsorted)) (let ((_let_0 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_1 (hAPP int nat (number_number_of nat) _let_0))) (let ((_let_2 (fun X_a X_a))) (let ((_let_3 (minus_minus X_a))) (let ((_let_4 (fun nat X_a))) (let ((_let_5 (power_power X_a))) (let ((_let_6 (times_times X_a))) (or (not (number_ring X_a)) (= (hAPP nat X_a (hAPP X_a _let_4 _let_5 (hAPP X_a X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_163519) BOUND_VARIABLE_163520)) _let_1) (hAPP X_a X_a (hAPP X_a _let_2 _let_3 (hAPP X_a X_a (hAPP X_a _let_2 (plus_plus X_a) (hAPP nat X_a (hAPP X_a _let_4 _let_5 BOUND_VARIABLE_163519) _let_1)) (hAPP nat X_a (hAPP X_a _let_4 _let_5 BOUND_VARIABLE_163520) _let_1))) (hAPP X_a X_a (hAPP X_a _let_2 _let_6 (hAPP X_a X_a (hAPP X_a _let_2 _let_6 (hAPP int X_a (number_number_of X_a) _let_0)) BOUND_VARIABLE_163519)) BOUND_VARIABLE_163520))))))))))) ) 16.50/16.59 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 16.50/16.59 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 16.50/16.59 ( complex, (hAPP real complex (of_real complex) pi), ii ) 16.50/16.59 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((Z_1 $$unsorted)) (= (hAPP real complex (of_real complex) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP complex real re Z_1))) (hAPP complex complex (hAPP complex (fun complex complex) (plus_plus complex) Z_1) (hAPP complex complex cnj Z_1))) ) 16.50/16.59 ( (one_one complex) ) 16.50/16.59 ( ii ) 16.50/16.59 ( (zero_zero complex) ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((M $$unsorted) (K_4 $$unsorted) (N_1 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int (fun int bool) (dvd_dvd int) K_4))) (or (not (= (one_one int) (hAPP int int (hAPP int _let_0 (gcd_gcd int) K_4) N_1))) (not (hBOOL (hAPP int bool _let_1 (hAPP int int (hAPP int _let_0 (times_times int) M) N_1)))) (hBOOL (hAPP int bool _let_1 M))))) ) 16.50/16.59 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (zero_zero int)) A_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) A_1) B))) (= (ti int A_1) (hAPP int int (hAPP int (fun int int) (div_mod int) A_1) B)))) ) 16.50/16.59 ( (one_one int), pls ) 16.50/16.59 ( pls, pls ) 16.50/16.59 ( pls, min_1 ) 16.50/16.59 ( min_1, pls ) 16.50/16.59 ( min_1, min_1 ) 16.50/16.59 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), pls ) 16.50/16.59 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s ) 16.50/16.59 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 16.50/16.59 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_4 ) 16.50/16.59 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_10 ) 16.50/16.59 ( t, (one_one int) ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((Z_1 $$unsorted)) (let ((_let_0 (fun nat nat))) (= (hAPP nat nat (hAPP nat _let_0 (times_times nat) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) Z_1) (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) Z_1) Z_1))) ) 16.50/16.59 ( (one_one nat) ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((I_1 $$unsorted)) (let ((_let_0 (zero_zero int))) (or (not (= _let_0 (ti int I_1))) (= _let_0 (hAPP int int (sgn_sgn int) I_1)))) ) 16.50/16.59 ( pls ) 16.50/16.59 ( min_1 ) 16.50/16.59 ( s ) 16.50/16.59 ( m ) 16.50/16.59 ( s1 ) 16.50/16.59 ( t ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((I_1 $$unsorted)) (let ((_let_0 (one_one int))) (let ((_let_1 (hAPP int int (sgn_sgn int) I_1))) (let ((_let_2 (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) I_1)))) (or (= (zero_zero int) (ti int I_1)) (and (or _let_2 (= (hAPP int int (uminus_uminus int) _let_0) _let_1)) (or (not _let_2) (= _let_0 _let_1))))))) ) 16.50/16.59 ( (one_one int) ) 16.50/16.59 ( pls ) 16.50/16.59 ( min_1 ) 16.50/16.59 ( s ) 16.50/16.59 ( m ) 16.50/16.59 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.50/16.59 ( s1 ) 16.50/16.59 ( t ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_163710 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (comm_semiring_1 X_a)) (= _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_163710) _let_0)))) ) 16.50/16.59 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.59 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.59 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.50/16.59 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.59 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.59 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 16.50/16.59 ( complex, ii ) 16.50/16.59 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.59 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((F $$unsorted) (L $$unsorted) (C_1 $$unsorted)) (let ((_let_0 (filter real))) (let ((_let_1 (fun _let_0 bool))) (or (not (hBOOL (hAPP _let_0 bool (hAPP real _let_1 (hAPP (fun real real) (fun real _let_1) (tendsto real real) F) L) (hAPP real _let_0 (at real) C_1)))) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) L) (zero_zero real)))) (not (forall ((R_2 $$unsorted)) (or (not (forall ((X $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (abs_abs real) (hAPP real real (hAPP real (fun real real) (minus_minus real) C_1) X))) R_2))) (= C_1 X) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real F X)) (zero_zero real)))))) )) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) R_2)))) ))))) ) 16.50/16.59 ( (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int int (number_number_of int) K_4) (ti int K_4)) ) 16.50/16.59 ( pls ) 16.50/16.59 ( (hAPP int int bit1 pls) ) 16.50/16.59 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.50/16.59 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.50/16.59 ( min_1 ) 16.50/16.59 ( s ) 16.50/16.59 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.59 ( m ) 16.50/16.59 ( s1 ) 16.50/16.59 ( t ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_163759 $$unsorted) (BOUND_VARIABLE_163760 $$unsorted)) (or (not (comm_semiring_1 X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_163759) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_163760) BOUND_VARIABLE_163759)))) ) 16.50/16.59 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.59 ( int, t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.50/16.59 ( int, skv_13, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.50/16.59 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.59 ( real, pi, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 16.50/16.59 ( real, (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.59 ( real, (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.59 ( complex, ii, ii ) 16.50/16.59 ( complex, ii, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 16.50/16.59 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((N_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)))) (or (not (hBOOL (hAPP int bool _let_0 X_1))) (hBOOL (hAPP int bool _let_0 (hAPP nat int (hAPP int (fun nat int) (power_power int) X_1) N_1))))) ) 16.50/16.59 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 16.50/16.59 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 16.50/16.59 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_14 ) 16.50/16.59 ) 16.50/16.59 (instantiation (forall ((Z_1 $$unsorted)) (= (hAPP real real sqrt (hAPP complex real re (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) Z_1) (hAPP complex complex cnj Z_1)))) (hAPP complex real (norm_norm complex) Z_1)) ) 16.50/16.59 ( (one_one complex) ) 16.50/16.59 ( ii ) 16.50/16.59 ( (zero_zero complex) ) 16.50/16.59 ( (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.59 ( (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 16.50/16.59 ) 16.50/16.60 (instantiation (forall ((Z $$unsorted) (W_1 $$unsorted)) (let ((_let_0 (fun int bool))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) Z) W_1)) (and (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) Z) W_1)) (not (= (ti int Z) (ti int W_1)))))) ) 16.50/16.60 ( (one_one int), t ) 16.50/16.60 ( (zero_zero int), (one_one int) ) 16.50/16.60 ( (zero_zero int), min_1 ) 16.50/16.60 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.60 ( (zero_zero int), s ) 16.50/16.60 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.50/16.60 ( (zero_zero int), (hAPP int int (number_number_of int) pls) ) 16.50/16.60 ( (zero_zero int), skv_4 ) 16.50/16.60 ( (zero_zero int), skv_10 ) 16.50/16.60 ( pls, (one_one int) ) 16.50/16.60 ( pls, pls ) 16.50/16.60 ( pls, min_1 ) 16.50/16.60 ( pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.50/16.60 ( min_1, pls ) 16.50/16.60 ( min_1, min_1 ) 16.50/16.60 ( s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.50/16.60 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.50/16.60 ( skv_4, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.50/16.60 ( skv_10, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.50/16.60 ) 16.50/16.60 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_163895 $$unsorted) (BOUND_VARIABLE_163896 $$unsorted)) (let ((_let_0 (inverse_inverse X_a))) (let ((_let_1 (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_163896))) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP X_a X_a _let_0 BOUND_VARIABLE_163895)) (hAPP X_a X_a _let_0 BOUND_VARIABLE_163896)))) (not (hBOOL (hAPP X_a bool _let_1 (zero_zero X_a)))) (hBOOL (hAPP X_a bool _let_1 BOUND_VARIABLE_163895))))) ) 16.50/16.60 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 16.50/16.60 ( int, (one_one int), pls ) 16.50/16.60 ( int, pls, pls ) 16.50/16.60 ( int, pls, min_1 ) 16.50/16.60 ( int, min_1, pls ) 16.50/16.60 ( int, min_1, min_1 ) 16.50/16.60 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), pls ) 16.50/16.60 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s ) 16.50/16.60 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 16.50/16.60 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_4 ) 16.50/16.60 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_10 ) 16.50/16.60 ( int, t, (one_one int) ) 16.50/16.60 ( real, (zero_zero real), pi ) 16.50/16.60 ( real, (zero_zero real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.50/16.60 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.60 ( real, pi, (zero_zero real) ) 16.50/16.60 ( real, pi, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 16.50/16.60 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.60 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.50/16.60 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 16.50/16.60 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 16.50/16.60 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.50/16.60 ( real, skv_2, (zero_zero real) ) 16.50/16.60 ( real, skv_8, (zero_zero real) ) 16.50/16.60 ( real, skv_9, (zero_zero real) ) 16.50/16.60 ) 16.50/16.60 (instantiation (forall ((N_1 $$unsorted)) (= (hAPP real int (archim2085082626_floor real) (hAPP real real (uminus_uminus real) (hAPP int real (real_1 int) N_1))) (hAPP int int (uminus_uminus int) N_1)) ) 16.50/16.60 ( (one_one int) ) 16.50/16.60 ( (zero_zero int) ) 16.50/16.60 ( pls ) 16.50/16.60 ( min_1 ) 16.50/16.60 ) 16.50/16.60 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_163985 $$unsorted)) (or (not (comm_monoid_mult X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) (one_one X_a)) BOUND_VARIABLE_163985) (ti X_a BOUND_VARIABLE_163985))) ) 16.50/16.60 ( bool, fFalse ) 16.50/16.60 ( bool, fTrue ) 16.50/16.60 ( int, pls ) 16.50/16.60 ( int, min_1 ) 16.50/16.60 ( int, s ) 16.50/16.60 ( int, m ) 16.50/16.60 ( int, s1 ) 16.50/16.60 ( int, t ) 16.50/16.60 ( (fun int bool), nat_neg ) 16.50/16.60 ( (fun int bool), zprime ) 16.50/16.60 ( (fun int bool), zEven ) 16.50/16.60 ( (fun int bool), zOdd ) 16.50/16.60 ( (fun int bool), (even_odd_even int) ) 16.50/16.60 ( (fun int bool), twoSqu1091635170sum2sq ) 16.50/16.60 ( (fun int bool), nat_is_nat ) 16.50/16.60 ( (fun int (fun int bool)), norRRset ) 16.50/16.60 ( (fun int (fun int bool)), quadRes ) 16.50/16.60 ( (fun int (fun int bool)), sRStar ) 16.50/16.60 ( (fun int (fun int bool)), d22set ) 16.50/16.60 ( (fun int (fun int bool)), sr ) 16.50/16.60 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 16.50/16.60 ( (fun int int), zfact ) 16.50/16.60 ( (fun int int), bit0 ) 16.50/16.60 ( (fun int int), bit1 ) 16.50/16.60 ( (fun int int), (fact_fact int) ) 16.50/16.60 ( (fun int int), pred ) 16.50/16.60 ( (fun int int), succ ) 16.50/16.60 ( (fun nat bool), (even_odd_even nat) ) 16.50/16.60 ( (fun nat bool), prime ) 16.50/16.60 ( (fun nat nat), suc ) 16.50/16.60 ( (fun nat nat), (fact_fact nat) ) 16.50/16.60 ( (fun nat nat), fact ) 16.50/16.60 ( (fun nat nat), nat_size ) 16.50/16.60 ( (fun nat nat), (size_size nat) ) 16.50/16.60 ( (fun (product_prod nat nat) bool), pred_nat ) 16.50/16.60 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 16.50/16.60 ( real, pi ) 16.50/16.60 ( (fun real real), ln ) 16.50/16.60 ( (fun real real), cos ) 16.50/16.60 ( (fun real real), sqrt ) 16.50/16.60 ( (fun real real), sin ) 16.50/16.60 ( (fun real real), arccos ) 16.50/16.60 ( (fun real real), arcsin ) 16.50/16.60 ( (fun real real), tan ) 16.50/16.60 ( (fun real real), arctan ) 16.50/16.60 ( (fun nat (fun nat bool)), coprime ) 16.50/16.60 ( complex, ii ) 16.50/16.60 ( (fun nat real), (real_1 nat) ) 16.50/16.60 ( (fun nat real), sin_coeff ) 16.50/16.60 ( (fun nat real), cos_coeff ) 16.50/16.60 ( (filter nat), sequentially ) 16.50/16.60 ( (fun int (fun int int)), (gcd_gcd int) ) 16.50/16.60 ( (fun int (fun int int)), legendre ) 16.50/16.60 ( (fun int (fun int int)), legacy_zgcd ) 16.50/16.60 ( (fun int (fun int int)), standardRes ) 16.50/16.60 ( (fun int (fun int int)), nat_tsub ) 16.50/16.60 ( (fun int (fun int int)), multInv ) 16.50/16.60 ( (fun int (fun int int)), z3mod ) 16.50/16.60 ( (fun int (fun int int)), z3div ) 16.50/16.60 ( (fun int (fun int int)), int_gcd ) 16.50/16.60 ( (fun int (fun int int)), int_lcm ) 16.50/16.60 ( (fun int (fun int int)), inv ) 16.50/16.60 ( (fun complex complex), expi ) 16.50/16.60 ( (fun complex complex), cnj ) 16.50/16.60 ( (fun real complex), cis ) 16.50/16.60 ( (fun int nat), nat_1 ) 16.50/16.60 ( (fun int nat), phi ) 16.50/16.60 ( (fun (fun int bool) bool), nat_nat_set ) 16.50/16.60 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 16.50/16.60 ( (fun nat (fun nat nat)), nat_gcd ) 16.50/16.60 ( (fun nat (fun nat nat)), nat_lcm ) 16.50/16.60 ( (fun (fun int bool) int), (the int) ) 16.50/16.60 ( (fun complex real), re ) 16.50/16.60 ( (fun complex real), im ) 16.50/16.60 ( (fun complex real), arg ) 16.50/16.60 ( (fun bool bool), fNot ) 16.50/16.60 ( (fun nat (fun real real)), root ) 16.50/16.60 ( (fun real (fun real real)), log ) 16.50/16.60 ( (fun real (fun real real)), powr ) 16.50/16.60 ( (fun bool (fun bool bool)), fimplies ) 16.50/16.60 ( (fun bool (fun bool bool)), fconj ) 16.50/16.60 ( (fun bool (fun bool bool)), fdisj ) 16.50/16.60 ( (fun int (fun int (product_prod int int))), negDivAlg ) 16.50/16.60 ( (fun int (fun int (product_prod int int))), posDivAlg ) 16.50/16.60 ( (fun int (fun int (product_prod int int))), divmod_int ) 16.50/16.60 ( (fun int (fun int (product_prod int int))), pdivmod ) 16.50/16.60 ( (fun int (fun int (product_prod int int))), norm_frac ) 16.50/16.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 16.50/16.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 16.50/16.60 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 16.50/16.60 ( (fun int (fun int (fun int bool))), zcong ) 16.50/16.60 ( (fun int (fun int (fun int bool))), zcongm ) 16.50/16.60 ( (fun int (fun int (fun int bool))), noXRRset ) 16.50/16.60 ( (fun int (fun int (fun int bool))), bnorRset ) 16.50/16.60 ( (fun int (fun int (fun int bool))), wset ) 16.50/16.60 ( (fun (product_prod int int) bool), frac_1 ) 16.50/16.60 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 16.50/16.60 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 16.50/16.60 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 16.50/16.60 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 16.50/16.60 ( (fun (fun nat rat) bool), vanishes ) 16.50/16.60 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 16.50/16.60 ( (fun code_code_numeral nat), code_c271388182l_size ) 16.50/16.60 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 16.50/16.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 16.50/16.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 16.50/16.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 16.50/16.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 16.50/16.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 16.50/16.60 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 16.50/16.60 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 16.50/16.60 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 16.50/16.60 ( (fun complex nat), complex_size ) 16.50/16.60 ( (fun complex nat), (size_size complex) ) 16.50/16.60 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 16.50/16.60 ( (fun nat (fun nat (product_prod int int))), bezw ) 16.50/16.60 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 16.50/16.60 ( (fun int (fun nat nat)), nat_aux ) 16.50/16.60 ( (fun int (fun (fun int bool) bool)), rsetR ) 16.50/16.60 ( (fun int (fun (fun int bool) bool)), resSet ) 16.50/16.60 ( (fun int (list int)), quickc666637781d_zero ) 16.50/16.60 ( (fun (product_prod int int) rat), frct ) 16.50/16.60 ( (fun int (fun int rat)), fract ) 16.50/16.60 ( (fun real (fun real complex)), complex_1 ) 16.50/16.60 ( (fun real (fun real complex)), rcis ) 16.50/16.60 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 16.50/16.60 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 16.50/16.60 ( (fun int real), (real_1 int) ) 16.50/16.60 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 16.50/16.60 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 16.50/16.60 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 16.50/16.60 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 16.50/16.60 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 16.50/16.60 ( (fun real nat), natfloor ) 16.50/16.60 ( (fun real nat), natceiling ) 16.50/16.60 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 16.50/16.60 ( (fun quickcheck_code_int int), quickcheck_int_of ) 16.50/16.60 ( (fun rat (product_prod int int)), quotient_of ) 16.50/16.60 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 16.50/16.60 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 16.50/16.60 ( (fun rat real), ratreal ) 16.50/16.60 ( (fun code_code_numeral int), code_int_of ) 16.50/16.60 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 16.50/16.60 ( (fun int quickcheck_code_int), quickcheck_of_int ) 16.50/16.60 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 16.50/16.60 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 16.50/16.60 ) 16.50/16.60 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_164001 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (ring_11004092258visors X_a)) (= (= _let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_164001) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (= _let_0 (ti X_a BOUND_VARIABLE_164001))))) ) 16.50/16.60 ( bool, fFalse ) 16.50/16.60 ( bool, fTrue ) 16.50/16.60 ( int, pls ) 16.50/16.60 ( int, min_1 ) 16.50/16.60 ( int, s ) 16.50/16.60 ( int, m ) 16.50/16.60 ( int, s1 ) 16.50/16.60 ( int, t ) 16.50/16.60 ( int, skv_14 ) 16.50/16.60 ( (fun int bool), nat_neg ) 16.50/16.60 ( (fun int bool), zprime ) 16.50/16.60 ( (fun int bool), zEven ) 16.50/16.60 ( (fun int bool), zOdd ) 16.50/16.60 ( (fun int bool), (even_odd_even int) ) 16.50/16.60 ( (fun int bool), twoSqu1091635170sum2sq ) 16.50/16.60 ( (fun int bool), nat_is_nat ) 16.50/16.60 ( (fun int (fun int bool)), norRRset ) 16.50/16.60 ( (fun int (fun int bool)), quadRes ) 16.50/16.60 ( (fun int (fun int bool)), sRStar ) 16.50/16.60 ( (fun int (fun int bool)), d22set ) 16.50/16.60 ( (fun int (fun int bool)), sr ) 16.50/16.60 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 16.50/16.60 ( (fun int int), zfact ) 16.50/16.60 ( (fun int int), bit0 ) 16.50/16.60 ( (fun int int), bit1 ) 16.50/16.60 ( (fun int int), (fact_fact int) ) 16.50/16.60 ( (fun int int), pred ) 16.50/16.60 ( (fun int int), succ ) 16.50/16.60 ( (fun nat bool), (even_odd_even nat) ) 16.50/16.60 ( (fun nat bool), prime ) 16.50/16.60 ( (fun nat nat), suc ) 16.50/16.60 ( (fun nat nat), (fact_fact nat) ) 16.50/16.60 ( (fun nat nat), fact ) 16.50/16.60 ( (fun nat nat), nat_size ) 16.50/16.60 ( (fun nat nat), (size_size nat) ) 16.50/16.60 ( (fun (product_prod nat nat) bool), pred_nat ) 16.50/16.60 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 16.50/16.60 ( real, pi ) 16.50/16.60 ( real, (hAPP int real (number_number_of real) min_1) ) 16.50/16.60 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.60 ( (fun real real), ln ) 16.50/16.60 ( (fun real real), cos ) 16.50/16.60 ( (fun real real), sqrt ) 16.50/16.60 ( (fun real real), sin ) 16.50/16.60 ( (fun real real), arccos ) 16.50/16.60 ( (fun real real), arcsin ) 16.50/16.60 ( (fun real real), tan ) 16.50/16.60 ( (fun real real), arctan ) 16.50/16.60 ( (fun nat (fun nat bool)), coprime ) 16.50/16.60 ( complex, ii ) 16.50/16.60 ( (fun nat real), (real_1 nat) ) 16.50/16.60 ( (fun nat real), sin_coeff ) 16.50/16.60 ( (fun nat real), cos_coeff ) 16.50/16.60 ( (filter nat), sequentially ) 16.50/16.60 ( (fun int (fun int int)), (gcd_gcd int) ) 16.50/16.60 ( (fun int (fun int int)), legendre ) 16.50/16.60 ( (fun int (fun int int)), legacy_zgcd ) 16.50/16.60 ( (fun int (fun int int)), standardRes ) 16.50/16.60 ( (fun int (fun int int)), nat_tsub ) 16.50/16.60 ( (fun int (fun int int)), multInv ) 16.50/16.60 ( (fun int (fun int int)), z3mod ) 16.50/16.60 ( (fun int (fun int int)), z3div ) 16.50/16.60 ( (fun int (fun int int)), int_gcd ) 16.50/16.60 ( (fun int (fun int int)), int_lcm ) 16.50/16.60 ( (fun int (fun int int)), inv ) 16.50/16.60 ( (fun complex complex), expi ) 16.50/16.60 ( (fun complex complex), cnj ) 16.50/16.60 ( (fun real complex), cis ) 16.50/16.60 ( (fun int nat), nat_1 ) 16.50/16.60 ( (fun int nat), phi ) 16.50/16.60 ( (fun (fun int bool) bool), nat_nat_set ) 16.50/16.60 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 16.50/16.60 ( (fun nat (fun nat nat)), nat_gcd ) 16.50/16.60 ( (fun nat (fun nat nat)), nat_lcm ) 16.50/16.60 ( (fun (fun int bool) int), (the int) ) 16.50/16.60 ( (fun complex real), re ) 16.50/16.60 ( (fun complex real), im ) 16.50/16.60 ( (fun complex real), arg ) 16.50/16.60 ( (fun bool bool), fNot ) 16.50/16.60 ( (fun nat (fun real real)), root ) 16.50/16.60 ( (fun real (fun real real)), log ) 16.50/16.60 ( (fun real (fun real real)), powr ) 16.50/16.60 ( (fun bool (fun bool bool)), fimplies ) 16.50/16.60 ( (fun bool (fun bool bool)), fconj ) 16.50/16.60 ( (fun bool (fun bool bool)), fdisj ) 16.50/16.60 ( (fun int (fun int (product_prod int int))), negDivAlg ) 16.50/16.60 ( (fun int (fun int (product_prod int int))), posDivAlg ) 16.50/16.60 ( (fun int (fun int (product_prod int int))), divmod_int ) 16.50/16.60 ( (fun int (fun int (product_prod int int))), pdivmod ) 16.50/16.60 ( (fun int (fun int (product_prod int int))), norm_frac ) 16.50/16.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 16.50/16.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 16.50/16.60 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 16.50/16.60 ( (fun int (fun int (fun int bool))), zcong ) 16.50/16.60 ( (fun int (fun int (fun int bool))), zcongm ) 16.50/16.60 ( (fun int (fun int (fun int bool))), noXRRset ) 16.50/16.60 ( (fun int (fun int (fun int bool))), bnorRset ) 16.50/16.60 ( (fun int (fun int (fun int bool))), wset ) 16.50/16.60 ( (fun (product_prod int int) bool), frac_1 ) 16.50/16.60 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 16.50/16.60 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 16.50/16.60 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 16.50/16.60 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 16.50/16.60 ( (fun (fun nat rat) bool), vanishes ) 16.50/16.60 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 16.50/16.60 ( (fun code_code_numeral nat), code_c271388182l_size ) 16.50/16.60 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 16.50/16.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 16.50/16.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 16.50/16.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 16.50/16.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 16.50/16.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 16.50/16.60 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 16.50/16.60 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 16.50/16.60 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 16.50/16.60 ( (fun complex nat), complex_size ) 16.50/16.60 ( (fun complex nat), (size_size complex) ) 16.50/16.60 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 16.50/16.60 ( (fun nat (fun nat (product_prod int int))), bezw ) 16.50/16.60 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 16.50/16.60 ( (fun int (fun nat nat)), nat_aux ) 16.50/16.60 ( (fun int (fun (fun int bool) bool)), rsetR ) 16.50/16.60 ( (fun int (fun (fun int bool) bool)), resSet ) 16.50/16.60 ( (fun int (list int)), quickc666637781d_zero ) 16.50/16.60 ( (fun (product_prod int int) rat), frct ) 16.50/16.60 ( (fun int (fun int rat)), fract ) 16.50/16.60 ( (fun real (fun real complex)), complex_1 ) 16.50/16.60 ( (fun real (fun real complex)), rcis ) 16.50/16.60 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 16.50/16.60 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 16.50/16.60 ( (fun int real), (real_1 int) ) 16.50/16.60 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 16.50/16.60 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 16.50/16.60 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 16.50/16.60 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 16.50/16.60 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 16.50/16.60 ( (fun real nat), natfloor ) 16.50/16.60 ( (fun real nat), natceiling ) 16.50/16.60 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 16.50/16.60 ( (fun quickcheck_code_int int), quickcheck_int_of ) 16.50/16.60 ( (fun rat (product_prod int int)), quotient_of ) 16.50/16.60 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 16.50/16.60 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 16.50/16.60 ( (fun rat real), ratreal ) 16.50/16.60 ( (fun code_code_numeral int), code_int_of ) 16.50/16.60 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 16.50/16.60 ( (fun int quickcheck_code_int), quickcheck_of_int ) 16.50/16.60 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 16.50/16.60 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 16.50/16.60 ) 16.50/16.60 (instantiation (forall ((Y_2 $$unsorted) (X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) Y_2) X_2))) (= X_2 (hAPP _let_0 real (complete_Sup_Sup real) (hAPP real _let_0 (hAPP real (fun real _let_0) (ord_atLeastAtMost real) Y_2) X_2))))) ) 16.50/16.60 ( (zero_zero real), pi ) 16.50/16.60 ( (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.60 ( (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.60 ( (zero_zero real), skv_3 ) 16.50/16.60 ( (zero_zero real), skv_5 ) 16.50/16.60 ( (zero_zero real), skv_7 ) 16.50/16.60 ( (zero_zero real), skv_12 ) 16.50/16.60 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.50/16.60 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.60 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.50/16.60 ( skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.60 ) 16.50/16.60 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_164053 $$unsorted)) (or (not (archim1727834104eiling X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_164053) (hAPP int X_a (ring_1_of_int X_a) (hAPP X_a int (archimedean_ceiling X_a) BOUND_VARIABLE_164053))))) ) 16.50/16.60 ( int, (one_one int) ) 16.50/16.60 ( int, (zero_zero int) ) 16.50/16.60 ( int, min_1 ) 16.50/16.60 ( real, (zero_zero real) ) 16.50/16.60 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.60 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.60 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.60 ( real, skv_5 ) 16.50/16.60 ) 16.50/16.60 (instantiation (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (times_times real))) (let ((_let_2 (hAPP real _let_0 _let_1 (hAPP complex real re X_1)))) (let ((_let_3 (hAPP complex real re Y_1))) (let ((_let_4 (hAPP real _let_0 _let_1 (hAPP complex real im X_1)))) (let ((_let_5 (hAPP complex real im Y_1))) (= (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) X_1) Y_1) (hAPP real complex (hAPP real (fun real complex) complex_1 (hAPP real real (hAPP real _let_0 (minus_minus real) (hAPP real real _let_2 _let_3)) (hAPP real real _let_4 _let_5))) (hAPP real real (hAPP real _let_0 (plus_plus real) (hAPP real real _let_2 _let_5)) (hAPP real real _let_4 _let_3)))))))))) ) 16.50/16.60 ( ii, ii ) 16.50/16.60 ( (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 16.50/16.60 ( (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 16.50/16.60 ) 16.50/16.60 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_164105 $$unsorted)) (let ((_let_0 (of_real X_a))) (or (not (real_algebra_1 X_a)) (= (hAPP real X_a _let_0 (hAPP real real (uminus_uminus real) BOUND_VARIABLE_164105)) (hAPP X_a X_a (uminus_uminus X_a) (hAPP real X_a _let_0 BOUND_VARIABLE_164105))))) ) 16.50/16.60 ( complex, (one_one real) ) 16.50/16.60 ) 16.50/16.60 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_164125 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (linordered_idom X_a)) (= (= _let_0 (hAPP X_a X_a (sgn_sgn X_a) BOUND_VARIABLE_164125)) (= _let_0 (ti X_a BOUND_VARIABLE_164125))))) ) 16.50/16.60 ( bool, fFalse ) 16.50/16.60 ( bool, fTrue ) 16.50/16.60 ( int, pls ) 16.50/16.60 ( int, min_1 ) 16.50/16.60 ( int, s ) 16.50/16.60 ( int, m ) 16.50/16.60 ( int, s1 ) 16.50/16.60 ( int, t ) 16.50/16.60 ( (fun int bool), nat_neg ) 16.50/16.60 ( (fun int bool), zprime ) 16.50/16.60 ( (fun int bool), zEven ) 16.50/16.60 ( (fun int bool), zOdd ) 16.50/16.60 ( (fun int bool), (even_odd_even int) ) 16.50/16.60 ( (fun int bool), twoSqu1091635170sum2sq ) 16.50/16.60 ( (fun int bool), nat_is_nat ) 16.50/16.60 ( (fun int (fun int bool)), norRRset ) 16.50/16.60 ( (fun int (fun int bool)), quadRes ) 16.50/16.60 ( (fun int (fun int bool)), sRStar ) 16.50/16.60 ( (fun int (fun int bool)), d22set ) 16.50/16.60 ( (fun int (fun int bool)), sr ) 16.50/16.60 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 16.50/16.60 ( (fun int int), zfact ) 16.50/16.60 ( (fun int int), bit0 ) 16.50/16.60 ( (fun int int), bit1 ) 16.50/16.60 ( (fun int int), (fact_fact int) ) 16.50/16.60 ( (fun int int), pred ) 16.50/16.60 ( (fun int int), succ ) 16.50/16.60 ( (fun nat bool), (even_odd_even nat) ) 16.50/16.60 ( (fun nat bool), prime ) 16.50/16.60 ( (fun nat nat), suc ) 16.50/16.60 ( (fun nat nat), (fact_fact nat) ) 16.50/16.60 ( (fun nat nat), fact ) 16.50/16.60 ( (fun nat nat), nat_size ) 16.50/16.60 ( (fun nat nat), (size_size nat) ) 16.50/16.60 ( (fun (product_prod nat nat) bool), pred_nat ) 16.50/16.60 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 16.50/16.60 ( real, (zero_zero real) ) 16.50/16.60 ( real, pi ) 16.50/16.60 ( (fun real real), ln ) 16.50/16.60 ( (fun real real), cos ) 16.50/16.60 ( (fun real real), sqrt ) 16.50/16.60 ( (fun real real), sin ) 16.50/16.60 ( (fun real real), arccos ) 16.50/16.60 ( (fun real real), arcsin ) 16.50/16.60 ( (fun real real), tan ) 16.50/16.60 ( (fun real real), arctan ) 16.50/16.60 ( rat, (zero_zero rat) ) 16.50/16.60 ( (fun nat (fun nat bool)), coprime ) 16.50/16.60 ( complex, ii ) 16.50/16.60 ( (fun nat real), (real_1 nat) ) 16.50/16.60 ( (fun nat real), sin_coeff ) 16.50/16.60 ( (fun nat real), cos_coeff ) 16.50/16.60 ( (filter nat), sequentially ) 16.50/16.60 ( (fun int (fun int int)), (gcd_gcd int) ) 16.50/16.60 ( (fun int (fun int int)), legendre ) 16.50/16.60 ( (fun int (fun int int)), legacy_zgcd ) 16.50/16.60 ( (fun int (fun int int)), standardRes ) 16.50/16.60 ( (fun int (fun int int)), nat_tsub ) 16.50/16.60 ( (fun int (fun int int)), multInv ) 16.50/16.60 ( (fun int (fun int int)), z3mod ) 16.50/16.60 ( (fun int (fun int int)), z3div ) 16.50/16.60 ( (fun int (fun int int)), int_gcd ) 16.50/16.60 ( (fun int (fun int int)), int_lcm ) 16.50/16.60 ( (fun int (fun int int)), inv ) 16.50/16.60 ( (fun complex complex), expi ) 16.50/16.60 ( (fun complex complex), cnj ) 16.50/16.60 ( (fun real complex), cis ) 16.50/16.60 ( (fun int nat), nat_1 ) 16.50/16.60 ( (fun int nat), phi ) 16.50/16.60 ( (fun (fun int bool) bool), nat_nat_set ) 16.50/16.60 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 16.50/16.60 ( (fun nat (fun nat nat)), nat_gcd ) 16.50/16.60 ( (fun nat (fun nat nat)), nat_lcm ) 16.50/16.60 ( (fun (fun int bool) int), (the int) ) 16.50/16.60 ( (fun complex real), re ) 16.50/16.60 ( (fun complex real), im ) 16.50/16.60 ( (fun complex real), arg ) 16.50/16.60 ( (fun bool bool), fNot ) 16.50/16.60 ( (fun nat (fun real real)), root ) 16.50/16.60 ( (fun real (fun real real)), log ) 16.50/16.60 ( (fun real (fun real real)), powr ) 16.50/16.60 ( (fun bool (fun bool bool)), fimplies ) 16.50/16.60 ( (fun bool (fun bool bool)), fconj ) 16.50/16.60 ( (fun bool (fun bool bool)), fdisj ) 16.50/16.60 ( (fun int (fun int (product_prod int int))), negDivAlg ) 16.50/16.60 ( (fun int (fun int (product_prod int int))), posDivAlg ) 16.50/16.60 ( (fun int (fun int (product_prod int int))), divmod_int ) 16.50/16.60 ( (fun int (fun int (product_prod int int))), pdivmod ) 16.50/16.60 ( (fun int (fun int (product_prod int int))), norm_frac ) 16.50/16.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 16.50/16.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 16.50/16.60 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 16.50/16.60 ( (fun int (fun int (fun int bool))), zcong ) 16.50/16.60 ( (fun int (fun int (fun int bool))), zcongm ) 16.50/16.60 ( (fun int (fun int (fun int bool))), noXRRset ) 16.50/16.60 ( (fun int (fun int (fun int bool))), bnorRset ) 16.50/16.60 ( (fun int (fun int (fun int bool))), wset ) 16.50/16.60 ( (fun (product_prod int int) bool), frac_1 ) 16.50/16.60 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 16.50/16.60 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 16.50/16.60 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 16.50/16.60 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 16.50/16.60 ( (fun (fun nat rat) bool), vanishes ) 16.50/16.60 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 16.50/16.60 ( (fun code_code_numeral nat), code_c271388182l_size ) 16.50/16.60 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 16.50/16.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 16.50/16.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 16.50/16.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 16.50/16.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 16.50/16.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 16.50/16.60 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 16.50/16.60 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 16.50/16.60 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 16.50/16.60 ( (fun complex nat), complex_size ) 16.50/16.60 ( (fun complex nat), (size_size complex) ) 16.50/16.60 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 16.50/16.60 ( (fun nat (fun nat (product_prod int int))), bezw ) 16.50/16.60 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 16.50/16.60 ( (fun int (fun nat nat)), nat_aux ) 16.50/16.60 ( (fun int (fun (fun int bool) bool)), rsetR ) 16.50/16.60 ( (fun int (fun (fun int bool) bool)), resSet ) 16.50/16.60 ( (fun int (list int)), quickc666637781d_zero ) 16.50/16.60 ( (fun (product_prod int int) rat), frct ) 16.50/16.60 ( (fun int (fun int rat)), fract ) 16.50/16.60 ( (fun real (fun real complex)), complex_1 ) 16.50/16.60 ( (fun real (fun real complex)), rcis ) 16.50/16.60 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 16.50/16.60 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 16.50/16.60 ( (fun int real), (real_1 int) ) 16.50/16.60 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 16.50/16.60 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 16.50/16.60 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 16.50/16.60 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 16.50/16.60 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 16.50/16.60 ( (fun real nat), natfloor ) 16.50/16.60 ( (fun real nat), natceiling ) 16.50/16.60 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 16.50/16.60 ( (fun quickcheck_code_int int), quickcheck_int_of ) 16.50/16.60 ( (fun rat (product_prod int int)), quotient_of ) 16.50/16.60 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 16.50/16.60 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 16.50/16.60 ( (fun rat real), ratreal ) 16.50/16.60 ( (fun code_code_numeral int), code_int_of ) 16.50/16.60 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 16.50/16.60 ( (fun int quickcheck_code_int), quickcheck_of_int ) 16.50/16.60 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 16.50/16.60 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 16.50/16.60 ) 16.50/16.60 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_0 (prod X_a X_b))) (= _let_0 (ti (fun (fun X_a bool) (fun (fun X_b bool) (fun (product_prod X_a X_b) bool))) _let_0))) ) 16.50/16.60 ( nat, nat ) 16.50/16.60 ( int, int ) 16.50/16.60 ( int, (product_prod int int) ) 16.50/16.60 ( (product_prod nat nat), (product_prod nat nat) ) 16.50/16.60 ( real, real ) 16.50/16.60 ( (product_prod int int), (product_prod int int) ) 16.50/16.60 ( quickcheck_code_int, quickcheck_code_int ) 16.50/16.60 ( code_code_numeral, code_code_numeral ) 16.50/16.60 ) 16.50/16.60 (instantiation (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) X_1))) (= (hAPP real real ln (hAPP real real (inverse_inverse real) X_1)) (hAPP real real (uminus_uminus real) (hAPP real real ln X_1)))) ) 16.50/16.60 ( (zero_zero real) ) 16.50/16.60 ( pi ) 16.50/16.60 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.60 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.60 ( skv_2 ) 16.50/16.60 ( skv_8 ) 16.50/16.60 ( skv_9 ) 16.50/16.60 ) 16.50/16.60 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_164157 $$unsorted)) (or (not (linordered_ring X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_164157) BOUND_VARIABLE_164157)))) ) 16.50/16.60 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.60 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.60 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.50/16.60 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.60 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.60 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))) ) 16.50/16.60 ( complex, ii ) 16.50/16.60 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.60 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 16.50/16.60 ) 16.50/16.60 (instantiation (forall ((C_1 $$unsorted) (D_1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted) (Ma $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (hAPP int (fun int _let_0) zcong C_1))) (let ((_let_2 (hAPP int (fun int int) (times_times int) D_1))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong A_2) B_1) Ma))) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int _let_2 B_1)) Ma)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int _let_2 A_2)) Ma))))))) ) 16.50/16.60 ( s1, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), s1, s, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.50/16.60 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.50/16.60 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.50/16.60 ) 16.50/16.60 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_164198 $$unsorted) (BOUND_VARIABLE_164199 $$unsorted) (BOUND_VARIABLE_164210 $$unsorted) (BOUND_VARIABLE_164211 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (ord_less_eq X_b))) (let ((_let_2 (number_number_of X_b))) (let ((_let_3 (fun X_b X_b))) (let ((_let_4 (ord_max X_b))) (let ((_let_5 (hAPP int X_b _let_2 BOUND_VARIABLE_164198))) (let ((_let_6 (hAPP int X_b _let_2 BOUND_VARIABLE_164199))) (let ((_let_7 (hAPP int X_b _let_2 BOUND_VARIABLE_164210))) (let ((_let_8 (hAPP int X_b _let_2 BOUND_VARIABLE_164211))) (or (not (number X_b)) (not (ord X_b)) (and (or (not (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 _let_5) _let_6))) (= _let_6 (hAPP X_b X_b (hAPP X_b _let_3 _let_4 _let_5) _let_6))) (or (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 _let_7) _let_8)) (= _let_7 (hAPP X_b X_b (hAPP X_b _let_3 _let_4 _let_7) _let_8)))))))))))))) ) 16.50/16.60 ( nat, pls, pls, pls, pls ) 16.50/16.60 ( nat, (hAPP int int bit1 pls), (hAPP int int bit1 pls), (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 16.50/16.60 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.50/16.60 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.50/16.60 ( int, pls, pls, pls, pls ) 16.50/16.60 ( int, (hAPP int int bit1 pls), (hAPP int int bit1 pls), (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 16.50/16.60 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.50/16.60 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.50/16.60 ( int, min_1, min_1, min_1, min_1 ) 16.50/16.60 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.60 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.50/16.60 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.50/16.60 ( real, min_1, min_1, min_1, min_1 ) 16.50/16.60 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.60 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.50/16.60 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.60 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))), (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))), (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))), (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 16.50/16.60 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.50/16.60 ( complex, min_1, min_1, min_1, min_1 ) 16.50/16.60 ( quickcheck_code_int, (one_one int), (one_one int), (one_one int), (one_one int) ) 16.50/16.60 ( quickcheck_code_int, (zero_zero int), (zero_zero int), (zero_zero int), (zero_zero int) ) 16.50/16.60 ( quickcheck_code_int, (hAPP int int bit1 pls), (hAPP int int bit1 pls), (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 16.50/16.60 ( code_code_numeral, pls, pls, pls, pls ) 16.50/16.60 ( code_code_numeral, (hAPP int int bit1 pls), (hAPP int int bit1 pls), (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 16.50/16.60 ) 16.50/16.60 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_164243 $$unsorted) (BOUND_VARIABLE_164244 $$unsorted)) (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat X_a))) (let ((_let_2 (power_power X_a))) (let ((_let_3 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)))) (or (not (linordered_semidom X_a)) (not (= (hAPP nat X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_164244) _let_0) (hAPP nat X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_164243) _let_0))) (not (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_164243))) (not (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_164244))) (= (ti X_a BOUND_VARIABLE_164244) (ti X_a BOUND_VARIABLE_164243))))))) ) 16.50/16.60 ( int, s, s ) 16.50/16.60 ( int, s, s1 ) 16.50/16.60 ( int, s1, s ) 16.50/16.60 ( int, skv_14, skv_14 ) 16.50/16.60 ( real, (hAPP int real (number_number_of real) min_1), (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.60 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) min_1) ) 16.50/16.60 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.60 ( complex, ii, ii ) 16.50/16.60 ) 16.50/16.60 (instantiation (forall ((B $$unsorted) (Q_3 $$unsorted) (R_4 $$unsorted) (B_5 $$unsorted) (Q_5 $$unsorted) (R_5 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (times_times int))) (let ((_let_3 (ord_less_eq int))) (let ((_let_4 (zero_zero int))) (let ((_let_5 (ord_less int))) (let ((_let_6 (plus_plus int))) (let ((_let_7 (hAPP int int (hAPP int _let_1 _let_6 (hAPP int int (hAPP int _let_1 _let_2 B_5) Q_5)) R_5))) (or (not (= _let_7 (hAPP int int (hAPP int _let_1 _let_6 (hAPP int int (hAPP int _let_1 _let_2 B) Q_3)) R_4))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_5 _let_7) _let_4))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_5 R_4) B))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_3 _let_4) R_5))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_5 _let_4) B_5))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_3 B_5) B))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_3 Q_5) Q_3))))))))))) ) 16.50/16.60 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m, (one_one int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m, (one_one int) ) 16.50/16.60 ) 16.50/16.60 (instantiation (forall ((N $$unsorted)) (let ((_let_0 (fun int (fun int bool)))) (let ((_let_1 (ord_less int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (hAPP int (fun int bool) _let_1 (zero_zero int)))) (let ((_let_4 (fun int _let_2))) (or (not (hBOOL (hAPP int bool _let_3 N))) (= (hAPP nat int (semiring_1_of_nat int) (hAPP (fun int bool) nat (finite_card int) (hAPP (fun int bool) (fun int bool) (collect int) (hAPP (fun int bool) (fun int bool) (hAPP _let_4 (fun (fun int bool) (fun int bool)) (combs int bool bool) (hAPP (fun int bool) _let_4 (hAPP (fun bool _let_2) (fun (fun int bool) _let_4) (combb bool _let_2 int) fconj) _let_3)) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) _let_1) N))))) (hAPP int int (hAPP int (fun int int) (minus_minus int) N) (one_one int))))))))) ) 16.50/16.60 ( (one_one int) ) 16.50/16.60 ( pls ) 16.50/16.60 ( min_1 ) 16.50/16.60 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.50/16.60 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.60 ) 16.50/16.60 (instantiation (forall ((X_a $$unsorted)) (or (not (linordered_semidom X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)) (one_one X_a)))) ) 16.50/16.60 ( bool ) 16.50/16.60 ( nat ) 16.50/16.60 ( int ) 16.50/16.60 ( (fun int bool) ) 16.50/16.60 ( (fun nat bool) ) 16.50/16.60 ( (product_prod nat nat) ) 16.50/16.60 ( real ) 16.50/16.60 ( rat ) 16.50/16.60 ( complex ) 16.50/16.60 ( (filter nat) ) 16.50/16.60 ( (product_prod int int) ) 16.50/16.60 ( quickcheck_code_int ) 16.50/16.60 ( code_code_numeral ) 16.50/16.60 ( (product_prod real real) ) 16.50/16.60 ( (fun nat rat) ) 16.50/16.60 ( (filter real) ) 16.50/16.60 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 16.50/16.60 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 16.50/16.60 ) 16.50/16.60 (instantiation (forall ((Ma $$unsorted) (N $$unsorted)) (let ((_let_0 (one_one int))) (let ((_let_1 (hAPP int int (number_number_of int) min_1))) (let ((_let_2 (ti int N))) (let ((_let_3 (ti int Ma))) (= (or (and (= _let_0 _let_2) (= _let_0 _let_3)) (and (= _let_1 _let_2) (= _let_1 _let_3))) (= _let_0 (hAPP int int (hAPP int (fun int int) (times_times int) Ma) N))))))) ) 16.50/16.60 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 16.50/16.60 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 16.50/16.60 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13 ) 16.50/16.60 ) 16.50/16.60 (instantiation (forall ((X_a $$unsorted) (X_2 $$unsorted)) (let ((_let_0 (fun X_a bool))) (= (ti X_a X_2) (hAPP _let_0 X_a (hilbert_Eps X_a) (hAPP X_a _let_0 (fequal X_a) X_2)))) ) 16.50/16.60 ( bool, fFalse ) 16.50/16.60 ( bool, fTrue ) 16.50/16.60 ( int, pls ) 16.50/16.60 ( int, min_1 ) 16.50/16.60 ( int, s ) 16.50/16.60 ( int, m ) 16.50/16.60 ( int, s1 ) 16.50/16.60 ( int, t ) 16.50/16.60 ( (fun int bool), nat_neg ) 16.50/16.60 ( (fun int bool), zprime ) 16.50/16.60 ( (fun int bool), zEven ) 16.50/16.60 ( (fun int bool), zOdd ) 16.50/16.60 ( (fun int bool), (even_odd_even int) ) 16.50/16.60 ( (fun int bool), twoSqu1091635170sum2sq ) 16.50/16.60 ( (fun int bool), nat_is_nat ) 16.50/16.60 ( (fun int (fun int bool)), norRRset ) 16.50/16.60 ( (fun int (fun int bool)), quadRes ) 16.50/16.60 ( (fun int (fun int bool)), sRStar ) 16.50/16.60 ( (fun int (fun int bool)), d22set ) 16.50/16.60 ( (fun int (fun int bool)), sr ) 16.50/16.60 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 16.50/16.60 ( (fun int int), zfact ) 16.50/16.60 ( (fun int int), bit0 ) 16.50/16.60 ( (fun int int), bit1 ) 16.50/16.60 ( (fun int int), (fact_fact int) ) 16.50/16.60 ( (fun int int), pred ) 16.50/16.60 ( (fun int int), succ ) 16.50/16.60 ( (fun nat bool), (even_odd_even nat) ) 16.50/16.60 ( (fun nat bool), prime ) 16.50/16.60 ( (fun nat nat), suc ) 16.50/16.60 ( (fun nat nat), (fact_fact nat) ) 16.50/16.60 ( (fun nat nat), fact ) 16.50/16.60 ( (fun nat nat), nat_size ) 16.50/16.60 ( (fun nat nat), (size_size nat) ) 16.50/16.60 ( (fun (product_prod nat nat) bool), pred_nat ) 16.50/16.60 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 16.50/16.60 ( real, pi ) 16.50/16.60 ( (fun real real), ln ) 16.50/16.60 ( (fun real real), cos ) 16.50/16.60 ( (fun real real), sqrt ) 16.50/16.60 ( (fun real real), sin ) 16.50/16.60 ( (fun real real), arccos ) 16.50/16.60 ( (fun real real), arcsin ) 16.50/16.60 ( (fun real real), tan ) 16.50/16.60 ( (fun real real), arctan ) 16.50/16.60 ( (fun nat (fun nat bool)), coprime ) 16.50/16.60 ( complex, ii ) 16.50/16.60 ( (fun nat real), (real_1 nat) ) 16.50/16.60 ( (fun nat real), sin_coeff ) 16.50/16.60 ( (fun nat real), cos_coeff ) 16.50/16.60 ( (filter nat), sequentially ) 16.50/16.60 ( (fun int (fun int int)), (gcd_gcd int) ) 16.50/16.60 ( (fun int (fun int int)), legendre ) 16.50/16.60 ( (fun int (fun int int)), legacy_zgcd ) 16.50/16.60 ( (fun int (fun int int)), standardRes ) 16.50/16.60 ( (fun int (fun int int)), nat_tsub ) 16.50/16.60 ( (fun int (fun int int)), multInv ) 16.50/16.60 ( (fun int (fun int int)), z3mod ) 16.50/16.60 ( (fun int (fun int int)), z3div ) 16.50/16.60 ( (fun int (fun int int)), int_gcd ) 16.50/16.60 ( (fun int (fun int int)), int_lcm ) 16.50/16.60 ( (fun int (fun int int)), inv ) 16.50/16.60 ( (fun complex complex), expi ) 16.50/16.60 ( (fun complex complex), cnj ) 16.50/16.60 ( (fun real complex), cis ) 16.50/16.60 ( (fun int nat), nat_1 ) 16.50/16.60 ( (fun int nat), phi ) 16.50/16.60 ( (fun (fun int bool) bool), nat_nat_set ) 16.50/16.60 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 16.50/16.60 ( (fun nat (fun nat nat)), nat_gcd ) 16.50/16.60 ( (fun nat (fun nat nat)), nat_lcm ) 16.50/16.60 ( (fun (fun int bool) int), (the int) ) 16.50/16.60 ( (fun complex real), re ) 16.50/16.60 ( (fun complex real), im ) 16.50/16.60 ( (fun complex real), arg ) 16.50/16.60 ( (fun bool bool), fNot ) 16.50/16.60 ( (fun nat (fun real real)), root ) 16.50/16.60 ( (fun real (fun real real)), log ) 16.50/16.60 ( (fun real (fun real real)), powr ) 16.50/16.60 ( (fun bool (fun bool bool)), fimplies ) 16.50/16.60 ( (fun bool (fun bool bool)), fconj ) 16.50/16.60 ( (fun bool (fun bool bool)), fdisj ) 16.50/16.60 ( (fun int (fun int (product_prod int int))), negDivAlg ) 16.50/16.60 ( (fun int (fun int (product_prod int int))), posDivAlg ) 16.50/16.60 ( (fun int (fun int (product_prod int int))), divmod_int ) 16.50/16.60 ( (fun int (fun int (product_prod int int))), pdivmod ) 16.50/16.60 ( (fun int (fun int (product_prod int int))), norm_frac ) 16.50/16.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 16.50/16.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 16.50/16.60 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 16.50/16.60 ( (fun int (fun int (fun int bool))), zcong ) 16.50/16.60 ( (fun int (fun int (fun int bool))), zcongm ) 16.50/16.60 ( (fun int (fun int (fun int bool))), noXRRset ) 16.50/16.60 ( (fun int (fun int (fun int bool))), bnorRset ) 16.50/16.60 ( (fun int (fun int (fun int bool))), wset ) 16.50/16.60 ( (fun (product_prod int int) bool), frac_1 ) 16.50/16.60 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 16.50/16.60 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 16.50/16.60 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 16.50/16.60 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 16.50/16.60 ( (fun (fun nat rat) bool), vanishes ) 16.50/16.60 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 16.50/16.60 ( (fun code_code_numeral nat), code_c271388182l_size ) 16.50/16.60 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 16.50/16.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 16.50/16.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 16.50/16.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 16.50/16.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 16.50/16.60 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 16.50/16.60 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 16.50/16.60 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 16.50/16.60 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 16.50/16.60 ( (fun complex nat), complex_size ) 16.50/16.60 ( (fun complex nat), (size_size complex) ) 16.50/16.60 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 16.50/16.60 ( (fun nat (fun nat (product_prod int int))), bezw ) 16.50/16.60 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 16.50/16.60 ( (fun int (fun nat nat)), nat_aux ) 16.50/16.60 ( (fun int (fun (fun int bool) bool)), rsetR ) 16.50/16.60 ( (fun int (fun (fun int bool) bool)), resSet ) 16.50/16.60 ( (fun int (list int)), quickc666637781d_zero ) 16.50/16.60 ( (fun (product_prod int int) rat), frct ) 16.50/16.60 ( (fun int (fun int rat)), fract ) 16.50/16.60 ( (fun real (fun real complex)), complex_1 ) 16.50/16.60 ( (fun real (fun real complex)), rcis ) 16.50/16.60 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 16.50/16.60 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 16.50/16.60 ( (fun int real), (real_1 int) ) 16.50/16.60 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 16.50/16.60 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 16.50/16.60 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 16.50/16.60 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 16.50/16.60 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 16.50/16.60 ( (fun real nat), natfloor ) 16.50/16.60 ( (fun real nat), natceiling ) 16.50/16.60 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 16.50/16.60 ( (fun quickcheck_code_int int), quickcheck_int_of ) 16.50/16.60 ( (fun rat (product_prod int int)), quotient_of ) 16.50/16.60 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 16.50/16.60 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 16.50/16.60 ( (fun rat real), ratreal ) 16.50/16.60 ( (fun code_code_numeral int), code_int_of ) 16.50/16.60 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 16.50/16.60 ( (fun int quickcheck_code_int), quickcheck_of_int ) 16.50/16.60 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 16.50/16.60 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 16.50/16.60 ) 16.50/16.60 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_164396 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (or (not (linordered_idom X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_164396) _let_2)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_164396) BOUND_VARIABLE_164396)) _let_2))))))) ) 16.50/16.60 ( nat, (one_one nat) ) 16.50/16.60 ( int, pls ) 16.50/16.60 ( int, min_1 ) 16.50/16.60 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 16.50/16.60 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.60 ( real, pi ) 16.50/16.60 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.50/16.60 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.60 ) 16.50/16.60 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (BOUND_VARIABLE_164417 $$unsorted) (BOUND_VARIABLE_164418 $$unsorted)) (let ((_let_0 (fun (filter X_a) bool))) (let ((_let_1 (fun X_a real))) (let ((_let_2 (fun X_a X_b))) (or (not (real_normed_vector X_b)) (not (hBOOL (hAPP (filter X_a) bool (hAPP X_b _let_0 (hAPP _let_2 (fun X_b _let_0) (tendsto X_a X_b) BOUND_VARIABLE_164417) (zero_zero X_b)) BOUND_VARIABLE_164418))) (hBOOL (hAPP (filter X_a) bool (hAPP real _let_0 (hAPP _let_1 (fun real _let_0) (tendsto X_a real) (hAPP _let_2 _let_1 (hAPP (fun X_b real) (fun _let_2 _let_1) (combb X_b real X_a) (norm_norm X_b)) BOUND_VARIABLE_164417)) (zero_zero real)) BOUND_VARIABLE_164418)))))) ) 16.50/16.60 ( nat, real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))), sequentially ) 16.50/16.60 ( real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (hAPP real (filter real) (at real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.50/16.60 ) 16.50/16.60 (instantiation (forall ((A_2 $$unsorted) (A_3 $$unsorted) (Ma $$unsorted)) (let ((_let_0 (fun int (fun int bool)))) (let ((_let_1 (fun (fun int bool) bool))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun (fun int bool) (fun int bool)))) (let ((_let_5 (member int))) (let ((_let_6 (hAPP int (fun int bool) norRRset Ma))) (let ((_let_7 (hAPP (fun int bool) int (hilbert_Eps int) (hAPP (fun int bool) (fun int bool) (hAPP _let_3 _let_4 (combs int bool bool) (hAPP (fun int bool) _let_3 (hAPP (fun bool _let_2) (fun (fun int bool) _let_3) (combb bool _let_2 int) fconj) (hAPP int (fun int bool) (hAPP _let_0 _let_0 (combc int int bool) (hAPP int _let_0 zcong A_2)) Ma))) (hAPP (fun int bool) (fun int bool) (hAPP (fun int _let_1) _let_4 (combc int (fun int bool) bool) _let_5) _let_6))))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (one_one int)) Ma))) (not (hBOOL (hAPP int bool (hAPP (fun int bool) (fun int bool) is_RRset A_3) Ma))) (not (hBOOL (hAPP (fun int bool) bool (hAPP int _let_1 _let_5 A_2) A_3))) (and (hBOOL (hAPP int bool (hAPP int (fun int bool) (hAPP int _let_0 zcong A_2) _let_7) Ma)) (hBOOL (hAPP (fun int bool) bool (hAPP int _let_1 _let_5 _let_7) _let_6)))))))))))) ) 16.50/16.60 ( (one_one int), zEven, t ) 16.50/16.60 ) 16.50/16.60 (instantiation (forall ((I_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_0 (fun nat nat))) (= (hAPP nat nat (hAPP int _let_0 nat_aux I_1) N_1) (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) (hAPP int nat nat_1 I_1)) N_1))) ) 16.50/16.60 ( (one_one int), (one_one nat) ) 16.50/16.60 ) 16.50/16.60 (instantiation (forall ((V_1 $$unsorted)) (let ((_let_0 (hAPP int int (number_number_of int) V_1))) (or (hBOOL (hAPP int bool nat_neg _let_0)) (= _let_0 (hAPP nat int (semiring_1_of_nat int) (hAPP int nat (number_number_of nat) V_1))))) ) 16.50/16.60 ( pls ) 16.50/16.60 ( (hAPP int int bit1 pls) ) 16.50/16.60 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.50/16.60 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.50/16.60 ( min_1 ) 16.50/16.60 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.60 ) 16.50/16.60 (instantiation (forall ((V_1 $$unsorted)) (or (not (hBOOL (hAPP int bool nat_neg (hAPP int int (number_number_of int) V_1)))) (= (zero_zero int) (hAPP nat int (semiring_1_of_nat int) (hAPP int nat (number_number_of nat) V_1)))) ) 16.50/16.60 ( pls ) 16.50/16.60 ( (hAPP int int bit1 pls) ) 16.50/16.60 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.50/16.60 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.50/16.60 ( min_1 ) 16.50/16.60 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.60 ) 16.50/16.60 (instantiation (forall ((P_5 $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (number_number_of int))) (let ((_let_2 (hAPP int int bit1 pls))) (let ((_let_3 (times_times nat))) (let ((_let_4 (hAPP int (fun int int) (minus_minus int) P_5))) (let ((_let_5 (hAPP int nat nat_1 (hAPP int int _let_4 (hAPP int int _let_1 (hAPP int int bit0 _let_2)))))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP int int _let_1 (hAPP int int bit1 (hAPP int int bit0 _let_2)))) P_5))) (= (hAPP nat nat (hAPP nat _let_0 _let_3 _let_5) _let_5) (hAPP nat nat suc (hAPP nat nat (hAPP nat _let_0 _let_3 (hAPP int nat nat_1 (hAPP int int _let_4 (one_one int)))) (hAPP int nat nat_1 (hAPP int int _let_4 (hAPP int int _let_1 (hAPP int int bit1 _let_2)))))))))))))) ) 16.50/16.60 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.60 ) 16.50/16.61 (instantiation (forall ((X_a $$unsorted)) (or (not (real_normed_vector X_a)) (not (forall ((K_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) K_2))) (not (forall ((A_4 $$unsorted) (B_4 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (times_times real))) (let ((_let_2 (norm_norm X_a))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP X_a real _let_2 (hAPP X_a X_a (hAPP real (fun X_a X_a) (scaleR_scaleR X_a) A_4) B_4))) (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real (norm_norm real) A_4)) (hAPP X_a real _let_2 B_4))) K_2)))))) ))) ))) ) 16.50/16.61 ( real ) 16.50/16.61 ( complex ) 16.50/16.61 ) 16.50/16.61 (instantiation (forall ((X_a $$unsorted) (P $$unsorted)) (= (hAPP X_a X_a (combi X_a) P) (ti X_a P)) ) 16.50/16.61 ( bool, fFalse ) 16.50/16.61 ( bool, fTrue ) 16.50/16.61 ( int, pls ) 16.50/16.61 ( int, min_1 ) 16.50/16.61 ( int, s ) 16.50/16.61 ( int, m ) 16.50/16.61 ( int, s1 ) 16.50/16.61 ( int, t ) 16.50/16.61 ( (fun int bool), nat_neg ) 16.50/16.61 ( (fun int bool), zprime ) 16.50/16.61 ( (fun int bool), zEven ) 16.50/16.61 ( (fun int bool), zOdd ) 16.50/16.61 ( (fun int bool), (even_odd_even int) ) 16.50/16.61 ( (fun int bool), twoSqu1091635170sum2sq ) 16.50/16.61 ( (fun int bool), nat_is_nat ) 16.50/16.61 ( (fun int (fun int bool)), norRRset ) 16.50/16.61 ( (fun int (fun int bool)), quadRes ) 16.50/16.61 ( (fun int (fun int bool)), sRStar ) 16.50/16.61 ( (fun int (fun int bool)), d22set ) 16.50/16.61 ( (fun int (fun int bool)), sr ) 16.50/16.61 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 16.50/16.61 ( (fun int int), zfact ) 16.50/16.61 ( (fun int int), bit0 ) 16.50/16.61 ( (fun int int), bit1 ) 16.50/16.61 ( (fun int int), (fact_fact int) ) 16.50/16.61 ( (fun int int), pred ) 16.50/16.61 ( (fun int int), succ ) 16.50/16.61 ( (fun nat bool), (even_odd_even nat) ) 16.50/16.61 ( (fun nat bool), prime ) 16.50/16.61 ( (fun nat nat), suc ) 16.50/16.61 ( (fun nat nat), (fact_fact nat) ) 16.50/16.61 ( (fun nat nat), fact ) 16.50/16.61 ( (fun nat nat), nat_size ) 16.50/16.61 ( (fun nat nat), (size_size nat) ) 16.50/16.61 ( (fun (product_prod nat nat) bool), pred_nat ) 16.50/16.61 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 16.50/16.61 ( real, pi ) 16.50/16.61 ( (fun real real), ln ) 16.50/16.61 ( (fun real real), cos ) 16.50/16.61 ( (fun real real), sqrt ) 16.50/16.61 ( (fun real real), sin ) 16.50/16.61 ( (fun real real), arccos ) 16.50/16.61 ( (fun real real), arcsin ) 16.50/16.61 ( (fun real real), tan ) 16.50/16.61 ( (fun real real), arctan ) 16.50/16.61 ( (fun nat (fun nat bool)), coprime ) 16.50/16.61 ( complex, ii ) 16.50/16.61 ( (fun nat real), (real_1 nat) ) 16.50/16.61 ( (fun nat real), sin_coeff ) 16.50/16.61 ( (fun nat real), cos_coeff ) 16.50/16.61 ( (filter nat), sequentially ) 16.50/16.61 ( (fun int (fun int int)), (gcd_gcd int) ) 16.50/16.61 ( (fun int (fun int int)), legendre ) 16.50/16.61 ( (fun int (fun int int)), legacy_zgcd ) 16.50/16.61 ( (fun int (fun int int)), standardRes ) 16.50/16.61 ( (fun int (fun int int)), nat_tsub ) 16.50/16.61 ( (fun int (fun int int)), multInv ) 16.50/16.61 ( (fun int (fun int int)), z3mod ) 16.50/16.61 ( (fun int (fun int int)), z3div ) 16.50/16.61 ( (fun int (fun int int)), int_gcd ) 16.50/16.61 ( (fun int (fun int int)), int_lcm ) 16.50/16.61 ( (fun int (fun int int)), inv ) 16.50/16.61 ( (fun complex complex), expi ) 16.50/16.61 ( (fun complex complex), cnj ) 16.50/16.61 ( (fun real complex), cis ) 16.50/16.61 ( (fun int nat), nat_1 ) 16.50/16.61 ( (fun int nat), phi ) 16.50/16.61 ( (fun (fun int bool) bool), nat_nat_set ) 16.50/16.61 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 16.50/16.61 ( (fun nat (fun nat nat)), nat_gcd ) 16.50/16.61 ( (fun nat (fun nat nat)), nat_lcm ) 16.50/16.61 ( (fun (fun int bool) int), (the int) ) 16.50/16.61 ( (fun complex real), re ) 16.50/16.61 ( (fun complex real), im ) 16.50/16.61 ( (fun complex real), arg ) 16.50/16.61 ( (fun bool bool), fNot ) 16.50/16.61 ( (fun nat (fun real real)), root ) 16.50/16.61 ( (fun real (fun real real)), log ) 16.50/16.61 ( (fun real (fun real real)), powr ) 16.50/16.61 ( (fun bool (fun bool bool)), fimplies ) 16.50/16.61 ( (fun bool (fun bool bool)), fconj ) 16.50/16.61 ( (fun bool (fun bool bool)), fdisj ) 16.50/16.61 ( (fun int (fun int (product_prod int int))), negDivAlg ) 16.50/16.61 ( (fun int (fun int (product_prod int int))), posDivAlg ) 16.50/16.61 ( (fun int (fun int (product_prod int int))), divmod_int ) 16.50/16.61 ( (fun int (fun int (product_prod int int))), pdivmod ) 16.50/16.61 ( (fun int (fun int (product_prod int int))), norm_frac ) 16.50/16.61 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 16.50/16.61 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 16.50/16.61 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 16.50/16.61 ( (fun int (fun int (fun int bool))), zcong ) 16.50/16.61 ( (fun int (fun int (fun int bool))), zcongm ) 16.50/16.61 ( (fun int (fun int (fun int bool))), noXRRset ) 16.50/16.61 ( (fun int (fun int (fun int bool))), bnorRset ) 16.50/16.61 ( (fun int (fun int (fun int bool))), wset ) 16.50/16.61 ( (fun (product_prod int int) bool), frac_1 ) 16.50/16.61 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 16.50/16.61 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 16.50/16.61 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 16.50/16.61 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 16.50/16.61 ( (fun (fun nat rat) bool), vanishes ) 16.50/16.61 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 16.50/16.61 ( (fun code_code_numeral nat), code_c271388182l_size ) 16.50/16.61 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 16.50/16.61 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 16.50/16.61 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 16.50/16.61 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 16.50/16.61 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 16.50/16.61 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 16.50/16.61 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 16.50/16.61 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 16.50/16.61 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 16.50/16.61 ( (fun complex nat), complex_size ) 16.50/16.61 ( (fun complex nat), (size_size complex) ) 16.50/16.61 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 16.50/16.61 ( (fun nat (fun nat (product_prod int int))), bezw ) 16.50/16.61 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 16.50/16.61 ( (fun int (fun nat nat)), nat_aux ) 16.50/16.61 ( (fun int (fun (fun int bool) bool)), rsetR ) 16.50/16.61 ( (fun int (fun (fun int bool) bool)), resSet ) 16.50/16.61 ( (fun int (list int)), quickc666637781d_zero ) 16.50/16.61 ( (fun (product_prod int int) rat), frct ) 16.50/16.61 ( (fun int (fun int rat)), fract ) 16.50/16.61 ( (fun real (fun real complex)), complex_1 ) 16.50/16.61 ( (fun real (fun real complex)), rcis ) 16.50/16.61 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 16.50/16.61 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 16.50/16.61 ( (fun int real), (real_1 int) ) 16.50/16.61 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 16.50/16.61 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 16.50/16.61 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 16.50/16.61 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 16.50/16.61 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 16.50/16.61 ( (fun real nat), natfloor ) 16.50/16.61 ( (fun real nat), natceiling ) 16.50/16.61 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 16.50/16.61 ( (fun quickcheck_code_int int), quickcheck_int_of ) 16.50/16.61 ( (fun rat (product_prod int int)), quotient_of ) 16.50/16.61 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 16.50/16.61 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 16.50/16.61 ( (fun rat real), ratreal ) 16.50/16.61 ( (fun code_code_numeral int), code_int_of ) 16.50/16.61 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 16.50/16.61 ( (fun int quickcheck_code_int), quickcheck_of_int ) 16.50/16.61 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 16.50/16.61 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 16.50/16.61 ) 16.50/16.61 (instantiation (forall ((X_a $$unsorted)) (or (not (real_normed_vector X_a)) (= (zero_zero real) (hAPP X_a real (norm_norm X_a) (zero_zero X_a)))) ) 16.50/16.61 ( nat ) 16.50/16.61 ( int ) 16.50/16.61 ( real ) 16.50/16.61 ( rat ) 16.50/16.61 ( complex ) 16.50/16.61 ( quickcheck_code_int ) 16.50/16.61 ( code_code_numeral ) 16.50/16.61 ) 16.50/16.61 (instantiation (forall ((N_1 $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (fact_fact nat))) (let ((_let_2 (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) N_1) (one_one nat)))) (= (hAPP nat nat _let_1 _let_2) (hAPP nat nat (hAPP nat _let_0 (times_times nat) _let_2) (hAPP nat nat _let_1 N_1)))))) ) 16.50/16.61 ( (one_one nat) ) 16.50/16.61 ) 16.50/16.61 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_164694 $$unsorted) (BOUND_VARIABLE_164695 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_164695) BOUND_VARIABLE_164694))) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_164695))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_164695) (one_one X_a)))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_164695) _let_2)) _let_2)))))) ) 16.50/16.61 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 16.50/16.61 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 16.50/16.61 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_14 ) 16.50/16.61 ( complex, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), ii ) 16.50/16.61 ) 16.50/16.61 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (one_one X_a))) (or (not (real_n2089651433ebra_1 X_a)) (= _let_0 (hAPP X_a X_a (sgn_sgn X_a) _let_0)))) ) 16.50/16.61 ( nat ) 16.50/16.61 ( int ) 16.50/16.61 ( real ) 16.50/16.61 ( rat ) 16.50/16.61 ( complex ) 16.50/16.61 ( quickcheck_code_int ) 16.50/16.61 ( code_code_numeral ) 16.50/16.61 ) 16.50/16.61 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (BOUND_VARIABLE_164782 $$unsorted) (BOUND_VARIABLE_164783 $$unsorted) (BOUND_VARIABLE_164784 $$unsorted) (BOUND_VARIABLE_164785 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (ord_less X_b))) (or (not (order X_b)) (not (order X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_164784) BOUND_VARIABLE_164785))) (not (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 (hAPP X_a X_b BOUND_VARIABLE_164782 BOUND_VARIABLE_164785)) BOUND_VARIABLE_164783))) (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) X) Y))) (hBOOL (hAPP X_b bool (hAPP X_b _let_0 (ord_less_eq X_b) (hAPP X_a X_b BOUND_VARIABLE_164782 X)) (hAPP X_a X_b BOUND_VARIABLE_164782 Y)))) )) (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 (hAPP X_a X_b BOUND_VARIABLE_164782 BOUND_VARIABLE_164784)) BOUND_VARIABLE_164783))))) ) 16.50/16.61 ( int, int, (number_number_of int), pls, min_1, pls ) 16.50/16.61 ( int, int, (uminus_uminus int), pls, (zero_zero int), (one_one int) ) 16.50/16.61 ( int, int, pred, min_1, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 16.50/16.61 ( int, int, succ, (one_one int), min_1, min_1 ) 16.50/16.61 ( int, int, succ, min_1, (zero_zero int), min_1 ) 16.50/16.61 ( real, real, cos, (zero_zero real), skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.61 ( real, real, cos, skv_2, (zero_zero real), skv_5 ) 16.50/16.61 ( real, real, (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.61 ( real, real, tan, pi, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.50/16.61 ( real, real, tan, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.50/16.61 ( real, real, tan, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real), pi ) 16.50/16.61 ( real, real, (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.61 ) 16.50/16.61 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_164842 $$unsorted) (BOUND_VARIABLE_164843 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (ring_n68954251visors X_a)) (= (= _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_164842) BOUND_VARIABLE_164843)) (or (= _let_0 (ti X_a BOUND_VARIABLE_164843)) (= _let_0 (ti X_a BOUND_VARIABLE_164842)))))) ) 16.50/16.61 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 16.50/16.61 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 16.50/16.61 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13 ) 16.50/16.61 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.50/16.61 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 16.50/16.61 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 16.50/16.61 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 16.50/16.61 ( complex, ii, ii ) 16.50/16.61 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 16.50/16.61 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 16.50/16.61 ) 16.50/16.61 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_164887 $$unsorted) (BOUND_VARIABLE_164888 $$unsorted)) (let ((_let_0 (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (minus_minus X_a))) (let ((_let_3 (fun nat X_a))) (let ((_let_4 (power_power X_a))) (or (not (comm_ring_1 X_a)) (= (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP nat X_a (hAPP X_a _let_3 _let_4 BOUND_VARIABLE_164887) _let_0)) (hAPP nat X_a (hAPP X_a _let_3 _let_4 BOUND_VARIABLE_164888) _let_0)) (hAPP X_a X_a (hAPP X_a _let_1 (times_times X_a) (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_164887) BOUND_VARIABLE_164888)) (hAPP X_a X_a (hAPP X_a _let_1 (plus_plus X_a) BOUND_VARIABLE_164887) BOUND_VARIABLE_164888))))))))) ) 16.50/16.61 ( nat, (one_one nat), (one_one nat) ) 16.50/16.61 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (one_one int) ) 16.50/16.61 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 16.50/16.61 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min_1) ) 16.50/16.61 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP int real _let_2 (hAPP int int bit0 _let_1))) (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) (hAPP int real _let_2 (hAPP int int bit1 _let_1)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 16.50/16.61 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 16.50/16.61 ) 16.50/16.61 (instantiation (forall ((B_5 $$unsorted) (Q_5 $$unsorted) (R_5 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (ord_less_eq int))) (let ((_let_3 (zero_zero int))) (let ((_let_4 (ord_less int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_4 (hAPP int int (hAPP int _let_1 (plus_plus int) (hAPP int int (hAPP int _let_1 (times_times int) B_5) Q_5)) R_5)) _let_3))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 _let_3) R_5))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_4 _let_3) B_5))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 Q_5) _let_3)))))))) ) 16.50/16.61 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m, (one_one int) ) 16.50/16.61 ) 16.50/16.61 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_0 (product_prod X_a X_b))) (let ((_let_1 (ti X_a A_1))) (or (not (= (hAPP _let_0 X_a (product_fst X_a X_b) (hAPP X_b _let_0 (hAPP X_a (fun X_b _let_0) (product_Pair X_a X_b) X_1) Y_1)) _let_1)) (= _let_1 (ti X_a X_1))))) ) 16.50/16.61 ( int, int, (one_one int), (one_one int), pls ) 16.50/16.61 ( int, int, (zero_zero int), (one_one int), s ) 16.50/16.61 ( int, int, s, (one_one int), s ) 16.50/16.61 ( int, int, s, (one_one int), s1 ) 16.50/16.61 ) 16.50/16.61 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_164989 $$unsorted) (BOUND_VARIABLE_164990 $$unsorted) (BOUND_VARIABLE_164991 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (zero_zero X_a))) (let ((_let_2 (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_164989))) (let ((_let_3 (= _let_1 (ti X_a BOUND_VARIABLE_164991)))) (or (not (field_inverse_zero X_a)) (not (number X_a)) (= (and (or _let_3 (= (ti X_a BOUND_VARIABLE_164990) (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) _let_2) BOUND_VARIABLE_164991))) (or (not _let_3) (= _let_1 _let_2))) (= _let_2 (hAPP X_a X_a (hAPP X_a _let_0 (inverse_divide X_a) BOUND_VARIABLE_164990) BOUND_VARIABLE_164991)))))))) ) 16.50/16.61 ( int, pls, min_1, min_1 ) 16.50/16.61 ( int, (hAPP int int bit1 pls), pls, pls ) 16.50/16.61 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)), t, t ) 16.50/16.61 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)), s1, s1 ) 16.50/16.61 ( int, min_1, m, m ) 16.50/16.61 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))), s, s ) 16.50/16.61 ( real, min_1, pi, pi ) 16.50/16.61 ( complex, min_1, ii, ii ) 16.50/16.61 ) 16.50/16.61 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_165040 $$unsorted)) (let ((_let_0 (uminus_uminus X_a))) (or (not (group_add X_a)) (= (ti X_a BOUND_VARIABLE_165040) (hAPP X_a X_a _let_0 (hAPP X_a X_a _let_0 BOUND_VARIABLE_165040))))) ) 16.50/16.61 ( bool, fFalse ) 16.50/16.61 ( bool, fTrue ) 16.50/16.61 ( int, (one_one int) ) 16.50/16.61 ( int, pls ) 16.50/16.61 ( int, min_1 ) 16.50/16.61 ( int, s ) 16.50/16.61 ( int, m ) 16.50/16.61 ( int, s1 ) 16.50/16.61 ( int, t ) 16.50/16.61 ( (fun int bool), nat_neg ) 16.50/16.61 ( (fun int bool), zprime ) 16.50/16.61 ( (fun int bool), zEven ) 16.50/16.61 ( (fun int bool), zOdd ) 16.50/16.61 ( (fun int bool), (even_odd_even int) ) 16.50/16.61 ( (fun int bool), twoSqu1091635170sum2sq ) 16.50/16.61 ( (fun int bool), nat_is_nat ) 16.50/16.61 ( (fun int (fun int bool)), norRRset ) 16.50/16.61 ( (fun int (fun int bool)), quadRes ) 16.50/16.61 ( (fun int (fun int bool)), sRStar ) 16.50/16.61 ( (fun int (fun int bool)), d22set ) 16.50/16.61 ( (fun int (fun int bool)), sr ) 16.50/16.61 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 16.50/16.61 ( (fun int int), zfact ) 16.50/16.61 ( (fun int int), bit0 ) 16.50/16.61 ( (fun int int), bit1 ) 16.50/16.61 ( (fun int int), (fact_fact int) ) 16.50/16.61 ( (fun int int), pred ) 16.50/16.61 ( (fun int int), succ ) 16.50/16.61 ( (fun nat bool), (even_odd_even nat) ) 16.50/16.61 ( (fun nat bool), prime ) 16.50/16.61 ( (fun nat nat), suc ) 16.50/16.61 ( (fun nat nat), (fact_fact nat) ) 16.50/16.61 ( (fun nat nat), fact ) 16.50/16.61 ( (fun nat nat), nat_size ) 16.50/16.61 ( (fun nat nat), (size_size nat) ) 16.50/16.61 ( (fun (product_prod nat nat) bool), pred_nat ) 16.50/16.61 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 16.50/16.61 ( real, (one_one real) ) 16.50/16.61 ( real, pi ) 16.50/16.61 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.61 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.50/16.61 ( (fun real real), ln ) 16.50/16.61 ( (fun real real), cos ) 16.50/16.61 ( (fun real real), sqrt ) 16.50/16.61 ( (fun real real), sin ) 16.50/16.61 ( (fun real real), arccos ) 16.50/16.61 ( (fun real real), arcsin ) 16.50/16.61 ( (fun real real), tan ) 16.50/16.61 ( (fun real real), arctan ) 16.50/16.61 ( (fun nat (fun nat bool)), coprime ) 16.50/16.61 ( complex, (one_one complex) ) 16.50/16.61 ( complex, ii ) 16.50/16.61 ( (fun nat real), (real_1 nat) ) 16.50/16.61 ( (fun nat real), sin_coeff ) 16.50/16.61 ( (fun nat real), cos_coeff ) 16.50/16.61 ( (filter nat), sequentially ) 16.50/16.61 ( (fun int (fun int int)), (gcd_gcd int) ) 16.50/16.61 ( (fun int (fun int int)), legendre ) 16.50/16.61 ( (fun int (fun int int)), legacy_zgcd ) 16.50/16.61 ( (fun int (fun int int)), standardRes ) 16.50/16.61 ( (fun int (fun int int)), nat_tsub ) 16.50/16.61 ( (fun int (fun int int)), multInv ) 16.50/16.61 ( (fun int (fun int int)), z3mod ) 16.50/16.61 ( (fun int (fun int int)), z3div ) 16.50/16.61 ( (fun int (fun int int)), int_gcd ) 16.50/16.61 ( (fun int (fun int int)), int_lcm ) 16.50/16.61 ( (fun int (fun int int)), inv ) 16.50/16.61 ( (fun complex complex), expi ) 16.50/16.61 ( (fun complex complex), cnj ) 16.50/16.61 ( (fun real complex), cis ) 16.50/16.61 ( (fun int nat), nat_1 ) 16.50/16.61 ( (fun int nat), phi ) 16.50/16.61 ( (fun (fun int bool) bool), nat_nat_set ) 16.50/16.61 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 16.50/16.61 ( (fun nat (fun nat nat)), nat_gcd ) 16.50/16.61 ( (fun nat (fun nat nat)), nat_lcm ) 16.50/16.61 ( (fun (fun int bool) int), (the int) ) 16.50/16.61 ( (fun complex real), re ) 16.50/16.61 ( (fun complex real), im ) 16.50/16.61 ( (fun complex real), arg ) 16.50/16.61 ( (fun bool bool), fNot ) 16.50/16.61 ( (fun nat (fun real real)), root ) 16.50/16.61 ( (fun real (fun real real)), log ) 16.50/16.61 ( (fun real (fun real real)), powr ) 16.50/16.61 ( (fun bool (fun bool bool)), fimplies ) 16.50/16.61 ( (fun bool (fun bool bool)), fconj ) 16.50/16.61 ( (fun bool (fun bool bool)), fdisj ) 16.50/16.61 ( (fun int (fun int (product_prod int int))), negDivAlg ) 16.50/16.61 ( (fun int (fun int (product_prod int int))), posDivAlg ) 16.50/16.61 ( (fun int (fun int (product_prod int int))), divmod_int ) 16.50/16.61 ( (fun int (fun int (product_prod int int))), pdivmod ) 16.50/16.61 ( (fun int (fun int (product_prod int int))), norm_frac ) 16.50/16.61 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 16.50/16.61 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 16.50/16.61 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 16.50/16.61 ( (fun int (fun int (fun int bool))), zcong ) 16.50/16.61 ( (fun int (fun int (fun int bool))), zcongm ) 16.50/16.61 ( (fun int (fun int (fun int bool))), noXRRset ) 16.50/16.61 ( (fun int (fun int (fun int bool))), bnorRset ) 16.50/16.61 ( (fun int (fun int (fun int bool))), wset ) 16.50/16.61 ( (fun (product_prod int int) bool), frac_1 ) 16.50/16.61 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 16.50/16.61 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 16.50/16.61 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 16.50/16.61 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 16.50/16.61 ( (fun (fun nat rat) bool), vanishes ) 16.50/16.61 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 16.50/16.61 ( (fun code_code_numeral nat), code_c271388182l_size ) 16.50/16.61 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 16.50/16.61 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 16.50/16.61 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 16.50/16.61 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 16.50/16.61 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 16.50/16.61 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 16.50/16.61 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 16.50/16.61 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 16.50/16.61 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 16.50/16.61 ( (fun complex nat), complex_size ) 16.50/16.61 ( (fun complex nat), (size_size complex) ) 16.50/16.61 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 16.50/16.61 ( (fun nat (fun nat (product_prod int int))), bezw ) 16.50/16.61 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 16.50/16.61 ( (fun int (fun nat nat)), nat_aux ) 16.50/16.61 ( (fun int (fun (fun int bool) bool)), rsetR ) 16.50/16.61 ( (fun int (fun (fun int bool) bool)), resSet ) 16.50/16.61 ( (fun int (list int)), quickc666637781d_zero ) 16.50/16.61 ( (fun (product_prod int int) rat), frct ) 16.50/16.61 ( (fun int (fun int rat)), fract ) 16.50/16.61 ( (fun real (fun real complex)), complex_1 ) 16.50/16.61 ( (fun real (fun real complex)), rcis ) 16.50/16.61 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 16.50/16.61 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 16.50/16.61 ( (fun int real), (real_1 int) ) 16.50/16.61 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 16.50/16.61 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 16.50/16.61 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 16.50/16.61 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 16.50/16.61 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 16.50/16.61 ( (fun real nat), natfloor ) 16.50/16.61 ( (fun real nat), natceiling ) 16.50/16.61 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 16.50/16.61 ( (fun quickcheck_code_int int), quickcheck_int_of ) 16.50/16.61 ( (fun rat (product_prod int int)), quotient_of ) 16.50/16.61 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 16.50/16.61 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 16.50/16.61 ( (fun rat real), ratreal ) 16.50/16.61 ( (fun code_code_numeral int), code_int_of ) 16.50/16.61 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 16.50/16.61 ( (fun int quickcheck_code_int), quickcheck_of_int ) 16.50/16.61 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 16.50/16.61 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 16.50/16.61 ) 16.50/16.61 (instantiation (forall ((P_5 $$unsorted) (Q_3 $$unsorted)) (let ((_let_0 (product_prod int int))) (let ((_let_1 (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) P_5) Q_3))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) Q_3))) (not (= (one_one int) (hAPP int int (hAPP int (fun int int) (gcd_gcd int) P_5) Q_3))) (= _let_1 (hAPP _let_0 _let_0 normalize _let_1))))) ) 16.50/16.61 ( (one_one int), (one_one int) ) 16.50/16.61 ( (zero_zero int), (one_one int) ) 16.50/16.61 ( s, (one_one int) ) 16.50/16.61 ) 16.50/16.61 (instantiation (forall ((X_a $$unsorted)) (or (not (linordered_semidom X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) (one_one X_a)))) ) 16.50/16.61 ( bool ) 16.50/16.61 ( nat ) 16.50/16.61 ( int ) 16.50/16.61 ( (fun int bool) ) 16.50/16.61 ( (fun nat bool) ) 16.50/16.61 ( (product_prod nat nat) ) 16.50/16.61 ( real ) 16.50/16.61 ( rat ) 16.50/16.61 ( complex ) 16.50/16.61 ( (filter nat) ) 16.50/16.61 ( (product_prod int int) ) 16.50/16.61 ( quickcheck_code_int ) 16.50/16.61 ( code_code_numeral ) 16.50/16.61 ( (product_prod real real) ) 16.50/16.61 ( (fun nat rat) ) 16.50/16.61 ( (filter real) ) 16.50/16.61 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 16.50/16.61 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 16.50/16.61 ) 16.50/16.61 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted)) (= (hAPP rat int (archim2085082626_floor rat) (hAPP int rat (hAPP int (fun int rat) fract A_1) B)) (hAPP int int (hAPP int (fun int int) (div_div int) A_1) B)) ) 16.50/16.61 ( (one_one int), (one_one int) ) 16.50/16.61 ( (zero_zero int), (one_one int) ) 16.50/16.61 ) 16.50/16.61 (instantiation (forall ((B_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (let ((_let_2 (hAPP int _let_0 (ord_less int) (zero_zero int)))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (zero_zero int)) A_2))) (= (and (hBOOL (hAPP int bool _let_2 B_1)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 B_1) A_2))) (hBOOL (hAPP int bool _let_2 (hAPP int int (hAPP int (fun int int) (div_div int) A_2) B_1)))))))) ) 16.50/16.61 ( (one_one int), t ) 16.50/16.61 ( (zero_zero int), (one_one int) ) 16.50/16.61 ( (zero_zero int), min_1 ) 16.50/16.61 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.61 ( (zero_zero int), s ) 16.50/16.61 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.50/16.61 ( (zero_zero int), (hAPP int int (number_number_of int) pls) ) 16.50/16.61 ( (zero_zero int), skv_4 ) 16.50/16.61 ( (zero_zero int), skv_10 ) 16.50/16.61 ( min_1, pls ) 16.50/16.61 ( min_1, min_1 ) 16.50/16.61 ) 16.50/16.61 (instantiation (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_165218 $$unsorted) (BOUND_VARIABLE_165219 $$unsorted) (BOUND_VARIABLE_165220 $$unsorted) (BOUND_VARIABLE_165221 $$unsorted) (BOUND_VARIABLE_165222 $$unsorted)) (let ((_let_0 (filter X_a))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_165222))) (or (not (real_normed_vector X_b)) (not (real_normed_vector X_c)) (not (topological_space X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (hAPP (fun X_a X_b) (fun X_b _let_1) (tendsto X_a X_b) BOUND_VARIABLE_165220) BOUND_VARIABLE_165221) _let_2))) (not (forall ((X $$unsorted)) (or (= (ti X_a X) (ti X_a BOUND_VARIABLE_165222)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP X_c real (norm_norm X_c) (hAPP X_c X_c (hAPP X_c (fun X_c X_c) (minus_minus X_c) (hAPP X_a X_c BOUND_VARIABLE_165218 X)) BOUND_VARIABLE_165219))) (hAPP X_b real (norm_norm X_b) (hAPP X_b X_b (hAPP X_b (fun X_b X_b) (minus_minus X_b) (hAPP X_a X_b BOUND_VARIABLE_165220 X)) BOUND_VARIABLE_165221))))) )) (hBOOL (hAPP _let_0 bool (hAPP X_c _let_1 (hAPP (fun X_a X_c) (fun X_c _let_1) (tendsto X_a X_c) BOUND_VARIABLE_165218) BOUND_VARIABLE_165219) _let_2)))))) ) 16.50/16.61 ( real, real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.61 ) 16.50/16.61 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (zero_zero real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 _let_2) (hAPP real real ln X_1)))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) _let_2) X_1))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (one_one real)) X_1)))))) ) 16.50/16.61 ( (one_one real) ) 16.50/16.61 ( pi ) 16.50/16.61 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.61 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.61 ( skv_2 ) 16.50/16.61 ( skv_8 ) 16.50/16.61 ( skv_9 ) 16.50/16.61 ) 16.50/16.61 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_165316 $$unsorted)) (or (not (linordered_idom X_a)) (not (number_ring X_a)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) BOUND_VARIABLE_165316) pls)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_165316)) (zero_zero X_a))))) ) 16.50/16.61 ( nat, pls ) 16.50/16.61 ( nat, (hAPP int int bit1 pls) ) 16.50/16.61 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.50/16.61 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.50/16.61 ( int, pls ) 16.50/16.61 ( int, (hAPP int int bit1 pls) ) 16.50/16.61 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.50/16.61 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.50/16.61 ( int, min_1 ) 16.50/16.61 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.61 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.50/16.61 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.50/16.61 ( real, min_1 ) 16.50/16.61 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.61 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.50/16.61 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.61 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 16.50/16.61 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.50/16.61 ( complex, min_1 ) 16.50/16.61 ( quickcheck_code_int, (one_one int) ) 16.50/16.61 ( quickcheck_code_int, (zero_zero int) ) 16.50/16.61 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 16.50/16.61 ( code_code_numeral, pls ) 16.50/16.61 ( code_code_numeral, (hAPP int int bit1 pls) ) 16.50/16.61 ) 16.50/16.61 (instantiation (forall ((P_1 $$unsorted) (A0 $$unsorted) (A1 $$unsorted)) (let ((_let_0 (product_prod nat nat))) (let ((_let_1 (fun _let_0 bool))) (or (not (hBOOL (hAPP _let_0 bool (hAPP (fun _let_0 _let_1) _let_1 (accp _let_0) nat_gcd_rel) (hAPP nat _let_0 (hAPP nat (fun nat _let_0) (product_Pair nat nat) A0) A1)))) (not (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_2 (fun nat bool))) (or (not (hBOOL (hAPP _let_0 bool (hAPP (fun _let_0 _let_1) _let_1 (accp _let_0) nat_gcd_rel) (hAPP nat _let_0 (hAPP nat (fun nat _let_0) (product_Pair nat nat) X) Y)))) (and (not (= (zero_zero nat) Y)) (not (hBOOL (hAPP nat bool (hAPP nat _let_2 P_1 Y) (hAPP nat nat (hAPP nat (fun nat nat) (div_mod nat) X) Y))))) (hBOOL (hAPP nat bool (hAPP nat _let_2 P_1 X) Y)))) )) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) P_1 A0) A1))))) ) 16.50/16.61 ( (ord_less nat), (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.61 ) 16.50/16.61 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_165375 $$unsorted) (BOUND_VARIABLE_165376 $$unsorted)) (or (not (comm_semiring_1 X_a)) (and (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) BOUND_VARIABLE_165376))) (not (= (one_one X_a) (ti X_a BOUND_VARIABLE_165375)))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_165375) (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_165375) BOUND_VARIABLE_165376)))) ) 16.50/16.61 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.61 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.61 ( int, skv_14, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.61 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.61 ) 16.50/16.61 (instantiation (forall ((P_5 $$unsorted)) (or (not (hBOOL (hAPP int bool zprime P_5))) (= (hAPP int nat nat_1 (hAPP int int (hAPP int (fun int int) (minus_minus int) P_5) (one_one int))) (hAPP int nat phi P_5))) ) 16.50/16.61 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.61 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.50/16.61 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.61 ) 16.50/16.61 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_165413 $$unsorted) (BOUND_VARIABLE_165414 $$unsorted)) (let ((_let_0 (fun (filter nat) bool))) (let ((_let_1 (fun nat X_a))) (or (not (metric_space X_a)) (not (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_0 (hAPP _let_1 (fun X_a _let_0) (tendsto nat X_a) BOUND_VARIABLE_165413) BOUND_VARIABLE_165414) sequentially))) (hBOOL (hAPP _let_1 bool (cauchy X_a) BOUND_VARIABLE_165413))))) ) 16.50/16.61 ( real, (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat real))) (hAPP _let_1 _let_1 (hAPP (fun real real) (fun _let_1 _let_1) (combb real real nat) (inverse_inverse real)) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real) ) 16.50/16.61 ) 16.50/16.61 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_165478 $$unsorted) (BOUND_VARIABLE_165479 $$unsorted)) (or (not (dvd X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_165478) BOUND_VARIABLE_165479))) (not (forall ((K_1 $$unsorted)) (not (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_165478) K_1) (ti X_a BOUND_VARIABLE_165479))) ))) ) 16.50/16.61 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (one_one int)) ) 16.50/16.61 ) 16.50/16.61 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_165523 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (times_times X_a))) (let ((_let_2 (one_one X_a))) (let ((_let_3 (minus_minus X_a))) (or (not (ring_1 X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_3 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_165523) BOUND_VARIABLE_165523)) _let_2) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_0 (plus_plus X_a) BOUND_VARIABLE_165523) _let_2)) (hAPP X_a X_a (hAPP X_a _let_0 _let_3 BOUND_VARIABLE_165523) _let_2)))))))) ) 16.50/16.61 ( nat, (one_one nat) ) 16.50/16.61 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 16.50/16.61 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.61 ( complex, ii ) 16.50/16.61 ) 16.50/16.61 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (one_one real))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (fun real real))) (let ((_let_4 (plus_plus real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 (zero_zero real)) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 X_1) _let_1))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 (hAPP real real (exp real) X_1)) (hAPP real real (hAPP real _let_3 _let_4 (hAPP real real (hAPP real _let_3 _let_4 _let_1) X_1)) (hAPP nat real (hAPP real (fun nat real) (power_power real) X_1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))))))))) ) 16.50/16.61 ( pi ) 16.50/16.61 ( (hAPP int real (number_number_of real) min_1) ) 16.50/16.61 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.61 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.61 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.61 ( skv_3 ) 16.50/16.61 ( skv_5 ) 16.50/16.61 ( skv_7 ) 16.50/16.61 ( skv_12 ) 16.50/16.61 ) 16.50/16.61 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_165558 $$unsorted) (BOUND_VARIABLE_165559 $$unsorted) (BOUND_VARIABLE_165560 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (fun X_a X_a))) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_165560) (zero_zero X_a)))) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_165559) (hAPP X_a X_a (hAPP X_a _let_2 (times_times X_a) BOUND_VARIABLE_165558) BOUND_VARIABLE_165560))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_165558) (hAPP X_a X_a (hAPP X_a _let_2 (inverse_divide X_a) BOUND_VARIABLE_165559) BOUND_VARIABLE_165560)))))))) ) 16.50/16.61 ( real, (zero_zero real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.50/16.61 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 16.50/16.61 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 16.50/16.61 ) 16.50/16.61 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_165651 $$unsorted) (BOUND_VARIABLE_165652 $$unsorted) (BOUND_VARIABLE_165653 $$unsorted) (BOUND_VARIABLE_165654 $$unsorted)) (let ((_let_0 (filter X_a))) (let ((_let_1 (fun _let_0 bool))) (or (not (metric_space X_b)) (not (metric_space X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (hAPP (fun X_a X_b) (fun X_b _let_1) (tendsto X_a X_b) BOUND_VARIABLE_165652) BOUND_VARIABLE_165653) (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_165654)))) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) BOUND_VARIABLE_165651))) (not (forall ((S_1 $$unsorted)) (or (not (forall ((X $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP X_a real (hAPP X_a (fun X_a real) (dist_dist X_a) X) BOUND_VARIABLE_165654)) S_1))) (= (ti X_a X) (ti X_a BOUND_VARIABLE_165654)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP X_b real (hAPP X_b (fun X_b real) (dist_dist X_b) (hAPP X_a X_b BOUND_VARIABLE_165652 X)) BOUND_VARIABLE_165653)) BOUND_VARIABLE_165651))))) )) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) S_1)))) ))))) ) 16.50/16.61 ( real, real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.50/16.61 ) 16.50/16.61 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int int pred (hAPP int int bit1 K_4)) (hAPP int int bit0 K_4)) ) 16.50/16.61 ( pls ) 16.50/16.61 ( (hAPP int int bit1 pls) ) 16.50/16.61 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.50/16.61 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.50/16.61 ( min_1 ) 16.50/16.61 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.50/16.61 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.50/16.61 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 16.50/16.61 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 16.50/16.61 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 16.50/16.61 ) 16.50/16.61 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (F $$unsorted) (G $$unsorted)) (let ((_let_0 (fun X_a X_b))) (or (not (forall ((X $$unsorted)) (= (hAPP X_a X_b F X) (hAPP X_a X_b G X)) )) (= (ti _let_0 F) (ti _let_0 G)))) ) 16.50/16.61 ( bool, bool, fNot, fNot ) 16.50/16.61 ( bool, (fun bool bool), fimplies, fimplies ) 16.50/16.61 ( bool, (fun bool bool), fimplies, fconj ) 16.50/16.61 ( bool, (fun bool bool), fconj, fimplies ) 16.50/16.61 ( bool, (fun bool bool), fconj, fdisj ) 16.50/16.61 ( bool, (fun bool bool), fdisj, fimplies ) 16.50/16.61 ( nat, bool, (even_odd_even nat), (even_odd_even nat) ) 16.50/16.61 ( nat, bool, (even_odd_even nat), prime ) 16.50/16.61 ( nat, bool, prime, (even_odd_even nat) ) 16.50/16.61 ( nat, nat, suc, fact ) 16.50/16.61 ( nat, nat, (fact_fact nat), nat_size ) 16.50/16.61 ( nat, nat, fact, suc ) 16.50/16.61 ( nat, nat, fact, fact ) 16.50/16.61 ( nat, nat, nat_size, nat_size ) 16.50/16.61 ( nat, nat, nat_size, (size_size nat) ) 16.50/16.61 ( nat, nat, (size_size nat), (fact_fact nat) ) 16.50/16.61 ( nat, nat, (size_size nat), nat_size ) 16.50/16.61 ( nat, (fun nat bool), coprime, coprime ) 16.50/16.61 ( nat, (fun nat nat), (gcd_gcd nat), (gcd_gcd nat) ) 16.50/16.61 ( nat, (fun nat nat), (gcd_gcd nat), nat_gcd ) 16.50/16.61 ( nat, (fun nat nat), nat_gcd, (gcd_gcd nat) ) 16.50/16.61 ( nat, (fun nat nat), nat_gcd, nat_lcm ) 16.50/16.61 ( nat, (fun nat nat), nat_lcm, (gcd_gcd nat) ) 16.50/16.61 ( nat, (fun nat (fun (product_prod nat nat) bool)), divmod_nat_rel, divmod_nat_rel ) 16.50/16.61 ( nat, real, (real_1 nat), sin_coeff ) 16.50/16.61 ( nat, real, (real_1 nat), cos_coeff ) 16.50/16.61 ( nat, real, sin_coeff, (real_1 nat) ) 16.50/16.61 ( nat, real, sin_coeff, sin_coeff ) 16.50/16.61 ( nat, real, cos_coeff, sin_coeff ) 16.50/16.61 ( nat, (fun real real), root, root ) 16.50/16.61 ( nat, (fun nat (fun nat bool)), (ord_gr676655987ssThan nat), (ord_gr676655987ssThan nat) ) 16.50/16.61 ( nat, (fun nat (product_prod nat nat)), divmod_nat, divmod_nat ) 16.50/16.61 ( nat, (fun nat (product_prod int int)), bezw, bezw ) 16.50/16.61 ( int, bool, nat_neg, zprime ) 16.50/16.61 ( int, bool, nat_neg, (even_odd_even int) ) 16.50/16.61 ( int, bool, zprime, (even_odd_even int) ) 16.50/16.61 ( int, bool, zEven, twoSqu1091635170sum2sq ) 16.50/16.61 ( int, bool, zEven, nat_is_nat ) 16.50/16.61 ( int, bool, zOdd, zOdd ) 16.50/16.61 ( int, bool, (even_odd_even int), nat_neg ) 16.50/16.61 ( int, bool, (even_odd_even int), (even_odd_even int) ) 16.50/16.61 ( int, bool, twoSqu1091635170sum2sq, zEven ) 16.50/16.61 ( int, bool, twoSqu1091635170sum2sq, twoSqu1091635170sum2sq ) 16.50/16.61 ( int, bool, nat_is_nat, twoSqu1091635170sum2sq ) 16.50/16.61 ( int, nat, nat_1, phi ) 16.50/16.61 ( int, nat, phi, nat_1 ) 16.50/16.61 ( int, nat, phi, phi ) 16.50/16.61 ( int, int, zfact, bit1 ) 16.50/16.61 ( int, int, bit0, (fact_fact int) ) 16.50/16.61 ( int, int, bit0, succ ) 16.50/16.61 ( int, int, bit1, bit1 ) 16.50/16.61 ( int, int, bit1, pred ) 16.50/16.61 ( int, int, (fact_fact int), bit0 ) 16.50/16.61 ( int, int, (fact_fact int), (fact_fact int) ) 16.50/16.61 ( int, int, pred, zfact ) 16.50/16.61 ( int, int, pred, bit1 ) 16.50/16.61 ( int, int, succ, (fact_fact int) ) 16.50/16.61 ( int, (fun int bool), norRRset, norRRset ) 16.50/16.61 ( int, (fun int bool), norRRset, sr ) 16.50/16.61 ( int, (fun int bool), quadRes, quadRes ) 16.50/16.61 ( int, (fun int bool), quadRes, sRStar ) 16.50/16.61 ( int, (fun int bool), sRStar, quadRes ) 16.50/16.61 ( int, (fun int bool), sRStar, quickc1265749348ro_rel ) 16.50/16.61 ( int, (fun int bool), d22set, norRRset ) 16.50/16.61 ( int, (fun int bool), sr, norRRset ) 16.50/16.61 ( int, (fun int bool), sr, d22set ) 16.50/16.61 ( int, (fun int bool), quickc1265749348ro_rel, quadRes ) 16.50/16.61 ( int, (fun int (fun int bool)), zcong, zcongm ) 16.50/16.61 ( int, (fun int (fun int bool)), zcong, noXRRset ) 16.50/16.61 ( int, (fun int (fun int bool)), zcongm, noXRRset ) 16.50/16.61 ( int, (fun int (fun int bool)), noXRRset, zcong ) 16.50/16.61 ( int, (fun int (fun int bool)), noXRRset, noXRRset ) 16.50/16.61 ( int, (fun int (fun int bool)), bnorRset, bnorRset ) 16.50/16.61 ( int, (fun int (fun int bool)), bnorRset, wset ) 16.50/16.61 ( int, (fun int (fun int bool)), wset, bnorRset ) 16.50/16.61 ( int, (fun int int), (gcd_gcd int), (gcd_gcd int) ) 16.50/16.61 ( int, (fun int int), (gcd_gcd int), int_gcd ) 16.50/16.61 ( int, (fun int int), legendre, legacy_zgcd ) 16.50/16.61 ( int, (fun int int), legendre, z3div ) 16.50/16.61 ( int, (fun int int), legacy_zgcd, z3div ) 16.50/16.61 ( int, (fun int int), standardRes, multInv ) 16.50/16.61 ( int, (fun int int), standardRes, inv ) 16.50/16.61 ( int, (fun int int), nat_tsub, z3mod ) 16.50/16.61 ( int, (fun int int), nat_tsub, int_lcm ) 16.50/16.61 ( int, (fun int int), multInv, standardRes ) 16.50/16.61 ( int, (fun int int), multInv, multInv ) 16.50/16.61 ( int, (fun int int), z3mod, nat_tsub ) 16.50/16.61 ( int, (fun int int), z3mod, z3mod ) 16.50/16.61 ( int, (fun int int), z3div, legendre ) 16.50/16.61 ( int, (fun int int), z3div, z3div ) 16.50/16.61 ( int, (fun int int), int_gcd, (gcd_gcd int) ) 16.50/16.61 ( int, (fun int int), int_lcm, z3mod ) 16.50/16.61 ( int, (fun int int), inv, multInv ) 16.50/16.61 ( int, (fun nat nat), nat_aux, nat_aux ) 16.50/16.61 ( int, real, (real_1 int), (real_1 int) ) 16.50/16.61 ( int, (fun int rat), fract, fract ) 16.50/16.61 ( int, (fun int (product_prod int int)), negDivAlg, pdivmod ) 16.50/16.61 ( int, (fun int (product_prod int int)), negDivAlg, norm_frac ) 16.50/16.61 ( int, (fun int (product_prod int int)), posDivAlg, divmod_int ) 16.50/16.61 ( int, (fun int (product_prod int int)), divmod_int, posDivAlg ) 16.50/16.61 ( int, (fun int (product_prod int int)), divmod_int, divmod_int ) 16.50/16.61 ( int, (fun int (product_prod int int)), pdivmod, norm_frac ) 16.50/16.61 ( int, (fun int (product_prod int int)), norm_frac, negDivAlg ) 16.50/16.61 ( int, (fun int (product_prod int int)), norm_frac, norm_frac ) 16.50/16.61 ( int, (fun (fun int bool) bool), rsetR, resSet ) 16.50/16.61 ( int, (fun (fun int bool) bool), resSet, rsetR ) 16.50/16.61 ( int, (fun (fun int bool) bool), resSet, resSet ) 16.50/16.61 ( int, quickcheck_code_int, quickcheck_of_int, quickcheck_of_int ) 16.50/16.61 ( int, (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), adjust, adjust ) 16.50/16.61 ( int, (fun int (fun int (fun int bool))), multInvPair, multInvPair ) 16.50/16.61 ( int, (fun (product_prod int int) bool), int_ge_less_than, int_ge_less_than ) 16.50/16.61 ( int, (fun (product_prod int int) bool), int_ge_less_than, int_ge_less_than2 ) 16.50/16.61 ( int, (fun (product_prod int int) bool), int_ge_less_than2, int_ge_less_than ) 16.50/16.61 ( int, (fun int (fun (product_prod int int) bool)), divmod_int_rel, divmod_int_rel ) 16.50/16.61 ( int, (fun int (product_prod int (product_prod int int))), xzgcd, xzgcd ) 16.50/16.61 ( int, (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))))), xzgcda, xzgcda ) 16.50/16.61 ( int, (fun int (fun (fun int bool) bool)), setS, setS ) 16.50/16.61 ( int, (list int), quickc666637781d_zero, quickc666637781d_zero ) 16.50/16.61 ( (fun int bool), bool, nat_nat_set, nat_nat_set ) 16.50/16.61 ( (fun int bool), int, (the int), (the int) ) 16.50/16.61 ( (fun int bool), (fun int bool), is_RRset, is_RRset ) 16.50/16.61 ( (fun int bool), (fun int (fun int int)), rRset2norRR, rRset2norRR ) 16.50/16.61 ( (product_prod nat nat), bool, pred_nat, pred_nat ) 16.50/16.61 ( (product_prod nat nat), (fun (product_prod nat nat) bool), nat_gcd_rel, nat_gcd_rel ) 16.50/16.61 ( real, nat, natfloor, natceiling ) 16.50/16.61 ( real, nat, natceiling, natfloor ) 16.50/16.61 ( real, nat, natceiling, natceiling ) 16.50/16.61 ( real, real, ln, sqrt ) 16.50/16.61 ( real, real, ln, arccos ) 16.50/16.61 ( real, real, cos, cos ) 16.50/16.61 ( real, real, cos, tan ) 16.50/16.61 ( real, real, sqrt, ln ) 16.50/16.61 ( real, real, sqrt, sqrt ) 16.50/16.61 ( real, real, sin, arcsin ) 16.50/16.61 ( real, real, sin, arctan ) 16.50/16.61 ( real, real, arccos, sqrt ) 16.50/16.61 ( real, real, arcsin, sin ) 16.50/16.61 ( real, real, arcsin, arcsin ) 16.50/16.61 ( real, real, tan, cos ) 16.50/16.61 ( real, real, arctan, arcsin ) 16.50/16.61 ( real, (fun real real), log, log ) 16.50/16.61 ( real, (fun real real), log, powr ) 16.50/16.61 ( real, (fun real real), powr, log ) 16.50/16.61 ( real, complex, cis, cis ) 16.50/16.61 ( real, (fun real complex), complex_1, rcis ) 16.50/16.61 ( real, (fun real complex), rcis, complex_1 ) 16.50/16.61 ( real, (fun real complex), rcis, rcis ) 16.50/16.61 ( (fun real bool), real, (complete_Sup_Sup real), (complete_Sup_Sup real) ) 16.50/16.61 ( rat, real, ratreal, ratreal ) 16.50/16.61 ( rat, (product_prod int int), quotient_of, quotient_of ) 16.50/16.61 ( complex, nat, complex_size, complex_size ) 16.50/16.61 ( complex, nat, complex_size, (size_size complex) ) 16.50/16.61 ( complex, nat, (size_size complex), complex_size ) 16.50/16.61 ( complex, real, re, im ) 16.50/16.61 ( complex, real, im, im ) 16.50/16.61 ( complex, real, im, arg ) 16.50/16.61 ( complex, real, arg, re ) 16.50/16.61 ( complex, real, arg, im ) 16.50/16.61 ( complex, complex, expi, expi ) 16.50/16.61 ( complex, complex, expi, cnj ) 16.50/16.61 ( complex, complex, cnj, expi ) 16.50/16.61 ( (product_prod int int), bool, frac_1, frac_1 ) 16.50/16.61 ( (product_prod int int), int, twoSqu1094008024sum2sq, twoSqu1094008024sum2sq ) 16.50/16.61 ( (product_prod int int), rat, frct, frct ) 16.50/16.61 ( (product_prod int int), (product_prod int int), negateSnd, negateSnd ) 16.50/16.61 ( (product_prod int int), (product_prod int int), negateSnd, normalize ) 16.50/16.61 ( (product_prod int int), (product_prod int int), normalize, negateSnd ) 16.50/16.61 ( (product_prod int int), (fun (product_prod int int) bool), norm_frac_rel, norm_frac_rel ) 16.50/16.61 ( (product_prod int int), (fun (product_prod int int) bool), norm_frac_rel, lazy_small_lazy_rel ) 16.50/16.61 ( (product_prod int int), (fun (product_prod int int) bool), posDivAlg_rel, posDivAlg_rel ) 16.50/16.61 ( (product_prod int int), (fun (product_prod int int) bool), posDivAlg_rel, upto_rel ) 16.50/16.61 ( (product_prod int int), (fun (product_prod int int) bool), lazy_small_lazy_rel, norm_frac_rel ) 16.50/16.61 ( (product_prod int int), (fun (product_prod int int) bool), lazy_small_lazy_rel, negDivAlg_rel ) 16.50/16.61 ( (product_prod int int), (fun (product_prod int int) bool), negDivAlg_rel, norm_frac_rel ) 16.50/16.61 ( (product_prod int int), (fun (product_prod int int) bool), upto_rel, posDivAlg_rel ) 16.50/16.61 ( quickcheck_code_int, nat, quickcheck_nat_of, quickcheck_nat_of ) 16.50/16.61 ( quickcheck_code_int, int, quickcheck_int_of, quickcheck_int_of ) 16.50/16.61 ( quickcheck_code_int, (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int)), quickc495462417de_int, quickc495462417de_int ) 16.50/16.61 ( code_code_numeral, nat, (size_size code_code_numeral), (size_size code_code_numeral) ) 16.50/16.61 ( code_code_numeral, nat, (size_size code_code_numeral), code_c271388182l_size ) 16.50/16.61 ( code_code_numeral, nat, code_c271388182l_size, (size_size code_code_numeral) ) 16.50/16.61 ( code_code_numeral, int, code_int_of, code_int_of ) 16.50/16.61 ( code_code_numeral, (fun nat nat), code_nat_of_aux, code_nat_of_aux ) 16.50/16.61 ( code_code_numeral, code_code_numeral, code_S1047413653umeral, code_S1047413653umeral ) 16.50/16.61 ( code_code_numeral, (fun code_code_numeral (product_prod code_code_numeral code_code_numeral)), code_d418564891umeral, code_d418564891umeral ) 16.50/16.61 ( (fun (product_prod real real) bool), (fun real (fun real (fun nat (product_prod real real)))), bolzano_bisect, bolzano_bisect ) 16.50/16.61 ( (fun nat rat), bool, vanishes, vanishes ) 16.50/16.61 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)), bool, ratrel, ratrel ) 16.50/16.61 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), bool, pair_less, pair_less ) 16.50/16.61 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), bool, pair_less, pair_leq ) 16.50/16.61 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), bool, pair_leq, pair_less ) 16.50/16.61 ) 16.61/16.61 (instantiation (forall ((I $$unsorted) (P_1 $$unsorted) (P_4 $$unsorted)) (or (not (forall ((I_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) I_2) P_4))) (not (hBOOL (hAPP nat bool P_1 I_2))) (hBOOL (hAPP nat bool P_1 (hAPP nat nat (hAPP nat (fun nat nat) (div_mod nat) (hAPP nat nat suc I_2)) P_4)))) )) (not (hBOOL (hAPP nat bool P_1 I))) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) I) P_4))) (hBOOL (hAPP nat bool P_1 (zero_zero nat)))) ) 16.61/16.61 ( (zero_zero nat), (even_odd_even nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.61/16.61 ) 16.61/16.61 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP quickcheck_code_int int quickcheck_int_of (hAPP int quickcheck_code_int (number_number_of quickcheck_code_int) K_4)) (hAPP int int (number_number_of int) K_4)) ) 16.61/16.61 ( (one_one int) ) 16.61/16.61 ( (zero_zero int) ) 16.61/16.61 ( pls ) 16.61/16.61 ( (hAPP int int bit1 pls) ) 16.61/16.61 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.61/16.61 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.61/16.61 ( min_1 ) 16.61/16.61 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.61/16.61 ) 16.61/16.61 (instantiation (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) X_1))) (= (hAPP int nat nat_1 (hAPP int int (fact_fact int) X_1)) (hAPP nat nat (fact_fact nat) (hAPP int nat nat_1 X_1)))) ) 16.61/16.61 ( (one_one int) ) 16.61/16.61 ( (zero_zero int) ) 16.61/16.61 ( min_1 ) 16.61/16.61 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.61/16.61 ( s ) 16.61/16.61 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.61/16.61 ( (hAPP int int (number_number_of int) pls) ) 16.61/16.61 ( skv_4 ) 16.61/16.61 ( skv_10 ) 16.61/16.61 ) 16.61/16.61 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (fun real real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) (zero_zero real)) X_2))) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP _let_1 (fun real _let_0) (deriv real) ln) X_2) (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) X_2)))))) ) 16.61/16.61 ( pi ) 16.61/16.61 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.61/16.61 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.61/16.61 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.61/16.61 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.61/16.61 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.61/16.61 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 16.61/16.61 ( skv_2 ) 16.61/16.61 ( skv_8 ) 16.61/16.61 ( skv_9 ) 16.61/16.61 ) 16.61/16.61 (instantiation (forall ((Nat_1 $$unsorted)) (let ((_let_0 (size_size nat))) (= (hAPP nat nat _let_0 (hAPP nat nat suc Nat_1)) (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP nat nat _let_0 Nat_1)) (hAPP nat nat suc (zero_zero nat))))) ) 16.61/16.61 ( (zero_zero nat) ) 16.61/16.61 ( (hAPP nat nat suc (zero_zero nat)) ) 16.61/16.61 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 16.61/16.61 ) 16.61/16.61 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_166127 $$unsorted) (BOUND_VARIABLE_166128 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (zero_zero X_a))) (let ((_let_3 (hAPP X_a _let_0 _let_1 _let_2))) (or (not (linord1117847801e_zero X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_166127) BOUND_VARIABLE_166128)) _let_2)) (or (and (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_166128)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_166127) _let_2))) (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_166128) _let_2)) (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_166127)))))))))) ) 16.61/16.61 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.61/16.61 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.61/16.61 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.61/16.61 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 16.61/16.61 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.61/16.61 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.61/16.61 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.61/16.61 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.61/16.61 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.61/16.61 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.61/16.61 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.61/16.61 ) 16.61/16.62 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_166173 $$unsorted) (BOUND_VARIABLE_166174 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (or (not (field X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 (inverse_divide X_a) BOUND_VARIABLE_166173) BOUND_VARIABLE_166174) (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_166173) (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_166174))))) ) 16.61/16.62 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.61/16.62 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.61/16.62 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.61/16.62 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 16.61/16.62 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.61/16.62 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.61/16.62 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.61/16.62 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.61/16.62 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.61/16.62 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.61/16.62 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.61/16.62 ) 16.61/16.62 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_166192 $$unsorted) (BOUND_VARIABLE_166193 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member X_a))) (let ((_let_3 (field_char_0_Rats X_a))) (or (not (field_char_0 X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_166193) _let_3))) (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_166193) BOUND_VARIABLE_166192)) _let_3))))))) ) 16.61/16.62 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 16.61/16.62 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 16.61/16.62 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_14 ) 16.61/16.62 ( complex, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), ii ) 16.61/16.62 ) 16.61/16.62 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_166216 $$unsorted)) (or (not (comm_monoid_add X_a)) (= (ti X_a BOUND_VARIABLE_166216) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (zero_zero X_a)) BOUND_VARIABLE_166216))) ) 16.61/16.62 ( bool, fFalse ) 16.61/16.62 ( bool, fTrue ) 16.61/16.62 ( int, pls ) 16.61/16.62 ( int, min_1 ) 16.61/16.62 ( int, s ) 16.61/16.62 ( int, m ) 16.61/16.62 ( int, s1 ) 16.61/16.62 ( int, t ) 16.61/16.62 ( (fun int bool), nat_neg ) 16.61/16.62 ( (fun int bool), zprime ) 16.61/16.62 ( (fun int bool), zEven ) 16.61/16.62 ( (fun int bool), zOdd ) 16.61/16.62 ( (fun int bool), (even_odd_even int) ) 16.61/16.62 ( (fun int bool), twoSqu1091635170sum2sq ) 16.61/16.62 ( (fun int bool), nat_is_nat ) 16.61/16.62 ( (fun int (fun int bool)), norRRset ) 16.61/16.62 ( (fun int (fun int bool)), quadRes ) 16.61/16.62 ( (fun int (fun int bool)), sRStar ) 16.61/16.62 ( (fun int (fun int bool)), d22set ) 16.61/16.62 ( (fun int (fun int bool)), sr ) 16.61/16.62 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 16.61/16.62 ( (fun int int), zfact ) 16.61/16.62 ( (fun int int), bit0 ) 16.61/16.62 ( (fun int int), bit1 ) 16.61/16.62 ( (fun int int), (fact_fact int) ) 16.61/16.62 ( (fun int int), pred ) 16.61/16.62 ( (fun int int), succ ) 16.61/16.62 ( (fun nat bool), (even_odd_even nat) ) 16.61/16.62 ( (fun nat bool), prime ) 16.61/16.62 ( (fun nat nat), suc ) 16.61/16.62 ( (fun nat nat), (fact_fact nat) ) 16.61/16.62 ( (fun nat nat), fact ) 16.61/16.62 ( (fun nat nat), nat_size ) 16.61/16.62 ( (fun nat nat), (size_size nat) ) 16.61/16.62 ( (fun (product_prod nat nat) bool), pred_nat ) 16.61/16.62 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 16.61/16.62 ( real, pi ) 16.61/16.62 ( (fun real real), ln ) 16.61/16.62 ( (fun real real), cos ) 16.61/16.62 ( (fun real real), sqrt ) 16.61/16.62 ( (fun real real), sin ) 16.61/16.62 ( (fun real real), arccos ) 16.61/16.62 ( (fun real real), arcsin ) 16.61/16.62 ( (fun real real), tan ) 16.61/16.62 ( (fun real real), arctan ) 16.61/16.62 ( (fun nat (fun nat bool)), coprime ) 16.61/16.62 ( complex, ii ) 16.61/16.62 ( (fun nat real), (real_1 nat) ) 16.61/16.62 ( (fun nat real), sin_coeff ) 16.61/16.62 ( (fun nat real), cos_coeff ) 16.61/16.62 ( (filter nat), sequentially ) 16.61/16.62 ( (fun int (fun int int)), (gcd_gcd int) ) 16.61/16.62 ( (fun int (fun int int)), legendre ) 16.61/16.62 ( (fun int (fun int int)), legacy_zgcd ) 16.61/16.62 ( (fun int (fun int int)), standardRes ) 16.61/16.62 ( (fun int (fun int int)), nat_tsub ) 16.61/16.62 ( (fun int (fun int int)), multInv ) 16.61/16.62 ( (fun int (fun int int)), z3mod ) 16.61/16.62 ( (fun int (fun int int)), z3div ) 16.61/16.62 ( (fun int (fun int int)), int_gcd ) 16.61/16.62 ( (fun int (fun int int)), int_lcm ) 16.61/16.62 ( (fun int (fun int int)), inv ) 16.61/16.62 ( (fun complex complex), expi ) 16.61/16.62 ( (fun complex complex), cnj ) 16.61/16.62 ( (fun real complex), cis ) 16.61/16.62 ( (fun int nat), nat_1 ) 16.61/16.62 ( (fun int nat), phi ) 16.61/16.62 ( (fun (fun int bool) bool), nat_nat_set ) 16.61/16.62 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 16.61/16.62 ( (fun nat (fun nat nat)), nat_gcd ) 16.61/16.62 ( (fun nat (fun nat nat)), nat_lcm ) 16.61/16.62 ( (fun (fun int bool) int), (the int) ) 16.61/16.62 ( (fun complex real), re ) 16.61/16.62 ( (fun complex real), im ) 16.61/16.62 ( (fun complex real), arg ) 16.61/16.62 ( (fun bool bool), fNot ) 16.61/16.62 ( (fun nat (fun real real)), root ) 16.61/16.62 ( (fun real (fun real real)), log ) 16.61/16.62 ( (fun real (fun real real)), powr ) 16.61/16.62 ( (fun bool (fun bool bool)), fimplies ) 16.61/16.62 ( (fun bool (fun bool bool)), fconj ) 16.61/16.62 ( (fun bool (fun bool bool)), fdisj ) 16.61/16.62 ( (fun int (fun int (product_prod int int))), negDivAlg ) 16.61/16.62 ( (fun int (fun int (product_prod int int))), posDivAlg ) 16.61/16.62 ( (fun int (fun int (product_prod int int))), divmod_int ) 16.61/16.62 ( (fun int (fun int (product_prod int int))), pdivmod ) 16.61/16.62 ( (fun int (fun int (product_prod int int))), norm_frac ) 16.61/16.62 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 16.61/16.62 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 16.61/16.62 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 16.61/16.62 ( (fun int (fun int (fun int bool))), zcong ) 16.61/16.62 ( (fun int (fun int (fun int bool))), zcongm ) 16.61/16.62 ( (fun int (fun int (fun int bool))), noXRRset ) 16.61/16.62 ( (fun int (fun int (fun int bool))), bnorRset ) 16.61/16.62 ( (fun int (fun int (fun int bool))), wset ) 16.61/16.62 ( (fun (product_prod int int) bool), frac_1 ) 16.61/16.62 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 16.61/16.62 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 16.61/16.62 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 16.61/16.62 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 16.61/16.62 ( (fun (fun nat rat) bool), vanishes ) 16.61/16.62 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 16.61/16.62 ( (fun code_code_numeral nat), code_c271388182l_size ) 16.61/16.62 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 16.61/16.62 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 16.61/16.62 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 16.61/16.62 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 16.61/16.62 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 16.61/16.62 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 16.61/16.62 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 16.61/16.62 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 16.61/16.62 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 16.61/16.62 ( (fun complex nat), complex_size ) 16.61/16.62 ( (fun complex nat), (size_size complex) ) 16.61/16.62 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 16.61/16.62 ( (fun nat (fun nat (product_prod int int))), bezw ) 16.61/16.62 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 16.61/16.62 ( (fun int (fun nat nat)), nat_aux ) 16.61/16.62 ( (fun int (fun (fun int bool) bool)), rsetR ) 16.61/16.62 ( (fun int (fun (fun int bool) bool)), resSet ) 16.61/16.62 ( (fun int (list int)), quickc666637781d_zero ) 16.61/16.62 ( (fun (product_prod int int) rat), frct ) 16.61/16.62 ( (fun int (fun int rat)), fract ) 16.61/16.62 ( (fun real (fun real complex)), complex_1 ) 16.61/16.62 ( (fun real (fun real complex)), rcis ) 16.61/16.62 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 16.61/16.62 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 16.61/16.62 ( (fun int real), (real_1 int) ) 16.61/16.62 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 16.61/16.62 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 16.61/16.62 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 16.61/16.62 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 16.61/16.62 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 16.61/16.62 ( (fun real nat), natfloor ) 16.61/16.62 ( (fun real nat), natceiling ) 16.61/16.62 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 16.61/16.62 ( (fun quickcheck_code_int int), quickcheck_int_of ) 16.61/16.62 ( (fun rat (product_prod int int)), quotient_of ) 16.61/16.62 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 16.61/16.62 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 16.61/16.62 ( (fun rat real), ratreal ) 16.61/16.62 ( (fun code_code_numeral int), code_int_of ) 16.61/16.62 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 16.61/16.62 ( (fun int quickcheck_code_int), quickcheck_of_int ) 16.61/16.62 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 16.61/16.62 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 16.61/16.62 ) 16.61/16.62 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_166230 $$unsorted) (BOUND_VARIABLE_166231 $$unsorted) (BOUND_VARIABLE_166232 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (times_times X_a))) (let ((_let_2 (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_166230))) (let ((_let_3 (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_166231))) (or (not (comm_semiring_1 X_a)) (= (hAPP X_a X_a _let_2 (hAPP X_a X_a _let_3 BOUND_VARIABLE_166232)) (hAPP X_a X_a _let_3 (hAPP X_a X_a _let_2 BOUND_VARIABLE_166232)))))))) ) 16.61/16.62 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 16.61/16.62 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 16.61/16.62 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 16.61/16.62 ) 16.61/16.62 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_166255 $$unsorted) (BOUND_VARIABLE_166256 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (zero_zero X_a))) (let ((_let_2 (ord_less_eq X_a))) (let ((_let_3 (inverse_inverse X_a))) (let ((_let_4 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_166255) BOUND_VARIABLE_166256))) (or (not (linord1117847801e_zero X_a)) (= (and (or (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) _let_1) _let_4))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_166256) BOUND_VARIABLE_166255))) (or (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 _let_4) _let_1))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_166255) BOUND_VARIABLE_166256)))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 (hAPP X_a X_a _let_3 BOUND_VARIABLE_166255)) (hAPP X_a X_a _let_3 BOUND_VARIABLE_166256)))))))))) ) 16.61/16.62 ( int, (one_one int), (zero_zero int) ) 16.61/16.62 ( int, (one_one int), t ) 16.61/16.62 ( int, (zero_zero int), (one_one int) ) 16.61/16.62 ( int, (zero_zero int), min_1 ) 16.61/16.62 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.61/16.62 ( int, (zero_zero int), s ) 16.61/16.62 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.61/16.62 ( int, (zero_zero int), (hAPP int int (number_number_of int) pls) ) 16.61/16.62 ( int, (zero_zero int), skv_4 ) 16.61/16.62 ( int, (zero_zero int), skv_10 ) 16.61/16.62 ( int, pls, min_1 ) 16.61/16.62 ( int, min_1, (zero_zero int) ) 16.61/16.62 ( int, min_1, pls ) 16.61/16.62 ( int, min_1, min_1 ) 16.61/16.62 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 16.61/16.62 ( int, s, (zero_zero int) ) 16.61/16.62 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 16.61/16.62 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), t ) 16.61/16.62 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_13 ) 16.61/16.62 ( int, t, (one_one int) ) 16.61/16.62 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 16.61/16.62 ( int, (hAPP int int (number_number_of int) pls), (zero_zero int) ) 16.61/16.62 ( int, skv_4, (zero_zero int) ) 16.61/16.62 ( int, skv_10, (zero_zero int) ) 16.61/16.62 ( real, (zero_zero real), pi ) 16.61/16.62 ( real, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.61/16.62 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.61/16.62 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.61/16.62 ( real, (zero_zero real), skv_3 ) 16.61/16.62 ( real, (zero_zero real), skv_5 ) 16.61/16.62 ( real, (zero_zero real), skv_7 ) 16.61/16.62 ( real, (zero_zero real), skv_12 ) 16.61/16.62 ( real, pi, (zero_zero real) ) 16.61/16.62 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.61/16.62 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 16.61/16.62 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.61/16.62 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (fun real _let_0))) (let ((_let_6 (fun real _let_4))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_4) (fun _let_0 _let_6) (combb bool _let_4 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_0 real (the real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 _let_1 _let_3))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 _let_9 (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 _let_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_0 (hAPP _let_5 _let_5 _let_10 (hAPP _let_2 _let_5 (hAPP _let_5 (fun _let_2 _let_5) (combb real _let_0 real) (fequal real)) cos)) _let_3))))))))))))))) ) 16.61/16.62 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_5 ) 16.61/16.62 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.61/16.62 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.61/16.62 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 16.61/16.62 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.61/16.62 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 16.61/16.62 ( real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 16.61/16.62 ( real, skv_3, (zero_zero real) ) 16.61/16.62 ( real, skv_5, (zero_zero real) ) 16.61/16.62 ( real, skv_5, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.61/16.62 ( real, skv_7, (zero_zero real) ) 16.61/16.62 ( real, skv_12, (zero_zero real) ) 16.61/16.62 ( complex, ii, ii ) 16.61/16.62 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 16.61/16.62 ( complex, (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 16.61/16.62 ) 16.61/16.62 (instantiation (forall ((P_5 $$unsorted)) (or (not (hBOOL (hAPP nat bool prime P_5))) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (dvd_dvd nat) P_5) (hAPP nat nat suc (zero_zero nat)))))) ) 16.61/16.62 ( (zero_zero nat) ) 16.61/16.62 ( (hAPP nat nat suc (zero_zero nat)) ) 16.61/16.62 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.61/16.62 ) 16.61/16.62 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) X_2) zEven))) (not (forall ((K_1 $$unsorted)) (not (= (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) K_1) (ti int X_2))) )))) ) 16.61/16.62 ( (one_one int) ) 16.61/16.62 ) 16.61/16.62 (instantiation (forall ((N_1 $$unsorted) (K_4 $$unsorted)) (let ((_let_0 (fun int int))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) K_4))) (= (ti int K_4) (hAPP int int (hAPP int _let_0 legacy_zgcd (hAPP int int (hAPP int _let_0 (times_times int) K_4) N_1)) K_4)))) ) 16.61/16.62 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.61/16.62 ( t, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.61/16.62 ( skv_13, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 16.61/16.62 ) 16.61/16.62 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int int bit1 (hAPP int int pred K_4)) (hAPP int int pred (hAPP int int bit0 K_4))) ) 16.61/16.62 ( pls ) 16.61/16.62 ( (hAPP int int bit1 pls) ) 16.61/16.62 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 16.61/16.62 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 16.61/16.62 ( min_1 ) 16.61/16.62 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.61/16.62 ) 16.61/16.62 (instantiation (forall ((X_a $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (zero_zero int) (hAPP X_a int (archim2085082626_floor X_a) (zero_zero X_a)))) ) 16.61/16.62 ( nat ) 16.61/16.62 ( int ) 16.61/16.62 ( real ) 16.61/16.62 ( rat ) 16.61/16.62 ( complex ) 16.61/16.62 ( quickcheck_code_int ) 16.61/16.62 ( code_code_numeral ) 16.61/16.62 ) 16.61/16.62 (instantiation (forall ((X $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (norm_norm real) (hAPP complex real im X))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real (norm_norm complex) X)) skv_1))) ) 16.61/16.62 ( (one_one complex) ) 16.61/16.62 ( ii ) 16.61/16.62 ( (zero_zero complex) ) 16.61/16.62 ) 16.61/16.62 (instantiation (forall ((X $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (norm_norm real) (hAPP complex real re X))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real (norm_norm complex) X)) skv_2))) ) 16.61/16.62 ( (one_one complex) ) 16.61/16.62 ( ii ) 16.61/16.62 ( (zero_zero complex) ) 16.61/16.62 ) 16.61/16.62 (instantiation (forall ((X $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (norm_norm real) (hAPP complex real im X))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real (norm_norm complex) X)) skv_3))) ) 16.61/16.62 ( (one_one complex) ) 16.61/16.62 ( ii ) 16.61/16.62 ( (zero_zero complex) ) 16.61/16.62 ) 16.61/16.62 (instantiation (forall ((Y $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int int))) (let ((_let_2 (hAPP int int (hAPP int _let_1 (plus_plus int) (hAPP int int (hAPP int _let_1 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) Y) _let_2))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) Y) _let_2))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (zero_zero int)) Y))) (= (ti int Y) (ti int skv_4)))))) ) 16.61/16.62 ( (one_one int) ) 16.61/16.62 ( pls ) 16.61/16.62 ( min_1 ) 16.61/16.62 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.61/16.62 ( s ) 16.61/16.62 ( m ) 16.61/16.62 ( s1 ) 16.61/16.62 ( t ) 16.61/16.62 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 16.61/16.62 ( (hAPP int int (number_number_of int) pls) ) 16.61/16.62 ( skv_4 ) 16.61/16.62 ( skv_10 ) 16.61/16.62 ) 16.61/16.62 (instantiation (forall ((Y $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (zero_zero real))) (or (not (= _let_2 (hAPP real real cos Y))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Y) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 _let_2) Y))) (= Y skv_5))))) ) 16.61/16.62 ( (zero_zero real) ) 16.61/16.62 ( pi ) 16.61/16.62 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 16.61/16.62 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.61/16.62 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 16.61/16.62 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 16.61/16.62 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.61/16.62 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 16.61/16.62 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 16.61/16.62 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 16.61/16.62 ( (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of real))) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP int real _let_2 (hAPP int int bit1 _let_1))) (hAPP int real _let_2 (hAPP int int bit0 _let_1)))) pi)))) ) 16.61/16.62 ( skv_3 ) 16.61/16.62 ( skv_5 ) 16.61/16.62 ( skv_7 ) 16.61/16.62 ( skv_12 ) 16.61/16.62 ) 16.61/16.62 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (norm_norm complex))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP complex real _let_0 (hAPP complex complex cnj X))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real _let_0 X)) skv_6)))) ) 16.61/16.62 ( (one_one complex) ) 16.61/16.62 ( ii ) 16.61/16.62 ( (zero_zero complex) ) 16.61/16.62 ) 16.61/16.62 (instantiation (forall ((X $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (norm_norm real) (hAPP complex real re X))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real (norm_norm complex) X)) skv_7))) ) 16.61/16.62 ( (one_one complex) ) 16.61/16.62 ( ii ) 16.61/16.62 ( (zero_zero complex) ) 16.61/16.62 ) 16.61/16.62 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (norm_norm complex))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP complex real _let_0 (hAPP complex complex cnj X))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real _let_0 X)) skv_8)))) ) 16.61/16.62 ( (one_one complex) ) 16.61/16.62 ( ii ) 16.61/16.62 ( (zero_zero complex) ) 16.61/16.62 ) 16.61/16.62 (instantiation (forall ((X $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (norm_norm real) (hAPP complex real im X))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real (norm_norm complex) X)) skv_9))) ) 16.61/16.62 ( (one_one complex) ) 16.61/16.62 ( ii ) 16.61/16.62 ( (zero_zero complex) ) 16.61/16.62 ) 16.61/16.62 (instantiation (forall ((X $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (norm_norm real) (hAPP complex real re X))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real (norm_norm complex) X)) skv_11))) ) 16.61/16.62 ( (one_one complex) ) 16.61/16.62 ( ii ) 16.61/16.62 ( (zero_zero complex) ) 16.61/16.62 ) 16.61/16.62 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (norm_norm complex))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP complex real _let_0 (hAPP complex complex cnj X))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real _let_0 X)) skv_12)))) ) 16.61/16.62 ( (one_one complex) ) 16.61/16.62 ( ii ) 16.61/16.62 ( (zero_zero complex) ) 16.61/16.62 ) 16.61/16.62 % SZS output end Proof for theBenchmark 16.61/16.64 EOF